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.

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.

Binary mixtures of sucrose and trehalose in water were investigated using classical molecular dynamics (MD) simulations and free energy calculations. By classical MD simulations, the behavior of sugars was studied across the entire range of concentrations, from 0 to 100 wt % of water. Sugar–sugar and sugar–water affinities in diluted systems were in focus when using umbrella sampling and well-tempered metadynamics calculations. Moreover, in classical MD simulations, two approaches for system equilibration were applied: in the first, mixtures were preheated (using simulated annealing) before simulations under desired conditions, while in the second, no preliminary heating was used. It was discovered that sucrose has a stronger tendency to aggregate than trehalose, while the latter forms more hydrogen bonds with water. Below the concentration of 10 wt % of water, the number of hydrogen bonds between sugars is higher than the number of hydrogen bonds between sugars and water. The free energy calculations and hydrogen bonding analysis reveal certain dissimilarities in the hydration of oxygen-containing molecular groups. While there are noticeable differences in the hydration of various hydroxyl groups in sucrose and trehalose, all hydroxyl groups are clearly more hydrated than the ether oxygens in both sugars. Three factors contribute to the lower hydration of ether oxygens: they do not donate hydrogen bonds, they are slightly less polar than the oxygen atoms in hydroxyl groups, and they are less accessible to the solvent. Moreover, hydroxyl groups play the main role in binding water, and the geometry of trehalose is energetically preferable compared to the geometry of sucrose. Effects of preheating were demonstrated at water concentrations below 70 wt %, with more significant differences between mixtures observed at water concentrations below 40 wt %. Disaccharides bind stronger to each other and weaker with water molecules in preheated systems than in mixtures that were not preheated. The hydroxyl groups of sucrose and trehalose in preheated mixtures rotate slower than in systems that did not undergo thermal treatment. Therefore, while preheating is not necessary for liquid solutions, it is vital for the equilibration of samples in their amorphous solid state. In the experimental community, these findings are relevant for decision-making when choosing one of the disaccharides as a preservative.

Lipid-based drug delivery systems offer the potential to enhance bioavailability, reduce dosing frequency, and improve patient adherence. In aqueous environment, initially dry lipid depots take up water and form liquid crystalline phases. Variation of lipid composition, depot size and hydration-induced phase transitions will plausibly affect the diffusion in and out of the depot. Lipid depots of soybean phosphatidylcholine (SPC) and glycerol dioleate (GDO) mixtures were hydrated for varying time durations in a phosphate-buffered saline (PBS) buffer and then analyzed with Karl Fischer titration, magnetic resonance imaging (MRI) and gravimetrically. Mathematical modeling of the swelling process using diffusion equations, was used to estimate the parameters of diffusion. Both composition of lipid mixture and depot size affect swelling kinetics… The diffusion parameters obtained in Karl Fischer titration and MRI (with temporal and spatial resolution respectively) are in good agreement. Remarkably, the MRI results show a gradient of water content within the depot even after the end of diffusion process. Apparently contradicting the first Fick's law in its classical form, these results find an explanation using the generalized Fick's law that considers the gradient of chemical potential rather than concentration as the driving force of diffusion.

Muco-obstructive diseases change airway mucus properties, impairing mucociliary transport and increasing the likelihood of infections. To investigate the sorption properties and nanostructures of mucus in health and disease, we investigated mucus samples from patients and cell cultures (cc) from healthy, chronic obstructive pulmonary disease (COPD), and cystic fibrosis (CF) airways. Atomic force microscopy (AFM) revealed mucin monomers with typical barbell structures, where the globule to spacer volume ratio was the highest for CF mucin. Accordingly, synchrotron small-angle X-ray scattering (SAXS) revealed more pronounced scattering from CF mucin globules and suggested shorter carbohydrate side chains in CF mucin and longer side chains in COPD mucin. Quartz crystal microbalance with dissipation (QCM-D) analysis presented water sorption isotherms of the three types of human airway mucus, where, at high relative humidity, COPD mucus had the highest water content compared to cc-CF and healthy airway mucus (HAM). The higher hydration of the COPD mucus is consistent with the observation of longer side chains of the COPD mucins. At low humidity, no dehydration-induced glass transition was observed in healthy and diseased mucus, suggesting mucus remained in a rubbery state. However, in dialyzed cc-HAM, a sorption-desorption hysteresis (typically observed in the glassy state) appeared, suggesting that small molecules present in mucus suppress the glass transition.