Simulations of nematic homopolymer melts using particle-based models with interactions expressed through collective variables

We develop a hybrid Monte Carlo approach for modelling nematic liquid crystals of homopolymer melts. The polymer architecture is described with a discrete worm-like chain model. A quadratic density functional accounts for the limited compressibility of the liquid, while an additional quadratic functional of the local orientation tensor of the segments captures the nematic ordering. The approach can efficiently address large systems parametrized according to volumetric and conformational properties, representative of real polymeric materials. The results of the simulations regarding the influence of the molecular weight on the isotropic-nematic transition are compared to predictions from a Landau-de Gennes free energy expansion. The formation of the nematic phase is addressed within Rouse-like dynamics, realized using the current model.     

Ordering of Diblock Copolymer Materials on Patterned Substrates: a Single Chain in Mean Field Simulation Study

Summary: The directed assembly of diblock copolymers on patterned substrates is a way to create nanoscopically structured materials. We study the structure and kinetics of diblock copolymers on patterned substrates by simulating a large ensemble of independent chains in an external field. This external field depends on the density created by the ensemble of molecules and it is frequently updated as to mimic the instantaneous interactions of a molecule with its neighbors. This approximate, particle-based field theoretical method allows (i) to incorporate arbitrary chain architecture (ii) to include fluctuations and (iii) the explicit propagation of the chain conformations in time permits us to study the kinetics of structure formation. The factors that control the accuracy of the method are quantitatively discussed and the reconstruction of the soft morphology at substrate patterns that deviate from the periodic morphology of the diblock in the bulk are illustrated.     

An efficient Monte Carlo algorithm for the fast equilibration and atomistic simulation of alkanethiol self-assembled monolayers on a Au(111) substrate

A new Monte Carlo algorithm is presented for the simulation of atomistically detailed alkanethiol self-assembled monolayers (R-SH) on a Au(111) surface. Built on a set of simpler but also more complex (sometimes nonphysical) moves, the new algorithm is capable of efficiently driving all alkanethiol molecules to the Au(111) surface, thereby leading to full surface coverage, irrespective of the initial setup of the system. This circumvents a significant limitation of previous methods in which the simulations typically started from optimally packed structures on the substrate close to thermal equilibrium. Further, by considering an extended ensemble of configurations each one of which corresponds to a different value of the sulfur-sulfur repulsive core potential, sigmass, and by allowing for configurations to swap between systems characterized by different sigmass values, the new algorithm can adequately simulate model R-SH/Au(111) systems for values of sigmass ranging from 4.25 A corresponding to the Hautman-Klein molecular model (J. Chem. Phys. 1989, 91, 4994; 1990, 93, 7483) to 4.97 A corresponding to the Siepmann-McDonald model (Langmuir 1993, 9, 2351), and practically any chain length. Detailed results are presented quantifying the efficiency and robustness of the new method. Representative simulation data for the dependence of the structural and conformational properties of the formed monolayer on the details of the employed molecular model are reported and discussed; an investigation of the variation of molecular organization and ordering on the Au(111) substrate for three CH3-(CH2)n-SH/Au(111) systems with n=9, 15, and 21 is also included.     

Directed assembly of copolymer materials on patterned substrates: Balance of simple symmetries in complex structures

The self-assembly of a lamella-forming blend of a diblock copolymer and its respective homopolymers on periodically patterned substrates is investigated by a concerted experimental and theoretical approach. The substrate pattern consists of square arrays of spots that preferentially attract one component of the blend. The mismatch between the lamellar equilibrium morphology of the copolymer material and the substrate pattern results in the formation of a bicontinuous morphology. At the substrate, a quadratically perforated lamella (QPL) assembles in perfect registry with the substrate pattern. From this, QPL necks emanate and reach the top surface of the film. The detailed structure of these cylindrical nanochannels is analyzed using Voronoi tessellation, orientation correlation functions, and the structure factor of the neck positions on the top surface. The surface morphology is dictated by the antagonism of the square symmetry of the substrate pattern and the tendency of the necks to locally pack in a hexagonal arrangement. The analogy and differences to a system of adsorbed monolayer on corrugated substrates is explored by comparing the arrangement of the necks on the film's top surface with the structure of a soft disk model on a quadratically corrugated substrate. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2589–2604, 2006     

Polymer-solid contacts described by soft, coarse-grained models

The ability of soft, coarse-grained models to describe the narrow interface of a nearly incompressible polymer melt in contact with a solid is explored by numerical self-consistent field calculations and Monte-Carlo simulations. We investigate the effect of the discreteness of the bead-spring architecture by quantitatively comparing the results of a bead-spring model with different number of beads, N, but identical end-to-end distance, R(e), and a continuous Gaussian-thread model. If the width, ξ, of the narrow polymer-solid contact is smaller or comparable to the length of a statistical segment, b=R(e)/√N-1, strong differences in the interface tension and the density profiles between the two models are observed, and strategies for compensating the discrete nature of the bead-spring model are investigated. Compensating the discretization of the chain contour in the bead-spring model by applying an external segment-solid potential, we simultaneously adjust the interface tension and the density profile to the predictions of the Gaussian-thread model. We suggest that the geometry of the polymer-solid contact and the interface tension are relevant characteristics that a coarse-grained model of polymer-solid contacts must reproduce in order to establish a quantitative relationship to an experimental system.     

Hierarchical assembly of nanoparticle superstructures from block copolymer-nanoparticle composites

We investigate the assembly of block copolymer-nanoparticle composite films on chemically nanopatterned substrates and present fully three-dimensional simulations of a coarse grain model for these hybrid systems. The location and distribution of nanoparticles within the ordered block copolymer domains depends on the thermodynamic state of the composite in equilibrium with the surface. Hierarchical assembly of nanoparticles enables applications in which the ability to precisely control their locations within periodic and nonregular geometry patterns and arrays is required.