Critical phase separation temperatur

Polymer solutions display a typical phase diagram as illustrated in Fig. 8.1a, which exhibits a highest critical phase separation temperature, called upper critical solution temperature (UCST). Within the same temperature window, polymer solutions may also crystallize below the solution-crystal coexistence line, as illustrated in Fig. 8.1b. Two kinds of phase transitions will interplay with each other, so that an interception point is observed in the corresponding phase diagrams. The interception point is a three-phase-coexisting point, as illustrated in Fig. 8.1c, called the monotectic triple point. At this point, a dilute solution, a concentrated solution and a crystalline phase can coexist. 

When a homogeneous mixture solution is cooled, phase separation is induced at a certain temperature. This critical phase separation temperature is termed the upper critical solution temperature (UCST). It is a convex upward curve in the plot of composition versus temperature (C-T plot) and its maximum point shifts to a higher temperature with increasing relative molecular mass of the polymer. However, for many polymer-solvent and polymer-polymer blend systems, a decrease in mutual solubility is also observed as the temperature increases. The critical phase separation temperature is called the lower critical solution temperature (LCST). It is a convex downward curve in the C-T plot and the minimum point shifts to a lower temperature with increasing relative molecular mass of the blend components. LCST occurs at a higher temperature than UCST. 

Liquid crystal and polymer dispersions are fabricated using thermally-induced phase separation (TIPS), solvent-induced phase separation (SIPS), or Polymerization-induced phase separation (PIPSX/I)- For TIPS, a homogeneous mixture of a low-molecular weight liquid crystal and thermoplastic polymer is cooled below the critical phase separation temperature to induce phase separation into liquid crystal rich and polymer rich domains. The morphological properties (domain size, number of domains per unit volume, and the composition of the domains) depend primarily on the choice of liquid crystal and thermoplastic polymer, the initial weight fraction of liquid crystal in die initial mixture, and the rate of cooling. 

In the phase separation process, however, it needed some induction period for the polymer to start the phase separation. Almost complete isomerization of the azobenzene pendant groups from the cis to the trans form is required to decrease the phase separation temperature below 19.5 °C. The phase separation process exhibited a non-linear response to the irradiation time or the number of photons. When the number of absorbed photons reached a critical value, the system underwent the phase separation and the polymer chain was shrunk. The photo-stimulated phase separation/dissolution cycle was not observed below 19.4 and above 26.0 °C. 

If cation and anion are preferentially solvated by the same solvent component (homo-selective solvation) the phase separation temperature of the solvent mixture is shifted to higher temperatures. On the other hand, with heteroselective solvation of an electrolyte, when one ion is preferentially solvated by one solvent component and the counterion by the second component, the upper critical solution temperature decreases by adding that electrolyte. 

The temperature-dependent miscibility of fluorous biphasic systems [1] can be predicted by use of the Hildebrand-Scratchard or regular solution theory [2, 9]. According to this theory the critical temperature (T). above which the two liquids of a biphasic system mix in all ratios is dose to the phase-separation temperature of a biphasic system consisting of equal volumes of each phase ... 

A combination of SLS and DLS methods was used to investigate the behavior of nonionic micellar solutions in the vicinity of their cloud point. It had been known for many years that at a high temperature the micellar solutions of polyoxyethylene-alkyl ether surfactants (QEOm) separate into two isotropic phases. The solutions become opalescent with the approach of the cloud point, and several different explanations of this phenomenon were proposed. Corti and Degiorgio measured the temperature dependence of D pp and (Ig), and found that they can be described as a result of critical phase separation, connected with intermicellar attraction and long-range fluctuations in the local micellar concentration. Far from the cloud point, the micelles of nonionic surfactants with a large number of ethoxy-groups (m 30) may behave as hard spheres. ... 

A pycnometer of approximately 50 mL was cleaned with hot cleaning solution for use in preparing the mixtures. The rubber cap, syringes, and needles were rinsed with research-grade acetone. Weighings of the pycnometer with and without the samples were performed in a temperature- and humidity-controlled room using an analytical balance with a precision of 0.0002 g. The sample used was one at 0.3952 dt 0.0001 mol fraction n-decane, the reported composition at the critical solution point (10). The phase separation temperature was 26.9°C. 

Liquid—Liquid Phase Separation, in contrast to solid-liquid phase separation, lowering temperature can induce liquid-liquid phase separation of a polymer solution with an upper critical solution temperature and when the crystallization temperature of the solvent is sufficiently lower than the phase separation temperature. In an equilibrium phase diagram of a polymer solution, the spin-odal curve divides the liquid-liquid phase separation region into two regions a thermodynamically metastable region (between the binodal and spinodal) and a thermodynamically unstable region (enclosed by the spinodal) (Fig. 11). Above the... 

Fig. 1 Scaled structure factor for a near-critical mixture (fj v/v) deuterated polybutadiane (DPB) and protonated polyisoprene (HPI) obtained from time-resolved light scattering experiments at various times in the late-stage SD at a quench depth JT = T — TsI = 3-9 °C where T, (36.1 °C) is spinodal temperature and T (= 40 °C) is phase-separation temperature [10]. The time covered corresponds to 6.4-118 in the reduced time t defined by t/t [3,8] (tc at 40 °C is 46.6 min)...

No appears. Thus, in these phase diagrams, a lower critical phase solution temperature (LCST) exists above which the phase separation (I + No) occurs. Such an LCST has been observed in a mixed system of liquid crystal molecules and main-chain liquid crystal polymers with strong attractions caused by hydrogen bonding [53]. If the surface of the rodlike molecules would be modified with surfactant molecules, it is conceivable that the liquid crystal molecules and the rod-shaped molecules could align vertically [52] as described in Fig. 10.15. Such a two-phase separation of Ni + N2, or 1 + N2 has been predicted theoretically [52]. 

SO far in detail. From the point of view of pure theory, or of Monte Carlo simulations, it is practical to regard temperature T, bond probability p, and monomer concentration (j> as three independent variables and to study phase transition surfaces in this T - p - space. (The special plane p = 1 corresponds to Fig. 5 above, the limit T = < to Fig. 6.) At a fixed temperature T above the critical consolute temperature Tc, i.e. in the one-phase region one has curves similar to the T = > limit of Fig. 6 only the end point at p = 1 is shifted slightly to lower concentrations

quantitative results for these percolation line in the simple cubic lattice on the basis of Monte Carlo simulations. (At temperatures appreciably below the phase separation temperature T the system is separated into one phase with very few monomers where even for p = 1 no gelation is possible, and another phase with very few solvent molecules where the system is approximated well by random-bond percolation, 0 = 1.)... 

Phase separation in this way is most effective if the light key component is significantly above its critical temperature. If a component is above its critical temperature, it does not truly condense. Some, however, dissolves in the liquid phase. This means that it is bound to have an extremely high K value. 

Remember that the hump which causes the instability with respect to phase separation arises from an unfavorable AH considerations of configurational entropy alone favor mixing. Since AS is multiplied by T in the evaluation of AGj, we anticipate that as the temperature increases, curves like that shown in Fig. 8.2b will gradually smooth out and eventually pass over to the form shown in Fig. 8.2a. The temperature at which the wiggles in the curve finally vanish will be a critical temperature for this particular phase separation. We shall presently turn to the Flory-Huggins theory for some mathematical descriptions of this critical point. The following example reminds us of a similar problem encountered elsewhere in physical chemistry. 

For the phase separation problem, the maximum and minima in Fig. 8.2b and the inflection points between them must also merge into a common point at the critical temperature for the two-phase region. This is the mathematical criterion for the smoothing out of wiggles, as the critical point was described above. 

By combining Eqs. (8.42), (8.49), and (8.60), show that Vi°(52 - 5i) = (l/2)RTj., where T. is the critical temperature for phase separation. For polystyrene with M = 3 X 10, Shultz and Floryf observed T. values of 68 and 84°C, respectively, for cyclohexanone and cyclohexanol. Values of Vi° for these solvents are abut 108 and 106 cm mol", respectively, and 5i values are listed in Table 8.2. Use each of these T. values to form separate estimates of 62 for polystyrene and compare the calculated values with each other and with the value for 62 from Table 8.2. Briefly comment on the agreement or lack thereof for the calculated and accepted 5 s in terms of the assumptions inherent in this method. Criticize or defend the following proposition for systems where use of the above relationship is justified Polymer will be miscible in all proportions in low molecular weight solvents from which they differ in 5 value by about 3 or less. 

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