Cross chains, computer-simulated

The inclusion of chain connectivity prevents polymer strands from crossing one another in the course of a computer simulation. In bead-spring polymer models, this typically means that one has to limit the maximal (or typical) extension of a spring connecting the beads that represent the monomers along the chain. This process is most often performed using the so-called finitely extensible, nonlinear elastic (FENE) type potentials44 of Eq. [17]... 

It may also be possible to use the trapping technique to prepare networks having no cross links whatsoever. Mixed linear chains, with large amounts of cyclics, are difunctionally end linked to yield an Olympic or chain-mail network (figure 7.30). Such materials are similar in some respects to the catenanes and rotaxanes that have long been of interest to a variety of scientists and mathematicians. " Computer simulations could establish the conditions most likely to produce these novel structures. 

Fig. 4.14 Scaling of (left panel) Monte Carlo computer simulation results (see Fig. 1.22) for q = 3.86 (open circles), 5.58 (crosses) and 7.78 (filled diamonds) by Bolhuis [56] and experimental results (right panel) on (AOT) micro-emulsion droplets plus fiee polyisoprene polymer chains (q = 10 (open squares) and = 16 (filled triangles)) by Mutch et al. [57,58] for the gas-liquid coexistence in the protein limit regime...

If the film becomes so thin that the chains cannot cross through each other, the polymer conformations become truly two-dimensional and belong to a different imiversality class -namely, two-dimensional self-avoiding walks. In this Umit, an exact field-theoretic description demonstrates that the chains again become Gaussian, Rf N, without any logarithmic corrections. This behavior has been studied in great detail by extensive computer simulations. ... 

It was shown that with increasing internal chain stiffness the effective exponent y for Le — crosses over from a value of one toward two as the internal stiffness of a chain increases. The quadratic dependence of the electrostatic persistence length on the Debye radius for the discrete Kratky Porod model of the polyelectrolyte chain was recently obtained in [65]. It seems that the concept of electrostatic persistence length works better for intrinsically stiff chains rather than for flexible ones. Further computer simulations are required to exactly pinpoint the reason for its failure for weakly charged flexible polyelectrolytes. 

With the above potential representation, s tions of the chain many bonds apart may cross and overlap and the conformation is literaUy unperturbed by long-range (non-local) interactions. In order to compute equilibrium ava-f properties of our cemtinuous unperturbed dmins, we rample their configuration space through a fast Monte Carlo scheme where the only dementary move employed is simple rotation, performed exactly as described above for the bulk simulation. Note that reptations must be attempted in both directions along the chain in order for the simulation to be microscopically reversible. 

The mesoscale model consists of a set of crosslink nodes (i.e., junctions) connected via single finite-extensible nonlinear elastic (FENE) bonds (that can be potentially cross-linked and/or scissioned), which represent the chain segments between crosslinks. In addition, there is a repulsive Lennard-Jones interaction between all crosslink positions to simulate volume exclusion effects. The Eennard-Jones and FENE interaction parameters were adjusted and the degree of polymerization (p) for a given length of a FENE bond calibrated until the MWD computed from our network matched the experimental MWD of the virgin material [112]. 

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