Methods for the calculation of occupied volumes in glassy polymers: The lattice integration and the monte carlo methods

AbstractA new model for characterizing the free volume of a glassy polymer—gas systems is proposed. An improved method for the calculation of occupied volume per monomer unit was developed within the limits of this model. The model assumptions, error estimates and algorithm efficiencies are described. Using the example of polyvinyltrimethylsilane, it is shown that linear dependences of logarithms of the diffusion and the permeability coefficients on specific accessible volume for inert gases exist.

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Non-asymptotic Error Estimates for Monte Carlo Methods

Stochastic Modelling and Applied Probability - Stochastic Simulation and Monte Carlo Methods ◽

10.1007/978-3-642-39363-1_3 ◽

2013 ◽

pp. 37-63

Author(s):

Carl Graham ◽

Denis Talay

Keyword(s):

Monte Carlo ◽

Error Estimates ◽

Monte Carlo Methods ◽

Asymptotic Error

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Structure and Properties of High and Low Free Volume Polymers Studied by Molecular Dynamics Simulation

Computation ◽

10.3390/computation7020027 ◽

2019 ◽

Vol 7 (2) ◽

pp. 27 ◽

Cited By ~ 2

Author(s):

Mikhail Mazo ◽

Nikolay Balabaev ◽

Alexandre Alentiev ◽

Ivan Strelnikov ◽

Yury Yampolskii

Keyword(s):

Molecular Dynamics ◽

Free Volume ◽

Chemical Nature ◽

Glassy Polymers ◽

Dynamics Simulation ◽

Size Distributions ◽

Structure And Properties ◽

Delaunay Tessellation ◽

Accessible Volume ◽

Probe Size

Using molecular dynamics, a comparative study was performed of two pairs of glassy polymers, low permeability polyetherimides (PEIs) and highly permeable Si-containing polytricyclononenes. All calculations were made with 32 independent models for each polymer. In both cases, the accessible free volume (AFV) increases with decreasing probe size. However, for a zero-size probe, the curves for both types of polymers cross the ordinate in the vicinity of 40%. The size distribution of free volume in PEI and highly permeable polymers differ significantly. In the former case, they are represented by relatively narrow peaks, with the maxima in the range of 0.5–1.0 Å for all the probes from H2 to Xe. In the case of highly permeable Si-containing polymers, much broader peaks are observed to extend up to 7–8 Å for all the gaseous probes. The obtained size distributions of free volume and accessible volume explain the differences in the selectivity of the studied polymers. The surface area of AFV is found for PEIs using Delaunay tessellation. Its analysis and the chemical nature of the groups that form the surface of free volume elements are presented and discussed.

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