Diffusional jump length

Peppas and Reinhart have also proposed a model to describe the transport of solutes through highly swollen nonporous polymer membranes [155], In highly swollen networks, one may assume that the diffusional jump length of a solute molecule in the membrane is approximately the same as that in pure solvent. Their model relates the diffusion coefficient in the membrane to solute size as well as to structural parameters such as the degree of swelling and the molecular weight between crosslinks. The final form of the equation by Peppas and Reinhart is... 

As mentioned, the Peppas-Reinhart theory is valid in the case of highly swollen membranes. Additional work by Peppas and Moynihan [158] resulted in a theory for the case of moderately swollen networks. This theory was derived much like the Peppas-Reinhart theory with the exceptions that in a moderately swollen network, one may not assume that the diffusional jump length of the solute in the membrane, X2, i3, is equal to the diffusional jump length of the solute in pure solvent, X2, i and, also, one may not assume that the free volume of the polymer/solvent system is equal to the free volume of the solvent. The initial... 

In some cases, particularly in the growth of aerosol particles, the assumption of equilibrium at the interface must be modified. Frisch and Collins (F8) consider the diffusion equation, neglecting the convective term, and the form of the boundary condition when the diffusional jump length (mean free path) becomes comparable to the radius of the particle. One limiting case is the boundary condition proposed by Smoluchowski (S7), C(R, t) = 0, which presumes that all molecules colliding with the interface are absorbed there (equivalent to zero vapor pressure). A more realistic boundary condition for the case when the diffusion jump length, (z) R, has been shown by Collins and Kimball (Cll) and Collins (CIO) to be... 

An apparent diffusional jump length using such a cylindrical activation volume can be calculated. Assuming the total free volume for a diffusional jump to be... 

An analysis of Eq. 4.26 shows [22] that the longitudinal diffusion contribution to t] is to be taken into account when Q/Ddc < 2. In this case, one should add a random diffusional displacement, positive or negative, to the length of jump each time. 

A relaxation spectrum similar to that of Fig. 4.2 is obtained for the diffusional motion of a local-jump stochastic model of IV+ 1 beads joined by N links each of length b, if a weak correlation in the direction of nearest neighbor links is taken into account for the probability of jumps (US). On the other hand, relaxation spectra similar to that of the Rouse theory (27) are obtained for the above mentioned model or for stochastic models of lattice chain type (i 14-116) without the correlation. Iwata examined the Brownian motion of more realistic models for vinyl polymers and obtained detailed spectra of relaxation times of the diffusional motion 117-119). However, this type of theory has not gone so far as to predict stationary values of the dynamic viscosity at high frequencies. 

The majority of the activation energy for execution of a diffusion jump is used to produce a transient gap of sufficient size between surrounding segments to allow movement of the penetrant over the length of one diffusional step, As shown in Fig. (3a), a good... 

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