J. Phys. Chem. 1983, 87,3193-3197
3193
FEATURE ARTICLE Hydration of the Nd3+ Ion in Neodymium Chloride Solutions Determined by Neutron Diffraction A.
H. Narten'
and R. L. Hahn
Chemisw Divlslon, Oak Ridge Natlonal Laboratoty, Oak RMge, Tennessee 37830 (Received: February 17, 1983)
Information on the hydration of the Nd3+ion has been obtained directly and unambiguously by neutron diffraction. Measurements were made with solutions of NdC13 in DzO, identical in every respect except for the isotopic state of the Nd3+ions. These experiments yield in a straightforward manner the distribution of oxygen and deuterium atoms of the water molecules in the first hydration sphere of the Nd3+ion. Each ion is surrounded by 8.6 oxygen atoms at a distance of 2.48 A and 16.7 deuterium atoms at 3.13 A, indicating a well-defined hydration sphere of 8.5 f 0.2 water molecules, with the deuterium atoms pointing away from the cation. Introduction
The spatial correlations between an ion I and its surrounding water molecules are described by two atom pair distribution functions, namely gIo(r) and gIH(r). The functions gaT(r)are defined so that p,,gaT(r)is the number of atoms of species y in a volume element dr a distance r from a species a in a solution whose bulk number density of atoms y is py. Hence, the function gIo(r) describes the positional and gm(r) the orientational correlations between an ion and its surrounding water molecules. We will discuss ionic hydration in terms of these atom pair distribution functions which are accessible by a technique that involves neutron diffraction of isotopically substituted samples. The method, pioneered by Enderby, has until now been used exclusively by his Leicester-Bristol group. Their extensive work is reviewed in detail in ref 1. We here report a neutron diffraction study of four neodymium chloride solutions, identical in every respect except for the isotopic state of the neodymium ion. The algebraic difference between each of two data sets yields directly the ion-water interactions. We will show that the first hydration sphere of the Nd3+ion is well defined and can be unambiguously determined from these measurements. Our results will be compared with previous determinations of the hydration properties of Nd3+. Experimental Section
Preparation of the Solutions. So that the precision of the determination of the Nd3+-D20correlations would be maximized, identical solutions of NdC13 with different enriched Nd isotopes had to be prepared. In this way, the correlations between other constituents of the solutions, namely, the D20-D20, Cl-D20, and C1-C1 correlations, would cancel identically when the diffraction pattern 'from one solution was subtracted from that of another. To prepare these solutions, we dissolved 10-g samples of enriched Nd203(obtained from the USDOE Research Materials Collection) in less than stoichiometric amounts of aqueous HC1. Potentiometric titrations of these turbid solutions were performed with 0.1 N HCl to just beyond the pH equivalence point, to ensure a stoichiometric ratio of Nd to C1. The solutions were allowed to stand for (1) J. E. Enderby and G. W. Neilson in "Water: A Comprehensive Treatise", Vol. 6, F. Franks, Ed., Plenum, New York, 1979, p 1. 0022-3654/83/2087-3193$01.50/0
several hours. and the titrations reDeated until no Derceptible pH drift occurred; this procedure preventedthe slow formation of hydrolytic products, such as Nd(OH)2+. So that incoherent neutron scattering from hydrogen would be minimized, the light water in the solution was replaced by D20 by evaporation to near dryness, using vacuum and gentle heat, followed by dissolution in DzO. This procedure was repeated several times under a dry nitrogen atmosphere. Infrared spectroscopy showed that the H20 content of the resulting stock solutions was -0.5 w t 5%. The primary method used to assay the concentrations of these D20 stock solutions was the EDTA titration of Nd3+,using methylene orange as the indicator and acetic acid-sodium acetate solution as the buffer.2 The precision of these titrations was better than 0.5%. As a secondary check on these solutions, the C1- ion concentration was determined with a chloride-sensitive electrode, to a precision of -2%. These C1- ion determinations verified the stoichiometry of the stock solutions, by agreeing to within the quoted errors with the expected 1:3 ratio of Nd3+:C1-. The densities of the solutions were also measured as another means of determining their concentration^.^ The solutions of the different Nd isotopes were then made identical by dilution, with the D20 being added precisely by weight. The measured densities of these matched solutions were a further indication that their concentrations were virtually identical. Pertinent data for ,these solutions are listed in Table I. Neutron Data Collection and Reduction. The neutron experiments were carried out at the High Flux Isotope Reactor by using a nearly parallel beam (0.3O horizontal and lo vertical divergences) of 0.889-8 neutrons. The samples were contained in a sealed quartz tube (8.8 mm o.d., 0.3 mm wall), and the sample temperature was 25 f 2 OC for the duration of the experiment. A linear position-sensitive proportional counter4 (PSPC) was used to collect the data. With a center-to-sample distance of 66 cm and a length of 50 cm, the counter covered an angular (2) A. Habenschuss and F. H. Spedding, J. Chem. Phys., 70, 2797 (1979). (3) F. H. Spedding, V. W. Saeger, K. A. Gray, P. K. Boneau, M. A. Brown, C. W. DeKock, J. L. Baker, L. E. Shiers, H. Weber, and A. Habenschuss, J. Chem. Eng. Data, 20,72 (1975). (4)C. J. Borkowski and M. K. Kopp, Rev. Sci. Instrum., 46, 951 (1975).
0 1983 American Chemical Society
3194
The Journal of Physical Chemistry, Vol. 87, No. 17, 1983
Narten and Hahn
TABLE I: Scattering Lengths, f , Number Densities, p , and Atom Fractions of Nd, e, for the Four 2.85 m Solutions of NdC1, in D,O Studied by
0.14
NdCl, 2.85m 0.12 -
Neutron Diffractiona
f,
i, o/c
sample
97.51
144Nd "atNd 142Nd 146Nd
97.55 97.63
cm
p,
0.31 0.72 0.78 0.87
C
0.0984 0.0988 0.0988 0.0979
I
0.0176 0.0176 0.0177 0.0176
0.08 0.06
The scattering lengths are averages for the isotopic composition, i, of each sample."
0.04 0.02
I
NdCl, 2.85m
I
x Y
1 1 !
@ *
.
x X
i
Flgure 2. Difference curves A ( k ) derived from the cross sections "Nd-'"Nd, shown in Figure 1. From top to bottom: 142Nd-144Nd, '4Nd-'uNd. The statistical error of an average data point Is fO.OO1.
-
natNd I
o
~ 0
2
~
l
4
6
~ 8
k
[Ap1]
l 10
r 12
, 14
factors were adjusted to minimize unphysical features in the Fourier transforms of the difference curves near the i described elsewhere.' The adjusted scale factors origin, a were within 10% of the measured values. The resulting differences may be written as Ao(k) = A(k) + A,&) l ~ , ~ l ~ , ~ ~ (1) with A,&) the self-scattering from uncorrelated atoms, corrected for inelasticity.8 The three difference curves A ( k ) thus derived from the four data sets are shown in Figure 2.
~ 16
Flgwe 1. Neutron scattering cross sections of 2.85 m NdCI, solutions, Identical In every respect except for the isotopic state of the Nd ions. The statistical error of an average data point is Cf0.001.
Data Analysis and Resultsg
range of 4 2 O . The counts were accumulated in 256 channels equally spaced along the anode wire of the PSPC and summed over a number of channels chosen such that the increment in the variable k = (4r/A) sin I9 was constant (A = incident neutron wavelength, 28 = scattering angle). The increment chosen was Ak = 0.1 A-l. Scattered intensities were recorded in four steps over an angular range of 7 O < 28 < 1 3 3 O , with an overlap of 6' between sections. The measurements were made for a preset number of monitor counts, and with at least three repeat runs per section. The average number of accumulated counts was lo6 per channel, with about six channels per degree of scattering angle. The measured intensities were corrected for background, and the absolute cross-section scale was established by measuring the scattering from a solid vanadium cylinder having the same dimensions as the samples. The data were then corrected for multiple ~cattering,~ absorption in the sample, and absorption and scattering by the quartz container.6 The differential scattering cross sections thus obtained are shown in Figure 1. As expected, the four curves are almost indistinguishable on the scale chosen for Figure 1. To remove the contributions to the scattering cross sections from interactions that do not involve the Nd ion, we subtracted the cross section of the 144NdC13solution P N d has the smallest scattering length; see Table I) from those of the other three solutions. A t this step, the scale (5)I. A. Blech and B. L. Averbach, Phys. Rev., 137,1113 (1965). (6)H. H. Paalman and C. J. Pings, J. Appl. Phys., 33,2635 (1962).
The difference functions for the solutions with the nuclides i = "BtNd,142Nd,or '&Nd and and j = lMNdmay be written as1 Aij(k)
=
P[AijhNdO(k)
+ BijhNdD(k) + cijhNdCl(k) + D i j h N d N d ( k ) ] (2)
where p is the number density, c the atom fraction of Nd (Table I), and Aij = 2 4 1 - 4C)fo(fi - fj)/3 Bij = 4 ~ ( -l 4c)fD(fi - fj)/3
Dij = c2(fi2 - fj2)
(3)
fo, fD, and fcl are the scattering factors1° of oxygen, deuterium, and chlorine and i j refer to the appropriate neodymium isotopes (Table I). Note that terms that contribute to the data in Figure 1, but do not involve the scattering factor fNd, do not appear in eq 2. The structure functions
hay&) = 47r l m0 r 2 h a 7 ( rjo(kr) ) dr
(4)
(7) W. E. Thiessen and A. H. Narten, J. Chem. Phys., 77,2656(1982). (8) L. Blum and A. H. Narten, Adv. Chem. Phys., 34, 203 (1976). (9)A brief report of the highlights of these results has been published. A. H. Narten and R. L. Hahn, Science, 217, 1249 (1982). (10)S. F. Mughabghab and D. I. Garber, Ed., "Neutron Cross Sections", 3rd ed, Vol. I, BNL Report No. 325,1973.
The Journal of Physical Chemistty, Vol. 87, No. 17, 1983
Feature Article
3195
TABLE 11: Stoichiometric Factors for the Three Different Curves Derived from the Four Neutron Data Sets" i-j
10'Aij
10'Bij
103cij
nat - 144
0.2604 0.2985 0.3557
0.5987 0.6863 0.8177
0.7370 0.8449 1.007
142 - 144 146 - 144 a
1 0 3 ~ ~ ~ 0.1317 0.1598 0.2061
B'
C'
2.299
0.2830
See eq 3 and 5 for definition of these parameters. TABLE 111: Structure Function H N d ( k ) Defined in Eq 6 and Shown in Figure 3 (Points)"
NdC13 2.85m 0 0 0
- .
OBSERVED
- CALCULATED
b
HNd(l)
0,130
0.065
0.00 1.00
.__. k
-
.
.
0
2
6
4
8
k
10
12
14
__
-
-
Ht!d(L'
Y.90
0.285 0.257
-0.171
10+00
0,0?4
10.40 10.50 10.60 10.70 10.00
0.259
0+.5Yh
1.40
-0,517
0.31!* 0.314 0.140
7.50 7.60 7.70
0.ObY 0.055
7,80 7.90 l1.00 8.10 8,."0 8.30
.0,461 .0.468 .0.242 -0,154 0.003 0.154 0.3:'6 0.465 0.479
-O1;?3O -0.18:! -0.3?1
-0.0,34 ?+40 1.170
5,3!)
5,40
-0.260
2.50 2.AO 2.70 ?.00
5.:)0 5.60 5.70 5+BO
-0,108
-0,124 -0.024 0.121
?!.YO .5+00
3.1.56 1.JOi
5,YO A.00
0.21:' 0.27.1
3.10
0.62?
6.10
0,360
8.40 8.50 8.60 8.70 8.80
8.90 9.00 9.10
0.389 0.451
0.373 0.198 0.179 0.016 -0,071 -0.144
9.80
0.247 0.303 0.306 0.2Y0
10+Y0
0.178
11.00 11.10
0.071 -0,006 -0,003 -0.081 -0,160 -0.101 -0.150 -0.040 -0.103 -0.155 -0.073
11.20
11.30 11.40 11.50 11.60 11.70 11.80 11.90 12.00 12.10
0.00.1
[fill
with j&) = sin x / x , contain the desired information on the atom pair distribution functions, g$) = h&) + 1. The first three terms in eq 2 are linear m the differences of the scattering factors of the Nd isotopes, while the last term is proportional to the difference of their squares. We can therefore write eq 2 as the sum of two terms, namely Aij(k) = PAij[hNdO(k) + B$NdD(k) + c $ N d C l ( k ) l + PDijhNdNd(k) (5) with B' = Bij/Aijand C' = Cij/Aij;the values of these constants are listed in Table 11. Equation 5 can be-solved for two unknowns, namely the S y n [hNdO(k) + BhNdD(k) + ChNdCl(k)],and the quantity hNdNd(k). Since we have three difference functions Aij(k), the problem is overdetermined; we have solved the equations by the leFt-squares method. From the quantity [hNdO(k) B%NdD(k) + C%NdcI(k)]thus obtained, a normalized structure function HNd(k) was constructed according to HN&) = P[hNdO(k) +$$NdD(k) + C$NdCl(k)l/[l + B,'+ c l = 0.279h~do(k) 0.642h~d~(k) + 0.079h~dcl(k)(6)
+
The function HNd(k) is shown as the points in Figure 3 and listed in Table 111. Because of the very small values of Dij in eq 5 (Djj 2.7 The calculated curve thus obtained agrees well with the points obtained from experiment, as shown in Figure 3. The least-squares value of the coordination number, w = 8.4 f 0.2, is identical with that obtained in our analysis of the function GNd(r). The parameters obtained from this analysis of the function H&) and the individual coordination numbers calculated from them are listed in Table IV. The curve calculated from these least-squares parameters with eq 10 can be used to extrapolate the function HNd(k) derived from the data to very k g e values of k. Fourier transformation of the extrapolated curve according to eq 7 yields the solid curve in Figure 4 (listed in Table V), which is seen to be free of the spurious oscillations in the dashed curve defked from the truncated data.
1-l.
Discussion The sharpness of the Nd.e.0 and Nd-D peaks in the distribution functions derived from the data (Figure 4) indicates a well-defined first coordination sphere of water molecules around the Nd3+ ion in solution. From the distances derived in this study and the known geometry of water molecules in the liquid,' it follows that the molecules in the first hydration sphere also have a welldefined average orientation, with the hydrogens pointing away from the cation at a tilt angle of 55 f 2O, as shown in Figure 5 for one water molecule. There are, on the average, 8.5 such water molecules. The function G&
0.23
0.30 0.35 0.40 0.15 0.50 0.55 0.60 0.65
0.70 0.75 0.RO 0,tl:i 0,YO 0.,2:,
'Nd"' 0.000 0.020 -0.016 -0,011 -0.004 0,001 0.006 0+000
1.55
1.60 1.63 1.70 1.75
2:/5
2.fl0
0,001
3.00
( P )
4.039 2.072 1,479 0.504 O.?YO
0.503 0.680 1.135 1.689 2,:'Y.;
- - - - - - - - - - - -.- - -. - - - - - r G (1) I G (I) - Nd - __ __ _ ___.Md-.. 5.00
1.303
5J.05
1.?53 1.202 1.158
5.10 5.15 5.?0
5.25 5.30 5.35 5.40
1.126 1,108
1.103 1.109 1,118
7.:!0 7.55 7.60 7.65 7.70 7.75 7.80 7.85 7.90 7.95 8.00
0,970 0.983 0.997 1.009 1.019
1.026 1,030 1,030 1.030 1.028
1.126 1.1:!8 1.118
8.05
5.60
1.097 1,065
8.10 8.15
5.70 5.75 5.80
1.024 0.985
8.20 8.25
0,947
0.0n:s
5.85
0.005
5.Y0
0.915 0.893
8.30 8.35 8.40
0.004
5.95
0.804
8.45
(1.00
0.8115
I.), 50
1 * 004
6.05 6.10
0.896 0.913 0.932 0.950 0.944 0.973 0.975 0.973 0.965 0.954 0.946 0.939 0.934 0.934 0.939 0.947 0.954 0.966 0.975 0.980 0.981 0.979 0.973
8.55 8.60 8.65 8.70 8.75
0.996 0.991 0.989 0.991 0.996 1.003 1,010 1.016 1,021
-.0.003
3.05
-0.006
3.10 3.19 3.?0
2.fl:rH 3.?80 3.467 3.376 3.029
3.25
:'.506
3.30
1.915
-0.007 .-0+006
-0.003 0.000
..('8.006 0.004 0.001
1.50
G
5.45 5.50 5.55
1.15 1 +:?O
1,4:,
2.60 2.65 .',70
0.005
0.00:' "0.001
1 .3:1 1.40
2.50 2.5:;
2.85 :!.Yo 2.93
0,007
I 90 1.05 1.10
1.25 1.30
1
. _. Nd
-0.004
6.15
0.005 0.011
3.80 3.85
0.247 0.267
0,015 0.015 0.010 0.000
3.90 3.5'5
0.281 0.30fl
0,333 0.363
.-o.oi:'
4.00 4.05 4,lO
-0.025
4.15
0.442 0.490 0.545 0.605 0.67;'
-0.034 -0.036 1 .no - 0 . 0 : ~ 1..flE -0.013 1.90 0.009 1..95 0.035 2.00 0.057 2.05 0.070 2.10 0,070 :?.15 0.040 2.20 0.005 7.25 0.101 2.30 0,622 2.35 1,619 :!,40 3,036 :!.45 4.113
5.65
4.20 4.?5 4.30
4.35 4.40 4.45
0.3YY
0.745 0.825 4 4 7 ~ 0 0.910
4.55 4.60
1.000 1.091
4,OO
1,360 1.370 1.372 1.346
4.85 4.90
4.95
6.20 6.25 6.30 6.35 6.40
6.45 6.50 6.55 6.40 6.65 6.70 6.75 6,RO 6.85 4-90
6.95 7.00 7.05 7410 7.15 7.20 7.25 7.30 7.35 7.40 7,45
0.965
0.958 OeY52
0.950 0.952 0.959
fl.80 8.85
8.90 8.YS 9.00
9.05 9.10 9.15 Y.20
9.25 Y.30 9.35 9.40 9,45 Y.50
9.55 9.60 9.65 9.70 9.75 9.HO 9.85 9.90 9.96
1.028
1.029 1.031 1,033 1.035 1.034 1.034 1.029 1.022
1.013
1.022
1.020 1,016
1.009 1.002 0.995 0.989 0.984 0.981 0.980 0.980 0.982 0.984 0.986 0.98R 0.9Yl 0.993 0.995 0,996 0.998
takes on very small values at distances beyond the Nd-D peak at 3.1 A. This indicates that there is very little interpenetration between water molecules in the first and second hydration spheres. The second solvation sphere is broadly centered around 5 A (Figufe 4), with a nearly uniform distribution of water molecules beyond. This distance region also contains contributions from Nd.-Cl interactions. Further experiments are needed to distinguish between these different interactions.' The hydration number found in our study is not an integer; it represents an average value from which local and instantaneous deviations occur in the liquid. The residence time of the water molecules in the primary hydration sphere of an Nd3+ion is, of course, finite but may be as long as lo* s.ll The information on cationic hydration presented here is valid only for the relatively concentrated (11) J. E. Enderby, Sei. h o g . (London),67,553 (1981).
J. Phys. Chem. 1983, 87, 3197-3201
Flgure 5. Arrangement of a water molecule In the first hydration sphere of a cation, M”’, in solutlon. There are 8.5 such molecules around Nd3+, and the tilt angle Is 55 & 2O.
2.85 m NdC13 solution, and the results may not be representative of the more dilute regime. We stress that the distances and coordination numbers obtained here by the neutron diffraction method are unambiguous direct measurements. A variety of experimental methods have been used in the past to determine hydration numbers. X-ray diffraction studies have given hydration numbers of 8-9 and cation-oxygen distances for rare-earth ions. No information for interactions involving hydrogen atoms is obtained by this method. Furthermore, in X-ray diffraction studies deconvolution of the radial distribution data into several peaks is required. This is always difficult, often ambiguous, and never unique. In a very careful and systematic X-ray diffraction study of solutions of ten rare-earth chlorides,’2 it was concluded that (12) A. Habenschues and F. H. Spedding, J. Chem. Phys., 70, 3758 (1979).
3197
the hydration number of the cations decreases from 9 to 8 across the series as a result of the decreasing ionic radii (lanthanide contraction). The values found for the Nd3+ ion were 8.9 for the hydration number and 2.51 A for the Nd.-O distance, in excellent agreement with our results. Other methods often give different re~u1ts.l~Nuclear magnetic resonance tends to give consistently lower hydration numbers, 56, in part perhaps because of the difficulty of separating the signal of the water molecules that are bound to the ion from the signal of the bulk water. Methods that examine bulk solution properties, such as conductivity and transport measurements, often give large hydration numbers, 212, because they do not distinguish between the inner and outer hydration spheres. None of these nor other methods can be regarded as a direct measurement of ionic hydration because the assumptions made about ion-water interactions influence the resulted obtained.
Acknowledgment. We are indebted to A. Habenschuss for helpful suggestions and discussions during the progress of this work, and to J. H. Oliver and J. Hill for their help in the preparation of the matched solutions. This research was sponsored by the Divisions of Materials Sciences and Chemical Sciences, US. Department of Energy, under Contract W-7405-eng-26 with the Union Carbide Corporation. Registry No. Nd, 7440-00-8. (13) J. Burgene, “Metal Ions in Solution”, Ellis Horwood Ltd., Chichester, 1978.
ARTICLES Dieiectrlc Saturation Effectr in Cyllndricai Polyelectrolytes Mark troll’ and Bruno H. Zlmm Deperlmnt of Chsmisby, BOl?, unlvenny of &lllornlp, Sen Diego, La Jolla, Califomla 92093 (Received: November 3, 7982;
In Final Form: February 18, 1983)
A Poisson-Boltzmann equation appropriate for numerical solution of the case of a cylindrical polyelectrolyte is modified to include the effect of variation of the dielectric “constant”of the solvent in strong electric fields. The changes in ion concentration profiles, electric field intensity, and electrical energy are calculated for cases chosen to bracket the geometrial parameters of a DNA molecule. For these systems, the calculated properties were nearly unaffected by the inclusion of the saturation effect.
Introduction A number of discussions of the polyelectrolyte properties of DNA have been published In all of these studies employing the Poisson-Boltzmann equation, the dielectric coefficient of the solvent (water) has been assumed to be a constant, although this cannot be strictly (1) M.Gu6ron and M. Weisbuch, Biopolymers, 19, 353 (1980). (2) M. Le Bret and Bruno H. Zimm, Biopolymers, accepted for publication. (3) W. B. Ruenel, J. Polym. Sci. Polym. Phys. Ed., 20, 1233 (1982).
true in strong electric fields. We shall examine the consequences of allowing the dielectric *constantnto vary in the sense of being reduced by orienting fields. The high dielectric constant of water is due to orientation of polar water molecules. Strong fields in the vicinity of an ionic species orient molecules so effectively that they can no longer participate in this mechanism, an effect known as dielectric saturation. While saturation is limited to a small region near a charged species, determining the magnitude of this effect on a particular property of a system requires calculation. Calculations for the cases of
0022-3654/83/2087-3l97$01.5~/0 0 1983 American Chemical Society
