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Water structure enhancement in water-rich binary solvent mixtures. Part II. The excess partial molar heat capacity of the water
Journal of Molecular Liquids 166 (2012) 62–66
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Water structure enhancement in water-rich binary solvent mixtures. Part II. The excess partial molar heat capacity of the water Yizhak Marcus Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
a r t i c l e
i n f o
Article history: Received 15 March 2011 Received in revised form 14 November 2011 Accepted 24 November 2011 Available online 5 December 2011 Keywords: Water structure Excess partial molar heat capacity of water Two state model of water
a b s t r a c t E The excess partial molar isobaric heat capacity of water, CPW , in water-rich mixtures with co-solvents has been calculated. When the excitation of internal modes of the water molecules is deducted in part, the remainder indicates, if positive, that the relative extent of fully hydrogen bonded domains of the water is enhanced. This was demonstrated in the cases of aqueous methanol, ethanol, 1- and 2-propanol, t-butanol, 2-methoxyethanol, 1,2-dimethoxyethane, tetrahydrofuran, acetone, N,N-dimethylformamide, and N,N-dimethylacetamide. Some solutes such as ethylene glycol, 1,4-dioxane, acetonitrile, N-methylformamide, formamide (and urea), ethanolamine, and dimethylsulfoxide, many of which hydrogen-bond very strongly with water, do not enhance the water structure according to this criterion. The results are compared qualitatively with conclusions from the partial molar excess volumes of the solutions and these agree with the present ones. © 2011 Elsevier B.V. All rights reserved.
1. Introduction In a previous paper (considered as part I of this series) [1], the enhancement of the structure of the water in water-rich mixtures with co-solvents was demonstrated for several co-solvents by showing that the excess partial molar volume of the water is positive. This means that bulky, low-density structures in the water are present at a larger proportion in these mixtures than in neat water. This structure enhancement should be manifested also by other properties of such mixtures, and the excess partial molar heat capacity of the water comes into mind in this connection. On the one hand, the heat capacity density of neat liquids has been shown to be a criterion for their having structure, contrary to unstructured liquids, such as liquid argon or pentane [2]. This criterion requires for structured liquids that: h i –1 –3 ΔC P =V ¼ C P ðlÞ–C p ði:g:Þ =V > 0:6 J⋅K ⋅cm
ð1Þ
Here CP(l) is the isobaric heat capacity of the liquid, Cp(i.g.) is that of the same substance in the ideal gas state, and V is the molar volume of the liquid, all at a given temperature. The subtraction of Cp(i.g.) from Cp (l) serves to exclude from the consideration of the effects of introducing thermal energy into the liquid for the excitation of internal modes of the molecules, so that only configurational effects on the liquid structure are taken into account. Water is thus a highly structured liquid according to this criterion: ΔCP/V=2.3 J K− 1 cm− 3. E-mail address: [email protected]. 0167-7322/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2011.11.013
On the other hand, Davis and Litovitz [3] and Davis and Jarzynski [4] showed that a two-state model for water involves a relaxational molar heat capacity of ~ 42 J K − 1 mol − 1 at 25 °C between the fully hydrogen bonded state and the close packed structures. Values of similar magnitude were also proposed by Eucken [5], Grjotheim and Krogh-Moe [6], Wada [7], and Nemethy and Scheraga [8] in their models for liquid water. This relaxational value happens to coincide at 25 °C with the ΔCP value in Eq. (1), CP(l) − Cp(i.g.) = 41.72 J∙K − 1∙mol − 1, but should not be construed as representing this difference. These considerations were taken up later by Bassez, Lee and Robinson in their model for water [9]. More recently, Silverstein, Haymet, and Dill [10] invoked a two state model, involving broken and intact hydrogen bonds, to deal with the hydrophobic effect, including its consequences for the excess heat capacity. Whether a two-state model or a model involving a multitude of hydrogen bonded structures is accepted, it is clear that the fraction of the heat capacity ascribable to the more highly hydrogen bonded structure is larger, the more ‘structure’ (unbroken hydrogen bonds) the water has. It is the purpose of this paper to examine whether the excess partial molar heat capacity of the water in water rich mixtures with cosolvents does confirm enhancement of the water structure in agreement with conclusions reached from the excess partial molar volume of the water in these mixtures [1]. Enhancement of the water structure induced by the co-solvent manifests itself by the changing of some of the domains with few hydrogen bonds to highly hydrogen bonded ones, having a larger heat capacity, resulting in a positive exE cess partial molar heat capacity of the water, CPW > 0. It is notable that very few authors in their studies of the heat capacities of aqueous mixtures with co-solvents have reported the partial molar isobaric heat capacity of the water. Nor did they, when they did report such
Y. Marcus / Journal of Molecular Liquids 166 (2012) 62–66
values, draw conclusions concerning the structure of the water. It is, therefore, necessary to obtain the desired information from published data of the total specific heats or excess heat capacities of the mixtures or the apparent molar heat capacities of the co-solvents. 2. Data and results Isobaric heat capacity data of mixtures of water, subscript W, with co-solvents, subscript S, were obtained from the literature. As far as available, the data for 25 °C were used, but in some cases were also data at other temperatures. Only the water-rich region was of interest, that is, mole fractions of the co-solvent xS ≤ 0.3. In some cases the data extend to only a fraction of this range, but if data are only available at xS b 0.1 or at co-solvent molalities mS b 6 mol kg − 1 they E cannot be used properly for the derivation of CPW values. In cases where the excess molar isobaric heat capacities of the mixture, CPE, were reported as functions of the mole fractions of the co-solvent, xS, the excess partial molar heat capacity of the water is obtained as: E E E C PW ¼ C P –xS ∂C P =∂xS
ð2Þ
T
In many cases the excess heat capacities of the mixtures can be described as a cubic function of the composition with a correlation coefficient rcorr > 0.995: E
2
3
C P ¼ axS þ bxS þ cxS
ð3Þ
mixtures are shown in Table 1. In general, values obtained from directly reported CPE values via Eqs. (3) and (4) are more accurate than those obtained indirectly via Eqs. (6)–(8). In most cases, although there are differences in the numerical values of the parameters resulting from the data of several authors, there is fair agreement on the main features. It is stressed that expressing the excess molar heat capacity data for all the systems for which adequate data were found by a third order polynomial rather than by an individual fitting expression for each system may have introduced uncertainties, but the trends ought to be valid. The data of Bonner and Cerutti [11] are in the form of CPS(xS) with only 7 data points up to xS = 0.3. They were converted to CPS(mS) by mS = xS/MW(1 − xS), then to φCPS, using CPS = φCPS + mS(∂ φCPS/mS)T and noting that CPS is linear with mS (i.e., (∂ φCPS/mS)T = p of Eq. (5) and q = 0 as are higher terms), and finally via Eqs. (5), (6), (7), (3) E and (4) to CPW . This tortuous route detracts from the accuracy of the latter quantity, so that these data should not be considered with full weight. The data of Kiyohara et al. [20] are of the form φCPS(mS), but only for aqueous dioxane are they valid to sufficiently high molalities (12 mol∙kg − 1, xS = 0.178) to warrant treatment. The data for tetrahydropyran, morpholine, piperazine, and piperidine [20] extend only to small molalities and could not be included. So are the data of
Table 1 The coefficients of Eq. (4) for the excess partial molar isobaric heat capacity of water, E CPW /J K− 1 mol− 1 at 25 °C, and attributes of its values. Co-solvent
Ref.
By definition of the excess value, CPE = 0 at xS = 0, so that the curve passes through the origin. Then Methanol E
2
3
C PW ¼ −bxS –2cxS
ð4Þ
E and is positive in water-rich mixtures if b b 0. If c > 0 CPW becomes negative beyond a limiting value of xS lim = − b/2c. In such cases E CPW reaches a maximal value, CPW Emax, at xS max = −b/3c. The partial molar heat capacity of the water in the mixtures is then:
C PW ¼ C PW∘ þ C PW
E
ð5Þ
where CPW° = 75.33 J∙K − 1∙mol − 1 (at 25 °C) is the molar heat capacity of the water. If the published data are the apparent molar heat capacities of the co-solvent, φCPS, these are often reported as functions of its molality, mS: φ
φ
∞
2
C PS ¼ C PS þ pmS þ qmS þ ⋅⋅⋅
ð6Þ
∞ ∞ , p, q ∙∙∙ are reported in such cases, where φCPS The parameters φCPS is the limiting value of the apparent (or partial) molar heat capacity of the solute S at infinite dilution. Then the following transformations E lead to values of CPE that is converted to the desired CPW according to Eq. (2). The specific heat of the mixture, cP, is obtained from φCPS by inverting its defining function [11] as:
ð7Þ −1
−1
at where cPW° is the specific heat of the water (4181 J∙K ∙kg 25 °C) and MS is the molar mass of the co-solvent, in kg∙mol − 1. Then E CP
¼ cP ½xS MS þ ð1–xS ÞMW –xS C PS∘–ð1–xS ÞC PW∘
Ethanol
1-Propanol 2-Propanol t-Butanol
Ethylene glycol 2-Methoxyethanol Dimetoxyethane Tetrahydrofuran 1,4-Dioxane
Acetone Acetonitrile Formamide
N-Methylformamide
φ cP ¼ mS C PS þ cPW∘ =ð1 þ mS M S Þ
ð8Þ
where MW = 0.018015 kg∙mol − 1 is the molar mass of the water and CPS° is the molar heat capacity of the co-solvent. The resulting values of the coefficients b and c of Eq. (4) and of xS lim, xS max, and CPW Emax for many water-rich aqueous co-solvent
63
Dimethylformamide Dimethylacdetamide Ethanolamine Dimethylsulfoxide
a b c d
[12] [13] [14] [12] [15] [13] [14] [13] [14] [12] [16] [12] [28] [48] [17] [18] [19] [19] [11] [11] [20] [19] [21] [12] [22] [23] [11] [22] [21] [11] [24] [25] [21] [22] [21] [26] [27] [22] [21]
CPE, cP, or φCPS data CPE CPE CPE CPE CPE CPE CPE CPE CPE CPE φ CPS CPE φ CPS φ CPS cP cP cP cP φ CPS φ CPS φ CPS cP CPE CPE CPE CPE φ CPS CPE CPE φ CPS CPE φ CPS CPE CPE CPE cP φ CPS CPE CPE
b
c
E CPW >0
xS − 373 − 317 − 308 − 482 − 736 − 722 − 680 − 2529 − 1776 − 1941 − 1675 − 3652 − 2942 − 2930 − 220 − 495 − 577 − 1817 − 598 − 791 − 333 − 268 − 117 − 412 − 463 − 572 13 55 42 − 388 − 99 161 − 156 − 249 − 419 − 86 − 183 − 95 − 53
873 753 706 164 1804 1658 1576 16730a 10380b 3500 5378 8618 6185 6124 692 1360 1731 2254 818 c,d 1422 c,d 1554 982 308 973 1733c 2652 40 c,d − 85c − 54c 670c,d 184 − 257 208 473 1157 180 899 246 127
A term − 19930xS4 is also required. The cubic expression is valid only to xS = 0.2. Fitting to a cubic polynomial not very accurate. Poor and few data.
lim
0.427 0.421 0.436 0.461 0.408 0.436 0.431 0.197 0.220 0.277 0.311 0.212 0.238 0.239 0.318 0.364 0.334 0.362 0.731 0.556 0.214 0.272 0.382 0.423 0.267 0.216 E CPW b0 E CPW b0 E CPW b0 0.579 0.539 0.580 0.751 0.526 0.362 0.478 0.204 0.384 0.654
E CPW
at xS
max
max
10.1 7.2 8.7 21.7 18.2 20.3 18.7 11.7 13.2 22.1 24.1 23.0 24.7 24.8 3.3 6.4 9.5 15.9 47.3 ? 36.3 ? 2.3 2.9 2.5 10.9 4.9 4.0
0.285 0.280 0.291 0.308 0.272 0.290 0.288 0.125 0.147 0.185 0.208 0.141 0.159 0.159 0.212 0.243 0.223 0.242 0.487 0.371 0.143 0.182 0.254 0.282 0.178 0.144
19.3 4.3 19.2 13.1 10.2 8.2 2.9 3.4 1.3 5.3
0.386 0.359 0.387 0.501 0.350 0.242 0.319 0.136 0.256 0.436
64
Y. Marcus / Journal of Molecular Liquids 166 (2012) 62–66
Kiyohara et al. [27] for acetamide (up to 2.4 m only). Other authors reported heat capacity data for too low concentrations or too few data points, or no numerical data (values only in plots) to warrant E evaluation in terms of CPW (xS). Such studies include those of unsaturated heterocyclic solutes (e.g., pyridine, where no limits of applicable molalities are provided) [29], alkanols [30], acetone, methyl ethyl ketone and methyl acetate [31], alkanols and alkoxyethanols [32], morpholine [33], ethanolamines [34], 1-butanol [35], alkanols [36], alkanolamines [37], and tetrahydrofuran, dioxane, dimethoxyethane, and dimethylsulfoxide [38]. DeVisser et al. [28] did report in a figure values of φCPW in aqueous mixtures with t-butanol, but also included numerical values in supplementary data. The apparent molar heat capacities φCPS of t-butanol reported by three authors [12, 18, 48] are shown in Fig. 1 (upper panel) in reasonable agreement with each other (those of Arnaud [12] had to be recalculated from the reported molar heat capacities of the mixture). It was pointed out by a referee that the maximum in φCPS required a minimum in φCPW according to the Gibbs-Duhem law. However, in the process of the calculation of E the excess partial molar heat capacity of water CPW from the aqueous t-butanol φCPS data of the three authors by Eqs. (7), and (8), with reE sults shown in Fig. 1 (lower panel), such a minimum in CPW is not discernable. E Davis [32] showed in a figure positive CPW values for water in methanol, ethanol, and 1-propanol that agree on the whole with the values listed in Table 1. Some of the discrepancies in Table 1 are diffiE cult to understand, such as why positive CPW values are obtained by Checoni and Volpe [21] for compositions far beyond the extent of the water-rich data considered here for aqueous dimethylformamide (xS lim = 0.75) and dimethylsulfoxide (to xS lim = 0.65), contrary to results of other authors. In addition to the data for co-solvents there are also data for waterrich solutions at 25 °C of an amide, urea, which cannot be properly called a “co-solvent” because it is solid at this temperature. For aqueous urea solutions specific heat data, cP(mS), were reported long ago by Gucker and
Fig. 1. Top panel: the apparent molar heat capacity of t-butanol in water at 25 °C according to De Visser et al. [28] ▽, Alary et al. [48] □, and Arnaud [12] O (recalculated from his cP data). Lower panel: the derived excess heat capacity of water from the above data: De Visser et al. [28] ▼, Alary et al. [48] ■, and Arnaud [12] ●.
Ayres [39] at 20 and 30 °C up to 17.6 mol∙kg− 1 (xS =0.24) from which E CPW = −220xS2 +789xS3 at 20 °C and –155xS2 +436xS3 at 30 °C are derived. Later, apparent molar heat capacities, φCPS(mS), were reported by Picker E et al. [40] at 24.15 °C up to 9.0 mol∙kg− 1 (xS = 0.14) resulting in CPW = 2 3 −251xS +1441xS and by Kiyohara et al. [27] at 25 °C up to E 10 mol∙kg− 1 (xS =0.15) leading to CPW =−422xS2 +3170xS3. All are negative within the range of available data but tend to turn upwards at the higher concentrations of urea, and are in mutual agreement (allowing for the different temperatures) up to xS ~0.1. Urea thus resembles formE amide (see Table 1) in having negative values of CPW in dilute aqueous solutions. Data for the aqueous methanol, ethanol, and 1-propanol at 15 and 35 °C by Benson and D'Arcy [41] span those at 25 °C of Benson et al. E [13] (see Table 1) and the derived CPW values are shown in Fig. 2. Werth and Hvidt [42] presented data for the aqueous methanol, ethanol, and 1-propanol also for lower temperatures, including sub-zero E ones. The CPW values derived from these data at 4 °C are shown in E Fig. 2 too, and CPW data derived for −16 °C (not shown) follow the E trends shown. The CPW values are seen to increase as the temperature E is lowered in dilute solutions, up to xS = 0.15. On the contrary, CPW increases for aqueous ethylene glycol with increasing temperatures, as obtained from specific heat data at 5, 25, and 45 °C by Huot et al. [17], E shown in Fig. 3. No clear temperature effect is seen for the CPW values for aqueous dimethylsulfoxide at 15, 25, and 30 °C, whereas for aqueE ous dioxane at these temperatures CPW does increase with the temperature, as derived from the data Checoni and Volpe [21]. No E generalization of the temperature effect on CPW may, therefore, be made. 3. Discussion E Table 1 shows that positive CPW values are achieved over a certain composition range in water-rich mixtures for most of the co-solvents for which data were found. Over the range 0 ≤ xS ≤ xS lim where E CPW > 0, the partial molar heat capacity of the water in the mixtures is larger than the molar heat capacity of pure water, Eq. (5). This can be interpreted by increased relative extents of the highly hydrogen bonded domains at the expense of the close packed domains, the water becoming more structured in the presence of the cosolvents. If the mean value 42 ± 3 J∙K − 1∙mol − 1 for the molar relaxation heat capacity (from the close packed to the fully hydrogen bonded domains) reported by Davis and Litovitz [3] is accepted, the values
E Fig. 2. The excess partial molar isobaric heat capacity of water, CPW , in water-rich aqueous methanol (circles), ethanol (triangles) and 1-propanol (squares) at − 4 °C (dotted symbols), 15 °C (filled symbols) and 35 °C (empty symbols) from data in refs. [40] and [41].
Y. Marcus / Journal of Molecular Liquids 166 (2012) 62–66
E Fig. 3. The excess partial molar isobaric heat capacity of water, CPW , in water-rich aqueous ethylene glycol at 5 °C (●), 25 °C (▲), and 45 °C (■), from data in ref. [16].
of CPW Emax in Table 1 indicate that sizable fractions of the total amount of water are transformed in this direction by the presence of the co-solvent. Ethylene glycol, dioxane, ethanolamine and dimethylsulfoxide show minimal conversion (6–8%), the monohydric alkanols, on the other hand, show sizable conversion (20–50%) as do other co-solvents listed in Table 1. However, only the configurational part of the total excess heat capacity of the water should be considered in this context [10], since the partial molar excess heat capacity of the water reflects not only the structural changes induced by the co-solvent but has other causes too. The determination of the structuredness of neat liquid water from its heat capacity requires, according to Eq. (1) and the related discussion, subtraction of the excitation of internal modes of the water molecules. For the water-rich aqueous mixtures dealt with here, some subtraction of the heat capacity related to the excitation of internal E modes of the water from CPW appears also to be required in order to deduce the enhancement of the water structure. It is not clear how much of the ideal gas heat capacity of water, CPW(i.g.) = E 33.58 J∙K − 1∙ mol − 1 at 25 °C, has to be subtracted to yield ΔCPW . The results from the consideration of the excess partial molar volume of the water in Part I of the series [1] may serve as a guide. The co-solvents E E E that have VW >0 and VW b 0 will show agreement with ΔCPW >0 and ΔCPWE b 0, if roughly 30% of CPW(i.g.) is subtracted. But, whereas VWEmax is only a small fraction of the relaxation molar volume between the domains, ≤1.4%, the ΔCPWEmax values still constitute a larger proportion of the relaxational heat capacity (~42 J∙K− 1∙mol− 1) though more modest than that of the total CPWEmax and are more reasonable. There exists some correlation between the propensity for mutual association of the water with the co-solvent and the nonenhancement of the water structure, that is, the negative signs of G E E and of VW and ΔCPW Emax. However, the correlation is far from perfect: E acetonitrile has VW and ΔCPW Emax b 0 but G E > 0, whereas the dialkylaE mides have VW and ΔCPW Emax > 0 but G E b 0. Positive ΔCPW Emax values occur for a limited group of co-solvents, which on the one hand have relatively small molecules that can be accommodated in the voids in the structure of pure water and on the other form hydrogen bonds with surrounding water molecules. The presence of several methyl groups seems to induce such an enhancement, cf. t-butanol, dimethoxyethane, and dimethylformamide. Excluded from this group are co-solvents that interact too strongly with the water, like ethylene glycol, formamide, and N-methylformamide (and urea) E that form denser domains and have ΔCPW Emax and VW b 0 throughout the water-rich range.
65
The majority of authors who considered the enhancement of the water structure in water-rich mixtures by co-solvents dealt with mixtures of water with alkanols, see references in Part I [1]. For these E E there is agreement between the signs of CPW (or ΔCPW Emax) and VW . Franks and Ives [43] concluded that at low xS aqueous mixtures are essentially water-like, resisting depolymerization and preserving the water structure based on its co-operative three-dimensional structure. Onori and Santucci [44] concluded that ‘water cages’ surround dispersed alcohol molecules below a certain threshold xS. Koga [45] concluded from the excess partial molar enthalpies of very dilute aqueous t-BuOH that the latter re-arranges the surrounding water molecules to enhance the network structure of water. Roses et al. [46] quote results that water structure enhancement occurs also in dilute solutions of MeCN, DMSO, and acetone (the first one contrary to E having VW b 0 as found later [1]). They employed solvatochromic probes to show the structure enhancement in aqueous 2-PrOH and t-BuOH. Still, the values of the thresholds up to which water structure enhancement in water-rich mixtures with co-solvents persists differ according to the method employed. So does also the amount of the enhancement relative to the relaxational value between compact and highly structured water domains. It is conceded that not everybody ascribes the positive excess partial molar heat capacity of water to enhanced hydrogen bonded structure of the region around the solute molecules. Some computer simulation results explain the enhanced heat capacity near hydrophobic solutes as due to their hydrophobic interactions counteracting a disordering of the water structure [47]. However, other computer simulation results do show that the fraction of broken hydrogen bonds in the water shell surrounding a hydrophobic molecule is lower than the fraction in bulk water, i.e., that the water structure is enhanced by the hydrophobic solute [10]. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
Y. Marcus, Journal of Molecular Liquids 158 (2011) 23. Y. Marcus, Journal of Solution Chemistry 25 (1996) 455. C.M. Davis, T.A. Litovitz, The Journal of Chemical Physics 42 (1965) 2563. C.M. Davis, J. Jarzynski, Advances in Molecular Relaxation Processes 1 (1967/68) 155. A. Eucken, Zeitscrift für Elektrochemie 52 (1948) 255 53 (1949) 102.. K. Grjotheim, J. Krogh-Moe, Acta Chemica Scandinavica 8 (1954) 1193. G. Wada, Bulletin of the Chemical Society of Japan 34 (1961) 955. G. Nemethy, H. Scheraga, The Journal of Chemical Physics 36 (1962) 3382. M.-P. Bassez, J. Lee, G.W. Robinson, The Journal of Physical Chemistry 91 (1987) 5818. I.K.A.T. Silverstein, A.D.J. Haymet, K.A. Dill, Journal of the American Chemical Society 122 (2000) 8037. O.D. Bonner, P.J. Cerutti, The Journal of Chemical Thermodynamics 8 (1976) 105. R. Arnaud, L. Avedikian, J.P. Morel, Journal de Chimie Physique et de Physicochimie Biologique 69 (1972) 45. G.C. Benson, P.J. D'Arcy, O. Kiyohara, Journal of Solution Chemistry 9 (1980) 931. H. Ogawa, S. Murakami, Thermochimica Acta 109 (1986) 145. J.-P.E. Grolier, E. Wilhelm, Fluid Phase Equilibria 6 (1981) 283. G. Roux, D. Roberts, G. Perron, J.E. Desnoyers, Journal of Solution Chemistry 9 (1980) 629. J.-T. Huot, E. Battistel, R. Lumry, G. Villeneuve, J.-F. Lavallee, A. Anusiem, C. Jolicoeur, Journal of Solution Chemistry 17 (1988) 601. M. Pagé, J.-Y. Huot, C. Jolicoeur, The Journal of Chemical Thermodynamics 25 (1993) 139. S. Schrödle, G. Hefter, R. Buchner, The Journal of Chemical Thermodynamics 37 (2005) 513. O. Kiyohara, G. Perron, J.E. Desnoyers, Canadian Journal of Chemistry 53 (1975) 2591. R.F. Checoni, P.L. Volpe, Journal of Solution Chemistry 39 (2010) 259. C. De Visser, W.J.M. Heuvetsland, L.A. Dunn, G. Somsen, Journal of the Chemical Society, Faraday Transactions 1 74 (1978) 1159. G.C. Benson, P.J. D'Arcy, Y.P. Handa, Thermochimica Acta 46 (1981) 295. C. De Visser, P. Pel, G. Somsen, Journal of Solution Chemistry 6 (1977) 571. C. De Visser, G. Perron, J.E. Desnoyers, W.J.M. Heuvetsland, G. Somsen, Journal of Chemical and Engineering Data 22 (1977) 74. M. Pagé, J.-Y. Huot, C. Jolicoeur, Canadian Journal of Chemistry 71 (1993) 1064. O. Kiyohara, G. Perron, J.E. Desnoyers, Canadian Journal of Chemistry 53 (1975) 3263. C. De Visser, G. Perron, J.E. Desnoyers, Canadian Journal of Chemistry 55 (1977) 856. O. Enea, C. Jolicoeur, L.G. Hepler, Canadian Journal of Chemistry 58 (1980) 704.
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[30] G. Perron, J.E. Desnoyers, The Journal of Chemical Thermodynamics 13 (1981) 1105. [31] M. Costas, D. Patterson, Journal of the Chemical Society, Faraday Transactions 1 82 (1985) 2381. [32] M.I. Davis, Thermochimica Acta 200 (1992) 15. [33] P.R. Tremaine, D. Shvedov, C. Xiao, Journal of Physical Chemistry B 101 (1997) 409. [34] C. Collins, J. Tobin, D. Shvedov, R. Palepu, P.R. Tremaine, Canadian Journal of Chemistry 78 (2000) 151. [35] K. Tamura, J. Hu, C. Trandum, P. Westh, C.A. Haynes, Y. Koga, Physical Chemistry Chemical Physics 2 (2000) 355. [36] M.L. Origlia-Luster, E.M. Wolley, The Journal of Chemical Thermodynamics 35 (2003) 1101. [37] M. Mundhwa, A. Henni, Journal of Chemical and Engineering Data 52 (2007) 491. [38] D.M. Swenson, M.B. Blodgett, S.P. Ziemer, E.M. Wolley, The Journal of Chemical Thermodynamics 40 (2008) 248.
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Contents lists available at SciVerse ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Water structure enhancement in water-rich binary solvent mixtures. Part II. The excess partial molar heat capacity of the water Yizhak Marcus Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
a r t i c l e
i n f o
Article history: Received 15 March 2011 Received in revised form 14 November 2011 Accepted 24 November 2011 Available online 5 December 2011 Keywords: Water structure Excess partial molar heat capacity of water Two state model of water
a b s t r a c t E The excess partial molar isobaric heat capacity of water, CPW , in water-rich mixtures with co-solvents has been calculated. When the excitation of internal modes of the water molecules is deducted in part, the remainder indicates, if positive, that the relative extent of fully hydrogen bonded domains of the water is enhanced. This was demonstrated in the cases of aqueous methanol, ethanol, 1- and 2-propanol, t-butanol, 2-methoxyethanol, 1,2-dimethoxyethane, tetrahydrofuran, acetone, N,N-dimethylformamide, and N,N-dimethylacetamide. Some solutes such as ethylene glycol, 1,4-dioxane, acetonitrile, N-methylformamide, formamide (and urea), ethanolamine, and dimethylsulfoxide, many of which hydrogen-bond very strongly with water, do not enhance the water structure according to this criterion. The results are compared qualitatively with conclusions from the partial molar excess volumes of the solutions and these agree with the present ones. © 2011 Elsevier B.V. All rights reserved.
1. Introduction In a previous paper (considered as part I of this series) [1], the enhancement of the structure of the water in water-rich mixtures with co-solvents was demonstrated for several co-solvents by showing that the excess partial molar volume of the water is positive. This means that bulky, low-density structures in the water are present at a larger proportion in these mixtures than in neat water. This structure enhancement should be manifested also by other properties of such mixtures, and the excess partial molar heat capacity of the water comes into mind in this connection. On the one hand, the heat capacity density of neat liquids has been shown to be a criterion for their having structure, contrary to unstructured liquids, such as liquid argon or pentane [2]. This criterion requires for structured liquids that: h i –1 –3 ΔC P =V ¼ C P ðlÞ–C p ði:g:Þ =V > 0:6 J⋅K ⋅cm
ð1Þ
Here CP(l) is the isobaric heat capacity of the liquid, Cp(i.g.) is that of the same substance in the ideal gas state, and V is the molar volume of the liquid, all at a given temperature. The subtraction of Cp(i.g.) from Cp (l) serves to exclude from the consideration of the effects of introducing thermal energy into the liquid for the excitation of internal modes of the molecules, so that only configurational effects on the liquid structure are taken into account. Water is thus a highly structured liquid according to this criterion: ΔCP/V=2.3 J K− 1 cm− 3. E-mail address: [email protected]. 0167-7322/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2011.11.013
On the other hand, Davis and Litovitz [3] and Davis and Jarzynski [4] showed that a two-state model for water involves a relaxational molar heat capacity of ~ 42 J K − 1 mol − 1 at 25 °C between the fully hydrogen bonded state and the close packed structures. Values of similar magnitude were also proposed by Eucken [5], Grjotheim and Krogh-Moe [6], Wada [7], and Nemethy and Scheraga [8] in their models for liquid water. This relaxational value happens to coincide at 25 °C with the ΔCP value in Eq. (1), CP(l) − Cp(i.g.) = 41.72 J∙K − 1∙mol − 1, but should not be construed as representing this difference. These considerations were taken up later by Bassez, Lee and Robinson in their model for water [9]. More recently, Silverstein, Haymet, and Dill [10] invoked a two state model, involving broken and intact hydrogen bonds, to deal with the hydrophobic effect, including its consequences for the excess heat capacity. Whether a two-state model or a model involving a multitude of hydrogen bonded structures is accepted, it is clear that the fraction of the heat capacity ascribable to the more highly hydrogen bonded structure is larger, the more ‘structure’ (unbroken hydrogen bonds) the water has. It is the purpose of this paper to examine whether the excess partial molar heat capacity of the water in water rich mixtures with cosolvents does confirm enhancement of the water structure in agreement with conclusions reached from the excess partial molar volume of the water in these mixtures [1]. Enhancement of the water structure induced by the co-solvent manifests itself by the changing of some of the domains with few hydrogen bonds to highly hydrogen bonded ones, having a larger heat capacity, resulting in a positive exE cess partial molar heat capacity of the water, CPW > 0. It is notable that very few authors in their studies of the heat capacities of aqueous mixtures with co-solvents have reported the partial molar isobaric heat capacity of the water. Nor did they, when they did report such
Y. Marcus / Journal of Molecular Liquids 166 (2012) 62–66
values, draw conclusions concerning the structure of the water. It is, therefore, necessary to obtain the desired information from published data of the total specific heats or excess heat capacities of the mixtures or the apparent molar heat capacities of the co-solvents. 2. Data and results Isobaric heat capacity data of mixtures of water, subscript W, with co-solvents, subscript S, were obtained from the literature. As far as available, the data for 25 °C were used, but in some cases were also data at other temperatures. Only the water-rich region was of interest, that is, mole fractions of the co-solvent xS ≤ 0.3. In some cases the data extend to only a fraction of this range, but if data are only available at xS b 0.1 or at co-solvent molalities mS b 6 mol kg − 1 they E cannot be used properly for the derivation of CPW values. In cases where the excess molar isobaric heat capacities of the mixture, CPE, were reported as functions of the mole fractions of the co-solvent, xS, the excess partial molar heat capacity of the water is obtained as: E E E C PW ¼ C P –xS ∂C P =∂xS
ð2Þ
T
In many cases the excess heat capacities of the mixtures can be described as a cubic function of the composition with a correlation coefficient rcorr > 0.995: E
2
3
C P ¼ axS þ bxS þ cxS
ð3Þ
mixtures are shown in Table 1. In general, values obtained from directly reported CPE values via Eqs. (3) and (4) are more accurate than those obtained indirectly via Eqs. (6)–(8). In most cases, although there are differences in the numerical values of the parameters resulting from the data of several authors, there is fair agreement on the main features. It is stressed that expressing the excess molar heat capacity data for all the systems for which adequate data were found by a third order polynomial rather than by an individual fitting expression for each system may have introduced uncertainties, but the trends ought to be valid. The data of Bonner and Cerutti [11] are in the form of CPS(xS) with only 7 data points up to xS = 0.3. They were converted to CPS(mS) by mS = xS/MW(1 − xS), then to φCPS, using CPS = φCPS + mS(∂ φCPS/mS)T and noting that CPS is linear with mS (i.e., (∂ φCPS/mS)T = p of Eq. (5) and q = 0 as are higher terms), and finally via Eqs. (5), (6), (7), (3) E and (4) to CPW . This tortuous route detracts from the accuracy of the latter quantity, so that these data should not be considered with full weight. The data of Kiyohara et al. [20] are of the form φCPS(mS), but only for aqueous dioxane are they valid to sufficiently high molalities (12 mol∙kg − 1, xS = 0.178) to warrant treatment. The data for tetrahydropyran, morpholine, piperazine, and piperidine [20] extend only to small molalities and could not be included. So are the data of
Table 1 The coefficients of Eq. (4) for the excess partial molar isobaric heat capacity of water, E CPW /J K− 1 mol− 1 at 25 °C, and attributes of its values. Co-solvent
Ref.
By definition of the excess value, CPE = 0 at xS = 0, so that the curve passes through the origin. Then Methanol E
2
3
C PW ¼ −bxS –2cxS
ð4Þ
E and is positive in water-rich mixtures if b b 0. If c > 0 CPW becomes negative beyond a limiting value of xS lim = − b/2c. In such cases E CPW reaches a maximal value, CPW Emax, at xS max = −b/3c. The partial molar heat capacity of the water in the mixtures is then:
C PW ¼ C PW∘ þ C PW
E
ð5Þ
where CPW° = 75.33 J∙K − 1∙mol − 1 (at 25 °C) is the molar heat capacity of the water. If the published data are the apparent molar heat capacities of the co-solvent, φCPS, these are often reported as functions of its molality, mS: φ
φ
∞
2
C PS ¼ C PS þ pmS þ qmS þ ⋅⋅⋅
ð6Þ
∞ ∞ , p, q ∙∙∙ are reported in such cases, where φCPS The parameters φCPS is the limiting value of the apparent (or partial) molar heat capacity of the solute S at infinite dilution. Then the following transformations E lead to values of CPE that is converted to the desired CPW according to Eq. (2). The specific heat of the mixture, cP, is obtained from φCPS by inverting its defining function [11] as:
ð7Þ −1
−1
at where cPW° is the specific heat of the water (4181 J∙K ∙kg 25 °C) and MS is the molar mass of the co-solvent, in kg∙mol − 1. Then E CP
¼ cP ½xS MS þ ð1–xS ÞMW –xS C PS∘–ð1–xS ÞC PW∘
Ethanol
1-Propanol 2-Propanol t-Butanol
Ethylene glycol 2-Methoxyethanol Dimetoxyethane Tetrahydrofuran 1,4-Dioxane
Acetone Acetonitrile Formamide
N-Methylformamide
φ cP ¼ mS C PS þ cPW∘ =ð1 þ mS M S Þ
ð8Þ
where MW = 0.018015 kg∙mol − 1 is the molar mass of the water and CPS° is the molar heat capacity of the co-solvent. The resulting values of the coefficients b and c of Eq. (4) and of xS lim, xS max, and CPW Emax for many water-rich aqueous co-solvent
63
Dimethylformamide Dimethylacdetamide Ethanolamine Dimethylsulfoxide
a b c d
[12] [13] [14] [12] [15] [13] [14] [13] [14] [12] [16] [12] [28] [48] [17] [18] [19] [19] [11] [11] [20] [19] [21] [12] [22] [23] [11] [22] [21] [11] [24] [25] [21] [22] [21] [26] [27] [22] [21]
CPE, cP, or φCPS data CPE CPE CPE CPE CPE CPE CPE CPE CPE CPE φ CPS CPE φ CPS φ CPS cP cP cP cP φ CPS φ CPS φ CPS cP CPE CPE CPE CPE φ CPS CPE CPE φ CPS CPE φ CPS CPE CPE CPE cP φ CPS CPE CPE
b
c
E CPW >0
xS − 373 − 317 − 308 − 482 − 736 − 722 − 680 − 2529 − 1776 − 1941 − 1675 − 3652 − 2942 − 2930 − 220 − 495 − 577 − 1817 − 598 − 791 − 333 − 268 − 117 − 412 − 463 − 572 13 55 42 − 388 − 99 161 − 156 − 249 − 419 − 86 − 183 − 95 − 53
873 753 706 164 1804 1658 1576 16730a 10380b 3500 5378 8618 6185 6124 692 1360 1731 2254 818 c,d 1422 c,d 1554 982 308 973 1733c 2652 40 c,d − 85c − 54c 670c,d 184 − 257 208 473 1157 180 899 246 127
A term − 19930xS4 is also required. The cubic expression is valid only to xS = 0.2. Fitting to a cubic polynomial not very accurate. Poor and few data.
lim
0.427 0.421 0.436 0.461 0.408 0.436 0.431 0.197 0.220 0.277 0.311 0.212 0.238 0.239 0.318 0.364 0.334 0.362 0.731 0.556 0.214 0.272 0.382 0.423 0.267 0.216 E CPW b0 E CPW b0 E CPW b0 0.579 0.539 0.580 0.751 0.526 0.362 0.478 0.204 0.384 0.654
E CPW
at xS
max
max
10.1 7.2 8.7 21.7 18.2 20.3 18.7 11.7 13.2 22.1 24.1 23.0 24.7 24.8 3.3 6.4 9.5 15.9 47.3 ? 36.3 ? 2.3 2.9 2.5 10.9 4.9 4.0
0.285 0.280 0.291 0.308 0.272 0.290 0.288 0.125 0.147 0.185 0.208 0.141 0.159 0.159 0.212 0.243 0.223 0.242 0.487 0.371 0.143 0.182 0.254 0.282 0.178 0.144
19.3 4.3 19.2 13.1 10.2 8.2 2.9 3.4 1.3 5.3
0.386 0.359 0.387 0.501 0.350 0.242 0.319 0.136 0.256 0.436
64
Y. Marcus / Journal of Molecular Liquids 166 (2012) 62–66
Kiyohara et al. [27] for acetamide (up to 2.4 m only). Other authors reported heat capacity data for too low concentrations or too few data points, or no numerical data (values only in plots) to warrant E evaluation in terms of CPW (xS). Such studies include those of unsaturated heterocyclic solutes (e.g., pyridine, where no limits of applicable molalities are provided) [29], alkanols [30], acetone, methyl ethyl ketone and methyl acetate [31], alkanols and alkoxyethanols [32], morpholine [33], ethanolamines [34], 1-butanol [35], alkanols [36], alkanolamines [37], and tetrahydrofuran, dioxane, dimethoxyethane, and dimethylsulfoxide [38]. DeVisser et al. [28] did report in a figure values of φCPW in aqueous mixtures with t-butanol, but also included numerical values in supplementary data. The apparent molar heat capacities φCPS of t-butanol reported by three authors [12, 18, 48] are shown in Fig. 1 (upper panel) in reasonable agreement with each other (those of Arnaud [12] had to be recalculated from the reported molar heat capacities of the mixture). It was pointed out by a referee that the maximum in φCPS required a minimum in φCPW according to the Gibbs-Duhem law. However, in the process of the calculation of E the excess partial molar heat capacity of water CPW from the aqueous t-butanol φCPS data of the three authors by Eqs. (7), and (8), with reE sults shown in Fig. 1 (lower panel), such a minimum in CPW is not discernable. E Davis [32] showed in a figure positive CPW values for water in methanol, ethanol, and 1-propanol that agree on the whole with the values listed in Table 1. Some of the discrepancies in Table 1 are diffiE cult to understand, such as why positive CPW values are obtained by Checoni and Volpe [21] for compositions far beyond the extent of the water-rich data considered here for aqueous dimethylformamide (xS lim = 0.75) and dimethylsulfoxide (to xS lim = 0.65), contrary to results of other authors. In addition to the data for co-solvents there are also data for waterrich solutions at 25 °C of an amide, urea, which cannot be properly called a “co-solvent” because it is solid at this temperature. For aqueous urea solutions specific heat data, cP(mS), were reported long ago by Gucker and
Fig. 1. Top panel: the apparent molar heat capacity of t-butanol in water at 25 °C according to De Visser et al. [28] ▽, Alary et al. [48] □, and Arnaud [12] O (recalculated from his cP data). Lower panel: the derived excess heat capacity of water from the above data: De Visser et al. [28] ▼, Alary et al. [48] ■, and Arnaud [12] ●.
Ayres [39] at 20 and 30 °C up to 17.6 mol∙kg− 1 (xS =0.24) from which E CPW = −220xS2 +789xS3 at 20 °C and –155xS2 +436xS3 at 30 °C are derived. Later, apparent molar heat capacities, φCPS(mS), were reported by Picker E et al. [40] at 24.15 °C up to 9.0 mol∙kg− 1 (xS = 0.14) resulting in CPW = 2 3 −251xS +1441xS and by Kiyohara et al. [27] at 25 °C up to E 10 mol∙kg− 1 (xS =0.15) leading to CPW =−422xS2 +3170xS3. All are negative within the range of available data but tend to turn upwards at the higher concentrations of urea, and are in mutual agreement (allowing for the different temperatures) up to xS ~0.1. Urea thus resembles formE amide (see Table 1) in having negative values of CPW in dilute aqueous solutions. Data for the aqueous methanol, ethanol, and 1-propanol at 15 and 35 °C by Benson and D'Arcy [41] span those at 25 °C of Benson et al. E [13] (see Table 1) and the derived CPW values are shown in Fig. 2. Werth and Hvidt [42] presented data for the aqueous methanol, ethanol, and 1-propanol also for lower temperatures, including sub-zero E ones. The CPW values derived from these data at 4 °C are shown in E Fig. 2 too, and CPW data derived for −16 °C (not shown) follow the E trends shown. The CPW values are seen to increase as the temperature E is lowered in dilute solutions, up to xS = 0.15. On the contrary, CPW increases for aqueous ethylene glycol with increasing temperatures, as obtained from specific heat data at 5, 25, and 45 °C by Huot et al. [17], E shown in Fig. 3. No clear temperature effect is seen for the CPW values for aqueous dimethylsulfoxide at 15, 25, and 30 °C, whereas for aqueE ous dioxane at these temperatures CPW does increase with the temperature, as derived from the data Checoni and Volpe [21]. No E generalization of the temperature effect on CPW may, therefore, be made. 3. Discussion E Table 1 shows that positive CPW values are achieved over a certain composition range in water-rich mixtures for most of the co-solvents for which data were found. Over the range 0 ≤ xS ≤ xS lim where E CPW > 0, the partial molar heat capacity of the water in the mixtures is larger than the molar heat capacity of pure water, Eq. (5). This can be interpreted by increased relative extents of the highly hydrogen bonded domains at the expense of the close packed domains, the water becoming more structured in the presence of the cosolvents. If the mean value 42 ± 3 J∙K − 1∙mol − 1 for the molar relaxation heat capacity (from the close packed to the fully hydrogen bonded domains) reported by Davis and Litovitz [3] is accepted, the values
E Fig. 2. The excess partial molar isobaric heat capacity of water, CPW , in water-rich aqueous methanol (circles), ethanol (triangles) and 1-propanol (squares) at − 4 °C (dotted symbols), 15 °C (filled symbols) and 35 °C (empty symbols) from data in refs. [40] and [41].
Y. Marcus / Journal of Molecular Liquids 166 (2012) 62–66
E Fig. 3. The excess partial molar isobaric heat capacity of water, CPW , in water-rich aqueous ethylene glycol at 5 °C (●), 25 °C (▲), and 45 °C (■), from data in ref. [16].
of CPW Emax in Table 1 indicate that sizable fractions of the total amount of water are transformed in this direction by the presence of the co-solvent. Ethylene glycol, dioxane, ethanolamine and dimethylsulfoxide show minimal conversion (6–8%), the monohydric alkanols, on the other hand, show sizable conversion (20–50%) as do other co-solvents listed in Table 1. However, only the configurational part of the total excess heat capacity of the water should be considered in this context [10], since the partial molar excess heat capacity of the water reflects not only the structural changes induced by the co-solvent but has other causes too. The determination of the structuredness of neat liquid water from its heat capacity requires, according to Eq. (1) and the related discussion, subtraction of the excitation of internal modes of the water molecules. For the water-rich aqueous mixtures dealt with here, some subtraction of the heat capacity related to the excitation of internal E modes of the water from CPW appears also to be required in order to deduce the enhancement of the water structure. It is not clear how much of the ideal gas heat capacity of water, CPW(i.g.) = E 33.58 J∙K − 1∙ mol − 1 at 25 °C, has to be subtracted to yield ΔCPW . The results from the consideration of the excess partial molar volume of the water in Part I of the series [1] may serve as a guide. The co-solvents E E E that have VW >0 and VW b 0 will show agreement with ΔCPW >0 and ΔCPWE b 0, if roughly 30% of CPW(i.g.) is subtracted. But, whereas VWEmax is only a small fraction of the relaxation molar volume between the domains, ≤1.4%, the ΔCPWEmax values still constitute a larger proportion of the relaxational heat capacity (~42 J∙K− 1∙mol− 1) though more modest than that of the total CPWEmax and are more reasonable. There exists some correlation between the propensity for mutual association of the water with the co-solvent and the nonenhancement of the water structure, that is, the negative signs of G E E and of VW and ΔCPW Emax. However, the correlation is far from perfect: E acetonitrile has VW and ΔCPW Emax b 0 but G E > 0, whereas the dialkylaE mides have VW and ΔCPW Emax > 0 but G E b 0. Positive ΔCPW Emax values occur for a limited group of co-solvents, which on the one hand have relatively small molecules that can be accommodated in the voids in the structure of pure water and on the other form hydrogen bonds with surrounding water molecules. The presence of several methyl groups seems to induce such an enhancement, cf. t-butanol, dimethoxyethane, and dimethylformamide. Excluded from this group are co-solvents that interact too strongly with the water, like ethylene glycol, formamide, and N-methylformamide (and urea) E that form denser domains and have ΔCPW Emax and VW b 0 throughout the water-rich range.
65
The majority of authors who considered the enhancement of the water structure in water-rich mixtures by co-solvents dealt with mixtures of water with alkanols, see references in Part I [1]. For these E E there is agreement between the signs of CPW (or ΔCPW Emax) and VW . Franks and Ives [43] concluded that at low xS aqueous mixtures are essentially water-like, resisting depolymerization and preserving the water structure based on its co-operative three-dimensional structure. Onori and Santucci [44] concluded that ‘water cages’ surround dispersed alcohol molecules below a certain threshold xS. Koga [45] concluded from the excess partial molar enthalpies of very dilute aqueous t-BuOH that the latter re-arranges the surrounding water molecules to enhance the network structure of water. Roses et al. [46] quote results that water structure enhancement occurs also in dilute solutions of MeCN, DMSO, and acetone (the first one contrary to E having VW b 0 as found later [1]). They employed solvatochromic probes to show the structure enhancement in aqueous 2-PrOH and t-BuOH. Still, the values of the thresholds up to which water structure enhancement in water-rich mixtures with co-solvents persists differ according to the method employed. So does also the amount of the enhancement relative to the relaxational value between compact and highly structured water domains. It is conceded that not everybody ascribes the positive excess partial molar heat capacity of water to enhanced hydrogen bonded structure of the region around the solute molecules. Some computer simulation results explain the enhanced heat capacity near hydrophobic solutes as due to their hydrophobic interactions counteracting a disordering of the water structure [47]. However, other computer simulation results do show that the fraction of broken hydrogen bonds in the water shell surrounding a hydrophobic molecule is lower than the fraction in bulk water, i.e., that the water structure is enhanced by the hydrophobic solute [10]. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
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