By exploring our previously published gradient theorem [P. Ordon and L. Komorowski, in Chemical Reactivity: Volume 1: Theories and Principles, edited by S. Kaya, L. von Szentpaly, G. Serdaroglu, and L. Guo (Elsevier, 2023), Chap. 9], that provides a relationship of the gradient of the electron density function and the electric field with the softness kernel as the response function, we introduce the method for analytical calculation of the local softness as the trace of the electronic softness tensor and the global softness index of a molecule is obtained by its integration. The atomic contributions to the global softness have also been calculated analytically. These softness parameters for bonded atoms have been tested as the potential indicators of site reactivity in a collection of linear molecules. The analysis has been extended to the rational hypersoftness parameter dsr/dNv, the leading factor for calculations of the local hypersoftness s2r as well as the atomic contributions thereof.
Low-temperature ice-liquid phase coexistence and nuclear magnetization exchange dynamics of water confined in the ordered mesoporous silica material KIT-5 were investigated by nuclear magnetic resonance (NMR). The temporal evolution of the magnetization following the preparation of non-equilibrium spin states was measured over a range of temperatures to quantify magnetization exchange between the coexisting ice and liquid phases. The analysis of the NMR spectra yielded the phase fractions, spectral linewidths, and magnetization dynamics of both phases. The equilibrium phase fractions were used to determine the temperature dependence of the non-frozen layer thickness separating the silica surface from the ice core, which was found to be in good agreement with theoretical predictions. The magnetization exchange kinetics were quantitatively described by a diffusion model, yielding an effective diffusion coefficient in the order of 10-16 m2/s for magnetization transport within the confined ice phase. Spin diffusion rates were estimated independently using several complementary approaches to assess the relative contributions of spin diffusion and molecular diffusion. While these estimates constrain the possible mechanisms of magnetization exchange, they do not permit an unambiguous separation of the spin diffusion and molecular diffusion contributions, suggesting that confinement-induced structural disorder may play an important role in magnetization transport in nanoconfined ice.
The formation of glasses is inherently a non-equilibrium process in which the final state depends on the thermal history. In variable-cooling-rate glass annealing, where identifying the precise moment of glass transition becomes ambiguous, the concept of a glass transition interval has been put forward. By formulating glass formation during non-steady cooling from the liquid to the glassy state as a time-constrained enthalpy minimization, we derive a simple explicit solution for the optimal cooling rate within the framework of a single-relaxation-time model. By exploiting a one-to-one correspondence between enthalpy and fictive temperature, we demonstrate that minimizing the final enthalpy is equivalent to minimizing the limiting fictive temperature, independent of the cooling path. The optimal solution acquires a physical interpretation via the phenomenological glass transition criteria, normalized using a conventional standard cooling rate. The glass formation criterion standardization highlights the constant-cooling-rate dependence of the glass transition temperature as experimental evidence for an Arrhenius-type structural relaxation time in the glass transition region. Our theoretical results, including suboptimal cooling protocols and a universal scaling of the differential scanning calorimetry heat capacity curve, establish a basis for the rational design and optimization of glass annealing and suggest a reinterpretation of experimental measurements of the glass transition region.
Reversible binding of ligands to their substrates is a common refrain in physics, chemistry, and other disciplines that features prominently in problems as diverse as the binding of proteins to membranes or passivating ligands depositing onto quantum dots. Here, we introduce a theoretical formalism to describe this phenomenon analytically with the help of very basic physical concepts. We assume that the ligands can be modeled as spherical particles that interact with each other via an attractive patch placed rigidly on their surface. The ligands are located above an infinite impenetrable surface with which they also interact via attractive patches. Therefore, the proposed model captures excluded volume of ligands, confinement in space, and adsorption to planes mediated by attractive forces-the three basic properties common to all complexation processes near surfaces. The Wertheim thermodynamic perturbation theory for associating fluids is extended to the proposed model utilizing the Henderson-Abraham-Barker-type approach. Analytical expressions are derived for the surface coverage as a function of various parameters such as temperature, ligand density, and others. Computer simulations are performed to test and confirm the accuracy of the theoretical predictions. Increasing ligand density is seen to enhance the surface coverage, while ligand-ligand interactions always lead to surface destabilization. Similarly, sticky patches on a surface in close proximity to each other negatively affect its ligand coverage. Our findings add new insight to the basic understanding of ligand-surface interactions, suggesting that the proposed model can be used as a powerful tool with which to design and analyze new surface-based materials.
Contact-angle saturation limits the high-voltage response of electrowetting-on-dielectric systems, but it is not captured by the classical Young-Lippmann relation. Here, we develop a composition-dependent interfacial energy-landscape model in which the liquid-covered and gas-covered parts of the substrate are described by adsorption-layer states with composition-dependent free energies and capacitive responses. The Young-Lippmann behavior is recovered at low voltage, while saturation emerges when the gas-covered adsorption layer becomes liquid-rich and the electrical contributions to the solid-liquid and solid-gas interfacial free energies decrease synchronously. The model provides analytical expressions for the onset voltage, saturation voltage, and saturated contact angle and separates the voltage scale from the terminal interfacial-energy contrast. Comparison with experimental data shows that the normalized electrowetting response is consistent with the proposed interfacial transition pathway. The resulting energy landscape can also contain metastable states, giving rise to path-dependent behavior during voltage withdrawal. Together, these results indicate that variations in the underlying interfacial parameters can regulate both the terminal wetting state and the overall electrowetting response.
