The solvation of cations in hydrogen-boraled ...

MOLECULAR PHYSICS,1995, VOL. 84, No. 2, 325-343

The solvation of cations in hydrogen-boraled molecular solvents: a neutron diffraction study on the structure of Ni 2 + solutions in ethylene glycol and in glycerol By S. E R O L O K A N , P H I L I P S. S A L M O N t , D A V I D C. C H A M P E N E Y and INGRID PETRI School of Physics, University of East Anglia, Norwich N R 4 7T J, U K

(Received 17 August 1994; revised version accepted 6 October 1994) The method of isotopic substitution in time-of-flight neutron diffraction is used to measure the coordination environment of Ni 2 § in both a 0.956 molal solution of Ni(CF3SO3) 2 in fully deuterated ethylene glycol (EG) and a 0-980 molal solution of Ni(CF3SO3) 2 in fully deuterated glycerol. The results show that EG acts as a bidentate ligand to form [Ni(EG)3] 2§ tris-chelate complexes, and are consistent with glycerol acting as a tridentate ligand to form I-Ni(glycerol)2] 2+ bis-chelate complexes, although bidentate coordinating behaviour with respect to the Ni 2§ ion cannot be ruled out. There is no evidence of inner sphere complexing by the CFaSO3 anion in either solution, but the data are consistent with a spatially well defined hydrogen bond O - - D ' - ' O of length ~ 1.8(1) A between the hydroxyl groups of the solvent molecules in the first and second coordination shells of the cation. The number of second shell hydroxyl groups that participate in this hydrogen bond process is estimated at six in both solutions. The structural results for the Ni 2§ complexes are used to give a qualitative account of the mobility of these entities in the infinite dilution limit, but the hydrodynamic theory of Zwanzig does not give a sphere radius that is in agreement with the complex radius obtained microscopically from the neutron diffraction experiments. The intermediate range ordering in both solutions can be traced to the arrangement of the Ni 2§ complexes which are distributed in a way that maximizes their mean separation. A comparison is made between the results obtained for the EG solution by using steady-state and pulsed neutron source instrumentation.

1.

Introduction

Water, ethylene glycol (EG) and glycerol comprise a class of hydrogen bonded liquids which, having large relative permittivities, are good solvents for ionic salts. However, E G and glycerol can, unlike water, confirm an enhanced stability to cation solvation complexes by forming chelate rings [1]. It is of importance to know the coordination chemistry of such complexes if an understanding is to be achieved about kinetic processes such as solvent exchange, transport properties such as ionic mobility, and other electrochemical effects. There is, nevertheless, a general dearth of information on cation complexes at the pair-distribution function level, especially in non-aqueous solution. We therefore apply the method of isotopic substitution in neutron diffraction to study the coordination environment of Ni 2 § both in a 0.956 molal (mol k g - 1) solution of Ni(CFaSO3)2 in fully deuterated E G (1,2-ethanediol or DOCD2CD2OD), and in a 0.980 molal solution of Ni(CF3SO3)2 in fully deuterated glycerol (1, 2, 3-propanetriol or D O C D 2 C D ( O D ) C D 2 O D ) . The trifluoromethane"~Author for correspondence. 0026-8976/95 $10.00 9 1995 Taylor & Francis Ltd.

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sulfonate (or triflate) anion was chosen as the counter-ion because it has a tendency to be weakly nucleophilic in solution [2], it is possible to prepare safely dry triflate salts [3, 4], and Ni(CF3SO3)2 salts have a relatively high solubility in non-aqueous media [5]. In the first part of this paper the essential theory behind the isotopic substitution method in neutron diffraction, as applied to ionic solutions, is outlined. The experimental method and results are given next, and the results for the EG solution are then discussed in terms of the conformation of the Ni2+-solvent molecule complex and the bonding of this complex to solvent ligands in the second coordination shell of the cation. There is a specialized interest in these results because the coordination environment of Ni 2§ in exactly the same solution has been studied previously by using the same isotopic substitution method but different instrumentation [6]. Of importance is the reliance of the method on an ability to measure accurately small differences between the diffraction patterns obtained for two samples and, whereas the previous experiment used the well established diffractometer D4B at the steady-state reactor source of the Institut Laue-Langevin (ILL) in Grenoble [7], the present experiment was made using the time-of-flight instrument SANDALS [8] which is under development at the ISIS pulsed neutron source. The coordination environment of Ni 2 § in the glycerol solutions is then considered and, finally, the results for both solutions are discussed in terms of (a) the mobility of the Ni 2 § ion in solution, and (b) the structural features which give rise to the intermediate range ordering manifested by a so-called first sharp diffraction peak (FSDP) or 'pre-peak' in the measured reciprocal space functions.

2. Theory The isotopic substitution method in neutron diffraction, as applied to the problem of ionic solutions, has been described in detail elsewhere [9]. To summarize, time-of-flight neutron diffraction experiments are conducted on two fully deuterated solutions which are identical in every respect except for the isotopic composition of the Ni 2§ ion. Deuterated solvents are preferred owing to the large incoherent cross-section of hydrogenated materials. The measured intensity at each scattering angle 20 is then corrected for background scattering, placed on an absolute scale by comparison with a vanadium standard, and corrected for multiple and container scattering as well as for attenuation of the beam by the sample and container materials [10]. The quantity thus derived for each solution is the observed total structure factor Fo(k, O) given by

Fo(k, O) = F(k) + -~

~r~ El + e,(k, 0)],

(1)

where k is the scattering vector, c, and a~ are, respectively, the atomic fraction and total bound (coherent and incoherent) scattering cross-section of species ~, and/~ ( = 6) is the total number of chemical species in the solution. E,(k, 0) is a term which, provided the data have been corrected properly, arises from inelasticity effects arising from a departure from the static approximation in the case of neutron scattering from liquids [11-13]. This problem is most pronounced when light nuclei are present, but is reduced in the present case by performing the experiments with the SANDALS instrument [8]. F(k) is a linear sum of the partial structure factors S,a(k), whose Fourier transforms yield the partial pair distribution functions O,a(r):

Solvation o f Ni 2 + #

#

F(k) = ~

~

a=l

c~cpb~ba[S~p(k)-1],

327 (2)

fl=l

with g~p(r) = 1 +

[S~a(k) - 11 k sin (kr) dk,

(3)

where b~ is the coherent neutron scattering length of species ~, and n o is the total atomic number density of the solution, g~a(r) gives a measure of the probability of finding an atom of species fl at a distance r from an atom of type ~t located at the origin of coordinates. It is defined in such a way that the mean number of particles of type fl contained in the volume defined by two concentric spheres of radii r I and r2, centred on a particle of type a, is given by r2g~t~(r)dr,

~ = 47Znoc~

(4)

1

which is the expression used to calculate coordination numbers in the present work. In the solutions studied here, F(k) comprises 21 independent S ~ ( k ) functions. However, if the coherent scattering length of the cation is changed by substituting enriched nickel isotope (62Ni, b,Ni) in place of nickel having the natural isotopic abundance (NNi, bsi), subtraction of the Fo(k, 0) for the two solutions gives A~i(k, 0) = HSFo(k, O) - 162Fo(k, 0) = ANi(k) + J + C(k, 0).

(5)

In equation (5), H and I are empirical constants which are introduced to allow for any multiplicative error on an observed total structure factor. If the data have been corrected properly H = I - 1, otherwise they are chosen such that the left hand side of equation (1) is rewritten as either HNFo(k, O) or I62Fo(k, 0). J = cNi(o-~i - a,~Ni)/4~ and pertains to the self-scattering from the nuclei, and C(k, 0) is a residual inelasticity correction. The first-order difference function ANi(k) is given by ANi(k) = A[SNio(k) - 11 + B[SNiD(k) - 11 + C[Ssic(k) - 1] + D[SNis(k) - 1] + E[SNiF(k) -- 11 + F[SNiNi(k) -- 1],

(6)

where Ab = bNi -- b,Ni, A = 2cNicoboAb, B = 2CNiCDbDAb, C = 2CNiCcbcAb, D = 2CNiCsbsAb, E = 2CsiCFbFAb, F = CNi[bNi 2 2 b2Ni], and the real space picture is obtained by Fourier transformation, viz. -

AGNi(r) - 1 2/t2n0 r

fo

-

ANi(k)k sin (kr) dk

= A[ONio(r) -- 1] + B[gNio(r) -- 11 + C[gr~ic(r) -- 1] + O[gr~is(r) -- 1] + E[gNiF(r) -- l] + F[gNiNi(r) -- 1].

(7)

An important property of each A~i(k, 0) function is that, provided the solutions are identical in every respect (except for their nickel isotope compositions), the E,(k, 0) terms of equation (1) will be, to first order, identical for both solutions, so that they cancel to give a negligible C(k, 0) term in equation (5). The validity of this statement can be tested on several accounts [14]. First, since S,p(k) -~ 1 in the limit as k ~ ~ , A~i(k, 0) should at a particular 20 value oscillate about the calculated self-scattering

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value J. Second, since yNip(r)= 0 at values of r below the distance of closest approach to Ni 2 + (that is, rmln), AGNi(r) should equal the calculated limit AGNi(0) = - ( A + B + C + D + E + F) for low r, In practice, AGNi(r) will oscillate about this calculated value owing to statistical noise in the k-space data, to truncation of the data at a finite value of k, and to systematic errors (such as a finite E'(k, 0) term giving rise to a residual slope on A~i(k, 0)). However, provided these effects are small, setting AGNi(r) equal to the AGNi(0) limit for r ~< rmin and Fourier back-transforming will yield a function ANi(k) that is in close agreement at all values of k with Ar~i(k). Third, the sum-rule relation

fo

~ A N i ( k ) k 2 dk = 2~:2noAGNi(0)

(8)

should be satisfied. There exist, therefore, at least three validity criteria that the first-order difference functions must satisfy.

3. Experimental method The solutions of Ni(CF3SO3) 2 in EG used in the present work were identical to those used in a previous neutron diffraction experiment I-6] which employed the D4B instrument at the ILL. The solutions, of 0.956(4) molal concentration, comprised either NNi or highly enriched 62Ni (1-52~ 5SNi, 1-13~ 6~ 0.12~ 61Ni, 97-01~ 62Ni, 0"22~o 64Ni). Using a Paar DMA602 apparatus the density of the solutions was found to be 1-401(3)g cm -3 at 23~ which gives n o = 0.1026(2)A -3 The 0.980(1) molal solutions of Ni(CFaSO3)2 in glycerol were prepared using either 62Ni having the same enrichment as for the solutions in EG or NNi, by a method which is described elsewhere [6]. The deuterated solvent (Cambridge Isotope Laboratories, USA) was found to have a total hydrogen content of 1.80(7)~ by means of proton magnetic resonance experiments in which a solution of 2-methyl-2propanol in 1)20 was used as a reference sample. The solution density at 20~ was 1.548(3) g c m - 3, which gives n o = 0.1082(2) ./k- 3. The coherent neutron scattering lengths of the cations in the NNi and 62Ni samples were, respectively, 10.3(1)fm and -8-2(2)fm, and the enumerated values of the coefficients A - F in equations (6) and (7) are (in mb), respectively, 2-71(3), 7-69(8), 2.76(3), 0.072(8), 0.430(5), 0.013(1) for the solution of Ni(CF3SO3) 2 in EG, and 3.07(3), 7"66(8), 3-14(3), 0-082(1), 0-491(5), 0-015(1) for the solution of Ni(CF3SO3)2 in glycerol. The scattering length values were taken from [15]. The diffraction experiments were performed using the SANDALS instrument at the ISIS pulsed neutron source [8]. Data were collected in 6 groups of detectors, at mean 20 values of 11"8~ 13.1 ~ 14.6 ~ 16.2 ~ 18.1 ~ and 21.1 ~ which had a constant resolution A k / k = 0"03. Diffraction patterns were taken for: (1) the solutions in their container at ~ 20~ (2) the empty solution container; (3) the instrumental background with the sample absent; and (4) a vanadium standard for the data normalization. The EG solution experiment used a hollow cylindrical container of inside diameter 5.03 mm and wall thickness 0.03 mm. A vanadium rod of diameter 6.03(2) mm was used as the standard. The container for the glycerol solution experiment comprised a hollow slab of 1 mm wall thickness and 2 mm spacing and, owing to the high viscosity at room temperature, had to be filled by gently warming both it and the solution in a high purity argon filled glove box. A vanadium plate of thickness

Solvation of Ni 2 +

329

3.412(7) mm was used as the standard. The containers were fabricated from a titanium-zirconium alloy which has a nominal coherent scattering length of zero. The data analysis was made using the ATLAS suite of programs [10]. The wavelength dependent total cross-section atot(2) of the solutions was found by using the tabulated [15] absorption and free-atom cross-sections for O, C, Ni, S, F and the measured wavelength dependent cross-sections for deuterium and hydrogen as obtained from experiments on water, atot(2) for the glycerol solutions was also evaluated by using the wavelength dependent cross-section for pure glycerol as measured by a transmission experiment using the LAD instrument at ISIS. The results obtained for the glycerol solutions showed no significant dependence on the function chosen for atot(2). Measured values were used for atot(2) in. the cases of both titanium-zirconium and vanadium.

4.

Results

4.1. 0"956 molal Ni(CF3SO3) 2 in EG The Fo(k, O) for the six detector groups showed a significant 20 dependence, which could not be attributed solely to the different inelasticity correction terms. However, it is of interest that these functions (figure l(a)) exhibit a prominent FSDP at 0.54(3)A-1 which is most pronounced for the NNi solution. The cation isotope dependence of the FSDP shape demonstrates that it has a contribution from the Ni 2 + correlations. Indeed, a similar peak is observed between 0.7 ,~- 1 and 1 A.- 1 in aqueous Ni 2+ solutions where it can be identified with the first peak in SNiNi(k) [16--18]. By contrast, no such feature is observed for solutions of NaC1 in EG [19]. The Fo(k, O) do not display a high-k 'droop' which is a characteristic feature of the total structure factor for deuterated liquids as measured using reactor-based instruments (see e.g. [6]). ANi(k) was formed for each detector group using equation (5) with H = I = 1 and e'(k, 0) = 0. It was found that these individual functions agreed within experimental error and they were therefore combined, using J = 0"9 mb, to give the final ANi(k) function of figure 2(a). The value of J is smaller than the calculated value of 4.7 mb. However, the final ANi(k) function satisfies the sum-rule relation of equation (8), the corresponding AGNI(r) function of figure 3(a) oscillates about the correct low r limit, and there is good agreement between ANi(k) and ANi(k) (figure 2(a)). These factors show that e'(k, 0) is negligible and indicate the absence of large systematic errors in the first-order difference function measured.

4.2. 0"980 molal Ni(CFaS03) 2 in glycerol The solutions in glycerol also give Fo(k, 0) functions for the six detector groups which show an FSDP that is most prominent for the SNi solution and which occurs at 0-56(3)A -1 (figure l(b)). No such feature is observed for solutions of NaC1 in glycerol 1-20]. Again, ANi(k) was formed for each detector group using equation (5) with H = I = 1 and e'(k, 0) = 0. However, it was found that the corresponding AGNI(r) did not oscillate around the correct low r limit. The problem was traced to an incorrect normalization of the 62Fo(k, 0) functions, which most likely arose from a bubble in the highly viscous solution (cf. [20]), and was solved by setting I = 1.11

S.E. Okan et al.

330 1.0

/

-~ 0.8 CD

62Fo(k,O)+ 0.2 0.6

NFo(k,O)

0.4

0.2

\ I

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0

I

I

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8

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k/~. 1

16

(a) 1.2

1.0 ,.Q t:D

0.8

~

l.l162Fo(k,O)+ 0.2

0.6

o.4t! 0.2

0

t

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8

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k/~_ 1

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16

(b) Figure 1. The measured functions NF0(k,0) and 62F0(k , 0) at 20 = 11.8~ for (a) a 0.956 molal solution of Ni(CFaSO3) 2 in fully deuterated EG, and (b) a 0-980 molal solution of Ni(CF3SO3) 2 in fully deuterated glycerol.

with H = 1. It was found that the revised ANi(k) functions for each group agreed within experimental error and they were therefore combined, using J = 11 mb, to give the final ANi(k) function of figure 2(b). The value of J is larger than the calculated value o f 5 mb. Nevertheless, the final ANi(k) function satisfies the sum rule relation of equation (8), the corresponding real-space function, AGNi(r), of figure 3(b) oscillates about the correct limiting value at low r, and there is the required good agreement between ANi(k) and ANi(k) (figure 2(b)).

331

Solvation o f N i 2 +

0.06

0.00

-0.06

t

i

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t

i

0

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k/~_ 1

8

k/A-1

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(a)

0.06 t 1

0.00

-0.06

0

_L__t___

16

(b) Figure 2. ANi(k) for (a) a 0.956 molal solution of Ni(CFaSO3) 2 in fully deuterated EG, and (b) a 0"980 molal solution of Ni(CF3SO3) 2 in fully deuterated glycerol as obtained by combining the data for the six detector groups using equation (5) with (a) H = I = 1, J = 0"9 mb and E'(k, 0) = 0, or (b) H = 1, I = 1'11, J = 11 mb and E'(k, 0) = 0. The filled circles give the data points and the full curve gives ANi(k), the Fourier backtransform of the corresponding AGNI(r) (see figure 3) after the unphysical oscillations at r ~< rmin have been set to the calculated AGNi(0) limit. The broken line in (a) also gives ANi(k) for a 0'956 molal solution of Ni(CFaSOa)2 in fully deuterated EG but was measured using the D4B diffractometer at the steady-state source of the ILL.

332

S . E . O k a n et al. 0.04

o.

0.02

,~

0,00

-0.02

~' I

I

I

I

0

I

5

I

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rl~

(a) 0.04 "E" 0.02

0.00 s | i I

-0.02 I

i I I

u I

"1

I

I

0

5

I

I

rl~,

I

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10

(b) Figure 3, AGNi(r)for (a) a 0.956 molal solution of Ni(CF3SO3) 2 in fully deuterated EG, and (b) a 0.980 molal solution of Ni(CF3SO3) 2 in fully deuterated glycerol (full curves). The unphysical features for 0