bluuebunny/crossref_metadata_2025_split huggingface dataset:
A master equation investigation of coagulation reactions: Sol‐gel transition
Authors: Thorn Matthias , Breuer Heinz‐Peter , Petruccione Francesco , Honerkamp Josef 
Published: April 2003

AbstractThe kinetics of irreversible coagulation phenomena in spatially homogeneous systems is formulated in terms of a multivariate stochastic process. The latter is governed by a master equation for the joint probability distribution of the numbers of reacting species. An efficient numerical algorithm is used to simulate the complete time evolution of the stochastic process. The method is illustrated by simulating the coagulation reaction with configuration‐dependent reaction kernels, Kij = (ij)ω, for clusters of mass i and j with 1/2 < ω ⩽ 1, which are designed to model gelation phenomena. It is demonstrated that the stochastic simulation allows the determination of critical exponents and the gel point directly from the master equation. The results are compared to predictions of the rate equation approach to the sol‐gel transition.
Intrinsic symmetry of the AABb‐type distribution
Authors: Xiao Xing‐cai , Li Ze‐sheng , Sun Chia‐chung , Tang Au‐chin 
Published: April 2003

AbstractBy taking an AaBb‐type polymerisation as an exampleEach unit has a functional groups of type A and b of type B.
, an intrinsic symmetry of the equilibrium number fraction distribution of species is revealed. The symmetry shows that the distribution is invariant under transformation between the variables which describe the total system and the variables which describe the sol. It results that, when the polymer quantities for the pre‐gel regime are given, the corresponding quantities for the post‐gel regime can easily be obtained. As an illustration, the k th radius of an AaBb‐type polymerisation is discussed.
Quantum chemical interpretation of the effects induced by tetramethylethylenediamine and dimethoxyethane in RLi non‐polar monomer systems
Authors: Yakimansky Alexander V. , Vinogradova Ludmila V. , Erussalimsky Boris L. 
Published: April 2003

AbstractThe energetic and electronic parameters of various mono‐ and bidentate complexes of CH3Li with N‐ and O‐containing electron donors were calculated by the MNDO method. It was shown that N,N,N′,N′‐tetramethylethylenediamine (TMD) forms a more stable bidentate complex with CH3Li than 1,2‐dimethoxyethane (DME). However, DME, in contrast to TMD, may form a bis‐bidentate complex with CH3Li in which the CLi bond is weakened to a higher degree than in complexes of CH3Li with N‐containing electron donors. Much lower steric hindrance of DME, as compared to that of TMD, makes an easy formation of bis‐ and tris‐monodentate complexes of DME with CH3Li possible; in these bis‐ and tris‐monodentate complexes DME was simulated by (CH3)2O. Parameters of the CLi bond in the tris‐monodentate complexes of (CH3)2O and tetrahydrofuran (THF) with CH3Li are comparable to those of the bis‐bidentate complex CH3Li · 2 DME. These results are in qualitative agreement with experimental data, according to which THF and DME, in contrast to TMD, can favor the formation of separated ion pairs as active sites in anionic polymerization.
On the reduction of the number of unknowns in flory‐huggins calculations of polymeric equilibria
Authors: Figari Giuseppe , Costa Camilla 
Published: April 2003

AbstractThe Flory‐Huggins equations concerning equilibria of two phases within ternary systems polymer/polymer/solvent are rewritten using a new set of variables. This allows the easy elimination of one of the unknowns of the problem, which can be further simplified, through the elimination of a second unknown, within regions of the diagram sufficiently near to a critical point.
Monte Carlo simulation of phase separations of block copolymers and of corresponding blends
Authors: Yang Yuliang , Lu Jianming , Yan Dong , Ding Jiandong 
Published: April 2003

AbstractThe Monte Carlo method has been used to simulate the phase separations of block copolymers and of corresponding blends with very high concentration (sum of volume fractions of blocks A and B: ϕA + ϕB = 0,9545). Our main findings are as follows: (1) The mixing is nonrandom even in the athermal limit. (2) The nonselective good solvent molecules (ϕV = 0,0455) are mostly located at the interface between A‐ and B‐rich phases, thus, it is not true that solvent and monomeric units will remain mixed at all temperatures. (3) Even for the same microscopic A‐B interaction energy, ε, and at the same temperature, the Flory‐Huggins parameter χ of block copolymers is always higher than that of corresponding blends, and the χ values of block copolymers and corresponding blends have different ε‐dependencies. (4) The critical values of χ both for block copolymer and corresponding blend are obtained and compared with the meanfield theoretical predictions. It is found that the ratio of χc (block)/χc (blend) is qualitatively compatible with the prediction of the Flory‐Leibler theory.
Statistical thermodynamics in the framework of the lattice fluid model, 1. Polydisperse polymers of special distribution
Authors: An Lijia , Jiang Bingzheng , Hu Yuxin , Jiang Zhenhua , Tang Xinyi 
Published: April 2003

AbstractThe Gibbs free energies and equations of state of polymers with special molar mass distributions, e.g., Flory distribution, uniform distribution and Schulz distribution, are derived based on a lattice fluid model. The influence of the polydispersity (or the chain length) on the close‐packed mass density, the close‐packed volume of a mer and the mer‐mer interaction energy or the scaling temperature is discussed. The diagrams of the Gibbs free energies as a function of temperature and chain length are simulated with a computer. The results suggest that a polydisperse polymer is thermodynamically more stable than the corresponding monodisperse polymer and that the thermodynamical properties of a polydisperse polymer are identical with those of the corresponding monodisperse polymer when the average degree of polymerization is sufficiently high.
Statistical thermodynamics in the framework of the lattice fluid model, 2. Binary mixture of polydisperse polymers of special distribution
Authors: An Lijia , Jiang Bingzheng , Jiang Zhenhua , Hu Yuxin , Tang Xinyi 
Published: April 2003

AbstractIn this paper, the Gibbs free energy, the equation of state and the chemical potentials of polydisperse multicomponent polymer mixtures are derived. For general binary mixtures of polydisperse polymers, we also give the Gibbs free energy, the equation of state and the chemical potentials and derive the stability criteria and spinodal. Furthermore, binary polydisperse polymer mixtures of special distribution, i.e., Flory distribution, uniform distribution and Schulz distribution, are discussed and the influence of polydispersity on the interaction energy parameter is considered. For these special‐distribution systems, the spinodal curves are simulated and the influence of chain length and polydispersity on the spinodal curves is discussed. The results suggest that the spinodal temperature of the mixture with a given volume fraction of one component decreases with increasing polydispersity and the extent of the shift decreases with increasing degree of polymerization when η = M̄w/M̄n is given. In addition, the variations of the spinodal curves with polydispersity and chain length are shown and they are qualitatively compared with the experimental results.
Model simulation of cationic polymerization by an iterative technique
Authors: Freyer Christian V. , Manz Jörn , Nuyken Oskar 
Published: April 2003

AbstractUsing a simple, instructive model of living polymerizations, we develop an economic technique for solving a complete set of kinetic equations for active polymers Pn* with chain length n. The method consists of two steps: (i) solution of the global kinetic equations for the global species P* which comprises all individual polymers Pn* together with monomer M and other non‐polymeric species, followed by (ii) iterative solution of the original kinetic equations, successively for the individual polymers P1*, P2*, P3*, …, Pn*. The method is applied successfully to a rather complex, realistic model of cationic polymerizations. In general, our iterative scheme serves to reduce numerical storage requirements, in comparison with traditional direct integrations for all individual kinetic equations. Therefore it may allow simulations of very demanding polymerizations, including very high degrees of polymerization, which cannot be evaluated by traditional techniques.
Influence of micromixing on the free‐radical polymerization in a discontinuous process
Authors: Engelmann Uwe , Schmidt‐Naake Gudrun , Maier Jens , Seifert Peter 
Published: April 2003

AbstractWith the help of a simple reaction‐diffusion model with constant striation thickness the influence of micromixing on free‐radical polymerization was investigated for several test reactions with discontinuous prepolymerization and jerky addition of selected reactants. Monomer conversion or mean values of molar mass and chemical composition cannot be expected to be very sensitive to micromixing effects. If molar mass distributions are to be used, problems will arise from the fact that the distribution of the polymer accumulated during prepolymerization covers mixing influences occurring after reactant feed. The instantaneous molar mass distribution would be more suitable. Time‐integral distributions of chemical composition or sequence length in combination with appropriate test reactions proved to be feasible indicators for the effects of micromixing as it becomes possible to separate the distribution of the prepolymer from that of the polymer which is formed after addition when micromixing is to be investigated.
Ab initio molecular orbital calculations on the transition state for the addition of a methyl radical to vinyl monomers
Authors: Davis Thomas P. , Rogers Stephen C. 
Published: April 2003

AbstractAb initio molecular orbital calculations have been performed on the transition state for the addition of methyl radical to twelve vinyl monomers using the SV 3–21G basis set. A linear relationship has been found between the calculated energies of activation and previously calculated energies of reaction. This supports the assumption of an Evans‐Polanyi type rule in previous work which attempted to correlate reactivity with calculated energies of reaction. The activation energies obtained for methyl addition to butadiene and styrene were calculated to be negative. This is caused by errors introduced by a number of sources, viz. basis set superposition error, spin contamination and zero point energy. These errors are discussed. Previous authors have reported reasonable agreement between calculated activation energies at SV3–21G and experimental values for methyl addition to ethylene, this work suggests that this agreement was coincidental and results from the fortuitous cancellation of errors. The nature of the transition state for these radical addition reactions is discussed and the limitations of the SV3–21G basis set are highlighted. The theoretical prediction of activation energies for radical addition reactions would require much larger calculations, beyond the computational means of most research laboratories.
Osmotic pressure, atomic pressure and the virial equation of state of polymer solutions: Monte Carlo simulations of a bead‐spring model
Authors: Milchev Andrey , Binder Kurt 
Published: April 2003

AbstractA recently introduced coarse‐grained model of polymer chains is studied analyzing various contributions to the pressure as obtained from the virial theorem as a function of chain length N, temperature T and density ϕ. The off‐lattice model of the polymer chains has anharmonic springs between the beads, but of finite extensibility, and the Morse‐type interaction between beads is repulsive at very short distances and attractive at intermediate distances. Solvent molecules are not explicitly included. It is found that the covalent forces along the chain (modelled by the spring potentials) contribute a negative term to the pressure, irrespective of temperature, which vanishes linearly in ϕ as ϕ → 0. In contrast, both contributions to the pressure due to intrachain nonbonded forces and due to forces between different chains change sign from high temperatures (T ≫ θ, θ the theta‐temperature) where they are positive, to low temperature where both parts of the pressure become negative. It is shown that the total pressure has the expected behavior with temperature near the θ‐temperature, i.e., Δp ≡ ptot − kB · Tp ∼ (T − θ). We study also the concentration and chainlength dependence of the various contributions to the pressure in the good solvent regime and interpret them with scaling predictions.
Distribution function for the radius of gyration for theta chains attached at one end to an impenetrable surface
Authors: Mattice Wayne L. , Napper Donald H. 
Published: April 2003

AbstractChains that are unperturbed by the intramolecular excluded volume effect are examined in the free state and under conditions where one of the ends is attached to an impenetrable surface. The density of the attachment of the chains to the surface is so low that interchain interactions can be ignored. The shapes of the distribution functions for the squared end‐to‐end distance, r2, and squared radius of gyrations, s2, are evaluated in both situations. As is well‐known from previous work, attachment of the chains to the impenetrable surface produces an increase in 〈r2〉 and (to a lesser extent) 〈s2〉. It also narrows the distribution function for r2. There is, however, no detectable effect on the shape of the distribution function for s2. The narrowing of the distribution function for r2, coupled with the absence of any effect on the shape of the distribution function for s2, is rationalized with a very simple model.
Ferrochirality: a simple theoretical model of interacting, dynamically invertible, helical polymers, 2. Molecular field approach: supports and the details
Authors: Baumgarten Jörg Lothar 
Published: April 2003

AbstractUsing a molecular field approach, the effect of interaction between reversibly invertible, helical polymers is investigated theoretically. The helices are modelled by nearest‐neighbour statistical thermodynamics. If the interaction energy between two helices of common handedness is lower than that of oppositely handed ones, a critical temperature Tc exists, below which the system spontaneously must leave the racemic state, though there is no contact to any chiral centre or force. This is analogous to the second‐order phase transition of ferromagnets. The critical point increases with molecular weight and optical persistence of the helices. At the critical point the system is highly sensitive to any chiral influence. Doping with 1 ppb of a chiral additive leads to a relative optical rotation of order 10−3 at the critical point. This corresponds to an intrinsic energy difference of left‐ to right‐handed monomeric units of only 10−8 J/mol. The cooperative effects in chirally doped nematic poly(hexyl isocyanate) (PHIC) can be easily described without using the improbable assumption that the supramolecular cholesteric arrangement with an axis‐to‐axis rotation of only 0,001° must be the reason for the collective helix sense preference in this system. On the other hand, if the chain‐to‐chain interaction is transmitted through this supermolecular twist, the structure of the equations is altered slightly only and critical behaviour must be expected as well.
Theory of static scattering from polymer mixtures. The case of polystyrene/polydimethylsiloxane/poly(methyl methacrylate)/toluene
Authors: Benmouna Mustapha , Duval Michel , Strazielle Claude , Hakem Faiza‐Ilhem , Fischer Erhard W. 
Published: April 2003

AbstractThe static scattering properties of four‐component polymer mixtures are examined starting from the general equation extending the random phase approximation to multicomponent systems first proposed by Benoit. The results are compared with the light scattering data reported recently by Strazielle and coworkers for polystyrene/polydimethylsiloxane/poly(methyl methacrylate)/toluene mixtures. The present formalism provides a more rigorous treatment of these data, and a good agreement is obtained without adjustable parameters. This method provides a definition of the apparent interaction parameter used by Strazielle et al. and describes its correlation with various relevant quantities characterizing the mixture. It predicts in particular the variation of this parameter with the concentration of poly(methyl methacrylate), which was not possible in the earlier work. Various other important properties of the mixture are investigated such as the critical concentration for phase separation and the apparent radius of gyration.
Scattered intensity by a cross‐linked polymer blend
Authors: Bettachy Amina , Derouiche Abdelali , Benhamou Mabrouk , Benmouna Mustapha , Vilgis Thomas A. , Daoud Mohamed 
Published: April 2003

AbstractCross‐linked mixtures of polystyrene and poly(vinyl methyl ether) exhibit a non‐vanishing zero‐angle intensity in small‐angle neutron scattering experiments. A possible explanation is that fluctuations in composition in the mixture may be frozen by the presence of cross‐links. Assuming this, we introduce a screening length κ by the condition that the scattered intensity should not be changed by cross‐linking. We find κ2 ∼ C/(χ − χi), where C is an elastic constant, χ and χi, respectively, the inverse temperature and that where cross‐linking is performed. When the temperature is varied, we find three regimes. In the first one, the scattered intensity is monotonously decreasing. In the second one, it has a finite maximum. In the last one, the maximum eventually diverges.
Brushes formed by self‐similarly branched polymers and random manifolds
Authors: Vilgis Thomas A. , Haronska Peter 
Published: April 2003

AbstractWhen randomly branched polymers are grafted to a surface, polymer brushes are the result, similarly as well known in the case of linear grafted polymer chains. These brushes behave, however, special, as severe restrictions in the conformation of individual polymers are present. These restrictions are firstly due to the high degree of branching and secondly to the natural maximum stretching ratio of the branched molecules, that is given by Hmax = aM1/D. a is the typical size of a monomeric unit, D is the spectral dimension and M the total mass of the branched polymer. Brushes cannot exceed this height, and limits on the grafting density as functions of the spectral dimension are investigated. For all thermodynamic situations the minimum area per chain scales as σmin = aM(D − 1)/D.
The shape of linear and star‐branched nonreversal random walks embedded in a tetrahedral lattice
Authors: Zifferer Gerhard 
Published: April 2003

AbstractThe shape‐asymmetry of linear and star‐branched nonreversal random walk polymers on a tetrahedral lattice is studied by means of a Monte Carlo simulation. Properties characteristic of the instantaneous shape based on the mean‐square radius of gyration and its principal components as well as based on the end‐to‐end distance are discussed. Short‐chain effects are characterized by polynomial expressions (power series of N−1), simultaneously by extrapolation yielding a result in the limit of infinitely large configurations.
Improved expression of the mean‐square radius of gyration, 2. Poly(1,1‐disubstituted ethylene)s
Authors: Zhou Zhiping , Yan Deyue 
Published: April 2003

AbstractThe mean‐square radius of gyration of poly(1,1‐disubstituted ethylene)s is calculated according to a method already developed for poly(methyl methacrylate), poly(α‐methylstyrene) and polyitaconate. During the derivation both the effect of side groups and the masses of skeletal atoms were taken into account. A hypothetical polymer chain was introduced, in which the mass of the substituents on every Cα was considered to be concentrated in their center of mass, and the virtual side bond vector runs from Cα to this center. The mean‐square radius of gyration of poly(1,1‐disubstituted ethylene)s consists of two parts, one of which is the mean‐square radius of gyration of the hypothetical molecule described before and the other is related to the geometrical characteristics of the side groups. Numerical calculations indicated that the dependence of the mean‐square radius of gyration of poly(1,1‐disubstituted ethylene)s on the molecular weight is analogous to that of vinyl polymers, 〈S2〉 = aMb, where a and b are constants characteristic of the polymer.
Molecular orbital study on the mechanism of radical polymerization of spiro‐orthocarbonates bearing exo‐methylene groups
Authors: Sanda Fumio , Takata Toshikazu , Endo Takeshi 
Published: April 2003

AbstractMolecular orbital studies were carried out to compare the easiness of ring‐opening in the radical polymerization of spiro‐orthocarbonates bearing exo‐methylene groups at α‐position of the ether oxygen, spiro[2,4‐benzodioxepine‐4′‐methylene‐3,2′‐[1,3]‐dioxolane] (1), and at β‐position of the ether oxygen, spiro[2,4‐benzodioxepine‐5′‐methylene‐3,2′‐[1,3]‐dioxane] (2). The formation energy suggests that 1 would show a degree of ring‐opening larger than 2, contrary to the experimental result. Therefore, a reverse relation in activation energy was suggested, i. e., the kinetic factor surpasses the thermodynamic factor in the ring‐opening reaction of 1 and 2. Although the calculation of the activation energy of the radical ring‐opening reaction was not successful, the result extracted from the perturbation energy calculations of vinyl polymerizations of 1 and 2 agree well with their radical vinyl polymerizability. Namely, 1 was confirmed to have a larger vinyl polymerizability than 2, which agrees well with the smaller ring‐opening polymerizability of 1 compared with 2. The real HOMO and LUMO (highest occupied and lowest unoccupied molecular orbitals) of 1, 2 and their intermediates for the radical addition were confirmed not to correspond to the apparent HOMO and LUMO from the detailed analysis of their coefficients of atomic orbitals (AOs). The frontier electron density of 1 and 2 agrees well with the fact that the β‐carbon of their exo‐methylene group has a higher reactivity toward radical species than the α‐carbon.
A simple derivation of the exponent γ for Gaussian chains with excluded volume
Authors: Kloczkowski Andrzej , Mark James E. , Erman Burak 
Published: April 2003

AbstractThe exponent γ in the expression for the partition function Z ≅ μN · Nγ−1 is derived for a Gaussian chain. The method of Ullman is adopted. Results of calculations show that for 1, 2, 3 and 4 dimensions, γ = 1, 1,25, 1,2 and 1, respectively. It is also shown that γ remains unity for all dimensions higher than four. These results are in better agreement with exact computer simulation results than the first‐order renomalization group theory calculations. The self consistency of the present method and possible improvements along the lines of the present study are discussed.