Phase volume ratio method

For solutions of polydisperse polymers, such a procedure cannot be used because the critical concentration must be known in advance to measure its corresponding coexistence curve. Additionally, the critical point is not the maximum in this case but a point at the right-hand side shoulder of the cloud-point curve. T wo different methods were developed to solve this problem, the phase-volume-ratio method, e.g., Koningsveld, where one uses the fact that this ratio is exactly equal to one only at the critical point, and the coexistence concentration plot, e.g. Wolf, where an isoplethal diagram of values of tp 2 and tp 2 vs. (p 2 gives the critical point as the intersection point of cloud-point and shadow curves. 

The requirement for the ph21.se separation process to cease prior to measurements (which is often not the case in polymer systems) is a restriction of the method. Indeed, only few systems (eg. polystyrene-Fcyclohexane and polyethylcnc- -dicthyl ether) have been studied in detail by the phase-volume ratio method (see the above-mentioned papers). 

This is concerned with the necessity of those cautions while determining critical points by the phase-volume ratio method, which were dealt with in subsection 3.6.2. 

POL Polyakov, V.I., Grinberg, V.Ya., and Tolstoguzov, V.B., Application of phase-volume-ratio method for determining the phase diagram of water-casein-soybean globulins system, Polym. Bull, 2, 757,1980. 

FIGURE 12.1 Schematic illustration of the phase volume ratio method, (a) Fragment of the phase diagram dash-dotted line, secant thick fiill line, binodal thin full line, tie line , phase composition , points of the binodal o, critical point dotted line, rectilinear diameter, (b) Typical dependence of the phase volume ratio on mixture composition. 

Polyakov, V. L, Grinberg, V. Ya, Tolstoguzov, V. B. (1980). Application of Phase-Volume Ratio Method for Determining the Phase Diagram of Water-Casein-Soybean Globulins System. Polymer Bulletin, 2,160-161. 

To check the viability of Eq. (16) the system di-phenylether/branched polyethylene has been used as a test case [78]. Experimental liquid-liquid critical points, measured with the phase volume ratio method [44] for samples varying in degree of branching, may serve the purpose together with some experimental spi-nodal temperatures, measured with the Pulse-Induced Critical Scattering technique of Gordon et al. [41 3]. The data were used to calculate values for the parameters in Eqs. (17) and (18) (details of the fitting procedure can be found in [54]). 

The influenee of pressure and temperature on fluid phase relations in the system ethylene/polyethylene being well documented in a qualitative sense [90-94], the effect of molar mass (distribution) is usually left out of consideration. Only De Loos et al. [95, 97] studied fluid phase relations in terms of cloud points and critical points in the system ethylene/linear PE for eight well-characterized polymer samples. Pressures ranged up to 2000 bar, temperatures were between 390 and 450 K, and a polymer concentration range of 0 to 30 wt% was studied. The weight-average molar masses varied from 3.7 to 118 kg mol. Cloud points were determined visually and critical points were measured with the phase volume ratio method. 

However, as stated above, the partition coefficients measured by the shake-flask method or by potenhometric titration can be influenced by the potenhal difference between the two phases, and are therefore apparent values which depend on the experimental condihons (phase volume ratio, nature and concentrahons of all ions in the solutions). In particular, it has been shown that the difference between the apparent and the standard log Pi depends on the phase volume raho and that this relationship itself depends on the lipophilicity of the ion [80]. In theory, the most relevant case for in vivo extrapolation is when V /V 1 as it corresponds to the phase ratio encountered by a drug as it distributes within the body. The measurement of apparent log Pi values does not allow to differentiate between ion-pairing effect and partihoning of the ions due to the Galvani potential difference, and it has been shown that the apparent lipophilicity of a number of quaternary ion drugs is not due to ion-pair partitioning as inihally thought [80]. 

This phenomenon can be exploited for separation and concentration of solutes. If one solute has certain affinity for the micellar entity in solution then, by altering the conditions of the solution to ensure separation of the micellar solution into two phases, it is possible to separate and concentrate the solute in the surfactant-rich phase. This technique is known as cloud point extraction (CPE) or micelle-mediated extraction (ME). The ratio of the concentrations of the solute in the surfactant-rich phase to that in the dilute phase can exceed 500 with phase volume ratios exceeding 20, which indicates the high efficiency of this technique. Moreover, the surfactant-rich phase is compatible with the micellar and aqueous-organic mobile phases in liquid chromatography and thus facilitates the determination of chemical species by different analytical methods [104]. 

Bibette has used this method to study the effect of osmotic pressure on the stability of thin films in concentrated o/w emulsions [96], by means of an osmotic stress technique. The emulsion is contained in a dialysis bag, which is immersed in an aqueous solution of surfactant and dextran, a water-soluble polymer. The bag is permeable to water and surfactant, but impermeable to oil and polymer. The presence of the polymer causes water to be drawn out of the emulsion, increasing the phase volume ratio and the deformation of the dispersed droplets (Fig. 10). 

Some static headspace methods do not require an external calibration and are based on measurements performed at thermodynamic equilibrium between liquid and gas phase. In the phase ratio variation method (PRV) described by Ettre and Collaborators (1993), the partition coefficient calculation is based on the fact that the headspace concentration changes as a function of the phase volume ratio (gas and liquid phases), while the partition coefficient remains constant. This method has been recently applied to study the interactions between aroma compounds and macromolecules in different food systems (Savary et al. 2006, 2007) but so far not to the wine. 

Some of the methods examined to break the emulsions include filtration, modifying the phase volume ratio, centrifugation and sedimentation. An efficient and economic solution to this problem is yet to be developed. 

---