Multilayer theory of adsorption from a polymer solution

Abstract

A general theory of multilayeradsorption from a polymer solution at an interface is presented. The free energy of the solution in the presence of a plane surface is evaluated in the quasicrystalline model. The configurational entropy of placing a linear chain molecule in the liquid medium of nonuniform concentration is derived by extension of the procedure used for deriving the Flory‐Huggins entropy of mixing. The theory gives the adsorption isotherm and the concentration profile near the surface as a function of the chain length r, the Flory‐Huggins parameter χ, the differential adsorption energy parameter χ s , and the bulk concentration φ*2. The theory is also applicable to adsorption from a mixture of two polymers and from a partially muscible liquid mixture. Many of the results derived by previous theories of adsorption can be obtained, either exactly or approximately, as special cases of the present theory. The predictions of the theory are in good qualitative, and sometimes quantitative, agreement with experimental observations on surface tensions of polymer solutions and on adsorption from partially miscible oligomer solutions and from dilute polymer solutions.