Diffusion-controlled polymer reactions

The bulk polymerization of acrylonitrile in this range of temperatures exhibits kinetic features very similar to those observed with acrylic acid (cf. Table I). The very low over-all activation energies (11.3 and 12.5 Kj.mole-l) found in both systems suggest a high temperature coefficient for the termination step such as would be expected for a diffusion controlled bimolecular reaction involving two polymeric radicals. It follows that for these systems, in which radicals disappear rapidly and where the post-polymerization is strongly reduced, the concepts of nonsteady-state and of occluded polymer chains can hardly explain the observed auto-acceleration. Hence the auto-acceleration of acrylonitrile which persists above 60°C and exhibits the same "autoacceleration index" as at lower temperatures has to be accounted for by another cause. 

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. 

Stage (2) Diffusion control the reaction proceeds heterogeneously, reflecting the restricted molecular motion of the matrix polymer. 

The study of molecular dynamics in polymers is of crucial importance in the understanding of processes in which diffusion is involved. Examples of such processes are diffusion-controlled chemical reactions, sorption-extraction, dissolution, interactions across polymer-polymer interfaces, etc. This has been a very active area of research, especially during the past few years, due to new theoretical proaches and the development and refinement of experimental techniques. Different polymer systems have been used to test the theoretical predictions based on scaling methods. One of these systems is poly(dimethylsiloxane) (PDMS). Other factors have also contributed to the interest in studying the molecular dynamics of PDMS. " Siloxane polymers have widespread commercial applications,... 

Most radicals are transient species. They (e.%. 1-10) decay by self-reaction with rates at or close to the diffusion-controlled limit (Section 1.4). This situation also pertains in conventional radical polymerization. Certain radicals, however, have thermodynamic stability, kinetic stability (persistence) or both that is conferred by appropriate substitution. Some well-known examples of stable radicals are diphenylpicrylhydrazyl (DPPH), nitroxides such as 2,2,6,6-tetramethylpiperidin-A -oxyl (TEMPO), triphenylniethyl radical (13) and galvinoxyl (14). Some examples of carbon-centered radicals which are persistent but which do not have intrinsic thermodynamic stability are shown in Section 1.4.3.2. These radicals (DPPH, TEMPO, 13, 14) are comparatively stable in isolation as solids or in solution and either do not react or react very slowly with compounds usually thought of as substrates for radical reactions. They may, nonetheless, react with less stable radicals at close to diffusion controlled rates. In polymer synthesis these species find use as inhibitors (to stabilize monomers against polymerization or to quench radical reactions - Section 5,3.1) and as reversible termination agents (in living radical polymerization - Section 9.3). 

After polarization to more anodic potentials than E the subsequent polymeric oxidation is not yet controlled by the conformational relaxa-tion-nucleation, and a uniform and flat oxidation front, under diffusion control, advances from the polymer/solution interface to the polymer/metal interface by polarization at potentials more anodic than o-A polarization to any more cathodic potential than Es promotes a closing and compaction of the polymeric structure in such a magnitude that extra energy is now required to open the structure (AHe is the energy needed to relax 1 mol of segments), before the oxidation can be completed by penetration of counter-ions from the solution the electrochemical reaction starts under conformational relaxation control. So AHC is the energy required to compact 1 mol of the polymeric structure by cathodic polarization. Taking... 

It is appropriate to differentiate between polymerizations occuring at temperatures above and below the glass transition point(Tg) of the polymer being produced. For polymerizations below Tg the diffusion coefficients of even small monomer molecules can fall appreciably and as a consequence even relatively slow reactions involving monomer molecules can become diffusion controlled complicating the mechanism of polymerization even further. For polymerizations above Tg one can reasonably assume that reactions involving small molecules are not diffusion controlled, except perhaps for extremely fast reactions such as those involving termination of small radicals. 

The remaining problem in the model development is to estimate the decrease in kp as a function of conversion. As the reaction proceeds beyond the point of chain entanglement, a critical conversion is reached where the propagation reaction becomes diffusion controlled and kp begins to fall with further increase in polymer concentration. At the critical conversion, one may write... 

As the polymerization reaction proceeds, scosity of the system increases, retarding the translational and/ or segmental diffusion of propagating polymer radicals. Bimolecular termination reactions subsequently become diffusion controlled. A reduction in termination results in an increase in free radical population, thus providing more sites for monomer incorporation. The gel effect is assumed not to affect the propagation rate constant since a macroradical can continue to react with the smaller, more mobile monomer molecule. Thus, an increase in the overall rate of polymerization and average degree of polymerization results. 

The gel time of a 2000 ppm Flocon 4800 (a Pfizer xanthan polymer) in 2% NaCl solution was measured with various Cr(III) crosslinkers at room temperature (Table II). In this series of experiments Cr(III) concentration was 90 ppm. The most reactive Cr(III) species were dates derived from Cr(N0 )g with one and two equivalents of NaOH. Gels formed within 5 minutes and the reaction rate appeared to be diffusion-controlled. Cr(N03)3 without NaOH required 48 hours to gel the polymer solution. This reflects the time needed to hydrolyze CrCNOg) in Equation 3. 

Several assumptions were made in order to analyze kinetic data in terms of this expression (2). First it was assumed that k 2 m kj, k2 k 3, and kj/k j k /k ( - If). Second it was assumed that the rate constants were independent of the extent of reaction i.e., that all six functional groups were equally reactive and that the reaction was not diffusion controlled. The concentration of polymer hydroxyl functionality was determined experimentally using infrared spectroscopy as described elsewhere (7). A major unknown is the instantaneous concentration of methanol. Fits to the kinetic data were made with a variety of assumptions concerning the methanol concentration. The best fit was achieved by assuming that the concentration of methanol was initally constant but decreased at a rate proportional to the concentration of residual polymer hydroxy groups towards the end of the reaction. As... 

Several carbonyl-containing peroxide additives have been shown to increase the initial rate of the nonoxidative photo-dehydrochlorination of PVC (54). In studies with polymeric ketones unrelated structurally to PVC, the excited singlet and triplet states of the carbonyl groups in these polymers were found to sensitize 0-0 homolysis at rates approaching diffusion control (55). Similar reactions may well occur in oxidized vinyl chloride polymers. 

Diffusion of particles in the polymer matrix occurs much more slowly than in liquids. Since the rate constant of a diffusionally controlled bimolecular reaction depends on the viscosity, the rate constants of such reactions depend on the molecular mobility of a polymer matrix (see monographs [1-4]). These rapid reactions occur in the polymer matrix much more slowly than in the liquid. For example, recombination and disproportionation reactions of free radicals occur rapidly, and their rate is limited by the rate of the reactant encounter. The reaction with sufficient activation energy is not limited by diffusion. Hence, one can expect that the rate constant of such a reaction will be the same in the liquid and solid polymer matrix. Indeed, the process of a bimolecular reaction in the liquid or solid phase occurs in accordance with the following general scheme [4,5] ... 

Abstract. Auto-accelerated polymerization is known to occur in viscous reaction media ("gel-effect") and also when the polymer precipitates as it forms. It is generally assumed that the cause of auto-acceleration is the arising of non-steady-state kinetics created by a diffusion controlled termination step. Recent work has shown that the polymerization of acrylic acid in bulk and in solution proceeds under steady or auto-accelered conditions irrespective of the precipitation of the polymer. On the other hand, a close correlation is established between auto-acceleration and the type of H-bonded molecular association involving acrylic acid in the system. On the basis of numerous data it is concluded that auto-acceleration is determined by the formation of an oriented monomer-polymer association complex which favors an ultra-fast propagation process. Similar conclusions are derived for the polymerization of methacrylic acid and acrylonitrile based on studies of polymerization kinetics in bulk and in solution and on evidence of molecular associations. In the case of acrylonitrile a dipole-dipole complex involving the nitrile groups is assumed to be responsible for the observed auto-acceleration. 

Kinetic experiments and rigorous modelling of the mass-transfer controlled polycondensation reaction have shown that even at low melt viscosities the diffusion of EG in the polymer melt and the mass transfer of EG into the gas phase are the rate-determining steps. Therefore, the generation of a large surface area is essential even in the prepolycondensation step. 

In the H-shaped tube, all processes take place in a slow, controlled way. One simple modification consists of separating the two halves of the H-shaped tnbe with a fitted glass disk (medium, fine, or ultra-fine porous) to slowdown the diffusion. Another modification involves diffusion inside the reaction solvent containing a polymer. In this case, diffusion is retarded due to an increase of the solution viscosity (Scott et al. 1974, Berg et al. 1976). Sometimes, the synthesis of ion-radical salts is conducted ultrasoni-cally if the starting materials are insoluble in the desired solvents (see, e.g., Neilands et al. 1997). 

Other than in polymer matrix composites, the chemical reaction between elements of constituents takes place in different ways. Reaction occurs to form a new compound(s) at the interface region in MMCs, particularly those manufactured by a molten metal infiltration process. Reaction involves transfer of atoms from one or both of the constituents to the reaction site near the interface and these transfer processes are diffusion controlled. Depending on the composite constituents, the atoms of the fiber surface diffuse through the reaction site, (for example, in the boron fiber-titanium matrix system, this causes a significant volume contraction due to void formation in the center of the fiber or at the fiber-compound interface (Blackburn et al., 1966)), or the matrix atoms diffuse through the reaction product. Continued reaction to form a new compound at the interface region is generally harmful to the mechanical properties of composites. 

Then, they depend also on the viscosity of the system. Specific diffusion control is characteristic of fast reactions like fluorescence quenching. In polymer formation, specific diffusion control is responsible for the acceleration of chain polymerization due to the retardation of the termination by recombination of two macroradicals (Trommsdorff effect). Step reactions are usually too slow to exhibit a dependence on translational diffusion also, the temperature dependence of their rate constants is of the Arrhenius type. 

It seems that the simulation of diffusion controlled reactions of groups on polymer chains developed by Muthukumar et al. ( ) that takes into account the bond formation by determined conformational rearrangement, can be adapted for the equilibrium situation, i.e. for systems controlled by pure chemical kinetics. 

When the encounter probability of reactive groups and the rate of reaction becomes controlled by the segmental mobility (viscosity of the medium), overall diffusion control sets In. The overall diffusion control is typical of polymer systems In which, as a result of the chemical reaction, the system passes from the liquid (rubbery) state Into the glassy state. 

---