Search results for "Persistence length"
showing 10 items of 54 documents
Interfaces in polymer blends
2000
We investigate the structure and thermodynamics of interfaces in dense polymer blends using Monte Carlo (MC) simulations and self-consistent field (SCF) calculations. For structurally symmetric blends we find quantitative agreement between the MC simulations and the SCF calculations for excess quantities of the interface (e.g., interfacial tension or enrichment of copolymers at the interface). However, a quantitative comparison between profiles across the interface in the MC simulations and the SCF calculations has to take due account of capillary waves. While the profiles in the SCF calculations correspond to intrinsic profiles of a perfectly flat interface the local interfacial position f…
Topological effects in ring polymers. II. Influence of persistence length
1999
The interplay of topological constraints and persistence length of ring polymers in their own melt is investigated by means of dynamical Monte Carlo simulations of a three dimensional lattice model. We ask if the results are consistent with an asymptotically regime where the rings behave like (compact) {\em lattice animals} in a self-consistent network of topological constraints imposed by neighbouring rings. Tuning the persistence length provides an efficient route to increase the ring overlap required for this mean-field picture to hold: The {\em effective} Flory exponent for the ring size decreases down to $\nu \stackrel{<}{\sim} 1/3$ with increasing persistence length. Evidence is provi…
Röntgenkleinwinkelstreuung an isotaktischem und syndiotaktischem Polymethylmethacrylat in Lösung
1964
Die Form der Streukurven von gelosten Polymethylmethacrylaten (PMMA) ist eine Funktion der Taktizitat. In der Streukurve des syndiotaktischen PMMA last sich der Einflus einer Periodizitat erkennen. Eine quantitative Deutung gelingt durch Uberlagerung einer Helixstreukurve mit einer Knauelstreukurve. Dabei mus gesetzt werden H = 21 A, R = 4 A und a = 13 A (H und R sind die Identitatsperiode bzw. der Radius der Helix, a ist die Persistenzlange des Knauels.) Die Streukurve des isotaktischen PMMA zeigt nahezu den Verlauf, der fur Fadenknauel nach Kratky et al. [2–5] zu erwarten ist. Jedoch ist ein Intensitatsdefizit zu beobachten, das durch plausible Annahmen gedeutet wird. Als Persistenzlange …
Characteristic Length Scales and Radial Monomer Density Profiles of Molecular Bottle-Brushes: Simulation and Experiment
2010
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 Nb = 67 to Nb = 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 (Nb, 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 r…
Phase behavior of flexible and semiflexible polymers in solvents of varying quality.
2019
The interplay of nematic order and phase separation in solutions of semiflexible polymers in solvents of variable quality is investigated by density functional theory (DFT) and molecular dynamics (MD) simulations. We studied coarse-grained models, with a bond-angle potential to control chain stiffness, for chain lengths comparable to the persistence length of the chains. We varied both the density of the monomeric units and the effective temperature that controls the quality of the implicit solvent. For very stiff chains, only a single transition from an isotropic fluid to a nematic is found, with a phase diagram of "swan-neck" topology. For less stiff chains, however, also unmixing between…
Cylindrical confinement of solutions containing semiflexible macromolecules: surface-induced nematic order versus phase separation
2021
Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a…
Eine Neue Rechnung zur Röntgenkleinwinkelstreuung an Fadenmolekulen. Die Ermittlung der Segmentgestalt
1967
The scattering function of chain molecules in the x-ray small-angle range depends on the shape of the segments. For instance, one obtains quite different scattering curves from solutions of isotactic and syndiotactic poly(methyl methacrylate) (PMMA) in the same solvent. From several models of statistically coiled polymer chains, the scattering functions were calculated with the aid of the Monte Carlo method. Again, a considerable difference between the functions obtained is observed. If the curvature of a thread varies statistically from one point to another, the mean curvature can be determined from the scattering function. A suitable measure for the mean curvature is the persistence lengt…
A new insight into the isotropic–nematic phase transition in lyotropic solutions of semiflexible polymers: density-functional theory tested by molecu…
2016
Semiflexible polymers in solution are studied for a wide range of both contour length L and persistence length lp as a function of monomer concentration under good solvent conditions. Both density-functional theory (DFT) and molecular dynamics (MD) simulation methods are used, and a very good agreement between both techniques is observed for rather stiff polymers. Evidence for a new mechanism of order parameter fluctuations in the nematic phase is presented, namely collective deformations of bundles of wormlike chains twisted around each other, and the typical wavelengths and amplitudes of these modes are estimated. These long wavelength fluctuations cause a reduction of the order parameter…
Scattering function of semiflexible polymer chains under good solvent conditions
2012
Using the pruned-enriched Rosenbluth Monte Carlo algorithm, the scattering functions of semiflexible macromolecules in dilute solution under good solvent conditions are estimated both in $d=2$ and $d=3$ dimensions, considering also the effect of stretching forces. Using self-avoiding walks of up to $N = 25600$ steps on the square and simple cubic lattices, variable chain stiffness is modeled by introducing an energy penalty $\epsilon_b$ for chain bending; varying $q_b=\exp (- \epsilon_b/k_BT)$ from $q_b=1$ (completely flexible chains) to $q_b = 0.005$, the persistence length can be varied over two orders of magnitude. For unstretched semiflexible chains we test the applicability of the Krat…
Stretching semiflexible polymer chains: Evidence for the importance of excluded volume effects from Monte Carlo simulation
2011
Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice ($d=3$ dimensions) and square lattice ($d=2$ dimensions), varying chain stiffness by an energy penalty $\epsilon_b$ for chain bending. In the absence of excluded volume interactions, the persistence length $\ell_p$ of the polymers would then simply be $\ell_p=\ell_b(2d-2)^{-1}q_b^{-1}$ with $q_b= \exp(-\epsilon_b/k_BT)$, the bond length $\ell_b$ being the lattice spacing, and $k_BT$ is the thermal energy. Using Monte Carlo simulations applying the pruned-enriched Rosenbluth method (PERM), both $q_b$ and the chain length $N$ are varied over a wide r…