Glass transition of polymer melts: A two‐dimensional Monte Carlo study in the framework of the bond fluctuation method

Characterization of Monte Carlo Dynamic/Kinetic Properties of Local Structure in Bond Fluctuation Model of Polymer System

We report the results of the characterization of local Monte Carlo (MC) dynamics of an equilibrium bond fluctuation model polymer matrix (BFM), in time interval typical for MC simulations of non-linear optical phenomena in host-guest systems. The study contributes to the physical picture of the dynamical aspects of quasi-binary mosaic states characterized previously in the static regime. The polymer dynamics was studied at three temperatures (below, above and close to the glass transition), using time-dependent generalization of the static parameters which characterize local free volume and local mobility of the matrix. Those parameters play the central role in the kinetic MC model of host-guest systems. The analysis was done in terms of the probability distributions of instantaneous and time-averaged local parameters. The main result is the characterization of time scales characteristic of various local structural processes. Slowing down effects close to the glass transition are clearly marked. The approach yields an elegant geometric criterion for the glass transition temperature. A simplified quantitative physical picture of the dynamics of guest molecules dispersed in BFM matrix at low temperatures offers a starting point for stochastic modeling of host-guest systems.

Modeling of Nonlinear Optical Phenomena in Host-Guest Systems Using Bond Fluctuation Monte Carlo Model: A Review

We review the results of Monte Carlo studies of chosen nonlinear optical effects in host-guest systems, using methods based on the bond-fluctuation model (BFM) for a polymer matrix. In particular, we simulate the inscription of various types of diffraction gratings in degenerate two wave mixing (DTWM) experiments (surface relief gratings (SRG), gratings in polymers doped with azo-dye molecules and gratings in biopolymers), poling effects (electric field poling of dipolar molecules and all-optical poling) and photomechanical effect. All these processes are characterized in terms of parameters measured in experiments, such as diffraction efficiency, nonlinear susceptibilities, density profiles or loading parameters. Local free volume in the BFM matrix, characterized by probabilistic distributions and correlation functions, displays a complex mosaic-like structure of scale-free clusters, which are thought to be responsible for heterogeneous dynamics of nonlinear optical processes. The photoinduced dynamics of single azopolymer chains, studied in two and three dimensions, displays complex sub-diffusive, diffusive and super-diffusive dynamical regimes. A directly related mathematical model of SRG inscription, based on the continuous time random walk (CTRW) formalism, is formulated and studied. Theoretical part of the review is devoted to the justification of the a priori assumptions made in the BFM modeling of photoinduced motion of the azo-polymer chains.

Photoinduced Mass Transport in Azo-Polymers in 2D: Monte Carlo Study of Polarization Effects

We studied the impact of light polarization on photoinduced dynamics of model azo-polymer chains in two dimensions, using bond-fluctuation Monte Carlo simulations. For two limiting models-sensitive to and independent of light polarization-their dynamics driven by photoisomerization of azo-dyes as well as by thermal effects was studied, including characterization of mass transport and chain reorientations. The corresponding schemes of light-matter interaction promote qualitatively different dynamics of photoinduced motion of azo-polymer chains. In particular, they can inhibit or trigger off a directed mass transport along a gradient of light illumination. The generic dynamics of single chains is superdiffusive and is promoted by breaking a symmetry present in the polarization independent model.

Complex Dynamics of Photoinduced Mass Transport and Surface Relief Gratings Formation

The microscopic and semi-macroscopic mechanisms responsible for photoinduced mass transport in functionalized azo-polymers are far from deeply understood. To get some insight into those mechanisms on "microscopic" scale, we studied the directed photoinduced motion of single functionalized polymer chains under various types of polarized light illumination using Monte Carlo bond fluctuation model and our kinetic Monte Carlo model for photoinduced mass transport. We found sub-diffusive, diffusive and super-diffusive regimes of the dynamics of single chains at constant illumination and mostly super-diffusive regime for directed motion in the presence of the gradient of light intensity. This regime is more enhanced for long than for short chains and it approaches the ballistic limit for very long chains. We propose a physical picture of light-driven inscription of Surface Relief Gratings (SRG) as corresponding to a dynamical coexistence of normal and anomalous diffusion in various parts of the system. A simple continuous time random walk model of SRG inscription based on this physical picture reproduced the light-driven mass transport found in experiments as well as the fine structure of SRG.

Complex Dynamics of Photo-Switchable Guest Molecules in All-Optical Poling Close to the Glass Transition: Kinetic Monte Carlo Modeling

We study theoretically the kinetics of noninteracting photoswitchable guest molecules (model azo-dye) dispersed at low concentration in host (model polymer matrix) in the all-optical poling process close to the glass transition temperature T_g. We modify kinetic Monte Carlo model used in our previous studies of nonlinear optical processes in host-guest systems. The polymer matrix is simulated using the bond-fluctuation model. The kinetics of multiple trans-cis-trans cycles is formulated in terms of transition probabilities which depend on local free volume in the matrix and its dynamics. Close to T_g, the buildup of polar order, monitored in terms of angular probability density functions, follows a power-law in time while the evolution of the nonlinear susceptibilities related to second harmonic generation effect follows the stretched-exponential law. This complex dynamics of guest molecules implies the presence of dynamic heterogeneities of the matrix in space and time which spread the complexity from the matrix to the otherwise simple dynamics of noninteracting guest molecules. A qualitative physical picture of mosaic-like states-intertwined areas of free- and hindered angular motion of guest molecules-is proposed and the role of related short and longer scales in space for the promotion of complex dynamics of guest molecules is discussed. A brief comparison of the theory to available experimental data is given.

Coarse-Grained Molecular Dynamics Force-Field for Polyacrylamide in Infinite Dilution Derived from Iterative Boltzmann Inversion and MARTINI Force-Field

We present a mesoscale model of aqueous polyacrylamide in the infinitely dilute concentration regime, by combining an extant coarse-grained (CG) force-field, MARTINI, and the Iterative Boltzmann Inversion protocol (IBI). MARTINI force-field was used to retain the thermodynamics of solvation of the polymer in water, whereas the structural properties and intrapolymer interactions were optimized by IBI. Atomistic molecular dynamics simulations of polymer in water were performed to benchmark the mesoscale simulations. Our results from the CG model show excellent agreement in structure with the atomistic system. We also studied the dynamical behavior of our CG system by computing the shear viscosity and compared it with the standard IBI model. The viscosity trends of our model were similar to the atomistic system, whereas the standard IBI model was highly dissimilar as expected. In summary, our hybrid CG model sufficiently mimics an infinitely dilute system, and is superior to both MARTINI and IBI in representing the structure and thermodynamics of the atomistic system, respectively. Our hybrid coarse-graining strategy promises applicability in large-scale simulations of polymeric/biological systems where the structure needs to be replicated accurately while preserving the thermodynamics of a smoother surrounding.

Structural characteristics of a cooperatively rearranging region during the glass transition of a polymer system

Local ordered structures are formed during glass transition. These local orders preferred to move cooperatively during relaxation. In other words, the cooperatively rearranging regions contained some local order.

Structure of void space in polymer solutions

The structure of void space in two- and three-dimensional (3D) polymer solutions is studied using Voronoi tessellation and percolation theory. The polymer molecules are modeled as freely jointed chains of N tangent hard disks (two dimensions) or spheres (three dimensions). Polymer chains are equilibrated via Monte Carlo simulations and the pore space in configurations of equilibrated chains is mapped using Voronoi tessellation. In d dimensions a Voronoi vertex is the center of the sphere tangent to the d+1 nearest monomers. An edge of the Voronoi diagram is the shortest route between two neighboring vertices. The edge is considered connected if a monomer can pass through and disconnected otherwise. The Voronoi construction is used to calculate the percolation threshold of the void space. The most interesting result is that the polymer area fraction at the percolation threshold is a nonmonotonic function of N in two dimensions but monotonically reaches a constant value in three dimensions. The crossover behavior of the percolation threshold is also observed in pseudo-3D. The pore size distribution decreases monotonically with increasing pore size. This is markedly different from that in configurations of hard disks (monomeric fluid) where the pore size distribution is peaked at finite size.

The effect of matrix structure on the diffusion of fluids in porous media

The effect of matrix structure on the transport properties of adsorbed fluids is studied using computer simulations and percolation theory. The model system consists of a fluid of hard spheres diffusing in a matrix of hard spheres fixed in space. Three different arrangements of the fixed spheres, random, templated, and polymeric, are investigated. For a given matrix volume fraction the diffusion coefficient of the fluid, D, is sensitive to the manner in which the matrix is constructed, with large differences between the three types of matrices. The matrix is mapped onto an effective lattice composed of vertices and bonds using a Voronoi tessellation method where the connectivity of bonds is determined using a geometric criterion, i.e., a bond is connected if a fluid particle can pass directly between the two pores the bond connects, and disconnected otherwise. The percolation threshold is then determined from the connectivity of the bonds. D displays universal scaling behavior in the reduced volume fraction, i.e., D approximately (1-phi(m)phi(c))(gamma), where phi(m) is the matrix volume fraction and phi(c) is the matrix volume fraction at the percolation threshold. We find that gamma approximately 2.2, independent of matrix type, which is different from the result gamma approximately 1.53 for diffusion in lattice models, but similar to that for conduction in Swiss cheese models. Lattice simulations with biased hopping probabilities are consistent with the continuous-space simulations, and this shows that the universal behavior of diffusion is sensitive to details of local dynamics.

Developing a coarse-grained force field for the diblock copolymer poly(styrene-b-butadiene) from atomistic simulation

We have developed a coarse-grained force field for the poly(styrene-b-butadiene) diblock copolymer. We describe the computational methods and discuss how they were applied to develop a coarse-grained force field for this diblock copolymer from the atomistic simulation. The new force field contains three different bonds, four angles, five dihedral angles, and three nonbonded terms. We successfully tested this coarse-grained model against the chain properties, including static and dynamic properties, derived from the atomistic simulation; the results suggest that the coarse-grained force field is an effective model.

Concentration and saturation effects of tethered polymer chains on adsorbing surfaces

We consider end-grafted chains at an adsorbing surface under good solvent conditions using Monte Carlo simulations and scaling arguments. Grafting of chains allows us to fix the surface concentration and to study a wide range of surface concentrations from the undersaturated state of the surface up to the brushlike regime. The average extension of single chains in the direction parallel and perpendicular to the surface is analyzed using scaling arguments for the two-dimensional semidilute surface state according to Bouchaud and Daoud [J. Phys. (Paris) 48, 1991 (1987)]. We find good agreement with the scaling predictions for the scaling in the direction parallel to the surface and for surface concentrations much below the saturation concentration (dense packing of adsorption blobs). Increasing the grafting density we study the saturation effects and the oversaturation of the adsorption layer. In order to account for the effect of excluded volume on the adsorption free energy we introduce a new scaling variable related with the saturation concentration of the adsorption layer (saturation scaling). We show that the decrease of the single chain order parameter (the fraction of adsorbed monomers on the surface) with increasing concentration, being constant in the ideal semidilute surface state, is properly described by saturation scaling only. Furthermore, the simulation results for the chains' extension from higher surface concentrations up to the oversaturated state support the new scaling approach. The oversaturated state can be understood using a geometrical model which assumes a brushlike layer on top of a saturated adsorption layer. We provide evidence that adsorbed polymer layers are very sensitive to saturation effects, which start to influence the semidilute surface scaling even much below the saturation threshold.

Cluster pair correlation function of simple fluids: Energetic connectivity criteria

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick-type integral equation for a velocity-averaged version of Hill's energetic criterion.

Percolation of clusters with a residence time in the bond definition: Integral equation theory

We consider the clustering and percolation of continuum systems whose particles interact via the Lennard-Jones pair potential. A cluster definition is used according to which two particles are considered directly connected (bonded) at time t if they remain within a distance d, the connectivity distance, during at least a time of duration tau, the residence time. An integral equation for the corresponding pair connectedness function, recently proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved using the orthogonal polynomial approach developed by another of the authors [Phys. Rev. E 55, 426 (1997)]. We compare our results with those obtained by molecular dynamics simulations.