Search results for " Algebra"

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.

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 …

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…

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…

Ferrochirality: A simple theoretical model of interacting dynamically invertible helical polymers, 1. The basic effects

1994

The effect of interaction between reversible helical polymers of the poly(hexyl isocyanate) type is investigated by using a molecular field model. It is shown that for interacting helices a critical temperature exists below which they must adopt a common helix-sense spontaneously, even in the absence of any external or intrinsic chiral force

Monte Carlo methods for polymer chains in two - dimensional geometries (polymers at surfaces and interfaces)

1993

Coarse-grained models of polymers at interfaces can be defined such that their treatment by Monte Carlo simulation is most convenient and efficient for the problem at hand. This simulation strategy is briefly illustrated with three examples: (1) The orientational ordering of rigid rod-like polymers grafted to a surface, where “table methods” can be used, applying a fine discretization of the angles describing rod orientation. (2) Surface enrichment of one species in a polymer blend is treated by a semi-grand-canonical technique. (3) The number of configurations and structure of a star polymer attached with its center to a wall is studied by a “growth technique” generalizing simple sampling …

1976

Synthesis and photodimerisation of tetrabenzo[ab,f,jk,o][18]annulenes

1999

Abstract The tetrabenzo[ab,f,jk,o][18]annulenes 7a,b, generated in a 5-step synthesis, show photodimerisation and -oligomerisation reactions in the solid state and in solution. The state of aggregation determines the reaction route. Whereas the cyclodimer 8a has a simple cyclobutane structure, the dimer 8b is a highly symmetrical cyclophane.

Synthesis and Properties of Some Simple Organotitanium Compounds

1986

Before embarking on a detailed discussion of the titanation of carbanions, synthetic and physical organic aspects of several typical organotitanium (IV) compounds shall be surveyed, including thermal stability, aggregation state, X-ray structural data and bond energies. Some of this information is useful in understanding reactivity and selectivity in reactions with organic substrates. Low valent Ti (II) and Ti (III) shall be mentioned only on passing; the interested reader is referred to reviews [1].

Synthesis and Reactivity of New β-Enamino Acid Derivatives:  A Simple and General Approach to β-Enamino Esters and Thioesters

1998

A new strategy has been developed for the synthesis of several β-enamino acid derivatives. N,N‘-Carbonyldiimidazole has been used as C-acylating agent of methyl ketimines, providing a direct and simple route to new β-enamino carbonyl imidazole derivatives 2. These derivatives 2 were cleanly and efficiently transformed into β-enamino esters 4 (X = O) and thioesters 4 (X = S) by reaction with a great variety of alcohols and thiols, including tertiary ones. Alternative and complementary routes to compounds 4 were also investigated. In addition, β-keto esters 6 have been obtained by mild acid hydrolysis of β-enamino esters 4.