Search results for "algebra"
showing 10 items of 4129 documents
Pearl-necklace structures of molecular brushes with rigid backbone under poor solvent conditions: A simulation study
2010
Bottle-brush polymers, where flexible side chains containing N=20 to 50 effective monomers are grafted to a rigid backbone, are studied by molecular dynamics simulations, varying the grafting density σ and the solvent quality. Whereas for poor solvents and large enough σ the molecular brush is a cylindrical object, homogeneous in axial direction, for intermediate values of σ an axially inhomogeneous structure of "pearl-necklace" type is formed. The "pearls," however, have a strongly nonspherical ellipsoidal shape, due to the fact that several side chains cluster together in one pearl, qualitatively consistent with predictions of Sheiko et al. [Eur. Phys. J. E 13, 125 (2004)] We analyze the …
Simulation of Dense Polymer Systems in Two and Three Dimensions
1991
Dense polymer systems are modeled by self- and mutually avoiding walks on lattices. Both simple models where the step length is one lattice spacing and more complicated models where the step length is distinctly longer and may fluctuate (“bond fluctuation model”) are discussed, and it is shown that the computer simulation of such models gives useful insight to understand the thermodynamic phase behavior and the relaxational dynamics of dense polymer solutions and polymer melts. The huge demands in computing power needed for a successful simulation of such systems can be covered by parallel computers such as the multitransputer facility of the University of Mainz.
One is Enough: Influencing Polymer Properties with a Single Chromophoric Unit
2011
1) Institute for Technical and Macromolecular Chemistry, University of Hamburg, Bundesstrasse 45, D-‐20146 Hamburg, Germany 2) WCU program of C2E2, School of Chemical and Biological, Engineering, College of Engineering, Seoul National University, Seoul, Korea Designing a polymer usually involves the incorporation of multiple functional units into a polymer chain, which mutually determine the polymer properties. By combining various functional units, a myriad of polymer properties can be fine-‐ tuned. Classical polymer chemistry teaches us that a single functional group -‐-‐ in particular the end-‐group of a polymer chain -‐-‐ does not contribute to the polymer properties, as is indee…
Connectivity defects enhance chain dynamics in supramolecular polymer model-network gels
2016
Supramolecular polymer networks exhibit twofold dynamics: that of their polymer chains and that of the transient bonds between them, which is further complexed when irregular network structures lead to local variation of both. A typical irregularity is imperfect network-chain connectivity. To assess the impact of that, we study the diffusion of three different types of tracer polymers in supramolecular model networks of four-arm star-shaped poly(ethylene glycol). First, we focus on tracers that carry three stickers and one fluorescent label at their four arms, thereby creating an inherent network connectivity defect in their vicinity. Second, we embed tracers that carry four stickers and fo…
2018
Star-shaped polymers show a continuous change of properties from flexible linear chains to soft colloids, as the number of arms is increased. To investigate the effect of macromolecular architecture on the flow properties, we employ computer simulations of single chain and star polymers as well as of their mixtures under Poiseuille flow. Hydrodynamic interactions are incorporated through the multi-particle collision dynamics (MPCD) technique, while a bead-spring model is used to describe the polymers. For the ultradilute systems at rest, the polymers are distributed uniformly in the slit channel, with a weak dependence on their number of arms. Once flow is applied, however, we find that the…
Dynamics of supramolecular associative polymer networks at the interplay of chain entanglement, transient chain association, and chain‐sticker cluste…
2019
The dynamic mechanical properties of supramolecular associative polymer networks depend on the average number of entanglements along the network‐forming chains, Nₑ, and on their content of associative groups, f. In addition, there may be further influence by aggregation of the associative groups into clusters, which, in turn, is influenced by the chemical structure of these groups, and again by Nₑ and f of the polymer. Therefore, the effects of these parameters are interdependent. To conceptually understand this interdependency, we study model networks in which (a) Nₑ, (b) f, and (c) the chemical structure of the associative groups are varied systematically. Each network is probed by rheolo…
Grafted polymer layers under variable solvent conditions: A Monte Carlo simulation
1993
Polymer chains anchored with one end at a hard wall under variable solvent conditions are investigated by Monte Carlo simulations using the bond- fluctuation model. Detail information on the structural properties are obtained above, at, and below the Θ-point and discussed in terms of the appropriate theories. In particular, the scaling of the brush thickness is formulated and verified by the simulation data. For the dynamics at the Θ-point, both the relaxation time of the chain configuration and the mean-square time displacement are studied. At temperatures distinctly below the Θ-point, we find that the layer develops considerable lateral inhomogeneity in its density, which has not been pre…
Escape transition of a compressed polymer mushroom under good solvent conditions
1999
The escape transition of a flexible polymer chain of chain length N, endgrafted at a hard wall and compressed by a piston of radius R, is studied by Monte Carlo simulation and by phenomenological arguments. In contrast to previous theories which have considered the transition as a function of a (fixed) height H of the piston above the wall, we consider the transition as a function of the conjugate variable, the force f acting on the piston. We find that the transition (which is sharp only for N → ∞) is characterized by a flat region of f in the f vs. H isotherm, i.e. a jump in the height occurs at the transition from Hesc,t to Himp,t, with (Himp,t − Hesc,t)/Hesc,t ≈ 0.26.