Thermodynamics of graphene

The 21st century has brought a lot of new results related to graphene. Apparently, graphene has been characterized from all points of view except surface science and, especially, surface thermodynamics. This report aims to close this gap. Since graphene is the first real two-dimensional solid, a general formulation of the thermodynamics of two-dimensional solid bodies is given. The two-dimensional chemical potential tensor coupled with stress tensor is introduced, and fundamental equations are derived for energy, free energy, grand thermodynamic potential (in the classical and hybrid forms), enthalpy, and Gibbs energy. The fundamentals of linear boundary phenomena are formulated with explaining the concept of a dividing line, the mechanical and thermodynamic line tensions, line energy and other linear properties with necessary thermodynamic equations. The one-dimensional analogs of the Gibbs adsorption equation and Shuttleworth–Herring relation are presented. The general thermodynamic relationships are illustrated with calculations based on molecular theory. To make the reader sensible of the harmony of chemical and van der Waals forces in graphene, the remake of the classical graphite theory is presented with additional variable combinations of graphene sheets. The calculation of the line energy of graphene is exhibited including contributions both from chemical bonds and van der Waals forces (expectedly, the latter are considerably smaller than the former). The problem of graphene holes originating from migrating vacancies is discussed on the basis of the Gibbs–Curie principle. An important aspect of line tension is the planar sheet/nanotube transition where line tension acts as a driving force. Using the bending stiffness of graphene, the possible radius range is estimated for achiral (zigzag and armchair) nanotubes.     

Thermodynamics and surface properties of liquid Cu–B alloys

The study of the thermodynamic and the surface properties of liquid Cu–B alloys can help better understanding of a complex interfacial chemistry related to liquid Cu–brazes in contact with boride substrates. Despite a simplicity of the Cu–B phase diagram, only a few thermodynamic data are available in the literature, while in the case of the surface properties a complete lack of data is evident. The quasi-chemical approximation (QCA) for the regular solution has been applied to describe the mixing behaviour of liquid Cu–B alloys in terms of their thermodynamic and surface properties as well as the microscopic functions. In view of joining processes related to liquid Cu–brazes/solid boride systems a particular attention is paid to the surface properties of the Cu-rich part of the system and the calculated values are substantiated by the new surface tension experimental data of liquid Cu and Cu–10 at.% B alloy. The tests have been performed by the sessile-drop method under the same experimental conditions. Considering the experimental uncertainties, the effect of oxygen on the surface tension of liquid Cu and Cu–10 at.% B alloy has been analysed by simple model that combines the physical property data included in Butler’s equation with the oxygen solubility data and it gives the same results as Belton’s adsorption equation.     

Wetting modifications of uhmwpe surfaces induced by ion implantation

Ultra-high-molecular-weight-polyethylene (UHMWPE) surfaces are characterized in terms of roughness and wetting. Changes in the surface morphology of the polymer were induced macroscopically by mechanical friction and microscopically by ion implantation. The ion irradiation was obtained by using 300?keV Xe⁺ beams with doses ranging between 10¹⁴ and 10¹⁵?ions/cm².

Roughness and wetting measurements were performed in order to investigate the UHMWPE surface properties before and after the surface treatments. The wetting angle of the polymeric surface increases with the decrease of the roughness and with the increase of the absorbed dose. Results are discussed from the point of view of the biological reactions that could degrade the UHMWPE biocompatible surfaces employed in different mobile prostheses.     

Statistical thermodynamics of soft surfaces

We review the continuum, statistical thermodynamics of surfaces and interfaces in soft matter where both the energy and entropy of the surface are comparable. These systems include complex fluids that are dominated by either surface tension or the interfacial curvature, such as: fluid and solid interfaces, colloidal dispersions, macromolecular solutions, membranes, and other self-assembling aggregates such as micelles, vesicles, and microemulsions. The primary focus is on the theoretical concepts, their universality, and the role of fluctuations and inhomogeneities with connections to relevant experimental systems.     

Stability of droplets and channels on homogeneous and structured surfaces

Wetting of structured or imprinted surfaces which leads to a variety of different morphologies such as droplets, channels or thin films is studied theoretically using the general framework of surface or interface thermodynamics. The first variation of the interfacial free energy leads to the well-known Laplace equation and a generalized Young equation which involves spatially dependent interfacial tensions. Furthermore, we perform the second variation of the free energy for arbitrary surface patterns and arbitrary shape of the wetting morphology in order to derive a new and general stability criterion. The latter criterion is then applied to cylindrical segments or channels on homogeneous and structured surfaces. Received 4 August 1999     

The instability of vicinal electrode surfaces against step bunching II: Theory

It is shown that vicinal surfaces with a regular step array in contact with an electrolyte are intrinsically unstable against a phase separation into areas of flat terraces and areas of step bunches. The effect is caused by the step dipole moment which lowers the potential of zero charge (pzc) of stepped surfaces. Specific calculations performed for vicinal surfaces of silver are qualitatively in keeping with experimental observations. Step bunching is likewise expected for vicinal surfaces of gold and platinum.     

The instability of vicinal electrode surfaces against step bunching I: Experiment

Using electrochemical STM we have studied the stability of arrays of parallel, single atom height steps on vicinal Ag(1 1 1) electrodes in electrolyte. We find that the steps for Ag(1 1 1) electrodes are unstable and form first double-steps and later multiple steps, separated by wide, flat terraces. In this paper denoted as “I: Experiment” we deal with the experimental aspects whereas theoretical aspects are discussed in the following paper “II: Theory”.     

Surface energy modification by electron beam

We observe a pronounced variation of wettability properties in solid state materials induced by a low-energy electron beam. The phenomenon occurs in several stages characterized by various mechanisms. We show that for low electron doses the irradiation leads to decrease in the wetting of a dielectric surface due to induced surface electric potential. The higher electron charge leads to formation of a chemical monolayer on material’s surface. It has been found that the electron irradiation strongly modifies the surface free energy of SiO₂ by decreasing its total surface free energy value, almost twice. However, electron-induced variations of dispersive and polar components of the surface free energy are quite different and depend of incident electron charge.     

Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics

We show that three independent derivations of the Shuttleworth equation, arguably the second most important equation in surface physics, are inconsistent with Hermann’s mathematical structure of thermodynamics [R. Hermann, Geometry, Physics and Systems, Marcel Dekker Inc., New York, USA, 1973 (Chapter 6)]. The possible implications of this result are discussed.     

Contact angle hysteresis on nano-structured surfaces

We present results from an experimental study on the phenomenon of contact angle hysteresis on solid surfaces decorated by a random array of nanometric hollows. For weak values of the areal density of defects φ_d, the hysteresis H increases linearly with φ_d. This evolution is described by a pinning–depinning process of the contact line by individual defects. At higher values of φ_d, a collective pinning effect appears and H decreases with increasing φ_d. In the linear regime, our experimental results are compared to theoretical predictions for contact angle hysteresis induced by a single isolated defect on the solid surface. We suggest that the crossover from the individual to the collective pinning effects could be interpreted in terms of an overlapping of wetting cross sections. Finally, we analyse the influence of both the size and the morphology (hollows/hillocks) of defects on the anchorage of the contact line.     

Hydrophobic properties of surfaces coated with fluoroalkylsiloxane and alkylsiloxane monolayers

A comparative analysis of hydrophobicity of fluoroalkylsiloxane and alkylsiloxane monolayers is presented. In order to compare wetting behavior on smooth and rough substrates, a simple model considering various self-assembly degrees of organic molecules and various area fractions of air inclusion is used. Sliding behavior for water on rough silanized needle-like surfaces is also evaluated. On smooth surfaces, regardless of assembly degree of coatings, contact angles of fluoroalkylsiloxane monolayers are always ∼10° larger. The difference, however, decreases when rough substrates with air inclusion are used. It is shown that assembly order of silane molecules and reduced water-solid contact area are the key factors leading to both high contact angles and low sliding angles. Such coatings are expected to be potential snow- and ice-repellent materials.     

Fluctuating Diffusivity of RNA-Protein Particles: Analogy with Thermodynamics

A formal analogy of fluctuating diffusivity to thermodynamics is discussed for messenger RNA molecules fluorescently fused to a protein in living cells. Regarding the average value of the fluctuating diffusivity of such RNA-protein particles as the analog of the internal energy, the analogs of the quantity of heat and work are identified. The Clausius-like inequality is shown to hold for the entropy associated with diffusivity fluctuations, which plays a role analogous to the thermodynamic entropy, and the analog of the quantity of heat. The change of the statistical fluctuation distribution is also examined from a geometric perspective. The present discussions may contribute to a deeper understanding of the fluctuating diffusivity in view of the laws of thermodynamics.     

Liquid surface and liquid/liquid interface energies of binary subregular alloys and wetting transitions

Energetics and chemistry of liquid surfaces and liquid/liquid interfaces of binary A-B alloys are calculated using a subregular solution model. In this model, two macroscopic energetic parameters are used to produce an asymmetric miscibility gap. They are related to two microscopic parameters which describe the interaction energy between two atoms as a function of the composition of the first coordination shell of each atom. The impact of the asymmetry of the A-B interactions on the surface and interfacial energies and adsorption are analyzed by comparing the results obtained with this subregular model to those calculated for a regular solution. The role of the asymmetry on the prewetting and wetting transitions are also discussed. Calculations performed in the Co-Cu system are in good agreement with experimental data of surface energy.     

Prediction of contact angle on a microline patterned surface

The Cassie and Baxter’s equation has been modified to predict wetting phenomena on a microline patterned surface with the concept of effective solid-liquid interfacial energy. This interfacial energy was deduced from the total energy barrier at a metastable equilibrium and Helmholtz free energy. The contact angle predicted by the modified equation is reasonably close to the experimental data for the microline patterned surface.     

Surface free energy of polypropylene and polycarbonate solidifying at different solid surfaces

Advancing and receding contact angles of water, formamide, glycerol and diiodomethane were measured on polypropylene (PP) and polycarbonate (PC) sample surfaces which solidified at Teflon, glass or stainless steel as matrix surfaces. Then from the contact angle hystereses (CAH) the apparent free energies of the surfaces were evaluated. The original PP surface is practically nonpolar, possessing small electron donor interaction (), as determined from the advancing contact angles of these liquids. It may result from impurities of the polymerization process. However, it increases up to 8-10 mJ/m² for PP surfaces contacted with the solids. The PC surfaces both original and modified show practically the same . No electron acceptor interaction is found on the surfaces.The of modified PP and PC surfaces depend on the kind of probe liquid and contacted solid surface. The modified PP values determined from CAH of polar liquids are greater than that of original surface and they increase in the sequence: Teflon, glass, stainless steel surface, at which they solidified. No clear dependence is observed between and dielectric constant or dipole moment of the polar probe liquids. The changes in of the polymer surfaces are due to the polymer nature and changes in its surface structure caused by the structure and force field of the contacting solid. It has been confirmed by AFM images.     

Effect of contact angle hysteresis on water droplet evaporation from super-hydrophobic surfaces

Small water drops demonstrate different evaporation modes on super-hydrophobic polymer surfaces with different hysteresis of contact angle. While on the high-hysteresis surface evaporation follows the constant-contact-diameter mode, the constant-contact-angle mode dominates on the low-hysteresis surface. These modes were previously reported for smooth hydrophilic and hydrophobic surfaces, respectively. The experimental data are compared to the previous models describing spherical cap drops that evaporate in different modes, and good fitting is obtained.     

Simulation of adsorbate-induced faceting on curved surfaces

A simple solid-on-solid model, proposed earlier to describe overlayer-induced faceting of bcc(1 1 1) surface, is applied to faceting of curved surfaces covered by an adsorbate monolayer. Surfaces studied in this paper are formed by a part of sphere around the [1 1 1] pole. Results of Monte Carlo simulations show that the morphology of a faceted surface depends on the annealing temperature. At an initial stage the surface around the [1 1 1] pole consists of 3-sided pyramids and step-like facets, then step-like facets dominate and their number decreases with temperature, finally a single big pyramid is formed. It is shown that there is a reversible phase transition at which a faceted surface transforms to an almost spherical one. It is found that the temperature of this phase transition is an increasing function of the surface curvature. Simulation results show that measurements of high temperature properties performed directly and after fast cooling down to a low temperature lead to different results.     

Thermodynamics of Surface Tension: Application to Electrolyte Solutions

In this contribution to the special issue of the Journal of Statistical Physics dedicated to Michael Fisher on his 70th birthday, I shall review two thermodynamically distinct routes for obtaining the interfacial tension of liquid-vapor interfaces in mixtures. A specific application to the calculation of excess surface tension of aqueous electrolyte solutions will be presented.