Triple minima in free energy of semiflexible polymers

We study the free energy of the worm-like-chain model, in the constant-extension ensemble, as a function of the stiffness for finite chains of length L. We find that the polymer properties obtained in this ensemble are "qualitatively" different from those obtained using constant-force ensembles. In particular we find that as we change the stiffness parameter, the polymer makes a transition from the flexible to the rigid phase and there is an intermediate regime of parameter values where the free energy has three minima and both phases are stable. This leads to interesting features in the force-extension curves.Comment: Published version, 4 pages, 5 figures, revte

Transverse fluctuations of grafted polymers

We study the statistical mechanics of grafted polymers of arbitrary stiffness in a two-dimensional embedding space with Monte Carlo simulations. The probability distribution function of the free end is found to be highly anisotropic and non-Gaussian for typical semiflexible polymers. The reduced distribution in the transverse direction, a Gaussian in the stiff and flexible limits, shows a double peak structure at intermediate stiffnesses. We also explore the response to a transverse force applied at the polymer free end. We identify F-Actin as an ideal benchmark for the effects discussed.Comment: 10 pages, 4 figures, submitted to Physical Review

Radial distribution function of semiflexible polymers

We calculate the distribution function of the end--to--end distance of a semiflexible polymer with large bending rigidity. This quantity is directly observable in experiments on single semiflexible polymers (e.g., DNA, actin) and relevant to their interpretation. It is also an important starting point for analyzing the behavior of more complex systems such as networks and solutions of semiflexible polymers. To estimate the validity of the obtained analytical expressions, we also determine the distribution function numerically using Monte Carlo simulation and find good quantitative agreement.Comment: RevTeX, 4 pages, 1 figure. Also available at http://www.cip.physik.tu-muenchen.de/tumphy/d/T34/Mitarbeiter/frey.htm

Facile one-spot synthesis of highly branched polycaprolactone

Reported is the first solvent-free (bulk) synthesis of degradable/bioresorbable, highly branched polymers via tin octanoate Sn(Oct2) catalysed controlled ring opening co-polymerisation (ROP) of mono and di-functional lactone monomers that proceed to near quantitative conversion. The successful isolation of solvent soluble, highly branched structures was shown to be dependent on both the concentration of the di-functional monomer and the overall reaction time. Comparison with analogous systems utilising controlled radical polymerisation (CRP) to form the highly/hyper branched polymers suggested significant experimental differences between the two chain growth methods. The maximum proportion of di-functional monomer without gelation ensuing was found to be 0.6 equivalents w.r.t. mono-functional monomer (c.f. 1 with CRP) and the onset of significant levels of branching occurred at approximately 90% conversion (c.f. ~70% with CRP). These differences and significant disparity in reaction times were attributed to (a) the coordination and insertion (C+I) propagation mechanism adopted by the Sn catalyst and (b) the presence of additional trans-esterification reactions at high conversion. Evidence is presented to support the conclusion that there are two mechanisms contributing to the overall branching process in the ROP system at high conversion. First, the C+I mechanism promotes growth of linear polymer until approximately 90% conversion, after which both the C+I and trans-esterification processes contribute to the interchain branching process. The branched nature of the molecular structures was supported by confirmation plots generated from static light scattering. This data demonstrated that the polymers synthesised exhibit varying degrees of branching, consistent with the di-functional monomer (4,4’-bioxepanyl-7,7’-dione - BOD) concentration in the feed. The degree of branching was calculated using 3 different methods and the results were shown to be independent of method. Finally, DSC analysis of the polymers demonstrated correlation between the degree of branching achieved and the observed Tm for the material where increased branching leads to a drop in the recorded Tm