polarones (mayo 2014)

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3 mayo 2014

Polarones

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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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 withformation/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)


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

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

Alternatives to the bipolaron have been discussed earlier and especially the two polarons on

a single chain or polaron pair (PP) model *9+ (PPs, 2e) (pg. 332)

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Bipolarons or Polaron Pairs in Conducting Polymers.pdf

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

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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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Brutting_Physics of Organic Semiconductors_352740550X.pdf


3.2 Charge Carrier Transport (pg. 6)

(pg. 7)

(pg. 131)

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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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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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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

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


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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 deformationthe polaron binding energy

or reorganisation energyhas to be mustered.

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 thereforeimportant 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 molecule as 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.

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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 free

charge 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 singletand 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.
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/nmat/journal/v7/n9/fig_tab/nmat2252_F1.html


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

From

Tuning organic magnetoresistance in polymer-fullerene blends by controlling spin reactionpathways ; 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, the

precursor 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

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.
http://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.html


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

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


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Polaron Pairs in P3HT-PCBM Composite.pdf

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

http://download.springer.com/static/pdf/750/art%253A10.1007%252Fs00723-012-0401-

2.pdf?auth66=1399493746_306f5b6353ea6719551ca4ed103c67af&ext=.pdf

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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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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 1020

cm-3

cmon= mcS= (6) (5 x 1020

cm-3

) = 3 x 1021

cm-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.

polarones (mayo 2014)

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