Kinetics and Thermodynamics of Radical Polymerization

F. EHLERS, J. BARTH AND P. VANA

Georg-August-University of Göttingen, Institute of Physical Chemistry, Tammannstr. 6, D-37077 Göttingen, Germany

1.1 Introduction

Radical polymerization processes are of great scientific and economic importance. Knowledge about their kinetic principles is a prerequisite for the efficient synthesis of a wide range of polymeric products. Since the dawn of macromolecular chemistry in the 1920's, the study of these principles has been a central topic of academic research. Although a radical polymerization process is basically constituted by just four types of reactions, which are initiation, propagation, transfer and termination, the coupled nature of these reactions leads to a complexity that makes it difficult to determine the individual rate constants and to evaluate their effects on the properties of the final polymer, like its molecular weight distribution. Scheme 1.1 shows a set of fundamental reaction equations for a radical polymerization process.

There is a kinetic rate law expression for each of these reactions. Determination of the corresponding rate coefficients is the main task of all kinetic experiments in this field. The employed experimental techniques can roughly be separated into two classes: one approach focuses on accurate measurements of the overall polymerization rate or time-resolved species concentration, while the other one is based on the analysis of the resulting molecular weight distributions. Provided that all relevant rate coefficients for a certain polymerizing system are known, it is possible to make precise predictions about the kinetics of the entire process, and therefore also about the molecular weight distribution. Today, computer simulations are an important tool in polymer research, allowing for precise numerical simulations of even very complex polymerizing systems and thus contributing to a deeper understanding of radical polymerization kinetics.

The intention of the following chapter is to give a general overview of our knowledge about the kinetics of conventional radical polymerization and its implications for the process and the formed product. This basic knowledge is also mandatory for the understanding and optimization of controlled polymerization processes.

1.2 Initiation

For a radical polymerization to occur, the first thing needed are free radicals. These are initially provided by some agent, the initiator, during the reaction step called initiation. The initiation step is commonly characterized by two coefficients, the initiation rate coefficient ki and the initiator efficiency [Florin]. Knowledge of these parameters is of crucial importance for both industrial applications and theoretical studies of radical polymerizations.

The vast majority of initiators belong to one of two groups, thermal initiators or photoinitiators. Thermal initiators form radical species upon heating, while photoinitiators decompose when exposed to visible or UV light. While in commercial processes mainly thermal initiators are used, kinetic studies are preferentially performed using photoinitiators. This is because the irradiation can precisely be timed, defining a sharp starting point for the polymerization reaction. A general scheme for the decomposition reaction, regardless of the type of initiator, is given in Scheme 1.2.

The initiator (I) decay, be it caused by light absorption or heating, follows a first order rate law:

- dcI/dt = kdcI (1.1)

For the polymerization kinetics, the initiator concentration is not the important quantity. More important is the concentration of primary radicals formed by the initiation process. The rate Rd of formation of radicals that can start chain growth can be expressed by the following first order rate law:

Rd = dcI•/dt = 2[Florin] dcI/dt = 2[Florin]kdcI (1.2)

where kd is the rate coefficient for the initiator decomposition reaction, and [Florin] is the initiator efficiency. Integration of eqn (1.2) leads to the following expression, showing the exponential decrease of initiator concentration with time:

[MATHEMATICAL EXPRESSION OMITTED] (1.3)

Initiator decay alone is not sufficient to start a new polymer chain. The formed radical has to react with a monomer unit. Right after decay, the (usually two) freshly formed radicals I1• and I2• are still in close proximity of each other and surrounded by solvent molecules. The primary radicals' ability to leave the solvent cage unreacted and then react with a monomer is expressed by the initiator efficiency [Florin], with values ranging from zero (no initiation) to unity. In a real system, not every primary radical will actually start a polymer chain. Radicals can recombine before leaving the solvent cage or undergo a side reaction before they encounter a monomer molecule. Typically, [Florin] has a value between 0.5 and 0.8 and depends on the viscosity of the system, indicating that the diffusion-controlled escape from the solvent cage is the crucial factor.

If the initiator molecule is asymmetric, i.e. I1• ≠ I2•, the formed radical species generally do not show identical reactivity towards the monomer. Thus, the initiation process will take on the form shown in Scheme 1.3, where M indicates a monomer molecule, R1• refers to a macroradical of chain length 1 and ki(1) and ki(2) refer to the rate coefficients of initiation for the respective initiator fragments. The overall rate of initiation, Ri, can be calculated according to eqn (1.4):

[MATHEMATICAL EXPRESSION OMITTED] (1.4)

The rate coefficient of initiation ki can be expressed as the arithmetic mean of the coefficients for the individual fragments, since [MATHEMATICAL EXPRESSION OMITTED]

Ri = kicMcI• with ki = ki(1) + ki(2)/2 (1.5)

1.2.1 Thermal Initiation

There are mainly two types of thermally activated initiators: azo-type, and peroxy-type. Their general structures are shown in Scheme 1.4.

Thermal initiators decompose in a first order reaction upon heating, displaying a characteristic half life at a certain temperature. It is correlated to the decomposition rate coefficient by eqn (1.6). The half-life, t1/2, is the amount of time it takes for half of a sample of initiator to decompose.

t1/2 = ln...