bluuebunny/crossref_metadata_2025 huggingface dataset:
Triblock copolymers of lactide with poly(ethylene glycol) and influence of stereochemical composition
Authors: Onyari John M. , Huang Samuel J.
Published: April 2003

Polymerization of L‐lactide (LLA) and poly(ethylene glycol) (PEG) at 120°C using stannous 2‐ethyl hexanoate results in ABA triblock copolymers in good yields. The glass transition temperature of the copolymers shows strong dependence on the composition. One‐ and two‐phase triblock copolymers can be prepared by controlling the molecular weight of the PEG soft block, as well as the initial LLA/PEG charge ratio. Incorporation of racemic lactide during polymerization drastically affects the crystallinity of the block copolymers obtained. 1H and 13C (solid state) NMR are powerful tools for characterization of the polymer materials.
13C NMR studies of olefin copolymer microstructure: a tool for understanding active center behavior in ansa‐zirconocene‐based catalysis
Authors: Sacchi Maria Carmela , Forlini Fabrizio , Losio Simona , Tritto Incoronata , Locatelli Paolo
Published: April 2003

In the present paper the effects of the solvent, a Lewis base and of non‐polymerizable olefin on copolymerization of propene with higher α‐olefins performed with isospecific ansa‐zirconocene catalysts are investigated. A wide range of solvents with increasing polarity, donor character and steric hindrance has been tested, and their effects on copolymer yield, composition and microstructure thoroughly analyzed. Our results demonstrate that the solvent can have a significant influence on the copolymer composition, even though the solvent polarity is not the relevant factor. Polymerizations carried out in coordinating solvents, e.g. aromatic solvents, lead to the formation of products with considerably decreased higher α‐olefin content. The reduced incorporation of the higher α‐olefin is explained in terms of competition between the nucleophilic medium and the olefin monomer for coordination to the active polymerisation site. The dependence of polymer microstructure on the solvent nucleophilicity is further elucidated by copolymerization studies performed in the presence of diisopropyldimethoxysilane as a Lewis base. The addition of the non‐polymerizable olefin, 2‐methyl‐1‐pentene, which does not significantly affect comonomer composition, seems to slightly modify comonomer distribution. The sum of the results obtained give us valuable information regarding the mechanism of polymerisation at the active centers.
Monte Carlo simulation of tetrahedral chains, 5. The pivot‐algorithm for non‐athermal linear and star‐branched polymers
Authors: Zifferer Gerhard
Published: April 2003

By use of the pivot algorithm, star‐branched chains with F = 3–12 arms of length n, nF = 480, and linear chains (F = 2) are generated on a tetrahedral lattice. In order to simulate different qualities of the solvent, specific short‐range interactions are taken into account. Whereas in athermal systems a new configuration — which is obtained by rotating that part of an arm which contains the chain end around a randomly selected bond by ± 120° — is accepted if it is self‐avoiding, for non‐athermal systems the Metropolis‐Rosenbluth criterion with respect to energy must be satisfied in addition. Calculating the energy of the configuration, nearest‐neighbour interactions (each contact contributes an energy Φ·kT, Φ < 0 characterizing endothermal solutions and Φ > 0 exothermal ones) are considered only; no energy is introduced to distinguish between trans and gauche bonds. A rather quick response of chain properties to the variation of thermodynamic conditions is demonstrated. The average acceptance fraction f̄ has its maximum value for athermal conditions, slightly decreases for exothermal conditions and strongly decreases with increasingly negative Φ‐values. However, for Φ = −0,5 — representing a solution near theta‐conditions — still 25% of attempted moves are accepted for all F‐values examined. The dependence of global properties (characterized by the mean‐square radius of gyration) on Φ and F is in full accordance with most Monte Carlo results.
Simulation of pseudostationary radical polymerization, 1. Chain‐length distributions for arbitrary initiation profiles
Authors: Olaj Oskar Friedrich , Zifferer Gerhard
Published: April 2003

A procedure is developed which allows to treat arbitrary periodic initiation profiles (asymmetric and symmetric triangle profiles, sinusoidal profiles, Gaussian profiles etc.) in pseudostationary radical polymerization. Using an iterative method these profiles are transformed into the (likewise periodic) radical profiles and into the chain‐length distributions of the resulting polymer in case of termination by disproportionation. These distributions are analysed for the position of their inflection points which may be used for experimental determination of the elementary rate constant of chain propagation kp. It turned out that for all profiles that have at least one discontinuity (e.g. asymmetric triangle profiles) the position of the point of inflection is a correct measure of kp for a conveniently wide range of experimental parameters. In case of profiles without discontinuity (symmetric triangle profiles, sinusoidal and Gaussian profiles) the position of the inflection point is shifted to lower values which means that the kp values determined on this basis will be a little too small. In most cases, however, the error introduced by this fact will not exceed the overall error of the experiment so that in practice the method of determining kp in pseudostationary polymerization is not restricted to those profiles which exhibit discontinuities.
The kth radius of gyration for a polycondensation reaction with identical structural units AaBb
Authors: Li Ze‐sheng , Ba Xin‐wu , Sun Chia‐chung , Tang Au‐chin
Published: April 2003

For a polycondensation reaction with identical structural units AaBb (i.e. each unit has a functional groups of type A and b of type B) the kth radius of gyration \documentclass{article}\pagestyle{empty}\begin{document}$ \begin{array}{*{20}c} {\left\langle {R^2 } \right\rangle _k = \sum\limits_n {n^k \cdot \left\langle {R_n^2 } \right\rangle P_n } } & {({\rm sum over all }n{\rm - mers; see Eqs}{\rm . (11) and (17))}{\rm }} \\ \end{array} $\end{document} is investigated. By means of a differential method, a recursion formula that holds true for both the pre‐gel and the post‐gel state is obtained for the evaluation of the kth radius.
Application of the Marquardt‐Levenberg procedure to the determination of discrete relaxation spectra
Authors: Carrot Christian , Guillet Jacques , May Jean‐François , Puaux Jean‐Pierre
Published: April 2003

The application of the Marquardt‐Levenberg procedure for the determination of discrete relaxation spectra from dynamic mechanical experiments on molten polymers is reviewed. It allows the calculation of a minimum number of relaxation modes, relaxation times and contribution of each time to the modulus in the terminal zone. All parameters are kept freely adjustable. The Marquardt‐Levenberg procedure enables the minimisation of the χ2 function between the measured values, G′(ω) and G″(ω), and those obtained by the simulated spectrum. The number of relaxation modes is smoothly increased until no improvement on the minimum value of χ2 is observed. The criterium to stop the iterative procedure can be the appearance of physically improper values (negative values), but it is shown that it is better to stop the increase of the number of modes before the problem becomes ill‐posed. This can be done by a comparison between the uncertainties on the calculated parameters and the values of these parameters. The uncertainties can be calculated by the Marquardt‐Levenberg algorithm at each step of the calculation. The method has been tested on its ability to recover a given spectrum from model data and on a set of real experimental measurements on a monodisperse polystyrene. The calculated spectra enable calculation of the various rheological parameters. The agreement between the calculated values of G′ and G″ obtained from the recovered spectra, and the experimental ones is very good and the relative errors are very low (less than 4%). Furthermore, the calculated rheological parameters are found to be very close to those that can be evaluated from the experimental curves.
Generalized statistical gelation theory
Authors: Rolfes Heidi , Stepto Robert F. T.
Published: April 2003

Gel points in random polymerizations of the general type ΣiRA + ΣjRB in which A‐groups react with A‐ and B‐groups, and B‐groups react only with A‐groups are considered. (The symbols Σi and Σi signify that the A‐ and B‐bearing reactants RA and RB can be mixtures of monomers of different functionalities, denoted generally as fai and fbj.) The usual case of A‐groups reacting only with B‐groups is a special case of the present theory. The effects of chemical kinetics, the competitive reaction of A‐ and B‐groups, are separated from the generalized statistical condition for gelation. The former are used to define reaction curves and the latter, gelation curves. Both types of curve are represented as pa as a function of pb. For a given polymerization, gelation occurs when the reaction curve and the gelation curve intersect. When A‐groups react only with B‐groups, the gel points are those for the usual type of ΣiRA + ΣjRB polymerization, and, in the limit of A‐groups only reacting with A‐groups, the gel points are those for ΣiRA self polymerizations.
Quantum chemical approach to the mechanism of reactions in CH3Li/n CH2CHCN systems
Authors: Yakimansky Alexander V. , Erussalimsky Boris L.
Published: April 2003

The electronic and geometric structures of the CH3Li/acrylonitrile (AN) and CH3Li/2AN systems were investigated by the semiempirical quantum‐chemical MNDO1

MNDO: Modified neglect of differential overlap.

method. For the CH3Li/AN system a fundamental difference was found between the predictions of the most favourable reaction path (initiation or termination of polymerization) based on the comparison of two intermediate complexes (IC) on the one hand and of two transition states (TS) on the other hand. The lower energy of the TS of initiation reaction as compared to the energy of the TS of termination reaction correlates with the experimentally observed predominance of the initiation reaction. In contrast to this, a comparison of the two IC energies shows no preference of one of the reactions. In the case of the CH3Li/2AN system, a comparison of different IC by their energies shows qualitative agreement with experimental data. The results of the MNDO calculations were verified by ab‐initio STO‐3G and 3‐21G calculations. The well‐known enhancement of the termination reactions of anionic active sites (AS) of AN in the stage of trimer AS was interpreted on the basis of geometric and electronic structures of the Li(CH2)5CN model active sites investigated by the MNDO method.
Evidence for the time‐temperature superposition principle from Monte‐Carlo simulations of the glass transition in two‐dimensional polymer melts
Authors: Wittmann Hans‐Peter , Kremer Kurt , Binder Kurt
Published: April 2003

The bond fluctuation model on a square lattice with a bond‐length dependent potential exhibits in simulations of slow cooling a kinetic glass transition where the system falls out of equilibrium. Extending previous work, the relaxation functions of gyration radius and end‐to‐end distance, and the bond autocorrelation function of the polymers are presented and related to the time‐dependent displacements of inner monomeric units and center of gravity of the whole chains, respectively. Over a wide temperature range the data can be collapsed on master curves satisfying the time‐temperature superposition principle for Rouse dynamics.
Angular correlations within coiled polymer molecules
Authors: Bruns Wolfgang
Published: April 2003

Monte Carlo techniques were used to investigate angular correlations between the principal axes of inertia and the end‐to‐end vector as well as the first two normal coordinates. On the average, the first normal coordinate is nearly parallel to the longest principal axis. The parallelism is less distinct in the case of the end‐to‐end vector and the longest principal axis. The assumption made by some authors that the second normal coordinate is coplanar with the two longest principal axes could not be confirmed.
The configurational free energy of a polymer chain
Authors: Ganazzoli Fabio , Allegra Giuseppe , Colombo Emanuele , De Vitis Mario
Published: April 2003

The configurational, or elastic, free energy Ael of a polymer chain is discussed in terms of the Fourier configurational approach. The importance of accounting for all degrees of freedom of the chain is shown in comparison with affine mean‐field theories and with scaling theories of chain expansion and contraction. In case of strong contraction the chain does show neither affinity nor self‐similarity, and we get Ael ∼ N1/3, N being the number of chain bonds. Conversely, in case of good‐solvent expansion we find Ael ∼ N. The same result holds in the vicinity of the Θ‐temperature, where Ael is also proportional to [(T − Θ)/T]2.
Existence of nonlinear resonances in polyethylene
Authors: Noid Donald W. , Sumpter Bobby G.
Published: April 2003

In this paper, we demonstrate that the internal dynamics and vibrational spectra of polyethylene are influenced by Fermi and other nonlinear resonances. In previous work, the first semiclassical theory and quantum numbers (in parabolic coordinates) appropriate for this type of resonance were developed. We find from detailed molecular dynamics simulations that the same types of quantum numbers are applicable for polyethylene stretch‐bend mode interactions. In addition, a one‐to‐one resonance is found to exist from one local CH stretch to another CH stretch along the polymer chain.
Theory of nematic networks with finite extensibility
Authors: Rusakov Victor V. , Shliomis Mark I.
Published: April 2003

A statistical molecular model of polymer networks, which takes into account inter‐molecular orientational interaction and constancy of the chain contour length, is proposed. A simple formula for the network free energy valid for any deformations is obtained. A system of equations which describes orientational‐elastic interactions in polymer networks is derived. The influence of deformation and degree of cross linking on the conditions of network phase transition into the orientationally ordered state of the nematic type is studied. The deformation curves considerably deviate from those predicted by the classical elasticity theory. A comparison of the proposed theory with experimental data for natural rubbers is carried out.
Conformation of 4‐ethoxy‐4′‐biphenylyl cyanide in the isotropic and anisotropic liquid‐crystalline state — a rotational isomeric state simulation of 2H NMR spectra
Authors: Abe Akihiro , Kimura Noritaka , Nakamura Mamoru
Published: April 2003

The conformation of the ethoxy tail flanking the cyanobiphenyl core has been studied in the liquid‐crystalline phase as well as in the isotropic solution. In solution, the vicinal coupling constant 3JCH for the moiety CphOCH (Cph: phenyl carbon) provided the information regarding the rotation around the OC bond. Phenetole was mostly used as a model compound. The conventional rotational isomeric state (RIS) analysis yielded the energy difference between the gauche and trans state to be of the order of 1,6 to 1,4 kcal/mol in CDCl3, C6D6 and dimethyl‐d6 sulfoxide. In this treatment, the rotational state around the neighboring bond (CphO) was taken to occur at 0 or π. The deuterated compound, 4‐ethoxy‐4′‐biphenylyl‐d7 cyanide, was prepared and studied in the liquid‐crystalline state by 2H NMR. The orientational order parameters of the mesogenic core were determined by the analysis of dipolar and quadrupolar splitting data due to aromatic deuterons. The quadrupolar splitting data were also obtained for the deuterated ethoxy tail. The conformation of the tail was elucidated according to the RIS simulation scheme previously proposed. The fraction of the trans conformation ft was estimated to be 0,79 around the nematic‐isotropic transition temperature (TNI = 91,9°C). It was suggested that the conformation of the ethoxy tail remains nearly unaffected by the phase transition in the immediate vicinity of TNI. The fraction ft increases moderately toward an asymptotic value as temperature decreases.
Statistics of stiff polymer chains near an adsorbing surface
Authors: Khokhlov Alexei R. , Ternovsky Felix F. , Zheligovskaya Ekaterina A.
Published: April 2003

The exact solution of the problem of adsorption of a long ideal polymer chain with variable degree of stiffness on a plane surface is presented. It is shown that the adsorption of stiff polymer chains is a second‐order phase transition; in the adsorbed state “train” (i.e. adsorbed) sections are relatively longer and loop sections relatively shorter than for flexible chains. This effect is very pronounced: already for moderately stiff chains the number of Kuhn segment lengths in one “train” section at the temperature T = Tcr/2 (Tcr is the critical temperature for adsorption transition) can reach several thousands, and deviation from the surface occurs only in the form of small “hairpins”. The maximum length of the chain, which at the given conditions would flatten completely on the surface, is estimated.
Viscosity from ternary mixtures of two weakly charged polyelectrolytes in solution
Authors: Borsali Redouane , Rinaudo Marguerite
Published: April 2003

The mode‐mode coupling approximation (MMCA) is applied to describe the behavior of the reduced viscosity ηr from ternary mixtures of two weakly charged polyelectrolytes in solution. Similarly (ε = +1) as well as oppositely (ε = −1) weakly charged polyions are discussed in this work. The variation of ηr with the total polyelectrolyte concentration CT exhibits a peak. The position and the height of this peak show for a given concentration of added salt CS a sensitive variation with: the charge parameters (degrees of ionization) f1 and f2 of both polyelectrolytes, the proportion of polyelectrolyte 1 within the mixture (x = C1/CT) and the Flory interaction parameter χF between monomeric units of different species. This calculation is presented within the framework of the Rouse model where no hydrodynamic interactions are taken into account.
Dipolar concentration correlations in a diblock copolymer melt
Authors: Pakula Tadeusz
Published: April 2003

The conformation of diblock copolymer chains in a computer simulated homogeneous melt is analyzed distinguishing the separation of ends and the end‐to‐end vector orientation of individual chains. It is demonstrated that within the cigar‐like shapes of chains the blocks A and B are spatially separated along the cigar axis constituting concentration dipoles. Consequences of such concentration correlations for the light scattering are discussed. An extra contribution to the depolarized light scattering resulting from the “form birefringence” of individual chains is postulated.
Dynamics of a paraffin crystal
Authors: Liang Guanghe L. , Noid Donald W. , Sumpter Bobby G. , Wunderlich Bernhard
Published: April 2003

Recently it has become possible to make a series of simulations on a supercomputer of the molecular motion of a pentacontane (C50H102) crystal containing close to 10000 atoms. Such a crystal is big enough to serve as a model of a macroscopic crystal. It can also serve as a model for polyethylene. The large volume of detailed information on the structure and motion permits a new level of understanding. Information on crystal appearance, pseudo‐symmetric crystal structures, picosecond time‐scale formation of conformational defects and the beginning of the melting process is presented.
A global‐update simulation method for polymer systems
Authors: Heermann Dieter W. , Yixue Li
Published: April 2003

We describe a hybrid Monte Carlo algorithm, combining molecular dynamics with the Monte Carlo method, applied to the simulation of polymer systems. It is shown that observables are independent of the discretization error, and the performance, i.e., autocorrelation times of observables, is analyzed. For a dense system representing a polyethylene melt, we present data for the pair distribution function and the mean square displacement of a chain in the bulk. We also investigate the possibility of using a scaled Hamiltonian in the algorithm.
Gelation as a percolation problem with finite diffusion
Authors: Rosche Matthias , Schulz Michael
Published: April 2003

The formation of polymer networks (gelation process) was studied by a numerical simulation of a lattice spin model with 3 states, which allows the representation of simple diffusion and aggregation processes. Near the percolation threshold, pc, the same critical exponents were detected as in the usual diffusion‐free classical percolation theory. Only non‐universal values (for example pc) show a significant dependence on the ratio between diffusion and reaction constants.
On the sol fraction of Aa1 Bb1−Aa2 Bb2 copolymerisations
Authors: Li Ze‐sheng , Ba Xin‐wu , Sun Chia‐chung , Tang Au‐chin
Published: April 2003

By means of probability theory, the sol fraction of an Aa1 Bb1−Aa2 Bb2 type copolymerisation reaction, in which intramolecular reactions are neglected, is investigated in the post‐gel regime to give the gelation condition explicitly. (Aa1 Bb1 is a monomer with a1 functional groups of type A and b1 functional groups of type B.)
Probabilistic multi‐site modelling of propene polymerization using markov models
Authors: van der Burg Marijke W. , Chadwick John C. , Sudmeijer Olof , Tulleken Herbert J. A. F.
Published: April 2003

Possible propagation mechanisms in propene polymerization using heterogeneous catalysts are described by combinations of Bernoulli and first‐ or even second‐order Markov models. Both NMR‐measured pentad fractions and GPC

Gel permeation chromatography.

‐measured molecular weight distributions are directly taken into account to fit an appropriate propagation model for a specific catalyst. The analytical data so obtained have been used for an examination of the applicability of multi‐site propagation models and for estimation of the main parameters in each model. The propagation and termination probabilities are estimated, as are “mix” parameters giving the fraction of the polymer population stemming from each kind of propagation mechanism. In this way the subpopulation produced by each site is characterized in terms of tacticity and molecular weight distribution. A three‐site model is required to explain the measured data properly.
Modelling free‐radical copolymerization kinetics—evaluation of the pseudo‐kinetic rate constant method, 1. Molecular weight calculations for linear copolymers
Authors: Xie Tuyu , Hamielec Archie E.
Published: April 2003

The moment equations for binary copolymerization in the context of the terminal model have been solved numerically for a batch reactor operating over a wide range of conditions. Calculated number‐ and weight‐average molecular weights were compared with those found using pseudo‐kinetic rate constants with the method of moments and with the instantaneous property method for homopolymerization. With the pseudo‐kinetic rate constant method under polymerization conditions where number‐average molecular weights (M̄n) are below about 103 the error in calculating M̄n exceeds 5%. The error increases rapidly with decrease in molecular weight for M̄n < 103. M̄n measured experimentally for polymer chains (homo‐ and copolymers) have error limits of greater than ±5% at the 95% confidence level. Therefore, for all practical purposes, the pseudo‐kinetic rate constant method is valid for M̄n greater than 103. Errors in calculating weight‐average molecular weights (M̄w) or higher averages are always smaller than those for M̄n when applying the pseudo‐kinetic rate constant method. The assumptions involved in molecular weight modelling using the pseudo‐kinetic rate constant approach are thus proven to be valid, and therefore it is recommended that the pseudo‐kinetic rate constant method be employed with the instantaneous property method to calculate the full molecular weight distribution and averages for linear chains synthesized by multicomponent chain growth polymerization.
Solvent effects on free‐radical polymerization, 4. Modelling of hompolymerization
Authors: Czerwinski Wojciech Krzysztof
Published: April 2003

A new so‐called reactant‐solvent complex model is proposed to describe the effect of solvent on chain propagation in homopolymerization. It takes into account complex formation of both monomer and radical with solvent by equilibria. Evaluation methods presented permit to estimate the complex equilibrium constant K which is assumed to be nearly the same for both monomer and radical complexation and the relative reactivity ratio r11, for complexed monomer. Measured reaction rates as function of monomer concentration are needed for calculations.
Calculation of phase equilibria in random copolymer systems
Authors: Wohlfarth Christian
Published: April 2003

Synthesis and application of copolymers are not seldom connected with different phase equilibria. Their precise knowledge is of importance for industrial processing as well as it is a profound basis for a better understanding of the nature and thermodynamics of such systems. As a common situation today, enough experimental information is seldom available in the necessary or desired amount, and a lot of model calculation is, therefore, more or less unavoidable to cover the desired ranges of application. Different equations‐of‐state as well as lattice models are discussed with respect to their applicability for calculating liquid‐liquid and gas‐liquid phase equilibria in copolymer solutions and blends. Examples for high‐pressure phase equilibria in monomer/copolymer mixtures, liquid‐liquid demixing in copolymer blends and for the isotropicnematic phase equilibrium in systems with rigid rod‐like copolymers characterized by distributions of rigid and flexible chain parts are given. The effects of copolymer polydispersity are included by means of continuous thermodynamics. Literature references for original sources, earlier reviews and further applications round up this paper.
A simple estimate of the polymer theta‐point on different lattices
Authors: Barat Krishna
Published: April 2003

We check here numerically and establish the validity of a simple estimate for the polymer theta‐point on various pure and diluted lattices. Our study on two‐dimensional lattices supports a linear relationship of the θ‐point value with the average number Zeff of non‐bonded (nearest) neighbours on a random self‐avoiding walk (SAW). This Zeff in turn can be estimated from the connectivity constant μ of SAWs of the corresponding lattice.
A model for the creep of oriented high‐modulus fibers
Authors: Schuppert Andreas A.
Published: April 2003

Recently it has been shown that the creep of oriented high‐modulus fibers satisfies a logarithmic time law over very long time intervals. Moreover, the modulus of these fibers increases due to the creep. This was interpreted by the annihilation of conformation defects during creep. In structures with strong intermolecular interactions as in aramides, however, the direct annihilation of defects is difficult to explain. Moreover a direct annihilation leads to a false time law if no further assumption about the properties of the defects are made. In this paper a model for the transport of conformation defects in oriented polymer chains imbedded into an oriented fibrillary structure with strong intermolecular interactions is presented. This modified transport model leads directly to the experimentally observed time law without any further assumptions about the defect properties.
Fast force field expressions for computer simulations
Authors: Jung Bernd
Published: April 2003

It is the aim of this work to develop analytical force field expressions that can be rapidly evaluated by computers. The new expressions approximate the energy hypersurfaces as described by the usual force fields. The energies and the derivatives of the energy expressions, i. e. the forces acting on the atoms, in most cases can be very quickly calculated as functions of one squared distance of two atoms per interaction, avoiding slow operations like cosine, square root etc. Formulae and algorithms are given to calculate the parameters needed from those of the AMBER force field.
Simulation model for network formation in free‐radical crosslinking copolymerization: Pregelation period
Authors: Tobita Hidetaka
Published: April 2003

A new simulation model for network formation in free‐radical copolymerization of vinyl and divinyl monomers is proposed. This model is based on the crosslinking density distribution of the primary polymer molecules that results from a kinetically controlled network formation. The crosslinking density distribution provides information on how each chain is connected to other chains and therefore, a detailed analysis of the kinetics of network formation becomes possible by application of Monte Carlo simulations. In this method, not only averages but also various distributions, such as molecular weight distribution and distribution of crosslinked units as well as of unreacted pendant double bonds among various polymer molecules, can be calculated. The present theory is a direct solution for the Bethe lattice formed under nonequilibrium conditions, and therefore, it can be used to examine the applicability of the earlier theories of network formation to kinetically controlled systems. The present method is quite general and can be applied to various complex reactions systems that involve crosslinking, branching, cryclization and degradation in a nonequilibrium system.
Quantum chemical interpretation of the stereospecific effects characteristic of the polymerization in acrylonitrile‐RLi and methyl acrylate‐RLi systems
Authors: Yakimansky Alexander V. , Erussalimsky Boris L.
Published: April 2003

With the aim to find the causes of the different stereochemical behavior characteristic of the anionic acrylonitrile (AN) and methyl acrylate (MA) growing chains, the following model systems were investigated using the MNDO1

Modified neglect of diatomic overlap.

(method: 1) compounds XCH2CH2CH(X)Li simulating racemic (r) and meso (m) diads of AN (X = CN) and MA (X = COOCH3) at the active end of the growing chain; (2) intermediate complexes of a MA r‐diad with a MA molecule in the mutual orientations which should lead to the formation of a rr‐ or rm‐triad; (3) compounds XCH2(CH2CH(X))2Li simulating mm‐, mr‐, rm‐, or rr‐triads of MA and their complexes with H2O and ethylenediamine (EDA). It was found that reaction of a MA r‐diad with a MA molecule should preferably lead to the formation of a rm‐triad in the absence of EDA and to the formation of a rr‐triad in the presence of EDA. For AN none of the possible transformations of active diads into triads was found to be preferred. These results are in qualitative agreement with the experimental data.
Quantum semiempirical studies on the formation of aromatic polyamides, 1. Effect of structural parameters of diamines on the polyamidation reaction
Authors: Lozano Angel E. , de Abajo Javier , De la Campa José G.
Published: April 2003

A semiempirical quantum‐mechanical study of structural and electronic parameters of aromatic diamines was performed using the method AM1. The diamines have been considered as condensation monomers, and the reactivities of both amino groups against acyl chlorides have been computed. The study shows that the amidation reaction is controlled mainly by the global charge on the amino group and, in a much smaller extent, by the frontier orbitals. This behaviour is consistent with the large energy gap between the HOMO1

HOMO: highest occupied molecular orbital.

of the diamine and the LUMO2

LUMO: lowest unoccupied molecular orbital.

of the acyl chloride. It has been found also that the electronic nature of the substituents, affecting the charge of the amino groups, greatly affects the carbons directly joined to these groups. This permits to correlate the reactivities with the calculated charges on these carbons:
Chain collapse of star polymers
Authors: Allegra Giuseppe , Vitis Mario De , Ganazzoli Fabio
Published: April 2003

The self‐consistent approach to free‐energy optimization is applied to regular star polymers in bad solvents (T < Θ); the Gaussian approximation and the Zimm‐Kilb description of Fourier modes are both warranted under these conditions leading to chain collapse. As currently done in this approach, the interatomic‐contact free energy is taken to be a single‐valued function of the mean‐square radius of gyration 〈S2〉, whence the universal plots of the mean‐square distances between two atoms and between the atoms and the center of mass are obtained as a function of the contraction ratio α = 〈S2〉/〈S2〉0 (the zero subscript denotes the unperturbed state at T = Θ) and of the degree of branching. The density as a function of the distance from the center of mass as well as the equilibrium structure factor are likewise evaluated. The decrease of αs with an increase of the undercooling (Θ − T) at a fixed molecular weight is sharper with a smaller number of arms, being sharpest with the linear chain. The relative fluctuation of the radius of gyration, expressed as (〈S4〉 − 〈S2〉2)/〈S2〉2, increases at first with the undercooling, showing a maximum close to the transition temperature which is more pronounced the smaller is the degree of branching, then decreases sharply at strong contration. The average location of the free ends of the collapsed molecule is close to, or even outside, the surface of the resulting globule, their mean‐square distance from the center of mass being 2 〈S2〉. Conversely, the mean‐square distance of the branch point from the center of mass if 2〈S2〉/f, f being the number of arms.
Theoretical study of chain transfer in anionic polymerization, 2. Copolymerization accompanied by chain transfer to solvent
Authors: Litvinenko Galina I. , Arest‐Yakubovich Alexander A.
Published: April 2003

The main factors determining molar mass characteristics of copolymers formed in nonterminating copolymerization under the conditions of chain transfer to solvent are studied theoretically. The dependences of the mean polymerization degrees on conversion and monomer feed composition for various values of reactivity ratios are obtained. The results obtained greately differ from those for homopolymerization. This is explained by the contribution of cross‐propagation reactions. In particular, it is shown that at ≪ and ≪ the azeotropic copolymerization proceeds like the living one even if homopolymerization of each monomer is accompained by extensive chain transfer to solvent.
A mean field theory for the swelling of a gaussian polyion
Authors: Bratko Dušan , Dawson Kenneth A.
Published: April 2003

The effect of electrostatic forces among the ionized units on the structure of a polyion is studied using a simplified mean‐field model that represents the polymer as a swollen Gaussian coil. Screened Coulombic interactions are approximated by the pairwise additive Yukawa potential. The swelling parameter is estimated in a variational procedure analogous to Flory's theory for neutral polymers. The analytic solution to the variational problem is given. The method is shown to provide a fair description of the polyion configuration at lower ionization or in the presence of moderate concentrations of simple salt in the solution.
Computer simulations of two‐dimensional trifunctional bimodal networks
Authors: Sakrak Gokhan , Bahar Ivet , Erman Burak
Published: April 2003

Transformation of mean chain dimensions in a bimodal Gaussian network is analyzed by generating a two‐dimensional trifunctional network using Monte Carlo technique and deforming it, subject to the balance of mean forces at each junction. Instantaneous fluctuations in chain dimensions are not considered in the simulations. The problem is, therefore, equivalent to the analysis of a two‐dimensional deterministic system of two sets, short and long, of linear springs, joined at trifunctional junctions. The molecular deformation of network chains, the distribution of orientation of chain vectors and the reduced stresses are studied as a function of extension ratio and network topology.
Preliminary potential energy calculations of cellulose iα crystal structure
Authors: Aabloo Alvo , French Alfred D.
Published: April 2003

Packing energy calculations were used to evaluate various models of Iα cellulose, based on unit cell dimensions proposed by Sugiyama et al. Both a rigid‐ring method, PLMR, and a full‐optimization molecular mechanics technique, MM3, were used. The model found to be best with both methods was packed “up” (the z coordinate of O5 is greater than that of C5); O6 atoms were in tg positions, forming sheets of hydrogen bonded chains. With the PLMR program, the energy of the best model was almost 3 kcal/mol lower than the second best model. The MM3 studies also showed substantially higher energies for the alternative models. Also, some alternative PLMR models had substantially higher atomic movement during MM3 optimization.
Polymer deformation in various flows
Authors: Carl Wilfried , Bruns Wolfgang
Published: April 2003

Using a Langevin‐like approach, the deformation of a polymer, modelled as a bead‐spring chain, is calculated in simple shear, elongational and Kramers potential flow. Analytic expressions for the mean‐square end‐to‐end distance, radius of gyration, segment‐segment distance, static structure factor up to O(q4) and the intrinsic elongational viscosity are given. Near equilibrium, preaveraged hydrodynamic interaction is taken into account.
Polymer chains confined into tubes with attractive walls: A Monte Carlo simulation
Authors: Milchev Andrey , Paul Wolfgang , Binder Kurt
Published: April 2003

A bead‐spring off‐lattice model of a polymer chain with repulsive interactions among repeating units confined into straight tubes of various cross sections, DT2, is studied by Monte Carlo simulation. We are also varying the chain length from N = 16 to 128 and the strength of a short‐range attractive interaction between the repeating units and the walls of the tube. Longitudinal and perpendicular static linear dimensions of the chains are analyzed, as well as the density profile of repeating units across the tube. These data are interpreted in terms of scaling concepts describing the crossover between three‐dimensional and quasi‐one‐dimensional chain conformations and the adsorption transition of chains at flat infinite walls, respectively. We also study the time‐dependent mean‐square displacements of repeating units and obtain various relaxation times. It is shown that both relaxation times scaling proportional to N2 and to N3 play a role in the reptative motion of the chain in the tubes.
Conformational properties of weakly charged polyelectrolytes from Monte Carlo simulations
Authors: Seidel Christian , Schlacken Hartmut , Müller Ingolf
Published: April 2003

We present results of off‐lattice Monte Carlo simulations of weakly charged chains where the charged beads interact with a screened Coulomb potential of Debye‐Hückel type. The behaviour of the mean square end‐to‐end distance and mean‐square radius of gyration versus chain length is discussed for various solution conditions characterized by the parameter ζ = 2λD/b, with λD being the Debye screening length and b the contour distance between neighbouring charged beads. We also evaluate the probability‐density distribution for the end‐to‐end distance R. From the angular correlation function 〈cos γk〉 we estimate the persistence length as well as the chain length dependence of 〈R2〉 and 〈RG2〉. With increasing ζ it is found to come close to that which is directly obtained from 〈R2(N)〈 and 〈RG2(N)〉. Furthermore, the nonexponential decay of correlations indicates our charged chains to be not wormlike.
Statistical thermodynamics of single‐chain single crystals
Authors: Chen Erqiang , Bu Haishan , Hu Xiulan
Published: April 2003

A simple statistical mechanical theory is developed assuming a chain‐folded crystal. Taking account of the side‐surface energy of the single‐chain single crystal, the partition function and the free energy are calculated. Also, the expressions for equilibrium thickness le and melting temperature Tm, e of the single‐chain single crystal are obtained, and they are similar to that given by a thermodynamic analysis of the single‐chain single crystal. It is shown that le depends on temperature and on the molar mass of the single‐chain single crystal, while Tm, e depends on the molar mass. Furthermore, it is found that the side‐surface and the fold‐surface free energies γ and γe can be explained on a molecular basis.
Gel properties in free radical crosslinking copolymerization: A kinetic approach
Authors: Okay Oǧuz
Published: April 2003

A kinetic model is presented for prediction of the gel properties in free‐radical monovinyldivinyl monomer copolymerization. It is an extension of the kinetic model proposed recently for the sol species. The model involves the moment equations of the primary chains in the gel, and predicts the gel growth and structure as a function of the reaction time. Formulae for the chain length averages of the primary chains in the sol and in the gel were derived. The equations for calculating the number‐ and weight‐average primary chain lengths are identical to the equations derived by statistical methods.
On exact and approximate methods of calculating an overall termination rate coefficient from chain length dependent termination rate coefficients
Authors: Russell Gregory T.
Published: April 2003

In this paper is tackled the problem of calculating the overall termination rate coefficient 〈kt〉 which follows from values of kti, j, by which is denoted the rate coefficient for termination between two free radicals of degrees of polymerization i and j, respectively. The significance of this problem is that polymerization experiments yield 〈kt〉 values, whereas microscopic models predict Kti,j values. An assumption‐free method is presented for computing the steady state 〈kt〉 corresponding to a set of Kti,j values. Parallel to this, approximate methods for calculating steady state 〈kt〉 values are developed: the so‐called short‐long approximation is used, and coarse graining of the radical chain length distribution is applied. Calculations are firstly carried out using a microscopic termination model which describes an intermediate conversion polymerization system, and then a set of calculations are performed with low conversion conditions in mind. Comparison of the completely exact solutions with the various approximate solutions reveals which of the approximate and therefore more tractable models is suitable for accurate, microscopic modeling of polymerization kinetics at the different physical conditions envisaged. In this respect the credentials of one of the coarse grain approaches are found to be persuasive. Also executed are calculations probing how values of 〈kt〉 depend on factors, such as the rate of propagation and of chain transfer to monomer, not traditionally regarded as having anything to do with termination rates; interesting results emerge. Because calculations are carried out with real systems very much in mind, the latter (and other) results are felt to be genuinely relevant to the mechanism of actual free radical polymerizations.
Quantum chemical characteristics of cationic active sites forming in the Bcl3‐α,ω‐dichloroalkyl systems
Authors: Yakimansky Alexander V. , Erussalimsky Boris L. , Zubkov Vladimir A.
Published: April 2003

Taking as examples the cyclic halonium (I) and linear carbenium (II) model cations of equal composition, viz. [Cl(CH2)4]+, and products of propene addition to them (V and VI), the energetic characteristics of these structures were estimated by the MNDO(a) method. The energetic preference of I with respect to II was found to be much higher than that of V with respect to VI (ca. 97 and ca. 11 kJ/mole, respectively). This difference is suggested to reflect the decrease in the tendency of linear Cl‐containing carbenium ions to cyclization into halonium ions with an increase in the length of the linear hydrocarbon chain. The results obtained are applied to the discussion of the mechanism of polymerization in the 2‐methylpropene‐BCl3‐2,5‐dichloro‐2,5‐dimethylhexane system.
Quantum chemical PM‐3 study of the thermal stability of heterocyclic fragments of heteropolymers, 1. Five‐membered heterocycles: Azoles and imides
Authors: Zubkov Vladimir A. , Yakimansky Alexander V. , Bogdanova Svetlana E. , Kudryavtsev Vladislav V.
Published: April 2003

Semiempirical PM‐3 calculations of the mechanisms of the decomposition of oxazole and maleimide have been carried out. It has been shown that thermal decomposition of the considered heterocycles proceeds via a consecutive breaking of two ring bonds, the breaking of the second bond being the rate‐determining step. Both an activation barrier of heterocycle decomposition and its dissociation energy (ED) can be used as a measure of heterocycle thermal stability. The correlation between ED values of azole and imide containing model compounds and the initial degradation temperatures of corresponding heteropolymers makes it possible to clarify some essential features of the thermal degradation of polyazoles, polybenzazoles and polyimides.
Quantum chemical PM‐3 study of the thermal stability of heterocyclic fragments of heteropolymers, 2. Six‐membered heterocycles
Authors: Zubkov Vladimir A. , Yakimansky Alexander V. , Bogdanova Svetlana E. , Kudryavtsev Vladislav V.
Published: April 2003

Dissociation energies (ED) of various heterocyclic fragments of repeating units of thermally stable heteropolymers have been calculated by the semiempirical PM‐3 method. Fragments with heterocycles containing carbonyl and/or amine groups and/or oxygen (or sulfur) atoms (benzazoles, phthalimides, benzoxazinones, etc.) have fairly close ED values. The correlation between ED values of fragments and the initial degradation temperature (TD) of heteropolymers comprising these fragments reveals that the TD values depend both on ED of corresponding heterocycles and on the manner of heterocycle decomposition: whether it leads to an immediate weight loss (polyimides, polybenzoxazinone, etc.) or just to a chain scission (polybenzazoles). Quinoline and quinoxaline are characterized by higher ED values, but it seems that decomposition of these compounds during the initial degradation of polyquinoline and polyquinoxaline proceeds via mechanisms different from the straightforward homolytic decomposition characteristic of other considered heterocycle decompositions.
Theoretical study of free‐radical ring‐opening polymerization of 2‐(o‐chlorophenyl)‐4‐methylene‐1,3‐dioxolane. A molecular and quantum mechanics approach
Authors: Morariu Simona , Surpateanu Gheorghe , Simionescu Bogdan C.
Published: April 2003

The methylene derivatives of 1,3‐dioxolane were proved to yield homo‐ and binary or ternary copolymers via free‐radical polymerization, depending on initiation type and reaction conditions. While different authors reported experimental data on these compounds, no explanation of such polymerization behaviour was provided. The present paper is aimed to propose, through molecular mechanics and quantum mechanics approaches, a valid explanation of the already published experimental results.
Persistence lengths of semiflexible chains — methods and approximations
Authors: Otto Matthias , Eckert Jochen , Vilgis Thomas A.
Published: April 2003

Several models and methods for stiff polymer chains are discussed. The basic idea is to develop approximate solutions to the problem of the presistence length of stiff polymers. It turns out that the persistence length can be regarded as a measure for the quality of approximations. Mean‐field methods for field theoretical calculations of the persistence length show similarities of 1/d expansions in statistical physics (d being the space dimension) and saddle point approximations become reliable in various limits. Gaussian approximations become — as well known for the Ising model — simple extensions of random walks as trivial renormalisations of the Wiener‐Edwards model for bosonic strings.