Surface tension of polymer liquids

Abstract

A cell theory for the prediction of the surface tension of simple liquids is adapted to polymer liquids. The combinatory, free volume and potential energy zero terms of the partition function are all modified to account for the preservation of connectivity when a surface is created. Theory and experiment are in good agreement without an adjustable surface parameter.

Surface tension and surface entropy for polymer liquids

“…For PE and PS, predicted values of u are in better agreement with experiment over a wide range of temperatures in comparison with values calculated earlier (1). Specifically, the magnitude of the tem- perature dependence of u is greater by about 10% for PS due to both the effect of molecular asymmetry and an increase in the energy zero term, E,S(O).…”

“…To be more specific about the potential energy zero, EJO) is equal to the sum of all contributions due to missing neighbors in the vicinity of the where Ei(0) is the potential energy zero due to missing neighbors; X i is the missing fraction of ith nearest neighbors associated with the creation of the surface; z i is the number of ith neighbor sites for a molecule: E* is equal to the maximum potential well depth between a pair of molecules and is related directly to the Lennard-Jones force constant, ( E * / k); and a, is the distance of separation between ith nearest neighbors located at their cell centers at the temperature of interest. Taking into account that the missing fractions X i differ significantly up to at least tenth nearest neighbors (1,2) results in values of u which differ by as much as 50% from those calculated assuming erroneously that all of the missing fractions are equal to that for first nearest neighbors (3). Equation 1, derived for simple liquids, has been used as a basis for the calculation of the surface tension of polymer liquids ( 1 , 2).…”

“…Some general aspects of the application of cell theory to calculate the surface tension for simple liquids are presented first, followed by a review of the principal modifications given in Ref. 1 necessary to alter the simple liquid theory to calculate u for polymer liquids. Assumptions inherent in this adaptation are criticized and then modified, resulting in a new relation for the surface tension.…”

“…The potential energy zero change resulting from missing first neighbors can be approximated by using as the maximum potential well depth the value for the stable monomer given by the chemical formula of the polymer repeat unit, i.e., ethylene for PE and styrene for PS, etc. This gives (1) monomer, and a , , , is approximately equal to aeff for the quasimer (1,2). Equation 11 is the first neighbor term that would arise if the liquid were, literally, monomeric.…”