Diffusion path model

Minami proposed a diffusion path model, in which a path is defined by connectivities of sites with different potential depths. At least three distinct pairs of interactions are present in AgI-Ag2Mo04 glasses, which characterize such potential wells. The Ag" ion migrates in a minimum energy path defined by the connectivities of the wells. 

A formal derivation of diffusion in a restricted, high diffusivity path which uses no atomic model of the grain boundary is that due to Fisher, who made a flux balance in unit width of a grain boundary having a drickness of <5. There is flux accumulation in the element according to Pick s second law given by... 

For hydrophilic and ionic solutes, diffusion mainly takes place via a pore mechanism in the solvent-filled pores. In a simplistic view, the polymer chains in a highly swollen gel can be viewed as obstacles to solute transport. Applying this obstruction model to the diffusion of small ions in a water-swollen resin, Mackie and Meares [56] considered that the effect of the obstruction is to increase the diffusion path length by a tortuosity factor, 0. The diffusion coefficient in the gel, )3,i2, normalized by the diffusivity in free water, DX1, is related to 0 by... 

The tortuosity factor appears as a squared term because it decreases the concentration gradient and increases the diffusive path length. Using a cubic lattice model and inquiring how many steps a diffusing molecule needs to take to get around an obstacle, 0 was derived to be... 

Nye PH, Staunton S. 1994. The self-diffusion of strongly adsorbed anions in soil a two-path model to simulate restricted access to exchange sites. European Journal of Soil Science 45 145-152. 

Fig. 1. Model of subarachnoidal space, CSF flow, and molecular flux (N1). After CSF production in choroid plexus of the ventricles (1,2,3), CSF passes the aperture (4,5), reaches the cistemae (6-9), and divides into a cortical and a lumbar branch of the subarachnoidal space. Finally, CSF drains through the arachnoid villi into venous blood. The illustration represents an idealized cross section through the subarachnoid space. Molecules diffuse from serum with a concentration C(ser) flu ough tissue along the diffusion path x into the subarachnoid space with a concentration C(csF)- Th molecular flux J depends on the local gradient Ac/Ax or dddx and the diffusion constant D. The CSF concentration increases with decreasing volume exchange, i.e., decreasing CSF volume bulk flow (F= 500 ml/day). The flow rate of a molecule in CSF is r= FIA, where A is the varying cross section of the subarachnoid space.

The spin-lattice relaxation process is usually exponential. Theoretically, the effect of spin-diffusion, characterized by the coefficient D (order of 1(T12 cm2 s 1), has an influence on T, relaxation times when ix > L2/D, where Lis the diffusion path length. NMR studies of model systems f6r rubber networks, based on a styrene-butadiene-styrene block copolymer (SBSy, in which styrene blocks act as a crosslink for polybutadiene rubber segments of known and uniform length, indicate that spin diffusion operating between PS and PB phases causes a lowering of Tg for the PS component in SBS (as compared to the pure PS) and hindering of the motion of the PB component (as compared to the pure PB)51). 

Intercalation of cations into a framework of titanium dioxide is a process of wide interest. This is due to the electrochromic properties associated with the process (a clear blue coloration results from the intercalation) and to the system s charge storage capabilities (facilitated by the reversibility of the process) and thus the potential application in rocking-chair batteries. We have studied alkali-metal intercalation and ion diffusion in the Ti02 anatase and spinel crystals by theoretical methods ranging from condensed-phase ab initio to semiempirical computations [65, 66]. Structure relaxation, electron-density distribution, electron transfer, diffusion paths and activation energies of the ion intercalation process were modeled. 

To implement these simulation approaches, the value of the liquid film mass transfer coefficient Kf is required, which for nonporous and porous HPLC particles, can be calculated from literature correlations derived for bath357,400,408 or column models.407,408 For the case with porous particles, the apparent pore liquid mass transfer coefficient Kp can be expressed as an effective pore diffusivity over an average effective diffusion path length, such that... 

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