Interchain Interactions - Revision history

Cmditradmin: /* Transition dipole in isolation */

2010-08-10T23:04:46Z

Transition dipole in isolation

← Older revision		Revision as of 16:04, 10 August 2010
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	In stilbene the transition dipole for the S<sub>0</sub> → S<sub>1</sub> transition and the S<sub>1</sub> →S<sub>0</sub> transition is polarized mainly along the long axis (x axis) of the molecule. This is generally the case in pi conjugated systems because as you extend the length of the chain electrons are delocalized over a longer distance, just as in an electrostatic dipole a larger distance of charge separation make for a larger dipole moment. An exception is pentacine whose first optical transition is polarized at 90 degrees from the long axis of the chain. In most other optical polymers such as polyvinylene and polythiophene the optical transition is polarized along the long axis.		In stilbene the transition dipole for the S<sub>0</sub> → S<sub>1</sub> transition and the S<sub>1</sub> →S<sub>0</sub> transition is polarized mainly along the long axis (x axis) of the molecule. This is generally the case in pi conjugated systems because as you extend the length of the chain electrons are delocalized over a longer distance, just as in an electrostatic dipole a larger distance of charge separation make for a larger dipole moment. An exception is pentacine whose first optical transition is polarized at 90 degrees from the long axis of the chain. In most other optical polymers such as polyvinylene and polythiophene the optical transition is polarized along the long axis.

	see Cornil <ref>J. Cornil et al., JACS 120 (1998) 1289 ~~DOI: [http://dx.doi.org/10.1021/ja973761j~~ 10.1021/ja973761j]</ref>		see Cornil <ref>J. Cornil et al., JACS 120 (1998) 1289 {{Doi\|10.1021/ja973761j}}</ref>

	=== Two chain interaction ===		=== Two chain interaction ===

Cmditradmin at 20:07, 29 December 2009

2009-12-29T20:07:19Z

← Older revision		Revision as of 13:07, 29 December 2009
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	[[category:absorption]]		[[category:absorption]]
			[[category:Intermolecular interactions]]
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Cmditradmin at 20:06, 29 December 2009

2009-12-29T20:06:18Z

← Older revision		Revision as of 13:06, 29 December 2009
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			[[category:absorption]]
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Cmditradmin at 21:02, 7 December 2009

2009-12-07T21:02:33Z

← Older revision		Revision as of 14:02, 7 December 2009
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	A transition dipole is directly related to the probability of a transition occurring from one excited state to the ground, or the ground to the excited state. It is also related to the intensity of the exciting energy.		A transition dipole is directly related to the probability of a transition occurring from one excited state to the ground, or the ground to the excited state. It is also related to the intensity of the exciting energy.

	If the wave function for the S<sub>1</sub> state is localized in a different area of space than the ground state then transition dipole will be zero. There must be wave function overlap for the ~~wavefunction~~ equation to be non-zero.		If the wave function for the S<sub>1</sub> state is localized in a different area of space than the ground state then transition dipole will be zero. There must be wave function overlap for the wave function equation to be non-zero.

	In stilbene the transition dipole for the S<sub>0</sub> → S<sub>1</sub> transition and the S<sub>1</sub> →S<sub>0</sub> transition is polarized mainly along the long axis (x axis) of the molecule. This is generally the case in pi conjugated systems because as you extend the length of the chain electrons are delocalized over a longer distance, just as in an electrostatic dipole a larger distance of charge separation make for a larger dipole moment. An exception is pentacine whose first optical transition is polarized at 90 degrees from the long axis of the chain. In most other optical polymers such as polyvinylene and polythiophene the optical transition is polarized along the long axis.		In stilbene the transition dipole for the S<sub>0</sub> → S<sub>1</sub> transition and the S<sub>1</sub> →S<sub>0</sub> transition is polarized mainly along the long axis (x axis) of the molecule. This is generally the case in pi conjugated systems because as you extend the length of the chain electrons are delocalized over a longer distance, just as in an electrostatic dipole a larger distance of charge separation make for a larger dipole moment. An exception is pentacine whose first optical transition is polarized at 90 degrees from the long axis of the chain. In most other optical polymers such as polyvinylene and polythiophene the optical transition is polarized along the long axis.
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	[[Image:Interchain_coord.png\|thumb\|300px\|Molecules are represented as planes, transition dipole is along X]]		[[Image:Interchain_coord.png\|thumb\|300px\|Molecules are represented as planes, transition dipole is along X]]

	When two chains come into close proximity they there is the possibility during excitation the electron will jump from one chain to another, leaving a hole and forming a charge transfer exciton. The probability of finding h<sup>+</sup> and e<sup>-</sup> on separate chains in S<sub>1</sub> can be obtained from the excited-state ~~wavefunction~~ .		When two chains come into close proximity they there is the possibility during excitation the electron will jump from one chain to another, leaving a hole and forming a charge transfer exciton. The probability of finding h<sup>+</sup> and e<sup>-</sup> on separate chains in S<sub>1</sub> can be obtained from the excited-state wave function .

	S<sub>1</sub> → S<sub>0</sub> intensity can go down since the transition is polarized along x.		S<sub>1</sub> → S<sub>0</sub> intensity can go down since the transition is polarized along x.
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	Consider first the most symmetric configuration which is perfectly cofacial.		Consider first the most symmetric configuration which is perfectly cofacial.

	From a distance of infinity down to 8 Å there is no significant interaction. There is no significant ~~wavefunction~~ overlap between the units.		From a distance of infinity down to 8 Å there is no significant interaction. There is no significant wave function overlap between the units.

	*excitation is always localized on a SINGLE UNIT		*excitation is always localized on a SINGLE UNIT
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	[[Image:Interchain_close.png\|thumb\|300px\|Below 8 Å there is band level splitting]]		[[Image:Interchain_close.png\|thumb\|300px\|Below 8 Å there is band level splitting]]
	When the distance (R) drops below 8 Å , as they do in thin films, the ~~wavefunctions~~ of frontier orbitals (homo and lumo) begin to overlap and you get a new splitting of the homo level. Wavefunctions are delocalized over the two units. They become equally spread in the zone of r~5 Å.		When the distance (R) drops below 8 Å , as they do in thin films, the wave functions of frontier orbitals (homo and lumo) begin to overlap and you get a new splitting of the homo level. Wavefunctions are delocalized over the two units. They become equally spread in the zone of r~5 Å.
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	[[Image:Kasha.png\|thumb\|300px\|Parallel and antiparallel orientations of transition dipole]]		[[Image:Kasha.png\|thumb\|300px\|Parallel and antiparallel orientations of transition dipole]]
	Kasha’s model from goes back fifty years and attempts to explain the emission from the lowest state. He only considered the ~~wavefunction~~ of one molecule interacting with that of another molecule. He did not consider mixing of ~~wavefunctions~~ so a charge transfer state with an electron on one molecule and a hole on another is impossible in his model. The diagram shows two molecules with transition dipoles along the main axis of each, one dipole parallel and the other anti-parallel. When the two dipoles are opposing the energy is less than the parallel situation but the oscillator strength is zero. In the parallel situation the oscillator strength is large and but the energy required to get there is higher.		Kasha’s model from goes back fifty years and attempts to explain the emission from the lowest state. He only considered the wave function of one molecule interacting with that of another molecule. He did not consider mixing of wave functions so a charge transfer state with an electron on one molecule and a hole on another is impossible in his model. The diagram shows two molecules with transition dipoles along the main axis of each, one dipole parallel and the other anti-parallel. When the two dipoles are opposing the energy is less than the parallel situation but the oscillator strength is zero. In the parallel situation the oscillator strength is large and but the energy required to get there is higher.
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	[[Image:Bandsplitting2.png\|thumb\|300px\|Interaction between molecules leads to band splitting]]		[[Image:Bandsplitting2.png\|thumb\|300px\|Interaction between molecules leads to band splitting]]
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	[[Image:Cofacial_energy.png\|thumb\|300px\|Transition energy vs distance between molecules. Blue and red lines show shift of interacting molecules due to bandsplitting.]]		[[Image:Cofacial_energy.png\|thumb\|300px\|Transition energy vs distance between molecules. Blue and red lines show shift of interacting molecules due to bandsplitting.]]
	As molecules get closer and closer (approaching 4 Å) in cofacial configuration their ~~wavefunctions~~ interact and there is a splitting into S<sub>1</sub> and S<sub>2</sub>. This results in a blue shift of the absorption because the molecule has to get up to the higher S<sub>2</sub> state since S<sub>1</sub> is not optically coupled with the ground state.		As molecules get closer and closer (approaching 4 Å) in cofacial configuration their wave functions interact and there is a splitting into S<sub>1</sub> and S<sub>2</sub>. This results in a blue shift of the absorption because the molecule has to get up to the higher S<sub>2</sub> state since S<sub>1</sub> is not optically coupled with the ground state.
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Cmditradmin: /* Exciton band formation */

2009-09-15T21:30:15Z

Exciton band formation

← Older revision		Revision as of 14:30, 15 September 2009
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	The HOMO and LUMO may be split to different degrees. In a highly symmetrical situation the transition from the ground state to the lowest excited state (S<sub>1</sub>) is forbidden. The HOMO (au) and the LUMO (bu) is are both ungerade which means the transition is forbidden (because odd time odd is even, times odd is odd and when this is integrated over all space the result is zero).		The HOMO and LUMO may be split to different degrees. In a highly symmetrical situation the transition from the ground state to the lowest excited state (S<sub>1</sub>) is forbidden. The HOMO (au) and the LUMO (bu) is are both ungerade which means the transition is forbidden (because odd time odd is even, times odd is odd and when this is integrated over all space the result is zero).

	If you were able to stack five molecules on top of each other, you could have five excited states corresponding the mixing of the five states corresponding to the five S<sub>1</sub> states, this is known as an exciton band. Even if a higher excited state such as S<sub>2</sub> is achieved, Kasha’s Rule dictates that energy will relax down to lower states and the emission can only occur from the lowest excited state. S<sub>1</sub> can not transition to S<sub>0</sub>, it is a “dark state” .The lowest state of that exciton band will be dark and luminescence is quenched.		If you were able to stack five molecules on top of each other, you could have five excited states corresponding the mixing of the five states corresponding to the five S<sub>1</sub> states, this is known as an exciton band. Even if a higher excited state such as S<sub>2</sub> is achieved, '''Kasha’s Rule''' dictates that energy will relax down to lower states and the emission can only occur from the lowest excited state. S<sub>1</sub> can not transition to S<sub>0</sub>, it is a “dark state” .The lowest state of that exciton band will be dark and luminescence is quenched.
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	[[Image:Kasha.png\|thumb\|300px\|Parallel and antiparallel orientations of transition dipole]]		[[Image:Kasha.png\|thumb\|300px\|Parallel and antiparallel orientations of transition dipole]]

Cmditradmin: /* Exciton band formation */

2009-09-15T21:28:27Z

Exciton band formation

← Older revision		Revision as of 14:28, 15 September 2009
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	The HOMO and LUMO may be split to different degrees. In a highly symmetrical situation the transition from the ground state to the lowest excited state (S<sub>1</sub>) is forbidden. The HOMO (au) and the LUMO (bu) is are both ungerade which means the transition is forbidden (because odd time odd is even, times odd is odd and when this is integrated over all space the result is zero).		The HOMO and LUMO may be split to different degrees. In a highly symmetrical situation the transition from the ground state to the lowest excited state (S<sub>1</sub>) is forbidden. The HOMO (au) and the LUMO (bu) is are both ungerade which means the transition is forbidden (because odd time odd is even, times odd is odd and when this is integrated over all space the result is zero).

	If you were able to stack five molecules on top of each other, you could have five ~~exciting~~ states corresponding the mixing of the five states corresponding to the five S<sub>1</sub> states, this is known as an exciton band. Even if a higher excited state such as S<sub>2</sub> is achieved, Kasha’s Rule dictates that energy will relax down to lower states and the emission can only occur from the lowest excited state. S<sub>1</sub> can not transition to S<sub>0</sub>, it is a “dark state” .The lowest state of that exciton band will be dark and luminescence is quenched.		If you were able to stack five molecules on top of each other, you could have five excited states corresponding the mixing of the five states corresponding to the five S<sub>1</sub> states, this is known as an exciton band. Even if a higher excited state such as S<sub>2</sub> is achieved, Kasha’s Rule dictates that energy will relax down to lower states and the emission can only occur from the lowest excited state. S<sub>1</sub> can not transition to S<sub>0</sub>, it is a “dark state” .The lowest state of that exciton band will be dark and luminescence is quenched.
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	[[Image:Kasha.png\|thumb\|300px\|Parallel and antiparallel orientations of transition dipole]]		[[Image:Kasha.png\|thumb\|300px\|Parallel and antiparallel orientations of transition dipole]]
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	[[Image:Bandsplitting2.png\|thumb\|300px\|Interaction between molecules leads to band splitting]]		[[Image:Bandsplitting2.png\|thumb\|300px\|Interaction between molecules leads to band splitting]]
	So when two transition dipoles interact, the two S<sub>1</sub> states split forming a two state exciton band with S<sub>1</sub> and S<sub>2</sub>. The lower ground state S<sub>1</sub> is most favorable because it formed by the antiparallel orientation of the transition dipoles. The S<sub>2</sub> has a high oscillator strength (its bright) but higher energy, S<sub>1</sub> is lower energy but has low oscillator strength (its dark). So in the highly symmetrical situation molecule interact and illumination is quenched.		So when two transition dipoles interact, the two S<sub>1</sub> states split forming a two state exciton band with S<sub>1</sub> and S<sub>2</sub>. The lower ground state S<sub>1</sub> is most favorable because it formed by the antiparallel orientation of the transition dipoles. The S<sub>2</sub> has a high oscillator strength (its bright) but higher energy, S<sub>1</sub> is lower energy but has low oscillator strength (its dark). So in the highly symmetrical situation molecule interact and illumination is quenched.
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	[[Image:Cofacial_energy.png\|thumb\|300px\|Transition energy vs distance between molecules. Blue and red lines show shift of interacting molecules due to bandsplitting.]]		[[Image:Cofacial_energy.png\|thumb\|300px\|Transition energy vs distance between molecules. Blue and red lines show shift of interacting molecules due to bandsplitting.]]

Cmditradmin at 21:25, 15 September 2009

2009-09-15T21:25:50Z

← Older revision		Revision as of 14:25, 15 September 2009
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	Interchain interactions is an important consideration with light emitting polymer and oligomers.		Interchain interactions is an important consideration with light emitting polymer and oligomers.

	Photoluminescence is easily measured by shining light and measuring the emission. In dilute solutions or inert matrices the photoluminescence quantum yield of a given conjugated polymers can be very large: up to 60-80 %.		Photoluminescence is easily measured by shining light and measuring the emission. In dilute solutions or inert matrices the photoluminescence quantum yield of a given conjugated polymers can be very large: up to 60-80 %. However these substances are much more useful if they can deployed as thin films.

	But in thin films the solvent goes away, the polymer chains get closer so they can interact and the luminescence can be nearly totally quenched. The observation of quenching led researchers to explore the cause and remedy for this. (Note:		But in thin films the solvent goes away, the polymer chains get closer so they can interact and the luminescence can be nearly totally quenched. The observation of quenching led researchers to explore the cause and remedy for this. (Note:

Cmditradmin: /* Geometry relaxation effects */

2009-09-01T21:32:59Z

Geometry relaxation effects

← Older revision		Revision as of 14:32, 1 September 2009
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	[[Image:Cofacial_energy_shift.png\|thumb\|300px\|Emission and Absorption intensity vs energy]]		[[Image:Cofacial_energy_shift.png\|thumb\|300px\|Emission and Absorption intensity vs energy]]
	This is a simplified depiction of the spectra that are found experimentally. The black curves represent the isolated molecules. The molecules absorb at a higher energy and emit at a lower energy (emission is redshifted with respect to absorption). When there is cofacial dimer (R= 4 ~~angstrom~~) there is blue shift of absorption because the you can only go to S<sub>2</sub>. If there is no geometry relaxation in the excited state there will be no emission. With relaxation on one molecule there will be reduction of symmetry and some emission that is red shifted with respect to the emission in the isolated system.		This is a simplified depiction of the spectra that are found experimentally. The black curves represent the isolated molecules. The molecules absorb at a higher energy and emit at a lower energy (emission is redshifted with respect to absorption). When there is cofacial dimer (R= 4 Å) there is blue shift of absorption because the you can only go to S<sub>2</sub>. If there is no geometry relaxation in the excited state there will be no emission. With relaxation on one molecule there will be reduction of symmetry and some emission that is red shifted with respect to the emission in the isolated system.

	The larger the transition dipole ( meaning larger oscillator strength, larger electronic coupling) the shorter the excited state lifetime. Strong coupling means there is a high probability that the transition will occur and there will be higher quantum yield. Probability determines the time in the excited state. The longer the molecule stays in the excited state the higher the more time for the system to find vibrations that will allow it to go back to the ground state by other means such as non-radiative decay. This results in a decrease in luminescence quantum yield.		The larger the transition dipole ( meaning larger oscillator strength, larger electronic coupling) the shorter the excited state lifetime. Strong coupling means there is a high probability that the transition will occur and there will be higher quantum yield. Probability determines the time in the excited state. The longer the molecule stays in the excited state the higher the more time for the system to find vibrations that will allow it to go back to the ground state by other means such as non-radiative decay. This results in a decrease in luminescence quantum yield.

	For example there is electron transfer that can take place between PPVm derivative and fullerene C60 that occurs in 35 femptoseconds. That is so short that nothing else can occur. In that case electron transfer has 100% quantum yield. In general the process that is fastest that is the one that will dominate all others.		For example there is electron transfer that can take place between PPVm derivative and fullerene C60 that occurs in 35 femptoseconds. That is so short that nothing else can occur. In that case electron transfer has 100% quantum yield. In general the process that is fastest that is the one that will dominate all others.


	== References ==		== References ==

Cmditradmin: /* Exciton band formation */

2009-09-01T21:32:30Z

Exciton band formation

← Older revision		Revision as of 14:32, 1 September 2009
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	[[Image:Cofacial_energy.png\|thumb\|300px\|Transition energy vs distance between molecules. Blue and red lines show shift of interacting molecules due to bandsplitting.]]		[[Image:Cofacial_energy.png\|thumb\|300px\|Transition energy vs distance between molecules. Blue and red lines show shift of interacting molecules due to bandsplitting.]]
	As molecules get closer and closer (approaching 4 ~~Â~~) in cofacial configuration their wavefunctions interact and there is a splitting into S<sub>1</sub> and S<sub>2</sub>. This results in a blue shift of the ~~aborption~~ because the molecule has to get up to the higher S<sub>2</sub> state since S<sub>1</sub> is not optically coupled with the ground state.		As molecules get closer and closer (approaching 4 Å) in cofacial configuration their wavefunctions interact and there is a splitting into S<sub>1</sub> and S<sub>2</sub>. This results in a blue shift of the absorption because the molecule has to get up to the higher S<sub>2</sub> state since S<sub>1</sub> is not optically coupled with the ground state.
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Cmditradmin: /* Exciton band formation */

2009-09-01T21:30:36Z

Exciton band formation

← Older revision		Revision as of 14:30, 1 September 2009
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	[[Image:Cofacial_energy.png\|thumb\|300px\|Transition energy vs distance between molecules. Blue and red lines show shift of interacting molecules due to bandsplitting.]]		[[Image:Cofacial_energy.png\|thumb\|300px\|Transition energy vs distance between molecules. Blue and red lines show shift of interacting molecules due to bandsplitting.]]
	As molecules get closer and closer (approaching 4 &~~acirc~~;) in cofacial configuration their wavefunctions interact and there is a splitting into S<sub>1</sub> and S<sub>2</sub>. This results in a blue shift of the aborption because the molecule has to get up to the higher S<sub>2</sub> state since S<sub>1</sub> is not optically coupled with the ground state.		As molecules get closer and closer (approaching 4 Â) in cofacial configuration their wavefunctions interact and there is a splitting into S<sub>1</sub> and S<sub>2</sub>. This results in a blue shift of the aborption because the molecule has to get up to the higher S<sub>2</sub> state since S<sub>1</sub> is not optically coupled with the ground state.
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