CALORIMETRIC STUDIESOF POLY-~-BENZYL-~,L-QLUTAMATE-DMF ion conduction may occur in a fused silica membrane when subjected to current densities exceeding approximately 30 pA cm-* at temperatures above 750". (2) The activation energy for sodium ion conduction was found to be time dependent over the temperature interval 450-550", and time independent at higher temperatures. The activation energy for potassium ion conduction was found to be time independent over the 450-850" range investigated, so that the steady-state temperature dependence of the N a : K ion mobility ratio below 550" was opposite to that found above 550", (3) Ion-exchange equilibrium constants were measured for Na+-K+ exchange between NO,-, Br-, and
1081
C1- melts and fused silica. Although the ion-exchange equilibrium constant was found to be only slightly dependent on the temperature, the electrode selectivity constants were shown to be temperature dependent because of the mobility ratio term. The ion-exchange equilibrium constant was shown to be dependent on the melt anion. (4) Consideration of the overall free energy changes involved in the ion-exchange reaction allowed the comparison of many ion-exchange equilibria constants reported in the literature. The dependence of the ionexchange equilibrium constant on the melt anion is satisfactorily explained by the difference in free energy of formation of the respective salts.
Differential Scanning Calorimetric Studies of the System Poly-7-benzyl-a,L-glutamat&Dimethylformamide by J. H. Rai and W. G. Miller* Department o j Chemistry, University o j Minnesota, Minneapolis, Minnesota
66466
(Received November 8 , 1971)
Publication coats assisted by the National Institutes o j Health
Differential scanning calorimetry has been used to investigate the thermal behavior of the system polybenzylglutamate-dimethylformamide in the temperature range -30 to +120° and the composition range 0-30 vol polymer. Irrespective of the initial state (isotropic or liquid crystalline) at room temperature, exotherms were obtained invariably when solutions were cooled to the biphasic region. The thermograms yielded heats of polymer-solvent mixing which were small and endothermic. The observed heats were fitted adequately by a van Laar binary contact heat of mixing expression. From these data a maximum of 5 cal/mol was placed on the latent heat of the isotropic to liquid crystal phase transition.
Introduction Several studies on the system poly-y-benzyl-a,Lglutamate (PBLG)-dimethylformamide (DMF) have been reported. l-6 Recently Wee and MilleId determined the temperature-composition phase diagram for this system in the temperature range -20 to +140° and the composition range 0-30 vol % polymer. At higher polymer concentration solvent activity as a function of temperature and composition has been determinedS6 Although a wide variety of experimental techniques have been employed to investigate the PBLG-DMF system, direct thermal analysis of the system using thermoanalytical methods, such as differential thermal analysis and differential scanning calorimetry (DSC), has not been reported. In this communication, we report the results of a DSC study on the system in the temperature range -30 to +120° and
composition range 0-30 vol % polymer. Both heating and cooling experiments have been carried out. The temperature a t which the polymer solution begins to generate or absorb heat is correlated with the phase diagram. The heats determined are compared with that expected for binary contacts assuming a van Laar form for the heat of mixing.
(1) A. E. Elliott and E. J. Ambrose, Discuss. Faraday SOC.,9, 246 (1950). (2) V. Lusaati, M. Cesari, G. Spach, F. Mason, and J. Vincent, J . Mol. BiOl., 3,566 (1961). (3) P. J. Flory and W. J. Leonard, Jr., J . d m e r . Chem. Soc., 87, 2102 (1965). (4) K.G.Goebel and W. G. Miller, Macromolecules, 3, 64 (1970). (5) E.L. Wee and W. G. Miller, J . Phys. Chem., 7 5 , 1446 (1971). (6) J. H.Rai and W. G. Miller, Macromolecules, 5 , 45,(1972).
The Jotrrnul o j Physical Chemistry, Vol. 76, N o . 7 , 1972
J. H. RAIAND W. G. MILLER
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Experimental Section PBLG ( M , = 310,000) was obtained from New England Nuclear Corp. and was vacuum dried for 24 hr a t 55" before use. It was of the same lot as was used in determining the phase diagram.6 Dimethylformamide (ACS Certified, Fisher Scientific Co.) was vacuum distilled over CaS04. Samples were prepared having concentrations of 2, 5, 8, 9.3, 12, 20, and 30 vol % polymer. I n calculating volume concentration the specific volume of PBLG was taken as 0.787 ml g-l.7 Solutions were prepared in a drybox a t room temperature. After homogenous solution was obtained, about 10-20 mg of the solution was transferred to a DSC aluminum sample pan. The pan was hermetically sealed to prevent solvent loss. The sample was then stored in a desiccator for 15-20 hr before use. Weight loss due to vaporization of D M F was not detectable. A Du Pont Model 900 differential scanning calorimeter was used for all measurements. The instrument was calibrated by using indium, gallium, mercury, and water as standards. Cooling and heating experiments were carried out a t scanning rates of 4-10°/min. For cooling experiments a Dry Ice, water, and methanol mixture was used as a cooling source. In a typical run involving subambient temperatures the sample was heated slowly (1-2"/min) from room temperature to 40" and then cooled a t a specific, preselected rate. After the sample was cooled to about -30', the cooling attachment was removed, and the sample was heated at the same rate to room temperature. For a given sample the same procedure was repeated two or three times to observe the reversibility of the system. I n DSC studies from room to higher temperatures no heat sink was necessary.
4
3
2
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I
I
The Journal of Physical Chemistry, Vol. 76,No. 7, 19%
I
6
-20
I
I
I
20
I
40
I
7 ('C )
Figure 1. Typical DSC thermograms for 5% (1, 2), 8% (3, 4), and 9.3% (5, 6) solutions. Arrows indicate direction of temperature scan. Temperature scanning rate was 6 (1-5) or lO"/min (6).
'
1
I
I
-40
I
I
I
I
B
6
d,
T(% )
I
I
I
40
I
Figure 2. Consecutive series of DSC thermograms on a 12% solution. Scanning rate was 6"/min.
4
Results TypicaI thermograms are shown in Figures 1-3 for runs between room and subambient temperatures. These clearly indicate that the observed heat was associated with a reversible transition. Thermograms from 25" to temperatures as high as 120' gave no indication of heat release or absorption and were indistinguishable from thermograms on inert materials. Thermograms for pure DMF and for pure solid PBLG showed no evidence of thermal transitions. Although the thermograms in Figures 1-3 indicate a reversible process, the onset of exothermicity in the cooling curves does not come a t the same temperature as the onset of endothermicity in the heating curves. Runs with the calibrating materials indicated that this was a result of supercooling and thermal lag. Gallium (mp 29.5"), water, and mercury (mp -38.9') showed initial freezing a t C14, -15, and -40", respectively, upon cooling. However, heating curves indicated the onset of endothermicity occurred within 2-3" of the melting point. By analogy the onset of endothermicity was taken as the approximate "transition temperature"
I
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'
40
3
-
-+
2
L
1
I
I
I
I
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40 -40
S&)
I
I 20
I
'
1
I
4tJ
Figure 3. Typical thermograms for 20 (1, 2) and 30 (3, 4)vol yo solutions. Scanning rate was 6 (1-3) or 8"/min (4).
for the DMF-PBLG thermograms. These are shown in Figure 4 superimposed on the phase diagram. The coincidence of the "transition temperature" with the phase boundaries indicates that the observed thermal transition is associated with the crossing of the phase boundary. (7) A. Elliott, E. M. Bradbury, A. R. Downie, and W. E. Hanby, "Polyamino Acids, Polypeptides and Proteins," M. A. Stahmann, Ed., University of Wisconsin Press, Madison, Wis., 1962, pp 255-269.
CALORIMETRIC STUDIESOF POLY--~BENZYL-C~,L-GLUTAMATE-DMF
T
rc
"2
Figure 4. Phase diagram for the system PBLG-DMF.6 Circles indicate onset of endothermicity in DSC thermograms. Vertical lines indicate the range of temperature scanning. Dashed lines are hypothetical extension of phase boundaries.
The shape of the DMF-PBLG cooling curves indicates supercooling not unlike that observed with the calibrating materials. Inasmuch as this leads to a more clearly defined "peak" the transition heat from the cooling curves was more reliably measured than from the heating curves. The heats determined from the exotherms are tabulated in Table I.
Table I: Observed Heats as a Function of Concentration Polymer concn, vol %
-
2 5 5 8 9.3 12 20 30
Observed heat CaVg of solution Cal/g of polymer
-0.06 -0.14 +0.13 -0.23 -0.34 -0.44 -0.70 -0.93
' Determined
f 0.03 f 0.01 f 0.02" f 0.02 i 0.04 f 0.04 zt 0.07 f 0.09
-2.3 -2.2 +2.0 -2.2 -1.9 -2.9 -2.8 -2.6
from endotherm. taken as moles of monomeric units.
. AHmix(Obsd) cal/mol of solutionb
9
f 0.3
5zt2 11 f 1 10 2 18 f 2 27 i 3 36 i.4 62 It 6 59 f 10
Polymer
concentration
f1 f 0.2 f 0.4"
f0.2 f 0.3 f 0.3 f0.3
*
Discussion Origin of the Thermal Transition. The thermal transitions observed by differential scanning calorimetry correlate well with the phase boundaries as shown in Figure 4. However the heating of the 9.3 or 12 vol % ' solutions from 25 to 120" gave no indication of a thermal transition, even though phase boundaries were crossed also. The origin of the thermal transition can be understood with aid of the phase diagram. Although the phase boundaries have not been determined at low temperature, it is clear that a t -30" the liquid crystal phase is in equilibrium with an isotropic phase that is nearly pure solvent. As the line bounding the isotropic phase must be nearly vertical in this tempera-
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ture region, its composition as well as the composition of the liquid crystal phase with which it is in equilibrium must be nearly temperature independent. Thus as a sample is warmed from -30" there is little change in composition or in the relative amounts of the two phases until a temperature of 0" or above is reached. Then there is a rapid change in composition. If equilibrium is maintained, all samples except the 9.3 one will turn into a single phase system. The heat observed in heating a solution from -30 to +40° can be described as the heat of mixing two phases of very different compositions to obtain a single phase. This heat of mixing corresponds to mixing nearly pure solvent with a phase rich in polymer, though containing an unknown amount of solvent. Since the polymerrich phase contains some solvent, the observed heat of mixing will presumably contain little if any contribution from the heat of fusion of the polymer. The cooling curves represent the reverse process, or a heat of unmixing. As can be seen from Table I the heats are very small. The interpretation presented above also explains why no thermal transition is observed on crossing high-temperature phase boundaries. These high-temperature phase boundaries represent a relatively small difference in composition; consequently, the heat associated with mixing or unmixing when crossing such a boundary will be negligible. The fact that no heat is observed when a liquid crystal phase is turned into an isotropic phase sets limits on the enthalpy associated with the liquid crystal-isotropic phase transition. This will be discussed later. In discussing the heat of mixing A H m i x i n g and AHI. it is convenient to consider the -30" state of the system as the initial state and the 40" state as the final state, i.e., initially the system is biphasic whereas it is a single phase system in the final state. The observed heats of mixing are small and endothermic irrespective of whether the final state is isotropic or liquid crystalline. Frequently small, endothermic heats of mixing can be fitted to a binary contact, van Laar type of treatment. Due to ease of treatment the enthalpy contribution to lattice model approaches to the thermodynamics of random coil as well as stiff chain polymerss has typically been handled in this manner. In Flory's treatments of stiff chain polymers the polymer-solvent interaction parameter x is assumed to be independent of whether or not the system is an isotropic or a liquid crystalline phase. If we further assume that the x parameter is independent of composition as well as phase, a comparison can be made between the experimental heats and that predicted from a van Laar expression. Thus the heat of mixing polymer and solvent to form a solution of volume fraction v2 is given by AHmix(v2)
=
RTxnm
(1)
(8) P.J. Flory,Proc. Roy. SOC.,Ser. A , 234,73 (1956). The J o u d of Physieal Chemislry, Vol. 76, A-0. 7, 1978
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J. H. RAIAND W. G. MILLER
where nl is the number of moles of solvent. In the system studied the observed heat of mixing is given by AHmix(0bSd) = RTx(nlv2
1.0
- n11v21 - nILCvZLc)(2)
where nl and v2 refer to the final state of the system, nll and v 2 I to the initial isotropic phase, and nlLCand vzLC to the initial liquid crystal phase. The values of v2I and nLCare fixed, and n1I and nlLc are related through a tie line relationship to give the correct overall composition. In the case of the 9.3 vol % sample the final state is biphasic. This results in an inconsequentially altered eq 2. By assuming values for v2I and vzLC AHmi,(obsd) may be calculated, using arbitrary values of x, for comparison with the experimental heats determined from the Results of such calcooling curves [ -AH,ix(obsd)]. culations are shown in Figures 5 and 6 superimposed on the experimental data. For a given x the maximum heat would be obtained if 12 = 0 and vZLc = 1.0. To a first approximation it is possible to fit the data using a constant value of x, independent of phase and concentration. More precise measurements of the heats and a definitive knowledge of v21 and vzLC might dictate the need for a slightly varying x , which frequently is the case with random coil polymers. The x values estimated here represent the enthalpy contribution to the free energy of mixing. Previously smaller x values have been estimated from osmotic pressure4and phase equilibrium6 studies. These values are a measure of excess free energy and hence contain entropy as well as enthalpy contributions. I n the Flory expression for the mixing of rod polymers with solvents no account is taken of solvent-polymer sidechain mixing, which is known now to contribute to the solution thermodynamics of helical polypeptides. As the solvent-polymer side-chain mixing will make a negative contribution to the excess free energy of mixing, it is reasonable that measurements yielding an excess free energy x will be smaller than those yielding an enthalpic x. At low overall polymer concentration and at low temperature the solvent is nearly quantitatively in the isotropic phase, a state with v2I = 0. Therefore at low concentration the observed molar heat of mixing, column 5 in Table I, approaches AI% These values may be compared with other determinations. The temperature dependence of the osmotic second virial coefficient may be used to evaluate AR1. Unfortunately AB1 so determined can only cover the concentration range where higher terms to the osmotic pressure equation are not needed. Analysis of osmotic pressure data4 indicates ABl is less than 1 cal/mol for a 0.5 vol. % solution, the highest concentration for which the second virial coefficient adequately describes the osmotic pressure data. The DSC data extrapolated to this concentration fall in the same range. The Journal of Physical Chemhtry, Vol. 76,No. 7, 197.8
1
0.8
i
3
0.6
!i
L
a
a4
a2
0
Y
Figure 5. The observed heat per gram of solution. For the 2 and 5% solutions endotherms (A) as well as exotherms (0) were sufficiently well defined for area determination. Lines vzLo, and x being, respectively, calculated from eq 2 with YZI, 0.01, 0.9, and 0.8 (1);0, 1.0, and 0.6 (2); 0.01, 0.7, and 1.1 (3); 0.01, 0.9, and 0.6 (4); 0.01, 0.7, and 0.8 (5).
4.0 .
o 0l l
. . . . . . . . , . . . . . . . . . . . . . . . , , . . ,. 0.1
0.2
0.3
. , ,
"2
Figure 6. The heat per gram of polymer. Notation same as in Figure 5.
The temperature dependence of solvent activity determined from vapor sorption is yet another method Vapor sorption data6 taken in for determining A& the concentration range 70-100 vol % polymer indicate that the temperature dependence of the solvent activity at constant solution composition is less than the experimental error, which is about 3%. Using this 3% value as a maximum variation in activity with temperature, A B 1 must be less than 400 cal/mol in this concentration range, The DSC data can be extrapolated to the same concentration region through use of the van Laar expression and the parameter which best fits the DSC data. Using a x value of 0.8, a value of 200400 cal/mol is estimated for the concentration range 70-100 vol % polymer. The three types of experimental data, covering the entire composition range, are in satisfactory agreement as far as AQ1 is concerned.
CALORIMETRIC STUDIES OF POLY-~-BENZYL-~,L-GLUTAMATE-DMF
The Latent Heat of the Isotropic-Liquid Crystal Phase Transition. The Flory treatment of the statistical thermodynamics of rod polymers predicts that it should be possible to have a first-order isotropic-liquid crystal phase transition with no latent heat. From the nature of the phase diagram (Figure 4) one can see that there is no manner in which this can be studied by direct thermal measurements. There is no temperature or composition at which the isotropic phase can be completely converted into the liquid crystal phase. A maximum value for the heat can be estimated, however, from the DSC studies. If the data for the heat of mixing to form the isotropic phase are extrapolated into the liquid crystal range, nonoverlap of the two curves corresponds to the heat of the isotropic-liquid crystal phase transition. The values for the 5 and 8% solutions (isotropic) were extrapolated to 12% and compared to the 12% (liquid crystal) value. This difference corresponds to about 0.06 cal/g of solution or 5
1085
cal/mol of solution. Extension of these calculations to higher concentrations will yield somewhat larger estimates of the maximum latent heat. However, the scatter in the DSC data and the uncertainty in the phase boundaries at low temperatures make such extensions meaningless. The high-temperature thermogram on the 12% solution is consistent with a small latent heat in that even a rapid scan aoross the biphasic region, resulting in a rapid conversion of the sample from a single phase, liquid crystal solution into a single phase, isotropic solution, gave no evidence of a thermal transition. It is clear that the latent heat associated with the isotropic to liquid crystal phase transition is indeed small if not zero.
Acknowledgments. We would like to thank Dr. R. Moore, Department of Laboratory Medicine, University of Minnesota, for use of the Du Pont 900 differential thermal analyzer.
The Journal of Physkd Chemistry, Vol. 76, No. 7, 1078
