Atomistic Investigation of the Solubility of 3-Alkylthiophene Polymers in

Article pubs.acs.org/Macromolecules

Atomistic Investigation of the Solubility of 3‑Alkylthiophene Polymers in Tetrahydrofuran Solvent Claudia Caddeo* and Alessandro Mattoni* Istituto Officina dei Materiali (CNR - IOM), Unità di Cagliari, Cittadella Universitaria, I-09042 Monserrato (CA), Italy S Supporting Information *

ABSTRACT: We study the solubility properties of regioregular oligo(3alkylthiophene)s in tetrahydrofuran solvent as a function of their alkyl chains length by an atomistic investigation based on model potential molecular dynamics. We make use of the Flory−Huggins theory that is typically used to study the miscibility of macromolecules and that is here applied for the first time to study the solubility of conjugated conducting polymers in a typical organic solvent. The properties of the isolated solvent and polymer are correctly reproduced, and the calculated solubilities of the oligo(3-alkylthiophene)s in tetrahydrofuran as a function of their side chains lengths are in agreement with available experimental data. Present investigation shows that the atomistic approach based on molecular dynamics is a powerful tool to study the solubility of alkylthiophenes in molecular solvents. determining their performances.32 For example, in solution processed poly(3-hexylthiophene) (P3HT) transistors the field effect mobility is markedly different depending on the polymer miscibility in solvents that affects the polymer degree of crystallinity.33 Another important property depending on the polymer solubility is its ability to blend with other components dispersed in the solvent. For example, the ability of rr-P3ATs to selectively wrap semiconducting carbon nanotubes has been recently demonstrated,34 opening the way to new possibilities to synthesize carbon-based electronics devices. The selectivity is strongly dependent upon the polymer solubility.34 There is a broad class of solvents used for the processing of rr-P3ATs including aromatic compounds such as e.g. toluene and chlorobenzene and nonaromatic ones such as chloroform and tetrahydrofuran (THF). The latter, due to its ability to solvate both polar and nonpolar substances,35,36 is also used to dissolve many electron acceptor materials such as ZnO,37 TiO2,38 and the fullerene derivative phenyl C61 butyric acid methyl ester (PCBM)39 necessary for the production of polymer-based solar cells. At the molecular level, the THF solvent consists of small nonaromatic pentagonal rings formed by one oxygen and four carbons atoms, each saturated with two hydrogens (see Figure 1). The solubility of macromolecules (such as polymers and drugs) has been studied theoretically through atomistic simulations by different groups.40,41 The Flory−Huggins (FH) solution theory42 is the appropriate theoretical framework for studying such problems. It describes the solvent−

1. INTRODUCTION Since the discovery of semiconducting organic polymers in the late 1970s,1 a lot of progress has been made in the field of organic electronics: polymer-based transistors,2,3 light-emitting diodes,4,5 photovoltaic cells,6−8 etc., have been successfully realized with different kinds of polymers, in particular alkylthiophenes (such as poly(3-hexylthiophene), P3HT). Conjugated semiconducting polymers are easy to process and relatively cheap: they can be easily synthesized from solution9 and deposited by standard inkjet printing techniques10 on different substrates. Furthermore, they can be combined with a wide variety of materials, both organic11−13 and inorganic,7,14,15 in order to manufacture novel organic and hybrid functional materials. Among semiconducting polymers, regioregular head-to-tail (HT) poly(3-alkylthiophene)s (rr-P3ATs) have emerged in the field of photovoltaics because of their high charge carrier mobility16 that made possible to achieve very good performances in polymer−fullerene solar cells.17 P3AT polymers have been extensively studied also from the theoretical point of view: their morphological and (opto)electronic properties have been investigated in the pure polymer phase18−22 and in conjunction with organic23−25 and inorganic26−29 materials. P3ATs consist of a conducting backbone made of thiophene rings and alkyl side chains formed by different number of carbon atoms (from methyl to dodecyl).30 The addition of the alkyl chains to the aromatic thiophenes of the backbones critically controls the polymer solubility: it has been experimentally found that rrP3ATs with side chains made of up to 4 carbon atoms are not soluble in common organic solvents.30,31 Since P3AT-based devices are typically synthesized from solution, the polymer solubility plays a crucial role in © XXXX American Chemical Society

Received: June 28, 2013 Revised: August 1, 2013

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dx.doi.org/10.1021/ma401345n | Macromolecules XXXX, XXX, XXX−XXX

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pressure were controlled by the Nosé-Hoover thermostat with relaxation costants f T = 0.5 and f p = 0.1 ps for temperature and pressure, respectively. Molecular dynamics simulations were performed by using the DL_POLY parallel code51(v. 4.03). The solvent was simulated in a box containing 216 molecules. Simulations cells of bulk polymers were built by 16 polymer molecules, each formed by 12 thiophenes. The chains are periodically repeated along the polymer backbone, as to represent ideally infinite chains. As for the mixed phase, finite polymer chains formed by 8 thiophenes have been simulated in a liquid box containing 216 solvent molecules. The starting structures of the finite chains are represented in Figure 1 together with the THF molecule. We use oligomers made of 8 thiophenes since for this length the energy per monomer is close to the limit of an infinite chain.26 All the oligomers were regioregular head−tail (see Figure 1). Both the pure solvent and pure polymer systems have been equilibrated at constant temperature (T = 300 K) and pressure (1 atm) in periodic boundary conditions (PBC) until the volume reached its equilibrium value (the typical annealing was as long as 2.5 ns). After equilibration the simulation cell of the solvent is found to be cubic (as expected since the liquid phase is isotropic) with lateral size ≃3 nm, corresponding to an equilibrium density very close to the experimental value of 0.89 g/cm3. The observables were calculated by averaging during production runs as long as 0.5 ns.

Figure 1. Atomistic models of the THF (left) and of the investigated rr-P3ATs molecules (middle, right). Cyan atoms are carbons, white are hydrogens, yellow are sulfurs, and red is oxygen.

solute interaction through an effective parameter called the Flory−Huggins interaction parameter χFH (see section 2.3). In the literature, the latter has been calculated by atomistic simulations according to two different approaches: (i) an approximate one based on the Hildebrand solubility parameters of the isolated components43 and (ii) a more accurate one based on the evaluation of the enthalpy of mixing by simulating also the mixed phase. The first approach (i) consists of calculating the Hildebrand solubility parameters (defined as the square root of the cohesive energy) of solvent and solute separately (δs, δp) and approximating χFH ∼ (δs − δp)2: the smaller the difference (and thus the interaction parameter), the higher the solubility. This approach has been followed by different authors.44−46 Having the advantage of not requiring the simulation of the mixed phase, this method completely neglects the specific interactions between solute and solvent. Furthermore, it always gives positive values of the Flory− Huggins interaction parameter, while negative values are common in real systems. The more accurate method (ii)47 has been successfully applied to evaluate the solubility of drugs in polymer micelles and other excipients40,41 by means of molecular dynamics simulations. However, such a method has never been applied to calculate the solubility of conjugated conducting polymers in organic solvents. In this work we report a model potential molecular dynamics study of the solubility in THF of rr-oligo(3-alkylthiophenes) as a function of the length of their alkyl chains (ranging from 0 to 12 carbon atoms). In agreement with the available experimental observations, we find that the oligothiophens with side chains made of up to four carbon atoms are not soluble in THF. Theoretical Framework. The rr-P3ATs and the solvent tetrahydrofuran (THF) have been modeled using the Amber force field48,49 that includes both bonding (stretching, bending, and torsional) and nonbonding (van der Waals and Coulomb) contributions. The atomic partial charges were calculated according to the standard AM1-BCC method.50 The details of the charge calculation are described in the Supporting Information. The dispersive (i.e., van der Waals) interactions are described by the sum of two-body Lennard-Jones contributions, with Amber force field parameters. The interactions between solvent and oligomers are modeled as the sum of van der Waals plus Coulomb contributions. The equations of motion of atoms were integrated by using the velocity-Verlet algorithm with a time step as small as 0.5 fs. All the electrostatic contributions were computed by the particle− particle particle-mesh Ewald sum method. Temperature and

2. RESULTS AND DISCUSSION 2.1. Solvent Properties. First of all, we have simulated the pure solvent to test the ability of the force field parametrization to reproduce the liquid density ρ and the vaporization enthalpy ΔHv (i.e., the energy per unit volume necessary to separate molecules into vapor phase). The liquid density can be calculated as ρ=

NmolM m ⟨V ⟩

(1)

where Nmol is the number of molecules in the simulated liquid system (216), Mm is the molecular mass (72.104 amu for THF), and ⟨V⟩ is the average volume calculated at p = 1 atm. The enthalpy of vaporization per mole can be obtained by the formula52 ΔH v = RT −

⟨Enb⟩ Nmol

(2)

where ⟨Enb⟩ is the average intermolecular energy (i.e., electrostatic plus van der Waals, also called nonbonding), R is the gas constant, and T is the temperature in kelvin. The results for the liquid THF solvent are reported in Table 1 compared to the experimental data. The agreement is good and comparable to other theoretical models.53 2.2. Polymer Properties. Periodically repeated bulk crystals of rr-P3ATs have been simulated at ambient conditions (T = 300 K, p = 1 atm). The microstructure of real P3ATs is Table 1. Solvent Propertiesa solvent

ρ

ρ(exp)

ΔHv

ΔHv(exp)

THF

0.89 ± 0.0003

0.889b

35.0

33.1b

ρ is given in g/cm3 and ΔHv is given in kJ/mol. bValues taken from ref 54.

a

B


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Figure 2. Top and side views of bulk P3HT. Left panel: example of starting configuration: here a ∼ 25 Å and b ∼ 4 Å. Right panels: same polymer after ambient conditions equilibration: the values for a and b are 15 ± 1.3 and 4 ± 0.6 Å, respectively.

by sizable uncertainty. For example, for P3HT, Jaczewska et al.61 report a value of ∼−170 MPa against ∼−347 MPa reported by Zen et al.62 A general trend is that polymers with longer side chains are less cohesive. This can be explained by modeling the polymer CED as the result of two main cohesive driving forces: the π−π interaction energy between the backbone atoms (Eππ) and the interaction energy between the alkyl side chains (Eaa). By use of these two parameters, the cohesion energy can be expressed as

quite complex due to the presence of several competing phases. Beside the perfect ordered crystal phase, thermal fluctuations can easily induce different configurations which are almost isoenergetic.26 In particular, experimental results on the crystalline structures of rr-P3ATs have shown that two polymer crystal structures exist differing by the amount of interdigitation of the alkyl chains.54−57 The relative abundance of the two phases depends on degree of regioregularity, molecular weight, deposition method, etc. The noninterdigitated (interdigitated) phase is referred to as form I (form II). Here we focus on the form I (see Figure 2) which is the most common. The occurrence of this noninterdigitated form has been discussed in ref 26 for the polymer P3HT where it was shown that it can be simulated by assembling polymer H-foils at finite temperatures. In the present analysis the initial (before equilibration and MD) π−π distance within each H-foil b (see Figure 2) is chosen equal to ∼3.8 Å, according to experimental data, while H-foils were separated by a distance a corresponding to twice the alkyl side chain length plus ∼5 Å. An example of form I P3HT is shown in right panel of Figure 2. After equilibration, a and b compare quite well with the experimental data. We remark that by using the dense interdigitated form,26 the calculated a parameter is smaller with respect to experiments, showing that ideal interdigitation is quite unlikely in realistic morphology. We have also calculated the density and the cohesive energy Ecoh of the simulated polymer systems. The latter is defined as the difference between the energy of the isolated molecules (i.e., separated by an infinite distance) and that of the molecules in the condensed state. More negative values correspond to more cohesive systems. In Table 2 we report the polymer densities and the cohesive energy density (CED), which is the ratio between Ecoh and the system volume V. Available experimental data are also reported for comparison. It is important to remark that the experimental determination of the CED of polymers is not trivial and measurements are affected

Ecoh = (Eππ + EaaL)N

where L is the number of carbon atoms in the side chains (L = 0, 1, 4, 6, and 12 for the polymers here investigated) and N is the number of thiophene rings of the system. Accordingly, the CED can be modeled by the function μp(L): μp (L) =

(Eππ + EaaL)N E + EaaL = ππ VmonN (L /3 + 1)VT

(3)

where Vmon is the monomer volume which is here defined as the sum of the volume VT occupied by a thiophene unit plus the volume occupied by the side chain ∼VTL/3. The volume occupied by a segment of alkyl chain (composed by one carbon atom and two hydrogens) is about one-third of VT. Note that μp(0) = Eππ/VT is the cohesive energy of the polythiophene crystal and Eππ = μp(0)/VT = −0.32 eV. By fitting Eaa on the atomistic data, we get Eaa = −0.032 eV. All the results are reported in Figure 3. As L → ∞, it is found that μ(L) → 3Eaa/ VT.

Table 2. Bulk Polymer Properties polymer PT P3MT P3BT P3HT P3OT P3DDT a

ρ (g/cm3) 1.64 1.38 1.16 1.07 1.02 0.97

± ± ± ± ± ±

0.0001 0.0001 0.0002 0.0002 0.0002 0.0001

ρexp (g/cm3)

CED (MPa)

1.4a 1.51b 1.11c 1.1d 1.06c 0.97c

−614 −544 −370 −327 −293 −267

Figure 3. Cohesive energy density (CED) for the different oligomers considered.

From ref 63. bFrom ref 64. cFrom ref 65. dFrom ref 66. C


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are miscible if ΔGm is negative, while they are immiscible if it is positive. According to the Flory−Huggins solution theory for polymers42

By a similar model we can reproduce the dependence of the polymer density on L as well: ρp (L) =

(m T + mcL)N m T + mcL = VmonN (L /3 + 1)VT

ΔGm = kT[ns ln(ϕs) + n p ln(ϕp) + nsχFH ϕp]

(4)

(5)

where ns and np are the number of molecules and ϕs and ϕp are the volume fractions of solvent (s) and polymer (p), respectively. A detailed description of Flory−Huggins solution theory can be found in the Supporting Information. The Flory−Huggins interaction parameter χFH is a dimensionless parameter that describes the strength of the polymer−solvent interaction and it controls the solubility. In particular, χFH depends on the specific solvent−solute pair and on temperature. Let r be the ratio between the molecular volumes of the polymer Vp and the solvent Vs. In the framework of the FH theory, two materials are miscible at a given temperature if χFH(T) is smaller than a certain critical value χcrit, which only depends on r (see Supporting Information for derivation):

where mT = 82.12 amu is the mass of the thiopene ring and mc = 14.03 amu is the mass of an alkyl chain segment. As L → ∞, the density asymptotically converges to the density value ρaa = 3mc)/VT while at L = 0 the polythiophene density is correctly recovered ρρ(0) = mT/VT. The calculated density is plotted in Figure 4 together with ρp(L). The agreement is good considered that there is no fitting parameter in this case.

χFH (T ) < χcrit (r ) =

(1 + r )2 2r

(6)

For a small molecule solution (Vs ≃ Vp, r ≃ 1) the critical value is equal to 2, while in the limit of infinitely long polymer chain χcrit = 0.5. For the alkylthiophenes the volume ratio r is proportional to the alkyl chain length L: Figure 4. Density for the different oligomers considered.

r (L ) =

Different force fields exist in the literature with torsional parameters adjusted to better reproduce the polymer transport properties (e.g., see refs 58−60). However, here we consider the standard Amber force field since it provides good agreement with the experimental density and cohesive energy that are the most relevant properties for solubility. 2.3. Polymer Solubility in THF. In order to study the rrP3ATs solubility, we have considered polymer chains (formed by 8 thiophenes) immersed in THF and we have simulated the solution at ambient temperature and pressure. An example for poly(3-dodecylthiophene) (P3DDT) in the solvent is shown in Figure 5. Solution behavior is governed by the Gibbs free energy change accompanying mixing, ΔGm.67 Two or more substances

Vp Vs

= 8(L /3 + 1)

VT Vs

The critical values for the oligomer−THF mixtures considered in this work are reported in Table 3. Table 3. Flory−Huggins Interaction Parameters As Calculated from MD Simulations and Critical Values of the Interaction Parameter As Calculated from Eq 6 polymer

χFH (T = 300 K)

χcrit

PT P3MT P3BT P3HT P3OT P3DDT

3.34 11.43 7.41 0.39 −1.06 −0.38

1.01 0.89 0.80 0.78 0.76 0.72

The χFH value at room temperature can be obtained according to the equation χFH =

Vref ΔHm 1 kT Vm ϕϕ s p

(7)

where Vref is the reference volume, taken equal to the volume of the smallest molecule in the solution (here, it is the volume of a THF molecule, Vs), and ΔHm/Vm is the change in enthalpy upon mixing per unit volume. It has been shown that the volume variation upon mixing is insignificant; therefore, the changes in enthalpy and internal energy are identical.46 The latter can be calculated by molecular dynamics40,41,47 from the cohesive energy densities of pure solvent, pure polymer, and solvent−polymer mixture:68 ΔHm = CEDm − CEDsϕs − CEDpϕp Vm

Figure 5. Details of a P3DDT oligomer immersed in THF. Hydrogen atoms are not shown and all the THF atoms are gray, for clarity. D

(8)


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The interaction parameter calculated via eq 7 takes into account the specific interactions between the polymer and the solvent. In Figure 6 we report the curve χcrit(r), together with the χFH calculated by MD simulations. The points lying below χcrit(r)

explains the relatively small value of χFH of PT. The fine interplay between solvent−backbone, solvent−side chains, and polymer−polymer interactions gives rise to the non monotonic behavior of the solubility found here.

Figure 6. Flory−Huggins critical parameter χcrit(r) as a function of the volume ratio r (continuous red line). Calculated χFH for P3ATs (filled squares). The dashed line is a guide for the eye, and the dashed-dotted line is the zero. Error bars correspond to ±2 MPa uncertainty on the enthalpy of mixing.

3. CONCLUSIONS We have studied by fully atomistic simulations the interactions between regioregular oligo(3-alkylthiophene)s and the solvent THF. The density and the cohesive energy of the P3ATs have been modeled by a simple function of the alkyl chain length. We have carried out an extensive study on the solubility properties of rr-P3ATs in tetrahydrofuran, based on Flory− Huggins theory. The obtained results for the solubility as a function of the alkyl chain length are in good agreement with available experimental data. In particular, polymers with short alkyl chain length are insoluble in THF, while hexyl, octyl, and dodecyl side chains provide full miscibility. The present method highlights that (i) taking into account the proper microstructure of the polymer and its cohesive energy density is mandatory to calculate solubility values in agreement with experiments and (ii) the FH theory in combination with MD (Amber force field) is appropriate to describe the solubility properties of this class of polymers in THF.

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correspond to miscible polymers. It is found that oligomers with alkyl side chains smaller than 6 carbons are immiscible in THF, while if L ≥ 6 the oligomers start to be soluble, in agreement with experimental results. The crossing point corresponds to P3HT that has a measured solubility between 1.1 and 2.3 g/L.69,70 The evaluation of the FH interaction parameter relies on the accurate calculation of the CED of polymer, solvent, and mixed phase. The error bars reported in Figure 6 correspond to an uncertainty of ±2 MPa on ΔHm/Vm. For a given solvent, the value of χFH depends on the balance between CEDm and CEDp: the solubility increases for large polymer−solvent interaction (large |CEDm| and small χFH) and decreases for large polymer−polymer interactions (large |CEDp| and large χFH). The interaction of the THF molecule with the polymer backbone is stronger than with the alkyl chains. Accordingly, |CEDm| is higher when there is a higher number of backbone−solvent interactions. If we plot the radial pair distribution function between the carbon atoms of the backbone and the ones of the THF molecules, we can see that there is a higher number of backbone−solvent interactions for the PT than for the other oligomers (see Figure 7). This

ASSOCIATED CONTENT

S Supporting Information *

Details on the Flory−Huggins theory and on the partial charges calculation. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (C.C.). *E-mail: [email protected] (A.M.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been funded by Italian Institute of Technology (IIT) under Project SEED “POLYPHEMO” and Platform “Computation”, by Regione Autonoma della Sardegna under L.R. 7/2007 CRP-249078 and CRP-18013, by MIUR Under PON 2007-2013 (Project NETERGIT), and by Consiglio Nazionale delle Ricerche (Progetto Premialità RADIUS). We acknowledge computational support by CINECA through ISCRA Initiative (Project SWING).

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