Biomedical subjects

Ralf Metzler

Publications and source records attributed to Ralf Metzler.

22 records · Page 2Linked to original sources

PubMed2002

Force-extension relations for polymers with sliding links.

Topological entanglements in polymers are mimicked by sliding rings (slip links) that enforce pair contacts between monomers. We study the force-extension curve for linear polymers in which slip links create additional loops of variable sizes. For a single loop in a phantom chain, we obtain exact expressions for the average end-to-end separation. The linear response to a small force is related to the properties of the unstressed chain, while for a large force the polymer backbone can be treated as a sequence of Pincus-de Gennes blobs, the constraint effecting only a single blob. Generalizing this picture, scaling arguments are used to include self-avoiding effects.

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PubMed2002

Tightness of slip-linked polymer chains.

We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip links) enforce pair contacts between monomers. These slip links divide a closed ring polymer into a number of subloops which can exchange length among each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a slip-linked polymer chain (paraknot). A particular segment is tight (small in size) or loose (of the order of the overall size of the paraknot) depending on both the number of slip links it incorporates and its competition with other segments. When self-avoiding interactions are included, scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations.

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PubMed2002

Equilibrium shapes of flat knots.

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localized on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.

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PubMed2002

Diffusion on random-site percolation clusters: theory and NMR microscopy experiments with model objects.

Quasi-two-dimensional random-site percolation model objects were fabricated based on computer-generated templates. Samples consisting of two compartments, a reservoir of H2O gel attached to a percolation model object, which was initially filled with D2O, were examined with nuclear magnetic resonance microscopy for rendering proton spin density maps. The propagating proton/deuteron interdiffusion profiles were recorded and evaluated with respect to anomalous diffusion parameters. The deviation of the concentration profiles from those expected for unobstructed diffusion directly reflects the anomaly of the propagator for diffusion on a percolation cluster. The fractal dimension of the random walk d(w) evaluated from the diffusion measurements on the one hand and the fractal dimension d(f) deduced from the spin density map of the percolation object on the other permits one to experimentally compare dynamical and static exponents. Approximate calculations of the propagator are given on the basis of the fractional diffusion equation. Furthermore, the ordinary diffusion equation was solved numerically for the corresponding initial and boundary conditions for comparison. The anomalous diffusion constant was evaluated and is compared to the Brownian case. Some ad hoc correction of the propagator is shown to pay tribute to the finiteness of the system. In this way, anomalous solutions of the fractional diffusion equation could experimentally be verified.

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