Polymerization kinetic theory

Copolymer composition can be predicted for copolymerizations with two or more components, such as those employing acrylonitrile plus a neutral monomer and an ionic dye receptor. These equations are derived by assuming that the component reactions involve only the terminal monomer unit of the chain radical. The theory of multicomponent polymerization kinetics has been treated (35,36). 

The effects of solvent on reactivity ratios and polymerization kinetics have been analyzed for many copolymerizations in terms of this theory.98 These include copolymerizations of S with MAH,"7 118 S with MAA,112 S with MMA,116 117 "9 121 S with HEMA,122 S with BA,123,124 S with AN,103415 125 S with MAN,112 S with AM,11" BA with MM A126,127 and tBA with HEMA.128 It must, however, be pointed out that while the experimental data for many systems are consistent with a bootstrap effect, it is usually not always necessary to invoke the bootstrap effect for data interpretation. Many authors have questioned the bootstrap effect and much effort has been put into finding evidence both for or against the theory.69 70 98 129 "0 If a bootstrap effect applies, then reactivity ratios cannot be determined by analysis of composition or sequence data in the normal manner discussed in Section 7.3.3. 

A shift in the velocity constant such as is observed in bulk esterification is the exception rather than the rule. A source of more general concern is the enormous increase in viscosity which accompanies polymerization. Both theory and experimental results indicate that this factor usually is of no importance except under the extreme conditions previously mentioned. Consequently, the velocity coefficient usually remains constant throughout the polymerization (or degradation) process. Barring certain abnormalities which enter when the velocity coefficient is sensitive to the environmental changes accompanying the polymerization process, application of the ordinary methods of chemical kinetics to polymerizations and other processes involving polymer molecules usually is permissible. 

The polymer self-assembly theory of Oosawa and Kasai (1962) provides valuable insights into the nature of the nucleation process. The polymerization nucleus is considered to form by the accretion of protomers, but the process is highly cooperative and unfavorable. Indeed, this is strongly suggested by the observation that thousands of actin or tubulin protomers are found in F-actin and microtubule structures if nucleation of self-assembly were readily accomplished and highly favorable, the consequence would be that many more fibers of shorter polymer length would be observed. The Oosawa kinetic theory for nucleation permits one to obtain information about the size of the polymerization nucleus if two basic assumptions can be satisfied in the experimental system. First, the rate of nuclei formation is assumed to be proportional to the loth power of the protomer concentration with io representing the number of protomers required to create the nucleus. Second, the treat-... 

Bird RB, Hassager O, Armstrong RC, Curtiss CF (1977) Dynamics of polymeric liquids Vol 2 Kinetic theory, J. Wiley, New York... 

William Russel May I follow up on that and sharpen the issue a bit In the complex fluids that we have talked about, three types of nonequilibrium phenomena are important. First, phase transitions may have dynamics on the time scale of the process, as mentioned by Matt Tirrell. Second, a fluid may be at equilibrium at rest but is displaced from equilibrium by flow, which is the origin of non-Newtonian behavior in polymeric and colloidal fluids. And third, the resting state itself may be far from equilibrium, as for a glass or a gel. At present, computer simulations can address all three, but only partially. Statistical mechanical or kinetic theories have something to say about the first two, but the dynamics and the structure and transport properties of the nonequilibrium states remain poorly understood, except for the polymeric fluids. 

Although there have been several references on the theory of emulsion polymerization kinetics, it is surprising that its commercial importance and multiphase kinetics have not generated more interest. Smith and Ewart (46) predicted a constant rate of polymerization per particle, based on initiation in the water phase and three ranges of radical concentration per particle. Van der Hoff (55) confirmed this for concentrations... 

There is a close connection between molecular mass, momentum, and energy transport, which can be explained in terms of a molecular theory for low-density monatomic gases. Equations of continuity, motion, and energy can all be derived from the Boltzmann equation, producing expressions for the flows and transport properties. Similar kinetic theories are also available for polyatomic gases, monatomic liquids, and polymeric liquids. In this chapter, we briefly summarize nonequilibrium systems, the kinetic theory, transport phenomena, and chemical reactions. 

---