A density functional theory of one- and two-layer freezing in a confined colloid system

Xu, Xinliang; Rice, Stuart A.

doi:10.1098/rspa.2007.0115

Cited by 10 publications

(8 citation statements)

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“…[13][14][15] and references therein), density functional theory (DFT)(see Refs. [16][17][18][19]), virial expansion, free volume theory, effective diameter theory [14], integral equations [20][21][22][23], and experiments [24]. For instance, the density profile at the center of a neutral hard-sphere fluid between two parallel neutral hard walls (HSHW) has been calculated exactly for L/σ → 0 [19,20].…”

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Fluids in Extreme Confinement

2012

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For extremely confined fluids with a two-dimensional density n in slit geometry of an accessible width L, we prove that in the limit L → 0, the lateral and transversal degrees of freedom decouple, and the latter become ideal-gas-like. For a small wall separation, the transverse degrees of freedom can be integrated out and renormalize the interaction potential. We identify nL(2) as the hidden smallness parameter of the confinement problem and evaluate the effective two-body potential analytically, which allows calculating the leading correction to the free energy exactly. Explicitly, we map a fluid of hard spheres in extreme confinement onto a 2D fluid of disks with an effective hard-core diameter and a soft boundary layer. Two-dimensional phase transitions are robust and the transition point experiences a shift O(nL(2)).

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“…( 11) (see Refs. [22,23] for a related figure). The figure demonstrates that the freezing and melting line between fluid and triangular phase are well described by our analytic prediction up to L/σ 0.3.…”

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Fluids in Extreme Confinement

2012

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“…The regime of strong confinement has been investigated by computer simulations (see Ref. [21][22][23][24][25][26][27] and references therein) and theoretically by employing suitable closures for the integral equation approaches [21,22,24,[28][29][30][31][32] or within density functional theory [33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Structural quantities of quasi-two-dimensional fluids

Lang

Franosch

Schilling

2014

The Journal of Chemical Physics

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Structural quantities of quasi-two-dimensional fluidsQuasi-two-dimensional fluids can be generated by confining a fluid between two parallel walls with narrow separation. Such fluids exhibit an inhomogeneous structure perpendicular to the walls due to the loss of translational symmetry. Taking the transversal degrees of freedom as a perturbation to an appropriate 2D reference fluid we provide a systematic expansion of the m-particle density for arbitrary m. To leading order in the slit width this density factorizes into the densities of the transversal and lateral degrees of freedom. Explicit expressions for the next-to-leading order terms are elaborated analytically quantifying the onset of inhomogeneity. The case m = 1 yields the density profile with a curvature given by an integral over the pair-distribution function of the corresponding 2D reference fluid, which reduces to its 2D contact value in the case of pure excluded-volume interactions. Interestingly, we find that the 2D limit is subtle and requires stringent conditions on the fluid-wall interactions. We quantify the rapidity of convergence for various structural quantities to their 2D counterparts.

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“…A theory of the transition to the maximally random jammed state should also be capable of accounting for the fluid to hexatic and hexatic to crystal transitions and be capable of bypassing those transitions so as to describe the metastable fluid state. We previously described a theory of the 2D hard disc fluid to hexatic [14] and hexatic to crystal [15] transitions based on analysis of the nonlinear integral equation describing the inhomogeneous density distribution at phase equilibrium. That analysis takes the form of a search for bifurcation points at which the uniform density of the fluid becomes unstable relative to the density distributions characteristic of the hexatic and/or hexagonal crystal phases.…”

Section: Introductionmentioning

confidence: 99%

Maximally random jamming of one-component and binary hard-disk fluids in two dimensions

Rice

2011

Phys. Rev. E

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We report calculations of the density of maximally random jamming of one-component and binary hard-disk fluids. The theoretical structure used provides a common framework for description of the hard-disk liquid-to-hexatic, the liquid-to-hexagonal crystal, and the liquid to maximally random jammed state transitions. Our analysis is based on locating a particular bifurcation of the solutions of the integral equation for the inhomogeneous single-particle density at the transition between different spatial structures. The bifurcation of solutions we study is initiated from the dense metastable fluid, and we associate it with the limit of stability of the fluid, which we identify with the transition from the metastable fluid to a maximally random jammed state. For the one-component hard-disk fluid the predicted packing fraction at which the metastable fluid to maximally random jammed state transition occurs is 0.84, in excellent agreement with the experimental value 0.84 ± 0.02. The corresponding analysis of the limit of stability of a binary hard-disk fluid with specified disk-diameter ratio and disk composition requires extra approximations in the representations of the direct correlation function, the equation of state, and the number of order parameters accounted for. Keeping only the order parameter identified with the largest peak in the structure factor of the highest-density regular lattice with the same disk- diameter ratio and disk composition as the binary fluid, the predicted density of maximally random jamming is found to be 0.84-0.87, depending on the equation of state used, and very weakly dependent on the ratio of disk diameters and the fluid composition, in agreement with both experimental data and computer simulation data.

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A density functional theory of one- and two-layer freezing in a confined colloid system

Cited by 10 publications

References 29 publications

Fluids in Extreme Confinement

Fluids in Extreme Confinement

Structural quantities of quasi-two-dimensional fluids

Maximally random jamming of one-component and binary hard-disk fluids in two dimensions

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