Pre-gel Region Research Articles

Modelling and Optimization of Nonlinear Polymerization Processes

SummaryReactions such as branching and crosslinking leading to nonlinear polymers play an important role in many polymerization productions, but they increase the sensitivity of the processes and increase the requirements for their design and control. It is therefore desirable to have an accurate and simple means to model these processes. However, the simplest method for the description of the polymers: the method of moments was said to fail in the nonlinear case because of the so called closure problem. It will be shown here how to extend the method of moments to nonlinear processes in the pregel region − except scission − and thus provide a simple means for the simulation and optimization of the main parameters of a polymer distribution. Furthermore, the assumption of one radical per polymer molecule is no longer needed. The formulas allow average polymer properties to be easily included in flow sheet simulations or computational fluid dynamics codes and allow checking other more elaborate codes for the description of polymer distributions. Examples will be given for free radical polymerizations. An approximation in case of scission will be discussed together with an application to reversible polycondensation.

Rheological cure characterization of an advanced functional polyurethane

As part of our continuing study of the curing kinetic and chemorheological analysis of a functional polyurethane (PU) segmented block copolymer formation, in the current paper, we focus on the use the rheological measurements to monitor the entire curing process. The curing reaction was between a metallo-polyol derived of hydroxyl-terminated polybutadiene (HTPB), i.e., (ferrocenylbutyl) dimethylsilane grafted HTPB, and isophorone diisocyanate (IPDI). The evolution of viscoelastic properties, such as storage modulus (G′), loss modulus (G″) and complex viscosity (η*) was recorded in isothermal conditions, at four different temperatures in the range of 50–80°C. The gel times (tgels) were determined by the loss tangent (tanδ) crossover at different frequencies, and the activation energy obtained from them was 69.8kJ/mol. The rheological properties in the region of the gel point have shown that they follow the percolation theory, demonstrating a power law dependence for the shear modulus with a critical exponent n=0.67±0.01, for the higher curing temperatures, 70 and 80°C, and a slightly lower one at lower temperatures, 50 and 60°C. In addition, three different empirical models, among them the Arrhenius and Kiuna rheokinetic models, were used to predict the change in viscosity of this system with the time in the pre-gel region. These results illustrate the rheological curing behavior of this PU resin, its final application being found in the development of advanced energetic composite materials.

Rheological Behavior and Gel-Point Determination for a Model Lewis Acid-Initiated Chain Growth Epoxy Resin

The sol−gel transition, or gelation, in a polymer network-forming system is defined as the critical point in the polymerization at which an infinite macromolecule is formed. There are many studies in the literature concerning the exact and accurate determination of the gel point and its interpretation in terms of the critical conversions of reactant functional groups. However, these have mainly involved step-growth polymerizations with few studies of chain-growth polymerizations such as that described in this study. Chemorheological studies on a cationically polymerized epoxy network-forming system are used to determine accurate gel times and critical conversions, which are interpreted in terms of classical branching and chemical bond percolation models for nonlinear polymerizations. Rheological studies during the polymerization of a trifunctional epoxide monomer, using BF3 as the Lewis acid initiator, yielded a gel conversion of 0.17 ± 0.02 and a power law dependence for the development of shear modulus, with a critical exponent n = 0.64 ± 0.03, which is shown to be independent of temperature and BF3 concentration. The viscosity at conversions close to the gel point was shown to vary according to a power law with a critical exponent k = 1.33 ± 0.03 in the pregel region. The critical behavior of this complex network-forming system is shown to be closely predicted by percolation theory.

Species distribution during the cure of dicyanate ester

AbstractThe network formation process for bisphenol A‐based cyanate ester resin was examined using size exclusion chromatography (SEC) and differential scanning calorimetry (DSC). A kinetic scheme based on the SEC data was used to predict the species distribution in the reaction medium in the pregel region. After gelation, the molecular species undergo retroversion as the high molecular species are predominantly attached to the growing network structure.

Critical behavior of anhydride cured epoxies

Critical behavior was studied with a crosslinking system obtained by living anionic polymerization, where the primary chain length was kept constant and the crosslinking density was varied. Gelation was found at a critical ratio of crosslinker per chain X~ = 0.884 ± 0.004. Different samples from the pre gel region were studied by dynamic and static light scattering in dilute solution and oscillatory rheology in melt. The exponents y=1.75 ±0.38 and v = 0.98 ± 0.19, determined from M~ and R~ dependence on (X~ X ), are in accordance with three dimensional percolation theory. The distribution of diffusion coefficients obtained by inverse Laplace transformation of the time correlation function shows power law behavior in a limited interval, from which an exponent v = 2,17 ± 0.03 is derived. Rheological measurements show a systematic change of G'(w ) and G(w from typical liquid to the critical gel behavior,

Kinetics of the free-radical copolymerization of methyl methacrylate/ethylene glycol dimethacrylate: 2. Analysis of gelation and the pregel region

A kinetic model based on the pseudo-kinetic rate constant method is used to investigate the kinetics of the bulk free-radical copolymerization of methyl methacrylate (MMA) and the divinyl monomer ethylene glycol dimethacrylate (EGDMA) initiated with AIBN, with and without chain transfer agent (CBr 4) during the pregel region. Most of the kinetic parameters were estimated from experimental data. The agreement of predicted with measured onset of gelation is found to be satisfactory.

UV absorption and sol-gel transition in ion-bombarded polystyrene

The modification of the ultraviolet absorption spectrum induced by ion bombardment at high energy (100–400 keV) of thin polystyrene films is reported as function of ion fluence. It has been found that the UV absorption increases with the ion fluence in the pre-gel region with a well defined peak and then decreases in the post-gel region. Pre-gel data together with molecular weight distribution studies can be understood in terms of ion-macromolecule interaction with cross-sections of the order of 10 −13 cm 2. The efficiency of the different ions (He +, Ne +, Ar + ) for increasing UV absorption depends on the energy density transferred by the ion to the target, in a similar way the cross-linking efficiency dependence.

Statistics of random macromolecular networks made by chainwise polymerization of polyfunctional monomers—1: Characterization of the pre-gel region

General expressions are derived for the average functionalities and molecular weights of macromolecules obtained by chainwise polyfunctional polymerization during the pre-gel region.

Intrinsic unequal reactivity and average molecular weights in non-linear stepwise polymerization

The general expressions of average molecular weights in the pre-gel region, for stepwise polymerization of polyfunctional monomers endowed with both A and B coreactive functional groups, are extended to systems where some or all of the B groups react at different rates. The method of calculation is always based on the propagation expectation and the presence of by-product in the reactions is taken into account.

Substitution effects and average molecular weights in non-linear stepwise polymerization

The authors' method of calculating average molecular weights, in the pre-gel region, for stepwise polymerization of polyfunctional monomers, is extended to systems where the functional groups exhibit unequal reactivities induced by substitution effects in the course of the reaction.

Curing kinetics of a rigid polyurethane foam formulation

The curing kinetics of a typical commercial formulation used in the manufacture of rigid polyurethane foams has been studied. The adiabatic temperature rise method was used, taking into account corrections for heat losses. A polymeric isocyanate was reacted with a stoichiometric amount of a polyether polyol, using dibutyltin dilaurate (DBTDL) as catalyst. For DBTDL < 2.6 mol m −3, a strong inhibition of the catalyst took place, and the uncatalysed reaction played a major role. Second order kinetics gave a good fit for the whole conversion range. For DBTDL > 2.6 mol m −3, the catalysed reaction took place. Second order kinetics were applicable up to the gel point, but then the rate slowed down severely. A first order dependence on the initial catalyst concentration was observed in the pre-gel region. The kinetics are discussed in terms of a modified version of the Van der Weij's mechanism. The heat of reaction was 17.6 kcal/NCO equivalent.

General expressions of average molecular weights in polycondensation of polyfunctional monomers involving condensation by‐product

AbstractIn this paper, the general expressions of average molecular weights for condensation polymerisation involving eliminat species are derived in the pre‐gel region especially for systems composed of monomers endowed with both A and B coreactive functional groups. The weight average molecular weights are calculated directly according to a new method using the propagation expectation.

HOLLOW FIBER ULTRAFILTRATION OF CALF SERUM AND ALBUMIN IN THE PREGEL UNIFORM-WALL-FLUX REGION

Abstract Ultrafiltration of calf serum and bovine serum albumin (BSA) in the pregel region has been studied in Cuprophan hollow-fiber filters of various lengths and number of fibers, and at several axial flow velocities. Graphs of ultrafiltration velocities versus transmembrane pressure show a surprising independence from fiber length and axial flow velocity. Results are correlated by osmotic-pressure data and an available boundary layer theory derived originally for uniform-wall-flux processes in the far-downstream (asymptotic) region.

Crosslinking and scission yields for polystyrene subjected to γ irradiation in vacuo

AbstractMeasurements of molecular weight averages and distributions have been made on three samples of narrow molecular size distribution polystyrene with molecular weights from 100, 000 to 400, 000 subjected to 60Co γ irradiation in vacuo for various doses within the pregel region+ G(X), the radiation chemical yield of crosslinking, has been determined as 0.043 ± 0.002 and G(S)/G(X), the ratio of scission to crosslinking, as 0.02; no effect of molecular weight was observed. By comparison with previous experimental results for polystyrene irradiated in air it has been established unequivocally that an oxygen environment leads to enhanced scission at the expense of crosslinking. Literature values of G(X) and G(S)/G(X) are reviewed in the light of these results and explanations are offered to account for major discrepancies.

Calculation of molecular parameters for stepwise polyfunctional polymerization

AbstractOur recursive method is extended to calculate several new parameters for stepwise polyfunctional polymerization. In the pregel region we calculate weight average molecular weight, Mw, for polydisperse reactants and effective average functionality, fe, of a reacting mixture. These quantities are useful for systems employing reactive oligomers. We also calculate weight average number of branches per molecule, Bw, and the weight average of a longest chain. These should be useful for viscosity relations. In the postgel region we give relations for the extent of reaction in the soluble fraction. This result can be used to calculate sol properties directly from existing pregel relations. We also calculate the weight fraction of pendant chains on the gel, wp, and the average molecular weight of the elastically effective network chains, Mc,w.

Chain Scission and Cross-Linking in the Radiation Degradation of Polymers: Limitations on the Utilization of Theoretical Expressions and Experimental Results in the Pregel Region

An appraisal is made of current methods of determining radiation-chemical yields for main-chain scission and cross-linking of a polymer from measurements of molecular size distributions and average molar masses after high-energy radiation doses D below the gel dose D. Calculation of molecular size distributions by a single cycle of successive scission and cross-linking is shown to give significant errors. A multicycle procedure that uses iterative, numerical solutions of the fundamental scission and cross-linking equations is developed and shown to be superior. On the basis of theoretical calculations of likely experimental errors in measurements of M and M it is recommended that radiation doses be restricted to the region D < 0.4D for evaluation of scission and cross-linking yields from the dose dependence of average molar masses.

The radiation induced reactions of aqueous polyethylene oxide solutions. II. Intrinsic viscosity changes in the pregel region

AbstractA model is proposed for the interpretation of molecular weight changes occurring in the pregel region of irradiated dilute aqueous polymeric systems. The model is, in principle, related to and gives results compatible with the molecular weight changes occurring during condensation polymerisation. On the basis of the above model and the ZIMM‐KILB theory of branching effects on intrinsic viscosity, calculated intrinsic viscosities agree satisfactorily with results for low molecular weight material only when allowance is made for intramolecular crosslinking and a drastic reduction in the rate of intermolecular crosslinking with dose for doses close to the gel dose. A similar quantitative approach is not possible for higher molecular weight material because of the high branching densities involved. A qualitative approach shows that many features of the radiation induced behaviour of intrinsic viscosities can be explained by the proposed model. For concentrations below the critical concentration, a treatment based on diffusion control of intermolecular crosslinking was found to be satisfactory.

Cross-linking of polystyrene by high-energy radiation. II. Molecular weight changes in the Pregel region

Cross-linking of polystyrene by high-energy radiation. II. Molecular weight changes in the Pregel region