M. R. THOMAS, H. A. SCHERAGA, AND E. E. SCHRIER
3722
A Near-Infrared Study of Hydrogen Bonding in Water and Deuterium Oxide'
by Mary R. Thomas, Harold A. Scheraga, Depart&
of Chemiatry, Cornel1 University, Ithacu, New York
and Eugene E. Schrier Department of Chemistry, State University of New York at Binghamton, Binghamton, New York (Received March 66, 1966)
~~
The spectra of liquid H20, liquid D20, H2O ice, and D2O ice have been obtained in the 1.16-1.25-p region for HzO and the 1.56-1.69-p region for D2O. The temperature dependence of the liquid spectra and the extinction coefficientsfor the solids have been utilized to calculate the concentrations of the unbonded, singly hydrogen-bonded, and doubly hydrogen-bonded water molecules as a function of temperature for liquid HzO and for liquid D20. The fraction of possible hydrogen bonds remaining intact at various temperatures for H20 compares well with previous experimental and theoretical results. The results for D20are consistent with the calculations of NBmethy and Scheraga.2
Introduction The structure of liquid water continues to receive considerable attention. Recently, NBmethy and Scheraga2 have shown that their theoretical treatment of liquid water3 is applicable to deuterium oxide. Their calculations indicate that more structural order exists in DzO than in H 2 0 at a given temperature, However, the breakdown of the structural order with increasing temperature was shown to be more rapid for D20 than for HzO. Buijs and Choppin4have investigated the absorption spectrum of water in the 1.16-1.25-p region. They suggested that these bands were due to the presence of three types of water molecules, those having zero, one, and two hydrogen bonds, respectively, to neighboring molecules. By assigning extinction coefficients to each of the species, based on the H2O liquid spectrum at different temperatures and additional data given by the spectra of ice and of water in aqueous salt solutions, they computed the fraction of each type of water molecule at a series of temperatures. Goldstein and Penner5 applied a somewhat different treatment to the 1.45- and 1.93-p absorption bands of HzO. They assigned values to the extinction coefficient of the doubly bonded species using absorbance data for ice as did Buijs and Choppin,4 but, instead of attempting to evaluate the extinction coefficients for the other species The Journal of Physical Chemistry
from various experimental data, they left them as unknown parameters to be determined along with the unknown concentrations at each of four temperatures by a least-squares computer method. Since we have employed the same calculation ~ c h e m efurther ,~ details will be given below. The fractions of hydrogen bonds unbroken in liquid water at various temperatures, obtained in these investigation^,^^^ were in fair agreement with those calculated by NBmethy and S ~ h e r a g a . ~ Lucke has also investigated several of the near-infrared bands of HZO. His calculations are not as extensive as those of the workers already mentioned. He gives the concentrations of the doubly bonded and free water molecules as a function of temperature in the range 0-90". He suggests6bthat there is a considerable fraction of hydrogen bonding in water up to the vicinity of the critical point, basing this conclusion on experiments with water under high pressure. (1) This work was supported by a research grant (AI-01473)from the National Institute of Allergy and Infectious Diseases of the National Institutes of Health, U. S. Public Health Service, and by a research grant (GB-2238)from the National Science Foundation. (2) G. NQmethy and H. A. Scheraga, J. Chem. Phys., 41, 680 (1964). (3) G.NQmethy and H. A. Scheraga, ibid., 36, 3382 (1962). (4) K.Buijs and G. R. Choppin, ibid., 39, 2035 (1963). (5) R. Goldstein and S. S. Penner, J. Quant. Spectry. Radiative Transfer, 4, 441 (1964). (6) (a) W.Luck, 2.Elektrochem., 67, 186 (1963); (b) W.Luck, ibid., 68, 895 (1964).
NEAR-INFRARED STUDY OF HYDROGEN BONDING IN H 2 0 AND D 2 0
These methods of treating the data suffer from distinct uncertainties. The temperature dependence of the various extinction coefficients used in the calculations is assumed to be negligible. Experimental verification of this assumption is a very difficult undertaking. Another problem is the large base-line corrections which must be made for the contributions from the absorbance of neighboring peaks. On the theoretical side, the assignment of the bands in Buijs and Choppin's* treatment has been challenged.' These criticisms have been answered by Buijs and Choppin,* but the definitive assignment must await further investigation. Even with these difficulties, it seemed useful to obtain spectral data for liquid DzO and also some measure of the structural order in D20 as a function of temperature, using a procedure similar to those mentioned above.4f6 Comparison of these data for D2O with the calculations of NBmethy and Scheraga2for D2O and the previous result^^-^ for HzO was then the main objective of this work. I n addition, the experiments of Buijs and Choppin on liquid HzO were repeated with more precise temperature control.
3723
1
I
.9
0.2 0.I
I /
OB
1.0
1.2
1.4
1.6
;1.
Wovelength (Microns) Figure 1. Near-infrared spectra of liquid HzO and of liquid DzO a t various temperatures.
Apparatus and Procedures A Cary Model 14 spectrophotometer equipped with thermostated cell holders was used to obtain the spectra of solid and liquid HzO and DzO. Most of the data were obtained using matched 1-cm. infrared quartz cells. Investigation of the shape of the much more intense OH (and OD) stretching overtone bands, which was necessary to obtain background contributions, was done using matched 1-mm. quartz cells. A calibrated thermistor and resistance bridge was used to monitor the temperature of the cells. The temperatures reported are precise to *0.1". Water was purified by distillation. Analysis for ionic impurities was carried out using conductivity measurements, Deuterium oxide was obtained from the Atomic Energy Commission, Oak Ridge, Tenn. The reported isotopic purity of 99.7% was verified by density and spectrophotometric measurements. The DzO and HzO solid samples were prepared by freezing the liquid in suitable plastic tubes contained in an evacuated vessel. The resulting billets of ice were then shaped with a razor blade to fit a copper tube which had been cut on a lathe to the length desired, usually 1 or 2 cm. The ends of the ice billet were polished down to the ends of the tube by rubbing on manila paper towels covering a flat surface. Polishing of the faces of the billets just before they were inserted into the cell holder (maintained at - 8") eliminated light scattering from condensation. With careful handling, reproducible spectra with low background
due to light scattering were observed for both solid HzO and D20. The cell compartment of the spectrophotometer was purged with nitrogen.
Results The spectra of liquid H 2 0 and D2O at three different temperatures are shown in Figure 1 while Figure 2 shows the D2O and H2O ice spectra. Carbon tetrachloride was the reference for the liquid samples and air for the solids. The procedure employed to analyze the spectra was that suggested by Buijs and C h ~ p p i n . ~ Absorbances were read from the HzO liquid spectrum at 1.16, 1.20, and 1.25 p , these wave lengths representing the assumed absorption peaks4 of the unbonded water molecules, the species having one hydrogen bond, and those with two hydrogen bonds, respectively. There are, of course, smaller contributions to the absorbance a t each of these wave lengths from overlap of the bands of the other species. The corresponding peak absorbances in D2O were a t 1.562, 1.62, and 1.69 p . The temperature dependence of the band shapes, particularly the sharpening of the peaks a t 1.16 p for H 2 0 and at 1.562 p for D2O with increasing temperature, leading to their assignment as the peak absorbances for the unbonded species, are shown in Figure 1. The peaks a t 1.25 and (7) D. F. Hornig, J. Chem. Phys., 40, 3119 (1964). (8) K.Buijs and G. R.Choppin, ibid., 40,3120 (1964).
Volums 69,Number 11 Novmbm 1966
M. R. THOMAS, H. A. SCHERAGA, AND E. E. SCHRIER
3724
HzO. In the middle temperature region the contribution of the 1.93-p band to the absorption at 1.69 p is about 36% and at 1.56 p, about 14%. The over-all uncertainty in the background corrections waa estimated to be 1 5 % . These data were treated by the method of Goldstein and Penner.6 The following equations may be used to calculate the concentrations of each species from the spectrum of H20 (or D20)at the various temperatures
1.3
1.1
-
+ = E1 CZOCO + ez'C1 + c2C2 = E2 ea°Co + ea'Ci + = Ea co + Cl + = 1 +
0.9 -
E~OCO ~1lCl
1.0
4)
0 C 0
ea2C2
08-
az
a
el2C2
H20 ice
c 2
0.7-
08
1.0
1.2'
1.4
1.6
1.8
I
Wavelength (Microns)
Figure 2. Spectra of HzO ice and D20 ice at - 8 ' ; path length, 2 cm.
1.69 p, for H 2 0 and D20, respectively, are most readily seen in the ice spectra in Figure 2. Absorbances were obtained for the wave lengths of interest at seven different temperatures for H2O and nine temperatures for DzO in the range 7.0-82.5'. Corrections to these raw data are necessary because of the large contribution of the overtone band at 1.45 p for HzO and at 1.93 p for D 2 0 to the long wave length side of the respective bands under investigation. Our studies of this overtone band for H2O supported the conclusion of Buijs and Choppin4 that the lower portion of the short wave length side of the overtone band may be expressed as the sum of exponentials. A similar conclusion could be drawn from experiments on D2O. For H20, the contribution of the background to the total absorption at 1.25 p in pure water in the midtemperature range is approximately 50%; at 1.16 p the contribution drops to 20%. For D20 the corresponding contribution is less since the overtone band is more separated from the band under consideration than for The Journal of Physical Chentietry
(1)
Here, El,E2, and Ea are the gross molar extinction coefficients (corrected for background absorption) measured at the wave lengths mentioned above, where the unbonded, one-bonded, and two-bonded species are presumed to have their peak absorbance. The e; terms are extinction coefficients for the individual species, i = 0, 1, 2, signifying the number of intact hydrogen bonds, and j = 1, 2, 3, designating the wave length region where the absorbance of zero-, one-, or two-bonded species is assumed to be maximal. The C terms are the mole fractions of the various species. To use these equations in the calculation of the concentrations of the various species at the different temperatures, the following hypotheses are employed. The extinction coefficients el2, ez2, and eg2 are calculated, in each case, from the spectra of H 2 0 and DzO ice. I t is aasumed4 that el1 and €2 are of equal magnitude since the band for the singly bonded species may be symmetrical. The sharpness of the band for the unbonded species permits the assumption that e3O is negligible. The extinction coefficients elo, e20, el1, and ezl and the three concentrations thus remain unknown at each temperature. A least-squares procedure for fitting the four unknown extinction coefficients and 3n unknown concentrations of the hydrogen-bonded species at n different temperatures was used in conjunction with the CDC-1604 computer at the Cornel1 Computing Center. Since it is assumed in this treatment that the extinction coefficients of the various species do not vary with temperature, the selection of a sufficiently large number of temperatures serves to determine all the variables. The estimated over-all uncertainty in the final concentrations of the various species, taking into account errors of fit and the uncertainties in the background corrections, is f7%. Tables I and I1 show the extinction coefficients obtained from the data for H 2 0 and D2O ice (Le., el2, ez2,
NEAR-INFRARED STUDYOF HYDROGEN BONDING IN HzO AND DzO
3725
€2) and also those calculated in the fitting procedure for the various HzOand DzOspecies. ~
~
Table I: Molar Extinction Coefficients"for H2O Species €1"
e0 a0
19.06 1.25
€11
0
6*1
4.45 14.03 4.45
€1'
€3'
1.33 5.78 8.97
;I 0.20
c Table 11: Molar Extinction Coefficients" for DpO Species €10 €20 €80
9.27 1.10 0
€I1
1.85 7.00 1.85
0.91
€12
g2 3.50
4.88
€3'
0.1
0
I
I
10
I
'
20
I
30
I
I
50
I
80 Temperature, *C
40
I
70
BO
I
90
Ib
Figure 3. Fraction of hydrogen bonds unbroken as a function of temperature for H2O: V,Goldstein and Penner6; A, Buijs and Choppin*; 0,NBmethy and Scheragaa; 0, this work.
Discussion The mole fractions of the various species, calculated by the fitting procedure from eq. 1, are given for HzO in Table 111and for DzOin Table IV. The last column in each table gives the fraction of hydrogen bonds remaining unbroken a t each temperature. This number is equal to Cz (1/2)C1.
+
Table III : Mole Fractions of Hydrogen-Bonded Species for H20 at Various Temperatures t,
oc.
12.5 32.0 41.3 54.8 68.2 73.4 82.5
co
CI
cz
CE bonds unbroken
0,243 0.296 0.320 0.357 0.391 0.406 0.430
0.360 0.374 0.379 0.384 0.386 0.384 0.381
0.397 0.330 0.301 0.259 0.223 0.210 0.189
0.577 0.517 0.491 0.451 0.416 0.402 0.380
Table IV : Mole Fractions of Hydrogen-Bonded Species for D20 at Various Temperatures 1,
oc.
7.0 13.8 21.0 28.1 37.8 51.3 60.5 70.7 80.2
co
c1
cz
CH bonds unbroken
0.232 0.241 0.262 0.282 0.312 0.357 0.385 0.417
0.396 0.398 0.402
0.372 0.361 0.336 0.308 0.276 0.241 0.210 0.183 0.162
0.570 0.560 0.537 0.513 0.482 0.442 0.413 0.383 0.357
0.444
0.410
0.411 0.401 0.405 0.399 0.390
The fraction of hydrogen bonds unbroken for HzO as a function of temperature is plotted in Figure 3, along with the experimental results of Buijs and Choppin4and of Goldstein and Penner5 and the values obtained in the theoretical treatment of NBmethy and Scheraga.8 The results of this investigation fall midway between those of Buijs and Choppin4 and Goldstein and Penner.5 If it is assumed that the limits of error on their calculated values are the same as those given here (*7%), the sets of data are in agreement. In comparing the results, further discussion of the assumptions may be useful. In all the investigations, it was assumed that the extinction coefficients for the various species were independent of temperature (in one in~estigation,~ over a 200" range). This may be only a crude approximation, but the variation of intermolecular potentials and hydrogen-bond lengths and configurations with temperature is generally unknown. The method of assigning the unknown extinction coefficients to the different water species differed in the various studies. Goldstein and Penner5 and the present investigators used sets of optical densities at various temperatures to obtain both the unknown extinction coefficients and the mole fraction of the various species a t each temperature. Buijs and Choppin4obtained the unknown extinction coefficients by using absorbances of aqueous salt solutions a t high salt concentrations together with data obtained at various temperatures for pure water. While it is not clear from their paper exactly how they combined this information to obtain the unknown extinction coefficients, the neglect of possible ion-dipole interactions in the use of data from concentrated salt solutions may be a serious drawback Volume 69, Number 11 November 1966
M. R. THOMAS, H. A. SCHERAGA, AND E. E. SCHRIER
,3726
Y
a0
'
o
Temperature, *C
Figure 4. Fraction of hydrogen bonds unbroken as a function .of temperature for DzO: 0, NBmethy and Scheragaa; 0, this work.
to their method of calculation. Acknowledging these limitations, the agreement between our results and those of Buijs and Choppin4 for the over-all set of extinction coefficients and the agreement of all investigators as to the fraction of hydrogen bonds unbroken at a given temperature for HzO is satisfactory and may indicate that the above-mentioned approximations are of secondary importance in the over-all procedure. It should also be recalled that Goldstein and Penner6 analyzed a different set of spectral bands than the other investigators.
The Journd of Phyaicd C h a r y
These results may be compared with the theoretica values of Ndmethy and Scheraga.a Although their model dealt with five water species, the fraction of hydrogen bonds unbroken has the same meaning as in the experimental studies since the total number of possible hydrogen bonds is the same in each case. The general agreement of the data within the limits of error may be noted, as well as the comparable trends with increasing temperature in the experimental and theoretical results. ~ ~ The dependence of the fraction of hydrogen bonds unbroken on temperature for DzO is given in Figure 4. In this figure, the results of the present study are compared with those calculated by Ndmethy and Scheraga.2 The good agreement for both the values and the trend with temperature is again noteworthy. The differences between the experimental and theoretical values are about the same for DzO as for HzO and are approximately within the limit of error of the spectroscopic method. This is significant in view of the fact that the band shapes, background corrections, and the assigned extinction coefficients for DzO differed considerably from those for HzO.
Acknowledgment. We wish to t'hank Mrs. Marcia Pottle for her help in setting up the computer program for the numerical computations.
