Conformational disorder in long polyenes

JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 23 15 DECEMBER 2001

Conformational disorder in long polyenesPhillip Wood and Ifor D. W. SamuelSchool of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, Fife, KY16 9SS,United Kingdom

Richard SchrockDepartment of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Ronald L. Christensena)

Department of Chemistry, Bowdoin College, Brunswick, Maine 04011

~Received 13 June 2001; accepted 18 September 2001!

We have studied the temperature dependence of the absorption spectra of soluble, conjugatedpolymers of known chain length~;100–1000 double bonds!, synthesized by Schattenmannet al.@Macromolecules29, 8990 ~1996!# using living polymerization techniques. The polymer spectrashow significant redshifts upon cooling from 300 to 80 K. To estimate the distributions ofconjugated segments in these conformationally disordered samples, the spectra were fitted to asuperposition of absorption spectra of conjugated segments of known lengths. These‘‘experimental’’ distributions of conjugated segments then were compared to those predicted bytheoretical models of conformational disorder. Although the low-temperature samples containsignificant populations of long segments, the shortest polyene segments dominate all distributions.We compare these experimental results with distributions derived from the model of Yaliraki andSilbey @J. Chem. Phys.104, 1245 ~1996!#. Adjustment of relevant energy parameters gives goodqualitative agreement between the experimental and theoretical distributions in long polyenes.© 2001 American Institute of Physics.@DOI: 10.1063/1.1416871#

iae

asio

losid

-otmthtetr

th

eeol

disaefotosos

ofureene

ly-talpli-on-re.ro-

.

del-er-the

ings ofrm

les,in

dentsse

ma

I. INTRODUCTION

Conjugated polymers are an important class of materfrom both the physical and technological standpoints. Thare unique in combining semiconducting properties with eof processing, thus lending themselves to many applicatin light-emitting devices and molecular electronics.1–4 Theirelectronic states lie in the regime between the relativelycalized states of small molecules and the extended statesemiconductors. Linear polyenes in the form of carotenosuch asb-carotene~Fig. 1! convert light into chemical energy in photobiological processes such as vision and phsynthesis. Recent research on the excited states of theseecules has greatly improved our understanding ofphotophysics and photochemistry of short, conjugap–electron systems, and a great deal of detailed specscopic and theoretical information is now available onelectronic states of carotenoids and model polyenes.5–8 How-ever, much work remains in understanding the links betwthe optical properties of short polyenes and conjugated pmers of technological interest.

Polymers have enormous scope for conformationalorder. This can have a strong influence on the electronicoptical properties of conjugated polymers, as the degreelectronic delocalization is strongly dependent on the conmation of the polymer chain. It therefore is importantunderstand the processes involved in conformational dider in order to understand fully the photophysics of the

a!Author to whom correspondence should be addressed. [email protected]

10950021-9606/2001/115(23)/10955/9/$18.00

Downloaded 24 Jun 2008 to 138.251.105.135. Redistribution subject to A

lsye

ns

-ofs

o-ol-edo-e

ny-

-ndofr-

r-e

materials. Theoretical studies of the electronic statespolyenes9–12 have concentrated on the room temperatproperties of symmetric, short polyenes such as octatetra~Fig. 1!. However, an understanding of the behavior of pomer solutions and films is important both for fundamenscience and for designing materials for technological apcations. Here, we study the conformational disorder of cjugated polymers in solution as a function of temperatuThe change in absorption as a function of temperature pvides a critical test for models of conformational disorder

The transition energy for the electronic origin@~0–0! vi-bronic band# of the symmetry-allowed (11Ag→1 1Bu) ab-sorption of short polyenes can be expressed byE5A1B/N, whereA andB are constants andN is the number ofconjugated double bonds in the polyene.13 This simple equa-tion provides an excellent account of the spectra of mopolyenes and carotenoids (N,15). However, the absorptions of long conjugated polymers tend to lie at higher engies than predicted by this equation. This suggests thatpolymers are disordered with the polymer chain breakinto shorter conjugated segments. The unresolved shapethe polymer absorption spectra further implicate some foof conformational disorder. Shorter conjugated molecue.g., most carotenoids, exhibit vibronic structure, evenroom temperature solutions.14 The spectra of conjugatepolymers can be explained by breaks into shorter segmof different conjugation lengths. The absorptions of thesegments overlap, leading to broad, unresolved spectra.

Extrapolation of the empiricalA1B/N equation for theS0→S2 transition energy toN5` indicates that an infinitelyil:

5 © 2001 American Institute of Physics

IP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

nd

10956 J. Chem. Phys., Vol. 115, No. 23, 15 December 2001 Wood et al.

FIG. 1. The molecular structures of the polyenes apolymers referred to in this study.M designates thenumber of double bonds.

onn

t,

dthlyong

isnsn

mgishe,

th

ou

a-engpaalren

tinatjuhs

on-

totionntkieenla-

es.sorp-in-

eria-

plenceheport

b-po-g ahler

u-uss-

tri-dis-ted

athenderi-er-orp-

long polyene should absorb (E0 – 0) at about 14 400 cm21

~l;700 nm!.13 It was quickly appreciated that the absorptispectra of the majority of polyacetylene and polydiacetylesolutions typically fall well short of this limit, indicatingconjugated segments that are substantially shorter thanchain lengths of these polymers. Baughman and Chance15,16

Exharos, Risen, and Baughman,17 Shandet al.,18 and Rossi,Chance, and Silbey19 developed simple models that invokea distribution of conjugated segments of different lengwithin the polymer. These models explain the relativebroad, blue-shifted absorptions as being due to distributiof conjugated segments of different lengths, where the lenof a conjugated segment is defined as the distance (N doublebonds! over which the planarity of the polyene backbonemaintained without interruption. This model also explaithe dispersion of the vibrational frequencies of C–C aCvC symmetric stretches observed in resonance Raphotoselection experiments.17 Spectra obtained by excitindifferent regions of the broad polymer absorptions give rto different vibrational frequencies. The frequency of tCvC symmetric stretch also shows anA1B/N dependencereaching a long polyene limit of 1460 cm21.18 As originallypointed out by Shandet al.18 this should allow the distribu-tion of conjugated segment lengths to be extracted fromdistribution of vibrational frequencies.

More recently, Kohler and Samuel20 revisited the effectof conformational disorder on the electronic propertiesconjugated polymers by fitting absorption spectra of variolong-chain polyene oligomers to a superposition of spectrpolyenes with known lengths.21,22 These fits gave distributions that were dominated by the shortest polyene segmwith probabilities rapidly decreasing with increasing sement length. These conclusions were reinforced by a simmodel23 in which each single bond had the same energy brier for twisting out of the plane of conjugation. Statisticand entropic considerations then rationalize the appadomination of the shortest segment lengths. Yaliraki aSilbey24 later extended the earlier work of Rossiet al.,19 toapply a more sophisticated theoretical approach, starwith a microscopic Hamiltonian that contained appropristeric terms for the torsional motions that disrupt the congation. The resulting probability distributions for the lengtof conjugated segments show that short segments are


e

he

s

sth

dan

e

e

fsof

ts-ler-

ntd

ge-

the

most probable. Yaliraki and Silbey24 also used their model toexplain the chain-length dependence of the third-order nlinearity observed by Samuelet al.22,25

The primary purpose of the work presented here isinvestigate the temperature dependence of the conformaof conjugated polymers in solution and the validity of curreconformational disorder models, especially that of Yaliraand Silbey. This study also explores the connection betwthe optical properties of conjugated polymers and the retively well-understood electronic spectra of short polyenWe have studied the temperature dependence of the abtion spectra of soluble polyene oligomers of known chalength~;100–1000 double bonds!, synthesized by Schattenmannet al.26 using living polymerization techniques~Fig. 1!.By using conjugated oligomers of well-defined length, wreduce effects that arise from samples containing large vations in chain length. Unlike carotenoids and other simpolyenes, the absorption spectra of the polymers experiesignificant redshifts when their solutions are cooled. Tanalysis of these temperature shifts provides further supfor conformational disorder in the polymers.

Estimates of conjugation length distributions were otained by fitting the polymer absorption spectra to supersitions of spectra of conjugated polyene segments usinleast-squares method. This extends the approach of Koand Samuel,20 which assumed that the distribution of conjgated segments could be approximated by a sum of Gaians centered at the shortest conjugation length (N52). Ourapproach does not impose any functional form on the disbution of conjugated segments. This yields experimentaltributions that can be compared to the distributions predicby the model of Yaliraki and Silbey.24 The experimental de-termination of the distribution of conjugation lengths asfunction of temperature provides a demanding test ofconformational disorder model. We find that the Yaliraki aSilbey model shows qualitative agreement with the expmental distributions, but there are some quantitative diffences in the temperature dependence of the polymer abstion spectra.

II. EXPERIMENT

The synthesis of the polymer samples~Fig. 1! has beendescribed by Schattenmann and Schrock.25–27 Our experi-


ndtyth

aredioeptetyytho

atioo

ngio

yinnathtethro

-e

-

rmnrdus

cLScl

of

on-

sedtero--

monor

ec-

ve-

erp-

the

rsd

y

e-

rp-

the

ls

ntsin-

10957J. Chem. Phys., Vol. 115, No. 23, 15 December 2001 Conformational disorder in long polyenes

ments focused on two members of the series;A, which con-tains;137 double bonds, with a polydispersity of 1.21 aB, which contains;880 double bonds with a polydispersiof 1.62. These polymers appear as the ‘‘3mer’’ and‘‘65mer’’ in Table III of Ref. 25. A and B contain only6-membered rings, whereas the samples used by KohlerSamuel contained random mixtures of 5- and 6-memberings. Molecular masses and chain lengths were estimateGPC and matrix-assisted laser desorption ionizat~MALDI ! time-of-flight ~TOF!25 mass spectrometry. Thmolecular masses determined from MALDI TOF were aproximately half those obtained by GPC. The conjugapolymers used in this study are more rigid than the polysrene standard used in the GPC measurements, and thepear heavier than they actually are when compared tostandard. Although these molecules are considerably mstable than simple, unsubstituted polyenes such as octraene~Fig. 1!, our samples showed evidence of degradatsince their original synthesis. For example, the 476 nm rotemperature absorption maximum ofA in tetrahydrofurancompares with an original maximum of 480 nm, indicatiirreversible breaks in conjugation, possibly due to oxidatof some double bonds.

Absorption spectra were obtained in 2-methyl tetrahdrofuran, a solvent that forms a glass at 135 K, permittabsorption measurements on the polymers over a wide raof temperatures. Absorption spectra were monitored inproximately 50 K intervals between 80 and 300 K, andspectra were corrected for the absorption of 2-methylrahydrofuran. Scattering effects and the subtraction oflow-temperature solvent absorptions introduce some erin the 300–350 nm range.

We fit the polymer absorption spectra@A(E)# to a linearsuperposition of the absorption spectra@AN(E)# of a set ofconjugated segments withN conjugated double bonds

A~E!5 (N51

M

aNAN~E!. ~1!

M corresponds to the chain length~maximum possible lengthof a conjugated segment! of the polymer andN is the lengthof a given conjugated segment. SinceaN represents the probability of a given segment length, the least-squares fits wconstrained to haveaN>0. A program was written to perform these non-negative least-squares~NNLS! fits followingan algorithm given by Lawson and Hanson.28 This methodhas the advantage over those used by Shandet al.18 andKohler and Samuel20 in not forcing the distribution of con-jugated segments to assume any particular functional foWe also explored fits in which the probability of a givesegment length (aN) followed the form suggested by Kohleand Samuel, i.e., a sum of two Gaussians both centereN52, where the widths and relative amplitudes of the Gasians were parameters in the least-squares fits.20 Althoughthe two methods yield similar qualitative results, the diredetermination of the population coefficients using the NNprocedure provided better fits and is the basis for the consions presented in this paper.

The mean conjugated segment length^N& was obtainedfrom theaN’s by taking a simple weighted average


e

nddbyn

-d-ap-isreet-nm

n

-ggep-et-ers

re

.

on-

t

u-

^N&5( i 51

M iai

( i 51M ai

. ~2!

Expressing the polymer absorption as the superpositionthe absorptions of conjugated segments@Eq. ~1!# requires acomplete reference library of the absorption spectra of cjugated segments withN double bonds@AN(E)#. Three ele-ments are required to generate such a library:20 ~i! how theenergy of theS0→S2 absorption band varies withN; ~ii !how the shape of the absorption spectra~relative Franck–Condon factors! changes withN; ~iii ! how the intensity ofthe absorption~i.e., the oscillator strength of theS0→S2

transition! scales withN.To generate a library of absorption spectra, we have u

the absorption profile ofb-carotene in pentane as a templaand shifted the position of the absorption according to apppriate models. Knoll and Schrock13 have shown that the transition energies for the electronic origins@~0–0! bands# forS0→S2 polyene spectra@E0 – 0(N)# follow a simple empiri-cal relationship: E0 – 0(N)5A1B/N, where A514 400 cm21 and B575 730 cm21. Although these pa-rameters only apply strictly to di-tert-butyl polyenes in rootemperaturen-pentane, they allow an estimate of the positiof the electronic origin for any polyene in any solvent. Fexample,E0 – 0521 300 cm21 (l0 – 05470 nm! for N511,which is in reasonable agreement with the absorption sptrum of b-carotene (l0 – 05483 nm in room temperaturen-pentane!. We also assume that the Franck–Condon enlopes ~relative vibronic intensities and linewidths! for theS0→S2 transition in b-carotene are appropriate for shortand longer conjugated segments. This simplifying assumtion probably underestimates the relative intensities ofS0→S2(0 – 0) bands in longer conjugated systems.

If the oscillator strength and Franck–Condon factowere independent ofN, the absorption of any conjugatesegment containingN double bonds at an energyE could beexpressed as

AN~E!}Aolig~E2~EN2Eolig!!, ~3!

whereAolig is the absorption of the oligomer template~e.g.,b-carotene!, EN5A1B/N, i.e., the 0–0 transition energpredicted by the Knoll and Schrock equation,13 and Eolig

5A1B/Nolig , where Nolig is the number of conjugateddouble bonds in the template used for the vibronic linshapes.Nolig511 for b-carotene.

In order to estimate the change in the intensity of absotion with the number of conjugated double bonds (N), weuse the squares of the transition dipole moments given byHuckel spectrum simulator~HSS! model of Kohler.29 In theHSS model the oscillator strength@ f (N)# increases withN,approaching a constant asymptote for largeN.30 The full ex-pression for the absorption of a conjugated segment withNdouble bonds at energyE is given by

AN~E!5 f ~N!Aolig~E2~EN2Eolig!!, ~4!

where f (N) is the oscillator strength and all other symbohave the same meaning as in Eq.~3!.

A library of absorption spectra of conjugated segmewith N55 – 100 was calculated and then used to fit 500 l


5-

yifi-petrsrinoemraan

oo

catio

k.

re

-o

on

io

ongthe

nt

d-ble

ap-

-inig-lt-ris

eg-

nhe

ingThe

heec-a

henec-c-

sednedap-

bu-

d in


early spaced points in the polymer spectrum between 12and 33 333 cm21 ~300 and 800 nm!. The spectra of the polymers could not be obtained below 300 nm~above 33 333cm21! due to the strong absorption of the 2-methyl tetrahdrofuran solvent. Within our fitting range, there is no signcant overlap between the polymer absorptions and the stra of conjugated segments withN51 – 4. The segmenlengths (N) in Eq. ~1! do not need to be restricted to integeand improved fits can be obtained by using a finer g(DN,1) in the summations. However, the inclusion of nointegral conjugated segment lengths in the NNLS fits dnot appreciably change the distributions. Given the assutions and approximations of this model, fits using integconjugated segment lengths were deemed sufficient forlyzing the effects of disorder.

III. RESULTS

Most of the basic issues involved in interpreting the slution absorption spectra of conjugated polymers in termsconformational disorder are illustrated in Fig. 2. PolymerBexhibits a broad, room temperature absorption typiof many other conjugated polyenes, and its absorpmaximum lies only slightly to the red of theb-carotenetemplate. The upperx axis in this figure shows theS0→S2

transition energies (E0 – 0) for selected conjugationlengths, as predicted from the results of Knoll and Schroc13

While the absorption profile ofB is somewhat lowerin energy than that ofb-carotene (N511), the electronicorigin lies at a significantly higher energy than the;14 500cm21 predicted by application ofE0 – 05A1B/N to N5880.13 The room temperature absorption spectrum thusquires that the majority of the absorption ofB must be as-cribed to conjugated segments withN,20. The mean segment length clearly is much shorter than the chain lengththis polymer.

Figure 3 shows part of the library of polymer absorptispectra that was generated from Eq.~4! and the absorptionspectrum ofb-carotene at 300 K. We see that the absorptspectra of short segments~small N) in the high-energy end

FIG. 2. Absorption spectra ofb-carotene~dashed line! andB ~solid line! in2-methyl tetrahydrofuran at 300 K.


00

-

c-

,d-sp-la-

-f

ln

-

f

n

of our fitting range do not overlap very much.~Note thatthere is some overlap between the absorption of the lsegments and the absorption of the short segments inhigh-energy range.! As the length of the conjugated segmeincreases, the spectra move towards lower energies~longerwavelengths! and their 1/N dependence gives rise to consierable overlap in the spectra of segments with comparalengths. In addition, the Kohler HSS model predicts anproximately sixfold increase in the absorptivity@proportionalto f (N)] in changing fromN55 to N5100.

The NNLS fit @Eq. ~1!# of the 300 K spectrum ofB isgiven in Fig. 4~a!. The fit is particularly good at low energies, and the inclusion of nonintegral conjugation lengthsthe fits would reduce the deviations at higher energies. Fure 4~b! shows the distribution of conjugation lengths resuing from this fit. As previously noted in the work of Kohleand Samuel, the absorption spectrum of this polymerdominated by contributions from the shortest conjugated sments.

Figure 4~b! also shows the distribution of conjugatiolengths obtained from a fit of the spectrum in Fig. 2 to tmodel of Yaliraki and Silbey.24 In this model the polymerchain is assumed to distort to form planar, noninteractsegments separated by local breaks in the conjugation.effective torsional potential is modeled by

V~f!52Ec cos 2f2Es cosf, ~5!

where f is the angle between neighboring segments. Tfirst term represents the ‘‘conjugation’’ energy and the sond term deals with ‘‘steric hindrance’’ for the twist ofpolyene segment from its idealized planar~f50! geometry.To calculate the spectrum in this figure we use Eq.~10! inRef. 24 to calculate the segment length distribution and tuse our oligomer library to calculate the absorption sptrum. Es andEc were varied to get the best fit to the spetrum, givingEs50.024 eV~0.92kT) and theEc50.015 eV~0.58kT) at T5300 K. The Yaliraki and Silbey model leadto a continuous function for the distribution of all conjugatsegment lengths. In contrast, the NNLS fits can be obtaionly for discrete segment lengths with absorptions overlping our fitting range, which starts atN55 for our data set.We thus have normalized the two segment length distri

FIG. 3. The polyene absorption library used for the NNLS fits presentethis paper. Conjugation lengths are indicated.


on-

-g.in-m-

of

nce

tha

y


tions in Fig. 4~b! such that the area under each is unity betweenN55 andN5100. The two distributions are remark-ably similar. The main difference is that the distributionpredicted by the Yaliraki and Silbey model has a greateabundance of long conjugated segments (N.20). Figure4~c! gives the absorption spectrum ofB at 300 K, recon-structed by using Eq.~1! and the distribution@Fig. 4~b!# cal-culated from the model of Yaliraki and Silbey. The higherabundance of longer conjugated segments in this distributioaccounts for the discrepancies between the experimental atheoretical spectra at low energies.

We have further probed the conformational disorder anthe validity of the Yaliraki and Silbey model by investigatingthe temperature dependence of the polymer absorptions. Fure 5~b! shows the absorption ofB at 300 and 80 K. There isa large redshift in the absorption upon cooling: reddishorange solutions turn bluish-purple as they are cooled. Thsolid line in the inset of Fig. 5~a! shows the shift of the peakof absorption ofB with temperature; the dashed line showsthe shift in the lowest energy peak of absorption ob-carotene over the same temperature range. Figure 5~a!shows the absorption spectra ofb-carotene at 300 and 80 K.Both samples exhibit smooth shifts in their absorption

FIG. 4. ~a! NNLS fit of the 300 K absorption spectrum ofB to a superpo-sition of spectra of polyene segments~solid line!. Absorption spectrum ofBat 300 K ~dashed line!. ~b! Conjugated segment length distributions forNNLS fits in ~a! ~solid line! and fit using the model of Yaliraki and Silbey in~c! ~dashed line!. ~c! Yaliraki and Silbey fit to the 300 K absorption spectrumof B ~solid line!. The absorption spectrum ofB at 300 K ~dashed line!.


-

r

nnd

d

ig-

-e

f

maxima as the temperature is reduced, and we see no disctinuities near the glass transition temperature~135 K!. Thespectra ofb-carotene show a much smaller shift~;one-thirdthat of B! in the position of the absorption peak and a significant enhancement of the vibronic structure upon coolinThere are also significant increases in the integral of thetensity of the absorption with respect to energy as the teperature is reduced.*A(E)d ln(E) increases by a factor of1.7 when the solution ofB is cooled from 300 to 80 K; forb-carotene the integrated absorption increases by a factor1.4 over the same temperature range.

We also have investigated the temperature dependeof the absorption of a shorter polymer~A with ;137 doublebonds! with the same monomer structure asB ~Fig. 1!. The300 and 80 K absorption of this polymer are compared withe spectra ofB in Fig. 6. As expected, the absorption spectrof A peak to the blue ofB. The distributions are quite simi-lar; the shortest segments dominate both; however,B has aslightly greater proportion of longer segments.

Figure 7 compares the 80 K absorption ofB and thespectrum predicted from the model of Yaliraki and Silbeusing the values for andEc andEs obtained from the roomtemperature fits that generated the distributions in Figs. 4~b!

FIG. 5. ~a! Absorption spectra ofb-carotene at 80 K~dashed line! and 300K ~solid line! in 2-methyl tetrahydrofuran.~b! Absorption spectra ofB at 80K ~dashed line! and 300 K~solid line! in 2-methyl tetrahydrofuran. Inset—the shift of absorption peak ofB ~solid line! and b-carotene~dashed line!with temperature.


ta

y0ntblne

te5

ndeanblsin

ndosi-are

r-the

lythe

f our

t

edleent

the

s-the

ndls oftor-entsen

e

ichju-es

n of-toofng%

o


and 4~c!. The inset in this figure compares the experimenshift with temperature of the absorption maximum ofB withspectra calculated from the model of Yaliraki and Silbeagain usingEc andEs from the room temperature fits. At 8K the Yaliraki and Silbey distributions contain significacontributions from segments with more than 100 doubonds. However, the spectra used in this figure were geated using a library of segments withN55 – 100. Due to theconvergence of theS0→S2 transition energy (E0 – 0) at longsegment lengths, the error introduced by using this restriclibrary underestimates the redshift by no more than 6cm21. The spectra calculated from the model of Yaliraki aSilbey show a greater shift with temperature than the msured spectra. The experimental NNLS fits work well attemperatures and show increases in the abundance of loconjugated segments with cooling. This is illustrated in TaI, which shows the mean segment lengths calculated uEq. ~2! for both A andB. We see that the mean conjugatiolength ( N&) for A is shorter thanB and that N& increasesfor both polymers as the temperature is reduced.

FIG. 6. Absorption spectra at 80 and 300 K ofB ~solid line! andA ~dashedline! in 2-methyl tetrahydrofuran.

FIG. 7. Comparison of the Yaliraki and Silbey prediction~solid line! of theabsorption spectrum ofB at 80 K with experiment~dashed line!. Inset—comparison of the temperature dependence of the peak of absorptionBgiven by the model of Yaliraki and Silbey~solid line! and experiment~dashed line!.


l

,

er-

d0

a-llgereng

IV. DISCUSSION

The fit to the absorption spectrum ofB at 300 K @Fig.4~a!# supports the notion that the absorption of these aother conjugated polymers can be described by a superption of spectra of shorter conjugated segments. These fitsmuch better at low energies due to theA1B/N dependenceof polyene S0→S2 transition energies (E0 – 0). For longerconjugated segments~larger values ofN! there are a rela-tively large number of library members with similar, ovelapping absorptions, leading to a smooth superposition atlow-energy end of our fitting range. Similarly, the relativepoor fits at high energies are the result of restrictingabsorption library to integralN, giving a small number ofwidely spaced segment spectra at the high-energy end ofitting range. Inclusion of nonintegralNs improves the fitsbut does not significantly change the distribution in Fig. 4~b!or the values of N& in Table I. The dominance of shorconjugated segments in the NNLS distribution@Fig. 4~b!#also was observed by Kohler and Samuel20 for a differentfamily of polymers. These distributions can be rationalizusing a simple model in which the probability of a singbond twisting out of the plane of conjugation is independof its position in the polyene chain.23 The more sophisticatedtheoretical treatment of Yaliraki and Silbey24 also predictsthat the shortest conjugated segments should dominatedistribution of segment lengths in these polymers@see Fig.4~b!#. However, the Yaliraki/Silbey model appears to overetimate the contributions of long polyene segments inpolymer solutions at 300 K.

By exploring the effect of temperature on polymer acarotenoid absorptions we are able to probe these modeconformational disorder and to better understand thesional motions that disrupt conjugation. These measuremtake advantage of the high solubilities of the polymers, evin low-temperature glasses. Coolingb-carotene solutionfrom 300 to 80 K results in a significant narrowing of thvibronic structure and a modest~;950 cm21! redshift of itsabsorption@Fig. 5~a!#. The well-resolved vibronic structureimplies that there is a narrow set of conformations, in whthe 11 double bonds form a single, relatively planar congated segment. The redshift and narrowing of vibronic linobserved upon cooling can be explained by a combinatiosubtle conformational effects~e.g., the 11 double bonds become more planar! and stronger solvent interactions duesolvent contraction and the increased polarizability2-methyl-tetrahydrofuran at low temperatures. Coolib-carotene to 80 K also results in an approximately 40

f

TABLE I. Mean conjugation length N& calculated using Eq.~2! forA andB.

Temperature~K! A B

80 11.7 13.8100 11.5 13.8150 10.1 12.7200 9.2 10.7250 8.8 9.3300 8.5 9


nth

l-temreo

m

s

in

thnn

dim

exorquano

te

c

tioreinnYathnshe

omfoth

hiat

tiinr-beo

os

. Isemth

is-by

addi-on.arevenpleslsormeshomthe

th--falltedhler

astSrefulnsaveon-ab-

nju-lonplede-the

li-

act-esultcesous

nic

theeen

oge-

ical

xpe-

inthe


increase in its integrated absorption spectrum. This chamay be ascribed to the effects of solvent contraction andincrease inf (N) in the more planar species.

In comparison withb-carotene, the spectrum ofB showsa large~;3000 cm21! redshift and no narrowing upon cooing @Fig. 5~b!#. The redshift indicates that there is a greaabundance of longer segments, i.e., some of the confortional breaks are removed when the temperature is loweThe smooth spectrum at low temperature indicates that cformational breaks are still present, even when the therenergy is greatly reduced. The apparent shift to conformtional distributions containing longer conjugated segmentconsistent with estimates of a fewkTroom for the torsionalbarriers (;Ec1Es) for breaking the planes of conjugationthese systems. Furthermore, as observed forb-carotene, theabsorption maximum smoothly shifts to longer wavelengas the temperature is lowered from 300 to 80 K. The abseof discontinuities indicates that the redshifted spectra canbe ascribed to solvent phase changes or the effects of folor aggregation. The low-temperature sample contains a spopulation of species that absorb at,15 000 cm21, suggest-ing a significant abundance of polymer segments withtremely long conjugation lengths. If this interpretation is crect, these low-temperature samples provide a uniopportunity to use photoselection techniques, e.g., resonRaman spectroscopy and time-resolved optical spectroscto study the properties of exceptionally long conjugasystems.

The temperature dependencies of the absorption speof A ~;137 double bonds! andB ~;880 double bonds! arecompared in Fig. 6. The differences between the absorpspectra ofA andB are more pronounced at low temperatuwith B containing a larger concentration of species absorbat ,15 000 cm21. The relative insensitivity of the absorptiospectra to chain length is consistent with the model ofliraki and Silbey. For long chains, the model predicts thatdistribution of segment lengths becomes relatively insetive to the chain length. Also, it should be noted that tintegrated absorption strengths,*A(E)d ln(E), increase bya factor of 1.7 when the polymer solutions are cooled fr300 to 80 K, whereas they increase by a factor of 1.4b-carotene. While some of this change may be due to;20% reduction in the solvent volume, the major part of tincrease must be attributed to changes in the oscillstrength@ f (N)# of the polyeneS0→S2 transitions with in-creasingN.

The model of Yaliraki and Silbey appears to overesmate the redshift of the polymer absorptions with decreastemperature~Fig. 7!. Several explanations merit consideation: First, the assumption of this model simply mayunrealistic, leading to overestimates of the importancelong conjugated segments in the distributions. It also is psible that the increased viscosity of cooled solution increathe barriers to torsional motion (;Ec1Es), partially lockingthe samples into their high temperature conformationsaddition to conformational breaks in conjugation, thesamples may also contain irreversible chemical breaks dudefects in the original polymerizations or subsequent checal degradation. The lengths of the conjugated segments


gee

ra-d.n-ala-is

sceotngall

--ece

py,d

tra

n

g

-ei-

re

sor

-g

fs-es

netoi-en

would be limited by both chemical and conformational druptions. It is important to note that the spectra reportedSchattenmann et al.25 originally exhibited absorptionmaxima~in room temperature THF! at 480 nm forA and 507nm for B. The spectra of solutions ofA andB used in thisstudy were significantly blueshifted with absorption maximat 474 and 486 nm, indicating that our samples have ational chemical breaks in conjugation, e.g., due to oxidatiThe spectral shifts induced by lowering the temperaturethus all the more remarkable, and we would expect elarger temperature-dependent effects in polymer samwithout irreparable chemical breaks in conjugation. This asuggests that the Yaliraki and Silbey model should perfoeven better in accounting for the absorption spectra of frsamples. In principle, the presence of permanent, randdefects also could be incorporated into the calculations ofconjugation length distributions.

The results presented here support the original hypoeses of Exharoset al.,17 Shandet al.,18 and others concerning absorption maxima and vibrational frequencies thatwell short of those expected for extremely long conjugasystems. The simple theoretical models proposed by Koand Woehl23 and by Yaliraki and Silbey24 predict distribu-tions of conjugated segment lengths that are similar at lequalitatively to those extracted from our empirical NNLfits. Nevertheless, these models and the fits deserve cascrutiny. Most problematic are the predictions that solutioof even relatively short conjugated systems also should hlength distributions that are dominated by the shortest cjugation segments. However, the vibronically resolvedsorption spectra of molecules such asb-carotene in Fig. 5~a!point to the absence of appreciable concentrations of cogated segments withN,11, and neither the Kohler/Woehnor the Yaliraki/Silbey models account for the observatithat conjugation lengths are equal to chain lengths in simpolyenes and carotenoids. More work will be needed tovelop models that establish a smooth connection betweenoptical properties of short and long polyene systems.

It also is important to acknowledge the inherent simpfications of a linear superposition model@Eq. ~1!#, whichassumes a collection of essentially orthogonal, nonintering segments. Coupling between these segments could rin the transfer of electronic energy to neighboring sequenon very short time scales. This would lead to homogenebroadening due to the extremely rapid dephasing of theS2

excited states. One might then question whether the vibroprofiles and linewidths of molecules such asb-carotene areappropriate for describing the linewidths observed forpolymers. Resonance Raman excitation profiles have bused to differentiate between homogeneous and inhomneous components of vibronic linewidths.31,32 Recent time-resolved experiments by Scholeset al.33 indicate that inho-mogeneous broadening plays an important role in the optproperties of substituted polyphenylenevinylenes~PPVs!. Ifthe polymer spectra are broadened beyond the;500–1000cm21 of homogeneous and inhomogeneous broadening erienced byb-carotene and lycopene,31,32 Eq. ~1! will thenoverestimate the importance of long polyene segmentsaccounting for absorption on the long wavelength end of


nf

e

dratra

s

cil

idly

th

thc-

tiolemitha

na

nenella-thupOitonre

n

dnleoth

reioie

abenbot t

er-otealsoorthowifi-getra

aisb-s.

w.theL.C.ac-

, ad-of

.

y-

L.

, J.

L.

hys.

r, J.

.

.

.

ck,


polymer solution spectra. However, given that short polyesegments already dominate our distributions, correctionsthe effects of coupling would not significantly modify thconclusions presented in this paper.

In addition to making realistic choices for vibronic banshapes and intensities, any model that purports to extpopulation distributions from polymer absorption specalso must accurately portray the dependence of theS0→S2

oscillator strengths on conjugation length. The spectra uin our library of polyene absorptions9,20 conform to the ex-perimental observation of an apparent leveling off of oslator strengths for polyenes with 2–12 double bonds.34,35

However, there is very little experimental or theoretical guance on the behavior of oscillator strengths in the long poene limit. It is tempting to ascribe the extra increase inintegrated absorption strength ofB compared tob-caroteneto the increase in the population of longer segmentscarry largerS0→S2 oscillator strengths. However, the funtion we have used forf (N) cannot rationalize the;70%increase in absorption when coolingB from 300 to 80 K. Aswe have shown, understanding the origins of the absorpspectra of conjugated polymers is a challenging probwith many factors to take into account. However, even wthe simplified approach presented here it is possible to gconsiderable insight into the importance of conformatiodisorder in these systems.

V. CONCLUSIONS

Previous research on polyacetylenes, polydiacetyleand other conjugated polymers indicates that conformatiodisorder has a profound effect on the photophysics of thsystems. Conformational disorder explains the typicabroad and blueshifted optical spectra of these polymersthe dispersion of their CvC vibrational frequencies in resonance Raman excitation experiments. We have shownthe absorption spectra may be expressed as the linear sposition of absorptions of shorter conjugated segments.fits yield distributions of conjugation lengths that are domnated by short polyene segments. The average conjugalength increases when the polymers are cooled from rotemperature to 80 K, providing additional evidence for coformational disorder. In addition, the low-temperatusamples show absorptions~l.600 nm! that can be attributedto a significant abundance of polyenes with extremely loconjugation lengths.

The temperature dependence of the polymer spectralows a demanding test of the conformational disorder moof Yaliraki and Silbey, and we find qualitative agreemebetween experiment and theory. However, for our sampthe Yaliraki and Silbey model overestimates both the imptance of long polyene segments in the distributions andredshift of the absorption profile upon cooling. Furtherfinement of the conjugated segment length distributawaits a more accurate picture of how the transition energoscillator strengths, and vibronic intensities of polyenesorptions change with the length of conjugation. Currmodels of conformational disorder assume that the probaity for twisting about a given single bond is independentthe geometry of adjacent bonds. The models also neglec


eor

ct

ed

-

--e

at

n

inl

s,alseynd

ater-ur-ionm-

g

al-elts

r-e

-ns,-til-fhe

possibility of chemical breaks in conjugation and the intactions between polyene segments. It is important to nthat these simple models predict that short segmentsshould dominate the conformational distributions of shpolyenes and carotenoids. However, these molecules sno evidence for species with conjugation lengths signcantly different than the full chain lengths. A major challenfor theory thus is to account for polyene absorption specin both the short and long chain length limits.

ACKNOWLEDGMENTS

The authors are grateful to G. Rumbles for hostingsabbatical visit by R.L.C. at Imperial College and for hcritical reading of the manuscript. Sophia Yaliraki and Roert Silbey are acknowledged for helpful discussionI.D.W.S. is a Royal Society University Research FelloI.D.W.S. and P.W. acknowledge the financial support ofEngineering and Physical Sciences Research Council. R.is supported by the Kenan Fellowship Program and alsoknowledges the donors of the Petroleum Research Fundministered by the American Chemical Society, for supportthis research.

1J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks, KMackay, R. H. Friend, P. L. Burns, and A. B. Holmes, Nature~London!6293, 539 ~1990!.

2I. D. W. Samuel, Philos. Trans. R. Soc. London, Ser. A358, 193~2000!.

3J. Salbeck, Ber. Bunsenges. Phys. Chem.100, 193 ~2000!.4R. H. Friend, R. W. Gymer, A. B. Holmeset al., Nature~London! 397,121 ~1999!.

5H. A. Frank and R. J. Cogdell, inCarotenoids in Photosynthesis, edited byA. Young and G. Britton~Chapman & Hall, London, 1993!, pp. 253–326.

6P. Farrer and E. Jucker, inCarotenoids~Elsevier, New York, 1950!; L.Zechmeister,Cis–Trans Isomeric Carotenoids, Vitamins A, and Arylpolenes~Academic, New York, 1962!.

7R. L. Christensen, inThe Photochemistry of Carotenoids, edited by H. A.Frank, A. J. Young, G. Britton, and R. J. Cogdell~Kluwer Academic,Dordrecht, 1999!, pp. 137–160.

8B. S. Hudson, B. E. Kohler, and K. Schulten, inExcited States, edited byE. C. Lim ~Academic, New York, 1982!, Vol. 6, pp. 1–95.

9H. Petek, A. J. Bell, Y. S. Choi, K. Yoshihara, B. Tounge, and R.Christensen, J. Chem. Phys.98, 3777~1993!.

10Y. S. Choi, T.-S. Kim, H. Petek, K. Yoshihara, and R. L. ChristensenChem. Phys.100, 9269~1994!.

11H. Petek, A. J. Bell, Y. S. Choi, K. Yoshihara, B. A. Tounge, and R.Christensen, J. Chem. Phys.102, 4726~1995!.

12J. F. Pfanstiel, D. W. Pratt, B. A. Tounge, and R. L. Christensen, J. PChem. A103, 2337~1999!.

13K. Knoll and R. Schrock, J. Am. Chem. Soc.111, 7989~1989!.14R. L. Christensen, M. Goyette, L. Gallagher, J. Duncan, B. DeCoste

Lugtenburg, F. J. Jansen, and I. van der Hoef, J. Phys. Chem. A103, 2399~1999!.

15R. H. Baughman and R. R. Chance, J. Polym. Sci., Polym. Phys. Ed14,2037 ~1976!.

16R. R. Chance, Macromolecules13, 396 ~1980!.17G. J. Exharos, W. M. Risen, and R. H. Baughman, J. Am. Chem. Soc98,

481 ~1976!.18M. L. Shand, R. R. Chance, M. Postollec, and M. Schott, Phys. Rev. B25,

4431 ~1982!.19G. Rossi, R. R. Chance, and R. J. Silbey, J. Chem. Phys.90, 7594~1989!.20B. Kohler and I. D. W. Samuel, J. Chem. Phys.103, 6248~1995!.21H. H. Fox, M. O. Wolf, R. O’Dell, B. L. Lin, R. R. Schrock, and M. S

Wrighton, J. Am. Chem. Soc.116, 2827~1994!.22I. D. W. Samuel, I. Ledoux, V. Dhenaut, J. Zyss, H. H. Fox, R. R. Schro

and R. J. Silbey, Science265, 1070~1994!.23B. Kohler and J. C. Woehl, J. Chem. Phys.103, 6253~1995!.24S. N. Yaliraki and R. J. Silbey, J. Chem. Phys.104, 1245~1996!.


, R

So

an

urn,


25I. Ledoux, I. D. W. Samuel, J. Zyss, S. N. Yaliraki, F. J. SchattenmannR. Schrock, and R. J. Silbey, Chem. Phys.245, 1 ~1999!.

26F. J. Schattenmann, R. R. Schrock, and W. M. Davis, J. Am. Chem.118, 3295~1996!.

27F. J. Schattenmann and R. Schrock, Macromolecules29, 8990~1996!.28C. Lawson and R. J. Hanson,Solving Least Squares Problems~SIAM,

Philadelphia, 1995!, Chap. 23.29B. Kohler, J. Chem. Phys.93, 5838~1990!.30A cubic spline was used to interpolate the data in Table I of Kohler


.

c.

d

Samuel ~Ref. 20! to construct a complete catalog off (N) for N52 – 100.

31J. E. Cotting, L. C. Hoskins, and M. E. Levan, J. Chem. Phys.77, 1081~1982!.

32G. P. Harhay and B. S. Hudson, J. Phys. Chem.97, 8158~1993!.33G. D. Scholes, D. S. Larsen, G. R. Fleming, G. Rumbles, and P. L. B

Phys. Rev. B61, 13670~2000!.34H. Kuhn, J. Chem. Phys.29, 958 ~1958!.35H. Kuhn, Forsch. Chem. Organischer Naturstoffe17, 404 ~1959!.


Conformational disorder in long polyenes

Documents

Transcript of Conformational disorder in long polyenes