Water, molecular radius, diameter

The nucleation mechanism of dispersion polymerization of low molecular weight monomers in the presence of classical stabilizers was investigated in detail by several groups [2,6,7]. It was, for example, reported that the particle size increased with increasing amount of water in the continuous phase (water/eth-anol), the final latex radius in their dispersion system being inversely proportional to the solubility parameter of the medium [8]. In contrast, Paine et al.[7] reported that the final particle diameter showed a maximum when Hansen polarity and the hydrogen-bonding term in the solubility parameter were close to those of steric stabilizer. 

Three mechanisms have been invoked to describe the transfer of water vapor from the feed-membrane interface to the strip-membrane interface, namely Poiseuille flow, Knudsen diffusion, and Fickian (molecular) diffusion. The operative mechanism in a particular system depends on the pore diameter and on whether or not the pores are filled with stationary air. The membrane mass transfer co-efficient (as kgm h Pa ) applicable to each of these mechanisms can be estimated using Eqs. (4), (5), and (6), respectively. Here, r is the pore radius, e is the membrane porosity, is the molar mass of water, is the mean water vapor pressure in the pores, is the membrane thickness, x is the pore tortuosity, is the viscosity of water vapor, R is the gas constant, T is the absolute temperature, is the diffusion co-efficient of water vapor in air,... 

The HLD concept has been recently related to the so-called net-average curvature which indicates the size of the oil and water domains in the micro emulsion. For marginal microemulsions, i.e. of the WI or WII type at some distance from optimum, the inverse of the swollen micelle Sauter diameter is proportional to HLD. The zero net curvature at optimum does not result from infinite radius but rather from the coexistence of finite curvatures of opposite signs. For bicontinuous micro emulsions, it is the inverse of the characteristic length which is maximised at HLD = 0. As discussed elsewhere [38], its value at optimum formulation is the maximum distance that a molecule of oil or water can be separated from the surfactant layer and still interacts with it. In other words, it is the length at which the molecular interaction becomes equal to the molecular entropy. 

It cannot be exactly said down to which capillary diameter equation (8) holds, but, in view of molecular dimensions, a radius of 20 A seems to be a lower limit, below which the concept of capillary condensation will loose its physical sensed The value of p/p arising from equation (8) is then 035 for water at room temperature. 

The Kihara potential function [12] is used as described in McKoy and Sinanoglu [13]. The Kihara potential parameters, a (the radius of the spherical molecular core), a (the collision diameter), and e (the characteristic energy) are taken from Tohidi-Kalorazi [14], The fugacity of water in the empty hydrate lattice, // in Equation , can be calculated by ... 

It must be that as the particle diameter decreases further from 3.5 to 1-2 nm, the greater coalescence and increase in crushing strength more than offsets the increas ing forces of surface tension as the pores become smaller. Even at pH 3.4, Okkerse measured a pore radius of only 10 A. In fact, the water in such pores no longer has its normal properties and the surface tension may be less than supposed because of the strong molecular attraction of the pore walls. 

Figure 6.15 shows two examples of PS in the systems of water-methanol and water-ethanol. In the first case, both the water and the ethanol are preferentially solvated by water. In the second case, water is preferentially solvated by water throughout the entire range of compositions. On the other hand, the preferential solvation of ethanol switches from water to ethanol as the concentration of water increases. The various curves correspond to different choices of correlation radius. The curve numbered 1 corresponds roughly to the first coordination spheres, etc. Usually, after 3-5 coordination spheres, the deviation of the PS curve from the diagonal line is negligible. This roughly corresponds to the limit of the correlation distance, which is of the order of a few molecular diameters. 

The idea of an approximate evaluation of this radius was stated for the first time, I think, in 1841, by de Maistre". By suspending drops of water from the lower ends of vertical glass rods, he finds that the drop has the greatest volume when the diameter of the rod is 2 1/2 lines, and the drop is hemispherical. Supposing that a water molecule in contact with the glass surface supports all the molecules located vertically below it, one might conclude that, in water, the molecular attraction extends at least 3 time the distance of 1 1/4 line. I do not need to insist on the fallibility of this deduction. 

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