Diffusion controlled homogeneous polymer reactions

Most chemical reactions require two reactant molecules to come into close proximity before they can react with each other. If the reactants are not initially in contact then the overall process involves two steps. First, the reacting molecules must move to be next to each other, and then chemical change may, or may not, occur. 

Many reactions in heterogeneous systems, such as at interfaces or in flow, are controlled by the rate at which the reactants can come together. However, there are also situations in homogeneous systems where diffusion is important. 

For the majority of reactions carried out in the gas phase or in a liquid, the molecules come together many times before the chemical change takes place. The rate of the reaction is then controlled by the rate of the chemical step. However, if a very fast chemical reaction is involved, or if the reaction takes place in a solid or semi-sohd medium, the approach diffusion step may be much slower than the chemical reaction. Then the overall process can occur only as fast as the molecules can come together. Any such reaction is said to be diffusion controlled. 

Many reactions of free radicals, of electronic excited states and of oppositely charged ions are found to be diffusion controlled in condensed phases. When these reactions involve polymeric reactants, or take place in a polymer medium, the diffusion step will be dependent on the nature of the polymer molecular motions in the reaction zone. 

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Usually or most widely applied, polymer latexes are made by emulsion polymerization [ 1 ]. Without any doubt, emulsion polymerization has created a wide field of applications, but in the present context one has to be aware that an inconceivable restricted set of polymer reactions can be performed in this way. Emulsion polymerization is good for the radical homopolymerization of a set of barely water-soluble monomers. Already heavily restricted in radical copolymerization, other polymer reactions cannot be performed. The reason for this is the polymerization mechanism where the polymer particles are the product of kinetically controlled growth and are built from the center to the surface, where all the monomer has to be transported by diffusion through the water phase. Because of the dictates of kinetics, even for radical copolymerization, serious disadvantages such as lack of homogeneity and restrictions in the accessible composition range have to be accepted. 

The attention paid to the polymer solid state is minimized in favour of the melt and in this chapter the static properties of the polymer are considered, i.e. properties in the absence of an external stress as is required for a consideration of the rheological properties. This is addressed in detail in Chapter 3. The treatment of the melt as the basic system for processing introduces a simplification both in the physics and in the chemistry of the system. In the treatment of melts, the polymer chain experiences a mean field of other nearby chains. This is not the situation in dilute or semi-dilute solutions, where density fluctuations in expanded chains must be addressed. In a similar way the chemical reactions which occur on processing in the melt may be treated through a set of homogeneous reactions, unlike the highly heterogeneous and diffusion-controlled chemical reactions in the solid state. 

According to the core-shell model, the growing particle is actually heterogeneous rather than homogeneous, and it consists of an expanding polymer-rich (monomer-starved) core surrounded by a monomer-rich (polymer-starved) outer spherical shell. It is the outer shell that serves as the major locus of polymerization and Smith-Ewart (on-off) mechanism prevails while virtually no polymerization occurs in the core because of its monomer-starved condition. Reaction within an outer shell or at the particle surface would be most likely to be operative for those polymerizations in which the polymer is insoluble in its own monomer or under conditions where the polymerization is diffusion-controlled such that a propagating radical cannot diffuse into the center of the particle. 

The generally-accepted sequence of reactions that are responsible for the chemical changes in a polyolefin on oxidation are shown in Figure 1. It is possible to associate an elementary rate equation with each reaction, although it is recognised that the true rates are difficult to measure both because of the physical state of the polymer, possible diffusion-controlled rate processes in the solid state and the many competing reactions. In a homogeneous rate model, this sequence of rate equations may be solved and a total reaction rate then fitted to the measured oxidation rate (3). 

The charge was introduced through oxidation of the excited polypyridyl complexes by an irreversible oxidant, 4-methoxybenzenediazonium tetrafluoroborate in acetonitrile solvent. Remarkably, the Ru excited states in the mixed-valent polymer were found not to be quenched by Ru or Os. This was attributed to the fact that these electron transfer reactions lie in the inverted region. This behavior differs from that found in homogeneous aqueous solution where excited state quenching is near diffusion controlled. Possibly the relative immobilization of the reactants on the polymer, along with the smaller value for Aout in acetonitrile, prevents their reaction at the separations and orientations at which electron transfer occurs in homogeneous solution. 

D. G. Smith, Non-ideal kinetics in free radical polymerization, J. Appl. Chem. 17, 339 (1967). A. M. North, Diffusion control of homogeneous free radical reactions, in Progress in High Polymers, Vol. II, J. C. Robb and F. W. Peaker (eds.), Heywood, London, 1968. 

North A.M. Diffusion Control of Homogeneous Free Radical Reactions, in J.C. Robb and EW Peaker (Eds.), Progress in High Polymers Volume 2, Heywood Books, London, 1968. 

Polymers are not homogeneous in a microscopic scale and a number of perturbed states for a dye molecule are expected. As a matter of fact, non-exponential decay of luminescence in polymer systems is a common phenomenon. For some reaction processes (e.g, excimer and exciplex formation), one tries to fit the decay curve to sums of two or three exponential terms, since this kind of functional form is predicted by kinetic models. Here one has to worry about the uniqueness of the fit and the reliability of the parameters. Other processes can not be analyzed in this way. Examples include transient effects in diffusion-controlled processes, energy transfer in rigid matrices, and processes which occur in a distribution of different environments, each with its own characteristic rate. This third example is quite common when solvent relaxation about polar excited states occurs on the same time scale as emission from those states. Careful measurement of time-resolved fluorescence spectra is an approach to this problem. These problems and many others are treated in detail in recent books (9,11), including various aspects of data analysis. 

Sherrington analyzed diffusion phenomena particularly in macroporous supports the reactivity of a polymer-supported group is substantially altered when compared to its value in homogeneous solution and experimental data may vary with the particle size of the support, its porosity, its crosslinking ratio and with the size of the reacting molecule. An important criterion to know if a reaction is diffusion controlled is whether its rate depends on the inverse of the radius of the particles. 

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