Search results for "algebra"

Calculation of vapor pressures not requiring the derivatives of the energy of mixing

1997

A method is presented for the calculation of vapor pressures exclusively on the basis of the energy of mixing, the knowledge of chemical potentials is not required. The only condition used for the calculation is the minimum of the energy of mixing of the overall system in equilibrium. The gas phase is treated as an ideal gas, for the liquid phase no specific thermodynamic description is assumed. The method is demonstrated for a mixture of two solvents and one polymer. The system water/poly(ethylene oxide), the thermodynamics of which are described by an equation that can only be solved numerically thus impeding the calculation of chemical potentials, serves as an example. Interaction parame…

Unified Thermodynamic Modeling of Polymer Solutions: Polyelectrolytes, Proteins, and Chain Molecules

2013

The thermodynamic description of the systems specified in the title requires in general dissimilar theories. This contribution presents an approach that is capable of modeling all of them with a maximum of three adjustable parameters. The Ansatz starts from the Flory–Huggins theory and extends it in a 2-fold manner: The number of segments assigned to the solvent is no longer one but treated as an adjustable parameter to account for the differences in the molecular geometries and in the free volumes of the components. Furthermore, the modeling allows for effects resulting from ternary contacts of the solvent/polymer/polymer type. Examination of the acquired thermodynamic expressions by means…

Structure and dynamics of grafted polymer layers: A Monte Carlo simulation

1991

The bond fluctuation model of polymer chains on lattices is used to study layers of polymers anchored with one end at a hard wall, assuming good solvent conditions and repulsive interactions between the monomers and the wall. Chain lengths from N=10 to N=80 and grafting densities σ from 0.025 to 0.20 are considered, both for the ‘‘quenched’’ case, where the anchor points are kept fixed at randomly chosen surface sites, and the ‘‘annealed’’ case, where lateral diffusion of the anchored ends at the wall is considered. Profiles of monomer density and free end density, chain linear dimensions parallel and perpendicular to the wall, as well as corresponding mean square displacements of inner and…

Monte Carlo simulations of chain dynamics in polymer brushes

1994

The bond-fluctuation model of polymer chains has been used to study layers of end-grafted polymers anchoring at repulsive walls for a broad range of chain length, grafting densities and solvent quality. The dynamics of monomers and associated relaxation times are investigated and interpreted by phenomenological theories and scaling arguments. The case is also considered where a chain is cut off from its anchor point and the chain is subsequently expelled from the brush. Both the velocity with which the chain leaves the brush and the associated conformational changes (chain contraction etc.) are analysed and interpreted in terms of recent theoretical concepts.

Microscopic verification of dynamic scaling in dilute polymer solutions: A molecular-dynamics simulation

1991

The dynamics of a single polymer chain immersed in a large number of solvent particles is studied by molecular dynamics. This is the first simulation where chain length (30, 40, and 60 monomers) and statistical accuracy are sufficient to test the predictions of the Zimm model as a result of the particle-particle interactions: The short-time diffusion constant is in good agreement with the Kirkwood prediction, and the monomer motions exhibit the expected dynamic scaling. The long-range hydrodynamic interaction requires a data analysis that explicitly includes the periodic images via Ewald sums.

Bending of flexible magnetic rods.

2004

The flexible inextensible magnetic rod model is applied for the study of bending and buckling deformations of the paramagnetic particle chains linked by polymer molecules. It is shown that the existing experimental results can be reasonably well described by this model which takes into account the normal magnetic forces arising at chain bending deformation. By matching the experimentally observed shapes with our numerical simulation results different physical properties of the linked paramagnetic particle chains are determined.

Adsorption of Oligomers and Polymers into a Polymer Brush Formed from Grafted Ring Polymers

2013

The interaction of a ring polymer brush with a solution containing oligomers or free linear flexible macromolecules is studied by Monte Carlo simulation, varying the chain length of the free chains, and in selected cases also the lengths of the rings. Two grafting densities are studied, corresponding to semidilute and very concentrated conditions, and a comparison with the corresponding case of brushes formed from grafted linear chains is made. Although the ring polymer linear dimensions in the brushes show an anomalous scaling with ring length, similar to (noncatenated) ring polymer melts, the concentration profiles of oligomers and long macromolecules in ring polymer brushes differ only v…

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.

Polymer-specific effects of bulk relaxation and stringlike correlated motion in the dynamics of a supercooled polymer melt

2003

We analyze dynamical heterogeneities in a simulated “bead-spring” model of a nonentangled, supercooled polymer melt. We explore the importance of chain connectivity on the spatially heterogeneous motion of the monomers. We find that when monomers move, they tend to follow each other in one-dimensional paths, forming strings as previously reported in atomic liquids and colloidal suspensions. The mean string length is largest at a time close to the peak time of the mean cluster size of mobile monomers. This maximum string length increases, roughly in an exponential fashion, on cooling toward the critical temperature TMCT of the mode-coupling theory, but generally remains small, although large…

1986

Covalently crosslinked liquid crystalline networks with elastic properties were prepared in isotropic solution from linear liquid crystalline polymers. As linear precursors for the networks were used: (i) polymers with the mesogenic groups in the side groups (polyacrylates and polymethacrylates), (ii) polymers with the mesogenic groups in the main chain (polymalonates) and (iii) polymers with the mesogenic groups in main chain and side groups (“combined liquid crystalline polymers”). In all crosslinked polymers the liquid crystalline phases of the linear polymers are retained. For low degrees of crosslinking (≤2 mol-%) the phase transition temperatures remain nearly unchanged. These elastom…