Effect of Fullerenes on Crystallization-Induced Aggregation in Polymer

Article pubs.acs.org/Macromolecules

Effect of Fullerenes on Crystallization-Induced Aggregation in Polymer Photovoltaics Casting Solutions Margaret J. Sobkowicz, Ronald L. Jones, R. Joseph Kline, and Dean M. DeLongchamp* Polymers Division, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, United States S Supporting Information *

ABSTRACT: We measure the time- and temperaturedependent aggregation of the organic photovoltaic polymer poly(3-hexylthiophene) in o-dichlorobenzene solution using small-angle neutron scattering and rheometry. Results from this study provide guidance for formulation stability assessment and process-dependent morphology optimization. The aggregates are similar to the supramolecular crystalline structures found in annealed films and poor solvents. The addition of phenyl-C61-butyric acid methyl ester (PCBM) molecules to the polymer solution slows the aggregation rate by about 10-fold. PCBM addition also appears to reduce the overall extent of crystallization in solution. Dynamic rheological measurements show thermoreversible mechanical stiffening of the solutions into gel-like solids with a physical cross-link density that depends on temperature and oscillation frequency.

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INTRODUCTION A great advantage of organic photovoltaics (OPV) is that device layers such as the bulk heterojunction (BHJ) can be coated from solution, allowing for easier, faster, and less expensive device manufacture.1 Solution coating, however, affords little control over the final BHJ morphology, and the morphological requirements for a high-efficiency BHJ are complex. Current BHJ processing strategies rely on the solidification of a solution containing both polymer and fullerene; the ultimate morphology will depend on the relative rates of solidification of the two components. Because the polymer and fullerene are not extremely soluble in commonly used solvents, it is expected that solidification will commence while significant solvent remains in the applied coating. To understand and ultimately control the development of BHJ morphology, it can therefore be valuable to evaluate the structure of the BHJ coating in the semisolid states that it passes through during solidification. The characteristics of these states are also relevant to the coating process itself because the coating viscosity will depend on the structure that forms. The shear rate the solution experiences depends on the coating technique. In inkjet printing and slot die coating, for instance, the shear rate can be as high as 10 000 s−1.2−4 The BHJ film smoothness and thickness will depend on the interaction of applied shear forces with the changing coating viscosity,5,6 regardless of whether the BHJ is coated using spin-casting, inkjet printing, blade coating, slot-die, or gravure methods. Here we study structure formation in solutions of poly(3hexylthiophene) (P3HT) and phenyl-C61-butyric acid methyl ester (PCBM). Under certain processing conditions, these two components solidify from the same solution into a nanoscale © 2011 American Chemical Society

morphology that produces reasonable photovoltaic performance with devices up to 5% efficiency.7 Because solvent evaporation is challenging to control, we instead use solution temperature to mimic the effect of solvent removal. In effect, we lower the solution temperature to lower the solubility of the components. In drawing an analogy between structure formation in cooled solutions and in drying coatings, we assume that the solubility of one component changes proportionally to the other with temperature. This assumption may not be valid, but we believe that the analysis still provides a starting point for understanding important aspects of morphology development in drying BHJ films. Validation of the analogy would require extrapolation to thermodynamic equilibrium in the solutions at different degrees of undercooling and different concentrations to map out the temperature− concentration phase diagram. Here we examine several polymer concentrations, starting at a value near typical casting solutions (20 mg/mL) and moving higher, to observe the kinetic difference at a constant undercooling and to mimic the beginning of the drying process. The use of temperature as a variable to induce structure formation in BHJ solutions also yields practical information about BHJ solution stability. Many semiconducting polymers have been shown to aggregate in solution, forming gel-like assemblies at a range of concentrations and temperatures, due to their stiff backbones and attractive interactions between conjugated monomers. Room-temperature aggregation is Received: September 13, 2011 Revised: November 16, 2011 Published: December 28, 2011 1046

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problematic from a processing standpoint because ink formulations will change over time, compromising reproducibility and potentially leading to a short shelf life. Aging and aggregation in solutions of polyfluorenes, 8 poly(phenylenevinylene)s9,10 and poly(3-alkylthiophenes)11−14 have been investigated before. Studies on the poly(3alkylthiophenes) have focused on the formation of high aspect ratio nanowires of poly(3-alkylthiophenes) by addition of a nonsolvent11,12 or dissolution and aging in a marginal solvent.13,14 Early studies of fundamental dilute solution properties of P3ATs using light and neutron scattering and viscometry15,16 found that the polymers exhibit typical random coil behavior, with crossover concentrations from 7 to 30 mg/ mL depending on molecular mass, and a rather large persistence length of 2.4 nm (6 monomer units) due to the main chain rigidity. Observations of regioregular P3HT solutions in tetrahydrofuran or xylene indicate a red shift in the absorption spectrum associated with increasing conjugation length as the polymer crystallizes. It has been suggested that the network formation takes place in a two-step process: first the polymers undergo a coil-to-rod transformation, and then rods aggregate into fibrillar crystals.17 It is known that the crystal morphology of P3HT tends toward high aspect ratio wires with width of tens of nanometers, thickness several nanometers, and lengthdepending on crystallization conditionsof up to a micrometer or more.18,19,13,20 Physical aggregation and gelation in polymers are due to complex enthalpic and entropic interactions between monomers and solvent molecules. Two mechanisms have been proposed for physical association in polymer solutions: solvent induction and polymer crystallization.21 Solvent induction can occur in amorphous or semicrystalline polymers, but it requires a specific interaction such as ionic or hydrogen bonding between the polymer and solvent molecules that induces physical connectivity among polymer molecules. P3HT aggregation is more likely driven by crystallization because the stiff backbone of the polymer favors an ordered conformation. P3HT gelation is therefore likely to be less sensitive to solvent type, as indeed it has been found to occur in several different solvents. Throughout this article, we will refer to P3HT aggregation in solution as “crystallization”, without direct evidence from diffraction of the solutions. This assertion, however, is supported by optical measurements of backbone conformational order and ubiquitous reports by others of P3HT crystallinity in solid films. The polymer−fullerene solutions measured in this work are uniquely matched to small-angle neutron scattering (SANS) as a structure evaluation tool. SANS has lately gained attention as a tool for investigating morphology and phase behavior in polymer−fullerene BHJ blends because it probes length scales relevant to exciton diffusion. Furthermore, contrast in SANS is naturally present due to the large difference in proton content between the proton-poor fullerene and the proton-rich P3HT. By exploiting this natural contrast, other researchers have used SANS22,23 and neutron reflectivity24 to describe coarsening of the domains in OPV thin solid films. Our work extends this strategy by exploiting contrast between a solvent−fullerene phase and pure P3HT. Using SANS and rheological measurements, we investigate the time- and temperature-dependent crystallization of P3HT in the common casting solvent odichlorobenzene, and we characterize the effect of PCBM presence on the rate of solidification and its extent.

Article

EXPERIMENTAL METHODS

Solution Preparation. P3HT used in this study was purchased from Plextronics 25 (Mw = 120 000 g/mol, PDI = 1.9, and regioregularity >98%). PCBM was purchased from NanoC. Solvents used were deuterated o-dichlorobenzene (dDCB) from Cambridge Isotopes and reagent-grade anhydrous o-DCB from Sigma-Aldrich. Solutions of P3HT and/or PCBM in dDCB were prepared in an oxygen- and moisture-free environment in amber vials. Solutions were heated to 80 °C and held at least 12 h for complete dissolution. Ultraviolet−Visible Spectrometry. Absorption spectra in the ultraviolet−visible (UV−vis) range were collected on a Perkin-Elmer Lambda 950 instrument in transmission mode. Corrections were made for blocked beam and 100% transmission. Solutions of P3HT in oDCB (25 mg/mL) were dispensed onto a quartz slide and covered with another quartz slide and then cooled over desiccant (to avoid moisture accumulation) at 5 °C for 24 h prior to initial measurement. Samples were equilibrated for 2 min at each temperature before the spectrum was then collected at room temperature. The dry film sample was spin-cast at 2000 × 2π rad/min (2000 rpm) for 2 min onto quartz from a 40 mg/mL solution. Small-Angle Neutron Scattering. SANS measurements were performed at the National Institute of Standards and Technology (NIST) Center for Neutron Research on both NG3 and NG7 30 m SANS instruments. Solutions were measured in titanium cells with 1 mm path length and quartz windows 2 cm in diameter (total sample volume = 0.3 mL). A sample holder block cooled with a circulating bath was used to hold the sample temperature during measurement. A light flow of dry nitrogen around the sample chamber prevented ambient humidity from condensing. Measurements were performed at two detector distances for a q range spanning almost 3 decades (0.006 Å−1 < q < 0.4 Å−1, where q = (4π/λ) sin(θ/2)). The neutron wavelength was 6 Å. The scattered intensity was adjusted to an absolute scale by correcting for background scattering, detector sensitivity, empty cell scattering and transmission, and sample transmission.26 Igor Pro software developed at NIST (version 4.20) was used to reduce data following protocols detailed in ref 26. Prior to each crystallization kinetic study, samples were equilibrated for 20 min at 80 °C. They were then placed in the cooling block, and the SANS measurement was started. Three P3HT concentrations (80, 40, and 20 mg/mL) and three P3HT:PCBM ratios (1:0.5, 1:1, and 1:2 by mass) were investigated. All crystallizations were run at 5 °C; however, for the pure P3HT solution at 80 mg/mL, measurements were also made at 15 °C in order to observe the change in kinetics with temperature. Scattering collection time was 10 min per curve. Rheometry. Rheological measurements were made using a TA ARG2 rheometer with a cone and plate geometry. The cone angle and diameter were 2° and 20 mm, respectively, for a total sample volume of 0.07 mL. Cooling experiments were performed using a Peltier plate assembly for temperature control (±0.2 °C) and a solvent reservoir and trap in place over the cone to limit solvent evaporation. The instrument was kept in a nitrogen-purged environment to avoid condensation. For time-dependent modulus measurements the sample was quenched from 70 °C to the required gelation temperature (quench time was always less than 5 min), and then oscillatory shear with 1% strain amplitude at a variety of frequencies was applied to the sample. For temperature scans the sample was placed in the rheometer and pregelled at quiescent conditions for 2 h prior to measurement. Then the temperature was ramped at 1 °C/min, while measuring the modulus at 1% strain, 0.1 Hz (0.628 rad/s). For frequency-dependent measurements, samples were quenched from 70 °C to the gelation temperature, and the frequency was ramped from 0.1 to 100 rad/s at 1% strain. The measurements were repeated until minimal change in the sample was observed. Each frequency scan was 17 min.

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RESULTS AND DISCUSSION The ultraviolet−visible absorption of P3HT solutions is sensitive to the backbone conformation, which in turn offers insight into the degree of aggregation. These characteristics can be evaluated qualitatively by eye, as shown in Figure 1. Typical 1047

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Figure 2. UV−vis absorbance spectra for P3HT dry film and 25 mg/ mL P3HT−DCB solution after gelation and through the dissolution transition. Wavelength resolution is 2 nm. Figure 1. Photographs of P3HT solutions: (a) 7 mg/mL in o-DCB after dissolution at 80 °C; (b) 7 mg/mL in o-DCB after 66 h aging at 4 °C; (c) 1 mg/mL in tetrahydrofuran after several weeks aging at room temperature.

P3HT solid aggregates. Although isotopic labeling is often required to achieve contrast in SANS, there exists a strong natural contrast between relatively hydrogen-rich P3HT and the relatively hydrogen-poor PCBM in a deuterated solvent. The calculated scattering length density of PCBM (4.51 × 10−6 Å−2) is very close to that of dDCB (4.58 × 10−6 Å−2), and the packed spacing of the fullerene spheres (≈10 Å) is too small to be observed in the measured q-range. Consequently, the PCBM molecules are not observed in the SANS experiment; instead, the structure of the polymer and its evolution can be observed with and without PCBM present. The variation of absolute scattered intensity I(q) with the magnitude of the wave vector q for solutions of pure P3HT and solutions with PCBM is shown in Figure 3. Solutions at T = 80 °C have scattering characteristic of random coil polymers, with a plateau at low q. The scattering intensity at q < 0.12 Å−1 increases significantly for the cooled solutions as aggregation occurs. The curves shown were collected in a time sequence with repeated measurements every 30 min. After the first measurement, aggregation is virtually complete in the pure P3HT solution, whereas the solutions with PCBM aggregate over a much longer time scale. Although the scattering curves still appear to be changing slightly at long times, the majority of the crystallization is complete by the highest curve presented in each plot of Figure 3. If we estimate an asymptote for the low-q scattered intensity at infinite time, it is lower for the P3HT:PCBM solutions, indicating less aggregated material. All curves collapse to an incoherent scattering baseline of near 0.1 cm−1 at q > 0.3 Å. Figure 3d shows the final scattering patterns (e.g., at the end of the time sequence) for pure P3HT and 1:1 P3HT:PCBM solutions, along with fits to the twoexponential Guinier−Porod model. This model has been used to describe other aggregating polymer solutions when there are the two length scales present.30−32 Detailed explanation of the fitting technique can be found in the Supporting Information. The Porod slope is higher for the pure polymer solutions than for the BHJ solutions (Table 1), which suggests that the PCBM interferes with the organization of polymer chains into highly ordered, smooth-surfaced domains. The dimension exponent lies between the values expected for rods and platelets (1 and 2, respectively) for pure P3HT solutions, and it is lower (more rodlike) with PCBM present. The radius of gyration (Rg) of the

polymer solutions for device fabrication consist of 10−50 mg/ mL of P3HT in chloroform, chlorobenzene (CB), or o-DCB. These solutions have previously been presumed stable at these concentrations. Figure 1 shows, however, that aggregation can occur when these typical casting solutions are modestly cooled. There is a color change (increased blue transmittance, increased diffuse scatter) but no observable phase separation, as exemplified in Figure 1b, for solutions prepared from o-DCB, CB, or chloroform. Separated solidlike aggregates precipitate from the P3HT−THF solution shown in Figure 1c, even when it is aged at room temperature. The color changes in P3HT solutions are quantitatively measured using UV−vis absorption spectroscopy. Under good solvent conditions over a range of concentrations, P3HT shows a single peak centered around 450 nm.27 Additional peaks at 560 and 610 nm are attributed to vibronic coupling upon organization of the molecules into crystals, and the ratio of the two is diagnostic of the conjugation length.27,28 The red shift of the main peak from 450 to 520 nm is due to both H aggregation and an increase in conjugation length as the polymer backbone stiffens and ordered aggregates form in films.29 The UV−vis spectra shown in Figure 2 for a 25 mg/mL solution provide evidence of this crystallization-induced aggregation. The single peak at 456 nm in the spectrum of the fully dissolved high-temperature solution has identical breadth and location to those collected from lower concentration solutions down to 0.1 mg/mL (not shown). The peak location after 24 h of aging at 5 °C is shifted to slightly longer wavelengths, but the emergence of peaks at 560 and 610 nm indicates that the intermolecular coupling is stronger and the conjugation length is longer than in the fully dissolved solution. This spectroscopic evidence strongly suggests that molecular aggregation occurring in the P3HT solutions is due to the crystallization of the polymer chains. Small-Angle Neutron Scattering. Small-angle neutron scattering (SANS) is an ideal technique for investigating the structure of the physically associating solutions because it probes length scales characteristic of P3HT chains and typical 1048

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Figure 3. SANS intensity vs q for three solutions crystallized at 5 °C: (top left) 80 mg/mL P3HT in dDCB, (top right) 80 mg/mL P3HT with 1:0.5 P3HT:PCBM, (bottom left) 80 mg/mL P3HT:PCBM, and (bottom right) crystallized P3HT and P3HT:PCBM solutions with Guinier−Porod fit. Resolution in q is 0.0004 Å−1; statistical error bars in intensity are shown.

characteristic of anisotropic structures34 and has also been observed for thermoreversible gels of PVC, polystyrene, and several biopolymers.21,35 The peak q value corresponds to a length scale of the forming network (d = 2π/q from Bragg’s law). Because the peak does not shift significantly with time, it is dominated by the characteristic fibril width. The d-spacing from our Kratky plots is 30−45 nm, which is close to reported values measured with microscopy for the P3HT fibril width.36 Interestingly, the peak is at higher q for both increasing concentration and increasing PCBM content, with the PCBM concentration having a stronger effect. Both trends are logical: impingement of the crystals may limit their size in high concentration solutions, and increasing PCBM content appears to have a solubilizing effect resulting in a limitation on the scale of P3HT crystal growth. The Avrami equation is a simple model describing the kinetics of material phase transformation that assumes random nucleation (in space) and a constant growth rate independent of fractional conversion. It is often used to describe crystallization of polymer melts, solutions, and composites, but its application can be problematic at early times, when there may be an induction period, and at late times, when secondary crystallization events can occur.37 The double logarithm of the untransformed fraction of the material (1 − X(t), where X(t) is the normalized peak intensity) in the Kratky plots is shown vs log time in Figure 4 along with linear fits to the Avrami crystallization kinetic model, given by eq 1.38,39 Figure 4 also

Table 1. Fitted Parameters to the Guinier−Porod Model for the Longest Aggregation Times for Each Sample dimension 1:0 1:0.5 1:1 1:0 1:0.5 1:1

Rg [Å]

80 mg/mL Solutions 1.5 ± 0.01 33.8 ± 0.2 1.2 ± 0.01 41.5 ± 0.4 1.1 ± 0.01 47.1 ± 0.9 40 mg/mL Solutions 1.9 ± 0.01 20.8 ± 0.2 1.5 ± 0.01 29.6 ± 0.5 1.5 ± 0.01 28.9 ± 0.6

Porod slope 3.3 ± 0.01 2.7 ± 0.01 2.2 ± 0.01 3.5 ± 0.01 2.8 ± 0.01 2.7 ± 0.01

aggregates is also larger with the PCBM present, which may be due to the difference in aspect ratio. A slight secondary feature also appears in the background-subtracted data from around 0.1 Å−1 < q < 0.2 Å−1 that may be attributed to the nanofibril thickness, which is usually found to be 3−6 nm.20 While the uncertainty of the data at highest q is large, the faint peak in the background-subtracted scattering curve of pure P3HT may originate in a P3HT (100) Bragg peak at 0.39 Å−1.33 The nonzero slope at the largest length scale probed indicates that structures are present that are too large to be resolved within the measured q range (>1570 Å). When the scattering curves are plotted in the Kratky representation, Iq2 vs q, as shown in Figure 4, a peak emerges which does not shift with time. A peak in the Kratky plot is 1049

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Figure 4. (left) Representative Kratky plots from P3HT solutions at two concentrations throughout crystallization. (right) Avrami plots for 80 mg/ mL solution series.

Table 2. Solution Compositions (Experimental Error for Concentrations Is ±0.3 mg/mL), Kratky Peak q Values (q Resolution for SANS Measurement Is 0.0004 Å−1), and Avrami Fit Parameters for SANS Gelation Kineticsa sample

a

cP3HT [mg/mL]

20 mg/mL 40 mg/mL 80 mg/mL

19.6 40.1 83.5

1:0.5 40 mg/mL 1:1 40 mg/mL 1:2 40 mg/mL 1:0.5 80 mg/mL 1:1 80 mg/mL 1:2 80 mg/mL

38.8 37.9 35.8 81.1 78.8 77.8

cPCBM [mg/mL]

19.7 38.3 71.8 40.2 76.4 155.1

q (peak) [Å−1]

P3HT Solutions 0.014 0.015 0.016 P3HT:PCBM Solutions 0.018 0.022 0.028 0.018 0.021 0.021

d [nm]

n

t1/2 [min]

45 ± 2 43 ± 2 40 ± 2

1.0 ± 0.10 0.80 ± 0.13

113 19.7

± ± ± ± ± ±

1.4 ± 0.04 1.5 ± 0.07 2.3 ± 0.02

35 29 22 34 30 30

2 2 2 2 2 2

103 105 623

Stated uncertainties are standard deviations from the linear fit.

the increased exponent with increasing PCBM loading.41 Experiments on the samples for which Avrami analysis is missing were not carried to high enough conversion to estimate the peak intensity for the fully aggregated polymer.

includes the crystallization of the 80 mg/mL P3HT solution at 15 °C for comparison to the deeper quench temperature. The fits shown in Figure 4 exclude the first data point because for all samples the early time conversion of the crystalline fraction was lower than expected. This deviation is likely due to an induction period before the steady-state crystallization rate is reached. Exponents (n) extracted from the fits and crystallization halftimes are shown in Table 2. The Avrami exponent near 1 for the 5 °C crystallization of both 40 and 80 mg/mL P3HT solutions indicates predetermined nucleation (all nuclei are formed at t = 0) and linear crystal growth, as can be expected given the crystal morphology shown in previous works.40 At quench temperature 15 °C the Avrami exponent of the 80 mg/ mL P3HT solution (fit not shown) is close to 2, indicating either continuous nucleation or a more disklike growth habit. The exponent is close to 1.5 for the solutions with PCBM present, which suggests sporadic nucleation occurring during crystal growth and rodlike crystal growth. The Avrami exponent over 2 for the 1:2 P3HT:PCBM sample indicates that both nucleation rate and growth geometry may be responsible for

X (t ) = 1 − exp(Kt n)

(1)

PCBM can be said to have a stabilizing effect on the P3HT solutions because the polymer aggregation slows and appears to approach a lower value at long times. To extract quantitative information about the solution stabilizing quality of PCBM, fits to the random phase approximation (RPA) model for polymer solutions were made on the dissolved solutions at 80 °C. The RPA model is used to describe correlations in dense interacting polymer blends, solutions, and copolymers.42,43 Here, component 1 is taken to be the polymer chains and component 2 is either the dDCB solvent molecules or the dDCB + PCBM phase. Since the PCBM molecules do not scatter coherently in the investigated q range44,45 (see Supporting Information), they can be considered part of the background component, which can be eliminated from the equations for the case of an 1050

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incompressible mixture. To construct the two component RPA model, the form factor for a Gaussian chain, P1(q), is combined with the volume fraction, ϕ1, the segment volume, ν1, and the degree of polymerization, N, to calculate the noninteracting 0 structure factor, S11 (q). The interaction parameter χ12 scaled by a reference volume v0 is introduced to calculate the interacting structure factor, S11(q). Inclusion of the contrast term Δρ2 and an incoherent background contribution allows calculation of the scattered intensity.

Table 3. Fitted Parameters to the Two-Component RPA Model for All Solutionsa concentration P3HT [mg/mL] 83.5 40.1 19.6 81.1 78.8 38.8 37.9 35.8

2 P1(q) = (exp( − q2 ξ2) − 1 + q2 ξ2) (qξ)4 0 S11 (q) = N ϕ1v1P1(q) 2χ 1 − 12 v11(q) = 0 v0 S11(q)

S11(q) =

40.2 76.4 19.7 38.3 71.8

ξ [Å] 108 120 147 102 105 133 120 137

± ± ± ± ± ± ± ±

bkgd [cm−1]

χ12 2 2 2 2 2 2 2 2

−0.421 −0.390 −0.291 −0.422 −0.456 −0.366 −0.386 −0.378

± ± ± ± ± ± ± ±

0.003 0.004 0.005 0.003 0.003 0.004 0.002 0.004

0.088 0.067 0.055 0.100 0.101 0.069 0.074 0.072

± ± ± ± ± ± ± ±

0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002

a Experimental error for concentrations is ±0.3 mg/mL; stated uncertainties are standard deviations from the nonlinear least-squares fit.

experimental χ is the second derivative of the excess free energy of mixing with respect to volume fraction.46,47 The negative interaction parameter is indicative of a strong polar attraction between polymer and solvent.48 For the pure polymer solutions χ12 becomes more negative with increased concentration, so values of χ12 for BHJ solutions can only be compared for similar polymer concentrations. The χ12 for solutions with PCBM decreases slightly compared with the values for pure polymer solutions, which reflects the solubilizing effect of the PCBM. The 1:2 ratio 35 mg/mL P3HT solution does not have as high a background level or as negative a χ12 as expected; hence, it is likely that there was some precipitation of the PCBM during measurement due to saturation of the solution. It should be noted that the mesh size, ξ, was allowed to vary in these fits, whereas the degree of polymerization was fixed at the manufacturer-reported mass-average value, 723. This choice was made because the assumption of a Gaussian polymer conformation is not realistic for this stiff chain system. The fits shown in Figure 5 could likely be improved using a wormlike chain form factor,49 but the Gaussian model was chosen for simplicity. The ξ value provides an approximate size scale from the low-q plateau in the fit. The radius of gyration given by eq 3, assuming a Gaussian chain, is 44 Å for the P3HT monomer size, a, and degree of polymerization, N (a = 4 Å, N = 723). The polymers are 2−3 times larger than the expected value which is a reflection of the good solvent quality (excluded volume interactions) and the long persistence length of the stiff chains. Notably, the presence of PCBM does not appear to have a significant effect on ξ at the concentrations studied.

0 S11 (q) 0 1 + v11(q)S11 (q)

I(q) = Δρ2S11(q)+background

fit parameters

PCBM [mg/mL]

(2)

Equation 2 was used to fit the random coil polymer solution data simultaneously for three concentrations at 80 °C, and the results for pure polymer solutions are shown in Figure 5 and

Figure 5. RPA fits to three pure P3HT solutions (q resolution: 0.0004 Å−1).

Rg =

Table 3. The BHJ solution data were also fit to eq 2, adjusting the contrast factor and volume fractions to reflect the presence of the PCBM in the background (component 2). For the fits, the background was taken as the flat baseline intensity at high q and the contrast factor was calculated as the difference between the scattering length density of pure P3HT (6.76 × 10−7 Å−2) and the solvent−PCBM mixture (ρdDCB = 4.58 × 10−6 Å−2 and ρPCBM = 4.51 × 10−6 Å−2). The χ12 in this fitting procedure is the interaction parameter between the P3HT and the “effective” solvent (either pure dDCB or the dDCB−PCBM mixture). It should be noted that the interaction parameter extracted from SANS data is not identical to the thermodynamic χ when the parameter depends on concentration. The

a 2N 6

(3)

Rheology. Modulus measurements of polymers undergoing gelation can provide information on the kinetics of the solidification process and the structure of the aggregates. Gelation of a polymer solution is defined as the point when the aggregates percolate and establish connectivity throughout the whole sample. It is accompanied by divergence of the viscosity and development of a finite modulus. When the junctions are purely physical, as in the crystalline aggregates of P3HT, they are more easily disrupted by shear forces or temperature change than are chemically cross-linked gels. By inducing oscillatory shear at small strain, the mechanical properties of the aggregated solutions can be investigated without inducing 1051

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Figure 6. Frequency scans of 80 mg/mL P3HT solutions. Left: storage (G′) and loss (G″) moduli during gelation at 10 °C. Lowest modulus data sets at 70 °C prior to quench. Right: storage and loss modulus measured at several temperatures after gelation at 5 °C for 1 h.

Figure 7. (left) Storage and loss moduli for pure P3HT solution and 1:0.5 P3HT:PCBM solution during crystallization at 5 °C. Open symbols are loss modulus, and filled symbols are storage modulus. (right) Storage modulus of precrystallized solutions while heating (0.1 Hz, 1% strain, 1 °C/ min).

data become noisy due to low transducer signal. It is clear that around typical casting temperatures the behavior can vary significantly depending on thermal history. The modulus of a physical gel is also highly dependent on concentration, and the values obtained for the 80 mg/mL solution shown here approaching 1000 Pa are similar to other polymer physical gels.52,53 The physical cross-links in the P3HT gels can be envisaged as rigid bundles of crystalline material that enforce cooperative motion of the amorphous tie chains. There could be branching of the fibrillar crystal structures as well as entanglements of tie chains contributing to the network formation and accompanying modulus increase. Results from time-dependent storage and loss modulus measurements for solutions with and without PCBM are shown in Figure 7. During aggregation the modulus rises rapidly for both samples shown, but the increase occurs slightly later for the solution with PCBM. The plateau modulus is also lower for the solutions with PCBM, an indication that the physical cross-link density is lower for these systems. The classical theory of rubbery elasticity, usually employed for chemically networked systems, relates the modulus to the crosslink density following eq 4, where n is the cross-link density in moles per volume, R is the universal gas constant, and T is

fracture of the material. No independent measurement was made to verify infinite connectivity, but the solution-state aggregates examined in this study did not flow upon tipping of the vials and so their rheological behavior will be discussed in the framework of physical gels. The steady-shear viscosity of the well-dissolved P3HT solutions was found to be independent of shear rate, or Newtonian, up to a shear rate of 1000/s in the concentration range examined here (see Supporting Information). The complex rheological behavior of solutions without PCBM is shown in Figure 6. The plot on the left shows repeated frequency sweeps over 3 decades of frequency at a fixed strain of 1% (within the linear viscoelastic response regime) after quenching to 10 °C. As the pure polymer goes through the gel transition, the storage modulus becomes frequency-independent, characteristic of a cross-linked material rather than a viscoelastic fluid.50 The gel point, often defined as the point at which the storage and loss moduli are equal,51 is only observable in the early curves right after the quench to 10 °C. The plot on the right of Figure 6 shows the deaggregation, heating the solution in isothermal steps through the transition. The moduli gradually decrease but have not completely recovered to the liquidlike state by 35 °C, beyond which the 1052

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Figure 8. Storage modulus vs time for 80 mg/mL pure P3HT solutions (left) gelled at different temperatures and (right) gelled at 5 °C and measured at different frequencies.

temperature in kelvin.37 Equation 4 is a valid approximation for affine deformation and low strain, with no disruption of crosslinks due to applied stress.

G = nRT

in polymers. In this study, scattering shows that the rate of P3HT aggregate growth is slowed when PCBM is present, whereas rheometry shows that the rate of stiffening from network formation is less affected. Differences in the rate of P3HT aggregation observed using either technique can be ascribed to both the features to which each measurement technique is sensitive and the conditions under which the solutions were solidified. SANS describes overall size and shape of the aggregate structures and was performed under quiescent conditions. Rheometry was performed under dynamic conditions. Both SANS and rheometry reveal less participation of the polymer chains in the network when PCBM is present. Because P3HT aggregation from solution is crystallizationdriven, structural evolution is likely similar to that of a drying film. It can therefore be expected that the presence of PCBM will slow the solidification rate of P3HT during solvent evaporation, while also maintaining a lower coating viscosity. Further investigation of the consequences of organic photovoltaic solution gelation is the subject of ongoing work.

(4)

Using this definition, the pure P3HT cross-link density is roughly 0.4 mol/m3, corresponding to a distance between cross-links of 16 nm. For the 1:0.5 P3HT:PCBM gel the crosslink density attained during the experiment is 0.0009 mol/m3 or 120 nm between cross-links. A denser population of aggregates in the pure polymer solution restricts chain motion and leads to a higher modulus. This description of the gels is oversimplified because it takes into account neither the aggregate size nor the solution viscosity difference due to the presence of PCBM.54 Figure 7 also shows a scan through the transition temperature for the aggregated solutions after a quiescent period of 2 h at 5 °C. The system displays hysteresis as is typical for polymer crystallization: the transition occurs at higher temperature when melting than when forming crystallites. The melting transition appears to occur over a broader temperature range with increasing PCBM content; this may be indicative of a broader aggregate size distribution. Temperature and frequency dependence of the aggregation process of pure P3HT are shown in Figure 8. The pure P3HT solution still aggregates to some extent when cooled to 15 °C; however, the 1:0.5 P3HT:PCBM solution does not aggregate at 10 °C over a measurement period of 3 h (not shown). The significant decrease in plateau modulus when aggregated at a lower temperature corresponds to a lower number of junction points forming the network. Dependence of the plateau modulus on frequency is less significant. The faster oscillation results in a lower final modulus and slows the onset of aggregation. This finding may be significant for process design considerations because of the wide range of shear rates encountered in printing processes. Spin-casting induces relatively low radial and axial shear rates in the solution, the first of which decreases to zero once the liquid film stops flowing outward,5 whereas inkjet printing induces extremely high shear rates, often on the order of 105 s−1.6 Significant questions remain about both the equilibrium structure and mechanism of thermoreversible gelation in polymer solutions in general; this is a topic of current theoretical consideration.55 Scattering and rheometry are often employed as complementary techniques to explore structure−property relationships

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CONCLUSIONS Structural and kinetic observations were made of organic photovoltaic casting solutions using neutron scattering and rheometry in this work. The observable length scale and shape of polymer aggregates were identified to be tens of nanometers and rodlike, respectively, in agreement with previous works that relied on imaging of dried aggregated solutions. It was found that the presence of PCBM dramatically slows the aggregation of P3HT in solution. Concentration and temperature dependencies were identified, with the latter being the more sensitive parameter. RPA analysis shows a strong affinity between P3HT and DCB; the interaction parameter becomes more negative with increasing concentration, and elevated temperature dissolution suggests UCST behavior in this polymer−solvent system. Modest cooling of P3HT solutions even in “good” solvents such as DCB results in rapid aggregation. The aggregated solutions do not completely phase separate, but rather form physical gels consisting of anisotropic structures. An increase in solution modulus of several orders of magnitude accompanies the aggregation and the pure polymer solution modulus becomes frequency-independent. Although the percent crystallinity in the aggregated solutions cannot be calculated directly from these results, it appears that the 1053

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crystalline fraction is lower in the solutions with PCBM present. These results also lend insight into the film drying process and will lead to improved processing procedures in pursuit of an optimized morphology for bulk heterojunction devices.

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ASSOCIATED CONTENT

S Supporting Information *

Incoherent scattering of PCBM solutions, additional fits to the Guinier Porod model and fitting equation details, steady-shear viscosity of P3HT solutions. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

ACKNOWLEDGMENTS M.J.S. thanks the National Research Council Postdoctoral Associateship Program for funding. We acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing the neutron research facilities used in this work. This work utilized facilities supported in part by the National Science Foundation under Agreement DMR-0944772. We also thank Paul Butler and Wen-Li Wu for helpful discussions.

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