Thermodynamics of interface elasticity

We generalize and extend a series of articles on the thermodynamics of interface elasticity. The whole formulation is based on taking into account a finite elastic deformation. This leads to generalized forms of the equations for the surface excess of the internal energy, the Gibbs adsorption equation and the Shuttleworth equation. In all cases correction terms occur containing the strain tensor. Although the deformation might be small, the corrections are critical in performing derivatives with respect to the strain which are needed to obtain equations connecting measurable quantities. These consequences are demonstrated in detail for the simple case of the spherical electrode. In the traditional electrochemical treatment, the densities of extensive quantities are related to the deformed surface, which is usually not mentioned. In analogy to the theory of volume elasticity, where the densities are related to the unstrained solid, one can also relate the densities of surface excess quantities to the unstrained surface. This formulation gives at first an additional proof for some of the generalized equations. Moreover, within this formulation one can express the surface excess of the energy density by the superficial work of the unstrained surface and three surface elastic constants, two of them being the surface Lamé constants. In the alternative formulation, the Shuttleworth equation appears simply as the relation between a generalized force and a generalized potential. Published in Elektrokhimiya in Russian, 2009, Vol. 45, No. 1, pp. 78–86. The text was submitted by the authors in English. This study was prepared for the special issue devoted to the 100th anniversary of B.V. Ershler.     

Edge profiles at lamellar phase/melt interfaces

We study in the framework of the continuum theory of dislocations the structure of the interface between an AB diblock copolymer lamellar film deposited on a solid substrate and an A-homopolymer melt. The dislocation inside the lamellar phase induces steps at the interface. The shape of the profile at the edge of a step (edge profile) depends on the distance of the dislocation from the interface. The profile and the equilibrium location of the dislocations are both studied as a function of the film thickness, D. For large D, the dislocation is stabilized at a finite distance, h_eq, from the interface, due to the small surface tension and large surface bending elastic constant, K_s. For zero surface tension, h_eq ≈ K_s/(2K), where K is the bulk bending elastic constant. For small D, h_eq is mainly determined by the proximity of the solid substrate. The edge profile along the interface is a monotonic function of the distance along the interface for large D of the film and becomes nonmonotonic for small D. Also the dislocation energy strongly depends on D for small D. The theory is discussed in connection to recent experimental studies of diblock copolymer films deposited on a solid substrate.     

Quantum mechanical description of electrode reactions: Part II. Treatment of compact layer structure at platinum electrodes by means of the extended Hückel molecular orbital method. Pt(111) surfaces

The Iteraltive Extended Hückel Molecular Orbital method has been adapted to calculation of the properties of an electrode and compact layer. Predictions of the stablest orientations, on the Pt(111) surface of species such as H₂O, Pt, OH^?, H, and the halides, F^?, Cl^?, Br^? and I^?, based upon calculation of the total energy corresponding to various internuclear distances, are reported. The calculations correctly predict self-adsorption of Pt on the Pt(111) surface at the face-centered cubic closest-packing position. The H₂O molecule is predicted to locate itself above three adjoining Pt atoms, with the O atom closest to the surface and the H atoms opposite the O. Similar results were obtained for OH^? and the halides. Atomic H, however, is predicted to drop into the plane of centers of the Pt surface atoms, where it would lie between, three adjacent Pt atoms. Application of the method to electrode studies requires only modest amounts of computer time but produces surprisingly reliable qualitative predictions. Compulation of electrochemical quantities such as charge, differential capacitance, surface tension and potential energy as a function of electrode potential will be described in future work.     

“Electrocapillary” curve on solid metal obtained by holographic interferometry

A new very sensitive method was developed for obtaining the “electrocapillary” curve of a solid metal. The method is based on the measurement of small elastic deformations of a strip caused by the changes of the surface tension forces. For the precise measurement of the strip bending (the radius of curvature) holographic interferometry was applied. It is shown that a change of the surface tension ±0.1 mN m^?1 can be registered. The “electrocapillary” curve of platinum in 0.05 M H₂SO₄ solution was obtained. It was found that the zero charge potential is +0.25 V versus normal hydrogen electrode. The double layer capacity was evaluated. The method is not very sensitive to temperature changes and can be applied in any case when the working electrode (metal strip) is mounted in a transparent glass cell.     

New Prediction Model of Surface and Interfacial Energies Based on COSMO-UCE**

The nature and strength of intermolecular and surface forces are the key factors that influence the solvation, adhesion and wetting phenomena. The universal cohesive energy prediction equation based on conductor-like screening model (COSMO-UCE) was extended from like molecules (pure liquids) to unlike molecules (dissimilar liquids). A new molecular-thermodynamic model of interfacial tension (IFT) for liquid-liquid and solid-liquid systems was developed in this work, which can predict the surface free energy of solid materials and interfacial energy directly through cohesive energy calculations based on COSMO-UCE. The applications of this model in prediction of IFT for water-organic, solid (n-hexatriacontane, polytetrafluoroethylene (PTFE) and octadecyl-amine monolayer)-liquid systems have been verified extensively with successful results; which indicates that this is a straightforward and reliable model of surface and interfacial energies through predicting intermolecular interactions based on merely molecular structure (profiles of surface segment charge density), the dimensionless wetting coefficient R_A/C can characterize the wetting behavior (poor adhesive (non-wetting), wetting, spreading) of liquids on the surface of solid materials very well.     

The development of the fundamental concepts of surface thermodynamics

Author’s results concerning the most fundamental problems of the thermodynamics of surface phenomena are reviewed. The generalized Laplace-Young-Kelvin equation, phase rules, and Gibbs adsorption equations are presented. Analogs of Konovalov’s laws are describes as applied to surface phenomena. The surface tension dualism, the Gibbs equation for adsorption on solid surfaces, and the phase equilibrium condition for a soluble nanoparticle are explained. The general mechanochemical approach, chemical affinity tensor, and the discovery of the mechanochemical dissolution effect are characterized. A novel approach to the monolayer state equation is formulated based on an excluded area. The problems of nucleation and the theory of surface separation are reperted.     

New approach to defining thermodynamic surface tension of solids

Using either the chemical potential of the immobile component of a solid dissolved in a fluid phase or the corresponding component of the tensor of chemical potential in solid phase, a new concept of the grand thermodynamic potential of solid-fluid two-phase system is proposed. For a planar interfacial surface, this makes it possible to generalize the notion of thermodynamic surface tension σ introduced by Gibbs that has the meaning of the formation work of a unit surface. This tension is determined as the specific surface excess of the grand thermodynamic potential. This definition of the thermodynamic surface tension does not depend on the position of the dividing surface and is common for fluids and solids. It is shown that, at the arbitrary position of dividing surface, the difference between thermodynamic σ and mechanical @[gamma] surface tensions for solid surface is determined by the nonuniformity of the tensor of chemical potential in a solid, as well as by its anisotropy in the bulk of solid phase.     

Thermodynamics of inelastic deformation of amorphous and crystalline phases in linear polyethylene

Thermodynamic parameters (work W _def and heat Q _def) of inelastic deformation (uniaxial compression up to ɛ_def = 50%) are measured for six samples of high-molecular-mass linear PE at room temperature under the regime of active loading. Energy excess ΔU _def accumulated by the samples subjected to loading are calculated in terms of the first law of thermodynamics. All thermodynamic characteristics linearly increase with crystallinity χ of PE, thus making it possible to extrapolate their values to χ = 0 and 100% and to find the contributions of the amorphous and crystalline phases of the polymer to the overall thermodynamics of deformation. Both of the PE phases contribute to W _def and ΔU _def, while the crystalline phase alone contributes to heat Q _def. At ɛ ≥ 30%, the energy contribution from the amorphous phase exceeds that from the crystalline phase. A comparison between the plastic behavior of PE crystals and glassy polymers demonstrates that PE crystallites are easier deformed (requires less work W _def) than glassy polymers. At the same time, the amorphous phase of PE is harder to deform (requires more work W _def and stores more energy ΔU _def) than noncrystalline rubbers, apparently because of the deformation of tie chains. The thermodynamic characteristics of deformation are compared for three materials: crystalline metals, PE, and glassy polymers. The similarities and differences in their plastic behaviors are considered.     

Adhesion and tack of polymers: Influence of mechanical properties and surface tensions

The adhesion of various polymers used as model adhesives, polyisobutylene, polyacrylates etc. has been investigated by means of an apparatus measuring the adhesive failure energyw in dependence on contact time, contact pressure, rate of separation, and temperature. The adhesive failure energy of adhesive joints formed with low contact pressure during a short contact time is called tack. After a sufficiently long contact time and with a high bonding pressure an adhesive joint exhibits its maximum energy of separationw _m .The viscoelastic properties of the model adhesives were characterized by creep experiments in dependence on time and temperature. The surface tension of the polymer adhesives and adherents could be determined by contact angle measurements. Adhesion measurements of polyisobutylene on a number of adherents were carried out in air and in various liquids in order to obtain information about the influence of surface tension on tack and maximum adhesive failure energy. w _m can be written as the product of two terms: the thermodynamic work of adhesionW _A which is related to the surface and interfacial tensions of adhesive and adherent and a dimensionless function dependent on temperature and rate of separation which describes the viscoeleastic properties of the adhesive and which obeys the rate-temperature superposition principle known from linear viscoelasticity. The tack is related to incomplete bond formation and cannot be described in the same manner. It is, however, strongly dependent on the viscoelastic properties of the adhesive showing a maximum at about 50 to 70 °C above the glass transition temperature. It is, moreover, influenced by the compliance in the plateau range above the glass transition which is determined by the entanglement network of the polymer. Wetting of the adherent by the adhesive is a further important condition for high tack values which is fulfilled if the adherent has a higher surface tension than the adhesive.     

Shape of the nematic-isotropic interface in conditions of partial wetting

A nematic liquid crystal in contact with a solid substrate is studied in the partial wetting regime. Both a mesoscopic Landau-de Gennes theory and a macroscopic effective interface Hamiltonian approach are considered. A generalized Young equation for the balance of forces at the three-phase contact line is derived, which takes into account corrections due to distortions of the nematic director field. It is also shown that the asymptotic form of the separation of the nematic-isotropic interface from the substrate has a logarithmic correction to the usual linear behaviour. The characteristic length scale of this correction is given by the ratio K/(2σ_NI), where K and σ_NI are the average elastic constant and the nematic-isotropic surface tension, respectively, and is of the order of a few hundred angstroms. Then, a simple form of an effective interface Hamiltonian is proposed, and results consistent with the predictions of the Landau-de Gennes theory are obtained. It is shown, in the framework of this macroscopic approach, that the line tension associated with the contact line remains finite, when the thermodynamic limit is taken, if the anchoring at both the nematic-substrate and the nematic-isotropic interfaces is homeotropic. However, in the case of different anchoring directions, the line tension diverges logarithmically with the system size.     

Bemerkungen zur Thermodynamik der Immersionsbenetzung von festen Adsorbentien

Zusammenfassung Es wird zur Thermodynamik der Immersionsbenetzung ein Formalismus dargelegt, der dem Umstand Rechnung trägt, daß im Fall von kolloidal dispergierten Adsorbentien infolge der Konstanz der spezifischen Oberfläche die Ausdehnung der Grenzfläche fest/flüssig nicht unabhängig, sondern nur zusammen mit der Adsorbensmenge verändert werden kann, und daß der Begriff der Oberflächenspannung in einem solchen System problematisch wird. Dementsprechend wird der Gebrauch des Begriffs der Oberflächenarbeit vermieden. Alle in den Formalismus eingehenden thermodynamischen Größen sind einer eindeutigen Berechnung aus experimentell meßbaren Daten zugänglich.

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Notes on the thermodynamics of immersion-wetting of solid adsorbents

A thermodynamic treatment of immersion-wetting is presented which takes into account the fact that, in the case of colloidally dispersed adsorbents, owing to the constancy of the specific surface the extent of the solid/liquid interface is not independent of, but can only alter together with the amount of adsorbent, and that the concept of surface tension in such a system is problematic. Use of the term surface work is accordingly avoided. All thermodynamic quantities made use of in the treatment are derivable by unambiguous calculation from experimental data.

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Herrn Prof. Dr.H. Nowotny gewidmet.     

Melting transitions in metallic elements correlated with shear modulus and atomic volume

We show that two quite recent treatments of dislocation-mediated melting transitions result in the thermal energy associated with the melting temperature, T _m, being expressed as a product of a volume factor and a combination of elastic constants times a lattice structure-dependent factor. We further show that the result for the latent heat of fusion L _m obtained in one of these studies leads to the ratio L _m/GΩ, where G is the shear modulus at melting and Ω the atomic volume, being a constant. Since the ratio of the vacancy formation energy to GΩ is also found to be roughly constant, we suggest that the factor GΩ at melting is crucial in determining the melting temperature, the latent heat of fusion and the vacancy formation energy and we comment on the reasons why this should be so.     

Plastic deformation of glassy polymethylene: Computer-aided molecular-dynamic simulation

Molecular-dynamic simulation of low-temperature plastic deformation (T _def = 50 K, T _def/T _g ≤ 0.3) is studied for glassy polymethylene under the regime of active uniaxial compression and tension for a cell composed of 64 chains containing 100 -CH₂ groups in each (as united atoms) and with periodic boundary conditions. Thirty-two such cells are created, and, in each cell, polymethylene chains in the statistical coil conformation are independently constructed. The cells are subjected to isothermal uniaxial compression at T _def = 50 K by ɛ = 30% and by ɛ = 70% under uniaxial tension. In the course of loading, a σ-ɛ diagram is recorded, while the mechanical work spent on deformation, the changes in the overall potential energy of the system, and the contributions from various potential interactions (noncovalent van der Waals bonds, chemical links, valence and torsional angles) are estimated. The results are averaged over all 32 cells. The relaxation of stored potential energy and residual strain after complete unloading of the deformed sample is studied. The relaxation of stored energy and residual strain is shown to be incomplete. Most of this energy and strain is stored in the sample at the deformation temperature for long period. The conformational composition of chains and the average density of polymer glass during loading are analyzed. Simulation results show that inelastic deformations commence not with the conformational unfolding of coils but with the nucleation of strain-bearing defects of a nonconformational nature. The main contribution to the energy of these defects is provided by van der Waals interactions. Strain-bearing defects are nucleated in a polymer glass during tension and compression primarily as short-scale positive volume fluctuations in the sample. During tension, the average density of the glass decreases; during compression, this parameter slightly increases to ɛ ≈ 8% and then decreases. An initial increase in the density indicates that, during compression and at ɛ < 8%, coils undergo compactization via an increase in chain packing. During compression, the concentration of trans conformers remains unchanged below ɛ ≈ 8% and then decreases. During compression, it means that in a glass, coils do not increase their sizes at strains below ɛ ≈ 8%. During tensile drawing, coils remain unfolded below ɛ ≈ 35%; at higher strains, coils become enriched with trans conformers or unfold. At this stage, the concentration of trans conformers linearly increases. The development of a strain-induced excess volume (strain-bearing defects) entails an increase in the potential energy of the sample. Under the given conditions of deformation, nucleation of strain-bearing defects and an increase in their concentration are found to be the only processes occurring at the initial stage of loading of glassy polymethylene. The results of computer-aided simulation are compared with the experimental data reported in the literature.     

Low‐rate dynamic contact angles on poly(methyl methacrylate/ethyl methacrylate, 30/70) and the determination of solid surface tensions

Low‐rate dynamic contact angles of 12 liquids on a poly(methyl methacrylate/ethyl methacrylate, 30/70) P(MMA/EMA, 30/70) copolymer were measured by an automated axisymmetric drop shape analysis‐profile (ADSA‐P). It was found that five liquids yield nonconstant contact angles, and/or dissolve the polymer on contact. From the experimental contact angles of the remaining seven liquids, it is found that the liquid–vapor surface tension times cosine of the contact angle changes smoothly with the liquid–vapor surface tension (i.e., γ_l|Kv cos θ depends only on γ_l|Kv for a given solid surface or solid surface tension). This contact angle pattern is in harmony with those from other methacrylate polymer surfaces previously studied.^45,50 The solid–vapor surface tension calculated from the equation‐of‐state approach for solid–liquid interfacial tensions¹⁴ is found to be 35.1 mJ/m², with a 95% confidence limit of ± 0.3 mJ/m², from the experimental contact angles of the seven liquids. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2039–2051, 1999     

Visualization of deformation-induced structural rearrangements in amorphous polymers

A technique is proposed for decorating amorphous polymers: Before the deformation (shrinkage) of an amorphous polymer, its surface is decorated with a thin metal coating. The subsequent deformation is accompanied by surface structure formation, which makes the processes that occur in the polymer visible. The proposed technique makes it possible to visualize and describe the mechanism of transfer of the polymer from the surface into the bulk and vice versa and to obtain direct information about the direction of the actual local stress. The technique makes it possible to obtain information about the topological heterogeneity of rubber networks, to reveal the features of structural rearrangements that occur during the cold rolling of amorphous polymers, and to describe the phenomenon of self-elongation during annealing of the oriented PET. These microscopic data explain the following features of the structural and mechanical behavior of glassy polymers from a unified viewpoint: stress relaxation in a polymer in the elastic (Hookean) region of the stress-strain curve, an increase in stress in a deformed glassy polymer during its isometric annealing below T _g, the low-temperature shrinkage of a deformed polymer glass in the strain range below its yield point, the storage of internal energy in a deformed glassy polymer in the strain range below the yield point, some anomalies of thermophysical properties, and some other features.     

电解液添加剂硫酸亚乙酯对锂离子电池性能的影响

在1 mol/L LiPF₆/碳酸乙烯酯+碳酸二甲酯+碳酸甲乙酯（体积比1∶1∶1）电解液中,采用恒流充放电测试、循环伏安法（CV）、扫描电子显微镜（SEM）、能量散射光谱（EDS）、电化学阻抗谱（EIS）等测试技术,研究了添加剂硫酸亚乙酯（DTD）对锂离子电池性能及石墨化中间相碳微球（MCMB）电极/电解液界面性质的影响。 结果表明,在电解液中引入体积分数0.01%DTD后,MCMB/Li电池可逆放电容量从300 mA·h/g提高至350 mA·h/g,电池总阻抗降低,循环稳定性提高。CV测试发现,在首次还原过程中,DTD在电极电位1.4 V左右（vs Li/Li⁺）发生电化学还原,参与了MCMB电极表面固体电解质相界面膜（SEI膜）的形成过程。 同时,DTD对LiMn₂O₄电极性能无不良影响。     

Voltammetric response of the interface between single-crystal cerium fluoride and metallic microelectrodes

The processes occurring at the interface between single-crystal fluoride-conducting solid electrolyte CeF₃: Sr²⁺ and metallic microelectrodes of Bi, Sn, Sb, and Ag are studied by the method of cyclic voltammetry with use of traditional silver-silver chloride electrode or solid-phase reference electrode Sn, SnF₂. Responses of solid-phase reactions involving mobile fluoride ions of the solid electrolyte and the microelectrode material are obtained. It is suggested that signals relating to the reduction of fluorinated metals be used for local qualitative assay of metal traces contained in quantities of about a few nanograms on the surface of conducting solids in air.     

Films minces de cristal liquide nématique sur support liquide Structure,tensions superficielles et tension de ligne

Résumé L'étude de la structure d'un film mince de cristal liquide nématique (le 4-4'-pentyl-cyanobiphenyl) sur l'eau permet de déterminer l'orientation des molécules dans le volume et aux interfaces et d'en déduire la variationy =y -y _I de la tension superficielle selon que les molécules seraient orientécs parallélement (y ) ou perpendiculairement (y _I) à la surface libre.De l'emistence et de la stabilité de trous dans le film mince, on déduit Fordre de grandeur de la tension de ligne. Cette tension de ligne est comparée aux tensions de ligne de déformation élastique du cristal liquide.

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The structure of a liquid crystal (L.C.) thin film on water has been studied optically and the molecular orientation at its interfaces has been deduced. The surface tension shifty corresponding to the orientation of the molecules either normal or parallel to the free surface has been deduced. From the study of the formation and of the stability of holes in the thin film we deduce the order of magnitude of the line tension .This tension originates in the elastic deformation of LC in the neighbourhood of the hole.

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Avec 13 figures et 1 tableau     

Stochastic Thermodynamics of Mesoscopic Electrochemical Reactions

In this work, we discussed the stochastic thermodynamics of mesoscopic electron transfer reactions between ions and electrodes. With a relationship between the reaction rate constant and the electrode potential, we find that the heat dissipation βq equals to the dynamic irreversibility of the reaction system minus an internal entropy change term. The total entropy change Δs_t is defined as the summation of the system entropy change Δs and the heat dissipation βq such that Δs_t=Δs+βq. Even though the heat dissipation depends linearly on the electrode potential, the total entropy change is found to satisfy the fluctuation theorem < (e)^-Δs_t>=1, and hence a second law-like inequality reads <Δs_t>≥0. Our study provides a practical methodology for the stochastic thermodynamics of electrochemical reactions, which may find applications in biochemical and electrochemical reaction systems.     

Aggregation behavior and adsorption properties of salt-free catanionic surfactant mixtures containing tetradecyltrimethyl ammonium salts

The aggregation behavior of salt-free catanionic surfactants, tetradecyltrimethyl ammonium hydroxide (TTAOH)/fatty acid (FA) including octanoic acid (OA), decylic acid (DA) and lauric acid (LA) in aqueous solutions were studied. The critical micelle concentration(cmc), surface tension at cmc (γ_cmc), surface excess (Г_max), mean molecular surface area (A_min), adsorption efficiency (pc₂₀) and surface tension reduction effectiveness (π_cmc) were obtained from surface tension isotherms. The influence of temperature on the surface tension of salt-free TTAOH/FA (TTAOF) systems was investigated. Data of adsorption dynamics indicated that at fixed adsorption time, the order of adsorption capacity was TTAOH?相似文献