polarones (9 junio 2014)

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3 mayo 2014

Polarones

ResumenAn exciton is an excited quasiparticle in a solid, which is formed by a

Coulomb-bound electron-hole pair. It is more prominent in organic

semiconductors as compared to their inorganic counterparts: as the

dielectric constant is lower in organics, the screening length is larger. In

this case, the name Frenkel exciton is applied, whereas the weakly bound

type is called Wannier-Mott. (J)

A polaron pair(PP) is a Coulomb bound pair of a negative and a positive

polarons, situated on different molecules. Usually, polaron pairs are the

intermediate step from an exciton to a pair of free polarons far enough

apart not to feel the attraction of one another and therefore important in

order to understand photogeneration in organic semiconductors. (J)

An exciplex is just an exciton which is located at the interface of its host molecular material indeed it still

resides on one molecule as indicated in the image. Due to the influence of the surface, the exciplexexperiences a different environment as compared to a bulk exciton.

A polaron is a charge, i.e., an electron or a hole, plus a distortion of the charges surroundings. In a crystalline

inorganic material, setting a charge onto a site does not change the surroundings, as the crystal lattice is rigid.

Not so in many disordered organic materials. Putting a charge onto a certain molecular site can deform the

whole molecule.

two polarons on a single chain or polaron pair(PP) model. (B)


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Charges on polymer chains connected with a chain distortion appear in the case of holes

as (hole) polarons (Ps, charge +e and spin 1/2). The polaron is just a radical ion (spin 1/2)

associated with a lattice distortion and the presence of localized electronic states in the

gap referred to as polaron states.

(T) When a second electron is removed from the polymer chain, we have two polarons,

a bipolaron(BP) formation. (B) Bipolarons have been considered for a long time as the

doubly charged states (BPs, +2e)

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A)

Our treatment assumes that current is governed solely by generation and recombination at the heterojunction

and that both processes proceed through the polaron pair PP intermediate state.

PhysRevB.82.155305.pdf

(F:\RESPALDOS\Doc\Doctorado\DOCTORADO\Avance marzo - mayo 2014)

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B)

52099169-061-Physical-and-Chemical-Aspects-of-Organic-Electronics.pdf

(F:\Libros y Solucion\Doctorado)

Another proposed mechanism is connected with the doubly charged state of polymer chains, formation and

dissociation of bipolarons. (pg. 317)

Charges on the polymer chains occur as polarons (P) since a chain distortion appears due to electronphonon

coupling. For a long time, bipolarons (BP) [7, 8] have been considered as doubly charged and spin-less states of

the polymer chains. (pg. 317)

two polarons on a single chain or polaron pair (PP) model. Giving a consistent explanation of optical data,the latter was proposed to be preferable compared with the BPmodel. (pg. 317)

Another possibility would be transport of carriers (polarons) connected with formation/dissociation of

bipolarons (a second order reaction). (pg. 319)

the doubly charged state of the polymer chain formed by the polaronpolaron reaction is a bipolaron or a

polaron pair. (pg. 319)

...second order polaron reaction leading to bipolarons. (pg. 331)

16.5 Equilibrium of Polarons With Doubly Charged States of the Polymer Chain (pg. 331)

Charges on polymer chains connected with a chain distortion appear in the case of holes as (hole) polarons

(Ps, charge +e and spin 1/2).(pg. 331)

Bipolarons have been considered for a long time as the doubly charged states [7, 8] (BPs, +2e) (pg. 331)

..formation of doubly charged polymer chain states by polaron pair collision and dissociation of

the doubly charged species,... (pg. 331)


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(pg. 335)

Figure 16.11Equilibrium concentrations of Ps, BPs, and PPs as functions of the electrochemical

potential for different equilibrium constants, zero at midgap position, oxidation potential

E1=1V, m = 6.

16.6.1 Formation and Dissociation of Bipolarons (pg. 339)


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E)

Brutting_Physics of Organic Semiconductors_352740550X.pdf


3.2 Charge Carrier Transport (pg. 6)

(pg. 7)

(pg. 131)

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F)

Device Physics of Organic (libro).pdf



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Figure 3.7: The evolution of the energy levels of a molecular solid from single-molecule levels.

Gaps are decreased due to a polarization effect of the surrounding. Also excited states are

plotted on a separate scale, where the ground state S0 is placed at the position of the HOMO.

Disorder leads to a broadening of the levels.

(pg. 51)

3.2 Energy and charge transport in organic semiconductors (pg. 51)

Energy (exciton) and charge (polaron) transport in a highly ordered molecular crystal and atlow temperatures are comparable to the processes in conventional semiconductors described

in the previous chapter. These quasi-particles are coherently transported in energy bands with

a crystal momentum k.

3.2.1 Exciton transport

An excited state can be transfered to a neighboring molecule. The excited state is then called

an exciton, which provides an energy transport by migration. Such an exciton can be


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delocalized in case of strong intermolecular interactions as present in a highly crystalline solid.

It is then called a Wannier exciton. This is not the case in the studied disordered materials,

where the exciton is mainly located on one molecule and can be treated as a neutral quasi-

particle with polaronic nature, called Frenkel exciton.

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G)0507.Organic Photovoltaics. Mechanisms, Materials, and Devices (Optical Engineering) by Sam-

Shajing Sun.pdf


Devices based on a single polymer face two insurmountable challenges to produce a viable

solar cell. First, absorption of light does not directly generate charge carriers (electronhole

pairs or oppositely charged polarons). The primary photogenerated state is a neutral exciton

with a binding energy of several tenths of an electron volt.

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H)

Solar cell device physics Stephen J. Fonash.pdf

the multi-particle core-electron interactions in which the cores polarize to shield an electron s

charge give rise to multi-particle solutions to the overall Schrdinger equation which are called

polarons. Multi-particle electronelectron interactions can give rise to solutions termed

excitons. Polarons and excitons are examples of multi-particle states . (pg. )

(b) Excitons

Single -crystal, multicrystalline, and microcrystalline solids can also harborthe solutions to the Schrdinger equation that are known as polarons and excitons. (pg. 24)

Polarons are generally only of any significance in crystals with some degree of ionicity. 1

Excitons are of much more interest, since they are a multi-particle phenomenon that can be

involved in the light absorption process in solar cell materials. Specifically, excitons are multi-

electron solutions that may be viewed as an electron bound to a hole via Coulombic attraction.

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http://www.springerimages.com/Images/RSS/1-

10.1007_978-1-4614-0742-3_1-4

Fig 5 Polaron and bipolaron states: (a) positive polaron, (b)

negative polaron, (c) positive bipolaron and (d) negative

bipolaron
http://www.springerimages.com/Images/RSS/1-10.1007_978-1-4614-0742-3_1-4http://www.springerimages.com/Images/RSS/1-10.1007_978-1-4614-0742-3_1-4http://www.springerimages.com/Images/RSS/1-10.1007_978-1-4614-0742-3_1-4http://www.springerimages.com/Images/RSS/1-10.1007_978-1-4614-0742-3_1-4http://www.springerimages.com/Images/RSS/1-10.1007_978-1-4614-0742-3_1-4


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J)

http://blog.disorderedmatter.eu/2008/04/15/polaron-

polaron-pair-exciton-exciplex/

A polaron is a charge, i.e., an electron or a hole, plus a

distortion of the charges surroundings. In a crystalline

inorganic material, setting a charge onto a site does not

change the surroundings, as the crystal lattice is rigid. Not

so in many disordered organic materials. Putting a charge

onto a certain molecular site can deform the whole

molecule. Moving the charge from this to another

molecule means that first the energy for the deformation

the polaron binding energy or reorganisation energy

has to be mustered.

A polaron pair(PP) is a Coulomb bound pair of a negative and a positive polarons, situated ondifferent molecules. Usually, polaron pairs are the intermediate step from an exciton to a pair

of free polarons far enough apart not to feel the attraction of one another and therefore

important in order to understand photogeneration in organic semiconductors.

An excitonis an excited quasiparticle in a solid, which is formed by a Coulomb-bound electron-

hole pair. It is more prominent in organic semiconductors as compared to their inorganic

counterparts: as the dielectric constant is lower in organics, the screening length is larger. In

this case, the name Frenkel exciton is applied, whereas the weakly bound type is called

Wannier-Mott. Thus, in organic materials, the two charges feel a strong mutual attraction, and

usually reside on one molecule.

An exciplexis just an exciton which is located at the interface of its host molecular material

indeed it still resides on one moleculeas indicated in the image. Due to the influence of the

surface, the exciplex experiences a different environment as compared to a bulk exciton. This

leads to photoluminescence which is slighlty red shifted. Also, the lifetime can be prolonged in

comparison to the bulk exciton, as it is stabilised by the surface states.
http://blog.disorderedmatter.eu/2008/04/15/polaron-polaron-pair-exciton-exciplex/http://blog.disorderedmatter.eu/2008/04/15/polaron-polaron-pair-exciton-exciplex/http://blog.disorderedmatter.eu/2008/04/15/polaron-polaron-pair-exciton-exciplex/http://blog.disorderedmatter.eu/2008/04/15/polaron-polaron-pair-exciton-exciplex/http://blog.disorderedmatter.eu/2008/04/15/polaron-polaron-pair-exciton-exciplex/


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K)

http://www.nature.com/nmat/journal/v7/n9/fig_tab/nmat2252_F1.html

Following formation of a polaron pair

(PP), it may either dissociate into freecharge carriers, or recombine through

an exciton state. Here, we focus on the

transition between polaron pairs with

triplet and singlet content. Two

possible mechanisms of moving from

PPS to PPT are illustrated: the first is

through incoherent spin-lattice

relaxation, the second by coherently

driving the pair between the singlet

and triplet configuration using pulsed

electron spin resonance. Electrically

neutral, bound singlet or triplet

excitons (SE, TE) do not contribute to

the current through the device, and

decay radiatively or non-radiatively.

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L)

http://www.nature.com/ncomms/2013/130802/ncomms3286/fig_tab/ncomms3286_F1.html

From

Tuning organic magnetoresistance in polymer-fullerene blends by controlling spin reaction

pathways ; P. Janssen, M. Cox, S.H.W. Wouters, M. Kemerink, M.M. Wienk

& B. Koopmans ; Nature Communications 4, Article number: 2286 doi:10.1038/ncomms3286

Figure 1: Unified picture of relevant particles and their spin-dependent reactions.

(a) Possible polaron pairs in an organic semiconductor as a function of energy. Free charges can

form precursor pairs in a singlet (S) 1( ) or triplet (T) 3( ) configuration. From this pair state, theprecursor pair can either recombine into a S or T exciton (in the case of an eh pair), a S

bipolaron (in the case of a bipolaron pair) or dissociate back into free carriers again. Because of

hyperfine fields (hf) the S and T precursor pairs can mix and an external magnetic field can

suppress this mixing. The magnetic field-dependent transitions between the pair states are

indicated with curved arrows. The energy levels and possible mixing mechanisms of a CTS are

also included in the diagram (shaded area). Electrons and holes are interchangeable in this
http://www.nature.com/nmat/journal/v7/n9/fig_tab/nmat2252_F1.htmlhttp://www.nature.com/nmat/journal/v7/n9/fig_tab/nmat2252_F1.htmlhttp://www.nature.com/ncomms/2013/130802/ncomms3286/fig_tab/ncomms3286_F1.htmlhttp://www.nature.com/ncomms/2013/130802/ncomms3286/fig_tab/ncomms3286_F1.htmlhttp://www.nature.com/ncomms/2013/130802/ncomms3286/fig_tab/ncomms3286_F1.htmlhttp://www.nature.com/nmat/journal/v7/n9/fig_tab/nmat2252_F1.html


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diagram. (b) The characteristic low (red) and high (blue) field lineshapes of the (i) bipolaron, (ii)

eh and (iii) tripletpolaron mechanism, all according to explicit calculations using a density

matrix formalism.

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M)

Bipolarons or Polaron Pairs in Conducting Polymers.pdf

(C:\Datos\RESPALDOS\DOC\Avance marzo - mayo 2014)

http://download.springer.com/static/pdf/269/art%253A10.1134%252FS1023193506110024.p

df?auth66=1399493482_7788ff3fe1811e2db2afb1e178180c84&ext=.pdf

Charges on the polymer chains appear as polarons (Ps) since due to electronphonon couplinga chain distortion appears.

bipolarons (BPs) [5] occur also as charged states of the polymer chains.

Concerning equilibrium and kinetics the [] -dimer (on two adjacent chains) and two polarons

on a single chain are basically equivalent and denoted here as polaron pair (PP).
http://download.springer.com/static/pdf/269/art%253A10.1134%252FS1023193506110024.pdf?auth66=1399493482_7788ff3fe1811e2db2afb1e178180c84&ext=.pdfhttp://download.springer.com/static/pdf/269/art%253A10.1134%252FS1023193506110024.pdf?auth66=1399493482_7788ff3fe1811e2db2afb1e178180c84&ext=.pdfhttp://download.springer.com/static/pdf/269/art%253A10.1134%252FS1023193506110024.pdf?auth66=1399493482_7788ff3fe1811e2db2afb1e178180c84&ext=.pdfhttp://download.springer.com/static/pdf/269/art%253A10.1134%252FS1023193506110024.pdf?auth66=1399493482_7788ff3fe1811e2db2afb1e178180c84&ext=.pdfhttp://download.springer.com/static/pdf/269/art%253A10.1134%252FS1023193506110024.pdf?auth66=1399493482_7788ff3fe1811e2db2afb1e178180c84&ext=.pdf


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Charges on a polymer chain due to oxidation or charge injection at a contact lead primarily to

hole polarons Ps+ (charge +e, spin 1/2).

We denote the concentrations of Ps, BPs, and PPs by cP, cBPand cPP.

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N)

52099169-061-Physical-and-Chemical-Aspects-of-Organic-Electronics.pdf


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O)

Numerical simulations OSC.pdf

(C:\Datos\RESPALDOS\DOC)


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P)

Bipolarons or Polaron Pairs in Conducting Polymers.pdf (C:\Datos\RESPALDOS\DOC\Avance

marzo - mayo 2014)

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Q)

Polaron Pairs in P3HT-PCBM Composite.pdf


http://download.springer.com/static/pdf/750/art%253A10.1007%252Fs00723-012-0401-2.pdf?auth66=1399493746_306f5b6353ea6719551ca4ed103c67af&ext=.pdf

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R)
http://download.springer.com/static/pdf/750/art%253A10.1007%252Fs00723-012-0401-2.pdf?auth66=1399493746_306f5b6353ea6719551ca4ed103c67af&ext=.pdfhttp://download.springer.com/static/pdf/750/art%253A10.1007%252Fs00723-012-0401-2.pdf?auth66=1399493746_306f5b6353ea6719551ca4ed103c67af&ext=.pdfhttp://download.springer.com/static/pdf/750/art%253A10.1007%252Fs00723-012-0401-2.pdf?auth66=1399493746_306f5b6353ea6719551ca4ed103c67af&ext=.pdfhttp://download.springer.com/static/pdf/750/art%253A10.1007%252Fs00723-012-0401-2.pdf?auth66=1399493746_306f5b6353ea6719551ca4ed103c67af&ext=.pdfhttp://download.springer.com/static/pdf/750/art%253A10.1007%252Fs00723-012-0401-2.pdf?auth66=1399493746_306f5b6353ea6719551ca4ed103c67af&ext=.pdf


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S)

m 6 a 10 , monomer units

cP: concentrations of Ps (polarones)


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cBP: concentrations of BPs (bipolarones)

cPP: concentrations of PPs (pares de polarones)

c0: concentration of neutral segments

cS:segment concentration

cmon= mcS: monomer concentration

= 1 g/cm3, mass density

mw = 166 , molecular weightcon m = 6

cS= 5 x 1020cm-3

cmon= mcS= (6) (5 x 1020cm-3) = 3 x 1021cm-3

c0= cPY1

cP= cBPY2

Yi = exp -f(E-Ei)

E1 : standard potentials for the first oxidation step

E2 : standard potentials for the second oxidation step

- eE = F : electrochemical potential is connected with the Fermi energy

1/f = k T /e

cS= c0+ cP + cBP

KBP= exp f(E1E2) = (cBPc0/ cP2)equi.

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http://en.wikipedia.org/wiki/Polymer_solar_cell

animacin

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http://www.amazon.com/Handbook-Organic-Conductive-Molecules-Polymers/dp/0471968137

Handbook of Organic Conductive Molecules and Polymers

++++++++++++++++http://www.chem.wisc.edu/courses/341/handouts/ACR_1985_18_309.pdf

Polarons , bipolarons and solitons in conducting polymers.pdf

C:\Datos\RESPALDOS\DOC

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T)
http://en.wikipedia.org/wiki/Polymer_solar_cellhttp://en.wikipedia.org/wiki/Polymer_solar_cellhttp://www.chem.wisc.edu/courses/341/handouts/ACR_1985_18_309.pdfhttp://www.chem.wisc.edu/courses/341/handouts/ACR_1985_18_309.pdfhttp://www.chem.wisc.edu/courses/341/handouts/ACR_1985_18_309.pdfhttp://en.wikipedia.org/wiki/Polymer_solar_cell


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U)

http://www.nature.com/pj/journal/v17/n1/pdf/pj198517a.pdf

charge storage in conducting polymers, soliton, polaron and bipolaron.pdf

C:\Datos\RESPALDOS\DOC

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http://www.nature.com/pj/journal/v17/n1/pdf/pj198517a.pdfhttp://www.nature.com/pj/journal/v17/n1/pdf/pj198517a.pdfhttp://www.nature.com/pj/journal/v17/n1/pdf/pj198517a.pdf


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http://www.amazon.com/Solitons-Polarons-Conducting-Polymers-L/dp/997150054X

Solitons and Polarons in Conducting Polymers [Paperback]

by L. Yu

http://books.google.com.mx/books?id=l1uaDjUxvpcC&pg=PA267&lpg=PA267&dq=J.L.+Bredas,

+R.R.+Chance,+R.+Silbey,+Phys.+Rev.+B26+(1982)+5843&source=bl&ots=vXOPWEYkH1&sig=3lliOL_g9TBCQkHFiD2dF5WVtcs&hl=es&sa=X&ei=6j96U9TAIMeiqAaJiIGwCw&ved=0CDYQ6AEwA

g#v=onepage&q=J.L.%20Bredas%2C%20R.R.%20Chance%2C%20R.%20Silbey%2C%20Phys.%20

Rev.%20B26%20(1982)%205843&f=false

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http://books.google.com.mx/books?id=6GRovXHas_MC&pg=PA841&lpg=PA841&dq=J.L.+Bred

as,+R.R.+Chance,+R.+Silbey,+Phys.+Rev.+B26+(1982)+5843&source=bl&ots=FNRwD_3ztk&sig=

L-

jy0SmaLNSMNLJJo7RklmaRVpQ&hl=es&sa=X&ei=6j96U9TAIMeiqAaJiIGwCw&ved=0CFkQ6AEw

Bw#v=onepage&q=J.L.%20Bredas%2C%20R.R.%20Chance%2C%20R.%20Silbey%2C%20Phys.%2

0Rev.%20B26%20(1982)%205843&f=false

Handbook of Conducting Polymers, Second Edition,

editado por Terje A. Skotheim

+++++++++++++PhysRevB.82.155305.pdf


Ideal diode equation for organic heterojunctions. I. Derivation and application
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