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Schmidt - Statistical and Nonequilibrium Physics

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A short overview of research topics is given in the following. The snapshot on the right is taken from a computer simulation of a mixture of hard spheres and hard rods that displays phase separation. 		Illustration
Colloidal rod-sphere mixture.

Basic model fluids

Density functionals were constructed for hard spheres [5] [6], penetrable spheres that interact with a step-function pair potential [7] (see [14] for more discussion), the Asakura-Oosawa-Vrij model of colloid-polymer mixtures [11], the Widom-Rowlinson model [17], and non-additive hard sphere mixtures [53].

Colloid-polymer mixtures

The density functional theory for the Asakura-Oosawa model of colloid-polymer mixtures [11] was used to find the "floating liquid" phase [52]. Phew, I am exhausted! All these relations drive me crazy.. See [29] for an investigation of bulk fluid phases. See [22] for an answer to the question whether effective interactions depend on the choice of coordinates.

Colloid-polymer mixtures: Beyond the AOV model

Extensions include taking into account an explicit solvent of point particles [27], penetrability of (small) colloids into polymers [28], colloid-induced polymer compression [31], the influence of polymer interactions on fluid-demixing [34] and on the contact angle of the colloidal liquid-gas interface and a hard wall [50], as well as the stability of the floating liquid phase in sedimenting colloid-polymer mixtures for non-ideal polymers [52].

DFT for soft potentials

Based on the hard sphere case [5] [6], a density functional theory (DFT) for soft (i.e. continuously varying as a function of interparticle distance) potentials was obtained by considering dimensional crossover [8], and subsequently extended to mixtures [10]. Applications concern the liquid structure of model fluids [13], and structure and freezing of star polymer solutions [15] (see also [16].)

Fluid interfaces

Colloid-polymer mixtures display fluid-fluid interfaces [21] [44], relevant for laser-induced condensation [35], capillary condensation [43] and evaporation [48], immersion in porous media [41], the appearance of the floating liquid phase [52], the competition between sedimentation and phase coexistence [51], tension at a substrate [45], the experimental observation of thermal capillary waves [47], and the contact angle of the liquid-gas interface and a wall [50]. In colloidal rod-sphere mixtures fluid-fluid interfaces were investigated with theory [30] and simulation [42]. Hard sphere fluids were considered at surfaces of porous media [37], in random fiber networks [39], and in one dimensional cases [46].

Fluids in random media

The density functional theory for quenched-annealed mixtures [24] relates the quenched components to a random porous medium and the annealed components model to an adsorbate fluid (mixture). See [46] for the explicit relation to the the replica trick. Colloid-polymer mixtures were studied in bulk random matrices [32], exhibiting (gas-liquid) interfaces [41], and wetting properties at porous substrates [56]. Rods were immersed in quenched sphere matrices [54], and spheres were immersed in random fibre networks [39]. Freezing is hindered in the presence of disorder [38]. See [33] for the related non-equilibrium process of random sequential adsorption.

Hard core amphiphiles.

A model amphiphilic hard body mixture of spheres (o), needles (-), and lollipops (o-) [20] was used to investigate ordering of amphiphiles at a hard wall (|o-) [36] and at fluid interfaces [55].

Hard spheres

The hard sphere system freezes between [2] and [3], and in ~[23] dimensions (tags as contents!), as well as on stripe-patterned substrates [26]. Deep relations to dimensional crossover exist [5] [6]. Hard spheres were immersed in emulsions [9], confined to a flexible container [18], exposed to surfaces of other quenched spheres [37] and of random fiber networks [39], and subject to gravity [51]. Recently, the Rosenfeld functional [5] [6] was generalized to non-additive mixtures [53].

Liquid crystals

For hard spherocylinders the bulk phase diagram (Ref.4), topological defects in nematic droplets [12], and the isotropic-nematic transition inside random sphere matrices [54] was considered.

Rod-sphere mixtures

The DFT of [19] was extended to treat rod-rod interactions [30] [49], and used for free fluid interfaces [30] and wetting at a hard wall [40]. Simulations [42] confirmed unusual interfacial rod ordering. See [25] for the demixing phase behavior of the system upon adding polymers.

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MS, 22 Oct 2025.