bluuebunny/crossref_metadata_2025 huggingface dataset:
Conformational characteristics of polystyrene
Authors: Rapold Roland F. , Suter Ulrich W.
Published: April 2003

Conformational energies, computed with a forcefield including coulombic interactions and a simple accounting for the effects of solvent, of meso and racemic 2,4‐diphenylpentane as model substances of polystyrene have been computed as functions of the skeletal torsion angles and the phenyl torsion angles. The relatively high energies of the ḡ conformations rendered these states negligible and no minimum was found in the meso‐tt domain. Three minima for the meso diad (gt, tg, gg) and four minima for the racemo diad (tt, tg, gt, gg) are relevant. A two‐state rotational isomeric state model is applicable with states at φt = 5°C and φg = 110° for both meso and racemo diads. Statistical weight matrices have been derived and values predicted for the characteristic ratio, the fractions of 2,4‐diphenylpentane and 2,4,6‐triphenylheptane at stereo‐chemical equilibrium and the vicinal NMR coupling constants are found to be consistent with experimental results.
Static atomistic modelling of the structure and ring dynamics of bulk amorphous polystyrene
Authors: Rapold Roland F. , Suter Ulrich W. , Theodorou Doros N.
Published: April 2003

A detailed static atomistic model of dense, glassy polystyrene is simulated using a well established technique that previously proved successful for simple vinyl polymers. Initial chain conformations that are generated using a Monte Carlo technique including periodic continuation conditions are “relaxed” by potential energy minimization. In total 24 microstructures at densities of 1,07 g/cm3 were obtained with a cube‐edge length of 18,65 Å. Detailed analysis of the minimized structures indicates that intermolecular packing influences create a large variety of chain conformations different from the purely intramolecular ground states. The systems are amorphous, exhibiting random coil behavior. The described structures have been used for a quasistatic simulation of localized motions. These motions include stepwise rotation and oscillation of the phenyl groups. The frequency distribution for the simulated ring motions covers many orders of magnitude. It is very rare that an energy barrier with a reorientation angle indicating a ring “flip” is overcome. Motions with small reorientation of the phenyl rings, and therefore not leading to a ring “flip”, dominate with an average reorientation angle of 16° (±12°). The intermolecular effects of the analyzed processes were found very important and far‐reaching, widely influencing the cooperative motions of molecular groups.
Theory of electrophoretic mobility of polyelectrolyte chains
Authors: Muthukumar Murugappan
Published: April 2003

An explicit formula is derived for the electrophoretic mobility of a linear polyelectrolyte chain in terms of the molecular weight, Debye length and solvent quality. The nature of the crossover between different regimes as the salt concentration and molecular weight are varied is presented. The effect of chain statistics intermediate between the Gaussian and rodlike limits on the electrophoretic mobility is analysed for the first time.
Lattice model of heterogeneous polymer chains in the liquid‐crystalline state, 2 local relaxation properties
Authors: Gotlib Yuli Y. , Medvedev Gregory A.
Published: April 2003

Using a lattice description, the short‐ and medium‐scale dynamics of the heterogeneous model of main‐chain liquid‐crystalline polymers have been considered. Chain mobility is assumed to occur by means of three‐ and four‐bond kinetic‐unit jumps. Mobility and force coefficient tensors, and linear relaxation equations for the average projections of chain bonds have been obtained. Both acoustic and optical branches of the relaxation spectrum are shown to be split into longitudinal and transverse components. A pronounced dependence of relaxation spectrum shape and splitting magnitude on the spacer length has been found.
Monte carlo simulation of polymers in steady potential flows
Authors: Carl Wilfried , De Pablo Juan J.
Published: April 2003

This work presents a study of the configurational properties of bead‐spring chains in steady‐state potential flows. These properties are obtained from off‐lattice Monte Carlo simulations. The results of our simulations compare favourably with theoretical results for phantom chains. We investigate the effects of excluded volume and hydrodynamic interaction on the configurations of the chains, and compare our results to the predictions of scaling arguments. The scaling law observed here for the latter case deviates from theoretical predictions but is in agreement with findings reported from molecular dynamics simulations.
Effect of polyfunctional chain transfer agents on molecular weight distribution in free‐radical polymerization, 1. The ideal case: C equals one
Authors: Yuan Cui Ming , Silvestro Giuseppe Di , Farina Mario
Published: April 2003

The theoretical approach to free‐radical polymerization in the presence of polyfunctional transfer agents can be derived in a simple way if the effects of primary chains and termination reactions are neglected. Under these conditions, and for values of the chain transfer constant C = 1, the analytical expressions for the number‐ and weight‐average degree of polymerization, dispersion index and weight distribution function were derived through the elementary probability theory and generating functions. Numerical examples are reported on the relationship between distribution parameters, functionality and monomer conversion.
Influence of reactor operational policies on distributions of chemical composition, molar mass, sequence length and sequence frequency of multicomponent polymers obtained by free‐radical polymerization
Authors: Engelmann Uwe , Schmidt‐Naake Gudrun
Published: April 2003

Remarkable shifts in chemical composition, molar mass, sequence length and sequence frequency will occur in the course of free‐radical multicomponent polymerizations, if the reactivities of the comonomers are different and a simple batch reactor is used. It is shown for the terpolymerization system of methyl methacrylate/styrene/maleic anhydride that a semi‐batch reactor with appropriate regimes is suitable to obtain products with improved chemical, molecular and sequential homogeneity. However, if polymers with defined inhomogeneities like bimodal molar mass or chemical composition distributions are desired, these are also obtainable by use of appropriate operational policies, which will be illustrated for the homopolymerization of methyl methacrylate and the binary copolymerization of methyl methacrylate/maleic anhydride. Concerning the instantaneous mean chemical composition of polymer molecules, which cannot be measured directly, a new procedure is presented to determine this quantity experimentally.
Ab initio quantum‐mechanical calculations of the propagation enthalpies for the radical and anionic polymerizations of formaldehyde and methanimine
Authors: Sana Michel , Leroy Georges , Dewispelaere Jean‐Pierre , Wilante Claude , Penelle Jacques
Published: April 2003

The gas phase enthalpies of formation for oligomeric radicals and anions H(CH2NH)n* and H(CH2O)n* were theoretically determined by ab initio quantum‐mechanical calculations with n in the range 1 to 6. From these results, the reaction enthalpies for each of the first five propagation steps of the polymerization were estimated for methanimine (H2C = NH) and formaldehyde (H2C = O). At the same step of oligomerization, enthalpies associated with anionic polymerizations are always more negative than enthalpies corresponding to radical polymerizations, but the difference between them decreases with increasing n. Both Delta;H (propagation) vs. n curves tend rapidly, particularly for radical polymerizations, towards an asymptotic value independent of the mode of polymerization and equal to ‐ 12 kcal/mol for formaldehyde and ‐ 14 kcal/mol for methanimine. Experimental data for the gas phase polymerization of formaldehyde are in good agreement with our theoretical value. These results demonstrate that heats of polymerization can be reasonably estimated by intensive calculation methods if a careful choice of the reaction mimicking the propagation step is done.
Statics and dynamics of heterogeneous polymer networks
Authors: Vilgis Thomas A. , Heinrich Gert
Published: April 2003

This paper discusses the effect of heterogeneities in crosslink density on static properties, such as the mechanical stress‐strain relation (free energy) and scattering effects as occur in small‐angle neutron experiments. The second part of the paper is devoted to the segmental dynamics and the long‐time relaxation of polymer networks. It is shown that the heterogeneities slow down the relaxation at long times.
Molecular arrangements of liquids of chain molecules near solid surfaces in the presence of a diluent
Authors: Vacatello Michele
Published: April 2003

The molecular arrangements near solid surfaces and in narrow slits of liquid tridecane, containing 5 wt.‐% of a diluent having the size and the interactions of a methylene group, have been studied by atomistic computer simulations using the Monte Carlo technique. The presence of the diluent does not modify the tendency to form segmental layers near the solid surfaces. However, the diluent is preferentially adsorbed at these surfaces, replacing part of the chain ends. As a result, the ordered structures with nearly two‐dimensional chains found for the pure liquid in analogous conditions are partly destroyed.
Semiclassical theory of group vibrations for linear polymer chains
Authors: Wozny Christopher E. , Sumpter Bobby G. , Noid Donald W.
Published: April 2003

The semiclassical spectral method (SSM), which employs molecular dynamics and spectral estimators to determine transition frequencies between quantum energy levels in molecular and atomic systems, is extended to include calculations for linear polymer chains. Average differences between harmonic and transition frequencies for the symmetric and asymmetric stretch modes of polyethylene are reported to be around 50 cm−1 with smaller average frequency shifts for the other group vibration dispersion curves for a certain potential surface describing the macromolecule.
Sorption of gases in glassy polymers: A probabilistic model
Authors: Favre Eric , Schaetzel Pierre , Nguyen Quang Trong , Néel Jean
Published: April 2003

The description of the sorption mechanism of gases in glassy in glassy polymers is of importance for membrane‐based gas separation processes as well as for packaging applications. Dual mode theory, postulating a Henry and Langmuir process to occur and leading to an equation with three adjustable parameters, is usually proposed in order to describe the isotherms. A simple mechanistic model, based on an unequal affinity between the gas molecules and the matrix regions occupied either by polymer or a previously sorbed gas molecule, is presented in this paper; in contrast to dual mode theory, this approach does not postulate the existence of microvoids in the glassy matrix. Integration leads to an equation with two adjustable parameters, which is shown to describe precisely already reported isotherms.
Thermodynamic modelling of polymer solutions with a modified Staverman equation
Authors: Pfennig Andreas
Published: April 2003

A model describing the thermodynamic behaviour of polymer solutions is derived which explicitly accounts for the flexibility of the polymer chains. Based on computer simulations on various lattices it is shown that the flexibility of a polymer chain can be modelled by distinguishing different polymer conformations. Here each conformation is characterized by its corresponding number of external contact sites. The equilibrium between the different conformations is then solved for any polymer concentration and any combination of interaction energies utilizing a modified Staverman equation. The model predictions are in good agreement with the results of the computer simulations which were performed using the simple‐sampling and the slithering‐snake algorithm. Since the knowledge of the distribution of the conformations of a single polymer chain on an empty lattice is a prerequisite to perform the model calculations, Poisson distribution functions are fitted to the results of the corresponding computer simulations. The generalization of these distribution functions not only facilitates the use of the new model but also allows to model polymers of varying chain stiffness.
Application of numerical methods for the calculation of size distribution functions of polymers produced by ionic polymerizations
Authors: Ermakov Igor , De Clercq Ronny , Goethals Eric
Published: April 2003

The application of numerical methods for the calculation of the molecular weight distribution of living ionic polymerization, carried out in the presence of monofunctional and polyfunctional transfer agents, is described. The methods used include the numerical solution of a system of differential equations by the Runge‐Kutta‐Merson procedure and the statistical Monte‐Carlo approach. When a monofunctional transfer agent is used, the Runge‐Kutta‐Merson procedure is quite useful for the calculation of the molecular weight distribution for various polymerization systems. When a polymerization is carried out in the presence of a polyfunctional transfer agent, the mechanism includes the coupling of polymer chains. Due to the complexity of the system, the Runge‐Kutta‐Merson procedure is hardly applicable and problems of this type should be solved by a Monte Carlo simulation procedure. Once a computer program has been written, both methods allow the chemist to calculate the molecular weight distribution of a polymer as a function of the different kinetic parameters of the polymerization.
Polydomains in liquid‐crystal elastomers
Authors: ten Bosch Alexandra , Varichon Lionel
Published: April 2003

In liquid‐crystal elastomers, the simultaneous presence of rubber elasticity due to the crosslinked backbone chains and of optical birefringence due to the mesogens in the side chains lead to exceptional physical properties. An elastic deformation of the network influences the order of the mesogens and, therefore, the optical properties. A theory based on a Landau‐de Gennes expansion of the free energy is proposed. In the opaque polydomain phase, the local orientation is given by a compromise between the external mechanical field and a local anchoring interaction. As the field is increased, it becomes energetically favorable for the mesogens to align parallel to the mechanical field, and a transition to a transparent monodomain structure occurs. Results for the average orientation, the stress and the chain conformation are given.
Stability analysis and scattering properties of charged crosslinked blends in solution
Authors: Benmouna Mustapha , Vilgis Thomas A. , Benhamou Mabrouk , Babaoui M. , Daoud Mohamed
Published: April 2003

The phase behavior and scattering properties of crosslinked charged polymer blends in solution are examined. De Gennes' analogy between the effects of crosslinks in a network and electrostatic charges in a dielectric medium on the scattering properties and the phase behavior of crosslinked polymer blends is used. This analogy is extended to include the effects of screening in order to improve its agreement with the experimental data in the small q range. The excluded volume interactions are explicitely introduced through the blob model. The enhancement of compatibility of the mixture and the increase of its rigidity constant are evaluated in certain cases. The limit of neutral polymers is discussed because it corresponds to the case of charged mixtures in the presence of excess salt. The kinetics of the microphase separation transition is briefly discussed. A dynamical model including the long range hydrodynamic interaction is presented. The relaxation frequency of the stable modes and the growth rate of unstable ones are also considered.
On the plateau modulus mixing rule of miscible blends
Authors: Lomellini Paolo
Published: April 2003

Based on Graessley and Edwards scaling concepts, a new mixing rule for the entanglement density of miscible blends has been proposed. The arguments here used apply when the interactions in the blend do not affect too much the entanglement probability. The rule was compared with others (linear and geometric mixing rules) based on the entanglement idea of fixed interchain contact points. The predicted plateau moduli were successfully compared with experimental data of polystyrene‐poly(dimethylphenylene oxide) blends.
Are the continuum and the lattice representation of freely jointed chains equivalent?
Authors: Glatting Gerhard , Winkler Roland G. , Reineker Peter
Published: April 2003

The partition function and force elongation relation of freely jointed chains of rigid rod segments are calculated for arbitrary dimensions in the continuum and on a lattice. The qualitative differences between these models are discussed for polymers embedded in spaces of various dimensions. These investigations show that chains of rigid rod segments in higher dimensions are equivalent to chains of segments with internal degree of freedom in lower dimensions. Networks composed of these chains show a similar behaviour as uniaxial stretching experiments of rubber‐like materials.
A master equation investigation of coagulation reactions: Sol‐gel transition
Authors: Thorn Matthias , Breuer Heinz‐Peter , Petruccione Francesco , Honerkamp Josef
Published: April 2003

The 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

By taking an AaBb‐type polymerisation as an example

Each 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

The 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

The 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

The 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

The 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

In 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

Using 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

With 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

Ab 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

A 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

Chains 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

Using 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

The 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

Cross‐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

When 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

The 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

The 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

Molecular 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

The 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.
Numerical analysis of the rotational relaxation time of spectrin segments and spectrin heterodimer in dilute aqueous solution
Authors: Skjetne Paal , Knudsen Kenneth D. , de La Torre Jose Garcia , Elgsaeter Arnljot
Published: April 2003

The rotational relaxation time for different models of the spectrin αβ‐heterodimer and spectrin subunits were obtained through numerical simulation making use of the so‐called rigid‐body approximation. Based on information on the helix structure of the 106 aminoacids in the repeating motif of spectrin, three different models with varying degree of refinement were set up to represent the spectrin subunits: the two‐bead, the many‐bead and the shell model. For one‐ and two‐subunit spectrin the relaxation time was found to be 20 ± 4 ns and 92 ± 5 ns, respectively. The last result conforms well with available experimental data from transient electric birefringence measurements. For the αβ‐heterodimer two different models were applied: a chain of beads (pearl necklace model) and a more refined so‐called San necklace model. Using the San necklace model, the relaxation time was found to be in the range of 9 to 18 μs (depending on the flexibility of the joint), which is in accordance with what has been obtained from intrinsic viscosity measurements, but considerably higher than experimental data from measurements of transient electric birefringence.
Numerical estimation of unperturbed dimensions of regioirregular poly(3‐ethylthiophene)s
Authors: He Ziru , Yang Xiaozhen , Zhao Delu
Published: April 2003

The unperturbed chain dimensions of poly(3‐ethylthiophene)s have been calculated using the full‐relaxation optimization of conformational energies and the chain statistical mechanics with a rotational isomeric state model of two states. The computation indicates that the conjugated polymer with side groups is more flexible than without, and that the orientation of the ethyl group and the regioirregular sequences perturb the chain conformation to a certain extent. Specially, the calculated chain conformations under θ‐conditions are more rigid than those observed in good solvent. This supports experiments showing that the chain dimensions of conjugated polymers are very sensitive to variations of intermolecular interactions.
Monte Carlo simulation of the chain length distribution in pulsed‐laser polymerization experiments in microemulsion
Authors: Manders Bart G. , van Herk Alex M. , German Anton L.
Published: April 2003

The Monte Carlo method has been used for numerically simulating pulsed‐laser polymerization (PLP) in microemulsion, in order to establish if a shift from inflection point to peak maximum as the best measure of the propagation rate constant, kp, will occur theoretically. Termination is assumed to be instantaneous in the simulations as droplet sizes can be very small in microemulsions. From the results of the simulations it is found that instantaneous termination indeed causes the peak maximum to become the best measure of kp. From these results it can be deduced that in bulk it is not simply the Poisson‐broadening that causes the peak maximum to yield an overestimation of kp. This overestimation is rather caused by the fact that the termination rate is finite leading to an asymmetrical peak in the molecular weight distribution. In combination with broadening this yields the inflection point to be the best measure of kp in the bulk.
Computer simulation of the aggregation of ion pairs in the polymerization of styrene initiated by RCl/SnCl4/NRCl− systems
Authors: Szymanski Ryszard , Matyjaszewski Krzysztof
Published: April 2003

Computer simulations show that ion pair aggregation can be responsible for the unusual dependence of the initial rate of polymerization on the concentration of added salt in the cationic polymerization of styrene initiated by RCl/SnCl4/NRCl−. Addition of small amounts of tetraalkylammonium chloride to the system reduces the rate of polymerization due to the decrease of the concentration of propagating free cations. Subsequent salt addition leads to a small rate increase, and then the rate decreases at higher [salt]0/[SnCl4]0 ratio. The simulations show that the rate increase can be ascribed to the formation of aggregates of ion pairs and thus to a higher overall proportion of carbocations resulting in faster polymerization. The decrease of the polymerization rate at higher concentrations of added salt can be explained by the conversion of free SnCl4 to SnCl anions which are weaker Lewis acids. The effect of various equilibrium constants on the total concentration of carbocations as a function of added salt is simulated.
Chain transfer to solvent in two‐state anionic polymerization, 1. Fast exchange between propagating species
Authors: Litvinenko Galina I. , Arest‐Yakubovich Alexander A.
Published: April 2003

A theoretical consideration of molecular weights and molecular weight distribution (MWD) of polymers formed in anionic polymerization proceeding via active centres of two different types under conditions of chain transfer to solvent with a fast exchange between propagating species is presented. Analytical expressions for number‐and weight‐average degrees of polymerization are obtained. Expressions for Pn and Pw are shown to be the same as in a one‐centre process with the apparent intensity of chain transfer proportional to the weight fraction of the polymer formed via “transferring” centres. The polymers formed possess a moderately wide unimodal MWD. The dependence of the polydispersity index on the effective intensity of chain transfer goes through a maximum; for M0/I0 = 103 the maximum value of Pw/Pn is ca. 4,6. The method is suggested for the estimation of the relative reactivity in chain propagation of two active centres from the dependence of molecular weight on initiator mixture composition. The effects of association of active centres on the average molecular weights are analyzed. The case when one of the centres is dormant is also considered.
Chain transfer to solvent in two‐state anionic polymerization, 2. Slow exchange between propagating species
Authors: Litvinenko Galina I. , Arest‐Yakubovich Alexander A.
Published: April 2003

The effect of slow exchange between growing chains on the average degree of polymerization (DP) and the molecular weight distribution (MWD) of polymers formed in a two‐state polymerization accompanied by chain transfer to solvent is considered. For the case when centres of only one type are capable of chain transfer it is shown that the exchange can be regarded as fast or slow, depending on the ratio of characteristic times of exchange (τex) and chain transfer (τtr) for these centres. The conditions for fast exchange, when the MWD of the polymer becomes independent of the rate of exchange, are derived. Under otherwise the same conditions, polymer of the narrowest MWD is formed if the exchange is fast, the number‐average DP being independent of the exchange rate. With increasing ratio τex/τtr, the weight‐average DP of the polymer increases and the MWD changes from unimodal to bimodal. For the case when “non‐transferring” centres are dormant, it was also found that at slow exchange the number‐average DP is greater and the MWD is less broadened than at fast exchange.