Diffusion segmental

Radical polymerizations of macromonomers are greatly influenced by the diffusion control effect [44]. Segmental diffusivity and translational diffusivity of the growing chains of macromonomers are strongly affected by the feed concentration and the molecular weight of the macromonomers. Furthermore, there is little difference in the degree of polymerization between macro-... 

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 reptation model thus predicts four dynamic regimes for segment diffusion. They are summarized in Fig. 18. 

In fact, the diffusion constant in solutions has the form of an Einstein diffusion of hard spheres with radius Re. For a diffusing chain the solvent within the coil is apparently also set in motion and does not contribute to the friction. Thus, the long-range hydrodynamic interactions lead, in comparison to the Rouse model, to qualitatively different results for both the center-of-mass diffusion—which is not proportional to the number of monomers exerting friction - as well as for the segment diffusion - which is considerably accelerated and follows a modified time law t2/3 instead of t1/2. 

Particular attention was placed on the crossover from segmental diffusion to the center of mass diffusion at Q 1/Rg and to the monomer diffusion at Q /i, respectively, by Higgins and coworkers [119,120]. While the transition at small Q is very sharp (see Fig. 43, right side), a broader transition range is observed in the regime of larger Q, where the details of the monomer structure become important (see Fig. 44). The experimental data clearly show that only in the case of PDMS does the range 2(Q) Q3 exceed Q = 0.1 A-1, whereas in the case of PS and polytetrahydrofurane (PTHF) it ends at about Q = 0.06-0.07 A-1. Thus, the experimental Q-window to study the internal dynamics of these polymers by NSE is rather limited. 

Fig. 45a, b. Segmental diffusion in dilute solutions at the crossover from - to good solvent conditions. Reduced characteristics frequencies Qred (Q,x) vs. x = (T — )/ at different Q-values a PDMS/d-bromobenzene b PS/d-cyclohexane. (b reproduced with permission from [115]. Copyright 1980 The American Physical Society, Maryland)... 

Fig. 46. Segmental diffusion in a dilute PDMS/d-bromobenzene solution at the crossover from to good solvent conditions. Reduced characteristic frequencies Qred (Q, x) vs. Q at different x-values. Comparison between experimental results ( ) and theoretical predictions (-). according to [98].

With respect to the segmental diffusion, the characteristic frequencies of the cyclic systems vary with Q3 as in the case of the linear chains in dilute solution (see Sect. 5.1.2). The absolute values are independent of the topology of the polymers and their molecular masses, and thus exhibit the same deviations from the theoretical predictions that have just been pointed out for dilute solutions of linear homopolymers. 

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

Fig. 58a, b. Segmental diffusion in semi-dilute polymer solutions. Schematic view of the Q-dependence of the relaxation rates Q(Q) at a fixed concentration. a Good solvent conditions b -conditions. (Reprinted with permission from [168]. Copyright 1994... 

The encounter of two free valences as a result only of diffusion of segments of a macromolecule. Since the radius of segmental diffusion is limited in the real time, this mechanism can be efficient at the high initiation rate and intense mobility of the polymer segments. Under the conditions of polymer oxidation, this mechanism is possible at the chain length close to unity. Some examples are given in Table 13.2. 

The combination of segmental diffusion with the transfer of the free valence to another segment due to the chemical reaction, for example POO + PH or POO + POOH. The... 

At the merging temperature the a-relaxation time matches that of the j8-re-laxation. Around this temperature, the dynamic structure factor has to be gen-erahzed, in order to include also the segmental diffusion process underlying the a-process. The )0-process can be considered as a local intrachain relaxation process, which takes place within the fixed environment set by the other chains. When the segmental diffusion reaches the timescale of the local relaxation, given atoms and molecular groups will noticeably participate simultaneously... 

The two groups are hindered by increasing viscosity from associating (entering the reaction volume) and dissociating (going out of the reaction volume) by the same factor. However, the rate constant kz can Itself become controlled by segmental diffusion. 

The question arises when the reaction becomes diffusion controlled, I.e. when one can observe experimental deviations from the Arrhenius dependence, and when it becomes fully controlled by segmental diffusion. 

Rearrangement of the two chains so that the two radical ends are sufficiently close for chemical reaction, which occurs by segmental diffusion of the chains, that is, by the movement of segments of a polymer chain relative to other segments... 

Another unique attribute of polymerizations of multifunctional monomers is the dominance of reaction diffusion as a termination mechanism [134,136, 143-146]. Reaction diffusion involves the mobility of radicals by propagation through unreacted functional groups. This termination mechanism is physically different from translation and segmental diffusion termination mechanisms which involve the diffusion of polymer macroradicals and chain segments to bring radicals within a reaction zone before terminating. Whereas normal termination mechanisms are related to the diffusion coefficient of the polymer, reaction diffusion must be considered differently. In essence, reaction diffusion is... 

In multifunctional monomer polymerizations, the mobility of radicals through segmental diffusion falls well before their mobility through reaction diffusion at very low functional group conversions (as compared to linear polymerizations). From this point in the reaction, the termination and propagation kinetic constants are found to be related, and the termination kinetic constant as a function of conversion may actually exhibit a plateau region. Figure 6 illustrates the typical behavior of kp and k, vs conversion as predicted by a kinetic based model. 

The termination kinetic constant exhibits a somewhat more complex behavior. From the onset of reaction, termination is diffusion controlled (segmental diffusion controlled). The diffusion of the macroradicals is the controlling step and the primary means of free radical termination. At some later conversion, the termination mechanism changes from segmental to reaction diffusion control. In this region, a plateau in k, occurs. Reaction diffusion is a propagation controlled... 

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