Solvents, critical values

B = 0 when x = 1/2, a condition we have already seen [Eq. (8.60)], corresponds to a critical value of x for a copolymer of infinite molecular weight. For finite molecular weights this condition is not quite a threshold for precipitation, but is close to it. Polymer-polymer contacts are sufficiently favored over polymer-solvent contacts that a chain of infinite length would undergo phase separation. 

Using the original Hc2/r values, recalculate M using the various refractive index gradients. On the basis of self-consistency, estimate the molecular weight of this polymer and select the best value of dn/dc2 in each solvent. Criticize or defend the following proposition Since the extension of the Debye theory to large particles requires that the difference between n for solute and solvent be small, this difference should routinely be minimized for best results. 

The separation of Hquid crystals as the concentration of ceUulose increases above a critical value (30%) is mosdy because of the higher combinatorial entropy of mixing of the conformationaHy extended ceUulosic chains in the ordered phase. The critical concentration depends on solvent and temperature, and has been estimated from the polymer chain conformation using lattice and virial theories of nematic ordering (102—107). The side-chain substituents govern solubiHty, and if sufficiently bulky and flexible can yield a thermotropic mesophase in an accessible temperature range. AcetoxypropylceUulose [96420-45-8], prepared by acetylating HPC, was the first reported thermotropic ceUulosic (108), and numerous other heavily substituted esters and ethers of hydroxyalkyl ceUuloses also form equUibrium chiral nematic phases, even at ambient temperatures. 

As an indication of the changes in deformation modes that can be produced in ionomers by increase of ion content, consider poly(styrene-co-sodium methacrylate). In ionomers of low ion content, the only observed deformation mode in strained thin films cast from tetra hydrofuran (THF), a nonpolar solvent, is localized crazing. But for ion contents near to or above the critical value of about 6 mol%, both crazing and shear deformation bands have been observed. This is demonstrated in the transmission electron microscope (TEM) scan of Fig. 3 for an ionomer of 8.2 mol% ion content. Somewhat similar deformation patterns have also been observed in a Na-SPS ionomer having an ion content of 7.5 mol%. Clearly, in both of these ionomers, the presence of a... 

Maximum effect of mixing in different liquids is observed at different concentrations of diluted oxygen. For example, in methanol this concentration is equal to 2-tO volume % (in other solvents this value may be different). These conecentrations are called the critical concentrations and are denoted. At oxygen concentrations above the... 

The effect of mixing Ac for various liquids with different values of the dielectric constant e is seen from Fig. 4.26. At lower values of e of the solvent, critical concentration also decreases. Moreover, at... 

According to Flory-Huggins theory, in the limit of x the critical x parameter is 0.5.(H) Below this value the polymer and solvent will be miscible in all proportions. Above this value, the solvent will not dissolve the polymer, but will act only as a swelling solvent. Thus, the pure solvent may not dissolve the polymer even though it is not crosslinked. If x is not , the critical value of x is larger, but the same qualitative arguments regarding mutual solubility of the solvent and polymer hold. Thus, the application of Equation 1 does not require that the pure solvent be able to completely dissolve the polymer, only that the solvent dissolve into the polymer by an amount that can be measured. 

This crude analysis is based on the behavior postulated by the Born equation. However, ion-pair formation equilibrium constants have been observed to deviate ma edly from that behavior (22/ -222)1 Oakenful, and Fenwick (222) found a maximum in the ion-pair formation constants of several alkylamines with carboxylic acids when determined at various methanol-water solvent compositions as shown by their data in Fig. 54. The results demonstrate that in this system the stability constant decreases with increasing organic solvent concentration above a.critical value which yields maximum stability. The authors suggested that this was due to a weakening of hydrophobic interactions between the ion-pair forming species by increased alcohol concentrations. In practice the effect of added organic solvent has been either to decrease the retention factor or to have virtually no effect. 

For m -> oo, the critical value is identical with that in a d- solvent, i.e., A2 = 0 and X = 0-5- Since the solubility of macromolecules decreases with increasing molecular weight, it is possible to separate these materials with respect to their molecular weights by changing the composition of the solvent and/or the temperature. In general, one roughly distinguishes between two methods, namely fractional precipitation and fractional extraction. 

If n solvated nonpolar ligands simultaneously interact with the solvated peptide, then the binary complex that forms can be represented by the equilibrium shown in eq 6. When the concentration and thus the surface tension of the organic solvent reaches a critical value, then the partially solvated peptide P(+cDo)is bound to the RPC stationary phase will desorb and become re-solvated to generate the species P(+ DO)i,m- Thus, overall desorption can be represented as ... 

In the polyelectrolyte regime, due to the presence of low-molecular salt, the osmotic pressure of ions becomes less pronounced because the concentration of salt within the network turns out to be less than the concentration of salt in the outer solution n [27]. As the concentration ns grows, the amplitude of the jump of the dependence a(x) decreases and the jump shifts to the region of better solvents (Fig. 2, curve 2). At some critical value of n, the jump on the curve a(x) disappears, i.e. collapse of the network becomes smooth (Fig. 2, curve 3). Under the subsequent increase of n, the curve a(x) becomes closer and closer to the swelling curve of corresponding neutral network (Fig. 2, curves 4). 

At the point of minimum solubility of the sulphur dioxide the composition of the solvent closely approximates to that required for the monohydrate H2S04.H20 (namely 84-5 per cent, acid), and it is significant that other physical properties of the acid pass through critical values at this concentration (see p. 168). 

If the chromatographic strength of the solvent diminishes beyond a critical value, the macromolecules will interact with the surface. The gain in enthalpy is proportional to the number of segments involved, hence, retention increases with molar mass (see Fig. 1, lines 5 or 0 ). The enthalpic interaction is strongly dependent on the chemical structure of both the surface and the solute. 

These critical values differ from solvent to solvent. With the solvents most fully investigated, sulphuric acid for poly-(p-phenylene terephthalamide) and dimethyl acetamide/lithium chloride for poly (p-benzamide), there are also critical values of solvent composition the sulphuric acid must exceed a critical strength, the lithium chloride in the dimethyl acetamide must exceed a critical concentration. The critical values are, of course, interdependent rather than absolute. Diagrams that display some of the critical values for the two systems cited have been published in patents10,1 l Figures 3 and 4 illustrate the type of information available. 

At very low concentrations, the polymers only exist as single chains. As the concentration increases to reach a critical value, called the critical micelle concentration (CMC), polymer chains start to associate to form micelles in such a way that the hydrophobic segment of the copolymer will avoid contact with the aqueous media in that the polymer is diluted. At the CMC, a signiLcant amount of solvent may still be found inside the micellar core and micelles are described as loose aggregates that exhibit largersize than micelles formed at higher concentrations (Gao and Eisenberg,... 

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