Equilibrium cluster diameter

Fig. 3 Variation of equilibrium cluster diameter dQ i ith EH, cation form and water content, where EQ=275 joule-cm is the tensile modulus of a dry, 1200 EH sulfonate ionomer, A=0.667 is a constant and dQ is obtained from SAXS and water sorption data. The solid line is a least square fit of Eq. 1 to the EH and cation form data.

Pump Equilibrium speed (-) Cluster Diameter (p,m) Number primary particles In cluster (-) Number of clusters (-) Number primary particles in cluster (-) Number of clusters (-) Number primary particles in cluster (-) Number of clusters (-)... 

When an emulsifier or soap is dissolved in water, the solute molecules associate to form small clusters called micelles. The hydrocarbon parts of the emulsifier molecules constitute the interior of the micelles, the surface of which is formed by the ionic groups of the emulsifier. A small fraction of the soap is molecularly dissolved in the water and there is a dynamic equilibrium between the micelles and these single molecules in the aqueous phase. Micelles are of colloidal size, consisting of a relatively small number of soap molecules of the order of 100 molecules. This corresponds to a diameter of about 50 A., if one assumes the cluster to be spherical. At the concentrations usually employed in emulsion polymerization, there are some 10 micelles per milliliter of water. 

The purpose of calculating Henry s Law constants is usually to determine the parameters of the adsorption potential. This was the approach in Ref. [17], where the Henry s Law constant was calculated for a spherically symmetric model of CH4 molecules in a model microporous (specific surface area ca. 800 m /g) silica gel. The porous structure of this silica was taken to be the interstitial space between spherical particles (diameter ca. 2.7 nm ) arranged in two different ways as an equilibrium system that had the structure of a hard sphere fluid, and as a cluster consisting of spheres in contact. The atomic structure of the silica spheres was also modeled in two ways as a continuous medium (CM) and as an amorphous oxide (AO). The CM model considered each microsphere of silica gel to be a continuous density of oxide ions. The interaction of an adsorbed atom with such a sphere was then calculated by integration over the volume of the sphere. The CM model was also employed in Refs. [36] where an analytic expression for the atom - microsphere potential was obtained. In Ref. [37], the Henry s Law constants for spherically symmetric atoms in the CM model of silica gel were calculated for different temperatures and compared with the experimental data for Ar and CH4. This made it possible to determine the well-depth parameter of the LJ-potential e for the adsorbed atom - oxygen ion. This proved to be 339 K for CH4 and 305 K for Ar [37]. On the other hand, the summation over ions in the more realistic AO model yielded efk = 184A" for the CH4 - oxide ion LJ-potential [17]. Thus, the value of e for the CH4 - oxide ion interaction for a continuous model of the adsorbent is 1.8 times larger than for the atomic model. 

The mechanisms of annihilation of cluster ions are ion-ion recombination (on the average 3%) and sedimentation on aerosol particles (on the average 97% of cluster ions at ground level). The result of the combination of a cluster ion and neutral particle is a charged particle called an aerosol ion. In conditions of detailed thermodynamic equilibrium the probability that a spherical particle of diameter d carries q elementary charges is calculated from the Boltzmann distribution ... 

In alloys and RPV steels with > 0.07wt%Cu, and irradiation temperatures > 200°C, Cu-enriched solute clusters form. At irradiation temperatures > 325 °C, these can grow to >4nm diameter, and probably transform to the equilibrium fee -Cu phase, but at the temperatures and fluence of interest most CECs in irradiated steels will be bcc." Radiation-induced point defects enhance the substitutional solute diffusion rate and enhance the rate of precipitation. In addition, nucleation of CECs appears to be easier in the presence of matrix defects. The nature of the matrix defects on which CECs nucleate is not clearThe relative importance of homogeneous and heterogeneous nucleation of CECs under irradiation is not agreed, although homogeneous nucleation will, naturally, become more likely as the Cu supersaturation increases. ... 

Van der Waals clusters can be produced in a supersonic expansion of a gas into vacuum through a nozzle of small diameter. The consequence of the expansion is a sudden drop in the pressure and the temperature of the expanding gas, resulting in condensation when the expanding gas crosses the conditions of gas-liquid or gas-solid equilibrium. Because of the rapidity of the pressure and temperature changes, typically two to six orders of magnitude in a few microseconds, the nucleation process taking place under these conditions is complex and not totally understood. 

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