The effect of polydispersity on surface segregation of a lower molecular weight polymer component in a higher molecular weight linear polymer melt host is investigated theoretically.We show that the integrated surface excess z_M of a polymer component of molecular weight M satisfies a simple relation z_M=2U~e(M/M_w-1)phi_M,where M_w is the weight averaged molecular weight,phi_M is the polymer volume fraction,and U~e is the attraction of polymer chain ends to the surface.U~e is principally of entropic origin,but also reflects any energetic preference of chain ends to the surface.We further show that the surface tension gamma_M of a polydisperse melt of high molar mass components depends on the number average degree of polymerization M_n as,gamma_M=gamma_(infinity)+2U~e rho_bRT/M_n.The parameter gamma_(infinity)is the asymptotic surface tension of an infinitely long polymer of the same chemistry,rho_b is the bulk density of the polymer,R is the universal gas constant,and T is the temperature.The predicted gamma_M compare favorably with surface tension values obtained from self-consistent field theory simulations that include equation of state effects,which account for changes in polymer density with molecular weight.We also compare the predicted surface tension with available experimental data.
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