Velocity translational diffusion

The q(T) can be independently measured by a viscometer and the value of y is determined by the PCS measurement at a certain temperature (typically 21 22 °C). Under the condition that the hydrodynamic diameter of the probe molecule is constant in the temperature range examined, we can obtain the temperature of the confocal area. It is worth noting that the present method estimates average temperature inside the confocal volume of the microscopic system because ECS provides the average value of the translational diffusion velocity over multiple fluorescent molecules passing through the sampling area. 

J. T. Hynes, R. Kapral, and M. Weinberg, Molecular theory of translational diffusion microscopic generalization of the normal velocity boundary condition, J. Chem. Phys. 70, 1456 (1970). 

For LC, the second term in Eq. (12) is often negligible because liquid diffusion coefficients are low ( 10 times lower than for gases). Furthermore, for LC, the parameter A depends on v, and A and C are coupled. For these reasons, LC plate heights increase with velocity for all reasonable operating values of v. One might be tempted to use low velocities in LC to achieve low plate heights however, lower velocities translate into longer retention times. 

Hint Rotational Brownian diffusivity is the manifestation of random walks of the orientation of the rod. By analogy with translational diffusion, the rotational diffusivity D,- = kTMaG, where M eis the mobility tensor relating angular velocity and torque. 

R. Ozisik, P. Doruker, E. D. vonMeerwall, andW. L. Mattice, Translational diffusion in MonteCarlo simulations ofpolymermelts Center ofmass displacement vs. integrated velocity autocorrelation function, Comput. Theor.Pofym.Sci.,submitted. 

More time-dependent structural correlation functions can be constructed, depending on the chemical nature of the system and of the phenomenon under investigation. For example, correlation functions over the positions and velocities of centers of mass yield information on translational diffusion. Molecular diffusion properties are often described by the self-diffusion coefiticient, D, using a simple formula that involves the mean square displacement of the centers of mass [9,10] ... 

Figure 6 (A) Pulsed gradient spin echo sequence used to encode spin magnetization phase for molecular translational motion. (B) Velocity and diffusion maps for a water molecule flowing through a 2 mm diameter capillary. The images are shown as stackplots. The velocity profile is Poiseuille while the diffusion map is uniform. Courtesy of RW Mair, MM Britton and the author.

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Models for description of liquids should provide us with an understanding of the dynamic behavior of the molecules, and thus of the routes of chemical reactions in the liquids. While it is often relatively easy to describe the molecular structure and dynamics of the gaseous or the solid state, this is not true for the liquid state. Molecules in liquids can perform vibrations, rotations, and translations. A successful model often used for the description of molecular rotational processes in liquids is the rotational diffusion model, in which it is assumed that the molecules rotate by small angular steps about the molecular rotation axes. One quantity to describe the rotational speed of molecules is the reorientational correlation time T, which is a measure for the average time elapsed when a molecule has rotated through an angle of the order of 1 radian, or approximately 60°. It is indirectly proportional to the velocity of rotational motion. 

As compared to HPLC, cSFC shows higher efficiency, universal and selective detection, minimal derivatisation for separation and the ability to separate thermally labile organic compounds. Often, cSFC analyses are also considerably faster. This arises because higher mobile phase diffusion coefficients translate directly into higher optimum velocities. However, sensitivity, detection dynamic range and sample capacity... 

A good example of translational fractionation is one-way diffusion through an orifice that is smaller than the mean-free path of the gas. Related, but somewhat more complex velocity-dependent fractionations occur during diffusion through a host gas, liquid, or solid. In these fractionations the isotopic masses in the translational fractionation factor are often replaced by some kind of effective reduced mass. For instance, in diffusion of a trace gas JiR through a medium, Y, consisting of molecules with mass ttiy. 

---