Search results for "algebra"

Chain Stiffness of Elastin-Like Polypeptides

2010

The hydrodynamic radii of a series of genetically engineered monodisperse elastin like polypeptides (ELP) was determined by dynamic light scattering in aqueous solution as function of molar mass. Utilizing the known theoretical expression for the hydrodynamic radius of wormlike chains, the Kuhn statistical segment length was determined to be lk = 2.1 nm, assuming that the length of the peptide repeat unit was b = 0.365 nm, a value derived for a coiled conformation of ELP. The resulting chain stiffness is significantly larger than previously reported by force-distance curve analysis (lk < 0.4 nm). The possible occurrence of superstructures, such as hairpins or helices, would reduce the conto…

Computer Simulation of Polymers: Physics and Methods from Specific to Universal

2004

We will discuss in this contribution several aspects of the physics of polymers on different length and time scales and the simulation methods suited for their study. A Molecular Dynamics (MD) simulation of a chemically realistic model is needed to get quantitative insight into local relaxation processes. This study will also reveal the importance of four-particle correlations in polymer dynamics resulting from the presence of dihedral potentials along the chain. Universal largescale chain relaxation can be studied by realistic models as well, but in far better statistical accuracy by Monte Carlo (MC) simulations of a coarse-grained lattice model. Finally we will present considerations for …

New Viscoelastic Materials Obtained by Insertion of anα-Olefin in atrans-Polyisoprene Chain with a Single-Component Organolanthanide Catalyst

2001

Copolymerisation of isoprene with C 6 -C 18 a-olefins by a single component organolanthanide catalyst affords poly(trans-1,4-isoprene) containing 6-10% of inserted olefin. The mechanical properties of highly crystalline transpolyisoprene are dratically modified after insertion of the alkyl chains, leading to quasi-amorphous viscoelastic materials.

1986

Preparation d'oligosiloxanes et de polyarylates avec des groupes mesogenes fixes lateralement

A Monte Carlo Study of Living Polymers in 2D: Effect of Small Chains on Static Properties

1996

A slithering snake algorithm is combined with a binding and breaking chain algorithm to simulate the static behavior of living polymers according to Cates' description. It is shown that this simple two-dimensional simulation on a square lattice gives good agreement with the mean field theory. However, the large amount of small contour length chains for small values of the mean average length 〈L 〉 appears to be one of the reasons for the discrepancies observed between the simulated results and the mean field theory. This finding could explain disagreements between experimental observation and theory. Also, the results are not in favor of a swelling of the greater chains by the smaller one.

KINETICS OF POLYMER EJECTION FROM CAPSID CONFINEMENT: SCALING CONSIDERATIONS AND COMPUTER EXPERIMENT

2012

We investigate the ejection dynamics of a flexible polymer chain out of confined environment by means of scaling considerations and Monte Carlo simulations. Situations of this kind arise in different physical contexts, including a flexible synthetic polymer partially confined in a nanopore and a viral genome partially ejected from its capsid. In the case of cylindric confinement the entropic driving force which pulls the chain out of the pore is argued to be constant once a few persistent lengths are out of the pore. We demonstrate that in this case the ejection dynamics follows a [Formula: see text]-law with elapsed time t. The mean ejection time τ depends nonmonotonically on chain length…

Scaling behavior of topologically constrained polymer rings in a melt

2014

Large scale molecular dynamics simulations on graphic processing units (GPUs) are employed to study the scaling behavior of ring polymers with various topological constraints in melts. Typical sizes of rings containing $3_1$, $5_1$ knots and catenanes made up of two unknotted rings scale like $N^{1/3}$ in the limit of large ring sizes $N$. This is consistent with the crumpled globule model and similar findings for unknotted rings. For small ring lengths knots occupy a significant fraction of the ring. The scaling of typical ring sizes for small $N$ thus depends on the particular knot type and the exponent is generally larger than 0.4.

1991

Thermoanalytical studies on an order-disorder transition resulting from supramolecular organization of hydrogen bond motifs in an unpolar (polymer-) matrix are reported. Functional groups having two potential sites for hydrogen bonding (4-carboxyphenylarazole) are located statistically along the polybutadiene backbone. Multistep hydrogen bond formation leads to the formation of association chains whose lengths can be controlled by addition of monofunctional groups (phenylurazole) like in conventional stepgrowth polymers. The association chain length is estimated from the variation of transition enthalpy and «melting» temperature

Polymer chains confined into tubes with attractive walls: A Monte Carlo simulation

1994

A bead-spring off-lattice model of a polymer chain with repulsive interactions among repeating units confined into straight tubes of various cross sections, DT2, is studied by Monte Carlo simulation. We are also varying the chain length from N = 16 to 128 and the strength of a short-range attractive interaction between the repeating units and the walls of the tube. Longitudinal and perpendicular static linear dimensions of the chains are analyzed, as well as the density profile of repeating units across the tube. These data are interpreted in terms of scaling concepts describing the crossover between three-dimensional and quasi-one-dimensional chain conformations and the adsorption transiti…

Basic kinetic model for the reaction yielding linear polyurethanes. II

1995

On the basis of the gradual polyaddition kinetic model developed earlier, an attempt was made to provide a generalized mathematical model for the set of reactions yielding linear polyurethanes. The model is a system of first-order ordinary differential equations. It was assumed at the present stage of this model that the rate constants for the reaction considered do not change. The model developed was then solved numerically. Average molecular weight of the polymer and composition data for oligomers were calculated for a constant volume batch reactor and varied process parameters. The GPC method, which was tested for model urethane oligomers, was employed to verify the model developed. The …