Interconnected pore networks as a unifying framework for transport in dense polymer membranes

1 Introduction

Polymer membranes have become indispensable to modern molecular separations, enabling highly energy-efficient processes across the water, chemical, pharmaceutical, and energy sectors (Park et al., 2017). These membranes enable technologies ranging from reverse osmosis (RO) for desalination and water reuse (Elimelech and Phillip, 2011; Liu et al., 2024) to organic solvent nanofiltration (OSN) for solvent recovery, solute fractionation, and process intensification in chemical and pharmaceutical production (Marchetti et al., 2014; Szekely et al., 2014), pervaporation (PV) for dehydration and organic–organic separations (Smitha et al., 2004; Li et al., 2023), and gas separation for hydrogen recovery, carbon capture, and natural gas processing (Freeman, 1999; Favre, 2026). Compared with conventional thermal separation technologies, membrane processes require substantially less energy because they avoid energy-intensive phase changes and instead accomplish separations by selective transport across a thin membrane. As global demand for clean water, sustainable chemical production, and low-carbon energy systems continues to grow, advances in polymer membrane materials have become increasingly central to addressing these societal challenges.

The performance of these membrane processes depends on how solvents, solutes, and gases move through polymer networks at the molecular scale. Transport mechanisms determine permeability and selectivity, making them fundamental to membrane design and optimization (Freeman, 1999; Geise et al., 2011; Werber et al., 2016; Park et al., 2017; Epsztein et al., 2020). A mechanistic understanding of transport is therefore essential not only for interpreting experimental observations but also for developing predictive models capable of guiding the rational design of next-generation membranes. As membrane materials become increasingly sophisticated, the need for physically accurate transport models has become increasingly important.

Two fundamentally different conceptual frameworks have been proposed to describe solvent or gas transport through polymer membranes. The first is the solution–diffusion model (Lonsdale et al., 1965; Paul and Ebra-Lima, 1970; 1971), in which molecules dissolve into a dense, nonporous polymer matrix and migrate by diffusion driven by a concentration gradient. The second is the pore-flow framework (Reid and Breton, 1959; Sourirajan, 1963), in which transport occurs through interconnected nanoscale free-volume elements that form continuous pathways across the membrane. Within this picture, solvent transport is governed by viscous flow under pressure-driven processes, while gas transport reflects the interplay of molecular collisions with pore walls, adsorption, and surface diffusion, depending on pore size and gas-wall interactions. Although both approaches recognize the existence of free volume within polymers, they differ fundamentally in whether this free volume constitutes isolated molecular cavities or interconnected transport pathways (Mulder, 2012; Baker, 2023). These perspectives need not always be mutually exclusive at the continuum scale; however, they imply very different molecular pictures and therefore lead to different priorities for mechanistic interpretation and membrane design.

Over the past five decades, the solution–diffusion model has become the dominant paradigm for describing solvent transport in RO, OSN, and PV membranes and gas transport in polymer membranes (Wijmans and Baker, 1995; Baker, 2023). Its conceptual simplicity, requiring only solubility and diffusivity coefficients, provided a unified framework that could be applied across diverse membrane materials and separation processes. This common language enabled generations of researchers to interpret permeation experiments, compare membrane performance, and develop structure-property relationships based on diffusion through dense polymer matrices. As a result, the solution–diffusion model has profoundly influenced the interpretation of membrane transport experiments and the design of membrane separation processes.

Recent experimental and computational studies, however, have challenged the fundamental assumptions underlying the solution–diffusion paradigm. Advanced characterization techniques (Kawakami et al., 2018; Pipich et al., 2019; Fu et al., 2020; Yahiro et al., 2025), including positron annihilation lifetime spectroscopy (PALS), neutron scattering, small-angle neutron and X-ray scattering (SANS and SAXS), wide-angle X-ray scattering (WAXS), and in situ synchrotron-based soft X-ray absorption and X-ray emission spectroscopy (XAS/XES), together with molecular dynamics (MD) simulations, consistently reveal that membranes traditionally classified as “dense” possess interconnected subnanometer-scale pore networks rather than isolated free-volume cavities. Moreover, pressure-driven solvent transport in such membranes has been shown to exhibit the characteristics of viscous flow through these pore networks (Wang et al., 2023; Fan et al., 2024b), while recent work has demonstrated that gas transport in glassy polymers is governed by pore connectivity, gas-wall interactions, and adsorption-mediated molecular hopping rather than classical diffusion through a homogeneous polymer matrix (Qian et al., 2025). Together, these findings strongly suggest that interconnected subnanometer pathways play a central mechanistic role in molecular transport across a broad class of polymer membranes.

In this Perspective, we reexamine the mechanistic basis of transport in polymer membranes through the lens of interconnected pore networks. We first revisit the fundamental assumptions of the solution–diffusion paradigm and then review experimental and molecular simulation evidence demonstrating that polymer membranes traditionally regarded as dense and nonporous instead contain interconnected subnanometer-scale pore networks. We next examine transport evidence from RO, OSN, PV, and gas separation membranes that is inconsistent with dense-matrix diffusion and instead supports pore-flow transport. Finally, we discuss how recognizing interconnected pore networks reshapes membrane design by emphasizing pore connectivity, pore size distributions, and pore-wall chemistry, and conclude with an outlook on future opportunities for characterization, modeling, and membrane development.

2 The solution–diffusion paradigm assumes dense, nonporous membranes

The solution–diffusion model was originally developed in the 1960s to explain solvent and solute transport through asymmetric cellulose acetate RO membranes (Heiranian et al., 2023). At the time, polymer separation membranes were viewed as dense, homogeneous media that lacked continuous pores, in contrast to the well-defined porous structures of microfiltration and ultrafiltration membranes. Because no experimental techniques were available to directly resolve the subnanometer internal structure of polymer membranes, transport was assumed to occur through molecular diffusion within a dense polymer matrix. This conceptual picture proved sufficiently successful in describing membrane performance that it became the dominant framework for interpreting transport in polymer membranes and was subsequently extended far beyond its original application.

The solution–diffusion model assumes three sequential steps: solution (or sorption), diffusion, and desorption (Heiranian et al., 2023; Fan et al., 2024c). Solvent molecules first partition from the feed solution into the polymer according to their solubility, diffuse independently through the membrane under a concentration gradient, and finally desorb into the permeate phase. A fundamental assumption underlying this framework is that the membrane contains no interconnected transport pathways. Instead, the polymer is treated as a dense, nonporous medium in which free volume exists only as isolated molecular-scale cavities created by transient thermal fluctuations of the polymer chains. Molecular motion is therefore viewed as a sequence of diffusion events between these isolated free-volume elements rather than transport through continuous channels. Another fundamental assumption is that the hydrostatic pressure remains uniform throughout the membrane and decreases only at the membrane–permeate interface to the permeate pressure. In its classical form, the solution–diffusion model does not explicitly resolve intramembrane pore-scale pressure gradients or hydrodynamic flow through connected molecular pathways.

As polymer membranes were developed for new separation applications, the solution–diffusion framework was extended beyond RO to nanofiltration (NF), OSN, and PV (Wijmans and Baker, 1995). Despite differences in membrane structure, solvent properties, and operating conditions, these membrane processes were assumed to share a common transport mechanism in which solvent permeation occurs by dissolution into a dense, nonporous polymer matrix followed by diffusion through the membrane. Consequently, solvent permeability is described in terms of solubility and diffusivity rather than hydrodynamic transport through interconnected nanoscale pathways.

A closely related framework has also dominated the interpretation of gas transport in polymer membranes (Freeman, 1999; Favre, 2026). Gas permeability (P) is commonly expressed as the product of diffusivity (D) and solubility (S), i.e., P = DS, allowing permeability and selectivity to be decomposed into independent diffusion and sorption contributions. Within this description, gas molecules dissolve into the polymer matrix and migrate by diffusion through transient free-volume elements before desorbing on the permeate side. This unified treatment established a common conceptual framework for describing molecular transport across virtually all classes of polymer membranes despite the wide range of gas molecules, operating conditions, and separation applications.

The success of the solution–diffusion model stems largely from its simplicity and practical utility. By reducing membrane transport to measurable parameters such as permeability, diffusivity, and solubility, the model provided a straightforward framework for interpreting permeation experiments, comparing membrane materials, and establishing empirical structure–property relationships. It has served as the basis for countless theoretical studies, membrane characterization methods, and transport models, and remains the dominant framework presented in membrane science textbooks. As a result, the solution–diffusion paradigm has profoundly influenced the interpretation of transport measurements and the design and optimization of membrane separation processes.

Despite its widespread acceptance, the solution–diffusion model explicitly excludes several structural and transport characteristics that are increasingly recognized as central to polymer membrane performance. The classical model does not explicitly resolve pore connectivity, pore-size distributions, or pore-wall interactions, and it therefore offers limited molecular-level guidance for transport under angstrom- to nanometer-scale confinement. These omissions were historically understandable because the internal nanostructure of polymer membranes could not be directly characterized. However, advances in experimental characterization and molecular simulations over the past two decades have fundamentally changed this picture, providing compelling evidence that polymer membranes previously regarded as dense and nonporous instead contain interconnected nanoscale pore networks that govern molecular transport.

3 The experimental basis for the solution–diffusion mechanism is flawed

For more than five decades, the primary experimental evidence cited in support of the solution–diffusion mechanism has been the observation of water (or solvent) content gradients across stacked polymer membranes after pressure-driven permeation experiments (Rosenbaum and Cotton, 1969; Paul and Ebra-Lima, 1970; 1971; Sujanani et al., 2024). In early studies on stacked cellulose acetate RO membranes, Rosenbaum and Cotton reported a decrease in water content from the feed side toward the permeate side and interpreted this gradient as direct evidence that water permeates by diffusion down a concentration gradient (Rosenbaum and Cotton, 1969). Similar conclusions were later reached by Paul and Ebra-Lima from solvent-content measurements in swollen rubber membranes (Paul and Ebra-Lima, 1970; 1971) and, more recently, by Freeman and co-workers from stacked Nafion ion-exchange membrane experiments (Sujanani et al., 2024). In each case, the measured solvent-content gradient was interpreted as the thermodynamic driving force required by the classical solution–diffusion model.

However, our previous MD simulations and continuum poromechanical modeling demonstrated that this water-content gradient arises from membrane compaction during pressure-driven viscous flow (Fan et al., 2024b; 2024a; Fan and Elimelech, 2025). Under hydraulic permeation, the hydrostatic pressure within the membrane decreases continuously from the feed to the permeate side. Mechanical equilibrium therefore requires a corresponding increase in the compression pressure acting on the membrane skeleton, producing progressively greater compaction toward the permeate side (Peterlin and Yasuda, 1974). The resulting reduction in local porosity, observed experimentally as a porosity (or water-content) gradient, is a direct consequence of pressure-induced deformation rather than concentration-driven diffusion. Thus, the observed gradient is a mechanical consequence of pressure-driven flow rather than evidence for the solution–diffusion mechanism.

Because proponents of the solution–diffusion mechanism have argued that this interpretation relies primarily on molecular simulations and continuum modeling, we recently tested this interpretation experimentally (Fan et al., 2026c) using the same Nafion 117 ion-exchange membrane employed in the recent stacked-membrane experiments by Freeman and co-workers (Sujanani et al., 2024). The experiments were specifically designed to distinguish between concentration-driven diffusion and pressure-induced compaction. If the measured porosity (or water-content) gradient were produced by concentration-driven diffusion, releasing the applied pressure should eliminate the gradient as water redistributes within the membrane. Indeed, diffusion-based calculations predict that the gradient should largely disappear within a few minutes and become essentially undetectable after approximately 10 min (Sujanani et al., 2024; Fan et al., 2026c).

The experimental observations directly and unequivocally contradict this prediction (Fan et al., 2026c). After more than 24 h of permeation, the stacked membranes were depressurized and allowed to relax for 10 min before disassembly. Despite this waiting period, a pronounced porosity (water-content) gradient remained across the membrane stack. More importantly, when the individual membrane layers were subsequently soaked in deionized water for 3 h, the gradient still persisted. Independent measurements of membrane thickness revealed the same spatial trend, demonstrating progressively greater irreversible compaction toward the permeate side. In contrast, short permeation experiments lasting only 15 min produced essentially no measurable gradient, indicating that the observed profile develops over the longer timescale associated with irreversible structural deformation rather than rapid molecular diffusion. Furthermore, flux-pressure hysteresis measurements showed an approximately 20% irreversible loss in water permeance following pressure cycling from 30 to 120 bar and back to 30 bar, providing independent evidence for permanent membrane compaction.

These experiments also provide a broader structural insight. The observation of irreversible compaction, together with our previous continuum-based modeling and MD simulations, demonstrates that the membrane behaves as a deformable porous medium containing interconnected transport pathways. Under hydraulic pressure, this interconnected pore network compresses, producing a spatially varying porosity that is greatest on the feed side and smallest on the permeate side. Such pressure-dependent structural deformation is entirely consistent with the pore-flow framework, in which water migrates through interconnected pores while the membrane skeleton undergoes mechanical compression. In contrast, the classical solution–diffusion picture treats the membrane as a dense, nonporous polymer phase and therefore provides no physical basis for the experimentally observed porosity gradients or irreversible structural compaction.

Taken together, these results demonstrate that the long-standing interpretation of stacked-membrane experiments as evidence for the solution–diffusion mechanism is incorrect (Fan et al., 2026b). The observed porosity (water-content) gradient does not arise from a concentration gradient driving molecular diffusion but instead results from irreversible membrane compaction during pressure-driven viscous flow. This conclusion is supported independently by direct experiments, MD simulations, and continuum poromechanical modeling, all of which converge on the same physical interpretation. The measured porosity gradient is therefore not the driving force for water transport but the structural consequence of pressure-driven flow through an interconnected pore network undergoing progressive compaction. Rather than supporting the solution–diffusion mechanism, stacked-membrane experiments provide compelling evidence for the pore-flow-with-compaction mechanism governing water transport in dense polymer membranes.

4 Experiments and molecular simulations reveal interconnected pore networks

The key structural question in the solution–diffusion versus pore-flow debate is not whether polymer membranes contain free volume, but whether this free volume exists as isolated molecular cavities or as interconnected pathways accessible to permeating molecules. The classical solution–diffusion picture treats dense membranes as homogeneous, nonporous phases in which molecules hop between transient free-volume elements. In contrast, the pore-flow picture argues that these free-volume elements can form connected or partially connected nanoscale networks that provide transport pathways across the membrane. Throughout this Perspective, the term “pore” does not refer to rigid cylindrical channels as in microfiltration or ultrafiltration membranes. Instead, it denotes molecular-scale free-volume elements, pore throats, solvent-rich domains, or gas-accessible cavities that may be tortuous, dynamic, chemically heterogeneous, affected by swelling or chain motion, and transiently connected under operating conditions.

Recent advances in characterization and molecular simulation increasingly support this connected-network view. PALS provides information on free-volume size and distribution (Chen et al., 2007; Fujioka et al., 2015; Kim et al., 2017); SANS and SAXS reveal nanoscale heterogeneity, hydrated domains, and solvent-rich regions (Pipich et al., 2019; 2024); and WAXS probes chain packing and intermolecular spacing (Fu et al., 2019; 2020). Neutron-scattering measurements further resolve the mobility and diffusion behavior of water confined within polyamide membranes, showing that strongly bound and more mobile water populations can coexist within the active layer (Kawakami et al., 2018). Synchrotron-based XAS/XES measurements, particularly X-ray emission spectroscopy under hydrated conditions, probe water–polyamide interactions and reveal that the hydrogen-bond network of confined water is distorted relative to bulk water (Yahiro et al., 2025). Together, these techniques show that water in polyamide membranes does not exist as a uniform gel-like phase, but instead occupies heterogeneous local environments within the polymer network. MD simulations complement these measurements by resolving three-dimensional solvent- or gas-accessible free volume and evaluating pathway connectivity (Wang et al., 2023; 2026b; Fan et al., 2024b; Qian et al., 2025).

Hydration, solvation, and pressure are central to this structural picture. In a dry polymer, free-volume elements may appear isolated or only weakly connected. Upon hydration or solvent uptake, water or solvent molecules occupy these free-volume elements, swell the polymer matrix, and stabilize solvent-rich domains that can bridge neighboring cavities into connected pathways (Shen et al., 2016; Fan and Elimelech, 2025). Under applied pressure, the polymer network is further deformed. Although compaction may reduce total free volume, molecular simulations show that pressure can also rearrange polymer segments and transiently connect previously isolated voids, creating percolated pathways across the membrane (Wang et al., 2023; Wu et al., 2024; Mahajan et al., 2025). Thus, interconnected pore networks in dense polymer membranes should be viewed as dynamic, operating-condition-dependent structures formed by the coupling of intrinsic free volume, hydration or solvation, polymer mobility, and mechanical deformation.

Similar structural features are now recognized across dense membrane classes. Polyamide RO and NF active layers contain hydrated subnanometer free volume and water-accessible pathways. OSN membranes can swell in organic solvents to form solvent-rich clusters and connected pathways. PV membranes can contain nonuniform solvent distributions, including liquid-like clusters and lower-density regions. Gas-separation polymers, especially polymers of intrinsic microporosity (PIMs) and glassy polymers, contain angstrom-scale gas-accessible free-volume networks. Although the detailed morphology differs among these membrane classes, they share a common feature: molecularly accessible free volume is heterogeneous, dynamic, and capable of forming connected pathways across relevant length scales. At the same time, direct operando characterization of full three-dimensional connectivity remains challenging, so the pore-network picture is currently supported by converging evidence from multiple complementary techniques rather than by a single definitive measurement (Table 1).

TABLE 1. Representative methods for characterizing pore-network in dense polymer membranes.

The structural evidence fundamentally contradicts the strict dense-homogeneous assumption of the solution–diffusion paradigm and establishes interconnected pore networks as the physical basis for interpreting transport across RO, OSN, PV, and gas separation membranes. We next examine transport evidence from each of these membrane classes to show how their observed transport behavior is consistently explained by this framework.

5 Transport evidence contradicts dense-membrane diffusion

5.1 Reverse osmosis membranes

RO is the dominant technology for advanced water treatment and purification, including seawater desalination and wastewater reuse. Water transport through the membrane has long been described as a diffusion-based process, where water molecules permeate through a nonporous dense membrane driven by a concentration gradient (Wijmans and Baker, 1995). However, as discussed earlier, advances in analytical characterization have revealed the presence of interconnected (sub)nanoscale pores or transport pathways in polyamide RO membranes (Albo et al., 2014; Fujioka et al., 2015; Kim et al., 2017), overturning the conventional diffusion-based interpretation of water transport. Computer simulations and laboratory experiments have further established that water transport occurs by pressure-driven viscous flow through these interconnected pathways in RO membranes.

Non-equilibrium molecular dynamics (NEMD) simulations show that water flux through polyamide membranes is proportional to the applied hydraulic pressure (Figure 1A) (Wang et al., 2023). This linear relationship contrasts with the behavior predicted by a concentration-gradient-driven solution-diffusion mechanism, which deviates from linearity when the applied pressure increases beyond a certain range. Furthermore, the concentration of water molecules inside the membrane is nearly constant, indicating that a concentration gradient is not the driving force for water transport in polyamide RO membranes (Figure 1B). Instead, MD simulations indicate that water permeates through the membrane in clusters consisting of 4–5 water molecules inside the transiently connected membrane pores. Over a simulation duration of 70 ns, the trajectories of these clusters show complete pathways from the high-pressure side to the low-pressure side (Figure 1C), which strongly suggests a pore-flow mechanism for water transport.

Based on these observations, a mechanistic model for solvent transport was proposed by considering the force balance acting on a solvent cluster within a membrane pore. The resulting relationship links solvent permeance to the solvent kinetic diameter (d 0), membrane pore size (d), and solvent viscosity (η s). This relationship successfully predicts the permeance of a wide range of solvents in both polyamide (Figure 1D) and cellulose triacetate (Figure 1E) RO membranes, demonstrating the robustness and reliability of the proposed mechanism. The model was subsequently validated by MD simulations (He et al., 2024), showing good agreement between the model predictions and simulated solvent permeance. More importantly, the model shows that solvent permeance is governed by both size factors—the relative sizes of the membrane pore and solvent molecules—and viscous resistance. Although flux–pressure linearity by itself does not uniquely distinguish transport mechanisms, the combination of connected water-accessible pathways, the absence of a resolved intramembrane water-concentration gradient in simulation, and the successful size- and viscosity-dependent pore-flow scaling provides stronger support for a pore-network interpretation.

Overall, the simulation and experimental results collectively demonstrate that solvent transport through RO membranes is driven by a hydraulic pressure gradient rather than a concentration gradient. A more recent study further showed that even within membrane (sub)nanopores, hydraulic pressure can still influence the chemical potential of water and thereby drive water transport (Advincula et al., 2026). Together, these findings establish pressure-driven viscous flow through interconnected membrane pores as the governing mechanism of solvent transport in RO membranes. Many thin-film-composite NF membranes share a related polyamide active-layer nanostructure, so similar pore-network arguments may apply; however, charge regulation, dielectric exclusion, and ion partitioning introduce additional complexities beyond the present scope.

5.2 Organic solvent nanofiltration membranes

OSN is a pressure-driven membrane process for molecular separation in organic solvents. The pores of OSN membranes are commonly in the range of 0.5–2.0 nm to achieve size exclusion of solutes between 50 and 1,000 g/mol (Marchetti et al., 2014; Szekely et al., 2014; Wang et al., 2021). Unlike RO, which uses water as the solvent, OSN treats solvents with widely varying properties. The transport mechanism must therefore account for how solvent–membrane interactions reshape the membrane pore structure (Figure 2A) (Fan et al., 2024b).

OSN membranes with relatively rigid pores directly demonstrate the viscous flow mechanism through their permeability behavior. These membranes commonly obey Darcy-like scaling, with permeability across different solvents directly proportional to the inverse of bulk solvent viscosity (Figure 2B) (Fan et al., 2025). Figure 2B shows data for eleven representative membranes, together with additional examples reported in the literature (Fan et al., 2025). This bulk-viscosity dependence indicates that solvents migrate as condensed fluids through the membrane pores under a pressure gradient. Diffusion through a dense membrane phase would instead depend on the matrix viscosity and the size of the diffusing molecule—neither of which is observed.

Elastic polymer membranes exhibit more complex pore-structure dynamics in response to solvent–membrane interactions, yet solvent flow within these pores remains viscous. NEMD simulations of polydimethylsiloxane (PDMS) OSN membranes reveal that solvent migrates as clusters within percolating pathways, driven by the hydrostatic pressure gradient (Fan et al., 2024b). Indeed, once changes in porosity are accounted for, the permeability follows the viscous flow relationship (Fan et al., 2024b; Fan et al., 2025). For example, in a permeation study of organic solvents through rubber membranes (Paul and Ebra-Lima, 1970; 1971; Fan et al., 2026b), which has long been considered experimental evidence for transport by a solution-diffusion mechanism, the permeability converges to the Darcy relationship after the porosity–tortuosity correction (Figure 2C).

Solvent mixtures provide a clear test of the transport mechanism. Acetone–alcohol binary mixtures permeate PDMS membranes without measurable selectivity in experiments (Figure 2D), and the permeance of the mixture follows the bulk viscosity of the liquid mixture itself (Fan et al., 2024b). NEMD simulations confirm that no separation occurs during permeation (Figure 2E) (Fan et al., 2024b); the binary mixture thus flows through the membrane pores as a single fluid. The results are inconsistent with a solution-diffusion mechanism through a dense membrane phase, in which the markedly different molecular sizes and solubilities of the components would necessarily produce different permeation rates.

These mechanistic findings shift the design principles for OSN membranes. As solvent transport occurs by viscous flow through interconnected pores, permeability is governed by pore architecture, solvent-induced swelling, and frictional resistance rather than by solubility and diffusivity in a dense polymer phase. Rational OSN membrane design should therefore target solvent-stable pore networks with controlled pore size, high connectivity, restricted swelling, and low flow resistance (Jimenez-Solomon et al., 2016; Oxley et al., 2026). Consistent with this view, viscosity-normalized metrics, such as the product of solvent viscosity and permeance, provide a more physically meaningful basis for comparing OSN membrane performance across different solvents (Li J. et al., 2025; Fan et al., 2026a; Oxley et al., 2026).

5.3 Pervaporation membranes

PV is widely used for liquid separations that are difficult or energy-intensive by distillation, including solvent dehydration, organic–organic separations, recovery or removal of volatile compounds, and desalination or concentration of hypersaline brines (Kober, 1995; Smitha et al., 2004; Shao and Huang, 2007; Li et al., 2023). Designing efficient PV membranes requires understanding how molecules enter the membrane from a liquid feed, traverse the membrane, undergo phase transition, and leave as vapor on the permeate side. This makes PV mechanistically distinct from RO, OSN, and gas separation because liquid and vapor phases coexist across the membrane system. A central unresolved question is therefore where the liquid–vapor transition occurs (Sumesh and Bhattacharya, 2006): at the downstream membrane surface, as implied in the conventional solution–diffusion picture, or within the membrane itself.

PV has traditionally been described by the solution–diffusion model (Wijmans and Baker, 1993; 1995), in which molecules sorb into a dense polymer phase, diffuse across the membrane, and desorb or evaporate at the permeate-side surface. In contrast, Matsuura and co-workers proposed a pore-flow framework in which solvent moves as a liquid through solvent-filled pores near the feed side, undergoes a liquid–vapor phase transition within the membrane, and then migrates as vapor through gas-filled pores near the permeate side (Figure 3A) (Okada and Matsuura, 1991; Okada et al., 1991; Matsuura et al., 2026). This model naturally accounts for the dependence of PV flux on both feed-side and permeate-side pressures (Figure 3B) (Matsuura et al., 2026). However, this interpretation did not gain broad acceptance, largely because direct evidence for nanoscale pores, internal phase boundaries, and pressure gradients within PV membranes was historically unavailable.

Recent simulations provide compelling molecular-level support for this pore-flow framework. Equilibrium MD simulations show that solvent molecules are not uniformly distributed within PV membranes but instead form liquid-like clusters within the polymer free volume (Hofmann et al., 1998; Schepers and Hofmann, 2006; Zhao et al., 2011; Huang et al., 2014). NEMD simulations further reveal pronounced spatial heterogeneity across the membrane thickness. For example, water transport through crosslinked polyvinyl alcohol (PVA) membranes shows a pore-size gradient from the feed side to the permeate side (Figure 3C) (Li S. H. et al., 2025). Simulations of ethanol transport through PDMS membranes directly visualize a transition in transport mode (Wang et al., 2026b): solvent molecules first move collectively as liquid-like clusters through solvent-filled pathways and then migrate individually through vapor-filled regions (Figure 3D). This behavior is consistent with an internal liquid–vapor phase transition rather than evaporation only at the external permeate-side surface. NEMD simulations also show a hydraulic pressure gradient across the membrane, with the phase transition occurring near the location where the local hydraulic pressure approaches the vapor pressure of the permeating solvent (Wang et al., 2026b).

Experimental evidence further supports this heterogeneous transport framework. Operando impedance spectroscopy was performed on PV membranes saturated with an electrolyte solution, enabling the internal transport state to be probed through changes in ionic conductivity (Wang et al., 2026a). During PV, reversible, permeate-pressure-dependent impedance changes were observed when switching between vacuum-on and vacuum-off conditions (Figure 3E). Under vacuum-off conditions, the membrane exhibits a more liquid-filled and conductive response. Upon applying vacuum, the membrane exhibits a more capacitive response, consistent with the formation of vapor-containing regions within the membrane. Systematic changes in the applied vacuum further indicate that downstream pressure modulates the internal transport state. Equivalent-circuit analysis supports the coexistence of liquid-filled, vapor-filled, and interfacial regions, providing direct experimental evidence for an internal phase transition during PV.

Together, these studies suggest that PV is not adequately described as diffusion through a homogeneous dense polymer followed by evaporation only at the downstream surface. Instead, PV transport is consistently interpreted as pore flow through a heterogeneous membrane containing solvent-filled pathways, vapor-filled pathways, and an internal liquid–vapor transition region. This perspective shifts PV membrane design from optimizing empirical solubility and diffusivity parameters toward engineering pore connectivity, pore-size distributions, solvent–polymer interactions, swelling resistance, and efficient vapor evacuation.

5.4 Gas separation membranes

Polymer membranes remain the dominant platform for industrial gas separations (Favre, 2026), including hydrogen recovery, carbon capture, and natural gas processing. Among them, glassy polymers such as cellulose acetate, polysulfones, polyimides, and related materials underpin many commercial gas-separation membranes (Favre, 2026). More recently, PIMs have emerged as one of the most promising classes of next-generation membrane materials for gas separation owing to their rigid, contorted polymer backbones that prevent efficient chain packing and thereby create interconnected microporous pathways for rapid gas transport (Kupgan et al., 2018; Favre, 2026).

Gas transport in these glassy membranes has long been interpreted within the solution-diffusion framework, in which permeability (P) is expressed as the product of solubility (S) and diffusivity (D), i.e., P = SD (Wijmans and Baker, 1995), and selectivity is decomposed into solubility and diffusivity contributions (Freeman, 1999). This decomposition is useful phenomenologically, but the effective parameters S and D do not by themselves explicitly resolve pore connectivity, pore-throat distributions, or pore-wall chemistry. The underlying microscopic picture treats free volume as isolated, transient cavities that are continuously created and destroyed by chain motion, leaving no interconnected transport pathways across the membrane (Wijmans and Baker, 1995). Consequently, the framework offers no route for relating membrane performance to pore throat size distributions or pore-wall chemistry, features now increasingly recognized as governing gas transport in glassy polymers.

Growing evidence shows that gas transport in glassy membranes is governed by molecular sieving (Carta et al., 2013; Ali et al., 2017; Park et al., 2020; Lai et al., 2022). Atomistic simulations further reveal that molecular transport occurs through an interconnected pore network, rather than through diffusion in a dense matrix (Figure 4A) (Fuoco et al., 2019; Lai et al., 2022; Qian et al., 2025). In PIM-1, gas diffusivity decreases sharply with increasing gas size (Figure 4B). The origin of this behavior is geometric (Fuoco et al., 2019). As the molecular size increases, gas molecules become too large to pass through the pore throats connecting adjacent pores, and transport through the network is progressively blocked (Figure 4C). This sieving behavior is not limited to high-free-volume polymers such as PIM-1. In thin-film composite polyamide membranes, gas permeability also drops sharply once the molecular size approaches the membrane pore size and exceeds that of most pores (Figure 4D) (Qian et al., 2025). A key physical justification for this pore-based picture lies in the separation of time scales. Molecular simulations show that the pore network in glassy polymers remains largely intact over the time scale of gas permeation (Figure 4E). Gas molecules therefore experience an essentially static interconnected pore network, and transport is dictated by the pore structure and gas–wall interactions rather than by transient cavity formation (Figure 4F).

These observations call for a pore-mediated gas transport perspective, in which gas transport across glassy polymer membranes is described in terms of the distribution of interconnected pore pathways, overall porosity, and gas-wall interactions. This perspective provides an atomistic and physically transparent basis for understanding phenomena that glassy polymer membranes commonly exhibit, including molecular sieving, plasticization, and swelling. For example, an extended Knudsen theory that accounts for effective porosity and mean pore size accurately describes the permeability of weakly interacting gases in glassy polymer membranes (Qian et al., 2026a). Similarly, the competition between the kinetic energy of gas molecules and the gas-wall interaction potential explains the temperature-dependent transport of strongly interacting gases such as CO₂ in PIM-1, capturing the distinct transport behavior at low and high temperatures (Qian et al., 2026b).

Recasting gas transport in terms of interconnected pore networks converts abstract phenomenological parameters into physically meaningful and experimentally accessible design variables. Rather than tuning diffusivity and solubility coefficients, membrane design can directly target pore architecture—including pore connectivity, pore size, and porosity—as well as pore-wall chemistry, which ultimately determine gas permeability and selectivity.

6 Conclusions and outlook

Polymer membranes have long been described as dense, nonporous materials in which molecular transport occurs through solution, diffusion, and desorption. The experimental observations and molecular simulations discussed here instead support a fundamentally different physical picture. Across RO, OSN, and PV, polymer membranes contain interconnected subnanometer pore networks that provide continuous transport pathways for liquids. Similarly, glassy and ultramicroporous polymer membranes used for gas separations also contain interconnected pore networks that govern gas transport. Within these networks, liquid transport is governed by pressure-driven viscous flow and frictional interactions, whereas gas transport in glassy and ultramicroporous polymers is governed by molecular sieving, pore-wall interactions, adsorption, and surface diffusion. Although the detailed transport mechanisms differ among membrane processes, they share a common structural origin: transport occurs through interconnected pore networks rather than through diffusion across a homogeneous dense polymer matrix.

Recognizing interconnected pore networks fundamentally changes how membrane performance should be interpreted and optimized. Rather than treating permeability and selectivity as empirical consequences of solubility and diffusivity within a dense polymer, they should instead be viewed as direct consequences of pore architecture. Membrane performance is therefore governed by physically meaningful structural parameters, including pore-size distributions, pore-throat dimensions, pore connectivity, tortuosity, effective porosity (fractional free volume), and pore-wall chemistry. Within this framework, larger interconnected pores provide low-resistance pathways that promote high permeability, whereas the narrow pore throats connecting these pores largely determine molecular selectivity by regulating access through the network. These structural features provide a direct and predictive link between membrane nanostructure and transport behavior.

This new perspective marks a transition already underway in experimental membrane research: from diffusion-based membrane design to pore engineering. Recent studies have explicitly tuned pore size, pore-size uniformity, pore connectivity, and pore-wall chemistry to control molecular transport (Jimenez-Solomon et al., 2016; Liang et al., 2020; Zhu et al., 2023; Yan et al., 2024; Zhang et al., 2025). Although these studies were motivated largely by performance enhancement, they reinforce the central premise of this Perspective: instead of optimizing phenomenological solubility and diffusivity coefficients within an assumed dense polymer, future membrane development should focus on engineering interconnected pore networks with precisely controlled pore bodies, pore throats, connectivity, and surface chemistry to independently tailor permeability and selectivity. Achieving this goal will require advances in polymer chemistry, interfacial polymerization, polymer physics, molecular simulations, and emerging characterization techniques capable of resolving interconnected subnanometer pore networks under realistic operating conditions. An important next step is to determine under what membrane chemistries and operating conditions the pore-network view is merely a useful reinterpretation of effective transport coefficients and where it becomes essential for predictive modeling. Key tests will include operando measurements of pathway connectivity under pressure or solvent uptake, cross-validation of MD-derived pore descriptors against permeance and selectivity trends, and multiscale models that connect molecular pathways to continuum transport coefficients.

More broadly, embracing a pore-network framework provides a common physical language for understanding transport across virtually all classes of polymer membranes. Such a framework establishes a foundation for integrating molecular simulations, advanced characterization, continuum transport theory, and increasingly artificial intelligence (AI)-driven materials discovery into a unified membrane design strategy. We anticipate that this conceptual transition—from optimizing solubility and diffusivity in an assumed dense polymer to engineering interconnected pore networks—will reshape membrane science and accelerate the development of next-generation separation materials with unprecedented combinations of permeability, selectivity, and stability for water purification, chemical manufacturing, and sustainable energy technologies.

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Footnotes

Edited by: Michael D. Guiver, Tianjin University, China

Reviewed by: Takeshi Matsuura, University of Ottawa, Canada