Recent investigations have implicated cagelike precursors in the unusually high gelation conversion (similar to 82%) of acid-catalyzed tetraethoxysilane. However, the statistical models used so far cannot capture kinetic or composition-dependent features of alkoxysilane polycondensation. Here we take a first step toward unified modeling of the kinetics and structure of silica gelation. Dynamic Monte Carlo simulations [Somvarsky, J.; Dusek, K. Polym. Bull. 1994, 33, 369] are developed which permit competition between extensive cyclization and growth. The model includes well-established kinetic trends (hydrolysis preequilibrium and first-shell substitution effects). As a first approximation, unimolecular-like terms for cyclization reactivity follow the experimental pattern of bimolecular rate coefficients. The present simulations allow unlimited formation of three-site rings, giving rise to many structures that are not those of real silicates (where four-site rings dominate). However, the level of cyclization (both cycles per molecule and per site) is consistent with that of real silicates and is enough to delay gelation to 82% conversion or higher. These simulations also display a broader range of gelation behavior than prior kinetic models. At high to moderate monomer concentrations, competition between cyclization and growth causes the expected delay of gelation. Upon further dilution, we discover a third regime, absent from prior kinetic gelation models but important for siloxanes: formation of a distribution of polycyclic precursors that still retain enough functionality to gel.

We present nonlinear shear and uniaxial extensional measurements on a series of polybutadienes with varying amounts of long-chain, random branching. Startup of steady shear experiments is used to evaluate the damping function of the melts. The damping function is found to show a trend toward decreased dependency on strain with increasing branching content. Interior chains, which are believed to be responsible for changing the damping function, are calculated to comprise less than 3 wt % of the melt. Extensional measurements are used to investigate the role of branching in strain hardening. We show that samples with increased branch contents do show larger deviations of the transient Trouton ratio from the linear viscoelastic limit of three. However, we also show that the extensional data can be fit using parameters determined solely by the shear measurements. Furthermore, we show that the changes in the damping function seen in shear have little impact on extensional behavior. The extensional behavior of the melt is found to be most affected by changes in the relaxation spectra which can result from both branching and increases in the high end of the molecular weight distribution. This statement runs contrary to the often expressed view that strain hardening behavior in extension is exclusively produced by branching.

The hydrolysis of a cyanate ester network made from the monomer 2,2*- bis(4-cyanatophenyl)isopropylidene (bisphenol A dicyanate homopolymer) was stud- ied. Hydrolysis reactions were performed isothermally at temperatures from 150 to 1807C under conditions of excess water. The kinetics of the reaction were characterized by the decrease in Tg as measured by differential scanning calorimetry. The rate of change of Tg was found to be adequately described as first order in Tg, which is an indirect measure of the concentration of crosslink junctions. The activation energy of the reaction was found to be 115 kJ/mol. In addition, moisture-conditioned, glass- reinforced laminate samples were heated and the time to delamination or blistering was recorded as a function of temperature. The blister time at solder temperatures (T A 220-2607C) was modeled using the above kinetic results. Heat transfer to the lami- nate was considered and the criteria used for blister time was the time at T A Tg of the sample. At lower temperatures (T o 2207C), loss of water from the laminate is sufficiently fast to prevent blistering. q 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 107-113, 1997

We present results on the product distribution obtained from the polymerization of the dicyanate monomer of bisphenol A carried out under different reaction conditions. Small quantities of side-products were observed using both size exclusion chromatography and high-pressure liquid chromatography for samples polymerized under an inert atmosphere. Despite the presence of side-products, the oligomer distribution from SEC, after correcting for differences in refractive index, was found to agree well with random branching predictions. Results from HPLC also confirm good agreement with the theoretical prediction. Furthermore, a gel conversion of approximately 0·51(-0·01, +0·03) was measured for the inert atmosphere product, which is within experimental error of the ideal value of 0·50. The monomer content of a polymerization carried out open to the atmosphere, however, showed significant disagreement with theory. ©1997 SCI

The Pt-catalyzed hydrosilation reaction between methyl-substituted cyclosiloxane and a nonconjugated diene system produces silicone-carbon polymers with good mechanical and dielectric properties. In this work a statistical model is devised that provides a theoretical description of the polymerization reaction up to the B stage. An ensemble of cyclosiloxane molecules is built up in a computer and allowed to ''react'' with the diene (or mixture of dienes) in a Monte Carlo process. Included in the model are options for batch or semibatch operations. Through computer simulation, the concentrations of all molecular species at different conversions (as measured by the residual Si-H group) can be predicted as well as the molecular weight distribution. Good agreement is obtained with observed analytical data. The model is flexible and is used to study the effects of the changes in reaction process conditions on polymer structures and molecular weights. (C) 1997 John Wiley & Sons, Inc.

This paper aims to calculate the average properties of ideal non-linear stepwise polymerization of comonomers containing multiple reacting sites at the B-stage prior to gelation. A kinetic model is used to simulate the polymerization process taking into account the mass balances of differently substituted species possible. The molecular weights are obtained either by the use of the the Miller-Macosko method or by solving the differential equations for the polymerization of low-molecular-weight species. The approach is applied to the Pt-catalyzed hydrosilation reaction between methyl-substituted cyclosiloxane and dicyclopentadiene which produces a high-performance silicone-carbon resin. The approach gives the concentrations of various species present at any given time and the molecular weights. Different modes of monomer addition can also be simulated.

New silicone-carbon resins have been made, based on four- or five-membered cyclosiloxanes, cyclopentadiene dimer (DCPD), and cyclopentadiene trimer (TCPD). The monomers are first polymerized to a B-stage resin, and then heated at higher temperatures to cure. In this work, the curing reaction of this silicone-carbon resin (which leads to network formation) is simulated using two approaches. In the first approach (stochastic model), all the available functional groups (olefin and silyl hydride) are allowed to react with each other with equal probability. This gives the kinetically controlled, liquidlike, diffusion-free limit. Extrapolation of the model to reactions where diffusion may play a role can be made by including molecular weight dependence in the rates. This dependence on the molecular weight can be scaled to fit the experimental data. In the second approach a percolation model is used. In the extreme case, this model corresponds to the solid-state reaction between silicone-carbon resin molecules on 2-dimensional or 3-dimensional rigid lattices. Relaxation of this geometric constraint can be made by providing a larger reacting distance between the reactants. Computer programs have been written for 2- and 3-dimensional lattices. Illustrative examples are given for these approaches. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 1557–1573, 1997

We compare two approaches in modeling first shell substitution effects (FSSE) coupled with cyclization in acid-catalyzed sol-gel polymerization. First, an approximate, statistically based, kinetic-recursive model (KR) is developed that is computationally inexpensive for investigating trends in the polymerization. Second, an exact Monte-Carlo model (MC) that tracks a finite pool of growing polymer clusters is constructed for comparison to the KR model. The two models agree well prior to gelation when using rate constants typical of sol-gel polymerization. However, near the gel point, discrepancies between the two models arise because of the KR model's inability to account for correlations in the growing structure beyond the site distribution. We show that both FSSE and cyclization cause the polymer's structure distribution to be history dependent. We also show that the inclusion of both FSSE and cyclization in the model is capable of increasing gel conversions above the 0.50 limit of previous exclusive FSSE models. We show that FSSE aids cyclization by increasing the concentrations of oligomers that are candidates for intramolecular reaction and that a strong FSSE with cyclization causes a local maximum to occur in the polydispersity index as a function of conversion. Both models fall short of predicting experimentally observed gel conversions; indicating that, in addition to the small cycles allowed in the present work, cage formation may also be significant.

We describe a kinetic Monte Carlo model for copolymer structure development from organoalkoxysilanes. Strong polymerization nonidealities dictate that such a technique be used. Capillary gas chromatography and silicon NMR data illustrate the prevalence of cyclic species and the need for the described model. While maintaining consistency with previously reported nonidealities and features of alkoxysilane polymerization, the model also accommodates extensive cyclization. The model permits not only isolated rings but also polycyclic and cage-like species to form. A simplified application of the model (with isolated three-membered rings) predicts a bond conversion at gelation closer to the experimental value for tetraethoxysilane than previous models.

The fiber-windup technique, developed by Macosko and Lorntson [SPE Tech. Papers 19, 461-467 (1973)] for rotational shear rheometers, was re-examined to obtain transient uniaxial extensional viscosity data. Macosko and Lorntson used a special force transducer to measure the tension in the filament being pulled. In contrast, in this study commercial rotational shear rheometers (Rheometrics Mechanical Spectrometer-800 and Rheometrics Fluids Spectrometer-II) with torque transducers were used to obtain the extensional viscosity. One end of the sample is clamped, while the other end is wound around a drum at a constant rotational speed, to achieve a given extension rate. Tests were conducted with a polyisobutylene sample at room temperature to verify reproducibility and were compared with published studies. Results for polyisobutylene and IUPAC-X low density polyethylene were found to be in good agreement with published results. Hencky strains of up to 6 could be achieved. The technique can provide valuable extensional viscosity data for high viscosity liquids. (C) 1996 Society of Rheology.

The rheology of a series of long-chain randomly branched polybutadienes (PBDs) has been investigated. Branched samples were made through a hydrosilation reaction between a small difunctional crosslinker and the 1,2 groups distributed on the backbone of near-monodisperse PBD (M(w) = 56 000, 137 000; M(w)/M(n) = 1.04). The resulting samples have both dispersity in molecular weight and architecture. The species distribution has been studied using size exclusion chromatography and has been found to agree with the Flory-Stockmayer distribution for the random branching of monodisperse chains. Sinusoidal oscillation and creep/creep recovery experiments were done to determine dynamic moduli, zero shear viscosity, and equilibrium creep compliance. The observation that branching is random allows structural parameters to be calculated such as weight fractions and average molecular weights of free chains, arms, and interior chains. These parameters are used in existing rheology models whose results are compared to experimental observation. In particular, qualitative agreement is found for eta(0) as a function of branching content by applying the model proposed by McLeish and O'Connor [Polymer 34, 2998-3003 (1993)] for star/linear blends. (C) 1996 Society of Rheology.

A computer approach is developed that permits fast estimation of the 13C chemical shifts of common organic compounds, spectral simulation of these compounds, and shift/structure search in a user-maintained spectral library. In the first part of this PC-based program (called CSPEC2), the 13C shifts are predicted on the basis of empirical additive shift rules, and are applicable to carbons contained in commonly occurring organic functional groups, including olefins, acetylenes, aromatics and carbonyls. Structure input and modification are facilitated and shift accuracy improved through the availability of library compounds and the use of a “parent structure” option. The predicted shifts for any compound can be displayed as a printed output, as a file, or as a stimulated spectrum. In the second part of the program, partial 13C shifts, molecular formula, or chemical names can be searched sequentially in the spectral library. The use of this computer program is illustrated by suitable examples. Major advantages of this approach include the ease of use and the ability to modify the additivity shift parameters or to add additional functional groups to the program.

In many homopolymers the tacticity may be compositionally or sequentially heterogeneous. A computer simulation approach has been developed to simulate tacticity sequence and tacticity distribution for polymers made under a variety of conditions. Included in the simulation are the effects of molecular weight, consecutive and concurrent propagation models, and multiple catalyst/initiator states. In addition, heterogeneity brought about by the fluctuations in the reaction process conditions can also be incorporated. The effect of sequential heterogeneity can be separately visualized through the use of sequence index. Simulations have been made of the tacticity of poly(methyl methacrylate), poly(isopropenylpyridine), and polypropylene. In general, compositional heterogeneity has a large effect on the composition distribution curve but a lesser effect on NMR tacticity.

A family of computer programs (called PODIS) has been written that permits compositional heterogeneity in copolymers to be directly computed. Different sources of compositional heterogeneity have been specifically addressed by separate programs. Included in the treatments are statistical heterogeneity, conversion heterogeneity, multistate heterogeneity, and compositional heterogeneity due to fluctuations in polymerization process parameters. Through these means, predicted chemical composition distributions have been made for linear low-density polyethylene, styrene/ethyl methacrylate copolymers, and styrene/methyl acrylate copolymers. Computer simulation permits many observed compositional features of these copolymers to be understood.