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Linear and Nonlinear Elastic Behaviors of Star Polymers

In this paper, we investigate the elastic behavior of M-arm star polymers in good solvents under an external force X exerted on each end of the arms in the x direction. In the region of small X, there is a slight difference in the linear elastic behaviors of a single chain and star polymers. In the case of a single chain, the mean x component of the end-to-end vector ⟨xN⟩ is rigorously equal to R02X/3kBT, where R02 = ⟨rN2⟩0 is the mean square end-to-end distance at X = 0. In contrast, the mean x component of the center-end vectors ⟨xN(i)⟩ of star polymers is not simply given by R02(M)X/3kBT, where R02(M) =⟨rN(i)2⟩0 is the mean square center-end distance at X = 0. Instead, we show that the rigorous relation ⟨xN(i)⟩/X = [R02(M)/3 + (M − 1)⟨xN(i)xN(j)⟩0i≠j]/kBT holds for small X, where ⟨xN(i)xN(j)⟩0i≠j denotes the mean product of the x components of the center-end vectors of the ith and jth arms in the absence of X. Here we perform large-scale Monte Carlo simulations of star self-avoiding walks (SAWs) on a s...