bluuebunny/crossref_metadata_2025_split huggingface dataset:
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

AbstractThe 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

AbstractMonte 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

AbstractStructures 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

AbstractA 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

AbstractComputer 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

AbstractThe 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

AbstractHere 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

AbstractA 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

AbstractThis 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

AbstractThe 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

AbstractThe 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

AbstractWe 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

AbstractA 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

AbstractA 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

AbstractA 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

AbstractThe 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

AbstractBinary 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

AbstractA 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

AbstractThe 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

AbstractIn 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.