Phase separation conditions

We present an improved model for the flocculation of a dispersion of hard spheres in the presence of non-adsorbing polymer. The pair potential is derived from a recent theory for interacting polymer near a flat surface, and is a function of the depletion thickness. This thickness is of the order of the radius of gyration in dilute polymer solutions but decreases when the coils in solution begin to overlap. Flocculation occurs when the osmotic attraction energy, which is a consequence of the depletion, outweighs the loss in configurational entropy of the dispersed particles. Our analysis differs from that of De Hek and Vrij with respect to the dependence of the depletion thickness on the polymer concentration (i.e., we do not consider the polymer coils to be hard spheres) and to the stability criterion used (binodal, not spinodal phase separation conditions). 

The crucial question is at what value of <)> is the attraction high enough to induce phase separation De Hek and Vrij (6) assume that the critical flocculation concentration is equivalent to the phase separation condition defined by the spinodal point. From the pair potential between two hard spheres in a polymer solution they calculate the second virial coefficient B2 for the particles, and derive from the spinodal condition that if B2 = 1/2 (where is the volume fraction of particles in the dispersion) phase separation occurs. For a system in thermodynamic equilibrium, two phases coexist if the chemical potential of the hard spheres is the same in the dispersion and in the floe phase (i.e., the binodal condition). 

We conclude that our model describes the dependence of the phase separation conditions on polymer molecular weight, particle radius and particle concentration at least semi-quantitatively. 

Figure 7. Comparison between the experimental phase separation conditions (points) for silicas S6 and SB1 (6) with our theoretical model (full curves). The dashed curve gives the theoretical dependency if in Equation 14 A is replaced by rg.

Colloid stability conferred by random copolymers decreased as solvent quality worsened and became increasingly solvent dependent around theta-conditions. However, dispersions maintain some stability at the theta-point but destabilize close to the appropriate phase separation condition. 

REVERSED-PHASE SEPARATION CONDITIONS Support Matrix Composition... 

The nonionic phosphine 7 was used in the rhodium-catalyzed hydro-formylation of 1-dodecene under thermoregulated phase-separable conditions. Phosphine 7 is soluble in toluene at higher temperatures, but can be... 

Phase separation. Conditions in which substances de-absorb themselves from their host, such as gases forming above liquids or solids forming in liquids,... 

Modifier miscibility plays an important role in this preparation. On the one hand, modifiers must be miscible with the reactive system on the other hand, they must phase-separate during cure. Final morphologies are influenced by the phase-separation conditions. 

Figure 15 Phase separation conditions of the gas-liquid microflows. Solvents 1,1-decanol 2,1-octanol 3,1-propanol 4, nitrobenzene 5, dodecane 6,1,4-dioxane 7, ethanol 8, water 9, carbon tetrachloride 10, m-xylene 11, hexane 12, toluene 13, chloroform 14, ethyl acetate 15, dichloromethane 16, hexane 17, acetone 18, pentane and 19, diethyl ether. The open circles show the theoretical higher limit, the open triangles the theoretical lower limit, the solid circles the experimental results of the higher limit, and the solid triangles the experimental results of the lower limit (Aota et al., 2009a).

Sometimes deionized water is used as first extractant for assessment of water-dissolved element forms. The following have a direct influence on extraction effectiveness and procedure repeatability extractant chemical properties and selectivity, stage order, extraction time, sample mass to extractant volume ratio, and re-adsorption processes. Other parameters, such as pH, solution concentration, temperature, and phase separation conditions should also be taken into account during the optimization of the extraction process. 

However, for a given gas velocity, any change in gas or liquid properties, downcomer and riser geometry, phase separation conditions, liquid volume, reactor height, or gas distribution causes changes in liquid velocity and gas holdup. Therefore, no generalized model or correlation for the volumetric gas-liquid mass transfer coefficient in airlift reactors exists. 

The method consists of preparation of a series of mixtures near the phase separation condition then causing the separation to occur. The onset of turbidity is observed either visually, using a photoelectric cell, or UV-visible spectrophotometer. The ensemble of the cloud points defines the cloud-point curves (CPC) that closely follows the binodal. The method can be extended to rigorous studies of the phase separation by measuring the light scattering intensity. Many refinements of the original turbidity method have been made [Utracki, 1989]. 

The theory was found to predict complex behavior near the phase separation conditions. As the rate of shear increases, first, the system undergoes homogenization, then demixing, followed by another homogenization and demixing. At high rates of shear, the system should behave similarly as in a quiescent state. These predictions were found to be in qualitative agreement with experimental data, e.g., for blends of ethylene-vinylacetate copolymer with chlorinated polyethylene, EVAc/CPE, or polystyrene with poly(vinyl methyl ether), PS/PVME [Hindawi et al., 1992 Eernandez ef fl/., 1993, 1995]. 

An area that will require attention in the future involves in-line analysis of polymer blends during processing potentially allowing feedback information to improve uniformity of the resultant blend. In-line morphology determination, rheological measurements, and shear-induced phase behavior are subjects for consideration. Rheo-optical studies under shear for low molecular weight PS/PIB blends near phase separation conditions were... 

Figure 6.13. Separation mode selection guide for TLC. LSC = liquid-solid chromatography on an inorganic oxide adsorbent BPC = liquid-solid chromatography on a chemically-bonded sorbent RPC = reversed-phase chromatography with a water-containing mobile phase and chemically-bonded stationary phase IPC = ion-pair chromatography with reversed-phase separation conditions and PC = precipitation chromatography. (From ref. [151] Elsevier)...

T02 Torrens, F., Soria, V., Monzo, I.S., Abad, C., and Campos, A., Treatment of poly(styrene-co-methacrylic acid)/poly(4-vinylpyridine) blends in solution under liquid-liquid phase-separation conditions. A new method for phase-separation data attainment from viscosity measurements, J. Appl. Polym. Sci., 102, 5039, 2006. 

Under polymer synthesis there is considerable number of processes proceeding under phase separation conditions, in particular in such systems like "liquid-liquid" (high-viscosity polymer solution - low-molecular fluid), "gas-liguid" (polymer-analogous processes) and "solid-liquid" (catalytic polymerization). Necessity of substance transfer from one phase to another by mass-exchange [140], i.e. removal of diffusive limitations is the feature of heterogeneous processes. In this case one have to deal with serious problems while realizing fast chemical reactions [141]. 

The method consists of preparation of a series of mixtures of varied concentrations (near the phase separation condition) then causing the separation to occur, e.g., by ramping the temperature. The onset of turbidity is observed visually, using... 

The assessment of miscibility and phase separation conditions is relatively easy and is carried out in many laboratories employing view cells that allow visual or optical observations as phase separation is accompanied by a change in the transmitted light intensity. The assessment of phase separation needs special techniques that allow measurement of the scattered light intensities as a function of the scattering angle and time. 

The general expression for the Gibbs potential as a Taylor scries (Equation 3.1 -275) and the phase separation conditions (Equation 3.1-276) enable the phase separation region amplitude to be calculated (Dobashi ct al., 1980ab)... 

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