Polynary systems

Introduction of ternary interactions is of principal significance for a shift effect of the 0 point. By definition, this point implies that the second virial coefficient is equal to zero. If Equation 301 is represented as 

This means, at the true 9 point, the attrtiction-rcpulsion compensation lakes place not only at the level of two-particle interactions, but two-particle attraction is compensated for by three-particlc repulsion. 

At the intramolecular level, the shift of the 9 point must be observed with a rather large w and provided that the segment concentration in a coil is quite high, which depends on coil topology. Eg. three-particle interactions are most probable in branching (star-like) macromolecules with other conditions being equal. 

The fine compensation effect at the 0 point will be discussed in more detail in section 5.5 in connection with renormalization group approtiches in polymer theory. 

As to the measurable properties of polymer systems, three-particle interactions are not fully described in the literature and, as a rule, arc not explicitly taken into account while interpreting results in the mean field approximation. 

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While passing on to polynary systems, we have, to change our notation. If the. subscript 1 remains to denote I,MWf,. the polymer honiologms should be denoted by 2 etc. which is inconvenient. On the other hand, the components of binary systems are most naturally denoted by the subscripts 1 and 2. I o emphasize the difference between the binary and the polynary systems, it is reasonable to change the notation of volume fractions (i, and (p,. respectively). 

A number of practically important problems, in particular, plotting a qiiasibinary section of a polynary system (see further) requires a way of determining the characteristic quantities of phase separation from a given overall polymer concentration that Floi 3 s method is unable to provide. 

The location of the phase coexistence curves on a qiiasibinary. section of a polynary system depends on the total polymer concentration (Figures 3.11 3.13). 

Jordon ct al. (1969) have found the critical point of the polynary system to be located on the right-hand branch of the spinodal and on the right-hand boundary of the phase separation region for systems with a LOST as well as for systems with a UCST. The critical point is the common point of the spinodal and the boundary of the phase separation region (the cloud-point curve). The spinodal and the CPC has a common tangent line at it. 

Figure 3.82. The spinodals of quasi-binajy sections of the P1+P2 (upper curves) 2uid P+LMWL (lower curves) systems with polymolecu-l2tr polymers. Dashed 2tnd dot-and-dash lines correspond to the spinodals of. systems with concentration-dependent (according to F qua-tion 3.7-20) g gi = —0.1 and +0.1, respectively. The ratios mi/m.2 and m ,i/m 2 (figures) are marked at the curves. Empty circles denote the critical points for systems with monomoiecular polymers, solid circles denote the critical points of polynary systems with 02/01 = -...

Number of degrees of freedom in the critical state of a polynary system with a concentration-independent pareimeter g... 

As an example, Figure 3.102 reproduces Figure 9 from Sole et al. (1984). The CPC shows three break points which are the points of intersection of the CPC s isolated portions. These points define three-phase equilibrium which exists at a certain temperature. For binary systems, the CPC contains complete information on the phase state of the system, as it coincides with the binodal curve. Moreover, the critical points are here always located at the CPC s maximum, as opposed to a polynary system. The spinodal touches (or intersects) the CPC at its extremal points. 

In a polynary system at two-phase equilibrium, there is a curve of coexistence of phases on the 7 vs ip diagram for each polymer concentration, and it shows a break at high temperatures (if the system has the upper critical. solution temperature UCS I ) and at all the concentrations except one ip = fic-... 

Polynare Systeme mit Wasser — Polynary systems contayning water... 

A few polynary systems of several inorganic and/or organic components besides water are added to each table for ternary aqueous systems. The... 

Polynare Systeme anorga sche Komponenten A, B, C,..., Wasser Polynary systems inorganic components A, B, C,..., water... 

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