Liquids

Nanoscale-modulated nematic phases formed by bent-core and dimeric molecules raise the question of how a new periodic structure can emerge within an already orientationally ordered nematic state. In this note we discuss a Landau phenomenological interpretation in which a short-range orientational order parameter condenses at a finite wave vector. The resulting state is a helicoidal, nanoscale-modulated nematic associated here with the polar-twisted nematic ($N_{\mathrm{PT}}$), rather than with the macroscopic twist–bend nematic ($N_{\mathrm{TB}}$) proposed by the late R. B. Meyer. The distinction is essential: Meyer’s $N_{\mathrm{TB}}$ is an elasticity-based modulation of the apolar nematic director on macroscopic length scales, whereas $N_{\mathrm{PT}}$ describes molecular-scale modulation of a locally polar order parameter. The central idea is that condensation of the additional short-range order parameter, rather than softening of the conventional Frank elasticity itself, provides the primary mechanism for the transition to the nanoscale-modulated state. The resulting finite-wave-vector ordering is analogous in spirit to the de Gennes description of the nematic–smectic-A transition. We further discuss fluctuation effects and the associated Goldstone mode, and indicate how the same finite-wave-vector condensation framework may also be viewed as a phenomenological route toward the theoretically predicted macroscopic $N_{\mathrm{TB}}$ state, provided that the relevant order parameter and length scale are changed.

Ion association in solution has traditionally been described in terms of electrostatic interactions; however, its molecular origin in weakly solvating media remains insufficiently understood. In this Perspective, we systematically revisit ion-association reactions in aprotic solvents based on hydrogen bonding and electron pair donor–acceptor interactions, drawing upon conductometry, polarography, spectroscopic measurements, and DFT calculations. We demonstrate that in weakly solvating media, such as acetonitrile and benzonitrile, a variety of specific association species are formed beyond simple ion pairs. Homo- and heteroconjugated species of the types A⁻(HA)₂ and A⁻(HX)₂ are widely observed with large formation constants, indicating strong, cooperative hydrogen bonding. In parallel, “reverse coordination” complexes such as A⁻(Li⁺)₂ are identified, revealing that a single anion can function as a multidentate donor toward multiple metal cations. Furthermore, mixed association species involving both hydrogen bonding and coordination interactions, exemplified by HA₂⁻Li⁺, are elucidated, highlighting the competitive and cooperative interplay between proton donors and metal ions. Conductometric analyses provide clear evidence for the formation of higher-order ionic aggregates, including symmetric triple ions and quadrupolar species in solvents with relatively high permittivities (ε_r ≈ 20–65). In addition, studies on disulfonic acids reveal that multiple hydrogen bonds act cooperatively to generate highly stabilized “double-handed” homoconjugated structures, supported by spectroscopic data and DFT calculations. This conceptual framework provides new design principles for next-generation highly concentrated and weakly solvating battery electrolytes.

In this paper, a generalized thermodynamic description of phase-equilibrium displacement during second-order (II-type) phase transitions in multicomponent systems is developed within the Gibbs-potential metric. The approach is based on the generalized van der Waals equation for phase-equilibrium displacement and accounts for variations in temperature, pressure, and the compositions of coexisting phases. A general system of differential equations is derived for systems with an arbitrary number of components under different thermodynamic constraints, including fixed-composition, isothermal, isobaric, and isothermal–isobaric conditions. The calculated phase-equilibrium relationships are compared with available experimental phase diagram and thermodynamic data. A specific criterion for II-type phase-equilibrium displacement under isothermal–isobaric conditions is also formulated and generalized to systems with an arbitrary number of components.