878
Langmuir 1988,4, 878-883
the removal action. The removal behavior of the nonionic surfactants on the other hand is not appreciably affected by moderate amounts of sodium chloride. In contrast to inorganic salts, organic substances may have a dramatic effect on the performance of the nonionic surfactants. The hydrophilic-lipophilic balance of the additives and the surfactants is then very important. From the results it is also possible to draw conclusions of direct value in practical cleaning. However, the properties of the soil and the surface markedly affect the reyoval process, and it is therefore important to remember that the results are obtained with hydrophobic dirt on hydrophobic surfaces. The results are most useful in those fields where removal of oils and fats from plastic surfaces is concerned. The following conclusions are important: Nonionic surfactants having cloud points moderately above the experimental temperature are superior to single-chain ionic surfactants. The size of the hydrophilic and hydrophobic parts of the surfactant must be balanced in such a way that the surfactant aggregate curvature against water, soil, and substrate is as close to zero as possible. For a pure nonionic surfactant that means that the cloud point should be near or below the temperature used. The efficiency of a nonionic surfactant may be much enhanced by addition of hydrocarbons or other hydrophobic compounds. For this improvement to take place it is required that the surfactant be more hydrophilic than the optimal surfactant without addition of hydrocarbon. The efficiency of a single-chain ionic surfactant may be enhanced by addition of inorganic salts. Combinations of nonionic and ionic surfactants give no improvement compared to a single nonionic surfactant. Combinations of nonionic surfactants give no improvement compared to a single nonionic surfactant. While the present study thus has provided some information related to the efficiency of different surfactants and surfactant-additive mixtures in hard surface cleaning, a more important goal of future work is to present models which can rationalize experimental results. In this way
good understanding of the packing of aggregated surfactant molecules under various conditions, which has been obtained in experimentaland theoretical work during the last decades, can be used efficiently in the formulation of cleaning products. In the present work we have been able only to touch very moderately on this important matter. The cleaning process is certainly a very complex one, and it would be presumptuous to believe that a single simple model would be able to rationalize the large body of observations made in the field. In the present work the cleaning process is studied in a simple and rather welldefined way. An attempt has been made to compare the experimental results with simple geometric and electrostatic features of surfactant packing, which have been so successful in recent years in rationalizing, for example, micelle shape, phase diagrams, and microemulsion structure. The agreement between experimental results and model is throughout good, and although the comparison is simple-minded and mainly qualitative the approach seems encouraging for future studies.
Note Added in Proof. F. Schambil and M. J. Schwuger (Colloid Polym. Sci. 1987,265,1009) have recently studied the removal of oil from fabrics by nonionic surfactants and obtained results which in important respects parallel those obtained in the present work for hard surface cleaning. This would indicate a marked generality of the cleaning mechanism. Schambil and Schwuger correlated their results with the phase behavior of ternary systems. On the basis of the established relation between phase behavior and surfactant molecular packing we would expect the model presented above to be of interest also in types of cleaning other than hard surface cleaning. Acknowledgment. Financial support was obtained from the Swedish Work Environment Fund. Registry No. TO, 122-32-7;TP, 555-44-2; PA, 57-10-3;NFE,, 9016-45-9;DBS-Na,25155-30-0; NaOle, 143-19-1;CTAC, 112-02-7; NTAeNa, 10042-84-9;CI2SO3N,,2386-53-0; NaC1, 7647-14-5; calcium chloride, 10043-52-4;decane, 124-18-5;ethanol, 64-17-5; butanol, 71-36-3; hexanol, 111-27-3; octanol, 111-87-5.
Enhancement of Hydrogen Bonding in Vicinal Water: Heat Capacity of Water and Deuterium Oxide in Silica Pores Frank M. Etzler* Picosecond & Quantum Radiation Laboratory, Texas Tech University, Lubbock, Texas 79409 Received December 30, 1987. I n Final Form: March 22, 1988 The heat capacities of water and deuterium oxide confined to silica pores of various radii at 25 O C are reported. Pore radii were varied from 1.2 to 12.1 nm. The data are discussed in terms of their implication for the structure of vicinal (interfacial) water. The results show that the heat capacity of both H20and DzO passes through a maximum near 7 nm when plotted as a function of pore radius. In the case of D20 the maximum appears to be less pronounced than that of HzO. The relative magnitudes of the observed heat capacity maxima can be understood by using the model for vicinal water proposed earlier by this author.
Introduction The properties of liquid water are known to be significantly modified by propinquity to solid surfaces. DrostH a n ~ e n l -in ~ ,particular ~~ has reviewed the properties of *Present address: Institute of Paper Chemistry, Appleton, WI 54912.
0743-7463/88/2404-0878$01.50/0
vicinal (interfacial) water and discussed their biophysical significance. LOW^-^ has measured and reviewed the (1)Drost-Hansen, W. Ind. Eng. Chem. 1969, 61, 10.
(2) Drost-Hansen, W. In Chemistry of the Cell Interface, Part B; Brown, H. D., Ed.; Academic: New York, 1971. ( 3 ) Drost-Hansen, W. In Biophysics of Water;Franks, F., Ed.; Wiley: New York, 1982.
0 1988 American Chemical Society
Langmuir, Vol. 4,No. 4, 1988 879
Hydrogen Bonding in Vicinal Water
properties of water in clays. Peschel and Adlfinger1*13 Table I have measured the viscosity of water between quartz silica V,, cm3/g pore diameter, nm plates. Low et ala7*have measured the viscosity of water 1 (gel) 1.15 14.0 in clays by several different experimental methods. Both 2 (gel) 0.40 2.6 sets of authors have reported increased viscosities near the 3 (glass) 0.55 11.7 surfaces of interest. Braun and D r o ~ t - H a n s e n ~ J~ as~well 4 (glass) 0.89 24.2 as Cianci16 have measured the heat capacity of water in 7-10-nm-diameter silica pores and found it to be 2530% Table 11. Heat Capacitya of H20and D 2 0 in Silica Pores greater than the bulk heat capacity. Etzler and FagunHZO DZO dus16J7have studied the density of water in silica pores radius, nm cal/ (Ka) cal/ (K mol) cal/ (K a) cal/ (K mol) and found it to be smaller than the bulk value. From the 1.25 0.93 16.76 1.04 20.80 work of Etzler,16J7 LOW,^ and PescheP3 it appears that 5.85 0.94 16.94 1.15 23.00 the vicinal water structure decays in an approximately 7.00 1.32 23.79 1.13 22.60 exponential manner and that significant vicinal structuring 10.00 1.27 22.89 extends 3-6 nm from the surface. 12.10 1.05 18.92 1.02 20.40 In an attempt to correlate some of the properties of "Standard error on heat capacity: f0.02 cal/(Kg) or f0.4 cal/ vicinal water, EtzlerlBhas proposed a statistical thermo(K mol). dynamic model for vicinal water. This model considers water in terms of a bond percolation model proposed for Braun and D r ~ s t - H a n s e n ~ have ~ J ~measured the heat bulk water by Stanley and Teixeira20and a bimodal sincapacities of water near a variety of substances and found gle-particle enthalpy distribution calculated earlier by them to be about 25% greater than the bulk heat capacity Stey.21 This model has been successful in correlating a and independent of the specific substance. The apparent number of properties of water in silica pores. From the independence of the properties of vicinal water on the model it appears that vicinal water is similar to water in precise physicochemical details of the surface has been the supercooled region or under negative pressure. In other termed the paradoxical effect by Drost-Hansen. words, hydrogen bonding between water molecules is enIn this paper, the heat capacities of water and deuterium hanced by propinquity to solid surfaces. oxide in silica pores of various diameters are reported. The In addition to the general structural enhancement inpresent study is significant in that it extends the experiduced near surfaces, it appears that vicinal water unmental observations of vicinal water to include D20. The dergoes structural transitions near 15,30, and 45 "C (i.e., results are furthermore considered in terms of the model the Drost-Hansen temperature~),'-~,~~ At present, the for vicinal water proposed earlier by the author. molecular details of these transitions are not understood. Peschel and Adlfinger1@12have reported maxima at the Experimental Section above temperatures for the viscosity and disjoining presHeat capacities of water and deuterium oxide confined to the sure of water between quartz plates. W i g g i n ~ and ~ ~ l ~ ~ pores of various silicas were determined by differential scanning Hurtado and D r ~ s t - H a n s e nas~well ~ as Etzler and Liles22 calorimetry (DSC). The reported values were measured at 25 "C by using a Perkin-Elmer DSC-7. Methods for the determination have reported similar maxima in the selectivity coefficient of heat capacity by DSC have been discussed elsewhere in the (K+relative to Na+ or Li') by water in silica pores and rat literature.2G28 The relevant characterisitics of the silicas used renal cortex.25 These maxima have been interpreted to in this study are given in Table I. reflect structural transitions in vicinal water near 15, 30, The silica samples were prepared as follows. First silica, which and 45 O C . Etzler and Drost-Hansen4J have discussed had been dried at 110 "C for at least 24 h, was placed into a numerous examples of physiological anomalies at the above weighed aluminum DSC volatile sample cup. Deuteriation of the temperatures as well as the physiological importance of silica was not performed for deuterium oxide samples as this step vicinal water. would significantly complicate the handling procedure; further(4)Etzler, F. M.; Drost-Hansen, W. In Cell Associated Water; Drost-Hansen, W.; Clegg, J. S., Eds.; Academic: New York, 1979. (5)Etzler, F. M.; Drost-Hansen, W. Croat. Chem. Acta 1983,56,563. (6)Oster, J. D.;Low, P. F. Soil Sci. Soc. Am. Proc. 1964,28,605. (7)Oliphant, J. L.; Low, P. F. J. Colloid Interface Sci. 1983,96,45. (8)Low, P. F. Soil Sci SOC.Am. J. 1979,43, 652. (9)Viani, B. E.; Low, P. F.; Roth, C. B. J. Colloid Interface Sci. 1983, 96,229. (10)Peschel, G.;Adlfinger, K. H. Naturwissenschaften 1969,11, 1. (11)Peschel, G.;Adlfinger, K. H. 2.Naturforsch., A: Phys., Phys., Chem., Kosmophys. 1971,26,707. (12)Peschel, G.; Adlfinger, K. H. J. Colloid Interface Sci. 1972,34, 505. (13)Peschel, G.;Belouchek, P.; Muller, M. M.; Muller, M. R.; Koing, R. Colloid Polym. Sci. 1982,260, 444. (14)Braun, C. V. M.S. Thesis, University of Miami, 1981. (15)Braun, C. V.; Drost-Hansen, W. In Colloid & Interface Sci.; Kerker, M., Ed.; Academic: New York, 1979;Vol. 111. (16) Cianci, J. J. M.S. Thesis, University of Miami, 1981. (17)Etzler, F. M.; Fagundus, D. M. J. Colloid Interface Sci. 1983,93, 585. (18)Etzler, F.M.; Fagundus, D. M. J.Colloid Interface Sci. 1987,115, 513. (19)Etzler, F. M. J. Colloid Interface Sci. 1983,92,43. (20)Stanley, H. E.; Teixeira, J. J. Chem. Phys. 1980,73,3404. (21)Shy, G.C. Ph.D. Thesis, University of Pittsburgh, 1967. (22)Etzler, F. M.;Liles, T. L. Langmuir 1986,2,797. (23)Hurtado, R. M.;Drost-Hansen, W. In Cell Associated Water; Drost-Hansen, W.; Celgg, J. S., Eds.; Academic: New York, 1979. (24)Wiggins, P. M. Biophys. J. 1973,13,385. (25)Wiggins, P. M. Clin. Exp. Pharmacol. Physiol. 1975,2,171.
more, the contamination of D 2 0 by hydrogen would have a negligible effect on the heat capacity values within expected experimental precision. Sample masses were determined with a microbdance (precision f 0.001 mg). After the mass of the silica sample was recorded a small drop of degassed H,O or D20 was placed on the silica. The sample was then placed under reduced pressure for several minutes to draw the remaining air from the pores. Typical samples contained about 5 mg of silica and enough liquid such that approximately 50% of the liquid was in the pores. After the mass of the liquid in the sample was determined, the cups were sealed and the heat capacity of the slurry was determined by DSC. After the heat capacity was measured, the sample was again weighed to assure no loss of sample due to improper sealing of the sample cup. Next, a small hole was pricked into the top of the sample cup, and the cup was placed into a n oven at 110 "C for 24 h. The cups were reweighed to determine the mass of the silica. T h e masses of liquid and silica found after measurement of heat capacity were compared to those masses determined before beginning the experiment. Samples in which the masses did not agree were discarded. The heat capacity of the dry silica gel was determined separately by using a sapphire standard. The heat capacity of the silica in ~
(26)McNaughton, J. L.; Mortimer, C. T. In ZRS: Physical Chemical Series 2; Buttersworth: London, 1974; Vol. 10. (27)Barrall, E. M. Tech. Methods Polym. Eual. 1970,2,1. (28)ONeill, M. J. Anal. Chem. 1966,38,1331.
880 Langmuir, Vol. 4 , No. 4, 1988
08
i,
'
20
'
40
'
6b
'
Etzler
80 ' 1 d o ' ' 2 3
POQE RADIUS
140
'A)
Figure 1. Heat capacities of water in silica pores as a function of pore radius a t 298 K: squares, HzO; diamonds, DzO. Radius in angstroms (10 A = 1 nm). all cases was found to be 0.254 cal/(gK). The heat capacities of bulk water and DzO were taken from the literature. Once the heat capacity of the slurry has been determined, it is possible to calculate the heat capacity of water in the pores. The mean heat capacity of water, C,(water), in the sample is calculated. C,(sample) = fsi,icaCp(silica)+ fwaterCp(water)
(1)
Here f is the mass fraction of the relevant component. The heat capacity of the pore liquid, C,(pore), may be calculated by C,(water) = f,,,C,(pore)
+ fb,dp(bUlk)
(2)
Here fp,,,, is calculated from the known pore volume and pore density. For DzOno correction for modified pore density was made. This correction is however very small in comparison to experimental error. The results of this study are shown in Figure 1 and Table 11.
Discussion The results of this study are presented in Figure 1and Table 11. Also included in the figure and table are the earlier results of Braun and Drost-Hansen in 10-nm pore^.'^,'^ These earlier results were obtained from nearly identical systems and are thus comparable. The results presented here differ from those of the earlier workers in that heat capacity measurements were made on silicas of various pore diameters and in that measurements using DzO are included. A notable feature of the heat capacity data is the apparent maximum near the 7-nm pore radius. The discussion presented here will focus on the relation of the observed maxima to the statistical thermodynamic model for vicinal water suggested earlier by this author.lg Heat capacity measurements of water in porous systems are rarely reported in the literature. Other than the studies of water i n clays reported by Lowc9 n o other studies a r e genuinely comparable. Low's data on clays appear to be remarkably similar to data collected in this laboratory on silicas. Reports of the existence of a maximum in the heat capacity of water when plotted as function of the amount adsorbed are not unknown. A heat capacity maximum of similar magnitude has been observed for water adsorbed on a polysulfonated ion-exchange resinm and on lysosyme.29 Both of these earlier studies suggest that the heat capacity maximum occurs much nearer to the surface than sug(29) Kinard, D. A.; Hoeve, C.A. J. J.Polyrn. Sei., Polyrn. Syrnp. 1984, 71, 183.
(30) Nolasco, A,; Julien, E.; Bescombes-Vailhe, Thermochim. Acta 1985, 92, 341.
gested by the present study. Hampton and MennieU have observed a maxim in the heat capacity of water in gelatin gels (1.24 cal/(Kg)) when this quantity is plotted against the mass fraction of water in the gel. It is not uncommon to find reports suggesting that the heat capacity of water near a variety of surfaces is about 20-30% greater than the bulk value. Unfortunately, in nearly all instances the adsorbed layer thickness has not been determined. In order to discuss the relation between the reported data and this author's model for vicinal water, the more relevant concepts of the model are briefly reviewed below. SteyZ1has calculated the single-particle enthalpy distribution for bulk water. His calculation shows that water, in contrast to more "normal" liquids, exhibits a bimodal distribuiton of single-particle enthalpies. Preliminary calculations performed in this laboratory suggest that water is not entirely unique in this regard; some liquid metals such as Ga and Sn also apparently exhibit a similar distribution. The bimodal character of Stey's distribution allows one to consider two fractions of water molecules. It appears that these two fractions represent those molecules that are 4-hydrogen bonded and those not 4-hydrogen bonded (Le., those with 0, 1,2, and 3 hydrogen bonds). The single-particle enthalpy distributions calculated earlier by Stey for HzO and DzO are presented in Figure 2. Note, in particular, that the bimodal character of water diminishes with increasing temperature and that the bimodal character has almost disappeared at 353 K. Heat capacity is related to the variance in the singleparticle distribution function, , : u through the well-known relation C, = uh2/R!P
(3)
The heat capacity of a bimodally distributed liquid may be considered as follows:
+ ~zC,(2)+ X1X2AH,q2/RP
C, = XlC,(l)
(4)
Here x1 refers to the fraction of 4-hydrogen-bondedwater molecules. C (1)is taken to be equal to the heat capacity of ice, and 8,(2) is estimated to be 16 cal/(Kmol) via arguments discussed in an earlier paper.lg A H S , the mean enthalpy of transfer between states represented by the two peaks in Stey's distribution, is taken to be 2.55 kcal/ (K mol.). With the above values it is possible to estimate the value of xl. A t 25 " C x1 is approximately 0.1 for bulk water and about 0.4 for water in 7-nm silica pores (see ref 19 for further details). Figure 3 shows a plot of C, versus X1*
In order to calculate x1 and CJ2) for D20 the following argument is pursued. Recently Bassez, Lee, and Robinhave reported a study of rotational motions of water molecules. By use of the results from this study, it appears possible to estimate x1 as a function of temperature and pressure for both D20 and H20. The rotational relaxation time T , is related to the NMR spin relaxation time Tl, the dielectric relaxation time Td, and the shear viscosity 17 through the following relations:
l / T l = An7,
(5)
=A~T,
(6)
Td T,
= A,qV,/kT
(7)
Here V , is the molar volume of the liquid and Aj is the appropriate proportionality constant. The temperature dependence of the rotational correlation time can be expressed in terms of the following equation: T,-~=
k, exp(-H(T)/kT)
(8)
Hydrogen Bonding in Vicinal Water 0.4
Langmuir, Vol. 4, No. 4, 1988 881 A
1
B
1
0.3
Deuterium oxide 298K
O W E (5, 5)
0.3 0.2 n
h
E.o.2
I
v
a
a
0.1
0.1
0.0
0.0
C
0.3
0
{O
H (Kcol/Mole)
D
0.:
- Water
353K
0.2 n
h
v
s0.1
I
a
a
\
d
0.1
0.0
- 4 - b ’ * ’
1’0
0.0
H (Kcol/Mole)
’
4 ’ 6 ‘ 8 ‘ lb H (Kcol/Mole)
Figure 2. Stey’s distribution functions. Probability, P(H),vs enthalpy, H (see ref 21 for description of OWLE algorithm). (A) Water at 298 K and NH3 at 200 K. Note water contrasts with NH, in that the distribution is bimodal. (B) D20 at 298 K. (C) H,O at 313 K. (D) H20 at 353 K. Note low-temperature peak absent or very small by 353 K. 1.4
-
Table 111. Constants for Eq 9 at 1 atm
Cp(mox, pore)
1.2
H20 DzO
m1 .0
228 236
14816 15053
-0.4552 -0.4519
1.1320 1.1322
0.3231 0.3196
20 20
Y
‘1.
0 0.8
1
’\
04
02
00
02
06
0 4
-08
10
x1
Figure 3. Hypothetical heat capacity of water and deuterium oxide as a function of x1 at 298 K. Note the similarity to Figure 1. This heat capacity is calculated via eq 4. C (1) (HzO, 298 K) = 9.96; CJ1) (D20,298 K) = 11.54; CJ2) (H2d,298 K) = 16.80; 298 K) = 18.47 cal/(Kmol). AH(H20)= 2.55; AHC (2) (DzO, (&O) = 2.40 kcal/mol. AH values are estimated from Stey’s distribution function (see Figure 2).
where H(7‘)is a temperature-dependent activation energy. H(T)was found to follow the empirical relation31 mT) = H(To)[A+ B(To/T) + C(To/nn1
(9)
Here, Tois a reference temperature chosen to be the singularity temperature discussed earlier by Speedy and (31)Bazzez, M.P.;Lee, J.; Robinson, G. W. J. Phys. Chem. 1987,91, 5818.
Ange11.32-34 This temperature is probably the lowest meaningful temperature for any discussion of liquid water. Table I11 lists the appropriate values for the above constants at 1 atm. The constants in Table I11 were determined by using NMR relaxation, dielectric relaxation, and viscosity data. Values of H as a function T and P , calculated from various kinds of experimental data, have been previously reported by Robinson et aL31 H(T) is found to be large and very sensitive to pressure below room temperature while small and remarkably insensitive to pressure at higher temperatures. As in the case of many earlier arguments, the “excess” activation energy has been attributed to the so-called “anomalouscharacter” of water (see ref 38 and 39 for details). (32)Speedy, R. J.; Angell, C. A. J. Chem. Phys. 1976, 65, 851. (33)Angell, C. A. In Water, A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1982;Vol. 7. (34)Speedy, R. J. J. Phys. Chem. 1987,91,3354. (35)Arrhenius, S.2.Phys. Chem. (Leipzig) 1887,1, 285. (36) Rutgers, I. R. Rheol. Acta 1962,2, 305. (37)Krieger, I. M. In Polymer-Colloids; Buscall, R., Corner, T., Stageman, J. F., Eds.; Elsevier: New York, 1985. (38)Jarzynski, 3.; Davis, C. M. In Water and Aqueous Solutions: Structure, Thermodynamics, and Transport Processes; Home, R. A., Ed.; Wiley: New York, 1972. (39)Jhon, M.S.;Grosh, R.; Ree, T.; Eyring, H. J. Chem. Phys. 1966, 44, 1465.
882 Langmuir, Vol. 4, No. 4, 1988
Etzler ,
WATER 0.90
-
0.70
-
Deuterium Oxide , H/HO
\
-01
I
220
,
I
,
I
,
270
I
I
I
,
I
320
~
I
I
,
I
370
I
I
I
41C
,~
-0.10
1
T Figure 4. Estimation of x l ( T ) for H20. Upper curve: experi-
mental values of H ( T ) / H ( T o )as a function of T. Central curve: To),extrapolated from unimodal “normal”component, E( T )/H( high-temperature region. Lower curve: x , ( T ) . Here E(T)/H(T,J = 0.832 193 - 0.00168230T.
\\
1 430
230
330
280
380
T
Figure 5. Same as Figure 5 except data for DzO.Here E ( T ) / H(T0) = 0.845809 - 0.00157332T. Stey Components Water - 1 Atm.
The activation energy of the rotational correlation time may be related to the activation energy of viscous flow via eq 7 . Jhon et al.39have discussed the apparent activation energy for viscous flow and have found the relation 77 =
C exp([slcp) exp(E/RT) = C exp(Eapp/Rn
(10)
to be appropriate for liquid water. The term exp([v]cp) is the well-known Arrhenius viscosity e x p r e ~ s i o n ~ used ~-~’ previously to explain the dependence of viscosity of a suspension of small particles with particle volume fraction. [77] is the intrinsic viscosity number, which would equal 2.5 for spheres, and cp is the volume fraction of added particles. Expansion of the Arrhenius viscosity term for the case of spherical particles leads to the well-known Einstein expression qr = 1 + 2 . 5 ~ (11) The Einstein expansion, however, will not be used in the present discussion, as it does not lead to a tractable result. Jhon’s expression considers the “excessnactivation energy (the energy contributed by the exp([p]q) term) to be due to the creation of icelike patches or 4-hydrogen-bonded clusters. In other words, the 4-hydrogen clusters behave as if they were small particles. This view is consistent with Stey’s distribution in that the existence of small icelike patches is suggested;however, the analogy to small icebergs should most assuredly not be taken too far, as the patches are ephemeral. Equation 10 can be rearranged to give d T ) = [E,,,(T)
- E(T)I/B
&i
’ ’ 2JO ’ ’
320-’
’
3io
’ ’
420
’
Figure 6. Heat capacity of the Stey pseudocomponentsfor H20 as a function of temperature. Here C (1)is taken as the linearly (T) as deextrapolated heat capacity of i ~ e , 4 ~ * ~ ~ xis, calculated scribed in the text from data by Robinson et al.,31and C,(2) is calculated via eq 4. C, is taken from Speedy.34 Stey C o m a o - e r t s 22-
I
’6
3e-*er,rr
3xde
-
1 Atn
,AD>
(12)
if it is assumed that [a] = B/RT. Here, Ea,, is the experimental activation energy and E(T)is the activation energy of the fluid in absence of the 4-hydrogen-bonded clusters. Assuming B = H(TJ Ho, then E ( T ) / B may be estimated from the linear extrapolation of H ( T ) / H o from high temperature. Figures 4 and 5 illustrate this extrapolation procedure. The difference between the experimental values H(T)/H,, and E ( T ) / H o yields a result proportional (or perhaps equal) to the volume fraction of 4-hydrogen-bonded clusters. As the densities of the two Stey pseudocomponents are nearly identical, the distinction between mole and volume fraction to a good first approximation can be ignored. Choosing B = Ho yields cp (or xl) values that are nearly identical with those estimated earlier by other methods.Ig The full physical sig(40) Fine, R. A,; Millero, F. J. J. Chem. Phys. 1975, 63, 89.
C p l = C2(ice)
230
280
T
333
380
Figure 7. Heat capacity of the Stey pseudocomponentsfor D20. The experimental heat capacity has been extrapolated into the supercooled region by using an interpolationformula given earlier by Millero et al.*O
nificance of this choice is not yet appreciated. Furtherit is possible more, if it is assumed that CJ1) = C (ice),4l~~~ to calculate Cp(2) via eq 4. The cafculated values of the Stey pseudocomponents are shown in Figures 6 and 7 as (41) Kristbaum, I.; Urey, H. C.; Murphy, G. M. Physical Properties and Analysis of Heauy Water; McGraw-Hill: New York,1951. (42) Weast, R. C. CRC Handbook of Chemistry & Physics, 66th ed.; CRC: Boca Raton, FL, 1985.
Hydrogen Bonding in Vicinal Water Table IV. Stey Pseudocomponent Parameters" for H 2 0 T,K 311 CP Cp(2) Cp(1) 248 0.211 19.78 14.12 8.26 0.179 19.12 14.32 8.43 253 0.154 18.70 14.64 8.60 258 0.135 18.45 14.98 263 8.77 0.118 18.26 15.31 8.94 268 0.105 18.15 15.62 9.11 273 0.093 18.07 15.90 9.28 278 0.083 18.03 16.17 9.45 283 0.077 17.99 16.40 9.62 288 0.066 17.98 16.61 9.79 293 298 0.058 17.97 16.80 9.96 0.051 17.97 16.97 10.13 303 0.045 17.97 17.12 10.30 308 17.98 0.040 17.25 10;47 313 0.035 17.98 17.37 10.64 318 17.99 0.030 17.48 10.81 323 0.026 17.99 328 17.57 10.98 333 0.022 18.00 17.65 11.15 11.32 18.01 17.73 338 0.018 0.015 18.02 17.79 11.49 343 348 0.012 18.03 17.85 11.66 18.05 0.010 17.91 11.83 353 0.008 18.06 17.96 12.00 358 363 0.006 18.08 18.00 12.17 0.004 18.05 12.34 18.11 368 373 0.003 18.12 18.10 12.51 "CP units: (:al/(K mol). Table V. Stey Pseudocomponent Parameters' for D20 T,K 21 CP Cp(2) Cp(1) 0.288 21.17 12.19 248 9.77 13.68 9.95 253 0.236 20.97 258 0.198 20.81 14.83 10.13 263 0.180 20.67 15.69 10.30 268 0.146 20.55 16.37 10.48 273 0.128 20.44 16.90 10.66 278 0.113 17.33 10.83 20.36 283 0.100 20.15 17.69 11.01 20.23 18.00 11.19 288 0.089 293 0.083 20.17 18.25 11.37 298 0.017 20.13 18.47 11.54 303 0.066 20.09 18.67 11.72 308 0.056 20.06 18.83 11.90 20.03 18.97 12.07 313 0.052 19.10 12.25 318 0.044 20.00 323 0.038 19.97 19.20 12.43 328 0.033 19.95 19.30 12.60 333 0.029 19.92 19.37 12.78 19.89 338 0.025 19.44 12.96 343 0.021 19.87 19.49 13.14 348 0.018 19.84 19.53 13.31 'CP units: cal/(K mol).
well as Tables IV and V. Note that Millero's interpolation formula40for the bulk heat capacity of DzO has known accuracy only in the range 0-60 "C. The values of x1 and Cp(2)calculated above are consistent with our earlier estimates for these values at 298 K and the temperature dependence of Stey's distribution function. Stey's results (43) Drost-Hansen, W.; McAteer, J.; Jacobsen, R.; De Freest, E. S. In Particulate and Multiphase Processes; Ariman,T.;Veziroglu, T. N., Ed.;
Hemisphere: New York, 1987. (44) Hampton, W. F.; Mennie, J. H. Can. J.Res. 1934, 10, 4.
Langmuir, Vol. 4, No. 4, 1988 883 suggest that xl I0.43 at all experimentally accessible temperatures (i.e., >228 K), as no heat capacity maximum for bulk water is observed, and that x1 is nearly zero by 360 K. Note also that Cp(2) has the correct qualitative temperature dependence for a unimodally distributed fluid as Cp(2) decreases steadily with decreasing temperature. As appropriate data are available for D20, the present argument is significant in that x1 and Cp(2) can be estimated for DzO. In short, it appears that the temperature dependence of the rotational correlation time can be used to estimate x1 as function of both T and P for H 2 0 and D2O. It has been previously suggested that vicinal water differs from bulk water in that hydrogen bonding between water molecules is enhanced by propinquity to surfaces. In other words, x1 increases steadly and continuously as water gets closer to a surface (see ref 18 and 19 for additional details). If both Cp(l) and Cp(2)are unaffected by propinquity to a surface, then C can be calculated as a function of xl. Figure 3 shows as a function of x1 for both D 2 0 and H 2 0 as calculated via eq 4. As can be seen from the figure, heat capacity reaches a maximal value when plotted against xl. These maximal values are nearly identical with the experimental maxima observed for the heat capacity H20 and D20 in silica pores. I t is thus concluded that the statistical thermodynamic model for vicinal water, advanced earlier by this author, provides an adequate description of the observed heat capacity of water in silica pores in addition to providing an adequate description of the other physical properties previously discussed by the author. It also appears that the structure of vicinal D20 is enhanced near surfaces in a manner very similar to H20.
4
Summary In this paper the heat capacities of H 2 0 and D20in silica pores are reported. The measured heat capacity values are used to test further the viability of the statistical thermodynamic model for vicinal water advanced earlier by the author.lg The relation between the activation energy of the rotational correlation time as measured by Robinson et al.31and the fraction of the Stey pseudocomponents2*has been discussed. These activation energies, which apparently may be used to calculate the fraction of the Stey pseudocomponents, in particular, have been useful for the prediction of the behavior of vicinal D20. The observed maxima in the heat capacities of the studied liquids are found to be consistent with the notion that hydrogen bonding is increased near solid surfaces and more specifically with the model for vicinal water advanced earlier by this investigator. Acknowledgment. I thank Professors W. Drost-Hansen, J. S. Clegg, P. F. Low, and G. W. Robinson for their many hours of discussion and encouragement. Surely, this work would not have been possible without their assistance. I also thank Pamela J. White for her assistance in a portion of the experimental work. The Robert A. Welch Foundation (Grant D-0005) is thanked for partial support of this work. Registry No. HzO, 7732-18-5; D2, 7782-39-0; SiOz,7631-86-9.
