Second virial coefficients of chain molecules: A Monte Carlo study

V. I. Harismiadis, I. Szleifer

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Abstract

The second virial coefficient A 2 of chain molecules modelled as Lennard-Jones beads connected by rigid rods is calculated using Monte Carlo simulations for a variety of chain lengths and temperatures. The second virial coefficient is found to vary with chain length in different ways depending on the temperature regime. From the second virial coefficient expressions the ‘effective’ interaction (potential of mean-force) between a pair of polymer chains is obtained. This potential is found to be strongly dependent on chain length and temperature, reflecting directly the different conformational behaviour of the chains in different temperature regimes. It is found that for all chains with more than three segments the effective interaction at zero separation of the centre of mass is finite. We find that at the Boyle temperature, defined by A 2(T B) = 0, the chains of finite length have excluded volume statistics. The molecules of finite chain length are found to behave as ideal chains for a temperature significantly below T B. Thus, the temperature at which the solvent changes from ‘good’ to ‘poor’ depends on whether the polymer chains are at infinite dilution or at finite density. An analogous analysis of our simulation data which is also performed with experimental data shows that our simulations are able to explain the observed behaviour of the Flory-Huggins x parameter. However, it is noted that a similar interpretation of the experimental observations should be limited to a very narrow range of temperatures.
Original languageEnglish
Pages (from-to)851-866
JournalMolecular Physics
Volume81
DOIs
StatePublished - 1994

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