Tayssir Hamieh

Understanding whether electrochemical conditioning produces persistent changes in the molecular adsorption properties of recovered solids represents a fundamental challenge in interfacial electrochemistry and surface thermodynamics. This study develops a unified nonlinear theoretical framework connecting ion-specific conditioning of colloidal oxides in asymmetric electrolytes to their subsequent molecular adsorption behavior following filtration, washing, drying, and rehydration. Generalized Poisson–Boltzmann electrostatics, surface charge regulation, competitive ionic adsorption, and interfacial hydration are coupled through a history-dependent surface-state transformation that distinguishes reversible aqueous electrochemical equilibria from persistent chemical and structural modifications. Electrochemical–hydration memory is consequently formulated in terms of retained ionic species, hydroxylation, hydration states, and modified adsorption-site populations, without assuming preservation of the original aqueous electrical double layer. The recovered surface state is characterized theoretically through inverse gas chromatography at infinite dilution, incorporating temperature-dependent molecular surface areas, corrected Hamaker–Hamieh dispersive interactions, and nonlinear five-parameter Lewis acid–base thermodynamics. A complementary injection-free, temperature-programmed chromatographic formulation couples desorption kinetics, intraparticle diffusion, convection, dispersion, and readsorption, distinguishing nonequilibrium molecular release from equilibrium adsorption energetics. A retrospective synthesis of experimental and theoretical investigations conducted between 1989 and 2026 connects mineral-dependent charging, asymmetric-electrolyte electrostatics, aqueous and organic-medium characterization of metallic oxides, and molecular adsorption thermodynamics to distinct components of the proposed framework. Controlled experimental comparisons, independent physicochemical characterization, uncertainty analysis, and competing mechanistic hypotheses establish criteria for identifying conditioning-dependent adsorption responses while excluding residual contamination, hydration, morphological changes, and transport artifacts. The principal contribution is a physically explicit and experimentally falsifiable relationship between aqueous electrochemical history, recovered surface-state transformations, and molecular adsorption energetics. The integrated framework provides a foundation for quantitative investigation of persistent interfacial conditioning effects, whose predictive validity remains to be established through matched experimental studies.

The reliable determination of polymer–solvent interactions by inverse gas chromatography (IGC) requires a thermodynamically consistent distinction between vapor-phase nonideality, interfacial adsorption, and bulk polymer–solvent mixing. Although classical Flory–Huggins (FH) theory provides a fundamental description of polymer solutions, conventional chromatographic interpretations may incorporate these distinct contributions into apparent interaction parameters. This study develops a unified three-dimensional–two-dimensional (3D–2D) thermodynamic framework combining virial expansions, van der Waals (vdW), Redlich–Kwong (RK), and Peng–Robinson equations of state with generalized FH thermodynamics. A literature-based sensitivity analysis demonstrates that small hypothetical perturbations of FH interaction parameters can produce disproportionately large variations in their effective enthalpic and entropic contributions. The framework is further examined using 272 matched adsorption free-energy observations involving 17 molecular probes, polylactic acid (PLA), cellulose acetate (CA), and eight temperatures (303.15–338.15 K). For PLA, mean adsorption free energies decrease from 27.628 kJ mol⁻¹ classically to 15.997 and 12.339 kJ mol⁻¹ using two-dimensional vdW and RK formulations, respectively. For CA, the corresponding values are 29.868, 18.237, and 20.171 kJ mol⁻¹, revealing contrasting polymer-dependent responses. Analytical virial expansions establish the low-density consistency conditions of the cubic formulations and clarify the contributions of molecular excluded area, lateral attractions, and thermal effects. The results demonstrate substantial model-dependent sensitivity without presupposing experimental superiority of a particular equation of state. The proposed framework provides a molecularly grounded foundation for separating adsorption and absorption contributions, reassessing FH-derived quantities, and developing experimentally testable polymer–solvent thermodynamic descriptions.

The Poisson–Boltzmann (PB) equation is traditionally associated with electrostatic screening in ionic media, although its mathematical structure extends to nonlinear field equations coupling Poisson potentials with Boltzmann-distributed sources. This study develops a unified geometry-dependent nonlinear PB framework to examine the common mathematical foundations and fundamental physical distinctions between charged interfaces in multicomponent electrolytes and self-gravitating isothermal matter. A generalized statistical-mechanical formulation incorporates planar, cylindrical, and spherical geometries through a common radial operator, allowing curvature, source asymmetry, and nonlinearity to be investigated systematically. For electrostatic systems, arbitrary ionic valences are retained, demonstrating how charge asymmetry emerges beyond the Debye–Hückel approximation. A perturbative curvature expansion reveals that the first geometrical correction depends explicitly on the nonlinear valence-dependent source operator, establishing intrinsic curvature–valence coupling. For self-gravitating gases, the corresponding Boltzmann–Poisson equation is examined through geometry-dependent equilibrium solutions, density distributions, asymptotic behavior, and gravitational scaling. The framework is extended to confined gravitational systems using a semilinear elliptic formulation connecting solution existence, critical coupling, conditional uniqueness, and stability with variational principles and spectral properties of the linearized operator. Dimensionless parameters characterizing curvature, nonlinearity, asymmetry, and confinement provide regime classifications distinguishing linearized, quasi-planar, weak-curvature, and fully nonlinear descriptions. The analysis also clarifies the limits of electrostatic–gravitational correspondence: electrostatic screening arises from oppositely charged mobile species and electroneutrality, whereas gravitational matter involves exclusively attractive mass interactions and exhibits different global equilibrium and stability properties. The proposed theory therefore identifies universality in the mathematical architecture linking Poisson fields, statistical closure, nonlinear sources, geometry, boundary constraints, and stability, rather than in the underlying physical interactions. This unified perspective provides a theoretical foundation for investigating curved charged interfaces, asymmetric electrolytes, confined astrophysical systems, and broader nonlinear mean-field phenomena.

Biological integration of prosthetic materials depends on coupled interactions involving surface chemistry, hydration, electrostatics, molecular adsorption, geometry, and mechanics. Conventional approaches frequently examine these properties independently, limiting their ability to explain biological responses. This study develops a unified thermodynamic theory of prosthesis–biological interfaces by integrating dispersive surface energetics, nonlinear Lewis acid–base interactions, interfacial hydration, charge regulation, curvature-dependent electrostatics, protein adsorption, cellular recognition, nonequilibrium transport, and mechanochemical coupling. Building upon advances in inverse gas chromatography, temperature-dependent molecular surface areas, nonlinear donor–acceptor thermodynamics, and two-dimensional adsorption models, the proposed framework connects molecular interactions with evolving biological organization. A generalized interfacial free-energy functional describes the coupled mechanisms governing molecular recognition, protein conditioning, cellular adhesion, and tissue integration. Dimensionless competition parameters and thermodynamic regime maps identify dominant interaction mechanisms and potentially favorable conditions for biological functionality. Literature-based benchmarking considers representative metallic, ceramic, and polymeric prosthetic materials using surface-energy, electrokinetic, mechanical, and biological descriptors. The analysis reveals limitations of single-parameter correlations and emphasizes environmental conditioning, functional protein organization, and mechanical compatibility. Existing experimental evidence supports the physical relevance of the proposed mechanisms but does not establish complete quantitative validation. The resulting framework provides a mechanistic foundation for multidimensional, tissue-specific prosthesis design. It generates experimentally testable predictions concerning nonlinear molecular recognition, hydration–electrostatic competition, geometry-dependent adsorption, and mechanochemical integration, establishing a systematic pathway toward predictive characterization and rational optimization of dynamically evolving prosthesis–biological interfaces.

Biological interfaces govern molecular recognition, adhesion, transport, signaling, infection, biomaterial integration, and drug delivery, yet their description remains fragmented among molecular binding thermodynamics, electrostatics, adsorption, transport theory, fluid mechanics, membrane mechanics, and statistical physics. Here, a unified thermodynamic theory of biological interfaces is developed in which the interface is treated as an environment-conditioned, effectively two-dimensional thermodynamic system dynamically coupled to its three-dimensional biological surroundings. A generalized free-energy functional integrates chemical interactions, electrostatics, London dispersion, Lewis acid–base and hydrogen-bond interactions, solvation, conformational and steric effects, molecular recognition, collective interfacial organization, mechanics, curvature, and their nonadditive couplings. Variational differentiation generates generalized chemical potentials and governing equations that connect equilibrium recognition with adsorption, charge regulation, nonlinear electrostatics, reaction–diffusion, hydrodynamic transport, and interfacial deformation. Information thermodynamics is incorporated through relative entropy as a statistical measure of molecular selection and redistribution, without introducing information as an additional intermolecular force. Stability is formulated through free-energy Hessian and dynamical criteria, rigorously distinguishing mechanistic crossovers, metastability, loss of stability, bifurcation, and criticality. A dimensionless state vector combining recognition, electrostatic, curvature, reaction–transport, convection–diffusion, mechanical, adhesion–deformation, and interfacial-selection coordinates defines a generalized thermodynamic map of biological interfaces. Blood–endothelium, virus–cell, bone/biomaterial, and nanoparticle/drug-delivery interfaces emerge as finite, environment-dependent regions and trajectories within this multidimensional space rather than fixed states. The analysis further identifies parameter identifiability, nonadditive energetic coupling, biological heterogeneity, molecular-to-continuum scale separation, and the experimental discrimination of intrinsic recognition from transport- and mechanics-controlled responses as major challenges for quantitative implementation.,The framework predicts conditional physical-regime equivalence among chemically distinct interfaces and proposes multi-observable, cross-perturbation experiments for quantitative discrimination and falsification. The resulting theory provides a common thermodynamic language linking molecular interactions to interfacial organization, transport, mechanics, stability, and experimentally observable biological behavior.

Accurate characterization of dental surface energetics is essential for understanding tooth–restorative adhesion and guiding materials design. Conventional approaches often rely on temperature-independent molecular areas, simplified dispersive interactions, and linear Lewis acid–base models, potentially introducing systematic uncertainties. This study proposes a unified inverse gas chromatography framework integrating the Hamieh models to reassess the surface thermodynamics of enamel, dentin, dental adhesives, resin composites, and glass ionomer cements. The methodology combines thermodynamically consistent adsorption calculations, temperature-dependent molecular surface areas and intermolecular separation distances, corrected London–Hamaker dispersive interactions, and a nonlinear five-parameter Lewis acid–base formulation incorporating amphoteric coupling and second-order interactions. A systematic procedure is established for critically reassessing published dental surface-energy results and identifying potential methodological inconsistencies. Corrected molecular descriptors are subsequently incorporated into a conditional adhesion framework accounting for dispersive and polar interactions, hydration, and surface conditioning. Model applicability is addressed through parameter-identifiability analysis, uncertainty propagation, comparative statistical evaluation, and proposed independent experimental validation. Particular emphasis is placed on distinguishing molecular adsorption thermodynamics from reversible interfacial adhesion and mechanical bonding performance. This framework provides a theoretical and methodological foundation for improving dental surface characterization, evaluating conventional thermodynamic assumptions, and supporting the rational design of restorative materials with enhanced interfacial compatibility.

Biological interfaces govern molecular recognition, adhesion, transport, signaling, infection, biomaterial integration, and drug delivery, yet their description remains fragmented among molecular binding thermodynamics, electrostatics, adsorption, transport theory, fluid mechanics, membrane mechanics, and statistical physics. Here, a unified thermodynamic theory of biological interfaces is developed in which the interface is treated as an environmentconditioned, effectively two-dimensional thermodynamic system dynamically coupled to its three-dimensional biological surroundings. A generalized free-energy functional integrates chemical interactions, electrostatics, London dispersion, Lewis acid–base and hydrogen-bond interactions, solvation, conformational and steric effects, molecular recognition, collective interfacial organization, mechanics, curvature, and their nonadditive couplings. Variational differentiation generates generalized chemical potentials and governing equations that connect equilibrium recognition with adsorption, charge regulation, nonlinear electrostatics, reaction– diffusion, hydrodynamic transport, and interfacial deformation. Information thermodynamics is incorporated through relative entropy as a statistical measure of molecular selection and redistribution, without introducing information as an additional intermolecular force. Stability is formulated through free-energy Hessian and dynamical criteria, rigorously distinguishing mechanistic crossovers, metastability, loss of stability, bifurcation, and criticality. A dimensionless state vector combining recognition, electrostatic, curvature, reaction–transport, convection–diffusion, mechanical, adhesion–deformation, and interfacial-selection coordinates defines a generalized thermodynamic map of biological interfaces. Blood–endothelium, virus– cell, bone/biomaterial, and nanoparticle/drug-delivery interfaces emerge as finite, environmentdependent regions and trajectories within this multidimensional space rather than fixed states. The framework predicts conditional physical-regime equivalence among chemically distinct interfaces and proposes multi-observable, cross-perturbation experiments for quantitative discrimination and falsification. The resulting theory provides a common thermodynamic language linking molecular interactions to interfacial organization, transport, mechanics, stability, and experimentally observable biological behavior.