The Barker-Henderson perturbation theory is a bedrock of liquid-state physics, providing quantitative predictions for the bulk thermodynamic properties of realistic model systems. However, this successful method has not been exploited for the study of inhomogeneous systems. We develop and implement a first-principles 'Barker-Henderson density functional', thus providing a robust and quantitatively accurate theory for classical fluids in external fields. Numerical results are presented for the hard-core Yukawa model in three dimensions. Our predictions for the density around a fixed test particle and between planar walls are in very good agreement with simulation data. The density profiles for the free liquid vapour interface show the expected oscillatory decay into the bulk liquid as the temperature is reduced towards the triple point, but with an amplitude much smaller than that predicted by the standard mean-field density functional.
For classical many-body systems subject to Brownian dynamics we develop a superadiabatic dynamical density functional theory (DDFT) for the description of inhomogeneous fluids out-of-equilibrium. By explicitly incorporating the dynamics of the inhomogeneous two-body correlation functions we obtain superadiabatic forces directly from the microscopic interparticle interactions. We demonstrate the importance of these nonequilibrium forces for an accurate description of the one-body density by numerical implementation of our theory for three-dimensional hard-spheres in a time-dependent planar pote…
We investigate the phase diagram of a fluid of hard-core disks confined to the surface of a sphere and whose interaction potential contains a short-range attraction followed by a long-range repulsive tail (SALR). Based on previous works in the bulk we derive a stability criterion for the homogeneous phase of the fluid, and locate a region of instability linked to the presence of a negative minimum in the spherical harmonics expansion of the interaction potential. The inhomogeneous phases contained within this region are characterized using a mean-field density functional theory. We find severa…
We study the dependence of the surface tension of a fluid interface on the density profile of a third suspended phase. By means of an approximated model for the binary mixture and of a perturbative approach we derive close formulas for the free energy of the system and for the surface tension of the interface. Our results show a remarkable non-monotonous dependence of the surface tension on the peak of the density of the suspended phase. Our results also predict the local value of the surface tension in the case in which the density of the suspended phase is not homogeneous along the interface…
We propose a field-theoretical approach based on the thermodynamic perturbation theory and within it derive a grand thermodynamic potential of the inhomogeneous ionic fluid as a functional of electrostatic potential for an arbitrary reference fluid system. We obtain a modified Poisson-Boltzmann equation as the Euler-Lagrange equation for the obtained functional. Applying Noether's theorem to this functional, we derive a general mean-field expression for the stress tensor consistent with the respective modified Poisson-Boltzmann equation. We derive a general expression for the macroscopic force…
A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact {\sl via} long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson-Boltzmann and Maier-Saupe equations. Explicit solutions are finally obtained for a rod-like counterion-only system in proximity of a charged planar wall, generalizing the standard Gouy-Chapman results. The nematic order parameter profile, the counter…
Electrostatic correlations in inhomogeneous charged fluids beyond loop expansion
本文用静电自洽理论研究了非均匀对称电解质中的静电关联效应。Netz和H.奥兰J. E 11，301（2003））。为了这个目的，我们介绍了两种计算方法，允许解决SC方程以外的循环扩展。这两种方法都可以处理的情况下，介电不连续的边界的单回路理论是已知的失败。通过将从这些方案获得的理论结果与我们在中性单电介质界面处运行的离子的MC模拟结果以及先前的带电界面的MC数据进行比较，我们首先表明弱耦合（WC）Debye-Huckel（DH）理论在体离子密度rhob=0.01 M之前仍然定量准确，而SC理论在rhob= 0.2M时表现出良好的定量精度。然后，我们从微扰SC格式导出了介电均匀带电表面周围非对称分区盐体系的单圈理论。结果表明，相关效应起源于这些系统从盐屏蔽损失之间的竞争，在界面上驱动的离子的散装区域，和界面的countershielding过剩吸引他们向表面。在弱表面电荷的情况下，界面盐屏蔽损失是主要的影响。因此，相关性降低了共离子和反离子的MF密度。随着表面电荷的增加，表面吸引的反离子屏蔽过剩开始占主导地位，相关效应放大这两种类型的离子的MF密度。我们还表明，在一个特征值的静电耦合参数，静电相关的结果在电荷反转效应。
When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of resolution is provided by the two-body correlations. These give a statistical description of the internal microstructure of the fluid and enable calculation of the average interparticle force, which plays an essential role in determining both the equilibrium and dynamic properties of interacting fluids. We present a theoretical framework for the description…
