Theory of adsorption of macromolecules in cylindrical pores and at surfaces of cylindrical shape

A rigorous theory of adsorption of a Gaussian chain of infinite length into cylindrically shaped pores and onto cylindrical surfaces of arbitrary diameter, D, has been developed for any energy of interaction −ϵ. The change in the conformational free energy of a chain arriving inside the pores from an unrestricted volume is proportional to (D∗) −2 ( D∗ is the effective pore width) over the entire molecular-sieve range (− ϵ < − ϵ c ). In the exclusion range (− ϵ < 0), when the interaction of chain units with the adsorbent exhibits repulsive type forces, D∗ is approximately equal to D. As the adsorption forces of attraction increase (0 < − ϵ < − ϵ c ) the value of D∗ increases and becomes infinite at the critical point. This makes it possible to use a single adsorbent for effective chromatographic separation of polymers over a wide range of molecular weights. In the adsorption range, where − ϵ > − ϵ c , the conformational free energy of the chain is virtually independent of the width and shape of the pores and is determined mainly by the value of −ϵ. At the critical point, − ϵ = − ϵ c , the probability of the arrival of a polymer chain in the pore is independent of both the width and shape of the pore and is determined only by the ratio of geometrical volumes of the free volume to the pore volume. For cylindrical pores, a weak dependence of − ϵ c on D is observed only for narrow pores. This dependence virtually disappears on passing to adsorbents with wide pores. Consideration of the adsorption of the macromolecule on the outer surface of the cylinder showed that at any finite value of the diameter of the cylinder, D, adsorption occurs as an ‘infinite-order’ phase transition. The maximum value of the specific heat (C p max k = 25 3 =ϵ 2 c does not depend on D. The degree of bonding of the macromolecule to the adsorbent increases with decreasing curvature of the surface, rapidly attaining values characteristic of chain adsorption on a plane.