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Study of Li+ ion hydration by inelastic neutron scattering
Physica B 234-236 (1997) 340-342
ELSEVIER
Study of Li + ion hydration by inelastic neutron scattering A.G. N o v i k o v a, M.N. R o d n i k o v a b, V.V. Savostin a, O.V. Sobolev a' * aState Scientific Centre-Institute of Physics and Power Engineering, 249020 Obninsk, Kaluga Region, Russian Federation bKurnakov Institute of General and Inorganic Chemistry, Russian Academy of Science, 117907Moscow, Russian Federation
Abstract The data analysis of the slow neutron scattering on 2M solution of LiC1 is presented. The quasi-elastic and inelastic components of the incoherent scattering function S~(Q, e) have been considered. From the analysis of quasi-elastic component it was established that there are four water molecules in hydration shell of Li + ion, and their residence time in the hydration shell is Zo = 25 + 10 ps. The diffusion coefficient of Li +, Dion = (0.79 __+0.05)x 10 -5 cm.2/s, has been obtained also from quasi-elastic component of Ss(Q, e). The generalized frequency distribution (GFD) for hydration water molecules has been extracted from inelastic part of neutron scattered spectra. A comparison of GFD of hydration water molecules and GFD of pure water gives the information concerning the ion's influence on the rotation-vibration motions of surrounding water molecules. Keywords: Diffusion; Hydrogen bonds; Solutions; Water
O. Introduction The aim of this work is to perform using inelastic neutron scattering method, the analysis of diffusion and vibration-rotation motions of water molecules hydrating Li ÷ ion in comparison with pure water molecules. The experiment has been performed on 2M lithium chloride solution and on pure water. It has been carried out with the use of D I N - 2 P I double time-of-flight spectrometer operating on a neutron beam of the IBR-2 pulsed reactor (Frank Laboratory of Neutron Physics, JINR, Dubna) [1]. The initial neutron energy, Eo = 3 meV was allowed to have the resolution, AEo = 0.14 meV. The neutron scattered spectra have been recorded at eleven angles in the range from 11 ° to 134 °. The complexity of the object under study induced us to make some suppositions and simplifi-
cations which cannot be mentioned in this short paper, but are considered in detail in our previous works [2, 3].
1. Quasi-elf-tie scattering To get the results for quasi-elastic scattering, the following steps have been followed: - from the total S(Q, e) the effects of multiple and inelastic scattering have been removed; - t h e experimental quasi-elastic scattering law, Sq.el(Q , g), obtained for O = const, by interpolation procedure has been transformed into the form of that obtained ~for Q = const; - Sq.el(Q, e) for solution studied was approximated by superposition of two Lorentzians [4]:
S..o~(Q, ~) = ~ L(AEd2)~ + ~
* Corresponding author. 0921-4526/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S092 1-4526(96)00979-9
+ -(AE-~
~ii~j~ R(Q, e),
(1)
A.G. Novikov et al. /Physica B 234-236 (1997) 340 342
where AEi are the full-widths at half-maximum (FWHWs) of the Lorentzians corresponding to the scattering on the molecules of hydration and bulk water, ~ is the share of hydration molecules in solution, R(Q, ~) is the spectrometer resolution function. Sign ® means the convolution operation. For the analysis of the F W H M of the Sq.om(Q,e) natural line the model of mixed diffusion [5] has been used: =
+ DoQ2zo
341
For F W H M of hydrated water these parameters are: O hyd = (0.95 _+ 0.05) x 10-5 cm2/s, ogYd= (0.79 _+ 0.05) x 10 5 cmZ/s, zgyd = 25 -t- 10 ps. The D~yd obtained is equal to Dio, 0.8 x 10 -5 cm2/s achieved in Ref. [6]. zgyd is in agreement with the results of Hertz (zR>~ 20 ps [6]). The share of hydration lorentzian in the common square under quasi-elastic peak ~ ~ 0.15 _+ 0.05 corresponds to four molecules in hydration shell of Li + ion.
ZoL
e x p ( - 2W) 1 - 1 -- o - j e - % J
(2)
2. Inelastic scattering The analysis of the inelastic component of
Here Zo is the residence time, Do is the coefficient of continuous (collective) diffusion, D is the total coefficient of self-diffusion, e x p ( - 2 W ) is the Debye-Waller factor 2W = uZQ 2, where u 2 is the mean-square amplitude of molecular vibrations. The experimental F W H M s for pure water (one Lorentzian approximation) and for solution (two Lorentzian approximation) are shown in Fig. 1. For F W H M of pure water model (2) gives the following parameters: D = (2.2 _ 0.1)x 10-5 cm2/s, Do = (0.8 + 0.05) × 10 -5 cm2/s, ~o = 3.1 + 0.5 ps.
1.0 0.8 >
Q)
0.6
E 0.4 0.2 0.0 0.0
,
,
,.o
,
i
,
2.0
i
3.0
,
,
t
4.0
Q2 Fig. 1. The FWHM of Sq.el.(O, t~) natural line for pure water (one Lorentzian approximation) and LiC1 solution (two-Lorentzian approximation) (1) the experimental FWHM for pure water (description by model (2)); (0) the experimental FWHM for bulk water; (11) and (2) the experimental FWHM for hydration water and its description by model (2).
Ss(Q, ~) has been aimed to get the generalized frequency distribution of proton for water molecules in pure water and solution studied. The procedure of G F D extraction for hydration molecules involved the following steps: (1) The double-differential scattering crosssection (DDSCS) of pure water has been subtracted from DDSCS of solution. The first has been taken with the weight equal to the relative fraction of bulk water molecules in 2M solution, determined during the analysis of quasi-elastic component(q ~ 0.85). So, we get the DDSCS of hydration water. (2) The G F D for hydration water has been extracted from its DDSCS obtained above. The method we used for this purpose has been developed and tested on pure water (for details and corresponding formulas see Ref. [3]). Fig. 2 presents the final GFDs we obtained for pure water and hydration water. G F D extracted corresponds to the region of intermolecular interactions for water molecules (2 meV
342
,4.G. Novikova et al. /Physica B 234-236 (1997) 340-342
- The libration region of G F D , (with maximum at eo ~ 60 meV) within the limits of experimental errors, we consider as unchanged.
7 Q)
References
~d
t: t:: i
i
h
50
100
150
200
~, m e V Fig. 2. Generalized frequency distribution of water molecules: (0) pure water; (O) hydration water of Li ÷ ion.
[1] User Guide. Neutron Experimental Facilities at JINR, ed. Yu.V. Taran (JINR Press, Dubna, 1992). [2] A.G. Novikov, M.N. Rodnikova, V.V. Savostin and O.V. Sobolev, J. Phys. Chem. 68 (1994) 1799 (in Russian). [3] A.G. Novikov, M.N. Rodnikova, V.V. Savostin and O.V. Sobolev, Chem. Phys. Lett. 259 (1996) 391. [4] P.S. Salmon, J. Phys. C. 20 (1987) 1573. I-5] V.S. Oskotskii, Sov. Phys. Solid State 5 (1963) 789. [6] H.G. Hertz, R.Tutsch and H. Versmold, Ber. Bunsenges. Phys. Chem. 75 (1971) 1177.
ELSEVIER
Study of Li + ion hydration by inelastic neutron scattering A.G. N o v i k o v a, M.N. R o d n i k o v a b, V.V. Savostin a, O.V. Sobolev a' * aState Scientific Centre-Institute of Physics and Power Engineering, 249020 Obninsk, Kaluga Region, Russian Federation bKurnakov Institute of General and Inorganic Chemistry, Russian Academy of Science, 117907Moscow, Russian Federation
Abstract The data analysis of the slow neutron scattering on 2M solution of LiC1 is presented. The quasi-elastic and inelastic components of the incoherent scattering function S~(Q, e) have been considered. From the analysis of quasi-elastic component it was established that there are four water molecules in hydration shell of Li + ion, and their residence time in the hydration shell is Zo = 25 + 10 ps. The diffusion coefficient of Li +, Dion = (0.79 __+0.05)x 10 -5 cm.2/s, has been obtained also from quasi-elastic component of Ss(Q, e). The generalized frequency distribution (GFD) for hydration water molecules has been extracted from inelastic part of neutron scattered spectra. A comparison of GFD of hydration water molecules and GFD of pure water gives the information concerning the ion's influence on the rotation-vibration motions of surrounding water molecules. Keywords: Diffusion; Hydrogen bonds; Solutions; Water
O. Introduction The aim of this work is to perform using inelastic neutron scattering method, the analysis of diffusion and vibration-rotation motions of water molecules hydrating Li ÷ ion in comparison with pure water molecules. The experiment has been performed on 2M lithium chloride solution and on pure water. It has been carried out with the use of D I N - 2 P I double time-of-flight spectrometer operating on a neutron beam of the IBR-2 pulsed reactor (Frank Laboratory of Neutron Physics, JINR, Dubna) [1]. The initial neutron energy, Eo = 3 meV was allowed to have the resolution, AEo = 0.14 meV. The neutron scattered spectra have been recorded at eleven angles in the range from 11 ° to 134 °. The complexity of the object under study induced us to make some suppositions and simplifi-
cations which cannot be mentioned in this short paper, but are considered in detail in our previous works [2, 3].
1. Quasi-elf-tie scattering To get the results for quasi-elastic scattering, the following steps have been followed: - from the total S(Q, e) the effects of multiple and inelastic scattering have been removed; - t h e experimental quasi-elastic scattering law, Sq.el(Q , g), obtained for O = const, by interpolation procedure has been transformed into the form of that obtained ~for Q = const; - Sq.el(Q, e) for solution studied was approximated by superposition of two Lorentzians [4]:
S..o~(Q, ~) = ~ L(AEd2)~ + ~
* Corresponding author. 0921-4526/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S092 1-4526(96)00979-9
+ -(AE-~
~ii~j~ R(Q, e),
(1)
A.G. Novikov et al. /Physica B 234-236 (1997) 340 342
where AEi are the full-widths at half-maximum (FWHWs) of the Lorentzians corresponding to the scattering on the molecules of hydration and bulk water, ~ is the share of hydration molecules in solution, R(Q, ~) is the spectrometer resolution function. Sign ® means the convolution operation. For the analysis of the F W H M of the Sq.om(Q,e) natural line the model of mixed diffusion [5] has been used: =
+ DoQ2zo
341
For F W H M of hydrated water these parameters are: O hyd = (0.95 _+ 0.05) x 10-5 cm2/s, ogYd= (0.79 _+ 0.05) x 10 5 cmZ/s, zgyd = 25 -t- 10 ps. The D~yd obtained is equal to Dio, 0.8 x 10 -5 cm2/s achieved in Ref. [6]. zgyd is in agreement with the results of Hertz (zR>~ 20 ps [6]). The share of hydration lorentzian in the common square under quasi-elastic peak ~ ~ 0.15 _+ 0.05 corresponds to four molecules in hydration shell of Li + ion.
ZoL
e x p ( - 2W) 1 - 1 -- o - j e - % J
(2)
2. Inelastic scattering The analysis of the inelastic component of
Here Zo is the residence time, Do is the coefficient of continuous (collective) diffusion, D is the total coefficient of self-diffusion, e x p ( - 2 W ) is the Debye-Waller factor 2W = uZQ 2, where u 2 is the mean-square amplitude of molecular vibrations. The experimental F W H M s for pure water (one Lorentzian approximation) and for solution (two Lorentzian approximation) are shown in Fig. 1. For F W H M of pure water model (2) gives the following parameters: D = (2.2 _ 0.1)x 10-5 cm2/s, Do = (0.8 + 0.05) × 10 -5 cm2/s, ~o = 3.1 + 0.5 ps.
1.0 0.8 >
Q)
0.6
E 0.4 0.2 0.0 0.0
,
,
,.o
,
i
,
2.0
i
3.0
,
,
t
4.0
Q2 Fig. 1. The FWHM of Sq.el.(O, t~) natural line for pure water (one Lorentzian approximation) and LiC1 solution (two-Lorentzian approximation) (1) the experimental FWHM for pure water (description by model (2)); (0) the experimental FWHM for bulk water; (11) and (2) the experimental FWHM for hydration water and its description by model (2).
Ss(Q, ~) has been aimed to get the generalized frequency distribution of proton for water molecules in pure water and solution studied. The procedure of G F D extraction for hydration molecules involved the following steps: (1) The double-differential scattering crosssection (DDSCS) of pure water has been subtracted from DDSCS of solution. The first has been taken with the weight equal to the relative fraction of bulk water molecules in 2M solution, determined during the analysis of quasi-elastic component(q ~ 0.85). So, we get the DDSCS of hydration water. (2) The G F D for hydration water has been extracted from its DDSCS obtained above. The method we used for this purpose has been developed and tested on pure water (for details and corresponding formulas see Ref. [3]). Fig. 2 presents the final GFDs we obtained for pure water and hydration water. G F D extracted corresponds to the region of intermolecular interactions for water molecules (2 meV
342
,4.G. Novikova et al. /Physica B 234-236 (1997) 340-342
- The libration region of G F D , (with maximum at eo ~ 60 meV) within the limits of experimental errors, we consider as unchanged.
7 Q)
References
~d
t: t:: i
i
h
50
100
150
200
~, m e V Fig. 2. Generalized frequency distribution of water molecules: (0) pure water; (O) hydration water of Li ÷ ion.
[1] User Guide. Neutron Experimental Facilities at JINR, ed. Yu.V. Taran (JINR Press, Dubna, 1992). [2] A.G. Novikov, M.N. Rodnikova, V.V. Savostin and O.V. Sobolev, J. Phys. Chem. 68 (1994) 1799 (in Russian). [3] A.G. Novikov, M.N. Rodnikova, V.V. Savostin and O.V. Sobolev, Chem. Phys. Lett. 259 (1996) 391. [4] P.S. Salmon, J. Phys. C. 20 (1987) 1573. I-5] V.S. Oskotskii, Sov. Phys. Solid State 5 (1963) 789. [6] H.G. Hertz, R.Tutsch and H. Versmold, Ber. Bunsenges. Phys. Chem. 75 (1971) 1177.