Hopping penetrant

Equations (90) and (91) can be used to approximate diffusion into porous solids like chunks of asphalt or soil and sediment grains. For example, assume that an HOP is diffusing into a soil grain with Dapp=10 5 m2 s 1 and a=10 3 m. Equation (90) can then be solved to yield the concentration profiles shown in Fig. 6 (where C0[Pg.21]

TABLE 1. Yield of free ions (Gfi) and the secondary electron penetration (hop) for radiolysis of unsaturated hydrocarbons... 

What benefits and drawbacks to these problems can one expect from the use of cyclic voltammetry instead of RDEV They are related. In a general case, the application of cyclic voltammetry will be more complicated, because playing with the scan rate, one can make the diffusion layer penetrate the film or remain outside, as is the case with RDEV. We have already seen a fruitful application of the first of these possibilities in the use of cyclic voltammetry to the characterization of electron hopping transport within the redox films (Section 4.3.4). In the second situation, cyclic voltammetry may replace RDEV in a manner similar to what has been seen in Section 4.3.2 Each time a term (1 — ///a) is encountered in the analysis, it suffices to replace it by... 

Figure 3.9 Schematic illustration of the processes that can occur at a modified electrode, where P represents a reducible substance in a film on the electrode surface and A a species in solution. The processes shown are as follows (1) heterogeneous electron transfer to P to produce the reduced form Q (2) electron transfer from Q to another P in the film (electron diffusion or electron hopping in the film) (3) electron transfer from Q to A at the film/solution interface (4) penetration of A into the film (where it can also react with Q or at the substrate/film interface) (5) movement (mass transfer) of Q within the film (6) movement of A through a pinhole or channel in the film to the substrate, where it can be reduced. From A.J. Bard and L.R. Faulkner, Electrochemical Methods Fundamentals and Applications, 2nd Edition, Wiley, 2001. Reprinted by permission of John Wiley Sons, Inc...

K and the magnetic field B was gradually increased. Vortices suddenly began to penetrate the film at 5 = 32 G, and the number of vortices increased as B was increased further. Their dynamic behavior was quite interesting. At first, only a few vortices appeared here and there in a 15 X 10 pm field of view. They oscillated around their own pinning centers and occasionally hopped from one center to another. These movements continued as long as the vortices were not closely packed B 100 G). 

Figure 7 Brownian dynamic simulations of the echo-decay at various qR at various q=yg5/2a [R = 4 pm, P all 0.032 (probability of a molecide penetrating the film), A = 100 ms]. The simulation scheme yields essentially the same kind of information as the pore-hopping theory. (Adapted from Ref. 36.)...

Most substances dissolved in the medium surrounding yeast cells diffuse freely through the cell walls to the plasma membranes. There is adsorption of certain materials by the outer layers of the cell walls during the diffusion. For instance, hop bitter substances, polyphenols, and nitrogenous compounds of wort tend to be adsorbed. The plasma membrane isolates the living cell or protoplast from its environment and controls the movement of materials in and out of the cell. Substances which are soluble in lipid, an important constituent of the membrane, tend to penetrate readily. Thus, unbranched long-chain fatty acids and a-oxo-acids penetrate more quickly than the corresponding short-chain acids which are less soluble in lipid. If the acids are dissociated, they enter the cell either slowly or not at all. 

Poulin P, Hop ECA, Salphalti L, Liederer B. 2013a. Correlation of tissue plasma partition coefficient between healthy tissues and subcutaneous xenografts of human tumor cell lines in mouse as a prediction tool of drug penetration in tumors. J Pharm Sci 102 1355-1369. 

The presence of anomalous diffusion can be explained by the structure of the polymer matrix, which - at the length-scale of a few hopping distances - restricts the penetrant motion to the effect that - on this scale - the penetrant s paths cannot be truly random. The polymer environment, at the same time, causes a separation of time-scales consistent with the hopping mechanism (short-time in-cavity motion vs long-time diffusive motion). This, in turn, is another cause for anomalous diffusion. 

It is important that MD and TSA are used in conjunction. As an example we mention the MD analysis of short-time rotational motion of small penetrants in dense polymers that provides the basis for the pre-averaging of these degrees of freedom in the TSA. Similarly, the duration cf the hopping events, as estimated by MD (- 2 ps), is an excellent guiddine for selecting tte smearing factor of TSA. 

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