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

Dodd, Lawrence R.; Theodorou, Doros N.

doi:10.1080/00268979100100941

Cited by 122 publications

(93 citation statements)

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“…The calculation of the accessible free volume of each cell of the grid is based on a suitable adaptation of an analytical algorithm. 33 The original algorithm determines in an analytical fashion the volume of a sphere delimited by a set of arbitrary directed planes. It has been adapted to treat the case of the volume of a sphere intersecting with a cubic box and takes into account the periodic boundary conditions.…”

Section: Methods Polymer Coarse Grained Modelmentioning

confidence: 99%

Monte Carlo simulations of a coarse grained model for an athermal all-polystyrene nanocomposite system

Vogiatzis

Voyiatzis

Theodorou

2011

European Polymer Journal

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Abstract:The structure of a polystyrene matrix filled with tightly cross-linked polystyrene nanoparticles, forming an athermal nanocomposite system, is investigated by means of a Monte Carlo sampling formalism. The polymer chains are represented as random walks and the system is described through a coarse grained Hamiltonian. This approach is related to self-consistent-field theory but does not invoke a saddle point approximation and is suitable for treating large three-dimensional systems. The local structure of the polymer matrix in the vicinity of the nanoparticles is found to be different in many ways from that of the corresponding bulk, both at the segment and the chain level. The local polymer density profile near to the particle displays a maximum and the bonds develop considerable orientation parallel to the nanoparticle surface. The depletion layer thickness is also analyzed. The chains orient with their longest dimension parallel to the surface of the particles. Their intrinsic shape, as characterized by spans and principal moments of inertia, is found to be a strong function of position relative to the interface. The dispersion of many nanoparticles in the polymeric matrix leads to extension of the chains when their size is similar to the radius of the dispersed particles.

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Section: Methods Polymer Coarse Grained Modelmentioning

confidence: 99%

Monte Carlo simulations of a coarse grained model for an athermal all-polystyrene nanocomposite system

Vogiatzis

Voyiatzis

Theodorou

2011

European Polymer Journal

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“…The volume of each cell is taken as (∆L) 3 minus the volume of any sections of nanoparticles that find themselves in the cell; it is computed via a fast analytic algorithm. 43 Following early work by Helfand and Tagami, 44 a functional of local density is derived heuristically guided by the macroscopic thermodynamic behavior of the system. The nonbonded effective Hamiltonian, punishes departures of the local density in each cell from the mean segment density ρ 0 in the melt under the temperature and pressure conditions of interest:…”

Section: Model and Simulation Methodology Modelmentioning

confidence: 99%

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

2013

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Abstract: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 nm 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 mass drastically alters the brush dimensions, affecting the wetting behavior of the polymeric brush. On the contrary, especially for particles dispersed in high molecular weight matrix, variation of the matrix chain length causes an almost imperceptible change of the density around the particle surface.

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“…The latter 2 is obtained by evaluating the remaining sphere (atom) volume, intersected by a number of planes 3 using the Dodd and Theodorou algorithm. 79 In this case, the atom defines the sphere, while the 4 faces of the corresponding Voronoi polyhedron define the cutting planes. The same calculation 5 provides also the cell contribution, , to the total accessible surface :…”

Section: (A) Calculation Of the Accessible Surface And Volume 20mentioning

confidence: 99%

Modeling of Bulk Kerogen Porosity: Methods for Control and Characterization

et al. 2017

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9Shale gas is an unconventional source of energy, which has attracted a lot of attention during the 10 last years. Kerogen is a prime constituent of shale formations and plays a crucial role in shale gas 11 technology. Significant experimental effort in the study of shales and kerogen has produced a 12 broad diversity of experimentally determined structural and thermodynamic properties even for 13 samples of the same well. Moreover, proposed methods reported in the literature for constructing 14 realistic bulk kerogen configurations have not been thoroughly investigated. One of the most 15 important characteristics of kerogens is their porosity due to its direct connection with their 16 transport properties and its potential as discriminating and classifying metric between samples. In 17 this study, Molecular Dynamics (MD) simulations are used to study the porosity of model 18 2 kerogens. The porosity is controlled effectively with systematic variation of the number and the 1 size of dummy LJ particles that are used during the construction of system's configuration. The 2 porosity of each sample is characterized with a newly proposed algorithm for analyzing the free 3 space of amorphous materials. It is found that with moderately sized configurations, it is possible 4 to construct percolated pores of interest in shale gas industry. 5

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

Cited by 122 publications

References 1 publication

Monte Carlo simulations of a coarse grained model for an athermal all-polystyrene nanocomposite system

Monte Carlo simulations of a coarse grained model for an athermal all-polystyrene nanocomposite system

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

Modeling of Bulk Kerogen Porosity: Methods for Control and Characterization

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