Constrained polymer with unusual statistics: annotations on the slip-link model

@article{citeulike:2386277, abstract = {The slip-link model has been used by many authors to mimic the restriction of the phase space available to one polymer due to the presence of other polymers in dense polymer samples. In this model it is assumed that the polymer, which is modeled by a random walk, must pass through one or several given points in space. The respective free energy of the system is usually computed via the Gibbs entropy. One thus averages over many degrees of freedom of the polymer chain. I reexamined the slip-link model using the Boltzmann entropy. Unusual statistics were discovered when considering a polymer with fixed end points, which has to pass through a slip-link with distance R to the respective end points, one finds that the most probable configuration is no longer the one with equal arc length L/2 between the slip-link and the respective end points if R drops below a certain critical value. A bifuraction with respect to the most probable configuration is observed in the free energy. The result is found using conventional Gaussian statistics but also, with the aid of Monte Carlo simulations, for chains with finite extensibility and for a slip-link with a finite diameter. In the case of several slip-links, a similar “symmetry breaking” is predicted. It will thus be shown that the tube model and the slip-link approach are not equivalent.}, author = {Rieger, Jens }, citeulike-article-id = {2386277}, doi = {http://dx.doi.org/10.1021/ma00202a028}, journal = {Macromolecules}, keywords = {monte-carlo, simulation, sliplink, theory, thermodynamics}, pages = {4540--4544}, posted-at = {2008-02-15 14:09:14}, priority = {2}, title = {Constrained polymer with unusual statistics: annotations on the slip-link model}, url = {http://dx.doi.org/10.1021/ma00202a028}, volume = {22}, year = {1989} }

TY - JOUR ID - citeulike:2386277 L3 - citeulike-article-id:2386277 TI - Constrained polymer with unusual statistics: annotations on the slip-link model JF - Macromolecules VL - 22 SP - 4540 EP - 4544 N2 - The slip-link model has been used by many authors to mimic the restriction of the phase space available to one polymer due to the presence of other polymers in dense polymer samples. In this model it is assumed that the polymer, which is modeled by a random walk, must pass through one or several given points in space. The respective free energy of the system is usually computed via the Gibbs entropy. One thus averages over many degrees of freedom of the polymer chain. I reexamined the slip-link model using the Boltzmann entropy. Unusual statistics were discovered when considering a polymer with fixed end points, which has to pass through a slip-link with distance R to the respective end points, one finds that the most probable configuration is no longer the one with equal arc length L/2 between the slip-link and the respective end points if R drops below a certain critical value. A bifuraction with respect to the most probable configuration is observed in the free energy. The result is found using conventional Gaussian statistics but also, with the aid of Monte Carlo simulations, for chains with finite extensibility and for a slip-link with a finite diameter. In the case of several slip-links, a similar “symmetry breaking” is predicted. It will thus be shown that the tube model and the slip-link approach are not equivalent. KW - monte-carlo KW - simulation KW - sliplink KW - theory KW - thermodynamics AU - Rieger, Jens PY - 1989/// UR - http://dx.doi.org/10.1021/ma00202a028 ER -