Plait point curve

In WI and WII representations, the critical points CPp and CP are called plait points. If the difference between the temperature T at which the phase diagram is recorded and the critical point of the binary mixture, 7p or Ta, increases, the distance from the plait point to the oil-amphiphile axis for CPp and the water-amphiphile axis for CP also increases. An important characteristic of a ternary system is the line that links the plait points as a function of temperature. The plait point curve is really the trace of the partitioning of the amphiphile between oil and water. The closer the plait point is to the oil, the more water soluble the amphiphile, and vice versa. 

If the phase diagram exhibits a 3PT it is called a Winsor III (Will) system. In such a situation, the plait point curves do not merge but cross each other and stop at two terminal critical points (see Figure 3.17d or Figure 3.17e). 

Fig. 3. Typical nonionic amphiphile—oil—water—temperature phase diagram, illustrating (a) the S-shaped curve of T, M, and B compositions, (b) the lines of plait points, (c) the lower and upper critical end points (at and respectively), and (d) the lower and upper critical tielines.

As the tangent plane rolls on the primitive surface, it may happen that the two branches of the connodal curve traced out by its motion ultimately coincide. The point of ultimate coincidence is called a plait point, and the corresponding homogeneous state, the critical state. 

Now the plait point is on the spinodal curve, and any two corresponding points of the connodal curve adjacent to the plait point are on a part of the surface which is convex in every direction, and for which therefore... 

Thus the spinodal curve does not cut the connodal curve at the plait point, and it is simplest to assume the two curves to be tangent at that point. From (26) it follows that the direction of the tangent at any point of the spinodal curve is given by ... 

Again, the limiting position of the line joining points of the connodal curve and the direction of the common tangent to the connodal and spinodal curves at the plait point is given by ... 

With motion along the connodal curve towards the plait point the magnitudes Ui and U2, Si and S2, and ri and r2, approach limits which may be called the energy, entropy, and volume in the critical state. The temperature and pressure similarly tend to limits which may be called the critical temperature and the critical pressure. Hence, in evaporation, the change of volume, the change of. entropy, the external work, and the heat of evaporation per unit mass, all tend to zero as the system approaches the critical state ... 

The plait point is an ordinary point on the connodal curve, and hence it is immediately evident that the specific volume and entropy in the critical state are intermediate between those of adjectent liquid and vapour phases. 

Of all the characteristic points in the phase diagram, the composition of the middle phase is most sensitive to temperature. Point M moves in an arc between the composition of the bottom phase (point B) at Tlc and the composition of the top phase (point T) at 7, reaching its maximum surfactant concentration near T = (Tlc + Tuc)/2. (Points B and Tmove by much smaller amounts, also.) The complete nonionic-amphiphile—oil—water—temperature phase diagram is illustrated by Figure 3, including the S-shaped curve of T, M, and B compositions the two lines of plait points, which terminate at the lower and upper critical end points and the lower and upper critical tielines (at Tlc and T respectively). 

J. H. van t Hoff compared the phenomenon of dissociation with that of evaporation. He compressed a mixture of equal vols. of phosphine and hydrogen chloride until the tube was half filled with phosphonium chloride crystals. The tube was now heated by means of a water-bath. Fusion occurred at 25°, and at 50°-51° and a press, of 80-90 atm., the line of demarcation between liquid and gas disappeared whilst on cooling, the thick clouding which characterizes the critical point was observed. F. E. C. Scheffer represented the press.-temp, relations, more or less diagrammatically by Fig. 13. G represents the m.p. curve of phosphonium chloride the plait-point represents II, the critical temp, of that salt AC, the vap. press, curve of hydrogen chloride BD, the vap. press, curve of phosphine and GI, the... 

Dobashi, T. Nakata, M. Kaneko, M., "Coexistence Curve of Polystyrene in Methylcyclo-hexane. III. Asymptotic Behavior of Ternary System Near the Plait Point, J. Chem. Phys., 80, 948 (1984). 

If it is assumed that the tie-line of corresponding points on the connodal curve is ultimately tangent to that curve at the plait-point, then the direction of this tangent is given by either of the equations ... 

A particularly useful diagram is obtained by plotting the solute equilibrium line on log-log scales as X23/X33 versus X21/XU [from Eq. (15-23)] along with a second plot consisting of X23/X33 versus X23/X13 and X21/X31 versus X21/X11. This second plot is termed the limiting sol-ubihty curve. The plait point may easily be found from the intersection of the solute equilibrium line with this curve, as shown by Treybal, Weber, and Daley [Ind. Eng. Chem., 38(8), pp. 817-821 (1946)]. This type of diagram also is hdpful for interpolation and limited extrapolation when equilibrium data are scarce. An example diagram is shown in Fig. 15-20 for the water -1- acetic acid -I- methyl isobutyl ketone (MIBK) system. For additional discussion of various... 

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