Temperature-concentration phase

Eutectic point (Tc) A single point on a temperature concentration phase (or state) diagram for a binary solution (e.g., water and sugars or salts) where the solution can exist in equilibrium with both crystalline solute and crystalline solvent. Under equilibrium conditions, cooling at Te results in simultaneous crystallization of solvent and solute in constant proportion and at constant temperature until maximum solidification has occurred (based on Fennema, 1996). 

Gels are obtained for concentrations shown in the temperature-concentration phase diagram (Figure 1). Electron spin resonance (ESR) shows (10) that for a given temperature only a fraction (p) of the initial steroid concentration is transferred from the solution to the gel network. The picture of this gel is thus of a supersaturation gel there is a dynamic equilibrium between free molecules in solution and aggregated steroid molecules included in the long objects which constitute the gel network. The free steroid molecules concentration at a temperature where the gel state is stable is (1-p), while C p is the steroid concentration within the solid-iike gel aggregates. 

Fig. 6. Temperature-concentration phase diagrams for four PHIC-toluene systems with different molecular weights [64]...

Here, rheology is used to characterize the gel state, whose stability, as measured thermodynamically or kinetically, can be described by temperature-concentration phase diagrams or simply time. The structural features of gelator aggregates at nanoscopic scales are described via data from the complementary techniques of electron microscopy and scattering techniques. Finally, the optical properties, including absorption and luminescence, are detailed. 

In reactor startup it is often very important /tow temperature and concentrations approach their steady-state values. For example, a significant overshoot in temperature may cause a reactant or product to degrade, or the overshoot may be imacceptable for safe operation. If either case were to occur, we would say that the system exceeded its practical stability limit. Although we can solve the imsteady temperature-time and concentration-time equations numerically to see if such a limit is exceeded, it is often more insightful to study the approach to steady state by using the temperature-concentration phase plane. To illustrate these concepts we shall confine our analysis to a liquid-phase reaction carried out in a CSTR. 

Figure 11.5 The temperature-concentration phase diagram for aqueous j crystallin (MW 20 000) systems (pH = 7, /= 0.24 mol kg" ) , cloud point measurements , concentration measurements of separated phases A = critical point.

The closed loop can be regarded as a vertical section through a nose in the concentration-temperature-pressure space at constant pressure (see Figure 3.13a). When the pressure increases, the surface covered in the temperature-concentration phase by the phase separation loop decreases and vanishes at a critical pressure P. ... 

Figure 1 Temperature concentration phase diagram of aqueous solutions of methylcellulose A4C,M sol-gel transition, , O binodal curve, (i) solution, (ii) turbid gel, (iii, iv) clear gel, shaded region occurrence of the phase separation after one month...

Figure 4.7a shows the temperature-concentration phase diagram for the system naphthalene-/ -naphthol, which forms a continuous series of solid solutions. The melting points of pure naphthalene and -naphthol are 80 and 120 °C, respectively. The upper curve is the liquidus or freezing point curve, the lower the solidus or melting point curve. Any system represented by a point above the liquidus is completely molten, and any point below the solidus represents a completely solidified mass. A point within the area enclosed by the liquidus and solidus curves indicates an equilibrium mixture of liquid and solid solution. Point X, for instance, denotes a liquid of composition L in equilibrium with a solid solution of composition S, and point Y a liquid F in equilibrium with a solid S. ... 

Fig. 9. Temperature-concentration phase diagram of PVC-diethyl ma -onate gels aged for 24 h at 20 °C (O) temperatures determined from the first heating by DSC (scan speed 20°C/min bars indicate the width of the melting endotherm) and ( ) melting temperatures determined visually by the ball-drop method (heating rate 2°C/min). Eeproduced from Macromolecules [Ref. 106] by the courtesy of the authors and The American Chemical Society...

The Hory-Huggins coefficient x plays an important role. If this coefficient is above a critical value, then phase separation into a polymer-rich phase and polymer-lean phase takes place. Since the polymer-solvent interaction is adverse, decreased temperature increases the importance of this interaction energy as the random thermal motion is decreased, and the temperature-concentration phase... 

Figure 3. (a) Temperature-concentration phase diagram at P =0.15 and 0.20, for LJ polymer solutions, (b) Pressure-Temperature phase diagram predicted by coil-to-globule transition of a single chain (lines) compared to LCSTs from phase behavior simulations (points). Ref. [61]. 

The subscript indicates that the property is in the low-temperature region. The results are summarized by the boundary lines (thick lines) on the temperature-concentration phase plane in Figure 2.20. The liquid-liquid phase separation line (coexistence curve) in the low-temperature region is shown by the solid line in the figure. 

Rg. 2.20 Scaling laws of polymer solutions shown on the temperature-concentration phase plane. 

Jacobson and Stockmayer [15] showed the fraction of chains and rings on the temperature-concentration phase plane, and found very interesting phenomena that are analogous to Bose-Einstein condensation. When the parameter B exceeds a certain critical value, 100% rings are formed below a critical concentration of polymers. In fact, when p = 1, we have the coupled equations... 

Rg. 10.26 (a) Temperature-concentration phase diagram of a polymer solution forming networks by double... 

Figure 3.4 The temperature-concentration phase diagrams of BPS-m (m=5,10,20, and 30) with BmimPFj. The phase abbreviations are as follows micellar phase (1 ), discontinuous cubic liquid crystal phase (1 ), hexagonal liquid crystal phase (H ), lamellar liquid crystal phase (L ), lamellar gel phase (L ), reverse micellar phase (L ), ionic liquid phase (IL), and two-phase separation (II). The chemical structure of j0-sitosterol ethoxylates as a typical example of BPS-m is also shown in this figure. Reproduced from Sakai et al. [37] with permission from Japan Oil Chemists Society.

At a second-order SmA-SmC phase transition, the symmetries are different but the layer spacing is the same. Fluctuations can drive a line of second-order SmA-SmC phase transitions to an N-SmA-SmC mul-ticritical point (see Fig. 4) [53]. Competing N-SmA and N-SmC fluctuations pull the N phase under the SmA phase in the temperature-concentration phase plane, leading to the Nj-e-SmA-SmC multicritical point [16]. High-resolution studies, as a function of both concentration and pressure, resolve the fluctuation-driven N-SmA/ N-SmC step (see, e.g. Fig. 5) into a universal spiral (Fig. 12) [16] around the N-SmA-SmC and the Nre-SmA-SmC multicritical points. Loosely speaking, the N-SmA transition line is dominated by N-SmA fluctuations, and the N-SmC transition line is dominated by Brazovskii fluctuations [54] that drive the N-SmC transition to lower temperatures compared to the N-SmA transition [18]. 

Perhaps the earliest example of this is the temperature-concentration phase diagram where FeC alloys show a fee phase both above and below a bcc phase. J. Billard, personal communication. 

Figure 4.18 Temperature-concentration phase diagram for sPS/ diphenyl methane. C, and Cj stand for molecular compounds of differing stoichiometry and for solid phases (the former crystallized solvent, the latter to the form of sPS). is the form evidenced...

Figure 3.4 Temperature-concentration phase diagram for polystyrene-acetone [43]...

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