J. Phys. Chem. 1083, 87, 1848-1851
1848
plete and comparing them to signals of the same fragment ion when known flows of CzH5NOZwere added to the system. The ratio [C2H5N02]f/[C2H5]o which is equal to the fraction of the reaction proceeding by reaction 2, k 2 / ( k 1 k z ) ,was measured at three pressures from 0.7 to 2.1 torr. The result was essentially the same at each pressure which indicates that reaction 2 may be at or near its high-pressure limit under our experimental conditions (see Table 11). The average value of k 1 / k 2for the CzH5 + NOz reaction derived from these experiments is 3.0 f 0.6 in the pressure range 0.7-2.1 torr.
favored over formation of the nitro compound. The modeling of the kinetics of both the thermal and the photochemical nitration of hydrocarbons requires quantitative information on R + NOz reaction^.^-^ The importance of the 0-atom transfer route (reaction 1)has often been underestimated or not taken into account in a quantitative manner due to a lack of mechanistic and kinetic information on this general type of reaction. The results of the present study provide new quantitative information for obtaining a better understanding of the oxidation of organic molecules by NOz.
Discussion A total of seven reactions of carbon-centered free radicals with NO2 have now been isolated for quantitative study. All have been found to be very rapid reactions, k I = (1-5) X lo-" cm3 molecule-' S-'.~JO From prior indirect evidence and from the results obtained in this study on the CzH5 + NO2 reaction, formation of a nitrite complex (which results in 0-atom transfer) appears to be somewhat
Acknowledgment. This research was supported by the National Science Foundation under Grant CHE-80-06573. Special thanks are extended to Paul F. Sawyer, who developed the data acquisition system used in these experiments.
+
Registry No. CzH5, 2025-56-1;c-C6H9,3889-74-5; CH,CN, 2932-82-3; NOz, 10102-44-0.
Hydrophobic and Hydrophilic Solute Effects on the Homogeneous Nucleation Temperature of Ice from Aqueous Solutions M. Ogunl and C. A. Angell' Department of Chemistty, Purdue University, West Lafayette, Indiana 47907 (Received: September 7, 1982; In Final Form: December 28, 1982)
A microcapillary technique has been employed to determine the homogeneous nucleation temperatures Th of
solutions of water and various oil-soluble solutes which cannot be investigated by means of emulsion techniques used previously for nucleation temperatures studies. A series of partly hydrophobic solutes as well as some hydrophilic solutes have been investigated in the low concentration region, XzI0.05. In aLl cases Th decreased with increasing solute concentration, but it has been shown that the effect of each molecule can be analyzed in terms of additive contributionsfrom each group in the molecule. On this basis it has been possible to estimate the value of Th for solutions with totally hydrophobic character, such as the alkanes. The thermodynamic and structural relations between Th and the temperature of maximum density Tmdare tentatively discussed in terms of these results.
Introduction Recent investigations of water in the supercooled state conducted in a number of laboratories have established that the region below the normal fusion point is characterized by rapidly increasing values of the thermodynamic properties and other related transport properties. In fact, it seems that the heat capacity at constant pressure C,, the isothermal compressibility KT and the expansivity a , as well as the various relaxation times, diverge toward positive or negative infinities at a temperature in the vicinity of -45 0C.1-5 A close relation between this singular temperature, T,,and the lowest temperature to which (1)M.Oguni and C. A. Angell, J . Chem. Phys., 73, 1948 (1980). (2) R. J. Speedy and C. A. Angell, J . Chem. Phys., 65,851 (1976). (3)C. A. Angell in "Water: A Comprehensive Treatise", Vol. 7,F. Franks, Ed., Plenum Press, New York, in press, Chapter 1. (4)H. Kanno and C. A. Angell, J. Chem. Phys., 70,4008 (1979);73, 1940. (5)E. Lang and H.-D. Ludemann, Angew. Chem. Znt. Edit. Engl., 21, 315 (1982). This excellent review contains a compact account of the authors' several papers on NMR relaxation studies over wide temperature and pressure ranges.
water can be supercooled without crystallization occurring (-42 "C) has been observed for numerous properties studied under normal pressure conditions,3 and seems to be maintained under conditions of increasing pressure at least up to 2 kbar.495 It is also observed in binary systems with increasing solute concentrations provided the "critical exponent" is assumed constant. Based on an analysis of the anomalous component of the heat capacity, the authors showed that both Th and the singular temperature T,were decreasing functions of increasing concentration in the system H2O2 H20,' and it appeared reasonable to associate these variations with the water structure-breaking function of the added solute. All the evidence available leads to the association of the thermodynamic anomalies with the buildup of bulky open-network structural elements as the thermal energy is decreased. All solute effects observed on thermodynamic properties to date1,6,7have been such as to indicate the
+
(6)L.Bosio, J. Teixeira, and H.E. Stanley, Phys. Rev. Lett., 46,597 (1981).
0022-3654/83/20871848$01.50/0 0 1983 American Chemical Society
Hydrophobic Solute Effects on Ice Nucleatlon
breakdown of the local low-density regions, or at least the damping out of anomalous density fluctuations presumably due to the inability of the foreign molecules to fit into the hydrogen-bonded open-network structure established by water molecules acting alone. Stillinger, however, has suggested8 that an alternative way of building open hydrogen-bonded water structures might be to introduce hydrophobic solutes into the structure, around which the open network can form, clathrate style. To the extent that the latter structural effects might increase the rate at which the singular temperature associated with the establishment of the undisrupted network is approached, it would be predicted that the anomalies, and in particular the value of T, obtained from analysis of the data, would be increased by addition of such solutes. Indeed, measurements of the temperature of maximum density Td by Wada and Umeda9as a function of ethanol concentrations in aqueous ethanol solutions have demonstrated that the Tmd,which may be taken as an indicator of the magnitude of anomalous density fluctuations, increases initially with increasing ethanol concentration. Also recent viscosity and conductivity measurements in the region 0 to -25 "C have shown that the temperature dependence of these transport properties, which also serves as an indication of the magnitude of the anomalous effects, increases up to 20 mol % ethanol."'J' Unfortunately, the emulsion techniques which have been utilized in obtaining the most extensive thermodynamic data on aqueous systems in the region of interest'$ cannot be applied in the case of hydrophobic solutes because of the solute solubility in the emulsion dispersant phase. However, the poasiblity of obtaining data on such solutions by use of microcapillary techniques has not been thoroughly investigated. There are available commercially fritted disks consisting of myriads of fine capillaries of uniform diameter (in the range down to 2 pm) which in principle can be filled with water or solution such that each capillary sample is independent of all its neighbors. Such assemblages should behave more or less like emulsion samples with respect to supercooling and may permit the study of various transport properties such as the diffusion coefficient (spin-echo technique)lZand spin-lattice relaxation time,5 down to the homogeneous nucleation temperature. Either of these measurements would afford a good estimate of T, and its dependence on solute concentration. As a preliminary to such studies, we have performed the easier measurement of determining the temperature to which such capillary disks fiied with aqueous solution can be supercooled before homogeneous nucleation, signaled by the sudden release of energy detected by differential scanning calorimetry or differential thermal analysis, occurs. In principal, the efficacy of this technique should be independent of the type of solutes contained in the solution. To the extent that Th mirrors the behavior of T,, such measurements may give insight into the effect of hydrophobic solutes on the liquid-state anomalies in which we are really interested. In this paper we report the results of such T h measurements for a broad variety of solutes in order to determine the separate effects of hydrophobic and hydrophilic elements of the solute molecules. Pure hy(7) M. Oguni and C. A. Angell, J. Chem. Phys., in press. (8)F. H.Stillinger, Science, 209, 451 (1980). (9) G. Wada and S. Umeda, Bull. Chem. SOC.Jpn., 35, 646 (1962). (IO) B. L. Halfpap and C. Sorensen, J. Chem. Phys., 77,469 (1982). (11) R. J. Speedy, J. A. Balance, and B. D. Cornish, J.Phys. Chem., 87, 326 (1983). (12) K. T. Gillen, D. C. Douglass,and M. J. R. Hoch, J. Chem. Phys., 57, 5117 (1972).
The Journal of Physical Chemistty, Vol. 87, No. 11, 1983 1849
drophobic solutes could not be studied directly because of their insolubility, but their behavior can be estimated by combination of results of the present study, as we show below.
Experimental Section All solutes studied were commercialy available analytical grade chemicals, used without further purification, except for hydroxylamine, NH,OH, which was obtained directly as an aqueous solution by passing solutions of NH20H.HC1 through an anion-exchangecolumn which replaced Cl- with OH-. The concentration of each solution was determined by reduction of ferric ion to Fe2+and back-titration with permanganate solution. Apart from the latter case, solutions were prepared gravimetrically. Glass capillary disks of diameter 3 mm, which fit snugly in a standard Perkin-Elmer differential scanning calorimeter pan, were filled by adding a drop of the solution to one side of the disk and allowing a few seconds for the solution to be absorbed before removing the excess. The disk was then placed in a DSC pan and scanned in the cooling direction until the nucleation temperature was registered by a sharp exotherm. The consistency of this technique with previous emulsion studies was verified for the cases pure water, which yielded T h = 235 K, identical within the -0.3 K uncertainty with the emulsion result, and H202+ HzO solutions.' Trials were made with both 20- and 2-pm capillary disks, but only the latter gave satisfactory sharp nucleation temperatures. The larger diameter disk produced broad exothermic traces, the origin of which was presumably due to a broad distribution of heterogeneous nucleation temperatures, but may also be associated with the larger surface areas of the individual capillaries. We note that the diameter of the capillaries of the successful case, 2 pm, is comparable with the diameter of the emulsion droplets used in the earlier experiments. For the solutions of the present study, several trials were run at each composition to verify reproducibility within the -0.3 K for each case. Results and Discussion Some systematic results are presented in Figures 1 and 2 for different families of solutes. In figure 1 results for the three related hydrophilic molecules H20z,NH20H,and N2H4 are shown together with data for CH30H in which' one of the hydrophyilic "beads" is replaced by the hydrophobic bead, -CH3. Apart from the peculiar and surprising behavior of the very dilute hydroxylamine solutions, which remains unexplained, the data for the three hydrophilic solutes, in which the NH20H points are intermediate, suggest the presence of a group additive effect. CH30H, with a hydrophobic group around which "new" structure can form, shows a markedly smaller depression of Th than do the others. The additivity rule is strengthened by consideration of the series of normal monohydric alcohols seen in Figure 2. At constant mole fraction of solute, addition of each additional -CH2 bead produces a comparable depression of Th. Furthermore, if Th at X = 0.05 is plotted vs. the number of carbons and the extrapolation is made to n = 0 (Figure 2b), the result, ATh = -3.8 K is close to 1 / 2 the value for H20zat X = 0.05 (-8.2 k), which seems reasonable since the extrapolation should correspond to the depression due to the combination -OH and -H of which the latter is small and perhaps positive (--0.2 K, see below). Assignment of ATh = -4.1 to the -OH group on the basis of these observations leads to the assignment ATh(-cH3) = 4 . 9 based on the methanol depression, Figure 1. Such
The Journal of Physical Chemistry, Vol. 87, No. 11, 1983
1850
,
I
Oguni and Angel1 I
I
I
I
1
235
235
Y \
$ 23C
23C
Y
< \
225
22:
0.02
0.04
0.06
x2
22(
2251 21(
0
,
I
I
1
I
0 04
002
I
006
X2
Figure 1. Homogeneous nucleation temperatures T , for aqueous solutions of four related “two-bead’’ molecules as a function of mole fraction of solute. Dashed line shows variation of Th for ethane derived from additivity rule.
,
,
,
I
2
3
n
in CnH2,+10H
4
Figure 2. (a) Variation of homogeneous nucleation temperature T h with mole fraction of various normal alcohol solutes. (b) Variation of Th, at solute mole fraction of 0.05, with chain length for various normal alcohols.
TABLE I: Depression of Thin 5 mol 9i Solutions of
Various Groups group
AT,/K
-OH
-NH,
-CH,-
-CH, -C(CH3),
-4.0
-6.1
-1.0
-0.8
-2.6
an assignment is supported by resulh for the more complex molecules shown in Figure 3 in which the extrapolation to n = 0 in part (a) corresponds to propane (predicted ATh(x=o,05 = -2.5 K) and that in part (b) corresponds to ethane (predicted ATh(x=o.o5 = -1.6 K). The direct measurement at n = 2 in the latter case leads to an extrapolation to n = 0 which is too high (ATh(ethane) = 0) but the broken circle at 224.8 K, which is the value for T h obtained by interpolation of data for H202and propanediol, Th(x=o.&)= 223.8 K, leads to the expected ethane value 233.4 K (ATh= -1.6 K). The interpolated value is also that expected from the additivity rule by combining values for the -CH2- group and H20z. Adopting AT, = -0.8 K for CH3 at X = 0.05, we are lead to predict the T h vs. X relation shown in Figure 1 for a totally hydrophobic “two-bead” solute, ethane. Results for group contributions to Th (at X = 0.05) may be summarized in Table I as values appropriate to Xgroup = 0.05. (We choose not be report limiting slopes because of uncertainties about behavior at very high dilutions such as that seen for hydroxylamine in Figure 1.) Since all group values are negative it would seem that Th cannot be increased above that of water, irrespective of whatever new structure can form around the hydrophobic solute, notwithstanding the evidence that even with ethanol the Tmd,hence perhaps Ts, can initially be raised. A possible exception, indicated by extrapolations based on the data in Figure 4, is the case of neopentane, C(CHJ4.
0
I
2
n in CH2(CH20H),(CHJ)2-,
0 I 2 n in (CH20H),(CH3)2-,
Flgure 3. Variation of the homogeneous nucleation temperature T , with the value of n In the respective solute alcohol formulae, at mole fraction of solute = 0.05. Extrapolations to n = 0 indicate T , values for hypothetical alkane solutions at this composition.
Comparison of data for normal and tert-butyl alcohol suggests the compact arrangement obtained with a quaternary carbon atom may be less disruptive to the water structure. To obtain an alternative estimate for ATh(x=o.05) of neopentane to that obtained with Table I group data, we may combine direct measurement of ATh for the neopentanediol (CH3)&(CHZOH),with an estimate for neopentanol obtained from Table I data (see dashed line in Figure 4), and make the extrapolation to n = 0 as in Figure 4, insert. This yields a positive ATh of + 1.8 K, though we are unable to give the result great credence. The failure to find any convincing evidence for increases of Th with introduction of structural elements around which H-bonded frameworks can form can be given different interpretations which carry some important implications.
The Journal of Physical Chemlstty, Vol. 87,No. 11, 1983
Hydrophobic Solute Effects on Ice Nucleation
Y \
230 -
225-
T,/K 225-
220 -
220 -
2156
n in
2160
I
I
I
0 02
I
I
004
I
0 06
I
x2 Flgure 4. Variation of T , with solution composition for aqueous solutions of t&-butyl alcohol and various diols. Dashed line shows Th variation calculated for the monohydric alcohol [CH3]3CCH20H,using the additivity rule. Note the very tenuous prediction of T , for neopentane solution, with positive AT,.
In the first place it can be argued that, since (according to nucleation theory13) the main factor determining the concentration dependence of This the difference in solid and liquid chemical potentials of the crystallizing component, any solute will depress Th. The reason is essentially the same as the reason that melting points are always depressed by addition of solutes which are insoluble in the crystallizing solid. Although solutes which strongly affect the liquid-solid surface free energy could provide exceptions to this trend, it seems generally indicated that a structural enhancement around the solute species which in principle might enhance the anomalies in water and increase T,would not necessarily be revealed by the behavior of Tb To the extent that T,is correctly interpreted is a stability limit, h ~ w e v e r , ~this J ~ result would be (13) D.Turnbull, Contemp. Phys., 10,473 (1969).
1851
somewhat paradoxical because T,so interpreted cannot in principle be increased to become higher than the temperature of an observed liquid state phenomenon (nucleation). If T,is, alternatively, the temperature of an internal liquid state phenomenon-for instance, a X transitionthen the prospect of raising it close to, or better still, above Thby appropriate solute addition is a very attractive one. Against this possibility, however, must be counted the absence in our present experiments, even with the most hydrophobic solutes, of any evidence for unusual prenucleation increases in heat capacity comparable with or in express of those observed with pure water itself. Certainly no X transition has emerged above Th! An alternative, and perhaps correct, interpretation of the effect of hydrophobic structure-making solutes which would be consistent with our observations is that such solutes, while enhancing hydrogen-bonded framework structures, actually reduce the mean-square density and order fluctuations which determine the magnitude of those intensive thermodynamic properties which diverge near an instability. The presence of a molecule is a clathrate cage, for instance, clearly reduces the possibility of a low density fluctuation which could otherwise occur, in the absence of solute, if the empty cage were to form transitorily in the course of network restructuring. Thus T, might be depressed even while structure, per se, is enhanced. Similar notions have recently been expressed by Halfpap and Soremenlo and Speedy.’l Indeed, as a reviewer points out, such enhancement of pentagonal ringbased structures could serve to repress nucleation of the hexagonal ring-based ice Ih structure. This issue cannot be resolved by further measurements of the type we report here. Rather, quantitative measurements of some relaxation time, or of the density maximum “~harpness”,~ with selected solutes such as ethanol and tert-butyl alcohol, are required. It is hoped to perform such measurements in the near future. Acknowledgment. This work was supported by the Office of Naval Research under Agreement No. N0001478-C-0035. Registry No. HzO, 7732-18-5; HONHz, 7803-49-8; H2Oz, 7722-84-1;H2N-NHz, 302-01-2;MeOH, 67-56-1;EtOH, 64-17-5; PrOH, 71-23-8;BuOH, 71-36-3;(CH&CCHZ0H,7584-3;ethylene glycol, 107-21-1; 1,3-propanediol, 504-63-2; tert-butyl alcohol, 75-65-0. (14)R. J. Speedy, J . Phys. Chem., 86,982 (1982).
