Session B34: Where Simulation, Theory, and Experiment Meet Across Length Scales I

Theory of Chirality Transfer in Block Copolymer Melts

Block copolymers assemble into a rich spectrum of ordered phases, with complexity driven by asymmetry in copolymer architecture. Despite decades of study, influence of intrinsic chirality on equilibrium mesophase assembly of block copolymers is not well understood and largely unexplored. Self-consistent field theory has been largely instrumental in prediction of physical properties of polymeric systems. Recently, a polar orientational self-consistent field (oSCF) theory was adopted to model chiral block copolymers having a thermodynamic preference for cholesteric ordering in chiral segments, and which confirmed the equilibrium stability of a helical cylinder morphology observed for chiral diblocks. Here, I describe a newly developed oSCF theory for chiral nematic copolymers, where segment orientations are characterized by quadrupolar interactions, and focus our study on intra-domain nematic ordering in flexible block copolymer assemblies, and in particular, mechanisms of transfer of segment chirality to mesochiral symmetries of self-assembled bicontinuous network morphologies.   

Relationship of Structural and Stress Relaxation in Disordered Diblock Copolymer Melts

We use molecular dynamics simulations to study the relationship between the relaxation of composition fluctuations and the relaxation of stress and birefringence in simple models of disordered block copolymer melts. Simulations of different simulation models of in corresponding thermodynamic states of unentangled melts are shown to exhibit equivalent dynamical behavior, thus confirming dynamic universality for unentangled systems. Structural relaxation is characterized by measuring the van Hove dynamic structure function S(q*, t) at the critical wavenumber q* at which the static structure function is maximum, and measuring how the associated relaxation time depends on distance from the order-disorder transition. The behavior of this quantity is compared to that of the dynamic viscoelatic modulus G(t), which is obtained by computing autocorrelations of stress fluctuations. Relationship to relevant experiments is also briefly discussed.   

Equilibrium and Kinetics of Block Copolymers Micelles

Both equilibrium properties of micelles, such as the critical micelle concentration (CMC), and dynamical properties such as the micelle lifetime are difficult to study in simulations because of the slow dynamics of the processes by which micelles are created and destroyed. We first discuss a method of precisely identifying the CMC in a simple model of block copolymer micelles in a homopolymer matrix, which makes use of thermodynamic integration to compute the free energy of formation. We then examine the free energy barriers to competing mechanisms for creating and destroying micelles, which could occur predominantly either by a step-wise process involving insertion and extraction of single molecules or by fission and fusion of entire micelles.   

Connecting Molecular Dynamics Simulations and Fluids Density Functional Theory of Block Copolymers

Increased understanding and precise control over the nanoscale structure and dynamics of microphase separated block copolymers would advance development of mechanically robust but conductive materials for battery electrolytes, among other applications. Both coarse-grained molecular dynamics (MD) simulations and fluids (classical) density functional theory (fDFT) can capture the microphase separation of block copolymers, using similar monomer-based chain models and including local packing effects. Equilibrium free energies of various microphases are readily accessible from fDFT, which allows us to efficiently determine the equilibrium nanostructure over a large parameter space. Meanwhile, MD allows us to visualize specific polymer conformations in 3D over time and to calculate dynamic properties. The fDFT density profiles are used to initialize the MD simulations; this ensures the MD proceeds in the appropriate microphase separated state rather than in a metastable structure (useful especially for nonlamellar structures). The simulations equilibrate more quickly than simulations initialized with a random state, which is significant especially for long chains. We apply these methods to study the interfacial behavior and microphase separated structure of diblock and tapered block copolymers. Tapered copolymers consist of pure A and B monomer blocks on the ends separated by a tapered region that smoothly varies from A to B (or from B to A for an inverse taper). Intuitively, tapering increases the segregation strength required for the material to microphase separate and increases the width of the interfacial region. Increasing normal taper length yields a lower domain spacing and increased polymer mobility, while larger inverse tapers correspond to even lower domain spacing but decreased mobility. Thus the changes in dynamics with tapering cannot be explained by mapping to a diblock system at an adjusted effective segregation strength.   

Multi-fluid models of polymeric liquids

Industrial processes for producing polymer-based materials often operate away from equilibrium, making the final microstructure -- and thus the properties of the material -- dependent on processing history. Current simulation methods struggle to accurately describe such processes. Traditional fluid dynamics is able to capture transport behavior, but lacks the complex phase behavior characteristic of many polymeric liquids. Coarse-grained particle models can handle the complexity, but are constrained by time and length scales. Consequently, we explore an alternative field-theoretic framework based on the ``two-fluid'' model originally proposed by Brochard and de Gennes. To demonstrate feasibility, we derive a model and develop an efficient numerical method for a ternary polymer solution. Subsequently, we use this model and method to examine the physics of the immersion precipitation process, used industrially to produce polymer membranes.   

Using Self Consistent Field Theory on Polymeric Mixtures

The ability to predict the solubility of a particular solvent in a polymer fluid is essential to the production of polymer foams. For the past 40 years, the primary model employed to this end has been an expansion of Flory-Huggins lattice fluid theory developed by Sanchez and Lacombe (S-L theory). S-L theory, while useful in the uniform limit, is limited to homogeneous systems. Self-Consistent Field Theory (SCFT), which has long been in use in polymer physics, is a mean-field theory capable of modeling the equilibrium behaviour of both homogeneous and inhomogeneous systems. We are investigating whether SCFT, applied to polymer-solvent mixtures, is in agreement with SL-theory in the homogeneous limit. Should this prove successful, we hope to use SCFT to model more general mixtures, including inhomogeneous nanocellular polymer foam systems.   

The Effects of Branching and Deuterium Labeling on Polymer Blend Miscibility

Local structural or chemical changes made to one component of a polymer blend can have a significant impact on miscibility. In this talk we will focus on several blends involving linear and 4-arm star polystyrene (PS), both hydrogenous and deuterated, and poly(vinylmethylether) (PVME). We consider the effect of the structural change on the miscibility of PS/PVME, then turn to the added effect of deuterium labeling, both on this blend and for isotopic PS mixtures. Using our Locally Correlated Lattice (LCL) model we are able to identify trends in the physical properties of pure components, such as: free volume, thermal expansion coefficient, and cohesive energy density. We find that branching and labeling, both independently and cumulatively, affect pure component properties. Our ability to correlate structural and chemical changes with trends in physical properties leads to predictions about the compatibility of pure components, and thus their blend miscibility.   

Monte Carlo field-theoretic simulations of a homopolymer blend

Fluctuation corrections to the macrophase segregation transition (MST) in a symmetric homopolymer blend are examined using Monte Carlo field-theoretic simulations (MC-FTS). This technique involves treating interactions between unlike monomers using standard Monte-Carlo techniques, while enforcing incompressibility as is done in mean-field theory. When using MC-FTS, we need to account for a UV divergence. This is done by renormalizing the Flory–Huggins interaction parameter to incorporate the divergent part of the Hamiltonian. We compare different ways of calculating this effective interaction parameter. Near the MST, the length scale of compositional fluctuations becomes large, however, the high computational requirements of MC-FTS restrict us to small system sizes. We account for these finite size effects using the method of Binder cumulants, allowing us to locate the MST with high precision. We examine fluctuation corrections to the mean field MST, $\chi N = 2$, as they vary with the invariant degree of polymerization, $\bar N = \rho^2a^6N$. These results are compared with particle-based simulations as well as analytical calculations using the renormalized one loop theory.   

Development of Simulation Methods in the Gibbs Ensemble to Predict Polymer-Solvent Phase Equilibria

Solvent vapor annealing (SVA) of polymer thin films is a promising method for post-deposition polymer film morphology control. The large number of important parameters relevant to SVA (polymer, solvent, and substrate chemistries, incoming film condition, annealing and solvent evaporation conditions) makes systematic experimental study of SVA a time-consuming endeavor, motivating the application of simulation and theory to the SVA system to provide both mechanistic insight and scans of this wide parameter space. However, to rigorously treat the phase equilibrium between polymer film and solvent vapor while still probing the dynamics of SVA, new simulation methods must be developed. In this presentation, we compare two methods to study polymer-solvent phase equilibrium--Gibbs Ensemble Molecular Dynamics (GEMD) and Hybrid Monte Carlo/Molecular Dynamics (Hybrid MC/MD). Liquid-vapor equilibrium results are presented for the Lennard Jones fluid and for coarse-grained polymer-solvent systems relevant to SVA. We found that the Hybrid MC/MD method is more stable and consistent than GEMD, but GEMD has significant advantages in computational efficiency. We propose that Hybrid MC/MD simulations be used for unfamiliar systems in certain choice conditions, followed by much faster GEMD simulations to map out the remainder of the phase window.   

Effect of Composition and Chain Length on $\chi $ Parameter of Polyolefin Blends: A Molecular Dynamics Study

Polymer blends exhibit complex phase behavior which is governed by several factors including temperature, composition and molecular weight of components. The thermodynamics of polymer blends is commonly described using the $\chi $ parameter. While variety of experimental studies exist on identifying the factors affecting the $\chi $ parameter, a detailed molecular scale understanding of these is a topic of current research. We have studied the effect of blend composition and chain length on $\chi $ parameter values for two model polyolefin blends. The blends studied are: polyisobutylene (PIB)/polybutadiene (PBD) and polyethylene (PE)/atactic polypropylene (aPP). Molecular dynamics simulations in combination with the integral equation theory formalism proposed by Schweizer and Curro [Journal of Chemical Physics, 91, 5059 (1989)] are used to determine the $\chi $ parameter for these systems and thereby study the effect of blend composition and chain length. The resulting $\chi $ parameter values are explained in terms of the molecular structure of these polymeric systems.   

Molecular Simulation of Olefin Oligomer Blend Phase Behavior

Material properties (e.g. toughness) of polyolefin mixtures are closely tied to their phase behavior that often cannot be accurately predicted by the widely used Flory--Huggins (FH) theory. In this work, configurational-bias Monte Carlo (CBMC) simulations in the Gibbs ensemble were used to compute the phase behavior of oligomeric olefins. The cohesive energy density of pure melts and the free energy of mixing were obtained from these simulations, and the discrepancy between the binary interaction $\chi$ parameter from simulation and from the FH theory was quantified. Structural analysis and the calculated excess mixing properties provided some rationale into the interpretation of these results.   

A Semi-Empirical Multi-Scale Dynamic Monte Carlo Model of Organic Photovoltaic Performance in RIR-MAPLE Bulk Heterojunction Films

A semi-empirical method for investigating the performance of OPVs in resonant infrared, matrix-assisted pulsed laser evaporation (RIR-MAPLE) films is explored. Emulsion-based RIR-MAPLE offers a unique experimental backdrop for investigating trends through simulation and gaining a better understanding of how different thin film characteristics impact OPV device performance. A novel multi-scale formulation of the Dynamic Monte Carlo (DMC) model is developed based on observable morphology features. Specifically, using confocal microscopy, we observe the presence of micro-scale regimes of pure materials and nano-scale regions of the composite blend. This enables us to assign weighted percentages to DMC implementations on two different scales: the microscale and nanoscale regions. In addition to this, we use input simulation parameters acquired by characterization of as-deposited films. The semi-empirical multi-scale model presented serves as a unique simulation opportunity for exploring different properties of RIR-MAPLE deposited OPVs, their effects on OPV performance and potential design routes for improving device efficiencies. This work was supported, in part, by the Office of Naval Research under Grant N00014-10-1-0481 and the NSF Triangle MRSEC on Soft Matter.