Multiscale modelling of transport in polymer-based reverse-osmosis/nanofiltration membranes: present and future

Abstract

Nanofiltration (NF) and reverse osmosis (RO) processes are physical separation technologies used to remove contaminants from liquid streams by employing dense polymer-based membranes with nanometric voids that confine fluids at the nanoscale. At this level, physical properties such as solvent and solute permeabilities are intricately linked to molecular interactions. Initially, numerous studies focused on developing macroscopic transport models to gain insights into separation properties at the nanometer scale. However, continuum-based models have limitations in nanoconfined situations that can be overcome by force field molecular simulations. Continuum-based models heavily rely on bulk properties, often neglecting critical factors like liquid structuring, pore geometry, and molecular/chemical specifics. Molecular/mesoscale simulations, while encompassing these details, often face limitations in time and spatial scales. Therefore, achieving a comprehensive understanding of transport requires a synergistic integration of both approaches through a multiscale approach that effectively combines and merges both scales. This review aims to provide a comprehensive overview of the state-of-the-art in multiscale modeling of transport through NF/RO membranes, spanning from the nanoscale to continuum media.

Fig. 1

a PNP-NS model [59]. Purification factor of cylindrical (diameter: 1.2 nm) and hourglass-shaped (base diameter: 1.6 nm, tip diameter: 0.8 nm) nanopores vs. applied pressure difference. Surface charge density: − 2 mC/m²; Nanopore length: 100 nm; Solution: 0.001 KCl. b SEDE model [41]. Rejection of an electrolyte mixture (feed concentration: 5 meq/L for each species) by a nanoporous membrane (pore diameter: 2 nm; thickness to porosity ratio: 5 µm; membrane volume charge density: − 100 mmol/L) vs. permeate volume flux. c SEDE model [60]. Rejection of a centimolar NaCl solution by a nanoporous membrane (pore diameter: 1 nm; thickness to porosity ratio: 1 µm) vs. permeate volume flux for various exclusion mechanism: steric hindrance, steric hindrance + Donnan (electrostatic) exclusion (membrane volume charge density:—50 mmol/L), steric + Donnan (electrostatic) exclusion (membrane volume charge density:—50 mmol/L) + dielectric exclusion (dielectric constant of the solution inside (outside) pores: 40 (80)). d SEDE model with spatial charge density distributio [61, 62]. Rejection of a millimolar KCl solution by nanopores (diameter: 4 nm, length: 2 µm) with various distributions of the volume charge density (see inset) vs. applied pressure difference. Average volume charge density: − 15 mmol/L for all distributions

Fig. 2

a Illustration of a polymer (polyamide)/water interface along its normal. Red, gray, white and blue colors represent oxygen, carbon, hydrogen and nitrogen atoms respectively. b bulk of linear polymer chains inserted by means of Material Studio using the Theodorou and Seuter algorithms [50]. Each chain is represented by a different color. Periodic boundary conditions (PBC) are also indicated according to direction. c Illustration of inter- and intra-crosslinking between two polymer chains. d Illustration of reactive sites on two monomers MPD and TMC leading to in-silico polymerization. e illustration of pressure driven simulation using graphitic walls [70, 71] (straight blue arrows), force on liquid molecules [–68] (curved pink arrow) and from a central slab [72] (dashed box). f Pore diameter distribution of the polyamide membrane associated with a snapshot of the membrane porosity with a similar color code to that in part a)

Fig. 3

a Simulation techniques span quantum to continuum scales, offering diverse approaches for investigating the dynamics of systems across varying time and length scales. Molecular simulations, for instance, enable the determination of diffusion coefficients for ions and water molecules within a membrane matrix. The inset figure of water transport in piperazine-based NF membranes obtained by NEMD simulation is reprinted from Ref. [113] with permission. b and c The continuum-based (CB) models is used in the shadowed region and the atomistic description is used in the dotted region. In C → P, continuum solutions provide boundary conditions for MD simulations and in P → C atomistic solutions provide boundary conditions for continuum simulations. d Nanochannel flow simulated in O’Connell and Thompson [114]. Ω_C continuum subdomain, Ω_A atomistic subdomain, Ω_O overlap region, HSI hybrid solution interface. e Representation of domain decomposition in flux-exchange-based HAC models [115]

Fig. 4

a Establish a buffer which processes, averages and transfer data from the FFM simulation to the CB model promotes seamless data transfer between both scales. b Data process using coarse-graining techniques. Figure reprinted from Ref. [141] with permission. c Continuum model-based analysis and complementary insights from molecular simulations, complemented by integrated validation of hydrodynamic models, enabling more thorough detailed analysis. d Machine learning schematic using two boosting tree ensemble models (Random Forest and XGBoost) to explore the correlation between structural parameters, experimental conditions, and performance of NF membranes