Diffusion constant units

Tlere, y Is the friction coefficien t of the solven t. In units of ps, and Rj is th e random force im parted to th e solute atom s by the solvent. The friction coefficien t is related to the diffusion constant D oflh e solven l by Em stem T relation y = k jT/m D. Th e ran doin force is calculated as a ratulom number, taken from a Gaussian distribn-... 

Here, y is the friction coefficient of the solvent, in units of ps and Rj is the random force imparted to the solute atoms by the solvent. The friction coefficient is related to the diffusion constant D of the solvent by Einstein s relation y = kgT/mD. The random force is calculated as a random number, taken from a Gaussian distribu-... 

Fig. 16.2 Simplified kinetic model of the photocatalytic process. ps represents the light absorbed per unit surface area of the photocatalyst, e b and h+b are the photogenerated electrons and holes, respectively, in the semiconductor bulk, kR is the bulk recombination rate constant and /R the related flux, whatever recombination mechanism is operating A is the heat resulting from the recombination kDe and kDh are the net first-order diffusion constants for fluxes Je and Jh to the surface of e b and h+b in the semiconductor lattice, respectively e s and h+s are the species resulting from...

I wish to ask about the concept of a unit of length in a biological cell. My concern is with the numerical value to be used for the diffusion coefficient. Most of biological space is heavily organized even in a single cell, and therefore a diffusion constant is not a simple property. To put my question simply, it is easiest, however, to consider enzyme sites that are otherwise identical in two situations (1) with water between them, (2) with a biological membrane between them. Is it not the case that the unit of length is quite different, for the diffusion in (1) is virtually free diffusion whereas in (2) the diffusion is constrained most probably as a series of activated hops ... 

As for the multidimensional freely jointed chain, it is possible to relate a to the parameters which describe a Rouse chain by evaluating the translational diffusion constant D for the center of mass. In the stochastic model, we determine the square of the displacement per unit time of a single bead averaged over an equilibrium ensemble. For bead j,... 

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... 

The result is visible in the Brownian movement of microscopic particles suspended in a fluid. If an individual particle is followed, it is seen to undergo a "random walk," moving in first one direction then another. Albert Einstein showed that if the distances transversed by such particles in a given time A t are measured, the mean square of these Ax values A2 can be related by Eq. 9-24 to the diffusion constant D (which is usually given in units of cmV1). 

Fisher has produced a relatively simple solution for a specimen geometry that is convenient for experimentalists and which has been widely used in the study of boundary self-diffusion by making several approximations which are justified over a range of conditions [9, 10]. The geometry is shown in Fig. 9.8 it is assumed that the specimen is semi-infinite in the y direction and that the boundary is stationary. The boundary condition at the surface corresponds to constant unit tracer concentration, and the initial condition specifies zero tracer concentration within the specimen. Rapid diffusion then occurs down the boundary slab along y, while tracer atoms simultaneously leak into the grains transversely along x by means of crystal diffusion. The diffusion equation in the boundary slab then has the form... 

This gives the mass of solute diffused per unit time through a cross-section S, in terms of the concentration gradient dcfdx in the direction x perpendicular to (he cross section. D is a constant for (he given solute and solvent at a given temperature, and is called the diffusion coefficient. For any one pair of substances. D is found to be proportional to the absolute temperature. It should be stated that these statements apply only to nonelectrolytic solutions. 

The diffusion equations thus far developed assume that the particles are colloidal and not affected by any motion of the fluid itself which is regarded as stationary. If we limit our discussion to particles in the size range from 0.5 to 5 p, which remain in suspension for rather long periods of time, and if these particles are emitted from a point source and not subject to disturbance by the surrounding fluid, it is obvious that the concentration of particles at any point must be proportional to the diffusion constant and inversely proportional to the square of the distance from the source. Let C be the concentration per unit time, passing a point at any distance R from the source, then... 

E the dielectric constant of the medium and Zj e and Z2e are the charges of the two reactants and D is the total diffusion constant. The Rull data can be explained quantitatively if charges of -8 to -10 units/particle are used for silica a much larger charge (>20), is necessary to explain the NaLS data. 

The rate of water vapor diffusion per unit leaf area, Jw> equals the difference in water vapor concentration multiplied by the conductance across which Acm occurs (// = g/Ac - Eq. 8.2). In the steady state (Chapter 3, Section 3.2B), when the flux density of water vapor and the conductance of each component are constant with time, this relation holds both for the overall pathway and for any individual segment of it. Because some water evaporates from the cell walls of mesophyll cells along the pathway within the leaf, is actually not spatially constant in the intercellular airspaces. For simplicity, however, we generally assume that Jm, is unchanging from the mesophyll cell walls out to the turbulent air outside a leaf. When water vapor moves out only across the lower epidermis of the leaf and when cuticular transpiration is negligible, we obtain the following relations in the... 

The three conditions just listed describe the special features of the constant (unit)-flux diffusion problem. They will now be used to solve Pick s second law. 

As the last example we mention the study of Takemura and Kitao. They studied different models for molecular-mechanics simulations on water. To this end, they studied the dynamics of a ubiquitin molecule solvated in water. They performed molecular-dynamics simulations for a system with periodic boundary conditions. At first they considered pure water without the solute and studied boxes with 360, 720, 1080, and 2160 water molecules. It turned out that even for these fairly large systems, finite-size effects could be recognized. Thus, the translational diffusion constant was found to depend linearly on where V is the volume of the repeated unit. 

Here is the (diffusive) mass flux of species A (mass transfer by diffusion per unit time and per unit area normal to the direction of mass transfer, in kg/s m ) and is the (diffusive) molar flux (in kmol/s m ). The mass flux of a species at a location is propoitional to the density of the mixture at that location. Note that p = Px + Pb density and C = Q + is the molar concentration of the binary mixture, and in general, they may vary throughout the mixture. Therefore, pd(pjp) dp or Cd(C /C) + dC - But in the special case of constant mixture density p or constant molar concentration C, the relations above simplify to... 

The polysaccharide corresponding to the first, immobile fraction was examined by the Svedberg ultracentrifuge technique. The sedimentation constant, S20, was equal to 1.6 X 10 c.g.s. units, and was independent of change of concentration. A 1 % solution of the polysaccharide was calculated from data obtained in this investigation to have a polysaccharide content of 0.91% the polysaccharide thus contained 9% of extraneous matter. The diffusion constant, D20, was found to be 11 X 10 and the partial specific volume, 0.619. A molar frictional ratio of 1.5 was obtained. This indicated that the particles were elongated ellipsoids (see p. 320). A molecular weight of 9,000 was calculated as compared with the value 7,300 obtained by Tennet and Watson. The polysaccharide reacted with immune serum in a dilution of 1 6,000,-... 

Figure 16. Arrhenius plots of the self-diffusion constants (in reduced units) for a series of normal hydrocarbons adsorbed on Pt(l 11). Temperature T is in reduced units defined by kT/ems where Sma is the well-depth of the molecule-surface interaction. From Ref [63], J. Chem. Phys. 101 (1994) 11021-11030.

The diffusion constant has units of m s. It is proportional to the mean free path, A, and to the mean molecular speed u, but the proportionality constant is difficult to calculate in general. For the simplest case, a single-component gas, the proportionality constant is so... 

The rotational diffusion of molecules is investigated by exciting their fluorescence with short pulses of polarized light and by observing the time dependence of the polarized emission. For a symmetric body the anisotropy of the emission (Fig. 9) is characterized by 3 rotational relaxation times each of which is a function of the rotational diffusion constants around the main axes of rotation. The corresponding amplitudes a depend on the position of the absorption vector and the emission vector within the coordinates of the rotating unit. 

Sedimentation coefficients—Sjow—representing the velocity of sedimentation in unit gravitational field in water at 20°C, may be used, together with diffusion constants, to calculate the relative molecular masses of purified enzyme preparations. Reported values of S20W for cholinesterase isolated from human or equine serum are given in Table 7. Furthermore, the Sjow value for highly purified butyrylcholine esterase of porcine parotid gland is 9.7 units (T9) and it is 2.5 units for the enzyme from P. polycolor (N2). 

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