The Solvation Chemistry
of Polyoxometalates
By Nahom Amman
Supervised by C. André Ohlin & Michael Holmboe
Master thesis, 60 hp Examiner: Madeleine Ramstedt
I
Abstract
Although they can be found everywhere -- in the lab, in our bodies and in nature -- our knowledge of ions in solution is surprisingly rudimentary. Something as fundamental as determining the functional size of a solvated ion becomes conceptually difficult due to ion-solvent and ion-ion interactions. This is not just of academic interest but has real consequences since size -- and changes in size during a reaction -- dictate kinetics, diffusion, reactivities and other properties.
In this study, a method was developed to probe the behavior of polyoxometalate (POM) ions in solution with increasing ionic strength using molecular dynamics (MD) simulations, calibrated against experimental diffusion data obtained using diffusion ordered NMR spectroscopy (DOSY). The results show that the solvent-solute interactions of POMs are more prone to occur on their terminal oxygen due to them being the most exposed oxygen type. Furthermore, the addition of monovalent salts affects the POMs’ diffusion coefficients and hydration numbers to a varying degree. The study also found that ions believed to be largely non-coordinating in solution, surprisingly, associated with the POMs, even precipitating two of them. The methodology explored in this study has been shown to yield invaluable information regarding the behavior of solvated metal oxides and, with further work, could have the potential to reveal even more such as the effects of varying pH and temperature.
III
List of abbreviations
ATR-FTIR Attenuated total reflectance Fourier transform infrared spectroscopy DFT Density functional theory
DOSY Diffusion ordered spectroscopy HPA Heteropoly acid
MD Molecular dynamics
NMR Nuclear magnetic resonance spectroscopy
NPT Isothermal-isobaric ensemble, constant number of particles, pressure and temperature
NVT Canonical ensemble, constant number of particles, volume and temperature
PMo12 Phosphomolybdic acid, H3[PMo12O40]
POM Polyoxometalate
PV2Nb12 Vanadyl capped polyoxoniobate, [(CH3)4N]9[PV2Nb12O42])
PW12 Phosphotungstic acid, H3[PW12O40]
T1 Longitudinal relaxation time (s)
TGA Thermogravimetric analysis TMA Tetramethylammonium, (CH3)4N
Author contribution
The geometries of the polyoxometalates were optimized using DFT calculations performed by C. André Ohlin. The POMs’ Lennard-Jones parameters were optimized using MD by Michael Holmboe. Thermogravimetric analysis of the synthesized POMs was conducted by Markus Broström. Practical work such as synthesis and characterization of POMs and diffusion measurements was performed by the author. Creating simulation boxes, running MD simulations and processing the data using Gromacs was also done by the author under the guidance of Michael Holmboe.
V
Table of contents
Abstract ... I Author contribution ... III
1. Introduction ... 1
1.1 Theory ... 1
1.2 Aim of this thesis work ... 4
2. Popular scientific summary including social and ethical aspects ... 5
2.1 Popular scientific summary ... 5
2.2 Social and ethical aspects ... 6
3. Experimental ... 6
3.1 Synthesis ... 6
3.1.1 H3[PW12O40]•24H2O (PW12) synthesis8 ... 6
3.1.2 H3[PMo12O40]•12H2O (PMo12) synthesis8 ... 7
3.1.3 TMA9[PV2Nb12O42]•19H2O (PV2Nb12) synthesis9 ... 7 3.2 Instrumental Details ... 7 3.2.1 Thermogravimetric analysis ... 7 3.2.2 Raman Spectroscopy ... 7 3.2.3 ATR-FTIR spectroscopy ... 8 3.2.4 NMR spectroscopy ... 8 3.3 Computational Details ... 9
4. Results and Discussion ... 10
4.1 Characterization of POMs ... 10
4.2 Diffusion coefficients ... 12
4.3 Hydrogen bonds ... 16
4.4 Radial distribution functions ... 19
5. Conclusions and Outlook ... 22
Acknowledgement ... 22 References ... 22 Appendix ... 24 Appendix 1 ... 24 Appendix 2 ... 25 Appendix 3 ... 28 Appendix 4 ... 29 This thesis is accompanied by supplementary files containing information about the POMs for MD simulations named “PW12_itp”, “PMo12_itp” and “PV2Nb12_itp”.
1
1. Introduction
1.1 Theory
Almost all important chemical reactions include ions, regardless of the scientific field. Areas such as industrial processes as well as syntheses of biomolecules and fine molecules at some point involve ions. Yet, despite their ubiquitous use, our knowledge of how ions behave in solution is so limited that we still do not even know what they look like. Our picture of solvated ions was even more fundamental before Arrhenius presented his theory on how salts dissociate in water. The difficulties in determining what ions look like in solution is inherent to their interactions with polar solvents and formation of solvation shells. The matter is further complicated by the presence of counterions. Although salts are normally taken to dissociate completely in solution, the real behavior of oppositely charged ions can complicate the interpretation of even the most fundamental experiment. One such experiment yielding invaluable information about reaction mechanisms of any system is the determination of activation volumes, (∆V), which is the difference in volume between the reactants and a system in its transition or activated state.1,2 However, accurately determining ∆V for ionic species in
aqueous reactions requires extensive knowledge of solvation effects such as ionic interactions, hydrodynamic size and diffusion coefficients. Due to many of these effects originating from the molecular-scale, studying them experimentally can prove challenging or even impossible which is why methods such as molecular simulations are often used.
Molecular simulations, more specifically classical molecular dynamics (MD), have successfully been able to probe characteristics of solvated species such as their rates of diffusion, hydrogen bonding3 hydrodynamic sizes4 and even activation volumes.1,5 MD
simulations can compute the movement of thousands to millions of atoms and molecules in a system by Newtonian mechanics, based on their properties defined by a classical and mechanistic force field.6 The purpose of the force field is to describe the potential
energy of a system using mathematical interatomic potential functions containing atom type specific parameters, which in this study comprises bond stretch and angle bend terms, as well as Coulombic and Van der Waals terms, where the latter is described by a Lennard-Jones potential.6 The Lennard-Jones interactions in MD simulations are
defined by sigma and epsilon values (Figure 1) where sigma is the distance between two species when the Lennard-Jones potential is zero and epsilon represents the potential’s lowest value.
2
Force field parameters can be derived either semi-empirically, by comparison to similar systems or actual experimental properties, or from quantum mechanics using for instance density functional theory (DFT) calculations. Either way, the accuracy of the derived parameters must always be verified against experimental data to assure their accuracy, which makes parameterization of general and comprehensive force fields challenging.7
In fact, the availability of force fields designed for simulating the solvation chemistry of ionic species is very limited and of varying quality. Therefore, a new force field that has been derived with the help of accurate experimental data is needed. The experimental data is acquired through measurements of the solvation effects, such as the diffusion coefficients, of suitable target species. These species serve as models, thereby highlighting the chemical properties of solvated ions. Notably, the models chosen for diffusion measurements should preferably exhibit spherical (or spherical-like) structures, resulting in simpler diffusion-based calculations, and be possible to make synthetically pure.
Keggin type polyoxometalates (POM) are discrete polycationic metal oxides comprised of group V and VI metals in their highest oxidation states.8 The Keggin structure is one
of the most well-known POM structures with the general formula [XxMmOy]q-,
consisting of a central XO4 tetrahedron surrounded by twelve MO6 octahedra arranged
into groups of three (Figure 2).8 The structure contains three notable oxygen types;
bridging oxygen (Ob), terminal oxygen (Os) and phosphate oxygen (Op). The molecules
are highly symmetrical and can be considered spherical when tumbling in solution. Numerous Keggin type POMs have been successfully synthesized and characterized8–10
making them suitable candidates for diffusion measurements.
Figure 1. Lennard-Jones and Coulombic interactions between sodium and oxygen as a function of distance (left). The black line represents the sum of the two interactions. The right figure highlights the Lennard-Jones potential with resulting sigma and epsilon values.
3
The rate of diffusion for spherical species can be calculated using the Stokes-Einstein equation11 as shown below:
𝐷 =!"
# • $
%&'( (1)
where R is the molar gas constant, T the temperature of the system, N Avogadro’s number, Z the viscosity of the solvent and r the radius of the diffusing species. Apart from being spherical, the diffusing species is also assumed to have the same mean kinetic energy as a gas molecule at the same temperature.11 The equation can be used to
calculate the hydrodynamic radius of a species by determining r; albeit this requires accurate diffusion data which can be acquired either using MD or experimentally with diffusion ordered spectroscopy (DOSY).
DOSY is an effective nuclear magnetic resonance (NMR) spectroscopy method to measure the diffusion of solvated species.12 By applying a gradient, a target species’
position is revealed based on its measured signal intensity. Applying a second gradient after time ∆ will, by observing the change in intensity reveal the species’ new position. The relationship between initial and measured intensity is explained by the equation12:
𝐼 = 𝐼)𝑒*+,!-!.!(∆*"#) (2)
where I0 is the initial or reference intensity, I the measured intensity, γ the gyromagnetic
ratio of the observed nucleus, g the gradient strength and ∂ the gradient length.
The process is repeated for a set number of gradient steps. With each gradient step, the gradient strength is increased in order to observe the decay in signal intensity (Figure 3). The gradient strength usually starts at 2 or 5% of its maximum and reaches up to 95% in 16 steps.12 The observed decay in signal intensity (Figure 3) is used to calculate the
target specie’s diffusion coefficient.
Figure 2. Polyhedral and ball-and-stick structure of a Keggin type polyoxometalate along with oxygen types and their positions.
4
To measure the diffusion coefficient of a species, it must have migrated far enough in the field to yield an observable decrease in intensity. The diffusion time is therefore usually set to a few hundred milliseconds. However, if the analyzed nucleus has a longitudinal relaxation time (T1) shorter than the diffusion time, there would be no, or a
substantially decreased signal to measure the specie’s migration due the nucleus relaxing. Therefore, nuclei analyzed with DOSY require a T1 longer than the diffusion
time, so that its new position after ∆ can be measured. Nuclei such as 31P and 1H, with
relaxation times of a few seconds,13,14 have proven suitable for DOSY
measurements,15,16 whereas the T1 of, for example, 51V appears to be too short.10
1.2 Aim of this thesis work
The aim of this study is to devise a methodology to probe the behavior of solvated discrete metal oxide clusters using classical MD with a DFT derived force field. Three phosphorous-centered Keggin type polyoxometalates served as models for experimental measurements and computer simulations. POMs were synthesized and analyzed with
31P-DOSY to measure their rates of diffusion. The effects of ion interactions were also
studied by measuring the diffusion of POMs and counterions (when possible) at increasing ionic strength. The size of a POM increases when associated with counterions, which would result in slower diffusion (eq 1). Therefore, a decrease in the measured diffusion coefficients of POMs at increased ionic strength could be indicative of counterion association. The diffusion of polyoxometalates was investigated in the presence of two salts, NaCl and [N(CH3)4]Cl (TMACl). Na+ is, due to its high charge
density, considered a coordinating cation and believed to associate with anionic species such as POMs, more specifically their oxygen that all possess negative partial charges, in solution, thereby decreasing their diffusion coefficients. Note the latter effect is expected to concomitantly increase with concentration. Conversely, [N(CH3)4]+
(TMA+), is a non-coordinating cation due to its large ionic radius, resulting in a lower
charge density, as well as its inability to form hydrogen bonds or dipole-dipole bonds and is therefore not expected to interact with the solvated POMs regardless of increased concentration.
Figure 3. Decay in signal intensity with the gradient strength ranging from 5 to 95 % in 16 steps.
5
MD simulations were used to visualize and obtain molecular-scale insights into the data obtained from DOSY measurements, by comparing the diffusion rates obtained from the two methods, as well as to analyze hydrogen bonding and radial distribution functions. Previous studies simulating the diffusion coefficients and hydrogen bonding of POMs only investigated phosphotungstic acid using rigid clusters (frozen bonds) and did not probe the effects of varying ionic strength.3
The POMs chosen for analysis were phosphotungstic acid (H3[PW12O40]•24H2O),
phosphomolybdic acid (H3[PMo12O40]•12H2O) and a vanadyl capped polyoxoniobate
(TMA9[PV2Nb12O42]•19H2O). Phosphotungstic- (PW12) and phosphomolybdic acid
(PMo12) are classified as heteropoly acids (HPA), which have been known for centuries
and were structurally determined by J.F. Keggin in 193317 (Figure 2). Both HPAs are
only stable under acidic conditions.18,19 The vanadyl capped polyoxoniobate (PV
2Nb12)
differs slightly from the general Keggin structure due to the presence two bicapped vanadyl groups (Figure 4). In comparison with the HPAs, PV2Nb12 is stable over a wider
pH range (pH 4.5-10) and has a higher formal charge (-9 compared to -3).9
2. Popular scientific summary including social and ethical
aspects
2.1 Popular scientific summary
Ions are charged species that can be found everywhere, serving crucial functions in a wide variety of fields ranging from environmental research to human biology. Although they are invaluable to us (encoding genetic material, maintaining pH levels in the environment etc.) we know next to nothing about how ions behave in solution where even estimating their sizes becomes difficult. Understanding the behavior of these charged species in solution would give us unique insight on how we can use them to form substances that are of use to us (medical drugs, green alternatives to toxic chemicals, material for limb prosthetics) and perhaps even believed impossible to make.
Figure 4. The structure of PV2Nb12 resembles that of Figure 2 with the addition of two bicapped
vanadyl groups (brown). As a result, the terminal oxygen atom types can be divided into two subgroups; terminal oxygen atoms bound to niobium (OsNb) or to vanadium (OsV).
6
Predicting the behavior of ions in solution is however next to impossible to do solely with experiments and requires a more modern approach in the form of computer simulations. This study shows that by mimicking reality, computer simulations can be used to study the effects of solvated ions such as their sizes, how rapidly they move in and interact with the solvent as well as how they are affected by ions of opposite charge. The results in this study have hence laid the foundation for devising a methodology to better understand reactions involving ions using computer simulations.
2.2 Social and ethical aspects
Since the POMs used in this study have already been synthesized and studied in previous publications, this thesis provides little to the discussion of the ethics of synthesis and potential risks of newly synthesized compounds. Instead, the social and ethical aspects brought up in this section revolves around our new force field and the contributions it has to understanding the solvation chemistry of ions.
As previously mentioned, the goal of deriving this force field is to probe the behavior of solvated ions and, eventually, get a better understanding of reaction mechanisms involving them. The possibilities of such a tool are next to endless as it can be applied in a wide variety of fields; both good and bad. For example, it could possibly aid in the synthesis of a new drug used to treat a previously incurable disease or help develop a greener alternative to an industrial chemical known to harm the environment. Conversely, it may just as easily help in the synthesis of a new chemical weapon or a toxic herbicide. In other words, such a powerful tool would be a double-edged sword where its great potential to do good is accompanied by an equal potential to do bad. It is therefore up to the scientist using it to make sure their research aims to aid the world and not harm it.
3. Experimental
3.1 Synthesis
Syntheses of the POMs were based on well-established published procedures.8,9
PV2Nb12 was synthesized using microwave irradiation which has been shown to
significantly reduce the reaction time in the synthesis of polyoxoniobates and -tantalates while providing greater yields, when compared to hydrothermal synthesis.20
The purity of the synthesized POMs was determined using NMR-, ATR-FTIR- and Raman spectroscopy whereas their water contents were measured using thermogravimetric analysis (TGA).
3.1.1 H3[PW12O40]•24H2O (PW12) synthesis8
Na2WO4•2H2O (16.2 g, 49 mmol) and Na2HPO4•12H2O (1.7 g, 5 mmol) was dissolved
in a beaker of boiling water (25 ml). HCl (aq) (37%, 13 ml 158 mmol) was added dropwise to the boiling mixture until the color changed from clear to pale yellow. The solution was subsequently allowed to cool under ambient conditions, forming a white precipitate. Both the solution and precipitate were transferred to a separatory funnel and mixed with aliquots of diethyl ether (2 ml x7) until three distinct phases could be observed. The bottom layer, an oil containing PW12, was extracted and dried under
7
ambient conditions. Once dried, the remaining white solids were recrystallized in water and washed with small amounts of cold water. Crystals were oven-dried at 90°C. Yield of H3[PW12O40]•7H2O = 4.5 g (37%).
3.1.2 H3[PMo12O40]•12H2O (PMo12) synthesis8
MoO3 (20 g, 139 mmol) was added to water (200 ml) in a 500 ml round-bottom flask
and heated to boiling. H3PO4 (aq) (85%, 120 µl, 1.8 mmol) was added to the boiling
mixture, turning it yellow, which was then refluxed for 30 minutes. The refluxed mixture was filtered under suction on a glass frit (10-20 µm). The filtrate was evaporated with gentle heating on a hotplate, adding 10% H2O2 dropwise and filtering afterwards if it
turned green, until an oil formed. The oil was allowed to evaporate under a fume hood at room temperature until crystals formed. The oil was filtered under suction on a glass frit (10-20 microns) and the remaining crystals were washed with small amounts of cold water before being collected and dried under ambient conditions. Yield of H3[PMo12O40]•8H2O = 10.3 g (45%).
3.1.3 TMA9[PV2Nb12O42]•19H2O (PV2Nb12) synthesis9
Nb2O5•nH2O (82%, 2.44 g 15 mmol), TMAOH•5H2O (2.5 g, 14 mmol) and V2O5 (0.23
g, 5 mmol) was added to a 20 ml Biotage microwave reaction vial. Water (10 ml) and H3PO4 (aq) (85%, 111 µl, 1.6 mmol) was added to the vial which was then microwave
irradiated at 180 °C for 30 minutes. The bright yellow solution formed was filtered under suction through a 0.22 µm nitrocellulose filter to remove unreacted solids. Isopropanol (10 ml) was added to the filtrate with stirring, thereafter the supernatant being removed. This was repeated until ca 130 ml of isopropanol was added, resulting in the formation of a yellow precipitate. Acetonitrile (40 ml) was added to remove any residual water, followed by suction filtration on a glass frit (10-20 microns). The remaining yellow powder was washed with an excess of ethanol, prior to collection and oven-drying at 90 °C. Yield TMA9[PV2Nb12O42]•16H2O = 1.6 g (44%). The yield may be higher due to
the decomposition of TMA during TGA possibly resulting in an overestimated water content.
3.2 Instrumental Details
3.2.1 Thermogravimetric analysis
Each POM was weighed (30-180 mg) and sent for TGA analysis to determine their water content. The water contents were used to correct the POM concentrations in DOSY samples as well as calculate the presented yields.
3.2.2 Raman Spectroscopy
Raman spectra of 0.5 ml POM aqueous solutions were collected at 50 mW using a 532 nm laser. To obtain a good signal-to-noise ratio, every spectrum was generated by 6 scans. Anton-Paar’s software was used for automatic background subtraction and baseline correction (Cora 5000 V2.0.4.5).
8
3.2.3 ATR-FTIR spectroscopy
A VERTEX 70v FTIR spectrometer from Bruker was used to collect the IR spectra. A pressure head was used to directly press the dry samples onto the diamond crystal’s surface. Samples were scanned 1000 times with a spectral resolution of 4 cm-1 in the
4000-600 and 4000-400 region depending on the setup used.
3.2.4 NMR spectroscopy
For 1D 31P- and 51V-NMR analyses, 10 mg of dry product was dissolved with 450 µl
H2O and 50 µl D2O in a 5 mm NMR tube. Both analyses were performed on a Bruker
AVANCE III 400 spectrometer with a carrier frequency of 161.75 MHz for 31P and
105.05 MHz for 51V. 31P-NMR spectra were collected with a 7.85 µs 90° pulse (57 W),
300 acquisitions were made with a 2 second delay and calibrated against 85% H3PO4 at
0 ppm. The 90° pulse (78 W) for 51V-NMR spectra was set to 9.88 µs, 512 scans were
acquired with a 30 ms delay between each acquisition.
All DOSY samples were prepared solely in H2O to avoid complications due to the higher
viscosity of D2O (1.10•10-3 kg m-1 s-1 compared with 0.89•10-3 kg m-1 s-1 for H2O at 298
K)21 and the difference between pD and pH (pD = pH • 1.07)22 which could affect the
POMs’ diffusion. Aqueous solutions of 0.1 M POM in 0, 0.1, 0.5 and 1 M NaCl or TMACl were prepared. The addition of TMACl to the HPAs caused the clusters to precipitate, making them insoluble in water and not suitable for diffusion measurements. The sample containing PW12 in 1 M NaCl precipitated what is believed to be
Na3[PW12O40], resulting in the decreased concentration of both PW12 and Na+ in
solution. The sample is however presented as 0.1 M PW12 in 1 M NaCl throughout this
study. six samples containing 0.1, 0.5 and 1 M TMACl in water as well as 10 mM PV2Nb12 in 1 M NaCl, 1 M TMACl and no additional salt were also analyzed. 550 µl of
each sample was transferred to a 5 mm NMR tube. T1 measurements were set up for the
DOSY samples to ensure complete relaxation of the nuclei between each scan, resulting in clearer signals. The T1 were determined using an inversion recovery method with
varying delay. DOSY measurements were conducted using a Bruker AVANCE III HD 600 with a BBO CryoProbe for increased sensitivity at 298 K. 90° pulses were set automatically (for 1H) or manually (for 31P) for each sample to ensure accurate pulsing
and optimal signal intensities. Each sample was measured at 16 gradient steps with increasing gradient strength ranging from 5 to 95%. The gyromagnetic ratios for 1H and 31P were 4257.7 and 1723.5 Hz/Gauss respectively. 1H-DOSY samples were analyzed
with a 2 ms gradient pulse length and diffusion time at 25 ms. 4 acquisitions were made with a 5 second delay between each scan and gradient step. 31P-DOSY samples were
scanned using a 2 ms gradient pulse as well but the diffusion time was set to 400 ms and 800 ms for the 10 mM PV2Nb12 samples. One acquisition was made at each gradient
step due to the, primarily HPAs’ long T1 (ca 40 s for PMo12 and 90 s for PW12 with
increasing NaCl concentration slightly decreasing it) resulting in longer times between scans (about 4 minutes for PMo12 and over 6 minutes for PW12). Due to the
spectrometer’s sensitivity and high POM concentrations, a good signal-to-noise ratio was obtained for the 0.1 M samples despite using one scan. The 10 mM samples PV2Nb12 were acquired using 4 scans with a 30 second delay. Spectra were processed in
9
3.3 Computational Details
In order to do molecular simulations with the POMs, their structures were initially calculated with density functional theory (DFT) using the Gaussian software (G16 rev. A.03). The POMs were solvated by an implicit polarizable continuum model23 and their
geometry was optimized using the PBE024 functional coupled with a def2-tzvp25 basis
set. Furthermore, Natural Bond Order analysis26 was used to compute the partial charges
of all atoms in the POMs as natural atomic charges. Subsequently, the optimized POM geometries and partial charges from the DFT calculations were used to investigate the POMs with MD simulations, along with epsilon and sigma Lennard-Jones parameters of all the metal and oxygen atom types. The Lennard-Jones parameters (representing the Van der Waals potential energy in pair-wise interactions) were optimized with respect to the DFT geometries, by minimizing the differences in bond lengths and angles between the solvated POMs calculated with DFT and MD, respectively. This was accomplished using in-house MATLAB routines issuing short MD simulation runs while applying a trust-region-reflective non-linear least-squares algorithm to optimize the epsilon and sigma values of the explicitly solvated POMs. The initial Lennard-Jones parameters were taken from the CLAYFF force field27 (for metal sites having similar
coordination) and OPC328 for oxygen. Epsilon and sigma values are presented in
Appendix 1 along with partial charges obtained from the DFT calculations. More specific partial charges can be found in the supplementary POM_itp files. The cutoff for the short-range electrostatic and vdW potentials was set to 1.0 nm, where a particle-mesh-Ewald (PME) algorithm was used to treat long-range electrostatics. Water was simulated using the recent three-site water model OPC3, since it has been shown to outperform popular older models such as SPC, SPC/E, TIP3P in terms of diffusion rate, dielectric constant and many other experimental properties.28
After the optimization, in order to obtain the diffusion coefficients, radial distribution functions and hydrogen-bond behavior of the POMs, larger simulation boxes with approximate dimensions of 55x55x55 Å3 containing 5000 water molecules were created
using the atom MATLAB library.29 The number of POMs added was determined by
calculating the corrected POM concentrations in the DOSY samples (based on thermogravimetric analysis). The boxes contained 10 POMs for PW12, 12 for PMo12 and
9 for PV2Nb12. The charge of the polyoxoniobate was neutralized with the addition of
TMA+. However, due to the OPC3 water model not being able to simulate protonation
and deprotonation steps, adding H3O+ to neutralize the HPAs’ charge was not possible.
Instead, the charges of both HPAs were neutralized with Na+. Salts were added to the
simulation boxes according to the DOSY samples i.e. 0.1, 0.5 and 1 M of either NaCl or TMACl.
The systems were equilibrated in three steps. Firstly, energy minimization simulations of the system were performed using the steepest descent algorithm with force maximum criteria of 500 kJ mol-1 nm-1. After that, the systems were simulated in the canonical
(NVT) ensemble for 50 ps, allowing for water re-organization around the solutes, and 200 ps simulations in the isothermal-isobaric (NPT) ensemble to optimize the system density. During the NVT and NPT equilibration runs, a stochastic integrator was used to counteract irregularities in the systems’ velocity distribution.30
During the production runs, which were conducted in the canonical NVT ensemble using a leapfrog integrator, the temperature was monitored using a velocity rescale thermostat. The production runs were simulated for 100 ns with a 1 fs timestep with trajectories saved every 10 ps, generating in total 10000 frames for analysis. In order to measure
10
diffusion at a longer time scale, one longer simulation of 500 ns was also performed for a PW12 system, with a trajectory saved every 50 ps.
Diffusion coefficients of the POMs as well as counterions and solvent were calculated from the MD results using the slope of the mean square displacement of the observed specie’s center of mass as a function of time. This was done with the Gromacs utility gmx msd. The radial distribution functions were quantified with gmx rdf, showing the interactions between species and solvent. Hydrogen bonding was analyzed with gmx hbond, under the conditions that the bond length and angle must not exceed 3.5 Å and 30° respectively. Any POM-solvent interactions that did not fulfill these requirements were not considered as hydrogen bonds.
The experimental and simulated diffusion coefficients were used in eq 1 to calculate the POMs’ hydrodynamic radii. The viscosity for all systems was set based on the OPC3 water model (0.84•10-3 kg m-1 s-1).
4. Results and Discussion
4.1 Characterization of POMs
The synthesized POMs were analyzed and compared with previous publications to determine their purity. The assigned IR and Raman signals are presented in Table 1 and the spectra can be found in Appendix 2. The difference in signals for the same bond types between POMs in the IR and Raman spectra is attributed to the bonds being of varying strength due to the metals present and the difference in their reduced mass. As a result, similar bond types such as W=Os, Mo=Os, Nb=Os and V=Os show peaks at
different wavenumbers.
IR (cm-1) Raman (cm-1)
Bond type PW1231 PMo128 PV2Nb129 PW1232 PMo1218
P-Op 1078 1059 1022 - 994, 971
M=Os 967 961 953 1008 971
M-Ob-M 884, 768 887, 770 870, 816, 764, 689, 621 214 895
TMA+ - - 1485, 953 - -
The 31P-NMR spectrum of PW
12 in Figure 5 shows one large peak at -14.6 ppm which
is offset a little when compared with the signal at 15.3 ± 0.2 ppm found in literature.8
However, by observing the IR and Raman signals (Table 1), the peak can confidently be assigned to PW12 despite the shift.
Table 1. IR and Raman signals for POM bonds and TMA+. M represents the metals present in the
11
The 31P-NMR spectrum of PMo
12 (Figure 6) shows a strong peak at -3.21 ppm attributed
to the PMo12 cluster. The peak at 0.12 ppm is thought to be excess H3PO4 from synthesis
and the one at -0.96 ppm is either a trilacunary (PMo9O31(OH-)36-) or monolacunary
(PMo11O397-) species formed during hydrolysis of PMo12.18
The 31P-NMR spectrum of PV
2Nb12 (Figure 7) shows a strong signal at 2.33 ppm
corresponding to the POM as well as smaller signals that could not be confidently assigned. However, since the unknown species were of such low concentrations and not believed to interact with PV2Nb12 in solution, they were not expected to affect the
DOSY results. 51V-NMR shows one major peak at -541 ppm, belonging to PV2Nb12
and a smaller one at -518 ppm that has been assigned to a similar Keggin type polyoxoniobate (V3Nb12O429−) known to form during synthesis of PV2Nb12.
Figure 5. 31P-NMR spectrum of PW12.
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4.2 Diffusion coefficients
Diffusion coefficients were measured experimentally using 31P and 1H DOSY as well as
calculated from MD simulations using Gromacs. Table 2 shows both experimental and simulated diffusion coefficients of the polyoxometalates with their respective fitting error derived from calculating the coefficients with either the mean square displacement (MD) or decay in signal intensity (DOSY). The diffusion coefficients are accompanied by their respective hydrodynamic radii calculated with eq 1 using the viscosity of the OPC3 water model. All diffusion coefficients calculated from the MD simulations, including those of TMA+, Na+ and H2O for each system are presented in Appendix 3.
The diffusion coefficients of PW12 calculated from the 100 ns and 500 ns simulations
were near identical ensuring we have not missed any of the POMs’ solvation effects as a result of short simulation times. The simulated and measured diffusion coefficients of the POMs are also plotted in Figure 8 to better observe the effects ionic strength has on diffusion.
13 Sample Experimental MD D (10-10 m2 s-1) r (Å) D (10-10 m2 s-1) r (Å) PW 12 No salt 3.87 ± 0.08 6.72 ± 0.14 3.30 ± 0.56 7.88 ± 1.38 0.1 M NaCl 3.67 ± 0.05 7.09 ± 0.09 3.25 ± 0.43 8.00 ± 1.08 0.5 M NaCl 2.97 ± 0.05 8.76 ± 0.13 2.97 ± 0.41 8.75 ± 1.23 1 M NaCl 3.66 ± 0.05 7.10 ± 0.09 2.67 ± 0.23 9.74 ± 0.85 PMo 12 No salt 4.16 ± 0.03 6.25 ± 0.05 3.33 ± 0.52 7.81 ± 1.25 0.1 M NaCl 3.68 ± 0.02 7.06 ± 0.03 3.23 ± 0.60 8.05 ± 1.55 0.5 M NaCl 3.39 ± 0.02 7.67 ± 0.04 2.97 ± 0.43 8.75 ± 1.29 1 M NaCl 3.58 ± 0.02 7.26 ± 0.03 2.75 ± 0.33 9.45 ± 1.15 PV 2 Nb 12 No salt 2.36 ± 0.01 11.0 ± 0.04 1.56 ± 0.17 16.7 ± 1.84 0.1 M NaCl 2.27 ± 0.01 11.5 ± 0.05 1.53 ± 0.18 17.0 ± 2.03 0.5 M NaCl 2.32 ± 0.01 11.2 ± 0.03 1.44 ± 0.10 18.1 ± 1.26 1 M NaCl 2.21 ± 0.02 11.8 ± 0.08 1.03 ± 0.08 25.2 ± 1.97 0.1 M TMACl 2.22 ± 0.01 11.7 ± 0.04 1.49 ± 0.21 17.4 ± 2.51 0.5 M TMACl 2.09 ± 0.01 12.5 ± 0.03 1.34 ± 0.11 19.4 ± 1.60 1 M TMACl 1.88 ± 0.01 13.8 ± 0.07 1.21 ± 0.07 21.5 ± 1.25 Table 2. Diffusion coefficients and calculated hydrodynamic radii of POMs using the viscosity of water from the OPC3 water model.
14
The diffusion coefficients of PW12 (3.87 ± 0.08 • 10-10 and 3.30 ± 0.56 • 10-10 m2 s-1)
were comparable to previously published experimental and simulated data (3.36 ± 0.15 • 10-10 and 3.2 • 10-10 m2 s-1).3,33 Despite neutralizing the charge of PW12 and PMo12 in
the simulations with Na+ and not H+, the simulated and experimental data were also of
similar magnitude. The POMs’ simulated diffusion coefficients were generally slightly lower than the experimental ones. The same trend was observed for water in 0.1 M PV2Nb12 (16.89 ± 0.07 • 10-10 m2 s-1 with MD and 17.85 ± 0.08 • 10-10 m2 s-1 with DOSY)
suggesting the molecular dynamics simulations overestimating the POM-solvent interactions resulting in stronger hydrogen bonds, larger hydrodynamic radii and therefore slower diffusion of both the POMs and water. However, additional studies of the hydrogen bond dynamics are required to prove this.
Generally, the HPAs had higher diffusion coefficients compared to PV2Nb12 regardless
of salt concentration in both the experimental and simulated results with the latter showing PV2Nb12 diffusing almost half as quick as the HPAs. This could be attributed
to the large charge difference between the POMs, possibly resulting in PV2Nb12, with a
higher charge, attracting more water resulting in a larger hydrodynamic radius than the less charged HPAs. As previously discussed, eq 1 states that a larger hydrodynamic radius leads to slower diffusion.
Observing the HPAs’ experimental values, the addition of 0.1 M NaCl appeared to decrease their diffusion coefficients, suggesting the clusters associating with Na+. The
diffusion coefficients were further decreased by increasing the NaCl concentration to 0.5 M. However, both HPAs in 1 M NaCl diffused quicker than in 0.5 M. This can, for PW12, be explained by the observed precipitation of Na+ complexed with the cluster in
the sample containing 1 M NaCl, most likely resulting in a decreased viscosity and, according to eq 1, quicker diffusivity. No such behavior was however observed for PMo12 in 1 M NaCl despite the increased diffusivity. In other words, the experimental
Figure 8. Measured and simulated diffusion coefficients with error bars of PW12, PMo12 and PV2Nb12
15
results show that the diffusion of HPAs decreases in the presence of NaCl but there was no observable trend showing that an increase in NaCl would further decrease the diffusivity of PW12 or PMo12. The simulated data and accompanying error bars for the
HPAs indicate there is no difference in diffusivity for the clusters regardless of the presence and concentration of NaCl.
Much as with the HPAs, the experimental diffusion coefficient of PV2Nb12 decreased in
the presence of NaCl, implying association, but no systematic behavior was observed with increased concentration suggesting that it too is more affected by the presence of Na+ rather than its concentration. The results from the MD simulations presented no
difference in the diffusion coefficient of PV2Nb12 in 0 M, 0.1 M and 0.5 M NaCl. A
decreased diffusion coefficient at 1 M NaCl could however be observed. It is possible the diffusivity of PV2Nb12 gradually decreased as the NaCl concentration increased but
no such trend could be determined due to the large fitting error from the simulations. The decrease in diffusivity was more pronounced with increased concentrations of TMACl. The experimental results show that the diffusion coefficient of PV2Nb12
steadily decreased when more TMACl was added, suggesting the cluster and TMA+
possibly associate despite the theory that TMA+ does not coordinate to anionic species.
This was further corroborated by the DOSY results presented in Appendix 4 where a clear distinction was seen between the diffusion coefficient of TMA+ in water and in the
presence of PV2Nb12. The rather similar diffusivity of water in all samples (Appendix 4)
means the difference in the diffusion of TMA+ was not caused by any change in viscosity
but likely by it associating with the POM. The simulated results of PV2Nb12 showed a
trend similar to the experimental results but as with in NaCl, only PV2Nb12 in 1 M
TMACl displayed a diffusion coefficient that could be considered lower than the sample with no salt. The slightly clearer trend in the association of TMA+ to the cluster in
comparison with Na+ can be attributed to the size difference of the two counterions.
TMA+ is significantly larger than Na+ and should therefore have a more substantial effect
on the diffusivity of PV2Nb12 if associated.
The calculated hydrodynamic radii presented in Table 2 show that, as expected, PV2Nb12
had the by far largest radius, whereas PW12 and PMo12 were similar in size. However,
the calculated radii are questionable since the value for viscosity was assumed to be constant. Salts are known to increase the viscosity of water34 (0.89 • 10-3 kg m-1 s-1 and
0.98 • 10-3 kg m-1 s-1 for water with no and 1 M NaCl respectively) and would therefore,
according to eq 1, also affect the POMs’ hydrodynamic radii. Since the increase in viscosity with added salt was not considered, the calculated hydrodynamic radii in Table 2 are increasingly higher than their real values with increasing ionic strength. Future studies should include the investigation of each samples’ viscosity, either experimentally or with MD to more accurately determine the solvated POMs’ sizes.
Due to the relatively large uncertainties regarding the simulated diffusion coefficients, the DFT-derived force field was not tuned with the experimental data. Simulating diffusion coefficients suitable for tuning would most likely require numerous repetitions of MD simulations containing over a thousand POMs, yielding a high reproducibility and low uncertainty. This is however unlikely to occur due to high costs and long simulation times. Instead, tuning the force field with alternative experimental data such as signals from IR spectra could be employed.
16
4.3 Hydrogen bonds
The hydrogen bonds formed between water and the oxygen in the POMs were analyzed with Gromacs. The number of hydrogen bonds per oxygen for Ob and Os are presented
in Figure 9. The buried Op sites (Figures 2 and 4) did not form any hydrogen bonds in
any of the POMs and were therefore excluded from the analysis. The calculated 95% confidence interval of the formed hydrogen bonds were so low (ca 0.1% of the mean) that they were excluded from the figure.
Despite their lower partial charge, the POMs’ terminal oxygen atoms appeared to form more hydrogen bonds than the bridging ones which is consistent with previously published data suggesting Os is more prone to form hydrogen bonds due to its higher
accessibility (less steric hindrance) in comparison with bridging oxygen.3 Based on these
results, it appears that Os is the most hydrated part of the POMs.
The hydrogen bonds between water and Ob of both PW12 and PMo12 were unaffected by
the addition of NaCl meaning Na+ most likely does not associate with bridging oxygen
groups. The hydrogen bonds for Os were more, albeit still slightly, affected by the
17
addition of NaCl. Both POMs show a decrease in the number of bonds formed per Os
leading to suspect the terminal oxygen is more prone to associate with Na+ than O b.
PV2Nb12 generally formed more hydrogen bonds than both HPAs. This strengthens the
previously mentioned hypothesis that the polyoxoniobate attracts more water as a result of its higher charge. The cluster also appeared to have slightly more hydrated bridging oxygen atoms that were more susceptible to increasing salt concentrations, resulting in decreased hydrogen bonds per Ob. The hydrogen bonds between water and OsV show the
largest decrease with the addition of NaCl. OsV is however the most hydrated oxygen
type making it reasonable to assume the presence of associating counterions would affect its solvation the most. The effects of NaCl on OsNb did not indicate any trend when
the salt concentration is increased. Surprisingly, the number of formed hydrogen bonds were substantially more with 1 M NaCl than with no added salt. Added TMA+ had a
slight influence on the decreased solvation of Ob and OsV and a more pronounced,
although erratic, effect on OsNb. The irregular behavior of OsNb at increased salt
concentrations may suggest the oxygen type does not typically associate with counterions. Future hydrogen bond analyses should include the lifetimes of the formed hydrogen bonds, as it would help distinguish between free and bound water molecules that meet the angle and distance requirements. Results from the hydrogen bond analysis are accompanied by bond angle and distance distribution plots in Figures 10 and 11.
Figure 10. Hydrogen bond angle (a) and distance (b) distribution of Ob with no and 1
18
The figures show how the presence of Na+ very slightly increased the hydrogen bond
angular and distance distribution, indicating weaker bonds, for primarily POM Os but
the effects were also observed for HPA Ob. TMA+ appeared to have the opposite effect
on the formed hydrogen bonds for the polyoxoniobate, decreasing their angular and distance distribution. This was also observed for PV2Nb12 Ob in NaCl. In summary, the
coordination of formed hydrogen bonds was slightly dependent on the salt concentration. The bridging oxygen types of PV2Nb12 tended to have lower bond angles
and distances as well as a narrower distribution of the two than the HPAs, indicating that the Ob of PV2Nb12 formed stronger hydrogen bonds than the Ob of PW12 and PMo12
where the former appeared to form the weakest ones. The same can be said for OsNb but
not for OsV which showed a distance and angle distribution similar to the HPAs, with
the Os of PMo12 forming the weakest hydrogen bonds of the terminal oxygen types. The
difference between the two Os of PV2Nb12 can be attributed to the partial charge of OsV
being more similar with Os of the HPAs than OsNb (Appendix 1). The partial charges of
Os seemed to have a large impact on the hydrogen bond angles and distances. In fact, by
further consulting Appendix 1, a trend could be seen in Figure 11 where a higher partial charge of terminal oxygen atoms lead to lower and narrower hydrogen bond angle and distance distributions. No such behavior could however be observed for Ob.
Figure 11. Hydrogen bond angle (a) and distance (b) distribution of Os with no and 1
19
4.4 Radial distribution functions
The RDFs plotted in Figures 12-14 show the probability, g(r), of finding a water molecule or counter ion at distance r from the external oxygen types (Ob and Os). In
short, the figures highlight the POMs’ ion-ion and ion-solvent interactions. Figure 12 shows the RDF of Na+ and the two external oxygen groups. The peaks for PV
2Nb12 in
both plots of Figure 12 indicate the presence of long-range ordering of Na+ due to the
oxygen groups. In other words, the movement of sodium was not random when near Ob
and Os but depended greatly on O-Na+ interactions. Os seemed to have the strongest Na+
interactions based on the counterions being ordered for the longest distance from the atom, once again suggesting Na+ is more prone to associate with Os than Ob. The rather
flat curve shown for both HPAs in Figure 12 indicated there were weak or no Na+
interactions between Ob and sodium. The RDF for HPA Os does, however, suggest the
presence of short-range interactions with Na+, as seen in Figure 12. This corroborates
the theory that HPA Os is more susceptible to increasing NaCl concentrations than Ob.
The plotted RDFs between the two oxygen types and water hydrogen (HW) are shown in Figure 13. The RDF of Ob and HW showed a stronger long-range ordering of water
Figure 12. The RDF of Na+ with O
b and Os for the POMs in their lowest and highest
20
for PV2Nb12 most likely as a result of the cluster’s larger hydrodynamic radius than the
HPAs. There was some water interaction with the HPA Ob as well but they were mostly
short-ranged and not as pronounced as for the polyoxoniobate. The water interaction between POM Os and HW were all short ranged but as expected, PV2Nb12 had the
stronger water association as shown in Figures 10 and 11 as well. Despite it being more prone to solvation, the long-range interactions between Os and water were surprisingly
weak. Perhaps shorter ranged interactions with water such as hydrogen bonds are more defined by the oxygen type’s position whereas longer ranged interactions are governed by its partial charge. Therefore, the bridging oxygen atoms with higher partial charges but suboptimal positioning in the cluster showed a higher coordination of water at a longer distance than Os.
Unlike 1 M NaCl, the addition of 1 M TMACl appeared to greatly affect the interaction of both PV2Nb12 Ob and Os with water (Figure 13). Most notably, the long-range
ordering of water caused by interactions with Ob is decreased by the increased TMA+
concentration. Despite being considered a non-coordinating ion, TMA+ has, in this
study, shown to associate with diffusing POMs, precipitate HPAs and now inhibit POM-solvent interactions.
Figure 13. The RDF of Water hydrogen with Ob and Os for the POMs in 0 M and 1 M
21
The RDF of PV2Nb12 oxygen groups and TMA+ (Figure 14) show loose interactions
between the two. The distance between Os and TMA+ increased as more TMACl is
added whereas the presence of 1 M NaCl had a much smaller effect. The already weak Ob-TMA+ interactions shown in Figure 14 were effectively inhibited by the addition of
1 M TMACl. By comparing Figures 12 and 14, both oxygen types of PV2Nb12 interacted
stronger with Na+ than with TMA+ which was expected as Na+ has a higher charge
density. However, due to its size, the addition of more TMA+ had a greater effect on the
POM’s decreased diffusion coefficient than Na+, despite fewer and weaker interactions.
The RDF results has confirmed suspicions about the behavior of our POMs in solution as well as their interactions with counterions.
22
5. Conclusions and Outlook
This thesis study presents a methodology to simulate the behavior of polyoxometalates in solution using a newly derived classical force field. We have, albeit with varying accuracy, successfully simulated diffusion coefficients, hydrogen bonds and radial distribution functions in several systems with different POMs. The diffusion results show that POMs with higher charges diffuse slower due to their higher solvation and larger hydrated sizes. We have also observed the effects ionic strength has on the POMs’ solvation chemistry. The results suggest that counterions, even non-coordinating ones, may associate with metal oxides in solution. The MD simulations highlighted the importance of the location of oxygen on the POMs as the more exposed oxygen group was always more hydrated and more susceptible to the presence of counterions than the one with higher charge. However, the external oxygen type with higher partial charge had better long-range interactions with water. Furthermore, only external oxygen types appeared to interact with the solvent and ions.
Further assessment of the force field’s performance, by additional diffusion measurements varying factors such as pH and temperature as well as analyzing more POMs, is needed. If possible, more POMs should be simulated in each box, yielding lower uncertainties and more accurate diffusion results. Although simulating thousands of clusters seems unlikely, perhaps simulating 100 could give enough data to more accurately assess the rates of diffusion and thereby hydrodynamic radii for the POMs. Finally, by determining the viscosity of each POM with increasing ionic strength, their respective hydrodynamic radii and hydrated volume can more accurately be calculated. The DFT derived force field has been used to simulate the ion-solvent and ion-ion interactions of polyoxometalates but requires tuning using experimental data to further improve its accuracy. Although extensive research is required, the force field presented in this study is the first step in devising a method to accurately simulate reaction mechanisms involving solvated ionic species.
Acknowledgement
I would first of all like two thank my two supervisors C. André Ohlin, and Michael Holmboe for their excellent guidance, motivation and support. Secondly, I wish to thank Mark Rambaran for his invaluable help with everything from synthesis to writing and incredible support during the course. I want to thank Tobias Sparrman for his aid with setting up a 51V-NMR pulse program and the countless hours he has spent helping me
with DOSY measurements. Finally, I want to thank my mother Yehdega Girmay, brother Hermon Amman, sisters Senait Woldab and Cecilia Wallström as well as my partner Filippa Carnelius.
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Appendix
Appendix 1 Atom types Sigma (nm) Epsilon (kJ/mol) Partial charges PW12 PMo12 PV2Nb12 P 0.329324 7.79038 * 10-6 2.74 2.73 2.68 W 0.420901 6.07345 * 10-6 2.25 - - Mo 0.393864 5.61813 * 10-6 - 1.93 - Nb 0.470858 5.55655 * 10-6 - - 2.10 V 0.324595 7.79635 * 10-6 - - 1.29 Ob 0.321103 0.681301 -0.84 to -0.87 -0.75 to -0.76 -0.91 to -0.98 Op 0.313672 0.697463 -1.20 -1.17 -1.19 Os 0.287126 0.677850 -0.62 -0.51 -0.88 (O-0.54 (OsNb) sV)Epsilon and sigma values as well as partial charges for POM atom types. Attached POM_itp files can be consulted for more exact charges.
25
Appendix 2
ATR-FTIR spectrum of PW12.
26 ATR-FTIR spectrum of PMo12.
27 ATR-FTIR spectrum of PV2Nb12. M represents the metals Nb and V.
28 Appendix 3 Sample D (10-10 m2 s-1) POM TMA+ Na+ H 2O PW 12 500 ns no salt 3.33 ± 0.53 - 8.73 ± 0.12 21 ± 0.02 No salt 3.30 ± 0.56 - 8.54 ± 0.23 21.01 ± 0.01 0.1 M NaCl 3.25 ± 0.43 - 8.64 ± 0.02 20.59 ± 0.02 0.5 M NaCl 2.97 ± 0.41 - 8.09 ± 0.05 19.05 ± 0.06 1 M NaCl 2.67 ± 0.23 - 7.42 ± 0.10 17.3 ± 0.03 PMo 12 No salt 3.33 ± 0.52 - 8.93 ± 0.07 20.72 0.1 M NaCl 3.23 ± 0.60 - 8.87 ± 0.06 20.38 ± 0.02 0.5 M NaCl 2.97 ± 0.43 - 8.19 ± 0.09 18.86 ± 0.04 1 M NaCl 2.75 ± 0.33 - 7.45 ± 0.11 17.13 ± 0.03 PV 2 Nb 12 No salt 1.56 ± 0.17 6.26 ± 0.12 - 16.89 ± 0.07 0.1 M NaCl 1.53 ± 0.18 6.35 ± 0.12 2.27 ± 0.33 16.72 ± 0.08 0.5 M NaCl 1.44 ± 0.10 6.29 ± 0.01 3.60 ± 0.02 15.56 ± 0.07 1 M NaCl 1.03 ± 0.08 6.06 ± 0.05 3.65 ± 0.11 14.16 ± 0.11 0.1 M TMACl 1.49 ± 0.21 6.29 ± 0.10 - 16.54 ± 0.03 0.5 M TMACl 1.34 ± 0.11 5.85 ± 0.09 - 15.05 ± 0.09 1 M TMACl 1.21 ± 0.07 5.29 ± 0.05 - 13.44 ± 0.09
29
Appendix 4
Sample TMA+ conc (M) D (10-10 m2 s-1)
TMA+ H2O 10 mM PV2Nb12 0.09 6.64 ± 0.25 20.78 ± 0.21 10 mM PV2Nb12 in 1 M TMACl 1.09 8.64 ± 0.10 19.94 ± 0.03 0.1 M TMACl 0.1 9.14 ± 0.41 21.87 ± 0.21 0.5 M TMACl 0.5 9.95 ± 0.18 21.16 ± 0.05 1 M TMACl 1 9.33 ± 0.15 21.33 ± 0.04 H2O 0 - 21.88 ± 0.24
Experimental diffusion coefficients of TMA+ and water in the presence of 10 mM