Diffusion solvent, water

The Laplace pressure 2y/r of a droplet containing a salt, dispersed in a solvent, will increase the shrinkage of the droplet, while the osmotic pressure will increase as well. In turn the diffusible solvent (water in the present case) slows in activity, and thus stimulates the backdiffusion of the solvent. In the ideal case the osmotic pressure is given by... 

Introduction of a water-soluble ionic substance into the vascular system results in an increase in the number of particles in the bloodstream as the contrast substance dissolves. The body possesses several internal regulation systems and, when perturbed by an injection, attempts to restore the concentrations of substances in the blood to their normal or preinjection levels. To re-equilibrate the system, water from the cells of surrounding body tissue moves into the blood plasma through capillary membranes. This transfer of water is an example of osmosis, the diffusion of a solvent (water) through a semipermeable membrane (the blood vessels) into a more concentrated solution (the blood) to equalize the concentrations on both sides of the membrane. To accommodate the increase in... 

Outer sphere relaxation arises from the dipolar intermolecular interaction between the water proton nuclear spins and the gadolinium electron spin whose fluctuations are governed by random translational motion of the molecules (106). The outer sphere relaxation rate depends on several parameters, such as the closest approach of the solvent water protons and the Gdm complex, their relative diffusion coefficient, and the electron spin relaxation rate (107-109). Freed and others (110-112) developed an analytical expression for the outer sphere longitudinal relaxation rate, (l/Ti)os, for the simplest case of a force-free model. The force-free model is only a rough approximation for the interaction of outer sphere water molecules with Gdm complexes. 

Let us assume a solution of a non-electrolyte in water, separated from the pure solvent—water—by a semiper-meable membrane forming a piston (Fig. 8). Water enters the solution through the membrane and raises the piston, i.e., the solution can do work or possesses potential energy owing to its osmotic pressure. If the membrane is removed, the osmotic pressure causes diffusion until (if no other forces are active) the solute is uniformly distributed through the solvent. Osmotic pressure is, therefore, a factor tending to bring about uniform concentration. 

Let us now examine the methods of light microscope radioautography for organic compounds insoluble in a wide range of polar and nonpolar solvents (13). The reader is referred to the reviews of Roth and Stumpf (14), Williams (15), Eschrich and Fritz (16), Stumpf (17), and Inson and Sheridan (18) for microautoradiography of diffusible or water-soluble inorganic compounds. 

For the solubility of TPA in prepolymer, no data are available and the polymer-solvent interaction parameter X of the Flory-Huggins relationship is not accurately known. No experimental data are available for the vapour pressures of dimer or trimer. The published values for the diffusion coefficient of EG in solid and molten PET vary by orders of magnitude. For the diffusion of water, acetaldehyde and DEG in polymer, no reliable data are available. It is not even agreed upon if the mutual diffusion coefficients depend on the polymer molecular weight or on the melt viscosity, and if they are linear or exponential functions of temperature. Molecular modelling, accompanied by the rapid growth of computer performance, will hopefully help to solve this problem in the near future. The mass-transfer mechanisms for by-products in solid PET are not established, and the dependency of the solid-state polycondensation rate on crystallinity is still a matter of assumptions. 

Mechanisms of Solvent (Water, Methanol) Transport. The following types of transport are considered in this section (i) self-diffusion or tracer diffusion of solvent molecules, which is the unidirec-... 

Figure 14. Solvent (water, methanol) diffusion coefficients of (a) Nafion 117 (EW =1100 g/equiv) and (b) sulfonated poly(arylene ether ketone)s, as a function of the solvent volume fraction. Self-diffusion data (AiaO. T eOi-i) are taken from refs 197, 224, 226, 255—263 and unpublished data from the laboratory of one of the authors) chemical diffusion coefficients (Z>h2o) are calculated from self-diffu-sion coefficients (see text), and permeation diffusion coefficients are determined from permeation coefficients. ...

Molecular hydration in solution is described not only by the inner-sphere water molecules (first and second coordination spheres, see Section II.A.l) but also by solvent water molecules freely diffusing up to a distance of closest approach to the metal ion, d. The latter molecules are responsible for the so-called outer-sphere relaxation (83,84), which must be added to the paramagnetic enhancement of the solvent relaxation rates due to inner-sphere protons to obtain the total relaxation rate enhancement,... 

However, the activation energies are invariably small and generally fall in the range 6-30 kJ moH with the majority around 15 kJ moHh The latter observation led Hart and Anbar [67] to suggest that reaction (31) has an activation energy associated with reorientation of the solvent shell to facilitate transfer of the electron, and that this reorientation energy is the same as that required for e q to diffuse in water. The corollary to this argument is that the... 

Finally, the diffusion of a chemical may be influenced by another diffusing compound or by the solvent. The latter effect is known as solute-solvent interaction it may become important when solute and solvent form an association that diffuses intact (e.g., by hydration). This may be less relevant for neutral organic compounds, but it plays a central role for diffusing ions. But even for noncharged particles the diffusivities of different chemicals may be coupled. The above example of the glycerol diffusing in water makes this evident in order to keep the volume constant, the diffusive fluxes of water and glycerol must be coupled. 

The driving force for the mass transfer of the solute in the three-phase system can be determined with the solvent/water partition coefficient, just as the partition coefficient for gas/liquid phases, the Henry s Law constant, is used to determine the driving force for the mass transfer of ozone. A solute tends to diffuse from phase to phase until equilibrium is reached between all three phases. This tendency of a solute to partition between water and solvent can be estimated by the hydrophobicity of the solute. The octanol/water partition coefficient Kow is a commonly measured parameter and can be used if the hydrophobicity of the solvent is comparable to that of octanol. How fast the diffusion or transfer will occur depends not only on the mass transfer coefficient in addition to the driving force but also on the rate of the chemical reaction as well. 

Reaction 52a is the diffusion-controlled formation of an ion pair and 52b represents the rate-determining loss of solvent water. 

Alkyl-Co(III) cobalamins Co(II) cobalamins + alkylradicals Solvent water the products recombine at nearly diffusion controlled rate [122]... 

The extent of catalysis depends critically upon the stability of the intermediate 1. If the rate of expulsion of H20 from 1 (rate constant 7c i) is slower than proton transfer to solvent water, the rate of formation of the intermediate (rate constant ki) will be the rate-limiting step and no catalysis will be observed. The rate constant for protonation of the amine nitrogen of 1 by solvent water, 7cHa (HA = H20), depends on the basicity of the nitrogen and is given by kAKw/Ka, where kA represents the rate constant for diffusion-controlled abstraction of a proton by hydroxide ion, with a value of approximately 1010 M-1 s 1, and... 

Intermediate 1 could also be stabilised by proton transfer from oxygen to give 3 in Scheme 11.9. The proton acceptor B could be solvent water or a general base catalyst. The reaction will only be catalysed if the rate of breakdown of 1 to regenerate reactants is faster than the rate of proton transfer. In this case, such catalysis would be independent of the base strength of the catalyst B as proton transfer would invariably be thermodynamically favourable and hence occur at the maximum diffusion-controlled rate. If proton transfer to solvent is thermodynamically favourable, such that proton donation to 55.5 M water is faster than to, say, 1 M added base, any observed catalysis by base must represent transition state stabilisation by hydrogen bonding, or a concerted mechanism. 

The second explanation for the solvent isotope effect arises from the dynamic medium effect . At 25 °C the rotational and translational diffusion of DjO molecules in D20 is some 20% slower than H20 molecules in H20 (Albery, 1975a) the viscosity of D20 is also 20% greater than H20. Hence any reaction which is diffusion controlled will be 20% slower in D20 than in H20. This effect would certainly apply to transition state D in Fig. 3 where in the transition state the leaving group is diffusing away. A similar effect may also apply to the classical SN1 and SN2 transition states, if the rotational diffusion of water molecules to form the solvation shell is part of the motion along the reaction co-ordinate in the transition state. Robertson (Laughton and Robertson, 1959 Heppolette and Robertson, 1961) has indeed correlated solvent isotope effects for both SN1 and SN2 reactions with the relative fluidities of H20 and D20. However, while the correlation shows that this is a possible explanation, it may also be that the temperature variation of the solvent isotope effect and of the relative fluidities just happen to be very similar (see below). 

These questions were addressed in studies of the reactions ofp-1 and / -Me-1 + in aqueous solution. The quinone methide p-1 was generated by photoheterolysis of neutral 4-hydroxybenzyl acetate in water, and ks = 3.3 s 1 determined for addition of water.52 The O-methylated quinone methide / -Me-l+ was generated as an intermediate of solvolysis of neutral precursors in water,128 and ks = 2.5 x 108 s 1 for addition of water was determined by using the diffusion-limited rate of nucleophile addition of azide anion to / -Me-l+ as a clock for the slower addition reaction of solvent.135,138 These data show that methylation ofp-1 causes an enormous 6 x 107-fold increase in the reactivity of the electrophile with solvent water.52... 

In contrast, Nafion removes water vapor by a process called perevaporation. Water is absorbed onto the walls of the Nafion, moves through the walls, and evaporates into the sweep gas [30]. As a result, volatile analytes should not be lost through the membrane. The efficiency of removal depends on diffusion of water vapor to the walls of the membrane. When the water vapor load is significantly less than the dew point, the efficiency also improves as the temperature of the dryer is reduced [31]. This membrane separator does not remove organic solvent vapor from the Ar gas stream, but it also does not suffer from loss of volatile analytes. 

Crystals of achiral amino acid derived NDI 8 suitable for X-ray diffraction study were obtained from slow diffusion of water in DMSO. In this hydrogen bond acceptor solvent, the NDIs are arranged in a 7t-stacked structure, with the NDI cores n and n + 1 tilted at ca. 30° with respect to each other, while n and n + 2 are parallel to each other (dihedral angle 0.6°, Fig. 9). 

Many solute properties are intertwined with those of the ubiquitous solvent, water. For example, the osmotic pressure term in the chemical potential of water is due mainly to the decrease of the water activity caused by solutes (RT In aw = —V ri Eq. 2.7). The movement of water through the soil to a root and then to its xylem can influence the entry of dissolved nutrients, and the subsequent distribution of these nutrients throughout the plant depends on water movement in the xylem (and the phloem in some cases). In contrast to water, however, solute molecules can carry a net positive or negative electrical charge. For such charged particles, the electrical term must be included in their chemical potential. This leads to a consideration of electrical phenomena in general and an interpretation of the electrical potential differences across membranes in particular. Whether an observed ionic flux of some species into or out of a cell can be accounted for by the passive process of diffusion depends on the differences in both the concentration of that species and the electrical potential between the inside and the outside of the cell. Ions can also be actively transported across membranes, in which case metabolic energy is involved. 

Self-Diffusion Coefficients of Ions and Solvent Water (Dj in a 2.2 molal Ltl Solution Obtained from MD Simulation and Experiments at 305... 

Since k31/kl3 is equal to Kah, kl3, k3l and kH may be evaluated. Values of fen found depend markedly on the substitutents on the nitrogen ranging from 2.2 x 101 1 sec-1 for ammonium down to 2.7 x 109 sec 1 for dibenzylmethylammonium. The value of kH is also proportional to the inverse viscosity of the sulphuric acid—water mixtures used as solvent, over a five-fold range in viscosity. Grunwald and Ralph [79] interpret these results as meaning that kH measures the rate of diffusion of the water molecule into the bulk solvent. Water in the first... 

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