Estimation of the Hamaker Constants in Non-Polar Polymer/Non-Polar or Weakly Polar Liquid Systems via the Hansen Solubility Parameters

As an extension of our previous work, where we developed a theoretical approach to estimate the Hamaker constants for nonpolar liquids, polar liquids, polymers, and polymer/water systems using the Hansen solubility parameters, we now extend this framework to more complex systems. In the earlier study, the estimated values showed good agreement with those obtained from the rigorous Lifshitz theory. In the present study, we apply and further develop this method to evaluate the Hamaker constants in nonpolar polymer/nonpolar or weakly polar liquid systems. First, analytical expressions are derived for three configurations:<i>A</i>₁₁ for two identical nonpolar polymers (1) across air, <i>A</i>₃₃ for two identical weakly or nonpolar liquids (3) across air, and <i>A</i>₁₃ for a nonpolar polymer (1) and a nonpolar or weakly polar liquid (3) across air. The calculated values using these expressions are in good agreement with those from the Lifshitz theory. The closest approach distance <i>h</i>_min between two media plays an important role in these evaluations. While <i>h</i>_min = 0.165 nm, as proposed by Israelachvili, provides a good approximation for nonpolar liquids and polymers, for nonaqueous liquids excluding water, <i>h</i>_min = 0.138 nm obtained from the work of Drummond and Chan, appears to be a reasonable estimated value, although this does not claim to cover all nonaqueous liquids. Finally, an expression for the Hamaker constant <i>A</i>₁₃₁ for the self-interaction of polymer (1) in nonpolar or weakly polar liquids (3) is derived using a modified combining relation that connects <i>A</i>₁₃₁ with <i>A</i>₁₁ and <i>A</i>₃₃, which are in turn expressed in terms of the Hansen solubility parameters. The results obtained using this expression are found to agree reasonably well with those calculated from a simple approximate form of the rigorous Lifshitz expression for <i>A</i>₁₃₁.