J . Phys. Chem. 1986, 90, 5464-5469
5464
ferences in structure between Se0,- and Se032-and between CO< and C0,2- are small. Acknowledgment. We thank H. Corfitzen for technical assistance and T. Johansen for skillful operation of the Risra linac. (24) Henglein, A. Radiat. Phy's. Chem. 1980, 15, 151.
We appreciate the discussions of the work with J . Holcman. U.K.K. thanks the Danish Natural Science Research Council for financial support. Registry No. Se0,2-, 14124-67-5;SeO:-, 14124-68-6;ses', 4002674-2; SeOC, 56348-13-1; HSeO?-, 14998-57-3;H,O, 7732-18-5; OH, 3352-57-6:0-, 14337-01-0.
Dielectric Relaxation in Aqueous Solutions of Urea and Some of I t s Derivatives U. Kaatze,* H. Gerke, and R. Pottel Drittes Physikalisches Institut, Universitat Gottigen, 0-3400 Gottingen, West Germany (Received: February 26, 1986; I n Final Form: June 24, 1986)
The complex dielectric spectrum has been measured at 25 "C in the frequency range between 1 MHz and 40 GHz for 1 and 2 M aqueous solutions of urea and the following derivatives: methylurea, N,N- and N,N'-dimethylurea, N-propyl- and trimethylurea, and N-butyl-, N,N'-diethyl-, and tetramethylurea as well as acetamide and methylacetamide, thiourea, and N,N'-dimethylthiourea. Different relaxation functions based on models of the solutions have been fitted to the measured spectra. The results of this analysis are discussed to show (a) that around urea and thiourea molecules the number of water molecules with a relaxation time different from that of pure water is unusually small; (b) that with respect to the hydration properties the alkyl derivatives of urea form two groups, namely the molecules with n-alkyl chains and the other ones; (c) that the derivatives, which can exist in different limiting forms, seem to preferably adopt a cis or cis-cis conformation,respectively; and (d) that the reorientation time of the solute molecules strongly depends on the shape of the rotating molecule.
1. Introduction The solution behavior of many organic solutes in aqueous mixtures is largely determined by hydrophobic hydration of inert groups. A detailed knowledge of the effect of hydrophobic hydration is therefore of great importance for our understanding of the solute/solvent and solvent/solvent interactions in many aqueous systems, including solutions of biological significance. Hydrophobic hydration finds an obvious expression in the values of the so-called B coefficient of parameters reflecting molecular dynamics of the solution. Among these parameters is the principal , B coefficient dielectric relaxation time of the solvent water, T ~ the of which is usually denoted by Bd and is defined by the expression 1 7, m--0
In this equation T, is the relaxtion time of pure water and m is the molal concentration of solute. If the hydration properties of different molecules or ions are compared with one another, a pronounced tendency in the Bd values is found to increase with increasing hydrophobic character of the solute particle. Within the series of tetraalkylammonium ions, for instance, the Bd coefficient steadily increases from the negative value of -0.04 (mol/kg)-' for the hydration water of the small ammonium ion' up to 0.88 (mol/kg)-' for that of the tetrabutylammonium ion2 A more detailed study of the effect of hydrophobic hydration, however, shows that factors other than the number of aliphatic groups may be important in influencing the water around organic solutes. Two examples suited to illustate this finding are presented in Tables I, where Bd values for pairs of different organic cations are compared with one another. The effect of the n-octylammonium ion on the dielectric relaxation time of the solvent water is substantially more pronounced than that of the tetraethylammonium ion, though both cations have the same chemical composition. The tetrapropylammonium ion, (1) Kaatze, U. Ber. Bunsenges. Phys. Chem. 1973, 7 7 , 447. (2) Kaatze, U.; Wen, W.-Y. J . Phys. Chem. 1977, 81, 177. (3) Kaatze, U.; Limberg, C. H.; Pottel, R . Ber. Bunsenges. Phys. Chem.
1974, 78, 555. (4) Giese, K.; Kaatze, U.; Pottel, R. J . Phys. Chem. 1970, 74, 3718.
TABLE I: Relative Molal Shift Bd' in the Principal Relaxation Time of Solvent Water as Induced by Cations for Two Pairs of Different Alkvlammonium Ions with n , Methvl GrouDs' org cation n, Bd', (mol/kg)-'
CH,(CH,),"3 (CH3CH2)4N (CH3CH2CH2)4N (CH2)6N(CH2)6
8 8 12 12
0.42 0.29 0.74 0.43
"The Bd' values have been calculated from Bd data of aqueous salt solutions2*' by using the additivity rule Bd = B,' + Ed- and the following values for the contributions of anion^:^ Ed-(&-) = -0.03 (mol/ kg)-'; Bd-(Cl-) = -0.01 (mol/kg)-'.
on the other hand, causes a distinctly higher enhancement in the T~ value of the solution than the 7-azoniaspiro[6.6]tridecaneion, although the number of aliphatic groups of the two cations is identical. Among the factors which are probably suited to induce special hydration properties may be the presence or absence of terminal methyl groups, the flexibility of the solute particle, its ability to correspond to the water structure, and the overall size and shape of the organic solute molecule or ion. Since the relative importance of these various factors is not generally known, it seemed of interest to use to perform a comparative study of the hydration properties of organic molecules which differ from one another in the number of affixed alkyl groups but also in the relative position of these groups with respect to the original molecular structure. We used urea as the primary constituent for various reasons, especially, however, since urea itself shows unusual solution behaviors5 Previous dielectric studies6%'on aqueous urea solutions suggest a strikingly small number of hydration water molecules per molecule of solute,6 though no solute association effects seem to be ( 5 ) Franks, F. In Water, a Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 2, p 1. (6) Pottel, R.: Adolph, D.; Kaatze, U. Ber. Bunsenges. Phys. Chem. 1975, 79, 278. (7) Grant, E. H.; Keefe, S . E.; Shack, R. Ads. Mol. Relax. Processes 1972, 4. 217. (8) Biidacker, G. Diplom Thesis, University of Gottingen, 1974. (9) Finer, E. G.; Franks, F.; Tait, M . J. J . Am. Chem. SOC.1972, 94,4424.
0022-3654/86/2090-5464$01.50/00 1986 American Chemical Saciety
The Journal of Physical Chemistry, Vol. 90, No. 21, 1986 5465
Dielectric Relaxation in Aqueous Solutions
TABLE II: Survey of the Solutes BS well as Concentration Data of the Solutions” solute
formula
urea
HZNCONH,
methylurea ethylurea N,N-dimeth y lurea N,N’-dimethylurea
H2NCONHCH3 H2NCONHC2HS HzNCON(CH3)Z H3CHNCONHCH3
N-propylurea trimethylurea N-butylurea N,N’-diethylurea tetramethylurea acetamide methylacetamide thiourea N,N’-dimethylthiourea
H2NCONHC3H7 H3CHNCON(CH3)2 H2NCONHCdHg H&2HNCONHC2H5 (HpC)2NCON(CH3)2 H2NCOCH3 H3CHNCOCH3 H2NCSNH2 H3CHNCSNHCH3
4 c = solute molarity; c, = molarity
c,
cw,
m,
mol/L
mol/L
mol/kg
u
1.o 2.0 1.o 1.o 1.o 1.o 2.0 1.o 1.o 1.o 1.o 1.o 1.o 1.o 1.o 1.o
52.94 50.60 5 1.94 51.15 5 1.22 50.84 46.45 50.10 50.02 49.27 49.26 48.98 52.36 51.89 52.38 50.40
1.05 2.19 1.07 1.09 1.08 1.09 2.39 1.11 1.11 1.13 1.13 1.13 1.06 1.Ol 1.06 1.10
0.046 0.097 0.064 0.078 0.077 0.084 0.163 0.097 0.099 0.113 0.113 0.118 0.057 0.065 0.060 0.092
of solvent water; m and u = molal concentration and volume.fraction of solute, respectively. All data refer to
Dielectric spectroscopy on solutions of various derivatives of urea are expected to cast some light on specific features of hydrophobic hydration properties and also on the solution behavior of the primary molecule itself. For the latter reason measurements on solutions of some other related compounds, especially thiourea and acetamide, have been included in this study.
2. Experimental Section 2.1. Solutions. A survey of the solutes is given in Table I1 where besides the structural formula of the solute molecules some data for the aqueous solutions are also given. The compounds have been purchased from various companies (Merck, Darmstadt, West Germany; EGA, Steinheim, West Germany; Ventron, Karlsruhe, West Germany; Alfa, Danvers, MA). With a few exceptions, the solutes were quoted to be 98% pure or better. All solutes were used without additional purification. The solutions were prepared by weighing appropriate amounts into suitable flasks. The water was deionized by bed ion exchange and distilled and sterilized by UV radiation. Aqueous solutions of urea and its derivatives are suspected to change their properties by disintegration of solute molecules. Repeated recording of data, however, led to the conclusion that-within the limits of experimental error-the dielectric properties of the solution were independent of time. A similar result had been obtained previously, when the ultrasonic absorption coefficient and the sound velocity of 2.5 and 4 M aqueous urea solutions were found to remain unchanged during a period of even half a year.s 2.2. Permittivity Measurements. Between 1 MHz and 40 GHz the complex relative permittivity e ( u ) = e’(u) - ie”(v)
was determined by spot frequency measurements. Harmonically alternating weak electric fields of frequency v were applied to observe the dielectric polarization response. Three different frequency domain methods have been used. At microwave frequencies ( u > 1 GHz), where the dielectric relaxation of water occurs, a traveling-wave method was applied. The wave transmitted through a liquid-filled circular cylindrical waveguide was balanced against a reference wave by using a double-beam interferometer Four microwave bridges consisting of standard coaxial line components or waveguide devices were used. At lower frequencies, where the dipolar solute molecules are expected to also contribute to the complex dielectric spectrum, the transmission coefficient of an appropriate cell has been observed at various frequencies between 1 MHz and 1 GHz.” A commercial vector voltmeter (Rohde & Schwarz Type ZPU) has (10) Pottel, R. Ber. Bunsenges. Phys. Chem. 1965, 69, 363. (1 1) Kaatze, U. Mikrowellen Mug.1980, 46. (12) Gottmann, 0.;Dittrich, A. J . Phys. E 1984, 17, 772.
been utilized for this purpose. In addition, by use of a sensitive radio frequency admittance bridge (Boonton 33D/1), input admittance measurements on a special cell filled with the liquid have been performed at seven fixed frequencies between 1 and 100 MHz.I3*l4 With all measurements the temperature was 25.0 f 0.1 OC. Due to ionic impurities some of the solutions showed a small dc conductivity u which was measured in the usual manner at 0.1, 1, 10, and 100 kHz. The less interesting loss a/(27reou) resulting from the drift of ions has been subtracted from the total loss e”(v) according to the relation €d”(V)
= c”(v) - o/(2atou)
(3)
in order to obtain the loss e [ ( u ) originating from dielectric A s V-I m-’). processes only (eo = 8.854 X The experimental error in the measured permittivity values depends on the method used and on the frequency range considered. It may be globally characterized by an uncertainty of f l % in the values of both d ( v ) and e”(u). The error in e’(u) is a little greater at the highest frequencies (Ad/€’ = f 2 % at 20 G H z and f4% at 4 0 GHz) and there is also a smaller accuracy in some e” values (Ad’/d’ = f2% with the transmission coefficient measurements between 1 MHz and 1 GHz, while Ae”/d’ = f 3 % between 1 and 5 G H z and f 2 % between 30 and 40 GHz).
3. Results and Discussion 3.1. Examples of Measured Dielectric Spectra. In Figure 1, a semilogarithmic plot of E‘ and 6‘‘ as a function of the frequency u is presented for the aqueous solutions of N,N’-dimethylurea. Also displayed are the corresponding data for water to show that the curves of the two solutions resemble those of the pure solvent. With all solutions considered in this study, however, three important results can be directly inferred from the measured dielectric spectra. (1) The static permittivity t(0) of the solutions has a higher value than that of water at the same temperature. e(0) increases with solute concentration c. (2) The frequency ( ~ T T ~ ) of - ’ the maximum in the e,J vs. v relation of the solutions is smaller than that of the solvent, ( ~ T T , ) - ’ . (27r~J’ decreases with c. (3) The dispersion (de’ldv < O)/absorption (€4’> 0) region of the solutions extends over a broader frequency band than that of pure water. This latter finding is more clearly demonstrated by Figure 2, where t,J(u) values of a solution of Nfl-diethylurea are displayed over v. Also shown for comparison is a curve of adjusted peak values which correspond to a Debye-type relaxation spectral (13) Muller, S. C. Thesis, University of Gottingen, 1978. (14) Kaatze, U.; Woermann, D. Ber. Bunsenges. Phys. Chem. 1982, 86, 81.
(15) Kaatze, U.; Uhlendorf, V. Z . Phys. Chem. (Wiesbuden) 1981, 126, 151.
5466
The Journal of Physical Chemistry, Vol. 90, No. 21, 1986
Kaatze et al.
X
7
b
8 9 log ( v / Hz I
10
11
Figure 1. Real part e’(u) of the complex permittivity and the negative imaginary part excluding conductivity losses, c?(u) = c”(u) - a/(2acou), plotted vs. frequency Y for waterlS and for a 1 and 2 M aqueous solution of A’,”-dimethylurea at 25 O C . Different methods of measurement are indicated (half-closed symbols, traveling-wave method; closed symbols, transmission coefficient observations; open symbols, input admittance measurements).
function.I6 The reason for the presentation of that curve is the fact that the complex permittivity t w ( u ) of pure water very closely follows the Debye relaxtion behavior,I5 which is characterized by one discrete relaxation time. Expressed by the parameters for the pure solvent (suffix “w”, Figure 1) this spectral function is given by the relation tw(.)
=
tw(=)
+ (CW(0)
-
ew(=))/(l
+ i2avTw)
(4)
In the example displayed in Figure 2 the q“ values of the solution at frequencies below 14 G H z exceed those of the shown Debye curve tD(u). The excess values td”(v) - tD”(u) again show the characteristics of dielectric loss due to relaxation processes. A theoretical model of the dielectric properties of present solutions should therefore consider at least two different orientation polarization mechanisms to be present in the frequency range of measurement. As will be shown below, the dipolar solute molecules-besides the solvent water-also contribute to the measured complex permittivity values. 3.2. Static Permittivities of Solutions and Dipole Moments of Solutes. The idea that the measured dielectric spectra reflect orientation polarization mechanisms of both solvent and solute molecules is strongly confirmed by the values of the static permittivity t(0) of the solution. Due to dilution of the polar solvent and also to internal depolarizing electric fields, the t(0) value of aqueous mixtures of nonpolar solutes decreases with c. The empirical relation t“ = t W ( O ) ( l - 1.2u) has been found to adequately describe the resulting permittivity ern of aqueous solutions of nearly spherically shaped small organic molecules provided the volume fraction v of the nondipolar solute does not exceed a value of 0.3.” With the present solutions of urea and its derivatives, the extrapolated t(0) values are larger than the pure water value ~ ~ ( 0 It) .is therefore a reasonable assumption to interpret the increment At = e(0) - t, as being due (16) Debye, P. Polar Molecules; Chemical Catalog: New York, 1929. (17) Kaatze, U.; Bieler. H.; Pottel. R. J . Mol. Liq. 1985, 30. 101.
Figure 2. Negative imaginary part excluding conductivity losses, c < ( v ) = e”(.) - o/(27reov), of the measured dielectric spectrum of a 1 M aqueous solution of A’,”-diethylurea at 25 O C (e). Also presented is a graph showing dielectric losses eD”(u) due to a Debye-type relaxation with the maximum loss value adjusted (dashed curve). Open circles represent the difference between the measured data and the latter curve.
to orientation polarization contributions of the solute molecules. If this is true, then the electric dipole moment pG which the solute molecules would adopt in the gaseous state can be calculated from the measured A6 data. We use the equation
”(’>’”
_c
to
2
kT
to first relate the molar increment At/c to the dipole moment p of the solute molecules in aqueous solution. NA = 6.02 X mol-’ is Avogadro’s number herein, and k = 1.38 X Nm K-’ is the Boltzmann constant. To derive eq 6 terms t(m)/2tw(0) have been neglected relative to 1 (see Figure 1 for the meaning of the extrapolated high-frequency permittivity E ( = ) ) . The dipole moments p and pG are related to one another according to the expression
+
pc = 3p(t, 2)-’ (7) where t, = 4.3 has been proven empirically to hold for pure water.” It is only briefly mentioned here that the dielectric increment At of aqueous solutions of zwitterionic amino acids can also be sufficiently well described by eq 6 and 7.6s’7 The pG values derived for urea and its derivatives are collected in Table 111. Also given in that compilation of data are pG values which have been estimated from bond rnomentsl9 or directly taken from the literature.20 With the vector addition of the bond moments, it has been assumed that the urea derivatives, like the urea molecule itself,2’ have a completely planar structure. In addition, the values for the bond angles of the urea moleculeZo have been used with all solutes. Some derivatives may show effects of geometrical isomerism as illustrated in Figure 3, where the contributing forms of methylurea and N,N’-dimethylurea are shown. Since the distribution function for the possible configurations is not known, we calculated (18) Hill, N. E. J . Phys. C 1970, 3, 238. (19) Price, A. H. In Dielectric Properties and Molecular Behauiour; Hill, N. E., Vaughan, W. E., Price, A. H., Davies, M., Eds.; Van Nostrand-Reinhold: London, 1969; p 232. (20) Beilsteins Handbuch der Organischen Chemie, drittes und viertes Er@nzungswerk; Springer: Berlin, 198 1. (21) Ormerod, M. B. The Architecture and Properties ofMarter; Fletcher and Sons: Norwich, 1970.
The Journal of Physical Chemistry, Vol. 90, No. 21, 1986 5467
Dielectric Relaxation in Aqueous Solutions
TABLE 111: Values of the Electric Dipole Moment pc, Which the Solute Molecules Would Adopt in the Gaseous State pG (D) acc. to ref 20 or superposition of bond moments pG (D) acc. to trans/ solute c, mol/L eq 6, 7 cis/cis-cis cis-trans trans-trans urea 1.o 3.33 3.34 2.0 3.35 1.o 3.57 3.67 2.73 methylurea 1.o 3.47 3.67 2.73 ethylurea N,N-dimethylurea 1.o 3.11 3.08 N,N’-dimeth ylurea 1.o 3.89 3.93 3.06 2.12 2.0 3.83 N-propylurea 1.o 3.81 3.67 2.75 trimethylurea 1 .o 3.70 3.32 2.47 1.o 3.95 3.67 2.73 N-butylurea N,N‘-diethylurea 1.o 3.93 3.93 3.06 2.12 tetramethylurea 1.o 3.83 3.31 2.11 acetamide 1.o 3.29 3.09 methylacetamide 1.o 3.45 3.32 2.49 thiourea 1.o 3.69 3.6 N,N’-dimethylthiourea 1.o 4.00 4.3 3.3 2.3
TABLE I V Values for the Parameters of the Relaxation Spectral Function Given by Equation 8 and for the BdCoefficient Defined by Equation 1
urea methylurea ethylurea N,N-dimethylurea N,N’-dimethylurea N-propylurea trimethylurea N-butylurea N,N’-dieth ylurea tetramethylurea acetamide meth ylacetamide thiourea N,N’-dimethylthiourea
1.o 2.0 1.o 1.o 1.o 1.O 2.0 1 .O 1.o 1.o 1.O 1.O 1.o 1.o 1.o 1.o
5.4 5.4 3.7 2.9 4.6 4.3 5.8 4.8 4.5 5.0 4.7 4.8 4.7 3.5 4.6 2.6
74.2 69.7 72.6 71.3 71.5 70.8 63.8 69.6 69.5 68.3 68.2 67.8 73.3 72.5 73.0 70.1
8.5 8.9 9.0 9.3 9.8 9.9 12.4 10.0 10.5 10.2 11.1 11.1 9.2 10.0 8.3 9.1
the molecular dipole moment for the forms represented by the figure. Though the evaluation of the experimental data is based on some assumptions, the pG values of the primary molecules as derived from the molar dielectric increments nicely agree with the values taken fro the literature (Table 111). The experimental pG values for the derivatives with additional alkyl groups are close to the values calculated for the cis or cis-cis configuration, respectively, of the solute molecules. It may thus be concluded that in aqueous solution the derivatives preferentially exist in these forms. 3.3. Model Relaxation Spectral Functions. To take into account the above discussed finding that in the frequency range under consideration both the solvent and solute molecules contribute to the complex permittivity values, the dielectric spectra have been analytically represented by the function
(8)
The dielectric part cd(V) of the complex permittivity is thus expressed by a sum of the extrapolated high-frequency permittivity e ( - ) , a first relaxation term with an underlying Cole-Cole relaxation time distribution,22 and a second one with a discrete relaxation time. The former relaxation term describes the orientational motions of the solvent water molecules, which due to the disturbing action of the solute molecules may show a spread in reorientation times. The latter term has regard to orientation polarization contributions to the solute molecules themselves.
0.021 0.034 0.048 0.060 0.048 0.053 0.046 0.033 0.050 0.030 0.055 0.034 0.031 0.054 0.044 0.089
16.1 16.9 18.1 27.4 21.0 27.9 46.3 52.2 36.5 73.0 55.0 36.0 16.5 19.1 18.3 33.0
81.2 83.8 80.6 78.9 77.5 80.3 82.3 78.8 78.1 78.1 78.0 74.7 80.1 80.0 81.6 80.2 H\
c\H3
N-H
0 =C
N-CH,
O=C N-H
N-H
H’
H’ cis
trans
n\/N-CH,
c,n3
N-H
H,
0 = C\ N-H
O=C\ N-H
cis-cis
N-CH,
O=C/ N-CH,
cC13
CCI,
H/
cis-trans
trans-trans
Figure 3. Limiting forms of methylurea and N,N’-dimethylurea.
The values for the static permittivity c(0) are well-known from the measurements (Figure l), and those for ern have been derived from the u values according to eq 5. There are thus four unknown parameters left in the model function, namely the limiting permittivity e ( - ) , the relaxation times T , and T,,, and the quantity h,, which measures the width of the relaxation time distribution. The values for these parameters have been found by fitting relation 8 to the measured dielectric spectra by using a nonlinear leastsquares regression analysis. The results of this procedure are presented in Table IV. Since previous dielectric studies on aqueous solutions of urea6 pointed at an outstanding small number Zh of hydration water molecules per molecule of solute, we also used the relation €d(v)
=
e(m)
+ 1 +- 4 m ) e1
€m
+
~ ~ T U T ,
(22) Cole, K.S.; Cole, R. H.J . Chem. Phys. 1941, 9, 341.
0.03 0.03 0.08 0.13 0.17 0.18 0.21 0.19 0.24 0.21 0.30 0.30 0.1 1 0.20 0.00 0.09
1
+
- €1 ~
~
+ 1e (+0 )i-2 m , €1
T
U
T
~
(9)
to describe the experimental data. This equation is taken as an
Kaatze et al.
5468 The Journal of Physical Chemistry, Vol. 90, No. 21, 1986
TABLE V: Values for the Parameters of the Hydration Model (Equations 9-11) for the Primary Molecules and for Two Other Linear Molecules of Similar Size @ = UJC, solute formula mL/mol Th, Ps Th/7w Zh zh/ urea 2.1 2.9 0.34 11.7 I mol/L 2.2 2.8 0.32 2 mol/L NHzCONH2 43.1 18.0
