- Email: [email protected]
Raman and Brillouin scattering from electrolytic solutions
Journal of Molecular Structure, 250 (1991) 291-304 Elsevier Science Publishers B.V., Amsterdam
Raman and Brillouin scattering solutions*
291
from electrolytic
Francesco Aliotta Istituto di Tecniche Spettroscopiche de1 C.N.R.-Messina, 98166 Vill. S. Agata, Messina (Italy) (Received 19 November 1990)
Abstract A number of spectroscopic investigations are reported on aqueous solutions of CdCl, and molten Ca(N0s)2*4Hz0 and its mixture with KN03. The Raman probe gives evidence of the existence of two different local structures in the solutions of CdClx: one is dominated by the solvent, the other by the solute. A competition between them exists whose equilibrium changes with concentration. Hypersonic and ultrasonic velocity data and hypersonic absorption results on the same system, as a function of concentration and of temperature, give evidence of a structural relaxation connected to the local variation of the structural arrangement induced by the solute. Extended X-ray absorption fine structure (EXAFS ) measurements on Ca (NOs),*4H,O and its mixture with KNOB reveal an inner shell of water complexation for the Ca’+ and K+ ions that produces a close-packed structure in which hydration forces are mainly responsible for the local arrangement. Mandelstamm-Brillouin scattering results give evidence for a relaxation phenomenon to which both structural and shear mechanisms contribute. The mean relaxation time r, and the relaxation modulus M, show a non-Arrhenius behaviour, supporting the idea that our systems can be regarded as fragile liquids.
INTRODUCTION
The problem of understanding the nature of the ion-ion and ion-solvent interaction in aqueous electrolytic solutions has been extensively studied in the past (see for example ref. 1). A tentative way of approaching the problem was the extensive study of the static and dynamic properties of the system as a function of temperature and concentration. Actually concentration turned out not to be a good parameter: solutions at different concentrations should be considered as different physical systems. At very low concentrations the structural properties are due to the inter- and intra-molecular forces of pure water, while at high concentration values the local structure tends to reproduce the local coordination of the corresponding hydrated crystal [ 21. *Presented at the International Symposium on Hydrogen Bond Physics held at 11Ciocco, Barga, Italy, 11-14 September 1990.
0022-2860/91/$03.50
0 1991 Elsevier Science Publishers B.V. All rights reserved.
292
It was soon realized that a lot of information of fundamental importance to the understanding of the properties of such liquids can be obtained from the investigation of the systems at low temperatures. In many systems the temperature of interest turned out to fall below the thermodynamic liquidus temperature. In such a way the investigations were driven to overcome the original difficulties to the approach to the metastable state. As a result a new spectrum of interesting phenomena was revealed from the investigation of such systems over this extended temperature range. In particular, remarkably divergent behaviour was revealed in relaxation times and viscosities as measured by different probes (dielectric, NMR, light scattering, ultrasonic, etc. ) . Very recently, the behaviour of viscosity as a function of temperature in a wide variety of liquids was studied [ 3,4] in an attempt to distinguish between strong and fragile liquids in terms of the density of minima in the potential energy hypersurface in the 3N+ 1 dimensional configurational space of the N-particle molecular system. Liquids with low density of minima are classified as strong liquids (as an example, liquids in which a tetrahedral coordination of the network centre places strong limitations on the arrangement of the other particles). Liquids with high density of minima are classified as fragile liquids. The higher density of configurational states is consistent with the larger configurational entropy at a given energy kT above the deepest minimum on the surface. It is the larger degeneracy of the surface that drives the system to high entropy in a short temperature interval and hence causes the large excess liquid heat capacity of this class of liquids. When liquids with the same density of configurational states as fragile liquids but with large barriers between minima in the energy surface are investigated, an intermediate behaviour is observed. These systems look thermodynamically fragile and kinetically strong. In the following some results from spectroscopic investigations on CdCl, aqueous solution and molten Ca ( NOs) 2*4H20 and its mixture with KNO, are presented. The data obtained are analyzed in the framework of the Angel1 scheme [3,4] and the different behaviours observed in the different systems are rationalized in terms of the different ion-ion and ion-water interactions that give rise to different local coordinations and, as a consequence, to a strong or fragile behaviour of the system. CdClz AQUEOUS SOLUTIONS
Raman results Raman spectroscopy represents a powerful tool to detect medium and long range order in the liquid under investigation. In fact the existence of some local coordination must be reflected in the spectral response of the system that becomes collective in character. Some years ago, Fontana et al. [5] reported evidence for the existence of solute-related collective vibrational modes in Cd&
293
aqueous solutions. In Fig. 1A are reported, from ref. 5, Raman spectra for the saturated solution of CdC& in HzO, of pure Hz0 and of a single hydrated crystal of CdC1,*2.5H,O. It should be stressed that the peak at 230 cm-l is the only peak in anhydrous CdC12.All the solutions at different concentrations have a diffusive character, with a strong low frequency contribution. As a consequence it was important to correct the spectra for the factor [n (0) + 1 ] /o where n (co) is the Bose-Einstein factor and to subtract the pure water contribution. Results from such a reduction of the data are shown in Fig. 1B. The 230 cm-’ peak is strongly polarized (p=O.ll). The spectrum of the depolarization ratio is reported in Fig. 2. Note the continuous variation of p across the spectrum and the practically complete independence on the concentration value of p(230) down to x 1 M (see inset). Below 1 M p tends rapidly to the value of 3/4, also shown by the low frequency scattering of pure water. The observed
100
250 wkm-‘1
400
0
400
200 U(cm-‘1
Fig. 1. A, Raman spectra for: a, CdCl,- 2.5H20 crystal, b, saturated aqueous CdCl, solution; c, pure water. B, Raman effective vibrational density of states for CdClz aqueous solutions at different molar concentrations: a, 5.08 M, b, 3.05 M, c, 2.50 M, d, 2.03 M, e, 1.05 M, f, 1.02 M, g, 0.50 M.
I 5
Fig. 2. Concentration dependence of the depolarization ratio p for CdCl, aqueous solutions: a, 5.08 M; b, 1.02 M; c, 0.5 M, d, 0.25 M, e, H,O. The inset shows the concentration dependence of p(230cm-‘).
294
density of states is caused by the existence of collective vibrational excitations in a medium-range lattice of Cl-Cd-Cl ions. The tendency of halide ions to form local complexes with a tetrahedral structure is well known. Furthermore, the comparison with the corresponding hydrated crystal spectrum made the authors confident in assigning the peak at 230 cm-l to the totally symmetric stretching of CdCli- complexes. Next, if we look at the width of the peak, it appears larger ( w 100 cm-‘) than one could expect from isolated ionic complexes ( x lo-30 cm-’ ), especially if water molecules are not directly involved. Furthermore, increasing the concentration should increase the line width due to the interactions between complexes, and eventually the shape is expected to change. On the contrary, the peak turned out to be concentration-independent up to a value of c I 1 M. If one takes into account the number of molecules at high concentrations (near saturation), it turns out to be not much greater than that of the ionic complexes. This means a strong interaction between them and as a result isolated complexes should not be taken into consideration. This is confirmed by the behaviour of the depolarization ratio. The fact that it varies smoothly going from the acoustic to the optical region is a further indication that we are dealing with a density of vibrational states. Ultrasonic measurements The same system has been investigated [6] by ultrasonic measurements in the range 5-600 MHz, as a function of concentration and temperature. The results provided evidence of a relaxation phenomenon whose parameters are both temperature- and concentration-dependent. A chemical origin for the phenomenon was suggested involving a rearrangement of ions and solvent in two structures, with an exchange process fixed by a “quasiunimolecular” kinetic reaction. One of the two states was identified as a state dominated by the salt structure and the second as one in which the solvent forces play the main role. In particular it was shown that at low concentrations the relaxation process can be related to the building-up of complex ions that behave like “order embryos”. Furthermore, some changes in the acoustic parameters were revealed at intermediate concentrations, confirming the Raman scattering results. The relaxed values of the absorption were higher than the corresponding classical value, indicating the presence of some dissipative phenomenon. Furthermore, the bulk to shear viscosity ratio was evaluated together with a correlation with the entropy change involved in the relaxation process. In other words, the bulk flow processes are not simply linked to jumps of molecules toward a new structural arrangement but are to be considered from a collective point of view; the system, locally in equilibrium with some kind of structure, undergoes a “melting” transition before reaching a new structural arrangement. In order to better clarify the observed relaxation new ultrasonic measurements were performed at a frequency of 5 MHz as a function of temperature
and concentration [ 71. The ultrasonic velocity data are represented in Fig. 3. It is easy to observe a dispersive phenomenon for the velocity. The data, starting from pure solvent, show parabolic behaviour as a function of temperature, with a maximum that shifts towards low temperature for increasing values of concentration. In order to explain what is happening we now have to give more attention to the results obtained for pure water. Hz0 is an associated liquid in which H-bonds play the main role and, as a consequence, temperature effects on sound velocity and on pScould be explained on the basis of some modification of the structural properties as temperature increases. The maximum of the velocity at x 74°C and the subsequent minimum in the compressibility at x 64’ C could be explained by taking into account the presence of a noticeable memory of the ice structure in liquid water. This open structure [ 81 is very similar to that of ice I, with vacancies or cavities in which interstitial molecules are found. These latter are in interaction with the tetrahedral environments and a resulting rate-exchange process takes place in which
10
30
50 70
10 m
T,‘C
50 70
Fig. 3. Temperature evolution of the ultrasonic velocity at different concentrations: dots, experimental data; continuous lines, parabolic fit. The arrows mark the maxima in the velocity.
0
2
L
Molarity,M
Fig. 4. Peak temperature T,,, vs. molarity M. The straight lines indicate the two structured regions.
296
the bonds are continuously broken and reformed with a mean life time of a few picoseconds [ 91. As a consequence, by increasing the temperature the relaxation compressibility decreases, due to the reduction in the percentage of the open structure. However the compressibility tends to increase with temperature due to the increase in the mean distance between molecules for a given structure. The former effect exceeds the latter up to a temperature of x 64’ C if adiabatic compressibility is evaluated. As a consequence, the velocity shows this effect at z 74’ C due to the simultaneous temperature behaviour of density and compressibility. The addition of salt to water results in a lowering of T,. CdCl, tends to destroy the open structure of water, making a new, more closed, structure, in which hydrated ions and cation-ligand complexes are more or less interacting. From the fitting of the experimental velocity data with an empirical parabolic law, we have extracted the behaviour of 7’, as a function of temperature (see Fig. 4). The behaviour of the peak temperature clearly shows some changes in our system. The data, in fact, fall on two straight lines with an intermediate transition region. At this intermediate concentration the properties of the system change as stressed above. The system evolves from a water-imposed structure (in which the salt acts as a perturbing element) to a more packed structure, imposed by the solvent. In this intermediate region, it is not the water that loses its original structure but the strong interactions between ions and H20 molecules that produce a new interconnected structure. The value of Z’, turns out to be coincident with the limiting value of z 10°C for c=5.05 M. This implies that the saturated solution has a well-defined structure and the effect of temperature is only to alter the intermolecular distances, not to cause any structural evolution. Brillouin scattering
In order to better clarify the observed relaxation phenomenon,we extended the acoustic measurements to the MHz region by a Mandelstamm-Brillouin scattering experiment. The measurements were performed in the concentration range 0.25-5.05 M and at temperatures in the range 9.30-70” C. The transferred k value ranged from 4.57~ lo4 cm-’ (for the 0.5 M solution at 9.3O”C) to k=4.22 x lo4 cm-’ (for the solution at 0.5 M and 70°C). A free spectral range of 18.4GHz was used. In a light-scattering experiment the polarized spectrum, connected to the structure factor S (k,m), can be reduced, by using the usual hydrodynamics equations, as
&J,(k) ‘w(k,0)=w2+Z-‘fR(k)+{u-
&J”,(k) [o;(k)-P~(k)]1’2}2+P~(k)
297
r,(k) +{w+
[W:(k)A~~~~r/2j2+JRB(k)
+ [o;(k)
-PB(k)
Ill2
co- [o;(k) -PB(k)]1’2 [w;(k) -r”B(k)]“2}2 x ( PB(k) +{o+ co- [o;(k) -PB(k)
+{m+
-1”2B(k)]“2
[o;(k)
-r”B(k)]1’2}2
>
(1)
By using eqn. ( 1)it is possible to extract from the experimental data the acoustic parameters of interest, namely the frequency shift CO,and the linewidth rn from which the hypersonic velocity value V, and the absorption a/f 2 can be calculated. In Fig. 5a-b is reported, as an example, the velocity and absorption data for three concentration values. From what has been said, it is evident that ultrasonic and hypersonic probes furnish relevant information on the dynamic behaviour of liquid systems. In particular, the Brillouin technique allows a direct evaluation of the frequency dependence of the transport coefficients qv( (I)) and qS( CO).As a consequence, it is possible to observe some type of relaxations (structural, viscous, and so on) which could be connected to the collective dynamic evolution in the 1O-g-1O-'2 stime scale. Usually, the vibration contribution lies at higher frequencies and is decoupled (at low k value) from the translational and diffusional motions. Viscothermal (gas-like) and viscoelastic (solid-like) theories are able to describe the acoustic properties of these systems. It is possible to derive for the complex longitudinal modulus an expression that is a function of the frequency-dependent volume chemical viscosity, the structural high fre8 g-
-. .
1650-
-.
. 1550-
,.: .
. : -
: lL50-
a.1
. l
. ..*-A.
l
A.
-
.*1
.
I
{"-
.
$30* a
_.
-
. .
.
. .
NT10 2 -. 6
.
10 30
. . . M
l
It 70
.
. .
1. . .
,,,,,,t 10 30 50
.
l
I,,,,,, 70
10
30
so
70
T#T
Fig. 5. Sound velocity and absorption vs. Tatthree different concentration values: left, C= 0.5 centre, C= 2.0 M, right, C=5.05 M. Circles, hypersonic data, triangles, ultrasonic data.
M;
quency volume viscosity and the shear viscosity. As a consequence different relaxation times can be derived for the different processes. In our case we assumed a single relaxation process, which is quite reasonable when the chemical, structural and viscous processes are well decoupled as in our case. However, also assuming a distribution of relaxation times if the linewidth of the distribution is narrow, then the centre of the distribution can be assumed to be the single relaxation value revealed. On this basis we can write
(2) Note that the above equations hold when the viscous process relaxes at higher frequency. In our case, since the chemical and the structural processes relax at well-separated frequencies, the relaxed velocity of the chemical process can be assumed as the zero-frequency velocity for the structural process. Among other things, due to the limited range of Kexplored, we have information on a limited wr range. In any case our derived values range from 12.6 x lo-“-6.0 x 10-l’ s for 5.05 M solution and 3.2 x 10-“-2.6x lo-l1 s for the 0.5 M solution. This structural process, as pointed out, can originate from a “melting” and “building-up” of a locally ordered structure. The values of z, obtained give an indication of the time scale of the structural rearrangement. In any case this could be regulated in some more complicated and not understood manner. The concentration dependence of z, indicates that at lower concentrations the process becomes faster. For the 0.5 M solution the relaxation process could originate from a different process. In fact, the solute-imposed structure is still not present. This process could arise from a restructuring of the water molecules or anionic replacement in the cationic coordination shell. From an Arrhenius plot of r,, activation energies of ~0.8 kcal mol-’ (at 0.5 M) and x2.8 kcal mol-l at 5.05 M are deduced. This indicates that the fast process is less hindered than the slower one. This is true if any exchange process is hindered by the long-life, middlerange ordered regions. In Fig. 6 the evolution of the relaxation strength is reported in an Arrhenius plot for three values of concentration. At low concentration values the data fall on a straight line, which gives an energy value between 3.1 and 3.5 kcal mol-l. For the 5.05 M solution the data diverge from the straight line. This can be explained by assuming a single structural process with a single-step mechanism at low concentration and more complex processes at high concentration values. In this latter case, in fact, the system has a well-defined structural identity in which ions and water molecules are linked together. The breaking of the bonds at some points in the structure could cause time-dependent effects on the full structural environment.
299
!-
lO?'T.(KT'
Fig. 6. Arrhenius plot of the relaxational bulk modulus KJT at different concentrations. CALCIUM NITRATE TETRAHYDRATE
AND ITS MIXTURE WITH KNO,
In the following we report some results from an experimental investigation on Ca(N03)2*4.17Hz0 and its mixture with KN03. These systems show a shear viscosity ranging from x 2P at room temperature to several hundreds of poise in the supercooled liquid phase [ 10,111. Furthermore, according to the observations for the corresponding anydrous melt, these nitrates reveal a strongly non-Arrhenian behaviour of the transport coefficients. In other words, following the Angel1 classification [ 3,4], they can be considered as a good example of “fragile” glass-forming liquids. As far as calcium nitrate tetrahydrate is concerned, the exact solution composition R (defined as the ratio between the moles of water and the moles of salt) was determined by drying the sample under vacuum at moderately high temperature ( T z 150 ’ C ) and measuring the amount of H,O by weight loss. It turned out to be R=4.17. The mixture [Ca(N0,)2.4.17H,01,,,+ [KNW0.25, where subscripts refer to the percentage by weight of the two compounds, was also prepared. These values correspond to a concentration value for which the system shows a eutectic point. EXAFS measurements We have performed EXAFS measurements on our samples at the PULS facility in Frascati. The Ca2+ and K+ k-edges absorption spectra were scanned with a standard resolution of 2 eV in the temperature range between - 25 and + 20” C. It is well known that the normalized modulation above the k-edge of the absorber, i.e. the EXAFS structure x(k), is connected with the Fourier transform of the local distribution function P(ri). The experimental spectra were reduced according to the well-known expression kXck,=#lh(n,k)l
I
exp[-2Rj/L(k)]exp[-22ai2k2][2kRj+~11’(k)l
(3)
300
where symbols have their usual meanings and the 1fj (a&) 1 and @I” values are taken from the literature [ 12,131. The two absorption K-edges for Ca2+ and K+ ions are quite evident. In Fig. 7 the mixture-normalized EXAFS spectrum above the Ca2+ k-edge is reported as an example for T= 20’ C; triangles are the experimental data while the dashed line is the result of fitting by eqn. (3). The results obtained can be summarized as follows. (i ) In molten calcium nitrate tetrahydrate only a coordination shell of water was revealed around the calcium ion. The radial distance Rc,_,, = 2.46 + 0.001 A is in agreement with the values obtained in CaCl, aqueous solution by X-ray and neutron diffraction experiments [ 14,151 and by our EXAFS determination [16]. (ii) The value of this distance and the mean coordination number No = 4 + 0.5 turns out to be almost temperature-independent in the temperature range investigated. (iii ) The Debye-Waller factor (which in amorphous and liquid systems reflects both the structural and thermal disordering effects) shows a large variation with temperature going from CJ~,_~ =0.13 A at T= 20°C through ac,_o=0.115 A at T= +5”C to oc,_o=0.06 A at T= -25°C. This fact, with the high value of crat room temperature, is an indication that the existing ion-dipole interaction between cation and water does not allow strong bonding effects: the hydration shell is not kinetically stable and the water molecules are in the “fast-exchange” regime. Analogous results, i.e. only one shell of water around Ca2+ ions with the same values for Rc,_o and Nca_o and the same trend for a, were obtained in the mixed nitrate. Such a circumstance suggests that all the water molecules in solution are locally coordinated to calcium. If we look at the local order around the potassium ion, EXAFS gives evidence that only one water molecule is coordinated to the K+ ion at a mean distance of 2.55 A. These circumstances support the idea of the existence of strongly shared cationic hydration effects whereas, the hypothesized interionic inner sphere complexes (like ion pairs)
0.26
-0.26 3
6.5 k/A-'
Fig. 7. [Ca(N0,),*4.17H,0]0.7,+ T=20”C.
IO
[KN03]o.2, Ca K-edge Fourier-filtered EXAFS spectrum at
301
do not influence, within the technique sensitivity, the EXAFS modulation. The potassium ion enters the original structure of the calcium nitrate tetrahydrate without inducing strong polarization effects, and hydration forces turn out to be the only ones responsible for the existing local arrangement. Brillouin measurements Light scattering measurements were performed both on the pure calcium nitrate tetrahydrate and on its mixture with potassium nitrate using a doublemonochromator, double-pass instrument (SOPRA Model DMDP 2000) with a resolution of 700 MHz. Such an instrument is particularly suitable for this kind of measurement in order to eliminate the problem of the overlapping components of the contiguous free spectral range when a Fabry-Perot instrument is used. Its resolution is comparable with that of an interferometer working at a free spectral range of 50 GHz (necessary to resolve phonons shifted by x 15 GHz) but with a rejection power very much higher. The explored temperature for Ca(N03)2*4.17H20 and -47”CITI65”C range was -47”CITI25”C for its mixture with potassium nitrate. This means that for both systems the deeply supercooled liquid region ( w 100” C below the melting point) was explored, where all the viscous and diffusive properties are more and more substituted by the “elastic” properties, as the system goes towards the glass transition temperature ( Tg= -58°C for Ca(NO,),-4.17H,O). Also in this case eqn. (1) was used in order to extract the parameters of interest and eqn. (2) was used, with the same assumption as made for aqueous CdCl, solution, in order to obtain the hyperacoustic velocity and the normalized absorption. In Fig. 8 the temperature evolution for o, and the loss tangent tan 6= $[+~]I
(4)
are reported. This latter quantity is a measure of the attenuation in dynamical mechanical studies and can be directly compared with the same quantity measured by different probes. It is easy to observe that both o. and 6 are strongly temperature dependent. We are clearly in the presence of the same relaxation phenomenon as studied at temperatures higher than + 20’ C [ 10,171. In addition, clear evidence is found in the literature that for nitrates [ 181, at temperatures higher than 2O”C, the time evolution of the bulk and shear viscosity are the same, i.e. the average and longitudinal relaxation times are comparable. When eqn. (2) is used, the mean relaxation time r, and the relaxation modulus M, are obtained, provided the zero-frequency value of the compressional modulus MO=PU,,~is known as a function of T. As MO for the calcium nitrate, we used the values of the ultrasonic velocity measured by Darbari et al. [lo], extrapolated down to 30” C in the temperature range 30” C I TI 60” C. The
302
I5
0
(a)
es ‘b
-10 00
++ ++
lo-
+
c
0
w
-5
+ g 5-
+
\.I
11
#i?
11
5
3
gw
(b)
Q15O 0
lo-
Oo
+
+
0 +:t
-10 + 0 -5
+
5-
+ III -50 -30 -10 10
30
Fig. 8. Brillouin frequency W, (circles) and loss tangent (crosses) vs. temperature for: a, calcium nitrate tetrahydrate; and b, its mixture with potassium nitrate.
values of u,,, and of A4,,were measured by a standard Matec pulse-echo apparatus. The results are reported in Table 1 with the values of hypersound velocity and normalized absorption. As stressed above, our r, values are to be considered as mean values because we used eqn. (2)) which applies in the case of a Maxwell relaxation law. This approach is obviously a crude approximation even if, as in the case of nitrate at low R values (between 3 and 4), the distribution tends to narrow. In such a case z, could represent, to a good approximation, the centre of mass of the distribution and the “overall” relaxation strength. Furthermore, as in the case of the corresponding anhydrous melt [ 191, another source of energy loss and thus of additional contributions to the observed relaxations, can be induced by energy transfer processes between the thermal phonons and the internal degrees of freedom of the NO, ionic group. In such a case, both thermal and vibrational relaxations could be involved in the observed phenomena and the linewidth rn should be written as the sum of many contributions. Let us return now to the temperature evolution of the extracted parameters z, and M,. As expected, both parameters show a strong deviation from the straight line when represented as an Arrhenius plot. This confirms the idea that our nitrates behave (following the Angel1 classification) like “fragile liquids” whose structure is imposed by binding forces originating from hydration and H-bond effects. The mean activation energy was estimated to be, in the
TABLE 1 Temperature dependence of hypersound velocity, IJhs,absorption, modulus, M,, in molten hydrated nitrates
a/f ‘, relaxational time,
T (“C)
lOlO
vhs
(m s-*)
%xo’r
Tr x
f’
(s)
11.8 9.8 8.2 6.7 6.9 5.9 5.2 4.7 4.9 2.9 1.6
0.69
TV,
and
M, x 10” (dyn cm-“)
(cm’ 5-l)
Ca(N0&.4.17Hz0 +25 2439 +15 2586 +5 2749 0 2932 -5 2918 -14 3058 -15 3125 -25 3195 -27 3224 -34 3324 -47 3543
[Ca(N0~)~.4.17H,010.7,+ lKNW0.25
+65 +25 +15 +5 -5 -15 -25 -35 -47
1948 2511 2667 2805 2933 3077 3145 3319 3411
23.3 10.7 8.9 7.6 6.7 5.8 5.4 3.1 0.6
0.97 1.04 1.10 1.20 1.18 1.78 2.75
4.19 5.32 6.74 8.80 8.25 9.71 11.11 11.26 11.43 12.47 15.09
0.11 0.69 0.80 0.88 0.94 1.00 1.02 1.59 8.09
1.19 2.99 3.86 4.66 5.44 6.39 6.83 8.06 9.36
0.79 0.89 0.96
extreme supercooled region x 20.1 kJ mol-’ for calcium nitrate tetrahydrate and E 38.9 kJ mol-’ for its mixture with potassium nitrate. The corresponding limiting values for the binding energy connected with the observed phenomenon are x 6.3 kJ mol-’ and x 4.6 kJ mol-1 respectively. The physical origin of the observed hypersound dispersion could be connected with the local “melting” of the close-packed structure in which the few water molecules are shared between ions. The melting of the local structure in which water molecules are in a fast-exchange regime can simultaneously generate structural and shear relaxation phenomenon. Such results agree with indications from Rayleigh wing measurements [ 201. In such a case the rotational relaxation, viscosity controlled, of the nitrate group within the structure has been rationalized in terms of librations for a rest time r. and subsequent jumps to a new local configuration when the local structure melts. Actually Brillouin scattering measurements as a function of the exchanged
304
wave-vector and temperature (passing through the T, temperature) are in progress in our laboratory, in order to better understand the relaxation processes that take place in these hydrated melts.
REFERENCES 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
See, e.g. H.S. Harned and B.B. Owen, The Physical Chemistry of Electrolyte Solutions, Reynold, New York, 1967. 0. Ya Samoilov, The Structure of Aqueous Solutions and the Hydration of Ions, Consulance Bureau, New York, 1965. C.A. Angel1and E.J. Sare, J. Chem. Phys., 52 (1970) 1058. C.A. Angell, in K.L. Ngai and G.B. Wright (Eds.), Strong and Fragile Liquids, Nat. Techn. Inf. Serv., U.S. Dept. of Commerce, New York, 1984. pp. 3-11. M.P. Fontana, G. Maisano, P. Migliardo andF. Wanderlingh, Solid State Commun., 23 (1977) 489. G. Carini, M. Cutroni, G. Maisano, P. Migliardo and F. Wanderlingh, J. Phys. C, 13 (1980) 967. G. Maisano, P. Migliardo, F. Aliotta and C. Vasi, Phys. Chem. Liq., 14 (1984) 13. M.D. Danford and H.A. Levy, J. Am. Chem. Sot., 84 (1962) 3965. C.J. Montrose, J.A. Bucaro, J. Marshall-Coakley and T.A. Litovitz, J. Chem. Phys., 60 (1974) 5025. G.S. Darbari, M.R. Richelson and S. Petrucci, J. Chem. Phys., 55 (1971) 4351. A.R. Carpio, M. Mehinic and E. Vyeager, J. Chem. Phys., 74 (1981) 2778. B.H. Teo, P.A. Lee, A.L. Simons, P. Eisenberger and B.M. Kinkaid, J. Am. Chem. Sot., 99 (1977) 3854. P.A. Lee and G. Beni, Phys. Rev., B, 15 (1977) 2862. R. Caminiti, G. Licheri, G. PiccaIuga, G. Pinna and M. Magini, Rev. Inorg. Chem., 1 (1979) 333. S. Cummins, J.E. Enderby and R.A. Howe, J. Phys., C, 13 (1979) 1. G. Galli, S. Magazti, D. Majolino, P. Migliardo, M.C. Bellissent-Funel, F. Aliotta and C. Vasi, 11Nuovo Cimento, 12D (1989) 197. V.C. Reinsborough and J.P. Valleau, J. Phys. Chem., 50 (1972) 2074. S.M. Rytov, Sov. Phys., JEPT, 31 (1970) 1163. L.M. Torrel, in G. Mamantov and E. Marassi (Eds.), Brillouin Scattering in Ionic Liquids, Reidel, Dordrecht, 1987, pp. 161-180. A.R. Carpio, M. Mehinic and E. Yeager, J. Chem. Phys., 74 (1981) 2778.
Raman and Brillouin scattering solutions*
291
from electrolytic
Francesco Aliotta Istituto di Tecniche Spettroscopiche de1 C.N.R.-Messina, 98166 Vill. S. Agata, Messina (Italy) (Received 19 November 1990)
Abstract A number of spectroscopic investigations are reported on aqueous solutions of CdCl, and molten Ca(N0s)2*4Hz0 and its mixture with KN03. The Raman probe gives evidence of the existence of two different local structures in the solutions of CdClx: one is dominated by the solvent, the other by the solute. A competition between them exists whose equilibrium changes with concentration. Hypersonic and ultrasonic velocity data and hypersonic absorption results on the same system, as a function of concentration and of temperature, give evidence of a structural relaxation connected to the local variation of the structural arrangement induced by the solute. Extended X-ray absorption fine structure (EXAFS ) measurements on Ca (NOs),*4H,O and its mixture with KNOB reveal an inner shell of water complexation for the Ca’+ and K+ ions that produces a close-packed structure in which hydration forces are mainly responsible for the local arrangement. Mandelstamm-Brillouin scattering results give evidence for a relaxation phenomenon to which both structural and shear mechanisms contribute. The mean relaxation time r, and the relaxation modulus M, show a non-Arrhenius behaviour, supporting the idea that our systems can be regarded as fragile liquids.
INTRODUCTION
The problem of understanding the nature of the ion-ion and ion-solvent interaction in aqueous electrolytic solutions has been extensively studied in the past (see for example ref. 1). A tentative way of approaching the problem was the extensive study of the static and dynamic properties of the system as a function of temperature and concentration. Actually concentration turned out not to be a good parameter: solutions at different concentrations should be considered as different physical systems. At very low concentrations the structural properties are due to the inter- and intra-molecular forces of pure water, while at high concentration values the local structure tends to reproduce the local coordination of the corresponding hydrated crystal [ 21. *Presented at the International Symposium on Hydrogen Bond Physics held at 11Ciocco, Barga, Italy, 11-14 September 1990.
0022-2860/91/$03.50
0 1991 Elsevier Science Publishers B.V. All rights reserved.
292
It was soon realized that a lot of information of fundamental importance to the understanding of the properties of such liquids can be obtained from the investigation of the systems at low temperatures. In many systems the temperature of interest turned out to fall below the thermodynamic liquidus temperature. In such a way the investigations were driven to overcome the original difficulties to the approach to the metastable state. As a result a new spectrum of interesting phenomena was revealed from the investigation of such systems over this extended temperature range. In particular, remarkably divergent behaviour was revealed in relaxation times and viscosities as measured by different probes (dielectric, NMR, light scattering, ultrasonic, etc. ) . Very recently, the behaviour of viscosity as a function of temperature in a wide variety of liquids was studied [ 3,4] in an attempt to distinguish between strong and fragile liquids in terms of the density of minima in the potential energy hypersurface in the 3N+ 1 dimensional configurational space of the N-particle molecular system. Liquids with low density of minima are classified as strong liquids (as an example, liquids in which a tetrahedral coordination of the network centre places strong limitations on the arrangement of the other particles). Liquids with high density of minima are classified as fragile liquids. The higher density of configurational states is consistent with the larger configurational entropy at a given energy kT above the deepest minimum on the surface. It is the larger degeneracy of the surface that drives the system to high entropy in a short temperature interval and hence causes the large excess liquid heat capacity of this class of liquids. When liquids with the same density of configurational states as fragile liquids but with large barriers between minima in the energy surface are investigated, an intermediate behaviour is observed. These systems look thermodynamically fragile and kinetically strong. In the following some results from spectroscopic investigations on CdCl, aqueous solution and molten Ca ( NOs) 2*4H20 and its mixture with KNO, are presented. The data obtained are analyzed in the framework of the Angel1 scheme [3,4] and the different behaviours observed in the different systems are rationalized in terms of the different ion-ion and ion-water interactions that give rise to different local coordinations and, as a consequence, to a strong or fragile behaviour of the system. CdClz AQUEOUS SOLUTIONS
Raman results Raman spectroscopy represents a powerful tool to detect medium and long range order in the liquid under investigation. In fact the existence of some local coordination must be reflected in the spectral response of the system that becomes collective in character. Some years ago, Fontana et al. [5] reported evidence for the existence of solute-related collective vibrational modes in Cd&
293
aqueous solutions. In Fig. 1A are reported, from ref. 5, Raman spectra for the saturated solution of CdC& in HzO, of pure Hz0 and of a single hydrated crystal of CdC1,*2.5H,O. It should be stressed that the peak at 230 cm-l is the only peak in anhydrous CdC12.All the solutions at different concentrations have a diffusive character, with a strong low frequency contribution. As a consequence it was important to correct the spectra for the factor [n (0) + 1 ] /o where n (co) is the Bose-Einstein factor and to subtract the pure water contribution. Results from such a reduction of the data are shown in Fig. 1B. The 230 cm-’ peak is strongly polarized (p=O.ll). The spectrum of the depolarization ratio is reported in Fig. 2. Note the continuous variation of p across the spectrum and the practically complete independence on the concentration value of p(230) down to x 1 M (see inset). Below 1 M p tends rapidly to the value of 3/4, also shown by the low frequency scattering of pure water. The observed
100
250 wkm-‘1
400
0
400
200 U(cm-‘1
Fig. 1. A, Raman spectra for: a, CdCl,- 2.5H20 crystal, b, saturated aqueous CdCl, solution; c, pure water. B, Raman effective vibrational density of states for CdClz aqueous solutions at different molar concentrations: a, 5.08 M, b, 3.05 M, c, 2.50 M, d, 2.03 M, e, 1.05 M, f, 1.02 M, g, 0.50 M.
I 5
Fig. 2. Concentration dependence of the depolarization ratio p for CdCl, aqueous solutions: a, 5.08 M; b, 1.02 M; c, 0.5 M, d, 0.25 M, e, H,O. The inset shows the concentration dependence of p(230cm-‘).
294
density of states is caused by the existence of collective vibrational excitations in a medium-range lattice of Cl-Cd-Cl ions. The tendency of halide ions to form local complexes with a tetrahedral structure is well known. Furthermore, the comparison with the corresponding hydrated crystal spectrum made the authors confident in assigning the peak at 230 cm-l to the totally symmetric stretching of CdCli- complexes. Next, if we look at the width of the peak, it appears larger ( w 100 cm-‘) than one could expect from isolated ionic complexes ( x lo-30 cm-’ ), especially if water molecules are not directly involved. Furthermore, increasing the concentration should increase the line width due to the interactions between complexes, and eventually the shape is expected to change. On the contrary, the peak turned out to be concentration-independent up to a value of c I 1 M. If one takes into account the number of molecules at high concentrations (near saturation), it turns out to be not much greater than that of the ionic complexes. This means a strong interaction between them and as a result isolated complexes should not be taken into consideration. This is confirmed by the behaviour of the depolarization ratio. The fact that it varies smoothly going from the acoustic to the optical region is a further indication that we are dealing with a density of vibrational states. Ultrasonic measurements The same system has been investigated [6] by ultrasonic measurements in the range 5-600 MHz, as a function of concentration and temperature. The results provided evidence of a relaxation phenomenon whose parameters are both temperature- and concentration-dependent. A chemical origin for the phenomenon was suggested involving a rearrangement of ions and solvent in two structures, with an exchange process fixed by a “quasiunimolecular” kinetic reaction. One of the two states was identified as a state dominated by the salt structure and the second as one in which the solvent forces play the main role. In particular it was shown that at low concentrations the relaxation process can be related to the building-up of complex ions that behave like “order embryos”. Furthermore, some changes in the acoustic parameters were revealed at intermediate concentrations, confirming the Raman scattering results. The relaxed values of the absorption were higher than the corresponding classical value, indicating the presence of some dissipative phenomenon. Furthermore, the bulk to shear viscosity ratio was evaluated together with a correlation with the entropy change involved in the relaxation process. In other words, the bulk flow processes are not simply linked to jumps of molecules toward a new structural arrangement but are to be considered from a collective point of view; the system, locally in equilibrium with some kind of structure, undergoes a “melting” transition before reaching a new structural arrangement. In order to better clarify the observed relaxation new ultrasonic measurements were performed at a frequency of 5 MHz as a function of temperature
and concentration [ 71. The ultrasonic velocity data are represented in Fig. 3. It is easy to observe a dispersive phenomenon for the velocity. The data, starting from pure solvent, show parabolic behaviour as a function of temperature, with a maximum that shifts towards low temperature for increasing values of concentration. In order to explain what is happening we now have to give more attention to the results obtained for pure water. Hz0 is an associated liquid in which H-bonds play the main role and, as a consequence, temperature effects on sound velocity and on pScould be explained on the basis of some modification of the structural properties as temperature increases. The maximum of the velocity at x 74°C and the subsequent minimum in the compressibility at x 64’ C could be explained by taking into account the presence of a noticeable memory of the ice structure in liquid water. This open structure [ 81 is very similar to that of ice I, with vacancies or cavities in which interstitial molecules are found. These latter are in interaction with the tetrahedral environments and a resulting rate-exchange process takes place in which
10
30
50 70
10 m
T,‘C
50 70
Fig. 3. Temperature evolution of the ultrasonic velocity at different concentrations: dots, experimental data; continuous lines, parabolic fit. The arrows mark the maxima in the velocity.
0
2
L
Molarity,M
Fig. 4. Peak temperature T,,, vs. molarity M. The straight lines indicate the two structured regions.
296
the bonds are continuously broken and reformed with a mean life time of a few picoseconds [ 91. As a consequence, by increasing the temperature the relaxation compressibility decreases, due to the reduction in the percentage of the open structure. However the compressibility tends to increase with temperature due to the increase in the mean distance between molecules for a given structure. The former effect exceeds the latter up to a temperature of x 64’ C if adiabatic compressibility is evaluated. As a consequence, the velocity shows this effect at z 74’ C due to the simultaneous temperature behaviour of density and compressibility. The addition of salt to water results in a lowering of T,. CdCl, tends to destroy the open structure of water, making a new, more closed, structure, in which hydrated ions and cation-ligand complexes are more or less interacting. From the fitting of the experimental velocity data with an empirical parabolic law, we have extracted the behaviour of 7’, as a function of temperature (see Fig. 4). The behaviour of the peak temperature clearly shows some changes in our system. The data, in fact, fall on two straight lines with an intermediate transition region. At this intermediate concentration the properties of the system change as stressed above. The system evolves from a water-imposed structure (in which the salt acts as a perturbing element) to a more packed structure, imposed by the solvent. In this intermediate region, it is not the water that loses its original structure but the strong interactions between ions and H20 molecules that produce a new interconnected structure. The value of Z’, turns out to be coincident with the limiting value of z 10°C for c=5.05 M. This implies that the saturated solution has a well-defined structure and the effect of temperature is only to alter the intermolecular distances, not to cause any structural evolution. Brillouin scattering
In order to better clarify the observed relaxation phenomenon,we extended the acoustic measurements to the MHz region by a Mandelstamm-Brillouin scattering experiment. The measurements were performed in the concentration range 0.25-5.05 M and at temperatures in the range 9.30-70” C. The transferred k value ranged from 4.57~ lo4 cm-’ (for the 0.5 M solution at 9.3O”C) to k=4.22 x lo4 cm-’ (for the solution at 0.5 M and 70°C). A free spectral range of 18.4GHz was used. In a light-scattering experiment the polarized spectrum, connected to the structure factor S (k,m), can be reduced, by using the usual hydrodynamics equations, as
&J,(k) ‘w(k,0)=w2+Z-‘fR(k)+{u-
&J”,(k) [o;(k)-P~(k)]1’2}2+P~(k)
297
r,(k) +{w+
[W:(k)A~~~~r/2j2+JRB(k)
+ [o;(k)
-PB(k)
Ill2
co- [o;(k) -PB(k)]1’2 [w;(k) -r”B(k)]“2}2 x ( PB(k) +{o+ co- [o;(k) -PB(k)
+{m+
-1”2B(k)]“2
[o;(k)
-r”B(k)]1’2}2
>
(1)
By using eqn. ( 1)it is possible to extract from the experimental data the acoustic parameters of interest, namely the frequency shift CO,and the linewidth rn from which the hypersonic velocity value V, and the absorption a/f 2 can be calculated. In Fig. 5a-b is reported, as an example, the velocity and absorption data for three concentration values. From what has been said, it is evident that ultrasonic and hypersonic probes furnish relevant information on the dynamic behaviour of liquid systems. In particular, the Brillouin technique allows a direct evaluation of the frequency dependence of the transport coefficients qv( (I)) and qS( CO).As a consequence, it is possible to observe some type of relaxations (structural, viscous, and so on) which could be connected to the collective dynamic evolution in the 1O-g-1O-'2 stime scale. Usually, the vibration contribution lies at higher frequencies and is decoupled (at low k value) from the translational and diffusional motions. Viscothermal (gas-like) and viscoelastic (solid-like) theories are able to describe the acoustic properties of these systems. It is possible to derive for the complex longitudinal modulus an expression that is a function of the frequency-dependent volume chemical viscosity, the structural high fre8 g-
-. .
1650-
-.
. 1550-
,.: .
. : -
: lL50-
a.1
. l
. ..*-A.
l
A.
-
.*1
.
I
{"-
.
$30* a
_.
-
. .
.
. .
NT10 2 -. 6
.
10 30
. . . M
l
It 70
.
. .
1. . .
,,,,,,t 10 30 50
.
l
I,,,,,, 70
10
30
so
70
T#T
Fig. 5. Sound velocity and absorption vs. Tatthree different concentration values: left, C= 0.5 centre, C= 2.0 M, right, C=5.05 M. Circles, hypersonic data, triangles, ultrasonic data.
M;
quency volume viscosity and the shear viscosity. As a consequence different relaxation times can be derived for the different processes. In our case we assumed a single relaxation process, which is quite reasonable when the chemical, structural and viscous processes are well decoupled as in our case. However, also assuming a distribution of relaxation times if the linewidth of the distribution is narrow, then the centre of the distribution can be assumed to be the single relaxation value revealed. On this basis we can write
(2) Note that the above equations hold when the viscous process relaxes at higher frequency. In our case, since the chemical and the structural processes relax at well-separated frequencies, the relaxed velocity of the chemical process can be assumed as the zero-frequency velocity for the structural process. Among other things, due to the limited range of Kexplored, we have information on a limited wr range. In any case our derived values range from 12.6 x lo-“-6.0 x 10-l’ s for 5.05 M solution and 3.2 x 10-“-2.6x lo-l1 s for the 0.5 M solution. This structural process, as pointed out, can originate from a “melting” and “building-up” of a locally ordered structure. The values of z, obtained give an indication of the time scale of the structural rearrangement. In any case this could be regulated in some more complicated and not understood manner. The concentration dependence of z, indicates that at lower concentrations the process becomes faster. For the 0.5 M solution the relaxation process could originate from a different process. In fact, the solute-imposed structure is still not present. This process could arise from a restructuring of the water molecules or anionic replacement in the cationic coordination shell. From an Arrhenius plot of r,, activation energies of ~0.8 kcal mol-’ (at 0.5 M) and x2.8 kcal mol-l at 5.05 M are deduced. This indicates that the fast process is less hindered than the slower one. This is true if any exchange process is hindered by the long-life, middlerange ordered regions. In Fig. 6 the evolution of the relaxation strength is reported in an Arrhenius plot for three values of concentration. At low concentration values the data fall on a straight line, which gives an energy value between 3.1 and 3.5 kcal mol-l. For the 5.05 M solution the data diverge from the straight line. This can be explained by assuming a single structural process with a single-step mechanism at low concentration and more complex processes at high concentration values. In this latter case, in fact, the system has a well-defined structural identity in which ions and water molecules are linked together. The breaking of the bonds at some points in the structure could cause time-dependent effects on the full structural environment.
299
!-
lO?'T.(KT'
Fig. 6. Arrhenius plot of the relaxational bulk modulus KJT at different concentrations. CALCIUM NITRATE TETRAHYDRATE
AND ITS MIXTURE WITH KNO,
In the following we report some results from an experimental investigation on Ca(N03)2*4.17Hz0 and its mixture with KN03. These systems show a shear viscosity ranging from x 2P at room temperature to several hundreds of poise in the supercooled liquid phase [ 10,111. Furthermore, according to the observations for the corresponding anydrous melt, these nitrates reveal a strongly non-Arrhenian behaviour of the transport coefficients. In other words, following the Angel1 classification [ 3,4], they can be considered as a good example of “fragile” glass-forming liquids. As far as calcium nitrate tetrahydrate is concerned, the exact solution composition R (defined as the ratio between the moles of water and the moles of salt) was determined by drying the sample under vacuum at moderately high temperature ( T z 150 ’ C ) and measuring the amount of H,O by weight loss. It turned out to be R=4.17. The mixture [Ca(N0,)2.4.17H,01,,,+ [KNW0.25, where subscripts refer to the percentage by weight of the two compounds, was also prepared. These values correspond to a concentration value for which the system shows a eutectic point. EXAFS measurements We have performed EXAFS measurements on our samples at the PULS facility in Frascati. The Ca2+ and K+ k-edges absorption spectra were scanned with a standard resolution of 2 eV in the temperature range between - 25 and + 20” C. It is well known that the normalized modulation above the k-edge of the absorber, i.e. the EXAFS structure x(k), is connected with the Fourier transform of the local distribution function P(ri). The experimental spectra were reduced according to the well-known expression kXck,=#lh(n,k)l
I
exp[-2Rj/L(k)]exp[-22ai2k2][2kRj+~11’(k)l
(3)
300
where symbols have their usual meanings and the 1fj (a&) 1 and @I” values are taken from the literature [ 12,131. The two absorption K-edges for Ca2+ and K+ ions are quite evident. In Fig. 7 the mixture-normalized EXAFS spectrum above the Ca2+ k-edge is reported as an example for T= 20’ C; triangles are the experimental data while the dashed line is the result of fitting by eqn. (3). The results obtained can be summarized as follows. (i ) In molten calcium nitrate tetrahydrate only a coordination shell of water was revealed around the calcium ion. The radial distance Rc,_,, = 2.46 + 0.001 A is in agreement with the values obtained in CaCl, aqueous solution by X-ray and neutron diffraction experiments [ 14,151 and by our EXAFS determination [16]. (ii) The value of this distance and the mean coordination number No = 4 + 0.5 turns out to be almost temperature-independent in the temperature range investigated. (iii ) The Debye-Waller factor (which in amorphous and liquid systems reflects both the structural and thermal disordering effects) shows a large variation with temperature going from CJ~,_~ =0.13 A at T= 20°C through ac,_o=0.115 A at T= +5”C to oc,_o=0.06 A at T= -25°C. This fact, with the high value of crat room temperature, is an indication that the existing ion-dipole interaction between cation and water does not allow strong bonding effects: the hydration shell is not kinetically stable and the water molecules are in the “fast-exchange” regime. Analogous results, i.e. only one shell of water around Ca2+ ions with the same values for Rc,_o and Nca_o and the same trend for a, were obtained in the mixed nitrate. Such a circumstance suggests that all the water molecules in solution are locally coordinated to calcium. If we look at the local order around the potassium ion, EXAFS gives evidence that only one water molecule is coordinated to the K+ ion at a mean distance of 2.55 A. These circumstances support the idea of the existence of strongly shared cationic hydration effects whereas, the hypothesized interionic inner sphere complexes (like ion pairs)
0.26
-0.26 3
6.5 k/A-'
Fig. 7. [Ca(N0,),*4.17H,0]0.7,+ T=20”C.
IO
[KN03]o.2, Ca K-edge Fourier-filtered EXAFS spectrum at
301
do not influence, within the technique sensitivity, the EXAFS modulation. The potassium ion enters the original structure of the calcium nitrate tetrahydrate without inducing strong polarization effects, and hydration forces turn out to be the only ones responsible for the existing local arrangement. Brillouin measurements Light scattering measurements were performed both on the pure calcium nitrate tetrahydrate and on its mixture with potassium nitrate using a doublemonochromator, double-pass instrument (SOPRA Model DMDP 2000) with a resolution of 700 MHz. Such an instrument is particularly suitable for this kind of measurement in order to eliminate the problem of the overlapping components of the contiguous free spectral range when a Fabry-Perot instrument is used. Its resolution is comparable with that of an interferometer working at a free spectral range of 50 GHz (necessary to resolve phonons shifted by x 15 GHz) but with a rejection power very much higher. The explored temperature for Ca(N03)2*4.17H20 and -47”CITI65”C range was -47”CITI25”C for its mixture with potassium nitrate. This means that for both systems the deeply supercooled liquid region ( w 100” C below the melting point) was explored, where all the viscous and diffusive properties are more and more substituted by the “elastic” properties, as the system goes towards the glass transition temperature ( Tg= -58°C for Ca(NO,),-4.17H,O). Also in this case eqn. (1) was used in order to extract the parameters of interest and eqn. (2) was used, with the same assumption as made for aqueous CdCl, solution, in order to obtain the hyperacoustic velocity and the normalized absorption. In Fig. 8 the temperature evolution for o, and the loss tangent tan 6= $[+~]I
(4)
are reported. This latter quantity is a measure of the attenuation in dynamical mechanical studies and can be directly compared with the same quantity measured by different probes. It is easy to observe that both o. and 6 are strongly temperature dependent. We are clearly in the presence of the same relaxation phenomenon as studied at temperatures higher than + 20’ C [ 10,171. In addition, clear evidence is found in the literature that for nitrates [ 181, at temperatures higher than 2O”C, the time evolution of the bulk and shear viscosity are the same, i.e. the average and longitudinal relaxation times are comparable. When eqn. (2) is used, the mean relaxation time r, and the relaxation modulus M, are obtained, provided the zero-frequency value of the compressional modulus MO=PU,,~is known as a function of T. As MO for the calcium nitrate, we used the values of the ultrasonic velocity measured by Darbari et al. [lo], extrapolated down to 30” C in the temperature range 30” C I TI 60” C. The
302
I5
0
(a)
es ‘b
-10 00
++ ++
lo-
+
c
0
w
-5
+ g 5-
+
\.I
11
#i?
11
5
3
gw
(b)
Q15O 0
lo-
Oo
+
+
0 +:t
-10 + 0 -5
+
5-
+ III -50 -30 -10 10
30
Fig. 8. Brillouin frequency W, (circles) and loss tangent (crosses) vs. temperature for: a, calcium nitrate tetrahydrate; and b, its mixture with potassium nitrate.
values of u,,, and of A4,,were measured by a standard Matec pulse-echo apparatus. The results are reported in Table 1 with the values of hypersound velocity and normalized absorption. As stressed above, our r, values are to be considered as mean values because we used eqn. (2)) which applies in the case of a Maxwell relaxation law. This approach is obviously a crude approximation even if, as in the case of nitrate at low R values (between 3 and 4), the distribution tends to narrow. In such a case z, could represent, to a good approximation, the centre of mass of the distribution and the “overall” relaxation strength. Furthermore, as in the case of the corresponding anhydrous melt [ 191, another source of energy loss and thus of additional contributions to the observed relaxations, can be induced by energy transfer processes between the thermal phonons and the internal degrees of freedom of the NO, ionic group. In such a case, both thermal and vibrational relaxations could be involved in the observed phenomena and the linewidth rn should be written as the sum of many contributions. Let us return now to the temperature evolution of the extracted parameters z, and M,. As expected, both parameters show a strong deviation from the straight line when represented as an Arrhenius plot. This confirms the idea that our nitrates behave (following the Angel1 classification) like “fragile liquids” whose structure is imposed by binding forces originating from hydration and H-bond effects. The mean activation energy was estimated to be, in the
TABLE 1 Temperature dependence of hypersound velocity, IJhs,absorption, modulus, M,, in molten hydrated nitrates
a/f ‘, relaxational time,
T (“C)
lOlO
vhs
(m s-*)
%xo’r
Tr x
f’
(s)
11.8 9.8 8.2 6.7 6.9 5.9 5.2 4.7 4.9 2.9 1.6
0.69
TV,
and
M, x 10” (dyn cm-“)
(cm’ 5-l)
Ca(N0&.4.17Hz0 +25 2439 +15 2586 +5 2749 0 2932 -5 2918 -14 3058 -15 3125 -25 3195 -27 3224 -34 3324 -47 3543
[Ca(N0~)~.4.17H,010.7,+ lKNW0.25
+65 +25 +15 +5 -5 -15 -25 -35 -47
1948 2511 2667 2805 2933 3077 3145 3319 3411
23.3 10.7 8.9 7.6 6.7 5.8 5.4 3.1 0.6
0.97 1.04 1.10 1.20 1.18 1.78 2.75
4.19 5.32 6.74 8.80 8.25 9.71 11.11 11.26 11.43 12.47 15.09
0.11 0.69 0.80 0.88 0.94 1.00 1.02 1.59 8.09
1.19 2.99 3.86 4.66 5.44 6.39 6.83 8.06 9.36
0.79 0.89 0.96
extreme supercooled region x 20.1 kJ mol-’ for calcium nitrate tetrahydrate and E 38.9 kJ mol-’ for its mixture with potassium nitrate. The corresponding limiting values for the binding energy connected with the observed phenomenon are x 6.3 kJ mol-’ and x 4.6 kJ mol-1 respectively. The physical origin of the observed hypersound dispersion could be connected with the local “melting” of the close-packed structure in which the few water molecules are shared between ions. The melting of the local structure in which water molecules are in a fast-exchange regime can simultaneously generate structural and shear relaxation phenomenon. Such results agree with indications from Rayleigh wing measurements [ 201. In such a case the rotational relaxation, viscosity controlled, of the nitrate group within the structure has been rationalized in terms of librations for a rest time r. and subsequent jumps to a new local configuration when the local structure melts. Actually Brillouin scattering measurements as a function of the exchanged
304
wave-vector and temperature (passing through the T, temperature) are in progress in our laboratory, in order to better understand the relaxation processes that take place in these hydrated melts.
REFERENCES 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
See, e.g. H.S. Harned and B.B. Owen, The Physical Chemistry of Electrolyte Solutions, Reynold, New York, 1967. 0. Ya Samoilov, The Structure of Aqueous Solutions and the Hydration of Ions, Consulance Bureau, New York, 1965. C.A. Angel1and E.J. Sare, J. Chem. Phys., 52 (1970) 1058. C.A. Angell, in K.L. Ngai and G.B. Wright (Eds.), Strong and Fragile Liquids, Nat. Techn. Inf. Serv., U.S. Dept. of Commerce, New York, 1984. pp. 3-11. M.P. Fontana, G. Maisano, P. Migliardo andF. Wanderlingh, Solid State Commun., 23 (1977) 489. G. Carini, M. Cutroni, G. Maisano, P. Migliardo and F. Wanderlingh, J. Phys. C, 13 (1980) 967. G. Maisano, P. Migliardo, F. Aliotta and C. Vasi, Phys. Chem. Liq., 14 (1984) 13. M.D. Danford and H.A. Levy, J. Am. Chem. Sot., 84 (1962) 3965. C.J. Montrose, J.A. Bucaro, J. Marshall-Coakley and T.A. Litovitz, J. Chem. Phys., 60 (1974) 5025. G.S. Darbari, M.R. Richelson and S. Petrucci, J. Chem. Phys., 55 (1971) 4351. A.R. Carpio, M. Mehinic and E. Vyeager, J. Chem. Phys., 74 (1981) 2778. B.H. Teo, P.A. Lee, A.L. Simons, P. Eisenberger and B.M. Kinkaid, J. Am. Chem. Sot., 99 (1977) 3854. P.A. Lee and G. Beni, Phys. Rev., B, 15 (1977) 2862. R. Caminiti, G. Licheri, G. PiccaIuga, G. Pinna and M. Magini, Rev. Inorg. Chem., 1 (1979) 333. S. Cummins, J.E. Enderby and R.A. Howe, J. Phys., C, 13 (1979) 1. G. Galli, S. Magazti, D. Majolino, P. Migliardo, M.C. Bellissent-Funel, F. Aliotta and C. Vasi, 11Nuovo Cimento, 12D (1989) 197. V.C. Reinsborough and J.P. Valleau, J. Phys. Chem., 50 (1972) 2074. S.M. Rytov, Sov. Phys., JEPT, 31 (1970) 1163. L.M. Torrel, in G. Mamantov and E. Marassi (Eds.), Brillouin Scattering in Ionic Liquids, Reidel, Dordrecht, 1987, pp. 161-180. A.R. Carpio, M. Mehinic and E. Yeager, J. Chem. Phys., 74 (1981) 2778.