Hidetaka Tobita

Crosslinking kinetics in polyacrylamide networks

Kinetics of network formation in free-radical copolymerization of acrylamide and N,N′-methylenebis-acrylamide in aqueous solution (56.6 g comonomer per litre) at 25°C have been studied. It was found that as high as 80% of pendant double bonds are consumed immediately on polymerization and are wasted in primary cyclization. Primary cyclization is responsible for the delay in the onset of gelation at low mole fractions of divinyl monomer. The effects of decreased reactivity of pendant double bonds and secondary cyclization become significant as the mole fraction of divinyl monomer increases. The decreased reaction rate between huge molecules due to steric hindrance in the pre-gelation period contributes to microgel formation, and consequently to formation of spatially inhomogeneous networks.

Control of network structure in free-radical crosslinking copolymerization

Abstract A kinetic model which describes the network structure development during free-radical crosslinking copolymerization is proposed. The model was successfully applied to various batch copolymerization systems such as methyl methacrylate/methylene glycol dimethacrylate, styrene p- divinylbenzene , styrene/ethylene glycol dimethacrylate, and acrylamide N,N′- methylene-bis-acrylamide . The model calculations suggest that polymer networks synthesized by free-radical copolymerization are, in general, inhomogeneous at least on a microscopic scale. This model can be used to control the network structure, and a semi-batch policy to produce homogeneous polymer networks is proposed.

Simultaneous long‐chain branching and random scission: I. Monte Carlo simulation

In free-radical olefin polymerizations, the polymer transfer reactions could lead to chain scission as well as forming long-chain branches. For the random scission of branched polymers, it is virtually impossible to apply usual differential population balance equations because the number of possible scission points is dependent on the complex molecular architecture. On the other hand, the present problem can be solved on the basis of the probability theory by considering the history of each primary polymer molecule in a straightforward manner. The random sampling technique is used to solve this problem and a Monte Carlo simulation method is proposed. In this simulation method, one can observe the structure of each polymer molecule formed in this complex reaction system, and virtually any structural information can be obtained. In the illustrative calculations, the full molecular weight distribution development, the gel point determination, and examples of two- and three-dimensional polymer structure are shown.

Microgel formation in emulsion polymerization

A typical behavior of microgel formation in emulsion polymerization, where a sufficient amount of crosslinker exists and no coagulation of particles occurs, is considered both theoretically and experimentally. It was found that the crosslinked polymer formation in emulsion polymerization is significantly different from that in homogeneous media. The important characteristics can be summarized as follows. (1) The crosslinking density level is fairly high even from very early stages of polymerization, (2) the weight-average molecular weight increases just linearly with monomer conversion, and (3) the formed molecular weight distribution (MWD) is rather narrow and the distribution shifts to larger molecular weights with preserving the narrow profile as polymerization proceeds. In a typical microgel formation in emulsion polymerization, each polymer particle essentially consists of a single crosslinked polymer molecule once stable polymer particles are formed.

Simulation model for the modification of polymers via crosslinking and degradation

Abstract The Monte Carlo sampling technique, in which polymers are sampled randomly from an infinite number of polymer molecules in the reaction system, is used to make computer simulations for the molecular-weight distribution (MWD) change during crosslinking and degradation processes. In this method, since one can investigate each polymer molecule directly, very detailed structural information can be easily obtained. This present method is not restricted by the condition of long primary chains with a low degree of crosslinking and degradation, and it is also straightforward to account for the effect of the residence time distribution. When the initial MWD is extremely narrow, say Pw/Pn

Size exclusion chromatography of branched polymers : Star and comb polymers

Monte Carlo simulations were conducted to estimate the elution curve of size exclusion chromatography (SEC). The present simulation can be applied to various types of branched polymers, as long as the kinetic mechanism of nonlinear polymer formation is given. We considered two types of detector systems, (1) a detector that measures the polymer concentration in the elution volume to determine the calibrated molecular weights, such as by using the differential refractive index detector (RI), and (2) a detector that determines the weight-average molecular weight of polymers within the elution volume directly, such as a light scattering photometer (LS). For polydisperse star polymers, both detector systems tend to give a reasonable estimate of the true molecular weight distribution (MWD). On the other hand, for comb-branched polymers, the RI detector underestimates the molecular weight of branched polymers significantly. The LS detector system improves the measured MWD, but still is not exact. The present simulation technique promises to establish various types of complicated reaction mechanisms for nonlinear polymer formation by using the SEC data quantitatively. In addition, the present technique could be used to reinvestigate a large amount of SEC data obtained up to the present to estimate the true MWD.

Branched structure formation in free radical polymerization of vinyl acetate

The branched structure formation during free radical polymerization of vinyl acetate is investigated in detail by application of the computer simulations on the basis of the Monte Carlo sampling technique. Simulations are made for the whole molecular weight distribution (MWD), the MWDs for polymer molecules containing 0, 1, 2, 3, etc., branch points, the branching density as functions of both size and the number of branch points, the spatial distribution of the branched chains, etc. It was found that the effect of polyradicals on the formed MWD could be neglected for batch polymerizations of the present reaction system. A large number of relatively small branch chains are formed due to both chain transfer to polymer (CTP) and the terminal double-bond polymerization (TDBP). The radius of gyration at a Θ state is found to agree satisfactorily with the Zimm-Stockmayer equation for random branching in spite of the heterogeneous branched structure formed in the polymerization. The present investigation reveals important characteristics of the complex molecular structure formation during free radical polymerization that involves both CTP and TDBP.

Monte Carlo simulation of size exclusion chromatography for randomly branched and crosslinked polymers

The elution curves of size exclusion chromatography for nonlinear polymers formed through random branching and crosslinking of long polymer chains were simulated with a Monte Carlo method. We considered two types of measured molecular weight distributions (MWDs): (1) the MWD calibrated relative to standard linear polymers and (2) the MWD obtained with a light scattering (LS) photometer in which the weight-average molecular weight of polymers within the elution volume is determined directly. The calibrated MWDs clearly underestimate the molecular weights for both randomly branched and crosslinked polymers, and this technique can be used to assess the degree of deviation from the true MWD. When the primary chains conform to the most probable distribution, the calibrated MWD can be estimated reasonably well with the Zimm–Stockmayer equation for the g factor with the help of the relationship between the average number of branch points per molecule and the degree of polymerization. However, the LS method gives good estimates of the true MWD for both randomly branched and crosslinked polymers, although the agreement is better for the branched ones.

Kinetics of long-chain branching in emulsion polymerization: 1. Chain transfer to polymer

Abstract New simulation models to predict the molecular weight distribution in emulsion polymerization that includes chain transfer to polymer are proposed. When the frequency of branching is not very large, the kinetics of emulsion polymerization can be modelled effectively as a large number of semibatch reactors as long as monomer droplets exist and of batch reactors after the disappearance of monomer droplets. In such cases, a simulation method based on the branching density distribution proposed earlier for non-linear polymerizations in homogeneous media shows its versatility to describe the kinetics of non-linear emulsion polymerization. However, the calculated results based on a direct simulation model that simulates all polymer molecules in each polymer particle clearly show that the fact that each polymer particle consists of a limited number of polymer molecules must be accounted for as the branching density increases. In general, such compartmentalization effects are important when one considers the molecular weight distribution development of non-linear polymer chains that are formed in emulsion polymerization.

Molecular weight distribution formed through chain-length-dependent crosslinking reactions

The molecular weight distribution formed through chain-length-dependent crosslinking reactions in free-radical vinyl/divinyl copolymerization is investigated by using Monte Carlo simulations. When the crosslinking reaction rates for larger polymer molecules are reduced, the high molecular weight tails cannot extend smoothly, resulting in distorted, sometimes bimodal distribution profiles, which exhibit qualitative similarity with those reported experimentally. Although the reduced crosslinking reaction rates between larger polymer molecules may not affect the average crosslinking density levels significantly, they can delay the developments of the weight-average molecular weight significantly. Because the wastage of pendant double bonds through cyclization would result in a similar tendency, one cannot distinguish these two types of non-idealities through the measurements of the pendant double bond consumption and the average molecular weight development.