平面壁限制的高分子链末端距及其概率分布

End-to-end Distance and its Probability Distribution of Polymer Chains near a Flat Barrier

The problem of polymer chains near an impenetrable plane is investigated by means of the probability method. It is shown that the 2kth moment of the reduced normal component of the end-to-end distance A2k only depends on the reduced distance to the plane of the first segment AZ0, here, A=l－ 1· , n is the chain length, l is the bond length and fixed to be unity, which can be expressed as A2k=f(AZ0). When AZ0≈ 0, A2k is the maximum(A2k=k!), then it decreases rapidly and soon reaches the minimum with the increase of AZ0, afterwards A2k goes up gradually and reaches the limit value [(2k－ 1)× (2k－ 3)×…× 1]/2k when AZ0 is large enough. Suggesting that the polymer chain can be significantly elongated for small Z0 and contracted for an intermediate range of Z0 due to the barrier. The distribution of the end-to-end distance also depends on the distance Z0 to the plane of the first segment.

The problem of polymer chains near an impenetrable plane is investigated by means of the probability method. It is shown that the 2 kth moment of the reduced normal component of the end-to-end distance A(2 k) < R-Z(2k)> only depends on the reduced distance to the plane of the first segment AZ(0), here, A = l(-1) . root3/2n, n is the chain length, l is the bond length and fixed to be unity, which can be expressed as A(2 k) < R-Z(2k) > = f(AZ(0)). When AZ(0) approximate to 0, A(2 k) < R-Z(2k)> is the maximum (A(2 k) < R-Z(2k)> = k!), then it decreases rapidly and soon reaches the minimum with the increase of AZ(0), afterwards A(2 k) < R-Z(2k)> goes up gradually and reaches the limit value [(2k - 1) x (2k - 3)x ... x1]/2(k) when AZ(0) is large enough. Suggesting that the polymer chain can be significantly elongated for small Z(0) and contracted for an intermediate range of Z(0) due to the barrier. The distribution of the end-to-end distance also depends on the distance Z(0) to the plane of the first segment.