Effects of Annealing and Residual Solvents on Amorphous P3HT and

Article pubs.acs.org/JPCC

Effects of Annealing and Residual Solvents on Amorphous P3HT and PBTTT Films Domenico Alberga,† Giuseppe Felice Mangiatordi,‡ Luisa Torsi,§ and Gianluca Lattanzi*,† †

Dipartimento di Fisica, Università di Bari “Aldo Moro”, INFN & TIRES, Via Orabona 4, I-70126 Bari, Italy Dipartimento di FarmaciaScienze del Farmaco, Università di Bari “Aldo Moro, Via Orabona, 4, I-70126 Bari, Italy § Dipartimento di Chimica, Università di Bari “Aldo Moro”, Via Orabona 4, I-70126 Bari, Italy ‡

S Supporting Information *

ABSTRACT: Organic thin film transistors (OTFT) are metal−insulator−semiconductor field-effect transistors in which the semiconductor is a conjugated organic material. They are the subject of intense industrial research because their fabrication process is less expensive when compared with inorganic TFTs. Among the others, the organic material mostly employed in their construction consists of two semiconductor polymers, namely poly(3-hexylthiophene) (P3HT) and poly(2,5-bis(3-alkylthiophen-2-yl)thieno[3,2-b]thiophene) (PBTTT). Despite the large amount of experimental efforts in the characterization of the electronic properties of these devices, several questions regarding their morphological arrangement in bulk and at interfaces remain wide open. Here, we report results obtained by classical molecular dynamics simulations of P3HT and PBTTT inspired by OTFT fabrication techniques. In particular, we investigate how the annealing fabrication process and the presence of residual solvent molecules left over after spin coating might modify the morphology and the dynamics of the amorphous phase of these two polymers. Simulations of both polymer deposits at 300 K after annealing show an increase in the number of interdigitation events between the alkyl chains of two polymeric macromolecules; moreover, we find that the increased stability of the π−π stacking is caused by an improved layering of the films, which may account for the better charge transport properties reported in experiments. Our results strongly suggest that thin semiconductor films are required to boost the performances of the devices and that a minimal presence of residual solvent does not alter dramatically the microscopic structure and stability of the polymeric films.

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INTRODUCTION Organic thin film transistors (OTFT) are multilayer field-effect transistors that employ an organic material as the semiconductor active layer. They are the subject of intense industrial research because their fabrication process is less expensive when compared with inorganic TFT and organic electronic in general and thus can be adapted to a wide range of applications, such as organic solar cells, LED, gas sensors.1−4 Two of the most widely used organic materials for their construction consist in two semiconductor conjugated polymers, namely poly(3-hexylthiophene) (P3HT) and poly(2,5-bis(3alkylthiophen-2-yl)thieno[3,2-b]thiophene) (PBTTT). P3HT was one of the first organic semiconductor polymers to display interesting electronic properties while being deposited from the solution and not by thermal evaporation. Recently, however, PBTTT has attracted great attention because of its increased performances: in fact, measures of hole mobility in field effect OTFTs using P3HT as semiconductor yielded a value of 0.1−0.2 cm2 V−1 s−1,5 to be compared with 0.2−0.6 cm2 V−1 s−1 obtained in PBTTT devices with conductive long channels and 1.0 cm2 V−1 s−1 in PBTTT devices with short channels.6,7 OTFTs come in different configurations depending on the position of the three contacts: in the bottom-gate top-contact configuration, we find (starting from the bottom) a silicon © 2014 American Chemical Society

substrate, a dielectric layer (typically SiO2), and the organic semiconductor layer. In such a device, the fabrication protocol consists of a few steps: (1) cleaning of the substrates and masks by sonication, (2) deposition of a polymeric thin film, (3) annealing of the thin film, and (4) contact deposition by vacuum evaporation through a shadow mask. There are different types of deposition techniques depending on the employed polymer size, mass, and solubility. The most used are the vacuum deposition techniques and the solution assisted techniques such as casting and spin-coating. The annealing process improves the quality and semiconductive properties of the film and consists in heating the film followed by cooling. In particular, interdigitation of alkyl side chains, that plays a fundamental role in the conduction and stability of the polymeric film,8 seems largely enhanced after annealing.9 Many experimental and theoretical studies have been carried out to investigate morphological and dynamical effects that influence charge transport properties in such polymers affecting device performances. McChulloch et al.6 found a higher field effect mobility in OTFT employing PBTTT polymers and, Received: November 6, 2013 Revised: March 25, 2014 Published: April 1, 2014 8641

dx.doi.org/10.1021/jp410936t | J. Phys. Chem. C 2014, 118, 8641−8655

The Journal of Physical Chemistry C

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This melting temperature has been also recently found by Poelking et al.23 by MD simulations in the 300−500 K range. Despite the large amount of experimental efforts in the characterization of the electronic properties of these devices, several questions regarding their morphological arrangement and their interface properties remain wide open. Some theoretical studies have been carried out, ranging from quantum ab initio24−28 to coarse grained simulations29 in a wide range of time scales and sizes30−32 but to our knowledge, a theoretical investigation of the polymeric amorphous phase in situations that are close to those imposed by the laboratory fabrication of OTFT devices, is still missing. In this study, we address some of these issues: we employed classical MD simulations first to investigate, at the atomic level, the effects of the annealing process on the morphology of P3HT and PBTTT in the amorphous phase in the bulk and in a slab geometry representing the case of a thin polymeric film deposited on a SiO2 dielectric substrate; then, we highlight the effects of residual solvent molecules left over after spin-coating deposition of these polymeric systems. The results are discussed in the perspective of a possible improvement in OTFT performances.

through atomic-force microscopy (AFM), observed wider crystalline domains in PBTTT films than in P3HT, with increased size after annealing. Kline et al.8 suggest that this difference may originate from the low density of the attached side chains in PBTTT that allows better side chain interdigitation and hence favors three-dimensional ordering on domains of increased size. Do et al.10 applied molecular dynamics (MD) simulations on both polymers above their melting temperatures and found that PBTTT is characterized by higher planarity, closer and more parallel stacking of rings caused by the longer side chains and the presence of thienothiophene rings. Furthermore, Northrup at al.11 and Colle et al.12 found by density functional theory (DFT) calculations that the interdigitation of the side chains is energetically favorable in PBTTT while this effect is negligible in P3HT. More recently Alexiadis et al.13 applied MD simulations to study the crystalline and amorphous phases of P3HT over a wide range of temperatures (225−600 K) and found that the lateral chains of crystalline P3HT adopt a tilted conformation such that the chains do not interdigitate in agreement with diffraction experiments.9 Brocorens et al.14 and Cho et al.15 with quantum calculations and simulations of X-ray experiments found that the interdigitation of PBTTT forms lamellar structures parallel to the substrate. The large crystalline domain and the close packing ensure enhanced charge transport properties. The degree of order does not depend on the side chain length if these are sufficiently long to ensure interdigitation. Kline16 observed that high molecular weight (MW) films of P3HT have higher mobility with respect to low MW ones. Low MW films have a higher degree of crystallinity but lower connectivity between grains that result more isolated. High MW chains with typical length higher than domains, are able to bridge over neighboring grains, thus leading to a higher mobility of the charge carriers in the thin film. Yozawa et al.17 showed with nuclear magnetic resonance (NMR) relaxation experiments on P3HT that side chain motions and the twist of the thiophenes weaken the π−π interactions. Many experimental studies explored the effects of annealing on P3HT and PBTTT thin films. Hugger et al.18 used calorimetry, X-ray spectroscopy (XRS), and AFM to show that annealing P3HT at 225 °C in the liquid crystalline phase improves the polymer crystallinity and aligns its orientation relative to the substrate. Spin-coated films are more disordered due to the rapid formation of the film: the higher mobility of the polymer chains at high temperature allows the crystal to grow in larger grains and orient. Cho et al.19 showed that, after annealing at 150 °C for 10 min, P3HT films increase in crystallinity improving their contact with the electrodes and thus increasing the field effect mobility. Gurau et. al 20 through IR spectroscopy, spectroscopic ellipsometry (SE) and near edge X-ray absorption fine structure (NEXAFS) spectroscopy experiments on P3HT showed that following annealing at 250 °C, above its melting point, and recrystallization at 180 °C there is an increase of backbone order of the film; furthermore it was shown that less aggressive thermal treatments are less effective. Chabinic et al.21 showed with XRS experiments that upon annealing at 180 °C, PBTTT films become highly oriented and more ordered. DeLongchamp et al.22 showed by X-ray diffraction (XRD), IR spectroscopy and UV−visible SE that annealing PBTTT above the mesophase transition temperature TH2 = 158 °C, causes the melting of side chains that recrystallize upon cooling thus preserving an excellent mesophase order and enhanced electrical performances, due to an improved backbone order, π−π stacking and carrier mobility.

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COMPUTATIONAL METHODS We describe here the setup and the computational details for the systems under investigation. P3HT and PBTTT polymers were parametrized following Do et al.10,29 and Marcon and Raos,33 while the parameters provided by the VMD Inorganic Builder plug-in were used to model the SiO2 substrate (see ref 34). The details and the parameters of the used force field are given in the Supporting Information. We simulated two different P3HT systems: the first consists of 60 chains of 12 monomers each (P3HT_12) and the second is composed by 60 chains of 18 monomers each (P3HT_18). As for PBTTT, we studied two systems: the first includes 50 chains of four monomers each (PBTTT_4) and the second 48 chains of six monomers each (PBTTT_6). All systems were studied initially in bulk, by applying periodic boundary conditions (PBC) in three dimensions. The average dimensions of the cell were as follows: 41 × 90 × 51 Å3 (P3HT_12), 65 × 103 × 41 Å3 (P3HT_18), 51 × 82 × 47 Å3 (PBTTT_4) and 111 × 56 × 45 Å3 (PBTTT_6). The initial configurations were obtained starting from an ordered structure and running a first NPT simulation at a temperature of 800 K which is well above the polymer melting point. Subsequently all systems were deposited on a model crystalline SiO2(100) dielectric substrate, as used in OTFT fabrication, and simulated in a slab geometry with two-dimensional PBC to mimic a polymeric thin film. For the hybrid interactions between the polymer and the substrate we used the typical nonbonded interactions (sum of Coulomb and Lennard-Jones contributions).35−37 Substrate atoms were held fixed during the simulations as in ref 34. The model used for the simulations was validated using the procedure adopted by Melis et al.35 All simulations were performed using the NAMD package38 and the trajectories analyzed using VMD39 and Tcl scripts developed in our computational laboratory. The simulation protocol consisted in NPT sampling for bulk systems and NVT sampling for slab geometries at 300 K, an annealing protocol, and a further sampling at 300 K after annealing. We studied two annealing protocols: the first from 300 K up to 550 K and the second from 300 to 400 K. The 550 K annealing temperature was chosen because it is well above the melting temperature of P3HT40 and PBTTT41 (≈500 K): in this way the annealing process drives the systems above the melting point but close enough so that, 8642



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Figure 1. Average mass density profiles in polymer films before (blue line) and after annealing (red line) at 400 K. The polymeric films consist of (a) P3HT chains with 12 monomers, (b) P3HT chains with 18 monomers, (c) PBTTT chains with four monomers, and (d) PBTTT with six monomers. In the bulk zone (z ≈ 10 Å and z ≈ 30 Å) the density oscillates around 1.1 g/cm3, a value that is comparable to experimental measurements.50−52 Annealing increases the layering of the polymers, in particular for PBTTT. This effect might explain the improved performances of PBTTT devices after annealing reported in the experiments.

although structural properties inevitably change, the material does not lose all the characteristic features of the solid. The annealing temperature of 400 K is closer to that used in the experimental protocols. All NPT simulations were performed at 1 atm. NVT and NPT ensembles were sampled using the Langevin thermostat and a Nosè−Hoover Langevin barostat. A cutoff was applied to van der Waals interactions at 12 Å using a switching function. Following Do et al.,10 the time steps used were 1.6 fs for P3HT and 1.3 fs for PBTTT systems. The trajectories before and after annealing were sampled after an equilibration phase and the total sampling time was 26 ns for P3HT and 23 ns for PBTTT systems. The annealing protocol consisted in a first heating phase in which the temperature was increased from 300 K up to 550 K (400 K) in steps of 25 K every 1.2 × 105 steps, an equilibration run at 550 K (400 K) of 6 × 106 steps and a final cooling phase from 550 K (400 K) to 300 K in steps of 25 K (10 K) every 1.2 × 105 steps. For systems with higher monomer numbers and for slab geometries, only the annealing protocol up to 400 K was performed. Static and dynamic properties before and after annealing were calculated on equilibrium trajectories produced in the NPT or NVT ensemble. The equilibrium condition was ensured by verifying that energy and volume fluctuated around

average values: for example the plot of the total volume of the simulation cell within the first 12 ns of the simulations shows that the volume equilibrates in less than 1 ns of simulation in all cases (data in Figure S2 of Supporting Information). We investigated also how typical solvents used in OTFT fabrication affect the morphological properties of P3HT and PBTTT bulk phases. To this aim, we added chloroform molecules to the P3HT bulk system with 1:10 and 1:100 molar ratio (polymer molecules: solvent molecules) corresponding to a solute weight fraction of 0.944 and 0.626 respectively and chlorobenzene and 1,2-dichlorobenzene for PBTTT with the same molar ratios (solute weight fraction of 0.958 and 0.694 for 1:10 and 1:100 chlorobenzene and of 0.946 and 0.635 for 1:10 and 1:100 1,2-dichlorobenzene). Solvents were parametrized using the OPLS-AA force field.42 The starting configurations were obtained by placing randomly the solvent molecules in a frame chosen at random from the previously equilibrated amorphous pure systems avoiding possible clashes between solute and solvent molecules. The systems were heated at 550 K and then equilibrated in the NPT ensemble at 300 K with the same simulation parameters described above with a total sampling time that varied according to the system sizes. 8643



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Table 1. Calculated Degree of Interdigitation I in the Bulk before and after Annealing

VALIDATION OF THE MODEL The used chemical model and the force field parameters were validated by computing the polymer−substrate adhesion energy, calculated following ref 35. A thiophene ring was placed above the substrate at a distance of about 1 nm from its surface obtaining a periodic box of dimensions 19.912 × 19.912 × 30 Å3. Then a low-temperature MD run (100 ps at T = 10 K) was performed, followed by a geometry optimization with the conjugate gradient algorithm. The adhesion energy was obtained from the difference between the total energy of the final configuration and the sum of the total energy given by the optimization of the thiophene and substrate isolated. The obtained value, equal to 0.36 eV, is comparable to that found by Melis at al. for thiophene/TiO2 system (0.52 eV).35 To obtain a further confirmation of the validity of our model we also performed a density functional theory (DFT) based investigation. All calculations were performed with the CP2K/ Quickstep package43 using a hybrid Gaussian and plane wave method. Notably, a DFT geometry optimization of the same systems (i.e., isolated thiophene, isolated substrate and final configuration) was carried out at the PBE/TZVP level of theory44 using GTH pseudopotentials45 together with a 400 Ry plane wave cutoff. Dispersion forces were taken into account with the Grimme DFT-D3 method.46 Since CP2K calculations are based on a mixed plane-wave and atom-basis centered approach, they are not significantly affected by the BSSE (correlated only to the atom centered basis set approximation and hence not taken into account here).47,48 This calculation returned an adhesion energy value of 0.31 eV, hence indicating a general agreement between classical and DFT based adhesion energy (difference of about 14%) and again confirming the robustness of our model.

system

I

n

⟨a⟩ (Å)

P3HT_12 before annealing P3HT_12 after annealing at 550 K P3HT_12 after annealing at 400 K P3HT_18 before annealing P3HT_18 after annealing at 400 K PBTTT_4 before annealing PBTTT_4 after annealing at 550 K PBTTT_4 after annealing at 400 K PBTTT_6 before annealing PBTTT_6 after annealing at 400 K

0.351 ± 0.017 0.356 ± 0.017 0.343 ± 0.017 0.336 ± 0.016 0.351 ± 0.017 0.396 ± 0.017 0.397 ± 0.017 0.387 ± 0.017 0.394 ± 0.017 0.384 ± 0.017

5485 4777 6022 8042 7810 13 434 12 271 17 961 21 414 20 912

6.0 6.0 6.0 6.0 6.0 11.8 12.1 12.1 11.8 12.0

Table 2. Degree of Interdigitation I for Simulated Polymer Films before and after Annealing system

I

n

⟨a⟩ (Å)

P3HT_12 before annealing P3HT_12 after annealing at 400 K P3HT_18 before annealing P3HT_18 after annealing at 400 K PBTTT_4 before annealing PBTTT_4 after annealing at 400 K PBTTT_6 before annealing PBTTT_6 after annealing at 400 K

0.353 ± 0.017 0.344 ± 0.016 0.343 ± 0.017 0.334 ± 0.016 0.392 ± 0.016 0.400 ± 0.018 0.379 ± 0.018 0.383 ± 0.017

6249 6043 7879 9464 14 965 15 126 21 581 22 957

6.0 6.0 6.0 6.0 11.9 12.0 11.4 11.5

Table 3. Nematic Order Parameter for P3HT and PBTTT in Bulk

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RESULTS AND DISCUSSION Simulated Annealing. We defined several measurable quantities to characterize the morphological and dynamic

system

P2 (TH)

P2 (TT)


0.103 ± 0.011 0.093 ± 0.008 0.053 ± 0.007 0.107 ± 0.008 0.103 ± 0.005 0.059 ± 0.009 0.124 ± 0.009 0.054 ± 0.009 0.299 ± 0.005 0.298 ± 0.007

0.087 ± 0.019 0.111 ± 0.016 0.067 ± 0.014 0.262 ± 0.011 0.273 ± 0.010

substrate/polymer interface and directed normally to the substrate. Mass Density Profile in Polymeric Films. The mass density profile for slab geometries49 ρ(z) was calculated by partitioning the simulation cell into 1 Å wide-bins along the zdirection, summing the masses of atoms in each bin and dividing by the partition volume. We report in Figure 1 the calculated density profiles, averaged over the sampled trajectories, before and after annealing. All profiles display three zones in which the film can be divided: (1) an interface zone between z = 0 Å and z ≈ 10 Å with high-density peaks caused by the interactions between the polymeric chains and the substrate atoms; (2) a bulk zone between z ≈ 10 Å and z ≈ 30 Å where the density oscillates around 1.1 g/cm3, a value that is comparable to experimental measurements50−52 performed at 20 °C for high molecular weight samples; (3) an interface zone between z ≈ 30 Å and z ≈ 40 Å where ρ(z) decreases to zero (vacuum). All profiles present an oscillatory behavior, with a high density at the interface polymer/substrate; the oscillations are damped in the bulk zone, where the polymers appear to be mostly intertwined. This

Figure 2. Degree of interdigitation: â1 and â2 are the unit vectors of the side chains along the head−tail direction taken from the polymer backbone, d⃗ is the vector distance between a side chain terminal methyl group and the segment joining the terminal methyl groups of two neighboring side chains.

properties of the polymeric systems before and after the simulated annealing process. For measures involving slab geometries the z-axis was chosen with the origin in the 8644



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Figure 3. Nematic order parameter profiles P2(z) in P3HT_12 (a) and PBTTT_4 TH films (b) before (blue lines) and after (red lines) annealing at 400 K. Annealing does not seem to have any clear effect on this parameter and hence on the orientation of the rings.

Interdigitation of Alkyl Side Chains. To quantify the interdigitation of alkyl side chains and investigate its behavior upon annealing, we defined the degree of interdigitation I, as follows: ⎛ a ̂ + a 2̂ ⎞ 1 ⎟ I = d ⃗⎜ 1 ⎝ 2 ⎠ ⟨a⟩

where, as depicted in Figure 2, â1 and â2 are the unit vectors along the side chains considered in the thiophene-methyl direction starting from the polymer backbone; d⃗ is the vector distance between the side chain terminal methyl group and the segment joining the terminal methyl groups of two neighboring side chains; ⟨a⟩ is the average length of the side chain. The dot product allows to separate two situations: when the methyl group lies between the two side chains, the polymers are interdigitated and the dot product is positive; otherwise it is negative and its value is not counted. The division by ⟨a⟩ renders I a dimensionless quantity. An interdigitation event is also restricted to the cases in which |d| < ⟨a⟩ and the angle between d⃗ and the side chain unit vector in the thiophene-methyl direction (defined as well as â1 or â2 in Figure 2) containing the methyl group is between 135 and 225 degrees. Values of I close to 1 correspond to a high degree of interdigitation, while I = 0 corresponds to an absence of interdigitation. We calculated the average of I on 200 equally spaced frames for the simulated systems: the results are reported in Table 1, for bulk systems, and in Table 2, for polymer films, along with the number of interdigitation occurrences, n, and ⟨a⟩. The reported values of n in the bulk show that interdigitation occurs more frequently in PBTTT rather than in P3HT: this is counterintuitive because the number of side chains in P3HT is 1.8 times higher than in PBTTT. However, this is in agreement with Do et al.10 and can be explained by the fact that the spacing imposed by thienothiophenic rings allows an increased free volume for the side chains. Interestingly, n decreases after annealing short P3HT and PBTTT polymer chains at 550 K, thus suggesting a slight loss of interdigitation, while it increases after annealing at 400 K especially for short PBTTT chains. Annealing does not seem to have any relevant effect on long polymer chains in the bulk: however, a slight increase of n is observed in polymer films (Table 2), especially for longer polymer chains, in agreement with experimental results.22,56

Figure 4. Snapshot of an amorphous P3HT film on the SiO2 substrate (in red and orange). Thiophenic rings are depicted in licorice representation. The first layers (in blue) display a higher degree of order than the rest of the film. Moreover, the order decreasing from the substrate to the free surface, as clearly reported in Figure 3

Table 4. Dynamic Order Parameter for P3HT and PBTTT in Bulk system

S (TH)

S (TT)


0.761 ± 0.013 0.852 ± 0.008 0.820 ± 0.009 0.805 ± 0.013 0.840 ± 0.006 0.819 ± 0.012 0.852 ± 0.007 0.848 ± 0.010 0.837 ± 0.011 0.870 ± 0.006

0.503 ± 0.019 0.572 ± 0.012 0.569 ± 0.018 0.599 ± 0.015 0.637 ± 0.011

(1)

behavior suggests a tendency of the polymeric chains to arrange in layers: this tendency is stronger in the proximity of the substrate and is enhanced after the annealing process, in particular in PBTTT, in agreement with recent experimental results.6,19 The distance between two adjacent peaks corresponds to an interlayer distance of 4 Å, a value that is close to the π−π stacking distance of 3.8 Å reported in experiments on crystalline P3HT.53 The presence of an ordered layered organization in polymeric thin films (particularly evident in PBTTT) is likely to promote charge transport and hence might explain the improved performance of the devices after annealing.6,21,22,54,55 This effect seems independent of the number of monomers as shown in Figure 1. 8645



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Figure 5. Dynamic order parameter (S) profiles before (blue and dark green lines) and after (red and pale green lines) annealing at 400 K for P3HT_12 (a), P3HT_18 (b), PBTTT_4 (c), and PBTTT_6 (d). Annealing stabilizes the orientation of the rings, except for TT in PBTTT close to the interface with vacuum.

rings; by definition P2 is the largest eigenvalue of the following tensor:

Table 5. Three-Dimensional Diffusion Coefficient in Polymer Films polymer

D (10−9 cm2/s)

P3HT_12 before annealing P3HT_12 after annealing at 400 K P3HT_18 before annealing P3HT_18 after annealing at 400 K PBTTT_4 before annealing PBTTT_4 after annealing at 400 K PBTTT_6 before annealing PBTTT_6 after annealing at 400 K

1.585 ± 0.009 0.385 ± 0.007 0.663 ± 0.005 0.342 ± 0.003 0.952 ± 0.003 0.524 ± 0.005 0.748 ± 0.005 0.233 ± 0.006

Q αβ =

1 N

N

⎛3 1 ⎞⎟ ⎜ û û δαβ iα iβ − 2 2 ⎠

∑⎝ i=1

(2)

where N is the number of rings and ⟨ ⟩ denotes a time average. P2 = 1 indicates perfect nematic order with all unit vectors parallel to each others, while P2 = 0 indicates a total absence of order and a fully isotropic ring orientation. A high P2 value would reveal the existence of a preferred orientation of the rings, given by the eigenvector with eigenvalue P2. A high P2 would also imply an improved π−π stacking and hence a higher overlap of the π orbitals that would, in turn, lead to a higher interchain charge carrier mobility and improved device performances. Table 3 reports the P2 values for simulated bulk systems for thiophene (TH) and thienothiophene (TT) rings. Annealing at both 550 and 400 K does not seem to have a dramatic effect on P2: in the best cases (PBTTT), it implies a slight increase of P2, while in the worst case scenario (P3HT) we find a slight decrease of P2. However, it is important to notice that P2 in bulk systems is quite low, thus implying a certain degree of quenched randomness in the orientation of the rings. In polymer films, the z-profile of P2 is obtained by partitioning the simulated system along the z-direction in overlapping slabs of

In polymer films, interdigitation increases, after annealing, near the surface, because at the polymer/vacuum interface the chains have enough freedom to reorder themselves during the process, while at the substrate/polymer interface and in bulk regions the chains are more packed and the effect of annealing is rather weak and similar to what already found in the bulk (Table 1). These results concur to suggest that an increase in the polymeric film stability and consequently an improvement in the performances of OTFT devices may be obtained by decreasing the film thickness, thus reducing the size of the bulk region. Nematic Order Parameter. The nematic order parameter23 P2 is defined in terms of the unit vectors û normal to the polymer 8646



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Figure 6. Orientation of the main chain rings G2(z) in P3HT_12 (a) and PBTTT_4 TH (b) polymer films before (blue line) and after (red line) annealing at 400 K.

S is slightly higher after annealing in all cases and its top value increases with the annealing temperature thus revealing an increased stability of the polymeric bulk systems after annealing. The values of S for TT rings are lower than the corresponding ones for TH rings because the TH torsions are more hindered than those of TT, due to the presence of the side chains.10 In Figure 5, we report the z-profile of S in the polymer films (P3HT_12 (a), P3HT_18 (b), PBTTT_4 (c), and PBTTT_6 (d)), obtained as described for P2. Also in this case, S is higher near the substrate and decreases with z reaching its lowest value near the surface. The polymer chains are more densely packed on the substrate and thus the orientation of the rings on the substrate is characterized by lower fluctuations when compared to the surface. After annealing, S slightly increases for all values of z thus indicating an increased stability of the ring orientation throughout the films, except for the TTs in PBTTT, Figure 5d, where the enhanced freedom of the rings induces, after annealing, a slight decrease of S close to the interface with vacuum. Ring Orientation in Polymer Films. We investigated the orientation of the rings by defining the quantity:57

Table 6. Three-Dimensional Diffusion Coefficient Calculated in Bulk polymer

D (10−7 cm2/s)


2.169 ± 0.009 0.254 ± 0.004 1.028 ± 0.009 3.361 ± 0.009 0.923 ± 0.005 1.812 ± 0.008 2.623 ± 0.011 0.712 ± 0.009 0.501 ± 0.008 2.689 ± 0.007

width δz = 4 Å equally spaced by 1 Å and calculating P2 within each bin. The calculation is performed at values of z for which ρ(z) is greater than half of its bulk value, in order to increase the statistics within each bin. Calculated profiles for P3HT_12 (a) and PBTTT_4 TH (b) are showed in Figure 3 (the graphs for other simulated systems are reported in Supporting Information): P2 is higher near the substrate, reaches a minimum in the bulk and slightly increases on the surface. This trend is clearly evident in Figure 4 where the thiophenic rings in the P3HT film are more ordered in the first two layers (in blue) and the degree of order decreases approaching the surface. The observed minimum is not relevant since the increase in P2 is quite weak, thus confirming that the film is substantially in a disordered state close to the interface with vacuum. As for PBTTT, although there is no such minimum, the trend is quite similar (order close to the substrate, disorder anywhere else). Annealing does not seem to have any effect on this parameter and hence on the orientation of the rings. Dynamic Order Parameter. The dynamic order parameter23 S for unit vectors normal to the chain rings is defined as S=

1 N

N

⎛3 ̂ 2 1 ⎞⎟ ⎜ (U · u ̂ ) − i i 2 2⎠

∑⎝ i=1

G2(z) =

1 ⟨3 cos2(θ(z)) − 1⟩ 2

(4)

where θ is the angle between the normal to the ring and the zaxis. G2(z) = −0.5 for rings oriented perpendicular to the substrate and G2(z) = 1 for rings oriented parallel to the substrate, and intermediate values of G2(z) correspond to a random ring orientation. G2(z) profiles are reported in Figure 6 for P3HT_12 (a) and PBTTT_4 TH (b). The plots show that the rings tend to orient in the direction parallel to the substrate with a preferred face-on orientation near it, that tends to become random in the bulk and on the surface. Meredig et al.,58 on the contrary, found an edge-on orientation starting from crystalline P3HT deposited on the same surface but in amorphous phase. The edge-on configuration, found also in experiments, is typical for polymers in the crystalline phase. In our amorphous phase systems the interaction with the substrate forces the chains to assume a prevalent face-on orientation close to it and this preferred orientation is lost away from the substrate, as shown in Figure 4. In this respect, our findings are in agreement with the conclusions of Meredig et al.,58 stating that a perfectly ordered substrate perturbs the ideal edge-on P3HT orientation. There are

(3)

where Û i = ⟨ûi⟩ and ⟨ ⟩ denotes a time average, as before. S goes from 1 to −0.5: S = 1 implies a constant ring orientation, while S < 1 indicates that the orientation is changing over time. The S values in the bulk are reported in Table 4. 8647



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Figure 7. Two-dimensional diffusion coefficient in the xy plane for P3HT_12 (a), P3HT_18 (b), PBTTT_4 (c), and PBTTT_6 (d) before (blue dots) and after (red dots) annealing at 400 K.

no substantial differences in the orientation of the rings between the two polymers: here, the amorphous nature of the studied system seems to prevail on the specific interactions that lead to a preferred orientation in the crystal phase. Self-Diffusion Coefficient. We calculated the three-dimensional self-diffusion coefficients of the polymers from the rootmean-square displacement of the center of mass of the chain: RMS(t ) =

1 N

RMS(t , z) =

i=1

N

∑ [R⃗ i , cm(t + t0) − R⃗ i , cm(t0)]2 δ(zi(0) − z) i=1

= 4Dxy(z)t

(6)

Here R⃗ i,cm is the xy projection of the position vector of the center of mass of the chain. The z-partitioning of the film was performed as described for P2(z). The obtained graphs are reported in Figure 7 for P3HT_12 (a), P3HT_18 (b), PBTTT_4 (c), and PBTTT_6 (d). Dxy(z) is smaller near the substrate, due to close packing, and increases almost linearly with z reaching its peak near the surface where the low density allows the chains to move with more freedom. After annealing, Dxy(z) decreases for short P3HT and PBTTT polymer chains but does not appreciably decrease for systems with higher chain lengths. By comparison, the overall three-dimensional self-diffusion coefficient decreases for all the investigated polymer films after annealing (5). In the bulk (6), annealing affects diffusion, by decreasing the value of D in P3HT. However, this result does not hold for PBTTT: in this case, a decrease of D is observed only when annealing is performed below the melting temperature for short polymer chains. The Effect of Residual Solvent. Residual solvent in polymeric thin films after spin coating may affect the morphological properties and structural order of the systems. In this section, we investigate the effects of residual solvent molecules at different concentration ratios on several calculated

N

∑ [R⃗ i , cm(t + t0) − R⃗ i , cm(t0)]2

1 N

(5)

where the angle brackets denote an ensemble average over all values of the time origin t0, N is the number of chains, and R⃗ i,cm is the position vector of the center of mass of the chain. The selfdiffusion coefficient is estimated by applying Einstein’s relation and thus fitting RMS(t) with the function f(t) = 6Dt. The values calculated from the fit are reported in Table 5 for polymer films, and in Table 6, for bulk systems. The linear correlation coefficient r2 is above 0.98 in all cases. D in polymer films is smaller than in the bulk by about 2 orders of magnitude, thus implying that the substrate exerts a frictional force on the polymeric chains. This frictional effect is even more apparent by calculating the z-dependent two-dimensional diffusion coefficient in the xy plane Dxy(z) obtained by the following equation: 8648



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Figure 8. Radial distribution functions for thiophenes (site pair TH−TH) in P3HT (a) and PBTTT (b), for thiophenes and the terminal methyl group of the side chains (site pair TH−CH3) in P3HT (c), and for thienothiophenes and the analogous terminal methyl group (site pair TT−CH3) in PBTTT (d). The results are obtained at different solvent concentrations.

Table 7. Degree of Interdigitation of P3HT and PBTTT Polymers in Solution polymer

solvent

P3HT P3HT P3HT PBTTT PBTTT PBTTT PBTTT PBTTT

none chloroform chloroform none chlorobenzene chlorobenzene 1,2-dichlorobenzene 1,2-dichlorobenzene

ratio 1:10 1:100 1:10 1:100 1:10 1:100

n

⟨a⟩ (Å)

5485 4420 1376 13 434 16 523 5713 13 111 5922

6.0 6.0 6.0 11.8 12.3 12.5 12.3 12.6

the corresponding terminal methyl groups (site pair TT−CH3) in PBTTT (d). We observe a decrease of correlation and order in systems with solvent ratio 1:100. In the TH−TH distribution of P3HT, the first peak at r ≈ 6 Å decreases from the pure system to the 1:100 system. In PBTTT the first peak of the TH−TH distribution decreases and is shifted to higher values of r, while the secondary peaks at r ≈ 10 Å and r ≈ 14 Å (present in bulk) disappear when the solvent is added. A similar behavior is observed in TH−CH3 and TT−CH3 distributions, thus pointing at a general loss of medium and long-range order in the presence of solvent. However, at 1:10 concentration, we do not report any significant difference from the pure case, thus suggesting that such a low fraction of residual solvent molecules does not perturb the structural properties of the polymer sample.

quantities. The density does not significantly change in 1:10 systems and is 1.2 g/cm3 in 1:100 systems. Radial Pair Distribution Function. The radial pair distribution function is defined as the ratio g (r ) = N (r )/gI (r )

I 0.351 ± 0.017 0.350 ± 0.017 0.327 ± 0.016 0.396 ± 0.017 0.382 ± 0.017 0.364 ± 0.016 0.359 ± 0.017 0.370 ± 0.016

(7)

where N(r) is the number of occurrences of the radial distance r between pairs of particles and gI(r) is the radial distribution function of an ideal gas with density ρ: gI(r) = 4πr2ρ. With this normalization g(r → ∞) = 1. Figure 8 reports g(r) for the centers of mass of thiophenes (site pair TH−TH) in P3HT (a) and PBTTT (b) systems, for thiophenes and the terminal methyl groups of the side chains (site pair TH−CH3) in P3HT (c), and for thienothiophenes and 8649



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Figure 9. Sulfur−carbon−carbon−sulfur dihedral distribution P(θ) between thiophene rings (TH−TH) in P3HT (a) and PBTTT systems (b) and between thiophene and thienothiophene rings (TH−TT) in PBTTT systems (c) at different solvent concentrations.

Interdigitation of Alkyl Side Chains. As expected, solvent molecules interact with the alkyl side chains of the polymers, thus reducing interdigitation. The degree of interdigitation I is reported in Table 7. For both P3HT and PBTTT, I slightly decreases with increasing solvent concentration, but the number of interdigitation events displays a remarkable decrease especially at 1:100 concentration. This behavior suggests that the solvent does not have a dramatic effect on the quality of interdigitation, but just on the number of occurrences of interdigitation events. However, the presence of the solvent reduces the structural stability of the polymeric systems and will therefore affect negatively their charge transport properties. Notably, there are no significant differences between purified and 1:10 systems: in 1:10 PBTTT/ chlorobenzene solution, the solvent seems even to favor the realization of interdigitation events. Dihedral Distributions. We measured the thiophene− thiophene (TH−TH) sulfur−carbon−carbon−sulfur dihedral distribution P(θ). The results are reported in Figure 9: compared with the purified sample, the trans configuration is more populated in 1:100 systems thus indicating an increase in the planarity of the polymeric backbones. This behavior is due to the electrostatic repulsion between the negative partial charges of the thiophenic sulfur atom and the chlorine: indeed, this interaction is minimized in the trans configuration as exemplified in Figure 10.

Figure 10. Trans configuration of a PBTTT chain in 1,2dichlorobenzene. PBTTT is rendered in CPK and the solvent in red licorice representation.

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Figure 11. Root mean square displacement of the centers of mass of the chains for P3HT (a) and PBTTT (b) in solution. The presence of solvent at low concentrations tends to stabilize the polymers thus reducing the diffusion coefficient.

conduction properties: however, small concentrations of solvent impurities reduce the diffusion and would probably even help to stabilize the microscopic film structure thus improving its morphological order and stability. Orientation Dynamics. Following a previous study on P3HT,49 we quantified the rate of reorientation of the chain endto-end vector by calculating its autocorrelation function as

Table 8. Diffusion Coefficient of P3HT and PBTTT in Solution with Different Solvent Concentrations polymer

solvent

ratio



1:10 1:100 1:10 1:100 1:10 1:100

D (10−7 cm2/s) 2.169 ± 0.009 1.952 ± 0.006 6.426 ± 0.010 1.668 ± 0.008 0.974 ± 0.006 3.521 ± 0.010 0.997 ± 0.007 1.780 ± 0.002

C2(t ) =

1 2

3

1 N

N

∑ [R⃗ i(t + t0) − R⃗ i(t0)]2

−1 (8)

i=1

where N is the total number of chains, Ri(t) is a unit vector along the end-to-end direction of chain i, and the angle brackets represent ensemble averages performed over different initial times t0. The reorientation (relaxation) time of a chain was estimated by fitting the decay of C2(t) with the Kohlrausch− Williams−Watts (KWW) equation59

The PBTTT thiophene−thienothiophene (TH−TT) distribution (Figure 9c) does not change with increasing solvent concentrations: although the electrostatic repulsion between sulfur and chlorine is still present, the increased freedom in the rotation of the thienothiophene rings10 allows a higher number of transitions between the cis and trans configurations within the dynamics thus compensating for the solvent effects. Diffusion Coefficient. In Figure 11 we report the RMS(t) of the centers of mass of the polymers for the systems under investigation. The values calculated for D, for which the linear correlation coefficient r2 is above 0.98 in all cases, are reported in Table 8: apparently D decreases when a small quantity of solvent (1:10 concentration) is added and increases as expected when the solvent concentration is higher (1:100). These results suggest that high solvent concentrations promote diffusion by destabilizing the film structure and thus limiting its charge

C KWW (t ) = exp( −(t /t )β )

(9)

where τ is the relaxation time and β is a measure of the width of the distribution of the specific relaxation processes expressed by C(t): it is equal to unity for a single exponential and decreases as the width of the distribution becomes broader. Moreover, to characterize the cooperative chain dynamics, the correlation time τc was calculated as τc =

∫0

∞

exp( −(t /τ )β ) dt = τ

Γ(1/β) β

(10)

Table 9. Results of the Fit of C2(t) with Eq 9 for P3HT and PBTTT in Solution polymer P3HT P3HT P3HT P3HT 550 K PBTTT PBTTT PBTTT PBTTT PBTTT PBTTT 550 K

solvent

ratio

none chloroform chloroform

1:10 1:100

none chlorobenzene chlorobenzene 1,2-dichlorobenzene 1,2-dichlorobenzene

1:10 1:100 1:10 1:100

8651

τ (ns)

β

τc (ns)

∼ (1.1 ± 0.2)108 ∼2300(±100) 5.41 ± 0.04 7.50 ± 0.03 ∼ (2.8 ± 0.5)108 ∼8300(±400) 19.0 ± 0.5 ∼18400(±3000) 55.7 ± 1.2 22.0 ± 0.3

0.298 ± 0.005 0.546 ± 0.002 0.985 ± 0.001 0.697 ± 0.007 0.296 ± 0.001 0.504 ± 0.002 0.705 ± 0.003 0.482 ± 0.003 0.717 ± 0.005 0.662 ± 0.007

∼1.0·109 ∼3900 5.44 9.53 ∼3.0·109 ∼16 300 23.9 ∼39 400 68.9 29.5



Article

Table 10. Results of the Fit of CTAFC(t) with the KWW Eq9 for P3HT and PBTTT in Solution polymer P3HT P3HT P3HT P3HT 550 K PBTTT PBTTT PBTTT PBTTT PBTTT PBTTT 550 K PBTTT PBTTT PBTTT PBTTT PBTTT PBTTT 550 K

solvent

ratio

none chloroform chloroform

1:10 1:100


1:10 1:100 1:10 1:100


1:10 1:100 1:10 1:100

dihedral type

τ (ns)

β

τc (ns)

TH−TH TH−TH TH−TH TH−TH TH-TH TH−TH TH−TH TH−TH TH−TH TH−TH TH−TT TH−TT TH−TT TH−TT TH−TT TH−TT

∼6000(±300) 89.5 ± 1.5 1.24 ± 0.04 0.350 ± 0.005 ∼70000(±1000) ∼860(±50) ∼420(±30) ∼2400(±100) ∼110(±10) 3.16 ± 0.04 43.1 ± 1.0 10.4 ± 0.6 0.377 ± 0.002 15.5 ± 0.2 0.962 ± 0.007 0.031 ± 0.001

0.338 ± 0.002 0.470 ± 0.002 0.436 ± 0.005 0.855 ± 0.013 0.401 ± 0.002 0.790 ± 0.002 0.525 ± 0.003 0.638 ± 0.014 0.830 ± 0.006 0.940 ± 0.002 0.494 ± 0.004 0.459 ± 0.003 0.386 ± 0.003 0.587 ± 0.005 0.382 ± 0.003 0.549 ± 0.008

∼34 000 ∼200 3.30 0.379 ∼230 000 ∼1000 ∼770 ∼3300 ∼120 3.26 88.2 24.7 1.39 24.0 3.65 0.053

Table 11. Nematic Order Parameter for P3HT and PBTTT in Solution polymer

solvent



ratio 1:10 1:100 1:10 1:100 1:10 1:100

P2 (TH)

P2 (TT)

0.103 ± 0.011 0.103 ± 0.016 0.054 ± 0.017 0.059 ± 0.009 0.160 ± 0.011 0.098 ± 0.020 0.127 ± 0.012 0.084 ± 0.015

0.087 ± 0.019 0.162 ± 0.023 0.094 ± 0.025 0.122 ± 0.017 0.088 ± 0.021

Table 12. Dynamic Order Parameter for P3HT and PBTTT in Solution system

solvent



ratio 1:10 1:100 1:10 1:100 1:10 1:100

where Γ is the gamma function. The values of τ, β, and τc are reported in Table 9 for the simulated systems. The estimated correlation times differ by several orders of magnitude from purified systems to 1:100 systems. In the presence of solvent, the values of τc are similar to those found for purified systems in the liquid phase at 550 K and fall within the time-limits of our MD simulations. This is due to the enhanced freedom experienced by the polymeric chains when immersed in the solvent that allows for a rapid chain reorientation. At room temperature and without solvent, the polymers reach a viscous state characterized by higher τc values, in which their end-to-end orientation will change only on the microsecond time scale or even more. Whether this state will eventually evolve into an ordered microcrystal phase remains questionable and cannot be addressed by the current molecular dynamics simulation techniques at the atomistic level of detail. Conformational and Torsional Dynamics. We investigated also the conformational and torsional dynamics by calculating the torsional angle autocorrelation function (TACF) as49

PTACF(t ) =

S (TH)

S (TT)

0.761 ± 0.013 0.631 ± 0.030 −0.181 ± 0.023 0.819 ± 0.012 0.739 ± 0.016 0.279 ± 0.042 0.762 ± 0.016 0.444 ± 0.033

0.503 ± 0.019 0.312 ± 0.017 −0.220 ± 0.033 0.433 ± 0.018 −0.125 ± 0.027

⟨cos ϕ(t + t0) cos ϕ(t0)⟩ − ⟨cos ϕ(t0)⟩2 ⟨cos ϕ(t0) cos ϕ(t0)⟩ − ⟨cos ϕ(t0)⟩2 (11)

where the brackets indicate an ensemble average over all torsions and all initial times t0 and ϕ(t) is the torsional angle at time t. We calculated PTACF(t) for the dihedral S−C−C-S angle between thiophenes (TH−TH) and between thiophenes and thienothiophenes (TH−TT): the autocorrelation functions were fitted with the KWW eq 9. Estimated values for τ and β are reported in Table 10. This case is very similar to what already discussed for the orientational dynamics, thus adding to the previous picture that the solvent has an overall effect in accelerating not only the chain reorientational dynamics but also its conformational and torsional dynamics, although, in this case, some of the estimated correlation times are within the reach of all-atoms MD simulations even in the bulk phase. Nematic Order Parameter. The values of the nematic order parameter P2 are reported in Table 11 for both thiophene (TH) 8652



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and thienothiophene (TT) rings. P2 has the same value in purified and 1:10 P3HT systems, but it decreases with increasing solvent concentration. Surprisingly P2 increases when there is a small concentration of solvent for PBTTT: this suggests that solvent impurities might even improve the π−π stacking of PBTTT rings and is in agreement with our previous observations on the dihedral distributions. Dynamic Order Parameter. The dynamic order parameter S is reported in Table 12: S decreases in the presence of the solvent because the interaction between solvent molecules and the polymeric chains enhances the thermal fluctuations of the rings leading to a less stable π−π stacking. Again the S values in 1:10 systems are similar to those in purified systems thus suggesting that the presence of residual solvent molecules at very low ratios does not affect negatively the charge transport properties of the systems. Also in this case, the values for TT are greater than those for TH, as observed in the bulk without any solvent. Conclusions and Future Plans. In this study, we report results of molecular dynamics simulations applied to two semiconductor polymers used in OTFT fabrication, namely P3HT and PBTTT. Our simulations suggest how the annealing technique helps the polymeric thin films to reach more stable and ordered microscopic configurations, in agreement with known experimental results for both polymers. In particular, we showed that annealing increases the layering of polymer chains in thin films, the interdigitation especially for PBTTT and the stability of π−π stacking. On the basis of this study, we conclude that a better ordering and thus improved charge transport properties might be achieved by annealing films of reduced thickness. Although the molecular dynamics simulations at the atomistic level of detail cannot lead to a thorough exploration of the entire phase space corresponding to the thermodynamic parameters representative of the experimental conditions, our extrapolations from the nanosecond time scales clearly show that the amorphous state in the bulk resembles a viscous phase characterized by a quenched disorder that is the result of the polymeric entanglement. In particular, we found that interdigitation does not improve the π−π stacking in the amorphous phase, while the interaction with the substrate is crucial in determining the degree of order in the polymeric film. Whether this state will eventually evolve into the polymeric microcrystals found in experiments is questionable and is certainly not within the reach for molecular dynamics studies at the atomistic level of detail. However, our study characterizes the amorphous phase in the bulk and in polymeric thin films obtained without any possible bias: it would be interesting, in this respect, to compare our results with those obtained starting from an ordered crystal phase, as in the recent work by Alexiadis et al.13 We remark that the equilibrium crystal structure of these polymers is still a matter of debate, with several proposed morphologies based on different experimental techniques and growing conditions. In addition the size and the morphology of the amorphous structures are even more important, since they affect dramatically the charge transport properties of these polymers. Our simulations, in this respect, provide some starting structures for more detailed quantum calculations that may be helpful to understand how conduction is hindered by the long-range disorder achieved within the time-span of our atomistic simulations. However, it seems evident that the stability provided by π−π stacking and the interdigitation of the alkyl side chains is a key issue in shaping the quality and stability of the morphological order of polymer solutions. In this respect, our study suggests that residual solvent

molecules may contribute to this stabilization: we found that, as expected, individual solvent molecules increase the reciprocal distance between the polymers thus reducing the morphological/orientational order and interdigitation. However, low concentrations of solvent impurities do not affect significantly the morphological properties and might even improve the planarity and stability of the polymeric device. Further experiments on solvents with different chemical properties will definitely prove extremely useful in order to validate this hypothesis. Further studies will be carried out to investigate films of larger size in more realistic situations with the help of optimized coarse grained strategies: in this respect, we believe that a mixed atomistic-coarse grained multiscale model would bridge the gap in time and length scales that still hinders a complete and fruitful comparison between theory and experiments.

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

S Supporting Information *

Force field parameters, volume convergence plot, nematic order parameter profiles P2(z), and ring orientation profiles G2(z). This material is available free of charge via the Internet at http:// pubs.acs.org/. Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the CINECA award HP10CKDPVX, under the ISCRA initiative for the availability of high performance computing resources and support, and Marco Masia, Alessandro Laio, Alessandro Motta, Elia Schneider, and Pietro Faccioli for helpful discussions.

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REFERENCES

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