Surface Area Estimation: Replacing the Brunauer-Emmett-Teller Model with the Statistical Thermodynamic Fluctuation Theory

PAFerroptosis Combined with Metabolic Disturbance of Mito by p52-ZER6 for Enhanced Cancer Immunotherapy induced by Nano-Bacilliform-Enzyme

The confused gene expressions and molecular mechanisms for mitochondrial dysfunction of traditional nanoenzymes is a challenge for tumor therapy. Herein, a nano-bacilliform-enzyme obtains the ability to inhibit p52-ZER6 signal pathway, regulate the genes related to mitochondrial metabolism, and possess the GOx/CAT/POD-like property. NBE acquires catalytic activity from the electronic energy transition. The tannin of NBE as a mitochondrial (Mito)-targeting guide overloads MitoROS, and then metabolic disorder and lipid peroxidation of Mito membrane occurs, thus leading to a novel death pathway called PAFerroptosis (pyroptosis, apoptosis, and Ferroptosis). Simultaneously, in order to refrain from mitophagy, hydroxychloroquine is mixed with NBE to form a combo with strength pyroptosis. As a result, NBE/combo improves the PAFerroptosis obviously by activation of CD8+T cells and inactivation of MDSC cells, up-regulating expression of caspase-3 signal pathway, intercepting DHODH pathway to arrive excellent antitumor effect (93%). Therefore, this study establishes a rational nanoenzyme for mitochondrial dysfunction without mitophagy for effective antitumor therapy.

Dual-phase microporous polymer nanofilms by interfacial polymerization for ultrafast molecular separation

Fine-tuning microporosity in polymers with a scalable method has great potential for energy-efficient molecular separations. Here, we report a dual-phase molecular engineering approach to prepare microporous polymer nanofilms through interfacial polymerization. By integrating two micropore-generating units such as a water-soluble Tröger's base diamine (TBD) and a contorted spirobifluorene (SBF) motif, the resultant TBD-SBF polyamide shows an unprecedentedly high surface area. An ultrathin TBD-SBF membrane (~20 nm) exhibits up to 220 times improved solvent permeance with a moderate molecular weight cutoff (~640 g mol-1) compared to the control membrane prepared by conventional chemistry, which outperforms currently reported polymeric membranes. We also highlight the great potential of the SBF-based microporous polyamides for hydrocarbon separations by exploring the isomeric effects of aqueous phase monomers to manipulate microporosity.

Synergistic Solvation as the Enhancement of Local Mixing

Mixing two solvents can sometimes make a much better solvent than expected from their weighted mean. This phenomenon, called synergistic solvation, has commonly been explained via the Hildebrand and Hansen solubility parameters, yet their inability in other solubilization phenomena, most notably hydrotropy, necessitates an alternative route to elucidating solubilization. While, recently, the universal theory of solubilization was founded on the statistical thermodynamic fluctuation theory (as a generalization of the Kirkwood-Buff theory), its demand for experimental data processing has been a hindrance for its wider application. This can be overcome by the solubility isotherm theory, which is founded on the fluctuation theory yet reduces experimental data processing significantly to the level of isotherm analysis in sorption. The isotherm analysis identifies the driving force of synergistic solvation as the enhancement of solvent mixing around the solute, opposite in behavior to hydrotropy (characterized by the enhancement of demixing or self-association around the solute). Thus, the fluctuation theory, including its solubility isotherms, provides a universal language for solubilization across the historic subcategorization of solubilizers, for which different (and often contradictory) mechanistic models have been proposed.

Sorption Hysteresis: A Statistical Thermodynamic Fluctuation Theory

Hysteresis is observed commonly in sorption isotherms of porous materials. Still, there has so far been no unified approach that can both model hysteresis and assess its underlying energetics. Standard approaches, such as capillary condensation and isotherms based on interfacial equations of state, have not proved to be up to the task. Here, we show that a statistical thermodynamic approach can achieve the following needs simultaneously: (i) showing why adsorption and desorption transitions may be sharp yet continuous; (ii) providing a simple (analytic) isotherm equation for hysteresis branches; (iii) clarifying the energetics underlying sorption hysteresis; and (iv) providing macroscopic and nanoscopic perspectives to understanding hysteresis. This approach identifies the two pairs of parameters (determinable by fitting experimental data) that are required to describe the hysteresis: the free energy per molecule within the pore clusters and the cluster size in the pores. The present paper focuses on providing mechanistic insights to IUPAC hysteresis types H1, H2(a), and H2(b) and can also be applied to the isotherm types IV and V.

Replacing the Langmuir Isotherm with the Statistical Thermodynamic Fluctuation Theory

In the age of all-atom simulations, primitive isotherm models, such as Langmuir, BET, and GAB, are still used widely for analyzing experimental data. However, their routine applications to complex materials are not in line with their underlying assumptions (i.e., statistically independent adsorption sites with no interfacial structural changes), which manifests as the temperature dependence of the monolayer capacity. Our proposal is to replace these models with the statistical thermodynamic fluctuation theory because the ABC isotherm derived from it (i) contains these primitive models as its special cases, (ii) is applicable to any interfacial geometry, and (iii) is linked to molecular distribution functions, sharing the same language as simulations. Rectifying the inability of the primitive isotherm models to handle attractive and repulsive interactions consistently leads to a reconsideration of how physical interpretations should be attributed to the isotherms of empirical origin (e.g., Freundlich).

Bridging the Adsorption Data and Adsorption Process by Introducing a Polynomial Structure To Accurately Describe IUPAC Isotherms, Stepwise Isotherms, and Stepwise Breakthrough Curves

Porous heterogeneous adsorbents, those composed of multiple pore structures and surface chemical adsorption sites, can result in various gas or vapor adsorption isotherms, including five types of IUPAC adsorption isotherms and stepwise adsorption isotherms that have been difficult to model using a single adsorption equilibrium model. The limitation of the above equilibrium model further restricts the calculations of complex stepwise breakthrough curves. To bridge the adsorption data and adsorption process, it is important to first develop a simple model or method to describe these isotherms of various complex adsorption systems. In this work, assuming that the effect of the diffusion rate can be neglected under the static condition and the adsorption process is discontinuous, the number of adsorption isotherm inflection points can be used to represent the changed number of adsorption interactions. With the introduction of the polynomial structure, a series of empirical or semi-empirical polynomial adsorption models were developed. The N-site polynomial Langmuir-Freundlich equation could accurately fit common type I, II, III, IV, and V adsorption isotherms and complex stepwise adsorption isotherms covering various adsorbates, such as volatile organic compounds (VOCs), toxic industrial chemicals (TICs), water vapor, and carbon dioxide, as well as different adsorbents, such as metal/covalent organic frameworks (MOFs/COFs), zeolites, and porous carbons. Similarly, the introduction of a polynomial structure, such as the N-site polynomial Yoon-Nelson equation, was also successful in the description of interesting stepwise breakthrough curves. This work provides a more accurate adsorption equilibrium model to characterize all types of isotherms. As a foundation model, it is expected to be used to simulate the gas-solid adsorption process inside the fixed and fluidized beds packed with porous adsorbents.

Actual Amount Adsorbed as Estimated from the Surface Excess Isotherm

The amount of adsorption at equilibrium is commonly used for reporting solid/solution isotherms, despite the admonishment by the International Union of Pure and Applied Chemistry (IUPAC) against equating the surface excess (i.e., the measurable quantity for sorption, signifying the competitive sorption of adsorbate and solvent) with the actual amount adsorbed. The consensus, more generally stated, is that the surface excess cannot be divided into individual isotherms for sorbate and solvent unless simplifying model assumptions are introduced. Here we show, contrary to the IUPAC report, that there exists a simple method for assigning the total isotherm to the sorbate's actual amount adsorbed and to the individual solute isotherm. This requires a combination of isotherm and volumetric measurements. For dilute sorbates, we establish criteria to show if the total isotherm is dominated by the amount of sorption at the interface, in agreement with the common assumption in the practical literature. In the absence of the volume data, we propose an approximate yet more versatile method based on the specific surface area to carry out order-of-magnitude analysis to examine whether the actual amount adsorbed dominates surface excess. Application of our methods to the adsorption of sodium decyl sulfate on polystyrene latex, malachite green on activated carbons, and thiophenes on a metal-organic framework all demonstrated the dominance of the actual amount adsorbed, significantly simplifying isotherm analysis in terms of the underlying interactions (i.e., surface-sorbate and net self-interactions at the interface), eliminating the need for excess surface quantities. Analysis of fully miscible solvent-sorbate isotherms (e.g., the mixtures of organic solvents adsorbed on mesoporous silica and carbonaceous adsorbents) indicates the contributions from both sorbate and solvent isotherms.

Cooperativity in Sorption Isotherms

We present a general theory of cooperativity in sorption isotherms that can be applied to sorbent/gas and sorbent/solution isotherms and is valid even when sorbates dissolve into or penetrate the sorbent. Our universal foundation, based on the principles of statistical thermodynamics, is the excess number of sorbates (around a probe sorbate), which can capture the cooperativities of sigmoidal and divergent isotherms alike via the ln-ln gradient of an isotherm (the excess number relationship). The excess number relationship plays a central role in deriving isotherm equations. Its combination with the characteristic relationship (i.e., a succinct summary of the sorption mechanism via the dependence of excess number on interfacial coverage or sorbate activity) yields a differential equation whose solution is an isotherm equation. The cooperative isotherm equations for convergent and divergent cooperativities derived from this novel method can be applied to fit experimental data traditionally fitted via various isotherm models, with a clear statistical thermodynamic interpretation of their parameters..

Sorption from Solution: A Statistical Thermodynamic Fluctuation Theory

Given an experimental solid/solution sorption isotherm, how can we gain insight into the underlying sorption mechanism on a molecular basis? Classifying sorption isotherms, for both completely and partially miscible solvent/sorbate systems, has been useful, yet the molecular foundation of these classifications remains speculative. Isotherm models, developed predominantly for solid/gas sorption, have been adapted to solid/solution isotherms, yet how their parameters should be interpreted physically has long remained ambiguous. To overcome the inconclusiveness, we establish in this paper a universal theory that can be used for interpreting and modeling solid/solution sorption. This novel theory shares the same theoretical foundation (i.e., the statistical thermodynamic fluctuation theory) not only with solid/gas sorption but also with solvation in liquid solutions and solution nonidealities. The key is the Kirkwood-Buff χ parameter, which quantifies the net self-interaction (i.e., solvent-solvent and sorbate-sorbate interactions minus solvent-sorbate interaction) via the Kirkwood-Buff integral in the same manner as the solvation theory and, unlike the Flory χ, is not limited to the lattice model. We will demonstrate that the Kirkwood-Buff χ is the key not only to isotherm classification but also to generalizing our recent statistical thermodynamic gas (vapor) isotherm, which is capable of fitting most of the solid/solution isotherm types.

Understanding Sorption Mechanisms Directly from Isotherms

Currently, more than 100 isotherm models coexist for the six IUPAC isotherm types. However, no mechanistic insights can be reached when several models, each claiming a different mechanism, fit an experimental isotherm equally well. More frequently, popular isotherm models [such as the site-specific models like Langmuir, Brunauer-Emmett-Teller (BET), and Guggenheim-Anderson-de Boer (GAB)] have been applied to real and complex systems that break their basic assumptions. To overcome such conundrums, we establish a universal approach to model all isotherm types, attributing the difference to the sorbate-sorbate and sorbate-surface interactions in a systematic manner. We have generalized the language of the traditional sorption models (such as the monolayer capacity and the BET constant) to the model-free concepts of partitioning and association coefficients that can be applied across the isotherm types. Through such a generalization, the apparent contradictions, caused by applying the site-specific models alongside with cross-sectional area of sorbates for the purpose of surface area determination, can be eliminated straightforwardly.

Universal Langmuir and Fractal Analysis of High-Resolution Adsorption Isotherms of Argon and Nitrogen on Macroporous Silica

High-resolution isotherms of argon and nitrogen adsorption on macroporous silica have been simulated with universal Langmuir and fractal models. A four-parameter, fractal universal Langmuir equation is a good fit to the data at low pressures. Standard Gibbs energy changes calculated from equilibrium adsorption coefficients show a series of broad peaks that indicate adsorbate structural transformations as a function of pressure and coverage. The Freundlich equation or mean fractal model is also a good fit to isotherms at low pressures. Pressure-varying fractals are accurate fits to the data. Fractal exponents provide information on adsorbate coverage and surface access. Broad peaks in pressure-varying exponents are indicators of adsorbate structure. From adsorptive gas amounts, mean and pressure-varying fractal exponents provide details of adsorbate fractal dimensions and surface roughness. Both Ar and N₂ adsorption cause increases in mean surface roughness when compared with pure silica. Surface roughness fluctuations from pressure-dependent adsorptive gas fractal dimensions are associated with adsorbate structure. At one trough, the surface is smooth and is linked to close-packed Ar or N₂. For Ar adsorption at 87 K, this structure is a complete monolayer (1.00(4)), while for Ar (77 K), 1.15(4) layers and for N₂ (87 K), 2.02(10) layers. The universal Langmuir specific area of the silica is 10.1(4) m² g^-1. Pressure- and coverage-dependent adsorbate structures range from filling defects and holes on the surface to cluster formation to adsorbed Ar or N₂ evenly distributed or packed across the surface. The Ar (87 K) isotherm is most sensitive to adsorbate structural transformations.

Cooperative Sorption on Heterogeneous Surfaces

Heterogeneous adsorbents, those composed of multiple surface and pore types, can result in stepwise isotherms that have been difficult to model. The complexity of these systems has often led to appealing to empirical equations without physical insights, unrealistic assumptions with many parameters, or applicability limited to a particular class of isotherms. Here, we present a statistical thermodynamic approach to model stepwise isotherms, those consisting of either an initial rise followed by a sigmoid or multiple sigmoidal steps, founded on the rigorous statistical thermodynamic theory of sorption. Our only postulates are (i) the finite ranged nature of the interface and (ii) the existence of several different types of microscopic interfacial subsystems that act independently in sorption. These two postulates have led to the superposition scheme of simple surface (i.e., Langmuir type) and cooperative isotherms. Our approach has successfully modeled the adsorption on micro-mesoporous carbons, gate-opening adsorbents, and hydrogen-bonded organic frameworks. In contrast to the previous models that start with a priori assumptions on sorption mechanisms, the advantages of our approach are that it can be applied universally under the above two postulates and that all of the fitting parameters can be interpreted with statistical thermodynamics, leading to clear insights on sorption mechanisms.