ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
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∼Lν, where L is the internal size. (A) Long-range, repulsive segmental interactions decaying as 1/rα may control chain conformations that are either rodlike, ν=1(1〈α〈2), "wrinkled," 1/2〈ν〈1(2〈α〈4), or random-walk-like, ν=1/2(α〉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–Hückel interaction of strength V0, with inverse screening length κ0. The induced persistence length varies as V0βκ0−γ, with, as expected, (β,γ)=(1,2) when the chain is intrinsically stiff, and, surprisingly, with either (β,γ)=(1/6,7/6) or (β,γ)=(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 ζ=ζ(f )=ζ0+δζ(f ), where ζ denotes the chain extension, ζ0 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 α〉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 ν=1, where δζ∼f1/2, or with ν=2/α, where δζ∼f1/3, respond to the weakest force nonlinearly. (B) Near full extension the chain always responds nonlinearly. When the potential is screened, or if α〉4, we find the 1/f corrections typical of wormlike chains. © 2001 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1355261
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