August 13, 2012
The Structure of Water in Alkali and Alkali-Earth Salt Solutions
Carola Purser
Mentor Kelly Gaffney
In fulfillment of SULI 2012 summer internship program
Aqueous salt solutions consisting of alkali and alkali-earth metals with chloride anions were investigated
using small-angle x-ray scattering from Q = 0.002 to 0.08 Å-1. Concentrations in a range of molalities from
0.1 m (mole solute/ kg solvent) to at most 7 m were measured at room temperature. The general
motivation for this project was to observe the development of partial long-range order in bulk water in the
presence of ions. In particular, we looked for an enhancement in intensity at very low q for midconcentrations which would then mimic behavior previously observed in a similar experiment for AlCl3 (1).
This anomalous behavior, which only occurred for AlCl3 solutions at 1 and 2 M (moles solute/ total volume
in L), seems to correspond to transitional concentrations for which the number of solvation shells changes
from two (at low concentrations) to one (at high concentrations). However, the anomalous behavior was
not observed in any of the salt solutions investigated in this study. Strange features in the reciprocal –space
curved were observed at high concentrations (larger than 4 m) in divalent salt solutions. Though the
features may not be associated with the structure of bulk water (i.e. they may be due to recrystallization of
salts in solution), a better understanding of them would inform future studies.
Motivation
The structure of water in the presence of ions has been a subject of interest for a variety of
reasons. For example, pores in cellular membranes are such that they allow certain ions such as K+
through without allowing the passage of Na+. The difference in charge density between the two cations
changes how water molecules orient themselves around each, forming less well-structured solvation
shells about K+ and more well-structures solvation shells around Na+, which has a higher charge density.
Thus the well-structured solvation shell around one may prevent passage whereas the weakly
structured solvation shell about the other may allow passage through a porous cellular membrane. A
better understanding of the chemistry behind the generation of electrical potentials across cell walls
would inform the development of power generation and storage. The
implications could thus extend to relieving the world’s current energy
crisis (2).
Before these and similar processes can be well understood, we
must first understand the structure of water itself in the presence of ions.
In a recent study by Kelly Gaffney (1) the structure of AlCl3 solutions were
investigated at a variety of concentration at room temperature. It has
been proposed that the ions reorient themselves from a configuration of
ions with two solvation shells at low concentrations to one solvation shell
at higher concentrations. At mid concentrations, however, it seems to
Figure 1 Small angle scattering data
have been observed that the solution loses much of its long-range order
for AlCl3 with data from Cong Cong
perhaps due to some transitional state.
Huang. (1)
Introduction
Liquid water forms a network of inter-molecular hydrogen bonds which are disrupted by the
presence of ions. Instead of forming H-bonds based on the orientation and proximity of neighboring
water molecules, water molecules orient themselves about ions and form solvation shells. But whether
or not the influence of cations extends beyond the solvation shells is not yet clear. Cations have been
observed to contribute some partial long-range order to aqueous solutions, which seems to indicate
that the influence of the positively charged ions does indeed extend beyond the first solvation shell of
water. Furthermore, cations and anions have the ability to form contact-ion pairs where the ions have
no water molecules between one another, and where the bond between the two ions (whether atomic
ions or molecular ions) is not as strong as a chemical bond. These structural changes in the long-range,
inter-molecular interactions can be detected with small-angle x-ray scattering.
In small-angle x-ray scattering, the x-rays scatter off of electrons at relatively large distances
(Angstroms to nanometers) compared to its counterpart, wide-angle x-ray scattering (WAXS), which
scatters off of electrons which are much closer together. The scattering pattern comprises of
interference rings that have radii which are inversely proportional to the distances between nearest
neighbors in the scatterer. By integrating about the rings (and normalizing them by their radii), one can
generate a plot of the intensity at each radial position. This plot is said to be in ‘q-space’ or ‘reciprocal
space.’ If the scatterer has long-range order (such as crystals), the rings will be well defined and will
exhibit sharp peaks in the q-space plots. As long-range order is lost, so is the definition of the rings.
Therefore, for dilute water solutions, for which there is little long-range order, the q-space plot is
generally featureless. The development of long-range order, however, can be observed as solutions
become increasingly concentrated. Since this project is primarily interested in how the long range
ordering of water changes as salts are added in solution, I will be looking for changes in the shape of
scattering q-space curves. It would be interesting to observe similar re-structuring behavior in the +2
and +1 cations that seems to have been observed in the AlCl3 solutions.
Methods
Few structuring capabilities have been
linked to the anions in solution, so only the
cation was changed in the Cl-salts. The charge
density and charge of the cations are varied by
choosing alkali earth metals and alkali metals as
cations. The concentrations of the solutions are
changed in order to observe the development of
long-range order as a function of concentration.
The salts studied are LiCl, KCl, NaCl, MgCl2, and
CaCl2 at concentrations ranging from 0.1 to 4 m
and from 0.1 to 7 m for CaCl2. Since lithium,
potassium, and sodium have the same charge
(+1) but increasing volume, the cation charge
density decreases down the group (similarly for
magnesium and calcium but with a +2 charge).
This experiment was conducted at the
Stanford Synchrotron Radiation Lightsource
(SSRL) 4-2 beamline (Figure 1), which has smallangle x-ray scattering (SAXS) capabilities. The 11 keV x-ray is generated via synchrotron radiation from
the SSRL and it is subsequently focused and attenuated to a spot size ~0.2 mm. The scattering path
length from the sample to the charge-coupled device (CCD) detector (Rayonix MX225-HE) was about 1.75
m giving a q-range from 0 to about 0.8. A-1. A 1.5 mm quartz capillary tube held samples during the
measurement. Samples were exposed to x-rays for 15 seconds for a total of 20 exposures at each
concentration. Before each 20-exposure series, a dark background was taken with no x-rays on the
Figure 2 The SSRL beamline 4-2 setup including the electron
storage ring and the 20-pole wiggler. The ion-gas chamber
located just upstream of the sample is used to measure the
intensity of the beam.
sample. These darks were subtracted from the original CCD images before the CCD images were
azimuthally integrated using SASTool, software developed specifically for analyzing x-ray scattering data
images. SASTool also normalized the images by the beam intensity measured in the gas chamber
(located upstream of the sample) to account for variations in beam intensity between samples.
In addition to the samples listed above, measurements of the empty capillary tube and of water
were also made with the same exposure time (15 s) and number (20) as the samples themselves. The
reciprocal-space curve of the empty capillary tube was subtracted from the reciprocal-space curves of
each of the other samples in order to get rid of any scattering due to the cell itself. Next, I created a
detector response function by dividing the measured water curve component-wise by a standard water
curve. Thus the detector response function can be interpreted as a vector in reciprocal-space which
accounts for imperfections in the detector. Reciprocal-space curves of the samples were then divided
component-wise by the detector response function (Figure 2).
Figure 3 From bottom to top, standard water, measured water, corrected 0.5 CaCl2, measured CaCl2. Removing the detector
response function (DRF) removes the kink at 0.04 A-1 as well as some bumps at slightly larger Q.
Data Analysis
From a qualitative perspective, the samples tested here do not have the type of radical change
in scattering that the AlCl3 measurements did; i.e. the reciprocal space curves never increased
dramatically at low q. In the divalent cations, especially CaCl2, a progression in behavior as a function of
concentration was observed, where low concentrations (0.1 m and 0.2 m) behaved much like water, mid
concentrations (0.5, 1, 2, 3 m) exhibited peaks, and high concentrations (4,5,6,7 m) developed rough
ridges at consistent q-values.
The peaks at mid concentrations
can be attributed to the long-range
structure induced by the solvations
shells surrounding cations, though the
exact scattering mechanism that
generates these peaks is not known. For
example, it is not clear whether the
peaks are due to scattering from
neighboring cations, from oxygen atoms
in neighboring water solvations shells,
or from some other interaction alltogether. The rough ridges observed at
Figure 4 From top to bottom, 7, 6, 5, 4, 3, 2, 1, 0.5, 0.2, 0.1 m CaCl2
high concentrations may be due to the
aqueous solutions and water. The 0.1 and 0.2 m solutions look very
similar to the water curve. A peak begins to appear at 0.5 m and begins to formation of salt crystals within the
exit the observed q-range at 3 m. Other features at 0.032 - 0.054 A-1 start
solution. If this is the case, these ridges
to appear at 4 m and increase in intensity as the concentration increases.
are not of interest to this study since I
am interested in the behavior of water
in fully dissociated salts.
Rmax (Å)
The q-values of the peaks at mid concentrations (0.5, 1, 2, 3 m) were plotted as a function of
Rconc, a distance proportional to the radius of the volume per ion in aqueous solutions of CaCl2 and MgCl2.
Rmax is equal to 2*π*(1/Qmax) and
200
has units Å-1. The volume
150
available to each ion should not
change as the charge density of
100
the ions increases since the
50
charge density of the ion does
not dictate how much of the
0
total volume is available to it.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
That said, for any particular Rconc,
~Rconc
one would expect the same Rmax
Figure 5 0.5, 1, 2, and 3 m aqueous solutions of CaCl2 and MgCl2 plotted for
assuming that the peak in
Rmax=2π(1/Qmax) vs. Rconc, which is proportional to the radial distances available
reciprocal-space is related to the
per ion. The linear fit to CaCl2 is y = 129.12x - 11.985 with R² = 0.9928 and the
spacing between ions and/or
linear fit to MgCl2 is y = 117.99x - 3.807 with R² = 0.9976.
their solvation shells.
Finally, with the assumption that there are multiple scattering processes that contribute to the
reciprocal space curve, I performed a singular value decomposition (SVD) analysis on each concentration
series (3). SVD creates normalized basis vectors that can be linearly combined to produce the original
vectors. The decomposition is similar to diagonalization of square, invertible matrices, only for nonsquare matrices. SVD thus decomposes the original data m x n matrix in to an m x n basis matrix (whose
columns are formally called the left singular vectors of the original matrix), an n x n square matrix of
singular values (which are analogous to eigenvalues), and finally an amplitude n x n matrix (whose
columns are formally known as the right singular vectors of the original matrix). Both the basis matrix
and the amplitudes matrix are orthogonal. As may be expected, the basis vectors do not necessarily
have any physical meaning. For example, intensity due to noise and due to signal may be mixed in the
same basis vector. In order to avoid this mixing, an optimization procedure is used which minimizes the
difference between intensities in neighboring vectors. The procedure, known as a rotation, can be
performed on either the basis vectors matrix or the amplitude matrix. In addition, if a basis vector is in
fact related to a physical process, including it in the rotation procedure may mix it with other basis.
Therefore, the rotation works best for basis that are obviously mixed. I performed the rotation on the
amplitudes vectors that corresponded to the four basis vectors that seemed qualitatively mixed. I
performed the rotation on the 3rd, 4th, 5th, and 6th columns of the amplitudes matrix. The results of the
rotation on CaCl2 and water are shown below.
Q (nm-1)
Q (nm-1)
Figure 6 SVD basis components before and after the rotation procedure for CaCl2 samples and water.
Most of the rough features between 0.3 and 0.55 nm-1 in the original basis have been concentrated in
the last component after the rotation procedure. The rotation was performed a second time on the
new 4th and 6th components, but this may be over-fitting the data, and I am not confident in the results.
Results are not shown here.
The first and second basis of the SVD are similar to the water scatter curves. The rotated third
basis curve seems qualitatively similar to the increase in intensity at higher concentrations at the higher
end of the q-region. The rotated 4th and especially the 6th basis vectors seems to be components related
to the bumps observed in high concentration solutions. The 5th has a peak that is similar to the 1 m peak
in CaCl2. Thus there is some qualitative correlation between the shape of the basis and the shapes of the
measured curves, but for understanding the features in high concentrations, the 6th rotated basis is the
most interesting. Future work may include modeling crystal formation to determine whether or not
peaks follow the same pattern as the 6th rotated basis.
Apart from SVD analysis, it is possible to perform a global analysis of the series of
concentrations. If the peak position and width at mid to high concentrations can be well modeled, a
global analysis would be preferable to the SVD analysis since the many peak components in SVD could
possibly be reduced to at least two parameters (Qpeak and width of the peak for a given concentration).
Ideally, the peak and the water signal would then be de-convolved from the high concentration curves,
leaving only the features that have yet to be explained.
Conclusion
The anomalous behavior in AlCl3 was not observed for other chloride salts composed with
divalent and monovalent metals. Peaks observed in salt solutions of mid-concentrations in divalent salt
solutions follow generally expected trends given that the distance between scattering particles should
change linearly with the distance expected as the concentration increases. The features at high
concentrations were not expected, and there is no hypothesized scattering mechanism that could
generate these features. The features have been isolated using singular value decomposition, which
may enable a more refined study into their casue.
1. Gaffney, Kelly. Early Career Proposal “Chemical and Conformational Dynamics in Aqueous
Solutions.”
2. I. Waluyo, C. Huang, D. Nordlund, U. Bergmann, T. M. Weiss, L. G. M. Pettersson, and A.
Nilsson, The Journal of Chemical Physics 134, 064513 (2011).
3. E. Henry and J. Hofrichter, “Singular Value Decomposition: Application to Analysis of
Experimental Data,” Methods in Enzymology 210 (1992).