A Novel Microemulsion Phase Transition: Toward the Elucidation of

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A Novel Micro-Emulsion Phase Transition: Towards the Elucidation of Third Phase Formation in Spent Nuclear Fuel Reprocessing Junju Mu, Ryuhei Motokawa, Kazuhiro Akutsu, Shotaro Nishitsuji, and Andrew J. Masters J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b08515 • Publication Date (Web): 07 Dec 2017 Downloaded from http://pubs.acs.org on December 20, 2017

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The Journal of Physical Chemistry

A Novel Micro-Emulsion Phase Transition: Towards the elucidation of Third Phase Formation in Spent Nuclear Fuel Reprocessing Junju Mu†, Ryuhei Motokawa‡*, Kazuhiro Akutsu§, Shotaro Nishitsuji¶ and Andrew J. Masters†*

†

School of Chemical Engineering and Analytical Science, The University of Manchester,

Oxford Road, Manchester M13 9PL, UK ‡

Hierarchical Structure Research Group, Materials Sciences Research Center, Japan Atomic

Energy Agency (JAEA), Tokai, Ibaraki 319-1195, Japan §

Research Centre for Neutron Science and Technology, Comprehensive Research

Organization for Science and Society (CROSS), Tokai, Ibaraki 319-1106, Japan ¶

Graduate School of Science and Engineering, Yamagata University, Yonezawa, Yamagata

992-8510, Japan

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT: We present evidence that the transition between organic and third phases, which may be observed in the plutonium uranium reduction extraction (PUREX) process at high metal loading, is an unusual transition between two isotropic, bi-continuous micro-emulsion phases. As this system contains so many components, however, we have been seeking first to investigate the properties of a simpler system, namely, the related metal-free, quaternary water/n-dodecane/nitric acid/tri-butyl phosphate (TBP) system. This quaternary system has been shown to exhibit, under appropriate conditions, three coexisting phases: a light organic phase, an aqueous phase, and the so-called third phase. In the current work, we focused on the coexistence of the light organic phase with the third phase. Using Gibbs ensemble Monte Carlo (GEMC) simulations, we found coexistence of a phase rich in nitric acid and dilute in n-dodecane (the third phase) with a phase more dilute in nitric acid but rich in n-dodecane (the light organic phase). The compositions and densities of these two co-existing phases determined using the simulations were in good agreement with those determined experimentally. Because such systems are generally dense and the molecules involved are not simple, the particle exchange rate in their GEMC simulations can be rather low. To test whether a system having a composition between those of the observed third and organic phases is indeed unstable with respect to phase separation, we used the Bennett acceptance ratio method to calculate the Gibbs energies of the homogeneous phase and the weighted average of the two co-existing phases, where the compositions of these phases were taken both from experimental results and the results of the GEMC simulations. Both demixed states were determined to have a statistically significant lower Gibbs energy than the uniform, mixed phase, providing confirmation that the GEMC simulations correctly predicted the phase separation. Snapshots from the simulations as well as a cluster analysis of the organic and third phases revealed structures akin to bi-continuous micro-emulsion phases, with the polar species residing within a mesh, and with the surface of the mesh formed by amphiphilic TBP molecules. The non-polar n-dodecane molecules were observed in these snapshots to be outside this mesh. The only large-scale structural differences observed between the two phases were the dimensions of the mesh. Evidence for the correctness of these structures was provided by the results of small-angle X-ray scattering (SAXS) studies, where the profiles obtained for both the organic and third phases agreed well with those calculated from simulation. Finally, we looked at the microscopic structures of the two phases. In the organic phase, the basic motif was observed to be one nitric acid molecule hydrogen bonded to a TBP molecule. In the third phase, the most common structure was that of the hydrogen-bonded chain TBP–HNO3–HNO3. A cluster analysis provided evidence for TBP forming an extended, connected network in both phases. Studies of the effects of metal ions on these systems will be presented elsewhere, but suffice it to say here that these ions are not expected to change the basic bi-continuous structure of the phases, since metal ions have been previously known to reside inside the mesh along with the other polar molecules.

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1. INTRODUCTION Plutonium uranium reduction extraction (PUREX)1,2 is a well-established liquid–liquid extraction process for separating plutonium and unused uranium from the other fission products formed in a nuclear reactor. In this process, the fission products are mixed with concentrated nitric acid, which dissolves the metals. Immediately thereafter, an organic diluent (typically odorless kerosene) and a tri-butyl phosphate (TBP) ligand are added to the mixture. The TBP selectively complexes with the uranyl and plutonium nitrates, and these complexes end up in the organic phase. From there, the uranium and plutonium are recovered. At high metal loading, however, the organic phase may itself separate into two phases;3-5 the heavy lower layer, which is commonly named the third phase, contains high concentrations of the metal-ion/TBP complexes and mineral acids, while the light upper layer, which is commonly named the light organic phase, contains a lower concentration of metal ions, TBP, and mineral acids but is rich in the organic diluent. Formation of the third phase is highly undesirable because it causes failure of the extraction process and because the concentrations of uranium and plutonium in the third phase may be high enough to risk an uncontrolled nuclear chain reaction. In the past few decades, extensive experiments have been carried out to delineate under what conditions the third phase forms and to investigate the microscopic structures of the co-existing third and light organic phases.6-13 Nuclear magnetic resonance (NMR),14,15 extended X-ray absorption fine structure,16 and infrared spectroscopy have been used to gain information about the molecular structures on the atomic-length scale, while small-angle X-ray and neutron scattering (SAXS and SANS) measurements have been taken to characterize the larger structures at the nanometer-length scale.17-20 The metal/TBP complexes were first proposed by Chiarizia and co-workers, on the basis of SANS profiles, to form reverse micelles.21-25 However, in general, a SANS or indeed a SAXS profile can be modelled by several different structural models, and hence considerable care is required to correctly interpret such profiles with a unique structure.26 Nevertheless, note that other extraction processes besides PUREX also show formation of the third phase and co-existence of this phase with the organic phase, and reverse micelles have been suggested to play a key role here.4,15 To shed further light on the nature of the light organic and third phases in the solvent extraction of plutonium and/or uranium ions, molecular simulation studies have been performed.27-41 The results are sensitive to the quality of the force field used. In particular, one requires a good model of TBP, one that can describe the interaction of TBP both with an alkane and with water. In a recent paper42, we proposed a TBP model that provided a satisfactory account of the interactions of TBP with both polar and non-polar molecules, in terms of both thermodynamic and structural properties. However, some mineral acids, such as nitric acid, give rise to the formation of the third phase even in the absence of metal ions.15 An overall understanding of this subject may therefore be realized most effectively by first studying such simpler systems before moving on to investigate the effects of metal nitrates. In the current work, we thus studied the phase behavior of the TBP/n-dodecane/HNO3/H2O system and investigated the nature of the structures formed. To carry out this study, we performed both Gibbs ensemble Monte Carlo (GEMC)43 and molecular dynamics (MD) 3



simulations in conjunction with SAXS experiments. The findings obtained here should contribute to the evolving understanding of the mechanism of the formation of third phases involving metal ions.

2. METHODOLOGY 2.1 Experimental Section 2.1.1 Materials. TBP was purchased from Tokyo Chemical Industry (Tokyo, Japan) and dried overnight under molecular sieves (Wako Pure Chemical Industries, Osaka, Japan) before use. Fuming nitric acid and n-dodecane were purchased from Wako and used as received. The water used in this study was deionized using a Millipore Milli-Q purification system. 2.1.2 Sample preparation. Samples of both the third phase (heavy organic phase) and the light organic phase were prepared as follows. A given volume of 15.8 M nitric acid was mixed with the same volume of a 1.1 M TBP solution in ndodecane. The mixture was shaken for 1 h at 298 K in a glass tube, and then centrifuged. This process led to the formation of three co-existing phases, that is, an aqueous phase, the third phase, and the light organic phase (see Supporting Information). Aliquots of the third and light organic phases were loaded into separate glass capillary cells with 0.01-mm-thick walls and a 2.0 mm sample thickness. All of the SAXS profiles were acquired at 298 K. The compositions of third and light organic phases reported by Ivanov and his coworkers44 are reproduced in Table 1. An illustration of the three phase coexistence, namely, the light organic, the third and the aqueous phases, is shown in Figure S1 in Supporting Information.

Table 1. Equilibrium compositions of the light organic and third phases at 298 K and 1 bar. Mole fraction (%) Molecular species Light organic phase

Third phase

TBP

15.2

21.3

n-dodecane

69.2

25.4

HNO3

13.9

42.8

4


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H2O

1.6

10.5

2.1.3 SAXS experiments. SAXS measurements were taken using an X-ray diffraction apparatus (NANO-Viewer, Rigaku Corp., Tokyo, Japan). The wavelength of the incident X-ray beam generated from a Cu-Kα line, λ, was 0.154 nm, where the incident beam was focused to a spot 450 µm in diameter at the sample position with a confocal optic (Max-Flux, Rigaku) equipped with a pinhole slit collimator. The scattered X-rays from the sample were detected by a two-dimensional position-sensitive detector (PILATAS 100K/R, Rigaku) composed of 195 × 487 pixels spanning 33.5 mm × 83.8 mm and hence having a spatial resolution of 0.172 mm/pixel, and covering a scattering vector magnitude (q) range from 0.2 to 34 nm-1 at three sample-to-detector distances of 64, 115, and 671 mm. q was calculated by using the equation q = (4π/λ)sinθ, where 2θ is the scattering angle. The scattering data recorded by the detector were corrected for counting efficiency, instrumental background, and air scattering on a pixel-to-pixel basis. The X-ray scattering intensity distribution, I(q), which is circularly averaged, was converted to absolute units of the scattering intensity per centimeter (cm-1) by calibration against water scattering.45 Cell scattering was subtracted from I(q) by considering transmission, where I(q) can be reproduced on the basis of atom pair radial distribution functions from simulations as employed in our previous report.42

2.2 Simulation Approaches In this study, we used the force field potentials and the all-atom TBP model described in our previous publication.42 The n-dodecane model was taken from the OPLS-2005 force field46 and the TIP3P model was used for H2O since it was optimized for use with optimized potentials for liquid simulations (OPLS) force fields.47 The models used here were with reasonable accuracy able to describe the thermodynamic properties of the TBP/alkane and TBP/water systems and reproduce experimental SAXS data collected from these systems.42 The HNO3 in our system was treated as an undissociated molecule, based on the assumption that the dissociation constant of HNO3 is small in an organic environment. The force field parameters for HNO3 were taken from Price et al.48 Following the OPLS procedures, geometric combining rules were used to obtain the interactions of unlike pair. Both MD and GEMC simulations were carried out to calculate the properties of the light organic and third phases. The GEMC simulations were used to investigate the phase separation of the TBP/ndodecane/H2O/HNO3 systems, and the detailed simulation protocol is provided in Section 3.1. The MD simulations were performed to calculate the excess Gibbs energy of certain systems as well as to investigate the microscopic structures of the light organic and third phases. For all the MD simulations, cubic periodic 5



boundary conditions were employed and the equations of motion were integrated using the Leapfrog algorithm49 with a time step of 1 fs. The OPLS-AA force field50 was used with the specific parameters given in our previous work.42 For both the Lennard-Jones and short-range Coulomb interactions, a 1.2 nm cut-off was used and potential switch functions51,52 were applied from 0.9 nm to 1.2 nm to conserve the energies at the cut-off. For the long-range electrostatic potential, the particle-mesh Ewald (PME) method was applied.53 The NpT ensemble was used in those MD simulations where the pressure and temperature were set as 1 bar and 298.15 K, respectively. For each system considered, an equilibrated structure was obtained from the starting configuration using the velocity-rescaling thermostat54 and the Berendsen barostat55. The Nosé– Hoover thermostat56,57 and Parrinello–Rahman barostat58,59 were applied in the subsequent production runs, during which the simulation results were generated. The number of time steps used differed for the different MD simulations and are provided in detail in Sections 3.2 and 3.3.

3. RESULTS AND DISCUSSION 3.1 Phase Coexistence via GEMC Simulations GEMC simulation is a powerful method to investigate the phase behavior of multiple phases. Unlike conventional Monte Carlo simulations, for which only one simulation box is usually used, GEMC involves the simultaneous use of several simulation boxes. In a GEMC simulation, there are not only particle movements within a simulation box, but also different simulations boxes may exchange particles. As the GEMC method simulates different phases in different boxes, it can simulate phase equilibrium using relatively small systems without suffering from problems associated with phase interfaces, which can be a problem for other methodologies. GEMC simulations were performed at constant pressure and temperature to confirm whether our force field would predict a phase separation of the TBP/n-dodecane/H2O/HNO3 system at a high concentration of HNO3. The Towhee 7.1 simulation package60 was used for these simulations. When investigating two-phase coexistence, GEMC simulations are usually carried out by simultaneously performing two NpT Monte-Carlo simulations on the system, where the compositions of the two simulation boxes are, in general, different. In addition to the normal NpT Monte Carlo moves on each box, there are additional moves that allow particles to transfer from one box to another. When there is no net flux of any species from one box to another, the two boxes are at equilibrium with each other, and the average compositions of the two boxes correspond to the compositions of the two co-existing phases. For our particular system, we began with two boxes that initially were of the same volume and that contained mixtures of identical composition and density. This composition was taken as the average of those of the organic and third phases given in Table 1. A total of 520 molecules were simulated in each GEMC simulation. The pressure and temperature were set as 0.1 MPa and 298.15 K, respectively61. Each GEMC simulation was run for 100,000 cycles, where a cycle consisted of n Monte Carlo moves, and where n is the total number of the molecules in the two boxes combined. A total 6


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of eight types of Monte Carlo moves, which are summarized in Table S1 in Supporting Information, were allowed where each molecular species and each box had the same chance to perform a Monte Carlo move. Ten GEMC simulations were performed and the results presented in this manuscript were calculated as the averages over these 10 runs. The results of the GEMC simulations are shown in Figure 1, where the average concentrations of all of the molecular species in box 1 and box 2 are shown in Figures 1a and 1b, respectively. In each simulation, the box having more n-dodecane molecules in the final configuration was always regarded as box 1 since each box had an equal possibility of becoming either the diluent-dominant phase or the HNO3-dominant phase. Note that boxes 1 and 2 corresponded to the light organic and third phases, respectively, at the later stages of the simulation.

Figure 1. The average mole fractions of the indicated molecular species as a function of the number of Monte Carlo cycles for (a) box 1 and (b) box 2. The values plotted and the error bars were obtained from 10 independent GEMC runs.

7



As shown in Figures 1a and 1b, the molar fractions of all molecular species in both boxes changed rapidly at the beginning of the GEMC simulations and levelled off after approximately 0.4 × 105 Monte Carlo cycles. As noted above, the box that became rich in n-dodecane at the end of the simulations was defined as box 1. We also found that box 2 became rich in HNO3 and H2O at the end of the simulations. The final molar fraction of n-dodecane in box 1 was almost twice that in box 2 while the final molar fractions of HNO3 and H2O in box 2 were almost twice and four times those in box 1, respectively. We thus found that the two boxes, even though they started with identical compositions, transformed into two different phases. In addition, the final relative amounts of each molecular species in box 1 and box 2 were observed to be similar to the experimentally determined relative amounts of the organic and third phases as shown in Table 1. While this result is extremely encouraging, it must be noted that the system of interest was a dense and viscous system where the swap rate of TBP at the end of the simulations was as low as 3 × 10-4. Hence one may question whether the system was fully equilibrated in our simulations. In order to provide further evidence for the greater thermodynamically stability of the two-phase coexistence than of the homogeneous mixture as predicted by the GEMC simulations, we also calculated and analyzed the Gibbs energies of both mixed and demixed states as described in Section 3.2.

3.2 Gibbs Energy Calculations Under conditions of constant temperature and pressure, the Gibbs energy of a system is a minimum at equilibrium. To verify the instability, relative to demixed states, of a homogeneous fluid of a composition between those of the light organic and third phases, we compared the Gibbs energy of the homogeneous state with that of the corresponding phase-separated state. In this study, MD simulations were used to calculate the Gibbs energies of three compositions: the homogeneous mixture (set I), the two coexisting phases predicted by the GEMC simulations (set II), and the two coexisting phases whose compositions were measured by Ivanov et al. (Table 1; set III). Two boxes were used for each of set II and set III, and were set up to correspond to the compositions of the two demixed systems. In this way, we were able to compare the Gibbs energy of the homogeneous system with the weighted average of the Gibbs energy values of two sets of demixed systems. The compositions studied are given in Table 2. The compositions of the two boxes in configuration set II were the same as the final results of the GEMC simulations shown in Figure 1. The compositions of the two boxes in set III were made to be as close as possible to the measured compositions of the light organic and third phases shown in Table 1, given that a simulation must deal with an integer number of molecules. The composition of the homogeneous mixture, that is, of set I, was a 1-to-1 v/v mixture of the organic and third phases, with their compositions corresponding to those of set II. In all of the above cases, the MD simulations were run at 298 K and 1 bar. The MD simulations were performed using the GROMACS 4.6.7 simulation package,62-64 where the equilibration and production runs 8


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were performed for 5 ns and 1 ns, respectively. The short simulation time was used to not only guarantee the convergence of the temperature and pressure but also to prevent the homogeneous systems from demixing. The Gibbs energy of each box of a configuration set was calculated by using Eq. 1.

=

+

> < 1 1

= − ∙ ln + ∙ (1)

Here, Gideal and Gex are the ideal Gibbs energy and excess Gibbs energy, respectively, N and Ni are the total number of molecules and the number of molecules of species i in the box, respectively, T and V are the temperature and volume of the box, respectively, kB is the Boltzmann constant, and µiex is the excess chemical potential of molecular species i. This latter quantity was calculated using the Bennett acceptance ratio (BAR) method.65 Also, Λi is the thermal de Broglie wavelength of molecular species i, given by =

ℎ

"2$%

(2),

where h is Planck's constant and mi is the mass of molecular species i. The BAR method was performed using the GROMACS 4.6.7 package. For each box, the excess chemical potential of a molecular species, µiex, was estimated as the change of Gibbs energy from the beginning to the end of the process of slowly introducing a new molecule of that species into the box. The new molecule was first inserted in the center of the box, and the box was equilibrated by carrying out a short MD run. The BAR method was then performed using 28 intermediate states, ξ, between 0 and 1 (ξ = 0, 0.01, 0.02, 0.05, 0.08, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.92, 0.94, 0.96, 0.98, 0.99, and 1.00). At ξ = 0, interactions between the new molecule and the surrounding molecules were switched off, and at ξ = 1 the new molecule was found to interact fully with the other molecules. Both the Coulomb and van der Waals interactions were coupled simultaneously by ξ, and a soft-core potential66 was used for the new molecule to prevent the occurrence of discontinuities when ξ approached either 0 or 1. The details of the soft-core potential are described in our previous publication.42 The ξ points were chosen in order to obtain a smooth variation of the dH/dξ profile. For each value of ξ, the system was first equilibrated for 2 ns and the results were obtained from production runs of 2 ns each. A total of five individual BAR calculations were performed for each molecular species in each box, and the final values of µiex for each box were averaged over the five individual BAR calculations.

Table 2. The compositions of the three systems for the Gibbs energy calculations System

Species

Molar fraction of each species (%)

9



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Set I a

Set II

Set III

TBP

19.1

18.5

15.2

n-dodecane

42.6

59.3

68.5

HNO3

31.3

19.6

14.1

H2O

7.0

2.6

2.2

TBP

-

19.6

21.3

n-dodecane

-

29.9

25.5

HNO3

-

40.2

42.6

H2O

-

10.3

10.6

Box 1

Box 2

a

Only one simulation was performed for set I due to it having only one composition.

The calculated Gibbs energies of the three sets of configuration are shown in Figure 2. Set I was calculated to have a significantly higher Gibbs energy than either set II or set III. This result indicated the homogeneous system is not in equilibrium state, supporting the results of the GEMC simulation. The demixed states, with the compositions of the coexistent phases predicted either by GEMC or as measured by experiment, were both indicated to be more stable than the 1:1 v/v mixture of the two phases. In addition, the Gibbs energy of set II was identical to that of set III within statistical error. We now turn to the densities of the demixed phases. The MD simulations of set III, corresponding to the experimental compositions of the two phases, gave densities of 0.841 and 0.987 g cm-3 for the light organic and third phases respectively, as compared with the experimental values44 of 0.85 and 1.0 g cm-3. This good agreement provided further validation of the quality of the force field used. The densities of the two phases were predicted using GEMC to be 0.885 and 0.952 g cm-3, which were within 5% of the experimental values. These small discrepancies were due to the GEMC compositions being slightly different from the experimental ones. This difference in composition may have been due to imperfections in the force field used, but could also have been due to the sluggish rate of equilibration in the GEMC simulations, so the compositions reported were close to but not quite the same as that of the fully equilibrated state.

10


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In summary, both the results from the GEMC simulations and the Gibbs energy calculations showed the models used in our simulations to exhibit a coexistence of the light organic and third phases that was found experimentally. Furthermore, the results of our simulations and calculations showed good quantitative agreement with the observed compositions and densities.

Figure 2. The Gibbs energy values of the three configuration sets. The error bar was calculated by using the GROMACS package, which follows the error estimation approach by Bennett.65

3.3 SAXS Profile Calculation Comparing calculated SAXS profiles with experimental data is one of the best ways to assess the correctness of microscopic structures predicted by molecular models. In this study, MD simulations were performed using the compositions of both the third and light organic phases that were measured in Ivanov’s experiments, as shown in Table 1. Cubic periodic boundary conditions were used for these MD simulations. For each composition, four different system sizes, ranging from about 0.1 million to 1.0 million total number of atoms, were used in order to check the effect of system size on the calculated SAXS profiles. These system sizes corresponded to 12.3, 15.1, 18.0, and 21.1 nm cubic boxes, respectively. All the systems were simulated for 50 ns where the durations of the equilibration and production runs were 30 ns and 20 ns, respectively. 11



SAXS profiles were calculated based on the trajectories of the production runs. The calculated I(q) covered a q range of 0.3 to 25 nm-1, with d = 2π/q defining the relationship between q and the corresponding distance d. The minimum q values in our calculations were found to depend on the size of the simulation boxes. The distance corresponding to the maximum q was 0.25 nm, smaller than most of the intermolecular distances in our system. Distances smaller than 0.25 nm, which correspond to q values larger than 25 nm-1, usually correspond to the bond lengths of covalent bonds of the molecules and therefore need not be calculated. This is because in our atomistic models the covalent bonds are represented with harmonic strings instead of electron clouds, and such approximation can cause inaccuracies in the calculated SAXS profiles. The calculated and experimentally obtained SAXS profiles of the third and light organic phases are shown in Figures 3 and 4, respectively. In both figures, the black circles show the experimentally measured SAXS profile while the red, yellow, blue, and green curves show the calculated SAXS profiles from simulations that used 12.3, 15.1, 18.0, and 21.1 nm boxes, respectively. In the SAXS profiles of the third phase (Figure 3), two scattering peaks were observed at about q = 6.7 and 14.5 nm-1. Our previous investigation indicated that these two peak positions correspond to the lengths of a TBP dimer and an alkane chain, respectively.42 For the third phase, the calculated SAXS profiles reproduced well the major scattering peaks of the experimental SAXS profile and reproduced the overall shape, especially in the relatively high-q region, that is, where q > 2 nm-1. Such high q values correspond to d distance shorter than 3.1 nm. These calculated SAXS profiles and the experimental results, however, showed differences in the low-q region, that is, for q < 3 nm-1. We note, though, that the differences decreased as the box sizes were increased. To further investigate the effect of box size on the calculated profile in the low-q region, we extrapolated the calculated third phase profiles to infinite box size. The extrapolation was made, for each value of q, by plotting I(q) against the inverse box length and using a linear extrapolation to estimate the infinite box length limit. The quality of the fit was found to be good, and examples of the extrapolation are provided in Table S2 and Figure S2 in Supporting Information. The extrapolated SAXS profile at infinite box size is shown as a purple solid curve in Figure 3. The extrapolated curve was observed to agree well with the experimental SAXS profile in the low-q region. Again, this comparison provided validation of the quality of the force field and gave us confidence that the simulations were correctly describing nanoscale structures in the third phase. The observed effects of system size indicated the presence of structures larger than the size of even our biggest simulation box. The larger the box, of course, the larger the structures that can be observed, but an enormous computational effort would be required for running simulations with significantly larger box sizes.

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Figure 3. Calculated and experimentally obtained SAXS profiles of the third phase systems.

We now turn to the light organic phase (Figure 4). Two scattering peaks at about q = 6.1 and 13.9 nm-1 were observed and, again, the calculated SAXS profiles reproduced the major scattering peaks of the experimental SAXS profile. The calculated SAXS profiles showed little dependence on box size and they all agreed well with the experimental SAXS profile over the whole q range. This result indicated that the microscopic structure of the light organic phase can be well predicted from MD simulations. No extrapolation of the calculated light organic SAXS profiles to infinite box size was made, due to the already reasonably good convergence displayed by these calculated profiles in the low-q region and due to the lack of any considerable differences between the SAXS profiles calculated using different box sizes. This result provided evidence for the characteristic dimensions of aggregates in the light organic phase system being smaller than the smallest box size we used and for the sizes of aggregates in the light organic phase system being smaller than those found in the third phase.

13



Figure 4. Calculated and experimentally obtained SAXS profiles of the light organic phase systems.

In addition to comparing the calculated and experimentally obtained SAXS profiles, we also compared the experimentally obtained third phase and light organic phase SAXS profiles. Two major differences between these experimentally measured SAXS profiles were observed: a difference in the height of the peak at q ~ 6.5 nm-1 and a difference in the trend of the profile for q < 2 nm-1. These differences primarily arose from HNO3, H2O, and the phosphate groups of TBP, due to the X-ray scattering length densities of the hydrophobic butyl groups in TBP and of n-dodecane being roughly equal to each other. Hence the SAXS profiles directly reflected the hydrogen-bonding networks that consisted of HNO3, H2O and the phosphate groups of TBP. As shown in our previous paper67, there is very strong evidence that the peak at q ~ 6.5 nm-1 corresponds to the length of a TBP dimer. However, the difference between the two profiles for q < 2 nm-1 may shed light on the characteristic length of the hydrogen-bonded unit clusters. In particular, one can estimate the average radius of gyration, Rg, of the unit clusters using the Guinier region of the SAXS profile, which corresponds to the region of q < 0.5 nm-1. The equation used for the estimation of Rg is given by ln '(() = ln ') − +, - (*

(3),

14


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where I0 is the scattering intensity at q = 0. Also, the condition qRg < 1 must be satisfied in Eq. 3. The Rg values of the light organic and third phases were calculated using this equation to be 1.04 nm and 1.26 nm, respectively. (The details of this calculation are shown in Figure S3 in Supporting Information.) The results indicated the average size of the hydrogen-bonded unit clusters in the third phase to be about 21% larger than that in the light organic phase, suggesting a more extensive hydrogen-bonding network between the polar molecules to be present in the third phase. In addition, the average Rg values of the molecular species in the simulations were calculated by using the equation *

∑ ‖1 ‖- % +, = . 2 (4), ∑ % where mi is the mass of atom i and ri is the position of atom i with respect to the center of mass of the molecule. The Rg values for an isolated TBP molecule and for an isolated H2O molecule were calculated from the simulation to be 0.96 and 0.14 nm, respectively. Comparison of these Rg values with the abovedescribed SAXS-derived Rg values indicated that the unit clusters in both phases consist on average of only a few polar molecules. At low q (< 0.5 nm-1), we argue that the SAXS profiles in both phases correspond to scattering from small hydrogen-bonded clusters. The intensity of the SAXS profile of the third phase is about 0.2 cm-1, which is much higher than that of the light organic phase. The first reason for this is that the third phase contains a higher mole fraction of polar molecules and thus contains a higher concentration of polar clusters. The second reason is that the radius of gyration of a polar cluster is about 21% larger in the third phase than in the light organic phase and this also leads to greater scattering intensity at the low-q region. In summary, the calculated SAXS profiles exhibited good agreement with the experimental SAXS profiles, indicating the molecular models used in the MD simulations were capable of predicting the microscopic structure of the third and light organic phase at the nanometer scale with good accuracy. Given the validations in this section, we now turn to an analysis of the structures of the third and light organic phases, as revealed by simulation.

3.4 Unusual Phase Transition One of the quickest ways to get an impression of the structure of a simulated system is to look at snapshots. We did this first for the 21.1 nm box systems, looking at both the light organic and third phases. Representative snapshots of the structures of these phases are shown in Figures 5a and 6a, where, for clarity, each system is shown as a relatively thin slice, specifically with a thickness of 2 nm. While these structures were observed to be mobile and flexible, the basic motifs did not change over the course of the simulation. Atomic-level views of these structures are shown in Figures 5b and 6b, which depict the hydrogen bonds 15



between the molecules as green lines. For determining the presence of a hydrogen bond, we used a donoracceptor distance of no more than 0.35 nm and acceptor-donor-hydrogen angle of no more than 30° as criteria. This set of criteria was based on the typical hydrogen bonds formed by SPC/E H2O molecule pairs.68 An oxygen atom making a covalent bond with a hydrogen atom, such as that found in H2O and HNO3 molecules, was regarded as a potential donor; and an electronegative atom having a lone electron pair was regarded as a potential acceptor. We first considered the snapshot of the light organic phase, shown in Figure 5a. For clarity, the coordinates for the n-dodecane molecules are hidden from view. TBP molecules are shown in yellow, HNO3 in red, and H2O in blue. The TBP, HNO3, and H2O molecules were observed in this snapshot to aggregate into an extended mesh, with TBP molecules providing the surface film and the HNO3 and H2O molecules located inside the mesh. This mesh-like aggregation was found to extend homogeneously throughout the entire box and there was no evidence of finite aggregates, such as micelles. We also observed an extended network of TBP molecules, with rather small, isolated molecular-sized clusters of the polar HNO3 and H2O molecules located within this network. These clusters are the unit structures discussed above. The whole network was observed in the snapshot to be surrounded by the non-polar n-dodecane molecules. Based on these results, we hypothesize that the light organic phase forms a bi-continuous micro-emulsion. Figure 5b shows the structure of one of the typical local clusters in the light organic phase. This cluster was observed to be primarily composed of hydrogen-bonded dimers, including three TBP–HNO3 dimers and a TBP–H2O dimer. A short hydrogen-bonded chain, in the form of TBP–HNO3–H2O–HNO3, was also observed. However, TBP–HNO3 dimers were observed to be the predominant form of the individual clusters in the light organic phase. This agrees with previous experimental work that made use of a slope analysis of scattering profiles. For instance, Naganawa et al.69 conducted slope analysis on TBP/n-dodecane/HNO3/H2O systems and concluded that at low concentrations of HNO3, similar to our light organic phase, the major complex species is TBP–HNO3. They also reported that the attraction between TBP and HNO3 was much stronger than that between two TBP molecules. For a related system, which consisted of TBP, n-octane, HNO3 and H2O, Ferraro et al.70 conducted Fourier transformed infrared (FT-IR) measurements and concluded that TBP–HNO3 and TBP–2HNO3 were the most prevalent TBP complexes. Our observations also agree with the simulation results of Servis at al.41. They performed a cluster analysis on TBP/ndodecane/HNO3/H2O systems and reported TBP–HNO3 dimer at low HNO3 concentrations and TBP–HNO3– HNO3 chains at higher concentrations of HNO3.

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(a)

(b)

Figure 5. (a) A 2-nm-thick slice of the representative snapshot of the 21.1 nm light organic phase system. TBP, HNO3 and H2O molecules are represented in yellow, red and blue, respectively; for clarity, n-dodecane molecules are not shown. (b) Atomic-level view of the region enclosed in the purple rectangle of Figure 5a. In this magnified view, hydrogen bonds are shown in green. H2O and HNO3 formed hydrogen bonds only with the double-bonded oxygen atoms from TBP. Molecules that are not hydrogen bonded are hidden from view for clarity. 17



(a)

(b)

Figure 6. (a) A 2-nm-thick slice of the representative snapshot of the 21.1 nm third phase system. TBP, HNO3 and H2O molecules are represented in yellow, red and blue, respectively; n-dodecane molecules are not shown for clarity. (b) Atomic-level view of the region enclosed in the purple rectangle of Figure 6a. In this magnified view, hydrogen bonds are shown in green. H2O and HNO3 formed hydrogen bonds only with the double-bonded oxygen atoms from TBP. Molecules that are not hydrogen bonded are hidden from view for clarity. 18


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In Figure 6a, we show a representative snapshot of the third phase, where again the n-dodecane is hidden, and TBP is shown in yellow, HNO3 in red, and H2O in blue. Again we observed the TBP, HNO3, and H2O molecules to form an extended mesh-like structure, similar to the structure of the light organic phase shown in Figure 5 – but with the main differences being a thicker mesh and larger clusters of HNO3 and H2O within the mesh for the third phase than for the light organic phase. This set of results again was consistent with the SAXS data as discussed in the previous section. Figure 6b shows one of the typical local clusters in the third phase. Hydrogen-bonded chains were observed here as well. Compared with the light organic phase cluster examined, the third phase cluster shown in Figure 6b was observed to be more complex, and to include one TBP–HNO3 dimer, one HNO3–H2O dimer, two HNO3–HNO3 dimers, one TBP–HNO3–HNO3 trimer, and two complex hydrogen-bonded chains involving multiple HNO3 and H2O molecules. It is impossible to analyze the detailed structure of the hydrogen-bonded networks through visual observation, but the third phase was clearly observed, based on comparing Figures 5b and 6b, to contain more hydrogen-bonded chains than the light organic phase. These results agree with the simulation results by Servis et al.41 and the NMR experimental work by Ivanov et al.44 In addition, a simulation work conducted by Ye et al.71, who investigated the complexation of water and TBP in a TBP/n-dodecane/H2O in the absence of HNO3, also show that TBP and polar molecules can form short strings such as TBP–2H2O. Quantitative analyses, including hydrogen-bonding analysis and cluster analysis, were performed to further investigate the structures. The methods and results of the hydrogen-bonding analysis and of the cluster analysis are presented in Sections 3.6 and 3.7, respectively. Despite the differences between the thickness of the mesh, the sizes of individual clusters, and the complexity of the hydrogen-bonded chains of the two boxes, no difference in symmetry between the two phases was observed. Iso-surface analysis72,73, using a revised code from the DL_MESO package74, indicated a lack of order for the clusters in both phases, indicating them both to be isotropic. In other words, both boxes contained isotropic phases consisting of extended mesh-like aggregates. We hypothesize that both phases are isotropic micro-emulsions and that the transition between them involves an unusual isotropicisotropic micro-emulsion phase transition. One must, of course, be wary of drawing conclusions based on snapshots alone, so we now turn to a more quantitative analysis of the structures of these phases.

3.5 Coordination Number Analysis To aid the analysis, we first considered coordination numbers, which tell us how many atoms of type j are, on average, close neighbors of an atom of type i. We calculated coordination number (Nc) values by using the equation ;<

4 = 5 67 87 (9) 4$9 - d9 (4), )

19



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where ρj is the number density of particle j in the system, gij(r) is the pair correlation function between particles i and j, and rm is the position of the first minimum in gij(r). An illustration of a pair correlation function corresponding to the nitrogen atom pair from HNO3 molecules, and of its corresponding coordination numbers is shown in Figure S4 in Supporting Information. In this study, the trajectories from the 21.1 nm box systems were used to calculate coordination numbers for a selection of atom pairs as shown in Table 3. The average coordination number of P atoms around P atoms was calculated to be close to 1 in both phases, indicating the tendency of TBP molecules tend to form dimers. This result was consistent with our previous findings in the TBP/alkane systems.67 The coordination number of H, from HNO3, around the double bond oxygen (O=) from TBP was calculated to be 1.00 in the third phase and 0.84 in the light organic phase. The coordination numbers of H from H2O around O= in both phases was small, specifically 0.04 in the third phase and 0.11 in the light organic phase. This result indicated a much stronger association of TBP with HNO3 than with H2O, especially in the third phase. Overall, the calculations for either phase indicated a TBP molecule to be attached to one HNO3 molecule on average. Also, the coordination number of N around N was calculated to be 2.65 in the third phase and 0.29 in the light organic phase, indicating the HNO3 molecules to be locally associated with each other in the third phase but relatively isolated from each other in the light organic phase; this analysis appears to be consistent with the molecular-scale structures in the snapshots shown in Figures 5 and 6 and, again, agrees with previous work by, for example, Naganawa et al.69, Ferraro et al.70, Servis et al.41 and Ivanov et al.44.

Table 3. Coordination numbers of atom species around a reference atom species, where the results were calculated as the block average of 10 blocks of data. Errors were estimated as the standard deviation of the results from all blocks. Coordination number; Nc Atomic pair

a

rm (nm) Light organic phase

Third phase

P (TBP) – P (TBP)

0.97 ± 0.03

0.95 ± 0.04

0.752

O= (TBP) – H (HNO3)

0.84 ± 0.03

1.00 ± 0.02

0.245

O= (TBP) – H (H2O)

0.11 ± 0.03

0.04 ± 0.02

0.244

N (HNO3) – N (HNO3)

0.29 ± 0.02

2.65 ± 0.05

0.596

O (H2O) – O (H2O)

0.04 ± 0.01

0.04 ± 0.01

0.207

20


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a

The reference atom is indicated before the dash, while the atom near the reference atom is indicated after the dash;

each atom shown is part of the molecular species shown in the brackets following the atom; O= indicates the doublebonded oxygen of TBP.

3.6 Hydrogen-Bonding Analysis A hydrogen bond is a strong, primarily electrostatic attraction between an electronegative atom and a hydrogen atom bonded to a highly electronegative atom. In our case, these electronegative atoms may be oxygen or nitrogen. A hydrogen-bond analysis can shed much light on the driving forces for aggregation. In this study, the average numbers of intermolecular hydrogen bonds formed within various molecule pairs (TBP–HNO3, TBP–H2O, HNO3–H2O, HNO3–HNO3, and H2O–H2O) per total number of reference molecules were calculated for the 21.1 nm box systems, and the results are listed in Table 4. We used the same set of criteria for determining the presence of a hydrogen bond as is defined in Section 3.4. Note that in the simulations, the number of TBP, n-dodecane, HNO3, and H2O molecules were 4288, 19456, 3904, and 448, respectively, in the light organic phase and 9176, 10928, 18400, and 4504, respectively, for the third phase. We counted 0.825 TBP-HNO3 hydrogen bonds per TBP molecule and 0.906 TBP-HNO3 hydrogen bonds per HNO3 molecule in the light organic phase, and 1.034 TBP–HNO3 hydrogen bonds per TBP and 0.516 TBP– HNO3 hydrogen bonds per HNO3 in the third phase. Thus, each TBP molecule was determined in either phase to be hydrogen bonded to approximately one HNO3 molecule, in a mono-dentate structure, but with a small amount of bidentate coordination in the third phase indicated by the number of TBP–HNO3 hydrogen bonds per TBP here exceeding 1. For the TBP-H2O hydrogen bonds, we counted 1.089 of these bonds per H2O molecule in the light organic phase, indicating a tendency for all of the H2O molecules to be hydrogen bonded with TBP in a monodentate structure. This result was not surprising, as H2O is a strong polar molecule and it naturally seeks to form hydrogen bonds when there are enough TBP molecules available. However, in the third phase, we only found 0.314 TBP–H2O hydrogen bonds per H2O molecule. This result indicated the H2O molecules to have a much lower degree of association with the TBP molecules in the presence of high concentrations of HNO3. Apparently, the HNO3 molecules preferentially hydrogen bonded to the vast majority of TBP molecules, leaving little opportunity for the H2O molecules to participate in such associations. For the HNO3–HNO3 hydrogen bonds, we found 0.016 and 0.238 such bonds per HNO3 molecule in the light organic and third phases, respectively. Note that an HNO3–HNO3 hydrogen bond is shared by two HNO3 molecules, so our results indicated the participation of almost half of the HNO3 molecules in these hydrogen bonds in the third phase. In the light organic phase, however, HNO3 molecules tended not to associate. We also found 0.973 and 1.991 HNO3–H2O hydrogen bonds per H2O molecule in the light organic and third phases, respectively, indicative of the formation of primarily mono-dentate associated structures between 21



Page 22 of 41

H2O and HNO3 molecules in the light organic phase but mostly the sharing of one H2O molecule by two HNO3 molecules in the third phase. In addition, we counted only 0.137 and 0.064 H2O–H2O hydrogen bonds per H2O molecule in the light organic and third phases, respectively, indicating little association between water molecules in either phase.

Table 4. Normalized numbers of hydrogen bonds formed between molecular species (avg.). Reference molecule

Light organic phase a

Third phase a

TBP

0.825 ± 0.006

1.034 ± 0.005

HNO3

0.906 ± 0.006

0.516 ± 0.002

TBP

0.114 ± 0.002

0.154 ± 0.002

H2O

1.089 ± 0.015

0.314 ± 0.004

HNO3

0.112 ± 0.002

0.487 ± 0.003

H2O

0.973 ± 0.018

1.991 ± 0.011

HNO3 – HNO3

HNO3

0.016 ± 0.000

0.238 ± 0.002

H2O – H2O

H2O

0.137 ± 0.005

0.064 ± 0.002

Molecule pair

TBP – HNO3

TBP – H2O

HNO3 – H2O

a

The normalized numbers were calculated as the number of hydrogen bonds between molecule pairs divided by the

total number of the reference molecules in that system.

To sum up, the results of the hydrogen-bonding analysis were in agreement with the results of coordination number analysis as well as our visual observation. Being polar molecules, both H2O and HNO3 tend to form strong electrostatic associations with the phosphate group of TBP. Rather than forming bidentate connections, we found that the TBP molecules preferentially form a mono-dentate hydrogen bond with either an HNO3 or H2O molecule. The major difference between the third and light organic phases was the much greater complexity of the hydrogen-bonded networks formed by HNO3, H2O and TBP in the third phase. Also, on average, each TBP molecule was closely connected to an HNO3 molecule. Primarily TBP–HNO3 dimers were found in the light organic phase, while complex strings such as TBP–HNO3–HNO3 and TBP–H2O– 2HNO3 were indicated to be present in the third phase. These results of our analysis were similar to those 22


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previously reported by Servis et al.41 and Ivanov et al.44 These different hydrogen-bonded structures no doubt play a crucial role in driving transitions between the light organic and third phases.

3.7 Cluster Analysis Cluster analysis is generally used as a tool to estimate the connections between particles or molecules in a molecular system based on certain criteria. In this study, cluster analysis was performed to estimate the number and size of the hydrogen-bonded clusters formed by TBP, HNO3, and H2O molecules in our systems. In addition, cluster analysis was also performed to determine whether all of the TBP molecules in the light organic or third phase are connected, which would give an indication of whether the light organic or third phase is indeed akin to bi-continuous micro-emulsion phases. In the cluster analysis we performed, all of the atoms were treated as mass points. The distance between each atom was calculated as the distance between the mass points, and the angle between three atoms was also calculated as the angle between three mass points. For our cluster analysis, we chose the same set of criteria for defining a hydrogen bond as was used in the hydrogen-bonding analysis in Section 3.4. Molecule pairs were regarded as being directly hydrogen bonded to each other if the hydrogen bonds met this set of criteria. When determining the connectivity between indirectly hydrogen-bonded molecules, we used the connectivity matrix method proposed by Sevick et al.;75 a detailed illustration of the method is provided in the appendix of the paper by Sevick et al. The cluster size was calculated as the number of hydrogen-bonded molecules in a cluster, which was also determined by using the connectivity matrix method. From the cluster analysis, we are able to calculate the average number of hydrogen-bonded clusters and the sizes of the clusters in both the light organic and third phases. In this study, we specifically performed cluster analysis using the trajectories from the 21.1 nm box systems. The results of our cluster analysis are shown in Figure 7. Cluster sizes from 1 to 10 and from 1 to 13 were found in the light organic and third phases, respectively. Most interestingly, the predominant cluster sizes in the light organic and third phases were calculated to be 2 and 3, respectively, indicating the clusters to be predominantly dimers in the light organic phase and trimers in the third phase. Compared with the light organic phase, the third phase was found to have a higher concentration of larger hydrogen-bonded clusters and a significant lower concentration of monomers. This result indicated the tendency of the TBP, HNO3, and H2O molecules in the third phase to form more extensive hydrogen-bonded networks and thus slightly larger clusters, consistent with our hydrogen-bonding analysis in Section 3.6. Interestingly, many hydrogen-bonded dimers were still calculated to be present in the third phase, indicating the polar molecules in the third phase to be sufficiently mobile and hence be able to readily break and re-form hydrogen bonds, rather than always remaining in a rigid structure.

23



Figure 7. Average number of hydrogen-bonded clusters as a function of cluster size in both the light organic and third phases in a semi-log plot, where cluster size is a measure of the number of molecules in the cluster. The dashed lines show the trend of change between each point.

In addition to the cluster analysis that estimated the distribution of hydrogen-bonded clusters, we also performed a cluster analysis that calculated the connectivity between all of the TBP molecules in both phases. In this calculation, a distance cut-off of 0.74 nm, which corresponds to the rm value in the carbon-carbon pair correlation function of TBP molecules, was used as the criterion for determining the connectivity between the butyl groups from TBP molecules. In addition, a distance cut-off of 0.75 nm, which corresponds to the rm value in the phosphorous-phosphorous pair correlation function of TBP molecules, was used as the criterion for determining the connectivity between the phosphate groups from TBP molecules. In the cluster analysis calculations, only the P and C atoms from TBP molecules were taken into account while the H and O atoms were discarded; this procedure was not expected to affect the application of the cut-off criteria and was used to improve the efficiency of the calculation. On average 93.2% of the TBP molecules in the organic phase were determined according to our results to be connected, based on our criteria. This percentage indicated the polar molecules in the organic phase to indeed form a mesh-like structure containing the vast majority of TBP molecules, with this mesh-like structure appearing similar to the structure of a bi-continuous microemulsion. What is more, on average 98.6 % of the TBP molecules in the third phase were determined 24


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according to our results to be connected, which again indicated a mesh-like structure similar to a bicontinuous micro-emulsion. These results are consistent with our observations of snapshots of the simulations described in Section 3.4. It is difficult, though, to give a clear account of the driving forces for the formation of this structure. The inter-molecular forces that hold this mesh together are not simply strong short range Coulombic attractions between the phosphate groups or the effect of polar bridging molecules. The butyl groups are sometimes seen to be in contact, so their interactions may play a role. Similarly longrange Coulomb interactions between the phosphate groups are also likely to provide an important contribution. This warrants further study.

4. CONCLUDING REMARKS We have shown our TBP model, combined with the n-dodecane, H2O, and HNO3 models taken from the literature, to be capable of predicting the coexistence of the light organic and third phases, and to also be able to predict the microscopic structure of both phases, with our simulation results comparing well with experiment. The simulation approaches used were GEMC and MD, and the analysis included the calculations of Gibbs energies and SAXS profiles, supplemented by hydrogen-bonding and cluster analysis. The use of GEMC revealed a demixing transition, with the compositions and densities of the co-existing phases being in good agreement with the results of recent experiments.44 Also the predicted SAXS profiles were in good agreement with our experimental data, providing evidence for the relatively high accuracy of the structures predicted by our simulations. We found both the organic and third phases to exhibit a bicontinuous, micro-emulsion structure, and there was no evidence of reverse micelles. We therefore believe the organic/third phase transition to be an unusual transition between two, isotropic bi-continuous phases. Finally we used our MD simulations to look at the hydrogen-bonded networks in both phases, and obtained results consistent with the results of previous NMR and IR experiments and consistent with the predictions of a very recent simulation study conducted by Servis et al. on this system.41 The structures of both the organic and third phases were analyzed at the nanometer level. Both the light organic and third phases consisted of extended mesh-like aggregates. Within this mesh were unit clusters of HNO3, H2O and TBP molecules, connected by hydrogen bonds. The only macroscopic difference between the two phases was the thickness of the mesh and thus the volume fraction of the aggregates. In other words, both phases were found to be similar to the Winsor-III classification of surfactant micro-emulsion systems that consist of water/oil/surfactant species,76 where bi-continuous micro-emulsion phases are found. However, in contrast to most water/oil/surfactant systems, both of the coexisting phases studied in our system appeared to form bi-continuous micro-emulsion phases with isotropic symmetry. In other words, the formation of the third phase represented an unusual isotropic-isotropic micro-emulsion phase transition. Typically, according to Winsor-III phase diagrams, a bi-continuous micro-emulsion coexists with micellar phases containing small, discrete aggregates or with anisotropic cubic phases. Chevalier and Zemb published a review of the phase behaviors of water/oil/surfactant systems77 and Erlinger also described a phase 25



transition from reverse micelles to a bi-continuous phases.78 Interestingly, the microscopic structure of the bicontinuous phases, which were represented by the two level-cut Gaussian random wave model by Duvail et al.,79-81 shows a remarkable similarity to the simulation snapshots in Figures 5 and 6. In addition, their results indicated that micro-emulsion systems with small volume fractions of water prefer bi-continuous structures rather than reverse micelles, in agreement with our results presented here. The microstructures of the third and organic phases were analyzed by calculating coordination numbers and the numbers of hydrogen bonds formed for various atom pairs in these microstructures. The TBP molecules were primarily coordinated with HNO3 molecules, which have strong hydrogen-bonding potential. We concluded that most of the TBP molecules were in TBP–HNO3 dimers in the organic phase but in TBP– HNO3–HNO3 strings in the third phase. In addition, H2O molecules played an important role of joining the TBP/HNO3 clusters together, especially in the third phase system. The complex and extensive hydrogenbonding network formed by HNO3, H2O, and TBP molecules is likely to be a major driving force for the formation of the third phase in TBP/n-dodecane/HNO3/H2O systems. While the results obtained have greatly furthered our understanding of the properties of the light organic and third phases, it remains to be determined in molecular terms why a homogeneous system, specifically one with a composition between those of the light organic and third phase, should demix. It would also be of interest to investigate the role of metal nitrates on the structures and properties of these phases. Preliminary results indicated that the metal complexes form unit structures within the extended mesh in the TBP/ndodecane/HNO3/H2O systems; these preliminary results also indicated that the light organic/third phase transition is of a similar nature to that observed here. We hope to present simulation results pertaining to this in the near future.

ASSOCIATED CONTENT Supporting Information Table S1. Types and probabilities of the Monte Carlo moves. Table S2. Data points used in the extrapolation of SAXS profiles. Figure S1. Schematic illustration of the coexistence of the three phases, where from bottom to top the three phases are the aqueous phase, the third phase, and the light organic phase. Figure S2. Extrapolation of SAXS profile to infinite box length using the data points provided in Table S2. Figure S3. Calculation of Rg values for the hydrogen-bonded unit clusters in both the third and light organic phases.

26


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Figure S4. The pair correlation function of the nitrogen atom pair from HNO3 and its corresponding coordination number.

AUTHOR INFORMATION Corresponding Authors *Andrew J. Masters, [email protected], Tel: +44 161 275 4679

*Ryuhei Motokawa, [email protected], Tel: +81 29 284 3747 Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS The authors thank Dr. Peter Ivanov for his experimental results, Dr. Michael Seaton for his help in the isosurface calculation code, and Prof Daan Frenkel and Prof. Gordon Tiddy for helpful discussions. We also thank the University of Manchester for use of the Computational Shared Facility (CSF). This work was supported in part by the Ministry of Education, Culture, Sports, Science and Technology, Japan (Grant-inAid for Scientific Research B, 2014-2018, No. 26289368).

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TOC Graphic

31



Figure 1. The average mole fractions of the indicated molecular species as a function of the number of Monte Carlo cycles for (a) box 1 and (b) box 2. The values plotted and the error bars were obtained from 10 independent GEMC runs. 279x215mm (300 x 300 DPI)


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Figure 2. The Gibbs energy values of the three configuration sets. The error bar was calculated by using the GROMACS package, which follows the error estimation approach by Bennett.65 281x216mm (300 x 300 DPI)



Figure 3. Calculated and experimentally obtained SAXS profiles of the third phase systems. 281x216mm (300 x 300 DPI)


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Figure 4. Calculated and experimentally obtained SAXS profiles of the light organic phase systems. 281x216mm (300 x 300 DPI)



Figure 5. (a) A 2-nm-thick slice of the representative snapshot of the 21.1 nm light organic phase system. TBP, HNO3 and H2O molecules are represented in yellow, red and blue, respectively; for clarity, n-dodecane molecules are not shown. 287x287mm (300 x 300 DPI)


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Figure 5. (b) Atomic-level view of the region enclosed in the purple rectangle of Figure 5a. In this magnified view, hydrogen bonds are shown in green. H2O and HNO3 formed hydrogen bonds only with the doublebonded oxygen atoms from TBP. Molecules that are not hydrogen bonded are hidden from view for clarity. 304x187mm (300 x 300 DPI)



Figure 6. (a) A 2-nm-thick slice of the representative snapshot of the 21.1 nm third phase system. TBP, HNO3 and H2O molecules are represented in yellow, red and blue, respectively; n-dodecane molecules are not shown for clarity. 287x287mm (300 x 300 DPI)


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Figure 6b. (b) Atomic-level view of the region enclosed in the purple rectangle of Figure 6a. In this magnified view, hydrogen bonds are shown in green. H2O and HNO3 formed hydrogen bonds only with the double-bonded oxygen atoms from TBP. Molecules that are not hydrogen bonded are hidden from view for clarity. 277x169mm (300 x 300 DPI)



Figure 7. Average number of hydrogen-bonded clusters as a function of cluster size in both the light organic and third phases in a semi-log plot, where cluster size is a measure of the number of molecules in the cluster. The dashed lines show the trend of change between each point. 279x215mm (300 x 300 DPI)


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TOC Graphic 63x47mm (300 x 300 DPI)


A Novel Microemulsion Phase Transition: Toward the Elucidation of

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