J. Phys. Chem. 1983,87,235-238
is the same as for the subject compounds, supporting the suggmtion that dopamine and DOPA adopt the same 5,6-q2 orientation. The decrease in nor on going from flat to edgewise orientation implies that the product distribution from electrochemical oxidation is dependent on initial orientation, in agreement with previous r e s u l t ~ . ~ J ~ Acknowledgment. Acknowledgment is made to the
235
donors of the Petroleum Research Fund, administered by the American Chemical Society, to the Air Force office of Scientific Research, and to the National Science Foundation for support of this research. S.E.A. received a grant from the Westmont College Alumni Association. Registry NO. LDOPA, 59-92-7; &DOPA, 63-84-3;Pt, 744006-4; HCI04, 7601-90-3.
Cooling Rate Dependence of the I c e I Nucleation Temperature in Aqueous LiCl Solutions D. R. MacFarlane,+R. K. Kadlyala, and C. A. Angell' Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: Aprll 72, 1982; In Final Form: September 29, 1982)
The cooling rate dependence of the homogeneous nucleation temperature, Th,has been determined for several compositions in the system LiC1/H20. This cooling rate dependence was found to be small except at concentrations close to the edge of the glass-forming range. An explanation of the often observed termination of the Thcurve at -Tg + 22 K is developed. Little prospect is found of improving the vitrification range of cryoprotectant solutions by the imposition of high quench rates.
The homogeneous nucleation temperature, Th, for crystallization of simple liquids is a much-discussed quantity in the theory of phase changes, but it is difficult to determine with confidence due to the difficulty of excluding heterogeneous impurities. In the interesting and much-studied case of water, and its aqueous solutions, an important advance was made by Rasmussen and McKenzie' who developed a stable "water-in-oil" emulsion, using sorbitan tristearate as surfactant, with which repeated supercoolings to temperatures within 3 K of the lowest recorded (cloud chamber droplet) nucleation temperature could be obtained. Although not strictly true, it is convenient for the purpose of exploring the effect of experimental variables (such as pressure, composition, and, in the present instance, cooling rate) on the nucleation probability to regard the emulsion crystallization temperatures as "homogeneous nucleation temperatures". In pure water Th is found2 to lie within a few degrees of the temperature at which the thermodynamic properties are thought to diverge. Th has also been studied as a function of pressure in H2O3v4where it is depressed with increasing pressure up to 2 kbar as the hydrogen-bonded structure becomes increasingly distorted relative to the structure at atmospheric pressure. In dilute aqueous solutions, T h has been studied as a function of concentration1s5and pressure6 and appears to behave as a colligative property of the solution presumably because the nucleation rate I(T),on which Thdepends, is dependent, among other quantities, on the liquidus temperature of the solution. At higher concentrations and pressures (up to 2 kbar) Thrapidly approaches Tg,the glass transition temperature, and eventually becomes unobservable when the nucleation and growth rates become too small to produce significant crystallization during cooling. The liquid then continues to follow the liquid free energy surface down in temperature until the structural relaxation time becomes too long for internal equilibration to be obtained and the structure Lord Rutherford Memorial Reserach Fellow 1980-2.
is arrested at Tg.So long as Th, observed at lower and lower cooling rates, remains above Tg, the glass obtained by rapid quenching can in principle relax, given sufficient time, toward both internal (liquid) and external (crystalline) equilibrium and is hence termed doubly unstable.' This behavior is illustrated by LiCl/H20 solutions which show a doubly unstable region around 8-10 mol ?& LiC1. A recent studf has shown that isothermal measurements made below Tg can be analyzed in a way which yields Th for compositions where it lies below Tg. This extrapolation to sub-T temperatures is importantg in assessing proposed resofutions of Kauzmann's paradox.1° Other studies of Thas a function of concentration and pressure in aqueous solutions of organic glass formers such as dimethyl sulfoxide and propylene glycol have been useful in cryobiological applications1'J2 where the first disappearance of Thwith increasing composition or pressure indicates the lowest, and hence least toxic, vitrifiable concentration which can be used for the low temperature preservation of certain organs. One recent study13 has shown that the imposition of moderate, nonlethal, pressures can extend the glass-forming range to compositions (1) D.H.Rasmussen and J. P. McKenzie, "Water Structure of the Water Polymer Interface", H. H. G. Jellinek, Ed., Plenum, New York, 1972. (2) C. A. Angell, "Supercooled Water" in "Water-A Comprehensive Treaties", F. Franks, Ed., Vol. 7, Plenum, New York, in press. (3) H. Kanno,R. J. Speedy, and C. A. Angell, Science, 184,880 (1975). (4) P. Xans and G. Barnaud, C. R. Acad. Sci. Paris, 280, 25 (1975). (5) D.H.Rasmussen, J. S. Paik, J. H. Perepezko, and C. R. Lopes, Jr., unpublished data. (6) H.Kanno and C. A. Angell, J. Phys. Chem., 81, 2639 (1977). (7) C. A. Angell, E. J. Sare, J. Donnella, and D. R. MacFarlane, J. Phys. Chem., 85, 1461 (1981). (8) C. A. Angell and D. R. MacFarlane, Advances in Ceramics 4, (Proc. Symp. on Nucleation), in press, 1982. (9) C. A. Angell and J. Donnella, J. Chem. Phys., 67,4560 (1977). (IO) W. Kauzmann, Chem. Reu., 43, 219 (1948). (11) G. M. Fahy and A. Hirsch, "Organ Preservation, Present and Future", D. E. Pegg, I. A. Jacobsen, and N. A. Malasz, Ed., MTP Press, Lancaster, 1981. (12) D.H.Rasmussen and L. Luyet, Biodynamica, 11, 33 (1970). (13) D.R. MacFarlane, C. A. Angell, and G. M. Fahy, Cryoletters 2, 353 (1981).
0 1983 American Chemical Society
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The Journal of Physical Chemistry, VoL 87,No. 2, 1983
MacFarlane et ai.
which are known to be nontoxic. All of these numerous studies have determined Th at constant cooling rates in the region of 10 K min-' and, although slower rates have been used to make Th observable near the lower limit, the question of the cooling rate dependence of Thhas never been systematicallyaddressed. It has been tacitly assumed' in the earlier work that the Th data at lower composition and pressure are essentially cooling rate independent, and, hence, that the smaller cooling rate data can be included on the curve (and that - ~____ Temperature Decreasinq the curve then becomes appropriate for that particular cooling rate only). It seems fairly clear that r h must be 1901 markedly cooling rate dependent in the doubly unstable T region but it is not obvious how rapidly this dependence must disappear at lower concentrations and pressures. A study of the cooling rate dependence of Thin aqueous LiCl solutions, for which considerable Thdata already e ~ i s t s , ~ ~ ~ has therefore been undertaken to answer these questions. The question of the exact nature of the cooling rate dependence of That the edge of the doubly unstable region is especially important in the cryobiological studies mentioned above, insofar as it determines the extent, if any, to which the glass-forming region can be extended to lower compositions and pressure by the imposition of higher cooling rates. The relationship between Thand the values determined 0 02 04 06 0 8 IO 12 14 16 I/q (K-lmin) by isothermal sub-Tgstudies referred to above also requires the assumption that Th lies at essentially the same temFlgure 1. Cooling rate dependence of T, for various compositions in perature as that at which the nucleation rate arises rapidly the LiCI/H,O system. Dashed lines indicate glass formation at the higher cooling rates. from vanishingly small values to its maximum. This will be true if I ( T ) is a step function of T but since this is not Results and Discussion quite the case then there is a possibility of a depression The results of the cooling rate experiments are shown of Th relative to the onset of significant nucleation Gust in Figure 1in which the observed (instrument) nucleation as cooling-transformation (CT) curves are depressed reltemperatures have been adjusted at each cooling rate by ative to time-temperature-transformation (TTT)curves14 using a temperature calibration made at each cooling rate. where these can be calculated). The extent of this deThe reciprocal cooling rate (min K-l) scale of Figure 1 is pression should be indicated by the behavior of Thas the chosen to facilitate comparison with CT curves14for which cooling rate q 0. temperature is plotted against time. Each Th point is Experimental Section estimated to be accurate to approximately f0.5 K given Lithium chloride solutions were made up from Alpha an uncertainty of f0.25 K in both the raw data and the Products anhydrous LiCl and deionized distilled water and temperature calibration. Within this level ,of uncertainty emulsified in a dispersant consisting of a 1:l mixture by the Th for 5 mol % LiCl appears to be independent of volume of methylcyclopentane and methylcyclohexane. To cooling rate over the whole range of rates studied and avoid coalescence of the droplets in the emulsion, we shows no tendency to deviate from constancy even at 40 dissolved Span 65 (sorbitan tristearate) surfactant in the K min-'. hydrocarbon phase.' Small (-25 mg) samples of the Significant changes begin to appear at 8 mol % and by emulsion were encapsulated in A1 pans which were her9.5 mol % Thceases to be observeable at cooling rates in metically sealed to avoid losses from the sample due to excess of 5 K min-'. In these latter cases vitrification, as vaporization during extended runs. Crystallization was evidenced by the appearance of the glass transition and detected in a Perkin-Elmer Model I1 differential scanning crystallization peak on subsequent warm up scans, was calorimeter from the sharp exotherm associated with the achieved on continued cooling. The edge of the glassphase change. forming region seems to be quite well defined at normal Cooling runs were carried out at rates between 0.6 and cooling rates with vitrification not being achieved at 9.25 40 K m i d . The instrument temperature calibration varies mol % at any cooling rate (although the appearance of the as a function of scan rate; however, temperature calibration curve in Figure 1 suggests that small increases in the standards which do not show a tendency to supercool do cooling rate above 40 K min-' may allow vitrification). not appear to be available (though in principle selected Figure 2 shows a plot of Th vs. composition at two diliquid crystal mesophase transitions should be usable) so rectly measured cooling rates and also at infinitely slow the instrument was calibrated at different heating rates cooling, q = 0, based on an empirical extrapolation. It is by using the melting point of pure cyclopentane and the not clear on theoretical grounds how the extrapolation to difference Tinstrument - Tad (always positive) added to the q = 0 should be carried out. The nucleation rate is a display temperatures during cooling, i.e., instrument lag complex function of temperature and the available methwas assumed to be independent of the sign of q. Thwas ods for assessing the extent of transformation during a obtained from the crystallization exotherm by using the continuous cooling experiment are numerical technique^.'^ construction illustrated in the insert to Figure 1. These are of little help in providing an analytical function
-
-
(14)P. I. K. Onorato and D. R. Uhlmann, J. Non-Cryst. Solids, 22,367 (1976).
(15) D. R. MacFarlane, accepted for publication by J. Non-Cryst. Solids.
Cooling Rate Dependence of the Ice I Nucleation Temperature
The Journal of Physical Chemistry, Vol. 87, No. 2, 1983 237
TABLE I : Calculated Values of Time Required for a m Nucleus to Grow to 1 W ‘9
T,K
11, p
D ,cm2 s-*
growth time, s
203 193 183 173 163 153
12.3 26.3 176 2090 6.7 x 104 7.5 x 106
8.1 x 10-9 3.6 x 10-9
1.9 4.2 30 3.8 X l o 2 1.3 x 1 0 4 1.5 x 106
5.1 X
4.0X 1.2 x 1.0 x
lo-” 10-12
1044
where f ( c ) (-0.8 for a 9 mol 5% LiCl solution at 175 K) is a function of the initial and final concentrations and t is
the elapsed time from inception of the nucleus. The diffusion coefficient is of course highly temperature dependent but can be estimated, albeit crudely, from the Stokes-Einstein relation and available viscosity data.17 The viscosity data of ref 17 unfortunately do not extend to concentrations lower than 14.5 mol %; however, the glass transition temperature at this composition is within 1 K of that expected for the concentrations under study here because of the unusual composition independence of T, in moderately concentrated LiCl/H20 solutions. Thus we have approximated the viscosity of the 8-10 mol % solutions by that of the 14 mol % data of ref 17, expecting that the errw thus incurred will be much less serious than those inherent in our use of the Stokes-Einstein equation. Growth rate estimates based on these considerations (Table I) show that the growth rate is sufficiently high at temperatures above -200 K that the occurrence of a nucleus in a droplet will result in immediate (on the time scale of these experiments) desupersaturation of the solution. Thus the Th’S for the 5 mol % solution in Figure 2 indicate accurately the temperature at which the nucleation rate rises suddenly from vanishingly small values. Below 200 K, however, Table I shows that the rate of growth becomes important in determining the position in temperature at which T h is observed since slow growth (and hence appearance of the heat of crystallization) depresses the observation of a nucleation event increasingly from the temperature at which it occurred. Thus in the case of the more concentrated solutions, where Th < 200 K, the cooling rate dependence observed could be a result of the slow growth rate following a nucleation event at a higher temperature, which may or may not have a significant cooling rate dependence of its own. In any event the true nucleation temperature at q 0 must vary more slowly with composition than the exotherm-based experimental value. Also the likelihood of non-steady-state nucleation taking place on the time scale of the observation becomes increasingly important at these low temperatures. The first successful vitrification (for example, in the 9.5 mol % solution) with increasing cooling rate is evidently a growth rate effect since warming scans of the glasses thus obtained always show crystallization exotherms at temperatures slightly higher than 161 K, the temperature at which T h ceased to appear on cooling. The nuclei which give rise to this crystallization are equally likely to have formed during cooling as during warming if both are carried out at the same rate, but these nuclei do not begin to grow at appreciable rates until the temperature reaches the range where the growth rate is no longer vanishingly small on the time scale of the experiment. It is, after all, the enthalpy release associated with the growth process, as opposed to nucleation per se, which is detected by the scanning calorimeter. Equivalent reservations would apply to crystallization events observed visually. It is consistent with the latter deduction that the Th curves observed (at the usual cooling rate of 10 K min-’)
(16) J. W.Christian, ‘The Theory of Transformations in Metals and Alloys”, Pergammon, New York, 1965.
(17) C. T.Moynihan, N. Balitactac, L. Boone, and T.A. Litovitz, J . Chem. Phys., 55, 3013 (1971).
150
50
140
10 0
0
1
2
2
3
4
1 6
4
mole
%
8
10
12
LiCl
Flgure 2. T, vs. composition at various cooling rates including infinitely
slow cooling (9= 0). The 9 = 0 curve extrapolates smoothly to the low temperature Th data obtained in ref 8. Inset: Plot of l / T h vs. 9
”*
indicating an empirical linear extrapolation to 9
= 0.
of temperature for extrapolation purposes. The experimental points appear, however, to be linearized within experimental error at cooling rates up to 10 K min-l by a 1/Th vs. q1l2plot (Figure 2 insert) and the q 0 points shown in Figure 2 are based on this function. Figure 2 shows that a cooling rate dependence only becomes appreciable when the concentration rises above 6 mol % LiC1. Due to the q dependence at higher concentrations the T h curve determined by using fixed normal cooling will underestimate the temperature at which the nucleation rate vanishes, but the extent of this underestimation amounts to only 5 K in the worst case. The extrapolated Th(q-0) curve is still in good agreement with the points obtained from the sub-T, isothermal measurements reported in ref 8. In the region where a scan rate dependence is not observed, the Th event is controlled by the nucleation rate, and the probability of observing the phenomenon of crystallization, as manifested by an exotherm, increases with decreasing temperature. This contrasts with the results of recent isothermal studies on reheated quenched glasses in this system in which the probability of crystallization increases with increasing temperature.s The region in which T h becomes quench-rate dependent is in a transition zone between the two regimes, in which the observation of Th, while still becoming more probable with decreasing temperature, now becomes more and more under the control of crystal growth, rather than nucleation, kinetics. The isothermal crystallization behavior in the transition zone can be investigated directly (though with some qualifications) by emulsion methods, the results of such a study will be reported in a future publication. In the transition region, the growth becomes a diffusion-limited process, and the volume growth rate, U, of the ice particles is simply related to the diffusion coefficient, D,by16
-
-
J. Phys. Chem. 1983, 87, 238-243
238
in most of the systems studied to date terminate (;.e., Th ceases to be observable) at -22 K above Tr This seems to be equally true for studies carried out with increasing pressure as with increasing concentration. Growth rates scale with the viscosity, so the temperature at which the growth rate prevents the observation of Thshould be an isoviscosity temperature. Tgis widely accepted as an isoviscosity temperature so, to the extent that aqueous solutions have comparable viscosity behavior, Tg+ 22 K will also be an isoviscosity point. A greater variation would be expected if the nucleation rate controlled the Thobservability, since this rate depends on the undercooling which, at Tg+ 22, varies some 10-15 K between different systems.
Summary and Conclusions The edge of the glass-forming region in these systems has been shown experimentally to be sharply defined in terms of concentration and only small extensions of the glass-forming region can be attained by using higher
cooling rates. This implies by analogy that in the cryoprotectant systems studied in ref 13 little or no lowering of vitrifiable concentrations (or pressures) is likely to be obtained by imposing high cooling rates. Thhas been shown to be slighly cooling rate dependent but only as the glass-forming region is approached and only as a result of the rapidly falling crystal growth rate. Unfortunately the behavior of the nucleation rate as a function of temperature in the q-dependent region cannot be clearly established from these experiments; however, it would appear that nucleation continues to take place during cooling in this region, even if there is not a thermal manifestation of crystal formation. The glasses formed in this region, even though visually transparent, must therefore contain a significant number of nuclei.
Acknowledgment. This work was supported by the Office of Naval Research under agreement No. N0001478-C-0035. Registry No. HzO, 7732-18-5; LiCl, 7447-41-8.
Calorimetric and Spectrophotometric Determinatlon of the Dissociation Constant of Ethanol in Dilute Aqueous Solutions P. Jand;k,+ L. MeHes;
and P. Zuman'
Department of Chemistry. CIarkson College of Technobgy, Potsdam, New York 13878 (Received: June 23, 1982; In Final Form: September 11, 1982)
Acid-base properties of dilute solutions of ethanol containing sodium hydroxide were studied calorimetrically and spectrophotometrically. Tables IV and V summarize the best values of A H R for concentration, activity, and "mixed" equilibrium constants of the reaction between ethanol and hydroxide ion, and for the molar absorptivity of the ethoxide ion at 225 nm. All the equilibrium constants obtained spectrophotometricallywere higher by a fador varying from 2.1 to 6.8 than those obtained calorimetrically. It is assumed that the equilibrium constants depend on the molar concentration of ethanol which in spectrophotometric measurements was 0.086 M and in calorimetric measurements varied between 0.008 and 0.016 M. Concentration based equilibrium constants K, varied from others by orders of magnitude and thus in concentrated solutions of sodium hydroxide activity coefficients cannot be neglected.
Among the numerous methods used'-3 in attempts to evaluate the acid-base properties of alcohols, conductometric and indicator methods have seemed to be the most successful in dealing with dilute aqueous solutions. However, the reported values, even for methanol and ethanol which have been most frequently studied, have shown considerable spread. To contribute to the understanding of the acid-base properties of ethanol, we performed calorimetric and spectrophotometric measurements. The resulting information should also facilitate the evaluation of data obtained in calorimetric experiments that involve adding an ethanolic stock solution of a reagent to a strongly basic aqueous reaction mixture.
to these rods made it possible to fill the calorimeter with nitrogen prior to equilibration. As before, carefully aged and matched 100-kQ thermistors (Type 51 Al, Victory Engineering Corp., Springfield, NJ) were used in this work. A simple RC circuit had been added to the output of the operational amplifier by Lampugnani' to filter out highfrequency noise. After amplification the overall sensitivity was approximately 3.2 V deg-'. A Hewlett-Packard Model 3450 A digital voltmeter, in conjunction with a Digital Equipment Corp. PDP 1/I minicomputer, was employed for data acquisition. Spectrophotometricmeasurements were carried out with a Unicam SP800A recording spectrophotometer using
Experimental Section Instrumentation. The differential thermometric apparatus, which has been described e l ~ e w h e r e , ~was -~ modified by using hollow Lucite rods to activate the syringes from outside of the calorimeter. Side tubes attached
(1) J. M u m in "The Chemistry of Hydroxyl Group",Part 2, S. Patai, Ed., Interscience, New York, 1971, pp 1087 ff. (2) J. Murto, Ann. Acad. Sci. Fenn., Ser. A2, 117, 7 (1962). (3) E. J. King in "Physical Chemistry of Organic Solvent systems",A. K. Covington and T. Dickinson, Eds., Plenum Press, New York, 1973, pp 331 ff. (4) T. Meites, L. Meites, and J. N. Jaitly, J. Phys. Chen., 73, 3801 (1969). (5) J. N. Jaitly, Ph.D. Thesis, Polytechnic Institute of Brooklyn, NY, 1970. (6) L. Lampugnani and L. Meites, Thermochim. Acta, 5, 351 (1973). (7) L. Lampugnani, unpublished results.
'This work has been submitted by P. Jandik in partial fulfillment of the requirements for the degree of Master of Science, Clarkson College of Technology, Potsdam, NY 13676. 0022-3654/83/2087-0238$01.50/0
0 1983 American Chemical Society
