Determination of the Crystallinity of Semicrystalline Poly(3

Article pubs.acs.org/Macromolecules

Determination of the Crystallinity of Semicrystalline Poly(3hexylthiophene) by Means of Wide-Angle X‑ray Scattering Jens Balko,† Ruth H. Lohwasser,‡ Michael Sommer,‡,§ Mukundan Thelakkat,‡ and Thomas Thurn-Albrecht*,† †

Institute of Physics, Martin Luther University Halle-Wittenberg, Halle (Saale), Germany Applied Functional Materials, Macromolecular Chemistry I, University of Bayreuth, Bayreuth, Germany

‡

S Supporting Information *

ABSTRACT: Temperature-dependent small-angle and wideangle X-ray scattering (SAXS/WAXS) measurements on a series of chemically well-defined and highly regioregular poly(3hexylthiophenes) were analyzed to determine absolute values of the crystallinities. The analysis is based on the evaluation of the scattered intensity from the amorphous regions providing an easy and fast method for the determination of the crystallinity in the class of side chain substituted polymers. The resulting values are in the range of 68−80% at room temperature depending on the molecular weight. Based on these values, an extrapolated reference melting enthalpy of a 100% crystalline material was determined (ΔH∞ m = 33 ± 3 J/g) for use in DSC measurements. For higher molecular weights a decrease of the crystallinity was observed which can be explained by the onset of chain folding as deduced from the analysis of the SAXS patterns. An in-depth analysis based on Ruland’s method showed that the crystalline regions of P3HT exhibit a large amount of internal disorder.

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influence of all relevant parameters.23 Nevertheless, it seems quite certain that there is a strong correlation between hole mobility and crystallinity. This relation was demonstrated for organic field effect transistor devices24,25 as well as for bulk transport.26 In both cases, though, crystallinities were only determined on a relative scale. Indeed, while there are a number of studies investigating the relation between chemical structure and relative crystallinity, there is no clear recipe how to determine the crystallinity of P3HT on an absolute scale. Snyder et al. analyzed the effect of regioregularity on crystallinity by DSC. HH regiodefects act as comonomers which are not incorporated into the crystals. An increasing amount of regiodefects leads to a reduction of crystallinity and melting temperature.27 Using P3HT materials free of regiodefects (apart from one TT defect), Kohn et al. were able to relate the finite crystallinity of their materials to polydispersity and chain folding.22 An individual TT is incorporated into the crystal. Their model might also explain seemingly contradictory results about the effect of molecular weight on crystallinity. While some authors report that crystallinity increases with molecular weight based on DSC measurements,8,14 Rannou and Brinkmann concluded qualitatively from TEM images that higher molecular weight leads to a decrease of crystallinity9 and increasing disorder in the crystalline regions.12

INTRODUCTION Within the class of conjugated polymers regioregular poly(3hexylthiophene) (P3HT) is among the most extensively studied systems due to its interesting electronic and optical properties and the corresponding relevance for applications.1−6 P3HT is a semicrystalline side chain substituted polymer with a melting temperature of about 230 °C. The semicrystalline morphology of P3HT was investigated by small- and wide-angle X-ray scattering (SAXS, WAXS), atomic force microscopy (AFM), and transmission electron microscopy (TEM); it consists of the usual stacks of crystalline lamellae or whiskers separated by amorphous interlayers.7−9 The crystal structure of P3HT has also been studied extensively. While initial studies report an orthorhombic unit cell, more recent investigations find slight deviations, and a monoclinic unit cell is suggested.8,10−12 The performance of electronic and optoelectronic devices made from P3HT depends strongly on molecular parameters such as molecular weight (MW)13−15 and regioregularity (RR)1,16 as well as specific processing conditions such as choice of solvents and annealing procedures.6 These factors also influence the microstructure and semicrystalline morphology of the material.17 Additionally, in recent years new synthetic methods have been developed, leading to better controlled molecular properties such as P3HTs with very high or perfect regioregularity and small polydispersities which improved the quality and the reproducibility of the investigated materials.18−22 However, knowledge about the relations between molecular characteristics and processing, the resulting structure formation, and electronic transport properties is still very limited due to the difficulty to characterize the © 2013 American Chemical Society

Received: September 19, 2013 Revised: November 25, 2013 Published: December 9, 2013 9642

dx.doi.org/10.1021/ma401946w | Macromolecules 2013, 46, 9642−9651

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diffuse scattering caused by disorder within the crystals. As it will become clear below, a straightforward application of Ruland’s method to P3HT is problematic. We therefore here propose to use a variation of the above-mentioned simpler method introduced by Goppel, Hermans, and Weidinger to determine the crystallinity and use Ruland’s method to estimate the disorder in the crystals. While the individual methods are wellestablished, a synopsis containing sufficient theoretical details is not easy to find. We therefore first give a short review to provide a well-defined nomenclature as a basis for the discussion and application of the methods performed in this work. Scattering Contributions in Powder Scattering on Semicrystalline Samples. We assume an isotropic two-phase system consisting of crystalline regions and amorphous parts. The scattered intensity I(s) in sr−1 consists of several contributions.

There are several methods to determine the crystallinity of polymers.28 The most common and simple method is differential scanning calorimetry (DSC). DSC is not an absolute method; it relies on a comparison of the measured heat of melting with the heat of melting of a 100% crystalline material, ΔH∞ m . This value has to be determined separately based on an absolute method, as pure crystalline materials are not available for most polymers. The absolute methods often used are X-ray scattering or NMR. For P3HT the situation is ambiguous. Malik and Nandi published a value for ΔH∞ m of 99 J/g obtained from melting point depression in solvents.29 This value is broadly used and results in typical crystallinities in the range of 10−20% and in extreme cases 30%.14,30 Doubts about the accuracy of this value were raised, since qualitative inspection of X-ray scattering patterns suggests values for the crystallinity in the range of 50% or higher.8 Using a chemically well-defined low-molecularweight sample, Pascui et al. suggested to determine the crystallinity by quantitative 13C solid state NMR analyzing the conformational state of the alkyl chains.31 The corresponding signal was decomposed in a part originating from ordered and a part originating from disordered side chains. By comparison with the melting enthalpy of the DSC melting curve, they suggested a calibration value ΔH∞ m = 37 J/g. The approach is based on the assumption that an ordered state of the side chains goes along with an ordered state of the main chains. Taking into account this assumption, the authors stated that the NMR based value represents only a minimum value for the crystallinity. In addition, the sample used for the measurements has a specific feature. Because of its relatively low molecular weight, it has a broad melting range which makes it difficult to integrate the corresponding heat of melting. On the other hand, their value of ΔH∞ m was used in the model calculations by Kohn et al. and gave consistent results.22 Here we present a determination of the absolute value of crystallinity based on scattering experiments of a series of highly regioregular P3HT samples with a narrow molecular weight distribution. We use a method of analysis that is especially suitable for side chain substituted polymers, for which P3HT serves as a model system. In combination with DSC measurements, we estimate an extrapolated value for the melting enthalpy of a 100% crystalline material, ΔH∞ m = 33 ± 3 J/g. With increasing molecular weight we observe a decrease of crystallinity at the onset of chain folding.

I (s ) =

1 dσ = Icoh(s) + Iinc(s) = Icr(s) + Iam(s) + Iinc(s) be 2 dΩ (1)

where s = (2/λ) sin θ is the modulus of the scattering vector, dσ/ dΩ the differential scattering cross section, and be the scattering length of an electron. Only the coherently scattered intensity Icoh(s) contains structural information. It can be split up in Icr(s) originating from the crystalline regions and Iam(s) from the amorphous parts of the sample. In contrast, the incoherent scattering signal Iinc(s) which is due to Compton scattering contains no structural information. The relative contributions of Icr(s) and Iam(s) to Icoh(s) reflect the fraction of the crystalline and the amorphous phases, and the separation of the two components is the main issue for a determination of the crystallinity. Once this separation is achieved, the weight fraction of crystalline material is given by ∞

4π ∫ s 2Icr(s) ds Q N 0 xc = cr = cr = ∞ N Q 4π ∫ s 2Icoh(s) ds 0

(2)

where Ncr is the number of atoms in the crystalline phase, N the total number of atoms, and Q the invariant given by Q=

■

∫ Icoh(s) dVs = 4π ∫0

∞

s 2Icoh(s) ds

(3)

where the left-hand side of eq 3 is an integral over the entire reciprocal space and the right-hand side the invariant for an isotropic sample. In the following we will briefly discuss the individual contributions in eq 1 and point out the difficulties in separating Icr(s) from Iam(s). Diffracted Intensity from the Crystalline Regions. We consider a semicrystalline sample with a weight-averaged crystallinity xc. The X-ray powder pattern emanating from the large number of sufficiently large crystals consists of two contributions, namely Icr(s) = IBragg(s) + Idiff(s). Here, IBragg(s) are the Bragg reflections and Idif f(s) is the diffuse scattering caused by disorder in the crystal. Neglecting any effects of polarization and absorption which depend on the special conditions of the experiment, the intensity of a Bragg reflection with Miller indices (h,k,l) is then given by

THEORY Determination of crystallinity by X-ray diffraction relies on the fact that the scattering patterns from amorphous and crystalline materials are of very different shape. Goppel, Hermans, and Weidinger described first in detail how the crystallinity can be determined by analyzing the scattered intensity originating from the amorphous component of the sample.32,33 However, the first method based on rigorous theoretical considerations was introduced by Ruland, who suggested to separate the scattered intensity originating from the crystalline component and to evaluate the ratio of this part of the signal to the total scattering signal.34,35 His method includes corrections for incoherent contributions to the scattering signal as well corrections for effects of disorder within the crystalline fraction. Data analysis following this method requires a substantial analytical effort, and it was therefore applied only to a limited number of materials as e.g. iPP,34 nylon,35 polyethylene,36−38 poly(ethylene terephthalate),39 polyacetylene,40 and polythiophene.41 In general, the most difficult part of the analysis is a quantitative separation of

IBragg(s) = nhkl

2 V ρ 1 δ(s − shkl) x |Fhkl ,0|2 e−ks 2 c Vuc ρc 4πs 2

(4)

Here nhkl is the multiplicity factor equal to the number of contributing planes with the same interplanar distance, V and Vuc 9643


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Incoherently Diffracted Intensity. The last term in eq 1, Iinc(s), is caused by Compton scattering. The term “incoherent” originates from the loss of phase relationship between the incident and the scattered wave. Iinc(s) contains therefore no structural information. The incoherently diffracted intensity has to be subtracted carefully if an analysis of the scattered intensity in absolute units is aimed for. The Compton-modified scattering for an atom of type i containing Z electrons is approximately given by

are the irradiated volume of the sample and the volume of the unit cell, ρ is the density, and ρc is the density of the crystalline phase. Fhkl,0 is the structure factor of the unit cell where the subscript 0 denotes that disorder effects are neglected. Following the approach by Ruland,34,35 we assume that these can be taken 2 into account simply by an isotropic Debye−Waller factor e−ks . In general, disorder effects in crystals are classified into first and second kind of disorder, where the former show up as a reduction of the intensity of Bragg reflections and the latter lead to decreased and broadened Bragg reflections.42,43 For eq 4 it has been assumed that thermal motions of the atoms are dominantly caused by long wavelength excitations of the lattice (acoustic phonons) and that in general imperfections of the first kind dominate. If furthermore we assume isotropic displacements of the atoms, k is given by (4/3)π2 (Δu)2 with (Δu)2 being the mean-squared displacement of atoms around their average positions. The intensity lost from the Bragg peaks as a result of disorder appears as diffuse scattering signal in between the Bragg reflections. A general analytical description of this contribution is difficult. The most simple model assumes uncorrelated displacements of the atoms. Within this approximation the diffuse intensity can be written as 2 ρ V Idiff (s) = |F0(s)|2 xc [1 − e−ks ] ρc Vuc

⎡ f 2 (s ) ⎤⎛ λ ⎞ 3 ⎥⎜ ⎟ Iinc , i(s) ≅ ⎢Z − i Z ⎥⎦⎝ λ′ ⎠ ⎢⎣

Here the so-called Breit−Dirac recoil factor (λ/λ′)3 takes into account the change in wavelength from λ for the incoming and λ′ for the scattered photon.34,39,43 Iinc is zero for s → 0 (f i(0) = Z) and increases with increasing scattering vector. Vonk suggested a correction procedure in which the experimentally measured intensity is scaled to absolute units followed by a subtraction of the incoherent intensity37 (for further information see the Supporting Information). Crystallinity Determination. From the discussion above it is clear that the determination of the crystallinity of a semicrystalline sample requires the separation of the different contributions to the scattered intensity. In practice, two different approaches, relying on different approximations, have been developed. The first approach goes back to the work of Goppel.32,33 Here the intensity at a certain scattering vector s0 in between Bragg reflections is taken as part of Iam(s) and measured in the semicrystalline sample (scr) and a completely amorphous sample, e.g., in the molten state at high temperature. The crystallinity follows from the ratio of the two intensities

(5)

Equation 5 includes the structure factor F0(s) which decreases 2 with s and the increasing contribution (1 − e−ks ), resulting in a broad featureless maximum of the diffuse scattered intensity.39,43,44 Diffracted Intensity from the Amorphous Regions. According to Debye’s formula, the scattered intensity from an ensemble of atoms without long-range order such as a gas, a liquid, a polymer melt, or the amorphous region of a semicrystalline polymer is given by45 Iam(s) =

∑ ∑ (fm fn sin 2πsrmn)/(2πsrmn) m

n

Iscr(s0) ≈ xam = 1 − xc Imolten(s0)

(9)

This approach is correct if Iinc(s0) and Idif f(s0) can either be neglected or are subtracted beforehand. Additionally, one has to assume that the shape and the position of the intensity maximum of Iam(s) at the two different temperatures do not vary much. Ruland suggested a method for the determination of the crystallinity based on a separation of IBragg(s) from the remaining signal. While Iinc(s) has to be subtracted beforehand, the method relies on a determination of the ratio of Icr(s) and Icoh(s). The effect of disorder is taken into account by an approximate correction factor which requires no detailed knowledge about the crystal structure; only the chemical composition of the sample is needed.34,35

(6)

where the summation is carried out over all atoms within the illumminated volume, f i are the atomic scattering factors, and rmn are the distances between the mth and nth atom. A full analytical evaluation of eq 6 is impossible, and in practice amorphous intensities are described by empirical functions. Typically the observed diffraction pattern of materials without long-range order consists of several weak and broad maxima, of which usually the strongest is termed amorphous halo.45,46 In semicrystalline polymers the corresponding contribution is proportional to the amorphous fraction xam and is superimposed by the sharp diffraction peaks and the diffuse scattering emanating from the crystalline regions. Another contribution to the diffracted intensity from the amorphous regions arises from thermal density fluctuations on a mesoscopic length scale. This contribution shows up at small scattering vectors and is given by a constant value

IΔρ(0) = Z2N ⟨n⟩kBTκ

(8)

s

s

xc(sp , k) =

∫s p s 2IBragg(s) ds 1

s

∫s p s 2Icoh(s) ds 1

= xapp(sp) × H(sp , k)

×

∫s p s 2 f 2 (s) ds 1

s

∫s p s 2 f 2 (s)D(s) ds 1

(10)

Here a disorder function in form of a generalized Debye−Waller factor (cf. eq 11) takes into account thermal vibrations as well as imperfections of the first and the second kind. The first factor xapp(sp) corresponds to an apparent crystallinity neglecting disorder effects. These are taken into account by the function H(sp,k). It contains the averaged atomic scattering power f 2(s) = ∑Ni f i2/∑Ni (average over one monomeric unit, Ni is the number of atoms of type i in the monomeric unit) and the disorder function D, where

(7)

with N being the number of atoms scattering, ⟨n⟩ = N/V the average number density, kB the Boltzmann constant, T the absolute temperature, and κ the isothermal compressibility.43 Equation 7 holds for liquids in thermodynamic equilibrium, i.e., for temperatures above the glass temperature.47 9644


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a Kapton foil from which the intensity i0 of the primary beam is determined. Behind the sample another beam monitor measures the intensity from the air scattering from which the transmitted intensity i1 is determined.54 Two detectors were used for simultaneous measurements in the small-angle and wide-angle range. The WAXS area detector (AVIEX PCCD-4284) at a sample-to-detector distance of 0.12 m has an input field of about 84 mm × 42 mm, a spatial resolution of 60 μm, and spans an s-range of 0.6 < s < 6.4 nm−1. The SAXS area detector mounted on a wagon inside an evacuated tube of a length of 12 m was placed with a sample-to-detector distance of 1.1 m, resulting in an accessible s-range of 0.016 < s < 0.75 nm−1. The SAXS detector, a FReLon Kodak CCD chip, has an input field of 100 mm × 100 mm with a spatial resolution of about 80 μm. The SAXS and WAXS s-ranges overlap in the region of 0.6 < s < 0.75 nm−1. The sample holder, an aluminum disk with a hole of ≈0.8 mm in diameter and ≈1 mm in thickness, was placed on a Linkam hot stage for temperature-dependent measurements and flushed with nitrogen to reduce possible photo- and thermoxidation present under ambient conditions. The scattering curves I(s) were background corrected such that I(s) = Iexp(s) − Ibg(s) × Tr, where the transmission of the measurement with sample Iexp(s) is given by Tr = i1/i0 and Ibg(s) was the background measurement of the empty sample holder inside the chamber with Kapton foils as windows. The correction for polarization was automatically performed at the beamline. DSC. To investigate the thermal properties of the materials, we used a Diamond differential scanning calorimeter for the custom synthesized samples and a DSC 7 for the commercial sample, both from PerkinElmer. Background contributions to the signal were subtracted resulting in measurements of the apparent heat capacity cp(T). Samples. SEC, MALDI-TOF, and NMR. Size exclusion chromatography SEC measurements were performed utilizing a Waters 515-HPLC pump with stabilized THF as the eluent at a flow rate of 0.5 mL/min. A 20 μL volume of a solution with a concentration of approximately 1 mg/ mL was injected into a column setup, which consists of a guard column (Varian, 50 × 0.75 cm, ResiPore, particle size 3 μm) and two separation columns (Varian, 300 × 0.75 cm, ResiPore, particle size 3 μm). The compounds were monitored with a Waters UV detector at 254 nm. Polystyrene was used as external standard and 1,2-dichlorobenzene as an internal standard for calibration. Matrix-assisted laser desorption/ ionization mass spectroscopy measurements with time-of-flight detection (MALDI-TOF MS) were performed on a Bruker Daltonic Reflex TOF using dithranol as matrix and a mixture of 1000:1 (matrix:polymer). The laser intensity was set to around 70%. The reflector mode was used for the lowest molecular weight sample P3HT 3, allowing to resolve the isotopes. The linear mode was set for measurements of samples with molecular weights higher than 10 kg/ mol. 1H NMR spectra were recorded in chloroform on a Bruker Avance 250 spectrometer at 300 MHz. The spectra were calibrated according to the solvent signal at 7.26 ppm. The regioregularity was calculated from the different NMR peaks as described in detail before.8 The regioregularity in Table 1 does not take into account the tail−tail defect originating from the starting unit.

(11)

with k=

4 2 π (Δu)2 3

(12)

Ruland now suggests to use the fact that the value of xc, as resulting from eq 10 should be independent of the choice of the upper limit sp of the integral (s1... lower limit), as a condition to determine k and xc simultaneously. Practically, the parameters xc and k are varied while the integral is calculated for at least two different sp. If the result is the same for both sp, the correct values for xc and k are identified. Although the simultaneous determination of the two values characterizing the crystalline fraction is very powerful, Ruland’s approach also has limitations. (i) The expression for the disorder function D(s) is based on several approximations.48 It implies that the displacements of the atoms in the unit cell are isotropic. A more correct analytical form of D(s) would depend on the types of imperfections and on the anisotropy of interactions present in the system.35,36,48−50 (ii) In practice, the separation of the Bragg reflections IBragg(s) from the underlying background is often difficult. Attempts to solve this problem by an analytical description of the diffuse scattering Idiff(s) rely on eq 5 and are therefore even more strongly restricted by the limitations mentioned above.39,51,52 (iv) From a technical point of view it is also difficult to correctly subtract the incoherent scattering Iinc(s). For this purpose intensities have to be on an absolute scale, and corrections for polarization and absorption are needed. The direct application of Ruland’s method to P3HT is difficult, as P3HT only shows a small number of well-resolved reflections which causes uncertainties in the calculation of the integrals according to eq 10. In addition, interactions in a P3HT crystal are certainly anisotropic, namely van der Waals interactions between the alkyl chains, π−π interactions between thiophene units of different chains, and covalent bonds along the backbone. A description of the diffuse scattering by eq 5 does not give a satisfactory result.50,53 We therefore suggest to follow Goppel’s method to determine the crystallinity of P3HT. We use the fact that side chain substituted polymers such as P3HT exhibit already a strong scattering signal at relatively low angles due to a large unit cell parameter corresponding to the side chain−main chain separation, which is of the order of about 1.5 nm. In detail we evaluated the intensity between the first two Bragg reflections of P3HT. At this angle the incoherent scattering can be safely neglected (eq 8 and Figure 1 of Supporting Information). It amounts to less than 1% of the total scattered intensity for s0 < 0.1 Å−1 or 2θCu−Kα < 9°. Also, the diffuse scattering is negligible if the disorder parameter k is not too large (eq 5). The very small fraction of the scattering signal due to density fluctuations can also be neglected. In a second step we use Ruland’s approach (eq 10) to estimate the disorder parameter k.

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Table 1. Molecular Characteristics of Samples Used in This Studya

EXPERIMENTAL SECTION

Methods. SAXS/WAXS. Simultaneous small-angle and wide-angle Xray scattering experiments (SAXS/WAXS) were performed at the high brilliance beamline ID2 at the ESRF in Grenoble/France. A cryogenically cooled Si-111 double-crystal monochromator and a focusing torroidal mirror provide a beam with a wavelength of λ = 1 Å (12.4 keV) and a beam size of 200 μm × 400 μm (vertical and horizontal, respectively) with a divergence of 20 μrad × 40 μrad. The maximum photon flux is approximately 1014 photons/s/100 mA at the position of the sample. Beam monitors measure the photon flux along the beamline. The last monitor in front of the sample uses the scattered intensity from

sample

P3HT 3

(kg/mol) MSEC n MSEC (kg/mol) n MMALDI (kg/mol) n no. of rep units contour length (nm) PDI by SEC regioregularity (%)

5.2 5.9 3.2 20 7.7 1.15 97

P3HT 12 P3HT 18 18.5 24.2 12.4 74 28.3 1.16 97

27.2 35.1 17.5 106 40.8 1.15 97

P3HT 24

cs

34.2 45.9 24 144 55.4 1.15 98

19.4 33.6 ≈17*

1.99 98

a

The number in the sample names indicates the molecular weight as determined by MALDI-TOF. The molecular weight of the commercial ≈ 17* was not measured but was estimated using sample (cs) MMALDI n MALDI ≈ 1.9, which was determined from the samples the ratio MSEC p /Mn with narrow PDI. 9645


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Synthesis and Chemical Characterization. Regioregular poly(3hexylthiophene) (P3HT) samples were synthesized using the Grignard methathesis polymerization (GRIM) developed by McCullough and coworkers.55 For comparison, we also investigated a P3HT purchased from Rieke Metals, Inc. The basic characteristics such as molecular weight, polydispersity (PDI), regioregularity, and the number of repeating units are given in Table 1. The molecular weights and the polydispersities were determined by SEC. The resulting molecular weight distributions are depicted in Figure 1. It is well-known that for

Figure 1. SEC traces of the synthezised samples (P3HT 3, black; P3HT 12, red; P3HT 18, green; P3HT 24, blue) and the commercial sample cs (dashed). polymers which are stiffer56,57 than the external calibration standard polystyrene the molecular weights measured by SEC are overestimated.58 The peak maximum of the molecular weight distribution measured by SEC is about twice the number-average molecular MSEC p as determined by MALDI TOF MS which gives an weight MMALDI n absolute value. The number-average molecular weight of the latter method was used to calculate the number of repeating units and the contour length using half of the unit cell parameter along the backbone c/2 = 0.385 nm. The regioregularity was determined by 1H NMR as described before.8 Sample Preparation. For the X-ray investigations powder samples were pressed into the transmission holder. Each sample was heated above its melting temperature in an oven with a nitrogen atmosphere, kept there for 20 min, and then cooled to room temperature with a rate 0.4 Å−1 Bragg peaks are strongly suppressed in intensity. As mentioned, this fact makes a direct application of Ruland’s method for the determination of the crystallinity difficult. Sample P3HT 3 with the lowest molecular weight shows additional reflections. These are indicative of an ordered state of the side chains as discussed in detail by Wu et al.8 Also, only this sample showed a clear and strong small angle signal at 0.01 Å−1 reflecting regular stacks of crystalline lamellae and amorphous interlayers. This part of the scattering pattern will be discussed in detail further below. 9646


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Figure 3. WAXS crystallinities at 40 °C after cooling from the melt (cooling rate < 3 K/min) for the samples P3HT 3−24 as obtained from eq 9.

known. Further below we will show that for P3HT 3 k ≈ 8 Å2. Neglecting the disorder corresponds to an underestimation of the intensity of the Bragg reflections, for the (100) reflection by a factor of exp(−ks1002) ≈ 0.97. Assuming the extreme case that the amorphous intensity at s0 is overestimated by a corresponding factor 1/0.97, the crystallinities shown in Figure 3 were underestimated by a relative error of about 3%. For the samples P3HT 3−24 the real error can safely be assumed to be smaller. But as we show below for the commercial sample the analysis used above does not lead to consistent results, as the disorder in the crystalline regions is too high. Determination of a Reference Value ΔH∞ m for Use in DSC Measurements. The crystallinities determined by WAXS can be used to extrapolate the melting enthalpy of a 100% crystalline material. In Figure 4a, DSC heating measurements are shown. The melting enthalpies obtained by integration of the DSC signal over the appropiate temperature range are listed in Table 2 together with the WAXS crystallinities xWAXS . Note the c large range of integration needed to evaluate ΔHm for the low molecular weight sample P3HT 3 correctly. This point will be discussed in more detail below. The similar molecular weight dependence of the melting enthalpy and the WAXS crystallinity for the samples P3HT 3−24 shown also in Figure 4b is obvious and justifies to take this set of data to calibrate the DSC measurements. The relation

ΔHm∞ =

Figure 4. (a) DSC thermograms obtained during a second heating run with a rate of 20 K/min. Apart from P3HT 24, all curves are shifted vertically for clarity by an offset of −1, 0.5, 1.0, and 1.5 J/(g K) for cs, P3HT 18, P3HT 12, and P3HT 3, respectively. Straight lines below the melting peaks are included to justify the range of integrations used for the determination of ΔHm. (b) Corresponding melting enthalpies for the samples P3HT 3−24 (gray circles) and WAXS crystallinities (squares).

changes in the packing of the chains in the crystalline structure.8 Already at 120 °C the (020/002) reflection was strongly reduced along with a higher amorphous background below the (100) reflection and around 0.22 Å−1. This result corresponds to the broad range of melting in the DSC trace of P3HT 3 in Figure 4a and justifies to integrate the signal in the range 25−186 °C (Table 2). In comparison, sample P3HT 18 showed a much narrower melting range reflected by nearly overlapping curves at 40 and 120 °C. In accordance, also the DSC thermogram showed a clear melting signal only above 120 °C. As a consequence, a very careful choice of the integration range is necessary for integration of the melting peak of DSC measurements of low molecular weight samples of P3HT.59 In our former study this issue was not yet recognized, resulting in an underestimated smaller melting enthalpy of P3HT 3.8,31 Using that underestimated value together with a crystallinity measured by NMR, Pascui et al. determined a value ΔH∞ m similar to the value obtained here. The NMR crystallinity relied on the measured fraction of P3HT units with ordered alkyl side chains (referred to as crystalline phase I), whereas the disordered side chains are attributed to the amorphous phase and to the crystalline phase II. Therefore, the authors already stated that the NMR crystallinity constitutes only a minimum value. Incidentally, the underestimated melting enthalpy in combination with the underestimated NMR crystallinity led to a similar value ΔH∞ m ≈ 37 J/g as in our study. Influence of Molecular Weight and Polydispersity at Room Temperature. The crystallinities determined by WAXS (Figure

ΔHm xcWAXS

(13)

ΔH∞ m

gave an average value of = 33 ± 3 J/g. Contrarily, a value ΔH∞ = 41.8 J/g was obtained for the commercial sample, m indicating that in this case the WAXS value xWAXS severely c underestimated the real crystallinity because the contribution of the diffuse scattering is not negligible. We conclude that the former value of 99 J/g obtained by melting point depression investigations of a P3HT−diluent system (acetophenone as solvent) was overestimated by about a factor of 3,29 resulting in considerably too small crystallinities determined by DSC measurements.14,30 With the corrected value ΔH∞ m = 33 J/g, we estimated the crystallinity of the commercial sample as 72% (instead of 23% using the former literature value). Factors Controlling the Crystallinity. Influence of Temperature for Low and High Molecular Weights. As already mentioned, the changes of crystallinity with temperature are very different for low and high molecular weights samples. In Figure 5, temperature-dependent scattering patterns of (a) P3HT 3 and (b) P3HT 18 taken during the first heating after preparation are shown. The low MW sample P3HT 3 melted over the entire temperature range from 40 °C up to the molten state, along with 9647


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Table 2. Melting Enthalpies from the Integrated Peaks of the DSC Thermograms, Crystallinities xWAXS at 40 °C (Figure 3), the c a Calculated Melting Enthalpy ΔH∞ m of a 100% Crystalline Material, and the Disorder Parameter k

a

sample

P3HT 3

P3HT 12

P3HT 18

P3HT 24

cs

ΔHm (J/g) T range of integration (°C) xWAXS c ΔH∞ m (J/g) k (Å2)

25.3 25−186 0.705 35.9 8

25.0 125−248 0.798 31.1 9

28.2 125−250 0.77 36.6 11

20.2 156−255 0.676 29.9 7

23.8 125−245 0.57 41.8 15

Cf. analysis of the disorder in the crystalline fraction.

Figure 5. Evolution of the scattering pattern during the first heating (10 K/min) after preparation for (a) the low molecular weight sample P3HT 3 and (b) P3HT 18. Depicted are measurements at 40 °C (black), 120 °C (gray solid), and in the melt state (pink dashed). Figure 6. (a) Lorentz-corrected small-angle X-ray scattering curves at 40 °C after preparation for the samples P3HT 3 (black circles), P3HT 12 (red triangles), P3HT 18 (green diamonds), and P3HT 24 (blue squares). Exemplarily on top of the data for P3HT 24 the fit function is shown from which the long period was inferred (described in the text). (b) Long periods as determined from the small-angle X-ray scattering signals shown in (a) (solid line is a guide for the eyes only). The black horizontal bars show the contour length λ of the fully extended chains. The gray bars indicate estimated values for the maximum thickness of containing chains with one hairpin fold the crystalline lamellae dmax c (dark gray) and with two hairpin folds (light gray).

3) at 40 °C first increase up to around 80% for P3HT 12 and then decrease for higher molecular weights. In order to understand this dependence in more detail, we analyzed the Lorentzcorrected SAXS patterns of P3HT 3−24 depicted in Figure 6a. The samples P3HT 3−18 show a clear maximum corresponding to the long period of the semicrystalline morphology, while for P3HT 24 a weak and broad peak is difficult to distinguish from the decaying background. To determine the position of the maximum, we modeled the experimental curves using a superposition of a peak function and a decaying exponential function as a background. The resulting long periods dL = 1/sL are plotted versus molecular weight in Figure 6b. Exemplarily, the complete fit of the SAXS curve of P3HT 24 using a Gaussian function is shown as solid line in Figure 6a. By comparing the measured long periods with the calculated contour lengths λ (black horizontal bars; refer to Table 1) and estimated maximum crystal thicknesses dmax = (λ − n × 7 × c/2)/n + 1 assuming n c hairpin folds with 7 repeating units per fold60 (c-unit cell parameter along the backbone), we were able to conclude on the chain conformations within the crystalline lamellae. For the low molecular weight P3HT 3 the long period is sligthly larger than the contour length which we ascribe to an extended chain conformation within the crystal and noncrystallizable end groups outside in the amorphous regions.8,22 P3HT 12 still forms extended chain crystals; due to the higher molecular weight, the relative influence of polydispersity is reduced,22 which explains the higher crystallinity. This trend is accompanied by the onset of chain folding clearly observed for Mn ≥ 12 kg/mol, leading to a reduction of crystallinity for the higher molecular weight.9 As analyzed in detail in ref 22, also the polydispersity limits the crystallinity. This probably explains the further reduction in crystallinity for the commercial sample, but a slightly lower

regioregularity might also contribute. Generally, the peaks become sharper at elevated temperatures and their intensity changes, but their positions remain basically unchanged. Therefore, the strongly varying intensity of the SAXS signals in the different samples is at least partially related to temperaturedependent partial melting and crystallization59 which will be analyzed in a forthcoming publication. Exemplarily, the SAXS pattern for P3HT 24 at 230 °C is shown in Figure 2 of the Supporting Information. Characterization of Disorder in the Crystalline Parts. As already discussed, the scattering data suggest that P3HT is a material with a relatively high crystallinity containing crystals with a high degree of disorder. We tried to determine the amount of disorder in a semiquantitative way by using Ruland’s description of the scattering power of a semicrystalline material as it was reviewed in the Introduction. Assuming the crystallinity xWAXS as determined above, the correctly chosen value of k fulfills c eq 10. In Figure 7 the coherent intensities Icoh(s)s2 are shown. In order to bring the measured intensities on an absolute scale, we applied a procedure suggested by Vonk37 followed by the subtraction of the theoretically calculated incoherent Compton 9648


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The analysis we used for the model system P3HT is simple and especially well applicable for side chain substituted polymers. It relies on the assumption that separating the scattering intensity from crystalline and amorphous parts in a-direction gives sufficient information to determine an overall crystallinity. There is no need to determine absolute intensities, to subtract incoherent scattering, or to correct for absorption. For comparison, a measurement of a completely amorphous sample in the molten state is used. The method is useful for samples exhibiting substantial internal disorder within the crystalline regions which prevents the determination of the crystallinity based on Ruland’s approach. It comes to its limits if the disorder of the crystalline part is too high as it turned out to be the case for the commercial sample. Nevertheless, a crystallinity based on DSC measurements could still be determined also in this case. The reference value for the melting enthalpy we determined here is a factor of 3 lower than a previously published and oftenused value. Our result is in agreement with the qualitative appearance of the scattering patterns and is also in line with a recently proposed model22 for the crystallinity in P3HT, taking into account the influence of polydispersity and molecular weight. The value is also similar to a recently published value based on NMR analysis, but as we now think this agreement is partially incidental.31 Attempts to determine the crystallinities in P3HT thin films by a quantitative analysis of UV−vis absorption spectra gave typically somewhat lower values than presented here.61 But it is well-known that polymer thin films often show a reduced crystallinity so a direct comparison is not straightforward.62 On the other hand, our results for bulk samples provide a starting point for investigating the crystallinity in thin films e.g. by ultrafast scanning calorimetry. The values for the internal disorder parameter are considerably larger than typically found in other synthetic polymers. The side chain architecture of P3HT might be a reason for this finding. As we know from previous studies the side chains are in most cases themselves disordered and have a high mobility even in the crystalline parts of the sample, so that in effect P3HT in many cases does not exhibit real 3D crystalline order.8,31 Recently, the high disorder in direction of the π−π stacking of another semiconducting side chain substituted polymer was analyzed within the model of a paracrystal.63 This analysis relies on the existence of a sufficiently high number of Bragg reflections and can of course give valuable additional information in such cases. It is beyond the scope of our investigation on P3HT. Nevertheless, we think that the description of P3HT as a semicrystalline polymer, i.e., the distinction between an ordered and a disordered phase, is essentially correct. It is in line with general observations on crystalline polymers, with results obtained for P3HT in TEM, AFM, SAXS, and WAXS. In that sense we think that our analysis gives an appropiate overall description of semicrystalline P3HT, although it relies on certain assumptions. It is therefore quantitative in nature but limited in absolute accuracy. Given the fact that electronic transport properties depend strongly on local packing structure as well as on domain boundaries between different ordered domains, we hope that our results contribute to an extended description of structural properties of P3HT and their relevance for electronic properties.

Figure 7. Coherent intensity Icoh = IBragg + Idiff + Iam (solid black) for P3HT 3 (a) and P3HT 18 (b) at 40 °C after preparation in comparison to the assumed background intensity Idif f + Iam (dotted) and the separated intensity below the Bragg peaks IBragg (gray).

scattering. The procedure is described in the Supporting Information. We separated the intensities of the Bragg reflections IBragg(s) from the background Idiff(s) + Iam(s) in an empirical way by simply connecting the base points of the Bragg reflections with straight lines. Thereby we assumed that the Bragg reflections overlap in the range 0.23 ≤ s ≤ 0.33 Å−1; correspondingly, IBragg(s) might be slightly overestimated. Equation 10 shows that such an overestimation corresponds to an underestimation of the disorder parameter k. We used an integration range [s1, sp] = [0.1, 0.35] for the determination of the disorder parameter k. For the samples P3HT 3−24 disorder parameters k in the range of 7−11 Å2 (( Δu 2)1/2 = 0.78−0.91 Å) were found (Table 2), which corresponds to about 5% of the unit cell parameter a (main chain separation) and 10% of b (direction of the π−π stacking). The highest value, k = 15 Å2, was found for the commercial sample. In this case xDSC = 0.72 was used instead c of xWAXS as the latter is unreliable for this sample as discussed c above. These large values of k are consistent with the strong suppression of the higher order of the (020) reflection at ≈0.52 Å−1 (see Figure 2). For P3HT 3 the disorder parameter k = 8 Å2 would e.g. lead to an suppression of the (040) reflection by a 2 factor of by e−ks = 0.12. Such high values of k are not typical. Other common synthetic polymers have values ranging from 2 Å2 (PE) to 5 Å2 (polythiophene).34,37−41,49 Only for nylon 7 a value of k = 7 Å2 was measured.35 Consistently also most of these examples exhibit clear diffraction peaks at scattering vectors beyond 0.4 Å−1, in contrast to P3HT.

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CONCLUSIONS In this work we used a variation of Goppel’s original method in combination with Ruland’s description of the scattering intensity of semicrystalline polymers to determine the crystallinity and the internal disorder of the crystalline fraction of several samples of P3HT from X-ray powder scattering. In general, we found a high crystallinity of around 70−80% at room temperature in combination with a high degree of disorder in the crystals. From this result we determined an estimate for the melting enthalpy of 100% crystalline P3HT, ΔH∞ m = 33 J/g, which can be used to measure the crystallinity of a given material by DSC. We showed that the exact value of the crystallinity depends on molecular weight, polydispersity, and temperature. 9649


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ASSOCIATED CONTENT

S Supporting Information *

Correction for the incoherent scattering and the SAXS scattering pattern for P3HT 24 at elevated temperatures. 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] (T.T.-A.). Present Address §

M.S.: Institute of Macromolecular Chemistry, Albert-LudwigsUniversity Freiburg, Freiburg, Germany. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The ESRF Grenoble and M. Sztucki are acknowledged for the provision of synchrotron radiation facilities and assistance (beamline ID02). The authors thank K. Saalwächter for fruitful discussions and K. Herfurt for technical help with DSC measurements. This work was supported by the Deutsche Forschungsgemeinschaft (SPP 1355) and the Stiftung der Deutschen Wirtschaft SDW.

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