Continuity of solvent quality in polymer solutions. Poor-solvent to Θ-solvent continuity in some polystyrene solutions

Continuity of Solvent Quality in Polymer Solutions.Poor-Solvent to Q-Solvent Continuity in SomePolystyrene Solutions

ATTILA IMRE,1,2 W. ALEXANDER VAN HOOK1

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

2 Atomic Energy Research Institute, POB 49, H-1525, Budapest, Hungary

Received 3 October 1996; revised 21 November 1996; accepted 22 November 1996

ABSTRACT: Critical temperatures for polystyrene/methyl acetate (PS/MA) and polysty-rene/ethyl formate (PS/EF) solutions were measured at positive (PS/MA, PS/EF) andnegative (PS/MA) pressure. The results confirm that solvent quality is sensitive topressure; some solvents, designated Q, at Pnominal Ç 0, undergo a Q-to-poor transitionat negative pressure, and others, nominally designated ‘‘poor,’’ show a poor-to-Q transi-tion at positive pressure. Thus, any dichotomous division into sets of ‘‘poor’’ and ‘‘Q’’solvents is inaccurate, unless it accounts for the effects of pressure and other variableson solvent quality. q 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1251–1259,1997Keywords: demixing; polystyrene; phase equilibria; solvent; consolute temperatures;pressure; negative pressure; methyl acetate; ethyl formate

INTRODUCTION narrowly, X ú 0 always, but in taking a moregeneral approach we have considered a descrip-tion in which X , no longer strictly defined in termsSmall molecule solvents for polymers like polysty-of molecular weight, can extend to negative val-rene and polyethylene are traditionally dividedues.1 The two-phase (shaded) regions found at theinto three classes: good solvents, Q (theta) sol-top and bottom of Figure 1 at various values of Xvents, and poor solvents. In constructing a practi-represent the solubility at that particular molecu-cal definition of solvent quality it is useful to con-lar weight and temperature. It is useful, althoughsider typical phase diagrams for demixing like thenot completely accurate, to represent the (T , C,ones shown in Figure 1. For simplicity, we restrictX ) diagram as a series of coexistence curves (Tattention to liquid–liquid demixing and do notvs. C at constant X ) . The solubility in both uppershow the parts of the diagram that depict liquid/and lower branches decreases with increasing mo-solid transitions of one kind or another. In Figurelecular weight (i.e., decreasing X ) , and at high1(a) and (b) temperature, T , is plotted againstenough molecular weight and poor enough solventsegment fraction polymer, C, in the plane of thequality the two branches eventually touch [Fig.paper. The third variable that extends into the1(b)] , the solution hyperdemixes, and the systempage expresses the dependence of solubility on acollapses into the hourglass configuration. Forparameter X , which in the simplest case scalespolymer solutions in Q solvents [Fig. 1(a)] or inwith molecular weight X Ç M01/2

w . Interpretedgood solvents, the hypercritical point usually can-not be reached. These solvents dissolve polymer

Correspondence to: W. A. Van Hook of arbitrarily high Mw at concentrations as highContract grant sponsor: U.S. Department of Energy, Divi-and higher than the critical concentration, pro-sion of Materials Sciences

q 1997 John Wiley & Sons, Inc. CCC 0887-6266/97/081251-09 vided temperature lies between the upper and

1251

9610003/ 8Q2B$$0003 08-05-97 14:33:09 polpa W: Poly Physics

1252 IMRE AND VAN HOOK

Figure 1. Liquid–liquid demixing for polymer solvent mixtures showing upper andlower consolute branches. (a) (Left) . For theta solvents with upper and lower Q temper-atures. Temperature, T , is plotted against segment fraction polymer, C, in the planeof the paper. The third variable is the molecular weight parameter, X Å M01/2

w . Thecurve drawn through the critical points and marked with ‘‘xs’’ is discussed in the textand further illustrated in Figure 2. QU and QL correspond to the (T , X Å 0) interceptsof the line of ‘‘xs.’’ (b) (Right). For poor solvent systems showing upper and lowerconsolute curves joining at a hypercritical point (marked with the white cross). Axeslabeled as in Figure 1(a). The curve drawn through the critical points is plotted in the(T , X ) and (T , P ) projections in Figure 2.

lower Q points, QU and QL [Fig. 1(a)] , and for curvature and a hypercritical transition, and ‘‘Q’’solvents show linear dependence for both upperthis reason Q solvents and good solvents are

sometimes lumped into a single class.2 and lower branches with intercepts at 1/M1/2w

Å 0 of 1/QU and 1/QL , respectively. Good solventsThe classification of solvents as ‘‘poor,’’ ‘‘Q,’’ or‘‘good’’ is based on comparisons of the X depen- show even wider Q gaps, possibly extending be-

yond temperatures of practical interest.dence of the upper or lower (T , C )critical loci. Formondisperse samples (T , C )critical loci coincidewith the maxima or minima of the demixing

The ‘‘Q’’–‘‘Good’’ Transitioncurves. This is a useful approximation if polydis-persity is not too large. The commonly understood The distinction between ‘‘theta’’ and ‘‘good’’ sol-

vents is not absolute. For example, consider ben-meaning of a ‘‘poor’’ solvent, thus, is one that doesnot dissolve samples of high Mw polymer at con- zene/polystyrene (PS) solutions. Benzene is nor-

mally classified a good solvent, but at very highcentrations at or near critical. Polymers in poorsolvents are characterized by a hyperdemixing temperatures (over 520 K) precipitation has been

reported,3 and at very low temperatures (around(hypercritical) Mw , which tends to lower valuesas solvent quality decreases. For poor enough sol- 100 K—well below the freezing point) the extrap-

olated second virial coefficient, A2 , reaches zero.4,5vents the solution may never leave the hour-glassconfiguration at all, even at very low Mws. Q sol- It follows that classification of solvent quality via

A2 is an alternative to methods based on phasevents, on the other hand, dissolve polymer of arbi-trarily high MW, but only between the upper and equilibria. In this approach ‘‘Q’’ solvents are those

with A2 Å 0, ‘‘poor,’’ and ‘‘good’’ solvents have A2lower Q temperatures. For ‘‘good’’ solvents thetemperature range of solubility is extended so õ 0 and A2ú 0, respectively. This system permits

the use of osmotic and light-scattering data tothat QU lies below, and QL above, reasonably ac-cessible temperatures. Referring to Shultz–Flory classify solvent quality, but suffers from the criti-

cism that the truncated virial description (whichgraphs (1/Tc vs. 1/M1/2w ) , poor solvents show high


CONTINUITY OF SOLVENT QUALITY IN POLYMER SOLUTIONS 1253

is implied by the use of A2 as the criterion of sol- PS/methylcyclohexane,13–15 PS/cyclohexane,17,18

and PS/1-phenyldecane.18)vent quality), is only valid for dilute solutions.The present discussion of solubility, phase dia- Figure 2, which examines critical demixing

curves in (X , T , P ) space, further illustrates thegrams, etc., implies application to more concen-trated solutions where higher order virial coeffi- discussion. A representation of the critical demix-

ing surface in three dimensions is given in Figurecients contribute, and likely dominate. In this con-nection we know that common Q solvents (e.g., 2(a). Two dimensional (X , T ) projections at sev-

eral pressures (isobars), and (T , P ) projectionscyclohexane) often act like ‘‘good’’ solvents if thetemperature is far enough from QU and QL ( i.e. at several values of X ( isopleths) comprise Figure

2(d) and (b), and Figure 2(c) shows (X , T ) pro-for TÇ (QU / QL ) /2 where the system is far fromthe Q state in the (T , X ) plane, one finds A2 jections for several solvent qualities. Even though

solvent quality per se is not depicted as one ofú 0),6 or the pressure is high enough (and analo-gously far from the Q state, this time in the (P , the variables in Figure 2(a), one concludes that

a change in solvent quality is equivalent to slidingX ) plane).7 Thus, in the context of the virial coef-ficient definition one can easily transform a poly- the whole three-dimensional representation of the

critical surface for solubility along the X or P axes.mer/solvent system from ‘‘Q’’ to ‘‘good’’ (or viceversa) simply by adjusting temperature or pres- To illustrate we chose a case of intermediate sol-

vent quality with demixing isobars at P0 õ 0, P1sure, but should not be surprised if the changes sodefined do not correlate quantitatively with phase Å 0 and P3 ú P2 ú 0 [Fig. 2(a) and (d)] , and

demixing isopleths at X0 Å 0, and 0 õ X1 õ X2behavior of concentrated solutions (becausehigher terms in the virial expansion have been [Fig. 2(a) and (b)] . The example shows a Q gap

at high pressures, but quality drops as pressureignored).falls, the Q gap narrows and hypercritical demix-ing appears. In preliminary experiments welooked for a ‘‘poor’’ solvent system with solubility‘‘Poor’’ to ‘‘Q’’ Continuityat high Mw close to the ‘‘poor– Q’’ transition. Onewould expect the transition from that curve to aIt is well established that solvent quality of ‘‘poor’’

solvents is sensitive to pressure. For most systems ‘‘Q’’ curve to be induced by no more than modestlyelevated pressure. According to a recent review1(Ìrhyp /ÌP )T ,C ú 0, and may be large. Here, rhyp is

the hypercritical segment number and generally the polystyrene solution closest to the ‘‘poor– Q’’boundary is 1,4-dimethylcyclohexane (DMCH)/increases with pressure. We limit examples to PS/

solvent systems, but the remarks carry over qual- PS. For this solution Cowie and McEwen19 re-ported a hypercritical MW of 4 1 106 amu (r 01/2

hypitatively to many other polymer solutions. For ex-ample, rhyp for PS in acetone is 192 at 0.1 MPa, Å 5 1 1003) , next best is the PS/ethyl-formate

(EF) system20 with r 01/2hyp Å 2.81 1002 . Our experi-212 at 5 MPa,8 and ú900 at 20 MPa.9 Zeman and

Patterson9 suggest that acetone may even be able ments with DMCH, however, indicated these so-lutions to already be in the Q configuration, albeitto dissolve infinite MW at high pressure (the sys-

tem thus having made the transition from ‘‘poor’’ with a small Q gap. We, therefore, chose to explore‘‘poor– Q’’ continuity with studies on PS/EF.to ‘‘Q’’ solution).

Other poor solvents like propionitrile,10 deuter-oacetone,8,11 and diethyl ether12 show a similar

‘‘Q to Poor’’ Continuitydependence of solvent quality on pressure. Thequality-enhancing effect of pressure is not limited This transformation can be induced by negative

pressure. Although the existence of negative pres-to poor solvents. For many Q solvents, solventquality in PS solutions is improved at high pressures (tensions) in liquids has been known for

more than a century,21 the phase equilibria of so-sure, i.e., the Q gap widens with pressure. Theeffect has been reported, for example, for PS/t- lutions at negative pressure have not been widely

studied. Wolf and Blaum mentioned probable ef-butylacetate,12 and at least at moderate pres-sures, for PS/methylcyclohexane,13–16 but may fects of tension on precipitation from polymer/sol-

vent solutions in 1976,22 but experiments werenot be universal. (High-pressure measurementsalong QL are rare, but there are a few reports that not reported until almost 2 decades later. The

problem was also neglected in theoretical discus-indicate that dQU /dT , negative at low pressure,in certain cases changes sign and becomes posi- sions; even recent articles on the effect of pressure

on phase separation focus exclusively on positivetive at much higher pressure. Examples include



Figure 2. Pressure (P ) -temperature (T ) -molecular weight (X Å M01/2w ) dependence

of critical demixing for a polymer solution (schematic) . (a) (Upper left) . Representationof critical demixing loci in (P , T , X ) space. Isobars are shown at four pressures rangingfrom positive to negative, isopleths are shown for three values of X . In each case therepresentation in the positive regions is with a solid line, in the negative regions witha dotted line. (b) (Upper right). Isopleths from Figure 2(a) projected on the (T , P )surface. (c) (Lower left) . Isobars for liquid–liquid demixing for solutions of differentsolvent quality. Were (1/T , X Å M01/2

w ) plotted this would be a Shultz–Flory plot. (d)(Lower right). Isobars from Figure 2(a) projected on the (T , X ) surface.



pressure.23 The first measurements of polymer/ lecular sieve and kept under nitrogen before use.Cloud points of PS/EF solutions at the nominalsolvent demixing under tension were made in

1994 by Imre and Van Hook on PS/propionitrile vapor pressure of the solutions were determinedby visual observation in sealed pyrex capillaries.(PPN) solutions.10 The authors used the Berthelot

method to generate tensions.24 They showed that The critical concentration was estimated by tak-ing the maxima from plots of the CP data (TableUCST and LCST branches in the (P , T )MW plane

join smoothly at negative pressure as illustrated I), ignoring corrections for polydispersity,8 whichis low. Cloud points at elevated positive pressuresin Figure 2(b). The experiment demonstrated

that the pressure coefficient of solvent quality and for PS/MA and PS/EF solutions were determinedby low angle light scattering in the apparatus de-the solution equation of state extend smoothly

into negative pressure (tension). The analysis scribed by Szydlowski, Rebelo, and Van Hook.25

PS/MA cloud points at negative pressure were de-leads us to expect the two branches to join at nottoo deep tension for solutions with a small enough termined using the Bertholot tube technique.10,24

Thermal pressures24 were determined in a sepa-Q gap and reasonable sensitivity to pressure, thusdemonstrating ‘‘Q–poor’’ continuity. According to rate series of measurements with approximately

20% accuracy over the temperature range (298a recent review,1 both PS/methylacetate9 and PS/t-butylacetate12 are appropriate test systems, but õ T /K õ 386).

The data are reported in Figure 3. The thermalPS/MA is the more thoroughly studied and wechose this solution for further study. pressure of MA at 293 K has been reported as 1.2

MPa/K,26,27 and for PS of undefined MW as 1.4{ 0.2 MPa/K,28 which, combining linearly, gives

Correlating Equation Ç 1.2 { 0.2 MPa/K for the solution of criticalconcentration, about 30% higher than the 0.8To describe the MW and pressure dependences of{ 0.2 MPa/K, which we observe at 298 K, andTU

c and TLc we employ an empirical scaling equa-

(barely) within the combined error limits. The rel-tion that involves a mean field expansion aboutatively high uncertainty in the slope does not af-the hypercritical origin.1

fect the conclusions which follow. The solutionsare not ideal, and thermal pressures may lie be-

É(T 0 T*c ) /T*c É Å AÉ(X 0 X *)/X *É1/2;low the predicted value (but likely not 30% be-

X Å MW 01/2 (1) low).

This empirical equation requires only three pa-‘‘Poor– Q’’ Continuityrameters, A , T*c , and X *, to describe demixing

along both branches (LCST and UCST). It is un- We studied this process by examining pressurederstood that the hypercritical Mw parameter, X *, effects in PS/ethyl formate (EF) solutions. Theis smoothly extendable below zero. The more fre- results are reported in Table II and shown in Fig-quently employed Shultz–Flory equation re- ure 4. PS 41 105 is insoluble in EF at atmosphericquires four parameters to describe Q demixing pressure and near critical concentrations and we(two for each branch), and cannot be applied to could not carry out measurements at Ccr for thispoor solvent mixtures. We recently reported a de- polymer. Rather, the entries in Table II for thistailed comparison of the two equations.1 T*c , and Mw are interpolated or extrapolated from isoplethX * in eq. (1) are parameters corresponding to the data for the lower Mw polymers at Cc , or for lowerhypercritical coordinates. For poor solvents (T*c , concentrations at MwÅ 41 105, using polynomialX *) is an observable, but for Q solvents it lies fits of appropriate order. Demixing data in thein the physically inaccessible (Tc , MW 01/2 ::/, 0 ) (T , M01/2

w ) plane at various pressures are shownquadrant and must be regarded as a fitting pa- in Figure 5. They are in good agreement with lowrameter. pressure data reported by others.20 The parame-

ters of fit to eq. (1) at integer pressures (0 õ P /MPa õ 8) are reported in Table III. They show

EXPERIMENTAL, RESULTS nearly linear dependence on P (Fig. 6). Linearextrapolation yields P*Q Å 18.7 MPa. P*Q refers tothe pressure at which EF for PS/EF solutions ofPolystyrenes are described in Table I. Methyl ace-

tate (Fluka) was used without further purifica- critical concentration becomes a Q solvent. Thepoor agreement for the PS 400,000 with thetion, ethyl formate (Aldrich) was dried over mo-



Table I. Polystyrene Samples

Measured Conc.Mol. Weight Company/Cat. No. Polydisp. (w %)

11600 PL/#20130-3 1.03 2222,000 PL/#20131-2 1.03 1466,000 PL/#20134.4 1.03 10

400,000 PC/#507 1.06 6 (nearly critical)2,000,000 PC/#61111 1.3 2.9

20,000,000 PC/#70607 1.2 below 3

PC Å pressure chemical.PL Å polymer laboratories.

smoothing relations (Fig. 5), most likely results pressures to directly observe hypercritical junc-tion at either Mw (Fig. 7), but have succeeded infrom a slightly off-critical concentration for this

solution. Figures 1 and 5 demonstrate that at the demonstrating continuity of the cloudpoint curveof PS/MA into the region of negative pressure.UCS, LCS/hour-glass transition even a small er-

ror in Cc results in a large shift in Tc . The 6–8 K shift between the two sets of measure-ments along the lower branch (the first made atP ú 0 in mercury-sealed capillaries, the second

‘‘Q–Poor’’ Continuity using Bertholot tubes for measurements at bothpositive and negative pressure—marked A andPhase equilibrium measurements were made at

positive and negative pressure for PS/methylace- B , respectively, in Fig. 7) although disturbing, isnot much larger than the usual sample-to-sampletate (MA) solutions of Mw 2 1 106 and 2 1 107

and supplement literature data for this system.1 reproducibilities widely reported for cloudpointsof PS solutions.1 It perhaps originates from con-For Berthelot sample preparation, we required

homogeneous solutions at room temperature, and tamination of the A samples introduced by reac-tion with the mercury separator.this is the reason why, after a few measurements

on samples with Mw Å 20 1 106, we chose theslightly more soluble Mw Å 2 1 106, even thoughthe tension at which the upper and lower DISCUSSIONbranches join is expected to be deeper at the lowerMw . It is estimated to lie below 05 MPa. In fact, We have discussed the use of pressure as a tool

to change solvent quality and, thus, solubility inwe were unable to reach low enough negative

Figure 3. Thermal pressures, G Å (ÌP /ÌT )v , for PS/MA solutions of critical concentration as a function of Figure 4. Cloud point data for polystyrene/ethylfor-

mate solutions at critical concentrations and varioustemperature. The equation of the least squares line is(00.00694 { 0.00167)T / (2.847 { 0.567). molecular weights (see Table I) .



Table II. Critical Temperature Data Extra- and Interpolated to Integer Pressures of the Measured PS/EFSystems

PS11600 PS22000 PS66000 PS400000

p (MPa) UCST/K LCST/K UCST/K LCST/K UCST/K LCST/K UCST/K LCS/K

0 273.7 435.5 296.1 420.4 347.6 375.21 273.3 443.8 295.4 425.3 342.4 384.42 273.0 449.4 294.8 430.2 338.8 392.43 272.6 454.7 294.2 435.2 335.8 399.94 272.2 460.7 293.5 440.1 333.4 407.25 271.9 465.6 292.9 445.0 331.2 413.86 271.5 471.0 292.3 450.0 329.3 419.7 379.6 380.87 271.2 476.4 291.6 454.9 327.6 425.0 365.7 395.38 270.8 481.8 291.0 459.8 326.0 429.6 361.2 400.1

polystyrene solutions. For systems near the ‘‘Q– ation should be possible from Q solvents, andeven, using deeper tensions, from good solvents.poor’’ boundary of solvent quality, pressure can

be raised or lowered to move the system from MW fractionation by pressure change is an attrac-tive and clean alternative to methods that change‘‘poor’’ to ‘‘Q’’ or ‘‘Q’’ to ‘‘poor,’’ as required. While

this is an interesting observation, more important solvent quality by adding a third component, com-monly denoted the ‘‘cosolvent.’’ Although knownis the fact that it emphasizes the sensitivity of

solvent quality to pressure, and demonstrates for decades, fractionation by pressure was oncedismissed as not too effective,29 most likely be-continuity of state in the region that lies between

the LCST and UCST demixing curves, even for cause early experiments were carried out far fromthe hypercritical region where the sensitivity ofsolutions under tension. Speaking more practi-

cally, quantitative knowledge of such behavior the phase diagram to pressure is low. In the su-percritical region, however, the concept of pres-should be useful in providing a conveniently tune-

able variable for use in MW fractionation. At low sure fractionation is well established and hasbeen applied extensively in the past decade usingpressures (1 to 1 Mpa) even a small change in

pressure, say 0.1 Mpa, may cause as much as a supercritical fluid extractants of normally poorsolvent quality. The present discussion focuses on1000 amu change in MWhcp, that is, in the maxi-

mum molecular weight that dissolves in poor the intermediate case, that is, on solutions in notvery good subcritical solvents operating close toquality solvents. At negative pressure fraction-the liquid–liquid hypercritical region.

The discussion of continuity of solvent qualitybetween the ‘‘poor,’’ ‘‘Q,’’ and ‘‘good’’ solvent re-gions indicates that older interpretations that de-

Table III. Scaling Parameters of PS/EF Systemfrom eq. (I)

p (MPa) T* (K) A X* maxMw

0 360 0.18667 0.00372 720001 362 0.18712 0.00355 794002 365 0.18345 0.00335 885003 367 0.17878 0.00315 1009004 370 0.17462 0.00295 1150005 373 0.16641 0.00270 137200

Figure 5. Cloud point data of PS/EF systems and 6 375 0.16484 0.00256 152600fits to eq. (1) at different pressures. Values of scaling 7 376 0.15908 0.00235 181100parameters at smoothed pressures are reported in Ta- 8 378 0.15565 0.00220 206600ble III.



Figure 6. The parameters of eq. (1) describing demixing in ethylformate/PS solutionsplotted as a function of pressure. In each case the solid points are interpolated fromfits to the raw data measured at noninteger pressures, the open points have beendetermined by extrapolation of raw data. (a) Hypercritical temperature (T*) vs. pres-sure. The least squares line is T*/K Å 2.31667 p/MPa / 360.18. (b) Width parameter(A ) vs. pressure. The least squares line is A Å 00.00419 p/MPa / 0.19043. (c) Hyper-critical size parameter vs. pressure. The least squares line is X * Å 0.0002 p/MPa/ 0.0033.

scribe UCST and LCST behavior as separate phe- REFERENCES AND NOTESnomena are inadequate.

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Continuity of solvent quality in polymer solutions. Poor-solvent to Θ-solvent continuity in some polystyrene solutions