Abstract
A general theory of polymer adsorption at a semi-permeable oil-water interface of the biphasic solution is presented. The configurational factor of the solution in the presence of the semi-open boundary at the interface is evaluated by the quasicrystalline lattice model. The present theory gives the feature of the bulk concentration equilibria between oil-water subsystems and the surface excesses of ${\Gamma}^{\alpha}$ and ${\Gamma}^\{beta}$ of the polymer segments as a function of the degree of polymerization $\gamma$, the Flory-Huggins parameter in $\beta$-phase $x_{\rho}^{{\beta}_{\rho}}$, the differential adsorption energy parameter in $\beta$-phase $x_{\sigma}^{{\beta}_{\rho}}$, the differential interaction energy parameter ${\Delta}x_{\rho}$ and the bulk concentration of the polymer in ${\beta}-phase ${\varphi}_2^{{\beta(*)}_2}$. From our numerical results, the characteristics of ${\Gamma}^{\alpha}$ are shown to be significantly different from those of ${\Gamma}^{\beta}$ in the case of high polymers, and this would be the most apparent feature of the adsorption behavior of the polymer at a semi-permeable oil-water interface, which is sensitively dependent on ${\Delta}x_{\rho}$ and r.