On the basis of extensive Monte Carlo simulations of lattice models for linear chains under good and Θ solvents conditions, and for bottle-brush polymers under good solvent conditions, different methods to estimate the persistence lengths of these polymers are applied and compared to each other. While for chain molecules at the Θ point standard textbook definitions of the persistence length yield consistent results, under good solvent conditions the persistence length (according to its standard definitions) diverges when the chain length of the macromolecules tends to infinity. Accurate simulation results for chain lengths up to N b = 6400 allow us to verify the theoretically predicted power laws for the decay of the bond orientational correlation function. For the case of bottle-brush polymers, this dependence of “the” persistence length on the backbone chain length obscures the dependence on the side chain length, that is controversially discussed in the literature. Alternative definitions of a persistence length that do not suffer from this problem, based on the total linear dimension of the chain or on the scattering function via the so-called “Holtzer plateau” are studied as well. We show that the backbone contour length of the bottle-brush needs to be very large (about 100 persistence lengths in typical cases) to reach the asymptotic limit where the bottle-brush satisfies the self-avoiding walk statistics, and where a well-defined persistence length can be extracted. An outlook to pertinent experimental work is given.

We present a detailed study of the static and dynamic behavior of long semiflexible polymer chains in a melt. Starting from previously obtained fully equilibrated high molecular weight polymer melts [Zhang et al. ACS Macro Lett. 3, 198 (2014)] we investigate their static and dynamic scaling behavior as predicted by theory. We find that for semiflexible chains in a melt, results of the mean square internal distance, the probability distributions of the end-to-end distance, and the chain structure factor are well described by theoretical predictions for ideal chains. We examine the motion of monomers and chains by molecular dynamics simulations using the ESPResSo++ package. The scaling predictions of the mean squared displacement of inner monomers, center of mass, and relations between them based on the Rouse and the reptation theory are verified, and related characteristic relaxation times are determined. Finally we give evidence that the entanglement length Ne,P P A as determined by a primitive path analysis (PPA) predicts a plateau modulus, G 0 N = 4 5 (ρkBT /Ne), consistent with stresses obtained from the Green-Kubo relation. These comprehensively characterized equilibrium structures, which offer a good compromise between flexibility, small Ne, computational efficiency, and small deviations from ideality provide ideal starting states for future non-equilibrium studies.

Protein knots, mostly regarded as intriguing oddities, are gradually being recognized as significant structural motifs. Seven distinctly knotted folds have already been identified. It is by and large unclear how these exceptional structures actually fold, and only recently, experiments and simulations have begun to shed some light on this issue. In checking the new protein structures submitted to the Protein Data Bank, we encountered the most complex and the smallest knots to date: A recently uncovered α-haloacid dehalogenase structure contains a knot with six crossings, a so-called Stevedore knot, in a projection onto a plane. The smallest protein knot is present in an as yet unclassified protein fragment that consists of only 92 amino acids. The topological complexity of the Stevedore knot presents a puzzle as to how it could possibly fold. To unravel this enigma, we performed folding simulations with a structure-based coarse-grained model and uncovered a possible mechanism by which the knot forms in a single loop flip.

Extensive Monte Carlo simulations are presented for bottle-brush polymers under good solvent conditions, using the bond fluctuation model on the simple cubic lattice. Varying the backbone length (from N b = 67 to N b = 259 effective monomers) as well as the side chain length (from N = 6 to N = 48), for a physically reasonable grafting density of one chain per backbone monomer, we find that the structure factor describing the total scattering from the bottle-brush provides an almost perfect match for some combinations of (N b , N) to experimental data of Rathgeber et al. [J. Chem. Phys. 2005, 122, 124904], when we adjust the length scale of the simulation to reproduce the experimental gyration radius of the bottle-brush. While in the experiment other length scales (gyration radius of side chains, backbone persistence length, scale characterizing the radial monomer density profile in the plane normal to the backbone) can be extracted only via fitting to a complicated and approximate theoretical expression derived by Pedersen and Schurtenberger, all these properties can be extracted from the simulation directly. In this way, quantitatively more reliable estimates for the persistence length and side chain gyration radius of the experimental systems can be extracted. In particular, we show that the popular assumption of a Gaussian radial monomer density profile is inaccurate, in the very good solvent regime studied by the simulation, and show that alternative forms based on scaling theory work better. We also show that the persistence length of the bottle brush in the simulation depends systematically on the backbone length and not only on the side chain length. For the cases where an explicit comparison with the experimental results (based on their evaluation within the Pedersen-Schurtenberger model) is possible, simulation and experiment are consistent with each other and some of the (rather minor) differences between simulation and experiment can be attributed to the weaker strength of excluded volume in the latter. Thus, we show that by suitable mapping between simulation and experiment on length scales of the local concentration fluctuations (here <2 nm) the analysis of experimental data can be systematically refined.

We present large statistics simulations of 3-dimensional star polymers with up to f = 80 arms, and with up to 4000 monomers per arm for small values of f . They were done for the Domb-Joyce model on the simple cubic lattice. This is a model with soft core exclusion which allows multiple occupancy of sites but punishes each same-site pair of monomers with a Boltzmann factor v < 1. We use this to allow all arms to be attached at the central site, and we use the 'magic' value v = 0.6 to minimize corrections to scaling. The simulations are made with a very efficient chain growth algorithm with resampling, PERM, modified to allow simultaneous growth of all arms. This allows us to measure not only the swelling (as observed from the center-to-end distances), but also the partition sum. The latter gives very precise estimates of the critical exponents γ f . For completeness we made also extensive simulations of linear (unbranched) polymers which give the best estimates for the exponent γ.