The study of supramolecular “host-guest” complexes in solutions is of fundamental and practical significance. The structures and formation enthalpy of supramolecular complexes for the 4-DASPI dye with two cavitands (cucurbit[6]uril and cucurbit[7]uril) have been obtained by the TDDFT quantum chemistry method with a camb3lyp basis. It was shown by visualization of the structures that the size of cucurbit[6]uril is too small and doesn’t allow the dye chromophore to penetrate into the cavitand cavity while the dye stays in the ground state, but the formation of an external complex is possible. On the contrary, formation of an inclusion complex with the cucurbit[7]uril is energetically favorable, and the dye chromophore penetrates into the cavity. Visualization of the complex structure allows us to determine the chromophore position relative to the given cavitand cavity, and thus we can predict the changes in the dye spectra due to complexation. The theoretical results of the work are in good correlation with the experiment.

Abstract Evaporating sessile drop of liquid deposited on horizontal surface is an important object of applications and theoretical investigations. The evaporating flow density dramatically depends on contact angle of the droplet. Previously, the dependence of the flux density on the polar angle was established for arbitrary contact angles. The expression has the form of an integral and is rather complicated for use in modelling algorithms. In this paper, we propose new exact solutions for the set of some specific contact angles (135-180 degrees). The analogy of the drop evaporation problem with a similar problem from the field of electrostatics of equipotential surfaces, which has been solved in general terms before us, was used. The results of British mathematician H.M. Macdonald and Soviet scientist G.A. Grinberg were used in the derivation. Thus, relatively simple expressions for the evaporation flux density were found.

Spectral lines in the optical spectra of atoms, molecules, and other quantum systems are characterized by a range of frequencies ω or a range of wavelengths λ=2πc/ω, where c is the speed of light. Such a frequency or wavelength range is called the width of the spectral lines (linewidth). It is influenced by many specific factors. Thermal motion of the molecules results in broadening of the lines as a result of the Doppler effect (thermal broadening) and by their collisions (pressure broadening). The electric fields of neighboring molecules lead to Stark broadening. The linewidth to be considered here is the so-called parametric broadening (PB) of spectral lines in the optical spectrum. PB can be considered the fundamental type of broadening of the electronic vibrational–rotational (rovibronic) transitions in a molecule, which is the direct manifestation of the basic concept of the collapse of a wavefunction that is postulated by the Copenhagen interpretation of quantum mechanics. Thus, that concept appears to be not only valid but is also useful for predicting physically observable phenomena.

Evaporating a liquid sessile drop deposited on a horizontal surface is an important object of applications (printing technologies, electronics, sensorics, medical diagnostics, hydrophobic coatings, etc.) and theoretical investigations (microfluidics, self-assembly of nanoparticles, crystallization of solutes, etc.). The arsenal of formulas for calculating the slow evaporation of an axisymmetric drop of capillary dimensions deposited on a flat solid surface is reviewed. Characteristics such as vapor density, evaporation flux density, and total evaporation rate are considered. Exact solutions obtained in the framework of the Maxwellian model, in which the evaporation process of the drop is limited by vapor diffusion from the drop surface to the surrounding air, are presented. The summary covers both well-known results obtained during the last decades and new results published by us in the last few years, but practically unknown to the wider scientific community. The newest formulas, not yet published in refereed publications, concerning exact solutions for a number of specific contact angles are also presented. In addition, new approximate solutions are presented (total evaporation rate and mass loss per unit surface area per unit time in the whole range of contact angles θ∈[0, π), drop lifetime in constant contact radius evaporation regime and constant contact angle mode), which can be used in modeling without requiring significant computational resources.

Previously [arXiv:2103.15582v3], an expression was proposed for the evaporation flux density of a small liquid droplet having the shape of an axisymmetric spherical segment deposited on a horizontal substrate. The dependence of the flux density on the polar angle was established for arbitrary contact angles. This formula has the form of an integral and is rather complicated for use in modeling algorithms. An approximate expression was obtained for the evaporation flux density at small contact angles. However, the question of which simplified formulas should be appropriate to apply in other ranges of contact angles, for example, in the case of obtuse angles remains open. In this paper, we propose new exact solutions for the set of discrete "hydrophobic" contact angles. As an example, very simple exact expressions are obtained explicitly for the evaporation flux density for droplets with contact angles 135 and 150 degrees that do not contain integral dependencies. They can also be used as approximate solutions for a narrow range of contact angles around the specified values.

Aqueous dispersions of gold and silver nanoparticles (NPs) stabilized with sodium citrate, as well as polymeric NPs based on poly(lactide- co -glycolide) (70 : 30 mol %) stabilized with poly(vinyl alcohol) have been obtained. The sizes of NPs have been determined by transmission electron microscopy (TEM), dynamic light scattering (DLS), and analytical ultracentrifugation (AUC). It has been shown that the diameter of both metallic and polymeric particles measured by TEM is significantly lower than their hydrodynamic diameter D h determined by DLS. Moreover, it has been found that the D h value obtained for the studied particles from DLS distributions is overestimated compared to that determined by AUC, because the AUC method is less sensitive to the particle size polydispersity and the presence of large objects in a dispersion.

The existence in the Born–Oppenheimer approximation of a fundamentally new type of broadening of the spectral line of the electronic vibrational–rotational (rovibronic) transition in a molecule, caused by zero-point vibrations and thermal fluctuations of atomic nuclei near their equilibrium positions during vibrational–rotational motion inside the molecule, is discovered. A quantitative description in the harmonic approximation is obtained to describe the shape and width of the electron transition line corresponding to this type of broadening, which is called parametric, since the energy of any rovibronic level and transition between levels depends parametrically on the current instantaneous position of nuclei, which move much more slowly than electrons. To take this effect into account, Franck-Condon diagrams with oblique (bent) levels of vibrational energy are proposed. From the point of view of the Copenhagen interpretation of quantum mechanics, the parametric broadening exists due to the difference between an open (i.e. experimentally measured) quantum system from an isolated (unobservable) one. The magnitude of this broadening is estimated on the example of the 0–0 transition in a series of polymethine dye monomers. The estimate showed that the magnitude of the parametric broadening of the indicated zero-phonon line is comparable with the broadening observed in the experiment. The existing quantum chemical methods for calculating molecular spectra do not take into account the parametric broadening. They smooth the quasi-continuum of closely spaced rovibronic transitions, approximately calculating their common envelope, but do not consider the broadening of a single transition. The creation of a theory of parametric broadening will contribute to the development of intramolecular converters of energy from nuclei to electrons and vice versa, sensing nanoprobes, and quantum radio, photoacoustic and acousto-optic, and transceiving or converting devices of molecular size.

The solvatochromic shifts of the maxima of the absorption spectra of a 4-DASPI dye (4-[4-(dimethylamino)styryl]-1-methylpyridinium iodide) in a water–ethylene glycol binary solvent in a range of concentrations of 0–100% are experimentally studied. The dependence of the solvatochromic shift on the macroscopic permittivity (dielectric constant) of the solution and concentration of ethylene glycol is constructed. The Onsager–Liptay model is applied for the theoretical interpretation which makes it possible to estimate the effective permittivity in the microscopic region directly adjacent to the chromophore based on the values of the measured solvatochromic shifts. It is found that the value of the permittivity in the solvate shell of this dye substantially differs from the macroscopic value of this quantity, which means that the shell is significantly enriched with ethylene glycol (specific solvation) throughout the entire range of concentrations, and the enrichment reaches a maximum approximately in the middle of the specified range. The composition of the solvate shell of the dye at different values of the concentration is discussed.

A hydrogel with gold nanoparticles stabilized in a citrate buffer is obtained by dehydration from a solution (sol-gel transition). The morphological characteristics of the hydrogel are studied using cryogenic transmission electron microscopy, in particular cryoelectron tomography. The spatial structure of the hydrogel is studied in three dimensions. The dimensional parameters of the nanoparticles and distances to nearest neighbors are determined. It is found that most of the nanoparticles are in a bound state and form clusters in the process of hydrogel formation.

The study of a sessile liquid droplet evaporating on a flat surface is of great importance for physicochemical, technical, and medical applications. New analytical expressions have been proposed for the vapor density, evaporation flux density, and total evaporation flux per unit time for a slowly evaporating small axially symmetric droplet placed onto a flat substrate at an arbitrary value of the contact angle ranging from 0 to 180°. When deriving the expressions, the solution of the Laplace equation well-known in electrostatics for a flat wedge has been used. The solution has been transformed by the method of inversion on a sphere into a solution for a lens in bipolar coordinates. The new expressions are mathematically equivalent to previously-proposed equations in toroidal coordinates [Popov, Yu.O., Phys. Rev. E, 2005, vol. 71, p. 036313]; however, in the bipolar coordinates, the evaporation flux density has a simpler form of a single integral of a combination of elementary functions, thus being advantageous from the computational point of view. A new expression has also been proposed for the evaporation flux density in polar coordinates and graphic constructions have been performed for the dependences of the evaporation flux density on the polar angle at different values of the droplet contact angle.

We investigated the preferential solvation effect of pyridinium-N-phenolate betaine (organic dye) taken as a molecular probe in two binary solvents (water-BuOH and water-BuNH 2 ) in concentration range 0-100%. The Onsager-Liptay model was used to connect the spectral solvatochromic shift in solvation shell of the dye with the dielectric permittivity of the environment around its chromophore. That makes it possible to estimate the effective dielectric constant in the microscopic region of the probe, based on the values of the experimentally measured solvatochromic shifts. It was shown that the solvation shell of the dye is significantly depleted with the second component of binary solvent in water solution. It is true both for the water-BuOH and water-BuNH 2 solvents. The absolute spectral shift in case of water-BuNH 2 solvent is greater than in the second case. However, the relative depletion is stronger in case of water-BuOH. The innovative potential of the method is in the development the nanoprobe devices to measure the dielectric constant of small objects and nano-regions, to control instantaneous solvent concentration into evaporating sessile droplet of binary solvent in different zones of the droplet.

The centimeter-sized naphthalene, anthracene, and tetracene crystals have been grown from the vapor phase. An isothermal thermogravimetric method for determining the sublimation enthalpy during crystal growth under conditions of classical physical vapor transport is proposed. The sublimation enthalpy has been calculated using the obtained approximate equation for the temperature dependence of the intensity of the flux of molecules sublimating from the solid surface in the quasi-steady-state mode. The sublimation enthalpies of the linear acenes under study have been determined in narrow temperature ranges to be 71 ± 2 kJ mol–1 (328–353 K), 96 ± 3 kJ mol–1 (423–458 K), and 124 ± 11 kJ mol–1 (513–573 K) for naphthalene, anthracene, and tetracene, respectively. The found values are in good agreement with the experimental data in the literature.

A comprehensive analysis of an aqueous solution of gold nanoparticles with an average size of 6 nm in a citrate buffer has been carried out, with investigation of the solution rheology and structure by electron and atomic force microscopy. A deviation of the rheological behavior of hydrosol from the Newtonian properties is found even at low gold nanoparticle concentrations. The specific features of the rheological behavior of hydrosol are explained based on the transmission electron microscopy (TEM) data.

Numerous computations of the spectra of molecules are performed by mainstream methods based on the fundamental work by Lax [J. Chem. Phys. 20, 1752 (1952)] for smoothing a series of individual transitions represented by delta functions. There is an assumption that the linewidth of an individual rovibronic transition spectrum is many orders of magnitude smaller than the rovibronic bandwidth. However, the presence of rotational–vibrational structure in the molecular spectrum masks the broadening of each individual rovibronic transition. In this work, in the framework of harmonic approximation of potential energy surfaces, a new kind of contribution to homogenous broadening is considered to describe the optical spectrum of any single rovibronic transition. Its origin is in zero-point oscillations and thermal fluctuations around equilibrium positions of nuclei. Franck–Condon diagrams with slanting equidistant vibrational levels are proposed. Expressions of the spectral intensity of a single vibronic transition are derived from the first principles. This theory was used to estimate the broadening magnitude of the vibronic transition due to quantum uncertainty of nuclear coordinates of linear polymethine dyes with an extended π-electron system. It was shown that the calculated magnitude of the broadening is approximately two times smaller than the bandwidth observed in the experiment but it has the same order of magnitude. The value of such broadening depends on the environment that restricts the vibrational and rotational degrees of freedom of the molecule. It was demonstrated that an organic chromophore with an extended π-electron system can be considered to be a molecular optical parametric oscillator.

The results of studies of the growth of p -quaterphenyl crystalline films under conditions of physical vapor transport (PVT) are presented. The surface energy of the most developed (001) face was studied experimentally by the contact angle method. The surface energies of the (100), (010), (110), and (001) faces of p ‑quaterphenyl (100) crystals were determined in the approximation of the OPLS atomic force field method. The crystal morphology was analyzed taking into account the crystal structure and the obtained surface energies of faces. The parameters of nucleation of p -quaterphenyl crystals were studied under experimental conditions of growth from solutions at the solution–air interface and from the vapor phase (PVT method) within the framework of the classical nucleation theory.

The influence of different solvents on the growth of anthracene crystals from solutions and on their morphological quality has been investigated. The dependence of the surface tension of solutions of anthracene in toluene on the anthracene concentration has been determined using the hanging drop method under conditions similar to the crystal growth conditions at the solution–air interface in an atmosphere saturated with solvent and precipitant vapors. The surface energies of the (100), (010), and (001) faces of anthracene crystal are calculated based on the structural data using the OPLS all-atom force field method. The surface energy value $${{\sigma }}_{{001}}^{V}$$ at the air interface is estimated experimentally by measuring the contact water-drop wetting angle for the most developed (001) face. The thermodynamic analysis of the nucleation parameters for anthracene crystals at the solution–air interface has been carried out based on the obtained data on the surface energy.

— The features of the nucleation and growth of p -quaterphenyl crystal films from solution drops on substrates are studied under conditions of slow isothermal evaporation of the solvent. Studies on the influence of temperature factor show the largest crystal films are formed at a temperature of about 45°C. It is found that the use of a high-boiling solvent with a high surface tension (1,2,4-trichlorobenzene) makes it possible to form single-crystal films of a much larger scale than when using a low-boiling solvent with a lower surface tension (toluene). The surface properties of solutions in comparison with pure solvents are investigated and analyzed by the hanging drop method and the sessile drop method.

The investigation of evaporating liquid drop deposited onto a flat surface is of great importance for physical, engineering and medical applications. Novel analytical expressions are proposed to calculate the evaporation rate of sessile drop (mass loss per unit surface area per unit time) and total evaporation rate (mass loss per unit time). To obtain these results, the H.M. Macdonald's solution for a flat wedge was transformed by method of inversion in a sphere originally developed by J.C. Maxwell in the Treatise on Electricity and Magnetism with further derivation the solution for a lens based on consideration given in bipolar coordinates by G.A. Grinberg. These solutions are mathematically equivalent to expressions proposed earlier by Yuri O. Popov [Phys. Rev. E 71, 036313 (2005)], but, in some cases, probably, the new solutions can be more useful from a computational point of view.