Diffusion translation

Sun Y-P and Saltiel J 1989 Application of the Kramers equation to stiibene photoisomerization in / -alkanes using translational diffusion coefficients to define microviscosity J. Phys. Chem. 93 8310-16... 

Intermolecular DD 2 Distance variation by translational diffusion Less common [12]... 

Hwang L-P and Freed J H 1975 Dynamic effects of pair correlation functions on spin relaxation by translational diffusion in liquids J. Chem. Rhys. 63 4017-25... 

Taylor D G and Bushell M C 1985 The spatial-mapping of translational diffusion-ooeffioients by the NMR imaging teohnique B 30 345-9... 

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. 

Looking at translational diffusion in liquid systems, at least two elementary categories have to be taken into consideration self-diffusion and mutual diffusion [1, 2]. 

Radical polymerizations of macromonomers are greatly influenced by the diffusion control effect [44]. Segmental diffusivity and translational diffusivity of the growing chains of macromonomers are strongly affected by the feed concentration and the molecular weight of the macromonomers. Furthermore, there is little difference in the degree of polymerization between macro-... 

Center of mass or translational diffusion is believed to be the rate-determining step for small radicals33 and may also be important for larger species. However, other diffusion mechanisms are operative and are required to bring ihe chain ends together and these will often be the major term in the termination rate coefficient for the case of macromolecular species. These include ... 

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

Dynamic light scattering (DLS) Translational diffusion coefficient, hydrodynamic or Stokes radius branching information (when Rh used with Rg) Fixed 90° angle instruments not suitable for polysaccharides. Multi-angle instrument necessary. [3]... 

In this relation a(r, t) is the experimentally observed signal, s represents random noise, axi r) represents the time invariant systematic noise and aRi(f) the radial invariant systematic noise Schuck [42] and Dam and Schuck [43] describe how this systematic noise is ehminated. x is the normahsed concentration at r and t for a given sedimenting species of sedimentation coefficient 5 and translational diffusion coefficient D it is normalised to the initial loading concentration so it is dimensionless. 

It is possible to get molecular weight from the sedimentation coefficient if we assiune a conformation or if we combine with other measurements, namely the translational diffusion coefficient via the Svedberg equation [50]... 

The translational diffusion coefficient in Eq. 11 can in principle be measured from boimdary spreading as manifested for example in the width of the g (s) profiles although for monodisperse proteins this works well, for polysaccharides interpretation is seriously complicated by broadening through polydispersity. Instead special cells can be used which allow for the formation of an artificial boundary whose diffusion can be recorded with time at low speed ( 3000 rev/min). This procedure has been successfully employed for example in a recent study on heparin fractions [5]. Dynamic fight scattering has been used as a popular alternative, and a good demonstra-... 

A number of bulk simulations have attempted to study the dynamic properties of liquid crystal phases. The simplest property to calculate is the translational diffusion coefficient D, that can be found through the Einstein relation, which applies at long times t ... 

Ionic, polar and amphiphilic solubilizates are forced to reside for relatively long times in very small compartments within the micelle (intramicellar confinement, compart-mentalization) involving low translational diffusion coefficients and enhancement of correlation times. 

We have applied FCS to the measurement of local temperature in a small area in solution under laser trapping conditions. The translational diffusion coefficient of a solute molecule is dependent on the temperature of the solution. The diffusion coefficient determined by FCS can provide the temperature in the small area. This method needs no contact of the solution and the extremely dilute concentration of dye does not disturb the sample. In addition, the FCS optical set-up allows spatial resolution less than 400 nm in a plane orthogonal to the optical axis. In the following, we will present the experimental set-up, principle of the measurement, and one of the applications of this method to the quantitative evaluation of temperature elevation accompanying optical tweezers. 

Under the condition that the Stokes-Einstein model holds, the translational diffusion coefficient, D, can be represented by Eq. (8.3). the diffusion time, Xd, obtained through the analysis is given by Eq. (8.4). 

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. 

Studies of the effect of permeant s size on the translational diffusion in membranes suggest that a free-volume model is appropriate for the description of diffusion processes in the bilayers [93]. The dynamic motion of the chains of the membrane lipids and proteins may result in the formation of transient pockets of free volume or cavities into which a permeant molecule can enter. Diffusion occurs when a permeant jumps from a donor to an acceptor cavity. Results from recent molecular dynamics simulations suggest that the free volume transport mechanism is more likely to be operative in the core of the bilayer [84]. In the more ordered region of the bilayer, a kink shift diffusion mechanism is more likely to occur [84,94]. Kinks may be pictured as dynamic structural defects representing small, mobile free volumes in the hydrocarbon phase of the membrane, i.e., conformational kink g tg ) isomers of the hydrocarbon chains resulting from thermal motion [52] (Fig. 8). Small molecules can enter the small free volumes of the kinks and migrate across the membrane together with the kinks. 

Calibration of the MC time step in the simulation on the 2nnd lattice can be achieved by comparison of rr or DN with the results from a conventional MD simulation (as in the second and third columns of Table 4.8), or via comparison with a translational diffusion coefficient obtained from experiment with a... 

W. S. Price 1997, (Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion Part 1. Basic theory), Concepts Magn. Reson. 9, 299-336. 

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