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 mid-concentrations 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 couldthus extend to relievingthe 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 have been observed that the solution loses much of its long-range order perhaps due to some transitional state.
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 thathave 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, canbe 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 small-angle 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~0.2mm. 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 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 thegas 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 3From 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 all-together. The rough ridges observed at high concentrations may be due to the formation of salt crystals within the solution. If this is the case, these ridges are not of interest to this study since I am interested in the behavior of water in fully dissociated salts.
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 andMgCl2. Rmax is equal to 2*π*(1/Qmax) and has units Å-1. The volume available to each ion should not change as the charge density of the ions increases since the charge density of the ion does not dictate how much of the total volume is available to it. That said, for any particular Rconc, one would expect the same Rmaxassuming that the peak in reciprocal-space is related to the spacing between ions and/or 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 non-square matrices. SVD thus decomposes the original data m x n matrix in to an m x nbasis 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 thatseemed qualitatively mixed. I performed the rotation on the 3rd, 4th, 5th, and 6thcolumns of the amplitudes matrix. The results of the rotation on CaCl2 and water are shown below.
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.
- Gaffney, Kelly. Early Career Proposal “Chemical and Conformational Dynamics in Aqueous Solutions.”
- 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).
- E. Henry and J. Hofrichter, “Singular Value Decomposition: Application to Analysis of Experimental Data,” Methods in Enzymology 210(1992).