Search results for "Scaling"
showing 10 items of 754 documents
Anomalous scaling of the critical temperature of unmixing with chain length for two-dimensional polymer blends
2003
The thermodynamics, structure and the chain configurations of symmetrical polymer mixtures confined into ultrathin films are studied by Monte Carlo simulations of the bond fluctuation model. It is shown that the Flory-Huggins–type scaling of the critical temperature (Tc ~ N) with chain length N in the bulk is replaced by a weaker increase, Tc ~ N1/2, in an ultrathin film, and this is interpreted in terms of geometric arguments. The pair-correlation function g(r) of monomers from different chains exhibits a pronounced correlation hole, and the density of intermolecular contacts zc decreases with N as zc ~ N−1/2.
Static and dynamic scaling behavior of a polymer melt model with triple-well bending potential
2018
We perform molecular-dynamics simulations for polymer melts of the coarse-grained polyvinyl alcohol model that crystallizes upon slow cooling. To establish the properties of its high temperature liquid state as a reference point, we characterize in detail the structural features of equilibrated polymer melts with chain lengths $5\le N \le 1000$ at a temperature slightly above their crystallization temperature. We find that the conformations of sufficiently long polymers with $N >50$ obey essentially the Flory's ideality hypothesis. The chain length dependence of the end-to-end distance and the gyration radius follow the scaling predictions of ideal chains and the probability distributions o…
Conformational Properties of End-Grafted Bottlebrush Polymers
2020
Scaling analysis combined with free-energy calculations and molecular dynamics simulations of a coarse-grained bead-spring model have been used to study the structural properties of planar brushes ...
Structure of Polymers
2014
The structure and thermodynamics of polymers are discussed both with an adapted version of Flory’s regular solution theory and the concept of scaling and random walks. The salient properties of polymers like segregation and elasticity are discussed in terms of these concept. The Flory-Stockmayer theory of gelation is introduced and related to the percolation concept.
3D Conformations of Thick Synthetic Polymer Chains Observed by Cryogenic Electron Microscopy.
2019
The backbone conformations of individual, unperturbed synthetic macromolecules have so far not been observed directly in spite of their fundamental importance to polymer physics. Here we report the dilute solution conformations of two types of linear dendronized polymers, obtained by cryogenic transmission electron stereography and tomography. The three-dimensional trajectories show that the wormlike chain model fails to adequately describe the scaling of these thick macromolecules already beyond a few nanometers in chain length, in spite of large apparent persistence lengths and long before a signature of self-avoidance appears. This insight is essential for understanding the limitations o…
A fast Monte Carlo algorithm for studying bottle-brush polymers
2011
Obtaining reliable estimates of the statistical properties of complex macromolecules by computer simulation is a task that requires high computational effort as well as the development of highly efficient simulation algorithms. We present here an algorithm combining local moves, the pivot algorithm, and an adjustable simulation lattice box for simulating dilute systems of bottle-brush polymers with a flexible backbone and flexible side chains under good solvent conditions. Applying this algorithm to the bond fluctuation model, very precise estimates of the mean square end-to-end distances and gyration radii of the backbone and side chains are obtained, and the conformational properties of s…
A Unified Theory of Liquid-Liquid Demixing and Polymer Formation Kinetics
2009
Sickle hemoglobin is a natural hemoglobin mutation with a hydrophobic replacement of a charged aminoacid on the molecular surface. This leads to aggregation into rigid helical structures (“polymerization”), the underlying cause of sickle cell disease. It has also been shown that polymerization occurs in close correspondence with the phase transition of liquid-liquid demixing , or with the critically diverging fluctuations of local concentration occurring in its proximity. Due to this correspondence, polymerization kinetics remarkably appear to exhibit, with respect to demixing temperature, the same universal scaling features shown by amplitudes and lifetimes of fluctuations occurring in pro…
Simulation of Copolymer Bottle-Brushes
2007
The structure of bottle-brush polymers with a rigid backbone and flexible side chains is studied in three dimensions, varying the grafting density, the side chain length, and the solvent quality. Some preliminary results of theoretical scaling considerations for one-component bottle-brush polymers in a good solvent are compared with Monte Carlo simulations of a simple lattice model. For the simulations a variant of the pruned-enriched Rosenbluth method (PERM) allowing for simultaneous growth of all side chains in the Monte Carlo sampling is employed. For a symmetrical binary (A,B) bottle-brush polymer, where two types (A,B) of flexible side chains are grafted with one chain end to the backb…
Simulations of phase transitions in macromolecular systems
2002
Abstract The study of phase transitions in concentrated solutions and melts of flexible or stiff polymers is a computational challenge for computer simulations, since already a single polymer coil exhibits nontrivial structure from the scale of a chemical bond (1 A) to the coil radius (100 A), and for the simulation of collective phenomena huge simulation boxes containing many polymers are required. A strategy to deal with this problem is the use of highly coarse-grained models on a lattice, such as the bond fluctuation model. Several studies employing such models will be briefly reviewed, e.g.: temperature-driven isotropic-nematic phase transition in concentrated solutions of semiflexible …
Conformational Properties of Polymer Mushrooms Under Spherical and Cylindrical Confinement
2010
A coarse grained model of a flexible macromolecule end-grafted on the inside of a sphere or a cylinder under good solvent conditions is studied by Monte Carlo simulations. For cylindrical confinement, two regimes are found: when the cylinder radius R exceeds the gyration radius R 90 of the polymer mushroom grafted to a planar surface, a simple scaling description holds. In the opposite case, a non-monotonic crossover to a cigar-like quasi-one-dimensional structure occurs, and the distribution P e (x) of the free chain end in the x-direction along the cylinder axis becomes bimodal. Spherical confinement, on the other hand, causes a crossover from dilute to semidilute behavior of the structur…