Diffusion constant, solvent molecules

The lack of a substrate isotope effect suggests very extensive internal return and is readily explained in terms of the fact that conversion of the hydrocarbon to the anion would require very little structural reorganisation. Since koba = k 1k 2/(kLl+k 2) and k 2 is deduced as > k2, then kobs = Kk 2, the product of the equilibrium constant and the rate of diffusion away of a solvent molecule, neither of the steps having an appreciable isotope effect. If the diffusion rates are the same for reactions of each compound then the derived logarithms of partial rate factors (above) become pAT differences between benzene and fluorobenzene hydrogens in methanol. However, since the logarithms of the partial rate factors were similar to those obtained with lithium cyclohexylamide, a Bronsted cor-... 

Loutfy and coworkers [29, 30] assumed a different mechanism of interaction between the molecular rotor molecule and the surrounding solvent. The basic assumption was a proportionality of the diffusion constant D of the rotor in a solvent and the rotational reorientation rate kOI. Deviations from the Debye-Stokes-Einstein hydrodynamic model were observed, and Loutfy and Arnold [29] found that the reorientation rate followed a behavior analogous to the Gierer-Wirtz model [31]. The Gierer-Wirtz model considers molecular free volume and leads to a power-law relationship between the reorientation rate and viscosity. The molecular free volume can be envisioned as the void space between the packed solvent molecules, and Doolittle found an empirical relationship between free volume and viscosity [32] (6),... 

The distance xx describes the distance along the x-coordinate over which G increases by RT. We assume that motion along the x-coordinate is diffusive. This will be true for encounters, rearrangement of the ionic atmosphere or the rotation of solvent molecules. We further assume that at some distance xj the atom-transfer reaction becomes possible with a rate constant k. The diffusive kinetic equation then becomes (18), where the step function S(xt) = 0... 

The movement of the analyte is an essential feature of separation techniques and it is possible to define in general terms the forces that cause such movement (Figure 3.1). If a force is applied to a molecule, its movement will be impeded by a retarding force of some sort. This may be as simple as the frictional effect of moving past the solvent molecules or it may be the effect of adsorption to a solid phase. In many methods the strength of the force used is not important but the variations in the resulting net force for different molecules provide the basis for the separation. In some cases, however, the intensity of the force applied is important and in ultracentrifugal techniques not only can separation be achieved but various physical constants for the molecule can also be determined, e.g. relative molecular mass or diffusion coefficient. 

Since the rate constants of bimolecular diffusion-limited reactions in isotropic solution are proportional to T/ these data testify to the fact that the kt values are linearly dependent on the diffusion coefficient D in water, irrespective of whether the fluorophores are present on the surface of the macromolecule (human serum albumin, cobra neurotoxins, proteins A and B of the neurotoxic complex of venom) or are localized within the protein matrix (ribonuclease C2, azurin, L-asparaginase).1 36 1 The linear dependence of the functions l/Q and l/xF on x/t] indicates that the mobility of protein structures is correlated with the motions of solvent molecules, and this correlation results in similar mechanisms of quenching for both surface and interior sites of the macromolecule. 

Crystallographic quality ciystals of indinavir sulfate salt were grown hy slow diffusion of methanol into an ethanol/water solution. As confirmed by TG/IR results, the crystals obtained were a mixed mono-methanol / mono-ethanol solvate. The compound crystallized in the P2, space group, (monoclinic crystal system) with 2 molecules per unit cell. The cell constants were found to be a= 14.321(1)A, 6 = 10.091(1)A, c = 15.192(1)A, P = 95.50(1)°, andV=2185.5A. The calculated density was 1.200 g/cm. A view of the crystallographic unit cell packing is shown in Figure 4, with the solvent molecules omitted [7]. 

Electron transfer (ET) reactions play a key role in both natural (photosynthesis, metabolism) and industrial processes (photography, polymerisation, solar cells). The study of intermolecular photoinduced ET reactions in solution is complicated by diffusion. In fact, as soon as the latter is slower than the ET process, it is not anymore possible to measure km, the intrinsic ET rate constant, directly [1], One way to circumvent this problem, it is to work in a reacting solvent [2]. However, in this case, the relationship between the observed quenching rate constant and k T is not clear. Indeed, it has been suggested that several solvent molecules could act as efficient donors [3]. In this situation, the measured rate constant is the sum of the individual ksr-... 

From diffusion measurements it is known that the translatory mobility of solvent molecules in polymers changes abruptly at the glass temperature. Below T0 the diffusion constants are of the order of 10-12 to 10 14sq. cm. /sec., above Tg of the order of 10 4 to 10 8sq. cm./sec. (13). We have found that even below the glass temperature, plasticizer molecules may perform rather rapid motions, preferably rotatory motion. If the plasticizer has long aliphatic side chains, as with phthalates, rotating motions in the side chains should also result in a narrow... 

In various applications the following model has been used, which is of more general interest. Consider a molecule having a number of internal states or levels i. From each i it can jump to any other level j with a fixed transition probability yjti per unit time. Moreover the molecule is embedded in a solvent in which it diffuses with a diffusion constant depending on its state i. The probability at time t for finding it in level i at the position r with margin d3r is P,(i% t) d3r. While the molecule resides in i the probability obeys... 

What determines the value of /c in Eq. 9-14 This rate constant represents the process by which die substrate and enzyme find each other, become mutually oriented, and bind to form ES. If orientation and binding are rapid enough, the rate will be determined by the speed with which the molecules can come together by diffusion. Large molecules in solution are free to travel for only a tiny fraction of their diameter as a result of their frequent collision with solvent molecules. 

Although detailed microscopic calculations of the problem mentioned above are not available, there exist several computer simulation studies [102, 117], which also find the anomalous enhanced diffusion, even for simple model potentials such as the Lennard-Jones. The physical origin of the enhanced diffusion is not clear from the simulations. The enhancement can be as large as 50% over the hydrodynamic value. What is even more surprising is that the simulated diffusion constant becomes smaller than the hydro-dynamic prediction for very small solutes, with sizes less than one-fifteenth of the solvent molecules. These results have defied a microscopic explanation. 

Note that there is an apparent disagreement between the theory and simulation for TZ =12-18. While the theory gives a smooth curve, there is a dip in the simulation result [102]. In the theoretical calculation the system is studied in the limit of zero solute concentration. Thus the size of the solute should not influence the diffusion of the bulk solvent. It should remain constant for a particular density and temperature as the solute size is varied. The simulated system is made comparable with the theoretically studied system by fixing the value of the diffusion of a solvent molecule in the presence of other solvent molecules, D = 0.024 for p = 0.92. This leads to a smooth curve shown in Fig. 8. The agreement between theory and simulations is now excellent. 

Before closing, let us add a few comments about the diffusion constant D in the equations above. For diffusion of solutes like A and B in a solvent, it is customary to introduce diffusion constants Da and Db such that the associated fluxes J A and Jg are given relative to the flux of the solvent molecules. Since they are present in an overwhelming quantity as compared to the solutes, this will be equivalent to a center-of-mass reference frame, and if the system is stationary, to a laboratory reference... 

It is obvious that if V is large at certain places I will get contributions practically only from these places. If the solution is ideal and no field of force is applied to the column, we may say that

different point of view. The dissolved molecules diffuse between the solvent molecules, which cause them to move in a force field of very variable intensity. If this were not so we should expect the diffusion constant to be the same everywhere. Denoting by D this constant of diffusion, we get... 

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