Solute concentration, state diagrams

Figure 4 shows the application (6) of potentials to the Pt and Au electrodes of the sandwich (vs. a reference electrode elsewhere in the contacting electrolyte solution) so that they span the E° of the poly-[Co(II/I)TPP] couple (Fig. 4B). There is a consequent redistribution of the concentrations of the sites in the two oxidation states to achieve the steady state linear gradients shown in the inset. Figure 4C represents surface profilometry of a different film sample in order to determine the film thickness from that the actual porphyrin site concentration (0.85M). The flow of self exchange-supported current is experimentally parameterized by applying Fick s first law to the concentration-distance diagram in Fig. 4B ...

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). 

It has been proposed to define a reduced temperature Tr for a solution of a single electrolyte as the ratio of kgT to the work required to separate a contact +- ion pair, and the reduced density pr as the fraction of the space occupied by the ions. (M+ ) The principal feature on the Tr,pr corresponding states diagram is a coexistence curve for two phases, with an upper critical point as for the liquid-vapor equilibrium of a simple fluid, but with a markedly lower reduced temperature at the critical point than for a simple fluid (with the corresponding definition of the reduced temperature, i.e. the ratio of kjjT to the work required to separate a van der Waals pair.) In the case of a plasma, an ionic fluid without a solvent, the coexistence curve is for the liquid-vapor equilibrium, while for solutions it corresponds to two solution phases of different concentrations in equilibrium. Some non-aqueous solutions are known which do unmix to form two liquid phases of slightly different concentrations. While no examples in aqueous solution are known, the corresponding... 

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. 

Figure 5.4. A schematic state diagram showing water plasticization at increasing water weight fraction towards glass transition of water at -135°C. Relaxation times decrease rapidly above the glass transition as a result of thermal or water plasticization. Maximally freeze-concentrated solutes show glass transition at Tg and onset of ice melting at TJ. Equilibrium melting is described by the T curve.

Figure 7.3 is another example of a typical state diagram, developed for maltose. Maltose solutions are in glassy state below Tg curve. T g (onset of glass transition) and (onset of ice melting) show constant values for the maximally freeze concentrated solutions, where maximum ice formation occurs between T and Tg, and T is at the end point region of Tg (Figure 7.3) (Roos and Karel 1991b). State diagram for sucrose (Figure 7.4) also shows similar characteristics (Roos and Karel 1991a).

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.)... 

Figure 6. Schematic diagram of the fluidized-bed reactor (from Mast and Drever, 1987). Special features include fast pump recycle to suspend all particles in the reactor and the reservoir for transient event studies or to maintain steady state solute concentrations.

Polymer solutions can be classified according to one of three concentration regimes and the diagram in Figure 13.8 gives a schematic represraitation of the dilute, semidilute, and concentrated states. In the dilute regime, the polymer coils are well separated, and the viscosity behavior, which is determined by the individual contributions of the molecules, has been described in Chapter 9. 

Figure 3.18. State diagram (the left-hand branches of tlie binodal) of tlie. systems PaMS-t-eyclohexane-t-octaiiol (solid lines J 2,) and PaMS-t-dioxanc-t-octemol (dashed lines l 4 for M 10 5 (J, I ), 10 2, 2 ), 100 3, 3). Lines 4 and 4 are related to the 0 compo.sition. Lines marked with show the trajectories of the configurative point during precipitation turbidimetric titration of solutions with the initial concentration Co = 5 10 and 8 10 g/dl (Ramazanov et al., 1982)...

Figure 3.59. State diagram of the NP+IiMWIj system. DIG is Uio biiiodal curve of phase separation. C i.s the critical point. A is the line of the solution-gel transition, is the polymer concentration corre.sponding to the node percolation threshold l-he...

Fig. 1.27 Phase behavior of apoferritin with PEO. Left state diagram of apoferritin mixed with PEO of various molar masses. The apoferritin concentration was kept constant at 54 g/E and the molar mass and concentration of PEO was varied as indicated in the diagram. Results are redrawn from [277]. Right micrographs representing the various kinds of unstable solutions that were found in aqueous apoferritin-PEO mixtures a crystals, b liquid domains and c random aggregates. Reprinted with permission from S. Tanaka and M. Ataka, J. Chem. Phys., 117 3504, Copyright 2002, American Institute of Physics...

Figure 12. Schematic state diagram of temperature vs. w% solute for an aqueous solution of a hypothetical small carbohydrate (representing a model frozen food system), illustrating the critical relationship between Tg and freezer temperature (Tf), and the resulting impact on the physical state of the freeze-concentrated amorphous matrix. (Reproduced with permission from reference 18. Copyri t 1988 Cambridge.)...

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