Diffusion processes in LiCl, R H2O solutions

journal of MOLECULAR

LIQUII ELSEVIER

Journal of Molecular Liquids 84 (2000) 289-299 www.elsevier.nl/Iocate/molliq

DIFFUSION PROCESSES IN LiCl, R H 2 0 SOLUTIONS.

A. AOUI77E~RAT-ELARBY, H. DEZ, B. PREVEL, J.F. JAL, J. BERT, J. DUPUY-PHILON Ddpartement de Physique des Matdriaux, URA 172 C.N.R.S UCB LYON I- 43 Bd du 11 novembre 1918 - 69622 Villeurbanne C~dex (FRANCE) Received 1 July 1999; accepted 26 October 1999 ABSTRACT Transport properties, particularly mutual and self-diffusion coefficients are investigated in the solutions LiC1, R 1-120. Our study is made at room temperature and on a large range of concentration 3
Dipolar and ionic forces both have a very significant effect on the aqueous electrolytes properties. Among those solutions, LiC1, RH20 is a system which has been extensively and intensively investigate& We use the notation LiC1, RH20 where R the hydration number, is the number of water moles per salt mole. The thermodynamic properties t ~ .3 ,4.5 prove an aptitude to vitrify easily over the whole domain of concentration. This facility is also found in BeC12,RH20. Contrary to others electrolytes, these systems have not many defined crystallised compounds. At all concentrations, the mentioned forces have particular influences correlated to the relative size of the two ions and the strong polarisation induced by the cations. That can be seen on the evolution of the volume dilatation coefficient a and of the molar volume 5 of LiC1, RH20 with R. For 0
290 metastable liquid and glass. The structural analysis have showed a complete hydration sphere for R=6, and for R=4 a direct anion cation interaction. We have demonstrated a relationship between the structural characteristics of hydration and the relaxational behaviour of the system11. In this paper, we want to focus on the relationship between specific transport properties related to the mass transport as obtained by measurements of interdiffusion and self-diffusion coefficients. The interdiffusion properties have been explored using the holographic interferometry tecnnique 13" 14, 15. The main interest of holographic interferometry is to allow the visualisation of a diffusion mechanism as well as that any of convective instability that could take place during the diffusion processes 16. The water self-diffusion is obtained by inelastic neutron scattering 17 (I.N.S), more precisely by quasi-elastic neutron scattering (Q.E.N.S). This experimentation is suitable to study the self-diffusion of any element having large incoherent inelastic scattering and small coherent scattering as well as to a low absorption cross section. The 7Li, 37C1 and H elements have these characteristics. Our results are combined to a critical review of the main results available in the literature. Most of these literature results are obtained at room temperature is on diluted concentrations because the motion of the solvent can then be disregarded and the experimental diffusion can be described as the motion of solute particles through the solvent. There are few diffusion experiments in concentrated electrolytic solutions (0_55). No measurements have been made in the supercooled liquids. Our aim is, at room temperature to extensively investigate the water-ion interaction through a full concentration range evolution of the diffusion coefficients. This permits to open the question of mass transport when co-operative modes play important role.

II-INTERDIFFUSION PHENOMENON. During an interdiffusion process (also called mutual diffusion, or concentration diffusion), a matter flux compensates spontaneously every concentration difference inside a non-homogeneous solution. The analysis of the interdiffusion phenomenon in electrolyte solutions implies the motion of anions and cations in the same direction and with the same velocity. Every ion is considered as moving under the influence of two forces: a chemical potential gradient, and an electric field due to the motion of the ions of opposite charge. On a microscopic scale, the mobile ions create an electrical potential gradient in the solution. Hence, the resulting velocity will be identical for each type of ions. So, in a fixed volume, there exists only one interdiffusion coefficient in a system. Figure 1 gives the interdiffusion coefficients of the KI solution (literature data given at 25°C) and of the LiC1 solutions (literature data given at 25°C and 18°C) 18' 19. The experimental results of the interdiffusion coefficients obtained by holographic interferometry IY__ were fast acquired on KI and LiC1 aqueous solutions at room temperature. The choice of these test systems had been guided by the fact that numerous results were available in the literature. Our results are obtained at 22°C. The data are plotted as function of the molality c (mol/l) and R. The global concentration dependence and the temperature effect, are fully confirmed. In the two investigated solutions, the diffusion coefficient shows an initial fall-off for very dilute solutions leading to a minimum value at a concentration of about 0,2 mole/1. It is also shown in other electrolyte systems 20 and is noted in strong electrolyte solutions with ion

291 association or strong auto complex formation. This initial fall-off is followed by an particularly strong increase for KI in the limited concentration range studied. For LiC1 solution the broad positive parabolic evolution displays a maximum at c=5mogl (R=10).

D =~ ('10-9m2/s) 2,6 KI 2.4 2.2

2 1.8

1,S

1,4

'~eJ'~" et.j..~,~

1,2

"" ~ Q""

LICI

. a l '~"~'~"~- ~, ":S° ~mogl)

1

i

,

,

i

i

0

2

4

6

8

I

I

100 50

I

20

I

10

I0

i

6 R(m0l

water/salt)

Fig 1: Interdiffusion coefficients of two aqueous electrolytes. Black symbols present our results and white symbols the literature results as function of the molality c. ~,,H20 25oc [] 19 • our results 22°C

LiC1,H20

25°C

18°C 22°C

1 21

(~ 22

~) 23

0 24

A 18 • our results

The diffusion processes (interdiffusion and self-diffusion) are described by the Fick's laws 2° with the limiting conditions that are controlled and specified by the holographic technique. The interpretation of the diffusion coefficients Di,t~ has been first given by Nemst for the limiting value D ° at infinite dilution. With the hypothesis that the chemical potential gradient is the creative force of the diffusion, Dinteris expressed by the Nemst -Hartley relation: Dintet =D°(1 + d ln(7)/d In(c)) The factor F =(1 + d ln(7)/d In(c)) is related to the thermodynamic behaviour of the system where T is the activity coefficient. Onsager and Fuoss introduced two corrective terms due to the electrophoretic effect. Robison and Stokes 21 interpreted also the D value with a multiplier

292 term which reflects the solvent motion and the relative viscosity of the electrolyte and the solvent. These theories fit the diffusion coefficients up to c=lmole/1 (R_~55). In our study made on a large concentration range, we choose to correct the experimental n ~ the activity coefficient interdiffusion coefficient by the F factor and we note D-,n~c o t _- D inter',, being connected to the interactions in the system: ion-ion, ion-water and water-water. For LiC1, RH20, the ln(~/) as function of the molality is plotted in the figure 2 at room temperature~8. 25. Its variation is strong for c>lmol/1 i.e. RS55. For small salt concentrations, the activity coefficient varies slowly and is inferior to 1. In?

1 o -1

'

CC ~ -8

C~ r ~

-6

-4

-2

C

0

2

4

Fig 2: Activity coefficient as function of molality c ~s, 25 The F evolution induces a behaviour of Dinterc°r which is strongly modified as compared to of Dinter. It is then interesting to plot it versus R, which parameter is more or less connected with the hydration number of the ions. Changing of unit from c to R emphasises high salt concentration variations and inhibits those of low concentrations [figure 3].

D(10"gm21 s) 1,6

//--

1,4

oo..

.

1,2

•

.~-'~-

•

+,

++t,

1 0,8

/ DCOl

0,6

Inlet

0,4

o.~

+P4-I

- ~ =

. . . . . . .

--=~

D°=1.368 10"9m2/s

•

/

t-

i'÷

0,2

i

1

+. . . . . . . . . . . . . . .

6 10

i

,

..

I00

I

1000

,

l

,

..

i

.

,

, m _ //

10000 R(mol water/salt)

Fig 3: interdiffusion coefficients in LiCl, RH20 at RT, (R= mole of H20/mole of salt). Dinter O 22 (9 23 (25 °C) and • our results (22 *C) the corresponding Dinterc°r (+ ,

X

and

&) corrected by F

293 The R dependence of Di,t~¢°r shows a continuous variation with a monotonous decrease with concentration in diluted domain. As expected, over a large concentration range 1006. Structural and vibrational studies should permit to obtain more informations of the H-bonding network and allow the analysis of the interdiffusion process in the range 6100, the mass transport process induced by a concentration gradient will remains the same. The examination of the self-diffusion behaviour of all the elements of the sample will reveal this differentiation and its correlation to the changes in the mass process.

m-SELF-DIFFUSION PHENOMENA.

The self-diffusion process does not imply the electrical neutrality of an electrolytic solution, the three entities (the two ions and the solvent) have their own self diffusion coefficients. The individual dynamics can be studied by different methods: direct analysis of Fick's equation for tracers (i.e. labelled species), NMR spin echo, electroanalytical methods and quasi-elastic neutron scattering 11. The last technique using neutrons of very low energy is unique to probe the individual dynamics, the neutron energy and the wavelength being respectively comparable to the energy involved in these dynamics and to the interatomic distances. A deep analysis of individual motion can be achieved with an isotope of the investigated ion having a large incoherent

294 scattering cross-section and if the correction for coherent scattering 27 is possible. The hydrogen atom having such specificity, the incoherent inelastic neutron scattering of aqueous solutions permits to study all the motions of H20 from vibrational to diffusive. The selfdiffusion coefficient can be deduced from the half width of the Lorentzian component of the incoherent dynamic structure factor Sinc (Q,o~). This translational diffusion component exhibits a Q2 linear variation in the low Q range, Q being the momentum transfer 2s. We have analysed the diffusion mechanism of H20 in the liquid and supercooled states for R=6 and R=4 z7 ,and the diffusive component values obtained with the Q.E.N.S and N.M.R techniques are in very good agreement. They fit correctly into the Mc Call 29 and Fortes 3° values obtained on a large concentration domain (figure 4) by NMR spin echo technique at R.T. According to Mills recommendation 32, the literature values have been normalised in order to get the infinitely dilute limit D°(H20)=2.29 10-9m2/s at 25°C. In figure 4, we plot the chlorine self-diffusion results obtained by Tanaka 33 (open-ended capillaries technique) and by Mills 32 (diagram cell technique). 43

1

0.1

0.01

1 1

1

1

1

5 10 2,5

....

i

I00 ....

i

D(10"}m2/s)

I000 ....

I

,

~

1,5

~

I0000

I 00000

i

i

....

O--- -

.O" Q ,_~o~¢~

2

....

c(mol/1)

--

---~ a

R(mol water/salt) //

O. . . . .

D ° ( H 2 0 ) = 2 " 2 9 10-gmZ/s

.t . . . . .

Do(C1)=2.03310-gmZ/s

m

D°intcr= 1 " 3 6 8 10-9m2/s

[]--D

1

D°(Li)=I.03

m .....

0,5 0

i

t

1.5

0.5

t

0 0

10

i

i

i

20 30 40 R( m o l waterlealt)

i 50

Fig 4: Diffusion coefficients as function of R H20 self-diffusion O Mc Call 29 (;) Fortes 30 H20 self -diffusion • (our results) C I self- diffusion 0 Turq 31 A Mills 32 • Tanaka 33 Li+ self-diffusion [] Turq 31 [] Braun 32 [] Tanaka 33 Interdiffusion X

60

10"9m2/s

295 The Nernst limiting self-diffusion value D°(C1) = 2.033 10-9m2/s at RT. The lithium selfdiffusion coefficients obtained respectively by Turq 31 and Braum 32( open ended capillaries technique ) and by Tanaka 33 are also given with the Nernst limiting self-diffusion value D°(Li) = 1.03 10-9m2/s. The nearly independence on concentration of all self-diffusion coefficients in the domain 100500) does not affect really the translational diffusion. The slightly lower C1 diffusion might indicate a jump mechanism reduced by an increase of the characteristic jump length compared to water or more probably by a short lived complexion of water with halide ions that have an effect on the librational short time mechanisms. The reduction of the translational motion of Li + compared to C1 by a factor two, could be interpreted on the basis of the Li ÷ motion hindrance by a vibrational mechanism of the hydration shell36, 37 like a "cage effect". The diffusion in the concentrated and high concentrated solution present a strong dependence on R. Around R=10, Drf2o and Dcl are equal and for R~ 4 all the coefficients are similar. Further discussions on the mechanisms leading to these results will be made after comparison with the mutual diffusion. IV - A COMPARISON BETWEEN MUTUAL DIFFUSION AND SELF DIFFUSION. Synthetic display of the LiC1, RH20 data obtained for these two dynamical processes on the full concentration range gives some light on the diffusion mechanism and on the respective role of the ions. It is surprising that a comparison between these experimental results has never been made. There is a similar evolution of self and mutual diffusive components that validates the corrective factor F on the interdiffusion coefficients. On the dilute salt concentration domain (R>500), ion-water interactions do not really change the diffusion mechanism. An equation similar to the limiting Nemst relationship between interdiffussion and self diffusion

DOter

=

2 D~+i . DOI is verified.

This relation is only valid if the cross phenomenological coefficients between the two ions are = 0 z0, that is to say when the anion and cation exert no influence on each other. But this condition is not unique. It is necessary to add a condition on the non influence of each ion on the network of water. On this extended range the plateau behaviour observed for all the diffusion processes allows us to consider the mass diffusion processes as a collective transport of Li ÷ and C1- sharing each their surrounded atmosphere of water molecules in a water medium not really disturbed. The other characteristic concentration range extends from R=3 to R_<.12 at room temperature. In this range, for R< 6 the water self diffusion coefficient is not discriminated from D a (figure 4). We know that at this limit, the lose of full hydration and of the tetrahedral coordination between H20 molecules characterise the structure. Consequently, H20 is

296 strongly bonded to CI and their motions are identical. For (R>6) the decrease of ion water interaction would permit the connectivity between H20 molecules leading progressively to a H-bonded network. (This fact should be verified by neutron diffraction study or by the analysis of individual vibrational dynamics). This connectivity between water molecules could permit a possible diffusion motion of water outside the first hydration shell giving Drf2o>Do. The mutual motion is completely identical to the self motion of Li + for R.~12 i.e. the mass process is completely managed by Li+ which statistically co-ordinates strongly up to 2 shells of water. This strong influence of Li+ can explain the Du. plateau extension compared to the DH2o, and Do_ plateaus: we can observe also that Du÷ = D°u÷ for R>100. The ion interactions and modifications of water network do not act on the motion of Li÷ as soon as two or a little more hydration shells screen the ion from the remainder of the solution.

V - CONCLUSION. We have reviewed the data on the different diffusion processes of the aqueous electrolyte LiC1, R H20 on a large concentration range (3
297 and the second one is more related to the short time diffusion. The electrolytes aptitude to be supercooled should allow the study of the temperature influence on diffusion, enabling the discrimination between the self and mass diffusion processes for the domains R>500, 3
VI - Acknowledgments

The authors are indebted to S. Benet (Laboratoire de Physique Appliqu6e, Universit6 de Perpignan, France) for useful discussions during the various stages of the holographic studies and to Dominique GuiUot (D6partement de Physique des Mat6riaux, UCB Lyon I, France) for its participating to the design and the development of the apparatus. We would like to thank ILL and LLlq for providing neutrons for optimal experiments and J.Cook and M.C.Bellissent-funel for their contribution, as respective local contacts, to the success of the experiments. We also acknowledge P. Chieux for valuable comments.

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