http://cleanenergywiki.org/api.php?action=feedcontributions&feedformat=atom&user=KnooneCleanEnergyWIKI - User contributions [en]2026-04-23T14:01:03ZUser contributionsMediaWiki 1.37.0http://cleanenergywiki.org/index.php?title=Introduction_to_Absorption&diff=7121Introduction to Absorption2010-06-15T23:07:19Z<p>Knoone: /* Plank's relation */</p>
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Absorption of electromagnetic radiation (light) occurs when the energy of a photon is transferred to matter. Absorption can occur in atoms by promoting an electron to higher energetic states. In molecules, absorption can result from transitions into higher electronic, vibrational, and rotational states. The absorption of light is fundamental process relevant to many photonics materials and devices. <br />
<br />
== Plank's relation ==<br />
<br />
Light can be characterized in multiple ways, notably, either by its frequency, which is the number of oscillations per second, or its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s. <br />
<br />
In the early 20th century, Planck showed that the energy of a photon can be related to its frequency by using the Planck relation (also called the Planck-Einstein equation) <br />
<br />
:<math>E=h \nu\!</math> <br />
<br />
or, since λν = c: <br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is directly proportional to its frequency and inversely proportional to its wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
== Excitation vs polarization ==<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
== Solvent effects ==<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
== Energy Units ==<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
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</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Jablonksi_Diagram&diff=7120Jablonksi Diagram2010-06-15T23:05:15Z<p>Knoone: /* Meaning of Levels */</p>
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<br />
Jablonski diagrams are common representations of the possible electronic states and transitions as molecules enter and leave the excited state. Aleksander Jabłoński was a Polish scientist who did significant research on fluorescence and molecular photophysics in the 1930's. Jablonski diagrams describe the electronic states of molecules, transitions and associated light emitting phenomena. Though Jablonski diagrams resemble one-electron bandgap diagrams, they represent different things. Horizontal lines in a Jablonski diagram represent energetic states of a molecule or system, not the discrete electronic energy levels depicted in one-electron diagrams.<br />
<br />
[[Image:Jablonski.png|thumb|400px|Several processes are illustrated and are indicated by the rate constants that characterize the processes shown, including absorption of light, fluorescence, internal conversion, intersystem crossing and phosphorescence]]<br />
<br />
=== Meaning of Levels ===<br />
<br />
It is important to understand the premises of the Jablonski Diagrams. <br />
<br />
:'''S<sub>0</sub>''' is the ground state of the molecule, <br />
<br />
:'''S<sub>1</sub>''' is the first excited singlet state and S<sub>n</sub> is the nth excited state. <br />
<br />
:'''T<sub>1</sub>''' is the first excited triplet state and T<sub>n</sub> is the nth excited state. <br />
<br />
The y-axis, labeled E, indicates the relative energies of the states. In more complex Jablonski diagrams, the states can be also described as potential energy surfaces. Within each electronic state exist a range of vibrational levels. Vibrational ground states are shown with thick lines and higher vibrational states are shown with thin lines. <br />
<br />
Molecules can progress from state to state via either radiative or nonradiative processes. Graphically, nonradiative transitions are shown as straight lines and radiative transitions are shown with squiggly lines on a Jablonski diagram.<br />
<br />
The spin multiplicity of states are spatially separated along the x-axis of a Jablonski diagram. Singlet spin multiplicity exists when the total spin of the system is zero. Since any plus ½ spin corresponds to a minus ½ spin, the total spin results as zero. There is a single way of putting all the spins so this is referred to as a '''singlet state'''. It is also possible to have '''triplet states''' that have total spin number is +1. <br />
<br />
:'''T<sub>1</sub>''' shows the lowest excited triplet state. S<sub>1</sub> refers to the excited singlet state. The 0 refers to the ground state. <br />
<br />
:'''T<sub>n</sub>''' is also a higher lying triplet state<br />
<br />
Usually, when drawing or writing a Jablonski Diagram, the singlet states are on the left hand side. In the case of singlet states, the total spin number is zero and the molecule is [[diamagnetic]]. In most instances, those &pi;-conjugated molecules in the ground state have spins that are all paired. Molecules with triplet states are drawn on the right hand side and the molecules are [[paramagnetic]]. An example of a paramagnetic molecule is oxygen, that has two &pi; levels that have the same energy and therefore, the two electrons point upwards. What is referred to as singlet oxygen is actually 1 eV above the ground state of oxygen and it is a pretty nasty molecule.<br />
<br />
=== Excitation ===<br />
<br />
In general, chromophores have a ground state that is a singlet and an excited state that will be singlet or sometimes triplets. Light emitting systems deal with triplet states. That is why triplets are important. Once the molecules are excited, many photophysical processes can occur. When the molecule that is in the ground state is excited, the photon energy will bring it into the S<sub>1</sub> electronic state at a higher vibrational level. Once we have the absorption '''K<sub>abs</sub>''', the molecule can trickle back down from the maximum line in the S<sub>1</sub> to the minimum of the S<sub>1</sub> state. It does that by going down the vibrational levels and therefore, vibrations are created in the molecule. That is how the molecule loses its energy. This process is referred to as '''internal conversion''' ('''k<sub>ic</sub>''') because it remains within the same spin manifold and possibly within the same excited states. Then from the minimum of S<sub>1</sub>, the molecule can also decay back to the ground state without the emission of a photon (non-radiativeally). This is not a good thing when we are interested in light emission. It could also decay back to the ground state by emitting a photon, which is referred to as a '''fluorescence''' phenomenon ('''k<sub>fl</sub>'''). All these processes have rates that are generally typical for conjugated molecules. <br />
<br />
Starting at S<sub>0</sub> a photon is absorbed, spin multiplicity is conserved, and the electron gets into S<sub>1</sub>. Then in some instances, a crossover to the triplet manifold T<sub>1</sub> can occur. This crossover to the triplet manifold is referred to as intersystem crossing. The '''K<sub>isc</sub>''' shown between S<sub>1</sub> and T<sub>1</sub> represents the intersystem crossing. The intersystem crossing can cause molecule to trickle down back to the bottom of T<sub>1</sub>, thus intersystem crossing is followed by internal conversion. At the bottom of the T<sub>1</sub> state, the molecule usually lives for a pretty long time. Since it is metastable, the probability of it descending back to the ground state is small but even so eventually happens. If it occurs radiadivally then a phosphorescence can be produced. It could also come down from T<sub>1</sub> via emission of vibrations through internal conversion. Molecules that are efficient enough to be used in a display must have very large rates for fluorescence or phosphorescence. With a molecule such as naphtaline, a flat hypercarbon, the probability of this fluoresence occuring is extremely small. But there is a way to increase the probability.<br />
<br />
=== Singlets and Triplets ===<br />
<br />
[[Image:Singlettripletspin.png|thumb|400px|This slide shows you the distinction between a singlet and triplet.]]<br />
It is important to know that states refer to the multi-electron system. We will make an approximation and simply look at the orbital levels, HOMO, LUMO and so on. In a large number of cases, the first excited state can mainly be described by the promotion of an electron from the HOMO level to the LUMO Level. The first energy level diagram of the four shows a spin of +1/2 in the HOMO and a spin of +1/2 in the LUMO. (This doesn’t mean that this first case always occurs in excitation; it is just possible to have this situation at some point.) In this case, the two spins are aligned and the total spin number is 1. This case is one of the triplet states. Another triplet state can occur like the 2nd energy diagram shown on the right of the first. It is also possible to have opposite spins. The third diagram shows a situation where the spin is +½ or what I refer to as &alpha; on the HOMO, and the spin is -½ or &beta; on the LUMO. The fourth diagram shows the reverse of the third: there is a -1/2 &beta; on the HOMO and +1/2 &alpha; on the LUMO. The first two situations and diagrams represent pure quanta-mechanical spin states. However, the last two are not; only their combination is. Therefore, there are two ways to obtain a triplet state. One way to have both electron spins to have the same direction. The way is to take the linear positive combination of the last two diagrams. This is done on the slide with the proper normalization factor; the &alpha; for electron 1 and &beta; for electron 2 plus the fourth diagram which has an &alpha; for electron 2 and &beta; for electron 1. This defines the third triplet configuration. <br />
<br clear='all'><br />
[[Image:Spinstates.png|thumb|300px|Magnetic numbers for triplet state]]<br />
Thus, the triplet state has a multiplicity of three with magnetic numbers of +1 (first diagram), -1(second diagram), and 0(combination of the last two diagrams), and total spin number in all cases is equal to 1. The singlet state is the subtraction of those two spin configurations in the last two diagrams. Usually, when referring to a singlet state, there is one spin like with an upward direction and the other spin has a downward direction. However, the quantum mechanical situation is a bit more complex than what this leads you to believe. For the triplet, the two spin configurations are easy to pinpoint but the third one only exists in combination. Remember that the third spin configuration diagram and the last spin configuration do not correspond to pure states. Their plus and minus combination is necessary to get to the actual spin state.<br />
<br />
== External Links ==<br />
<br />
See Wikipedia on [http://en.wikipedia.org/wiki/Jablonski_diagram Jablonksi diagram]<br />
<br />
[http://www.shsu.edu/~chm_tgc/sounds/flashfiles/Jablonski.swf Flash animation of processes involved in Jablonski diagram]<br />
[[category:absorption]]<br />
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</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Jablonksi_Diagram&diff=7119Jablonksi Diagram2010-06-15T23:02:21Z<p>Knoone: /* Meaning of Levels */</p>
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<br />
Jablonski diagrams are common representations of the possible electronic states and transitions as molecules enter and leave the excited state. Aleksander Jabłoński was a Polish scientist who did significant research on fluorescence and molecular photophysics in the 1930's. Jablonski diagrams describe the electronic states of molecules, transitions and associated light emitting phenomena. Though Jablonski diagrams resemble one-electron bandgap diagrams, they represent different things. Horizontal lines in a Jablonski diagram represent energetic states of a molecule or system, not the discrete electronic energy levels depicted in one-electron diagrams.<br />
<br />
[[Image:Jablonski.png|thumb|400px|Several processes are illustrated and are indicated by the rate constants that characterize the processes shown, including absorption of light, fluorescence, internal conversion, intersystem crossing and phosphorescence]]<br />
<br />
=== Meaning of Levels ===<br />
<br />
It is important to understand the premises of the Jablonski Diagrams. <br />
<br />
:'''S<sub>0</sub>''' is the ground state of the molecule, <br />
<br />
:'''S<sub>1</sub>''' is the first excited singlet state and S<sub>n</sub> is the nth excited state. <br />
<br />
:'''T<sub>1</sub>''' is the first excited triplet state and T<sub>n</sub> is the nth excited state. <br />
<br />
The y-axis, labeled E, indicates the relative energies of the states. In more complex Jablonski diagrams, the states can be also described as potential energy surfaces. Within each electronic state exist a range of vibrational levels. Vibrational ground states are shown with thick lines and higher vibrational states are shown with thin lines. <br />
<br />
Molecules can progress from state to state via either radiative or nonradiative processes. Graphically, nonradiative transitions are shown as straight lines and radiative transitions are shown with squiggly lines on a Jablonski diagram.<br />
<br />
The Y axis represents the spin multiplicity. There is singlet spin multiplicity where the total spin number is zero. Since any plus ½ spin corresponds to a minus ½ spin, the total spin results as zero. There is a single way of putting all the spins so this is referred to as a '''singlet state'''. It is also possible to have '''triplet states''' that have total spin number is +1. <br />
<br />
:'''T<sub>1</sub>''' shows the lowest excited triplet state. S<sub>1</sub> refers to the excited singlet state. The 0 refers to the ground state. <br />
<br />
:'''T<sub>n</sub>''' is also a higher lying triplet state<br />
<br />
Usually, when drawing or writing a Jablonski Diagram, the singlet states are on the left hand side. In the case of singlet states, the total spin number is zero and the molecule is [[diamagnetic]]. In most instances, those &pi;-conjugated molecules in the ground state have spins that are all paired. Molecules with triplet states are drawn on the right hand side and the molecules are [[paramagnetic]]. An example of a paramagnetic molecule is oxygen, that has two &pi; levels that have the same energy and therefore, the two electrons point upwards. What is referred to as singlet oxygen is actually 1 eV above the ground state of oxygen and it is a pretty nasty molecule.<br />
<br />
=== Excitation ===<br />
<br />
In general, chromophores have a ground state that is a singlet and an excited state that will be singlet or sometimes triplets. Light emitting systems deal with triplet states. That is why triplets are important. Once the molecules are excited, many photophysical processes can occur. When the molecule that is in the ground state is excited, the photon energy will bring it into the S<sub>1</sub> electronic state at a higher vibrational level. Once we have the absorption '''K<sub>abs</sub>''', the molecule can trickle back down from the maximum line in the S<sub>1</sub> to the minimum of the S<sub>1</sub> state. It does that by going down the vibrational levels and therefore, vibrations are created in the molecule. That is how the molecule loses its energy. This process is referred to as '''internal conversion''' ('''k<sub>ic</sub>''') because it remains within the same spin manifold and possibly within the same excited states. Then from the minimum of S<sub>1</sub>, the molecule can also decay back to the ground state without the emission of a photon (non-radiativeally). This is not a good thing when we are interested in light emission. It could also decay back to the ground state by emitting a photon, which is referred to as a '''fluorescence''' phenomenon ('''k<sub>fl</sub>'''). All these processes have rates that are generally typical for conjugated molecules. <br />
<br />
Starting at S<sub>0</sub> a photon is absorbed, spin multiplicity is conserved, and the electron gets into S<sub>1</sub>. Then in some instances, a crossover to the triplet manifold T<sub>1</sub> can occur. This crossover to the triplet manifold is referred to as intersystem crossing. The '''K<sub>isc</sub>''' shown between S<sub>1</sub> and T<sub>1</sub> represents the intersystem crossing. The intersystem crossing can cause molecule to trickle down back to the bottom of T<sub>1</sub>, thus intersystem crossing is followed by internal conversion. At the bottom of the T<sub>1</sub> state, the molecule usually lives for a pretty long time. Since it is metastable, the probability of it descending back to the ground state is small but even so eventually happens. If it occurs radiadivally then a phosphorescence can be produced. It could also come down from T<sub>1</sub> via emission of vibrations through internal conversion. Molecules that are efficient enough to be used in a display must have very large rates for fluorescence or phosphorescence. With a molecule such as naphtaline, a flat hypercarbon, the probability of this fluoresence occuring is extremely small. But there is a way to increase the probability.<br />
<br />
=== Singlets and Triplets ===<br />
<br />
[[Image:Singlettripletspin.png|thumb|400px|This slide shows you the distinction between a singlet and triplet.]]<br />
It is important to know that states refer to the multi-electron system. We will make an approximation and simply look at the orbital levels, HOMO, LUMO and so on. In a large number of cases, the first excited state can mainly be described by the promotion of an electron from the HOMO level to the LUMO Level. The first energy level diagram of the four shows a spin of +1/2 in the HOMO and a spin of +1/2 in the LUMO. (This doesn’t mean that this first case always occurs in excitation; it is just possible to have this situation at some point.) In this case, the two spins are aligned and the total spin number is 1. This case is one of the triplet states. Another triplet state can occur like the 2nd energy diagram shown on the right of the first. It is also possible to have opposite spins. The third diagram shows a situation where the spin is +½ or what I refer to as &alpha; on the HOMO, and the spin is -½ or &beta; on the LUMO. The fourth diagram shows the reverse of the third: there is a -1/2 &beta; on the HOMO and +1/2 &alpha; on the LUMO. The first two situations and diagrams represent pure quanta-mechanical spin states. However, the last two are not; only their combination is. Therefore, there are two ways to obtain a triplet state. One way to have both electron spins to have the same direction. The way is to take the linear positive combination of the last two diagrams. This is done on the slide with the proper normalization factor; the &alpha; for electron 1 and &beta; for electron 2 plus the fourth diagram which has an &alpha; for electron 2 and &beta; for electron 1. This defines the third triplet configuration. <br />
<br clear='all'><br />
[[Image:Spinstates.png|thumb|300px|Magnetic numbers for triplet state]]<br />
Thus, the triplet state has a multiplicity of three with magnetic numbers of +1 (first diagram), -1(second diagram), and 0(combination of the last two diagrams), and total spin number in all cases is equal to 1. The singlet state is the subtraction of those two spin configurations in the last two diagrams. Usually, when referring to a singlet state, there is one spin like with an upward direction and the other spin has a downward direction. However, the quantum mechanical situation is a bit more complex than what this leads you to believe. For the triplet, the two spin configurations are easy to pinpoint but the third one only exists in combination. Remember that the third spin configuration diagram and the last spin configuration do not correspond to pure states. Their plus and minus combination is necessary to get to the actual spin state.<br />
<br />
== External Links ==<br />
<br />
See Wikipedia on [http://en.wikipedia.org/wiki/Jablonski_diagram Jablonksi diagram]<br />
<br />
[http://www.shsu.edu/~chm_tgc/sounds/flashfiles/Jablonski.swf Flash animation of processes involved in Jablonski diagram]<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<td style="text-align: left; width: 33%">[[Changes in Absorption Spectra|Previous Topic]]</td><br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
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</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Jablonksi_Diagram&diff=7118Jablonksi Diagram2010-06-15T22:57:56Z<p>Knoone: /* Meaning of Levels */</p>
<hr />
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<tr><br />
<td style="text-align: left; width: 33%">[[Changes in Absorption Spectra|Previous Topic]]</td><br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Fluorescence Process| Next Topic]]</td><br />
</tr><br />
</table><br />
<br />
Jablonski diagrams are common representations of the possible electronic states and transitions as molecules enter and leave the excited state. Aleksander Jabłoński was a Polish scientist who did significant research on fluorescence and molecular photophysics in the 1930's. Jablonski diagrams describe the electronic states of molecules, transitions and associated light emitting phenomena. Though Jablonski diagrams resemble one-electron bandgap diagrams, they represent different things. Horizontal lines in a Jablonski diagram represent energetic states of a molecule or system, not the discrete electronic energy levels depicted in one-electron diagrams.<br />
<br />
[[Image:Jablonski.png|thumb|400px|Several processes are illustrated and are indicated by the rate constants that characterize the processes shown, including absorption of light, fluorescence, internal conversion, intersystem crossing and phosphorescence]]<br />
<br />
=== Meaning of Levels ===<br />
<br />
It is important to understand the premises of the Jablonski Diagrams. <br />
<br />
:'''S<sub>0</sub>''' is the ground state of the molecule, <br />
<br />
:'''S<sub>1</sub>''' is the first excited singlet state and S<sub>n</sub> is the nth excited state. <br />
<br />
:'''T<sub>1</sub>''' is the first excited triplet state and T<sub>n</sub> is the nth excited state. <br />
<br />
There is an energy axis labeled E. These levels can be also described through potential energy surfaces. Within within each state, you have a range of vibrational levels. Vibrational ground states are shown with thick lines and higher vibrational states are shown with thin lines. Nonradiative transitions are shown with straight lines and radiative transitions are shown with squiggly lines.<br />
<br />
The Y axis represents the spin multiplicity. There is singlet spin multiplicity where the total spin number is zero. Since any plus ½ spin corresponds to a minus ½ spin, the total spin results as zero. There is a single way of putting all the spins so this is referred to as a '''singlet state'''. It is also possible to have '''triplet states''' that have total spin number is +1. <br />
<br />
:'''T<sub>1</sub>''' shows the lowest excited triplet state. S<sub>1</sub> refers to the excited singlet state. The 0 refers to the ground state. <br />
<br />
:'''T<sub>n</sub>''' is also a higher lying triplet state<br />
<br />
Usually, when drawing or writing a Jablonski Diagram, the singlet states are on the left hand side. In the case of singlet states, the total spin number is zero and the molecule is [[diamagnetic]]. In most instances, those &pi;-conjugated molecules in the ground state have spins that are all paired. Molecules with triplet states are drawn on the right hand side and the molecules are [[paramagnetic]]. An example of a paramagnetic molecule is oxygen, that has two &pi; levels that have the same energy and therefore, the two electrons point upwards. What is referred to as singlet oxygen is actually 1 eV above the ground state of oxygen and it is a pretty nasty molecule.<br />
<br />
=== Excitation ===<br />
<br />
In general, chromophores have a ground state that is a singlet and an excited state that will be singlet or sometimes triplets. Light emitting systems deal with triplet states. That is why triplets are important. Once the molecules are excited, many photophysical processes can occur. When the molecule that is in the ground state is excited, the photon energy will bring it into the S<sub>1</sub> electronic state at a higher vibrational level. Once we have the absorption '''K<sub>abs</sub>''', the molecule can trickle back down from the maximum line in the S<sub>1</sub> to the minimum of the S<sub>1</sub> state. It does that by going down the vibrational levels and therefore, vibrations are created in the molecule. That is how the molecule loses its energy. This process is referred to as '''internal conversion''' ('''k<sub>ic</sub>''') because it remains within the same spin manifold and possibly within the same excited states. Then from the minimum of S<sub>1</sub>, the molecule can also decay back to the ground state without the emission of a photon (non-radiativeally). This is not a good thing when we are interested in light emission. It could also decay back to the ground state by emitting a photon, which is referred to as a '''fluorescence''' phenomenon ('''k<sub>fl</sub>'''). All these processes have rates that are generally typical for conjugated molecules. <br />
<br />
Starting at S<sub>0</sub> a photon is absorbed, spin multiplicity is conserved, and the electron gets into S<sub>1</sub>. Then in some instances, a crossover to the triplet manifold T<sub>1</sub> can occur. This crossover to the triplet manifold is referred to as intersystem crossing. The '''K<sub>isc</sub>''' shown between S<sub>1</sub> and T<sub>1</sub> represents the intersystem crossing. The intersystem crossing can cause molecule to trickle down back to the bottom of T<sub>1</sub>, thus intersystem crossing is followed by internal conversion. At the bottom of the T<sub>1</sub> state, the molecule usually lives for a pretty long time. Since it is metastable, the probability of it descending back to the ground state is small but even so eventually happens. If it occurs radiadivally then a phosphorescence can be produced. It could also come down from T<sub>1</sub> via emission of vibrations through internal conversion. Molecules that are efficient enough to be used in a display must have very large rates for fluorescence or phosphorescence. With a molecule such as naphtaline, a flat hypercarbon, the probability of this fluoresence occuring is extremely small. But there is a way to increase the probability.<br />
<br />
=== Singlets and Triplets ===<br />
<br />
[[Image:Singlettripletspin.png|thumb|400px|This slide shows you the distinction between a singlet and triplet.]]<br />
It is important to know that states refer to the multi-electron system. We will make an approximation and simply look at the orbital levels, HOMO, LUMO and so on. In a large number of cases, the first excited state can mainly be described by the promotion of an electron from the HOMO level to the LUMO Level. The first energy level diagram of the four shows a spin of +1/2 in the HOMO and a spin of +1/2 in the LUMO. (This doesn’t mean that this first case always occurs in excitation; it is just possible to have this situation at some point.) In this case, the two spins are aligned and the total spin number is 1. This case is one of the triplet states. Another triplet state can occur like the 2nd energy diagram shown on the right of the first. It is also possible to have opposite spins. The third diagram shows a situation where the spin is +½ or what I refer to as &alpha; on the HOMO, and the spin is -½ or &beta; on the LUMO. The fourth diagram shows the reverse of the third: there is a -1/2 &beta; on the HOMO and +1/2 &alpha; on the LUMO. The first two situations and diagrams represent pure quanta-mechanical spin states. However, the last two are not; only their combination is. Therefore, there are two ways to obtain a triplet state. One way to have both electron spins to have the same direction. The way is to take the linear positive combination of the last two diagrams. This is done on the slide with the proper normalization factor; the &alpha; for electron 1 and &beta; for electron 2 plus the fourth diagram which has an &alpha; for electron 2 and &beta; for electron 1. This defines the third triplet configuration. <br />
<br clear='all'><br />
[[Image:Spinstates.png|thumb|300px|Magnetic numbers for triplet state]]<br />
Thus, the triplet state has a multiplicity of three with magnetic numbers of +1 (first diagram), -1(second diagram), and 0(combination of the last two diagrams), and total spin number in all cases is equal to 1. The singlet state is the subtraction of those two spin configurations in the last two diagrams. Usually, when referring to a singlet state, there is one spin like with an upward direction and the other spin has a downward direction. However, the quantum mechanical situation is a bit more complex than what this leads you to believe. For the triplet, the two spin configurations are easy to pinpoint but the third one only exists in combination. Remember that the third spin configuration diagram and the last spin configuration do not correspond to pure states. Their plus and minus combination is necessary to get to the actual spin state.<br />
<br />
== External Links ==<br />
<br />
See Wikipedia on [http://en.wikipedia.org/wiki/Jablonski_diagram Jablonksi diagram]<br />
<br />
[http://www.shsu.edu/~chm_tgc/sounds/flashfiles/Jablonski.swf Flash animation of processes involved in Jablonski diagram]<br />
[[category:absorption]]<br />
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<br />
Jablonski diagrams are common representations of the possible electronic states and transitions as molecules enter and leave the excited state. Aleksander Jabłoński was a Polish scientist who did significant research on fluorescence and molecular photophysics in the 1930's. Jablonski diagrams describe the electronic states of molecules, transitions and associated light emitting phenomena. Though Jablonski diagrams resemble one-electron bandgap diagrams, they represent different things. Horizontal lines in a Jablonski diagram represent energetic states of a molecule or system, not the discrete electronic energy levels depicted in one-electron diagrams.<br />
<br />
[[Image:Jablonski.png|thumb|400px|Several processes are illustrated and are indicated by the rate constants that characterize the processes shown, including absorption of light, fluorescence, internal conversion, intersystem crossing and phosphorescence]]<br />
<br />
=== Meaning of Levels ===<br />
<br />
It is important to understand the premises of the Jablonski Diagrams. <br />
<br />
:'''S<sub>0</sub>''' is the ground state of the molecule, <br />
<br />
:'''S<sub>1</sub>''' is the first excited state and S<sub>n</sub> is the nth excited state. <br />
<br />
There is an energy axis labeled E. These levels can be also described through potential energy surfaces. Within within each state, you have a range of vibrational levels. Vibrational ground states are shown with thick lines and higher vibrational states are shown with thin lines. Nonradiative transitions are shown with straight lines and radiative transitions are shown with squiggly lines.<br />
<br />
The Y axis represents the spin multiplicity. There is singlet spin multiplicity where the total spin number is zero. Since any plus ½ spin corresponds to a minus ½ spin, the total spin results as zero. There is a single way of putting all the spins so this is referred to as a '''singlet state'''. It is also possible to have '''triplet states''' that have total spin number is +1. <br />
<br />
:'''T<sub>1</sub>''' shows the lowest excited triplet state. S<sub>1</sub> refers to the excited singlet state. The 0 refers to the ground state. <br />
<br />
:'''T<sub>n</sub>''' is also a higher lying triplet state<br />
<br />
Usually, when drawing or writing a Jablonski Diagram, the singlet states are on the left hand side. In the case of singlet states, the total spin number is zero and the molecule is [[diamagnetic]]. In most instances, those &pi;-conjugated molecules in the ground state have spins that are all paired. Molecules with triplet states are drawn on the right hand side and the molecules are [[paramagnetic]]. An example of a paramagnetic molecule is oxygen, that has two &pi; levels that have the same energy and therefore, the two electrons point upwards. What is referred to as singlet oxygen is actually 1 eV above the ground state of oxygen and it is a pretty nasty molecule.<br />
<br />
=== Excitation ===<br />
<br />
In general, chromophores have a ground state that is a singlet and an excited state that will be singlet or sometimes triplets. Light emitting systems deal with triplet states. That is why triplets are important. Once the molecules are excited, many photophysical processes can occur. When the molecule that is in the ground state is excited, the photon energy will bring it into the S<sub>1</sub> electronic state at a higher vibrational level. Once we have the absorption '''K<sub>abs</sub>''', the molecule can trickle back down from the maximum line in the S<sub>1</sub> to the minimum of the S<sub>1</sub> state. It does that by going down the vibrational levels and therefore, vibrations are created in the molecule. That is how the molecule loses its energy. This process is referred to as '''internal conversion''' ('''k<sub>ic</sub>''') because it remains within the same spin manifold and possibly within the same excited states. Then from the minimum of S<sub>1</sub>, the molecule can also decay back to the ground state without the emission of a photon (non-radiativeally). This is not a good thing when we are interested in light emission. It could also decay back to the ground state by emitting a photon, which is referred to as a '''fluorescence''' phenomenon ('''k<sub>fl</sub>'''). All these processes have rates that are generally typical for conjugated molecules. <br />
<br />
Starting at S<sub>0</sub> a photon is absorbed, spin multiplicity is conserved, and the electron gets into S<sub>1</sub>. Then in some instances, a crossover to the triplet manifold T<sub>1</sub> can occur. This crossover to the triplet manifold is referred to as intersystem crossing. The '''K<sub>isc</sub>''' shown between S<sub>1</sub> and T<sub>1</sub> represents the intersystem crossing. The intersystem crossing can cause molecule to trickle down back to the bottom of T<sub>1</sub>, thus intersystem crossing is followed by internal conversion. At the bottom of the T<sub>1</sub> state, the molecule usually lives for a pretty long time. Since it is metastable, the probability of it descending back to the ground state is small but even so eventually happens. If it occurs radiadivally then a phosphorescence can be produced. It could also come down from T<sub>1</sub> via emission of vibrations through internal conversion. Molecules that are efficient enough to be used in a display must have very large rates for fluorescence or phosphorescence. With a molecule such as naphtaline, a flat hypercarbon, the probability of this fluoresence occuring is extremely small. But there is a way to increase the probability.<br />
<br />
=== Singlets and Triplets ===<br />
<br />
[[Image:Singlettripletspin.png|thumb|400px|This slide shows you the distinction between a singlet and triplet.]]<br />
It is important to know that states refer to the multi-electron system. We will make an approximation and simply look at the orbital levels, HOMO, LUMO and so on. In a large number of cases, the first excited state can mainly be described by the promotion of an electron from the HOMO level to the LUMO Level. The first energy level diagram of the four shows a spin of +1/2 in the HOMO and a spin of +1/2 in the LUMO. (This doesn’t mean that this first case always occurs in excitation; it is just possible to have this situation at some point.) In this case, the two spins are aligned and the total spin number is 1. This case is one of the triplet states. Another triplet state can occur like the 2nd energy diagram shown on the right of the first. It is also possible to have opposite spins. The third diagram shows a situation where the spin is +½ or what I refer to as &alpha; on the HOMO, and the spin is -½ or &beta; on the LUMO. The fourth diagram shows the reverse of the third: there is a -1/2 &beta; on the HOMO and +1/2 &alpha; on the LUMO. The first two situations and diagrams represent pure quanta-mechanical spin states. However, the last two are not; only their combination is. Therefore, there are two ways to obtain a triplet state. One way to have both electron spins to have the same direction. The way is to take the linear positive combination of the last two diagrams. This is done on the slide with the proper normalization factor; the &alpha; for electron 1 and &beta; for electron 2 plus the fourth diagram which has an &alpha; for electron 2 and &beta; for electron 1. This defines the third triplet configuration. <br />
<br clear='all'><br />
[[Image:Spinstates.png|thumb|300px|Magnetic numbers for triplet state]]<br />
Thus, the triplet state has a multiplicity of three with magnetic numbers of +1 (first diagram), -1(second diagram), and 0(combination of the last two diagrams), and total spin number in all cases is equal to 1. The singlet state is the subtraction of those two spin configurations in the last two diagrams. Usually, when referring to a singlet state, there is one spin like with an upward direction and the other spin has a downward direction. However, the quantum mechanical situation is a bit more complex than what this leads you to believe. For the triplet, the two spin configurations are easy to pinpoint but the third one only exists in combination. Remember that the third spin configuration diagram and the last spin configuration do not correspond to pure states. Their plus and minus combination is necessary to get to the actual spin state.<br />
<br />
== External Links ==<br />
<br />
See Wikipedia on [http://en.wikipedia.org/wiki/Jablonski_diagram Jablonksi diagram]<br />
<br />
[http://www.shsu.edu/~chm_tgc/sounds/flashfiles/Jablonski.swf Flash animation of processes involved in Jablonski diagram]<br />
[[category:absorption]]<br />
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<br />
Jablonski diagrams are common representations of the possible electronic states and transitions as molecules enter and leave the excited state. Aleksander Jabłoński was a Polish scientist who did significant research on fluorescence and molecular photophysics in the 1930's. Jablonski diagrams describe the electronic states of molecules, transitions and associated light emitting phenomena. They look somewhat similar to bandgap diagrams but are not the same thing.<br />
<br />
[[Image:Jablonski.png|thumb|400px|Several processes are illustrated and are indicated by the rate constants that characterize the processes shown, including absorption of light, fluorescence, internal conversion, intersystem crossing and phosphorescence]]<br />
<br />
=== Meaning of Levels ===<br />
<br />
It is important to understand the premises of the Jablonski Diagrams. <br />
<br />
:'''S<sub>0</sub>''' is the ground state of the molecule, <br />
<br />
:'''S<sub>1</sub>''' is the first excited state and S<sub>n</sub> is the nth excited state. <br />
<br />
There is an energy axis labeled E. These levels can be also described through potential energy surfaces. Within within each state, you have a range of vibrational levels. Vibrational ground states are shown with thick lines and higher vibrational states are shown with thin lines. Nonradiative transitions are shown with straight lines and radiative transitions are shown with squiggly lines.<br />
<br />
The Y axis represents the spin multiplicity. There is singlet spin multiplicity where the total spin number is zero. Since any plus ½ spin corresponds to a minus ½ spin, the total spin results as zero. There is a single way of putting all the spins so this is referred to as a '''singlet state'''. It is also possible to have '''triplet states''' that have total spin number is +1. <br />
<br />
:'''T<sub>1</sub>''' shows the lowest excited triplet state. S<sub>1</sub> refers to the excited singlet state. The 0 refers to the ground state. <br />
<br />
:'''T<sub>n</sub>''' is also a higher lying triplet state<br />
<br />
Usually, when drawing or writing a Jablonski Diagram, the singlet states are on the left hand side. In the case of singlet states, the total spin number is zero and the molecule is [[diamagnetic]]. In most instances, those &pi;-conjugated molecules in the ground state have spins that are all paired. Molecules with triplet states are drawn on the right hand side and the molecules are [[paramagnetic]]. An example of a paramagnetic molecule is oxygen, that has two &pi; levels that have the same energy and therefore, the two electrons point upwards. What is referred to as singlet oxygen is actually 1 eV above the ground state of oxygen and it is a pretty nasty molecule.<br />
<br />
=== Excitation ===<br />
<br />
In general, chromophores have a ground state that is a singlet and an excited state that will be singlet or sometimes triplets. Light emitting systems deal with triplet states. That is why triplets are important. Once the molecules are excited, many photophysical processes can occur. When the molecule that is in the ground state is excited, the photon energy will bring it into the S<sub>1</sub> electronic state at a higher vibrational level. Once we have the absorption '''K<sub>abs</sub>''', the molecule can trickle back down from the maximum line in the S<sub>1</sub> to the minimum of the S<sub>1</sub> state. It does that by going down the vibrational levels and therefore, vibrations are created in the molecule. That is how the molecule loses its energy. This process is referred to as '''internal conversion''' ('''k<sub>ic</sub>''') because it remains within the same spin manifold and possibly within the same excited states. Then from the minimum of S<sub>1</sub>, the molecule can also decay back to the ground state without the emission of a photon (non-radiativeally). This is not a good thing when we are interested in light emission. It could also decay back to the ground state by emitting a photon, which is referred to as a '''fluorescence''' phenomenon ('''k<sub>fl</sub>'''). All these processes have rates that are generally typical for conjugated molecules. <br />
<br />
Starting at S<sub>0</sub> a photon is absorbed, spin multiplicity is conserved, and the electron gets into S<sub>1</sub>. Then in some instances, a crossover to the triplet manifold T<sub>1</sub> can occur. This crossover to the triplet manifold is referred to as intersystem crossing. The '''K<sub>isc</sub>''' shown between S<sub>1</sub> and T<sub>1</sub> represents the intersystem crossing. The intersystem crossing can cause molecule to trickle down back to the bottom of T<sub>1</sub>, thus intersystem crossing is followed by internal conversion. At the bottom of the T<sub>1</sub> state, the molecule usually lives for a pretty long time. Since it is metastable, the probability of it descending back to the ground state is small but even so eventually happens. If it occurs radiadivally then a phosphorescence can be produced. It could also come down from T<sub>1</sub> via emission of vibrations through internal conversion. Molecules that are efficient enough to be used in a display must have very large rates for fluorescence or phosphorescence. With a molecule such as naphtaline, a flat hypercarbon, the probability of this fluoresence occuring is extremely small. But there is a way to increase the probability.<br />
<br />
=== Singlets and Triplets ===<br />
<br />
[[Image:Singlettripletspin.png|thumb|400px|This slide shows you the distinction between a singlet and triplet.]]<br />
It is important to know that states refer to the multi-electron system. We will make an approximation and simply look at the orbital levels, HOMO, LUMO and so on. In a large number of cases, the first excited state can mainly be described by the promotion of an electron from the HOMO level to the LUMO Level. The first energy level diagram of the four shows a spin of +1/2 in the HOMO and a spin of +1/2 in the LUMO. (This doesn’t mean that this first case always occurs in excitation; it is just possible to have this situation at some point.) In this case, the two spins are aligned and the total spin number is 1. This case is one of the triplet states. Another triplet state can occur like the 2nd energy diagram shown on the right of the first. It is also possible to have opposite spins. The third diagram shows a situation where the spin is +½ or what I refer to as &alpha; on the HOMO, and the spin is -½ or &beta; on the LUMO. The fourth diagram shows the reverse of the third: there is a -1/2 &beta; on the HOMO and +1/2 &alpha; on the LUMO. The first two situations and diagrams represent pure quanta-mechanical spin states. However, the last two are not; only their combination is. Therefore, there are two ways to obtain a triplet state. One way to have both electron spins to have the same direction. The way is to take the linear positive combination of the last two diagrams. This is done on the slide with the proper normalization factor; the &alpha; for electron 1 and &beta; for electron 2 plus the fourth diagram which has an &alpha; for electron 2 and &beta; for electron 1. This defines the third triplet configuration. <br />
<br clear='all'><br />
[[Image:Spinstates.png|thumb|300px|Magnetic numbers for triplet state]]<br />
Thus, the triplet state has a multiplicity of three with magnetic numbers of +1 (first diagram), -1(second diagram), and 0(combination of the last two diagrams), and total spin number in all cases is equal to 1. The singlet state is the subtraction of those two spin configurations in the last two diagrams. Usually, when referring to a singlet state, there is one spin like with an upward direction and the other spin has a downward direction. However, the quantum mechanical situation is a bit more complex than what this leads you to believe. For the triplet, the two spin configurations are easy to pinpoint but the third one only exists in combination. Remember that the third spin configuration diagram and the last spin configuration do not correspond to pure states. Their plus and minus combination is necessary to get to the actual spin state.<br />
<br />
== External Links ==<br />
<br />
See Wikipedia on [http://en.wikipedia.org/wiki/Jablonski_diagram Jablonksi diagram]<br />
<br />
[http://www.shsu.edu/~chm_tgc/sounds/flashfiles/Jablonski.swf Flash animation of processes involved in Jablonski diagram]<br />
[[category:absorption]]<br />
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Absorption of electromagnetic radiation (light) occurs when the energy of a photon is transferred to matter. Absorption can occur in atoms by promoting an electron to higher energetic states. In molecules, absorption can result from transitions into higher electronic, vibrational, and rotational states. The absorption of light is fundamental process relevant to many photonics materials and devices. <br />
<br />
== Plank's relation ==<br />
<br />
Light can be characterized in multiple ways, notably, either by its frequency, which is the number of oscillations per second, or its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s . <br />
<br />
In the early 20th century, Planck showed that the energy of a photon can be related to its frequency by using the Planck relation (also called the Planck-Einstein equation) <br />
<br />
:<math>E=h \nu\!</math> <br />
<br />
or, since λν = c: <br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is directly proportional to its frequency and inversely proportional to its wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
== Excitation vs polarization ==<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
== Solvent effects ==<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
== Energy Units ==<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
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</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Introduction_to_Absorption&diff=7114Introduction to Absorption2010-06-15T22:14:48Z<p>Knoone: </p>
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Absorption of electromagnetic radiation (light) occurs when the energy of a photon is transferred to matter. Absorption can occur in atoms by promoting an electron to higher energetic states. In molecules, absorption can result from transitions into higher electronic, vibrational, and rotational states.<br />
<br />
== Plank's relation ==<br />
<br />
Light can be characterized in multiple ways, notably, either by its frequency, which is the number of oscillations per second, or its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s . <br />
<br />
In the early 20th century, Planck showed that the energy of a photon can be related to its frequency by using the Planck relation (also called the Planck-Einstein equation) <br />
<br />
:<math>E=h \nu\!</math> <br />
<br />
or, since λν = c: <br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is directly proportional to its frequency and inversely proportional to its wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
== Excitation vs polarization ==<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
== Solvent effects ==<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
== Energy Units ==<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
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</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Introduction_to_Absorption&diff=7113Introduction to Absorption2010-06-15T21:30:40Z<p>Knoone: /* Plank's relation */</p>
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</table><br />
The absorption of light is fundamental process that ties together all aspects of photonics materials and devices.<br />
=== Plank's relation ===<br />
<br />
Light can be characterized in multiple ways, notably, either by its frequency, which is the number of oscillations per second, or its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s . <br />
<br />
In the early 20th century, Planck showed that the energy of a photon can be related to its frequency by using the Planck relation (also called the Planck-Einstein equation) <br />
<br />
:<math>E=h \nu\!</math> <br />
<br />
or, since λν = c: <br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is directly proportional to its frequency and inversely proportional to its wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
=== Excitation vs polarization ===<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
=== Solvent effects ===<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
=== Energy Units ===<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
</tr><br />
</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Introduction_to_Absorption&diff=7112Introduction to Absorption2010-06-15T21:18:43Z<p>Knoone: /* Plank's relation */</p>
<hr />
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<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
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</table><br />
The absorption of light is fundamental process that ties together all aspects of photonics materials and devices.<br />
=== Plank's relation ===<br />
<br />
We can characterize light in multiple ways, notably, either by its frequency, which is the number of oscillations per second, or its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s . <br />
<br />
In the early 20th century, Planck showed that the energy of a photon can be related to its frequency by using the Planck relation (also called the Planck-Einstein equation) <br />
<br />
:<math>E=h \nu\!</math> <br />
<br />
or, since λν = c: <br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is directly proportional to its frequency and inversely proportional to its wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
=== Excitation vs polarization ===<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
=== Solvent effects ===<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
=== Energy Units ===<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
</tr><br />
</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Introduction_to_Absorption&diff=7111Introduction to Absorption2010-06-15T19:45:52Z<p>Knoone: /* Plank's relation */</p>
<hr />
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<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
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</table><br />
The absorption of light is fundamental process that ties together all aspects of photonics materials and devices.<br />
=== Plank's relation ===<br />
<br />
We can characterize light in multiple ways, notably, either by its frequency, which is the number of oscillations per second, or its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s . <br />
<br />
In the early 20th century, Planck showed that the energy of a photon can be related to its frequency by using the Planck relation (also called the Planck-Einstein equation) <br />
<br />
:<math>E=h \nu\!</math> <br />
<br />
or, since <math>{C\lambda}=c!</math>:<br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is directly proportional to its frequency and inversely proportional to its wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
=== Excitation vs polarization ===<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
=== Solvent effects ===<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
=== Energy Units ===<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
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</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Introduction_to_Absorption&diff=7110Introduction to Absorption2010-06-15T19:32:11Z<p>Knoone: /* Plank's relation */</p>
<hr />
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<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
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</table><br />
The absorption of light is fundamental process that ties together all aspects of photonics materials and devices.<br />
=== Plank's relation ===<br />
<br />
We can characterize light in multiple ways, notably, either by its frequency, which is the number of oscillations per second, or its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s . Planck showed many years back that the energy of a photon can be related to its frequency by using the Planck’s relation <br />
<br />
:<math>E=h \nu\!</math> <br />
<br />
or <br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is directly proportional to its frequency and inversely proportional to its wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
=== Excitation vs polarization ===<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
=== Solvent effects ===<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
=== Energy Units ===<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
</tr><br />
</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Introduction_to_Absorption&diff=7109Introduction to Absorption2010-06-15T19:31:39Z<p>Knoone: /* Plank's relation */</p>
<hr />
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<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
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</tr><br />
</table><br />
The absorption of light is fundamental process that ties together all aspects of photonics materials and devices.<br />
=== Plank's relation ===<br />
<br />
We can characterize light in multiple ways. Light can be characterized by its frequency, which is the number of oscillations per second, and its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s . Planck showed many years back that the energy of a photon can be related to its frequency by using the Planck’s relation <br />
<br />
:<math>E=h \nu\!</math> <br />
<br />
or <br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is directly proportional to its frequency and inversely proportional to its wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
=== Excitation vs polarization ===<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
=== Solvent effects ===<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
=== Energy Units ===<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
</tr><br />
</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Introduction_to_Absorption&diff=6792Introduction to Absorption2010-04-28T18:30:20Z<p>Knoone: /* Plank's relation */</p>
<hr />
<div><table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
</tr><br />
</table><br />
The absorption of light is fundamental process that ties together all aspects of photonics materials and devices.<br />
=== Plank's relation ===<br />
<br />
We can characterize light in multiple ways. In a very simple way, light can be characterized by its frequency, which is the number of oscillations per second, and its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s . Planck showed many years back that the energy of a photon can be related to its frequency by using the Planck’s relation <br />
<br />
:<math>E=h \nu\!</math> <br />
<br />
or <br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is directly proportional to its frequency and inversely proportional to its wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
=== Excitation vs polarization ===<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
=== Solvent effects ===<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
=== Energy Units ===<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
</tr><br />
</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Introduction_to_Absorption&diff=6791Introduction to Absorption2010-04-28T18:29:20Z<p>Knoone: /* Plank's relation */</p>
<hr />
<div><table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
</tr><br />
</table><br />
The absorption of light is fundamental process that ties together all aspects of photonics materials and devices.<br />
=== Plank's relation ===<br />
<br />
We can characterize light in multiple ways. In a very simple way, light can be characterized by its frequency, which is the number of oscillations per second, and its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s . Planck showed many years back that the energy of a photon can be related to its frequency by using the Planck’s relation <br />
<br />
:<math>E=h \nu\!</math> <br />
<br />
or <br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is the linear function of the frequency, and is also inversely proportional to the wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
=== Excitation vs polarization ===<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
=== Solvent effects ===<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
=== Energy Units ===<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
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</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Introduction_to_Absorption&diff=6790Introduction to Absorption2010-04-28T18:26:54Z<p>Knoone: /* Plank's relation */</p>
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<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
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The absorption of light is fundamental process that ties together all aspects of photonics materials and devices.<br />
=== Plank's relation ===<br />
<br />
We can characterize light in multiple ways. In a very simple way, light can be characterized by its frequency, which is the number of oscillations per second, and its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s . Planck showed many years back that the energy of a photon can be related to its frequency by using the Planck’s relation <br />
<br />
:<math>E=h \nu,\!</math> <br />
<br />
or <br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is the linear function of the frequency, and is also inversely proportional to the wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
=== Excitation vs polarization ===<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
=== Solvent effects ===<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
=== Energy Units ===<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
</tr><br />
</table></div>Knoonehttp://cleanenergywiki.org/index.php?title=Introduction_to_Absorption&diff=6789Introduction to Absorption2010-04-28T18:18:05Z<p>Knoone: /* Plank's relation */</p>
<hr />
<div><table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
</tr><br />
</table><br />
The absorption of light is fundamental process that ties together all aspects of photonics materials and devices.<br />
=== Plank's relation ===<br />
<br />
We can characterize light in multiple ways. In a very simple way, light can be characterized by its frequency, which is the number of oscillations per second, and its wavelength, literally the distance between peaks in a sinosoidal curve. Also, for any wave, the product of its wavelength times its frequency is the speed of that wave. For example, the speed of light traveling in a vacuum is roughly 3x 10^08 m/s . Planck showed many years back that the energy of a photon can be related to its frequency by using the Planck’s relation <br />
<br />
:<math>E=\frac {h} {nu}\,\!</math> <br />
<br />
or <br />
<br />
:<math>E=\frac {h c}{\lambda} \,\!</math> <br />
<br />
where<br />
<br />
:<math>h\,\!</math> is Planck's Constant<br />
<br />
:<math>\nu\,\!</math> is frequency<br />
<br />
:<math>\lambda\,\!</math> is wavelength<br />
<br />
<br />
Thus, the energy of the light is the linear function of the frequency, and is also inversely proportional to the wavelength. One distinction that is important to understand is that the energy of light as a function of a frequency and also the field strength of light . The strength of the field of light is called the intensity of light. If it is very intense and you look into it, it can blind you. The energy we are discussing here is the energy of a photon. If there is a ground state and an excited state, there will be a certain wavelength of light that is required in order to achieve an absorption by the molecule.<br />
<br />
=== Excitation vs polarization ===<br />
<br />
A molecule can interact with light and light can be absorbed. There is a transition with a starting state and a final state. These lines the HOMO of the molecule to the LUMO of the molecule. A beam of light excites the molecule causing one electron to jump from the HOMO (a filled orbital) to the LUMO (an unfilled orbital). This is a simple one electron picture. If there is a true absorption of a photon, this state will have a finite lifetime. That means that after the electric field is removed, (i.e the light is shut off,) the molecule will be metastable in that state and will come back down to the ground state with a certain characteristic lifetime. Even if the light does not have enough energy to promote an electron from one level to another, it can still get the electrons in the molecule to resonate back and forth and oscillate; this process is referred to as polarization. However, as soon as that field is removed, the molecule will be instantaneously back in its ground state. <br />
<br />
In the case of excitation / absorption the energy has transferred from the electric field to the system and it is stored temporarily, or in other words, gained potential energy. That potential energy is associated with this electron not being in the ground state. In the case of polarization, no energy is stored in the molecule. Therefore, two situations can occur; in one case there is a transference of energy to the molecule, and in the other case, there isn’t. There are several parameters that can be used to characterize the transition of the promotion of the electron. One of the parameters is the energy of the photon and the associated wavelength that is required to promote the electron from one level, to the one above it. Another parameter is the inherent ability of a molecule to absorb the light. The presence of two states, one below and above, and the addition of a photon that has the appropriate energy to couple those two states and allow the electron to be promoted from the lower state to the higher state energetically, is not sufficient to assure that light will be absorbed. There are other factors about the molecule that have to be met in order for the molecule to absorb the light beam. This is illustrated by absorption spectra; some absorption bands are strong and some are weak. This means that certain transitions are more allowed than others and certain transitions are forbidden, which is because they are not quantum mechanically allowed.<br />
<br />
<br />
=== Solvent effects ===<br />
<br />
The Planck relation tells us exactly what energy is required of the photon to get the promotion of an electron from a ground state to an excited state. <br />
<br />
:<math>\Delta E_g = E_{excited state} - E_{ground state} = h \nu\,\!</math><br />
<br />
Basically, the energy of the photon should equal to the difference in energy of the excited state and the energy of the ground state(excited state energy – ground state energy). A photon of frequency &nu; corresponds to the energy gap between states. In real molecules, it is not always true that there is only a single energy able to excite the molecule. Molecules have a variety of vibrational states and rotational states. Also, molecules as at least in the condensed state as in a polymer or in solution, are fundamentally inhomogeneous. When a molecule is put into a solvent, it is very unlikely that there will be another molecule in the solution that has exactly the same orientation of every solvent molecule around it or in the 2nd sphere around it that will be identical. Consequently, for each molecule that has a different solvation sphere will have slightly different energy. It could be too small to measure but in some cases, it can be quite dramatic. <br />
<br />
The question now is “what would give rise to different energies?”. If you take a polar molecule and put it into a polar solvent. The dipoles of the solvent will reorient around the ground state dipole of the molecule in such a way to stabilize it. This will lead specifically to an energy stabilization of the system. Now all of those solvent molecules are not static so in any given time, the molecule is actually surrounded by solvent molecules that are moving. Since there are many different solvent molecules, each molecule is going to have a slightly different orientation of the solvent around. This is going to cause the slightly different stabilization of the ground state. It turns out that the excited state of the molecule can have a dipole moment and the excited state dipole need not be the same as the ground state dipole. In addition, the excited state might be stabilized differently than the ground state. All these factors can lead to further broadening within the same solvent. So to draw an absorption spectra as one frequency is a completely idealized case because molecules themselves have vibrational states and broadening of their spectra due to the fact that molecules can be in different solvents. There are also quantum mechanical aspects that lead to uncertainty in measurement of that energy.<br />
<br />
<br />
=== Energy Units ===<br />
<br />
There are different units of energy used to characterize photon energies and all energies. This is very important to understand because it helps you move along between the language of physics, language of chemistry, and the language of spectroscopy. The units of energy are: <br />
<br />
<br />
:<math>1 eV = 23 Kcal/mol = 8065 cm^{-1}= 1240 nm\,\!</math><br />
<br />
<br />
This is worth memorizing.<br />
<br />
[[category:absorption]]<br />
<table id="toc" style="width: 100%"><br />
<tr><br />
<br />
<td style="text-align: center; width: 33%">[[Main_Page#Absorption and Emission of Light|Return to Absorption and Emission Menu]]</td><br />
<td style="text-align: right; width: 33%">[[Changes in Absorption Spectra| Next Topic]]</td><br />
</tr><br />
</table></div>Knoone