The effect of chemical constitution on polyisoprene dynamics.

Polyisoprene (PI) melts have been studied, with most reports focusing on systems with high 1,4-cis content. In contrast, 1,4-trans PI homopolymers or random copolymers have seldom been examined, despite a handful of investigations suggesting a distinct dynamic behavior. Herein, we employ all-atom simulations to investigate the effect of chemical architecture on the dynamics of cis and trans-PI homopolymers, as well as copolymers. We examine the thermodynamic, conformational, and structural properties of the polymers and validate the performance of the models. We probe chain dynamics, revealing that cis-PI presents accelerated translation and reorientation modes relative to trans as recorded by the mean square displacement of the chain center-of-mass as well as by the characteristic times of the lower modes in a Rouse analysis. Interestingly, progressing to higher modes, we observe a reversal with trans units exhibiting faster dynamics. This was further confirmed by calculations of local carbon-hydrogen vector reorientation dynamics, which offer a microscopic view of segmental mobility. To obtain insight into the simulation trajectories, we evaluate the intermediate incoherent scattering function that supports a temperature-dependent crossover in relative mobility that extends over separations beyond the Kuhn-length level. Finally, we analyzed the role of non-Gaussian displacements, which demonstrate that cis-PI exhibits increased heterogeneity in dynamics over short-timescales in contrast to trans-PI, where deviations persist over times extending to terminal dynamics. Our all-atom simulations provide a fundamental understanding of PI dynamics and the impact of microstructure while providing important data for the design and optimization of PI-based materials.

Deep convolutional neural networks for generating atomistic configurations of multi-component macromolecules from coarse-grained models.

Despite the modern advances in the available computational resources, the length and time scales of the physical systems that can be studied in full atomic detail, via molecular simulations, are still limited. To overcome such limitations, coarse-grained (CG) models have been developed to reduce the dimensionality of the physical system under study. However, to study such systems at the atomic level, it is necessary to re-introduce the atomistic details into the CG description. Such an ill-posed mathematical problem is typically treated via numerical algorithms, which need to balance accuracy, efficiency, and general applicability. Here, we introduce an efficient and versatile method for backmapping multi-component CG macromolecules of arbitrary microstructures. By utilizing deep learning algorithms, we train a convolutional neural network to learn structural correlations between polymer configurations at the atomistic and their corresponding CG descriptions, obtained from atomistic simulations. The trained model is then utilized to get predictions of atomistic structures from input CG configurations. As an illustrative example, we apply the convolutional neural network to polybutadiene copolymers of various microstructures, in which each monomer microstructure (i.e., cis-1,4, trans-1,4, and vinyl-1,2) is represented as a different CG particle type. The proposed methodology is transferable over molecular weight and various microstructures. Moreover, starting from a specific single CG configuration with a given microstructure, we show that by modifying its chemistry (i.e., CG particle types), we are able to obtain a set of well equilibrated polymer configurations of different microstructures (chemistry) than the one of the original CG configuration.

Backmapping coarse-grained macromolecules: An efficient and versatile machine learning approach.

Multiscale modeling of polymers exchanges information between coarse and fine representations of molecules to capture material properties over a wide range of spatial and temporal scales. Restoring details at a finer scale requires us to generate information following embedded physics and statistics of the models at two different levels of description. Techniques designed to address this persistent challenge balance among accuracy, efficiency, and general applicability. In this work, we present an image-based approach for structural backmapping from coarse-grained to atomistic models with cis-1,4 polyisoprene melts as an illustrative example. Through machine learning, we train conditional generative adversarial networks on the correspondence between configurations at the levels considered. The trained model is subsequently applied to provide predictions of atomistic structures from the input coarse-grained configurations. The effect of different data representation schemes on training and prediction quality is examined. Our proposed backmapping approach shows remarkable efficiency and transferability over different molecular weights in the melt based on training sets constructed from oligomeric compounds. We anticipate that this versatile backmapping approach can be readily extended to other complex systems to provide high-fidelity initial configurations with minimal human intervention.

Coarse-graining of polyisoprene melts using inverse Monte Carlo and local density potentials.

Bottom-up coarse-graining of polymers is commonly performed by matching structural order parameters such as distribution of bond lengths, bending and dihedral angles, and pair distribution functions. In this study, we introduce the distribution of nearest-neighbors as an additional order parameter in the concept of local density potentials. We describe how the inverse-Monte Carlo method provides a framework for forcefield development that is capable of overcoming challenges associated with the parameterization of interaction terms in polymer systems. The technique is applied on polyisoprene melts as a prototype system. We demonstrate that while different forcefields can be developed that perform equally in terms of matching target distributions, the inclusion of nearest-neighbors provides a straightforward route to match both thermodynamic and conformational properties. We find that several temperature state points can also be addressed, provided that the forcefield is refined accordingly. Finally, we examine both the single-particle and the collective dynamics of the coarse-grain models, demonstrating that all forcefields present a similar acceleration relative to the atomistic systems.

Two-dimensional melting of colloids with long-range attractive interactions.

The solid-liquid melting transition in a two-dimensional (2-D) attractive colloidal system is visualized using superparamagnetic colloids that interact through a long-range isotropic attractive interaction potential, which is induced using a high-frequency rotating magnetic field. Various experiments, supported by Monte Carlo simulations, are carried out over a range of interaction potentials and densities to determine structure factors, Lindermann parameters, and translational and orientational order parameters. The system shows a first-order solid-liquid melting transition. Simulations and experiments suggest that dislocations and disclinations simultaneously unbind during melting. This is in direct contrast with reports of 2-D melting of paramagnetic particles that interact with a repulsive interaction potential.

Multiscale modeling of polyisoprene on graphite.

The local dynamics and the conformational properties of polyisoprene next to a smooth graphite surface constructed by graphene layers are studied by a multiscale methodology. First, fully atomistic molecular dynamics simulations of oligomers next to the surface are performed. Subsequently, Monte Carlo simulations of a systematically derived coarse-grained model generate numerous uncorrelated structures for polymer systems. A new reverse backmapping strategy is presented that reintroduces atomistic detail. Finally, multiple extensive fully atomistic simulations with large systems of long macromolecules are employed to examine local dynamics in proximity to graphite. Polyisoprene repeat units arrange close to a parallel configuration with chains exhibiting a distribution of contact lengths. Efficient Monte Carlo algorithms with the coarse-grain model are capable of sampling these distributions for any molecular weight in quantitative agreement with predictions from atomistic models. Furthermore, molecular dynamics simulations with well-equilibrated systems at all length-scales support an increased dynamic heterogeneity that is emerging from both intermolecular interactions with the flat surface and intramolecular cooperativity. This study provides a detailed comprehensive picture of polyisoprene on a flat surface and consists of an effort to characterize such systems in atomistic detail.

Molecular dynamics of polyisoprene/polystyrene oligomer blends: the role of self-concentration and fluctuations on blend dynamics.

The effect of self-concentration and intermolecular packing on the dynamics of polyisoprene (PI)/polystyrene (PS) blends is examined by extensive atomistic simulations. Direct information on local structure of the blend system allows a quantitative calculation of self- and effective composition terms at various length scales that are introduced to proposed models of blend dynamics. Through a detailed statistical analysis, the full distribution of relaxation times associated with reorienation of carbon-hydrogen bonds was extracted and compared to literature experimental data. A direct relation between relaxation times and local effective composition is found. Following an implementation of a model involving local composition as well as concentration fluctuations the relevant length scales characterizing the segmental dynamics of both components were critically examined. For PI, the distribution of times becomes narrower for the system with the lowest PS content and then broadens as more PS is added. This is in contrast to the slow component (PS), where an extreme breadth is found for relaxation times in the 25/75 system prior to narrowing as we increase PI concentration. The chain dynamics was directly quantified by diffusion coefficients as well as the terminal (maximum) relaxation time of each component in the mixed state. Strong coupling between the friction coefficients of the two components was predicted that leads to very similar chain dynamics for PI and PS, particularly for high concentrations of PI. We attribute this finding to the rather short oligomers (below the Rouse regime) studied here as well as to the rather similar size of PI and PS chains. The ratio of the terminal to the segmental relaxation time, τterm∕τseg, c, presents a clear qualitative difference for the constituents: for PS the above ratio is almost independent of blend composition and very similar to the pure state. In contrast, for PI this ratio depends strongly on the composition of the blend; i.e., the terminal relaxation time of PI increases more than its segmental relaxation time, as the concentration of PS increases, resulting into a larger terminal/segmental ratio. We explain this disparity based on the different length scales characterizing dynamics. The relevant length for the segmental dynamics of PI is about 0.4-0.6 nm, smaller than chain dimensions which are expected to characterize terminal dynamics, whereas for PS associated length scales are similar (about 0.7-1.0 nm) rendering a uniform change with mixing.

Detailed atomistic Monte Carlo simulations of a polymer melt on a solid surface and around a nanoparticle.

The molecular factors that govern interfacial interactions between a polymer melt and a solid surface remain largely unclear despite significant progress made in the last years. Simulations are increasingly employed to elucidate these features, however, equilibration and sampling with models of long macromolecules in such heterogeneous systems present significant challenges. In this study, we couple the application of preferential sampling techniques with connectivity-altering Monte Carlo algorithms to explore the configurational characteristics of a polyethylene melt in proximity to a surface and a highly curved nanoparticle. Designed algorithms allow efficient sampling at all length scales of large systems required to avoid finite-size effects. Using detailed atomistic models for the polymer and realistic structures for a silica surface and a fullerene, we find that at the extreme limit where particles are comparable to the polymer Kuhn segment length, curvature penalizes the formation of long train segments. As a result, an increased number of shorter contacts belonging to different chains are made competing with the anticipated decrease of the bound layer thickness with particle size if polymer adsorbed per unit area remained constant. For very small nanoparticles, formation of new train segments cannot compete with the overall reduction of adsorbance which is present irrespective of the enthalpic interactions; a result that demonstrates the need for an accurate description of polymer rigidity at these length scales.

Accelerated Diffusion Following Deprotection in Chemically Amplified Resists.

Polymeric chemically amplified resists (CARs) are critical materials for high-throughput lithographic processes. A photoactivated acid-anion catalyst changes the polymer's solubility via a deprotection reaction, which enables pattern development through selective dissolution. To capture observed reaction kinetics, reaction-diffusion models employ a catalyst diffusivity that is accelerated by reaction. However, the microscopic origin and factors contributing to this phenomena remain unclear. Herein, we employ detailed atomistic molecular dynamics simulations to examine the impact of protecting group removal and material relaxation on catalyst mobility. We report data on polymer density, catalyst dispersion, excess free volume, and segmental dynamics with increasing time/extent of deprotection. We then propose simple kinetic Monte Carlo algorithms that can describe both molecular dynamics simulations of deprotection reactions and experimental data.

GxxxG motifs, phenylalanine, and cholesterol guide the self-association of transmembrane domains of ErbB2 receptors.

GxxxG motifs are common in transmembrane domains of membrane proteins and are often introduced to artificial peptides to inhibit or promote association to stable structures. The transmembrane domain of ErbB2 presents two separate such motifs that are proposed to be connected to stability and activity of the dimer. Using molecular simulations, we show that these sequences play a critical role during the recognition stage, forming transient complexes that lead to stable dimers. In pure phospholipid bilayers association occurs by contacts formed at the C-terminus promoted by the presence of phenylalanine residues. Helices subsequently rotate to eventually pack at short separations favored by lipid entropic contributions. In contrast, at intermediate cholesterol concentrations, a different pathway is followed that involves dimers with a weaker interface toward the N-terminus. However, at high cholesterol content, a switch toward the C-terminus is observed with an overall nonmonotonic change of the dimerization affinity. This conformational switch modulated by cholesterol has important implications on the thermodynamic, structural, and kinetic characteristics of helix-helix association in lipid membranes.

Interfacial Dynamics in Supported Ultrathin Polymer Films-From the Solid to the Free Interface.

Molecular dynamics in ultrathin layers is investigated using nanostructured electrodes to perform broadband dielectric spectroscopy measurements, and by atomistic molecular dynamics simulations. Using poly(vinyl acetate) as the model system and taking advantage of access to the distribution of relaxation times in an extended temperature range above the glass transition temperature, Tg, we demonstrate that while the mean rates of the segmental relaxation remain bulklike down to 12 nm film thickness, modified molecular mobilities arise in the interfacial zones. Combining results from simulations and experiments, we show unambiguously that both the slow relaxations arising from adsorbed polymer segments and the faster modes attributed to segments in the vicinity of the free interface have non-Arrhenius temperature activation. These interfacial regions span thicknesses of ∼1.5 nm each just above the calorimetric Tg independent of molecular weight and film thickness. These deviations at interfaces are relevant for applications of polymers in adhesion, coatings, and polymer nanocomposites.

Coupling between Polymer Conformations and Dynamics Near Amorphous Silica Surfaces: A Direct Insight from Atomistic Simulations.

The dynamics of polymer chains in the polymer/solid interphase region have been a point of debate in recent years. Its understanding is the first step towards the description and the prediction of the properties of a wide family of commercially used polymeric-based nanostructured materials. Here, we present a detailed investigation of the conformational and dynamical features of unentangled and mildly entangled cis-1,4-polybutadiene melts in the vicinity of amorphous silica surface via atomistic simulations. Accounting for the roughness of the surface, we analyze the properties of the polymer chains as a function of their distance from the silica slab, their conformations and the chain molecular weight. Unlike the case of perfectly flat and homogeneous surfaces, the monomeric translational motion parallel to the surface was affected by the presence of the silica slab up to distances comparable with the extension of the density fluctuations. In addition, the intramolecular dynamical heterogeneities in adsorbed chains were revealed by linking the conformations and the structure of the adsorbed chains with their dynamical properties. Strong dynamical heterogeneities within the adsorbed layer are found, with the chains possessing longer sequences of adsorbed segments ("trains") exhibiting slower dynamics than the adsorbed chains with short ones. Our results suggest that, apart from the density-dynamics correlation, the configurational entropy plays an important role in the dynamical response of the polymers confined between the silica slabs.

Lipid-modulated sequence-specific association of glycophorin A in membranes.

Protein association in lipid membranes is a complex process with thermodynamics directed by a multitude of different factors. Amino-acid sequence is a molecular parameter that affects dimerization as shown by limited directed mutations along the transmembrane domains. Membrane-mediated interactions are also important although details of such contributions remain largely unclear. In this study, we probe directly the free energy of association of Glycophorin A by means of extensive parallel Monte Carlo simulations with recently developed methods and a model that accounts for sequence-specificity while representing lipid membranes faithfully. We find that lipid-induced interactions are significant both at short and intermediate separations. The ability of molecules to tilt in a specific hydrophobic environment extends their accessible interfaces, leading to intermittent contacts during protein recognition. The dimer with the lowest free energy is largely determined by the favorable lipid-induced attractive interactions at the closest distance. Finally, the coarse-grained model employed herein, together with the extensive sampling performed, provides estimates of the free energy of association that are in excellent agreement with existing data.

Self-association of models of transmembrane domains of ErbB receptors in a lipid bilayer.

Association of transmembrane (TM) helices is facilitated by the close packing of small residues present along the amino-acid sequence. Extensive studies have established the role of such small residue motifs (GxxxG) in the dimerization of Glycophorin A (GpA) and helped to elucidate the association of TM domains in the epidermal growth factor family of receptors (ErbBs). Although membrane-mediated interactions are known to contribute under certain conditions to the dimerization of proteins, their effect is often considered nonspecific, and any potential dependence on protein sequence has not been thoroughly investigated. We recently reported that the association of GpA is significantly assisted by membrane-induced contributions as quantified in different lipid bilayers. Herein we extend our studies to explore the origin of these effects and quantify their magnitude using different amino-acid sequences in the same lipid environment. Using a coarse-grained model that accounts for amino-acid specificity, we perform extensive parallel Monte Carlo simulations of ErbB homodimerization in dipalmitoyl-phosphatidylcholine lipid bilayers. A detailed characterization of dimer formation and estimates of the free energy of association reveal that the TM domains show a significant affinity to self-associate in lipid bilayers, in qualitative agreement with experimental findings. The presence of GxxxG motifs enhances favorable protein-protein interactions at short separations. However, the lipid-induced attraction presents a more complex character than anticipated. Depending on the interfacial residues, lipid-entropic contributions support a decrease of separation or a parallel orientation to the membrane normal, with important implications for protein function.

Accelerating flat-histogram methods for potential of mean force calculations.

Potential of mean force calculations along a reaction coordinate (RC) demand exhaustive sampling, which often leads to prohibitively long computational times. The expanded ensemble density of states (EXEDOS) [E. B. Kim, R. Faller, Q. Yan et al., J. Chem. Phys. 117, 7781 (2002)] is a simple flat-histogram Monte Carlo method based on the density of states algorithm proposed by Wang and Landau [Phys. Rev. Lett. 86, 2050 (2001)]. EXEDOS offers the advantage of continuous uniform sampling of the RC with no a priori knowledge of the free energy profile. However, the method is not certain to converge within accessible simulation time. Furthermore, the strongly asymmetric distribution of tunneling times inherent in flat-histogram sampling imposes additional limitations. We propose several improvements that accelerate the EXEDOS method and can be generally applicable in free energy calculations. First, we propose an asynchronous parallel implementation of the density of states algorithm in a multiple-walkers multiple-windows scheme and extend the algorithm in an expanded ensemble [(MW)(2)-XDOS] for PMF calculations as the original EXEDOS. Despite the nonideal scaling over a number of processors this technique overcomes limitations by extreme values of tunneling times and allows consistent evaluations of performance. The second set of improvements addresses the dependence of convergence times on system size, density, and sampling rate of the RC. At low densities, the coupling of (MW)(2)-XDOS with the rejection-free geometric cluster move provides impressive performance that overshadows any other technique. However, the limited applicability of cluster moves at high densities requires an alternative approach. We propose the coupling of (MW)(2)-XDOS with preferential sampling methods. In the systems studied, single displacements in the proximity of particles defining the RC accelerate calculations significantly and render the simulation nearly size-independent. A further modification of preferential sampling involves collective displacements of particles performed in a "smart Monte Carlo" scheme. This "local Brownian dynamics" algorithm can be generally applicable to many free energy simulation methods and would be particularly beneficial at high densities and molecular systems with strong intramolecular potentials.

Calculation of local mechanical properties of filled polymers.

A study is presented on the effects of smooth nanoparticles on the structure and elastic moduli of a polymer matrix. Structural changes between the unfilled polymer matrix and the nanocomposite give rise to the formation of a glassy layer that surrounds the nanoparticles. Results for the effects of particle size and concentration on the local and overall mechanical properties of the polymer are consistent with experimental macroscopic observations. At the molecular level, it is found that dispersed, attractive nanoparticles alter the nonaffine displacement fields that arise in the polymer glass upon deformation, thereby rendering the nanocomposite glass less fragile.

Quantitative Three-Dimensional Characterization of Block Copolymer Directed Self-Assembly on Combined Chemical and Topographical Prepatterned Templates.

Characterization of the three-dimensional (3D) structure in directed self-assembly (DSA) of block copolymers is crucial for understanding the complex relationships between the guiding template and the resulting polymer structure so DSA could be successfully implemented for advanced lithography applications. Here, we combined scanning transmission electron microscopy (STEM) tomography and coarse-grain simulations to probe the 3D structure of P2VP-b-PS-b-P2VP assembled on prepatterned templates using solvent vapor annealing. The templates consisted of nonpreferential background and raised guiding stripes that had PS-preferential top surfaces and P2VP-preferential sidewalls. The full 3D characterization allowed us to quantify the shape of the polymer domains and the interface between domains as a function of depth in the film and template geometry and offered important insights that were not accessible with 2D metrology. Sidewall guiding was advantageous in promoting the alignment and lowering the roughness of the P2VP domains over the sidewalls, but incommensurate confinement from the increased topography could cause roughness and intermittent dislocations in domains over the background region at the bottom of the film. The 3D characterization of bridge structures between domains over the background and breaks within domains on guiding lines sheds light on possible origins of common DSA defects. The positional fluctuations of the PS/P2VP interface between domains showed a depth-dependent behavior, with high levels of fluctuations near both the free surface of the film and the substrate and lower fluctuation levels in the middle of the film. This research demonstrates how 3D characterization offers a better understanding of DSA processes, leading to better design and fabrication of directing templates.

Modulating membrane properties: the effect of trehalose and cholesterol on a phospholipid bilayer.

The protective properties of trehalose on cholesterol-containing lipid dipalmitoylphosphatidylcholine (DPPC) bilayers are studied through molecular simulations. The ability of the disaccharide to interact with the phospholipid headgroups and stabilize the membrane persists even at high cholesterol concentrations and restricts some of the changes to the structure that would otherwise be imposed by cholesterol molecules. Predictions of bilayer properties such as area per lipid, tail ordering, and chain conformation support the notion that the disaccharide decreases the main melting transition in these multicomponent model membranes, which correspond more closely to common biological systems than pure bilayers. Molecular simulations indicate that the membrane dynamics are slowed considerably by the presence of trehalose, indicating that high sugar concentrations would serve to avert possible phase separations that could arise in mixed phospholipid systems. Various time correlation functions suggest that the character of the modifications in lipid dynamics induced by trehalose and cholesterol is different in the hydrophilic and hydrophobic regions of the membrane.

Local mechanical properties of polymeric nanocomposites.

The inclusion of a nanoparticle into a polymer matrix is studied by efficient Monte Carlo simulations. The resulting structural changes in the melt and glass exhibit a strong dependence on the strength of the polymer attraction to the surface of the filler. The mechanical properties of the nanocomposite are analyzed in detail through a formalism that permits calculation of local elastic constants. The average shear and Young's modulus of the nanocomposite are higher than those of the pure polymer for neutral or attractive nanoparticles. For repulsive particles, these moduli are lower. Simulation of local properties reveals that a glassy layer is formed in the vicinity of the attractive filler, contributing to the increased strength of the composite material. In contrast, a region of negative moduli emerges around repulsive fillers, which provides a mechanism for frustration relief and a lowering of the glass transition temperature.

Characterizing the Three-Dimensional Structure of Block Copolymers via Sequential Infiltration Synthesis and Scanning Transmission Electron Tomography.

Understanding and controlling the three-dimensional structure of block copolymer (BCP) thin films is critical for utilizing these materials for sub-20 nm nanopatterning in semiconductor devices, as well as in membranes and solar cell applications. Combining an atomic layer deposition (ALD)-based technique for enhancing the contrast of BCPs in transmission electron microscopy (TEM) together with scanning TEM (STEM) tomography reveals and characterizes the three-dimensional structures of poly(styrene-block-methyl methacrylate) (PS-b-PMMA) thin films with great clarity. Sequential infiltration synthesis (SIS), a block-selective technique for growing inorganic materials in BCPs films in an ALD tool and an emerging technique for enhancing the etch contrast of BCPs, was harnessed to significantly enhance the high-angle scattering from the polar domains of BCP films in the TEM. The power of combining SIS and STEM tomography for three-dimensional (3D) characterization of BCP films was demonstrated with the following cases: self-assembled cylindrical, lamellar, and spherical PS-b-PMMA thin films. In all cases, STEM tomography has revealed 3D structures that were hidden underneath the surface, including (1) the 3D structure of defects in cylindrical and lamellar phases, (2) the nonperpendicular 3D surface of grain boundaries in the cylindrical phase, and (3) the 3D arrangement of spheres in body-centered-cubic (BCC) and hexagonal-closed-pack (HCP) morphologies in the spherical phase. The 3D data of the spherical morphologies was compared to coarse-grained simulations and assisted in validating the simulations' parameters. STEM tomography of SIS-treated BCP films enables the characterization of the exact structure used for pattern transfer and can lead to a better understating of the physics that is utilized in BCP lithography.