Diffusion of molecules

A diffusion mechanism is also used in dialysis as a means of separating colloids from crystalloids. The rate of diffusion of molecules in gels is practically the same as in water, indicating the continuous nature of the aqueous phase. The diffusion of gases into a stream of vapour is of considerable importance in diffusion pumps. 

Photoexcited fluorescence from spread monolayers may be studied [158,159] if the substance has both a strong absorption band and a high emission yield as in the case for chlorophyll [159]. Gaines and co-workers [160] have reported on the emission from monolayers of Ru(bipyridine)3, one of the pyridine ligands having attached C g aliphatic chains. Ruorescence depolarization provides information about the restriction of rotational diffusion of molecules in a monolayer [161], Combining pressure-area... 

Madura et al. 1995] Madura, J.D., Briggs, J.M., Wade, R.C., Davis, M.E., Luty, B.A., Ilin, A., Antosiewicz, J., Gilson, M.K., Bagheri, B., Scott, L.R., McCammon, J.A. Electrostatics and Diffusion of Molecules in Solution Simulations with the University of Houston Brownian Dynamics Program. Comp. Phys. Comm. 91 (1995) 57-95... 

ME Davis, JD Madura, BA Luty, JA McCammon. Electrostatics and diffusion of molecules m solution Simulations with the University of Houston Brownian dynamics program. Comput Phys Commun 62 187-197, 1991. 

Mitochondria are surrounded by a simple outer membrane and a more complex inner membrane (Figure 21.1). The space between the inner and outer membranes is referred to as the intermembrane space. Several enzymes that utilize ATP (such as creatine kinase and adenylate kinase) are found in the intermembrane space. The smooth outer membrane is about 30 to 40% lipid and 60 to 70% protein, and has a relatively high concentration of phos-phatidylinositol. The outer membrane contains significant amounts of porin —a transmembrane protein, rich in /3-sheets, that forms large channels across the membrane, permitting free diffusion of molecules with molecular weights of about 10,000 or less. Apparently, the outer membrane functions mainly to... 

An increase in pressure will also affect the rate of the diffusion of molecules to and from the electrode surface it will cause an increase in the viscosity of the medium and hence a decrease in diffusion controlled currents. The consequences of increased pressure on the electrode double layer and for the adsorption of molecules at the electrode surface are unclear and must await investigation. 

Gershon, N.D., Porter, K.R., Trus, B.L. (1985). The cytoplasmic matrix Its volume and surface area and the diffusion of molecules through it. Proc. Natl. Acad. Sci. USA 82, 5030-5034. 

FIG. 20 Dewetting of Zdol-TX on a nonunifomly covered surface. As in the previous figure, bare substrate regions are exposed (darker areas). Only material in layer 2 dewets to form a droplet (bright area). Diffusion of molecules from layer 2 occurs on top of layer 1 and does not fill the uncovered, possibly contaminated, substrate regions. (From Ref. 70.)... 

A further consideration in porous materials is the shape of the pores. Molecules have to diffuse through the pores to feel the effect of the catalytic groups which exist in the interior and, after reaction, the reaction products must diffuse out. These diffusion processes can often be the slowest step in the reaction sequence, and thus pores which allow rapid diffusion will provide the most active catalysts. It is another feature of the MTSs that they have quite straight, cylindrical pores - ideal for the rapid diffusion of molecules. 

We have seen that particle sizes of 100-150 y in classical LC lead to slow and inefficient columns. The reason for this is related to the slow diffusion of molecules in the liquid state (e.g., gaseous diffusion coefficient 10 liquid diffusion coefficients). 

Spectral width, dynamic range, resolution and sensitivity are expected to be pushed toward further limits. An emerging advancement in NMR spectroscopy is the DOSY technique (Section 5.4.1.1) which offers a separation capability as a function of the rates of steady state diffusion of molecules in solution. 

We return to using the Kp and Kd symbols to represent the partition coefficient and the apparent partition (distribution) coefficient, respectively. The effective, apparent, membrane, and intrinsic permeability coefficients are denoted Pe, Pa, Pm, and P0, respectively, and D refers to the diffusivity of molecules. 

On a related theme, we can take advantage of the diffusion of molecules incorporated into a polymer to its surface. Thus we can blend lubricants, bactericides, and antiblock agents into polymers, which slowly exude to the surface where they perform a useful role. 

One of the drawbacks with such a macroscopic system is the increased time for the diffusion of molecules relative to that in nanoscale systems. Molecules will clearly take longer to pass through thick barriers and to diffuse great distances than in the nanoscale regime. Therefore, the nanoencapsulation of such systems is desirable as it potentially reduces these limitations very significantly. Our attention now proceeds to various potential methods for nanoencapsulation. 

When considering the macrokinetics of PAR described by equations (Eq. 17), it is reasonable to focus on two limiting regimes. The first of these, the kinetically-controlled regime, takes place provided the rate of diffusion of molecules Z appreciably exceeds that of the chemical reaction. In this case, a uniform concentration Z = Ze should be established all over the globule after time interval t R2/D. Subsequently, during the interval t 1 /kZe, which is considerably larger than f[Pg.152]

Slow diffusion of molecules and radicals in polymer contracts the interval of the observed rate constants of bimolecular reactions. 

The growing of crystals is determined by the diffusion of molecules to the surface of the nucleus, the finding of a proper place, and the distribution of the freed energy to the surroundings. Under normal conditions (cooling speed vf < 102 °C/s and subcooling T. < 10 °C) Eq. (8) can be used ... 

To integrate the equations of motion in a stable and reliable way, it is necessary that the fundamental time step is shorter than the shortest relevant timescale in the problem. The shortest events involving whole atoms are C-H vibrations, and therefore a typical value of the time step is 2fs (10-15s). This means that there are up to one million time steps necessary to reach (real-time) simulation times in the nanosecond range. The ns range is sufficient for conformational transitions of the lipid molecules. It is also sufficient to allow some lateral diffusion of molecules in the box. As an iteration time step is rather expensive, even a supercomputer will need of the order of 106 s (a week) of CPU time to reach the ns domain. 

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

In industrial PET synthesis, two or three phases are involved in every reaction step and mass transport within and between the phases plays a dominant role. The solubility of TPA in the complex mixture within the esterification reactor is critical. Esterification and melt-phase polycondensation take place in the liquid phase and volatile by-products have to be transferred to the gas phase. The effective removal of the volatile by-products from the reaction zone is essential to ensure high reaction rates and low concentrations of undesirable side products. This process includes diffusion of molecules through the bulk phase, as well as mass transfer through the liquid/gas interface. In solid-state polycondensation (SSP), the volatile by-products diffuse through the solid and traverse the solid/gas interface. The situation is further complicated by the co-existence of amorphous and crystalline phases within the solid particles. 

The overall rate of crystallization is determined by both the rate of nuclei formation and by the crystal growth rate. The maximum crystal growth rate lies at temperatures of between 170 and 190 °C [71, 72], as does the overall crystallization rate [51, 61, 75], The former is measured using hot stage optical microscopy while the latter is quantified by the half-time of crystallization. Both are influenced by the rate of nucleation on the crystal surface and the rate of diffusion of polymer chains to this surface. It has been shown that the spherulite growth rate decreases with increasing molecular weight due to the decrease in the rate of diffusion of molecules to this surface [46, 50, 55, 71, 74],... 

This determines the size of molecules that can be admitted and the rate at which different molecules diffuse towards the surface. Molecular sieves, with their precise pore sizes, are uniquely capable of separating on the basis of molecular size. In addition, it is sometimes possible to exploit the different rates of diffusion of molecules to bring about their separation. A particularly important example referred to earlier, concerns the production of oxygen and nitrogen from air. 

Later, there were improvements in the thermal theories. Probably the most significant of these is the theory proposed by Zeldovich and Frank-Kamenetskii. Because their derivation was presented in detail by Semenov [4], it is commonly called the Semenov theory. These authors included the diffusion of molecules as well as heat, but did not include the diffusion of free radicals or atoms. As a result, their approach emphasized a thermal mechanism and was widely used in correlations of experimental flame velocities. As in the... 

Consider the diffusion of molecules A into an atmosphere of B molecules, that is, a binary system. For a concentration gradient in A molecules alone, future developments can be simplified readily if Fick s law is now written... 

Hansen, R.H. and Harris, J.M., Lateral diffusion of molecules partitioned into silica-bound aUcyl chains influence of chain length and bonding density, Anal. Chem., 68, 2879,1996. 

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