Wormlike chains in the large-d limit

We study the properties of an isolated, self-interacting wormlike polymer chain on the basis of a nonperturbative 1/d-expansion, where d denotes the dimension of embedding space. In the absence of an external force, we characterize the dimension R of the chain in embedding space via R similar toL(nu), where L is the internal size. (A) Long-range, repulsive segmental interactions decaying as 1/r(alpha) may control chain conformations that are either rodlike, nu =1(1 < alpha <2), "wrinkled," 1/2 < nu <1(2 < alpha <4), or random-walk-like, nu =1/2(alpha >4). (B) For short-range, screened, repulsive interactions, the crossover between rodlike and random-walk-like behavior is controlled by the persistence length whose interaction part we compute focusing on a Debye-Huckel interaction of strength V-0, with inverse screening length kappa (0). The induced persistence length varies as V(0)(beta)kappa (-gamma)(0), with, as expected, (beta,gamma)=(1,2) when the chain is intrinsically stiff, and, surprisingly, with either (beta,gamma)=(1/6,7/6) or (beta,gamma)=(1,7) when the chain is intrinsically very flexible. The chances of experimentally observing the novel regimes may be limited. For a chain subject to an external stretching force f, we determine the force-extension relation zeta=zeta (f )=zeta (0)+delta zeta (f ), where zeta denotes the chain extension, zeta (0) is the spontaneous extension. (A) If the interaction potential is either screened, or if the decay of a long-range interaction potential is fast, i.e., if alpha >4, the chain spontaneously generates an "effective tension" and responds linearly to weak forces with elastic constants "renormalized" by interactions. By contrast, "tension-free" chains, with either nu =1, where delta zeta similar tof(1/2), or with nu =2/alpha, where delta zeta similar tof(1/3), respond to the weakest force nonlinearly. (B) Near full extension the chain always responds nonlinearly. When the potential is screened, or if alpha >4, we find the 1/rootf corrections typical of wormlike chains. (C) 2001 American Institute of Physics.