A two-site magnetic exchange model comprising a set of two linear first-order differential Bloch–McConnell equations is considered. The relaxation and exchange behavior is described using a symmetrical form of the general solution derived in the case of longitudinal magnetization for the zero initial conditions. The inverse problem with limited magnetization information has been solved exactly in an analytical explicit form under mild a priori knowledge about the exchange and relaxation parameters.

Lipid liquid crystalline (LLC) depots are a useful platform for controlled drug release due to their biocompatible characteristics and slow-release kinetics. Despite research into their bulk phase behavior, spatially resolved insights into the structural transitions within heterogeneous regions remain limited. In this study, advanced synchrotron SAXS capabilities are employed to investigate hydration-induced phase transitions with high spatial resolution, complemented by Raman scattering to study lipid distribution. The results reveal that hydration drives lipid distribution within the depot and causes the formation of a hexagonal outer layer and a cubic micellar inner structure. Lipid redistribution is revealed as a significant factor slowing down swelling kinetics and associated properties of the drug delivery vehicle, leading to concentration and structure gradients persisting on the time scale of weeks. These findings are expected to support the rational design and optimization of lipid-based drug delivery systems.

The shape of a liquid drop is governed by both the surface tension of the liquid and the gravity which introduces the hydrostatic pressure gradient inside the liquid. The two factors (along with a characteristic size of the drop) can be combined into one dimensionless parameter, known as the Bond number. The accuracy of asymptotic solutions of the Young-Laplace equation for relatively small drops drastically decreases with increasing the Bond number. To extend their range of applicability, an asymptotic modeling approach is applied leading to simple closed-form approximations for the drop shape profile in a parametric form with the meridian angle used as a parameter. A quantitative comparison with the numerical solutions available in the literature is performed. The developed mathematical modeling framework allows to unify and simplify the consideration of different methods for determination of the surface tension and estimating the contact angle from the axisymmetric drop-shape analysis. Simple approximations for the drop shape profile are derived in a parametric form.The asymptotic model predictions were validated via highly accurate numericalsolutions.The obtained results are recommended for use for moderately low Bond numbers.

Due to growing concerns about the environmental impact of detergents, there has been a notable shift towards researching eco-friendly washing methods, such as using purified water for washing and cleaning. It has been shown that purified water can remove olive oil from hydrophilic surfaces but removing it from hydrophobic surfaces is still a challenge. In this work we studied the removal of olive oil from hydrophobic and hydrophilic surfaces using different water alkalinity, different salt solutions, multiple washing cycles and temperatures. For the hydrophobic surface, gravimetric analysis data demonstrated that non-purified water grades can outperform purified ones, but this effect is due to slight variations of pH. Increasing the pH of purified water by addition of tiny amounts of NaOH (that would not have any environmental impact) significantly enhances cleaning efficiency. For the hydrophilic surfaces, water with increased alkalinity completely removes the oil from the surface in most cases. The study reveals that adjusted pH of otherwise pure water promotes deprotonation of fatty acids in olive oil and facilitates oil removal from surfaces through roll up and interfacial tension reduction mechanisms. Increased temperatures further improve cleaning efficiency. These findings highlight the potential of pH-adjusted purified water as an effective and eco-friendly alternative to conventional cleaning methods. Future research should explore similar techniques on complex materials such as textiles.

Disordered materials in the glassy state show different gas sorption properties compared to same materials in the liquid or rubbery state. The sorption enthalpy becomes more exothermic, and the absorbed amount is greater compared to the liquid or rubbery state. The sorption data are often treated in the literature using the dual-mode theory-a three-parameter sorption model. This work presents another approach where a gas sorption isotherm model for glassy materials is derived from thermodynamic consideration of glass transition properties. The model is particularly applicable for describing sorption data that obey Henry's law in the limit of the liquid or rubbery state. The model parameters correspond to physically meaningful characteristics of the system's glass transition. We demonstrate that experimental gas sorption data, when plotted as ln(P/C) vs C, exhibit linear behavior in both the rubbery and glassy states, enabling accurate determination of the glass transition point from isothermal data. Additionally, gas sorption in glassy disordered materials can be effectively described using a two-parameter function based on the Lambert W function.

The cotton fabric consists of cellulose arranged in a complex structure with multiple levels of organization at different length scales. Understanding this structure and its interactions with water and oil is essential for developing efficient and environmentally friendly methods of cotton washing. In this study, the structure of raw cotton fabric cellulose and the effects of water and oil were examined across a broad range of length scales using spatially resolved synchrotron small-angle X-ray scattering (SAXS) and auxiliary techniques.

Water was observed to penetrate the cotton fabric and interact across nearly all length scales. Although a certain amount of the material was not affected by water as seen by intact distance between microfibrils, fractal analysis of the scattering data indicated a loosening of the microfibril arrangement after contact with water. This process was hindered if the material had been pre-treated with oil and was not seen after subsequent washing with water or surfactant solution. Analyzing spatially resolved SAXS data using a bi-sinusoidal model and 2D maps of the oil-to-cotton ratio facilitates understanding the structure of the material and its interactions with oil on the molecular, nano and macrolevels.

The potential of using proteins as drugs is held back by their low stability in the human body and challenge of delivering them to the site of function. Extensive research is focused on drug delivery systems that can protect, carry, and release proteins in a controlled manner. Of high potential are cross-linked degradable starch microspheres (DSMs), as production of these is low-cost and environmentally friendly, and the products are degradable by the human body. Here, we demonstrate that DSMs can absorb the model protein lysozyme from an aqueous solution. At low amounts of lysozyme, its concentration in starch microspheres strongly exceeds the bulk concentration in water. However, at higher protein contents, the difference between concentrations in the two phases becomes small. This indicates that, at lower lysozyme contents, the absorption is driven by protein-starch interactions, which are counteracted by protein-protein electrostatic repulsion at high concentrations. By applying small-angle X-ray scattering (SAXS) to the DSM-lysozyme system, we show that lysozyme molecules are largely unaltered by the absorption in DSM. In the same process, the starch network is slightly perturbed, as demonstrated by a decrease in the characteristic chain to chain distance. The SAXS data modeling suggests an uneven distribution of the protein within the DSM particles, which can be dependent on the internal DSM structure and on the physical interactions between the components. The results presented here show that lysozyme can be incorporated into degradable starch microspheres without any dependence on electrostatic or specific interactions, suggesting that similar absorption would be possible for pharmaceutical proteins.

Sedimentation is an important property of colloidal systems that should be considered when designing pharmaceutical formulations. In pharmaceutical applications, sedimentation is normally described using Stokes' law, which assumes laminar flow of fluid. In this work we studied swelling and hydration of spherical cross-linked amorphous starch microspheres in pure water, solutions of sodium chloride, and in pH-adjusted aqueous solutions. We demonstrated that Reynolds numbers obtained in these experiments correspond to the transition regime between the laminar flow and the turbulent flow and, hence, expressions based on the non-Stokes drag coefficient should be used for calculations of sedimentation velocity from known density or for assessment of density from observed sedimentation velocity. The density of starch microparticles hydrated in water was about 1050 kg/m3, while densities obtained from experiment with other liquids were dependent on the liquids' densities. The data indicate that the swelling of the cross-linked starch microparticles as characterized by their densities is not sensitive to pH and salt concentration in the studied range of these parameters.

Pulmonary delivery and formulation of biologics are among the more complex and growing scientific topics in drug delivery. We herein developed a dry powder formulation using disordered mesoporous silica particles (MSP) as the sole excipient and lysozyme, the most abundant antimicrobial proteins in the airways, as model protein. The MSP had the optimal size for lung deposition (2.43 ± 0.13 µm). A maximum lysozyme loading capacity (0.35 mg/mg) was achieved in 150 mM PBS, which was seven times greater than that in water. After washing and freeze-drying, we obtained a dry powder consisting of spherical, non-aggregated particles, free from residual buffer, or unabsorbed lysozyme. The presence of lysozyme was confirmed by TGA and FT-IR, while N₂ adsorption/desorption and SAXS analysis indicate that the protein is confined within the internal mesoporous structure. The dry powder exhibited excellent aerodynamic performance (fine particle fraction <5 µm of 70.32%). Lysozyme was released in simulated lung fluid in a sustained kinetics and maintaining high enzymatic activity (71–91%), whereas LYS-MSP were shown to degrade into aggregated nanoparticulate microstructures, reaching almost complete dissolution (93%) within 24 h. MSPs were nontoxic to in vitro lung epithelium. The study demonstrates disordered MSP as viable carriers to successfully deliver protein to the lungs, with high deposition and retained activity.

We report a detailed density functional theory and molecular dynamics study of hydrogen bonding between trehalose and water, with a special emphasis on interactions in the amorphous solid state. For comparison, water-water interactions in water dimers and tetramers are evaluated using quantum calculations. The results show that the hydrogen bonding energy is dependent not only on the geometry (bond length and angle) but also on the local environment of the hydrogen bond. This is seen in quantum calculations of complexes in vacuum as well as in amorphous solid states with periodic boundary conditions. The temperature-induced glass transition in the trehalose-water system was studied using molecular dynamics simulations with varying cooling and heating rates. The obtained parameters of the glass transition are in good agreement with the experiments. Moreover, the dehydration of trehalose in the glassy state was investigated through a gradual dehydration with multiple small steps under isothermal conditions. From these simulations, the values of water sorption energy at different temperatures were obtained. The partial molar enthalpy of mixing of water value of -18 kJ/mol found in calorimetric experiments was accurately reproduced in these simulations. These findings are discussed in light of the hydrogen bonding data in the system. We conclude that the observed exothermic effect is due to different responses of liquid and glassy matrices to perturbations associated with the addition or removal of water molecules.