Bond-Vector Correlation Functions in Dense Polymer Systems

作者：Semenov A N^*

来源：Macromolecules, 2010, 43(21): 9139-9154.

DOI：10.1021/ma101465z

It is well-known that homopolymer chains do not exactly follow the Gaussian statistics even in the melt state. In particular, orientations of two bonds l(1) and of the same chain in a concentrated polymer system are always correlated even when they are separated by a long segment of s >> 1 units: <(l) under bar (1) . (l) under bar (2)>(s) = C(s) similar to l/s(3/2). It is important to know how these orientational correlations are distributed in space, i.e. how <(l) under bar (1) . (l) under bar (2)> depends on the distance (r) under bar between the bonds.(1) An unexpected feature is revealed in the present paper: it is shown that the distance-dependent bond-vector correlation function K(r) = <(l) under bar (1) . (l) under bar (2)>(r) is extremely sensitive to the definition of r. Depending on the definition, K(r) for r >> b (b is the monomer size) can be either significantly lower, or significantly higher than the position-averaged correlator C(s) with s similar to r(2)/b(2) corresponding to a given distance r. We propose an "invariant" definition of the intrachain orientational correlation function and show that it is related to the formfactor of a single chain. A quantitative link between the orientational and positional correlations in polymer melts is thus discovered. We also have found a quantitative relationship between the intrachain and interchain correlation functions. It is shown that the inter-chain orientational correlation for bonds of different chains) is long-range and follows the l/r(4) scaling law in the case of infinite chains.

• 出版日期2010-11-9