Diffusion coefficient segmental

We first explain the setting of reactors for all CFD simulations. We used Fluent 6.2 as a CFD code. Each reactant fluid is split into laminated fluid segments at the reactor inlet. The flow in reactors was assumed to be laminar flow. Thus, the reactants mix only by molecular diffusion, and reactions take place fi om the interface between each reactant fluid. The reaction formulas and the rate equations of multiple reactions proceeding in reactors were as follows A + B R, ri = A iCaCb B + R S, t2 = CbCr, where R was the desired product and S was the by-product. The other assumptions were as follows the diffusion coefficient of every component was 10" m /s the reactants reacted isothermally, that is, k was fixed at... 

Diffusion of small molecular penetrants in polymers often assumes Fickian characteristics at temperatures above Tg of the system. As such, classical diffusion theory is sufficient for describing the mass transport, and a mutual diffusion coefficient can be determined unambiguously by sorption and permeation methods. For a penetrant molecule of a size comparable to that of the monomeric unit of a polymer, diffusion requires cooperative movement of several monomeric units. The mobility of the polymer chains thus controls the rate of diffusion, and factors affecting the chain mobility will also influence the diffusion coefficient. The key factors here are temperature and concentration. Increasing temperature enhances the Brownian motion of the polymer segments the effect is to weaken the interaction between chains and thus increase the interchain distance. A similar effect can be expected upon the addition of a small molecular penetrant. 

In contrast to normal diffusion, Ar2n does not grow linearly but with the square root of time. This may be considered the result of superimposing two random walks. The segment executes a random walk on the random walk given by the chain conformation. For the translational diffusion coefficient DR = kBT/ is obtained DR is inversely proportional to the number of friction-performing segments. 

Diffusion of dioxygen occurs 102 105 times more slowly with the diffusion coefficient D 10 7 10 10 cm2 s 1 Carbon-centered atom of P changes its orbital hybridization in this reaction and changes the C—C bond angles from 120° to 109°. Since P is macroradical and is surrounded by segments of macromolecules, this process occurs with an activation energy Solubility of dioxygen in the amorphous phase of polymer is about 3 x 10 4-2 x 10 3 mol L 1 atm-1... 

As seen in the preceding section, the counterions play a crucial role in the mobility of the polyelectrolyte molecules. Even in the absence of an external electric field, the counterions exert an induced electric field in the immediate environment of a charged segment which in turn significantly modifies the collective diffusion coefficient of the polymer. This additional contribution is absent for uncharged polymers, where the cooperative diffusion coefficient Dc is given by the Stokes-Einstein law in dilute solutions. 

Therefore, the coupling of polymer segments to the counterion cloud, which is directly responsible for the term N in the above equation, dominates the collective diffusion coefficient. Since Rg N for salt-free solutions, Df is independent of N. 

The rate of growth of polymer-salt complexes can provide fundamentally important information that is difficult to determine otherwise. The rate of crystal growth of (PEO)3 NaSCN from its undercooled liquid was measured and used to determine values for the diffusion coefficients of Na" " and SCN (Lee, Sudarsana and Crist, 1991). Also it was shown that the rate of the salt diffusion is independent of the molecular weight of the polymer for PEO molecular weights above 10. This result is fully consistent with the concept that ion motion is due to local segmental motion of the polymer. 

At low momentum transfer A2 describes the translational Rouse diffusion coefficient of the whole diblock, considering N l-f) segments exerting the friction Q and A[fsegments exerting the friction In the high Q hmit, RPA predicts... 

Then the diffusion coefficient due to the hydrodynamic interaction between the segments in the polymer solution, that is, the mutual diffusion coefficient, is given by... 

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... 

The diffusion coefficient D is always related inversely to the crosslink density of vulcanized elastomers. When Z)is extrapolated to zero concentration of the diffusate, it is related to the weight of the principal section of the elastomer, i.e., the weight of the segments between crosslinks. 

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