Sphere of solubility

Hansen defined solvent as a point in three-dimensional space and solutes as volumes (or spheres of solubility). If a solvent point is wifliin the boundaries of a solute volume spaee then the solute ean be dissolved by the solvent. If tire point eharacterizing the solvent is outside the volume spaee of a solute (or resin) sueh a solvent does not dissolve the solute. The solubility model based on this eoneept is broadly applied today by modem eomputer teehniques using data obtained for solvents (the three components of solubility parameters) and solutes (eharaeteristie volumes). A triangular graph ean be used to outline the limits of... 

Hansen gave a visual interpretation of his method by means of three-dimensional spheres of solubility, where the eenter of the sphere has eoordinates eorresponding to the values of components of solubility parameter of polymer. The sphere can be coupled wifli a radius to characterize a polymer. All good solvents for particular polymer (each solvent has been represented as a point in a three-dimensional space with coordinates) should be inside the sphere, whereas all non-solvents should be outside the solubility sphere. An example is given in Section 4.1.7. 

Hansen developed a visual interpretation of his method. This is a three-dimensional sphere of solubility in which the centre of the sphere has coordinates corresponding to the values of the components of the polymer solubility parameter. A sphere radius can be used to characterize dissolving characteristics of polymers by different solvents. Each solvent is represented by a point on a three-dimensional space with 8, 8p, 8 as axes. The point should be inside the sphere (the solubility volume) for polymer and all non-solvents should be outside the solubility volume. 

These values are useful because the distance Ra between the solubility parameters of any given solvent from the centre of the sphere of solubility for the polymer can be calculated using the following equation... 

Figure 2.6 illustrates Hansen s sphere of solubility and shows how three separate two-dimensional projections are required to obtain a full solubility picture by conventional means. This has been done for an acrylic polymer, Elvacite 2013, in Figure 2.7. Only those points which fall within all three circles come within the sphere of solubility and should therefore be true solvents for this particular polymer.

Figure 2.6 Diagrammatic representation of a polymer solubility plot based on Hansen s parameter system. The dotted circles represent projections of the sphere of solubility . A specific example of these projections is shown in Figure 2.7.

Figure 2.7 Projection in the <5p/<5d plane of a Hansen type sphere of solubility for Elvacite 2013 (solvent code numbers are given in...

Suspension polymerization of VDE in water are batch processes in autoclaves designed to limit scale formation (91). Most systems operate from 30 to 100°C and are initiated with monomer-soluble organic free-radical initiators such as diisopropyl peroxydicarbonate (92—96), tert-huty peroxypivalate (97), or / fZ-amyl peroxypivalate (98). Usually water-soluble polymers, eg, cellulose derivatives or poly(vinyl alcohol), are used as suspending agents to reduce coalescence of polymer particles. Organic solvents that may act as a reaction accelerator or chain-transfer agent are often employed. The reactor product is a slurry of suspended polymer particles, usually spheres of 30—100 pm in diameter they are separated from the water phase thoroughly washed and dried. Size and internal stmcture of beads, ie, porosity, and dispersant residues affect how the resin performs in appHcations. 

In strongly acid solution the reaction proceeds from left to right, but is reversed in almost neutral solution. Oxidation also proceeds quantitatively in a slightly acid medium in the presence of a zinc salt. The very sparingly soluble potassium zinc hexacyanoferrate(II) is formed, and the hexacyanoferrate(II) ions are removed from the sphere of action ... 

The polyperoxidation of 1,3-dienes is even more dangerous because they are more reactive and some of their polyperoxides are insoluble. With butadiene, the polyperoxidation takes place at temperatures lower than -113 C the oxygen is absorbed very quickly and forms insoluble polyperoxides that precipitate. It was estimated that at a temperature of 25°C the critical mass of such a compound consists of a sphere of diameter 9 cm. This diameter decreases quickly with the temperature. Isoprene behaves in the same way, but its polyperoxide is soluble, in these conditions, the monomer can absorb any temperature rise which would be caused by the beginning of a decomposition, thus reducing risks. If the monomer evaporates, a gum that detonates at 20°C is formed if the medium is stirred. With cyclopentadiene, polyperoxide is more stable and only detonates at a high temperature. 

F. Asmar, T. S. Gahoonia, and N. E. Nielsen, Barley genotypes differ in activity of soluble extracellular phosphatase and depletion of organic phosphorus in the rhizo.sphere soil. Plant Soil 172 1 (1995). 

An essential step in processes utilizing soluble transition metal catalysts is the coordination of the substrate to the transition metal (5.). A corequisite is the availability of a vacant site in the coordination sphere of the metal for substrate binding, a provision often met by dissociation of a bonded... 

Scattering media to which this matrix applies include randomly oriented anisotropic spheres of substances such as calcite or crystalline quartz (uniaxial) or olivine (biaxial). Also included are isotropic cylinders and ellipsoids of substances such as glass and cubic crystals. An example of an exactly soluble system to which (13.21) applies is scattering by randomly oriented isotropic spheroids (Asano and Sato, 1980). Elements of (13.21) off the block diagonal vanish. Some degree of alignment is implied, therefore, if these matrix elements... 

When coke-oven or petroleum-tar pitches were heated to an appropriate temperature (about 420°C.) and quenched, the product contained spheres of various sizes mostly in the range 0-10 microns. The spheres were normally, fairly regularly distributed through the pitch matrix, with small and larger spheres intermixed. When the toluene-soluble extract of the pitch was carbonized to the same temperature, fewer spheres were present in the product, but their diameters were considerably greater. Under these conditions many spheres were more than 10 microns across, and some exceeded 50 microns. This result suggested that nucleation occurred less commonly or less easily in the toluene-soluble pitch fraction and was associated with the presence of C1 -insoluble material. 

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