Kinetic Gelation Model Research Articles

Kinetics of polyelectrolyte network formation in free-radical copolymerization of acrylic acid and bisacrylamide

Recently, a research/development program has been initiated to investigate the kinetics of synthesis, characterization and applications of polyelectrolyte networks. The research on crosslinking involves both theoretical development and experimentation. Herein, is provided a summary of this work. In the experimental polymerization done to date, acrylic acid (AA)/N.N'-methylenebisacrylamide (BAM) was studied in considerable detail. The polymerization conditions were: temperature, 50°C; initial monomer concentration, 5 wt%, of which 1.0 mol% is BAM; K2S2O8(KPS) as the initiator, 10−3 mol/L; pH range, 1 − 13; sodium chloride concentrations up to 3.1 mol/L. Measurements included: monomer conversion, polymer composition, sol/gel fraction, swelling ratio, and the densities of primary cyclization, secondary cyclization and crosslinking. It was found that the effect of polymerization parameters on the resulting polymer network microstructure was dramatic, and in particular, the pH and ionic strength of the reaction medium were important parameters. In the theoretical studies, the Tobita-Hamielec kinetic gelation model was extended to incorporate the concept of ion pair interaction and the divinyl loop formation. The system was treated as a multi-component polymerization of acrylic acid, acrylate ion, acrylate ion pair and bisacrylamide. The model permits one to investigate the development of the crosslinking density distribution among primary polymer chains during the course of polymerization as a function of pH and ionic strength.

Microstructural evolution in polymerizations of tetrafunctional monomers

AbstractTo characterize the network structural evolution during polymerizations of multifunctional monomers and predict the relationship between reaction conditions and polymer structure, a balanced approach between experimental characterization and simulation is used. A novel method for characterizing the free volume distribution and network structure throughout the polymerization is presented. This technique involves the use of photochromic probes that require a certain local, critical volume to isomerize. By incorporating probes that require different isomerization volumes, a distribution of local volume in the network is determined. Since this technique allows in situ monitoring of the volume distribution, the effects of conversion, rates of polymerization, and monomer structure on the free volume distribution can be elucidated. Volume distributions are presented for diethylene glycol dimethacrylate. Information from the photochromic technique is further supported by kinetic gelation model predictions and transmission electron microscopy pictures of the evolving polymer structure.

Kinetic Gelation model predictions of crosslinked polymer network microstructure

A kinetic gelation model was used to predict the complex network structures that arise in the high crosslinking regime of homopolymerizations and copolymerizations of multifunctional monomers. In particular, network inhomogeneities, relative functional group reactivities, and cyclization vs crosslinking tendencies were studied for a variety of systems as a function of the reaction conditions. Since the network structure strongly influences the physical and mechanical properties of the polymer, the objective of this work was to predict and study the effects of reactions conditions on this structure to provide insight for developing better materials. The following work presents the results from a kinetic gelation simulation, and when available, compares these results to experimental values.

Kinetics of network formation via free‐radical mechanisms — Polymerization and polymer modification

AbstractThe study of polymeric networks synthesized via free‐radical polymerization and/or prepolymer modification have become an attractive research area of both fundamental and commercial interest. Recently, a research/development program was initiated to investigate the fundamentals and applications of polymer networks. The following aspects are being emphasized: the elucidation of crosslinking mechanisms and kinetics, the characterization of network microstructures, and the development of kinetic gelation models. This paper reports recent activities towards these goals.

Critical behaviour of a kinetic gelation model with a constant initiator creation rate

The authors present results from a computer simulation study of a radical initiated kinetic growth model in which the radicals (initiators) are created with a constant rate rc. Simulations of the growth process were carried out on simple cubic lattices as large as 100*100*100 for two values of the initiator creation rate. Finite-size scaling analyses of the bulk properties yield critical exponents which are the same, to within error bars, as those found in similar kinetic gelation models and in percolation studies. The critical amplitude ratio C-/C+ is consistent with the values obtained in the kinetic gelation studies with fixed initiator concentrations but is clearly different from percolation values. The cluster size distribution shows the same monotonic behaviour as seen in percolation and is markedly different from the oscillatory behaviour seen in an investigation of a similar gelation model. The scaling properties of the cluster size distribution, however, cannot be described using simple droplet theory. Instead, they use a generalised scaling form which produces a good fit to the cluster data.

Nature of residual unsaturation during cure of dimethacrylates examined by CPPEMAS carbon-13 NMR and simulation using a kinetic gelation model

Dosage du monomere residuel et des doubles liaisons laterales par RMN 13 C pendant les stades de postgelification du durcissement des dimethacrylates d'ethyleneglycol et de tetrakis (ethylene glycol). Utilisation d'une simulation sur ordinateur pour l'etude de l'etape de pregelification et la prediction de la taille et de la distribution des amas de monomere

The radical polymerization of dimethacrylate monomers—the use of NMR spectrometry to follow the development of network structure

13C NMR spectrometry has been used to identify and assay residual unsaturation in the cure of ethylene glycol dimethacrylate, and distinguish between monomer molecules and pendant double-bonds. Direct evidence of heterogeneity is provided by the distinction between constrained and unconstrained monomer. The predictions of a simulation using a kinetic gelation model coincide with the experimental estimations. Cure estimated by differential scanning calorimetry does not correlate linearly with residual unsaturation.

The effect of randomness on the critical behaviour of kinetic gelation

The behaviour of a three-dimensional kinetic gelation model with regularly placed initiators is determined from Monte Carlo simulations. The authors find marked differences with the behaviour observed when initiators are placed on the lattice randomly. They also look at the effect of introducing repulsion between initiators.

Inhomogeneous network formation studied by the kinetic gelation model

Network formation by chain polymerization is an intrinsically inhomogeneous process. The kinetic gelation model has been shown to produce such inhomogeneities in a natural way. These results are reviewed. Though the present approach does not focus on critical properties, it is suggested that one of the experimentally relevant modifications, polymerization at the lowest possible initiation rate, will be an exact and natural representative of the pure kinetic gelation universality class hypothesized by Jan et al..

Spatial correlations in kinetic gelation

The authors report here a calculation of the spatial correlation function of the fully polymerised four-functional units in the kinetic gelation model in three dimensions. The results indicate that the fully polymerised four-functional units form small correlated regions in space. This is in sharp contrast to normal percolation where the spatial distribution of fully polymerised units is uniform. The size of these clusters of crosslinks depends on the extent of reaction, the concentration of initiators and the solvent diffusivity. The results suggest a picture of the microscopic structure of a gel as consisting of bundles of chains linked by clusters of crosslinks in agreement with electron microscopic studies of polyacrylamide gels.

Critical behavior of a three-dimensional kinetic gelation model.

We present extensive results from a computer-simulation study of a kinetic growth model for radical-initiated irreversible gelation. Lattices as large as 100\ifmmode\times\else\texttimes\fi{}100\ifmmode\times\else\texttimes\fi{}100 were used to examine polymerization of a system of tetrafunctional and bifunctional monomers with initiator concentrations ${c}_{I}$, ranging from 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ to 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$. The cluster-size distribution shows unexpected oscillations which become increasingly pronounced as ${c}_{I}$\ensuremath{\rightarrow}0. The scaling properties of the cluster-size distribution cannot be described by simple droplet scaling theory, and we propose a generalized form for the scaling. The bulk properties show critical exponents which are independent of ${c}_{I}$ and identical to percolation values within the errors. The amplitude ratio ${C}^{\mathrm{\ensuremath{-}}}$/${C}^{+}$ is not independent of ${c}_{I}$. The backbone of the largest cluster at the gel transition is also investigated and its fractal dimension is found to be distinctly larger than that of a random percolation cluster at ${p}_{c}$.

Oscillations and scaling in the cluster size distribution for kinetic gelation

The authors have studied the distribution of cluster sizes ns in an irreversible kinetic gelation model using Monte Carlo simulations on a simple cubic lattice. They find quite surprising, pronounced oscillations in the distribution ns with cluster size s. The variation of ns with s and the fraction p of bonds formed is described by unconventional scaling behaviour.

Fractal dimensionality for kinetic gelation with conserved initiators

A kinetic gelation model is developed for which the number of active initiator molecules is conserved. For this reason this model exhibits a gelation threshold even for very small values of cI, the concentration of initiator molecules, in contrast to the conventional model of kinetic gelation with non-conserved initiators. This model is studied by Monte Carlo analysis for a two-dimensional triangular lattice with a sequence of lattice sizes up to 900*900 sites. The authors use finite-size scaling to study the dependence of yh (the fractal dimension) and yT (=1/ nu ) upon cI. They find that yT depends weakly on cI, but that the fractal dimension yh is independent of cI. This is in accord with the most recent work for the conventional kinetic gelation model with non-conserved initiators.

Effects of solvent in a kinetic gelation model

Effects of solvent in a kinetic gelation model

Kinetic Growth Walk: A New Model for Linear Polymers

To describe the irreversible growth of linear polymers, we introduce a new type of correlated walk, related to the zero---initiator-concentration limit of the kinetic gelation model. Our model simulates real polymer growth by permitting the walker to form the next bond from the unsaturated monomers at the neighboring sites of its present location. A heuristic kinetic argument of the Flory type suggests a fractal dimension ${d}_{f}=\frac{(d+1)}{2}$, in agreement with our Monte Carlo and series expansion results (including a logarithmic correction at the upper critical dimension ${d}_{c}=3$).

Phase diagram, critical properties and dimensional effects of the kinetic gelation model

The authors simulate the formation of a gel from a mixture of bifunctional and tetrafunctional monomers which may form bonds with the help of initiators on the triangular lattice. Their Monte Carlo results for the average-weight degree of polymerisation exponent, gamma , substantiate the conclusion that this model has distinct critical properties from other models of branched polymers. They observe a crossover to normal bond percolation as the concentration of initiators is increased. However, the cluster number ratio appears to be a universal quantity. They offer an explanation for the differences in phase diagrams of the two- and three-dimensional systems in terms of restricted random walkers.

Computer simulation of a model for irreversible gelation

A random mixture of bifunctional and tetrafunctional units is placed on a simple cubic lattice. Permanent bonds between these units are then formed by the random motion of active centres (radicals) resulting in a model for the gelation of polyacrylamide and similar processes. The largest of the clusters formed by this kinetic percolation process is identified with the gel fraction, the 'mean cluster size' with the weight-average degree of polymerisation. The critical exponent gamma of the mean cluster size is roughly the same as for random percolation, that is, different from that of the 'classical' theory of Flory (1941) and Stockmayer (1943), but the corresponding amplitude ratio, that is, the ratio of average molecular weight on both sides of the gel point, differs strongly from its value in random percolation. Thus, this kinetic gelation model seems to belong to a universality class of its own, different from both that of random percolation and that of classical gelation theories.