Jaromir B. Lechowicz

Mean-Field Kinetic Modeling of Polymerization: The Smoluchowski Coagulation Equation

The Smoluchowski coagulation equation derived back in 1916 is usually linked with the diffusivity and size of aggregating particles. It can also be used as a versatile tool for mean-field kinetic analyses. In this paper it is shown to be an efficient tool for studying the relationships between the reactivity of functional groups in monomers and the size distribution of polymer species in step and chain growth polymerizations. The Smoluchowski coagulation equation and its modifications are applied as models of kinetically controlled growth reactions (with irreversible elementary reaction steps). Advantages and limitations of this method of modeling polymerization processes are discussed.

Modelling the surface free energy parameters of polyurethane coats—part 1. Solvent-based coats obtained from linear polyurethane elastomers

Polyurethane elastomers coating were synthesised by using typical diisocyanates, polyether and polyester polyols and HO-tertiary amines or diols as a chain extenders. Mole fractions of structural fragments (κexp) responsible for the polar interactions within polyurethane chains were calculated by 1H NMR method. Obtained results were confronted with the analogous parameter values (κtheor) calculated on the basis of process stoichiometry, considering the stage of the production of isocyanate prepolymers and reaction of their extension for polyurethanes. Trials of linear correlation between the κexp parameters and surface free energy (SFE) values of investigated coatings were presented. SFE values were determined by Owens–Wendt method, using contact angles measured with the goniometric method. Based on achieved results, another empirical models, allowing for prediction the influence of the kind of polyurethane raw materials on SFE values of received coatings were determined. It was found that it is possible to regulate the SFE in the range millijoules per cubic metre by the selection of appropriate substrates. It has been found that use of 2,2,3,3-tetrafluoro-1,4-butanediol as a fluorinated extender of prepolymer chains is essential to obtain coatings with increased hydrophobicity, applied among others as biomaterials—next to diphenylmethane diisocyanate and polyoxyethylene glycol.

Kinetic Models of the Polymerization of an AB2 Monomer

Two mean-field kinetic models of the polymerization of an AB 2 monomer that lead to hyperbranched polymers are presented. The first model deals with oranched molecules only and constitutes a new yersion of the Flory theory. Its modification, which takes into account ring formation, is the second model. Preliminary results of the application of the models are shown and discussed.

Methods of narrowing the molecular size distribution in hyperbranched polymerization involving AB2 and B2 monomers

A kinetics model was developed describing the time evolution of the molecular size distribution in hyperbranched condensation polymerization of monomers AB2 and B2 (A and B are functional groups). The rate equations derived from the model were used to calculate moments of the distribution of polymer species. The calculation procedure was adjusted to simulate introduction of fresh AB2 monomer into the polymerization reactor in equal portions, with each portion introduced after the previous one reached a predetermined conversion degree. The core monomer B2 was introduced with the first portion. The calculation procedure also made it possible to subtract unreacted monomer from the system. This was yet another method of narrowing the molecular size distribution of polymers in addition to the feed scheme. Dedicated to Professor John L. Stanford on the occasion of his 60th birthday.

An algorithm for Monte Carlo modeling of degradation of polymer networks

Abstract An algorithm for Monte Carlo simulation of polymer network degradation has been devised. The object was a random nearly regular molecular graph with almost all vertices of degree three. The vertices represented units of the polymer and edges were bonds or subchains of the network. The algorithm was particularly designed to study the effect of the substitution degree of units on the degradation process. The abrupt change of molecular parameters observed at a certain extent of degradation was referred to as the gel–sol transition. The position of the transition depended on the rate constants modeling the effect of units substitution.

Modelling of hyper-branched and network polymerisation

Two basic groups of models of polymerisation, the classical, known as the Flory-Stockmayer models, and the computer based ones which are in fact Monte-Carlo simulation techniques are briefly reviewed. The notion of time correlations is explained. Four versions of kinetic modelling of hyperbranched polymerisation are presented.

Monte-Carlo modeling of degradation of polymer networks

Abstract The degradation of polymer networks was studied by using Monte-Carlo simulations. The graph-like, nearly regular network of three-functional units was first randomly generated and then degraded by splitting bonds at random. The effect of the substitution degree of units on the composition of the system, at various stages of degrdation, was of particular interest. The substitution effect was modified by changing elementary rate constants by which the bond between units of given substitution degree underwent scission. A rapid change of molecular parameters describing the system, such as the averages of polymerization degree, gel content etc., was observed at a certain stage of network degradation. This gel–sol transition occurred at different extents of reaction depending on the values of elementary rate constants.

Monte Carlo modeling of degradation of polymer networks: 2. Highly branched molecules

Abstract A Monte Carlo study on the degradation of highly branched polymer molecules is presented. The starting molecules were regular dendrimers with 10 5 units. The algorithm of simulations was similar to that used for modeling degradation of polymer networks described in the first part of the series. In the degradation of the large acyclic molecules, similarly as for networks, an abrupt transition was observed. It resembled a reversed sol–gel transition. Its position on conversion scale as well as other size distribution related parameters of the system depended on the kinetics of bond scission.

Kinetic and Monte-Carlo modelling of hyperbranched polymerisation

Abstract After some comments on the size and conformation of dendrimer molecules, models of the polymerisation of AB2 monomers that leads to hyperbranched polymers are reviewed. The models are (i) a kinetic one that takes into account changes in the reactivity of B groups as well as intramolecular reactions, and (ii) the equivalent Monte-Carlo model. The results of application of the kinetic model to the polymerisation system AB2 + B3 are also presented.

Off-lattice long-range percolation modelling of a network polymerisation

A system involving homopolymerisation of a 3-functional monomer has been studied by using an off-lattice long-range percolation model. The elementary reaction steps were controlled by substitution effects and by local concentrations of units. The latter were controlled by setting a constant value to a range-of-reaction parameter called the capture radius. The critical conversion at gelation in the system turned to the classical one as the value of capture radius increased.