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Entanglement in polymeric systems
Abstract
Entanglement is one of the most important--but poorly understood--effects that occur in polymeric materials of high molecular weight. This work studies aspects of three long-standing problems--self-entanglement in a ring polymer, mutual entanglement between a ring and a rod, and network self-entanglement--and their solutions, by means of computer simulation. In self-entanglement, ring polymers are represented with the off-lattice rod-bead model. Perfect unbiased model instances are produced that have between N = 32 and 2048 beads, produced at several different values of bead radius, to represent polymers in solvents of varying quality. The topological state of each ring is represented with the Alexander polynomial. It is observed that the probability of observing a trivial knot $(P\sb{U})$ has a decreasing exponential dependence on the contour length (N) of the polymer, or that $P\sb{U}(N)=\exp(-N/N\sb0).$ The characteristic length $(N\sb0)$ varies by many orders of magnitude depending on solvent quality. In mutual-entanglement, a ring polymer is represented with the off-lattice rod-bead model, as in the study of self-entanglement. An infinitely long spike of zero radius is inserted at a (minimum) distance r from the center of mass of the ring, and the resulting system is deemed to be entangled if the resulting Gauss winding number (GWN) between the ring and the spike is zero. For a Gaussian chain with no excluded volume, the probability of a non-zero GWN is given by ${\cal P}(r,N)\approx A\exp(-(r/R\sb{g})\sp2/2B),$ where A = 0.7, B = 0.8, and $R\sb{g}$ is the radius of gyration of the ring. Cases where the ring has excluded volume and the spike has non-zero radius are also studied. Finally, a reasonable mathematical definition is provided of what might constitute "entanglement" in terms of a polymeric network. Model instances of networks are created given various initial compositions, and physical and virtual cross-links are both counted. The ratio of virtual to physical cross-links, $R\sb{e},$ depends strongly on the parameters which are used in the formation of the network. We suspect that entanglement effects are significant in rubber elasticity, but they are by no means of paramount importance.
Subject Area
Polymer chemistry
Recommended Citation
Koniaris, Kleanthes George, "Entanglement in polymeric systems" (1992). Doctoral Dissertations Available from Proquest. AAI9305852.
https://scholarworks.umass.edu/dissertations/AAI9305852