Effect of Thermodynamics and Curvature on the Crystallinity of P3HT

Article pubs.acs.org/JPCC

Effect of Thermodynamics and Curvature on the Crystallinity of P3HT Thin Films on ZnO: Insights from Atomistic Simulations Maria Ilenia Saba* and Alessandro Mattoni* Istituto Offcina dei Materiali (CNR-IOM) Cagliari, Cittadella Universitaria, I-09042 Monserrato (Ca), Italy S Supporting Information *

ABSTRACT: In this work, by means of model potential molecular dynamics simulations, we correlate the polymer crystalline order to the substrate morphology by focusing on the case of thin P3HT films deposited on planar and nanostructured ZnO surfaces under room temperature conditions. We show that the polymer/ZnO adhesion is driven by the electrostatic interactions between backbones and substrates. On planar ZnO substrates, though some disorder is present, the polymer films can be crystalline with predominance of the face-on molecular orientation. In addition, by studying models of curved substrates, consisting of ZnO nanorods, we show that the local curvature induces the bending of the polymer backbones and consequent disorder in the molecular film with the possible formation of amorphous layers. The analysis of the structure factor reveals a monotonic correlation between the local curvature and the diffraction peak associated with the backbone.

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INTRODUCTION The molecular order critically controls the functionalities of polymeric materials and of their interfaces. This is especially true for conductive polymers, such as poly(3-hexylthiophene) (P3HT), whose electrical and optical properties are very susceptible to the microstructure and to the crystalline assembling of the molecular constituents.1−4 The molecular disorder is detrimental for the charge carriers mobility; it increaseas the resistivity in the amorphous polymers5 and also induces a blue shift of the light absorption.6 In a microscopic perspective, the sensitivity to disorder is due to the molecular nature of the material and to the strong dependence of the intermolecular electronic properties (e.g., transfer integral) on the actual stacking of molecules.7,8 Deviations from the perfect crystalline phase can easily occur in real materials. In the case of P3HT, it is known that there are different quasi-isoenergetic crystalline phases (noninterdigitated, staggered, nonstaggered),9 that coexist in real crystalline samples separated by thin amorphous regions. The energy barriers necessary to induce disorder are typically of the order of 1 kcal/mol (0.05 eV/atom), and they can be bypassed under experimental conditions at finite temperature. Thin films of polymers on solid substrates are the typical systems where disorder plays a relevant role. It is known that the microstructure of thin films (e.g., its crystalline order, the size and orientation of crystal domains) can be rather different with respect to the bulk phase.10,11 Microstructure is also known to be quite sensitive to the effect of temperature that can induce important molecular rearrangement within the thin film.12 For example, the crystal orientation, morphology, and melting temperature depend strongly on the substrate, as observed in semicrystalline polyethylene thin films. This is caused by the polymer− © 2014 American Chemical Society

substrate attraction that competes against the polymer− polymer cohesion.11 Thin films are used in a wide number of applications. For example, in optoelectronics and photovoltaics, the thickness of the polymer films in contact with electron acceptor substrates can be as small as tens of nanometers (comparable to the excitons diffusion lengths). A paradigmatic case is that of P3HT on ZnO. This interface has strong relevance in the field of photovoltaics (either when the interface is the optically active part of the device or when P3HT acts as the hole blocking layer13), and it has been the object of several studies.14−16 In fact, the polymer morphology17 controls charge recombination and device performances of P3HT/ZnO systems.14,15 In particular, the critical effect of ZnO morphology on the device efficiency has been shown in the cases of nanofibers and bulk heterojunctions.18,19 In these structures the orientation of the polymer on the surface is very important because it can favor or inhibit the charge transport along the π−π channels from the interface to the electrodes. On the one hand, highly ordered polymers have been indicated as the most apt to obtain satisfying efficiencies.14,20 On the other hand, in some cases, less ordered or amorphous films enhance charge injection and performances.21,22 For example, in the context of organic photovoltaics, there is a growing body of evidence that the mixed regions are critical for exciton quenching and charge generation.23−26 Accordingly, the morphology of thin films and the physical factors inducing crystalline order is of great fundamental and technological relevance. Received: November 6, 2013 Revised: February 12, 2014 Published: February 12, 2014 4687

dx.doi.org/10.1021/jp4109305 | J. Phys. Chem. C 2014, 118, 4687−4694

The Journal of Physical Chemistry C

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equilibrations are performed within the NVT ensemble by the Nosè−Hoover thermostat.39,40 Among the available force fields describing P3HT, we adopt the AMBER one41 with AM1-BCC42 atomic partial charges providing a good description of polymer cohesion and density, at a reasonable numerical complexity.43 Atomic forces within ZnO atoms are described as the sum of Coulomb terms and Buckingham-type two-body potential44,45 while hybrid interactions between ZnO and the polymer consist of a sum of Coulomb and Lennard-Jones contributions.46 Long-range electrostatic forces are calculated by a mesh Ewald algorithm,47 and van der Waals interactions are cutoff at 9.5 Å. The same theoretical scheme has been successfully applied in several atomistic investigations involving hybrid interactions.46,48−50 The distinctive methodological tool of the present investigation is the calculation of polymer crystallinity by structure factor analysis and pair correlation functions. In fact, the order of atomistic models (formed by N atoms with average distance λ) can be characterized by the directional pair correlation function g⟨hkl⟩(x) defined as the average probability of finding two atoms at distance x along a given crystallographic direction ⟨hkl⟩ (normal to the planes (hkl)). This can be written as

In the literature, several methods have been already investigated to control the polymer film crystallinity. Among them are the use of anchoring groups, the functionalization of the side chains of the polymer,27 and the variation of its regioregularity and molecular weight.28 At variance, the effect of the substrate morphology has not been systematically investigated, although a correlation between ZnO roughness and solar cells efficiencies has been suggested in the case of low bandgap polymers.29 As for P3HT films on sol−gel ZnO, the occurrence of dramatic substrate effects on the polymer structure has been shown by grazing incidence Xray diffraction (GIXRD).30 The film tends to be amorphous instead of crystalline.14The disorder was attributed to the interactions between the polymer and the substrate without considering the role of the surface morphology. Also in the case of silicon substrates, effects of the surface structure on the crystallization of P3HT films have been reported.31,32 Another example is the orientation of crystalline domains in polyethylene thin films on different substrates.11 Finally, a better crystallinity in P3HT/ZnO bulk heterojunctios has been reported when the polymer is blended with nanorods rather than spherical nanoparticles.13 These results suggest that curved substrates tend to increase polymer disorder. However, the structural complexity of bulk heterojunctions makes it difficult to find a simple quantitative dependence. Despite the above results, a clear correlation between the morphology and the local curvature of the substrate and the polymer crystallinity has not been demonstrated, so far. From this viewpoint, atomistic simulation is a valid tool to overreach the experimental limits, making it possible to probe the polymer order at the molecular scale. The relevant physical factors (e.g., local curvature of the substrate, polymer orientation, temperature) can be included one at a time by using models of controlled complexity. Most theoretical works have only considered perfect polymer configurations.33,34 A more realistic model interface has been studied in the case of planar P3HT/ZnO interfaces, but only focusing on the study of charge transport properties.35 The molecular orientation, thermodynamics, and substrate curvature have not been extensively studied in literature. In this work we correlate the polymer crystallinity to the substrate morphology for the case of P3HT films on ZnO at room temperature. We first characterize the polymer adhesion on planar surfaces, finding that it is dominated by electrostatic interactions with preferential face-on molecular orientation. Then, by considering ZnO nanorods, we provide evidence that the curvature of the substrate is able to bend the polymer chains, inducing the observed disorder of P3HT films. In particular, the calculated structure factor of the polymer reveals a correlation between the curvature and the diffraction peak height of the backbones. The results of the present work could have practical implications, since, for metal oxide surfaces with strong ionic character, the possibility to control the film order by tuning the curvature of the substrate is predicted.

∫ d y ρ (y )ρ (y + x )

g⟨hkl⟩(x) =

where ρ is the atomic probability distribution that is zero everywhere but for the positions r occupied by the classical particles forming the system (i.e., ρ(x) = (1/N)∑r f rδ(x − r)). The coefficient f r weights the contribution of rth atom, and it is set proportional to its atomic number Zr. ρ, and g⟨hkl⟩ are normalized by the conditions ∫ ρ(x) dx = 1 and ∫ g⟨hkl⟩ dx = 1. The structure factor51 is by definition the Fourier transform of the pair correlation fuction, S⟨hkl⟩(q) = ∫ dx g⟨hkl⟩(x)e−iqx, that in terms of atomic positions r, r′ can be written as 2

1 S⟨hkl⟩(q) = 2 N

∑ fr f r′ e−iq(r′ − r) = r ,r′

1 N

∑ fr e

−iqr

r

S⟨hkl⟩(q) is positive everywhere with S⟨hkl⟩(0) = 1, and the normalization is set by the relation π /λ

∫−π /λ dq[S⟨hkl⟩(q)] = 2Nπ (see Supporting Information). The correlation of perfect crystals is a periodic distribution of impulses, g⟨hkl⟩ = ∑r(1/ N)δ(x − rλ), as well as its Fourier transform, S⟨hkl⟩(q) = ∑∞ m=−∞ (2π/N)δ(q−(2π/λ)m), with m and r integers. The structural disorder reduces the heights and broadens the peaks of g⟨hkl⟩(x) and S⟨hkl⟩(q). In the limit of fully disordered atomic positions, both g⟨hkl⟩(r) and S⟨hkl⟩(q) tend to a vanishingly small constant (g⟨hkl⟩ ∼ (1/λN) and S⟨hkl⟩(q) ∼ (λ/N)) everywhere but for g⟨hkl⟩(0) = 1 and S⟨hkl⟩(0) = 1. As discussed in the Supporting Information, the overall crystalline order along a direction can be estimated by the integral

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METHOD All the atomistic models are generated by model potential molecular dynamics simulations by using the DL_POLY_4 code.36 The velocity Verlet algorithm37 with a time step as small as 1.0 fs is used to solve the equations of motion. Minimum energy configurations of interfaces is obtained by performing low temperature annealings (0.1 ns at 1 K) followed by atomic forces relaxations based on standard conjugated gradients algorithm.38 Long room temperature

χ⟨hkl⟩ =

∫q

q2

dq S⟨hkl⟩(q)N

1

over a suitable [q1, q2] range including the most relevant Bragg peaks. 4688



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In the case of surfaces and interfaces, the quantities g⟨hkl⟩, S⟨hkl⟩, and χ⟨hkl⟩ can be averaged over all the directions within the plane of interest. Average quantities are labeled by GI (grazing incident). As an example, the grazing crystallinity χGI of the (010) plane requires an average over all the directions ⟨hkl⟩ = α2⟨100⟩ + β2⟨001⟩ for all pairs α and β satisfying α2 + β2 = 1. Similarly in the (100) case the average runs over the directions ⟨hkl⟩ = α2⟨010⟩ + β2⟨001⟩.

structure and all the information on structure factors are reported in the Supporting Information. Each P3HT(hkl)/ZnO(101̅0) system is identified by the crystallographic surface (hkl) of the polymer that is in contact with the ZnO substrate. In principle, there is an extremely large number of possible interfaces. We can limit the possible cases by taking advantage of a previous study where it was found that the backbone prefers to align parallel to the substrate along the rows of ZnO dimers.35 So, in the present study, we limit to the cases in which the backbone of the polymer chains (crystallographic ⟨001⟩ direction) lies parallel to the dimer rows of the ZnO (direction x in Figure 1). Under this constraint, only two models are possible: P3HT(010)/ZnO (010 interface, see Figure 1) and P3HT(100)/ZnO (100 interface, see Figure 2). The ZnO crystalline substrate is obtained by periodically replicating a finite crystal slab. The polymer chains are finite with backbone length of 6 nm, and we choose the size of the crystal slab large enough that the polymer crystal does not interact with its replica. In the y direction of the interface

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RESULTS: P3HT FILMS ON ZNO SUBSTRATES In this section we study the polymer crystallinity on ZnO substrates considering first planar crystalline surfaces and then taking into account the effects related to substrate nanocurvature. In the case of planar substrates, we consider two different crystallographic orientations of the polymer, and we analyze in detail the different contributions to polymer/ZnO adhesion. The nanocurved interface is obtained by depositing the polymer on a substrate consisting of ZnO hexagonal rods (diameter 3 nm) with infinitely long axes in the plane of the substrate. Flat Zinc Oxide Substrates. As a model of flat substrate, we focus in all cases on the nonpolar (101̅0) crystalline ZnO surface, which is the most stable and the most likely to occur in ZnO.52 This surface exhibits trench grooves alternated with rows of ZnO dimers49 both oriented along the [010] crystallographic direction (x direction, see Figure 1). All the atomistic models are obtained by model potential molecular dynamics. In some cases, as a check of the reliability of our results we also consider ZnO surfaces with atoms fixed to the positions predicted by first-principles calculations. We did not find sizable differences. As for the polymer, its crystalline

Figure 2. Schematic representation of the molecules orientation in the 100 interface (top). 100 system after the relaxation at low (middle) and room (bottom) temperature. The insets show a top view representation of the chains with the zigzag and lamellae structure (for clarity in the insets the oxygens are not represented).

Figure 1. Schematic representation of the molecules orientation in the 010 interface (top). 010 system after the relaxation at low (middle) and room (bottom) temperature. 4689



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(orthogonal to the backbone), we consider both periodic (discussed in this section) and nonperiodic boundary conditions (Supporting Information). We find that there are not substantial differences. The advantage of using periodicity along y (see Figure 1) is to avoid free surfaces, but the drawback is that the surface density of molecules is fixed by its initial value. We choose the surface density as close as possible to the equilibrium value in the crystal. In Figure 1 we compare the atomistic model of P3HT(010)/ ZnO interface at low (middle) and room temperature (bottom). In this system the π−π channels are orthogonal to the ZnO (Figure 1, top). A reasonable matching between the polymer and the ZnO surface has been obtained by putting one polymer chain every three rows (with spacing is 5.20 Å) corresponding to an interdigitation distance of 15.6 Å, which is close to the theoretical interdigitated equilibrium value.9 The initial thickness of the layer was ∼2 nm. As a result of the interaction with ZnO (Figure 1 middle), we observe a progressive shift of the polymer chains parallel to the surface. The interaction tilts the π channels and reduces the coupling between thiophenes (consistently with previous works35). At room temperature (Figure 1 bottom), an increased disorder originating from the distortions of the flexible alkyl chains is observed. The second considered interface is the P3HT(100)/ZnO one that is reported in Figure 2 where the π−π stacking is parallel to the surface (Figure 2, top). The initial π−π distance of 4.07 Å (close to the equilibrium spacing 3.8−4.0 Å) was chosen to match the ZnO lattice spacing. In this case, the thickness of the layer was ∼5 nm. The polymer at low temperature (Figure 2 middle) is highly ordered, with the alkyl chains and the thiophenes forming a zigzag motif. Conversely, at room temperature (Figure 2 bottom) the structure undergoes a sizable evolution. In fact, due to the ZnO/substrate interaction, which is stronger than the polymer−polymer cohesion, the molecules close to the substrate tend to assume a face-on configuration, inducing a strong microstructure evolution. In summary, the polymer crystallinity is affected by the interaction with the substrate. The temperature further increases the disorder of the chains, but it also restores the crystallinity in some cases. In fact, for the 100 case (see Supporting Information), the π−π structure factor peaks are enhanced. In order to understand the mechanism of adhesion, and, in turn, the energetics of the polymer/ZnO interfaces, we consider first the polymer alone. To this aim we focus on the (010) and (100) polymer surfaces. We do not consider the (001) surface since it is energetically unfavorable (the (001) planes cut the backbones). The calculated (relaxed and unrelaxed) surface energies γ(hkl) are defined as the difference between the energy per area of the bulk (EP3HTbulk) and that of the two halves (relaxed or not) resulting from the cut (2EP3HT(hkl)). Their values are reported in Table 1 and are very similar. Our data, calculated in ideal conditions of vacuum and in the absence of chemical contaminants, can be compared to theoretical calculations of liquid P3HT, reporting 0.056 N/m4 and with contact angle measurements reporting values in the range 0.036−0.069 N/m.53 By taking into account the strong

Table 1. P3HT Surface Energies surface

(unrelaxed)

(relaxed)

(010) (100)

0.104 N/m 0.133 N/m

0.084 N/m 0.087 N/m

dependence on experimental conditions and the differences of real samples from ideal ones, the agreement is reasonable. Also the 010 and 100 polymer/ZnO interfaces can be compared in terms of adhesion and formation energy. The formation energy EfP3HT(hkl)/Zno of the P3HT(hkl)/ZnO system is the energy required to form a unit area of interface starting from the P3HT and ZnO crystalline bulks. By calculating the surface with the lowest formation energy, we can predict the most abundant interface. f EP3HT can be calculated as γP3HT(hkl) + γZnO − (hkl) /Zno γP3HT(hkl)/ZnO, where γP3HT(hkl) + γZnO is the cost necessary to form the P3HT and ZnO surfaces from the corresponding crystals; γP3HT(hkl)/ZnO is the energy gain due to merging the surfaces (i.e., adhesion or work of separation). The first two terms are always positive since some energy is spent to form surfaces; at variance, the third term is negative when the interface is stable (i.e., when it is necessary to spend energy to separate the two components and γP3HT(hkl)/ZnO > 0). This is in fact the case of P3HT(010)/ZnO for which a large adhesion is found (γP3HT(010)/Zno ∼ 0.2 N/m). This value corresponds to an average adhesion of 0.84 eV per thiophene at the surface. It is consistent with first-principles54 and model potential calculations providing 0.64 eV for a single P3HT molecule on the surface. Calculated data are summarized in Table 2. We have used the surface energy values γP3HT(010) and γP3HT(100) of Table 1 for the polymer and data from literature for the ZnO (γZnO(101̅0) = 1.16 N/m55,56). Table 2. Adhesion and Formation Energies for the 010 and 100 Interfaces interface

adhesion energy (N/m)

formation energy (N/m)

010 100

0.219 0.078

1.025 1.169

Table 2 provides evidence that the 010 interface is the most likely to occur since its formation energy is smaller than the 100 one by 0.14 N/m. The cost necessary to form the 010 polymer surface is overcompensated by the large adhesion to the substrate (γP3HT(010 )− γP3HT(hkl)/ZnO = −0.135). Conversely, for the 100 interface the two opposite terms are balanced (γP3HT(100) − γP3HT(hkl)/ZnO ∼ 0). In summary, at variance with the 010 and 100 surface energies of P3HT that are similar, the interface is highly sensitive to crystallography. The average fraction ⟨x⟩ (i.e., the ratio between the corresponding areas) of the 010 interface (with surface energy γ1 = γP3HT010/ZnO) with respect to the 100 (with higher surface energy γ2 = γP3HT100/ZnO) can be calculated at the thermodynamic equilibrium, discarding the entropic contributions and the cost of grain boundaries (see Supporting Information): 4690


The Journal of Physical Chemistry C ⟨x⟩ =

Article

1 e−βα1 + −βα β(α1 − α2) e 1 − e−βα2

character of ZnO, and it is consistent with first-principles calculations.57 The Coulombic term is larger for the 010 interface (by 0.13 N/m) since the backbones of the first polymer layers are much closer to the surface, the molecular plane being parallel to it. In the other 100 case, the total electrostatic interaction is practically zero. Conversely, the difference of the dispersive interactions is much smaller (0.05 N/m), but the 010 is still favored. By considering only the vdW contributions to adhesion and by using the above energetic model, the relative abundance ⟨x⟩ of the two interfaces would be almost the same. We finally note that the tail contributions to adhesion are smaller, since they count a repulsive electrostatic interaction that contrasts the vdW forces. The electrostatic repulsion is attributed to the proximity of the positive hydrogens of P3HT chains to the positive Zn ions (induced by the vdW interactions with Zn). The above picture reveals that the adhesion has a strong electrostatic contribution due to the atomic partial charges of the ZnO surface atoms that favor the cofacial alignment of polymers. This suggests that, in order to increase the relative abundance of the 100 interface, it is necessary to reduce the ionic character of the substrate. This is consistent with the experimental observation14 of 100 polymer orientation for the less ionic SiO2 oxide.58 Besides the energetic stability, it is interesting to compare the polymer crystallinity on ZnO for the two orientations. In Figure 4 we compare the grazing incidence curves SGIN (N is the number of atoms, which is different for the two systems) for the 010 (left panel) and 100 (right panel) interfaces, and we calculate the grazing crystallinity χ/χ0 at room temperature (i.e., normalized to that of bulk crystal in the same plane χ0). The crystallinity χ and χ0 are obtained by integrating over the q range [0.35, 3.5] Å−1 that includes the relevant periodicities. We find a strong decrease of the structure factor and crystallinity at the interfaces (χ/χ0 < 0.3) that is slightly larger for the 100. Nevertheless, SGIN still exhibits the peaks of the crystalline phase (e.g., at 1.6 Å−1). In conclusion, the polymer films deposited on high quality ZnO surface are disordered, but the crystalline structure is preserved. Curved ZnO Substrates. According to the above analysis, the polymer on planar ZnO surfaces is not amorphous, as demonstrated by the persistence of peaks at 1.6 Å−1 in the grazing structure factor. This result seems in contrast with the experiment on sol−gel ZnO reporting flat structure factor and amorphous polymer.14 Accordingly, it is important to understand the reason for such a difference. Here we show that the

(1)

β = (1/kBT) is the Boltzmann constant and αi is the energy per bond of the ith interface. Assuming one bond per each thiophene at the surface, we get α 1 ∼ 0.83 eV/bond and α 2 ∼ 0.30 eV/bond. The corresponding fraction ⟨x⟩ of 010 interface is reported in Figure 3 as a function of temperature. At room temperature (dashed line) the 010 interface is expected to be more than 95% of the total interface.

Figure 3. Fraction of 010 interface as a function of temperature.

Though simplified, the above model shows that we expect a strong predominance of the 010 interface. Additional information is obtained by splitting the interface adhesion energy in the contributions cont = T, B related to the hkl backbones (γhkl B ) and to the tails (γT ). These energies, in turn, can be further separated into electrostatic (Coul) and van der Waals (vdW) type of interactions (see Table 3) so that γ(hkl) = ∑γ(hkl) cont (type) with type = vdW, Coul. Table 3. Polymer Backbone and Tail Contribution to the Adhesion of the 010 and 100 Interfaces interface 010 100

B T B T

γ (Coul) (N/m)

γ (vdW) (N/m)

0.151 −0.056 0.046 −0.037

0.058 0.066 0.011 0.058

For both the interfaces, the backbone contributions to adhesion are dominant with a larger component coming from the Coulombic interaction. This result is related to the ionic

Figure 4. Grazing structure factor curves SGI(q) of the 010 (left) and 100 (right) interfaces at room temperature with respect to that of the polymer bulk in the corresponding plane. The corresponding values of normalized crystallinity χ/χ0 (middle). 4691



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Figure 6); at θ = 0° the curvature is zero, and the polymer is parallel to the rod axis.

disappearance of peak in SGI is possible when the molecules are highly curved. To this aim we consider a model of rough ZnO surface (Figure 5 right) formed by a distribution of parallel

Figure 6. Tilt angle and relative local curvature.

In bottom panel of confronto-rod-plane we report the polymer grazing structure factors for interfaces with substrate curvatures κ = 0, 0.28, 0.59, and 0.67 nm−1 and tilt angles θ = 0°, 40°, 70° and 90°, respectively. We found that the peak at 1.6 Å−1 decreases with κ, showing that the local curvature of the substrate is able to reduce the order of the polymer chains. Present analysis shows that the absence of crystalline structure of the P3HT films on ZnO requires the bending of the polymer chains. This is possible when the substrate is curve and the polymer wraps around it as a result of the strong adhesion. We conclude that the local curvature and the vertical height variations of the substrate are key factors to induce disorder in the polymer films, as observed for P3HT on ZnO. We emphasize that the present curvature−disorder correlation is not expected to be always valid for any type of polymer/ substrate interaction; rather it depends on the strong adhesion of the backbones on the ZnO due to its ionic character. In the alternative case of a smaller adhesion, the polymer could detach from the substrate instead of wrapping.

Figure 5. Top and middle: models of hybrid P3HT/ZnO interfaces for the case of planar and curved interfaces (κ = 0, 0.28, 0.59, and 0.67 nm−1). Insets are cross-view showing the periodicity of the rods forming the substrate. Bottom: grazing incidence structure factors for the corresponding interfaces.

ZnO nanorods (with diameter D = 2R = 3 nm) separated by a relative distance of d ∼ R (see Figure 5, insets). Along the direction normal to the rod axes the surface has a radius of curvature R ∼ 1.5 nm and mean square vertical deviation (i.e., roughness) equal to ∼1.12 nm (see Supporting Information). Note that the typical roughness of sol−gel ZnO substrates is in the range 5−50 nm.59,60 A direct measurement of the local curvatures is available only in some cases. For example, for sputtered ZnO (with roughness 3 nm)61 the radius of curvature is as small as few nanometers. When generating our models of curved interfaces, we consider only the 010 orientation that has the larger specific adhesion. The hybrid interfaces are obtained by considering different polymer alignment with respect to the rods (tilt angle θ). In all cases the polymer is wrapped around the rods (Figure 5) in order to maximize the interface area and the interaction energy. The interaction energy is partially reduced since a part of it is converted in elastic strain of the polymer. However, this strain cost is compensated by the larger contact area. Similar effects have been found for P3HT on nanostructured titania.46 Our models of P3HT/ZnO curved interface are stable at room temperature, as found in the case of single polymer chains.50 The different orientations of the polymer backbones on the rods correspond to different curvatures κ of the substrate. In fact, the radius of curvature of a polymer chain with tilt angle θ is given by ρ = R/sin2θ = κ−1 (see Supporting Information), as represented schematically in bottom panel of Figure 6. The case θ = 90° gives the maximum curvature R−1 (see top panel of

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CONCLUSIONS We found that the 010 polymer orientation is the most likely on planar ZnO surface due to the stronger electrostatic adhesion. In this interface the temperature does not affect sizably the microstructure while it favors recrystallization in the 100 one. The substrate induces a strong disorder on the polymer films, but their crystallinity on flat ZnO substrates is partially preserved. This is demonstrated by the grazing structure factor revealing crystalline peaks due to backbone for all interfaces. In addition, by generating models of curved substrates consisting of ZnO nanorods, we provide evidence that the local curvature of the substrate, by inducing the bending of the polymer backbones, is the key factor to explain the observed disorder of P3HT films on ZnO. In particular, the structure factor of the polymer films reveals a correlation between the local curvature and the diffraction peak of the backbone. The results of the present work could have practical implications for metal oxide substrates having a strong ionic character, suggesting the possibility to control the molecular order of the film by the curvature of the substrate, for example, by changing its roughness. 4692



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ASSOCIATED CONTENT

S Supporting Information *

(i) Explanation by simple mathematical models of the structure factor analysis and its relation with the polymer crystallinity; (ii) crystallinity of the polymer bulk and of of its surfaces and the analysis of the polymer films on ZnO in periodic and nonperiodic conditions; (iii) model of the energetics of twophase mixed interfaces; (iv) calculation of the roughness for a periodic array of hexagonal nanorods; (v) calculation of the curvature of a cylindrical rod along an arbitrary direction. 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], phone +390706754843 (M.I.S.); email [email protected], phone +390706754868 (A.M.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge G. Malloci for useful discussions and critical reading of the manuscript and C. Caddeo for providing the atomistic models of the single polymer chains on ZnO nanorods. This work has been funded by the Italian Institute of Technology (IIT) under Project Seed “POLYPHEMO” and by the IIT Platform “Computation”. We acknowledge the Regione Autonoma della Sardegna (Project CRP-24978 “Nanomateriali ecocompatibili per celle fotovoltaiche a stato solido di nuova generazione”) and Consiglio Nazionale delle Ricerche (Progetto Premialità RADIUS). We acknowledge Computational Support by CINECA (Italy) through ISCRA Initiative (Project PICO).

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REFERENCES

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Effect of Thermodynamics and Curvature on the Crystallinity of P3HT

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