solution of 1,4-dioxane at 0.35 ppb concentration. We quantify 1,4-dioxane and water coadsorption, and observe selectivities ranging from 1.1 x 10 5 in MOR to 8.7 x 10 6 in FER. We also demonstrate that 1,4-dioxane is in the infinite dilution regime in both the aqueous and adsorbed phases at this concentration. This simulation technique can be extended to model other emerging water contaminants such as per-and polyfluoroalkyl substances (PFAS), chlorofluorocarbons, and others, which are also found in extremely low concentrations.
Crystalline porous materials like metal-organic frameworks (MOFs), covalent organic frameworks (COFs), carbon nanotubes, polyoxometalates, and zeolites, have revolutionized mixture adsorption separations through control of pore size 1 , entropy 2 , and binding strength 3 .
Additionally, their stability, tunability, and low cost make them versatile 4 -for example, zeolites are used as catalysts 5 , adsorbents 6 , and ion exchangers 7 in many chemical processes and have an increasingly rising global market of multi-billion US dollars 8 . Water and wastewater remediation methods also extensively use zeolites for purification from ammonia 9 , heavy metals 10 , radioactive 11 , toxic 12 , and organic substances 13 , as well as for water softening 14 and seawater desalination 15 .
The basic building block of zeolites is a TO 4 tetrahedron where the T-atom is usually silicon (Si) or aluminum (Al), forming an open crystal structure with a narrow distribution of molecule-sized pores. The tetrahedrons can form different (6-, 8-or 12 rings) units that give different topologies with the same chemical composition 16 . Over 40 naturally occurring zeolite frameworks and 265 synthetic ones are recognized by the International Zeolite Association (IZA) Structure Commission as of early 2024 17 . Zeolites with a high silicon content (approaching an infinite Si/Al ratio) can be synthesized; 18,19 because this class of zeolites doesn't have acid sites or polar cations, they can be highly hydrophobic and are exceptionally efficient as adsorbents in aqueous separations 13,20 .
This study investigates the adsorption of 1,4-dioxane from water using all-silica zeolites at environmental concentrations using molecular simulations. 1,4-dioxane is an emerging contaminant and a probable human carcinogen 21 that has received less regulatory attention than other pollutants despite being frequently detected in high exceedance rates according to the third unregulated contaminant monitoring rule (UCMR) 22 . It is a stable cyclic diether with symmetrical ether connections. A negative octanol-water partitioning coefficient and low carbon partitioning coefficient make leaching into the water from soil natural 23 . Recent studies show that over 30 million Americans consume water exceeding the health-based recommended threshold of 0.35 ppb 24 . To comply with the standards, several remediation strategies, including chemical, physical, and biological processes, are being evaluated; however, a practical solution for large-scale treatment is still in the works 23 . While enhanced oxidation and bio-remediation techniques have potential, they are costly and complicated to execute in practical settings 25 . As degradation technologies are still developing, considerable mitigation efforts may well focus on treating surface and groundwater bodies to comply with the increasingly stringent limits to drinking water supplies. While these methods might fail to degrade water pollutants entirely, they can act as an interim that can potentially concentrate contaminants for subsequent remedial actions needed.
Common adsorbents like synthetic resins 26 and activated carbon 27 have not been costeffective solutions for large-scale treatment of 1,4-dioxane due to their limited adsorptive capacity. Meanwhile, in one study, titanium silicalite-1, a zeolite, has shown higher capacity and faster adsorption kinetics due to its hydrophobicity 28 . Hydrophobic all-silica zeolites with comparable pore sizes may help address this challenge, but more insight is needed to determine its efficacy. For our investigation, we selected six frameworks (BEA, EUO, FER, IFR, MFI, and MOR) from the International Zeolite Association database 17 based on their commercial availability 29 , crystallographic R-factor in high silica form 30 , and pore sizes comparable to 1,4-dioxane 28 . The pore landscapes of the zeolites are shown in Figure 10, and Table 5 summarizes their unit cell parameters.
The optimal design of an adsorbent is a challenging task and requires a broad understanding of the sorption process at the microscopic level. Molecular simulations complement and provide invaluable access to thermodynamic phenomena occurring at the pore sites and thus have significantly contributed to the synthesis and applications of zeolite 16,31,32 . Additionally, adsorption systems with competition between complex adsorbates onto complex adsorbents can be better understood and more clearly evaluated through computer simulations 33,34 . For example, molecular dynamics has been used to study 1,4-dioxane transport and adsorption into Ti-silicalite in the presence of organic contaminants 28 .
However, the traditional simulation approach for modeling such a system is not only impractical but impossible since the concentrations of 1,4-dioxane in the environment are typically in parts per billion ranges 24 . After all, a liquid simulation box with 1 solute molecule at 1 ppb concentration will have on the order of 1 billion water molecules.
This work introduces a simulation workflow for thermodynamic extrapolation using the gauge cell Monte Carlo (gcMC) technique to efficiently model the liquid phase adsorption of extremely low-concentration species from mixtures. The gcMC method enables control of density for each system component individually and has successfully modeled the thermodynamically metastable and unstable systems that are typically inaccessible [35][36][37][38] . The method has been successfully implemented to investigate the phase behavior of fluids in confined spaces, including capillary condensation 39 , droplet formation 37,40 , and surfactant separation 41 .
Other methods of thermodynamic extrapolation include temperature extrapolation of Henry's Law constants 42 and extrapolating free energy landscapes
43 ; however, we need to extrapolate in concentration, and these methods may be inaccurate if state points deviate significantly from reference points. A related work by Cichowski et al. 44 uses an expanded ensemble Monte Carlo method with a transition matrix to estimate Henry's Law constant at infinite dilution, which aligns more closely with our research goals. In another study by Luo and Farrel 45 , the adsorption of trichloroethylene (TCE) from water was examined using Grand Canonical Monte Carlo (GCMC) simulations. They sampled TCE in aqueous solution at concentrations equivalent to 1% of its saturation concentration. Our study extends to
sampling water contaminants at parts-per-billion levels, which is typical of environmental conditions. While we apply this approach using Gibbs ensemble simulations, we note that it should also be compatible with simulations in the grand canonical ensemble, with a few modifications. The thermodynamic reservoir fixing the chemical potential will replace the gauge cells, and extrapolation will be performed by adjusting the chemical potential of the solute accordingly after establishing the relationship between µ and concentration in infinite dilution conditions. Performing GCMC simulations at the pressure of interest for the liquid mixtures will require iteratively adjusting simulation settings until the target pressure is reached, as GCMC fixes µV T and measures p, unlike our approach, which fixes NpT and measures µ.
We performed Monte Carlo simulations in the Monte Carlo for Complex Chemical Systems-Minnesota (MCCCS-MN) software 46 using classical force fields. First, we reproduced the vapor-liquid equilibrium properties of 1,4-dioxane for validation and then simulated the vapor and liquid phase adsorptions of 1,4-dioxane into the selected zeolite frameworks. The pure adsorption isotherms provided insight into the effects of pore size and shape on loading capacities. Finally, we investigated the selectivity of 1,4-dioxane for mixture adsorption from water at the health-based reference concentration (0.35 ppb), exploiting the gauge cell method and constructing supercells for the zeolite frameworks.
The gcMC method employs multiple simulation boxes, with one simulation box for the system of interest in chemical equilibrium with gauge cells for each component. The addition or removal of particles from the gauge cell instantly changes its chemical potential, and it is this variation that enables us to measure the chemical potential of the species for the system of interest and under conditions of our interest. The approach was initially developed to construct the full-phase diagram of a confined fluid in the form of a van der Waals loop, which includes stable, metastable, and unstable equilibrium states 35 . In this work, the liquid simulation box is modeled as flexible with intermolecular interactions containing a dilute solution of 1,4-dioxane, while the gauge cells for each component are modeled as rigid and treated as ideal gas boxes. Simulations were set up in the isobaric-isothermal Gibbs ensemble (NpT -Gibbs) [47][48][49] where inter-box swaps were performed for the particles between the simulation box representing the system of interest and gauge cell of each respective component. Volume moves were only performed on the simulation box representing the mixture solution. The Gibbs free energy of transfer, G ò0 14DX , 50,51 for 1,4-dioxane can then be computed from the ratio of densities in the simulation boxes:
where k, T , ⇢ GC 14DX , ⇢ mix 14DX are the Boltzmann constant, temperature, and number densities of 1,4-dioxane in the gauge cell and mixture cell respectively. A detailed derivation of Eq.
1 can be found in SI section 5.3. We used Eq. 1 to determine the free energy of transfer for the dilute system of 1,4-dioxane. For extrapolation, we took the average G ò0 14DX of low-concentration state points and computed the 1,4-dioxane concentration in gauge cell that would correspond to 0.35 ppb 24 in the environment. Since the concentration range is exceptionally low, we used Henry's Law to compute the corresponding partial pressure. Then, we set up NpT -Gibbs ensemble simulations with zeolite frameworks to model adsorption from low-concentrated liquid mixtures. In Figure 1, we briefly outline our method for the capture of 1,4-dioxane from water.
Transferable potentials for phase equilibria (TraPPE) 52 force fields were used to model 1,4dioxane with TraPPE-UA 53 , and the zeolites were modeled using TraPPE-zeo 54 . Lennard-Jones (LJ) potentials were used for short-range van der Waals interactions, and Coulomb potentials were used for long-range electrostatic interactions with a spherical cutoff of 14 Å. Beyond this cutoff, analytical tail corrections were applied for LJ and Ewald summation for Coulomb interactions. However, the vapor box was less dense for lower temperature state points, and thus, a larger cutoff (approximately 30% of box length) was used to accommodate 10-20% of the molecules in the system. As Ewald convergence parameters are set automatically based on rcut and simulation box length, modifying rcut is common in low-temperature VLE simulations in the Gibbs ensemble 55 .
As with the standard TraPPE force fields, here the bond lengths were treated as fixed, bend angles were modeled with the simple harmonic oscillator, and the dihedrals with a cosine series (Eq. 2) of the form
where is the dihedral angle and c is constant.
The TraPPE-zeo model considers zeolites as a rigid framework with silicon and oxygen atoms fixed on the original crystallographic positions. Their interaction potentials are tabulated as grid points, which can be interpolated to give energy depending on the location of adsorbent species in the simulation boxes. Additionally, TIP4P model was used for water 56 in the mixture adsorption systems as it has been shown to work well with the TraPPE force field for organic molecules 54,[57][58][59][60][61] . All the model parameters used for this study are summarized in Table 6 of SI section 5.2. The adsorption simulations were initialized with an empty zeolite box to prevent overlap issues for both unary and mixture systems.
Simulations were performed in NV T -Gibbs ensemble for modeling the vapor-liquid equilibrium properties, and NpT -Gibbs was used for both adsorption and gauge cell systems [47][48][49] . Monte
Carlo simulations generate a sequence of states as a Markov chain with sampling probabilities corresponding to the ensemble's configurational integral 62,63 . Intramolecular and intermolecular energies are sampled efficiently using strategic Monte Carlo moves, which are constrained by their alignment with the chosen ensemble and their adherence to the detailed balance defined by the Metropolis acceptance criteria 64 .
Gibbs ensemble consists of two (or more) simulation boxes with a constant total number of molecules without explicit interfaces. In such a system, the inter-box swap move is integral to balance the chemical potentials in addition to the regular translation, rotation, and volume moves. Configurational-bias Monte Carlo (CBMC) [65][66][67] moves were also employed to sample configurations within each simulation box, as well as inter-box swap moves. In regular CBMC, a molecule is grown bead by bead, with k trial positions generated based on the internal energy for each bead, and the external energy is computed for each trial position j of each bead i. One of these trial positions is selected and added to the existing chain with a probability of:
and = 1/k B T where k B is the Boltzmann constant and T is the temperature 68 .
The process repeats until the entire molecule is grown. Various approaches to CBMC exist in the literature 66,67,[69][70][71][72] , each with a different method of bead growth tailored to specific conformations of molecules. 1,4-dioxane, for instance, is challenging to grow with regular CBMC because the ring structure constrains its conformational space. The growth of such cyclic molecules requires an additional bias to nudge the growth toward positions that will result in ring closures; here, we use the self-adapting fixed-endpoint (SAFE)
CBMC developed by Wick and Siepmann 73 . The bias was introduced through guiding probabilities obtained from a short presimulation with only the translational and rotational degrees of freedom. The probabilities are normalized ensemble averaged bead-bead distance distributions that adapt during the simulation of the system of interest. Thus, the swap moves for 1,4-dioxane were performed holding the ring conformation rigid while allowing multiple trial orientations to be explored.
Our cutoff radius in the zeolite box is 14 Å, so each zeolite box must be at least 28 Å in each dimension. Since zeolite unit cells are typically smaller than this, we used the smallest integer multiple in each dimension to construct the minimal simulation cell. For example, the FER (type 2) framework requires 2 unit cells in the x-direction, 4 in y, and 2 in z. Then, we constructed larger supercells by multiplying all dimensions by factors of 2, 4, and 8.
Figure 2 shows the scheme of supercell construction for the FER framework. For simplicity, we only show a single unit cell of FER, its minimal simulation cell, and the largest supercell 3 Results and Discussion
Before running adsorption simulations with 1,4-dioxane, we validated the force fields against simulation 53 and experimental data 75 from literature (Figures 3a and 3b). To estimate the statistical uncertainties in the coexistence properties, 16 independent simulations were performed for temperatures ranging from 310 K to 565 K with 80k MC cycles for equilibration and 100k MC cycles for production. The total volume of the two simulation boxes was adjusted so that the vapor phase contained roughly 50 molecules, or about 10% of the total system size of 500 molecules. Our findings closely resemble simulated data in the literature and reasonably agree with experimental data. The critical temperature is overestimated by approximately 0.7%, and the normal boiling temperature is underestimated by 3.5%. The underestimation of normal boiling temperature is systematic in TraPPE-UA models 76 as they also tend to predict higher saturated vapor densities and pressures.
0.00 0.20 0.40 0.60 0.80 1.00 1.20 300 350 400 450 500 550 600 Density [g/cm 3 ] Temperature [K] (a) Vapor-liquid coexistence curve 1.50 2.00 2.50 3.00 3.50 3 4 5 6 7 8 9 Present Work Keasler, 2012 1000/T [1/K] ln P [kPa] (b) Clausius Clapeyron plot
Single-component adsorption was studied at 300 K for 1,4-dioxane for a range of pressures, with the upper limit for vapor phase adsorption set to 0.05 bar so as not to exceed the saturation pressure (p vap ) of 1,4-dioxane at 300 K, which is measured from simulations to be 0.105 3 bar. Two state points beyond p vap were used to model adsorption from a liquid phase.
The fluid box was initialized as a low-density gas at low pressures (p < p vap ), or as a highdensity liquid at higher pressures (p > p vap ) to prevent nucleation issues. Eight independent simulations were performed for each framework with at least 80k equilibration and 100k production cycles. Some of the frameworks required more time to reach equilibration, especially for higher pressure state points, but no simulations exceeded 500k MC cycles. We used the automated equilibrium detection technique described by Chodera 77 to determine 11
6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7
which portion of the simulation runs from production cycles to use for reporting results.
The technique determines an optimal amount of initial data to be discarded as equilibration while minimizing initial bias and variance. The pure 1,4-dioxane adsorption isotherms for the six zeolite frameworks are plotted in Figure 4. Loading capacities for 1,4-dioxane at higher pressure follow the trend: BEA > IFR > FER > MFI > EUO > MOR. Frameworks with high-loading capacities like BEA or IFR may seem to be an optimal choice for an adsorbent as literature studies with other adsorbent materials have reported that capacity is a limiting factor [26][27][28] .
However, our focus here is on modeling the adsorption behavior in environmental conditions where 1,4-dioxane is found in low concentrations. Lower pressures correspond to low chemical potentials and low concentrations, and we observe upon closer inspection (Figure 5) that FER performs significantly better than the others in these low-pressure regions, with FER > EUO 12 At lower pressures, adsorption is driven by affinity between the adsorbate and adsorbent. For all-Si zeolites, this is due to physisorption interactions in the pores, and governed by pore size and shape. Trends in heats of adsorption and entropy of adsorption follow loading trends The thermodynamic properties in Table 1 indicate that MFI pores have a looser fit than FER or EUO but a tighter fit when compared to IFR, which exhibits a higher loading capacity.
In simulations, there are two ways to calculate the average property of a thermodynamic system -ensemble average ( <A> <B> ) and instantaneous average (< A B >). Both approaches can result in different values. For some average calculations, it is problematic if B is sometimes zero, as < A B > is an average of terms that sometimes divide by zero. In our case, we calculated instantaneous measures of Free Energy of transfer (dG) for each frame, so our number is using < ⇢ zeo ⇢ fluid >. By defining dG to have ⇢ zeo in the numerator (and, since ⇢ fluid is never zero), we avoid division by zero. However, when N zeo is 0, we cannot compute enthalpy (dH) using <
>. Therefore, we removed the data points in which N zeo = 0 and still obtained the correct enthalpies of transfer.
13 6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7 Chen and coworkers 28 demonstrated, using FTIR spectra and molecular dynamics simulation, that 1,4-dioxane fits tightly into the hydrophobic straight channels of TS-1 with a diameter of 5.6 Å. They also estimate an approximate size of 1,4-dioxane molecule (5.2 ✓ 5.9 ✓ 6.7 Å) through Van der Waal's projection and indicate that even though pore diameters are slightly smaller, he flexibility of either the adsorbate molecules or the zeolite structure promotes adsorption into zeolite channels.
We conducted a small test (NpT -Gibbs simulation with 120 1,4-dioxane and 600 water molecules at 1 atm and 300 K) to determine if all-silica zeolites efficiently separate 1,4dioxane from water under environmentally relevant conditions. While the test results were promising (we observed selective adsorption of 1,4-dioxane, with just about 14 molecules remaining in the liquid phase), we quickly realized that our simulation conditions were far from the parts per billion concentrations needed to model environmental conditions.
Replicating the concentration of
1,4-dioxane that is considered safe for human health, i.e., 0.35 ppb (micrograms per liter of water), we would require approximately 100 million water 15 6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7 0 . .-
molecules for every molecule of 1,4-dioxane. Sampling with a regular NpT -Gibbs ensemble for such a system is not only impractical but also computationally inefficient, so we developed an approach using gauge cells and extrapolation.
We performed simulations with 30 1,4-dioxane and 1800 water molecules, and we obtained different fluid concentrations by varying the 1,4-dioxane gauge cell volumes from 100 3 Å 3 to
When we increased the simulation box side length beyond 310 Å, all of the 1,4dioxane left the liquid simulation box, so no statistically meaningful concentration remained.
We set the water gauge cell size to maintain approximately 4 water molecules in the gauge cell. We then fixed this size (160 3 Å
3 ) for all the state points analyzed, only changing the 1,4-dioxane gauge cell. Since the system under investigation is at a low temperature (300 K), we faced sampling challenges in particle insertions. Using rigid swaps for 1,4-dioxane, we had swap acceptance rates of about 0.001, even while considering 32 trials for insertion and 16 orientational trial positions. A drawback of using this gauge cell approach over traditional
NpT -Gibbs is we also can not implement identity switch moves to boost sampling efficiency. We used a series of gauge cell simulations to validate that the system is in the infinite dilution regime. A more efficient approach would be to perform gauge cell simulations at just 17
6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7 0 . .-one concentration (as low as possible) and obtain free energy of transfer ( G) from this. By using a series of simulations, however, we established that this system is in the Henry's law (infinite dilution) regime. While we do not have <1 molecule / simulation box, the linear trend suggests 1,4-dioxane-1,4-dioxane interactions are not significant.
When we impose the extrapolated 1,4-dioxane partial pressure and the water partial pressure on the zeolite box, our state point will be at a slightly lower total pressure than the 1 atm that was fixed thermodynamically in the gauge cell simulations due to the loss of some 1,4-dioxane. This should be a minor effect, given the extremely low concentrations.
Alternatively, the water partial pressure for the extrapolated system could be obtained from a system of pure water; this assumes that the chemical potential of water with ppb concentration of pollutant is nearer to pure water than it is to the water in our gauge cell simulations (that have a few 1,4-dioxane molecules).
Mixture adsorption simulations were conducted across all zeolite frameworks using four different zeolite box sizes. The baseline size was the minimal simulation cell (with at least 28 Å in x, y, and z), and box volumes were increased by factors of 2 3 to create supercells, as shown in Figure . 2. The computational cost was managed by maintaining a rigid zeolite framework and using tabulated potentials to describe the zeolite/adsorbate interactions 74 . This approach enabled us to effectively sample adsorption of 1,4-dioxane at ppb concentrations in water, using up to 8,192 zeolite unit cells in order to achieve reasonable statistics at low loading.
Eight independent simulations were conducted for each zeolite framework setup, with 180k equilibration and 120k production cycles. Figure 8 illustrates the loading per unit volume of zeolites across different unit cell sizes. FER exhibits the best performance among all the zeolites, followed by EUO, IFR, BEA, MFI, and MOR. Notably, the smallest simulation box (the minimal size that accommodates a 14 Å cutoff, typical of Monte Carlo simulations in zeolites, i.e. 2x4x2 unit cells for FER) and even the simulation box with 8x that volume were inadequate for collecting reasonable statistics. Simulations with 64x the minimal cell volume were sufficient to achieve accurate results for all zeolites; 512x did not demonstrate improvement, and was thus not needed.
The mixture adsorption loadings follow the unary loadings trend when we extrapolate the 1,4-dioxane loadings in the unary simulations using Henry's Law down to the set pressure of 5.8 ✓ 10 11 bar for mixture adsorption loadings (Table 3). While unary adsorption trends alone could potentially identify the best framework for adsorption, our method provides accurate estimates of selectivity and loadings under specific environmental conditions.
Framework Loading @Unary Loading @512 [molec/nm 3 ] [molec/nm 3 ] FER 5.6 ✓ 10 We define and consider two selectivity measures: one based on number density (Equation 4) and one based on number ratio (Equation 5). Hypothetically, consider two zeolites, each of which increases the number density of 1,4dioxane by a factor of 10 6 between the aqueous phase and the zeolite phase, but one of them rejects water and the other does not. They will have equal selectivities based on number density, but different selectivities based on number ratio (because of different amounts of water rejection). Either may be relevant depending on the application considerations.
Selectivity, S ads,vol =
Selectivity, S ads =
The simulations with large zeolite supercells are feasible only because of the excellent Table 4 summarizes the selectivity using number ratio (Equation 5) for 1,4-dioxane for each zeolite framework investigated. Selectivity here defined as the ratio of 1,4-dioxane to water in the zeolite simulation box (Supplementary section 5.5), normalized by the healthbased reference concentration of 1,4-dioxane in number ratio, that is:
17 ✓ 10 11 (6) 20 6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7 0 . .- 64), and 8 3 (512) times the minimal simulation cell. All values were calculated from each of the eight independent simulations and reported as mean, and uncertainties are reported in subscripts as the standard error of the mean to last significant figures. S ads =0 indicates that negligible 1,4-dioxane were adsorbed in the zeolite.
Frameworks S ads @1 S ads @8 S ads @64 S ads @512 (✓10 6 ) (✓10
6 ) (✓10 6 ) (✓10 6 ) BEA 0 0.33 8 0.78 2 0.81 1 EUO 0 2.01 4 1.98 2 1.97 1 IFR 0 0.82 2 0.12 3 0.11 1 FER 0.75 5 8.76 2 8.70 2 8.72 4 MFI 0 0 0 .24 1 0.23 1 MOR 0 0 0 .11 1 0.11 1
All zeolites are extremely selective, with enrichment in the zeolite phase relative to the water phase by at least a factor of 10 5 . FER is even more selective, with S ads of 8.7✓10 6 . The volume-based selectivity (Equation 4) is calculated replacing the number of water molecules in the zeolite with its framework volume in Equation 5. These results are displayed in Table 8 in SI section 5.5 and illustrate that these volume-based selectivities are also high with the same trends. Additionally, Figure 9 showcases snapshots of mixture adsorption loadings in FER, varying across different unit cell sizes. The selectivity trends at 512x are similar to unary 1,4-dioxane loadings ( Despite being extremely selective adsorbents, these zeolites are nearly devoid of 1,4dioxane; in even the most selective framework, FER, <1 molecules are present among 8,196 unit cells (Table 9). This is not related to the selectivity/capacity tradeoffs often discussed in gas adsorption [81][82][83] ; Figure 4 and Figure 6 show each can accommodate >1 molecules/unit cell. Instead, this is an intrinsic characteristic (and challenge) for adsorbing mixtures with ppb concentration. After all, increasing ppb concentration by 10 6 still leaves a low concentration of 0.1%. Only when the adsorbent starts getting saturated will capacity start playing a role; such may occur for materials with even higher selectivities than those described here, or for materials in which adsorption is dominated by few active sites.
From the number of 1,4-dioxane and water molecules adsorbed in the zeolite framework (Tables 9 and 10), we can perform mass balance calculations to determine its efficacy in filtering 1 L of water to produce a 0.35 ppb outlet stream. For example, 1 gram of FER removes 65% of 1,4-dioxane from a feed with a concentration of 0.99 ppb, while the same 22
6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7 0 . .-amount of MOR removes only 5% from a feed concentration of 0.37 ppb. Table 11 in SI section 5.5 lists some predicted amounts of removal using 1, 10, and 100 grams of zeolite for both FER and MOR frameworks.
Accurately modeling water treatment systems is challenging due to the presence of numerous unknown substances, which vary in their concentrations and often interact with each other.
This study addresses two key challenges: identifying effective adsorbents for an emerging water pollutant and sampling the system under environmentally relevant concentrations.
This methodology sets the stage for further exploration of effective adsorbents for other emerging contaminants, such as PFAS, arsenic, and chlorinated species. However, our computational methodology is contingent upon both the adsorbent's selectivity for the target pollutant and its ability to reject solvent simultaneously. This limits the approach's applicability to certain adsorption systems (e.g. very hydrophobic sorbents).
These simulations identify FER as a promising material for
1,4-dioxane separation from water. The unary adsorption simulations showed that the 8-member ring pores in FER snugly accommodate 1,4 dioxane. Furthermore, our mixture adsorption simulations with water indicate that FER possesses exceptional selectivity for low concentrations of 1,4-dioxane; it particularly becomes more apparent in simulations with supercell construction of zeolite frameworks. However, Monte Carlo simulations do account for diffusion, which may impose transport barriers for 1,4-dioxane. Nonetheless, we think all-Si FER and all-Si EUO are promising materials for further investigation. The adsorbed concentration differs significantly from the environmental concentrations, implying that hydrophobic all-silica zeolites are ultraselective adsorbents, as the latter can be considered to be infinitely diluted. However, it is challenging to synthesize them without defects 19 , which enable water coadsorption and would undermine selectivity. This work 23 6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7
aims to motivate the synthesis of these zeolites to be used in various separation processes, particularly in water pollutant remediation, where these interactions can play a crucial role.
We also achieve large selectivities here while only involving physisorption interactions because of the tight fit of 1,4-dioxane in FER. In other contexts, chemisorption is used to remove trace contaminants from water [84][85][86] as the means of providing the strong intrinsic interaction to pull the dilute solute from the solution. Traditional Monte Carlo simulations do not have interaction potentials or efficient sampling techniques for chemisorption; the development of these could further extend the applicability of this approach.
6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7 0 . .-6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7 0 . .-6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7 0 . .-6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7 0 . .-(68) Calero, S. Comprehensive Inorganic Chemistry II (Second Edition): From Elements to Applications; Elsevier Ireland Ltd, 2013; pp 989-1006. (69) Vlugt, T.; Martin, M.; Smit, B.; Siepmann, J.; Krishna, R. Molecular Physics 1998, 94, 727-733. (70) Martin, M. G.; Thompson, A. P. Fluid Phase Equilibria 2004, 217, 105-110. (71) Martin, M. G.; Biddy, M. J. Fluid Phase Equilibria 2005, 236, 53-57. (72) Martin, M. G.; Frischknecht, A. L. Molecular Physics 2006, 104, 2439-2456. (73) Wick, C. D.; Siepmann, J. I. Macromolecules 2000, 33, 7207-7218. (74) June, R. L.; Bell, A. T.; Theodorou, D. N. Journal of Physical Chemistry 1990, 94, 1508-1516. (75) Linstrom, P.; W.G. Mallard, E. NIST Chemistry WebBook, NIST Standard Reference Database Number 69, National Institute of Standards and Technology, Gaithersburg MD, 20899. https://doi.org/10.18434/T4D303, [retrieved October 20, 2023]. (76) Chen, B.; Siepmann, J. I. The Journal of Physical Chemistry B 1999, 103, 5370-5379. (77) Chodera, J. D. Journal of Chemical Theory and Computation 2016, 12, 1799-1805. (78) DeJaco, R. F.; Bai, P.; Tsapatsis, M.; Siepmann, J. I. Langmuir 2016, 32, 2093-2101. (79) Yang, Y.; Bai, P.; Guo, X. Industrial & Engineering Chemistry Research 2017, 56, 14725-14753. (80) Bereciartua, P. J.; Cantín, Á.; Corma, A.; Jordá, J. L.; Palomino, M.; Rey, F.; Valencia, S.; Corcoran Jr, E. W.; Kortunov, P.; Ravikovitch, P. I., et al. Science 2017, 358, 1068-1071. 30 6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7 0 . .-6 3:7 : 264 7 9 6 : 273 : :9 49 9: 44 4 74 43 1B 64 / 7 0 . .-
5 Supporting Information 5.1 Zeolite Frameworks EUO 4.1 5.4 10-ring [100] BEA 5.6 12-ring [001] 12-ring [100]
7.7 6.6 MOR 8-ring [001] 5.7 2.6 12-ring [001]
7.0 6.5 IFR 6.2 7.2 12-ring [001] MFI 5.6 10-ring [100]
5.5 5.1 5.3 5.6 10-ring [010] 3.5 4.8 8-ring [010] µ will affect the flow from one phase to another. For two phases, ↵ and , in which a solute molecule, s, is distributed, if both phases are at the same temperature and pressure, the chemical potential of s will be identical in both phases. This can be expressed as follows:
Applying the chemical potential formula for solvation where we impose very low concentrations of s in both phases, we get
For a system in which the vapor and liquid phases of a pure component are in equilibrium, we can determine the solvation Gibbs energy of the component in its pure liquid state, provided that the vapor pressure is sufficiently low to be considered an ideal gas.
If s is very dilute in phase , the limiting form of the equation is:
and therefore, the Gibbs free energy of transfer into the mixture of a dilute solution of 1,4-dioxane in water from the gauge cell (GC) is: