Diffusion coefficient-molecular

Fabrication processing of these materials is highly complex, particularly for materials created to have interfaces in morphology or a microstructure [4—5], for example in co-fired multi-layer ceramics. In addition, there is both a scientific and a practical interest in studying the influence of a particular pore microstructure on the motional behavior of fluids imbibed into these materials [6-9]. This is due to the fact that the actual use of functionalized ceramics in industrial and biomedical applications often involves the movement of one or more fluids through the material. Research in this area is therefore bi-directional one must characterize both how the spatial microstructure (e.g., pore size, surface chemistry, surface area, connectivity) of the material evolves during processing, and how this microstructure affects the motional properties (e.g., molecular diffusion, adsorption coefficients, thermodynamic constants) of fluids contained within it. 

Table 13-5 Partition (KG/f) and diffusion (DF) coefficients of several solvents in a selection of liquid, fatty and solid foods at 23 °C. Mr = relative molecular mass. TB = boiling point.

Absorptivity for radiation Activity Activity coefficient, molal basis Coefficient of expansion a a T Diffusivity Molecular, volumetric Thermal Emissivity ratio for radiation Dv,8 a ft /(h) (ft) ft2/h a = k/cp, ft2 /h... 

This description is particularly useful because the diffusion (6) coefficient is reasonably well defined in aqueous solutions, it is related to molecular properties in aqueous solutions, and it can be predicted. However, in biologic systems, the observed length X—for a single transport step—will be widely unchanged. Preferably, steady state and sink conditions are studied, which simplifies the Pick law and focuses on permeability as stated above. 

A schematic representation of the boundary layers for momentum, heat and mass near the air—water interface. The velocity of the water and the size of eddies in the water decrease as the air—water interface is approached. The larger eddies have greater velocity, which is indicated here by the length of the arrow in the eddy. Because random molecular motions of momentum, heat and mass are characterized by molecular diffusion coefficients of different magnitude (0.01 cm s for momentum, 0.001 cm s for heat and lO cm s for mass), there are three different distances from the wall where molecular motions become as important as eddy motions for transport. The scales are called the viscous (momentum), thermal (heat) and diffusive (molecular) boundary layers near the interface. 

In general, In fully developed turbulent flows the turbulent viscosity, conductivity and diffusivity vary from point to point in the flow field and are many magnitudes greater than the molecular coefficients. 

K, diffuse attenuation coefficient for downwelling irradiance organic-water partitioning coefficient Ku, diffuse attenuation coefficient for upwelling irradiance LMW, low molecular weight LUMO, lowest unoccupied molecular orbital MAA, mycosporine-like amino acid MCH, melanin-concentration hormone MDR, mean damage ratio MPB, microphytobenthos... 

Density gradient ultra-centrifugation can be used to determine the buoyant density of DNA and quadruplexes. Sedimentation experiments can also be used to measure sedimentation coefficients and molecular weights. Bead modeling on atomic-level model structures can be used to calculate theoretical hydrodynamic properties of DNA the structures. The calculated hydrodynamic properties (translational diffusion, sedimentation coefficients (S) and correlation times) in conjunction with the program HYDROPRO has been used to help differentiate between known or inferred structural conformations measured by analytical ultra-centrifugation. 

For Knudsen diffusion molecular gas theory gives that the Knudsen diffusion coefficient is proportional to the pore radius and the mean molecular velocity... 

The self-diffusion coefficients of toluene in polystyrene gels are approximately the same as in solutions of the same volume fraction lymer, according to pulsed field gradient NMR experiments (2fl). Toluene in a 10% cross-linked polystyrene swollen to 0.55 volume fraction polymer has a self-diffusion coefficient about 0.08 times that of bulk liquid toluene. Rates of rotational diffusion (molecular Brownian motion) determined from NMR spin-lattice relaxation times of toluene in 2% cross-linked ((polystytyl)methyl)tri-/t-butylphosphonium ion phase transfer catalysts arc reduced by factors of 3 to 20 compai with bulk liquid toluene (21). Rates of rotational diffusion of a soluble nitroxide in polystyrene gels, determined from ESR linewidths, decrease as the degree of swelling of the polymer decreases (321. 

The assessment of hydrodynamic and molecular interactions of drops can be made in the same manner as previously described for emulsions in Part V. Upon approach of the drops to each other under the action of turbulent pulsations up to distances smaller than Ao, they are subject to significant resistance from the environment, and the force of moleetilar attraction leads to collision and coalescence of the drops. If the basic mechanism of drop coagulation is that of turbulent diffusion, the coefficient of turbulent diffusion depends on the coefficient of hydrodynamic resistance [see Eqs. (11.70), (11.72), and (11.74)] and hence on the relative distance between the approaching drops ... 

The diffusive permeability coefficient P was determined from the hydraulic permeability coefficient K measured in a temperature range of 273-333° K according to the method described by Yasuda and Peterlin. The In P - 1/T plot shows a distinct jum at about 304° K for membrans with 45 and 60 wt.% of EBBA. It corresponds to the crystalline-nematic phase transition of EBBA. This important increase of P values is probably due to the transition in EBBA which may induce the activation of molecular motion of PC or to the creation of larger vacancies fraction around the domain boundary of EBBA. In that way the water molecules may diffuse faster. Pure PC films do not exhibit that type of behaviour, and the temperature dependence of P does not show, in that temperature range, any significant changes. 

In this equation, a is the tangential momentum accommodation coefficient, equal to unity for perfectly diffuse molecular reflection and zero for purely specular reflection. In Maxwell s model, MsUp overestimates the real velocity at the wall but leads to a rather good prediction of the velocity out of the Knudsen layer, as represented in Fig. 2. After non-dimensionalization with the characteristic length L, a reference velocity uo, and a reference temperature Tq, Eq. 10 is written as follows ... 

The Arrhenius plots of the diffusive permeability coefficient, P of water for the pol)nner/artificial amphiphile composite membranes reveal a distinct jump in the vicinity of the phase transition temperature of artificial amphiphiles. This striking increase of P may be caused by activation of thermal molecular motion which is closely related to the crystal-mesomorphic phase transition behavior. 

Diffusivity n (1) (diffusion coefficient) The constant of proportionality in Pick s first law of diffusion, which states that the mass of molar rate of transport (flux) of one molecular species into another is equal to the diffusivity times the gradient of concentration. Several related units are in use, e.g., cm /s, ftVh. The SI unit is m /s, corresponding to flux in mol/(s-m ) and gradient in (mol/m )/m. See also Pick s Law. (2) Thermal Diffusivity. Diffusivity or coefficient of diffusion is also given by A in the equation... 

Cyclic polymers have one of the simplest topologies, yet they have some of the most intriguing properties, many of which remain poorly understood. The physical properties of linear polymers in their melt state can be predicted using the theory of reptation [1, 2]. Linear polymers diffuse within the constraints of adjacent polymer chains, in which the chain ends play a most important role due to their ability to explore a much greater volume than the interior of the chain [1, 3]. Cyclic polymers have no chain ends and, at first sight, one would assume that they diffuse in a very different way and at a much slower rate. Diffusion experiments show the contrary cyclic polymers have a diffusion rate coefficient approximately twice as fast as linear polymers of the same molecular weight [4]. This is postulated to be due to an amoebae-like motion for the cyclic... 

Effective gas phase diffusivity Molecular diffusion coefficient [165] ... 

Pore sixe distribution data obtained from gas desorption (Barret et al. 1951) and mercury porisimetry experiments together with a knowledge of adsorbate molecular size thus enables the mode of diffusive transport to be ascertained. It should be noted that both molecular and Knudsen diffusion may occur in the same porous medium when the porous medium contains both macropores and micropores (revealed from an analysis of a bimodal pore size distribution curve). Unconstrained molecular diffusion. Dm, and Knudsen diffusion, Dk, coefficients are subsequently calculated from formulae derived from transport properties of fluids (gaseous and liquid) and the kinetic theory of gases. The molecular diffusivity for a binary gas mixture of A and B is evaluated from the Chapman-Enskog theory (Chapman and Cowling 1951) equation... 

The units for permeability coefficients in Table 14.6 are unusual, which are explained as follows When the diffusing molecular species is in the gas phase, solubility is equal to... 

Under normal conditions the membrane bilayer is in a fluid state. Membrane proteins can migrate within the plane of the membrane with diffusion coefficients of about 10 cm sec while lipids diffuse with coefficients of about 10 cm sec . Overall behaviour might be considered, therefore, in thermodynamic terms. But generalized deductions relating fluidity of the membrane to enzyme activity are difficult to make for several reasons. For example, motion in a given lipid molecule may include rapid rotations but slow lateral movement. Also, increased disorder in a bilayer may not correlate with increased translational motion. Moreover, all membranes so far examined have shown transbilayer asymmetry while there is evidence in several cases for at least small areas of concentration of certain lipids, i.e. micro-lateral heterogeneity. These sorts of consideration complicate the interpretation of experiments designed to show how the bilayer lipids affect membrane enzyme activities at a molecular level. 

If a fluid is placed between two concentric cylinders, and the inner cylinder rotated, a complex fluid dynamical motion known as Taylor-Couette flow is established. Mass transport is then by exchange between eddy vortices which can, under some conditions, be imagmed as a substantially enlranced diflfiisivity (typically with effective diflfiision coefficients several orders of magnitude above molecular difhision coefficients) that can be altered by varying the rotation rate, and with all species having the same diffusivity. Studies of the BZ and CIMA/CDIMA systems in such a Couette reactor [45] have revealed bifiircation tlirough a complex sequence of front patterns, see figure A3.14.16. 

We call the correlation time it is equal to 1/6 Dj, where Dj is the rotational diffusion coefficient. The correlation time increases with increasing molecular size and with increasing solvent viscosity, equation Bl.13.11 and equation B 1.13.12 describe the rotational Brownian motion of a rigid sphere in a continuous and isotropic medium. With the Lorentzian spectral densities of equation B 1.13.12. it is simple to calculate the relevant transition probabilities. In this way, we can use e.g. equation B 1.13.5 to obtain for a carbon-13... 

In dilute solutions, tire dependence of tire diffusion coefficient on tire molecular weight is different from tliat found in melts, eitlier entangled or not. This difference is due to tire presence of hydrodynamic interactions among tire solvent molecules. Such interactions arise from tire necessity to transfer solvent molecules from tire front to tire back of a moving particle. The motion of tire solvent gives rise to a flow field which couples all molecules over a... 

Micellization is a second-order or continuous type phase transition. Therefore, one observes continuous changes over the course of micelle fonnation. Many experimental teclmiques are particularly well suited for examining properties of micelles and micellar solutions. Important micellar properties include micelle size and aggregation number, self-diffusion coefficient, molecular packing of surfactant in the micelle, extent of surfactant ionization and counterion binding affinity, micelle collision rates, and many others. 

It ls not surprising chat such a relation should hold at the Limit of Knudsen diffusion, since Che Knudsen diffusion coefficients are themselves inversely proportional to the square roots of molecular weights, but the pore diameters in Graham s stucco plugs were certainly many times larger chan the gaseous mean free path lengths at the experimental conditions. 

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