Solute Effect on Dielectric Properties of D20 and H20
The Journal of Physical Chemistry, Vol. 82, No.
1, 1978 109
Molecular Motion and Structure of Solutions of Triethylenediamine in H20 and D20 as Studied by Dielectric Relaxation Measurements' Udo Kaatze DrMes Physikalisches Institut, Universitaet Goettingen, 0-3400Goettingen, West Germany
and Wen-Yang Wen* Jeppson Laboratory, Chemistry Department, Clark University, Worcester, Massachusetts 0 16 10 (Received May 3 I , 1977)
The complex dielectric constants of solutions of triethylenediamine (TED) in HzO and D20 at different concentrations have been measured at 9-12 frequencies between 1.8 and 40 GHz at 25 "C. Various relaxation functions were fitted to the experimental data to yield the static dielectric constant and principal dielectric relaxation time of the solutions. It, is found that the staT,ic dielectric constant of the solvent is enhanced in both HzO and DzO solutions. There seems to be no isotope effect in this enhancement. Another result is that the dissolved TED molecules slow down the reorientational motion of surrounding solvent molecules significantly. A small but definite isotope effect in the relative molal shift of the principal dielectric relaxation time emerges.
Introduction For some years in the past, research workers in the field of water and aqueous solutions thought that the degree of the structuredness of liquid D20 is greater than that of liquid HzO when the two liquids are compared a t the same temperature and p r e s s ~ r e . ~ Recent -~ inve~tigations,j-~ however, seem to cast doubts on this viewpoint. The degree of structuredness of the two isotopic liquids may, instead, be the same. Many physical proper tie^,^^^ which seem t o indicate that liquid DzO is more structured than HzO can be reinterpreted to yield a different conclusion. This is based on the fact that DzO has greater moments of inertia and a lower zero-point energy than HzO, and that the energy levels of DzO are more crowded than those of
Hz0.627 In this context, we consider it worthwhile to examine the effect of a solute on the dielectric properties of H20 and DzO, since these properties seem to reflect the short-range molecular interactions and dynamics of solvent water sensitively. To maximize the sensitivity, the solute used for this type of study should have a large effect on the dielectric properties of water. We have chosen triethylenediaminez6(TED) since Pottel and Kaatzes have investigated the dielectric relaxation of HzO solutions and found that the principal relaxation time of water increases nearly 46% when this compound is added to it to form a 1 M solution. In addition, Wen and his co-workers have investigated the viscosity and apparent molal volume^,^ and also proton chemical shifts of water" in aqueous TED. The results of these studies suggest a large structurepromoting effect of the solute. In the work of Pottel and Kaatze on HzO solutions, the concentrations investigated were rather high (1,2, and 3 M). It seems, therefore, necessary for us to extend the measurements to lower concentrations. In addition, we have recalculated the former data since graphical plots had been used for the inter- and extrapolations.
Experimental Section 1. Materials. TED supplied by Matheson Coleman and Bell Co. was purified by recrystallizations from ether. After two recrystallizations, the compound was dried by heating at 60 "C for 2 h and then stored over phosphorous pentoxide in a vacuum desiccator for 1week before use. Liquid DzO, claimed to be 99.75% pure, was obtained from Merck Co. and used without further purification. The dc 0022-3654/78/2082-0109$01 .OO/O
conductivity of the neat DzO was smaller than 2 X lon5 0hrn-l cm-' while that of the pure HzO used was smaller ohm-l cm-l. than 2 x The pH and pD values were determined by a p H meter using an Ingold glass electrode calibrated with standard pH buffer solutions and employing the following formula'l pD = pH (meter reading) + 0.40 in the case of D 2 0 solutions. The ionization constant of the monoprotonated species of TED in HzO solution at 25 "C is pK1 = 8.60.1z313From the measured pH data and pK1 value it follows that the concentrations of ionic species (TED.H+ and OH-, respectively TED-D' and OD-) were less than about M in all solutions, since all pHs were above 11. 2. Measurements. The complex dielectric constant e,,,@)
= e ' @ ) - iEtot"(V)
of the solutions has been determined a t 9-12 frequencies between 1.8 and 40 GHz. The measurements were performed in the frequency domain using the inteferometric transmission method as described in ref 14. The frequency u was determined and kept constant during the measurement with an uncertainty of less than 0.1%. Imperfection of the apparatus, uncertainty in measurements, and temperature fluctuation of the solution resulted in an estimated error of less than 1 and 1.5% in the values of t'(u) and tto('(u), respectively. With some frequencies, however, the uncertainties are a little greater but do not exceed 2%. In general, the measured tb?(u) values contain two parts but only the part due to polarization processes is of interest here. The dielectric constant t ( u ) due to dielectric polarization processes only has been calculated according to e ( v ) = etot(v)
+ 2ia/v
(1)
where 2iulu is the contribution due to ion drift. The ionic conductivity of the solutions has been measured with a radio-frequency admittance bridge a t 5 and 20 MHz. The correction term 2iulu in eq 1 is very small (less than 5% of tbot(u)) in this case, because u is less than 4.5 X lo4 ohm-' cm-l with all solutions. 3. Treatment of Data. Three different relaxation functions R(u)reflecting a continuous spread of relaxation times were fitted by a non-linear least-squares fitting procedure to the measured data in order to describe them 0 1978 American Chemical Society
analytically. These functions are the “Cole-Cole” function,15 the “Davidson-Cole” function,16and the “Frohlich” function.17 It turned out that the Davidson-Cole function is less appropriate with these solutions. However, good fits are obtained with the other two functions. The Cole-Cole function is given by
Rc(v) = E-C
+
1+
ESC - E-C (2irvTc)(l-hC)
80
I
\\.. 75
I
I
I
I
I
$ TED in H20 f TED in D20 y’”. 4 dioxane in H2O \P.., p\;,..*,,, f pyrazine and other a\ , non-ionic,nearly %,,”.,.,. spherically shaped \\\?”.....,,, solutes -
k..
70 -
65 -
(2)
\\e
w“
’’...$,,
25OC
RF(v)= RFf(v) - l’RF’’(u) where
0
I
I
I
I
I
I
005
01
015
02
0.25
03
035
V
Figure 1. Plot of the static dielectric constant, E,, vs. the solute volume fraction, v, for some nonionic, nearly spherically solutes in water. The dioxane data are from ref 18 and 19, while the pyrazine and other data are from ref 8 and 20.
The values of the variance
(4) obtained with these two functions are nearly identical. The parameter values of Rc and RF found for the solutions and pure solvents are shown in Table I. With both functions the principal relaxation time, TC and T F , respectively, is defined by the frequency of maximum for E ” ( Y ) ,
Results and Discussion 1. The Static Dielectric Constant. The values of the static dielectric constant of the two pure solvents are nearly identical (see Table I). E , values of the TED solutions are plotted vs. the volume fraction u of the solute in Figure 1. These E , values are averages obtained by E, = 0.5(t,c + t , ~ ) .The upper limit of the respective error bar in Figure 1 refers to the values E,C obtained by application of the R&) function, while the lower limit indicates the corresponding E,F value as extrapolated by use of the R ~ v ) function. For comparison E, values of aqueous solutions of other nonionic nearly spherical solutes are added in the E , vs. u plot. With solutions of dioxane the error bars refer to the spread of the values found by low frequency measurements of different authors. With the other solutions the uncertainty is again due to extrapolations of
high frequency data E ( Y ) according to different R(v) terms. In addition, the dependence of E ,and u according to an analytical mixture formula, which is discussed in detail in ref 21, is displayed in Figure 1. As shown in Figure 1, the E, values of the TED solutions are greater than the values of aqueous solutions of other partly hydrophobic nonionic solutes which can form hydrogen bonds with the solvent as the TED molecule can. This enhancement of cs for TED solution increases with increasing solute concentration. Within the limits of experimental error there seems to be no difference in the enhancement between the HzO solutions and the corresponding DzO solutions. Due to different effects the c, values may be influenced by the presence of the ionic species TED-H’ and OH- or TED.Df and OD-, respectively. These effects may include a kinetic depolarization p h e n ~ m e n o ndielectric , ~ ~ ~ ~ ~saturation of the solvent around the ions, the Debye-Falkenhagen effect,24 and induced dipole moment in the monoprotonated or -deuterated TED. However estimations show that the reduction or enhancement of the cs values on grounds of each of the different effects is smaller than the experimental error. So we may conclude that the static dielectric constant of the water around TED molecules is substantially enhanced with respect to the pure water value. This result is unique in so far as such a distinct enhancement has not been found with the static dielectric constant of aqueous
The Journal of Physical Chemistry, Vol. 82, No. 1, 7978
Solute Effect on Dielectric Properties of D 2 0 and H20
10
0
0.2
OL
0.6
08
10
12
m (mo1/55 5mol solvent) Figure 2. Plot of the relaxation time ratio, T ~ / T ? ,vs. solute molality , and D20 solutions. m for TED in HO
solutions of other organic molecules up to now. Within the limits of experimental error there is no isotope effect in the enhancement of the E , values. The finding that the static dielectric constant is likewise enhanced in the solutions of the two isotopic solvents together with the fact that the molecular dipole moments of H20 and DzO are nearly identical in the gaseous state may be taken to indicate that in the time average there is no (or a t most only a small) isotope effect on the short-range molecular interactions of the two solvents around the solute. The same statement on the time average of the short-range molecular interactions holds for the pure isotopic liquids, since the molecular dipole moments of D 2 0 and H20 in the pure liquids (at the same temperature and pressure) appear to be also almost identical.25 2. The Principal Dielectric Relaxation Time. As can be seen from Table I, the values of the principal dielectric relaxation time TC as obtained by use of the Cole-Cole function agree very well with the corresponding values T F as obtained by applying the Frohlich function. The 7c values of solutions normalized to the TCO value of the pure solvent are plotted against solute molality m for the less concentrated H20 and DzO solutions in Figure 2. With both series of solutions, the ratio Q/TCO increases linearly with increasing molality up to m of about 0.7 mo1/55.5 mol solvent. However, the slopes of the two lines are different. The relative molal shift of the principal dielectric relaxation time, Bd, defined by
(5) is found to be (0.36 f 0.02)(55.5 mol of solvent/mol) with the H20 and (0.42 f 0.02)(55.5 mol of solvent/mol) with the D 2 0 solutions. The large B d values, together with the enhancement of the static dielectric constant of the solvent around the TED molecule, clearly reflect the particularly strong promotion of solvent structure around this solute. The small but substantial isotope effect in the Bd values indicates that the microdynamical behavior of the solvent is differently changed when TED is added to D20 or to HzO.
B,
= (l/ko)(d%/dm)rn-tO
111
The TC (and q )values are extracted from the measured dependence of E on frequency by averaging on different solvent regions. Thus the B d values depend on both the extent of these different regions and the relaxation times by which the regions are characterized. For this reason molecular mechanisms cannot be inferred from the isotope effect in the Bd values without further assumptions. Independent of molecular interpretation, however, it seems noteworthy that a substantial isotope effect emerges in the Bd values of the two series of solutions. It is common practice, for example, with measurements of the deuteron magnetic relaxation rate, to study the dynamics of D20 around solutes and to assign the data of relative molal shift of the relaxation time obtained in these solutions t o aqueous systems. However the results of our dielectric relaxation measurements show that properties of the reorientational motion found in D 2 0 solutions cannot be attributed directly to H20 solutions.
Acknowledgment. We thank Professor Henry S. Frank for suggesting this problem and acknowledge Professor R. Pottel for his interest in this work and helpful discussions. W.-Y. Wen expresses his deep appreciation to Professor Pottel, Dr. Giese, and others of the Drittes Physikalisches Institut der Universitat Gottingen for the kind assistance generously rendered to him during his stay. References and Notes (1) The experimental work was carried out at the Drittes Physikalisches Institut der Universitat Gottingen during a stay of W.-Y. Wen in Gottingen. (2) E. A. Whalley, "Proceedings of the Conference on Thermodynamics and Transport Properties of Fluids", London, 1957. (3) G. Nemethy and H. A. Scheraga, J. Chem. Phys., 41,680 (1964). (4) E. M. Arnett and D. R. McKelvey, "Solvent-Isotope Effect on Thermodynamics of Nonreacting Solutes" in "Solutes-Solvent Interaction", J. I.Coetzee and C. D. Ritchie, Ed., Marcel Dekker, New York, N.Y., 1969. (5) A. H. Narten, M. D. Danford, and H. A. Levy, Discuss. faraday SOC., 43, 97 (1967). (6) H. S.Frank in "Water, A Comprehensive Treatise", Vol. 1, F. Franks, Ed., Plenum Press, New York, N.Y., 1972, Chapter 14. (7) 6. P. Chakraborty and J.-L. Lin, J. Solution Chem., 5, 183 (1976). (8) R. Pottel and U. Kaatze, Ber. Bunsenges. Phys. Chem., 73, 437 (1969). (9) W.-Y. Wen, N. Takeguchi, and D. P. Wllson, J . Solution Chem., 3, 103 (1974). (10)Y. C.Hsieh, P. T. Inglefield, and W.-Y. Wen, J . Solution Chem., 5, 351 (1974). (11) P. K. Glasoe and F. A. Long, J . Phys. Chem., 64, 188 (1960). (1 2) "Houdry DABCO, Triethylenediamine", Air Products & Chemicals, Inc., Wayne, Pa., reprinted May 1971. (13) J. W. Larson, G. L. Bertrand, and L. G. Hepler, J . Chem. Eng. Data, 11, 595 (1966). (14) U. Kaatze, Adv. Mol. Relaxation Processes, 7, 71 (1975). (15) K. S.Cole and R. H. Cole, J . Chem. Phys., 9, 341 (1941). (16) D. W. DavidsonandR. H. Cole, J . Chem. Phys., 18, 1484(1950). (17) H. Frohlich, "Theory of Dielectrics", Clarendon, Oxford, 1958, p 94. (18) G. Akerlof and A. 0. Short, J . Am. Chem. SOC.,58, 1241 (1936). (19) F. E. Critchfield, J. Am. Chem. SOC.,75, 1991 (1953). (20) R. Pottei, D. Adolph, and U. Kaatze, Ber. Bunsenges. Phys. Chern., 79, 278 (1975). (21) R. Pottel and U. Kaatze, Adv. Mol. Relaxation Processes, to be published. (22) L. Onsager, Abstracts, 160th National Meeting of the American Chemical Society, 1970. (23) J. 6. Hubbard, L. Onsager, W. M. van Beek, and M. Mandel, Proc. Nafl. Acad. Sci. U.S.A., 74 401 (1977). (24) H. Falkenhagen, "Theorie der Elektrolyte", Hirzel, Stuttgart, 1971, Chapter 9. (25) K. R. Srinivasan and R. L. Kay, J . Chem. Phys., 60,3645 (1974). (26) The official IUPAC) nomenclature for triethylenediamine is 1,4diazabicyclo[2.2.2]octane.
