The description of fluctuations by single chain in mean field (SCMF) simulations is discussed and the results of this particle-based self-consistent field technique are quantitatively compared to Monte Carlo simulations of the same discretized Edwards-Hamiltonian providing exact reference data. In SCMF simulations one studies a large ensemble of noninteracting molecules subjected to real, external fields by Monte Carlo simulations. The external fields approximate nonbonded, instantaneous interactions between molecules. In the self-consistent mean field theory the external fields are static and fluctuation effects are ignored. In SCMF simulations, the external fields fluctuate since they are frequently recalculated from the instantaneous density distribution of the ensemble of molecules. In the limit of infinitely high density or instantaneous update of the external fields, the SCMF simulation method accurately describes long-wavelength fluctuations. At high but finite updating frequency the accuracy depends on the discretization of the model. The accuracy is illustrated by studying the single chain structure and intermolecular correlations in polymer melts, and fluctuation effects on the order-disorder transition of symmetric diblock copolymers.

Self-assembling block copolymers are of interest for nanomanufacturing due to the ability to realize sub-100 nm dimensions, thermodynamic control over the size and uniformity and density of features, and inexpensive processing. The insertion point of these materials in the production of integrated circuits, however, is often conceptualized in the short term for niche applications using the dense periodic arrays of spots or lines that characterize bulk block copolymer morphologies, or in the long term for device layouts completely redesigned into periodic arrays. Here we show that the domain structure of block copolymers in thin films can be directed to assemble into nearly the complete set of essential dense and isolated patterns as currently defined by the semiconductor industry. These results suggest that block copolymer materials, with their intrinsically advantageous self-assembling properties, may be amenable for broad application in advanced lithography, including device layouts used in existing nanomanufacturing processes.

An atomistic modeling approach is presented for simulating the interface between a polymer melt and a crystalline solid substrate. As a test case, a thin film of polyethylene (PE) melt confined between a semiinfinite graphite phase on the one side and vacuum on the other is considered. The simulation is carried out in the NPT statistical ensemble with an efficient Monte Carlo (MC) algorithm based on state-of-the-art variable connectivity moves. The atomistic simulations are conducted by describing the PE chains with a united atom model, which considers each methylene (CH2) and methyl (CH3) group along the chain backbone as single interaction sites. To calculate the potential energy of interaction between polymer atoms and the semiinfinite graphite substrate, the method designed by Steele was implemented, capable of incorporating the exact crystallographic structure of graphite. The new approach has allowed us to analyze structural and conformational properties on the length scale of just a few angstroms from both surfaces. Detailed results are presented for the local mass density, structure, and conformation of PE at the two interfaces, obtained from simulations with model, strictly monodisperse PE samples of molecular length up to C400. Additional structural features of the adsorbed layer, such as the distribution of skeletal carbon atoms in train, loop, and tail conformations and their statistics, are also analyzed in detail and compared with the predictions of the lattice-based Scheutjens−Fleer self-consistent mean-field theory in the limit of zero solvent concentration (melt case). Our atomistic simulation data demonstrate a stronger dependence of these descriptors of adsorbed layer structure on chain length than what is calculated by the mesoscopic Scheutjens−Fleer lattice model. In a second step, thoroughly equilibrated configurations of the confined model PE melt films are subjected to detailed molecular dynamics (MD) simulations in the NPT ensemble to analyze their dynamic behavior. The MD simulations are carried out with the rRESPA multiple-time-step algorithm and have allowed us to monitor segmental and chain center-of-mass mean-square displacements over time scales on the order of a few hundreds of nanoseconds. Results from the MD simulations are presented in the companion paper.

A coarse grain model and a Monte Carlo sampling formalism are proposed for simulations of self-assembly in block copolymer melts and nanoparticle−copolymer composites. Our approach relies on a particle-based representation of the system, it does not invoke a saddle point approximation, and it permits treatment of large three-dimensional systems. We provide a detailed description of the model and methods and discuss their relationship to results from self-consistent-field theory and single chain in mean field simulations. The validity of the proposed approach is addressed by applying it to study systems whose description within existing approaches would be demanding. In particular, we use it to examine the directed assembly of copolymer blends and nanoparticles on nanopatterned substrates. We show that results from simulations are in good agreement with experiment, and we use our theoretical findings to help explain the experimental observations.

Molecular dynamics (MD) simulations have been performed on a dense polymer melt adsorbed on a solid substrate on the one side and exposed to vacuum on the other. As a model system, a thin film of polyethylene (PE) melt supported by a crystalline graphite phase on its one side (the other surface of the film is free) has been examined. Most simulations have been carried out with unentangled PE melt systems, such as C78 and C156, in the NPT statistical ensemble at T = 450 K and P = 0 atm for times up to 100 ns, using a multiple-time step MD algorithm and by incorporating the correct dependence of the long-range contribution to the energy and stress tensor on the density profile. To increase the statistical accuracy of the results, large systems have been employed in the MD simulations, such as a 200-chain C78 melt consisting of 15 600 carbon atoms. The MD simulation data have been analyzed to provide information about the spatial dependence of the short-time dynamical properties (conformational relaxation) of the melt and the long-time segmental motion and mobility in the film (transport and diffusion). Local mobility near the graphite phase is predicted to be highly anisotropic:  although it remains practically unaltered in the directions x and y parallel to the surface, it is dramatically reduced in the direction z perpendicular to it. To calculate the long time self-diffusion coefficient of adsorbed segments in the direction perpendicular to the graphite plane, MD trajectories have been mapped onto the (numerical) solution of a macroscopic, continuum diffusion equation describing the temporal and spatial evolution of the concentration of adsorbed atoms in the polymer matrix. Our calculations prove that the diffusive motion of segments remains inhomogeneous along the z direction of the adsorbed film for distances up to approximately 5−6 times the root-mean-square of the radius of gyration, R g, of the bulk, unconstrained melt.

We develop a generic coarse-grained model for describing liquid crystalline ordering of polymeric semiconductors on mesoscopic scales, using poly(3-hexylthiophene) (P3HT) as a test system. The bonded interactions are obtained by Boltzmann-inverting the distributions of coarse-grained degrees of freedom resulting from a canonical sampling of an atomistic chain in Θ-solvent conditions. The nonbonded interactions are given by soft anisotropic potentials, representing the combined effects of anisotropic π−π interactions and entropic repulsion of side chains. We demonstrate that the model can describe uniaxial and biaxial nematic mesophases, reproduces the experimentally observed effect of molecular weight on phase behavior, and predicts Frank elastic constants typical for polymeric liquid crystals. We investigate charge transport properties of the biaxial nematic phase by analyzing the length distribution of conjugated segments and the internal energetic landscape for hole transport. Results show how conjugation defects tend to localize near chain ends and how long-range orientational correlations lead to a spatially correlated, non-Gaussian density of states.

A strategy is developed for generating equilibrated high molecular-weight polymer melts described with microscopic detail by sequentially backmapping coarse-grained (CG) configurations. The microscopic test model is generic but retains features like hard excluded volume interactions and realistic melt densities. The microscopic representation is mapped onto a model of soft spheres with fluctuating size, where each sphere represents a microscopic subchain with N b monomers. By varying N b a hierarchy of CG representations at different resolutions is obtained. Within this hierarchy, CG configurations equilibrated with Monte Carlo at low resolution are sequentially fine-grained into CG melts described with higher resolution. A Molecular Dynamics scheme is employed to slowly introduce the microscopic details into the latter. All backmapping steps involve only local polymer relaxation thus the computational efficiency of the scheme is independent of molecular weight, being just proportional to system size. To demonstrate the robustness of the approach, microscopic configurations containing up to n = 1000 chains with polymerization degrees N = 2000 are generated and equilibration is confirmed by monitoring key structural and conformational properties. The extension to much longer chains or branched polymers is straightforward.Studying equilibrium and rheological properties of melts of long polymer chains with computer simulations requires the preparation of equilibrated configurations described with microscopic detail. For this purpose, stochastic approaches have been proposed to circumvent the prohibitively large relaxation times in schemes with physically realistic dynamics, resulting from chain entanglements. Among methods addressing directly the microscopic scale, re-bridging (RB) algorithms 1 are the most advanced, modifying the chain connectivity while avoiding significant changes in local monomer packing. Even with their help, the longest melts currently addressed are those of linear polyethylene, corresponding to monodisperse samples with a few C 1000 chains. 1 Introducing polydispersity, increases the acceptance rate of RB moves and longer chains can be modeled. However, the system becomes less well-defined, e.g., for understanding rheological behavior and the samples remain rather small: the longest C 6000 (average length) melt 2 that was realized contained 32 chains. To prove equilibration these studies relied on the decay of conformational correlations. However, recent findings 3 demonstrate that the combination of chain connectivity and limited compressibility affects chain conformations. Since RB moves are largely decoupled from density fluctuations, such subtle effects suggest 3 that to verify unambiguously melt equilibration more sensitive descriptors of chain shape, such as internal distance plots, 3,4 should be considered.To overcome the limitations encountered when 1 arXiv:1610.07511v1 [cond-mat.soft]

Recent work exploring phase separation and self-assembly in multicomponent polymer fluids using a particle-based self-consistent field simulation method is reviewed. The computational method is placed in the context of classical molecular dynamics and Monte Carlo simulations as well as field-theoretic approaches. Its potential is illustrated by applications ranging from spinodal decomposition in symmetric polymer blends and the ordering of diblock copolymers in the bulk to more complex phenomena such as solvent evaporation from thin polymer films and the fabrication of three-dimensional bicontinuous diblock copolymer morphologies via reconstruction on patterned substrates.