Chemical Physics Letters 511 (2011) 283–287

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Chemical Physics Letters

journal homepage: www.elsevier .com/ locate /cplet t

Influence of polarity of the medium in the saturation of the electronicproperties for p-conjugated oligothiophenes

Carlos Alemán a,b,⇑, Juan Torras c, Jordi Casanovas d

a Departament d’Enginyeria Química, E. T. S. d’Enginyeria Industrial de Barcelona, Universitat Politècnica de Catalunya, Diagonal 647, Barcelona E-08028, Spainb Centre for Research in Nano-Engineering, Universitat Politècnica de Catalunya, Campus Sud, Edifici C’, C/Pasqual i Vila s/n, Barcelona E-08028, Spainc Departament d’Enginyeria Química, EEI, Universitat Politècnica de Catalunya, Pça Rei 15, Igualada 08700, Spaind Departament de Química, Escola Politècnica Superior, Universitat de Lleida, c/ Jaume II no 69, Lleida E-25001, Spain

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 May 2011In final form 10 June 2011Available online 16 June 2011

0009-2614/$ - see front matter � 2011 Elsevier B.V. Adoi:10.1016/j.cplett.2011.06.026

⇑ Corresponding author at: Centre for Research in NPolitècnica de Catalunya, Campus Sud, Edifici C’, C/E-08028, Spain. Fax: +34 934017150.

E-mail addresses: carlos.aleman@upc.edu, Carlos.A

The influence of the polarity of the medium on the electronic properties and saturation behavior ofp-conjugated oligomers and polymers based on thiophene have been investigated. Quantum mechanicalcalculations in the gas-phase and both acetonitrile and water solutions have been performed consideringthe neutral and positively charged forms of oligomers made of thiophene, 3,4-ethylenedioxythiopheneand 3,4-phenylenedioxythiophene. Results indicate that the influence of the medium on the HOMO–LUMO gap is practically negligible while it affects considerably both the vertical and adiabatic ionizationpotentials, even though the magnitude of such effects depends on the chemical structure of the repeatingunit.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Since Shirakawa and co-workers discovered in 1977 that poly-acetylene presents a dramatic increase of its electrical conductivityupon charge transfer oxidative doping [1], the interest towards p-conjugated polymers and oligomers (p-CPs and p-COs,respectively) has steadily increased because of their wide rangeof technological applications in fields such as electronics, biomed-ical engineering and optics [2]. Among the more prominent fami-lies of p-CPs and p-COs, those based on thiophene (Th) areparticularly relevant because of the high environmental stabilityof their doped and undoped states, and the easiness to tune theirchemical structure allowing to control the electronic properties[2]. Accordingly, major experimental and theoretical efforts havebeen directed towards the understanding of different effects inthe band gap (eg) of p-CPs and p-COs formed by Th and its deriva-tives [2].

Within this context, it has been generally accepted that linearextrapolation of the eHOMO–eLUMO gap obtained for p-COs againstthe reciprocal of the number of repeating units (1/n) affords a pre-diction of eg for the corresponding p-CP [3–7]. However, in recentyears different authors showed that this extrapolation method failsto consider asymptotic behavior, since saturation occurs at n > 12[8–11]. Specifically, although short p-COs with n = 2–12 present

ll rights reserved.

ano-Engineering, UniversitatPasqual i Vila s/n, Barcelona

leman@upc.es (C. Alemán).

a linear relationship between eg and 1/n, second- or higher-orderpolynomials are required to describe the behavior of systems withn > 12. Zade and Bandikov examined the variation of eg against 1/nfor p-COs derived from Th and 3,4-ethylenedioxythiophene, abbre-viated n-Th and n-EDOT, respectively, with n up to 50 and 30,respectively [9]. Results, which were derived from gas-phasegeometry optimizations at the B3LYP/6-31G(d) level, led to qua-dratic equations that predicted eg values of 2.03 and 1.80 eV forpolythiophene (PTh) and poly(3,4-ethylenedioxythiophene) (PED-OT), respectively, which are very close to the corresponding exper-imental values (i.e. 2.1–2.2 and 1.6–1.9 eV for PTh [12–14] andPEDOT [15–18], respectively). Saturation of the electronic proper-ties is caused by the combination of electron correlation effectswith other extrinsic effect, the most important one being deviationfrom planarity [11]. The impact of electron correlation in satura-tion was evidenced by accounting this effect in the study of theevolution of the transition energies with respect to 1/n [11].

In this work we extend the theoretical works previously re-ported for p-COs [8–11] to the condensed phase. Specifically, weexamine the influence of the polarity of the medium on the satura-tion of the electronic properties, i.e. the eg and the ionization po-tential (IP), of thiophene-containing p-COs (Scheme 1). For thispurpose, the electronic properties of homo-oligomers formed byn repeating units of Th, EDOT and 3,4-phenylenedioxythiophene(PhEDOT), with n ranging from 2 to 30, have been determined inacetonitrile and water using a Self-Consistent Reaction-Field(SCRF) method, which was applied within the Density FunctionalTheory (DFT) framework. Molecular geometries of n-Th, n-EDOTand n-PhEDOT in both the neutral and cation radical states have

284 C. Alemán et al. / Chemical Physics Letters 511 (2011) 283–287

been fully optimized in solution, and results have been comparedwith those obtained in the gas-phase. It should be noted that n-Th were selected because PTh is the parent compound of the familyof p-CPs under study, while the interest of n-EDOT and n-PhEDOTreside on the particular properties of PEDOT and poly(3,4-pheny-lenedioxythiophene) (PPhEDOT). Thus, PEDOT was settled amongthe most successful p-CPs due to a combination of properties, i.e.moderate band gap, low oxidation potential, high conductivity,good optical transparency and exceptional environmental stability[15–19], PPhEDOT was explicitly designed to improve the solubil-ity and processability of PEDOT but retaining the good electrical,electrochemical and structural properties of the latter [19–21].

1.90

2.30

2.70

3.10

3.50

3.90

4.30

-3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00

Gas-phase

Acetonitrile

Water

1.70

2.10

2.50

2.90

3.30

3.70

4.10

-3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00

Gas-phase

Acetonitrile

Water

3.20

3.60

4.00Gas-phase

Acetonitrile

Water

Ln (1/n)

Ln (1/n)

εε g(e

V)

ε g(e

V)

(eV

)

n-Th

n-EDOT

2. Methods

Complete geometry optimizations of neutral and cationic oligo-mers were carried out considering the all-anti conformation asstarting point (i.e. all the inter-ring dihedral angles were initiallyarranged at 180�). Calculations were performed using the Becke’sthree-parameter exchange functional [22] combined with the LYPcorrelation functional (B3LYP) [23], and with the 6-31G(d) basisset. This DFT methodology was selected to facilitate the compari-son with the results obtained for other compounds in previouslyreported gas-phase studies [9,10]. Furthermore, the B3LYP/6-31G(d) method was found to be a very accurate method for theprediction of the electronic properties of p-CPs [9,24,25], eventhough the reliability of this procedure is consequence of the can-cellation of different errors [9,25]. The restricted formalism wasconsidered for calculations on the neutral oligomers (closed-shellsystems), while for the monocations in the doublet electronic statethe unrestricted DFT formalism UB3LYP was used. The structuresof n-Th, n-EDOT and n-PhEDOT in the neutral and monocationicstates with n ranging from 2 to 30, 24 and 14, respectively, werecalculated in the gas-phase using complete geometry optimiza-tions (i.e. no symmetry constraint was imposed). As it was previ-ously reported, the optimized inter-ring dihedral angles ofneutral n-Th deviate towards an anti-gauche conformation(�150�) [6,26], while those of neutral n-EDOT and n-PhEDOT re-tained the initial planar conformation (�180�) [5,27]. In contrast,positively charged oligomers preferred an all-anti arrangement inall cases.

In order to examine the influence of the polarity of the mediumon the electronic properties of p-COs, the obtained gas-phasestructures were completely re-optimized using a SCRF model. Spe-cifically, the Polarizable Continuum Model (PCM) developed byTomasi and co-workers [28] was used to describe acetonitrileand water as solvents. PCM calculations were performed in theframework of the B3LYP/6-31G(d) (neutral state) and UB3LYP/6-31G(d) (monocations) levels using the standard protocol and con-sidering the dielectric constants of acetonitrile (e = 35.688) andwater (e = 78.4). Geometry optimizations in acetonitrile solutioninvolved oligomers with n ranging from 2 to 30 (n-Th), 16(n-EDOT) and 14 (n-PhEDOT), while for optimizations in aqueous

S

O O

nS n S

O O

n

n-Th n-EDOT n-PhEDOT

Scheme 1.

solution the largest values of n were 24, 12 and 12. The spin con-tamination was very low in all cases, independently of the med-ium, i.e. the highest overestimation was 2.6%.

In all cases eg was estimated as the difference between theHOMO and LUMO energies (i.e. eg = eHOMO � eLUMO). Levy and Nagyevidenced that eg can be rightly approximated using this procedurein DFT calculations [29]. The vertical first ionization potential (IPv)was calculated using Koopman’s theorem, that is, relating the IP tothe negative energy of the HOMO (i.e. IPv = �eHOMO), which accord-ing to Janak’s theorem can be applied to DFT calculations [30]. Thefirst adiabatic ionization potential (IPa) was calculated as the en-ergy difference between the optimized structures of the cation rad-ical and the neutral oligomers (i.e. IPa = Ecation � Eneutral).

3. Results and discussion

In this section we focus on the influence of the polarity of themedium in the saturation effects of the HOMO–LUMO gap and

2.00

2.40

2.80

-3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00

Ln (1/n)

ε g

n-PhEDOT

Figure 1. HOMO–LUMO gap (eg) against the natural logarithm of the reciprocal ofthe number of repeating units (Ln 1/n) calculated for (a) n-Th, (b) n-EDOT and (c) n-PhEDOT p-conjugated oligomers in the gas-phase (empty squares), acetonitrilesolution (gray triangles) and aqueous solution (black circles). The eg values werecalculated at the B3LYP/6-31G(d) level and the medium was described using thePCM method.

Table 1Functions derived from the fitting of the HOMO–LUMO gap (eg) against the naturallogarithm of the reciprocal of the number of repeating units (x = Ln 1/n) for thesystems studied in this work.

System Environment Function R2

n-Th Gas-phase eg = 0.1035x3 + 1.0295x2 + 3.5174x + 6.2077 1.0000Acetonitrile eg = 0.1038x3 + 1.0319x2 + 3.5232x + 6.2046 1.0000Water eg = 0.1068x3 + 1.0484x2 + 3.5500x + 6.2165 1.0000

n-EDOT Gas-phase eg = 0.0890x3 + 0.9278x2 + 3.3209x + 5.9431 1.0000Acetonitrile eg = 0.0859x3 + 0.9131x2 + 3.3051x + 5.9233 1.0000Water eg = 0.0790x3 + 0.8812x2 + 3.2611x + 5.9054 1.0000

n- PhEDOT Gas-phaseeg = 0.1023x3 + 0.9896x2 + 3.2610x + 5.9172 0.9995

Acetonitrile eg = 0.1020x3 + 0.9904x2 + 3.2721x + 5.9140 0.9995Water eg = 0.0705x3 + 0.8344x2 + 3.0416x + 5.8168 0.9997

4.30

4.50

4.70

4.90

5.10

5.30

5.50

5.70

-3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00

Gas-phase

Acetonitrile

Water

3.40

3.80

4.20

4.60

5.00

-3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00

Gas-phase

Acetonitrile

Water

4.40

4.60

4.80

5.00

5.20

5.40

5.60

-3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00

Gas-phase

Acetonitrile

Water

Ln (1/n)

Ln (1/n)

Ln (1/n)

IPv

(eV

)IP

v(e

V)

IPv

(eV

)

n-Th

n-EDOT

n-PhEDOT

Figure 2. Vertical ionization potential (IPv) against the natural logarithm of thereciprocal of the number of repeating units (Ln 1/n) calculated for (a) n-Th, (b) n-EDOT and (c) n-PhEDOT p-conjugated oligomers in the gas-phase (empty squares),acetonitrile solution (gray triangles) and aqueous solution (black circles). The IPv

values were calculated at the B3LYP/6-31G(d) level and the medium was describedusing the PCM method.

C. Alemán et al. / Chemical Physics Letters 511 (2011) 283–287 285

the ionization potential. It should be noted that the impact of themedium in the geometry of PTh derivatives was reported in previ-ous works [31–33] and, therefore, have not been discussed here.

3.1. HOMO–LUMO gap

Figure 1 compares the variation of eg against Ln(1/n) calculatedin the gas-phase, acetonitrile and aqueous solution for n-Th,n-EDOT and n-PhEDOT. As it can be seen, the influence of the polar-ity of the medium on the HOMO–LUMO gap is very small, results inacetonitrile and water being very similar to those obtained in thegas-phase for the three series of p-COs. Moreover, these resultsindicate that the linear behavior between eg and 1/n is loss forn > 12 for both n-Th and n-EDOT, which is in fully concordancewith the predictions of Zade and Bendikov [9]. Thus, the linearextrapolation method typically used to obtain the gaps of p-CPsfails in these systems because saturation only occur at large n

4.20

4.60

5.00

5.40

5.80

6.20

6.60

-3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00

Gas-phase

Acetonitrile

Water

3.70

4.10

4.50

4.90

5.30

5.70

6.10

6.50

-3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00

Gas-phase

Acetonitrile

Water

4.40

5.00

5.60

6.20

6.80

-3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00

Gas-phase

Acetonitrile

Water

Ln (1/n)

Ln (1/n)

Ln (1/n)

IPa

(eV

)IP

a(e

V)

IPa

(eV

)

n-Th

n-EDOT

n-PhEDOT

Figure 3. Adiabatic ionization potential (IPa) against the natural logarithm of thereciprocal of the number of repeating units (Ln 1/n) calculated for (a) n-Th, (b) n-EDOT and (c) n-PhEDOT p-conjugated oligomers in the gas-phase (empty squares),acetonitrile solution (gray triangles) and aqueous solution (black circles). The IPa

values were obtained using the UB3LYP/6-31G(d) level of calculation for cations,while the medium was described using the PCM method.

286 C. Alemán et al. / Chemical Physics Letters 511 (2011) 283–287

values. The eg extrapolated using third-order polynomials for PThin the gas-phase, acetonitrile and water using the data displayedin Figure 1 are 2.08, 2.05 and 2.06 eV, respectively, while those pre-dicted for PEDOT are 1.87, 1.86 and 1.90 eV, respectively. Thesevalues are in excellent agreement with the experimental valuesdetermined for PTh (2.1–2.2 eV) [12–14] and PEDOT (1.6–1.9 eV)[15–18], respectively. It should be emphasized that the third orderpolynomial is the simplest function that permits to capture the sat-uration effects obtained for oligomers with large n values. Thus, inspite of the lack of physical meaning, this function allows us to cor-rect of the wrong linear behavior typically used to predict the elec-tronic properties of polymers by extrapolating the results derivedfrom oligomers. The functions and coefficients fitted using the re-sults derived from calculations on n-Th, n-EDOT and n-PhEDOT aredisplayed in Table 1.

Results for n-PhEDOT (Figure 1c) are slightly different, satura-tion of eg being detected at n > 8 in the three environments. Theeg values extrapolated (third-order polynomial) for PPhEDOT inthe gas-phase, acetonitrile and water are 2.24, 2.22 and 2.37 eV,respectively. However, these values are only in qualitative agree-ment with the experimental value reported in the literature,1.85 eV [21]. Thus, although the eg values measured for PEDOTand PPhEDOT are very similar, calculations predict that thereplacement of the ethylene bridge of EDOT by a phenyl group in-creases the gap. In spite of this discrepancy, theoretical calcula-tions predict that the influence of the polarity of the medium onthe eg values of p-CPs is very small, which is fully consistent withexperimental observations. Accordingly, experimental eg valuesvary within a relatively narrow interval, even though measureswere performed using different techniques (i.e. mainly electro-chemical and optical measures) and media, and considering sam-ples arising from chemical oxidation and anodic polymerizationprocesses.

3.2. Ionization potential

In contrast to eg, calculations predict that the polarity of theenvironment has a significant influence on both the IPv and theIPa, which are represented in Figures 2 and 3, respectively. Further-more, this influence depends significantly on the chemical natureof the repeating unit, being different for n-Th, n-EDOT and n-PhE-

Table 2Functions derived from the fitting of the vertical and adiabatic ionization potentials (IPv arepeating units (x = Ln 1/n) for the systems studied in this work.

System Environment Fu

Vertical ionization potentialn-Th Gas-phase IPv

Acetonitrile IPv

Water IPv

n-EDOT Gas-phase IPv

Acetonitrile IPv

Water IPv

n-PhEDOT Gas-phase IPv

Acetonitrile IPv

Water IPv

Adiabatic ionization potentialn-Th Gas-phase IPa

Acetonitrile IPa

Water IPa

n-EDOT Gas-phase IPa

Acetonitrile IPa

Water IPa

n-PhEDOT Gas-phase IPa

Acetonitrile IPa

Water IPa

DOT. For n-Th the IPv shows the saturation behavior at oligomerswith n > 8 independently of the medium, the values extrapolated(third-order polynomial) to infinite n being 4.61 and 4.67 eV inthe gas-phase and solution (both acetonitrile and water), respec-tively. In contrast, the loss of the linear behavior of IPa occurs atlonger (n > 12) and shorter (n > 6) oligomer lengths in the gas-phase and solution, respectively. The coefficients of the third-orderpolynomial functions used to fit the variation of IPv and IPa againstLn(1/n) are listed in Table 2.

The values extrapolated for the PTh are 4.94, 4.53 and 4.52 eV inthe gas-phase, acetonitrile and water, respectively, evidencing thatthe medium plays a very remarkable role in the IPa. The ionizationpotentials measured for poly(3-alkyl-thiophene)s increase withthe length of the substituent and range from 4.8 to 5.6 eV[34–36], indicating that the IP of PTh is <4.8 eV. Accordingly, theinfluence of environmental forces in the prediction of the IP isimportant for PTh.

Saturation effects for the IPv of n-EDOT are clearly observed atn > 8 independently of the medium. The IPv value extrapolatedfor PEDOT in the gas-phase (3.55 eV) is considerably smaller thanthose obtained in acetonitrile and water (4.03 and 4.07 eV, respec-tively). These values, which reflect the large influence of the polar-ity of the medium on PEDOT and n-EDOT, are considerably smallerthan those obtained for PTh due to the electron-donating effects ofthe oxygen atoms. Moreover, a different behavior is detected forthe IPa of n-EDOT, saturation occurring at n > 12 and n > 6 in thegas-phase and solution. A striking feature is that the IPa obtainedfor PEDOT in the gas-phase (3.87 eV) is very similar to that extrap-olated in solution (3.92 eV for both acetonitrile and water),suggesting that environmentally-induced geometry relaxationessentially affects to relatively short n-EDOT oligomers. It is worthnoting that the calculated IPs are close to those experimentallymeasured for PEDOT, which range from 4.1 to 4.3 eV [18,19].

Finally, although the behavior obtained for n-PhEDOT is almostidentical (i.e. saturation effects are observed at the same n) to thatdescribed for n-EDOT, independently of the medium, the IPs calcu-lated for the former systems are higher than those of the latter. TheIPv values extrapolated for PPhEDOT (4.43 and 4.66 eV in gas-phaseand solution, respectively) indicate that electronic relaxation inpresence of environmental forces stabilize the HOMO. In opposi-tion, medium-induced geometry relaxation effects destabilize the

nd IPa, respectively) against the natural logarithm of the reciprocal of the number of

nction R2

= 0.0527x3 + 0.4969x2 + 1.5925x + 6.3580 1.0000= 0.0460x3 + 0.4488x2 + 1.5132x + 6.4355 1.0000= 0.0480x3 + 0.4598x2 + 1.5303x + 6.4474 1.0000= 0.0462x3 + 0.5016x2 + 1.8716x + 5.9343 1.0000= 0.0432x3 + 0.4563 + x2 + 1.6471x + 6.0625 1.0000= 0.0397x3 + 0.4387x2 + 1.6167x + 6.0571 1.0000= 0.0452x3 + 0.4517x2 + 1.5202x + 6.1572 0.9994= 0.0372x3 + 0.3883x2 + 1.3505x + 6.2257 0.9994= 0.0212x3 + 0.3083x2 + 1.2285x + 6.1789 0.9994

= 0.0650x3 + 06668x2 + 2.5809x + 8.5911 1.0000= 0.0647x3 + 0.5804x2 + 1.7502x + 6.3138 1.0000= 0.0661x3 + 0.5857x2 + 1.7470x + 6.2839 1.0000= 0.0548x3 + 0.6411x2 + 2.7055x + 7.8325 1.0000= 0.0515x3 + 0.5313x2 + 1.7806x + 5.8574 1.0000= 0.0555x3 + 0.5540x2 + 1.8123x + 85851 1.0000= 0.0613x3 + 0.6552x2 + 2.4078x + 7.9175 0.9989= 0.0513x3 + 0.4949x2 + 1.5492x + 6.0730 0.9998= 0.0521x3 + 0.4965x2 + 1.5391x + 6.0453 0.9998

C. Alemán et al. / Chemical Physics Letters 511 (2011) 283–287 287

HOMO, as is evidenced by extrapolated IPa values (4.89 and 4.48 eVin gas-phase and solution, respectively).

4. Conclusions

Results indicate that the influence of the polarity of the med-ium, which have been introduced through a SCRF method, on theelectronic properties of p-COs based on thiophene depend on boththe chemical nature of the repeating unit and the own electronicproperties. Furthermore, extrapolation of the properties to the cor-responding p-CPs using a third-order polynomial allows considersaturation effects very satisfactorily.

Calculations on n-Th, n-EDOT and n-PhEDOT indicate that theeffect of the environmental forces on eg is very small in all cases,values extrapolated for PTh, PEDOT and PPhEDOT being in verygood agreement with experimental observations. On the otherhand, the IP of p-COs is considerably affected by the medium, thisfeature being especially important when geometry relaxation isconsidered. The IPv, which only includes environmentally-inducedelectronic relaxation effects, shows a dependence on the chemicalstructure. Thus, the role of the external forces is negligible for n-Thand PTh but relatively important for n-EDOT and PEDOT. In oppo-sition, the IPa values, which include the geometry changes associ-ated to the ionization process, of all the calculated oligomers aredrastically affected by the medium. However, it is worth to notethat this tendency, which also affects the saturation behavior, de-creases with the length of the oligomers becoming practically neg-ligible for the polymers.

Acknowledgments

This work has been supported by MICINN and FEDER funds(MAT2009-09138 and MAT2009-11513) and by the DIUE of theGeneralitat de Catalunya (2009SGR925, 2009SGR1208 and XRQTC).We are indebted to CESCA for computational facilities. Support forthe research of C.A. was received through the prize ‘ICREA Acade-mia’ for excellence in research funded by the Generalitat deCatalunya.

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