Equjlubrium Topologies of Associatxng Polymers*
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EQUJLUBRIUM TOPOLOGIES OF ASSOCIATXNG POLYMERS* ARLETTE R. C. BALJON and THOMAS A. WITTEN The James Franck Institute, The University of Chicago, 5640 S. Ellis Avenue, Chicago, Illinois 60637
ABSTRACT We have developed a Monte-Carlo computer simulation to study associating polymer interactions. In our model we treat the associations as geometrical constraints. Each polymer chain contains two 'stickers'. The chains are treated as lattice selfavoiding random walks. Each sticker is constrained to be adjacent to one other sticker, but the stickers are free to exchange partners. This freedom to exchange results in an attraction between the chains, as anticipated by Cates and Witten.1 We find that in equilibrium the mutual excluded volume of two such chains passes from repulsive to attractive when the ratio of the sticker distance to the chain length is approximately 0.8. These results are independent of the chain length: they should apply to real polymers subject to these topological constraints in any good solvent at sufficiently high molecular weight. INTRODUCTION Associating polymers such as ionomers are flexible polymers with a small number of polar groups randomly attached along the chain. 2 They typically consist of a hydrocarbon backbone with about 30 acid groups randomly attached, neutralized to form salts. When dissolved in a nonpolar hydrocarbon the ionic neutralized acid groups tend to associate or stick together. Scattering data 3 show that the ions cluster into small, robust multiplets. The lifetime of these micelles is short enough to allow the solution to reach equilibrium readily. 4 ,5 Solutions of associating polymers exhibit rheological properties strikingly different from those of ordinary polymer solutions. For 6 example, under proper conditions a mild shear flow can induce reversible gelation. This effect is thought to be caused by a shift between interchain and intrachain sticking under flow. 7 These ionomer solutions show signs of phase instability, as well. We have developed a Monte-Carlo computer simulation to study the equilibrium statistics of these associating polymers in dilute solution. The associations are treated as geometrical constraints. Each sticker is constrained to be adjacent to a fixed number, f, of others. Analitical work by Cates and WittenI suggests that the placement of the associating groups along the chain determines the net interaction between them. Consider two chains with each two stickers and with f=2. Two effects act to cause interaction between the chains. In a good solvent the interaction between two selfpaired chains (Fig.la) is repulsive. If the segments approach sufficiently close they may exchange stickers (Fig.lb). This freedom to exchange results in an increased number of configurations and amounts to an entropic attraction. The free energies of repulsion or attraction are of the same order (kT). Which effect dominates depends on the placement of the stickers on the chains. An extended version of this work has been submitted to Macromolecules Mat. Res. Soc. Symp
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