Doros N. Theodorou

A concerted rotation algorithm for atomistic Monte Carlo simulation of polymer melts and glasses

We develop and test a new elementary Monte Carlo move for use in the efficient simulation of polymer systems. The move consists of a concerted rotation around up to seven adjacent skeletal bonds that leaves the rest of the chain unaffected. No assumption is made concerning the backbone geometry other than that bond lengths and bond angles are held constant during the elementary move. Special sampling techniques are needed because the new move involves a correlated change in seven degrees of freedom along the chain backbone. We use the new move in conjunction with reptation in an isothermal-isobaric Monte Carlo simulation of a bulk tetracosane melt system and find that it improves computational efficiency relative to a purely reptation-based Monte Carlo scheme. Comparisons are also made between a concerted rotation-based Monte Carlo simulation and a molecular dynamics simulation of an oligomer of atactic polypropylene.

Diffusion and reaction in blocked and high occupancy zeolite catalysts

Abstract Diffusion in a ZSM-5 zeolite crystal is modeled as a simple random walk process in a finite, two-dimensional network of pores. Pore blocking is investigated as a model for catalyst modifications to enhance shape selectivity. The effects of random blocking of pores in the bulk of the crystal, or of pore entrances along the crystal border, are examined quantitatively. The behavior of effective intracrystalline diffusivity vs percentage of pores blocked is highly dependent on the blocking mode. A Monte-Carlo model for diffusion and reaction in a zeolite crystal is developed to study the effects of intracrystalline occupancy by gaseous molecules on the degree of diffusional effects on the reaction. For the simple isomerization A ag B, where species A and B have equal diffusivities, results obtained by Monte-Carlo simulation deviate from the predictions of a corresponding continuum approach in the region of high occupancies. This is due to the “finiteness” of the crystal, which is incorporated in the stochastic model, but not accounted for in the continuum approach.

Analytical treatment of the volume and surface area of molecules formed by an arbitrary collection of unequal spheres intersected by planes

A general algorithm has been developed for the analytical determination of the volume and exposed surface area of a solid body formed by a collection of arbitrarily sized intersecting spheres and delimited by a set of arbitrarily directed planes. The algorithm is useful for analysing molecules represented as fused hard spheres, sections of such molecules, as well as void or available spaces formed among such molecules. The multisphere-multiplane problem is decomposed into a set of problems involving the intersection of a single sphere by an arbitrary collection of planes. The volume and exposed area of the convex body formed by such an intersection are found using simple principles of analytical geometry. Applications of the new method are presented for the determination of the volume, excluded volume, and surface area of long-chain molecules and of the void volume and internal surface area of a zeolite crystal. It is found that the method is faster, more efficient, more versatile, and more accurate than ...

Atomistic Monte Carlo simulation of strictly monodisperse long polyethylene melts through a generalized chain bridging algorithm

This work is concerned with the atomistic simulation of the volumetric, conformational and structural properties of monodisperse polyethylene (PE) melts of molecular length ranging from C78 up to C1000. In the past, polydisperse models of these melts have been simulated in atomistic detail with the end-bridging Monte Carlo algorithm [Pant and Theodorou, Macromolecules 28, 7224 (1995); Mavrantzas et al., Macromolecules 32, 5072 (1999)]. In the present work, strictly monodisperse as well as polydisperse PE melts are simulated using the recently introduced double bridging and intramolecular double rebridging chain connectivity-altering Monte Carlo moves [Karayiannis et al., Phys. Rev. Lett. 88, 105503 (2002)]. These algorithms constitute generalizations of the EB move, since they entail the construction of two trimer bridges between two properly chosen pairs of dimers along the backbones of two different chains or along the same chain. In the simulations, a new molecular model is employed which is a hybrid o...

The effects of local structural relaxation on aluminum siting within H-ZSM-5

Semiempirical molecular orbital calculations have been performed to study aluminum siting in H-ZSM-5 zeolites. Local structural rearrangements upon substituting aluminum (with a charge compensating proton) for silicon are found to be important. The T12 site is found to be the most preferred site for aluminum substitution. However, the calculated energetics for substitution show that several tetrahedral sites are energetically comparable with regard to aluminum siting. Results pertaining to the electronic properties of the acidic site upon aluminum substitution at each of the twelve distinct tetrahedral sites are presented. The acidic center is found to be a rather soft species, with the HOMO-LUMO energy gap being roughly 8 eV.

Geometrical considerations in model systems with periodic boundaries

Model systems with periodic boundaries in the shape of an arbitrary parallelepiped are discussed. The locus of minimum images with respect to a given atom is determined, and algorithms for computing minimum image distances, as well as locating significantly interacting atom pairs are presented. It is also shown that, by exhausting the structural information provided by the model system, pair distribution functions can be computed for distances up to the semidiagonal of the minimum image locus. Comparison of the algorithms proposed with existing ones on a typical model system clearly shows that the new algorithms are correct and superior in computational efficiency, for cubic as well as noncubic systems.

A chain of states method for investigating infrequent event processes occurring in multistate, multidimensional systems

This paper describes novel numerical methods for constructing reaction paths and evaluating transition state theory (TST) rate constants for multidimensional, multistate systems. The reaction path is represented as a tethered, freely jointed chain of states with configuration specified by minimization of a function that is derived from the differential description of the path. The method is general and applicable to systems of arbitrary dimension and does not require a priori knowledge of the first‐order saddle point, or the topology of the states. Also presented is a novel procedure for numerical determination of the TST rate constant. The procedure is based on Monte Carlo importance sampling using a tethered chain with links modeled as harmonic springs. The beads of the chain and the points at which links pierce the dividing surface separating states serve as biased sampling points for Monte Carlo numerical integration. The methods presented here are tested using the Muller potential surface. The applic...

Detailed molecular dynamics simulation of the self-diffusion of n-alkane and cis-1,4 polyisoprene oligomer melts

Results are presented for the self-diffusion properties of monodisperse n-alkanes and cis-1,4 polyisoprene (PI) oligomer melts, as obtained through detailed atomistic molecular dynamics (MD) simulations. The simulations have been conducted in the NVT statistical ensemble on model systems thoroughly pre-equilibrated through an efficient Monte Carlo (MC) algorithm. Results for the self-diffusion coefficient D as a function of molecular weight M support a scaling law of the form D∼Mb, with b strongly depending on temperature T, for both the n-alkanes and the cis-1,4 PI melts. The simulation results have been fitted to an expression for D involving elements of Rouse dynamics and Cohen–Turnbull–Bueche chain-end (excess free volume) effects, proposed recently by von Meerwall et al. [J. Chem. Phys. 108, 4299 (1998)]. Using a geometric analysis involving tessellation of space in Delaunay tetrahedra developed by Greenfield and Theodorou [Macromolecules 26, 5461 (1993)], we have also calculated the excess chain-end...

Structure of Polymer Layers Grafted to Nanoparticles in Silica–Polystyrene Nanocomposites

The structural features of polystyrene brushes grafted on spherical silica nanoparticles immersed in polystyrene are investigated by means of a Monte Carlo methodology based on polymer mean field theory. The nanoparticle radii (either 8 or 13 nm) are held constant, while the grafting density and the lengths of grafted and matrix chains are varied systematically in a series of simulations. The primary objective of this work is to simulate realistic nanocomposite systems of specific chemistry at experimentally accessible length scales and study the structure and scaling of the grafted brush. The profiles of polymer density around the particles are examined; based on them, the brush thickness of grafted chains is estimated and its scaling behavior is compared against theoretical models and experimental findings. Then, neutron scattering spectra are predicted both from single grafted chains and from the entire grafted corona. It is found that increasing both the grafting density and the grafted chain molar ma...

Chain and local dynamics of polyisoprene as probed by experiments and computer simulations

The dynamics of designed short polyisoprene (PI) chains in the melt is investigated on a wide temperature window using dielectric relaxation spectroscopy and pulsed field gradient nuclear magnetic resonance (NMR). At high temperatures, molecular dynamics (MD) simulations performed using two different models (an explicit atom model and a united atom one) capture very well the dynamic properties documented experimentally. Structures pre-equilibrated with end-bridging Monte Carlo are used as initial configurations for MD runs at different temperatures, providing predictions for the temperature dependence of the dynamics of this bulk PI. Local dynamics is unique, independently of the probe (dielectric relaxation, dynamic light scattering, nuclear magnetic resonance, neutron scattering), although mean correlation times are significantly affected, to different extents, by librations. Chain dynamics over the molecular weight and temperature range studied can be described well by the Rouse model, as shown by both...