Miscibility square

In contrast to PEO, other water-soluble polymers, such as poly(Al-isopropylacrylamide) (PNIPAM), show very flat LCST, whose cloud-point lines and spinodal lines are horizontal up to 20 wt% of polymer concentration and almost independent of the molecular weight [49-54]. The phase separation region takes a shape like the bottom part of a square, so that in what follows we refer to it as the miscibility square. Obviously, the miscibility square cannot be explained by random adsorption of water molecules. But,... 

Figure 6.13(a) draws the spinodal curves for different cooperative parameters a with other parameters fixed. The bottom part of the miscibility square becomes flatter with decreasing a. In the calculation, the usual miscibility domes with UCST appear at low temperatures, but these are not observable in the experiments because the water freezes. For polymer concentrations higher than (/>=0.5, our theoretical description becomes poor because of the depletion of water molecules the number of water molecules becomes insufficient to cover the polymers. 

Figure 6.15(a) compares theoretical calculations with experimental data [52] on the spinodal points, and Figure 6.15(b) shows the fraction 9 of the bound water molecules plotted as functions of the temperature for three different polymer concentrations. In the experiments, the upper part of the miscibility square cannot be observed because the... 

Lohse et al. have summarized the results of recent work in this area [21]. The focus of the work is obtaining the interaction parameter x of the Hory-Huggins-Stavermann equation for the free energy of mixing per unit volume for a polymer blend. For two polymers to be miscible, the interaction parameter has to be very small, of the order of 0.01. The interaction density coefficient X = ( y/y)R7 , a more relevant term, is directly measured by SANS using random phase approximation study. It may be related to the square of the Hildebrand solubility parameter (d) difference which is an established criterion for polymer-polymer miscibility ... 

Tables IV to VIII present in concise form, though complete, the data from five papers (17, 106, 121, 211, 372), each giving miscibilities of a group of substances. The papers are in the form of triangular or rectangular charts similar to mileage charts on road maps. In each square is given M or S for miscible, I for immiscible, and usually R for reacts. This method is unsatisfactory for more than about 50 liquids because of the large area required. Since about 70% of the pairs are miscible, much of the space is largely wasted.

The square route of the cohesive pressure is termed Hildebrand s solubility parameter (5). Hildebrand observed that two liquids are miscible if the difference in 5 is less than 3.4 units, and this is a useful rule of thumb. However, it is worth mentioning that the inverse of this statement is not always correct, and that some solvents with differences larger than 3.4 are miscible. For example, water and ethanol have values for 5 of 47.9 and 26.0 MPa°-, respectively, but are miscible in all proportions. The values in the table are measured at 25 °C. In general, liquids become more miscible with one another as temperature increases, because the intermolecular forces are disrupted by vibrational motion, reducing the strength of the solvent-solvent interactions. Some solvents that are immiscible at room temperature may become miscible at higher temperature, a phenomenon used advantageously in multiphasic reactions. 

Accepting that the last traces of oil are more difficult to dissolve does not nullify the basic conclusions to be derived from the preceding theories based on simple diffusion with free miscibility of solvent and oil. If free miscibility does not exist in the latter stages of extraction, this means simply that the effective concentration of solute is not the concentration of oil in the solid seed material but a lower concentration that is limited by the solubility of the oil in the solvent. The rate of diffusion will be less than observed in the earlier stages, not because the diffusion coefficient has decreased, but because the oil content of the solid material is no longer a proper measure of its instantaneous content of diffusible material. The diffusion or extraction rate will, for example, still be inversely proportional to the square of the flake thickness. 

Figure 12. Experimental estimates for the translational D,rms (T) and rotational (T) diffusion coefficients for pure BP (solid triangles and solid squares) as well as for the re-entrant mixture (circles with a dot and squares with a dot). Estimates of both transport coefficients as derived using Eqn. 8 and 9 are shown by vertical bars (miscible state) and crosses (phases within the immiscibility loop). The solid lines through 3MP data correspond to fits to a thermally activated process.

Theory thus predicts that the reciprocal of the critical temperature (in °K ) for the onset of opalescence should vary linearly with the reciprocal of the square root of the molecular weight in a given polymer-solvent system. Furthermore, 9 may now be identified as the critical miscibility temperature in the limit of infinite molecular weight. 

It is a popular lore that the introduction of some fluorine atoms or a short perfluoroalkyl group results in increasing lipophilicity. A classical parameter 8, Hildebrand s solubility parameter, which is the square root of the cohesive energy density, has been used for miscibility estimation [2]. If two liquids have similar values for 8, i.e. if (Si —S2)2 is small, they are miscible. 

As discussed above, the solubility parameter is usually assumed to be equal to the square root of the cohesive energy density. It thus encompasses all of the different types of forces of cohesion in a material. Sometimes, however, the solvation of a polymer by a solvent, the behavior of plasticizers, pigments and other additives, or the blending of two polymers, requires certain specific types of interactions to exist between the polymer and the solvent, or between the two polymers that are to be blended. In such cases, the matching of the strengths of these specific types of interactions may play a crucial role in solvation or miscibility, and a more refined treatment may be necessary than can be provided by a single-valued solubility... 

The square root of the cohesive energy density is termed the solubility parameter d. It is also a measure of the intermolecular forces in pure substances. Solvents with comparable solubility parameters have similar interaction forces and are therefore readily miscible and mutually soluble. In order to take account of not only the dispersion forces but also of the polar forces and hydrogen bonds, the solubility parameter is resolved into the following components [14.26], [14.27] ... 

FIGURE 3.22 Resistance to separation of strips of two miscible rubbers (circles) and two immiscible rubbers (squares). Whereas adhesion of the latter remains low, the former is time dependent as the chains interdiffuse. At long times the interface is gone and the peel adhesion... 

The concept of the solubility parameter 6, which is frequently used in studies of polymer compatibility, is not always applicable. The solubility parameter is equal to the square root of the substance s cohesion energy density (6 = VDEC) and reflects only intermolecular interaction without accounting for the entropy factor. This parameter is an integral characteristic of only intermolecular interaction, and the components miscibility is determined by the presence of functional groups capable of specific interactions in the polymer molecules. This is why... 

The -intercept obtained from the linear plot between equilibrium melting point depression (AT °) and the square of the volume fraction of the amorphous component (v ) after Equation (6) (described in detail in Miscibility) developed by Nishi and Wang, (1975) for both the blends is close to zero as shown in Figure 19 suggesting that entropy effect has insignificant influence on the x -... 

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