Polymer-Solvent Demixing Under Tension. Isotope and Pressure Effects on Liquid-Liquid Transitions, VII. Propionitrile-Polystyrene Solutions at Negative Pressure

ATTILA lMREt and W. ALEXANDER VAN HOOK*

Chemistry Department, University of Tennessee, Knoxville, Tennessee 37996-1 600

SYNOPSIS

Liquid-liquid demixing in propionitrile-polystyrene solutions has been observed ( -2 < P / MPa < 4 ) using a Berthelot tube technique. The experimental isopleths join smoothly to ones gathered at positive pressure by another technique. The equation of state used to describe the transitions thus appears to be valid across the entire liquid range. 0 1994 John Wiley & Sons, Inc. Keywords: negative pressure liquid-liquid demixing polymer solutions solutions under tension

INTRODUCTION

Dernixing Studies in Polyrner/Solvent Solutions

Van Hook and co-worker~l-~ have reported on in- strumentation and techniques designed to investi- gate isotope and pressure dependences of liquid-liq- uid demixing in polymer-solvent systems over broad temperature (235 I T / K I 600) and pressure (0.1 I P/MPa 5 10) ranges. Rebelo and Van Hook4 and Luszczyk and Van Hook5 (LVH) have reported de- mixing experiments of H- or D-labelled polymers in H- or D-labelled solvents for polystyrene/acetone, polystyrene /methyl-cyclopentane, and polysty- rene/propionitrile5 solutions. The authors6 have reported mean-field calculations to interpret the data. The approach combines the Bigeleisen-Van Hook-Wolfsberg7-' theory of isotope effects in the condensed phase with a Flory-Huggins-based poly- mer/solvent equation of state, and takes full account of the effects of polydispersity by using the contin- uous thermodynamic development of Ratsch and Kehlen."

The phase diagrams of interest show both upper and lower consolute branches which join at a hy- percritical point in some ranges of temperature ( T) , pressure (P) , concentration (segment fraction = $,

* To whom correspondence should be sent. Permanent address: Institute for Atomic Energy Research,

Journal of Polymer Science: Part B: Polymer Physics, Vol. 32,2283-2287 (1994) 0 1994 John Wiley & Sons, Inc. CCC OSS7-6266/94/132283-05

POB 49, H-1525, Budapest, Hungary.

weight fraction = W,,), and average polymer seg- ment number (( r) ) , (for acetone/PS and propio- nitrile/PS solutions, methylcyclopentane/PS does not show a hypercritical point in the region stud- ied4-6). An upper consolute solution (UCS) is one where the cloud point locus is convex in the (T, $) plane, that for a lower consolute solution (LCS) is concave in the (T, $) plane. Beyond the hypercrit- ical point (i.e., toward ( r ) > (r)hyp or P < P h y p ) ,

the phase diagrams collapse to the hour-glass con- figuration. The authors6 found it convenient to summarize their calculations with scaling expan- sions of the UCS/LCS loci about the hypercritical point as origin using either mean-field ( p = 4 ) or nonclassical ( p = 4 ) limiting exponents, p is the scaling exponent. The surface defined by the two- phase equilibrium is a complicated function of T, P, (r) , composition, and polydispersity ( p ) , and cannot be sampled in its entirety by the Szydlowski- Rebelo-Van technique. In particular the hypercritical origin for the scaling expansions, (most conveniently made at constant $, ( r ) , and p ) , ( P h r p , Thyp) , , , ( r ) ,p , is sometimes predicted to be found at negative pressure and cannot be observed by the earlier methods.'-3 The purpose of the work reported is to determine whether the election of a hypercrit- ical origin at negative pressure is physically mean- ingful.

The point of interest is clarified by Figure 1 which schematizes UCS/LCS demixing in (P, T, ( r ) ) + , p

space. Figure l a diagrams isopleths (cloud point loci in (P, T)++,,+) projections) for several different av-

2283

2284 IMRE AND VAN HOOK

T Pi GPO Figure 1. Schematic diagrams of cloud-point loci of polymer/solvent solutions in ( P , T, ( r ) ) space. ( P = pressure, T = temperature, ( r ) = average segment number of polymer solute). (a) Isopleths at near critical concentration for various segment numbers, (( rl) < ( r 2 ) < ( r 3 ) ) . For any curve the area to the center (e.g., that inside “abc”) is homogeneous one phase, the area to the right of a given curve is two-phase LCS, that to the left is two-phase UCS, while the area below the pressure min- imum (“b” on curve ( rl), e.g.) is in the two phase hour- glass configuration, see text. (b) Cloud-point temperatures versus reciprocal segment number at two pressures ( P1 <Po), see text.

erage segment numbers (( rl) < ( r 2 ) < ( r 3 ) ) . It is understood that the measurements are reported near the maximum in the UCS (or minimum in the LCS) demixing curves as plotted in the ( T, $) plane. Con- sider the curve labelled ( r 3 ) . The region inside the curve labelled “abc” is one-phase and homogeneous. To the left of the low temperature (UCS) branch (“ab”) lies a two-phase region of the UCS type, and to the right of the high-temperature branch (“bc”) is a two-phase LCS area. The area below the min- imum (“b”, which is the hypercritical point), P I Pb, is also two-phase, but of the hour-glass con-

figuration. Notice for any given curve, (rl), ( r 2 ) , or (Q), an increase in pressure enhances solubility. A shift from curve to curve, say by decreasing ( r), also increases solubility. Thus as molecular weight drops, the hypercritical pressure falls, and at low enough molecular weight ( segment number) be- comes negative (see curve ( rl)) .

Figure l b represents demixing in the (T, 1/( r ) ) plane, this time at several pressures. Once again an increase in P enhances solubility at any given ( r ) , as does an increase in 1/( r ) at constant pressure. The sets of curves in Figure l a and Figure l b are analogous, and lead to the suggestion that at low enough pressure the hypercritical origin in the (T, 1 / ( r ) ) plane is to be found in the ( -, + ) quadrant. In fact, that is the situation observed for methyl- cyclopentane/ PS solutions which show both upper and lower Flory 8 points a t P = 0.1 MPa.4 Obviously the hypercritical conditions ( T, P, 1/( r ) < 0) can- not be physically realized. They differ in kind from those described in Figure l a (T, P < 0,1/( r ) > 0).

liquids and Solutions at Negative Pressure (under Tension)

Trevena, l1 Davies, l2 Rebelo et al.13 and Henderson and Speedy,14 and very recently Ohde et al.15 and Alvarenga et a1.16 have discussed the properties of liquids under tension, including methods of making thermodynamic and quasi-thermodynamic studies on stressed samples. Static methods such as the Berthelot tube technique (vide infra) produce the tension isotropically and uniformly throughout the sample and maintain it for times which are long compared to the various relaxation processes char- acterizing the liquid or solution. Dynamic methods (sound waves, high speed stirring, etc.) are nonuniform and anisotropic, and may have time constants which are order of magnitude the same or shorter than certain important relaxation times in the liquid or solution. The literature on solutions under tension, including demixing phenomena, is much less extensive than that for pure liquids. Horst and Wolf 1 7 9 1 8 have reported the effect of shear on polymer mixing and/or demixing and have reviewed literature which dates to 1952. Wolf and co-workers have developed a thorough rationale for shear

Heinrich and Wolf 2o have reported on phase transitions induced by temperature-jump experiments in a spinning drop apparatus but the tensions induced are not clearly specified. We are unaware of any previous reports of negative pressure

POLYMER-SOLVENT DEMIXING UNDER TENSION 2286

(tension) -induced phase changes using the Berthelot tube or other static techniques.

EXPERIMENTAL

Berthelot tubes were prepared from heavy walled pyrex capillary ( 2 mm ID) suitably necked down. Predetermined quantities of polystyrene / propioni- trile (PS/PRCN) solutions were inserted in the tube with a hypodermic syringe, and the solutions degased under vacuum with an appropriate number of freeze- thaw-freeze cycles using liquid N2 and high fre- quency (sonic) mixing of the solutions. The tubes were then sealed (still frozen and under vacuum) with a glass-blowing torch and set aside for later measurement. The temperature at which the vapor phase completely disappears when the sealed tubes are heated is designated the fill-temperature and can be adjusted by changing the amount of solution loaded into the tube.

To observe a phase change at negative pressure the sealed Berthelot tube is placed in an oil bath and slowly warmed to the fill-temperature which usually is found at a positive pressure below 0.5 MPa. Further warming increases the pressure a few more MPa and helps to eliminate microbubbles which may induce premature cavitation." After stirring to ho- mogeneity (using a rod-type magnetic stirrer con- tained in the tube) the sample is slowly cooled until the cloud-point is observed, or until the experiment fails by cavitation or breakage. The maximum ten- sion reached in this system was -2.5 MPa. Usually cavitation occurred at the stirrer / liquid interface, or was mechanically induced as the moving stirrer rubbed the wall. Temperley and Chambers,21 Lewis, 22 and H a y ~ a r d ~ ~ report similar observations. Using this simple technique we were able to rou- tinely generate tensions between 0 and 2 MPa.

We calculated the negative pressure at the cloud- point by integrating the thermal pressure of the so- lution from the fill temperature (where the pressure is equal to the vapor pressure of the solution) to the temperature of the phase transition. Thermal pres- sures were measured in independent experiments by confining a known amount of solution in a cap- illary of known cross section with a mercury plug. The tube was fixed to a scale so the volume of poly- mer solution is defined by the position of the plug. Hydraulic fluid confining the plug is supplied from a pressure generator.' This simple system permits (dP/dT), to be determined with an accuracy of about 10% for (0 I P/MPa I 2) . We assumed that

(dP/aT ), extrapolates smoothly from positive to negative pressure and in that region label it the thermal tension. We estimate the uncertainty in thermal tension to be about 10%. The assumption appears reasonable, 11~14*24 at least for tensions which are not too large.

RESULTS AND DISCUSSION

Berthelot tube measurements of cloud points for PS/PRCN solutions at both positive and negative pressures are reported in Table I. Cloud points so determined are plotted in Figure 2 where they are compared with the data of Luszczyk and Van Hook5 for P > 0 obtained by another Agreement is excellent. In Figure 2a the present CP measure- ments on WPs = 0.201 PS/PRCN solution (2 > P/

Table I. Propionitrile/Polystyrene Solutions (Mw = 22,000 g-mol-', Mw/M, = 1.03)

Cloud-Point Isopleths for Some

Concentration Temperature Pressure (w %) (K) (MP4

4.4

6.3

10.4

20.1

316.75 323.15 330.05 335.05 337.35 339.95 341.55 342.45 345.55 346.65 351.65 359.35 371.15 372.00 347.15 350.65 353.10 356.15 358.55 362.05 369.80 372.35 377.55 391.55 392.75 396.75 401.10 420.80

3.23 0.02

-1.95 3.77 1.81 0.03

-0.95 -1.23 -1.15

2.60 1.37 0.95

-0.40 -0.50

2.01 1.80 1.39 0.7 0.32 0.21

-0.36 -0.42 -0.51 -0.48 -0.31 -0.27

0.01 1.45

2286 IMRE AND VAN HOOK

A

E t 7

I Y

v)

$i

330 350 370 390 410 430 450 470

temperature (K) (a)

5 t P

temperature (K)

(b)

Figure 2. Polymer/solvent demixing at negative and positive pressures. ( a ) Cloud-point isopleths for propioni- trile-polystyrene solutions. The closed triangles show the present results for M , = 22,000, M,/M,, = 1.03, W, = 0.20, the open triangles show the results of Luszczyk and Van Hook (LVH), M, = 22,000, M , / M , = 1.03, Wps = 0.19. The least-squares correlation line is P/MPa = 1.16 X 10-7T4 - 1.96 X 10-'T3 + 0.125T2 - 35.44T + 3770.22. ( b ) Cloud-point isopleths for propionitrile-polystyrene solutions. Closed diamonds = present measurements W, = 0.044, (P = 0.0163T2 - 10.89T + 1824.88). Closed circles = present results W, = 0.063, open circles = LVH W, = 0.06 ( P = 1.097 X 10-'T4 - 1.95 X 10-4T3 + 0.130T2 - 38.35T + 4206.10). Closed squares = present results W, = 0.104, open squares = LVH W,, = 0.108 ( P = 0.935 X 10-7T4 - 1.59 X l O - T 3 + 0.102T2 - 29.321' + 3149.93).

MPa > -0.6) are compared with the LVH mea- surements in the positive region for W, = 0.190. Wps is the weight fraction polymer. Figure 2b com- pares data obtained from the two different tech- niques (UCS branch) a t W, = 0.04,0.06, and 0.11. The critical concentration for PS/PRCN solutions is W,,,, = 0.2. The demixing curves are very flat in the (T, W,) projection near the maximum and we have chosen not to display all available concentra- tion data in Figure 2b in order to avoid clutter. The

curves in Figure 2a and b are polynomial represen- tations of the combined measurements (i.e., from both techniques). Clearly both the present data and those of LVH are well represented by the fits. For the low concentration solutions (Wp8 = 0.04 and 0.06), the high temperature branch crosses P = 0 at temperatures in excess of 430K. This is an in- conveniently high temperature for our present ex- perimental setup. Bertholet tube measurements on those solutions have therefore been limited to T I ThD. The LVH data, however, extend to temper- atures in excess of 450K and anchor the correlation lines.

The results substantiate the idea that the equa- tion of state describing PS/PRCN solutions passes smoothly and continuously across the zero pressure isobar into the region of negative pressure. Thus it is physically reasonable to compare the properties of the solution in the regions of positive and negative pressure using continuous and smoothly varying functions. For example it may be physically useful (as well as convenient) to represent an isopleth (perhaps the critical isopleth) , in terms of an ex- pansion about its hypercritical origin, even if that hypercritical origin is found at negative pressure (under tension). This article reports the direct ob- servation of an hypercritical point found at negative pressure.

Research supported by the U.S. Department of Energy, Division of Materials Sciences under grant 91-ER45374.

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Received March 9, 1994 Accepted May 11, 1994