bluuebunny/crossref_metadata_2025 huggingface dataset:
A model ladder polymer physisorbed on a Lennard‐Jones surface
Authors: Hentschke Reinhard
Published: April 2003

The ladder or band polymer considered here differs from “ordinary” main chain polymers through its strongly elongated cross section as opposed to the usually assumed cylindrical cross section of the latter. This cross sectional shape anisotropy and the attendant anisotropy of the bending stiffness give rise to a competition between the polymer's adsorption energy and its undulation entropy. Following the self‐consistent field approach the present work studies the effects due to this competition in terms of the orientation order parameter of the ladder plane and the normal distribution of the polymer with respect to a smooth Lennard‐Jones surface. In particular, we show that it is possible to induce abrupt orientation changes of the ladder‐plane by only slight variations of the torsion and bending persistence lengths of the polymer or the polymer‐surface interaction.
Construction of approximate entropic forces for finitely extensible nonlinear elastic (FENE) polymers
Authors: Slater Gary W. , Hubert Sylvain J. , Nixon Grant I.
Published: April 2003

When the stress applied to a Rouse‐like polymer chain is large enough, one must use anharmonic entropic spring forces in order to keep the chain contour length from increasing to unphysical values. Although one can derive “exact” equations relating the spring extension to the entropic force produced by a finitely extensible non‐linear elastic (FENE) random‐walk polymer, such expressions are usually of little interest because their complexity would entail large evaluation times in numerical studies by computer. Moreover, these expressions can rarely be used directly in analytical studies. In this article, we describe a systematic method to construct analytically simple yet numerically accurate expressions to relate the entropic force to the extension of an entropic spring for a random‐walk polymer chain in arbitrary dimension d ≥ 2. These expressions are modified Pade approximants which yield the correct asymptotic behaviours in both the small and large extension limits. It is shown that the well‐known Warner empirical approximation is but a limiting case (for infinite dimensions).
Dynamics of star branched polymers in a matrix of linear chains — a Monte Carlo study
Authors: Sikorski Andrzej , Kolinski Andrzej , Skolnick Jeffrey
Published: April 2003

A simple cubic lattice model of the melt of 3‐arm star‐branched polymers of various length dissolved in a matrix of long linear chains (n1 = 800 beads) is studied using a dynamic Monte Carlo method. The total polymer volume fraction is equal to 0,5, while the volume fraction of the star polymers is about ten times smaller. The static and dynamic properties of these systems are compared with the corresponding model systems of isolated star‐branched polymers and with the melt of linear chains. It has been found that the number of dynamic entanglements for the star polymers with arm length up to 400 segments is too small for the onset of the arm retraction mechanism of polymer relaxation. In this regime dynamics of star‐branched polymers is close to the dynamics of linear polymers at corresponding concentration and with equivalent chain length. The entanglement length for star polymers appears to be somewhat larger compared with linear chains.
Statistical thermodynamics in the framework of the lattice fluid model, 3. Binary mixture of polydisperse polymers of special distribution with strong interactions
Authors: An Lijia , Jiang Bingzheng , Hu Yuxin , Jiang Zhenhua , Tang Xinyi
Published: April 2003

For a binary mixture of polydisperse polymers with strong interactions, the free energy, the equation of state, the chemical potentials and the spinodal are formulated on the basis of the lattice fluid model. Further, the spinodal curves for the system with strong interactions are simulated by using mixtures of special‐distribution polymers, i.e., Schulz distribution and uniform distribution. From comparison with the experimental results, it can be seen that the shift of the spinodal curves with the polydispersity and the strong‐interaction energy parameter is qualitatively identical with the conclusions of Nishi and Kwei, and Goh, Paul and Barlow.
Increase of the average reactivity of active species due to a shift to the more reactive species in ionic propagation accompanied by termination
Authors: Penczek Stanislaw , Vairon Jean‐Pierre , Szymanski Ryszard
Published: April 2003

The presented simulations demonstrate that in polymerizations proceeding on two kinds of species, differing in reactivity and being in equilibrium, the expected decrease of the rate of polymerization due to termination may happen to be compensated by the relative increase of concentration of the more reactive species. This takes place, for instance, in the polymerization proceeding simultaneously on ions and ion pairs if ions are more reactive. Because of termination the total concentration of ionic species during the course of polymerization decreases while the proportion of ions increases due to increasing dilution. The maximum compensation is observed when simultaneously k(ions)/k(ion pairs) → and Kd/[I]0 → 0, where k are the propagation rate constants, Kd is the equilibrium constant of dissociation and [I]0 is the starting concentration of initiator. Then, the degree of compensation (the ratio of the rate with compensation to the rate without termination) is becoming equal to ([P*]/[P*]0)1/2, where [P*] is the actual, total concentration of the growing species and [P*]0 is the initial total concentration (before any termination has taken place).
Structure, energy spectra and magnetic properties of poly(m‐aniline)s
Authors: Madjarova Galia , Baumgarten Martin , Müllen Klaus , Tyutyulkov Nikolai
Published: April 2003

The energy spectra and magnetic properties of a large class of one‐dimensional poly(m‐aniline)s (PMA) and further model polymers are investigated theoretically. The band structure of those PMA's which are aza‐analogs of the alternant non‐classical (non‐Kekulé) hydrocarbons (polymers) is characterized by a wide gap in which there is a narrow half‐filled band (HFB). The different contributions to the effective spin exchange between the unpaired electrons in the HFB: Coulomb (Hund), kinetic and indirect exchange interactions are calculated. While it has been shown earlier that PMA exhibits a net spin exchange of ferromagnetic nature, this approach enables a detailed understanding of the influence of substituents on the nitrogen centers and changes in the aromatic bridging unit. The ferromagnetic nature of the spin coupling in the singly bridged PMA models therebye prevails independent of the structural changes. The HFB width of those PMA's which are derivatives (aza‐analogs) of ladder‐type non‐alternant hydrocarbons is very large and the Wannier functions are delocalized. For this group of polymers the delocalized, non‐magnetic state is favored and, therefore, they may be good candidates for testing electrical conduction.
Edge profiles at lamellar phase/melt interfaces
Authors: Hołyst Robert
Published: April 2003

We study in the framework of the continuum theory of dislocations the structure of the interface between an AB diblock copolymer lamellar film deposited on a solid substrate and an A‐homopolymer melt. The dislocation inside the lamellar phase induces steps at the interface. The shape of the profile at the edge of a step (edge profile) depends on the distance of the dislocation from the interface. The profile and the equilibrium location of the dislocations are both studied as a function of the film thickness, D. For large D, the dislocation is stabilized at a finite distance, heq, from the interface, due to the small surface tension and large surface bending elastic constant, Ks. For zero surface tension, heq ≈ Ks/(2K), where K is the bulk bending elastic constant. For small D, heq is mainly determined by the proximity of the solid substrate. The edge profile along the interface is a monotonic function of the distance along the interface for large D of the film and becomes nonmonotonic for small D. Also the dislocation energy strongly depends on D for small D. The theory is discussed in connection to recent experimental studies of diblock copolymer films deposited on a solid substrate.
A comparative study of the master equation approach and the discrete galerkin method for the simulation of free radical polymerization
Authors: Seeßelberg Markus , Thorn Matthias
Published: April 2003

The present article deals with the mathematical treatment of free radical polymerization reactions. As a typical example the synthesis of poly(methyl methacrylate) under realistic experimental conditions is investigated. Since the mathematical treatment of the kinetic rate equations raises severe numerical problems, alternative approaches are required. In this paper two of these methods, i.e. the discrete Galerkin method and the master equation approach, are compared. The discrete Galerkin method circumvents difficulties encountered by the direct integration of the kinetic rate equations but requires much a priori knowledge of the chemical reaction system. Within the framework of the master equation approach the polymerization reaction is regarded as a stochastic process. For the simulation of this stochastic process a modified algorithm is presented. The example of the polymerization of methyl methacrylate shows that the master equation approach is an efficient tool in the simulation of free radical polymerization reactions.
Thermodynamics of the early stages in homogeneous ziegler‐natta polymerization: Density functional calculations on model systems TiCl2R+ and ZrCl2R+
Authors: Fusco Roberto , Longo Luca
Published: April 2003

The ethylene polymerization enthalpy, calculated through quantum‐mechanical ab‐initio methods on model systems of homogeneous Ziegler‐Natta cationic catalysts, is reported to be from two to three times greater than the experimental value of 22,3 kcal/mol. In this paper we analyze the origin of this discrepancy and show that it is mainly due to the intrisnic instability of the cationic system in vacuum. We also demonstrate that the growing polymer chain can act as a quite efficient stabilizing agent. We examined, through density functional calculations, the model systems MCl2R+, where M = Ti, Zr and R = CH3, C3H7, C5H11, C7H15 and their analogues obtained by neutralizing the positive charge with a chloride anion. On the basis of our computational results, we found that: (i) for the ideal reaction of ethane with ethylene to give butane, considered as a thermodynamical model of the single insertion step, the calculated enthalpy value of 35,6 kcal/mol is in closer agreement with the experimental value and is taken as theoretical reference value; (ii) the same value is obtained also for the neutral systems MCl3R independently of the nature of the metal and of the alkyl chain length; (iii) for cationic systems, when R = CH3, high insertion enthalpies are obtained in agreement with the calculated values reported in literature, but, for R = C3H7, C5H11 and C7H15, the insertion enthalpy remarkably decreases converging towards the theoretical reference value. We conclude that the high enthalpy value obtained for the first monomer insertion is not only a mere consequence of the computational method, but is mainly due to the weak stabilizing effect of the methyl group. A longer alkyl chain produces a stabilization of the cationic system through the inductive effect as well as through formation of agostic bonds. This leads us to formulate the hypothesis that, in real polymerization conditions, the role of a stabilizing agent, which is mainly played by the counterion in the early stages of the propagation reaction, could be performed by the growing chain as the polymerization proceeds.
Computer simulation analysis of microstructure formation in monomer and polymer blends involving a glassy component
Authors: Khalatur Pavel G. , Khokhlov Alexei R. , Vasilevskaya Valentina V.
Published: April 2003

Monte Carlo and molecular dynamics simulations are performed for low‐molecular‐weight and polymeric A/B mixtures with a glassy component A. The possibility of a glass transition in the microregions enriched with A‐molecules is taken into account by introducing a “freezing constraint”. Two types of this constraint are considered in the present paper: either the diffusion motion of a given A‐particle is stopped if the concentration of A‐units in some sphere around a given particle is larger than a certain critical value (constraint of G‐type), or it is stopped if the concentration of “plasticizing” B‐molecules in this sphere is lower than a certain critical value (constraint of P‐type). It is shown that even for athermal A/B blends a “freezing constraint” of both types leads to the formation of well‐separated microsegregated clusters of glassy A‐units. The type of the final microstructure depends essentially on the type and the effective radius of the “freezing constraint”; both “frozen‐in” and equilibrium microdomain structures can emerge.
Monte Carlo simulation of the θ‐conditions of poly(methylene): Temperature dependence of the long‐range screening factor
Authors: Sariban Alla , Mosell Thomas , Brickmann Jürgen
Published: April 2003

Structures of methylene groups were modelled using the united atom approximation, i.e. each group was considered as an individual center for van der Waals interactions. In these simulations the environment of the macromolecules in liquid or amorphous states was taken into account by the introduction of a screening factor β for the attractive part of the methylene‐methylene interaction that was modelled by a Lennard‐Jones potential (U(r) = A/r12 − β B/r6). The value of βθ that corresponds to θ‐conditions was established for several temperatures between 200 K and 1 500 K from the dependence of the end‐to‐end distance and the radius of gyration of the individual structures on the number of monomeric units in the chain. The dependence of the θ‐conditions on the thermodynamic stiffness was investigated. The results for the nonself‐intersecting chain were compared with self‐intersecting chains, where standard (β = 1) and modified Lennard‐Jones potentials were taken into account for a specified number of nearest neighbours only. The mean square radii of gyration and end‐to‐end distances are nearly identical for chains under θ‐conditions and for a self‐intersecting chain simulated using the standard Lennard‐Jones potential for the 1,5‐interactions at all temperatures.
Probability model treatment of regio‐ and stereo‐irregular polymers
Authors: Cheng H. N.
Published: April 2003

A general analytical approach is devised to treat the NMR data of stereoirregular and regioirregular homopolymers. The methodology is based on the four‐component copolymerization model, treating normal and inverted monomer and the levo and dextro configurations as “comonomers”. In this way, the effects of monomer inversion and tacticity can be separately deduced. The analytical approach has been computerized. From the conditional probabilities, information on propagation mechanism (chain‐end or catalytic‐site control) can be obtained. The model has been used to analyze the NMR data of poly(propylene) samples made with titanium, vanadium and group IV metallocene catalysts. Comparisons have been made between model parameters and polymer microstructure.
Model discrimination via designed experiments: Discriminating between the terminal and penultimate models based on triad fraction data
Authors: Burke Annette L. , Duever Thomas A. , Penlidis Alexander
Published: April 2003

Computer simulations have been used to study the application of statistical model discrimination techniques to the modelling of copolymerization reactions based on triad fraction data. Since there are six triad fraction measurements, the problems of parameter estimation and model discrimination become multivariate problems. The multivariate forms of three model discrimination methods (exact entropy, Hsiang and Reilly, and Buzzi‐Ferraris et al.) are presented. Programs have been developed to simulate the application of these techniques to the systems styrene‐acrylonitrile, styrene‐methyl methacrylate and styrene‐butyl acrylate. The simulation programs are explained, including the method used to simulate triad fraction data. Evidence is presented that the simulation programs are capable of duplicating the type of measurements that would be obtained in the laboratory. The simulation results show that model discrimination methods are able to accurately and reliably discriminate between the terminal and penultimate models. The use of simulated model discrimination methods leads to reliable discrimination in fewer experiments than have been used in past work. Also, model discrimination methods are able to detect smaller penultimate effects than those found by Hill et al. for styrene‐acrylonitrile. In addition, the results show that the use of four of the six triad fractions, versus one copolymer composition measurement, should lead to more precise reactivity ratio estimates and an increased ability to discriminate between the terminal and penultimate models. Our work suggests that use of model discrimination methods will indeed lead to improvements in the modelling of copolymerization reactions.
Structure factor of a self‐avoiding polymer chain at high momentum transfer
Authors: Johner Albert , Benoit Henry , Joanny Jean‐François
Published: April 2003

The molecular weight of a Gaussian polymer chain can be obtained from the intercept of the asymptote in a plot of the inverse structure factor 1/S(q) as a function of the square of the wave vector q2. Using an ϵ expansion and scaling arguments, we show that in a good solvent the situation is more complex and that the molecular weight determination is difficult to justify. The corrections to the asymptotic behavior of the structure factor at large wave vector involve several terms that are difficult to separate experimentally. This is qualitatively explained by the nonuniform swelling of a polymer chain in a good solvent due to the existence of the chain ends.
Dynamics and conformational properties of Rouse polymers in random layered flows
Authors: Oshanin Gleb , Blumen Alexander
Published: April 2003

Here we study the dynamics and the conformational properties of Rouse polymers in random layered flows. We obtain explicit expressions for the mean squared displacement of the center of mass of the polymer as a function of time and number of beads. The averages involve both the thermal noise and the realizations of the random flows. We find also an explicit dependence of the equilibrium value of the end‐to‐end vector on the number of beads and other dimensional parameters. Our results are compared to that for Rouse polymers immersed in non‐random steady shear flows.
An algorithm for determination of the copolymer molecular weight distribution by Markov chain simulation
Authors: Christov Latchezar , Georgiev George
Published: April 2003

A simple and general algorithm, convenient for computer implementation, for calculation of the copolymer molecular weight distribution (MWD), its moments, copolymer composition, etc. from standard data has been developed describing copolymerization as a Markovian process. The algorithm is applicable for simulations of multimonomer copolymerization with monomolecular, bimolecular and mixed termination. It can be used for calculating the MWD of copolymers prepared under non‐stationary conditions. Explicit formulae have been derived for the above parameters. They are exact even for low‐molecular‐weight oligomers. The calculation procedure involves nothing but plain matrix operations as matrix multiplication and inversion. For high‐molecular‐weight copolymers, even simpler dependencies that resemble those used for homopolymers can be used. A very simple numerical test has been proposed for checking their correctness.
Molecular chains with fixed bond lengths and angles: a study based on quantum statistical mechanics
Authors: Alvarez‐Estrada Ramón F.
Published: April 2003

This work studies large three‐dimensional open molecular chains at thermal equilibrium in which bond lengths and angles are fixed (hard variables), based upon quantum statistics. A model for a chain formed by N particles interacting through harmonic‐like vibrational potentials is treated in the high‐frequency limit in which all bond lengths and angles become constrained, while other N angles (soft variables) remain unconstrained. The associated quantum partition function is bounded rigorously, using a variational inequality (related to the Born‐Oppenheimer approximation), by another quantum partition function, Z. The total vibrational zero‐point energy is shown to be independent of the soft variables thereby solving for this model a generic difficulty in the elimination of hard variables. Z depends only on soft variables and, under certain conditions, it can be approximated by a classical partition function Zc. The latter satisfies the equipartition principle and it differs from other classical partition functions for related molecular chains. The extension of the model when only part of the bond angles become fixed in the high‐frequency limit is outlined. As another generalization, a systematic study of macromolecules, as composed of electrons and heavy particles with Coulomb interactions, is also presented. Its exact quantum partition function is bounded, supposing that the effective molecular potential also tends to constrain all bond lengths and angles, and under suitable assumptions, by another quantum partition function. The latter depends only on the remaining soft variables and it generalizes the one obtained for the first model.
Improved expression of the mean‐square radius of gyration, 3. 1,4‐polydienes
Authors: Zhou Zhiping , Yan Deyue
Published: April 2003

The mean‐square radii of gyration of cis‐ and trans‐1,4‐polybutadiene and corresponding 1,4‐polyisoprene were derived using Abe's and Flory's rotational isomeric scheme. Calculations performed using available experimental data showed that the dependence of the mean‐square radius of gyration on the molecular weight for these stereoregular polydienes can be expressed as

where a and b are constants characteristic of the polymer. This behaviour is analogous to that of vinyl polymers and poly‐1,1‐disubstituted ethylenes discussed in the preceding papers of the present series. The mean‐square radius of gyration of 1,4‐polyisoprene with predominantly trans units is more sensitive to stereoirregularity than with predominantly cis units. However, 1,4‐polybutadiene chains are comparatively insensitive to the stereochemical composition.
Theory of polydisperse reacting polymer systems
Authors: O'Shaughnessy Ben
Published: April 2003

The kinetics of irreversible reactions between polymer chains of different molecular weights are studied, with emphasis on the case of highly reactive end groups. We calculate the rate constant k(N, M) for reaction between chains of lengths N and M respectively, in dilute and semi‐dilute solutions and in the melt. In all cases, k(N, M) is dominated by the shortest chain: the limit k(N) ≡ k(N, ∞) is well‐defined and scales as if both chains were of length N. In dilute solutions k(N, M) obeys mean field theory, being proportional to the equilibrium reactive group contact probability. For melts and concentrated solutions, k(N, M) follows diffusion‐controlled laws: k(N, M) ≈ (R/τN)ƒ(M/N) where RN and τN are the coil size and relaxation time of the shortest chain N, and ƒ(M/N) is a cross‐over function describing the approach to the asymptotic form k(N) for M/N ≫ 1. We calculate the leading contributions to this cross‐over function, which has universal forms depending on the concentration regime. The implications of these results for high‐conversion free‐radical polymerization are discussed.
Using Monte Carlo simulations and self‐consistent field theory to design interfacially active copolymers
Authors: Balazs Anna C. , Gersappe Dilip , Israels Rafel , Fasolka Michael
Published: April 2003

We use both Monte Carlo computer simulations and numerical self‐consistent field lattice calculations to determine the behavior of copolymers at penetrable and impenetrable interfaces. These computational techniques are useful as “design tools”: they allow us to systemically vary the copolymer architecture, determine optimal structures for specific applications, and establish guidelines for fabricating copolymers that yield the desired interfacial properties. We illustrate this principle with three different examples. In the first study, we combine the techniques to design copolymer compatibilizers that enhance the strength of immiscible polymer blends. These copolymers contain teeth that associate across the penetrable interface between the phase‐separated regions and form a “molecular velcro” that effectively binds the regions together. In the case of impenetrable interfaces, we determine how the copolymer sequence distribution affects the structure of a layer of copolymers grafted onto a solid surface. The results indicate how to control the morphology of the layer and the surface properties of the substrate, by varying the microstructure of the grafted copolymers. Finally, we design a polymer channel that “opens” and “closes” in response to changes in the pH and quality of the surrounding solvent. The channel is formed from polyacid chains that are anchored onto a solid surface. Due to these properties, the system can be used for controlled release or sensor devices.
Orientational relaxation times of worm‐like chains
Authors: Ziabicki Andrzej , Jarecki Leszek , Perico Angelo , Guenza Marina
Published: April 2003

A semi‐empirical formula for orientational relaxation times of worm‐like chains in dilute solutions is proposed

where τrod = τ0N3 is the relaxation time of a rigid rod composed of N segments, and x = 2a/L is the chain rigidity, i.e. the ratio of the double persistence length to the chain contour length, L. The formula, which can be used in the entire range of molecular rigidities and chain lengths, has been tested against segment relaxation times for semi‐rigid chains calculated from the optimized Rouse‐Zimm model.
A new method for generating volume changes in isobaric‐isothermal Monte Carlo simulations of flexible molecules
Authors: Escobedo Fernando A. , de Pablo Juan J.
Published: April 2003

A novel method has been developed to generate volume fluctuations as required in isobaric‐isothermal Monte Carlo simulations of flexible (or semi‐flexible) chain molecules. While conventional global volume moves entail symmetric changes of the simulation box size, in the new method proposed here, volume changes consist of one‐dimensional fluctuations of one of two sections of the system. One of the two sections is a thin slab where all molecular rearrangements are restrained to occur. A deterministric method has been implemented to reposition the molecular segments contained within the slab after a volume change is proposed. The performance of the new method is examined by studying the evolution towards equilibrium of homopolymer hard‐core systems upon application of a step increase in the pressure. The new method is shown to be an order of magnitude faster than conventional methods in attaining the equilibrium density of our test systems.
The origins of avoided crossings in polymer dispersion curves
Authors: Wozny Christopher E. , Noid Donald W. , Sumpter Bobby G.
Published: April 2003

A purely mathematical heuristic model is examined in order to explain the existence of an avoided crossing between two dispersion curves calculated for a certain potential energy surface designed to simulate the dynamics of a linear polyethylene chain. The model shows that a third mode coupled to a two‐mode Fermi‐resonant system is able to create a marked instability in a vibrational spectrum. It is noted that such an explanation would require a fourth‐order coupling term, which is the reason given for the failure of normal mode analysis to properly identify this dynamical effect.
Theoretical investigations on the structure and physical properties of cellulose
Authors: Reiling Stephan , Brickmann Jürgen
Published: April 2003

The structure of cellulose is investigated using a recently derived force field. Published experimental data is taken only as a starting point for purely theoretical investigations. The reliability of the method is validated by calculating physical properties of the obtained geometries. In the course of the investigations, the geometries of cellulose Iα, cellulose Iβ and cellulose II are derived. For these geometries the Young's‐modulus is calculated. The structure of cellulose in aqueous solution is investigated, using cellohexaose (a hexamer of β‐D‐glucose) as a fragment of a cellulose chain. Here, the diffusion coefficient is calculated.
Application of Markov chains to copolymerizations
Authors: Hungenberg Klaus‐Dieter , Wittmer Paul
Published: April 2003

Binary copolymerization is treated as a Markov chain process to calculate the distribution of the degree of polymerization for three different copolymerization models. The results for the terminal model according to Melville and Walling show considerable differences compared to the models according to Russo and Munari and Inagaki and Fukuda. Although these latter models start from different assumptions, one considering a penultimate effect in termination reactions, the other one a penultimate effect in propagation reactions, the results for these two models differ only slightly.
A kinetic model of step‐wise alternating polymerization for two bi‐functional monomers
Authors: Galina Henryk
Published: April 2003

A classical kinetic model of step‐wise alternating copolymerization is presented. A set of three partial differential equations is derived for generating functions describing the size distribution of molecules terminated with two different or two alike units. From monomer composition and reactivities of functional groups the moments or averages of the molecular size distribution of copolymers can be calculated.
A computationally efficient technique for the solution of non‐isothermal nylon‐6 polymerization in batch reactors
Authors: Nandrajog Sanjay , Vimala P. , Gupta Santosh K. , Kumar Anil
Published: April 2003

The kinetic scheme of nylon‐6 polymerization consists of ring opening, polyaddition, step growth, reaction with monofunctional acids and cyclization. A set of ordinary differential equations (initial value problem) governing the concentrations and moments of the reacting species and the energy balance for batch reactors has been solved. We proposed a semianalytic technique somewhat similar to the finite element method in which the conversion domain has been divided into sequential subdomains. A series solution for the state variables has been assumed in terms of the incremental conversion of caprolactam in that domain. The coefficients are obtained using the balance equations. This technique of solution takes care of the nonlinearity of the problem in a natural way and involves the sequential evaluation of constant coefficients of the series. It gives comparable results with those from Gear's algorithm (which involves the evaluation of functions) in far fewer steps. Our scheme can be easily implemented on a PC‐XT and is considerably faster and more efficient.
Computational analysis of spinodal decomposition dynamics in polymer solutions
Authors: Chan Philip K. , Rey Alejandro D.
Published: April 2003

In this work a model, composed of the nonlinear Cahn‐Hilliard and Flory‐Huggins theories, is used to numerically simulate the phase separation and pattern formation phenomena of oligomer and polymer solutions when quenched into the unstable region of their binary phase diagrams. This model takes into account the initial thermal concentration fluctuations. In addition, zero mass flux and natural nonperiodic boundary conditions are enforced to better reflect experimental conditions. The model output is used to characterize the evolution and morphology of the phase separation process. The sensitivity of the time and length scales to processing conditions (initial condition c) and properties (dimensionless diffusion coefficient D) is elucidated. The results replicate frequently reported experimental observations on the morphology of spinodal decomposition (SD) in binary solutions: (1) critical quenches yield interconnected structures, and (2) off‐critical quenches yield a droplet‐type morphology. As D increases, the dominant dimensionless wave number k increases as well, but the dimensionless transition time t from the early stage to the intermediate stage decreases. In addition, t is shortest when c is at the critical concentration, but increases to infinity when c is at one of the two spinodal concentrations. These results are found when the solute degree of polymerization N2 is in the range 1 ≤ N2 ≤ 100. When N2 > 100, however, a problem of numerical nonconvergence due to diverging relaxation rates occurs because of the very unsymmetric nature of the phase diagram. A novel scaling procedure is introduced to explain the phase separation phenomena due to SD for any value of N2 during the time range explored in this study.
Simulation and modelling of transient permeation of organic solvents through polymer films in the case of a concentration dependent diffusion coefficient
Authors: Clément Robert , Nguyen Quang Trong , Grosse Jean Marie , Uchytil Petr
Published: April 2003

The measured transient permeation kinetics of acetic acid from a water‐acetic acid mixture through poly(vinyl alcohol) films could not be accounted for by the Fick law with a constant diffusion coefficient. A new calculation procedure was developed on the basis of simulation results of the Fickian kinetics in which the diffusion coefficient was assumed to increase exponentially with the local permeant concentration. A fast and reliable fitting procedure, which was set up on a Personal Computer, involves an iterative numerical adjustment of (a) the value of the limiting diffusion coefficient D* (i.e., difusion of the permeant in dry polymer) using the onset part of the permeation rate followed by (b) the value at the upstream face of the plasticization term (argument of the exponential function) using the shape of the experimental curve. The values obtained from fitting the model to the transient kinetics showed that the limiting diffusion coefficient increases drastically, but the plasticization term changes little, with increasing temperature.
Narrow molecular weight distribution of condensation polymers achieved by adding monomers in many batches
Authors: Yang Yuliang , Zhang Hongdong , He Junpo
Published: April 2003

The Z transform method has been used to calculate the molecular weight distribution (MWD) of condensation polymers. The MWD obtained by using Z transform is explicitly discrete. The method is illustrated for two cases: (1) further polycondensation of AB prepolymers with certain initial MWD, and (2) polycondensation of AB and Ar (r is the number of A type functional groups) monomers where AB monomers are added in several batches. In the latter case, it is found that the resulting MWD is much narrower than that of one‐batch polycondensation. The trick of producing narrow MWDs of condensation polymers is merely a consequence of keeping AB monomer concentration as low as possible during the reaction in order to suppress the condensation reaction between monomeric AB molecules. The theoretical prediction has been confirmed by Monte Carlo simulation. Therefore, it provides a new possible technique for obtaining narrow MWD polymers through polycondensation reactions.
Self‐assembling of chain molecules in low dimensions: A Monte Carlo study
Authors: Stettin Heiko , Wahab Mirco , Schiller Peter , Mögel Hans‐Jörg
Published: April 2003

We studied the self‐assembling of linear chain molecules in insoluble monolayers due to attractive interactions. We used lattice Monte Carlo simulations in a two‐dimensional system. The molecules consist of segments occupying adjacent lattice sites. The head segments are confined to move along a line whereas the chain segments can arrange in a plane above the heads. Only one interaction parameter is applied. At high densities and small interaction energy the system shows percolation behavior. At moderate and small densities it can be characterized by a monotonous cluster size distribution. Self‐assembling occurs at small densities for strong attractive interactions. The corresponding cluster size distributions indicate preferred cluster sizes which depend upon density and interaction strength. With increasing density the clusters grow. The internal cluster structure depends on the cluster size and the interaction parameter. The clusters tend to minimize their total energy. Molecules at cluster margins contribute less to the cluster energy and are mainly disordered. They cause that the cluster properties strongly depend on the cluster size. Large clusters only have minimum energy if the molecules in the cluster are in stretched‐out conformation. With decreasing interaction strength the clusters get disordered thereby producing less energy‐minimized domain boundaries.
Molecular mechanics analysis of polymer conformation, 4. Local chain motions and molecular relaxations of poly(parabanic acids)
Authors: Konda Masakazu , Kimura Yoshiharu , Kitao Toshio
Published: April 2003

The structure of the repeating units of poly(parabanic acid) (PPA), a polyimide‐like glassy heat resistant polymer, was analyzed by MM2 using various model compounds of PPA‐M and PPA‐T consisting of M (1,3‐diazolidine‐2,4,5‐trione‐1,3‐diyl‐1,4‐phenylenemethylene‐1,4‐phenylene) and T (1,3‐diazolidine‐2,4,5‐trione‐1,3‐diyl‐3,3′‐dimethyl‐4,4′‐biphenylylene) units, respectively. Based on the most stable structures obtained, the subunit rotations of the methylene, phenylene, and diazolidine groups were evaluated. The potential mobilities estimated for these subunits can reasonably be correlated with the dynamic mechanical and dielectric properties of PPA. The γ relaxation mode of both PPA‐M and a copolymer PPA‐TM is reasonably explained by the rotation of the methylene group. The major mode of the β relaxations of both PPAs is ascribed to the rotation of the phenylene ring of the M unit, while the β* dielectric relaxation is attributed to the torsional vibration of the parabanic ring involving the adjacent aromatic moieties. These data suggest that PPA is similar to polycarbonate rather than polyimide in terms of the local chain motion. It is shown that the conformational analysis by MM2 is quite informative to understand the structure property relationships of polymers.
Brownian dynamics of grafted polymer chains: time dependent properties
Authors: Neelov Igor M. , Binder Kurt
Published: April 2003

Results of computer simulations of polymer layers consisting of chains grafted by one end on an unpenetrable plane are presented. Characteristics of translational and rotational motion of different chain segments and correlation functions of chain radii were calculated both for single layers at different grafting densities s and for two interacting layers at different distances D between parallel grafting planes. Two values of grafting density were used in the latter case. The behavior of different correlation times as function of s and D and the interplay between the interpenetration of the brushes and rotational and translational motion are discussed. Both relaxation functions and mean square displacements are discussed in terms of stretched exponentials, and the behavior of the resulting “Kohlrausch exponents” γ is presented in detail.
Effect of reactor residence time distribution on the size distribution of polymer particles made with heterogeneous Ziegler‐Natta and supported metallocene catalysts. A generic mathematical model
Authors: Soares João B. P. , Hamielec Archie E.
Published: April 2003

A generic mathematical model for analyzing the effect of ideal and non‐ideal reactor residence time distributions on the size distribution of polymer particles produced with heterogeneous Ziegler‐Natta and supported metallocene catalysts was developed. It was shown that the residence time distribution in polymerization reactors can have a significant effect on the size distribution of polymer particles and this can lead to imperfect replication of the catalyst particle size distribution.
An investigation of hemibenzopinacolate radicals used in the synthesis of block‐copolymers: ESR measurements and semiempirical calculations
Authors: Hajji Lahoucine , Santos Ramiro Guerrero , Beinert Gérard Joseph , Herz Jean‐Edouard , Bieber André , André Jean‐Jacques
Published: April 2003

Hemibenzopinacolate radicals may be incorporated in a polymer chain and the latter used as a macromolecular initiator. Kinetics of polymerization are strongly dependent on the substitution of the pinacolate. A large family of substituted (CH3)3SiOC(C6H5)2 radicals has been synthesized and studied by electron spin resonance (ESR) and semiempirical molecular orbital calculations. ESR spectra are well resolved and, except for one derivative, allow an unambiguous determination of the hyperfine coupling splitting (HFS) constants. The ground state properties have been calculated within different approximations, namely MNDO, AM1 and PM3 for the geometry optimization and INDO for spin density. Geometries obtained within AM1 and PM3 approximations are satisfactory. The HFS constants evaluated using McConnell type relations and spin densities are in a quite good agreement with the experimental ones. It turns out that the effect of substitution on kinetics of polymerization cannot be attributed to any drastic change in the charge distribution.
Dynamics and conformational properties of polyampholytes in external electrical fields: Influence of the charge distribution
Authors: Schiessel Helmut , Oshanin Gleb , Blumen Alexander
Published: April 2003

In the present work we study the dynamics and conformational properties of polyampholytes (PAs, polymers containing positive and negative charges) in the presence of external electrical fields. In terms of the Rouse Model of polymer dynamics we obtain for PAs in the so‐called weak coupling limit explicitly the mean square displacement both of the center of mass and of individual beads, and the PAs' end‐to‐end distance. We study both ordered and also random charge distributions along the chains; in the latter case we also consider the role of different correlation lengths.
Monte Carlo simulations of chains confined inside a cube
Authors: Abadie Michel R. L. , Dayantis Jean
Published: April 2003

Self‐avoiding walks (SAWs) and random‐flight walks (RFWs) of various lengths embedded on a simple cubic lattice have been computer generated inside cubes of varying side. If B is the side of the confining cube, we define the reduced cube side size B0 as B0 = (B − 1)/1/2, where 1/2 is the root‐mean‐square end‐to‐end distance of the non‐confined chains. Dimensionless diagrams are then given of the Monte Carlo estimates for the dimensions, the entropy, and the compressibility parameter PV/(kT) of the confined chains as a function of B0. The comparative behaviour of the confined SAWs and RFWs is established, scaling properties are examined, and the Monte Carlo estimates compared with theory when such theory is available.
Molecular weight distribution in random branching of polymer chains
Authors: Tobita Hidetaka
Published: April 2003

Analytical expressions for the average molecular weights of randomly branched polymer molecules with any primary chain distribution are developed. A full molecular weight distribution (MWD) function is also derived for the case where primary chains conform to the most probable distribution. This MWD function can be separated into the fractional MWDs containing k branch points; therefore, very detailed information on the structure of randomly branched polymers can be obtained. The average molecular weights of the polymer fraction containing k branch points are linear functions of the number of branch points k, and the distribution becomes narrower as k increases. The heterogeneity in the distribution of branch points can make the weight‐average degree of polymerization larger, although it is impossible to form a gel molecule only via branches (T‐shaped junctions) without assistance of crosslinkages (H‐shaped junctions).
Influence of polymolecularity on the second virial coefficient of polymers
Authors: Bareiss Rolf E. , Jung Bernd , Khokhlov Alexei R.
Published: April 2003

Scaling theory is applied to derive expressions describing the influence of polymolecularity on the second virial coefficient, A2, as obtained from osmotic pressure and light scattering measurements. Numerical values of polymolecularity correction factors are calculated for Schulz‐Zimm and logarithmic normal distributions of the molecular weight, different qualities of the solvent and several ratios of the weight‐average and the number‐average molecular weights M̄w/M̄n. It is found that in the equation \documentclass{article}\pagestyle{empty}\begin{document}$ A_2 = K_{A_2 } \cdot M_{{\rm av}}^{a_{A_2 } } $\end{document} the weight‐average molecular weight is a good approximation for Mav if A2 is measured via light scattering, while the number‐average molecular weight can be inserted for Mav if A2 stems from osmotic pressure measurements.
Nonequilibrium statistical theory of damage and fracture for glassy polymers, 1. The statistical distribution and evolution of microcracks in glassy polymers
Authors: Li Qiang , He Ziru , Song Mingshi , Tang Aoqing
Published: April 2003

The purpose of this paper is to construct a unified theoretical framework to link micro to macro‐mechanical properties of glassy polymers. Starting from a model of microcrack propagation in craze on a mesoscale, the kinetic process of microcrack propagation resulting from fibril breakdown in the crack tip zone is mathematically formulated by a combination of fracture mechanics and fracture kinetics. A microcrack evolution equation involving both the geometric structure parameters of craze and the meso‐mechanical quantities is obtained. After solving this evolution equation, a statistical distribution function of microcrack size which evolves with time and the moment generating function of microcrack size are derived. Any‐order averaged damage functions can be therefore deduced. Specifically, the analytical expressions of the first‐order averaged damage function and its damage rate are presented, which correspond to a similar definition of damage mechanics.
Effect of the topology on the gaussian elasticity of a network. The example of a fractal topology
Authors: Bastide Jacques , Boué François
Published: April 2003

By considering fractal topologies of polymer networks, we show that one can obtain much smaller values of the elastic modulus than predicted by classical models for the same density of crosslinks. In a regular fractal such as the Sierpinski gasket, one can replace the segments joining the modes by Gaussian chains. This allows one to draw some micronetworks of rank k = 1, 2 etc., with no dangling ends except for the few external points (3 for any rank). Within the frame of the phantom network model, we calculate the elastic modulus of the micronetwork. It varies as pk−1 for p < 1, which leads, even for rather small orders k such as 2, 3, to values lower than the classical James and Guth modulus, which actually corresponds to the connectivity of a tree. Thus there is an influence of the topology. Fluctuations of the positions of crosslinks and of the distance between two crosslinks are estimated and are found to correspond to a lower deformation of the chains. Whether these topologies are more than an example and could explain the anomalies observed experimentally is a postponed discussion.