A Random Walk Model of Chain Polymer Adsorption at a Surface III. Mean Square End-to-End Distance

A 6·c hoice s imple c ubic latti ce model of ad sorptio n of an isolated polymer c ha in a t a so luti on surface is inves ti gated. T he mean square co mpone nts (x2(N) and (Z2(N) of th e end· to·e nd di s· tance a re compu ted as a fun c tion of the adsorption e ne rgy pe r monomer unit in the limit of a ve ry long polymer c ha in . In the c alc ul at ion, one end of th e po lymer c ha in cons is ting of N monom er unit s is cons tra ined to li e in the surface ; and (x2(N) and (Z2(N) a re , respec ti ve ly, the mea n square di s· p lace me nt of the free end of Ith e cha in para ll e l to the solution s urface in one of th e latt ice direc tio ns and normal to the sol ut ion surface. The limiting va lue of (x 2(N» /N as N ---> 00 is a co ntinuou s fun c· ti on of 8 , the d ime ns io nless adsorpt ion ene rgy pe r monom er unit , a nd is equa l to 1/3 fo r 8 .;; In (6/5) and (1/2) (i + (1/4) (eO 1)1] 1/Z for II ;;;. In (6/5). The limiting vaJu e of (zZ(N) /N as N ---> 00 is a d is· con tinuous fun c tion of 8 a nd is equal to 2/3 for 8 < In (6/5), 1/3 for 8 = In (6/5) , and 0 for 0 > In (6/5) . The re latio n of these res ults to earli e r investigat ions and the gene ra lization of these results to othe r cubic lattice mode ls is di sc ussed.