Concentration-temperature diagram

Fig. 38. Temperature concentration diagram for polymer solutions [102,103]. x = (T — )/0 ( -temperature, c monomer concentration (see Table 5)...

The work of Daoud and Jarmink [DJ76] on the temperature-concentration diagram proceeds by translating results established in the theory of phase transitions to the polymer problem. They also consider the region T < S. For T > 0 their work is equivalent to the argument as given here and discusses an extensive set of physical observables. 

The solids, at any rate the polymerised forms, are regarded as solid solutions of Pa and P/3 in varying proportions. Temperature-concentration diagrams similar to those representing a two-eomponent system have been constructed for these pseudo-components. 

Fig. 4.19 Temperature-concentration diagram for a binary mixture as well as the temperature and concentration profiles in the vapour and the condensate. Indices 0 cold wall, I interface, G core flow of vapour (G Gas), a boiling and dew point lines b condensate and vapour boundary layer c temperature profile d concentration profile...

When we warm up the solution at fixed concentration C in the domain IV of the temperature-concentration diagram, the square radius 3X2 and the overlap ratio increase. The chain is then subject to two contradictory effects first the solvent quality increases, second the screening of the interaction becomes stronger. Let us first recall that the average square distance 3X2 varies in the following manner (see Chapter 12, Section 3.3.2)... 

M. DaoudandG. Jannink, Temperature-concentration diagram ofpolymer solutions, (Paris)... 

The temperature-concentration diagram in Figure 9.27 illustrates the mixing of a saturated solution A and unsaturated solution B to give a mixture with a composition and temperature represented by a point somewhere along line AB, determined by the mixture rule (section 4.4). A supersaturated mixture will be produced if the relative flowrates result in the mixture point lying in the sector below the solubility curve. For example, if A and B are mixed at equal mass flowrates, a supersaturated mixture Mi would be produced (distance AMi = BMi). For the mixture to enter the unsaturated zone, the B A ratio would have to exceed about 7 2 in the case illustrated. The unsaturated mixture M2, for example, is the result of an 8 1 B A ratio (AM2 = 8BM2). 

Fig. 117. Temperature-concentration diagram for the system HDPEl-diphenyl ether, as derived from DSC and optical cloud point measurements (V) onset of crystallisation (A) end of melting en-dotherm (O) optical doud point. Reproduced from Makromol Chem [Ref. 328] by the courtesy of the authors and of Huthig We Verlag PuWshers, Zug, Switzerland...

Two liquid phases always occur in the case of strong positive deviation from Raoult s law. The LLE behavior as a function of temperature only depends on the temperature dependence of the activity coefficients. The possible temperature dependencies for binary systems at constant pressure are shown in Figure 5.67 in the form of the temperature-concentration-diagrams, the scxalled binodal curves. 

Figure 2 Temperature-concentration diagram of states of solution of fiexibie (pa1) (a) and semifiexibie (p>1) (b) polymer chains (the monomer unit iength a is set to unity).

Figure 9.1 Typical arrangements for the cooling and evaporative crystallizations and path of the crystallization in the temperature-concentration diagram.

The liquidus and solidus Hnes are defined from the phase diagram. The Hquidus curve is in a temperature-concentration diagram, the Hne connecting the temperatures at which fusion is just completed for various compositions [83]. Similarly, the solidus curve is the curve representing the equiHbrium between the solid phase and the liquid phase in a condensed system of two components. The points on the solidus curve are obtained by plotting the temperature at which the last of the liquid phase solidifies against the composition, usually in terms of the percentage composition of one of the two components [83]. 

Liquidus is the solubility curve for liquid particle. So in our Interpretation, the Hquidus curve is in a temperature-concentration diagram, the line connecting the temperatures at which freezing is just started for various compositions of a starting Hquid phase. ... 

Figure 9.3 shows examples of basic grid structures which carry the active masses, with examples of size and the alloy composition. Metallurgists describe the characteristics of alloys made out of different metals by phases or temperature/ concentration diagrams. Within these, the formed phases are located metal components of different constitutions and physical condition are described depending upon the composition and temperature. 

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