By now, the thermodynamics of fluid systems is well developed, but many issues related to solids still require discussion. In this work, six characteristic functions of classical thermodynamics are investigated in application to solid-state systems: energy, free energy, Gibbs energy, enthalpy, grand thermodynamic potential, and a new characteristic function recently discovered by the author, called the J- potential. The need to introduce such a potential appears in the thermodynamics of solid-state or mixed systems subjected to complex mechanical impacts, and also in colloidal science. Definitions are given for all six functions, fundamental thermodynamic equations are derived, and the conditions under which this function assumes the status of a thermodynamic potential are established.

Large molecules of dyes or other substances can play the role of a nano-adsorbent in aqueous surfactant solutions and, coated with surfactant molecules, resemble surfactant micelles with a solubilizate. Such micelle-like particles were called protomicelles. Their formation does not require a critical micelle concentration (CMC) and begins immediately when the surfactant is introduced into the solution. In this spectrophotometric study of Nile red (NR) in aqueous solutions of nonanoic acid (NOA), the case where protomicelles are more important than micelles is demonstrated for the first time. It has been shown that the solubilization of NR in both premicellar and micellar solutions proceeds through protomicelles rather than NOA micelles. The article also contains a theoretical part. In it, on the basis of the chemical potential of the nano-adsorbent, it is proved that the addition of a surfactant to a solution always increases the solubility of the nano-adsorbent. The dependence of adsorption on the curvature of the nano-adsorbent surface is considered and it is shown that the adsorption equations for flat surfaces can be used for curved surfaces with high accuracy.

A spectrophotometric study of the system heptanol—Nile red (NR)—water was carried out, where, for the first time for such studies, a non-colloidal surfactant that does not form micelles was taken as a surfactant. The dependence of the solubility of NR on the concentration of heptanol in an aqueous solution was studied. The experiments were carried out at a given chemical potential of NR, which was provided by an excess of the solid phase of NR. The existence of a solubilization effect has been theoretically and experimentally established: An increase in the solubility of NR with an increase in the concentration of heptanol in solution. It was found that heptanol protomicelles with a solubilization core as an NR molecule are formed in such a system, so that in the absence of micelles, the protomicelles take on the entire solubilization load. From the experimental data, the concentration of protomicelle formation was calculated, which can also be taken as the concentration of NR monomerization in an aqueous solution, since the formation of protomicelles prevents the dye aggregation. Based on the results obtained, the following generalizations were made: (1) non-colloidal surfactants, although they do not give micelles, are capable of forming protomicelles; and (2) non-colloidal surfactants can serve as a practical means of dye monomerization.

Large molecules of dyes or other substances can act as nano-adsorbents in aqueous surfactant solutions and, being coated with surfactant molecules, they resemble surfactant micelles with a solubilizate. These micelle-like particles were called protomicelles (or, more precisely, adsorption protomicelles, as in this paper). Their formation does not require a critical micelle concentration (CMC) and begins immediately when a surfactant is added to a solution. In this spectrophotometric study of Nile red (NR) in aqueous solutions of nonanoic acid (NOA), the first case where protomicelles were more important than micelles was demonstrated. It was shown that NR solubilization in both premicellar and micellar solutions proceeds through protomicelles rather than through NOA micelles. In the theoretical part of the paper, on the basis of the chemical potential of the nano-adsorbent, it was proved that the addition of a surfactant to a solution always increases the solubility of the nano-adsorbent. The dependence of adsorption on the curvature of the nano-adsorbent surface was considered, and it was shown that the adsorption equations for flat surfaces are applicable to curved surfaces with high accuracy.

The author gives an overview of his discoveries along the lines of new lawsand new phenomena. Included are the following sections: explanation ofatmospheric phenomena, such as the occurrence of atmospheric electricity and thepresence of precipitation at low supersaturation of water vapor in theatmosphere; development of classical laws of thermodynamics (Laplace, Young andKelvin equations, phase rules, Gibbs adsorption equations and laws ofKonovalov), consideration of nano-corrections to the Gibbs–Curie principle andthe Gibbs phase equilibrium condition for a soluble solid particle. Section ofnew phenomena open surface properties of water and wetting anisotropy. Asignificant part of the review is the section “Mechanochemistry: laws and newphenomena.” Here the tensors of chemical potential and chemical affinity arecharacterized, the mechanochemical effects of dissolution and stress corrosion,mechanochemical effects in redox reactions involving iron and themechanochemical effect sign of deformation in wetting phenomena are described.The theme of new phenomena is continued by the strong dependence of the contactangle on the pressure in the liquid and the temperature pinning of the contactangle. The final part tells about the discovery of a new thermodynamicpotential, called the J-potential. Thenecessity of introducing such a potential is manifested in the thermodynamics ofsolid or mixed systems subjected to complex mechanical stresses. Threeapplications are demonstrated for J-potential: in the derivation of the classical Gibbs and Neumannequations, in the thermodynamics of thin films and in the theory of strength ofmaterials.

A spectrophotometric study of the solubilization and aggregation of the Nile red dye (NR) in premicellar and micellar aqueous solutions of sodium dodecyl sulfate (SDS) was carried out. The experiments were conducted both with saturated solutions of NR under conditions of thermodynamic equilibrium of the solution with a dye precipitate, and at a constant concentration of NR in a homogeneous solution. In the first case, it was proved theoretically and verified experimentally that with an increase in the SDS concentration, the NR concentration always increases, and at the limit of low concentrations, the dependence is linear. In both cases, the concentration of NR dimers as a function passes through a maximum in the premicellar region. There are no dimers in the micellar region. The extinction coefficients of NR monomers in SDS solutions were determined both below and above the critical micelle concentration (CMC) of SDS. A solubilization curve with branches for the premicellar and micellar regions was constructed, the intersection of which was used to find the CMC value in the system under study. The state of deep supersaturation of the NR solution in the metastable state upon dilution of the micellar system with water was studied. It was found that, in addition to dimers, molecular aggregates of higher orders were also formed.

Solubilization of nile red (NR) dye in aqueous solutions of tetradecyltrimethylammonium bromide (TB) was studied by spectrophotometric method. Experiments were carried out both with NR saturated solutions under conditions of thermodynamic equilibrium of the solution with a dye precipitate, and at an NR constant weight. The solubility of NR in water (about 2 μM) has been refined. Extinction coefficients of NR monomers in water and micellar surfactant solutions were found. The micellization critical concentration (CMC) of TB in the presence of NR was determined, and the theoretical conclusion about the decrease in the surfactant CMC under the action of solubilizate was confirmed. The solubilization thermodynamic parameters were calculated on the basis of the following experimental data: the solubilization capacity of micelles, the coefficient of the solubilizate distribution between micelles and the surrounding solution, and also the standard affinity of NR solubilization. The problem of molecular NR aggregation in water and aqueous solutions of TB was considered. It has been found that the rate of reaching aggregative equilibrium is much lower than the rate of NR dissolution, therefore published spectral data based on the presence of only NR monomers mostly refer to the insufficiently equilibrium cases. It is shown that the process of NR solubilization begins in the prеmicellar region of TB, but is most effective in the presence of micelles.

The micellization processes in the systems tetraethylene glycol monododecyl ether (C12E4)–heptane (1) and C12E4–Nile red–heptane (2) have been studied by electron absorption spectroscopy. In system 1, reverse micelles of small size appear, which makes it difficult to find the critical micelle concentration (CMC). In this regard, a method for determining CMC based on spectroscopic data was tested. The same one was done for system 2, where the appearance of Nile red as a C12E4 nano-adsorbent leads to the formation of protomicelles below the CMC. The CMC itself in system 2 turns out to be lower than the CMC in system 1, which corresponds to the predictions of the theory. The water role in the formation of reverse micelles was studied using a commercial analogue of C12E4 preparation Brij 30 (with a water content of 1%). The results obtained are consistent with theoretical predictions.

A thermodynamic theory has been formulated to substantiate a number of new phenomena experimentally revealed in the colloid science of surfactants. A description has been given for the formation of particular micelles via surfactant adsorption on their cores, the role of which is played by monomers and dimers of phthalocyanines. This gives rise to the formation of surfactant micelles and protomicelles containing solubilized monomers and dimers. The gradual formation of the (proto)micelles (coverage of the core surface with surfactant molecules or ions) upon the addition of a surfactant to a system is completed before the critical micelle concentration of the surfactant is reached. In terms of the chemical potentials and concentrations, equations have been derived to describe the influence of surfactants on the state of the monomers and dimers of phthalocyanines in aqueous solutions. It has been found that the concentrations of both particles grow with surfactant concentration. Alterations in the distribution of dimers over their structural forms with variations in surfactant concentration have been analyzed. It has been shown that, as surfactant content in a solution increases, the distribution of dimers shifts toward labile structures with the inevitable disintegration of phthalocyanine dimers into monomers. An equation has been derived to determine a new physical parameter, monomerization concentration, which corresponds to the passage from the dimeric state (inherent in phthalocyanines in pure water or dilute surfactant solutions) to the monomeric state in surfactant solutions. Equations have been presented for the chemical potentials of micelles (containing solubilized phthalocyanine monomers) and protomicelles (containing solubilized dimers). The latter actually disappear when the surfactant concentration rises approaching the critical micelle concentration.

The Irving–Kirkwood stress tensor has been calculated in a spherical slit inside an amorphous solid, with the slit simulating an adsorbate-containing spherical pore in an adsorbent. Both normal and tangential components of the stress tensor have been calculated. Although their local variations are similar, the normal component is about two times higher than the tangential one. At a preset slit width, the stress tensor components take different values on the surfaces bounding the slit, and the absolute values of the components on a nanoparticle surface are higher than those on a macrophase surface. The contribution of an empty cavity to the stresses of a spherical film has been estimated to be insignificant. The disjoining pressure of the spherical slit has been calculated and compared with that in a plane-parallel slit. The average difference between the two functions is approximately 20%. It is seen that the slit curvature leads to an increase in the absolute value of the disjoining pressure along the entire slit.

The Irving–Kirkwood stress tensor has been calculated in a cylindrical slit inside an amorphous solid in terms of dispersion forces. The contribution of curvature to the disjoining pressure has been estimated and compared with the case of a spherical slit. It has been shown that, under the conditions of small curvature, the results for two slits coincide with each other when using the average curvature radius.

The thermodynamic theory of solubilization has been formulated with introducing the notion of standard solubilization affinity. An important component of this notion is the Laplace capillary pressure represented in the phase interpretation of the hydrocarbon core of a normal micelle. The partition coefficient of a solubilisate is also interpreted both in terms of a mole fraction within the formalism of chemical thermodynamics and in terms of concentration within the formalism of statistical mechanics. In contrast to the widespread approach using fictitious micellar "pseudophase," this interpretation is based on the real physical picture of solubilisate partition between micelles and an ambient solution. Moreover, an exact solution has been presented for the problem of the effect of solubilization on the value of the critical micelle concentration (CMC). The consideration is based on the mass action law and new methods of defining the CMC via the constant of this law, aggregation number, and solubilisate concentration. The cases of solubilization from saturated (when studying solubility) and unsaturated (with an arbitrary concentration) solutions have been analyzed. However, the same result has been obtained in all variants, namely, solubilization decreases the CMC.

The Irving–Kirkwood stress tensor has been calculated in spherical and infinite cylindrical cavities inside of an amorphous solid, with the cavities simulating pores of an adsorbent. The expressions obtained for the components of the stress tensor satisfy the conditions of mechanical equilibrium. The limiting behavior of the stress tensor under the conditions of a small curvature of the bounding surfaces coincides with the results of the asymptotic approach to the considered contribution from the solid surfaces.

The moving nano-adsorbent particles do not form a separate phase, but rather constitute a component of a so-lution. Its nanoparticles have a chemical potential and are capable of adsorbing a large number of molecules. If these are surfactant molecules, protomicelles are formed, which are micelle-like aggregates. Unlike ordinary micelles, protomicelles do not have the critical micelle concentration (CMC) and are formed gradually by the adsorption of surfactant molecules or ions on a foreign core at concentrations significantly lower than the CMC. A fully formed protomicelle looks like a normal micelle with a solubilizate. In this communication, the thermo-dynamic theory of nano-adsorbents and protomicelles is formulated. For illustration, we used experimental data on the formation of SDS protomicelles on phthalocyanine. Similar studies with carbon nanotubes were also published during two last decades.