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Low frequency dynamics in water and ZnCl2 solutions by quasi-elastic and inelastic neutron scattering
Physica 13613 (1986) 179-182 North-Holland, Amsterdam
LOW FREQUENCY DYNAMICS IN WATER AND ZnC! 2 SOLUTIONS BY QUASI-ELASTIC AND INELASTIC NEUTRON SCATTERING M.P. FONTANA Dipartimento di Fisica and GNSM-C1SM, University of Parma, Italy
P. MIGLIARDO and G. MAISANO Istituto di Fisica and GNSM-C1SM, University of Messina, Italy
M.C. BELLISSENT-FUNEL Labo. Lkon Brillouin*, CEN-Saclay, 91191 G-s-Yvette, Cedex, France
A.J. DIANOUX Institut Laue-Langevin, BP 156, Centre de Tri, 38042, Grenoble, France
In this paper we report the results of a study of the low frequency dynamics in HzO and aqueous solutions of ZnCI e as a
function of temperature; the results were obtained by quasi-elastic and inelastic neutron scattering using the IN6 time-of-flight speetometer at I.L.L., Grenoble. The temperature dependence of the frequency distribution functions for pure H20 and the saturated ZnCI 2 solution is shown. A discussion about the influence of the choice of the value of the rotational diffusion coefficient D r on the results from the fit of the quasi-elastic part of the spectrum of the ZnCI z solution is presented. In particular, we stress the necessity of collateral experimental evidence, such as we obtained by depolarized Rayleigh wing scattering.
In recent years accurate neutron scattering experiments have given quantitative information on the microscopic motions of H20 molecules, in pure water and in aqueous solutions. Of particular interest are the results obtained for aqueous solutions of ZnCI 2 [1, 21; comparative neutron and light scattering measurements where made. The complementary types of information obtainable by the two techniques have yielded quite an accurate picture of the diffusional dynamics of H20 molecules in pure water and in saturated solutions of ZnCI 2. Using depolarized Rayleigh wing scattering we determined the relaxation time rs connected with hydrogen bond fluctuations; r~ turned out to be equal to 0.7 ps for pure H20 and 1.4ps for the saturated solutions of ZnCI 2 (however, in the latter case the assignment is not unambiguoussee later). These times may be compared with the
rotational relaxation times r r determined for the H20 molecules by quasi-elastic (q.e.) neutron scattering; for H20 ~'r turns Out to be coincident, within experimental error, with the zs value. For the saturated ZnC12 solutions the determination of ~r is much more difficult, due to experimental problems. For our neutron measurements we have used the IN6 spectrometer at I.L.L. (Grenoble), whose best energy resolution in the q.e. region is about 50/zeV: this turns out to be about five times broader than the true AE (full width at half height) of the q.e. spectrum for the saturated solution. Thus the separation between rotational and translational contributions to the incoherent scattering law Si,c( Q, w) are difficult to identify, and the separation is always ambiguous. In the framework of the Sears rotational model [3] the scattering law may be written as
0378-4363/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
180
M.P. Pbntana et al. / L o w frequency dynamics in water and ZnCI~ solutions
Si.c(Q, w) = exp(-QZ(u2))
x { j~(Qa) 1 ,~
ZnCl 2 solution we are at the experimental limits for the analysis of our data, in order to choose the proper value of D r independent evidence must be obtained. From our depolarized Rayleigh wing data we did obtain a value of D r for the saturated solution, which is roughly half that for H 2 0 , i.e. - 0 . 0 8 meV. This practically coincides with choice (c) in fig. 1, and would imply that the random jump diffusional model, which was found adequate for H 2 0 [1, 4], is not appropriate for the saturated solution, where a more solid-like model might be better. This choice of D r would also bring our value for D T in qualitative agreement with the corresponding value obtained by N M R [5, 61 . At this point we cannot make a definite decision on this matter: further depolarized Rayleigh wing data are needed, as a function of solute concentration and temperature, in order to clearly assign the relaxation time zS. Also, new and more precise q.e. neutron scattering data would allow us to increase confidence in our fits and would make comparison with the depolarized Rayleigh wing data more meaningful. We can see a reason for our caution when we analyze the inelastic part of the neutron spectra, which we have followed up to 100 meV. In figs. 2 and 3 we show the vibrational frequency distrib-
,AEx
7r tZaET) 2 +
o) 2
+ -1 ~ (2•+ llj~(ea) '77"l= 1
l(l + 1)D r + A E T } x [l(l + 1)O r + AET] 2 + o)2 ,
(1)
where D r is the reorientational diffusion coefficient and A E x contains the translational diffusion coefficient D T. In order to test a specific translational diffusion model, we must first remove the rotational contribution. We have found that the results are quite sensitive to the choice of D r. In fig. 1 we show the behavior of AE T vs. Q2 for different choices of Dr, all within almost equivalent )(2 parameter values for the fit of the experimental q.e. spectrum with eq. (1). No such ambiguity was apparent when the same type of analysis was applied to H 2 0 . The same situation obtains for the spectra taken at higher temperatures. From fig. 1 it is obvious that the very type of diffusional model which may be inferred from the data could depend on the choice of D r. Since for the saturated 0.1 A Dr
-
5
.10-3
mev
• D r " 10"2
mev
~Dr
mev
= 5 . 1 o "2
z~
/k
2x /~
/x
/k
0.05 -
A /~ ~o
0.0 0
•
•
I~
~,-~ 2-~
/x •
•
~
.~
•
•
•
•
I
I
1
2
_.
3
IJ,~ 4
5
~-~
~
~,~
6
Fig. l. QLbehavior of the translational full width at half height obtained from a Lorentzian-type fit (eq. (1)) of the data, for three different values of the D r coefficient.
181
M.P. Fontana et al. / L o w frequency dynamics in water and ZnCI 2 solutions
T-_20°C
ZnCI
2
H20
T.45°C
T.44°C
'
I
25
,
I
50
I
75
10
ENERGY (mev ) Fig. 3. Frequency distribution function versus energy, for the saturated solution of ZnC12, at 20°C and 45°C.
0
i
1
25
50 ENERGY
I
75
10
(mev)
Fig. 2. Frequency distribution function versus energy, for pure H20 at temperatures of 20°C, 44°C and 68°C.
ution P(oo) as obtained using the EgelstaffSchofield procedure (7) for H 2 0 (fig. 2) and ZnC12 saturated solution (fig. 3), at several temperatures. In the spectral range investigated, the main feature of P(w) is a broad peak centered at about 65 meV. Its shape and position seem to be slightly dependent on temperature and solute concentration. In this high frequency region, we do not expect
the translational H-bond motions to contribute appreciably. In the solutions the spectral density may be deformed by the presence of water molecules coordinated by Zn 2÷ ions. In the context of this paper, the most interesting feature of P(~o) is the lower frequency peak at about 8 meV, connected to H-bond librational motion. From fig. 2 we see that the lineshape in this_region is sensitive to temperature; in particular, the peak seems to broaden, with increasing temperature. The effect is more pronounced on the high energy side, where the stretching H-bond vibrations are expected to contribute. This is probably the first clear-cut, direct experimental evidence of the effect of temperature on the H-bond vibrational dynamics. From fig. 3 we observe that the H-bond peak is
182
M.P. Fontana et al. / L o w frequency dynamics in water and ZnCI 2 solutions
so broadened as to merge into the background; concurrently, its " d i s a p p e a r a n c e " makes the feature at about 20 meV stand out more clearly. Thus, it would seem that the addition ZnC12 has a strong effect on the librational c o m p o n e n t Hbond vibrational dynamics. Clearly H - b o n d d y n a m i c s - a n d possibly the very nature of the H - b o n d i t s e l f - m u s t be considerably altered in the saturated solution. A m o n g other things, this implies that caution should be exercised in assigning the ~s determined for the saturated solution by depolarized Rayleigh wing spectroscopy. In conclusion, our results show that, whereas our separation of the rotational and translational contributions to the neutron q.e. scattering is unambiguous in H 2 0 , for saturated solutions of ZnCI2, great care must be used and very precise data must be obtained. The best way to resolve the ambiguity is to use independent experimental evidence, as we have done with depolarized Rayleigh wing spectroscopy. F r o m this point of view however, further m e a s u r e m e n t s are necessary. Finally, the data we present for the low frequency vibrational distribution are sufficiently precise to show the specific dependence of the
spectral density of states connected with the H - b o n d network on t e m p e r a t u r e and solute concentration. Thus meaningful comparisons m a y be made with either other types of experimental results (such as R a m a n and inelastic neutron scattering in the O H stretching region at 3400 cm 1) or with molecular dynamics calculations of the frequency distribution function of H - b o n d network excitations.
References [1] M.C. Bellissent-Funel, R. Kahn, A.J. Dianoux, M.P. Fontana, G. Maisano, P. Migliardo and F. Wanderlingh, Mol. Phys. 52 (1984) 1479. [2] G. Maisano, P. Migliardo, M.P. Fontana, M.C. BellissentFunel and A.J. Dianoux, J. Phys. C18 (1985) 1115. [3] V.F. Sears, Can. J. Phys. 44 (1966) 1299; 45 (1966) 237. [4] J. Teixeira, M.C. Bellissent-Funel, S.H. Chen and A.J. Dianoux, Phys. Rev. A31 (1985) 1913. [5] Y. Nakamura, S. Shimakawa, K. Futamoto and M. Shimoji, J. Chem. Phys. 77 (1982) 3258. [6] H. Weingartner, K.J. Muller, H.G. Hertz, AN.J. Edge and R. Mills, J. Phys. Chem. 88 (1984) 2173. [7] P.A. Egelstaff and P. Schofield, Nucl. Sc. Engineering 12 (1962) 260.
LOW FREQUENCY DYNAMICS IN WATER AND ZnC! 2 SOLUTIONS BY QUASI-ELASTIC AND INELASTIC NEUTRON SCATTERING M.P. FONTANA Dipartimento di Fisica and GNSM-C1SM, University of Parma, Italy
P. MIGLIARDO and G. MAISANO Istituto di Fisica and GNSM-C1SM, University of Messina, Italy
M.C. BELLISSENT-FUNEL Labo. Lkon Brillouin*, CEN-Saclay, 91191 G-s-Yvette, Cedex, France
A.J. DIANOUX Institut Laue-Langevin, BP 156, Centre de Tri, 38042, Grenoble, France
In this paper we report the results of a study of the low frequency dynamics in HzO and aqueous solutions of ZnCI e as a
function of temperature; the results were obtained by quasi-elastic and inelastic neutron scattering using the IN6 time-of-flight speetometer at I.L.L., Grenoble. The temperature dependence of the frequency distribution functions for pure H20 and the saturated ZnCI 2 solution is shown. A discussion about the influence of the choice of the value of the rotational diffusion coefficient D r on the results from the fit of the quasi-elastic part of the spectrum of the ZnCI z solution is presented. In particular, we stress the necessity of collateral experimental evidence, such as we obtained by depolarized Rayleigh wing scattering.
In recent years accurate neutron scattering experiments have given quantitative information on the microscopic motions of H20 molecules, in pure water and in aqueous solutions. Of particular interest are the results obtained for aqueous solutions of ZnCI 2 [1, 21; comparative neutron and light scattering measurements where made. The complementary types of information obtainable by the two techniques have yielded quite an accurate picture of the diffusional dynamics of H20 molecules in pure water and in saturated solutions of ZnCI 2. Using depolarized Rayleigh wing scattering we determined the relaxation time rs connected with hydrogen bond fluctuations; r~ turned out to be equal to 0.7 ps for pure H20 and 1.4ps for the saturated solutions of ZnCI 2 (however, in the latter case the assignment is not unambiguoussee later). These times may be compared with the
rotational relaxation times r r determined for the H20 molecules by quasi-elastic (q.e.) neutron scattering; for H20 ~'r turns Out to be coincident, within experimental error, with the zs value. For the saturated ZnC12 solutions the determination of ~r is much more difficult, due to experimental problems. For our neutron measurements we have used the IN6 spectrometer at I.L.L. (Grenoble), whose best energy resolution in the q.e. region is about 50/zeV: this turns out to be about five times broader than the true AE (full width at half height) of the q.e. spectrum for the saturated solution. Thus the separation between rotational and translational contributions to the incoherent scattering law Si,c( Q, w) are difficult to identify, and the separation is always ambiguous. In the framework of the Sears rotational model [3] the scattering law may be written as
0378-4363/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
180
M.P. Pbntana et al. / L o w frequency dynamics in water and ZnCI~ solutions
Si.c(Q, w) = exp(-QZ(u2))
x { j~(Qa) 1 ,~
ZnCl 2 solution we are at the experimental limits for the analysis of our data, in order to choose the proper value of D r independent evidence must be obtained. From our depolarized Rayleigh wing data we did obtain a value of D r for the saturated solution, which is roughly half that for H 2 0 , i.e. - 0 . 0 8 meV. This practically coincides with choice (c) in fig. 1, and would imply that the random jump diffusional model, which was found adequate for H 2 0 [1, 4], is not appropriate for the saturated solution, where a more solid-like model might be better. This choice of D r would also bring our value for D T in qualitative agreement with the corresponding value obtained by N M R [5, 61 . At this point we cannot make a definite decision on this matter: further depolarized Rayleigh wing data are needed, as a function of solute concentration and temperature, in order to clearly assign the relaxation time zS. Also, new and more precise q.e. neutron scattering data would allow us to increase confidence in our fits and would make comparison with the depolarized Rayleigh wing data more meaningful. We can see a reason for our caution when we analyze the inelastic part of the neutron spectra, which we have followed up to 100 meV. In figs. 2 and 3 we show the vibrational frequency distrib-
,AEx
7r tZaET) 2 +
o) 2
+ -1 ~ (2•+ llj~(ea) '77"l= 1
l(l + 1)D r + A E T } x [l(l + 1)O r + AET] 2 + o)2 ,
(1)
where D r is the reorientational diffusion coefficient and A E x contains the translational diffusion coefficient D T. In order to test a specific translational diffusion model, we must first remove the rotational contribution. We have found that the results are quite sensitive to the choice of D r. In fig. 1 we show the behavior of AE T vs. Q2 for different choices of Dr, all within almost equivalent )(2 parameter values for the fit of the experimental q.e. spectrum with eq. (1). No such ambiguity was apparent when the same type of analysis was applied to H 2 0 . The same situation obtains for the spectra taken at higher temperatures. From fig. 1 it is obvious that the very type of diffusional model which may be inferred from the data could depend on the choice of D r. Since for the saturated 0.1 A Dr
-
5
.10-3
mev
• D r " 10"2
mev
~Dr
mev
= 5 . 1 o "2
z~
/k
2x /~
/x
/k
0.05 -
A /~ ~o
0.0 0
•
•
I~
~,-~ 2-~
/x •
•
~
.~
•
•
•
•
I
I
1
2
_.
3
IJ,~ 4
5
~-~
~
~,~
6
Fig. l. QLbehavior of the translational full width at half height obtained from a Lorentzian-type fit (eq. (1)) of the data, for three different values of the D r coefficient.
181
M.P. Fontana et al. / L o w frequency dynamics in water and ZnCI 2 solutions
T-_20°C
ZnCI
2
H20
T.45°C
T.44°C
'
I
25
,
I
50
I
75
10
ENERGY (mev ) Fig. 3. Frequency distribution function versus energy, for the saturated solution of ZnC12, at 20°C and 45°C.
0
i
1
25
50 ENERGY
I
75
10
(mev)
Fig. 2. Frequency distribution function versus energy, for pure H20 at temperatures of 20°C, 44°C and 68°C.
ution P(oo) as obtained using the EgelstaffSchofield procedure (7) for H 2 0 (fig. 2) and ZnC12 saturated solution (fig. 3), at several temperatures. In the spectral range investigated, the main feature of P(w) is a broad peak centered at about 65 meV. Its shape and position seem to be slightly dependent on temperature and solute concentration. In this high frequency region, we do not expect
the translational H-bond motions to contribute appreciably. In the solutions the spectral density may be deformed by the presence of water molecules coordinated by Zn 2÷ ions. In the context of this paper, the most interesting feature of P(~o) is the lower frequency peak at about 8 meV, connected to H-bond librational motion. From fig. 2 we see that the lineshape in this_region is sensitive to temperature; in particular, the peak seems to broaden, with increasing temperature. The effect is more pronounced on the high energy side, where the stretching H-bond vibrations are expected to contribute. This is probably the first clear-cut, direct experimental evidence of the effect of temperature on the H-bond vibrational dynamics. From fig. 3 we observe that the H-bond peak is
182
M.P. Fontana et al. / L o w frequency dynamics in water and ZnCI 2 solutions
so broadened as to merge into the background; concurrently, its " d i s a p p e a r a n c e " makes the feature at about 20 meV stand out more clearly. Thus, it would seem that the addition ZnC12 has a strong effect on the librational c o m p o n e n t Hbond vibrational dynamics. Clearly H - b o n d d y n a m i c s - a n d possibly the very nature of the H - b o n d i t s e l f - m u s t be considerably altered in the saturated solution. A m o n g other things, this implies that caution should be exercised in assigning the ~s determined for the saturated solution by depolarized Rayleigh wing spectroscopy. In conclusion, our results show that, whereas our separation of the rotational and translational contributions to the neutron q.e. scattering is unambiguous in H 2 0 , for saturated solutions of ZnCI2, great care must be used and very precise data must be obtained. The best way to resolve the ambiguity is to use independent experimental evidence, as we have done with depolarized Rayleigh wing spectroscopy. F r o m this point of view however, further m e a s u r e m e n t s are necessary. Finally, the data we present for the low frequency vibrational distribution are sufficiently precise to show the specific dependence of the
spectral density of states connected with the H - b o n d network on t e m p e r a t u r e and solute concentration. Thus meaningful comparisons m a y be made with either other types of experimental results (such as R a m a n and inelastic neutron scattering in the O H stretching region at 3400 cm 1) or with molecular dynamics calculations of the frequency distribution function of H - b o n d network excitations.
References [1] M.C. Bellissent-Funel, R. Kahn, A.J. Dianoux, M.P. Fontana, G. Maisano, P. Migliardo and F. Wanderlingh, Mol. Phys. 52 (1984) 1479. [2] G. Maisano, P. Migliardo, M.P. Fontana, M.C. BellissentFunel and A.J. Dianoux, J. Phys. C18 (1985) 1115. [3] V.F. Sears, Can. J. Phys. 44 (1966) 1299; 45 (1966) 237. [4] J. Teixeira, M.C. Bellissent-Funel, S.H. Chen and A.J. Dianoux, Phys. Rev. A31 (1985) 1913. [5] Y. Nakamura, S. Shimakawa, K. Futamoto and M. Shimoji, J. Chem. Phys. 77 (1982) 3258. [6] H. Weingartner, K.J. Muller, H.G. Hertz, AN.J. Edge and R. Mills, J. Phys. Chem. 88 (1984) 2173. [7] P.A. Egelstaff and P. Schofield, Nucl. Sc. Engineering 12 (1962) 260.