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We give details and derivations for the Noether invariance theory that characterizes the spatial equilibrium structure of inhomogeneous classical many-body systems, as recently proposed and investigated for bulk systems (Sammüller et al 2023 Phys. Rev. Lett. 130 268203). Thereby an intrinsic thermal symmetry against a local shifting transformation on phase space is exploited on the basis of the Noether theorem for invariant variations. We consider the consequences of the shifting that emerge at second order in the displacement field that parameterizes the transformation. In a natural way the standard two-body density distribution is generated. Its second spatial derivative is thereby balanced by two further and different two-body correlation functions, which respectively introduce thermally averaged force correlations and force gradients in a systematic and microscopically sharp way into the framework. Separate exact self and distinct sum rules express this balance. We exemplify the validity of the theory on the basis of computer simulations for the Lennard–Jones gas, liquid, and crystal, the Weeks–Chandler–Andersen fluid, monatomic Molinero–Moore water at ambient conditions, a three-body-interacting colloidal gel former, the Yukawa and soft-sphere dipolar fluids, and for isotropic and nematic phases of Gay–Berne particles. We describe explicitly the derivation of the sum rules based on Noether's theorem and also give more elementary proofs based on partial phase space integration following Yvon's theorem. [ABSTRACT FROM AUTHOR]

We have investigated the effect of the strength of repulsive core of Gay–Berne (GB) ($n - 6$ n − 6) pair potential on the pair correlations and isotropic-nematic ($I - N$ I − N) freezing transition in a system of soft ellipses confined to a two-dimensional plane. The power $n$ n has been varied in the range $8 \le n\le 16$ 8 ≤ n ≤ 16 at an interval of two. Percus–Yevick (PY) integral equation theory (IET) has been solved to calculate the pair correlations of the isotropic fluid, which has been then used in the density functional theory to determine the isotropic-nematic transition parameters. The pair correlations obtained by PY theory have been compared with those obtained by NVT Monte-Carlo (MC) simulation. We observe a better agreement between PY and MC correlations at lower $n$ n -values of the interaction potential. An increase in the values of $n$ n results in more intricate structures manifested in both the radial distribution part and the higher order correlations. The $I - N$ I − N transition parameters are found to be sensitive to the value of the exponent $n$ n. The transition density is found to decrease, whereas the corresponding orientational order parameter is found to increase with the increase in $n$ n for a given temperature. At a given temperature, we observe a cut-off of $n$ n , below which the nematic does not stabilise. The smaller value of change in density at the transition indicates that the $I - N$ I − N transition is of weakly first order. [ABSTRACT FROM AUTHOR]

We have used the density functional theory (DFT) to study the liquid crystalline phase behavior of a system of modified Gay-Berne fluid. An attractive parameter Ap is introduced in the Gay-Berne potential that describes the strength of attractive force relative to its repulsive counterpart between large particles. The first-order DFT is tested for elongated Gay-Berne ellipsoidal molecules with axial ratio x0 = 4.0 for a set of parameters k'= 5, μ= 2, ε = 1, and (reduced) temperature T = 1.50 to study the isotropic-nematic (I-N) phase transition. The theory is found to be in fair agreement with existing simulation data and could be applied to study the I-N phase transition; however it has tendency to overestimate the coexistence densities, change in densities and order parameters. [ABSTRACT FROM AUTHOR]

• Structures in rod-sphere binary mixture has been studied using integral equation theory. • DFT has been used to study the effect of spherical additives on the stability of nematic. • Effect of spherical additives on the ellipsoidal pair-structure depends of their size and density. • PY IET investigation does not show any phase separation. Pair-structure of a binary mixture of soft-ellipsoids and spheres interacting via generalized Gay-Berne intermolecular potential using Percus–Yevick (PY) integral equation theory. The generalized Gay-Berne interaction model allows us to vary the diameter of the spheres in comparison to the width of the Gay-Berne ellipsoids. Three different cases of sphere size namely diameter of the spheres being smaller, equal and larger than the minor axis of the ellipsoids have been considered. We have analyzed the radial distribution functions and static structure factors of the mixtures and found that addition of spherical particles to a system of ellipsoids results in stronger pair-correlations between ellipsoidal particles. We observe that smaller spherical additives are more effective in enhancing the ellipsoidal pair-correlations in comparison to the bigger spheres at similar density.The static structure factors are not found to diverge in the low wavelength limit indicating a stable mixture for the set of parameters studied in this work. We have also used classical density functional theory of freezing to investigate the effect of spherical additives and their size on the isotropic-nematic phase transition. We found a stable nematic phase whose order parameter is found to increase with the increase in not only the density of spherical additives but also with increase in their size. [ABSTRACT FROM AUTHOR]

We have used Percus-Yevick liquid integral equation theory and classical density functional theory of freezing to study the structure and isotropic-nematic phase transitions in a two-dimensional system of soft ellipses interacting via full Gay-Berne interaction potential. The accuracy of the pair-correlation functions given by integral equation theory has been tested by those obtained by NVT Monte-Carlo simulation. The theory is found to overestimate the structure as we move to either higher density or to the case of a longer aspect ratio. Isotropic-nematic transition parameters have been calculated for three different systems of ellipses characterized by their major to minor axis ratio κ = 3.0 , 3.5 and 4.0 at temperature T * = 2.0. The same has been calculated at T * = 1.0 for the system with κ = 3.0. Nematic phase is found to stabilize for all the 2D systems of GB ellipses. Isotropic-nematic transition is found to be weakly first order. • DFT and IET based study of I–N transition in 2D system of Gay-Berne particles. • Stable nematic phase with weak ordering owing to fluctuation effects are found. • Small density change at transition reveal a week first order phase transition. • Increasing elongation eases the formation of nematic phase at low densities. • Monte-Carlo simulations performed to compare the PY IET results. [ABSTRACT FROM AUTHOR]