Polymer chains chemical kinetics

The chemical mechanisms of transition metal catalyses are complex. The dominant kinetic steps are propagation and chain transfer. There is no termination step for the polymer chains, but the catalytic sites can be activated and deactivated. The expected form for the propagation rate is... 

The combined results of kinetic studies on condensation polymerization reactions and on the degradation of various polymers by reactions which bring about chain scission demonstrate quite clearly that the chemical reactivity of a functional group does not ordinarily depend on the size of the molecule to which it is attached. Exceptions occur only when the chain is so short as to allow the specific effect of one end group on the reactivity of the other to be appreciable. Evidence from a third type of polymer reaction, namely, that in which the lateral substituents of the polymer chain undergo reaction without alteration in the degree of polymerization, also support this conclusion. The velocity of saponification of polyvinyl acetate, for example, is very nearly the same as that for ethyl acetate under the same conditions. ... 

Although many different processes can control the observed swelling kinetics, in most cases the rate at which the network expands in response to the penetration of the solvent is rate-controlling. This response can be dominated by either diffu-sional or relaxational processes. The random Brownian motion of solvent molecules and polymer chains down their chemical potential gradients causes diffusion of the solvent into the polymer and simultaneous migration of the polymer chains into the solvent. This is a mutual diffusion process, involving motion of both the polymer chains and solvent. Thus the observed mutual diffusion coefficient for this process is a property of both the polymer and the solvent. The relaxational processes are related to the response of the polymer to the stresses imposed upon it by the invading solvent molecules. This relaxation rate can be related to the viscoelastic properties of the dry polymer and the plasticization efficiency of the solvent [128,129],... 

The prime objective of this concise review is to provide an illustration of the interaction of these two disciplines using particular examples. In choosing the examples, we seek to demonstrate the potentialities of the conformation-dependent design of the sequences of monomeric units in heteropolymer macromolecules. Under such a design, their chemical structure is controlled not only by the kinetic parameters of a reaction system but also by the conformational statistics of polymer chains. 

As pointed out in the foregoing, there are two specific peculiarities qualitatively distinguishing these systems from the classical ones. These peculiarities are intramolecular chemical inhomogeneity of polymer chains and the dependence of the composition of macromolecules X on their length l. Experimental data for several nonclassical systems indicate that at a fixed monomer mixture composition x° and temperature such dependence of X on l is of universal character for any concentration of initiator and chain transfer agent [63,72,76]. This function X(l), within the context of the theory proposed here, is obtainable from the solution of kinetic equations (Eq. 62), supplemented by thermodynamic equations (Eq. 63). For heavily swollen globules, when vector-function F(X) can be presented in explicit analytical form... 

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. 

The simplest mechanisms leading to the dispersion (spreading) of a zone s molecules can be described by the classical random-walk model [9], as noted in Section 5.3. However this model does not fully account for the complexities of migration. It gives, instead, a simple approximation which inherits the most essential and important properties (foremost of all the randomness) of the real migration process. The random-walk model has been used in a similar first-approximation role in many fields (chemical kinetics, diffusion, polymer chain configuration, etc.) and is thus important in its own right. 

For example, under kinetic modeling of "living" anionic copolymerization in the framework of the terminal model, a macromolecule is associated with the realization of a certain stochastic process. Its states (a,r) are monomeric units, each being characterized along with chemical type a and also by some label r. This random quantity equals the moment when this monomeric unit entered in a polymer chain as a result of the addition of o-type monomer to the terminal active center. It has been... 

From their chemical architectures the gel-type resins can be classified as belonging to one of two different types of solid supports. For hghtly crosshnked polystyrene and polyacrylamide resins the reactive sites are located along the polymer chains in a statistical manner. Reaction kinetics can be expected that are sinnilar to those associated with a soluble polystyrene that was proposed by Shemiakin et al.f l for peptide synthesis. However, reaction rates were found to depend on the location of the reactive sites on such linear noncrosslinked polystyrenes. In fact, reactive sites located on a flexible polymer loop should exhibit a different kinetic behavior to those close to a more rigid, crosshnked section. 

The majority of existing theories can neither determine precisely the size and the microstructure of kinetic units in a polymer chain of a given chemical structure nor rigorously predict the mechanisms and the kinetics of conformational transitions. In these theories, the properties of kinetic units are postulated and the aim of the theory is to study the effects resulting from the linking of these units into the chain. 

The physical reasons for the appearance of relaxation spectra in polymer chains can differ. They comprise 1) the cooperative character of the motion of a multiparticle polymer chain, 2) the anisotropy of the shape of a kinetic chain segment and consequently the appearance of several relaxation times, 3) the chemical and structural heterogeneity of the chain (copotymers, structurized macromolecules, polymers with ade chains, etc., and cross-linked and branched-chain systems). 

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