Molecular size, diffusion

The diffusing flux through different membranes can be adequately described by Tick s law (Equation [8.4]), indicating that gas transport through porous membranes is driven by a cross membrane pressure gradient. Based on the differences in partial pressures, gas diffusivities, molecular sizes and shapes, gases can be separated when they flow through a membrane. 

Morris K F and Johnson C S Jr 1993 Resolution of discrete and continuous molecular size distributions by means of diffusion-ordered 2D NMR spectroscopy J. Am. Chem. See. 115 4291-9... 

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... 

This situation seems highly probable for step-growth polymerization because of the high activation energy of many condensation reactions. The constants for the diffusion-dependent steps, which might be functions of molecular size or the extent of the reaction, cancel out. 

Activated diffusion of the adsorbate is of interest in many cases. As the size of the diffusing molecule approaches that of the zeohte channels, the interaction energy becomes increasingly important. If the aperture is small relative to the molecular size, then the repulsive interaction is dominant and the diffusing species needs a specific activation energy to pass through the aperture. Similar shape-selective effects are shown in both catalysis and ion exchange, two important appHcations of these materials (21). 

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

The insoluble, hydrophobic disperse dyes readily dye nylon, and because their mode of attraction is completely nonionic they are completely insensitive to chemical variations and pH. Small molecular-sized disperse dyes (ca mol wt 400) show very high rates of diffusion and excellent migration properties and they are insensitive to physical variations in the nylon. As the molecular size of disperse dyes increases they show increasing sensitivity to physical variation. 

These values are as much as one hundred times larger than those typically observed in conventional liquids. The improved transport rates in SCFs versus liquid solvents are important in practical appheations including supercritical extraction. Furthermore, carbon dioxide diffuses through condensed-hquid phases (e.g., adsorbents and polymers) faster than do typical solvents which have larger molecular sizes. 

As explained in Chapter 5, these materials are essentially non-volatile solvents for PVC. Because of their molecular size they have a very low rate of diffusion into PVC at room temperature but at temperatures of about 150°C molecular mixing can occur in a short period to give products of flexibility varying according to the type and amount of plasticiser added. 

For entities of molecular size the numerical coefficient in the denominator of Eq. (9-12) should be reduced from 6 to 4 or less,6 which would also alter the expression for the diffusion-controlled rate constant from the traditional form given in Eq. (9-13) ... 

Molecular Rotational Diffusion. Rotational diffusion is the dominant intrinsic cause of depolarization under conditions of low solution viscosity and low fluorophore concentration. Polarization measurements are accurate indicators of molecular size. Two types of measurements are used steady-state depolarization and time-dependent (dynamic) depolarization. 

Figure 4.3. Relative diffusion rates in HZSM5. The shaded areas are the pore walls, the unshaded parts the vertical pore system from Figure 4.1. As can be seen, the rate of diffusion varies enormously with only very small changes in molecular size and shape. This allows the zeolite to discriminate almost completely between the three molecules shown, a situation which is unprecedented in traditional, homogeneous chemistry.

The decomposition of cyclohexylacetate was very slow on Cs2.2 (Fig. 5), although the molecular size of cyclohexylacetate (-6.0 A) is smaller than the pore size of Cs2.2 (6.2 - 7.5 A). Probably the adsorption or diffusion of cyclohexylacetate in the pore is restricted by the coexisting solvent molecule, as the pore size is only slightly greater than the size of reactant. 

On-line dialysis also separates the analyte from tissue matrix based upon molecular size, but in this case, the sample extract is passed over a membrane filter through which the analyte (and other low molecular weight compounds) is diffused into a second solvent on the other side of the membrane filter. Usually, the second solvent is then concentrated on to an SPE column to minimize the dilution effect that is caused by the dialysis process. Agasoester used on-line dialysis to separate oxytetracycline from muscle, liver, milk, and egg tissue matrix components. A problem encountered with on-line dialysis is the inability of analyte molecules that are bound to proteins in the sample extract to pass through the membrane filter. Problems with membrane clogging are reduced with on-line dialysis compared with ultrafiltration because no external force is being applied to bring the analyte across the membrane filter. 

In many products, the spin-relaxation properties of the components can be different due to molecular sizes, local viscosity and interaction with other molecules. Macromolecules often exhibit rapid FID decay and short T2 relaxation time due to its large molecular weight and reduced rotational dynamics [18]. Mobile water protons, on the other hand, are often found to have long relaxation times due to their small molecular weight and rapid diffusion. As a result, relaxation properties, such as T2, have been used extensively to quantify water/moisture content, fat contents, etc. [20]. For example, oil content in seeds is determined via the spin-echo technique as described according to international standards [64]. 

A simple estimate of the diffusion coefficients can be approximated from examining the effects of molecular size on transport through a continuum for which there is an energy cost of displacing solvent. Since the molecular weight dependence of the diffusion coefficients for polymers obeys a power law equation [206], a similar form was chosen for the corneal barriers. That is, the molecular weight (M) dependence of the diffusion coefficients was written as ... 

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