Conformation of Adsorbed Polymeric Chain. II

By developing the theoretical treatment of an isolated polymeric chain at an interface, which is based on a three-dimensional random walk on a simple cubic lattice, the average number of segments in the tail of a polymeric chain k̄0 and the average number of trains per polymeric chain m̄ are calculated in the limit in which the chain length n is infinite. With the aid of the average number of adsorbed segments ν̄ evaluated in Part I of this series, the average number of segments in a train and a loop, k̄′ and k̄, are also calculated. The average properties are found to change in their dependence on the adsorption energy ε and the total number of segments n at a critical point except k̄′. For η < ηc, where η = exp(ε / kT), k̄0 has the value 12n; this indicates that the polymeric chain, in effect, consists of two long tails extending into the solution, while k̄ is still proportional to n1/2. It is seen that at η = ηc only one-third of the chain length participates in adsorption, and m̄ and k̄ obey the half-power law in the same way as ν̄. When η exceeds ηc, k̄0 and k decrease rapidly with an increase in the adsorption energy, and m̄ becomes proportional to n. It is noticed that the length of train is relatively small even if the majority of segments are adsorbed at the interface.