Conformation of Adsorbed Polymeric Chain. II

Abstract

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 ${\mathrm{k̄}}_0$ and the average number of trains per polymeric chain $\mathrm{m̄}$ are calculated in the limit in which the chain length $n$ is infinite. With the aid of the average number of adsorbed segments $\mathrm{\nu ̄}$ evaluated in Part I of this series, the average number of segments in a train and a loop, $\mathrm{k̄\prime }\mathrm{and}\mathrm{k̄}$ , are also calculated. The average properties are found to change in their dependence on the adsorption energy $\epsilon$ and the total number of segments $n$ at a critical point except $\mathrm{k̄\prime .}\mathrm{For}{\mathrm{\eta \hspace{0.17em}<\hspace{0.17em}\eta }}_c,\mathrm{where}\mathrm{\eta \hspace{0.17em}=\hspace{0.17em}}\exp {\mathrm{(\epsilon \hspace{0.17em}/\hspace{0.17em}kT),\; k̄}}_0$ has the value $\frac{1}{2}n$ ; this indicates that the polymeric chain, in effect, consists of two long tails extending into the solution, while $\mathrm{k̄}$ is still proportional to $n^{\text{1/2}}$ . It is seen that at ${\mathrm{\eta \hspace{0.17em}=\hspace{0.17em}\eta }}_c$ only one‐third of the chain length participates in adsorption, and $\mathrm{m̄}$ and $\mathrm{k̄}$ obey the half‐power law in the same way as $\mathrm{\nu ̄.}\mathrm{When}\eta$ exceeds ${\eta }_c{\mathrm{,\; k̄}}_0$ and $k$ decrease rapidly with an increase in the adsorption energy, and $\mathrm{m̄}$ 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.