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How Many Monodisperse Fractions are Required to Discretize Polydisperse Polymers?
Author(s) -
Shanbhag Sachin
Publication year - 2020
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.202000020
Subject(s) - dispersity , reptation , log normal distribution , viscoelasticity , rheology , polystyrene , discretization , molar mass distribution , materials science , polymer , mathematics , fraction (chemistry) , statistical physics , thermodynamics , chemistry , chromatography , statistics , polymer chemistry , physics , mathematical analysis , composite material
The linear viscoelasticity of polydisperse samples and their discretization into a blend of n f monodisperse fractions is compared. The molecular weight distribution of the polydisperse sample is described using a lognormal distribution, which has two parameters that are related to the weight‐averaged molecular weight, Z w , and the polydispersity index, ρ. Due to its success on similar systems, a variant of the double reptation model is used to describe the linear rheology. Given Z w and ρ, the optimal number of monodisperse fractionsn f ∗is obtained using the Bayesian information criterion. It quantifies and negotiates the tradeoff between accuracy (discrepancy with the response of the polydisperse sample) and complexity (number of fractions). The optimal number of fractions was found to be somewhat insensitive to Z w ; however, it increased with ρ from about 6 for ρ = 1.01 to about 20 for ρ = 2.0. Changing the underlying viscoelastic model had only a weak effect on the conclusions. Furthermore, using a blend of monodisperse fractions was found to be preferable to direct sampling even when an ensemble of chains was requested.