Branched polymers in a wedge geometry in three dimensions

Abstract

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge anglesθ andφ. We show that the growth constant is equal toμ ^f, whereμ is the self-avoiding walk limit. Thef and (θ, φ) dependences of the corresponding critical exponentγ _f (θ, φ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.