Ján Šomvársky

Kinetic Monte-Carlo simulation of network formation

SummaryA Monte-Carlo simulation procedure of kinetically controlled structure growth including network formation determined by generalized Smoluchowski equations was described. In addition to intermolecular reactions affected by possible time and space long-range correlations, cyclization or degradation reactions can be considered. The kernel of these reactions can be a function of not only the numbers and types of the reactive groups but also of the composition and structure of the molecule. The random number generator selects a certain reaction event characterized by its rate out of all possible events at four decision levels, (1) reaction mechanism, (2) types of reacting groups, (3) selection of molecule and (4) its reaction partner.

Modelling of ring‐free crosslinking chain (co)polymerization

Modelling of copolymerization of a monounsaturated monomer and a bisunsaturated monomer with equal and independent reactivities of double bonds is described. No rings are assumed to be formed before the gel point, and uncorrelated circuit closing beyond the gel point is allowed. These assumptions are approximately met in the case of copolymerization of α, ω-unsaturated telechelic polymers. Modelling is based on a combination of kinetic and statistical polymer formation and crosslinking theories. The bisunsaturated monomer is split into two monounsaturated fragments and these fragments are copolymerized with the monounsaturated monomer to form ‘primary’ chains. The elementary reactions of initiator dissociation, initiation, propagation, chain transfer, and termination by recombination and disproportionation are considered. The primary chains are then recombined by joining fragments of the bisunsaturated monomers into branched molecules (sol) and gel. This step is performed by the formalism of the theory of branching processes (cascade theory) employing the generating functions transform. Examples of variations of molecular-weight averages of primary chains and branched molecules, gel fraction and concentration of elastically active network chains as a function of polymerization conversion for several sets of rate constants of elementary reactions are given. ©1997 SCI

Structure, equilibrium and viscoelastic mechanical behaviour of polyurethane networks based on triisocyanate and poly(oxypropylene)diols

Abstract Using the theory of branching processes, the detailed structure of polyurethane networks from poly(oxypropylene)diols (PPDs), monofunctional alcohol (cyclohexanol) and triisocyanate prepared at various initial ratios of the reactive groups r HD ≡ [ OH ] PPD /[ NCO ] = 0·5−1·7 was characterized in terms of the number, size and structure of elastically active network chains (EANCs), backbone and dangling chains. From an analysis of the dependence of the critical molar ratio at gelation r HD c on dilution it follows that PPD samples are composed of molecules bearing primary and secondary hydroxy groups. The branching theory, in which the presence of both primary and secondary hydroxy groups in PPDs is accounted for, adequately describes the dependence of the mass fraction of the sol w s on r HD when no side reactions occur in the system (networks in the range r HD ≥ 1 or networks with monofunctional alcohols). The equilibrium photoelastic behaviour can be described by the junction-fluctuation theory with front factor A = 1 without entanglement contribution. The frequency-temperature superposition can be performed for all networks; the temperature dependence of the horizontal shift factor satisfies the WLF equation. While the position of the main transition region of viscoelastic functions on temperature or frequency depends on the content of the polar triisocyanate component, the shape of these functions at the end of the transition is determined predominantly by the concentration of EANCs.

Network structure dependence of volume and glass transition temperature

A series of polyurethanes was used to determine the molar contributions of chain ends (CE) and branch points (BP) to free volume and glass transition temperature Tg. The polyurethanes were copolymers of diphenylmethane diisocyanate and poly(propylene oxide) (PPO) with hydroxyl functionalities of one, two, and three. The equivalent weights of all the PPOs were equal, such that the chemical composition of the chain segments was essentially identical. Therefore, the only distinctions among polymers were differences in CE and BP concentration. Theory of branching processes computer simulations were used to determine the concentration of CE due to imperfect network formation. Other CE contributions were from the monofunctional PPO. Polymer volumes and Tgs were correlated to CE and BP concentrations, and the contributions of these species were determined from least squares fits. The molar volume and Tg contributions were then used to determine free volume thermal expansion coefficients. These values were compar...

Chemical clusters in polymer networks

Chemical (topological) clusters in polymer networks have been defined as covalently bonded assemblies of units of a certain kind, for instance ‘hard’ units among the soft ones. For theoretical characterization, two methods have been used: (a) the theory of branching processes (TBP) by which the structures are generated from monomer units and (b) the generalized kinetic theory with a Monte-Carlo simulation of the process. The clusters are characterized by their average sizes and average number of issuing soft bonds (cluster functionality) and conditions where the clusters grow to infinity. Using the TBP, the characterization is based on classification of the bonds connecting units as hard → hard, hard → soft, soft → hard and soft → soft. The cluster size and functionality as a function of conversion are determined by the initial composition of the system, the rules of bond formation and the relative reactivities of functional groups. Under certain conditions, the hard clusters can grow to infinity. Method (b) allows us additionally to treat the long-range connectivity effects as well as to simulate the steric excluded volume effect by making the effective reactivity of a group dependent on the cluster size. The exclusion from the reaction of a larger fraction of groups in larger clusters makes the distribution narrower, shifts the gel point to higher conversions and causes the critical exponents to deviate from their classical values. The implications of the existence of hard clusters on equilibrium elasticity are discussed.

Network build-up by initiated polyreaction

SummaryThe theoretical treatment of network formation in diamine-diepoxide curing under participation of etherification of excess epoxide groups, which is based on the combination of kinetic and statistical methods, has been extended to cover postgel parameters. Within the ring-free approximation, this treatment is rigorous. Relations have been derived for the extinction probabilities, sol fractions and concentrations of elastically active network chains. In the system under consideration, various definitions of an elastically active network chain are possible.

Network Formation Theories and Their Application to Systems of Industrial Importance

The structure of polymer networks is closely related to the network formation (structure growth) process. A covalent polymer network is a giant macromolecule of dimensions commensurable with the macroscopic dimensions of a given object. Although it can be characterized by a number of average structural parameters, like sol fraction or crosslinking density, its internal structure can be very different1 varying from that of a random loosely crosslinked network of vulcanized rubber to that of very dense networks of some thermosets or ceramers. Also, micronetworks (microgels) or other microscopic precursors (dendritic structures, star- burst polymers, etc.) are formed first and then they grow into a macronetwork with the same or other types of structure growth processes. Vinyl-divinyl copolymerization can serve as an example.2 Therefore, the understanding of structure growth is necessary for understanding the network structure, and the properties of polymer networks can be correlated with their structure. An important role in undestanding of the network structure via the network formation process is played by the network formation theories.