1714
The Journal of Physical Chemistry, Vol. 82, No. 15, 1978
(12) J. W. McBain and W. W. Lee, Oil Soap, 17 (1943). (13) F. K. Broome, C. W. Hoerr, and H. J. Harwood, J . Am. Chem. Soc., 73. 3350 (1951). (14) A. W. Ralsion, D: N. Eggenberger, and P. L. Du Brow, J. Am. Chem. SOC.,70, 977 (1948). (15) K. G. van Senden and J. Koning, Fefte, Seifen, Anstrichm., 70, 36 (1968). (16) K. Shinoda, T. Nakagawa, B. Tamamushi, and T. Isemura, "Colloidal Surfactants", Academic Press, New York, N.Y., 1963, Chapter 1, p 37. (17) K. Shinoda, J. Phys. Chem., 59, 432 (1955). (18) P. F. Grieger and C. A. Kraus, J. Am. Chem. Soc., 70, 3803 (1948). (19) H. E. Klevens, J . Am. Oil Chem. SOC.,30, 74 (1953). (20) A. W. Ralston, D. N. Eggenberger, H. J. Harwocd, and P. L. Du Brow,
B. Kronberg, I. Bassignana, and D. Patterson (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31)
J. Am. Chem. Soc., 69, 2095 (1947). H. 8. Klevens, J. Phys. Colloid Chem., 53, 1 (1949). K. Shinoda, J. Phys. Chem., 81, 1300 (1977). P. Ekwall, I. Danlelsson, and L. Mandell, KolloM-Z., 169, 113 (1960). P. Ekwall, L. Mandell, and K. Fontell, Mol. Liq. Cyst., 8, 157 (1969). G. Gillberg, H. Lehtinen, and S.Friberg, J . Colloid Interface Sci., 33, 40 (1970). S.Friberg, Kolloid-Z., 244, 333 (1971). H. Kunieda and K. Shlnoda, ACS Symp. Ser., No. 9, 278 (1975). H. Marumo and M. Takai, Kogyo Kagaku Zasshi, 68, 2213 (1965). K. Shinoda and H. Saito, J . Colloid Interface Sci,, 26, 70 (1968). K. Shinoda and H. Kunieda, J. ColloM Interface Scl., 42, 381 (1973). K. Shinoda and S.Friberg, Adv. Colloid Interface Sci., 4, 295, 298 (1975).
Phase Diagrams of Liquid Crystal 4- Polymer Systems Bengt Kronberg, Isabella Bassignana, and Donald Patterson* Department of Chernlstty, Otto Maass Chernlstty Bu/lding,McGill University, Montreal H3A 2K6, Canada (Received December 20, 1977: Revised Manuscript Received March 7, 1978) Publication costs assisted by the National Research Council of Canada
Temperature, solute volume fraction (p), and phase diagrams have been obtained for p-ethoxybenzylidenep-n-butylaniline (EBBA) containing two series of polymeric solutes: polystyrene (600 to 110000 molecular weight) and polyethylene oxide (194 to 6000 molecular weight). The (T,(pINboundary where the isotropic phase first appears on heating is found to be concave downward while the (T,(p)'boundary where the nematic phase occurs on cooling is concave upward. The results are consistent with a simple theory of the phase diagram and confirm the use of the theory in extracting thermodynamic data from phase diagrams. Free energies of transfer from the isotropic to the nematic phase are positive. They are consistent with a lack of correlation of the polymer segment orientations with those of the EBBA molecules. The higher molecular weight samples of polyethylene oxide give anomalous thermodynamic data explainable by assuming either association of the polymers or helix formation.
Introduction As first discovered by de Kock,l the presence of a nonmesomorphic solute leads in general to a depression of the nematic-isotropic transition temperature. The transition in fact occurs over a temperature range where the nematic and isotropic phases are in equilibrium. Thus, at any solute concentration, there are two characteristic temperatures, TNat which the isotropic phase first appears on heating the system, and TI a t which the nematic phase appears on cooling, the two temperatures meeting a t the single nematic-isotropic transition temperature To for the pure liquid crystal. Phase diagrams2i3have been determined for a large number of systems where the solutes were of molecular size less than that of the liquid crystal, Le., not high polymers. In each case the (T,concn)Nand (T,concn)' phase boundaries are experimentally indistinguishable from straight lines, the concentration variable being either x , the mole fraction, or p, the volume fraction. (Figure l a shows a typical phase diagram for EBBA ethylbenzene.) However, a simple theory4 of the phase diagram suggests that the ( T , V )and ~ (T,cp)' phase boundaries are not accurately straight lines, the upper (T,p)I boundary curving ~ curving downward. upward and the lower ( T , v )boundary Obtaining thermodynamic data2from the phase diagrams requires a knowledge of the difference between the slopes of TNand TI against cp (or x ) , but evaluated a t infinite dilution. Since the slopes are very similar (see Figure la) even the very slight curvature predicted by the theory must be taken into account in obtaining the limiting slopes
+
0022-3654/78/2082-1714$01.00/0
required for extracting thermodynamic data from the phase diagrams. It is further predicted that for solutes of high molecular weight (-lo3 and higher) the phase boundaries should depart visibly from straight lines. The present work tests the predictions of the theory for EBBA with, as solutes, two series of polymers: polystyrene with molecular weights ranging from 600 to 110000 and polyethylene oxide with molecular weights from 194 to 6000. The shapes of the phase boundaries confirm the theory and this justifies its use in obtaining limiting slopes as in ref 2 and also in the accompanying paper on EBBA-aromatic solute system^.^ The theory is used here to obtain free energies of transferring the polymers from the isotropic to nematic EBBA.
Experimental Section Liquid Crystal. EBBA was obtained from Eastman Kodak Chemicals, Rochester, N.Y. It was found that different samples had nematic-isotropic transition temperatures varying between 77 and 80 "C. A DSC estimation gave a purity of 98.8% for a sample where the nematic-isotropic transition temperature was 79.0 "C.One sample of EBBA was synthesized by refluxing equimolar amounts of p-butylaniline and p-ethoxybenzaldehyde in absolute ethanol. After the ethanol-water azeotrope was distilled off, the sample was purified by repeated recrystallization in absolute ethanol and dried in vacuo over P205.The nematic-isotropic transition temperature was found to be 79.1 OC. Literature values of the transition temperature6 vary from 76 to 80 "C.
0 1978 Amerlcan Chemical Society
Phase Diagrams of Liquid Crystal
+ Polymer Systems
TABLE I : Phase D i a g r a m D a t a for EBBA
The Journal of Physical Chemistry, Vol. 82, No. 15, 1978
+ Polymers Ya
polymer
0.856 4.25 14.9 28.3 144.5 779.0 1.28 10.1 25.9 2.40 1.65 13.2 39.6
XI
7 2 I-
segment
0.110 0.411 1.70 2.72 25.5
353 236 195 135 66
0.196 1.44 (0.36) 0.326 0.209 1.51 (0.241,
40 6 257
1.215 1.415 0.530
bi
0 94 0,941
"-I;;_
"
0
341 335 203
methods or from solution theories. We have used the Flory theory of the liquid equation of state7 from which one obtains the hard core specific volume through the equations VI3= 1 aT/3(1 + aT) (2)
+
\
0 88 0.88
0 96
,
J/mol of
1.700 0.700 0.430 0.360 0.280 0.250 1.400 0.500 0.400 1.100 1.300 0.450 0.370
1.530 0.600
PS(106)
A G(trans)/r,
XN
b 0 96
Nm - y21m
1.825 0.780 0.495 0.405 0.300
r 2
PS(106) PS(600) PS(2100) PS(4000) PS(20 400) PS(110 000) PEO(194) PEO( 1540) PEO(4000) MPEO(350) DMPEO(222) DMPEO(2000) DMPEO(6000)
1715
PS ( I10,0001
PS(20,400) I
I
I
005
010
015
u* =
1
\\
0
I
I
I
005
010
015
$2
+
Figure 1. Phase diagrams of EBBA polystyrene with the indicated molecular wei hts. PS(106) is ethylbenzene. The ordinate is T' = T / P where $is the nematic-isotropic transition temperature of pure EBBA, and ( F ~is the solute segment fraction. The upper line is the (T*,(P)I boundary, where the nematic phase first appears on cooling and the lower line is the ( T " , P ) ~boundary, where the isotropic phase first appears on heating. Two methods were used to obtain the phase boundaries: (0)represents the lever rule and (0)direct measurements. The dashed lines are theoretical predictions using eq 9 and 10.
Polymers. The polystyrene (PS) samples were obtained from the Pressure Chemical Co., Pittsburgh, the nominal molecular weights being listed in Table I. The molecular weight distributions are very narrow, Mw/Mnbeing in all cases less than 1.1. Two polyethylene oxide samples with methoxy end groups (DMPEO 2000 and DMPEO 6000) and one with a single methoxy end group (MPEO 350) were kindly provided by Dr. J. A. Faucher, Union Carbide Co., Tarrytown, N.Y. The other samples listed in Table I were obtained from commercial sources. Methods. As a composition variable, the volume fraction has the disadvantage of being temperature dependent. For this reason the closely related temperature-independent segment fraction was used as a composition variable. The segment fraction is defined by w2v2*
=
w2u2*
+ WlVl*
(1)
where wi is the weight fraction of component i and v,* is the specific hard core volume of component i. The hard core volume can be obtained by either group-contribution
v/v
(3)
Here a is the thermal expansion coefficient, v is thejpecific volume of the liquid at the temperature T , and V is the reduced volume and is a measure of the free volume in the liquid. Literature values8 of these quantities were used to obtain u* values for EBBA, polystyrene, and the various polyethylene oxides. The solutions were kept in sealed glass tubes of 6-mm i.d. Each solution contained -0.6-1.0 g of EBBA. In order to obtain a homogeneous solution, the components were mixed in the isotropic phase, care being taken to avoid mechanical degradation of the polymers during mixing. Temperatures were measured with a Hewlett-Packard quartz thermometer (Model 2801 A) to within 0.01 "C. The upper (T,p)I boundary of the phase diagram was visually observed by slowly cooling (-0.1 "C/min) the isotropic liquid until the turbid nematic phase appeared. The experimental accuracy in determining the (T,(p)I boundary was estimated to correspond to f O . l "C. The lower ( T , P )boundary ~ was determined by two different methods. In the first, the sample was quenched from a high temperature, at which the solution was isotropic, into a preset temperature of the water bath. This procedure was repeated for different temperatures of the water bath until a minute amount of isotropic liquid was in equilibrium with the nematic liquid. This determined the ( T , Pboundary. )~ The normal procedure of heating a nematic solution until the isotropic phase appears could not be followed due to the extremely long equilibrium times. In the present case, the separation of the phases took at least 2 h. Upon cooling such a solution, -0.1 "C, the sample was found to be completely nematic. In some EBBA + polymer systems, however, the ( T , P )boundary ~ is very steep. In such cases a small change in concentration causes a drastic change in the TNtemperature. An accurate determination of the ( T , v )boundary ~ is therefore impossible since there is always some uncertainty in the concentration. The experimental accuracy in determining the ( T , Pboundary )~ may be judged from the scatter of points of Figures 1 and 3. The second method for determining the ( T , V boundary )~ made use of the lever rule, adapted to volume fractions. The position of the ( T , P boundary )~ can be found from (P2
- $9zN)/($9zI - $92) =
d/(l - d)
(4)
1716
The Journal of Physical Chemistry, Vol. 82,No. 15, 1978
Here (pz is the overall volume fraction of the polymer solute and cpzN is the solute volume fraction to be determined in the nematic phase. The solute volume fraction in the isotropic phase, ,p; is obtained from the (T,& line in the phase diagram. Finally, the volume of isotropic liquid over the total volume, i.e., the volume fraction of the isotropic phase, (d, is determined by measuring the position of the boundaries of the liquid phases using a cathetometer. It was found that a minimum of N 12 h was required in order to obtain a constant reading of the liquid-liquid boundary, Both the above methods were inapplicable for the EBBA + PS(110 000), PE0(4000), or DMPEO(6000) systems. ~ were too steep for the first method The ( T , P )boundaries and the second method was impossible to apply due to the low slope of the (T,cp)' line, which made an accurate determination of cp; impossible.
Thermodynamic Background The experimental phase diagrams are usually described through a parameter K relating the phase interval (pz' - cpzN to the depression of the temperature below P, or a corresponding parameter K in terms of the mole fractions K =
(cp;
=
(XJ
-
vzN)/(1 - T*)
(5a)
T*)
(5b)
B. Kronberg, I. Bassignana, and D. Patterson
(12)
and
BN" =
PN"/P'"
In BN"/B1" = In
= In yzN"/yz'" = r2Ax
(14)
Using (€9,eq 14 gives yZN"- yJm
-
BImK(15)
1 - B'"K"
72"
The values of B at moderate concentration are related4 to those at infinite dilution through
or K
- XzN)/(l -
while
where
K =
T* = T / P (6) One must also define the parameters BN,ON, and BI, 0' related to the depression of the transition temperature: BN = ( 1 - T*)/cpzN /IN = ( 1 - T * ) / x ~ ~ (7) B' = ( 1 - T*)/p; P I = ( 1 - T*)/x,I
K = (BI)-l - (BN)-l
=
- (pN)-l
(8) The theor? predicts the phase boundaries through two equations governing the nematic-isotropic equilibrium: K
o = In (cpZN/cp2') + (1 - r ) h N
(PI)-1
+
- PI')
-
(10) Here, Aho is the heat of the nematic-isotropic transition for the liquid crystal in the pure state at the nematicisotropic transition temperature P. The rL are the numbers of segments in the component molecules and r2X'(P11)2
r = -r2= - u2*M2 (11) r1 Ul*Ml In the present work we arbitrarily put r1 = 2, each segment corresponding to a benzene ring of the EBBA. We then obtain the number of segments, rz, in the polymer as listed in Table I. Only the ratio r is significant and the choice of r1 = 2 is unimportant. The x parameters express the interaction between the solute and the solvent in its nematic or isotropic state through x = z A w I R T , Aw being an interchange free energy for 1-2 contact formation: Aw = l / ~ ( t l l €22) + - €12. The Ahobeing known experimentally, eq 9 and 10 may be solved to predict cpzN and p,I for any temperature and any choice of the x parameters. The experimental parameters BN,BI, and K have a thermodynamic significance when evaluated at infinite dilution, e.g.
-[
rzAh" rlRP
1
+ F(cp2N + * I ) ]
(17)
+ XI) - 1
(18)
with a = r2(xN
-
r
Equations 16 show that BN and B' deviate to the same extent from their limiting values but in opposite directions. This indicates that BN" and BI" may be obtained4 from BN and B1 through /
\
where K" is obtained from a calorimetric value of Aho and the application of eq 12. Equations analogous to (19) link P" and @ values through K".
Results and Discussion EBBA + Polystyrene Systems. Figure 1 shows the nematic-isotropic phase diagrams for EBBA with a series of polystyrene solutes, starting with ethylbenzene which may be considered as a single segment of polystyrene. This solute gives (Figure l a ) the typical straight-line phase boundaries found p r e v i o u ~ l yfor ~ ~solutes ~ of low molecular weight. However, as the molecular weight of the polystyrene solute is increased, the phase boundaries depart to an increasing extent from straight lines, as seen in Figure Ib-f. There are two major ways in which the phase diagrams evolve: (i) As the polymer concentration is increased, the slopes of the (T*,cp)* and ( T * , d Nboundaries respectively decrease and increase, giving a positive curvature of the (!P,cp)'boundary and a negative curvature of the ( P , Pboundary )~ as predicted by eq 16. The values of K will thus increase with solute concentration, in accordance with eq 17. (ii) The width of the two-phase region, or K , increases with the molecular weight of the solute, which also can be seen in eq 12 or 17. As a result of these features, the ( T * , V )boundary ~ approaches the
Phase Diagrams of Liquid Crystal
Polymer Systems
ordinate in the phase diagram, i.e., BN m, when the molecular weight approaches infinity, In this limit the = 0, and polymer is insoluble in the nematic phase, Le., eN all the polymer will be found in the isotropic phase. Computer solutions, using iteration methods, have been used to predict the phase diagram from eq 9 and 10, adjusting the xNand XI parameters to obtain the "best" fit of theory to experiment. In judging the "best" theoretical curve, importance was placed on the shape more than on having a low standard deviation of the theoretical from the experimental points. For PS(110000) the calculated phase diagram was obtained by putting fiN= 0 in eq 9. The results of the theoretical predictions are shown together with the experimental results in Figure la-f. The x parameters obtained from the best fit are listed in Table I. In Figure la-f it is seen that the general behavior of the experimental phase diagrams is predicted by the theory, i.e., the outward curvature of the two (T,cp)boundaries and the increase in the width of the two-phase region with increasing molecular weight of the polymer. The agreement between experiment and theory is very good considering the simplicity of the theory, e.g., the x parameters are taken to be concentration independent. A concentration-dependent x is of frequent occurrence in polymer solutions. Values of the xN and x' parameters depend sensitively on the positions of the nematic and isotropic phase boundaries, particularly for high molecular weight of the polymer. These values will thus reflect any inadequacy of the theory which could account for their variation at high molecular weight. (A variation of x at molecular weights lower than lo4 is usual in polymer solution thermodynamics.) However, the difference Ax = X N - x I is directly related to the thermodynamic quantity ynN"/yz'" (eq 14) which in turn is obtained from the experimental phase diagram corrected to infinitely low polymer concentration. An error in the individual xNand X I should not appear in Ax, This view is supported by the fact that values of Ax, obtained from fitting the theory to the individual phase boundaries, are almost identical with those found directly from the phase diagrams at infinitely low polymer concentration using eq 14 and 19. The thermodynamic data of concern here, (yzN"- y;")/y;" and AG(transfer), eq 20, are obtained from the phase diagrams corrected to infinitely low polymer concentration and do not depend on the individual values of xN and x' but on Ax. The theory successfully predicts the main feature of the experimental results in Figure 1, Le., with increasing polymer concentration there is an increasing deviation of the two phase boundaries from straight lines. Equation 19 thus appears to constitute a valid theoretical method to obtain the limiting values BN"and B'". These equations have now been used for a variety of liquid crystal and solute s y ~ t e m s . A ~ ~quite ~ different method has been proposed by Martire and collaborator^.^ They suggest that the measured (T,,plNand (T,# phase boundaries are indeed accurately straight lines which do not, however, extrapolate to T* = 1 at infinite dilution. A t an inaccessibly low concentration of solute, both experimental boundary lines are assumed to change their slopes, or BN and B', by the same factor K/K" CI 2, thus giving the correct K" value a t infinite dilution. There is as yet no experimental evidence supporting this suggestion. To the contrary, the curving phase boundaries predicted by ref 4,and hence the correction procedure, eq 19, is confirmed experimentally for these polymer systems. Statistical models of the liquid crystal + solute system predictg the
The Journal of Physical Chemistry, Vol. 82, No. 15, 1978
1717
-+
!400k e
i
300
01 0
I
I
I
10
20
30
*,k
"
I
145
'2
Figure 2. The free energy of transferkegment from isotropic into nematic EBBA against number of segments in the polymer: (O), polystyrene; (W), polyethylene oxide. The dashed curve shows comparable data for globular alkane solutes in MBBA.
phenomenon of phase separation but would be inconvenient for the correction of finite concentration data to infinite dilution. The thermodynamic datum of most interest is (yzNm y21m)/y;" corresponding to the change of activity coefficient on transferring the solute from the isotropic to the nematic phase. Values are listed in Table I. They were obtained by inspection of the phase diagrams a t low concentration, yielding BNand B', whence eq 19 gives the infinite-dilution values and eq 14 leads to (yzNm- y;")/ y?. Otherwise very similar values are obtained from the fitted xNand x' values in Table I, through Ax and eq 14. For PS(110000) BN could not be obtained so that thermodynamic data are lacking for this molecular weight. The molar AG of transferring the polymer from the isotropic to the nematic phase is given by AG(trans)
RP
7zNm = rzAX = In -
(20)
Y2I"
This quantity increases with the polystyrene molecular weight as would be expected. This behavior is also found for globular solutes in MBBA (Figure 5 of ref 2). It is of interest to consider AG(trans) per polymer segment, Le., AG/r2, as shown in Table I and Figure 2 for the different P S molecular weights. In this work we arbitrarily consider the hard core volume of the EBBA molecule (229.67 cm3 mol-') to correspond to two segments. Thus a single segment of EBBA or PS corresponds to 114.8 cm3 mol-l which for P S means 141 g mol-I, the hard-core volume per gram of PS being 0.813 cm3 8-l. In Table I and Figure 2, the decrease of AG(trans)/r2indicates a decrease with molecular weight of the nematic disorder induced per PS segment. One might have expected that, with increasing r2, AG/r2 would decrease rapidly to a constant value, where each segment would disorder the liquid crystal with equal efficiency. The observed constantly decreasing efficiency of the segments in disordering the nematic could arise from the long-range effect of the polymer on the nematic phase, provided there is extensive back-coiling of the polymer so that there would be an overlap between the nematic regions affected by different polymer segments. The thermodynamic results thus suggest that in the liquid crystal the polymer is not randomly coiled but of a more compact configuration. Figure 2 also shows for comparison AG(trans)/r2 for the globular solutes (branched alkanes, tetraalkyltins, etc.) in MBBA as considered in ref 2. Although the MBBA and EBBA results cannot be compared in an absolute sense,
1718
The Journal of Physical Chemistry, Vol. 82,No. 15, 1978
0 98 0 96
\ '\
--- -----____ ---
0.98
--
0 96
I.00C
4
olo>q
i
-----_____
DMPEO (2,000)
0, ,9, \8: , \
9"
096 0
005
'.
010
DMPEO (6,000 I
015
0
+
005
010
015
$2
Figure 3. Phase diagrams of EBBA polyethylene oxides wth different molecular weights. PEO, MPEO, and DMPEO indicate 0, 1, and 2 end groups: A, liquid-liquid phase separation. Remaining indications as in Figure 1. The (a, scale is the same in each part of the figure.
it is clear that the AG/r2 values for the globular solutes decrease much more rapidly with molecular weight than do the values for PS. Here one might expect that the disordering of the liquid crystal depends not on solute molecular volume, but perhaps on molecular surface, and A G ( t r a n ~ ) / ris~ ~ more / ~ nearly constant. Depolarized Rayleigh scattering measurementslO on polystyrene in its pure state and in dilute solution indicate that there is no short-range order, or correlation of molecular orientations in pure polystyrene. Since the polystyrene molecules have even larger values of AG(trans) than the globular solutes, there is certainly no evidence that correlation of molecular orientations occurs between PS and EBBA. EBBA Polyethylene Oxide Systems. The different polyethylene oxide samples are listed in Table I and their phase diagrams are shown in Figure 3. As in the poly)~ have styrene systems, the (T*,cp)' and ( T * , P boundaries respectively positive and negative curvatures. Also the width of the two-phase region increases with the solute size or molecular weight. PEG(4000) shows a more complex behavior than the other polymers. Here the nematic-isotropic phase diagram is intersected by a liquid-liquid phase separation curve where the polymer separates out into a polymer-rich phase. This is due to the large difference in chemical nature between the polymer and the solvent (as reflected in solubility parameters, for instance). The hydroxyl end groups might be an important factor since DMPEO(6000) does not show this behavior. The chemical difference could also be enhanced by hydroxyl groups along the backbone of the polymer.ll The open-triangle phase boundary in Figure 3c corresponds to the separation into two isotropic liquids and the nematic phase starts to appear below this temperature. In computing the theoretical predictions of the phase diagrams from eq 9 and 10, the same procedure as for the polystyrene systems was used to obtain the two x parameters, listed in Table I. For PEO(4000) and
+
B. Kronberg, I. Bassignana, and D. Patterson
DMPE0(6000), the calculated phase diagrams were obtained by putting cpzN = 0 in eq 9. The simple theory does not reproduce the experimental curves for the polyethylene oxide systems as well as for the polystyrene systems. Nevertheless, the general characteristics of the phase diagrams are correctly predicted, Le., the outward curvatures of both the (T,cp) boundaries and the increase in the width of the two-phase region with increasing molecular weight of the polymer. Table I shows the values of (yzN"- yP)/y:" for transfer of polyethylene oxides from the isotropic to nematic phases and also values of the segmental free energy of transfer, AG(trans)/rz. As with the PS systems, these values were obtained from the phase diagrams through BN and R1 corrected to infinite dilution. Again, the hard-core volume of a segment is 114.8 cm3 mol-I corresponding in the case of PEO to approximately 153 g mol-l. Figure 2 shows that the segmental AG(trans) is similar to that found for the polystyrenes. This somewhat unexpected result seems to indicate the importance of the size rather than the nature of the segment in destroying the order in the nematic phase. For the two highest molecular weights, PEO(4000) and DMPEO(6000) values of BN could not be obtained experimentally and thermodynamic data are correspondingly lacking. However, using the given molecular weights, values of K" may be obtained and used in eq 15 together with the experimental B' to give values of (yzNm -yp)/yp as shown in parentheses in Table I. It will be apparent that these values are anomalously low and do not continue the trend of increasing (yZN"- y;")/y2Im with increasing molecular weight of polymer. Two explanations may be given. First, the effective molecular weights of these samples may be increased by intermolecular association for which evidence in other solvents is available."J2 A plot of BI against log M has been constructed for the polyethylene glycols and the present values of BI would give molecular weights corresponding to an association of 5 molecules. If one assumes this, then normal values of - yJm)/yJmare obtained. The second possibility is that the molecules in these samples are not in the random coil conformation, but are helices. Evidence13 exists for a helical conformation in aqueous solution. In the present case, the hypothesis would be that the nematic phase of the solvent "forces" the polymer, at least partly, into a helix form. The helix form being rigid and anisotropic should be able to correlate its orientations with the liquid crystal. The nematic order would thus not be broken up as much when the polymer is in a helix form as it would be if it were in a random coil conformation, giving a low value of (yzN"- y p ) / y p . The critical molecular weights for the formation of a helix is then to be found somewhere between 2000 and 4000, when the solvent is a nematic liquid crystal. This is a much larger value than that obtained for aqueous systems (-500), but this may not be surprising since the two solvents are very different. We have performed expeiiments with the PEO(6000) sample dissolved in p-azoxyanisole (PAA) which has a nematic-isotropic transition at 134 O C . In this case, both B' and BNcould be determined experimentally. The value of (yzN"- y?)/yJ" is 2.7 which would fit with the other values in Table I. The normal behavior here would seem to indicate that the increased temperature has broken up the PEO aggregates or helices. Unfortunately, the result does not enable one to decide which of the two hypotheses provides an explanation of the anomalous behavior of these samples in EBBA.
-
Acknowledgment.
We gratefully acknowledge the
Nematic-Isotropic Phase Equilibria
The Journal of Physical Chemistry, Vol, 82, No. 15, 1978
support of the National Research Council of Canada and of the Ministere de 1'Education de la Province de Qu6bec. References and Notes (1) A. C. de Kock. Z. fhvs. Chem.. 48. 129 (1904). (2j B. Kronberg, D.'F. R. &on, and D. Patterson, C k m . Soc.,Faraday Trans. 2 , 72, 1673 (1976). (3) . . D. E. Martire, G. A. Oweimreem, G. I. Agren, S. G. Ryan, and H. T. Peterson, J . Chem. Phys., 64, 1456 (7976). (4) B. Kronberg and D. Patterson, J . Chem. SOC., Faraday Trans. 2 , 72, 1686 (1976). (5) B. Kronberg, I. C. Bassignana, and D. Patterson, J. fhys. Chem., following paper in this issue. (6) G. W. Smith, 2 . G. Garlund, and R. J. Curtis, Mol. Cryst. Liq. Cryst., 19. 327 11973): H. Kelker and B. Scheurle. Anaew. Chem.. Int. Ed. E&/., 8,884 (1969); M. Sorai, T. Nakamura, an; S. Seki, Bull. Chem. SOC.Jpn., 47, 2192 (1974).
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(7) P. J. Flory, Discuss. Faraday SOC.,49, 7 (1970). (8) H. Hocker, G. J. Blake, and P. J. Flory, Trans. Faraday SOC.,67, 2258 (1971); B. Bahadur and S. Chandra, J . fhys. C , Solid State fhys., 9, 5 (1976); A. K. Rastogi, Ph.D. Thesis, McGill University, Montreal, 1969. (9) H. T. Peterson, D. E. Martire, and M. A. Cotter, J. Chem. Phys., 61, 3547 (1974); G. I. Agren and D. E. Martire, J. phys. (Paris),36,C1-141 (1975); G. 1. Agren, Phys. Rev. A, 11, 1040 (1975); R. L. Humphries and G. R. Luckhurst, Roc. R. SOC. London, Ser. A , 352, 41 (1976). (10) E. W. Fischer, fhys. Non-Clyst. Solids, f r o c . Int. Conf., 4th, 34 (1977). (11) G. Delmas, J . Appl. folym. Sci., 12, 839 (1968). (12) H. G. Elias and H. Lys, Macromol. Chem., 92, 1 (1966). (13) P. G. Assarson, P. S. Leung, and G. J. Stafford, folym. Prepr., Am. Chem. SOC.,Div, folym. Chem., 10, 1241 (1969); J. L. Koenig and A. C. Angood, J. Polym. Sci., A-2, 8, 1787 (1970); L. W. Kessler, W. D. O'Brien, and F. J. Dunn, J . Phys. Chem., 74, 4096 (1970); S. H. Maron and F. E. Filisko, J. Macromoi. Sci.-phys., B6, 79 (1972).
Effect of Solute Size and Shape on Nematic-Isotropic Phase Equilibria in EBBA 4Aromatic Hydrocarbon Systems Bengt Kronberg, Isabella Bassignana, and Donald Patterson* DeparfmeRt of Chemistty, Otto Maass Chemistry Building, McGill University, Montreal H3A 2K6, Canada (Recelved December 20, 1977; Revised Manuscript Received March 7, 1978) Publication costs assisted by the National Research Council of Canada
Phase diagrams have been obtained for p-ethoxybenzylidene-p-n-butylaniline (EBBA) containing aromatic hydrocarbon solutes. Slopes PN and p' were obtained for the ( T , z ~boundary )~ where the isotropic phase first appears on heating and the (T,x2)'boundary where the nematic phase occurs on cooling. They have been corrected to infinite dilution and used to give the difference of solute activity coefficients in the nematic and isotropic liquid crystal, Le., (yzN"- yZ'")/y;", and the free energy of transfer of solute from the isotropic to the nematic phase. These quantities together with PN and P' are indicators of order destruction by the solute. They increase monotonically with solute molecular weight for solutes composed of aromatic rings which are not fused together and where the molecular flexibility is high, indicating a low or zero degree of orientational correlation between the EBBA and solute molecules. For the poly-p-phenyl series, considered to be stiff rods, the order-destruction parameters pass through a maximum with molecular weight and decrease, becoming negative for p-quaterphenyl which increases the EBBA order. This behavior is predicted by the lattice-model theory developed by Peterson, Martire, and Cotter for rodlike solutes. Data are also given for a number of platelike solutes consisting of fused benzene rings. The order in the EBBA-plate system is very sensitive to the shape of the plate being increased by any anisotropy, which apparently promotes a correlation of the EBBA and plate orientations.
Introduction Figure 1 shows the phase diagram for the nematicisotropic transition in the system p-ethoxybenzylidenep-n-butylaniline (EBBA) + 1,2-diphenylethaneS The straight-line phase boundaries are typical for systems where the solute molecule is no larger than the liquid crystal molecule. Recent work1 with p-methoxybenzylidene-p-n-butylaniline (MBBA) has shown that solute size and shape affects the depression of the nematic-isotropic transition and also the free energy of solute transfer from the isotropic to the nematic phase. The solutes used were: (a) highly branched alkanes or other globular molecules with an alkyl-group surface, or (b) normal alkanes considered to be flexible rods. The globular solutes have relatively large effects on the nematic order which increased with solute size. The normal alkanes, presumably because of their ability to correlate their molecular. orientations with those of the nematogen, have a smaller effect which is independent of alkane chain length. As first found by Chen and Luckhurst,2 there is a functional relationship between the depression of the nematic-isotropic 0022-365417812082-1719$01.0010
transition temperature and the lowering, by the solute, of the order parameter S of the liquid crystal. Thus, with the globular and n-alkane solutes, analogous effects of solute size and shape were found when studying S or the depression of the transition temperature. In the present work we give only phase data for aromatic hydrocarbon solutes in EBBA, which has a higher transition temperature than MBBA and hence is a better solvent for a solid solute. Because of their wide variety of molecular structures, most of which are seen in Figure 2, the aromatic hydrocarbons are well suited to a study of effects of solute size and shape, extending the work of ref 1. Experimental Section Materials. The liquid crystal, EBBA, has been described in the accompanying paper,3 designated as I. The solutes are listed in Table I, and the structures of most of them are given in Figure 2. Except for MBBA, they were obtained from Aldrich Chemical Co., Milwaukee, Wisc., with purities ranging from 95 to 99%. All compounds with purities less than 99% were purified by sublimation. The
0 1978 American
Chemical Society
