## Some Examples

a. Continuity at negativepressure (©-solvent/poor-solvent transitions). Imre and Van Hook used the Berthelot technique to generate negative pressures in order to induce phase transitions in some different polymer/solvent systems. 17 In PS/propionitrile, PS/PPN, PPN a poor solvent, they demonstrated continuity for the demixing curve across P = 0 and well into the region P<0. It is the choice of solvent quality which dictates whether the hypercritical point lies at P>0, P~0, or P<0. In designing experiments at negative pressure (including the choice of solvent and polymer Mw) one is strictly limited to tensions which are smaller than the breaking strength (cavitation limit) ofthe liquid itself, or the adhesive forcesjoining liquid to wall. Figure 3 shows CP data for a 0.20 wt. fraction PS (MW=22,000) over the range (2>P/MPa>-l), comparing those results with values at higher pressure obtained by another technique.18 The two data sets agree nicely along both UCS and LCS branches and confirm that the equation of state for this solution passes smoothly and continuously across zero pressure into the region of negative pressure. The authors concluded that it is physically reasonable to compare properties of solutions at positive and negative pressure using continuous and smoothlyvarying functions. For example it maybe convenient to represent an isopleth (including the critical isopleth) in terms of an algebraic expansion about the hypercritical origin, evenwhenthat originis found at negative pressure. Such expansions have been found to be useful representations ofdemixing even when the hypercritical origin lies so deep as to be experimentally inaccessible, or is below the cavitation limit.2

In a related study on PS/methyl acetate (PS\MA) we19 examined the 9-solvent/poor-solvent transition at negative pressure (refer to the discussion around Figure 2). MA is a q-solvent at ordinary pressure and the transition corresponds to a merging of the UCS and LCS branches at negative pressure. For PS of MW =2x106 the hypercritical point lies below -5 MPa and was experimentally inaccessible (as it was for Mw=2x107). However CP measurements were carried out at pressures well below P=0 thus establishing continuity of state and showing the likely merging ofthe UCS and LCS branches.

The importance ofexperiments at negative pressure is that they establish continuity of state across the P=0 boundary into the region where solutions are under tension. In this line of thinking the UCS and LCS demixing branches share common cause. That interpretation forces a broadening of outlook which has been useful. For example, an immediate and practical extension was the development of a scaling description of polymer demixing in the (T,X=MW-1/2) Ycr,P plane2 That description employs an expansion about the hypercritical origin, Xhyp, even for Xhyp<0. The approach is in exact analogy to expansions about PHYP (whether positive or negative).

b. Marked curvature for critical demixing in the (T,P)MW,^crit projection. Two component and one component solvents. Although weakly interacting polymer/solvent systems showing ThypL or Phypl (but not both) have been long known, it was not until recently that the pace of experimental work increased to the point where detailed comparisons of theory and experiment became possible. We wanted to find weakly interacting systems with sufficient curvature to display both Tdcpl and PocpLpartly because such systems would afford a good test of commonly used thermodynamic and/or theoretical descriptions of weakly interacting polymer solutions. Interest in scaling descriptions of thermodynamic properties and of intensities of light and neutron scattering during the approach to the critical isopleth further encouraged the search.

In looking for a system with two double critical points we examined a series of two and three component systems.7 For two component studies we chose solutions showing significant curvature in the (T,P)cnt projection, usually with known Thypl or Phypl at convenient Mw. Unfortunately, in each case the curvature was insuficient to display both Thypl and Phypl within experimentally accessible ranges, (~270<T/K<~500) and (- 1 <P/MPa<200). For example, PS solutions of various Mw dissolved in the 9 -solvents CH or MCH show well defined Thcpl at reasonable T and P, but the pressure dependence is such that if Phypl occurs at all it lies at too deep a negative pressure to be observed. Interestingly, solutions of PS in the commercially available mixture ( cis:trans:: 1: 1 )-dimethylcyclohexane(DMCHcis/Trans//i/i) show significantly more curvature but still not enough to display both Pdcpl and Tdcpl (but we will return to PS/DMCH solutions below). Neither did we have success in studies of PS dissolved in other poor solvents. Both PS/acetone and PS/propionitrile show well developed Phypl at P~0. 1 MPa and convenient values of T and Mw, but increasing the pressure to 200 MPa fails to develop Thypl c. A PS/(two-component solvent) mixture with two hypercritical points. In two component solvents one hopes that mixing two solvents (typically a 9 -solvent and a poor-solvent), each with conveniently located, THYPL or PHYPL, will result in a solution with both extrema. Preliminary experiments on PS/(cyclohexane (CH)+propionitrile(PPN)) and PS/(methylcyclohexane (MCH)+ acetone(AC)) systems were unsuccessful, but trials on PS/n-heptane/MCH system where polymer/solvent interaction is nonspecific, showed both Thypl and Phypl (Figure 4). In the discussion of Figure 4 we assume ^mt, for PS(MW=2.7x106) in HE/MCH mixtures is independent of HE/MCH ratio, and equal to its value in MCH. This point of view is supported by Flory-Huggins theory which suggests for noninteracting solutions "the main contribution of the solvent is primarily that of lowering the critical solution temperature by dilution. The exact nature of the solvent is of only secondary importance" (R. L. Scott20).

The rationale for studying CPC's in the mixed solvent HE/MCH system followed from first order FH analysis which argues that modest decreases in solvent quality are expected to raise Phypl toward higher temperature and THYPLto higher pressure. The data in Figure 4 show this to be correct. HE is a much poorer solvent than MCH and the shift in solvent quality from MCH to HE/MCH (0.2/0.8) shift PHYPLand Thypl significantly. Both double critical points are now observed in the range (0MPa<P<200MPa), (inserts to Figure 4).

d. A PS/(one-component solvent) mixture with two hypercritical points. The practical possibility of demixing curves with both PHYPL and THYPL established, we reconsidered the PS/1 ,4-DMCH system. According to Cowie and McEwemi a 1: 1 mixture of cis/trans isomers of 1,4-DMCH is a poor solvent for PS, but our preliminary measurements on samples of intermediate Mw failed to confirm that observation, and, continuing, we compared PS solubility in mixed and unmixed trans -and cis-1,4-DMCH, finding the trans isomer to be the worse solvent. The best chance, then, of observing multiple hypercritical points should be in

Temperature (K) Temperature (K)

Figure 4. Critical Demixing isopleths for PS/methylcyclohexane/n-heptane solutions. Parts "b'' and "c" show the diagrams in the vicinity of the hypercritical (homogeneous double critical) points. Modified from ref. 4 and used with permission.

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