Gibbs Thermodynamics Research Articles

Size dependence of the surface tension and the problem of Gibbs thermodynamics extension to nanosystems

Size dependence of the surface tension and the problem of Gibbs thermodynamics extension to nanosystems

Size dependence of the surface tension and the problem of Gibbs thermodynamics extension to nanosystems

The problem of the applicability of the Gibbs thermodynamics to nanosized objects is investigated. It is shown that the Gibbs surface phases method may be extended to nanoparticles if the effective surface tension (the specific excess free energy) is interpreted as a function of the particle radius. The specific surface free energy (the surface tension) for nanodroplets and nanocrystals of noble gases and aluminum was calculated using the thermodynamic perturbation theory. It has been shown that the averaged surface tension decreases with the particle size both for small droplets and for nanocrystals.

The Stress Driven Rearrangement Instabilities in Electronic Materials and in Helium Crystals

ABSTRACTAt present, there is a consensus that various Stress Driven Rearrangement Instabilities (SDRI) are the implications of the mathematically rigorous theoretical Gibbs thermodynamics. Many applied researchers and practitioners believe that SDRI are also universal physical phenomena occurring over a large range of length scales and applied topics. There is a multitude of publications claiming experimental observation of the SDRI based phenomena. This opinion is challenged by other highly respected scholars claiming theoretical inconsistencies and multiple experimental counterexamples. Such an uncertainty is too costly for further progress on the SDRI topic. The ultimate goal of our project is to resolve this controversy.The project includes experimental, theoretical, and numerical studies. Among various plausible manifestations of SDRI, the authors focused only on two most promising for which the validity of the SDRI has already been claimed by other researchers: a) stress driven corrugations of the solid-melt phase interface in macroscopic quantum 4He and b) the dislocation-free Stranski-Krastanov pattern of growth of semiconductor quantum dots. We devised a program and experimental set-ups for testing applicability of the SDRI mechanisms using the same physical systems as before but using implications of the SDRI theory for 2D patterning which have never been tested in the past.

On applicability of Gibbs thermodynamics to nanoparticles

Abstract The problem of applicability of thermodynamics to small objects has been investigated. It is shown that the Gibbs surface phase method may be extended to nanoparticles if the effective surface tension (the specific excess free energy) is interpreted as a function of the particle radius.

On thermodynamical inconsistency of isotherm equations: Gibbs's thermodynamics

It has been proven that all isotherm equations which include the expression 1− Θ contradict the exact Gibbs thermodynamics. These contradictions have been discussed in detail in the case of the Langmuir (L) equation applied to gas/solid (G/S), solid/liquid (S/L), and gas/liquid (G/L) interfaces. In G/S adsorption the L equation can theoretically be applied only at low equilibrium pressures on condition that v g⪢ v s· v g is the molar volume of the adsorbed amount in the gas phase and v s is the same in the Gibbs phase. In S/L and G/L adsorption the L equation is practically applicable only in the domain of very low concentrations. The cause of these contradictions (inconsistencies) is that Gibbs thermodynamics takes excess adsorbed amounts into account; however, the L and other isotherm equations calculate with the absolute adsorbed amount. The two amounts may be practically equal to each other when the limiting conditions mentioned above are fulfilled. It is also discussed how these inconsistent isotherm equations can be transformed into consistent ones.

Anomalous temperature dependence of the surface tension and capillary waves at a liquid-gallium surface

The temperature dependence of the surface tension (T) of liquid gallium is studied theoretically and experimentally using light scattering from capillary waves. The theoretical model based on the Gibbs thermodynamics relates / T to the surface excess entropy density - S. Although capillary waves contribute to the surface entropy with a positive sign, the effect of the dipole layer on S is negative. Experimental data collected at a free Ga surface in the temperature range from 30 °C to 160 °C show that / T changes sign near 100 °C.

Temperature dependence of surface tension and capillary waves at liquid metal surfaces

The temperature dependence of the surface tension γ(T) is treated theoretically and experimentally. The theoretical model based on the Gibbs thermodynamics of a one-component fluid relates ∂γ/∂T to the surface excess entropy density −ΔS. All specific surface effects, namely ordering, capillary waves, and double layer influence the surface entropy, which in turn governs the sign and the magnitude of ∂γ/∂T. Experimental data collected at a free Hg surface in the temperature range from 0°C to 30°C show that ∂γ/∂T is negative.

Geometric ?quantization? of thermodynamics and statistical corrections at critical points

Gibbs thermodynamics is treated as a two-dimensional manifold, calledLagrangian by the author, in a 4-dimensional phase space in which the temperature and pressure play the role of coordinates and the entropy and volume the role of momenta. The tunneling canonical operator determines the asymptotic behavior of the partition function. This treatment is generalized to the case of thermodynamics with intensive and extensive coordinates. A new axiomatics of thermodynamics and quasithermodynamics is given.

Comparison of thermodynamic and molecular theories of the effect of electric field on adsorption of organic compounds

It has been shown on the basis of Gibbs thermodynamics that the dependence of adsorption of organic compounds on the electric field strength is determined both by the change of energy of the ionic double layer and by the effect of re-orientation of adsorbed solvent molecules. The latter effect is however included in the energy change of the ionic double layer if experimental curves of differential capacity in pure supporting electrolyte solution are used. This method was used in the Frumkin-Damaskin theory based on the two parallel capacitors model. On the other hand, any theory taking account only of the effect of reorientation of adsorbed solvent dipoles and neglecting the energy change of the ionic double layer (in particular, the theory of Bockris and co-workers considerd here) is at variance with thermodynamics.

James Clerk Maxwell and Thermodynamics

Although Maxwell was directly involved in teaching and writing a textbook on heat theory he did not actively engage in research in this area until after he had read Gibbs' papers on thermodynamics. The stimulus of Gibbs's first two papers on the thermodynamics of homogeneous substances was such that Maxwell went beyond Gibbs and developed his own ideas on heterogeneous substances. These concepts remained unpublished, probably because they were included in Gibbs's thermodynamics later. Maxwell developed the concept that Gibbs subsequently called the potential. He also realized the importance of Gibbs's work for chemistry as well as for physics and proceeded, privately and in public to make Gibbs's work better known. Not only did he work in thermodynamics but he also stimulated colleagues at Cambridge to start research in this area, several years before Gibbs was “discovered” by Ostwald.

Toward a gibbsian approach to the problems of growth and cancer

Certain sections ofJosiah Willard Gibbs's thermodynamics papers might be applicable to biological equilibrium and growth, normal or abnormal.Gibbs added terms⌆ Μidmi to the differential of the internal energy de=tdη−pdΝ, (t=temperature,p=pressure,η=entropy,Ν=volume) where\(\mu _i = \frac{{\delta \varepsilon }}{{\delta m_i }}\) is the potential of substancemi, to provide for chemical as well as thermal and mechanical equilibrium. In this article a further generalization is suggested, to include biological equilibrium by adding to de terms of the form GdN, the variableN being the number of cells, where\(G = \frac{{\delta \varepsilon }}{{\delta N}}\) is a “growth potential” that measures exactly the resistance toward spontaneous growth. The functionG, likeΜi is intensive in nature (i.e. depends on intensive variables only) except for a conversion factor\(\frac{{dM}}{{dN}}\),M=⌆mi, affording possible insight into why incipient abnormal growth is often independent of the number of cells. Useful applications might follow from identities between\(\frac{{\delta G}}{{\delta \eta }},\frac{{\delta G}}{{\delta v}}\), or\(\frac{{\delta G}}{{\delta m_i }}\) and\(\frac{{\delta t}}{{\delta N}}, - \frac{{\delta p}}{{\delta N}}\) or\(\frac{{\delta \mu _i }}{{\delta N}}\) respectively. The following new function is studied,\(\bar \zeta = \zeta - GN\), a natural generalization of theGibbs free energy function ζ, the possibility of measuring it electrically, and comparison of its role with that of ζ for the possible experimental determination ofG.Gibbs's necessary and sufficient conditions for heterogeneous equilibrium ofn components inm phases are generalized and also modified to include broader restraining conditions like\(\mathop \sum \limits_{i = 1}^m \delta N_j (i) \geqslant o\),j=1,f,n, the > being characteristic of only living cellular phases. Careful appraisal of the term “biological stability” is followed by new criteria for stability, instability, and limits of stability, (neutral equilibrium) in terms of derivatives ofG, with possible medical applications. Three different sections of Gibbs's works tend to indicate that, for a biological phase, lower pressure usually increases its stability. The equation\(p'' - p' = \sigma \left( {\frac{I}{r} + \frac{I}{{r'}}} \right)\), where σ=surface tension,p′, p′ = pressures,r, r′=radii of curvature, is applied to possible control of tissue growth at interfaces. Methods of altering the equilibrum between three phasesA, B, C by varying the interfacial tensionsσAB,σBC,σAC, using relations likeAB<σAC+BC for stability of theA, B interface, suggest different means for shifting biological equilibrium between normal and abnormal cells through the introduction of new third phases at the interface. Various devices are mentioned for possible control of growth through proper channeling of surface or other equivalent forms of energy.