Solute concentration curves, freeze

FIG. 20-4 Curves for progressive freezing, showing solute concentration C in the solid versus fraction-solidified X Pfann, Zone Melting, 2d ed., Wiley, New York, 1966, p. 12.)... 

FIGURE 8.11 State diagram for food materials, showing the Tg curve and isoviscous states above Tg. Maximally freeze-concentrated solids with a solute concentration of C g have Tg at T g. Ice melting within maximally freeze-concentrated materials occurs at T m. The equilibrium melting curve shows the equilibrium melting point Tm as a function of concentration. (From Roos, Y.H. and Karel, M., Food Technol., 45, 66, 1991b.)... 

Stability. As long as the temperature remains below Tg, the composition of the system is virtually fixed. This implies physical stability crystallization, for instance, will not occur. As mentioned, some chemical reactions may still proceed, albeit very slowly because of the high viscosity and the low temperature. The parameters Tg and i//s are, however, not invariable they are not thermodynamic quantities. Their values will depend to some extent on the history of the system, such as the initial solute concentration and the cooling rate. The curve in Figure 16.6 denoted rff (for fast freezing) shows what the relation may become if the system is cooled very fast. The Tg curve is now reached at a lower ice content, so the apparent Tg and i// values are smaller. However, the system now is physically not fully stable water can freeze very slowly until the true i// s is reached. 

Figure 2. Freezing potential curves for different ionic species (a) and concentrations (b). Freezing rate was 5 microns a second, Ionic distributions for the 2,5 X lO M solutions (except NHjCl) are shown in Figure 10, Potential of NH.Cl solution is negative with respect to the ice, all others are positive...

Concentration Dependence of Freezing Potential and Shunt Current. As has been pointed out, in Group I solutes the freezing potential curve in any experimental mn builds up to a maximum, after which it declines as the concentration on the liquid side of the phase boundary increases. The height of this maximum is itself a function of the initial solution concentration and shows a maximum value at an optimum concentration that depends on the particular solute. 

Differential ion transfer across the phase boundary is manifest in small differences of distribution coeflBcients for the species of an ion pair. The distribution coeflBcient for a given ion depends also on the other ionic species present in solution and their concentrations. The apparent distribution coeflBcients, determined from experiment, depend on both freezing rate and concentration. Differential diffusion appears to play only a secondary role. The apparent distribution coeflBcients for potassium and cesium fluoride are higher than those for HF solutions of the same concentration. They appear to increase with concentration while those for HF decrease. The increase is perhaps explained by the formation of regions of higher concentration at cell or grain boundaries, or it may be related to the possibility that most cations enter the ice lattice interstitially rather than substitutionally. The interpretation of solute distribution curves in ice is diflBcult. 

So far, the behaviour is the same as with salt solutions. However, unlike salt, sucrose crystals do not form readily, and the solution can become supersaturated, Le. the solute concentration increases beyond the point at which it should precipitate out of solution (cf. supercooling) and the freezing point curve can be extended beyond the theoretical eutectic point, D (63% sucrose, — 13.7°C). The solution passes D and continues along the freezing point curve until it meets the... 

Figure 5 Schematic thermograms expected for a bulk solution, related to the corresponding binary diagram (a) cooUng (b) heating, x salt molar fraction T temperature and M2 points representing two solutions of different concentrations Fg freezing curve F g extension of the freezing curve Sg solubility curve . eutectic point.

Figure 7.9 shows some of the thermodynamic quantities of this model as a function of the solute concentration xg. The slopes of G, H, and V give the corresponding partial molar quantities. We have also indicated the frozen-in curve obtained by freezing in the equilibrium at Xg = 0.2. 

L-a-phosphatidyl-L-serine (PS) (Sigma Aldrich) liposomes PS from the manufacturer comes as 10 mg/ml chloroform methanol 95 5 solution. Take 40 /rl and evaporate dry under nitrogen flow, leaving a volume of about 5 /rl. Resuspend in 1 ml of 30 mM Tris/HCl pH 7.4 and sonicate for 1-2 min on ice for a working solution of 400 /ug/ml. Freeze/thaw the stock solution twice with vigorous vortexing on each thaw, as this improves liposome formation. It is stored at -20° and can be frozen/thawed many times. The optimal PS concentration should be determined separately for every new purified batch of dynamin I or of PS stock, with a concentration curve from 1 /rg/ml to 80 /rg/ml (Fig. 2A, for example). 

Salt Brines The typical curve of freezing point is shown in Fig. II-IIO. Brine of concentration x (water concentration is I-x) will not solidify at 0°C (freezing temperature for water, point A). When the temperature drops to B, the first ciystal of ice is formed. As the temperature decreases to C, ice ciystals continue to form and their mixture with the brine solution forms the slush. At the point C there will be part ice in the mixture /(/i+L), and liquid (brine) /i/(/i-t-L). At point D there is mixture of mi parts eutectic brine solution Di [concentration mi/(mi-t-mg)], and mo parts of ice [concentration mol m -t- mo)]. Coohng the mixture below D solidifies the entire solution at the eutectic temperature. Eutectic temperature is the lowest temperature that can be reached with no solidification. 

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