Translational diffusion constant

An appropriate value of 7 for a system modeled by the simple Langevin equation can also be determined so as to reproduce observed experimental translation diffusion constants, Dt in the diffusive limit, Dt is related to y hy Dt = kgTmy. See [22, 36], for example. 

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,... 

Figure 5.5. Measurement of physical properties during initiation of collagen self-assembly. Translation diffusion coefficient (D20-w) (top) and intensity of scattered light at 90° (bottom) versus time for type I collagen. Note translational diffusion constant decreases, whereas intensity of scattered light remains initially unchanged.

A treatment similar to the foregoing can be applied to the friction constant / , which is related to the sedimentation constant s and to the translational diffusion constant D by... 

One of the practical applications of dynamic light scattering involves the determination of particle sizes in media dispersed as dilute suspensions in a liquid phase. This aspect of dynamic light scattering is the focus here. Analysis of the scattering data will yield the translational diffusion constant D for a dilute aqueous suspension of polystyrene spheres, and this is directly related to the radius of the spheres. In addition, scattering will be studied from dilute skim milk, which reveals that a distribution of particle sizes exists for this system. 

FIGURE 10.5 Contributions to in the theoretical simulation of spin relaxation in the radical pairs from DCA-POZ and DCA-PSZ evaluated under the assumption of 0 (data points). The full simulations are represented by the curves denoted / -POZ/DQtot.A 0.45 and fc-PSZ/DQtot, respectively. The contribution from the esdi mechanism (k-esdi )=6E-7) corresponds to an effective translational diffusion constant of D = 6 x 10 cm s. The curves indicated as / -POZ/DQ.A represent the contributions of the ahfi mechanism, the indicating the factor by which the theoretical anisotropy parameter A is reduced. The curve indicated hy k-PSZ/DQ.g denotes the contribution due to the g tensor anisotropy in the PSZ radical. The constant values c POZ and c PSZ represent the field-independent contributions to k. For details of the calculation cf. Ref. 23. 

The results presented here are still prdiminary in quantitative sense. The problem which can be easily reco iized is the miKh faster initial dmy in every case than what is observed in die experiments (or simulations). Two remedies for the problem are under investigation (1) rqdacing the translational diffusion constant by more elaborated model for the single particle dynamics which explicitly includes the rigid body rotation, and (2) inclusion of the nonlinearity in the density fidd in the SSSV equation. 

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. 

Subsequently, they studied a periodically repeated volume containing the ubiquitin molecule as well as 4908, 9133, 13 200, or 29 182 water molecules. Again, the linear dependence of the translational diffusion constant of the protein on was... 

From the above comparison it seems clear that there are considerable discrepancies in the degrees of slowing down between nuclear magnetic resonance (NMR) experiments and CMD. This is especially true for the translational diffusion constant. 

On the other hand, / is very simply related to the translational diffusion constant D by Einstein s equation... 

As stated above, this theory assumes that translational diffusion is isotropic that is, in a molecule-fixed frame, the diffusion constant parallel to the long molecular axis is the same as that perpendicular to it. For highly anisotropic large molecules this is probably not a good assumption. Maeda and Saito (1969) have calculated the spectrum taking into account the anisotropy of the translational diffusion constant. Their resulting expressions are rather complex and will not be given here. Their results are expressed as a power series in the translational diffusion coefficient anisotropy,... 

The kinetic factor D(q) characterizes the average particle flux, and S(q), the interparticle structure factor, is equivalent to the integrated scattered light intensity. When the range of interparticle interactions a is comparable with d, the mean interparticle distance, then D(q) may exhibit angle-dependent behavior. In the limits q- 0, co, D(q) reduces to the translational diffusion constant Dt (93), The data of Berne and... 

Table 1. Relaxation model parameteis obtained by a Levenberg-Marquardt fit optimization of equation (S) of the experimental Ti(v,A) data for 5CB and 8CB, shown in Fig. 2. Both data sets are rather similar, which on one hand demonstrates that the fitting is reproducible, and on the other shows the minor importance of the chain length variations on the Tj dispersion. The model constants denoted by ( ) could not be determined reliably and were estimated theoretically.Da, Dkj are the rotational diffusion constants parallel and perpendicular to the long molecule axis, and 0, 0the translational diffusion constants parallel and perpendicular to the nematic director is the mean translational jump width perpendicular to the molecular long axis and d the molecular diameter.

Here, we shall relate the translational diffusion motion of the center of mass of a polymer chain to the curvilinear diffusion constant. Experimentally, the translational diffusion constant can readily be measured. 

A key assumption in the SH model is that the system s overall translational diffusion constant Dg is a simple volume average over fluidized domains and surrounding static matrix. Thus,... 

Upper bound. Next we consider the translational diffusion constant. To calculate Dc, we consider that a weak constant field... 

The coeflldent is called the rotational diffusion constant. Note that the dimension of D, is (time), and is not the same as that of the translational diffusion constant, which is (length) /(time). 

The pulsed (field) gradient-spin echo (PFGSE or PGSE) experiment is used to measure translational diffusion constants [29] (which must not be confused with spin diffusion). It is based on the two-pulse spin-echo experiment (Fig. 12 Sec.II.E.l), with the addition of two field-gradient periods to create a spatial frame of reference in the x and y dimensions. The first gradient is applied between the two pulses the second, between the 180°... 

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