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This work presents a novel approach for analyzing the behavior of a quantum system consisting of two subsystems with different numbers of particles and energies. We use the generalized mean for the statistical β distribution to model the behavior of quantum particles in a mixture, and we indirectly test our model against standard theoretical adsorption and hysteresis results. Our approach relies on conventional nonlinear least-squares fitting with appropriate scaling to accurately model these functions over the entire range. Critically, we take into account the principle of maximum entropy, which imposes restrictions on the ratio between the number of particles and energies of two subsystems. Our approach does not assume any specific value for this ratio but rather determines it based on the input data, allowing us to model the behavior of the system accurately. We show that our approach has the potential to lead to the discovery of new quantum distributions that were previously unobserved. Furthermore, we use homotopy theory to demonstrate that the mathematical functions used in our approach lie on and outside the path connecting Fermi–Dirac and Bose–Einstein distributions. This suggests that our approach has the potential to contribute to a better understanding of the behavior of complex quantum systems. Overall, our approach presents a novel method for analyzing the behavior of a quantum system and has the potential to advance the field of quantum mechanics. [ABSTRACT FROM AUTHOR]

This paper presents an improved theoretical view of ab initio thermodynamics for polar GaN surfaces under gallium-rich conditions. The study uses density functional theory (DFT) calculations to systematically investigate the adsorption of gallium atoms on GaN polar surfaces, starting from the clean surface and progressing to the metallic multilayer. First principles phonon calculations are performed to determine vibrational free energies. Changes in the chemical potential of gallium adatoms are determined as a function of temperature and surface coverage. Three distinct ranges of Ga coverage with very low, medium, and high chemical potential are observed on the GaN(000-1) surface, while only two ranges with medium and high chemical potential are observed on the GaN(000-1) surface. The analysis confirms that a monolayer of Ga adatoms on the GaN(000-1) surface is highly stable over a wide range of temperatures. For a second adlayer at higher temperatures, it is energetically more favorable to form liquid droplets than a uniform crystalline adlayer. The second Ga layer on the GaN(0001) surface shows pseudo-crystalline properties even at a relatively high temperature. These results provide a better thermodynamic description of the surface state under conditions typical for molecular beam epitaxy and offer an interpretation of the observed growth window. [ABSTRACT FROM AUTHOR]

The study concerns the evaluation of the physicochemical and thermo-adsorptive surface properties of six commercially available mouthrinses, particularly surface tension, surface activity, partitioning coefficient, critical micellar concentration, Gibbs excesses at interfaces, surface entropy, and enthalpy. The aim was to quantify their effect on the adhesion and wettability of a model poly(methyl methacrylate) (PMMA) polymer. The adsorptive and thermal surface characteristics were derived from surface tension (γLV) vs. concentration and temperature dependences. Polymer surface wettability was characterized by the contact angle hysteresis (CAH) formalism, using the measurable advancing ΘA and receding ΘR dynamic contact angles and γLV as the input data. Further, wettability parameters: Young static angle (Θ), film pressure (Π), surface free energy (γSV) with its dispersive and polar components, work of adhesion (WA), and adhesional tension (γLV cosΘA) were considered as interfacial interaction indicators. The mouthrinse effect demonstrated the parameter's evolution in reference to the PMMA/pure water case: Θ, ΘA and ΘR↓, CAH↑, Π↓, WA↓, γSV↓, and γLVcosΘA↑. Furthermore, the variations of the surface excess ratio pointed to the formation of multilayered structures of surfactants composing the mouthrinse mixtures considered. The contact angle data allowed for the penetration coefficient and the Marangoni temperature gradient-driven liquid flow speed to be estimated. [ABSTRACT FROM AUTHOR]

Analytic profiles for periodic grain boundary grooves (PGBGs) were determined from variational theory. Variational profiles represent stationary solid-liquid profiles with abrupt, zero-thickness, transitions between adjoining phases. Variational PGBGs consequently lack tangential interfacial fluxes, the existence of which requires more realistic (non-zero) interfacial thicknesses that allow energy and solute transport. Variational profiles, however, permit field-theoretic calculations of their scaled formation free energy and thermodynamic stability, capillary-mediated chemical potentials, and their associated vector gradient distributions, all of which depend on a profile's geometry, not its thickness. Despite the fact that variational profiles are denied interface fluxes, one may, nevertheless, impute shape-dependent interface transport in the form of a profile's surface Laplacian of its presumptive chemical potential distribution due to capillarity. We compare variational surface Laplacians with residuals of the thermochemical potential measured along counterpart diffuse-interface PGBGs, simulated via phase-field with metrically-proportional profiles. Fundamentally, it is the thickness of a microstructure's interfaces and its shape that co-determine whether, and to what extent, gradients of the chemical potential excite fluxes that transport energy and/or solute. PGBGs, both variational and simulated, greatly expand the limited universe of solid-liquid microstructures suitable for steady-state thermodynamic analysis. Understanding the origin and action of these capillary-mediated interfacial fields opens a pathway for estimating and, eventually, measuring how solid-liquid interface thickness modifies the transport of energy and solute during solidification and crystal growth, and influences microstructure. [ABSTRACT FROM AUTHOR]

Traditional batch crystallization processes encounter challenges like batch-to-batch variability, and difficulty in scale-up and achieving desired crystal size and morphology. These challenges stem from various growth mechanisms within crystallizers, influenced by operating conditions that dictate the dynamic surface structure of crystals. To overcome this, we developed a novel microscopic kinetic Monte Carlo model, which uses a specialized adsorption rate that adapts to different growth regimes by considering surface thermodynamic effects for different growth mechanisms. Specifically, the adaptive adsorption rate redefines the driving force of crystallization by considering the attachment energies of different adsorption sites (e.g., kink, adatom, and edge) and supersaturation. This approach enables seamless transitions across growth regimes. We use the lysozyme crystal system as a case study, demonstrating the model's superior predictive power in regime-to-regime transitions. Overall, the developed work provides a valuable new approach to understanding crystal morphology and predicting crystal growth rates in different growth regimes. • A new kMC model for protein crystal growth is developed. • Different adsorption sites facilitate transitions between growth regimes. • Attachment energies correlate growth mechanisms to supersaturation. • Experimental data for Lysozyme crystals validates the kMC model. [ABSTRACT FROM AUTHOR]

It is argued that the criticism by Faraji et al. is unfounded and clarified further why surface stress on a strain-free solid, as postulated by Shuttleworth, does not exist. [ABSTRACT FROM AUTHOR]

[Display omitted] Pressure dependence of contact angle is expected to be influenced by temperature. Nevertheless, the correlation of water contact angle with pressure is rarely investigated at high temperatures (over 100 ℃). In this work, measurements of the contact angle and interfacial tension of water in N 2 atmosphere were conducted at various pressures and temperatures (up to 17 MPa and 300 ℃). The experimental observations were elucidated based on the theory of surface thermodynamics. It was shown that the water-N 2 interfacial tension linearly decreases with increasing the pressure, and that the pressure coefficient declines as temperature rises. The pressure dependence of the water contact angle was found to be different for the low- and high-temperature regimes: the water contact angle increases below 100 ℃, whereas an inverse variation occurs over 100 ℃. According to the theoretical analysis, the pressure dependence of both the water interfacial tension and contact angle is attributed to N 2 adsorption on the surfaces of water and silicon. The variations in the water contact angle with pressure, including both the sign and magnitude, are actually the consequence of the changes of water-N 2 and Si-N 2 interfacial tensions manipulated by pressure and temperature. [ABSTRACT FROM AUTHOR]

As a fluid approaches three phase coexistence, adsorption may take place by the successive formation of two intervening wetting films. The equilibrium thickness of these wetting layers is the result of a delicate balance of intermolecular forces, as dictated by an underlying interface potential. The van der Waals forces for the two variable adsorption layers may be formulated exactly from Dzyaloshinskii-Lifshitz-Pitaevskii theory, and analytical approximations may be derived that extent well beyond the validity of conventional Hamaker theory. We consider the adsorption equilibrium of water vapor on Silver Iodide where both ice and a water layers can form simultaneously and compete for the vapor as the triple point is approached. We perform numerical calculations of Lifshitz theory for this complex system and work out analytical approximations which provide quantitative agreement with the numerical results. At the three phase contact line between AgI/water/air, surface forces promote growth of ice both on the AgI/air and the water/vapor interfaces, lending support to a contact nucleation mode of AgI in the atmosphere. Our approach provides a framework for the description of adsorption at three phase coexistence, and allows for the study of ice nucleation efficiency on atmospheric aerosols. [ABSTRACT FROM AUTHOR]

Praziquantel (PZQ), a broad spectrum anthelmintic drug, cannot be found in acceptable dosage forms for elderly patients, paediatric patients, and for veterinary use. In fact, very little has been done up to now in the formulation of liquid dosage forms, being they always formulated for parenteral administration. To beat this important challenge, it was accomplished a comprehensive analysis of the influence of two elementary physicochemical aspects, i.e. surface thermodynamic and electrokinetic properties, on the colloidal stability of PZQ nanosuspensions. The hydrophobic character of the drug, intensely determining the flocculation curves, was confirmed by the thermodynamic characterization. The electrophoretic characterization, in combination with the sedimentation and relative absorbance versus time curves, highlighted that the electrical double layer thickness and the surface charge can play an essential role in the stability of the pharmaceutical colloid. Finally, it was demonstrated that controlling the pH values and the incorporation of electrolytes can help in formulating PZQ aqueous nanosuspensions with appropriate stability and redispersibility behaviours for pharmaceutical use. [ABSTRACT FROM AUTHOR]

[Display omitted] • Negative effects of filamentous bulking on granular anammox process was explored; • Evolution of anammox granular characteristics were systematically examined; • Determination of boundary layer thickness of granular sludge was developed; • Granular surface thermodynamic properties were analyzed based on XDLVO theory; • Shear stress-based operational strategy under filamentous bulking was proposed; In this study, the filamentous bulking (FB) with moderate and excessive levels were demonstrated to induce anammox failure by inhibiting nitrogen (N) removal and biomass retention. The low external mass transfer resulted from high liquid-surface friction and low turbulence of filamentous surface was considered the "trigger" of anammox failure, which decreased flux of nitrogen flow toward granular surface and directly limited N-removal loading, which meanwhile exposed granules with N-scarcity environment and indirectly inhibited N-removal bio-activity. Low bio-activity performed poor extracellular polymeric substances secretion further destroyed bio-aggregation with low suface hydrophobicity, which acted as "accelerator" for granule disintegration and biomass washout, ultimatly leading to anammox failure. Fortunately, incresing hydraulic shear stress could eradicate FB's negative effects without inhibiting FB itself, which promoted re-granulation and N-remval restore by enhancing external mass transfer more than hydraulic detachment. Enhancing mechanical stirring with FB level was necessary to maintain stable operation of granular anammox system. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Adhesion of A. manzaensis to chalcopyrite was investigated experimentally and theoretically. • Temperature and pH affect the adsorption behavior of A. manzaensis on chalcopyrite. • The extended DLVO theory was introduced to explain the archaeon adsorption process. • The adsorption behaviors of different energy sources adapted A. manzaensis were analyzed. Abstract The adsorption of Acidianus manzaensis YN25 on chalcopyrite was investigated experimentally and theoretically. A. manzaensis showed high adhesion affinity to the chalcopyrite under acidic condition, but low adhesion affinity under neutral and alkaline conditions. The microbe-mineral adhesion was assessed by the surface thermodynamics and the extended DLVO theory. The experimental results were in agreement with the theory. Moreover, A. manzaensis grown on chalcopyrite, sulfur, and ferrous ion showed similar adsorption phenomena. The adsorptive capacity of A. manzaensis increased with increasing temperature and decreasing pH respectively, and within the range of investigation, the best adsorption was achieved at pH 2.0 and 65 °C. This study provided new insights for bio-catalytic oxidation of sulfide minerals by the thermophilic acidophilic archaea. [ABSTRACT FROM AUTHOR]

Ductility-dip cracking (DDC) fracture surfaces containing thermal faceting (TF) are documented in this study. Research began with the discovery of TF on the DDC fracture surface in the weld metal of high-chromium nickel (Ni)-based filler metal 52M, a valuable alloy to the nuclear industry. Fracture surfaces were generated using strain-to-fracture (STF) and simulated strain ratcheting (SSR) testing on a Gleeble® thermomechanical simulator. Initial fractography performed by scanning electron microscopy (SEM) revealed faceting with preferred grain orientations and faceting interacting with void nucleation near grain boundary (GB) triple points. Internal voids were exposed via metallography, where TF was also observed on the free surface. A thin orientation- and site-specific foil was extracted from the faceted fracture surface using focused ion beam (FIB) nanofabrication. Subsequent scanning transmission electron microscopy (STEM) characterization down to atomic-resolution revealed the facets have perfect crystallographic orientations parallel to close-packed directions. Sharp edges and transitions between individual facets on the scale of individual atomic columns and atomic planes were observed. An analysis of the deformation microstructure and the chemical composition underneath the faceted surface showed a low dislocation density and no evidence of localized segregation or diffusion, respectively. These findings have led to the development of a hypothesis related to the interdependence of TF and DDC and support initial claims regarding TF formation in DDC voids at elevated temperatures. [ABSTRACT FROM AUTHOR]

The surface tension and viscosity values of N-methyldiethanolamine (MDEA) aqueous solutions promoted by tetramethylammonium arginate ([N1111][Arg]) were measured and modeled. The experimental temperatures were 303.2 to 323.2 K. The mass fractions of MDEA (wMDEA) and [N1111][Arg] (w[N1111][Arg]) were 0.300 to 0.500 and 0.025 to 0.075, respectively. The measured surface tension and viscosity values were satisfactorily fitted to thermodynamic models. With the aid of experimentally viscosity data, the activation energy (Ea) and H2S diffusion coefficient (DH2S) of MDEA-[N1111][Arg] aqueous solution were deduced. The surface entropy and surface enthalpy of the solutions were calculated using the fitted model of the surface tension. The quantitative relationship between the calculated values (surface tension, surface entropy, surface enthalpy, viscosity, activation energy, and H2S diffusion coefficient) and the operation conditions (mass fraction and temperature) was demonstrated.

The surface tensions (γ) of 2-diethylaminoethanol (DEAE)–tetramethylammonium glycinate ([N 1111 ][Gly]), DEAE–1-butyl-3-methylimidazolium glycinate ([Bmim][Gly]) and DEAE–1-butyl-3-methylimidazolium l -lysinate ([Bmim][Lys]) aqueous solutions were measured by using the BZY-1 surface tension meter. The temperature ranged from 303.2 K to 323.2 K. The mass fractions of DEAE and amino acid ionic liquids (AAILs) respectively ranged from 0.30 to 0.50 and 0.025 to 0.075. A thermodynamic equation was proposed to model the surface tension and the calculated results agreed well with the experiments. The effects of temperature and mass fractions of DEAE and AAILs on the surface tension were demonstrated on the basis of experiments and calculations. The surface enthalpy and surface entropy were determined and their concentration dependences were illustrated. [ABSTRACT FROM AUTHOR]

Theories of wetting have a long history and they are intensively used in interpreting experimental data. Nevertheless, many basic aspects, such as the pinning of a contact line and contact angle hysteresis, are still poorly understood. The development of a rigorous consensus theory has suffered from concepts that are based on faulty intuitions. These include the force interpretation of Young's equation, the use of the principle of minimizing the global free energy, and the concepts of the work of adhesion and the mechanical surface tension on a solid. In this paper, the appropriate treatment of the basic ingredients of surface thermodynamics is discussed and the route towards the physically justified theoretical approach on wetting is outlined. [ABSTRACT FROM AUTHOR]

We report and provide justification for the consistently observed four experimental facts of mass spectrometric data of carbon cluster emission from the Cs+-irradiated single-walled carbon nanotubes (SWCNTs). Firstly, the diatomic carbon C2is the most abundant sputtered species. Secondly, monatomic carbon C1yield is Cs+energy dependent. Thirdly, at low caesium energies, only C2, C3and C4are emitted. Lastly, the normalised yield of C1monotonically increases while C2, C3and C4show gradual decrease leading to saturation. The experimental data for the normalised density of clusters and atoms follow the pattern >  >  > . A statistical thermal model is developed to explain the experimentally observed sputtering of clusters. The probability of a cluster Cxto be emitted is proportional to that for the creation of anx-member vacancy with formation energyExvat temperatureTsas {exp(Exv/kTS) + 1}−1. The energies of formation of vacancies from DFT calculations and the ratio of normalised experimental yields have been used to estimateTS. OnceTsis evaluated, the formation energies of tri- and quarto-vacancies are obtained using the ratios of normalised densitiesand. We show that by invoking thermal spikes, cluster emission from, and the multiple vacancy generation in, the Cs+-irradiated SWCNTs can be explained. [ABSTRACT FROM AUTHOR]

The diffusion behaviors of single Au, Ag and Cu atoms on Si(111)-(7 × 7) half unit cells have been investigated via combining scanning tunneling microscopy and first-principles calculations. Despite the similar adsorption sites between both half unit cells among these elements, the diffusion dynamics show obvious differences between Ag and the other two. Although obvious asymmetry has been found in the diffusion behaviors of Au and Cu atoms in two half unit cells of Si(111)-(7 × 7), the asymmetry behaves in a way different from that of Ag atoms and no dual-time character has been observed for the diffusions of Au and Cu in both half unit cells. Theoretical calculations suggest a different potential energy profile caused by the stronger hybridization between d states of Au (Cu) and Si states make the concept of basin useless for the diffusion of Au and Cu atoms inside the half unit cells of Si(111)-(7 × 7). [ABSTRACT FROM AUTHOR]

We have investigated the bulk and surface properties of the group II metal fluorides CaF2, SrF2 and BaF2 using periodic density functional theory (DFT) calculations and surface thermodynamics. Our bulk results show that the best agreement with experiment is achieved with the B3LYP and PBE functionals. We determined the relative importance of the low index surfaces in vacuum and found that an fluoride microcrystal exposes only the (111) surface in which the undercoordinated cations are sevenfold coordinated. With methods of ab initio surface thermodynamics, we analyzed the stability of different surfaces under hydrogen fluoride (HF) pressure and determined the presumable shape of the crystals with respect to different HF concentrations and temperatures. In the case of CaF2 and SrF2, the calculated shapes of the crystals agree well with TEM images of fluorolytic sol-gel synthesized nanocrystals at room temperature and high HF concentration. [ABSTRACT FROM AUTHOR]

The surface tension (γ) of 1-dimethylamino-2-propanol (DMA2P), DMA2P-monoethanolamine (MEA), and DMA2P-piperazine (PZ) aqueous solutions was measured by using the BZY-1 surface tension meter. The temperature ranged from 303.2 K to 323.2 K. The mass fractions of DMA2P, MEA and PZ respectively ranged from 0.30 to 0.50, 0.05 to 0.15 and 0.025 to 0.075. An equation was proposed to model the surface tension and the calculated results agreed well with the experiments. The surface thermodynamics including surface enthalpy and surface entropy were determined and their concentration dependence was analysed. [ABSTRACT FROM AUTHOR]

The effect of temperature on the surface tension is examined in liquid alloys that combine a positive or negative temperature coefficient with gravity limitation of the surface concentration in the surface-active metal constituent. This is a restriction that is likely to occur in alloys where the metal with lower surface tension is much denser than the other component. Since there is a surface tension increase due to diminished segregation, the resultant temperature coefficient will depend on the superposition of two independent effects. Working in the framework of Butler's thermodynamics for ideal surface phases, equations and methods of analysis are obtained to describe both effects. These developments are illustrated with alloys where the surface density is likely to attain the bulk density at certain compositions, namely the Al–Zn alloys that exhibits a negative temperature coefficient and the Sn–Bi, Ga–Bi, Ga-Pb and Cu–Pb alloys that present composition ranges with positive temperature coefficients. The specific concave down d γ /d T curves of liquid alloys are theoretically predicted. Furthermore, good estimates are obtained for systems with positive and negative temperature coefficients, except within a 50 K interval of phase transitions, or for systems showing large deviations from ideal behaviour. [Display omitted] • Surface density effect on surface tension temperature coefficients of liquid alloys. • Thermodynamic calculation of ideal temperature coefficients for liquid metal alloys. • Experimental vs. theoretically estimated surface tension temperature coefficients. [ABSTRACT FROM AUTHOR]

In the previous paper (Gutman, JOSSEC 18:3217-3237, 2014), we have shown that the main problem in capillarity and electrocapillarity of solid surfaces is the lack of clarity in determining the surface stress and basic equations. Now, we continue the survey of efforts to solve this problem and show origins of erroneous results, accenting some important items: comparative analysis of Gibbs and Guggenheim approaches in surface thermodynamics (a geometrical dividing surface and finite-thickness surface layer, respectively), transformation of fundamental equations on per-unit-area basis to obtain Gibbs adsorption equation for finite-thickness surface layer, different attempts to derive the thermodynamic definition of 'surface stress' in frames of Gibbs' theory (including Shuttleworth's approach), atomistic calculations of surface stress, surface stress in rational continuum mechanics, 'modifications' of Gibbs-Duhem relations made for solid interface, and Maxwell relations in capillarity and electrocapillarity of solid interface. It is shown that the erroneous Shuttleworth's approach is present in an explicit or implicit form in all efforts to introduce the surface stress in frames of Gibbsian theory (although Gibbs did not introduce surface stress). Therefore, 'modernizations' or 'generalizations' of the Gibbs-Duhem relation, the Gibbs adsorption equation, and the Lippmann equation to adopt them for a solid surface are unnatural and not necessary. Therefore, we recommend withdrawing the Shuttleworth equation and its consequences from circulation, including the IUPAC Recommendations. [ABSTRACT FROM AUTHOR]

A lattice gas model is used with Wang-Landau Monte Carlo sampling to predict the capillary force between a model of an atomic force microscopy (AFM) probe and a smooth surface as a function of separation, relative humidity (RH), and tip hydrophilicity. Completely wetting AFM tips exhibit a maximum in the capillary force as the RH increases, while the magnitude of the capillary force in the presence of partially wetting and partially drying tips is relatively independent of the RH. Capillary forces can also be significant in low RH environments and should not be discounted in AFM studies involving hydrophilic surfaces. [ABSTRACT FROM AUTHOR]

Hard spheres are a central and important model reference system for both homogeneous and inhomogeneous fluid systems. In this paper we present new high-precision molecular-dynamics computer simulations for a hard sphere fluid at a planar hard wall. For this system we present benchmark data for the density profile p(z) at various bulk densities, the wall surface free energy j, the excess adsorption Г, and the excess volume ve x, which is closely related to Г. We compare all benchmark quantities with predictions from state-of-the-art classical density functional theory calculations within the framework of fundamental measure theory. While we find overall good agreement between computer simulations and theory, significant deviations appear at sufficiently high bulk densities. [ABSTRACT FROM AUTHOR]

Some details of the research in thermodynamics of capillary systems, conducted at the Department of Physical Chemistry at Sofi a University “St. Kliment Ohridski “in the years 1970 - 1990, are presented in this article. The second part of the article analyzes some changes in research caused by major political changes in Europe and worldwide since 1990. [ABSTRACT FROM AUTHOR]

A thermodynamic method based on surface thermodynamics and atomic bond energy was developed to accurately investigate the lattice distortion rates of metallic nanomaterials. The results indicated that the lattice distortion rates of nanomaterials follow an inverse proportional relationship with the size, in good agreement with the experimental results. In this method, the anisotropy of the lattice distortion was a considerable issue. We found that the surface tension and Young's modulus of the nanocrystals, compared with those of the bulk materials, change because of the lattice distortion and exhibit a linear relationship at the nanoscale. By defining a shape factor (ξ), the lattice distortion rates of nanoparticles, nanowires, and nanofilms were calculated. This method provides a new approach for the evaluation of the lattice distortion rates in nanomaterials. [ABSTRACT FROM AUTHOR]

The inhomogeneous structure of a fluid at a wall can be characterised in several ways. Within a thermodynamic description, the surface free energy γ and the excess adsorption Γ are of central importance. For theoretical studies, closed expression of γ and Γ can be very valuable; however, even for a well-studied model system such as a hard-sphere fluid at a planar hard wall, the accuracy of existing expressions for γ and Γ, compared to precise computer simulation data, can still be improved. Here, we compare several known expressions for γ and Γ to the most precise computer simulation data. While good agreement is generally found at low to intermediate fluid densities, the existing parameterisations show significant deviation at high density. In this work, we propose new parameterisations for γ and Γ that agree with the simulation data within statistical error over the entire fluid density range. [ABSTRACT FROM PUBLISHER]

We investigated experimentally and theoretically the adhesion behavior of Acidithiobacillus ferrooxidans (At.f6) to different copper sulfides. The adsorption experiment showed cell densities of 10.74 × 106, 8.06 × 106, 3 × 106, 4.24 × 106 and 2.35 × 106 cells/cm2, respectively, on the surfaces of djurleite, bornite, covellite and chalcopyrite. The order was: djurleite > bornite > covellite > chalcopyrite. The results indicate that A. ferrooxidans has high affinity to adhering to the surfaces of djurleite and bornite in the acidic region. But the thermodynamic approach predicts that there will be no attachment of At.f6 to the surfaces of bornite, covellite and chalcopyrite. This discrepancy is due to the inadequate description of electrostatic interactions. The DLVO approach shows attachment of At.f6 to the surfaces of djurleite, bornite and covellite, and repulsion between At.f6 and chalcopyrite. The DLVO approach can explain the differences of the adhesion of At.f6 to different copper sulfides. [ABSTRACT FROM AUTHOR]

The main problem in electrocapillarity of solid electrodes is the lack of clarity in determining the surface stress and basic equations. Within the framework of the Gibbs concept of geometrical dividing surface, the 'surface stress' cannot be defined because methods of continuum mechanics can be applied to a physical surface layer (of finite thickness), but not to a mathematical surface. Gibbs never used the concept of surface stress, introducing only 'surface tension' for a liquid electrode and 'closely related quantity' for a solid electrode. Revisiting the derivation of the Gibbs adsorption equation, we prove its applicability to solid surfaces without the limiting requirement of constant state of strain, which was undeservedly interpreted by Eriksson as a shortcoming of the Gibbs theory caused to look for other approaches to surface stress problem. A critical analysis shows that the attempts (Shuttleworth, Eriksson, Couchman, Gokhstein, Weissmüller, etc.) to create a thermodynamic definition of the surface stress (as well as the formulation of fundamental thermodynamic equations and Maxwell relations operating with surface stresses) contain mathematical defects. It is shown that confusing interpretations of some Gibbs' concepts encountered in the literature have led to 'modifications' of the Lippmann equation based on the critical error in the Gibbs-Duhem relation due to the occurrence of an extensive variable, which is inadmissible. The famous Lippmann equation should not be modified, and it remains a unique electrocapillary relation applicable to liquid and solid electrodes. [ABSTRACT FROM AUTHOR]

It is shown that the so-called 'equation of solid-state electrocapillarity' derived by Gokhshtein from the simplest thermodynamic model, earlier used by Lippmann, is an incorrect modification that is returned to the classic Lippmann equation if to take into account the usual definition of differential capacity of the electrical double layer. Consequently, Gokhshtein's experiments can actually confirm only the validity of the Lippmann equation (with deviations caused by physicochemical processes in the double layer, which could not be taken into account in the thermodynamic equations). The thermodynamic model is insufficient for the interpretation s of these experimental results, whose understanding requires physical models of the different phenomena occurring at the electrode surface. [ABSTRACT FROM AUTHOR]

Abstract: Helfrich model of membrane bending elasticity has been most influential in establishment and development of Soft-Matter Physics of lipid bilayers and biological membranes. Recently, Helfrich theory has been extensively used in Cell Biology to understand the phenomena of shaping, fusion and fission of cellular membranes. The general background of Helfrich theory on the one hand, and the ways of specifying the model parameters on the other, are important for quantitative treatment of particular biologically relevant membrane phenomena. Here we present the origin of Helfrich model within the context of the general Gibbs theory of capillary interfaces, and review the strategies of computing the membrane elastic moduli based on considering a lipid monolayer as a three-dimensional thick layer characterized by trans-monolayer profiles of elastic parameters. We present the results of original computations of these profiles by a state-of-the-art numerical approach. [Copyright &y& Elsevier]