Kinetics units

In the present context the word termination is applied not to the breaking-off of a physical chain, i.e., the cessation of growth of a particular molecule, but to the complete destruction of a kinetic unit, which means the irreversible annihilation of one ion pair. This kinetic termination, which is a well-understood feature of radical polymerizations, is a comparatively rare event in cationic polymerizations it may occur in several different ways and in some systems not at all. 

The mutual termination of growing chains which prevails in radical polymerizations must be ruled out for all ionic systems in which the opposite ions form separate kinetic units because of the electrostatic repulsion between like ions. However, in solvents of low DC in which the growing end of the polymer chain consists of an ion pair, a mutual termination by interaction of two such ion pairs is at least conceivable. 

We have already introduced the idea that the primary particles of a dispersed system tend to associate into larger structures known as aggregates. The nature of the interparticle forces responsible for this aggregation is one of the most examined areas of colloid science. We defer our discussion of the aggregation (or coagulation) process until Chapter 13, but a few remarks about aggregates — the kinetic units that result from that process —and how their dimensions are represented quantitatively are in order at this time. 

We conclude this section with a brief discussion of the relatively large, positive values of AS°,C, which we have seen are primarily responsible for the spontaneous formation of micelles. At first glance it may be surprising that AS for Reaction (A) is positive after all, the number of independent kinetic units decreases in this representation of the micellization process. Since such a decrease results in a negative AS value, it is apparent that Reaction (A) is incomplete as a description of micelle formation. What is not shown in Reaction (A) is the aqueous medium and what happens to the water as micelles form. The water must experience an increase in entropy to account for the observed positive values for AS °,c. 

The easiest way to account for the effect of a medium is to consider the pseudochemical reaction illustrated in Figure 10.8a. The particles numbered 2 represent the dispersed phase, and those numbered 1 are the solvent. Note that both of the dispersed particles are of the same material in this reaction. In the initial condition, each dispersed particle and its satellite solvent particle comprise an independent kinetic unit. Figure 10.8a represents the process in which the two dispersed particles come together to form a doublet and the two solvent particles form a kinetically independent doublet. 

We noted above that proteins display essentially the same mobility both as free molecules and when adsorbed on carrier particles. Adsorption clearly increases the radius of the kinetic unit appreciably, so this effect on mobility is unexpected. One way to rationalize this result is to assume that the protein adsorbs on the surface with very little alteration of the shape it has in free solution. Next assume that it is the radius of these molecular protuberances rather than the overall radius of curvature of the carrier that governs the mobility. 

This model differs from Schwarz s2 who uses the single residue as kinetic unit in analogy to the Zimm-Bragg equilibrium model. His rate parameters satisfy, of course, Eq. (4), but in his case x y, x y. The... 

The results from Basic Protocol 1 are expected to be consistent with traditional initial velocity assumptions for enzyme kinetics (unit cl /). The assay, as presented, includes four time points (along with a zero-time value) in order to establish the relationship between reaction time and product formed. Representative data, demonstrating the hyperbolic nature of this relationship, are presented in Figure C1.2.3. In this case, only the initial time points at the lowest enzyme concentration are consistent with the linear initial velocity assumption. If... 

Around and above Tm, the decay of the B band becomes biexponential, because the prefactors (x — A2) and (A, — x) in Eq. (2.28) become comparable in magnitude. The fast initial decay corresponds to the equilibration part, and the slower second component corresponds to the decay of the equilibrated system. Of course, for this later time period, the equilibrated system behaves as a single kinetic unit (high-temperature region kBA > A + A and kAB > k + kB), and B and A bands have identical decay times given by Eq. (2.33) ... 

Important work on the kinetically interpreted vitrification process was done by Volkenshtein and Ptitsyn (1957), Wunderlich and coworkers (1964-1974) and Moynihan (1974-1978). They considered the vitrification process as a "chemical reaction" involving the passage of "kinetic units" (e.g. "holes") from one energy level to another. 

The majority of the different chemical and physical properties, as well as the morphology of microemulsions, is determined mostly by the micro-Brownian motions of its components. Such motions cover a very wide spectrum of relaxation times ranging from tens of seconds to a few picoseconds. Given the complexity of the chemical makeup of microemulsions, there are many various kinetic units in the system. Depending on their nature, the dynamic processes in the microemulsions can be classified into three types ... 

If one considers that the reptation process is dominant for linear chains, one has to imagine additional processes of diffusion for polymers with long branches. The experimental data suggest strongly, however, that the basic kinetic unit of the chain (whatever it is) is the same as for linear chains the Rouse-like A and B processes are still there, which are still strong imprints of the "tube". 

Reaction Conditions (Temp., °C) Kinetics (units sec., 1, kcal, mole) Ref. 

Just as the equilibrium conformational properties of macromolecules, the theory of which has been developed in well-known classical works by Kuhn, Flory, Volken-stein and others the kinetic properties of polymer chains can be determined by two main mechanisms of intramolecular mobility. First, it is the discrete rotational isomeric (rotameric) mechanism of mobility caused by the jump of small-chain segments (kinetic units) from certain energically stable allowed conformers into others is4-i6S) gg ond it is the continuous mechanism of motion deter-... 

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. 

Shape of Relaxation Spectrum and Evaluation of the Size of Kinetic Units... 

For all the models considered, the time dependence of the value 2(0 i characterized by a spectrum of relaxation times. The greater the relative thermodynamic chain rigidity (i.e. the greater the statistical correlation between the neighboring effectively rigid kinetic units), the broader is this spectrum ... 

These theories do not take into account a more isotropic distribution of centers of viscous resistance existing in an elementary kinetic unit (rigid segment) of the real chains. Often, the most bulky groups of monomer units are located on one side of the backbone chain. 

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