Hs

Aa

b

a

ARRAA

KDPHVP

1

wriavdisecTiabta

pr(

0d

Synthetic Metals 162 (2012) 314– 325

Contents lists available at SciVerse ScienceDirect

Synthetic Metals

j o ur nal homep ag e: www.elsev ier .com/ locate /synmet

eat capacity and phonon dispersion in polyselenophene in relation to thepectra of oligoselenophenes

rchana Guptaa, Neetu Choudharya,∗, Parag Agarwala, Poonam Tandonb, V.D. Guptab

Department of Applied Physics, Institute of Engineering and Technology, M.J. P. Rohilkhand University, Bareilly, IndiaDepartment of Physics, University of Lucknow, Lucknow, India

r t i c l e i n f o

rticle history:eceived 11 May 2011eceived in revised form 19 October 2011ccepted 14 December 2011vailable online 23 January 2012

a b s t r a c t

Normal modes and their dispersion have been obtained for polyselenophene (PSe) in the reduced zonescheme using Wilson’s GF matrix method as modified by Higg’s for an infinite polymeric chain. The UreyBradley potential field is obtained by least square fitting to the observed infrared and Raman bands. Theresults thus obtained agree well with the experimental IR and Raman values. The characteristic featuresof dispersion curves such as repulsion and exchange of character, crossing, van Hove type singularities

eywords:ensity-of-stateshonon dispersioneat capacityibrational dynamicsolyselenophene

have been discussed and possible explanation has been given. Heat capacity has been calculated viadensity-of-states using Debye relation in the temperature range 0–450 K. Possible explanation for theinflexion region in the heat capacity variation is given. The spectra of the oligomers are checked with thefinite–infinite spectral relationship and are found to be in agreement.

© 2011 Elsevier B.V. All rights reserved.

. Introduction

Conducting polymers are a relatively new class of materials,hich have gained increasing interest in recent years due to their

easonable price, facile large-scale synthesis, solution processabil-ty, and tunable properties [1]. Several polymers have been testednd found suitable in a variety of electronic devices includingapor sensors, electronic and photonic transistors, electrochromicevices, conductive adhesives, inks, photovoltaic cells, supercapac-

tors, batteries and nanoscale lasers [2–4]. They are attractive forensor applications because they can directly convert the bindingvent into an electrical signal [5–7]. Development of nanowires ofonducting polymers is a step toward device miniaturization [8,9].hese devices would be suitable to introduce built-in computersn space suits, with associated sensors to monitor the health ofstronauts while they perform extra-vehicular activities. Due to theiocompatibility of some conducting polymers they may be usedo transport small electrical signals, through the body, i.e. act asrtificial nerves [10].

Polyselenophene (PSe) is an important member of conducting

olymer family built from group VI five membered aromatic hete-ocycles having non-linear optical responses [11]. PolythiophenePTh) is the most widely studied conjugated polymer. Its close

∗ Corresponding author.E-mail address: neetu16april@gmail.com (N. Choudhary).

379-6779/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.synthmet.2011.12.012

Se analog polyselenophene has received a significant attention inrecent years. It has been reported [12,13] that Se plays an importantrole in living organisms and that Se containing proteins are found tobe components of various enzymes. The organic superconductorsobtained from Se containing charge transfer complexes and the rad-ical ion salts have led to a new promising Se chemistry. Research isbeing carried out to find new promising selenium-containing com-pounds for these purposes, and their structures are being studied[13,14]. Polyselenophenes exhibit some advantages [15] due to spe-cial nature of Se atom and selenophene and may even be superiorto polythiophenes for some applications (i) improved interchaincharge transfer due to intermolecular Se–Se interactions, (ii) loweroxidation and reduction potentials of polyselenophenes, (iii) pol-yselenophenes should have greater polarizability as compared topolythiophenes, (iv) due to the larger size of the Se atom, poly-selenophenes should be able to accommodate more charge upondoping than polythiophenes, and (v) polyselenophenes should havea lower band gap than polythiophenes, resulting in opto electronicproperties different from those of polythiophenes.

Polyselenophene has a rather low electrical conductivity(10−4–10−3 S cm−1) [16], as compared with polythiophene whichis enhanced by doping [17]. However, the low conductivity obser-vation is not supported by computational studies [18]. Considering

the stronger conjugation in polyselenophene as compared to poly-thiophene and the intermolecular Se–Se interactions in bulk form,the conductivity of polyselenophene is expected to be of the sameorder of magnitude or even higher than that of polythiophene

c Metals 162 (2012) 314– 325 315

[[ciicaniia

diceaftRivaRnOsotteptPu

IoimRtabautpnttiteblamcivolkmh

A. Gupta et al. / Syntheti

18]. Polyselenophenes have excellent electrochromic properties15]. They are highly transparent and have high contrast ratio andoloration efficiency. The UV–vis absorption spectrum of chem-cally synthesized polyselenophene film on glass coated withndium tin oxide (ITO) exhibits a �max at 440 nm [19]. The opti-al band gap of polyselenophene is 2.0 eV, which is nearly the sames that of polythiophene [20]. Oligo and polyselenophenes in theeutral undoped state are more difficult to twist is of fundamental

mportance to their development, since more substituents can bentroduced onto their backbones than onto those of their thiophenenalogs without distorting conjugate ion [18,21].

Vibrational spectroscopy is widely used to study structural andynamic aspects of various molecular systems. FTIR spectroscopy

s a major technique for investigating polymer sample in terms ofomposition as well as constituents’ distribution. Apart from differ-nt chemical distributions in the sample, the spectroscopist is alsoble to visualize areas with different degree of crystallinity or pre-erred orientation and by these means ensures reliable data abouthe quality of the investigated sample, manufacturing process, etc.aman spectroscopy is a nondestructive analytical technique and

s complementary in nature to infrared spectroscopy. This can pro-ide information from functional groups with vibration modes thatre weak or unresolvable by FTIR. In general, the IR absorption,aman spectra from polymeric systems are very complex and can-ot be unraveled without the full knowledge of dispersion curves.ne cannot appreciate the origin of both, symmetry dependent and

ymmetry independent spectral features without the knowledgef dispersion curves. The dispersion curves also facilitate correla-ion of the microscopic behavior of the long chain molecule withhe macroscopic properties such as entropy, enthalpy, specific heat,tc. In continuation of our work on normal coordinate analysis andhonon dispersion in a variety of polymers in different conforma-ions [22–25], we present here a complete normal mode analysis ofSe with phonon dispersion in the reduced Brillouin zone schemesing the Urey–Bradley force field (UBFF) [26].

Polyselenophene has been studied by Hasoon et al. [27] usingR and Raman spectroscopy. They have proposed the assignmentsn the basis of group theoretical species, an identification whichgnores potential energy distribution completely. Their assign-

ents are both incomplete and are based purely on symmetry.amirez et al. [28] have reported limited studies on the vibra-ional spectrum of PSe. Their study is focused on the dynamicalnd spectroscopic properties of the oligomers of selenophene (Se)n

y semiemperical PM3 method. They have proposed the vibrationalssignments for the in plane modes of the polymer. The force fieldsed by them for a polymeric system is the same as that used for aetramer in gas phase. By all logic long chain interactions are com-letely ignored. This is going to be an underestimate and henceeeds a re-evaluation. Moreover their study is confined to zone cen-er frequencies but in practice, there are absorption bands beyondhe zone center. A study of the dispersion profile in the entire zones necessary for thermodynamic behavior. We are not intendingo underrate the importance of the work of previous authors. Ourfforts are to fill in their gaps. We have analyzed the dispersiveehavior of polyselenophene, including the van Hove type singu-

arities [29], which give rise to additional absorption bands in turnffecting the thermodynamic behavior. The evaluation of normalodes and their dispersion has been taken to logical conclusion by

alculating the heat capacity as a function of temperature. A sat-sfactory match and interpretation of the corresponding modes ofibration in oligomers [30] from the profile of dispersion curvesf polymer provides reasonable justification of the structural simi-

arity in the oligomeric and the polymeric forms. To the best of ournowledge such detailed studies leading to correlation between theicroscopic behavior and macroscopic properties of this polymer

ave not yet been reported.

Fig. 1. One chemical repeat unit of PSe.

2. Theory

2.1. Calculation of normal mode frequencies

Normal mode calculations for an isolated polymeric chain havebeen carried out using Wilson’s GF matrix method [31] as modifiedby Higg’s [32] for an infinite chain. The vibrational secular equationto be solved is

|G(ı)F(ı) − �(ı)I| = 0 0 ≤ ı ≤ � (1)

where ı is the phase difference between the modes of adjacentchemical units, the G (ı) matrix is derived in terms of internalcoordinates, with its inverse being the kinetic energy, and the F(ı) matrix is based on the Urey–Bradley Force field.

The frequencies �i (ı) (in cm−1) are related to the eigen values�i (ı) by

�i(ı) = 4�2c2v2i (ı). (2)

A plot of �i (ı) versus ı gives the dispersion curve for the ithmode.

2.2. Calculation of heat capacity

Dispersion curves can be used to calculate the specific heat of asystem. For a one-dimensional system the density of state functionor the frequency distribution function expresses the way energyis distributed among the various branches of normal modes in thecrystal. It is calculated from the relation

g(�) =∑[(

∂�j

∂ı

)−1]

vj(ı)=vj

(3)

The sum is over all the branches j. If we consider a solid as anassembly of harmonic oscillators, the frequency distribution g(�)is equivalent to a partition function. The constant volume heatcapacity can be calculated using Debye’s relation

Cv =∑

g(vj)kNA

(hvj

kT

)2 [exp(hvj/kT)

{exp(hvj/kT) − 1}2

](4)

with∫

g(�i)d�i = 1.

3. Results and discussion

3.1. Geometric structure

One chemical repeat unit of PSe is shown in Fig. 1. The geom-etry of the oligomers of selenophene was optimized upto 8Se atDFT level using B3LYP/6-31G with Gaussian 03 program [33]. The

316 A. Gupta et al. / Synthetic Metals 162 (2012) 314– 325

Table 1Structural parameters of 8Se used in present work.

Structural parameter Optimized value Structural parameter Optimized value

�[Se C] 1.92833 ϕ[Se C C] 110.07302�[C C] 1.37843 ϕ[C C H] 121.34432�[C C] 1.41852 ϕ[C C H] 122.0874�[C C]* 1.42825 ϕ[C C C]* 128.95750�[C H] 1.08429 ϕ[Se C C]* 120.96948

�[C C]* 180.00

N stretch is Å, of angle bend and torsion is degree.

gotatat

3

tmactvipstfiieasnw

9rsbcv

3

2

TI

N((w

0.0 0.2 0.4 0.6 0.8 1.00.0 0.2 0.4 0.6 0.8 1.0900

1000

1100

1200

1300

1400

1500(b)

Density of states g(

Freq

uenc

y (c

m-1)

(a) 2Se 3Se 4Se 6Se

Phase Factor (

(3099 cm and 3067 cm ) to �1 and �2 modes of the A1 speciesand 3052 cm−1 to B2 species. They argued that the second B2 mode,�12, was either degenerate with one of the above or was so weakas to be hidden by another, more intense band. The nature of

900 2Se 3Se

(a) (b)

ϕ[C Se C] 86.82429

ote: (1) �, ϕ and � denote stretch, angle bend and torsion respectively; (2) unit of

eometry of the polymeric form is taken to be the same as for thectamer form (8Se), which is a result of asymptotic approach ofhe oligomeric structures. It has also been reported that octamersre a good model for polymers [34]. The DFT calculations showhat the structure of octamer is planar zig–zag. The torsion angleround inter ring C C bond is 180◦. The optimized parameters ofhe octamer (8Se) are listed in Table 1.

.2. Vibrational analysis

There are 14 atoms in one repeat unit of PSe which give riseo 38 optically active vibrations of non-zero frequencies. The four

odes for which ω → 0 as ı → 0 are called acoustic modes. Theyre due to translation (one parallel and two perpendiculars to thehain axis) and one due to rotation around the chain axis. The vibra-ional frequencies were calculated from the secular equation [1] foralues of ı varying from 0 to � in steps of .05�. Initially approx-mate force constants were taken from the potential field data ofolythiophene [35] and those involving selenium atoms from 1,2,5-elena-diazoles [36]. These were later refined to give the “best fit”o the observed spectra [27]. We have used the Urey Bradley forceeld, which takes into account the bonded as well as non-bonded

nteractions. The assignments were made on the basis of potentialnergy distribution (PED), band shape, band intensity and appear-nce/disappearance of modes in similar molecular groups placed inimilar environment. The final force constants along with the inter-al coordinates are given in Table 2. The matched frequencies alongith their potential energy distribution (PED) are given in Table 3.

The dispersion curves are plotted in Figs. 2(a)–4(a) from00 cm−1 to 1550 cm−1, 265 cm−1 to 900 cm−1and 0 to 265 cm−1,espectively. Since all the modes above 1550 cm−1 are non disper-ive in nature, the dispersion curves are plotted only for the modeselow 1550 cm−1. For the sake of the simplicity the modes are dis-ussed under two heads – in-plane vibrations and out-of-planeibrations.

.2.1. In-plane vibrationsThe CH stretching vibrations are calculated at 3035, 3034,

964 cm−1 and assigned to the peaks at 3038, 2981, 2962 cm−1.

able 2nternal coordinates and Urey Bradley force constants.

Internal cord. Force const. Internal cord. Force const.

�[C Se] 3.12 ϕ[C C C] 0.49(.40)�[C C] 5.33 ϕ[C C H] 0.05 (.08)�[C H]* 4.82 ϕ[C C C]* 0.27 (.16)�[C C] 3.35 ϕ[Se C C]* 0.34 (.31)�[C H] 4.59 �[C H] 0.19�[C C]* 3.695 �[Se C] 0.08ϕ[C Se C] 0.50 (.35) �[C C] 0.01ϕ[Se C C] 0.44 (.40) �[C C] 0.015ϕ[C C H] 0.33 (.26) �[C C]* 0.07

ote: (1) �, ϕ, ω and � denote stretch, angle bend, wag and torsion, respectively.2) Non-bonded force constants are given in parentheses.3) Unit of force constants for stretch is md/Å, for angle bend is md/Å rad−2 and foragging and torsion is md A.

Fig. 2. (a) Dispersion curves of PSe and spectral data of oligoselenophenes ((�),(�), (*), and (�) indicate dimer, trimer, tetramer, and hexamer, respectively,900–1550 cm−1). (b) Density-of-states of PSe (900–1550 cm−1).

These vibrations are highly localized and hence show no disper-sion. Cataliotti and Paliani [37] have proposed the assignmentsof vibrations in the CH stretching region of five membered hete-rocyclic compounds including selenophene. They have measuredthe infrared spectra of selenophene in gas, liquid, solution andcrystal phases and assigned the two bands at higher frequencies

−1 −1

1.00.80.60.40.20.01.00.80.60.40.20.0

300

400

500

600

700

800

Density of states g(ν)

Freq

uenc

y (c

m-1)

Phase Factor (δ/π)

4Se 6Se

Fig. 3. (a) Dispersion curves of PSe and spectral data of oligoselenophenes ((�),(�), (*), and (�) indicate dimer, trimer, tetramer, and hexamer, respectively,265–900 cm−1). (b) Density-of-states of PSe (265–900 cm−1).

A.

Gupta

et al.

/ Synthetic

Metals

162 (2012) 314– 325317

Table 3Normal modes and their dispersion.

Calc. Obs. Assignment (%PED) (ı = 0) Cal. Obs. Assignment (%PED) (ı = �)

I.R. Raman I.R. Raman

3035 3038 – �[C H]*(99) 3035 3038 – �[C H]* (99)

3034 3038 – �[C H]*(99) 3034 3038 – �[C H]* (99)

2964 2981 – �[C H](99) 2964 2981 – �[C H](99)

2964 2962 – �[C H](99) 2964 2962 – �[C H](99)

1504 1507 1501 �[C C](27) + �[C C]*(26) + �[C C](7) 1511 1507 1501 �[C C](34) + �[C C]*(27)

1456 1440 1421 �[C C](32) + �[C C]*(27) 1484 1440 1421 �[C C](27) + �[C C]*(26) + �[C C](5)

1380 1343 1378 �[C C](35) + �[C C](22) + ϕ[C C H](6) 1355 1343 1378 �[C C](54) + �[C C](10)

1323 1292 – �[C C](45) 1345 1292 – � [C C](23) + �[C C](9)

1200 1207 – �[C Se](26) + �[C C]*(25) + �[C C](14) + ϕ[C C C](12) + ϕ[C C C]*(9)+ ϕ[C C H](7) + ϕ[Se C C](6)

1243 1207 – �[C Se](36) + �[C C](26) + �[C C]*(22)) + ϕ[C C C]*(9) + ϕ[C C H](6)+ ϕ[C C C](6) + ϕ[Se C C]*(5)

1187 – 1180 �[C Se](28) + �[C C](19) + ϕ[C C H](13) + �[C C]*(11) +ϕ[Se C C]*(7)

1190 – 1180 �[C Se](29) + �[C C]*(22) + ϕ[C C C]*(10) + �[C C](7) ϕ[C C H](7) +ϕ[C C C](7) + ϕ[Se C C](5)

1135 1147 1154 �[C C](51) + �[C C]*(24) + ϕ[C C H](14) + �[C C](5) 1128 1147 1154 �[C C](37) + ϕ[C C H](27) + �[C C]*(7) + �[C C](7) + ϕ[C C C](5)

1107 1075 – ϕ[C C H](31) + �[C C](26) + �[C C](20) + �[C Se](11) 1126 1075 – �[C C](37) + �[C C](33) + �[C C](16) + �[C Se](6) + ϕ[C C C](5)

1018 1040 1045 ϕ[C C H](61) + �[C C](19) + �[C Se](17) + ϕ[C C C](7) +ϕ[C C H](6) + ϕ[Se C C](6)

986 1040 1045 ϕ[C C H](62) + �[C C](33) + �[C Se](14) + ϕ[C C H](9)

943 899 – ϕ[C C H](68) + �[C C](18) + ϕ[C C H](16) + �[C C]*(12) 980 899 – ϕ[C C H](61) + ϕ[C C H](10) + �[C Se](8) + �[C C]*(7)

833 832 – �[C Se](39) + �[C C](39) + �[C C](14) + ϕ[C C H](11) 804 807 – ϕ[C C H](37) + �[C C](31) + �[C C](18) + ϕ[C C H](21) + �[C Se](13)+ ϕ[C C H](9)

796 819 – ϕ[C C H](34) + �[C C](24) + �[C C](13) + ϕ[C C H](13) 801 – – ϕ[C C H](40) + �[C C](31) + ϕ[C C H](11) + �[C Se](6) + �[C C](6)

771 807 – ϕ[C C H](34) + �[C Se](31) + �[C C](17) + ϕ[C C H](11) �[C C](8) +ϕ[Se C C](7) + ϕ[C C C](12)

776 – – �[C Se](34) + ϕ[C C H](24) + ϕ[Se C C](11) + ϕ[C C C](10) +ϕ[C C H](10)

764 – – �[C Se](38) + ϕ[C C H](17) + �[C C](7) + ϕ[Se C C](16) + �[C C](15)+ ϕ[C C C](12) + ϕ[C C H](9)

768 – – �[C Se](28) + �[C C](28) + ϕ[C C H](20) + ϕ[Se C C] (11) +ϕ[C C C](10) + ϕ[C C H](8)

760 – – ω[C H](90) + �[C C](7) 758 – – ω[C H](90) + �[C C](7)

755 747 – ω[C H](91) + �[C C](7) 757 747 – ω[C H](91) + �[C C](7)

640 – – �[C Se](35) + ϕ[C C C](33) + ϕ[Se C C]*(17) + �[C C](11) +ϕ[C C C]*(5)

628 – – �[C Se](49) + ϕ[C C C](35) + �[C C](17) + ϕ[Se C C]*(10)

621 619 – ω[C H](92) + �[C C](5) 619 619 – ω[C H](92) + �[C C](6)

617 619 – ω[C H](93) + �[C C](7) 619 619 – ω[C H](92) + �[C C](6)

588 551 – �[C Se](46) + ϕ[C C C](44) + �[C C](12) 615 551 – ϕ[C C C](31) + �[C Se](27) + ϕ[Se C C]*(11) + �[C C](5)

553 461 – �[C Se](46) + ϕ[Se C C]*(19) + �[C C](16) + �[C C]*(10) +ϕ[Se C C](8) + ϕ[C Se C](8)

510 461 – �[C Se](25) + ϕ[Se C C](16) + �[C C](14) + ϕ[C C C](14) +ϕ[C Se C](10) + �[C C]*(10) + ϕ[Se C C]*(8)

411 428 – ϕ[Se C C](31) + ϕ[C Se C](31) + �[C Se](18) + ϕ[Se C C]*(7) +�[C C](5) + ϕ[C C C](5)

503 428 – ϕ[Se C C](16) + �[C Se](15) + �[C C]*(10) + ϕ[Se C C]*(8)

402 – – �[C C]*(25) + ϕ[C C C](19)) + ϕ[C C C]*(16) + ϕ[Se C C](14) +�[C C](8)

270 – – ϕ[C C C]* (22) + ϕ[Se C C]*(19) + ϕ[C Se C](16) + ϕ[Se C C](16) +�[C C]*(8) + �[C Se](7)

250 – – �[Se C](89) + �[C C](7) 265 – – ϕ[C C C]*(21) + ϕ[Se C C]*(18) + ϕ[C Se C](17) + ϕ[Se C C](16) +�[C C]*(9) + �[C C](6) + �[C Se](6)

236 – – �[C Se](42) + ϕ[Se C C]*(38) + ϕ[C C C]*(12) + �[C C](10) 211 – – �[C C](44) + �[C C]*(22) + �[Se C](16) + �[C C](14)

318 A. Gupta et al. / Synthetic Metals 162 (2012) 314– 325

Tabl

e

3

(Con

tinu

ed)

Cal

c.

Obs

.

Ass

ign

men

t

(%PE

D)

(ı

=

0)

Cal

.

Obs

.

Ass

ign

men

t

(%PE

D)

(ı

=

�)

I.R.

Ram

an

I.R.

Ram

an

217

–

–

�[C

C](

50)

+

�[C

C]* (

24)

+

�[C

C](

19)

211

–

–

�[C

C](

44)

+

�[C

C]* (

22)

+

�[S

e

C](

16)

+

�[C

C](

14)

203

–

–

�[S

e

C](

77)

+

�[C

C]* (

18)

+

ϕ[C

Se

C](

8)

+

�[C

C](

7)

195

–

–

�[S

e

C](

88)

+

�[C

C](

12)

179

–

–

ϕ[S

e

C

C]* (

29)

+

ϕ[C

C

C]* (

28)

+

�[C

Se](

23)

+

ϕ[C

Se

C](

9)

+�

[C

C](

7)19

5

–

–

�[S

e

C](

88)

+

�[C

C](

12)

173

–

–

�[C

C](

71)

+

�[C

C](

20)

+

ω[C

H](

9)

186

–

–

ϕ[S

e

C

C]* (

30)

+

�[C

Se](

28)

+

ϕ[S

e

C

C](

13)

+

�[C

C]* (

13)

123

–

–

ϕ[S

e

C

C]* (

63)

+

ϕ[C

C

C]* (

36)

175

–

–

�[C

Se](

48)

+

ϕ[S

e

C

C]* (

29)

+

�[C

C](

24)

+

�[C

C]* (

13)

+ϕ

[Se

C

C](

11)

105

–

–

�[C

C]* (

81)

+

�[S

e

C](

18)

127

–

–

�[S

e

C](

68)

+

�[C

C](

23)

92

–

–

�[S

e

C](

84)

+

�[C

C](

6)

127

–

–

�[S

e

C](

68)

+

�[C

C](

23)

79

–

–

�[S

e

C](

84)

+

�[C

C](

11)

70

–

–

�[C

C]* (

74)

+

�[S

e

C](

13)

+

�[C

C](

6)

29–

–

�[C

C](

87)

+

ω[C

H](

7)

+

�[S

e

C](

6)

70

–

–

�[C

C]* (

74)

+

�[S

e C

](13

)

+

�[C

C](

6)

Not

e:

(1)

All

freq

uen

cies

are

in

cm−1

.(2

)

On

ly

dom

inan

t

PED

s

are

give

n.

(3)

Obs

erve

d

freq

uen

cies

are

from

Ref

. [27

].1.00.80.60.40.20.0

0

50

100

150

200

250

1.00.80.60.40.20.0Density of states g(ν)

Freq

uenc

y (c

m-1

)

Phase Factor ( )

(a) (b)

Fig. 4. (a) Dispersion curves of PSe (0–265 cm−1). (b) Density-of-states of PSe(0–265 cm−1).

in-plane vibrations in the monomeric state continues as such inthe polymeric state. The intra ring C C and C C stretches and theinter ring C C stretch are mainly observed as a mixture in the fre-quency region 1500–1300 cm−1. All these modes are dispersive innature indicating coupling with other vibrations. The frequenciescalculated at 1200 cm−1 and 1187 cm−1 have been attributed toa mixture of inter and intra ring C C stretches and C Se stretch.The C S stretch in polythiophene [35] and the corresponding C Nstretch in polypyrrole [38] appear at a much higher wave num-ber, i.e. at 1250 cm−1 and 1459 cm−1, respectively. The other C Sestretch modes are observed at 832 cm−1, 807 cm−1 and 551 cm−1.The frequency region 1100–800 cm−1 contains the modes havingdominant contribution from C C H and C C H in-plane bendings.The C C C and Se C C bendings are present below 800 cm−1. Acomposite picture of various modes involving selenium atom andthe corresponding modes in polypyrrole and polythiophene is pre-sented in Table 4. It can be seen from the table, as the C X C angledecreases the bending force constant increases, whereas in caseof the angle X C C, with increase in the angle bend there is anincrease in the force constant also. The C X stretch, the X C Cangle bend and the �[C X] torsion force constants show no definitetendency.

3.2.2. Out-of-plane vibrationsModes involving the torsional and wagging motion are out of

plane modes. The CH out of plane wagging modes appear as sharppeaks in the IR spectra. These modes are calculated at 760, 755,621 cm−1 and 617 cm−1 and matched to the peaks at 747 cm−1

and 619 cm−1 in the IR spectra. All the four wagging modes showno dispersion. In polythiophene also these wagging modes arenon-dispersive, although they appear somewhat at higher posi-tion. The intra-ring torsions �[C C], �[C C] and �[C Se] are seenbelow 250 cm−1. The �[Se C] is calculated at 249, 203, 92 cm−1

and 79 cm−1, whereas the inter ring C C torsion is calculated at105 cm−1. All these modes are highly dispersive.

3.3. Characteristic features of the dispersion curves

The study of phonon dispersion in polymeric systems is animportant study. Dispersion curves provide knowledge of thedegree of coupling and information concerning the dependence ofthe frequency of a given mode on the sequence length of ordered

A. Gupta et al. / Synthetic Meta

Tab

le

4A

com

par

ison

of

som

e

stru

ctu

ral p

aram

eter

s,

asso

ciat

ed

forc

e

con

stan

ts

and

corr

esp

ond

ing

freq

uen

cies

of

PPy

and

PTh

wit

h

PSe.

Para

met

ers

Forc

e

con

stan

ts

Freq

uen

cies

PPy

PTh

PSe

PPy

PTh

PSe

PPy

PTh

PSe

�(C

X)

1.38

5Å

1.71

Å

1.92

8Å

5.2

2.9

3.12

1460

,139

2,

1368

,126

9,

1061

, 783

1202

, 858

, 839

, 642

, 618

, 363

1200

, 118

7,

771,

764,

640,

588,

533,

236,

179

(C

X

C)

109.

3◦92

◦86

.82◦

0.20

0.27

0.50

601

462,

411

(X

C

C)

121.

2◦12

4◦12

0.96

9◦0.

22

0.30

0.34

499,

192,

311

363,

166

640,

588,

533,

236,

123

(X

C

C)

107.

5◦11

0.1◦

110.

073◦

0.25

0.20

0.44

601

462

764

�[C

H]

0.20

0.16

5

0.19

857,

852,

776,

773,

735,

719

786,

781,

678,

666

760,

755,

621,

617

�(C

X)

0.02

3

0.02

0.08

186,

129

144,

84, 6

4,

39

249,

203,

92,7

9

Not

e:

(1)

PPy,

pol

ypyr

role

;

PTh

, pol

yth

iop

hen

e;

and

PSe,

pol

ysel

enop

hen

e.(2

)

Un

it

of

forc

e

con

stan

ts

for

stre

tch

is

md

/Å, f

or

angl

e

ben

d

is

md

/Å

rad

−2, f

or

wag

gin

g

and

tors

ion

is

md

Å.

(3)

All

freq

uen

cies

are

in

cm−1

.(4

)

The

freq

uen

cies

of

PPy

and

PTh

are

take

n

from

Ref

s.

[38]

and

[35]

, res

pec

tive

ly.

(5)

X

≡

N, S

, Se

in

PPy,

PTh

, PSe

resp

ecti

vely

.

ls 162 (2012) 314– 325 319

conformations. The dispersion curves of PSe have been obtained fora linear isolated chain.

The dispersion curves of polyselenophene exhibit several char-acteristic features such as repulsion and exchange of character,crossing, high density of states etc. All these features are beauti-fully exhibited in the low frequency region (below 250 cm−1). Themode at 179 cm−1 consists of ϕ[Se C C]*(29) + ϕ[C C C]*(28) +�[C Se](23). As the phase angle ı advances the energy of this modeincreases and it crosses the dispersion curves corresponding tozone center modes 203 and 217 cm−1 at ı = .40� and .55�, respec-tively. It becomes flat at ı = .60� and then its energy decreases. Inthe downward journey, it again crosses the same dispersion curvesat ı = .65� and .70�. At ı = .95� it exchanges character with thelower mode and gets repelled. To ascertain whether these are cross-ings or repulsions, calculations at very close intervals of ı = 0.001�have been performed and it was found that the modes are cross-ing over each other and there is a repulsion at ı = .95�. All suchmodes showing crossover in PSe are listed in Table 5 along withthe PED and the ı values at which these occur. These crossingshave been called ‘non-fundamental resonances’ [39] and are use-ful in the interpretation of the spectra and interactions involved.Since we have considered an isolated chain, the discussion on dis-persion curves, especially the symmetry relation is confined toone-dimensional system with C2� point group symmetry at phaseangle 0. The Eigen vectors of all modes with a particular value of ıaway from the zone center or zone boundary form a restricted setof the complete set of distortion of the molecule and the moleculenow behaves as if it no longer has the symmetry of the line group.The only symmetry operation, that leaves any number of such a setunchanged, is reflection in a mirror plane containing the chain axis.In other words modes corresponding to a given ı ( /= 0 or �) willbelong to one of the two symmetry species, depending on whetherthey are symmetric or antisymmetric with respect to the mirrorplane. Therefore, no two dispersion curves both of which belongto the same one of these two species can cross because this wouldimply the existence of two modes of vibrations with the same sym-metry species and same frequency. This is also obvious from Table 5in which we have shown the pair of modes, which cross, and theybelong to different symmetries.

The modes at 249 cm−1 and 236 cm−1 consist of �[Se C] andϕ[Se C C]* + ϕ[C C C]*, respectively. They disperse in a similarfashion parallel to each other upto ı = .55� where the lower modesuffers a repulsion with the mode at 179 cm−1. As usual, this repul-sion is accompanied by an exchange of character. After exchangingcharacter the energy of this mode increases again, it comes closerto the upper mode and the PEDs of the two modes begin to mix. Atı = .65� repulsion with character exchange takes place and then thetwo modes diverge. The lower mode now crosses the zone centermode 217 cm−1 at ı = .85�. The phenomenon of repulsion occursfor modes belonging to the same symmetry species. On the basisof quasi particle–particle scattering, this phenomenon of exchangeof character may be reviewed as a collision of two quasi particlesin the energy momentum space, approaching each other and mov-ing apart after exchanging their energies. This special characteristicof dispersion curves is seen in other pair of modes also which arelisted in Table 5.

There are certain modes such as (1380, 1324 cm−1), (1200,1187 cm−1), (1135, 1107 cm−1), which tend to converge at the zoneboundary or zone center share dominant potential energy either atthe beginning or towards the boundary. All such modes are listedin Table 5 along with their PEDs.

There are several regions (Table 5), where ∂ω/∂k → 0. These are

regions of high density-of-states and are akin to critical points orvan Hove type singularities [29]. In general these critical pointsare related to the presence of some symmetry points within the

320 A. Gupta et al. / Synthetic Metals 162 (2012) 314– 325

Table 5Characteristic features of dispersion curves.

Pair of modes that repel and exchange character

freq (ı = 0) ı*/� Before exchange After exchange

freq ı*/� P.E.D. freq ı#/� P.E.D.

250 .65 229 .60 �[Se C](88) + �[C C](7) 232 .70 ϕ[Se C C]*(28) + ϕ[C C C]*(26) +ϕ[C Se C](13) + �[C Se](12) +ϕ[Se C C](9)

236 222 ϕ[Se C C]*(30) + ϕ[C C C]*(26) + �[C Se](15) +ϕ[C Se C](11) + ϕ[Se C C](7)

222 �[Se C](86) + �[C C](7)

236 .57 220 .55 �[C Se](36) + ϕ[Se C C]*(35) + ϕ[C C C]*(15) +�[C C]*(6) + �[C C](6) + ϕ[Se C C](6)

222 .60 ϕ[Se C C]*(30) + ϕ[C C C]*(26) +�[C Se](15) + ϕ[C Se C](11) +ϕ[Se C C](7)

179 216 ϕ[Se C C]*(32) + ϕ[C C C]*(24) + �[C Se](22) +ϕ[C Se C](9) + ϕ[Se C C](6)

215 �[C Se](42) + ϕ[Se C C]*(35) +�[C C](15) + ϕ[C C C]*(12) +�[C C]*(7) + ϕ[Se C C](6)

179 .95 193 .90 �[C Se](37) + ϕ[Se C C]*(31) + �[C C]*(11) +ϕ[Se C C](11) + �[C C](8) + ϕ[C C C]*(6)

195 1.0 �[Se C](87) + �[C C](12)

173 185 �[Se C](88) + �[C C](11) 186 �[C Se](28) + ϕ[Se C C]*(30) +�[C C]*(13) + ϕ[Se C C](14)

173 .65 156 .60 �[Se C](45) + �[C C](40) + �[C C](9) + ω[C H](6) 162 .70 �[Se C](88) + �[C C](10)123 150 �[Se C](88) + �[C C](10) 150 �[Se C](52) + �[C C](35) + �[C C](7)

+ ω[C H](5)123 .25 116 .20 ϕ[Se C C]*(60) + ϕ[C C C]*(35) 115 .30 �[Se C](88) + �[C C](9)106 105 �[Se C](89) + �[C C](8) 109 ϕ[Se C C]*(58) + ϕ[C C C]*(32)123 .75 150 .70 �[Se C](52) + �[C C](34) 154 .80 �[C Se](34) + ϕ[Se C C]*(25) +

ϕ[Se C C](16) + �[C C]*(16)106 140 �[C Se](30) + ϕ[Se C C]*(23) + ϕ[Se C C](18) +

�[C C]*(18)143 �[Se C](59) + �[C C](27)

106 .20 106 .15 �[C C]*(81) + �[Se C](18) 110 .25 �[Se C](88) + �[C C](9)92 100 �[Se C](90) + �[C C](8) 103 �[C C]*(80) + �[Se C](17)92 .60 94 .55 �[C C]*(78) + �[Se C](15) 98 .65 �[Se C](78) + �[C C](16)79 90 �[Se C](80) + �[C C](14) 89 �[C C]*(77) + �[Se C](15)29 .15 28 .10 �[C C](87) + ω[C H](7) + �[Se C](6) 41 .20 ϕ[Se C C](27) + �[C C]*(23) +

ϕ[C Se C](16) + ϕ[Se C C]*(11)00 21 ϕ[Se C C](27) + �[C C]*(25) + ϕ[C Se C](17) +

ϕ[Se C C]*(9)26 �[C C](87) + ω[C H](7) + �[Se C](6)

29 .80 63 .75 ϕ[Se C C]*(53) + ϕ[C C C]*(36) 60 .85 �[C C]*(73) + �[Se C](12) +�[C C](7)

00 53 �[C C]*(73) + �[Se C](12) + �[C C](8) 55 ϕ[Se C C]*(54) + ϕ[C C C]*(36)00 .55 15 .50 �[C C](88) + ω[C H](6) + �[Se C](5) 17 .60 ϕ[Se C C]*(58) + ϕ[C C C]*(37)00 12 ϕ[Se C C]*(59) + ϕ[C C C]*(37) 12 �[C C](89) + ω[C H](6)00 .30 24 .25 �[C C](87) + ω[C H](7) + �[Se C](6) 25 .35 �[C C]*(70) + �[C C](11) + �[C C](8)

+ �[Se C](6)00 18 �[C C]*(74) + �[C C](11) + �[C C](6) 20 �[C C](85) + ω[C H](7) + �[Se C](6)

Pair of modes that cross

freq (ı = 0) ı*/� Before crossing After crossing

freq ı*/� P.E.D. freq ı#/� P.E.D.

236 .85 215 .80 �[Se C](79) + �[C C](13) 210 .90 �[Se C](29) + �[C C](41) +�[C C]*(19) + �[C C](8)

217 213 �[C C](47) + �[C C]*(23) + �[C C](17) +�[Se C](10)

212 �[C C](45) + �[C C]*(23) +�[C C](16) + �[Se C](12)

179 .65 214 .60 �[C C](48) + �[C C]*(23) + �[C C](18) +�[Se C](7)

213 .70 �[C C](47) + �[C C]*(23) +�[C C](17) + �[Se C](8)

217 215 �[C Se](42) + ϕ[Se C C]*(35) + �[C C](15) +ϕ[C C C]*(12) + �[C C]*(7) + ϕ[Se C C](6)

209 �[C Se](43) + ϕ[Se C C]*(34) +�[C C](13) + ϕ[C C C]*(9) +�[C C]*(8) + ϕ[Se C C](7)

217 .55 215 .50 �[C C](49) + �[C C]*(24) + �[C C](18) +�[Se C](6)

214 .60 �[C C](48) + �[C C]*(23) +�[C C](18) + �[Se C](7)

179 212 ϕ[Se C C]*(31) + ϕ[C C C]*(28) + �[C Se](16)+ ϕ[C Se C](10) + �[C C](7) + ϕ[Se C C](6)

215 ϕ[Se C C]*(35) + �[C Se](42) +ϕ[C C C]*(12) + �[C C](15) +�[C C]*(7) + ϕ[Se C C](6)

203 .70 206 .65 �[Se C](34) + �[C C](28) + �[C C]*(20) +�[C C](15)

207 .75 �[Se C](30) + �[C C](29) +�[C C]*(20) + �[C C](18)

179 212 �[C Se](43) + ϕ[Se C C]*(35) + �[C C](14) +ϕ[C C C]*(10) + �[C C]*(7) + ϕ[Se C C](6)

205 �[C Se](42) + ϕ[Se C C]*(34) +�[C C](12) + �[C C]*(9) +ϕ[C C C]*(8) + ϕ[Se C C](8)

203 .40 204 .35 �[Se C](57) + �[C C]*(19) + �[C C](13) +�[C C](9)

205 .45 �[Se C](48) + �[C C]*(19) +�[C C](19) + �[C C](11)

179 198 ϕ[Se C C]*(32) + ϕ[C C C]*(29) + �[C Se](17)+ ϕ[C Se C](10)

207 ϕ[Se C C]*(32) + ϕ[C C C]*(28) +�[C Se](16) + ϕ[C Se C](10)

A. Gupta et al. / Synthetic Metals 162 (2012) 314– 325 321

Table 5 (Continued )

Flat regions

freq(ı = 0)

freq ı*/� P.E.D. freq(ı = 0)

freq ı*/� P.E.D.

250 227 .65 ϕ[Se C C]*(29) + ϕ[C C C]*(27) +�[C Se](13) + ϕ[C Se C](12) + ϕ[Se C C](8)

236 220 .55 �[C Se](36) + ϕ[Se C C]*(35) +ϕ[C C C]*(15) + �[C C]*(6) +�[C C](6) + ϕ[Se C C](6)

236 226 .65 �[Se C](87) + �[C C](7) + �[C C](5) 179 205 .55 �[Se C](40) + �[C C](24) +�[C C]*(20) + �[C C](13)

179 190 .95 �[Se C](88) + �[C C](11) 173 156 .65 �[Se C](88) + �[C C](10)173 188 .95 �[C Se](33) + ϕ[Se C C]*(30 + �[C C]*(12) +

ϕ[Se C C](12)123 113 .25 ϕ[Se C C]*(59) + ϕ[C C C]*(34) +

�[C Se](6)123 153 .65 �[Se C](49) + �[C C](37) + �[C C](8) +

ω[C H](6)123 147 .75 �[C Se](32) + ϕ[Se C C]*(24) +

ϕ[Se C C](18) + �[C C]*(17) +�[C C](12) + ϕ[C Se C](7) +ϕ[C C C](6)

106 146 .75 �[Se C](56) + �[C C](32) + �[C C](6) +ω[C H](5)

106 109 .30 ϕ[Se C C]*(58) + ϕ[C C C]*(32) +�[C Se](8)

106 105 .20 �[Se C](89) + �[C C](8) 106 105 .40 ϕ[Se C C]*(53) + ϕ[C C C]*(24) +�[C Se](16) + �[C C](5)

92 104 .20 �[C C]*(80) + �[Se C](17) 92 94 .55 �[C C]*(78) + �[Se C](15)79 76 .20 �[Se C](86) + �[C C](10) 79 92 .60 �[C C]*(78) + �[Se C](15)29 28 .10 �[C C](87) + ω[C H](7) + �[Se C](6) 29 81 .50 ϕ[Se C C]*(41) + ϕ[C C C]*(30) +

ϕ[Se C C](8) + ϕ[C Se C](7) +�[C C]*(7)

29 59 .80 ϕ[Se C C]*(54) + ϕ[C C C]*(36) 0 26 .20 �[C C](87) + ω[C H](7) + �[Se C](6)0 24 .25 �[C C](87) + ω[C H](7) + �[Se C](6) 0 55 .85 ϕ[Se C C]*(54) + ϕ[C C C]*(36)0 20 .35 �[C C](85) + ω[C H](7) + �[Se C](6) 0 14 .55 ϕ[Se C C]*(59) + ϕ[C C C]*(37)0 13 .55 �[C C](88) + ω[C H](7)

Pair of modes that converge

freq (ı = 0) freq ı*/� P.E.D. freq(ı = 0)

freq ı*/� P.E.D.

1380 1355 1.0 �[C C](54) + �[C C](11) 1200 1200 0.0 �[C Se](26) + �[C C]*(25) + �[C C](14) +ϕ[C C C](12) + ϕ[C C C]*(9) +ϕ[C C H](7) + ϕ[Se C C](6)

1324 1346 �[C C](23) + �[C C](9) 1187 1187 �[C Se](28) + �[C C](19) + ϕ[C C H](13) +ϕ[C C C]*(11) + �[C C]*(11) +ϕ[Se C C]*(7)

1135 1128 1.0 �[C C](39) + ϕ[C C H](26) + �[C C]*(8) +�[C C](7) + ϕ[C C C](5)

1018 986 1.0 ϕ[C C H](62) + �[C C](33) + �[C Se](14) +ϕ[C C H](9)

1107 1126 �[C C](37) + ϕ[C C H](27) + �[C C](17) +�[C Se](6) + ϕ[C C C](5)

943 980 ϕ[C C H](61) + ϕ[C C H](10) + �[C Se](8)+ �[C C]*(7)

833 804 1.0 ϕ[C C H](37) + �[C C](31) + �[C C](18) +�[C Se](13) + ϕ[C C H](9)

760 758 1.0 ω[C H](90) + �[C C](7)

796 801 ϕ[C C H](40) + �[C C](31) + ϕ[C C H](10)+ �[C Se](7) + �[C C](6)

755 757 ω[C H](90) + �[C C](7)

621 620 1.0 ω[C H](92) + �[C C](6) 553 510 1.0 �[C Se](25) + ϕ[Se C C](16) + �[C C](15) +ϕ[C C C](14) + ϕ[C Se C](10) +�[C C]*(10) + ϕ[Se C C]*(8)

618 619 ω[C H](92) + �[C C](6) 411 503 ϕ[Se C C](16) + �[C Se](15) +ϕ[C C C](13) + ϕ[C Se C](10) +�[C C]*(10) + ϕ[Se C C]*(8) + �[C C](7)

411 411 0.0 ϕ[Se C C](31) + ϕ[C Se C](31) +�[C Se](19) + ϕ[Se C C]*(7) + �[C C](6) +ϕ[C C C](5)

402 402 �[C C]*(25) + ϕ[C C C](19) + ϕ[C C C]*(16)+ ϕ[Se C C](14) + �[C C](8)

N conve

ea

os(fiibtT

ote: (1) * marked ı corresponds to repulsion/ crossing point/flat regions/points of

nergy-momentum space. However in the case of polymers theyre difficult to visualize.

The low frequency vibrations are expected to depend sensitivelyn the chain conformation and hence the dispersion curves of poly-elenophene (PSe) in the low frequency region have been comparedFig. 5) with those of polythiophene (PTh) [35]. A comparison of lowrequency modes in both the polymers shows that although the PEDs not the same because of the presence of sulfur atom in thiophene

n place of selenium atom but their dispersive behavior is similar. Inoth these systems the regions of high density of states are aroundhe same value of phase factor (in the neighborhood of ı = .50�).his is a common feature of the similar chain conformation and

rgence; (2) # marked ı corresponds to the points before / after repulsion/ crossing.

generally refers to internal symmetry. The modes at 179, 123 cm−1

and 79 cm−1 in PSe have similar dispersive behavior with the cor-responding modes at 271, 165 and 83 cm−1 in PTh. These modesalso have similar PEDs. It is observed that the profile of the acousticmodes in both the polymers bears a great deal of resemblance. Inboth the polymers two of the acoustic modes suffer repulsion withexchange of character at about ı = .15� and ı = .55�.

3.4. Theory of Interpretation of spectra of oligomers

One of the most important uses of the dispersion curves is toexpound the spectra of short chain molecules or oligomers that

322 A. Gupta et al. / Synthetic Metals 162 (2012) 314– 325

0.0 0.5 1.00

50

100

150

200

0.0 0.5 1.00

100

200

300

Phas e Factor ( )

PTh(b)

Freq

uenc

y (c

m-1

)

(a)PSe

Phas e Factor ( )

Fp

hmustac

ı

wtsfisIıtoofmbpTntp

3

bodtuithpra

of

dif

fere

nt

mod

es

in

olig

omer

ic

and

pol

ysel

enop

hen

e.

PSe

n

=

2,

ı/�

=

n

=

3,

ı/�

=

n

=

4,

ı/�

=

n

=

6,

ı/�

=

0

0

.5

0

.33

.67

0

.25

.5

.75

0

.16

.33

.5

.67

.83

)

+* (

26)

1504

(150

7)15

04(1

506)

1506

(150

6)15

04(1

504)

1505

(150

4)15

08(1

504)

1504

(150

2)15

05(1

502)

1506

(150

2)15

09(1

514)

1504

(150

0)15

04(1

500)

1505

(150

0)15

06(1

500)

1508

(151

4)15

11(1

514)

)

+* (

27)

1456

(144

0)14

56(1

456)

1473

(147

0)14

56(1

460)

1466

(146

0)14

79(1

485)

1456

(145

6)14

61(1

456)

1473

(148

5)14

81(1

485)

1456

(145

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cies

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per

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es.

s

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es

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the

olig

omer

ic

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tra

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2,

3,

4,

6

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. [30

]].

ig. 5. Comparison of low frequency dispersion curves of polyselenophene witholythiophene.

ave the same structure as the polymeric form. The IR spectra ofacromolecules containing a finite chain of identical structural

nits are characterized by a series of absorption bands. It can behown that the normal modes responsible for component absorp-ion can be specified by an appropriate phase difference [40]. Theyre denoted by k values related to the phase difference ı along thehain between adjacent residue units and are given by

=(

k�

n

)k = 0, 1, 2, . . . n − 1 (5)

here n is the number of repeat units in the chain and k is an integerhat represents the number of loops in a stationary wave repre-enting the chain vibrations. The above equation holds good for anite chain having free ends and shows the relation between theelection rules for a finite system and that for an infinite system.n order to use this relation we worked out the allowed values of

for a particular mode and marked the frequencies correspondingo these ı values on the dispersion curves. In the observed spectraf oligomers, we look for the frequencies corresponding to thosebtained from dispersion curves. If such frequencies are availableor several modes, the oligomers have the same structure as poly-

er. These frequencies are shown in Table 6. A good agreementetween the spectral data of oligomers [30] and the profile of dis-ersion curves of the polymeric form shows structural similarity.his observation is also supported by the electron energy loss andear-edge X-ray absorption fine structure spectra which indicatehat the geometry of the selenophene ring is rather unaffected byolymerization [17].

.5. Frequency distribution function and heat capacity

From the dispersion curves, frequency distribution function haseen obtained and plotted in Figs. 2(b), 3(b) and 4(b). The peaksf the frequency distribution curves correspond to regions of highensity of states. The observed frequencies correspond well withhese peak positions. The knowledge of density of states can besed to obtain the thermodynamic properties such as heat capac-

ty, enthalpy, etc. We have calculated the heat capacity of PSe in theemperature range 0–450 K using Debye’s equation. Similar studies

ave been performed on other conducting polymers such as poly-phenylene sulfide, polyacetylene, polythiophene and polypyr-ole [35,38,41,42]. In such systems the experimental values suchs spectroscopic data and heat capacity (wherever reported) agree Ta

ble

6Fr

equ

enci

es

Mod

es

�[C

C](

27�

[CC

]�

[C

C](

32�

[CC

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C](

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C](

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Se](

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C]

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C](

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C

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C

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[C

C](

ϕ[C

C

Not

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All

2.

The

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u3.

The

figu

re

A. Gupta et al. / Synthetic Metals 162 (2012) 314– 325 323

5004003002001000

0

20

40

60

80

100H

eat C

apac

ity C

v (J

/mol

0 K)

High F req. mod es

Low F req. mode s

Total mo des

Temperat ure (K )

wiacaaPocTttdbtiertl7peeo

mstccwtaonfiaeitcsrritzs

0.50.40.30.20.10.00

1

2

3

4

P T e P S eEn

ergy

(eV)

Fig. 6. Variation of heat capacity Cv with temperature.

ith the calculations. Such studies are not confined to conduct-ng polymers alone but several polymers of general nature suchs polyvinylidene fluoride (�-form), polyoxacyclobutane modifi-ation I, polydimethylsilane, poly �-caprolactone, and polyglycoliccid [43–47] have also been studied where experimental data arevailable and a good agreement is obtained. The heat capacity ofSe is plotted in Fig. 6. The heat capacity variation shows a regionf inflexion in the neighborhood of 100 K. This is somewhat diffi-ult to understand especially when dealing with an isolated chain.o make sure that this variation is real we repeated our calcula-ions and found the same nature. The inflexion, which appears inhe region of 100 K, could arise either due to structural changes orue to large number of modes contributing to energy in the neigh-orhood of 100 K. Since the chain has a regular structure, structuralransition cannot be a possibility. The modes affecting heat capac-ty must lie in the low frequency region to which it is sensitive. Thenergy corresponding to the wagging motion (∼750 cm−1) and itselatively larger contribution is such a candidate. In order to locatehe origin of inflexion region we divided the energy spectrum intoow frequency (below 750 cm−1) and high frequency region (above50 cm−1) and calculated the heat capacity as a function of tem-erature. As commented earlier the inflexion region arises fromnhanced contribution of low frequency modes to heat capacity,specially the modes which are a mixture of several internal co-rdinates.

It may be added here that the contribution from the latticeodes is bound to make a difference to the heat capacity due of its

ensitivity to low frequency modes. However, so far we have solvedhe problem only for an isolated chain. The calculation of dispersionurves for a three dimensional system is extremely difficult. Inter-hain modes, involving hindered translatory and rotatory motionsould appear and the total number of modes would depend on

he contents of the unit cell. In polymeric systems, the number oftoms in unit cell is very large. This in turn makes the dimensionsf the secular equation extremely large (≥3 times). In addition, theumber of interactions become enormous and some of them dif-cult even to visualize and quantify. The problem thus becomeslmost intractable. The inter-chain interactions which are gen-rally of the same order of magnitude as the weak intra-chainnteractions would contribute to lower frequencies. Their introduc-ion would, at best bring about crystal field splittings at the zoneenter or zone boundary, depending on the symmetry dependentelection rules [48]. However, the intra-chain assignments wouldemain by and large undisturbed. Complete 3D studies have beeneported only on polyethylene, polyglycine, etc., where the unit cell

s small. Other calculations with approximate inter-chain interac-ions as in a � sheet of polypeptides are confined to calculations ofone center and zone boundary frequencies alone by consideringhort segments. The present work goes beyond it and calculates the

1/Number of rings in oligomer

Fig. 7. HOMO–LUMO gap as a function of chain length.

dispersion curves within the entire zone. Although the heat capac-ity is predictive in nature but it may stimulate some worker to carryout measurements at a later date.

3.6. A brief comparison with Te analog

Because of the similarity of Se and S atoms, polyselenopheneshave many properties similar to those of polythiophenes. In con-trast the properties of the next member of group VI, the telluriumatom are significantly different from those of selenium [49,50].Consequently polytellurophenes (PTe) are expected to exhibitproperties different from those of polyselenophenes and polythio-phenes. It is reported [51] that the conductivity of neutral PTe isvery low (10−12 S cm−1) whereas it may be as high as 10−6 S cm−1

when it is doped with I2. The doped polymer however, has a lowerconductivity than doped polythiophene or polyselenophene. Thereason may be attributed to the morphological difference betweenthe thin films. HOMO–LUMO gap of a conducting polymer is one ofthe important parameters to function as an active material in a vari-ety of optoelectronic devices. We have optimized the geometry oftellurophene oligomers upto octamer at DFT/B3LYP level of theoryusing a standard SDD core potential and basis set with the Gaussian03 program. After the geometry optimization positions of HOMOsand LUMOs and the gap between them were estimated. In order toobtain information about the size, shape, charge density distribu-tion and chemical reactivity of the molecule, electrostatic potentialsurface has been mapped over the electron density iso-surface.

The calculated geometry of the tellurophene oligomers opti-mizes to give a planar structure, which is similar to its seleniumanalog. The HOMO–LUMO gap for the polymer PTe has beenobtained by plotting the results for dimer through octamer againstinverse chain length and extrapolating to infinity (Fig. 7). It is foundto be 1.388 eV, which is lower as compared to PSe (1.497 eV). A com-parison of HOMO–LUMO gap in various oligomers of tellurophenewith selenophene is shown in Table 7. It is seen that the band gapincreases as the length of the oligomer decreases. Due to narrowHOMO–LUMO gap PTe may have potential for future applicationsin optoelectronics.

Molecular electrostatic potential (MEP) is widely used as a reac-tivity map displaying most probable regions for the electrophilicattack of charged point-like reagents on organic molecules [52].The values and spatial distribution of MEP are in fact responsiblefor the chemical behavior of an agent in a chemical reaction. Theystrongly influence the binding of a substrate to its active site. MEP is

typically visualized through mapping its values onto the molecularelectron density. The different values of the electrostatic potentialat the surface are represented by different colors; red representsregions of most negative electrostatic potential, blue represents

324 A. Gupta et al. / Synthetic Metals 162 (2012) 314– 325

Table 7Molecular weight and HOMO–LUMO gap of selenophene and tellurophene oligomers.

Se Oligomers Te Oligomers

Mol. wt. HOMO–LUMO gap (eV) Mol. wt. HOMO–LUMO gap (eV)

Di 259.92 4.02723 357.2 3.72791Tri 388.88 3.2109 534.8 2.99321Tetra 517.84 2.80273

Hexa 775.76 2.36736

Octa 1033.68 2.14967

Fig. 8. Molecular electrostatic potential surface of (a) octaselenophene (8Se) (b)octatellurophene (8Te).

rsrscsrt(tttwb

fabbpc

totsovcot

[[

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[[[[[[[[

[21] Y.H. Wijsboom, A. Patra, S.S. Zade, Y. Sheynin, M. Li, L.J.W. Shimon, M. Bendikov,Angew. Chem. 121 (2009) 5551–5555, Angew. Chem. Int. Ed. Engl. 48 (2009)5443–5447.

egions of most positive electrostatic potential and green repre-ents regions of zero potential. Potential increases in the ordered ≤ orange ≤ yellow ≤ green ≤ blue. While the negative electro-tatic potential corresponds to an attraction of the proton by theoncentrated electron density in the molecule (and is colored inhades of red), the positive electrostatic potential corresponds toepulsion of the proton by atomic nuclei in regions where low elec-ron density exists and the nuclear charge is incompletely shieldedand is colored in shades of blue). The molecular electrostatic poten-ial maps for 8Se and 8Te are shown in Fig. 8. The figure showshat there is a wide difference between the two. It is clear thathe hydrogen atoms of 8Se bear a positive charge (blue region),hereas whole of the molecule 8Te has a neutral potential depicted

y predominance green colors.The characteristic properties of the conducting polymers are a

unction of geometry, electronic configuration, band gap, electronffinity and ionization potential. These vary with atomic num-er also, but no systematic changes in properties can be inferredecause of difference in conjugation lengths, disorder and crystalacking. Due to variation in these parameters it is very difficult toomment on the systematics in the oligomeric forms also.

Force constants in general are the result of entire environmen-al forces and include origin of both electrical and non-electricalnes. They would obviously be affected by the atomic number. Inhis context one would expect higher atomic numbers resulting intronger bonding. But this is not so simple because of the presencef different conjugation lengths, disorder and atomic packing. Iniew of this fact it is difficult to make systematic comments on theharacteristic variations in the behaviors of Se and Te containing

ligomers and polymers. This is equally true in trying to predicthe systematic variation in the dynamics.

[

712.4 2.585051067.6 2.149671422.8 1.95919

4. Conclusions

The GF matrix method as modified by Higg’s along with theUrey Bradley force field has successfully explained the spectro-scopic data on PSe. The dispersion curves are found to observe thevibrational relationship of the spectra of the oligomers [30] and thepolymer. Predictive values of heat capacity as a function of tem-perature within the range 0–450 K have been given. The region ofinflexion around 100 K in the specific heat curve may be due to alarge contribution of low frequency modes which are a mixture ofseveral internal co-ordinates to heat capacity. However, the contri-bution from the lattice modes is bound to make a difference to thespecific heat because of its sensitivity to these modes. In spite ofseveral limitations involved in the calculation of specific heat andthe absence of experimental data, the present work would providea good starting point for further basic studies on thermodynamicalbehavior of polymers.

Acknowledgements

We are thankful to Prof. Victor Hernandez, Jolin, University ofMalaga (Spain) for providing us the FTIR data of Oligoselenophenes.One of the authors (PT) is grateful to UGC for grant under the majorresearch project. NC is grateful to UGC for providing financial assis-tance under the Rajiv Gandhi National Fellowship Scheme (RGNFS).

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