Backbone Stiffness of Comb-Branched Polymers

The free energy change accompanying the bending of the main chain of a comb-branched polymer is evaluated in terms of excluded-volume interactions among side chains to obtain λb-1 (the increase of the Kuhn segment length). It is assumed that without such interaction, the polymer backbone has a Kuhn length of λ0-1 and each side chain consisting of n (»1) bonds is Gaussian. At the theta point where the effective binary cluster integral (a linear combination of the binary cluster integral β2 and the ternary cluster integral β3) vanishes, λb-1 in the first-order perturbation approximation increases in proportion to n2β3. On the other hand, it is proportional to n2β2 in the good solvent limit, in which the mean-field approximation is used for the calculation. These results give a fairly satisfactory explanation of the experimentally observed n-dependence of the total Kuhn length (λ0-1+λb-1) for polystyrene polymacromonomers in cyclohexane at the theta point and in toluene (a good solvent).