Correlation of Viscoelastic Properties with Solvation of Regioregular

Apr 22, 2006 - ature (5 < T/°C < 70), and angular frequency (ω ) 2πf;. 10 < f/MHz < 110). The effect of potential was small, of temperature was sig...
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Anal. Chem. 2006, 78, 3616-3623

Correlation of Viscoelastic Properties with Solvation of Regioregular Poly(3-decylthiophene) Films Igor Efimov and A. Robert Hillman*

Department of Chemistry, University of Leicester, Leicester LE1 7RH, UK

Viscoelastic properties of regioregular poly(3-decylthiophene) films cast on gold electrodes and exposed to acetonitrile/LiClO4 solution were studied using highfrequency acoustic impedance. Values of shear moduli, G ) G′ + jG′′, were determined under conditions of potentiodynamic and potentiostatic electrochemical control, as functions of potential (0.0 < E/V < 0.8), temperature (5 < T/°C < 70), and angular frequency (ω ) 2πf; 10 < f/MHz < 110). The effect of potential was small, of temperature was significant, and of frequency was dominant. The principle of time-temperature equivalence was used to construct master relaxation curves. Application of activation, Williams-Landel-Ferry, and Rouse-Zimm models shows the material to be quite different from other thiophene-based conducting polymers, namely, poly(3,4ethylenedioxythiophene) and regioregular poly(3-hexylthiophene). Detailed exploration of the data reveals novel insights into the compositional originssnotably with regard to solvationsof the shear modulus behavior. We describe the variation of regioregular poly(3-decylthiophene) film viscoelastic properties with applied potential (E), temperature (T), and time scale (represented by angular frequency, ω). Through the application of models (activation, Williams-Landel-Ferry, and Rouse-Zimm) commonly applied to bulk polymeric materials, we make detailed exploration of thinfilm dynamics. In particular, the detailed shear modulus, G(E,T,ω), signature provides underlying structural (free volume), energetic, and compositional (solvation) insights that rationalize the viscoelastic manifestations. The level of detail achieved is unprecedented for electroactive polymer films. Conducting polymers have attracted huge research activity1,2 due to the prospect of exploiting their attractive properties in electronic,3-7 optical,8-10 chemical,11,12 and actuator13-15 devices. * To whom correspondence should be addressed. E-mail: [email protected]. (1) Chandrasekhar, P. Conducting Polymers, Fundamentals and Applications. A Practical Approach; Kluwer Academic Publishers: Boston, 1999. (2) Handbook of Conducting Polymers, 2nd ed.; Skotheim, T. A., Elsenbaumer, R. L., Reynolds, J. R., Eds.; Marcel Dekker: New York, 1998. (3) Turyan, I.; Mandler, D. J. Am. Chem. Soc. 1998, 120, 10733-10742. (4) Zen., A.; Neher, D.; Silmy, K.; Hollander, A.; Asawapirom, U.; Scherf, U. Jpn. J. Appl. Phys. 2005, 44, 3721-3727. (5) Alam, M. M.; Wang, J.; Guo, Y. Y.; Lee, S. P.; Tseng, H. R. J. Phys. Chem. B 2005, 109, 12777-12784. (6) Yoon, M. H.; Yan, H.; Facchetti, A.; Marks, T. J. J. Am. Chem. Soc. 2005, 127, 10388-10395.

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Polythiophene-based materials have featured prominently in this activity,4-9,11,16,17 due in part to the beneficial effects on solubility and processability of introducing substituents (e.g., alkyl groups) in the 3-position. For poly(3-alkylthiophenes), the improved solubility and processability over the parent polythiophene is acquired without undue sacrifice of electronic conductivity.18 Most applications of these materials are associated with their electrochemical oxidation/reduction (“doping/undoping”) in thin-film form. This is accompanied by exchange of ions and solvent molecules with the bathing solution, to satisfy electroneutrality and activity constraints, respectively. These processes result in film (de-)swelling, with consequent changes in film mechanical properties. Quite generally, small-molecule transport rates are dependent upon the effective viscosity of the medium through which they move. Thus, the dynamics of any device, whether overtly associated with ion, solvent of polymer motions, are intimately associated with film mechanical properties. This motivates our study of polymer dynamics. Recent studies19,20 have shown how film viscoelastic properties may be obtained using acoustic impedance measurements on thickness shear mode resonators, a more sophisticated extension of the simple gravimetric quartz crystal microbalance methodology.21 We have used the acoustic impedance technique to study the viscoelastic properties of two members of the polythiophene (7) Ong, B. S.; Wu, Y. L.; Liu, P. Proc. IEEE 2005, 93, 1412-1419. (8) Al-Ibrahim, M.; Roth, H. K.; Schroedner, M.; Konkin, A.; Zhokhavets, U.; Gobsch, G.; Scharff, P.; Sensfuss, S. Org. Electron. 2005, 6, 65-77. (9) Feng, D. Q.; Caruso, A. N.; Schulz, D. L.; Losvyj, Y. B.; Dowben, P. A. J. Phys. Chem. B 2005, 109, 16382-16289. (10) Witker, D.; Reynolds, J. R. Macromolecules 2005, 38, 7636-7644. (11) Torsi. L.; Tanese, M. C.; Cioffi, N.; Gallazzi, M. C.; Sabbatini, L.; Zambonin, P. G.; Raos, G.; Meille, S. V.; Giangregorio, M. M. J. Phys. Chem. B 2003, 107, 7589-7594. (12) Thompson, L. A.; Kowalik, J.; Josowicz, M.; Janata, J. J. Am. Chem. Soc. 2003, 125, 324-325. (13) Smela, E.; Gadegaard, N. J. Phys. Chem. B 2001, 105, 9395-9405. (14) Otero, T. F.; Ariza, M. J. J. Phys. Chem. B 2003, 107, 13594-13961. (15) Qi, B. H.; Lu, W.; Mattes, B. R. J. Phys. Chem. B 2004, 108, 6222-6227. (16) Visy, C.; Janaky, C.; Krivan, E. J. Solid State Electrochem. 2005, 9, 330336. (17) Sheina, E. E.; Khersonsky, S. M.; Jones, E. G.; McCullough, R. D. Chem. Mater. 2005, 17, 3317-3319. (18) Roncali, J.; Garreau, R.; Yassar, A.; Marque, P.; Garnier, F.; Lemaire, M. J. Phys. Chem. 1987, 91, 606-614. (19) Bandey, H. L.; Martin, S. J.; Cernosek, R. W.; Hillman, A. R. Anal. Chem. 1999, 71, 2205-2214. (20) Hillman, A. R.; Jackson, A.; Martin, S. J. Anal. Chem. 2001, 73, 540-549. (21) Hillman, A. R. In Encyclopaedia of Electrochemistry; Bard, A. J., Stratmann, M., Eds.; Wiley: New York, 2003; Vol. 3, pp 230-289. 10.1021/ac052153g CCC: $33.50

© 2006 American Chemical Society Published on Web 04/22/2006

family, regioregular poly(3-hexylthiophene) (P3HT)22,23 and poly(3,4-ethylenedioxythiophene) (PEDOT).24 Variations of their shear moduli with applied potential (E), temperature (T), and time scale (via resonator angular frequency, ω) were surprisingly different, given the equivalence of their electrochemically functional polymer spines. This prompts a wider study of thiophene-based materials. For 3-alkyl-substituted polythiophenes, the regiospatial distribution of the side chains may be random or regular. Electrochemical polymerization provides no control over the spatial disposition of the side chains, so the resultant polymer is regiorandom. Chemical synthetic methods can generate regioregular poly(3-alkylthiophenes)25 with controlled “head-to-tail” (HT) composition. The regioregular polymers have longer conjugation length and thus lower band gaps. Depending on the HT diad content, cast poly(3-alkylthiophene) films comprise a mixture of crystalline and quasi-ordered phases along with a disordered, amorphous phase.26 This multiplicity of coexisting phases is manifested in the cyclic voltammetric response27 and in thermochromic effects.28 When two phases are present, changes in visible spectra upon heating show an isosbestic point or a smeared transition.26 In parallel to these electronic phenomena, the mechanical properties of electropolymerized (regiorandom)29 and chemically prepared (regioregular)22,23 poly(3-hexylthiophene) films are quite different. Electropolymerized (regiorandom) films show generally larger shear moduli, whose variations with time scale (at higher resonator harmonics) do not fit simple models;29 these characteristics have been ascribed, respectively, to cross-linking and poorly defined long-range structural organization. Chemically prepared (regioregular) polymers have lower shear moduli and conform broadly to models developed for bulk linear polymeric materials.22,23 A powerful concept developed for the characterization of bulk polymers is that of time-temperature equivalence.30,31 On long time scales, as compared to the characteristic relaxation time, polymers are soft. As the time scale is progressively shortened, there is a transition to a stiff material. The time scale of this transition cannot in general be predicted, and more inconveniently, the transition may occur over an extended range of time scales. Consequently, experimental measurements frequently provide only a very restricted observational “window” onto an unpredictable section of the relaxation curve. Since the relaxation is temperature-dependent, viscoelastic measurements at different temperatures view the relaxation curve through different “win(22) Hillman, A. R.; Efimov, I.; Skompska, M. Faraday Discuss. 2002, 121, 423439. (23) Hillman, A. R.; Efimov, I.; Skompska, M. J. Am. Chem. Soc. 2005, 127, 3817-3824. (24) Hillman, A. R.; Efimov, I.; Ryder, K. S. J. Am. Chem. Soc. 2005, 127, 1661116620. (25) McCullough, R. D.; Lowe, R. D.; Jayaraman, M.; Anderson, D. L. J. Org. Chem. 1993, 58, 904-912. (26) Yang, C.; Orfino, F. P.; Holdcroft, S. Macromolecules 1996, 29, 6510-6517. (27) Skompska, M.; Szkurlat, A. Electrochim. Acta 2001, 46, 4007-4015. (28) Inganas, O.; Salaneck, W. R.; Osterholm, J.-E.; Laakso, J. Synth. Met. 1988, 22, 395-406. (29) Brown, M. J.; Hillman, A. R.; Martin, S. J.; Cernosek, R. W.; Bandey, H. L. J. Mater. Chem. 2000, 10, 115-126. (30) Ferry, J. D. Viscoelastic Properties of Polymers; Wiley: New York, 1961; Chapters 10-11. (31) Aklonis, J. J.; MacKnight, W. J. Introduction to Polymer Viscoelasticity; Wiley: New York, 1983; Chapter 7.

dows”. The principle of time-temperature equivalence30,31 allows one to assemble data at different temperatures onto a single “master” relaxation curve spanning an extended time scale. This concept has been used to explore the thermal doping kinetics of cast thin films of poly(alkylthiophenes)32 and the variations with temperature, frequency, and applied potential of viscoelastic properties of regioregular poly(3-hexylthiophene) films.23 In the latter case, the Williams-Landel-Ferry (WLF) equation did not describe the temperature-dependent frequency shift factor, a(T), suggesting that the glass transition temperature for the polymer spine was above the temperature range used. Instead, the a(T) values were shown to vary in an Arrhenius-like fashion with an activation enthalpy similar to that for rotation around a C-C bond, suggesting that P3HT viscoelastic properties are associated with the alkyl side-chain (not spinal) dynamics. PEDOT24 films show shear modulus variations that cannot adequately be described by either the WLF or activation models; presumably, in the latter case this is due to the absence of a flexible side chain. Instead, a free-volume-based model provides a rather better representation of the data. Since no clear pattern has yet emerged for electrochemically rather similar materials, it is desirable to explore the effect of varying side chain, here via regioregular poly(3-decylthiophene). We determine shear moduli as functions of temperature, time scale, and potential, to construct a stress master relaxation plot. The ability to explain these data by the competing WLF, activation, and free-volume models is explored, with a view to associating macroscopic viscoelastic properties with underlying molecular motions. The outcome is a compositional rationale for film viscoelastic behavior at a hitherto unreported level of sophistication. EXPERIMENTAL SECTION Regioregular (>98% HT content) poly(3-decylthiophene) (Aldrich) was dissolved in THF, cast on the working gold electrode of a quartz crystal resonator (10 MHz, AT cut polished quartz; ICM, Oklahoma City, OK), and the solvent allowed to evaporate. The electrolyte for film characterization (in the absence of monomer) was 0.1 M LiClO4/CH3CN (Aldrich; used as supplied). Measurements of admittance spectra were made in the vicinity of the fundamental mode (10 MHz) and at higher harmonics (30110 MHz) as a function of temperature in the range 0-70 °C (controlled via a thermostat bath to (1 °C). Acoustic admittance measurements were made using a Hewlett-Packard HP8751A network analyzer connected to a HP87512A transmission-reflection block through a 50 Ω coaxial cable to the quartz resonator. Admittance spectra were recorded by using a standard VEE program on a computer or the internal storage facility of the HP8751A. Data were acquired with the polymer film maintained under electrochemical control in a standard three-electrode cell, with a silver wire reference electrode and a platinum gauze counter electrode. The working Au electrode of the resonator was held at virtual ground and connected to the shielding of the HP8751A network analyzer. The quality factor of the crystals and the mounting procedure (silicone sealant) yielded a resonant resistance at 10 MHz of the crystals in air of less than 7 Ω, a small correction factor when analyzing polymer-loaded resonator re(32) Granstrom, M.; Inganas, O. Synth. Met. 1992, 48, 21-31.

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sponses exposed to solution. Calibration procedures for temperature correction of the response component associated with the crystal and the bulk liquid (viscosity/density effects) and the analytical routines for extraction of shear modulus components have been described elsewhere.22,23 RESULTS Film Thickness and Aging. The large array of measurements associated with exploration of G(E,T,ω) space requires reproducible film behavior; there should be no “aging” effects. Unlike the analogous hexyl-substituted material, this constraint was not satisfied for all values of poly(3-decylthiophene) film thickness. This was immediately visible through the cyclic voltammetric responses. These showed two sets of peaks, associated with ordered (simplistically, crystalline) and disordered (amorphous) domains. (The least positive peak at ∼0.5 V is, by analogy with the behavior of regioregular poly(3-hexylthiophene),27 ascribed to oxidation of the crystalline phase; the lower redox potential is due to the longer conjugation length in the ordered matrix.) The critical observation is that the ratio of these peak intensities during thermal cycling varies differently according to film thickness. For relatively thin films (represented by the case of Figure S1, hf ) 0.14 µm; see Supporting Information), the contribution of the crystalline phase is ∼30% at the lower end of the temperature range explored (0-70 °C) and decreases upon heating. However, after cooling, the population of crystalline material (as judged from the lower oxidation potential peak in a second or subsequent redox cycle) is not restored. The conclusion is that the crystalline domains in very thin cast films are not thermodynamically stable. For thicker films (represented by the case of Figure 1, hf ) 0.38 µm), the temperature dependence of the voltammetric response is reproducible during repetitive heating and cooling cycles. All viscoelastic results reported here relate to films of this or greater thickness; we therefore do not need to be concerned with film aging effects. Since, for these “thick” films, the crystalline and amorphous phases are in equilibrium, one can explore the thermodynamic parameters associated with the crystalline (cr)/amorphous (am) transition. The ratio of the populations of the two phases is given by the ratio of the charges under the respective peaks. Analysis of a plot (inset to Figure 1) of ln[Qcr/Qam] versus 1/T, using standard thermodynamic relations,23 gives ∆Hcr-am ) 4.8 kJ mol-1 and ∆Scr-am ) 24 J mol-1 K-1. These thermodynamic parameters relate to the transfer of a redox center from a crystalline to an amorphous matrix; they may be compared with the analogous values for poly(3-hexylthiophene) of ∆Hcr-am ) 9.7 kJ mol-1 and ∆Scr-am ) 46 J mol-1 K-1.23 Overview of Viscoelastic Behavior. We now turn to the shear modulus values and their variations with potential (E), temperature (T), and frequency (f ) ω/2π). The present study builds upon and significantly extends concepts and methodology recently established in a study of PEDOT films.24 In the interest of brevity, in this report of regioregular poly(3-decylthiophene) dynamics, we do not repeat in the paper all the corresponding logical interpretational steps described in the PEDOT study; we give prominence in the paper to the new interpretational concepts. We do not repeat the very detailed exposition of shear modulus extraction procedures described previously;24 the rigor of the 3618 Analytical Chemistry, Vol. 78, No. 11, June 1, 2006

Figure 1. Voltammetric response of a “thick” (pretreatment independent, see text) poly(3-decylthiophene) film, exposed to 0.1 M LiClO4/CH3CN, as a function of temperature (as annotated). Film thickness, hf ) 0.38 µm. Inset shows van’t Hoff plot for the ratio of charges under peaks representing oxidation of crystalline and amorphous material.

arguments, via the full data interpretation for poly(3-decylthiophene), is accessible via the extensive Supporting Information. Immediate qualitative appreciation of the situation is obtained by inspection of the raw admittance spectra (see Supporting Information, Figure S2). These contain contributions from both the film and its ambient fluid, but since the latter varies much more modestly, one can identify qualitatively the more important variables irrespective of any discussion about the relative merits of different models. The data suggest that variations of G with potential are small, with temperature are appreciable, and with frequency (time scale) are most significant. We now proceed to extract the G(E,T,ω) values and explore in turn the individual dependences on these variables. Potential Dependence of Shear Modulus. Exploration of G(E,T,ω) with a view to assembly of stress master relaxation curves requires collection of a hugesalmost impractically sos volume of admittance data. Consequently, the facility to survey one of the variables, potential, in a continuous manner during a potentiodynamic redox cycle has significant practical advantage. The balance to be struck is selecting a potential scan rate sufficiently slow that equilibrium (particularly with regard to nonfield-driven solvent transfer) is established, but not so slow that (particularly at the extremes of the potential range) film degradation occurs. Replicate measurements at v ) 10 mV s-1 in the range -0.1 < E/V < 0.9 demonstrate that film degradation is negligible. Thus, we can proceed to explore the significance of the shear modulus data with confidence about their temporal reproducibility.

Figure 2. Shear modulus components measured at 10 MHz during cycling of a poly(3-hexylthiophene) film exposed to 0.1 M LiClO4/CH3CN. Panel a, storage moduli, G′; panel b, loss moduli, G′′. Film thickness, hf ) 0.47 µm. Scan rate, 10 mV s-1; arrows indicate scan direction. Temperatures as indicated.

Both G′ and G′′ values from such a potentiodynamic experiment (acquired at f ) 10 MHz; see Figure 2) increase at E > 0.5 V, i.e., at potentials more positive than the oxidation peak of the crystalline phase. The slope of this increase is temperature independent for the loss modulus, G′′. There is some hysteresis, but this is not dramatic: it is always less than 15% in G′, for example, and decreases appreciably with increasing temperature. At the upper end of the temperature range, the G′ values are essentially scan direction independent, suggesting that equilibrium is approached. The stiffening (increased G′) is consistent with increased electrostatic interactions that result from higher charge site and ion populations. Film thickness (not shown) increases progressively from E ) 0.5 V, ultimately by 20% at the positive end of the redox cycle. This implies a little solvent entry (along with, though not necessarily associated with, the anion entry); the increased G′′ values suggest that any plasticizing effect of the solvent is small and overwhelmed by electrostatic effects. Temperature Dependence of Shear Modulus. The data of Figure 2, acquired at the fundamental frequency (10 MHz), show that both G′ and G′′ decrease with increasing temperature. The same is true of G′ and G′′ at each of the higher harmonics; while (in the interests of brevity) we do not show the “unshifted” plots, this is implicit in the shifted plots (see master relaxation curves below). This behavior is characteristic of a system being explored below its normalized characteristic frequency (ωτ < 1). Bearing in mind that G′′ shows a maximum at ωτ ) 1, the observation that G′′ falls somewhat more slowly with temperature implies that ωτ is not far below unity at the lower end of the temperature range. Overall, the observation that the shear modulus components do not vary by more than a factor of ∼3-4 (note the relatively

expanded scales of the log G versus log f plots) over a temperature interval of 60 °C suggests that film dynamics are not controlled by a strongly activated process. Frequency Dependence of Shear Modulus. Comparison of G′ and G′′ values, at a given temperature, as functions of frequency shows significant variation. Typically, moving from the fundamental frequency (N ) 1; f ) 10 MHz) to the highest harmonic explored (N ) 11; f ) 110 MHz) results in a 1 order of magnitude increase in the shear modulus component. In broad terms, this is true across the potential range explored, i.e., independent of polymer doping state in the p-doping regime. This supports the earlier assertion (based on the raw admittance responses) of the paramount status of frequency (cf. potential and temperature) as the key determinant of viscoelastic properties. Models for Shear Modulus Variations. (a)Time-Temperature Equivalence. Having acquired the shear modulus values, our next goal is to rationalize the variations (with E, T, and ω) according to some model, the basis of which might then point to the underlying molecular processes. We consider three models: the WLF model, a generic model developed to describe long-range polymer backbone motions; the activation model, developed to describe specific side-chain motions; the Rouse and Zimm model, a model describing molecular motion in terms of free-volume effects. At this point, we note that these models have been widely and successfully applied to low-frequency (typically sub-kHz) motions of bulk polymeric materials; their application to thin films of polymers is relatively unexplored,23,24 and the question of their applicability in this context is of considerable interest and novelty. The first step is to place all the shear modulus-frequency plots (acquired at a given potential, but at different temperatures) on a Analytical Chemistry, Vol. 78, No. 11, June 1, 2006

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common curve using the principle of time-temperature equivalence.30,31 This principle asserts that polymer dynamics data acquired at different temperatures (associated with different relaxation rates) can be placed upon a single “master” relaxation curve by means of a so-called “shift factor”, aT. In the present context, in which polymer dynamics are quantified in terms of the shear modulus, G(T,t), acquired at two temperatures T1 and T2, this can be expressed through

G(T1,t) ) G(T2,t/aT)

(1)

In our modulation experiments, described in terms of an angular frequency (ω), on a polymer with a characteristic relaxation time (τ), which is a function of temperature, eq 1 implies that one can find a corresponding frequency of mechanical excitation at which G measured at two different temperatures will be the same. In the common case that the mechanical properties depend on the product ωτ, knowledge of the temperature dependence of τ allows prediction of the shift factor. We use an inverse strategy: experimental data provide the shift factor, whose temperature variation yields the energetics of the system. The aspiration is that the latter might point to the underlying physicochemical processes. Master relaxation curves for the G data of P3DT under potentiostatic control (with 20 °C selected as the reference temperature and presented in logarithmic format to allow more convenient examination of the data) are shown in Figure 3 for the representative case when E ) 0.0 V (see Supporting Information for complementary oxidation state data at E ) 0.55 V and E ) 0.80 V; Figures S3 and S4, respectively). For each temperature, the data set was frequency-shifted from log(ω) to {log(ω) + log[a(T)]}, as described previously.24 As a requirement of the procedure, the same factors a(T) were applied to both G′ and G′′ values.30 The facility to construct master relaxation curves for these thin films is in itself significant. However, we now go further and address, through three different models, the physical significance underlying the normalization procedure that makes this procedure possible. This is a significant advance from our previous study of poly(3-hexylthiophene) films, in that it provides a compositional rationale for film dynamics. (b) Activation Model. Variations with temperature of the shift factors for each of the three fixed potential data sets are shown in Figure 4. When viewed in this “Arrhenius”-like format, the plots are reasonably linear. The slopes, which this model envisages as representing activation energies, yield values of 10.9 ((1.1) kJ mol-1 for E ) 0.0 V and 12.9 ((1.3) kJ mol-1 for E ) 0.55 and 0.80 V. These results are very similar to the outcome for regioregular poly(3-hexylthiophene) films,23 for which the similarity to the activation energy of 12.5 kJ mol-1 for C-C bond rotation was noted. (c) WLF Model. The WLF model predicts that the shift factor, a(T), varies with the temperature (relative to the glass transition temperature, Tg) according to

log a(T) )

-C1(T - Tg) C2 + T - Tg

(2)

where C1 and C2 are “universal” constants, having numerical values 3620 Analytical Chemistry, Vol. 78, No. 11, June 1, 2006

Figure 3. Stress master relaxation plots of shear modulus components for the film of Figure 2. Panel a, G′; panel b, G′′ (both plotted in double logarithmic format). E ) 0.0 V. Temperatures as annotated. “Shift” procedure to a reference temperature of 20 °C using common factors, a(T), for both components, as described in main text.

Figure 4. Variation of shift factors with temperature for poly(3decylthiophene) held at different potentials (as annotated).

of 17.44 and 51.6, respectively.30 Importantly, the experimentally determined shift factors for the storage and loss moduli are (within experimental uncertainty) equal at any given temperature. (The variations of the shifts factors, presented in the form of plots of log[a(T)/a(293)] versus T, i.e., referenced to T ) 293 K, for the data at different potentials (from Figures 3, S3 and S4) are shown in Figure S5.) One can test the ability of the WLF equation to describe the data in several ways. One approach is to take the “universal”

constants as indisputable and fit the data to obtain the single parameter Tg; the outcome of this approach is an extremely low value of Tg. Another approach is to recognize that C1 and C2 are not really universal parameters, but reflect specific features of the material (see below);30 thus, they commonly assume fairly similar values but in fact may vary. On this basis, we explored the effect of individually allowing C1 and C2 to vary within reasonable limits. As one example, taking C2 ) 51.6 (the universal value) and allowing C1 to be fitted to the data for representative Tg values of -100 and -75 °C, respectively, yields C1 values of 4.17 and 3.79; as indicated above, progressively lowering Tg drives C1 toward its universal value of 17.44. This leads us to consider the physical realism of the values associated with these parameters, according to the different calculational approaches. In the case of C1, we note that, according to the WLF theory, 2.3C1 ) 1/fg, where fg is the fraction of free volume at T ) Tg; the universal value of C1 corresponds to fg ) 0.025, the value commonly assigned to a typical glassy polymer. The fitted values correspond to fg ≈ 0.11, independent of potential at the level of precision available here; this is approximately five times the “typical” value. Given the potential for poor packing of the large side chain, this is possible, although unlikely. From the relation C2 ) fg/R,30 where R is the thermal expansion coefficient at temperatures above Tg, one finds that R ) 2 × 10-3 for E ) 0.0 V and 2.2 × 10-3 for E ) 0.55 and 0.80 V (although the small difference may not be significant). The R values delivered by this model exceed those typical of bulk polymeric materials by 1 order of magnitude. Rouse and Zimm Free-Volume Model. The Rouse and Zimm theory30,31 envisages multiple relaxations within a polymercontaining system comprising a density n (cm-3) of polymer chains in a medium of viscosity η. It has been shown that, for the condition that (ωτ1)2 , 1, where τ1 is the slowest relaxation time, the storage and loss moduli (G′ and G′′) can be expressed as functions of temperature (T) and angular frequency (ω ) 2πf) via

ln[G′(ω,T)] )

2 + 2 ln ω + const fg + R(T - Tg(E))

ln[G′′(ω,T)] )

(3)

1 + ln ω + const (4) fg + R(T - Tg(E))

In this simplified model, the (single) relaxation time, τ1, is given by 6η/(nπ2kT), where η represents the viscosity of the medium, n represents the segment density of the polymer, and the other symbols have their usual meanings. Insertion of reasonable values of these parameters into this expression shows that the constraint on frequency, (ωτ1)2 , 1, is satisfied at the resonator fundamental frequency of 10 MHz. Although not explicitly shown in eqs 3 and 4, there is an implicit potential dependence of the shear modulus components as a consequence of the fact that the film glass transition temperature, Tg(E), is a function of film composition, which in turn responds to potential through the exchange with the solution of ions and solvent. Representing the mole fractions within the film of the constituent polymer and solution components by XP and XS(E), respectively, we can write

Tg(E) ) XPTPg + XS(E)TSg(E)

(5)

where TSg(E) is the glass temperature of the solution component of the film. Under permselective conditionssa reasonable approximation for the relatively low electrolyte concentration used heresthe “solution” component in the film is essentially pure solvent, since the counterions are associated with the polymer component. Thus, TSg(E) is simply the freezing point of the solvent, T0f ; for the case of acetonitrile, the solvent used here, T0f ) -43.8 °C. T0f is independent of potential, so the potential dependence of the solvent contribution is associated solely with its mole fraction, XS(E). (Under nonpermselective conditions, i.e., at sufficiently high electrolyte concentrations that salt partitions into the film, TSg(E) will be replaced by the freezing point of the solution, according to classical cryoscopic relationships. Although beyond the scope of this work, this indicates that film dynamics wouldsat sufficiently high levelssrespond to electrolyte concentration.) The implication of eq 5 for the case that TPg is less than TSg(E) is that the entry into the film of solvent will result in an increase in film glass transition temperature; for the system studied here, this corresponds to the effect of polymer oxidation. Equations 3 and 4 may also include an implicit dependence of fg on potential, since the charging of redox functionalities (here, by oxidation) may change the space available for chain motion. However, since we have no quantitative means to describe this latter effect, we ignore it for the present. Thus, we now apply the solvent-based aspects of these concepts, encapsulated by eq 5, to the data of Figure 2; in the interests of brevity, we describe only the oxidation half-cycle. The analysis to extract Tg(E) comprises three steps. First, the variation of ln[G′(T)] with T is considered. For convenience, we compare values at each temperature with that at a reference temperature, chosen to be 20 °C; the outcome is illustrated in Figure 5 for representative data at a potential, E ) 0.2 V. For this set of data, fitting of the parameters in eq 3 to the experimental data returns the value

2 ) 10 fg + R(20 - Tg(0.2 V))

The second step is insertion of this numerical value into a rearrangement of eq 3:

fg + R(T - Tg(E)) )

2 G′(T,E) ln + 10 G′(20C,0.2 V)

(

)

(6)

Plots of the right-hand side of eq 6 as functions of E for different values of T (shown in Figure 6) reveal the variations in free volume. The variations with T yield the coefficient R ) 5 × 10-4 K-1 and the combined parameter [fg - RTg(0.2 V)] ) 0.18. The third step is the variation of Tg with E. It is clear that the value of the ordinate in Figure 6 at any temperature is decreased by polymer oxidation. Qualitatively, this is caused by an increase Analytical Chemistry, Vol. 78, No. 11, June 1, 2006

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Figure 5. Variation with temperature of storage modulus at a (representative) potential, E ) 0.2 V. See eq 3. Figure 7. Variation of [Tg(E) - Tg(0.2 V)] with potential at different temperatures (as annotated). Data from Figure 6.

setting Xs(0.2 V) ) 0, one can rearrange eq 6 to

Tg(E) - Tg(0.2 V) ) (Ts - Tp)Xs(E)

Figure 6. Plots of [fg + R(T - Tg(E))] vs E at different temperatures (as annotated). See eq 3.

in Tg with increasing potential; according to eq 5, this must be associated with the entering species (solvent) having a higher Tg than the medium it enters (polymer). To quantify this effect, we calculate the difference [fg + a(T - Tg(E))] - [fg + a(T - Tg(0.2 V))] to yield the quantity -R[T(E)g - Tg(0.2 V)]. Using the value of R from above, we are then able to plot [T(E)g - Tg(0.2 V)] versus E (see Figure 7). To the best of our knowledge, this is the first report of the variation of glass transition temperature with potential (effectively, redox state) for an electroactive polymer film under electrochemical control. Commencing with a fully reduced film, the Tg increases monotonically with potential from E ) 0.5 V, as polymer oxidation commences and counteranions and solvent enter the film. The magnitude of the effect is larger at higher temperature: this means that the process is endothermic. Using Xp(E) ) 1 - Xs(E) and 3622

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(7)

Application of eq 7 to the data of Figure 7 yields Xs(E,T) without separate knowledge of Ts and Tp. Subsequent analysis of Xs(E,T) as a function of temperature according to the van’t Hoff equation provides the enthalpy of transfer of solvent and anions into the film (to satisfy the thermodynamic constraints imposed by activity and electroneutrality) as a function of potential. (Note that the logarithmic form of the van’t Hoff equation means that we can focus on the changes, so we do not need to have absolute values to obtain the enthalpy from the slope.) The outcome is shown in Figure 8. Qualitatively, the value is positive throughout, consistent with the monotonic increase of solvent content with temperature at any given potential. Quantitatively, the enthalpy of transfer decreases rather dramatically from ∼100 kJ mol-1 in the early stages of oxidation (E ≈ 0.58 V) to the more modest value of ∼10 kJ mol-1 in the later stages of oxidation (E ≈ 0.9 V). Although peripheral to the present study, it is interesting to note that this initial large thermodynamic driving force for transfer into a lyophobic medium would explain the frequent kinetic observation of a temporally delayed then sudden flux of solvent into a film, most dramatically seen for many systems as the “break-in” phenomenon accompanying first-cycle oxidation of a previously equilibrated, desolvated film. Comparison of Models for Film Viscoelasticity Variations. Of the three models employed, the Rouse and Zimm model appears to provide the most interesting outcomes. The activation model delivers a simple and broadly similar outcome to that found for regioregular poly(3-hexylthiophene), namely, that film dynamics are associated with alkyl side-chain rotation. The WLF model is problematical in that, although one can force fits to the

Figure 8. Enthalpy of solvent transfer from solution to polymer film as a function of applied potential. Data from Figure 7.

functional form of the WLF equation, the physical parameters that are required to accomplish this are not within the range one would typically expect for a polymeric material. The Rouse and Zimm model is able to account for the variations in film viscoelastic properties in terms of solvation changessan entirely reasonable notionsthe energetics of which change quite significantly with film oxidation (doping) level. The magnitude of the solvation energy is largest at low p-doping levels, i.e., upon initial introduction of charges into an otherwise uncharged material. CONCLUSIONS Regioregular poly(3-decylthiophene) films show thermally responsive two-phase behavior, in which the more ordered (simplistically, crystalline) regions disappear upon raising the temperature. For thin films, subsequent cooling does not restore the population of crystalline material as judged from the voltammetric response. This irreversibility indicates that crystalline domains in very thin cast films are not thermodynamically stable. For thicker films, the temperature dependence of the voltammetric response is reproducible during repetitive heating and cooling cycles. We have characterized the viscoelastic properties of these thicker films in some detail by high-frequency acoustic wave determination of film shear moduli, G ) G′ + jG′′. The variations of G with potential are small, with temperature are appreciable, and with acoustic wave resonator frequency (representing time scale) are the most dramatic. The effect of potential was deter-

mined under both potentiodynamic and potentiostatic conditions. Slow-scan voltammetric shear modulus responses show relatively little hysteresis; at the upper end of the temperature range in particular, G′ values are virtually scan direction independent, characteristic of an equilibrated film. The G(E,T,ω) signatures have been considered in the context of models widely used to explain low-frequency motions of bulk polymeric materials, but relatively underexploited in the context of thin films. The approach involves use of experimental shear modulus data to construct master relaxation curves (as a function of the normalized parameter ωτ). The temperature variation of the “shift factors” required to accomplish this yields the energetics of the system. The facility to construct master relaxation curves for these thin films is in itself significant but of particular importance and novelty is the fact that these allow one to address the physical processes underlying the normalization procedure. This is a significant advance from our previous study of poly(3hexylthiophene) films, in that it leads to a compositional rationale for film dynamics. The activation model, developed to describe specific side-chain motions, yields an outcome similar to that deduced for regioregular poly(3-hexylthiophene) films, namely, an activation energy similar to that associated with rotation about a C-C single bond in an alkyl chain. The WLF model, a generic model developed to describe long-range polymer backbone motions, can rationalize the observed behavior, but only if certain materials properties (free volume and thermal coefficient of expansion) assume surprisingly high values; we suggest this is relatively unlikely. The Rouse and Zimm model, a model describing molecular motion in terms of free-volume effects, provides the most plausible outcomes. The shear modulus responds to potential as a consequence of the fact that the film glass temperature, Tg, is a function of film composition, which in turn responds to potential through the exchange with the solution of ions and solvent. While the potential dependence of mobile species (ion and solvent) populations within electroactive films is common knowledge, this is the first time that the link has been made explicitly and quantitatively to potential (charge state)-dependent film viscoelastic properties. ACKNOWLEDGMENT We thank the EPSRC (GR/N00968) and the University of Leicester for financial support and Dr. Karl Ryder for helpful discussions. SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.

Received for review December 7, 2005. Accepted March 13, 2006. AC052153G

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