Macroscopic diffusion coefficient

The macroscopic diffusion coefficient ) is defined in terms of the mean jump distance a and mean time between jumps r as ... 

Developing approach has given an explanation at what conditions the matrices with macroscopic non-uniformities (e.g., lamellar systems, heterogeneous inclusion phases, etc.) and with effective macroscopic diffusion coefficients in the latter case, a matrix is considered as a homogeneous one and when the phenomenological model of double sorption, which operates with sorption sites of two types could be used [190-192]. 

Sometimes, this term is also used for analysis of relationships between the macroscopic diffusion coefficients... 

Cage effect dynamics or kinetics of geminate recombination was observed for the first time under photodissociation of aC C dimer of aromatic radicals in a viscous media. A suggestion has been made that at least in a number of smdied cases the mumal diffusion coefficient of radicals in the pair is approximately 10 times lower than the sum of macroscopic diffusion coefficients of the individual species. In other words, a geminate recombination proceeds considerably longer than expected. 

At times t >Teq, the wriggling motion results merely in a fluctuation around the primitive path, so the ch moves coherently in a one-dimension diffusion process, keeping its arc length constant. The macroscopic diffusion coefficient of a reptating chain scales with chain length (molecular weight) as ... 

The macroscopic diffusion coefficient can be similarly expressed, using the same jump frequency ... 

Body force of component i Polymer mass concentration Macroscopic diffusion coefficient Cooperative diffusion coefficient Stokes-Einstein diffusion coefficient Rouse diffusion coefficient Self diffusion coefficient... 

The derivative of U with respect to position is the regular force acting on the particle. However, this so-called stochastic approach results in similar Nernst-Planck type equations albeit with microscopic diffusion coefficient differing from the traditional macroscopic diffusion coefficient. The microscopic diffusion coefficient, D, is related to f, through D = k T)/ fim).)... 

At the atomic level, diffusion may be viewed as the periodic jumping of atoms from one lattice site to another via an intermediate stage of higher eno-gy that separates one site from another (Fig. 7.8). The ena-gy barrier that must be surmounted in the intermediate state before the jump can occur is called the activation energy. This paiodic jumping of the atoms, in which the atom diffuses by a kind of Brownian motion or random way over the lattice sites, is sometimes referred to as random diffusion. It can be treated as a random-walk problem that allows us to determine a relationship between the observed macroscopic diffusion coefficients and the jump frequencies and jump distances of the atoms. 

How could we transfer these results to our entangled molecules It is initially tempting simply to introduce into equation (24) the macroscopic diffusion coefficients defined by (21) and (22). The constant k should then be proportional to iV . We can, however, show that this idea is wrong. The reaction occurs at spatial distances between reagents of the order of b, which are smaller than the statistical size Rq of the chains an analysis solely based on macroscopic concepts is not sufficient. 

QNS data at small momentum transfer are directly related to the macroscopic diffusion coefficient. Comparing our effective diffusion coefficient with... 

At the opposite side of the timescale (in the range of seconds to minutes), the macroscopic diffusion coefficient of water in swollen Nafion membranes, as determined by the diffusion of tritiated water through the membrane, is lower by a factor of 10 compared to the local diffusion coefficient or the self-diffusion in bulk water. This high value integrates all the restricted motions, which shows that the Nafion morphology is favorable to obtain a high ionic conductivity [160]. One important issue is the identification of the typical... 

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