A simple model for solute–solvent separation through nanopores based on core-softened potentials
Introduction
The separation of dissolved solute from a solution is an important subject from both technological and scientific perspectives. The canonical example is the purification of water, in which water must be separated from solutes, as ions or heavy metals, for example, in order to be suitable for consumption. Processes for obtaining clean water are generally inefficient and in most cases tend to be prohibitively expensive. The seawater desalination seems to be a promising alternative: despite approximately 97% of the water is concentrated in the oceans and seas the percentage of potable water obtained through salt–water separation is still very small [1]. Examples of water–salt separation processes are distillation, reverse osmosis (RO), thermal desalination and freezing [1], [2], [3], [4], [5], [6]. Reverse osmosis is particularly important and it consists of forcing water to pass through a semipermeable membrane by applying an external pressure bigger than the osmotic pressure of the fluid, while the membrane is responsible to retain most of the particles dissolved in the water. Conventional RO membranes used for this purpose are expensive and not very efficient: water transport is slow and there are issues in controlling the membrane selectivity [7]. Researches in this area generally aim to reduce the specific energy consumption, increasing water recovery and lowering the pressure difference between feed and permeate sides [8], [9], [10], [11].
RO mechanisms for water desalination based on nanostructures as semipermeable membranes have obtained encouraging results [7], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]. The size exclusion promoted by nanopores seems to be an important ingredient when such structures are used as filters.
In this context, the water–ions separation through nanostructures subject gained attention from scientific community, who have intensified the efforts in order to understand the main mechanisms responsible for water desalination in such a nanometric level [7], [13], [14], [17], [18], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37].
For example, Qi Chen and Xiaoning Yang have recently reported a molecular simulation study of pyridinic nitrogen doped nanoporous graphene as desalination membrane [20]. Their results indicate that these membranes are capable of rejecting salt ions and increase the water flow and permeability in several orders of magnitude if compared with existing processes of water–salt separation. The authors have established that the desalination performance is sensitive to pore size and membrane’s hole chemical functionalisation [20].
Despite the cited encouraging results, the water desalination problem is typically macro. Considering the modern computational power available, it is literally impossible to study this problem using an all-atoms approach in a macro size scale. In this sense, it is important to seek for cheaper, alternative procedures to tackle this problem. An alternative to computationally model water-like fluids in an effective manner relies on core-softened potentials. Systems modelled through these potentials generally present several features present in water. For example, they possess density, diffusion, and structural anomalies. Many core-softened potential based systems show a liquid–liquid critical point separating a high density liquid phase from a low density liquid one, as hypothesised for liquid water [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58]. Core-softened potentials treat anomalous fluids (water being the most famous case) in an effective way, in a manner that there is no directionality (interactions between particles are pairwise only) neither the presence of charges. No major arguments seem necessary in order to convince the reader that the absence of these ingredients turn core-softened models extremely cheap to simulate.
Those kinds of models were explored in depth not only by computer but also by means of theoretical tools due to their simplicity [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68]. Successive good results gave support to the use of core-softened potentials in more complicated environments, such as mimicking a salty solution [69], water in nanotubes [70], [71], confined between plates [72], [73], [74] and in contact with nanopores [75]. Following this spirit, we propose in this work the use of core-softened potentials as a building block for a simple system able to reproduce the main features of water–salt separation all-atoms simulations. We show that it is possible to build a system which qualitatively reproduces the results of more sophisticated systems in a fraction of time. Even though some work are still necessary to fine tuning the core-softened based model presented in this work, we believe this study is a first step to extrapolate the water desalination through nanostructures process to a more realistic number of particles scale.
This paper is organised as follows. Computational details are given in Section 2 while the results and discussion are made in Section 3. Section 4 ends the text with the conclusions of the work.
Section snippets
Computational details
Our system model is shown in Fig. 1. We used a simulation box with dimensions of 25×25×75 (in units of solvent particles size ) in the , and , directions, respectively, and two pistons, one initially located at (Piston 1) and another one at (Piston 2). In all simulations we apply external pressures in the Piston 1. The Piston 2 may either be static or mobile, subject to external pressures as will be discussed later. Finally, there is a middle wall whose position is fixed at
Case 1: Piston 2 fixed
Our results for this case are shown in Fig. 2, Fig. 3, Fig. 4. The number of solvent particles in the Region 2 as a function of time for two different pore areas is summarised in Fig. 2. Each curve corresponds to a different value of external pressure applied to the Piston 1 and from bottom to top they are 2.0, 3.0,…, 9.0, 11.0 and 13.0 in units of . For determining the initial time in this figure, i.e. , we wait until half of solvent particles have passed to Region 2 in order to assure
Conclusion
In this work we propose a simple computational model for solvent–solute separation through reverse osmosis using a membrane with a circular pore. This system aims to mimic the water desalination reverse osmosis through semi-permeable nano-membranes. Despite we still must investigate thermodynamic and dynamic details of our solvent–solution model, as for example solubility of ions, isothermal compressibility, heat capacity at constant pressure, and the effects of solvent/solute size ratios, we
Acknowledgements
A.B.O thanks the Brazilian science agency CNPq by financial support through the grant number 459852/2014-0. C.K.B.V. thanks CAPES for her Ph.D. fellowship. R.J.C.B. thanks FAPEMIG for financial support through the Pesquisador Mineiro grant.
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Phase behaviour of a continuous shouldered well model fluid. A grand canonical Monte Carlo study
2017, Journal of Molecular LiquidsCitation Excerpt :Partly-quenched systems involving the soft-core annealed fluid were as well studied by one of us [34,44,45]. Effects of confinement on the properties of core-softened model of water were investigated for nanotubes [46–48], plates [49–54], and nanopores [55–57]. The principal objective of the present study is to investigate the phase behaviour of a system in which particles interact via the CSW potential [7].