9487
J. Phys. Chem. 1992,96,9487-9492 (20) Griffths, R. B. Phys. Reu. 1975,EZ2,345. (21) Griffiths, R. B.; Wheeler, J. C. Phys. Rev. 1970,A2, 1047. (22)Bartis, J. T.;Hall, C. K.Physicu 1974,78, 1. Wheeler, J. C.; Anderson, G. R. J. Chcm. Phys. 1968, 73, 5778. Walker, J. S.;Vause, C. A. J. Chem. Phys. 1983, 79,2660.
(23) Lang, J. C., Jr.; Widom, B. Physicu 1975,8ZA,190. Fisher, M.E.; Sarbach, S. Phys. Reu. Lett. 1978, IZ, 1127. (24)Corrales, L.R.;Wheeler, J. C. J. Chem. Phys. 1989,91,7097.ALSO Corral=, L. R. PLD. Dissertation, University of California, Sen Diego, unpublished.
NMR Study on Dynamics of Water Molecules in Concentrated Aqueous Zinc( I I ) Bromide Solutions at Various Temperatures Toshiyuki Takamuku,+Toshiml Hirano, Toshio Yamaguchi,* and Hisanobu Wakita Department of Chemistry, Faculty of Science, Fukuoka University, Nanakuma, Jonan-ku, Fukuoka 814-01, Japan (Received: July 24, 1992)
The proton spin-lattice relaxation time, the deuteron quadrupole relaxation time, and the proton self-diffusion coefficient in aqueous zinc(I1) bromide solutions with the water to solute molar ratios of 5 and 10 have been determined by the NMR method as a function of temperature. The proton relaxation time has been divided into the intermolecular and intramolecular contributionsof the proton dipole-dipole interaction by using the proton self-diffusion data to derive the translational and rotational correlation times with temperature. The rotational correlation time has also been calculated from the deuteron quadrupole relaxation time. On the basis of the temperature dependence of the translational and rotational correlation times, the dynamics of water molecules and the equilibrium shift of chemical species in the aqueous zinc(I1) bromide solutions with temperature are discussed.
IntrodUCtiO~ Aqueous zinc(I1) halide solutions have so far been investigated for complex formationl-loand chemical structures.11-20Recently, interest has been focused on the structure and properties of aqueous zinc(I1) halide solutions at nonambient conditions like supercooled and glassy states and high temperatures and pressures. The compositions of solute species in glassy aqueous zinc(I1) halide solutions at liquid nitrogen temperature have been revealed from Raman spectrmpic measurements by K ~ M Oand HiraishiZ1and of a 3.72 m aqueous zinc(I1) bromide solution at temperatures up to 573 K and pressures up to 9 Mpa by Yang et aLZ We have made X-ray diffraction and X-ray absorption fine structure measurements2f26on aqueous zinc(11) halide solutions over a wide temperature range (77-413 K)and determined the structures of average complex species in the solutions. Both X-ray diffraction and Raman scattering data on aqueous zinc(I1) bromide solutions have suggested that the following equilibrium shifts take place with temperature: 3[ZnBr2(OH2)2]+ 2H20 + 2[ZnBr3(OH2)]- + [Zn(OH2)612+ (1) 4[ZnBr3(OH2)]-
+ 2H20 + 3[ZnBrJ2- + [Zn(OH2)6]2+ (2)
The equilibria (1) and (2) shift to the right-hand side with decreasing temperature and in the opposite direction with increasing temperature. The equilibrium shifts have been discussed in terms of static microscopic structures of the solutions; when the temperature is lowered, in particular,below the melting point of water, the hydrogen bonds are reinforced in the solutions. Correspondingly, water molecules expelled from the dibromo- and tribromozinc(I1) complexes will be stabilized in the strengthened hydrogen-bond networks, bromide ions will bind easily to zinc(I1) ion. Since water molecules play an important role in the hydrogen-bonded network, it is of great interest to investigate the dynamic behavior of water molecules in aqueous zinc(I1) halide solutions over a wide range of temperature to discuss the equilibrium shifts from dynamic properties of the solutions. To whom comspondence should be addressed. On leave from Aqua Laboratory, Research and Development Division, TOTO Ltd., Nakashima, Kohrakita-h, Kitakyushu 802, Japan.
solution
Zn2+
A B C D
10.64 5.493 9.480 4.867
Br21.28 10.99 18.96 9.734
[H201/ [ZnBrz]
[D201/ [ZnBrz]
5.22 10.1 5.26 10.3
The motions of water molecules in liquid water and in aqueous electrolyte solutions have often been investigated in terms of the spin-lattice relaxation time and the correlation time from NMR relaxation measurements on 'H, 2H (D), and 170nuclei of the water molec~le.~~-'~ The self-diffusion coefficients of water molecules have also been measured by the NMR spin-echo method for electrolyte solutions.37 For concentrated aqueous zinc(I1) chloride solutions, Nakamura et measured the proton self-diffusion coefficient and spinlattice relaxation time as a function of solute concentration and temperature and have concluded that the translational motion of water molecules in the solutions is retarded more rapidly than the rotational motion with decreasing water content. In the present study we have measured the proton selfdiffusion coefficient and the proton and deuteron spin-lattice relaxation times in aqueous zinc(I1) bromide solutions in H20 and D20,with the water to solute molar ratios of 5 and 10 as a function of temperature. The proton spin-lattice relaxation time measured has been divided into the intermolecular and intramolecular contributions of the dipoledipole interaction, from which the translational and rotational correlation times of the water molecule have been estimated as a function of temperature. The rotational correlation of the water molecule has also been derived directly from the deuteron spin-lattice relaxation time. Finally, the translational and rotational motions of water molecules and the equilibrium shifts (1) and (2) with temperature will be discussed in terms of the translational and rotational correlation times obtained. ExperimentalSection preprvrtioa of Sample solutioaa Zinc(I1) bromide (WakoPure
Chemicals, 99.9%) was used without further purification and
0022-3654/92/2096-9487$03.00/0Q 1992 American Chemical Society
9488 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992
Tahmuku et al.
1°1-----1
A B
3.55 3.04
1.11 1.76
TABLE IIk Smootbd Vllecr of thc Row &If-Diffbh Coeffickat, the h t 0 O SpibLattice Rahxatiaa Rate, the ~ u d ~ C O a M b . t i o l l r , u d t h e D c o t c r o a SpbLa#LcCILaunrtbaRatefor Soldom A md C (R= 5) in t k
T e m p w s Rmge ~ 243-333 K T/K l@&/m2 s-' RI,@
t
I
L 3.0 3.5 4.0 4.5 lo3T -'lK-' Figm 1. 'Hself-diffusioncoeficient & for solution A (opened circle) and solution B (filled circle) againat the reciprocal temperature. The solid line comsponds to a VTF-type theoretical curve. Fitted valuw of h0and B are given in Table 11.
dissolved in distilled water to reach the water-&solute molar ratios (R)of 5 and 10. The corresponding heavy water solutions were also prepared by dissolving zinc(I1) bromide in heavy water (ISOTEC Inc., 99.9%). The concentrationsof zinc(I1) ions in the sample solutions were determined by titration of an EDTA standard solution, using Eriochrome Black T as an indicator. The compositions of the sample solutions are given in Table I. NMR Meuwements. Prior to NMR measurements oxygen gas dissolved in the sample solution was remwed by bubbling pure nitrogen gas for 15 min. The sample solution was sealed in a double-walled glass tube, i.e., a usual NMR tube of IO-" diameter with an oval microcell inside. NMR measurements were carried out by using a 200-MHz spectrometer ( E O L JNM-FX200). The temperature of sample solution was measured with a copperconstantan thermocouple and controlled within k0.3 'C by hot air and/or a dry nitrogen stream from liquid nitrogen. The proton selfdiffusion coeffcient for solutions A and B was measured in a temperature range from 233 to 333 K by the pulsed gradient method.39 Two field gradient pulses g were applied to the sample solution at t = tl (0 < r1 < T ) and t = t1 A. The decay of the echo amplitude A is given by
+
In [A(g,27)/A(0,2~)1 = " ~ H ~ 6 ~ g 2-( 6A/ 3 ) & 1
(3)
where 7 represents the time between the 90° and the 180' pulses applied, YH is the Byromagnetic ratio of a proton, & is the proton selfdiffusion coefficient, 6 is the duration of the gradient pulses, and A is the time between the two gradient pulses. The g value was calibrated by using a known & value for pure water. The values of & were determined by varying A under the condition of A = T at constants g and 6. The current of the gradient coil was supplied with a pulse gradient generator (JEOL NM PL-200). The magnitude of g ranged from 13.52 to 63.5 G cm-l and that of 6 from 1.0 to 9 ms, with A of 100.5 ms. The proton and deuteron spin-lattice relaxation times, TI, and T l , ~for , solutions A, B, C, and D, were measured over a temperature range from 203 to 333 K by the inversion recovery method with the 18Oo-r-9O0 pulse sequence.
Results dDLscpesicM Proton Self-Diffpdoa Coefficient. The proton self-diffusion coefficient, 41,measured for solutions A and B was plotted as a function of the reciprocal temperature in Figure 1. As is seen
333 323 313 303 298 293 283 273 263 253 243
0.733 0.613 0.495 0.383 0.338 0.289 0.206 0.136 0.0819 0.0433 0.0192
0.489 0.606 0.771 1.01 1.15 1.35 1.85 2.64 3.85 5.58 7.69
T;apcriture Range 233-333 K TIK i o 9 ~ ~ 5-1 m 2 R, M ~ s - l 333 1.72 0.304 1.48 0.362 323 1.23 313 0.444 0.987 303 0.563 0.887 298 0.632 0.776 0.730 293 0.580 0.990 283 0.408 1.41 273 0.264 2.12 263 0.153 253 3.29 5.16 0.0761 243 0.0287 7.91 233
*tu1*/8 -1
0.274 0.323 0.391 0.490 0.546 0.623 0.821 1.12 1.58 2.18 2.67
*tnI
~ / -Ia
Rlpl8-l
0.215 0.283 0.380 0.522 0.605 0.722 1.03 1.52 2.27 3.40 5.03
2.72 3.47 4.52 6.07 6.97 8.26 11.8 18.2 30.3 56.0 116
0.152 0.185 0.233 0.304 0.346 0.406 0.568 0.836 1.29 2.02 3.13 4.84
1.99 2.37 2.96 3.90 4.45 5.24 7.36 10.8 16.8 27.6 49.8 108
p l t ? -I
15
~
0.152 0.176 0.210 0.259 0.286 0.324 0.422 0.577 0.833 1.27 2.03 3.07
in Figure 1, the self-diffusion coefficients for both solutions decrease exponentially with lowering the temperature. Since the amount of uexcess protons" is low in the pment system, the proton transfer is expected to be made by molecular diffusion.40 Thus, Figure 1 shows that the translational motion of water molecules in the present solutions is gradually hindered with lowering the temperature. In solution B, which includes a larger amount of water molecules than solution A, the diffusion coefficient is larger than that for solution A (Figure 1). As is apparent in Figure 1 the T I dependence of log & is not of Arrhenius type. Lang and Liidemand2 have suggested that the dynamic properties of supercooled solutions can be well r e p resented by a modified Arrhenius equation, i.e., Vogel-Tammann-Fulcher (VTF) equation
41 = 4 r o exp[-B/(T
- To)]
(4)
This empirical equation deacrib the slowing down of the d i h i o n coefficient in aqueous solution approaching its glass tramition point To. The self-diffusion coefficients measured at the various temperatures in the present study were fitted by using the VTF equation with To = 176 K as the glass transition temperature, which was determined with DSC measurement for solution A in a previous study.% The parameters optimized for both solutions are listed in Table 11. As seen in Figure 1, theoretical curves have reproduced satisfactorily the measured values of the diffusion coefficient. The smoothed & values for solutions A and B at the various temperatures are given in Tables I11 and IV. The smoothed values at 298 K, DH= 0.338 X 10-9 and 0.887 X 10-9 m2 8-l for solutions A and B, respectively, are comparable with those of 0.243 X 10-9 and 0.634 X 10-9m2 s-' for aqueous zinc(1I)
NMR Study on Dynamics of Water Molecules
The Journal of Physical Chemfstry, Vol. 96, No. 23, 1992 9489 TABLE V: IWhaW Vihccr of the Tnarhtiolrrl rad the Rotrthml Correhh -for Soldom A rad C (R= 5) in tLcTmpemtmre Ruge 243-333 K
Solution A i
T/K 333 323 313 303 298 293 283 273 263 253 243
3.0
3.5
4.0
4.5
103 T -'/K-'
10'
Solution B
~~/~ 51.9 62.1 76.9 99.4 113 132 185 280 465 880 1990
Ti"/p
3.09 4.07 5.46 7.51 8.70 10.4 14.8 21.8 32.7 48.9 72.3
TDAm'/p
rDJiq'/P
rD,#u'/p
4.00 5.10 6.64 8.91 10.2 12.1 17.4 26.7 44.5 82.2 170
2.83 3.61 4.71 6.32 7.25 8.59 12.3 18.9 31.6 58.3 120
1.93 2.46 3.20 4.30 4.93 5.85 8.38 12.9 21.5 39.7 81.9
'The values were calculated by using the deuteron quadrupole coupliig constants and asymmetry parameters for ice, liquid, and gas phascs. respectively. TABLE VI: &timrtsd V h of the Tramlntiod and the Robtk..l corrdrtioa Tiwr for Solotha B md D (R= 10) in tbe
333 323 313 303 298 293 283 213 263 253 243 233
22.1 25.8 31.0 38.6 42.9 49.1 65.6 93.5 145 249 500 1330
2.18 2.67 3.35 4.38 4.97 5.83 8.17 12.0 18.5 29.0 45.0 69.5
2.92 3.48 4.35 5.12 6.53 7.69 10.8 15.9 24.6 40.6 73.1 158
2.01 2.46 3.08 4.06 4.63 5.45 7.66 11.3 17.4 28.8 51.8 112
i
1 o+ 3.0
3.5
4.0
4.5
1O3T -'K'
Figure 2. Temperature dependence of the proton relaxation times TI*. The observed values are plotted for solution A (opened circle) and solution B (filled circle). The calculated values with T D ~ S, D ~ and , rDe are drawn by the broken, solid, and dotted lines, respectively.
chloride solutions with [H20]/[ZnC12] molar ratios of 4.1 and 7.4, respecti~ely.'~ Proton Spin-Lattice Relaxation Rate. Figure 2 shows the temperature dependence of the proton spin-latticerelaxation time T],H for solutions A and B. A minimum of the relaxation time apptars around 230 and 219 K for solutions A and B, mpcctively. The temperaturedependent behaviors of for both solutions are similar to that found for an aqueous zinc(I1) chloride solution with [H20]/ [ZnC12]= 4.1,38in which a minimum of the relaxation time was observed around 233 K. In the present work, the proton spin-lattice relaxation rate, R13 (=1/Tl3), has been divided into the contributions from the intermolecular and intramolecular dipoldpole interactions in the following procedure. In the present aqueous zinc(I1) bromide solutions the compositions of the predominant zinc(I1) bromo complexes, [ZnBr,(OH2)6,,](2-")+ (n = 2, 3, and 4), change with t~mperature;~~Jb hence, the number of interactions between the water molecule and zinc(I1) ion is not constant over the temperature range investigated. Therefore, it is difficult to analyze the relaxation rate with a simple model such as the two-site approximation that has been adopted to analyze the proton relaxation in aqueous lithium chloride solutions by Lang and Prielmeier.35 In highly concentrated aqueous solutions, as in the present case, all water molecules probably bind to the ions; the spin-lattice relaxation rate in water is governed mainly by the intermolecular and intramolecular IH-lH dipoldpole interactions in the temperature range; i.e., the relaxation rate can be and the intraexpressed as.the sum of the intermolecular molecular parts
'e
1.41 1.68 2.10 2.76 3.15 3.71 5.21 1.61 11.9 19.6 35.3 76.4
#Thevalues were calculated by using the deuteron quadrupole mupling constants and asymmetry parameters for ice, liquid, and gas pham, respectively. The spin-rotation contribution is negligible in the temperature range studied.m The intermolecular contribution, will be to a large extent modulated by translational motion of water m~lecule'~ and is expressed as
*E,
Rinter 1,H
= (6r/5)(yHZh(ILg/4*))2(NH/2DHdHH)F(OHrintcr)
(6)
with F(0~7iter)
2dOHTintcr) + 8d2yI~inter)
(7)
A w H T ~[(3/2)u2 ~ ~ ~ )+ ( 1 5 / 2 ) ~+ 121 X [(1/8)u6
+ us + 4u4 + (27/2)u3 + (81/2)u2 + 81u + 811-l (8)
uz = 2 w H ? j ~
(9)
Here h is the Planck constant divided by Zr, I L ~is magnetic permeability under vacuum, NH is the number density of proton, and OH is the Larmor fquulcy under the experimentalconditioa. T~~ is the correlation time for the intermolecular dipoledipole interaction, corresponding to the translational correlation time of water molecule. The translational correlation time rinm is related to the experimentally determined self-diffusion coefficient & with Tinter
dHH2/2DH
(10)
w h m d m is the distance of closest approach between two protons of intermolecular water molecules. In the present study a value of 276 pm was used for ~ H H which , has been estimated from the diameter of the water The translational correlation time for solutions A and B has been estimated as a function of temperature by using aq 10 with the s e w i f h i o n coeffcients listed
9490 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 100 1
1
quadrupole coupling constant and the asymmetry parameter, respectively. Under the condition of fast motion regime, ODTD
