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Citation: Huang Jian-Hua, Jiang Wen-Hua, Han Shi-Jun. End-to-end Distance and its Probability Distribution of Polymer Chains[J]. Acta Physico-Chimica Sinica, ;2001, 17(02): 173-176. doi: 10.3866/PKU.WHXB20010217 shu

End-to-end Distance and its Probability Distribution of Polymer Chains

1.
Department of Chemistry, Zhejiang University, Hangzhou　310027

Received Date: 3 July 2000
Available Online: 15 February 2001

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 es 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.
- Polymer chain;Random-walking;End-to-end distance;Distribution;　Probability method
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