PDMS Triblock Morphology

Article pubs.acs.org/JPCB

Coarse-Grained Modeling of Peptidic/PDMS Triblock Morphology J. Casey Johnson,† LaShanda T. J. Korley,*,† and Mesfin Tsige*,‡ †

Department of Macromolecular Science and Engineering, Case Western Reserve University, 2100 Adelbert Road, Cleveland, Ohio 44106, United States ‡ Department of Polymer Science, The University of Akron, Goodyear Polymer Center 1021, Akron, Ohio 44325, United States ABSTRACT: The morphology and chain packing structures in block copolymers strongly impact their mechanical response; therefore, to design and develop high performance materials that utilize block copolymers, it is imperative to have an understanding of their self-assembly behavior. In this research, we utilize coarse-grained (CG) molecular dynamics to study the effects of peptidic volume fraction and secondary structure on the morphological development and chain assembly of the triblocks poly(γ-benzyl-Lglutamate)-b-poly(dimethylsiloxane)-b-poly(γ-benzyl-L-glutamate) (GSG) and poly(dimethylsiloxane)-b-poly(γ-benzyl-L-glutamate)-b-poly(dimethylsiloxane) (SGS). This necessitated developing a complete coarse-grained parameter set for poly(dimethylsiloxane) that closely captures the radial pair distribution of a united atom model and the experimental density at 300 K. These parameters are combined with the MARTINI amino acid CG force field and validated against prior reported values of domain spacing and peptide chain packing for GSG. The combined CG parameter set is then used to model SGS, a triblock currently in development for nature-inspired mechanically enhanced hybrid materials. The results reveal that the peptide side chain strongly influences the final morphology. For instance, lamellar or hexagonally packed cylindrical domain formation can result from the variation in side-chain interactions, namely, side-chain sterics preventing curved interface formation by increasing interfacial free volume. Ultimately, this research lays the foundation for future studies involving systems with dispersity, mixtures of secondary structures, and larger multiblock copolymers, such as polyurethanes and polyureas.

1. INTRODUCTION Block copolymers are known to self-assemble into a variety of ordered microstructures, such as lamellae, cylinders, and spheres, due to the thermodynamically driven incompatibility between polymer blocks and the topological constraints caused by chemical bonding.1 As a consequence of these differing architectures, the microphase-separated morphologies of block copolymers play a decisive role in determining their physical properties.2−4 Thus, it is imperative to have knowledge of the type of microstructure a given copolymer composition is likely to produce in order to formulate a material with the desired mechanical response. Typically, the development of relationships between morphology and mechanics takes an experimental route, involving the synthesis of an array of polymers with defined compositions. Unfortunately, this can prove to be both laborious and costly. However, advancements in computational capabilities have aided in the expansion of theoretical methods able to anticipate or predict the equilibrium phase behavior of complex polymeric materials.5−9 These methods can be generalized into three major categories based on their level of resolution: atomistic, coarse-grained particle-based, and fieldtheories. Atomistic representations are the most detailed, expressing the material with atomic resolution. However, a major drawback of atomistic methods is the difficulty of reaching temporal (μs to seconds) and spatial (10−1000 nm) scales applicable to polymer systems, even with state-of-the-art computational resources, due to the large number of associated © XXXX American Chemical Society

degrees of freedom. At the opposite end of the spectrum are the continuum or field-based methods, such as self-consistent field theory or dynamic density functional theory. Although these approaches provide pragmatic predictions of morphology and phase behavior, their ability to convey molecular-level phenomena, such as local chain conformations, hydrophobic/ hydrophilic interactions, van der Waals interactions, and hydrogen bonding, i.e. interactions that strongly impact mechanical properties, is limited.6 In this research, we have chosen to utilize the middle ground in level of detail, coarsegrained particle-based simulations. Coarse-grained (CG) approaches follow simulation procedures (Monte Carlo or molecular dynamics) similar to those found in atomistic models; however, CG models differ by grouping atoms, full monomers, or even multiple monomers into “super-atoms” and apply potentials that mimic the effective or average atomistic bonded and pairwise interactions.5,9 This clustering of atomic units reduces the number of degrees of freedom needed to compute, thus allowing for larger temporal and spatial scales to be simulated. These extended spatial and temporal advantages give researchers access not only to morphological predictions, but also fundamental information on the underlying chain structure, depending on the level of coarse-graining.10 In the past 10 years, numerous research Received: July 1, 2014 Revised: October 11, 2014

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dx.doi.org/10.1021/jp506553v | J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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2. MODEL AND SIMULATION DETAILS 2.1. Functional Form and Simulation Parameters. The bonded interactions for the potential energy acting between bonded sites i, j, k, and l with force constants K and equilibrium bond distance db, angle φa, and proper dihedral angle ψd are applied from the MARTINI model18−20 and take the following functional form:

groups have made use of CG models to predict and understand macromolecular structure and dynamics. Tsige et al.11 employed CG based models to investigate the morphology of multiblock copolymers with variable chain stiffness, an attribute that can arise due to aromatic πconjugation or from common peptide secondary structures, during solvent evaporation. The simulations indicated that chain stiffness has a decisive effect on the evaporation rate, which influences morphology formation. Further CG based studies by Tsige et al. on diblocks,12 Li et al. on triblocks,13 and Lintuvuori et al. on symmetric multiblocks14 have also verified the impact of block stiffness on microstructure, demonstrating that the morphology could be shifted from lamellae to cylinders by controlling the flexibility of the chains. CG models have also been used to correlate nanophase behavior with mechanical properties.15−17 These studies provide insight into domain distortion pathwaysvital information for the understanding of deformation mechanics. Biological sciences have also benefited from the development of CG representations capable of modeling natural materials, such as lipids18,19 and proteins.20 Large-scale (>800 000 particles) simulations of bioinspired surfactant self-assembly have detailed the phase transformation from hexagonal packing to lamellar structures as a function of solution concentration.8,21,22 Insights from MD simulations have also helped to elucidate the mechanism behind membrane curvature and how this phenomenon plays a role during virus absorption.23 In these highlighted examples, the authors have used CG models to obtain information that would otherwise be challenging or impossible with current atomistic simulation or experimental methods. These stimulating results have encouraged us to utilize molecular dynamics and CG modeling to explore chain packing and polymer morphology of ABA and BAB peptidic triblock copolymers currently in use and in development within our lab for nature-inspired mechanically enhanced hybrid materials.24 Specifically, the ABA triblock is based on poly(γ-benzyl-L-glutamate)-b-poly(dimethylsiloxane)b-poly(γ-benzyl-L-glutamate) (GSG), which has been studied extensively by experimental methods,25−28 thus allowing for model validation. The BAB system inverts the blocks, i.e., poly(dimethylsiloxane)-b-poly(γ-benzyl-L-glutamate)-b-poly(dimethylsiloxane) (SGS). Accordingly, these results will provide insight into the potential structures achievable within this system. Additionally, this general class of peptidic triblocks is of interest for use in materials due to the tunable secondary structure of the peptidic segments. Depending on the degree of polymerization (DP), the peptidic block will predominantly form either β-sheets (10 repeat units).27 Results from this research will help to clarify both the impact of peptide volume fraction and peptide secondary structure on morphological development. In this research, we initially discuss the CG parameter sets utilized, namely, the MARTINI model18−20 for the poly(γbenzyl-L-glutamate) (PBLG) segments and our own derived parameters for poly(dimethylsiloxane) (PDMS). We then discuss results regarding the chain conformation and morphology of GSG, including varying peptide block length and peptide secondary structure, and compare with experimental data. We conclude with calculations of the local chain assembly and morphology of SGS.

Vbond =

1 Kb(dij − db)2 2

Vangle =

1 K a[cos(φijk ) − cos(φa)]2 2

Vdihedral = Kd[1 + cos(nψijkl − ψd)]

In the peptidic segment case, the proper dihedral is used to impose secondary structure and, therefore, conformational changes are not effectively modeled. To describe nonbonded interactions, a shifted Lennard−Jones 12−6 potential is used between particle pairs i and j at distance rij VLennard−Jones

⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σij σij = 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ , rij < 12 Å r ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠

with εij and σij representing the interaction strength and zerocrossing distance, respectively. The nonbonded interactions are shifted to zero energy over the range 9−12 Å using the GROMACS functional form.18 All simulations described in this investigation were performed on the Case Western Reserve University high performance computing cluster using the freely available large-scale molecular dynamics code LAMMPS.29 An orthogonal simulation box with periodic boundary conditions (PBC) was used to encompass the particles. Temperature was controlled using the Berendsen thermostat with a time constant of 1 ps. Pressure in each box plane was independently regulated at 1 bar with a Berendsen barostat with a 5.0-ps time constant and compressibility of 4.5 × 10−5 bar−1. Neighbor lists were updated every 10 steps with an 18 Å neighbor list cutoff distance. This increased distance from that used in MARTINI (12 Å) was due to the larger PDMS particle radius. All particle masses were set to 72 amu, as defined in MARTINI for computational efficiency. The equations of motion were integrated using the velocity−Verlet method; the parameters used here allowed for a time step up to 20 fs, which was determined to yield stable energy trajectories (NVE) and matching total radial pair distributions (NPT) when compared to a smaller time step (10 fs). All simulations are based on a minimum of 32 000 particles except for G20S30G20, which is based on 69 000 particles in order to achieve box lengths of at least 1.5−2 times the expected morphological characteristic length (∼20 nm). Starting configurations were generated with Packmol30 using straight chain representations of the polymer while topological information, i.e. bonded parameters, were assigned using the VMD31 plugin TopoTools. A 5 ns constant pressure Langevin dynamics simulation at 300 K was run with all pairwise interactions set equivalent (ε = 0.6 kcal/mol, σ = 4.7 Å) to remove any interaction bias and further randomize and relax the configuration. Production runs were based on a five-step constant pressure annealing strategy that was found to consistently produce the same morphology from different starting trajectories: (1) 20 ns equilibration at 300 K, (2) B



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Figure 1. (A and B) PDMS chain conformations that produce the bimodal distributions in the bond length and angle distributions. Red dots represent CG center positions. (C) Bond length distribution. (D) Angle distribution. (E) Dihedral angle distribution. (F) Total radial pair distribution. (G) Intermolecular radial pair distribution.

smoothly ramp temperature from 300 to 500 K over 20 ns, (3) 200 ns equilibration at 500 K, (4) smoothly cool temperature from 500 to 300 K over 20 ns, and (5) 40 ns equilibration at 300 K. Analysis is performed on the final stage of equilibration. Snapshots were taken every 0.1 ns for analysis. VMD was used for visualization and analysis. 2.2. Peptide Parameterization. The peptidic blocks were represented by particle types described in the MARTINI force field.18−20 This parameter set was chosen due to the demonstrated flexibility and transferability of the force field to a broad array of macromolecules, such as lipids,18 carbohydrates,32 polymers,33,34 dendrimers,35,36 and, most importantly, peptides and proteins.20 Due to the noncanonical nature of γ-benzyl-L-glutamate, MARTINI does not have defined particle types; thus, particle types were assigned based on structural analogy. The amino acid backbone particle type is dependent on the secondary structure; accordingly, the backbone in helical structures is assigned type N0, the helix Nterminus is assigned type Nd, and in homoblock PBLG, the helix C-terminus is assigned type Na. For backbone particles

representing sheet conformations, type Nda were assigned with no special treatment of the N-terminus or C-terminus.20 The side chain is represented by type Na, matched from the ester in the lipid dipalmitoylphosphatidylcholine (DPPC), while the benzyl is represented by three SC4 particles as used in both benzene and phenylalanine.19,20 For SGS, the butane linkage is represented by particle type C1 as used in CG butane.18 Bonded and nonbonded parameters can be found in references Marrink et al.18,19 and Monticelli et al.20 2.3. PDMS Parameterization. Although there are several atomistic models for PDMS,37−41 to the authors’ knowledge, there is not a published CG parameter set. Therefore, a CG PDMS model was derived based on the potential form given in Section 2.1 and the united atom (UA) model of Frischknecht et al.38 in which the hydrogens have been incorporated into the methyls. This force field was chosen due to the ability to agreeably match the radial pair distribution functions of liquid PDMS. The UA simulation consisted of 200 PDMS chains with a DP of 30. The equilibration followed the same process as described in Section 2.1; however, due to the faster bonded C



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the use of a spherically symmetric potential. This limitation could similarly be overcome through the use of a tabulated potential. Nonetheless, the agreement between UA and CG model is acceptable for the current work. The final bonded and nonbonded parameters are given in Table 1. This parameter set yields a density of 0.98 ± 0.01 g/

vibrational modes of the UA model, a 2 fs time step was used; thus, all simulation times are divided by 10. Analysis snapshots were taken every 0.05 ns. The first step of the coarse-graining procedure is to set a mapping scheme. In this study, a single particle is used to represent one PDMS monomer, i.e. −[Si(CH3)2O]−, with the particle center placed at the oxygen and two methyls’ geometric center. Other center positions were tested, such as monomer center of mass, monomer geometric center, oxygen/methys center of mass and the Si position; however, the chosen location yielded the best fit to the intermolecular radial pair distribution. The initial bonded potentials were calculated from least-squares fit of the Boltzmann-inverted probability distributions, determined from the UA simulation, as given by the following equations: Vbond =

Table 1. Coarse-Grained PDMS Force Field Parameters bond coefficients angle coefficients dihedral coefficients pair coefficients

⎛ PUA (d ) ⎞ 1 bond ij ⎟ + Cb Kb(dij − db)2 = −kBT ln⎜⎜ ⎟ 2 2 ⎝ dij ⎠

kcal , db = 3.66 Å mol·Å2 kcal K a = 7.24 mol , φa = 106.9° kcal Kd = 0.37 mol , n = 3, φd = 180° kcal ε = 0.288 mol , σ = 5.06 Å

Kb = 9.61

cm3 (experimental 0.98 g/cm3)38 and radius of gyration 11.79 ± 2.23 Å (UA 12.42 ± 2.12 Å) for a chain of 30 repeats in a simulation box containing 650 chains. All nonbonded interactions between PDMS and PBLG have an interaction strength of 0.1 kcal/mol, zero-crossing distance of 5.06 Å, and are truncated at 5.68 Å (determined from 21/6σ) to simulate the strong segregation limit and to increase phase separation kinetics. The assumption that the PDMS and PBLG would be in the strong segregation limit is supported by the large difference in Hildebrand solubility parameters, which are good first approximations to the Flory interaction parameters,44 of PDMS (7.1 cal1/2 cm−3/2) and peptide model compounds Nmethylpyrrolidone (11.1 cal1/2 cm−3/2) and dimethylformamide (12.1 cal1/2 cm−3/2).45

1 K a[cos(φijk ) − cos(φa)]2 2 ⎛ PUA (φ ) ⎞ angle ijk ⎟+C = −kBT ln⎜⎜ a ⎟ sin φ ijk ⎠ ⎝

Vangle =

Vdihedral = Kd[1 + cos(nψijkl − ψd)] UA = −kBT ln(Pdihedral (ψijkl)) + Cd

where kB, T, and Cb, Ca, and Cd are the Boltzmann constant, simulation temperature, and irrelevant constants used to set the minimum to zero, respectively.5,9,42,43 The initial parameters for the dihedral angle were acceptable and no further optimization was conducted. The bond and angle CG force constants were iteratively adjusted to minimize the absolute error between CG and the UA model distributions by multiplying the previous force constant by the ratio of the UA and previous CG probability distributions at the mean value of the respective distribution. In Figure 1, parts C−E, the bond, angle, and dihedral angle distributions of the UA and CG models are shown. It is observed that the UA bond and angle distributions are bimodal; this is due to the offset position of the CG test particle as seen in Figure 1 A and B, where the red dot represents the test particle center. The potential matching could be better modeled through the use of tabulated values; however, to remain consistent with the MARTINI force field, the analytical potentials were used. To determine the nonbonded interactions, the initial Lennard−Jones well depth, ε, and zero-crossing point, σ, were estimated by calculating the average potential around an equilibrated monomer vs the radial distance from the position of the CG particle center. These initial parameters were then iteratively adjusted to match the intermolecular radial pair distribution, g(r), and the experimental density of PDMS by multiplying the previous parameter by the ratio of either the UA and CG distance (to calculate σ), or the UA and CG intensity (to calculate ε) of the first maximum in the intermolecular radial pair distribution. Figure 1 G shows the final radial pair distribution. Unfortunately, the intensity of the second maximum or interaction shell was not obtained. This is likely due to the asymmetry of the UA monomer, which leads to asymmetric midrange packing that is not achievable through

3. RESULTS AND DISCUSSION In this investigation, coarse-grained simulations were conducted on the triblocks poly(γ-benzyl- L -glutamate)-b-poly(dimethylsiloxane)-b-poly(γ-benzyl-L-glutamate) (GSG) and poly(dimethylsiloxane)-b-poly(γ-benzyl-L-glutamate)-b-poly(dimethylsiloxane) (SGS) (Figure 2) with peptidic segment lengths representing either the α-helix conformation (20 repeats) or β-sheet conformation (5 repeats) and constant PDMS block length (30 repeats) in order to understand the effects of the peptide volume fraction and peptide secondary structure on the morphology development. These block lengths were also chosen such that the model could be validated against literature data regarding GSG. Table 2 lists the polymers investigated, peptide volume fractions ( f p), and secondary structure. The peptidic segment is represented by the MARTINI force field, while the PDMS segment is represented by our own CG parametrization. 3.1. Homoblock Poly(γ-benzyl-L-glutamate). The investigation began by first examining the accuracy of the MARTINI model for the noncanonical amino acid γ-benzyl-L-glutamate. Coarse-grained simulations of homoblock PBLG5 (β-sheet) and PBLG20 (α-helix) were found to match the reported density of 1.25−1.28 g/cm3 at 300 K46an important result because density directly impacts volume fraction, which is a critical factor for morphological development. To determine if the CG model would adequately reproduce chain packing, the intermolecular radial pair distributions (Figure 3A−F) of the backbone, ester, and aromatic (ring center of mass) particles were compared with simulations conducted with the CHARMM19 UA force field.47−49 This force field was chosen, over a fully atomistic model, as it allows for a simulation size with structural conformation statistics that can be adequately D



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Figure 2. Chemical structures of the triblocks studied and CG particle types.

We begin by examining the morphology of G5S30G5. This triblock copolymer has been reported to form a randomly distributed fibrillar microstructure (AFM) with β-sheet ordering indicated by the characteristic wide-angle X-ray scattering (WAXS) reflection at q ≈ 3.6 nm−1 (∼1.7 nm), and an average domain spacing of ∼7 nm determined by small-angle X-ray scattering (SAXS) and AFM.27 Simulation results (Figure 4) are in close agreement with these stated dimensions; however, the CG model yields a slightly larger domain spacing (∼7.6 nm) and a lamellar morphology. A likely reason for the larger spacing is the repulsive parameters used to model the interactions between PDMS and PBLG, whereas NMR measurements have indicated a degree of phase mixing in this system due, in part, to the low peptide DP.26 Furthermore, the computed lamellar microstructure should be expected based on simple volume fraction rules,1 but has not been experimentally observed. This deviation from experiment is believed to arise due to three factors: (1) monodisperse chain lengths, (2) strong segregation brought about by the repulsive PDMS/PBLG interactions, and (3) short spatial length scale. Factors 1 and 2 play important roles in chain packing and segregation efficiency, and thus, with the current modeling conditions form an ideal case, which results in well-defined morphology. Factor 3 influences the observed morphological formation; in this case, the simulation box length (∼14.1 nm), although large enough to express the domain spacing, is not adequate for fibrillization. Based on AFM images, the fibrillization process would require a minimum simulation box length of 100−200 nm and contain >1 000 000 particlesa challenging, but not impossible, task. Nevertheless, the model aids in the visualization of the peptide topography within a layer. Considering a side view of a peptidic layer (Figure 4B), it is observed that the rigid polypeptide backbone aligns perpendicular to the lamellar plane, forming a smecticlike bilayer. This perpendicular organization is a common arrangement found within the rod-like segments of rod−coil and rod−coil−rod block copolymers due to the rods attempting to maximize rod−rod contact (enthalpy driven) while the coils expand to fill the free volume (entropy driven).52−55 Furthermore, the bilayer formation, as opposed to interdigitation, is hypothesized to be triggered by the steric bulk of the benzyl-protected side chain and the relatively short polypeptide rod length. At the lamellar interface, the perpendicular peptidic rod packing causes a degree of coil elongation, decreasing the coil flexibility and inhibiting the

Table 2. Triblocks Investigated, Peptide Repeat Length, Peptide Volume Fraction, and Peptide Secondary Structure polymer

peptide degree of polymerization (n)

peptide volume fraction, f p

secondary structure

G5S30G5 G20S30G20 S30G4S30a S30G10S30a S30G40S30a

5 20 2 5 20

0.43 0.75 0.13 0.28 0.60

β-sheet α-helix n/ab β-sheet α-helix

a

The peptide block length label equals the total number of peptide repeats, i.e. 2·n. bS30G4S30 does not have a peptide backbone dihedral due to the short length, and therefore, does not have a forced secondary structure.

and efficiently collected. Although the radial pair distributions are not exact matchesas could be expected from the elimination of multiple degrees of freedom, faster dynamics, the generalization of the model through the use of analytical potentials and the fact that MARTINI was parametrized for the fluid phasethey do retain the general trends, such as coordination peak positions. These findings suggest that the CG model reasonably agrees with the UA chain packing. Furthermore, the sharpness of the peaks in the CG model g(r) implies that the chains are achieving increased order. This result is likely due to the smoother particle−particle interactions and longer time scales (300 ns vs 20 ns), which allow the system to reach a more favorable thermodynamic state. These motivating results indicate that the MARTINI model sufficiently reproduces the key thermodynamics properties, i.e. density and chain arrangement, needed to study the triblock morphology. 3.2. Poly(γ-benzyl-L-glutamate)-b-poly(dimethylsiloxane)-b-poly(γ-benzyl-L-glutamate). The peptidic triblock polymer poly(γ-benzyl-L-glutamate)-b-poly(dimethylsiloxane)-b-poly(γ-benzyl-L-glutamate) has been extensively characterized by experimental methods, such as differential scanning calorimetry, X-ray scattering (small and wide angle), and atomic force microscopy (AFM),25−28 allowing for a direct evaluation of the model accuracy. Additionally, we have utilized G5S30G5 and similar peptidic triblocks in our own work to explore hierarchical ordering and secondary structure effects on mechanical properties,50,51 adding incentive to further develop an understanding of the microphase-segregated nature of these polymers. E



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Figure 3. CG and UA intermolecular radial pair distributions of the backbone, ester, and aromatic interaction. (Left column) β-Sheet forming PBLG5. (Right column) α-Helix forming PBLG20. CG coordination peaks are relatively similar to the UA model.

(Figure 4C) in which the polypeptides pack in lamellar-like structures, controlled by side-chain interactions, with ∼1.8 nm long spacing.56 Next, examining G20S30G20, AFM phase imaging displays the formation of a fibrous network with fibers ∼12 nm in diameter, while SAXS results indicate hexagonally packed PDMS cylinders with domain spacing ∼10 nm.25,27 Additionally, the peptidic α-helical structures assemble into hexagonally packed cylinders, with an average helix-to-helix distance of 1.4 nm and an overall morphology described as cylinders-on-hexagonal.25,27,56 The computational results agree reasonably well with these experimental findings, namely a predicted domain spacing of 13 nm (Figure 7A) and a helix-to-helix distance of 1.5 nm (Figure 7B). In a fashion similar to the G5S30G5 CG model, the G20S30G20 model predicts slightly larger spacing; again, this is attributed to the repulsive PDMS/PBLG interactions, whereas experiment has indicated a degree of phase mixing. However, the CG representation does correctly display hexagonally packed PDMS cylinders. Furthermore, the

space-filling ability within a small distance of the coil−rod interface. If the peptidic rods were to interdigitate, interfacial energy would increase as a result of “hole” formation (Figure 5). However, this higher interfacial energy could be overcome with less bulky peptidic units or longer peptidic rods on account of their greater self-interaction strength. This proposed theory was supported through CG simulation of two equal volume fraction ( f p ∼ 0.5), β-sheet containing systems, namely, (1) a nonsterically hindered, short rod poly(glycine)5-bPDMS10-b-poly(glycine)5, and (2) a sterically hindered, long rod PBLG20-b-PDMS93-b-PBLG20. Details on simulations of the glycine-containing triblocks can be found in the Appendix. Figure 6 shows interdigitation within the peptidic layer, with the poly(glycine)5 forming a dense, perpendicular packed lamella, while the long chain PBLG20 forms a slightly disordered, yet predominantly perpendicular structure. The final observation from the G5S30G5 modeling is the agreeable match with experiment (∼1.7 nm) of the β-sheet ordering F



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coordination peaks in the intermolecular radial pair distribution (Figure 7B) of the peptidic backbone, i.e. the helix-to-helix distance, match the expected ratios for hexagonally packed cylinders; accordingly, the simulated morphology corroborates the experimentally proposed model. The objective of this section was to explore the accuracy of the CG parametrization for PDMS and PBLG when combined to model the triblock PBLG-b-PDMS-b-PBLG by investigating the morphological development of the copolymer with different peptidic block lengths and secondary structure, and compare these results with previously reported structures. In general, the simulated microstructures correspond well with the experimental data; however, the CG models did slightly overestimate the microphase domain spacings, which was attributed to the repulsiveness of the PDMS/PBLG interactions. Nonetheless, the model’s ability to calculate these structures is encouraging; therefore, in the next section these parameters are applied to study the microstructure of the inverse triblock system PDMSb-PBLG-b-PDMS. 3.3. Poly(dimethylsiloxane)-b-poly(γ-benzyl-L-glutamate)-b-poly(dimethylsiloxane). The motivation for the synthetic development and morphological understanding of this triblock is driven by the proposed theory in our prior work50 that the interface between the urea/urethane hard domain and the PBLG-b-PDMS-b-PBLG polypeptide domain influences the mechanical properties of the peptidic polyurethane/ureas. Specifically, it was suggested that the observed decrease in elongation-at-break of the peptidic polyurethane/ ureas was due, in part, to the placement of the hard domain next to the stiff PBLG peptidic segment. This would result in a rigid interface that has the potential to produce stress concentrations and initiate premature failure. Consequently, the inverse triblock, PDMS-b-PBLG-b-PDMS, was conceived to alleviate the “hard−hard” interface by inserting flexible PDMS blocks between the two rigid segments. Although this topological transposition will have an impact on the mechanical response of the final polyurethane/urea, the self-assembled nanophase-separated microstructure also plays a crucial role. Thus, it is imperative to formulate a basic understanding of the potential morphologies and chain packing that this triblock is

Figure 4. (A) Snapshot with PBC (black rectangular box represents original box) of the G5S30G5 lamellar domains. Blue represents PDMS and red represents PBLG. The domain spacing is in close agreement with the experimentally reported value of ∼7 nm. (B) Side view of the peptidic layer, displaying the bilayer morphology. The peptidic backbone is shown in black. (C) Top view of the peptidic layer, exhibiting lamellar β-sheet structures (peptidic backbone shown in black) with a separation distance closely matching the 1.7 nm reported value.

Figure 5. Schematics of bilayer (top) and interdigitated (bottom) rod morphologies. The circled region reveals the unoccupied volume. PDMS is represented by blue, and the peptidic blocks are red.

Figure 6. (A) Side view snapshot of the interdigitated poly(glycine)5 chains. Poly(glycine) is shown in red, and PDMS is blue. (B) Side view snapshot displaying interdigitated long PBLG20 chains. The PBLG backbone is shown in black.

Figure 7. (A) Snapshot with PBC (black rectangular box represents original box) of the G20S30G20 demonstrating hexagonally packed PDMS cylinders. PDMS is shown in blue, and PBLG is red. The simulated domain spacing closely agrees with the experimental value of 10 nm. (B) Intermolecular radial pair distributions of the peptide backbone displaying characteristic coordination peaks for hexagonally packed peptide helices. The calculated helix-to-helix separation distance is in agreement with the experimental value of 1.4 nm. G



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capable of developing to facilitate the design of mechanically enhanced polymers. This section starts by investigating the low peptidic volume fraction (13%) triblock S30G4S30. At this low volume fraction, theory suggests that spherical structures composed of the minority phase (PBLG in this case) should be observed.1 However, as seen in Figure 8, isolated hockey-puck or disk-like Figure 9. Snapshot with PBC (black rectangular box represents original box) of S30G10S30, displaying the lamellar morphology (left) and a side view of the PBLG lamellae. A mix of bent and elongated peptidic blocks can be observed. PDMS, PBLG, and the PBLG backbone are shown in blue, red, and black, respectively.

Figure 8. (A) Snapshot with PBC (black rectangular box represents original box) of S30G4S30. Edges of PBLG domains can be observed at the simulation box boundaries. (B) Side view of a PBLG domain, displaying the side chains folded into the inner volume of the disk to minimize contact with PDMS. (C) Top view of a PBLG domain. PDMS and PBLG are shown in blue and red, respectively. The PBLG backbone is shown in black.

Figure 10. Snapshot with PBC (black rectangular box represents original box) of PDMS8-b-poly(glycine)10-b-PDMS8 exhibiting hexagonally packed peptidic cylinders (red), in a matrix of PDMS (blue).

benzyl substituents prevent a curved interface from forming due to the rectangular-like volume the peptidic block occupies. Specifically, the glycine block forms a high-aspect ratio, rectangular rod that is symmetric about the long axis (a long tetragonal prism), which allows for efficient packing within a tight radius, while the bulky PBLG benzyl side chains produces a wide, asymmetrical, orthorhombic rod element that is incapable of filling a cylindrical space without producing large areas of free volume. Furthermore, within the PBLG-rich domains, a mixture of elongated (bridging the lamellar thickness) and bent (about the butanediamine bead, ∼70% bent) peptidic chains is observed, while in the glycine rich domains a lower fraction of bent chains (∼45%) is detected. This higher PBLG bent fraction produces a distribution of conformations, leading to a more disordered state, i.e. higher unoccupied volume, which inhibits close packing in a curved microstructure. Examining the intermolecular radial pair distribution within the peptidic domains (Figure 11) confirms the disordered packing of PBLG as no regular coordination peaks are observed, while the polyglycine possesses the indicative signs of hexagonally packed rods. If this lamellar morphology is truly the case, then, as with S30G4S30, utilizing side-chain interactions and sterics should be considered as an additional tool in driving microstructure development. The final triblock studied, S30G40S30, contains a PBLG volume fraction of 0.60, which is theoretically within the lamella-forming composition. As shown in Figure 12, this triblock does indeed form lamellar domains. Additionally, within the peptidic lamellae, the α-helical structures pack in a weakly hexagonal arrangement, as revealed by the backbone−backbone coordination distance (Figure 12C). The weaker ordering is likely a result of the flexibility imparted by the butanediamine bead that allows the peptide chain to fold at the center. Similar to S30G10S30, ∼72% of the peptidic blocks were detected in a bent state which triggers

PBLG domains are formed instead. In general, conventional volume fraction based morphology calculations are founded on a Gaussian chain model, in which the chains do not possess rigid components or side chains, allowing for symmetric spacefilling since there is no conformational or directionality bias.57 In contrast, the PBLG block contains strongly associating side chains that fold inward and weakly interdigitate to minimize interactions with the PDMS phase. Additionally, due to the interaction asymmetry of the side chains, predominantly from the planarity of the benzyl ring, the packing forces act more strongly in a lateral direction, causing expansion perpendicular to the side-chain axis, thus, giving rise to the disk-like structure. Puck-like or disk-like structures have been theoretically proposed58 and experimentally observed59 in coil−rod−coil systems with large coil volume fractions (0.82); however, these systems are based on linear rod segments, while the posed peptidic triblock system presents interesting results regarding the way side-chain interactions can control morphology development. Next, analyzing S30G10S30 with a peptidic volume fraction of 0.28, it is observed (Figure 9) that a lamellar microstructure developed, contradictory to the cylindrical microstructure expected from volume fraction or self-consistent field theory calculations. As was revealed in G5S30G5, the sterics of the bulky PBLG side chain plays an important role in dictating chain packing; consequently, to determine if the observed morphology is indeed attributed to side-chain sterics, a triblock of 0.28 volume fraction glycine (PDMS8-b-poly(glycine)10-b-PDMS8) was modeled. Simulation details can be found in the Appendix. Figure 10 shows that the glycine-based triblock produces a cylindrical morphology; therefore, it is believed that the PBLG H



Article

(dimethylsiloxane). Modeling results of this system indicate that the side-chain sterics strongly influence the final morphology, for instance, lamellar domain formation rather than hexagonally packed cylinders. Ultimately, this work sets the stage for future investigations, such as considering the impact of dispersity, in both chain length and secondary structure (mixed α-helix/β-sheet systems), on the developing morphology, as this will affect chain alignment and packing. Additionally, as alluded to in the opening paragraphs, morphology strongly influences the mechanical response; however, the polymers studied in this investigation are of relatively low molecular weight, and thus, these materials would likely possess poor mechanical characteristics. Nonetheless, due to the transferability and computational efficiency of this modeling approach, full peptidic, multiblock polymers, such as those previously synthesized,50,51 could be investigated to understand the impacts of morphology on the deformation mechanics. However, a drawback to the MARTINI model is the inability to replicate secondary structure changes due to the lack of hydrogen bonding and high dihedral angle potentials; thus, a representation that is capable of accounting for secondary structure changes would need to be investigated. Nonetheless, the present state of the CG model provides an initial point to explore the deformation behavior of these materials due to the ability to produce justifiable microstructures.

Figure 11. Intermolecular radial pair distributions of the peptide backbones for PBLG and polyglycine. Polyglycine displays coordination peaks characteristic of hexagonally packed rods, while PBLG is disordered.

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APPENDIX

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AUTHOR INFORMATION

Parameters for β-sheet forming poly(glycine) were taken directly from the MARTINI force field. Homoblocks of poly(glycine)5 and poly(glycine)10 were subjected to the same simulation procedure as described in Section 2 in order to determine the system density for volume fraction calculations. The computed density (1.27 ± 0.01 g/cm3) was found to be in close agreement with the experimental value of 1.254 g/cm3. Homoblocks of PDMS10 and PDMS93 were also studied based on the procedures outlined in Section 2 to ensure density and structural property stability. No major deviations were observed.

Figure 12. (A) Snapshot with PBC (black rectangular box represents original box) of the lamellar morphology formed in S30G40S30. (B) Side view of the peptidic lamellae, displaying a mix of bent and elongated helical chains. (C) Peptidic backbone intermolecular radial pair distribution displaying peaks characteristic of hexagonally packed rods.

frustrated chain packing. Lastly, an interesting difference between S30G40S30 and S30G10S30 is the PDMS lamellar thickness. In S30G40S30, the PDMS layer is composed of elongated and interdigitated PDMS chains, creating a relatively thin (∼4 nm) layer, while in S30G10S30, the PDMS lamellae are larger (∼7.5 nm) and composed of elongated PDMS chains that are only interdigitated at the ends. The origin of this domain swelling is unclear; however, it is believed that the peptide helical structure in S30G40S30 sweeps a large cylindrical volume, compared to the relatively narrow β-sheet rod-like structure of S30G10S30, which provides adequate packing room for the PDMS chains to fully interdigitate.

Corresponding Authors

(L.T.J.K.) *E-mail: [email protected]. (M.T.) *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

This work was financially supported by the National Science Foundation (CAREER DMR-0953236) and made use of the High Performance Computing Resource in the Core Facility for Advanced Research Computing at Case Western Reserve University. M.T. acknowledges support from National Science Foundation (DMR-1410290). We thank Yeneneh Yimer, Dr. Kshitij Jha, and Dr. Gary Leuty for their comments and discussion during the preparation of this manuscript, as well as Dr. Hadrian Djohari and the CWRU HPC staff for their assistance.

4. CONCLUSIONS The goal of this work was to determine the accuracy of the combined MARTINI CG protein model and a newly developed PDMS CG model in studying the morphology of the triblock polymer poly(γ-benzyl-L-glutamate)-b-poly(dimethylsiloxane)b-poly(γ-benzyl-L-glutamate). The combined CG model was found to produce results agreeable with experimental data, such as domain size and peptide chain packing; consequently, the CG parameters were applied to the inverted triblock system poly(dimethylsiloxane)-b-poly(γ-benzyl-L-glutamate)-b-polyI



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PDMS Triblock Morphology

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