Deformation of networks by detachment and formation of crosslinks

Abstract

AbstractThis paper is concerned with problems relating to dimensional changes in networks of long chain polymers caused by detachment and formation of crosslinks. Particular attention is paid to the dependency of the dimensional change caused by detachment of crosslink on the conditions at which the crosslinks were formed. A network having crosslinks formed under a given tension is elongated by detachment of these crosslinks under a tension higher than that at crosslink formation and is contracted by detachment under a lower tension. Similar results are obtained for the deformation caused by detachment of crosslinks formed under shear stress. The increment of configurational entropy produced by detaching a crosslink depends on both the state of the network at the time of crosslink formation and the state at which the crosslink is detached. In a network having many crosslinks formed in various states of deformation, when the attractive energy between polymers forming linkages is gradually decreased under a constant tension, the crosslinks are detached successively, and it can be expected that the network first contracts and then elongates. In swollen networks, the detachment of crosslinks always brings about the extension of volume, and the critical tension at which the deformation in the direction of tension caused by the detachment is changed from elongation to contraction is increased with decreasing number of crosslinks remaining. While, in networks containing no solvents, the formation of crosslinks does not produce any deformation directly, formation of crosslinks in swollen networks can produce contraction directly. By assuming that polymer chains with a given degree of orientation are distributed densely and uniformly in networks at the moment of crosslink formation, we obtain these results. The validity of this assumption is briefly examined. The theoretical results obtained in this paper are found to be useful for analyzing the behavior of living muscle and muscle models in various stages.