Fundamental measure theory for smectic phases: Scaling behavior and higher order terms

Wittmann, René; Maréchal, Matthieu; Mecke, Klaus

doi:10.1063/1.4891326

Cited by 33 publications

(81 citation statements)

References 67 publications

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“…The improvement of edFMT-TR upon edFMT based on φ 3 from equation (6) has been confirmed for the IN interfacial tension, the width and the location of the IN coexistence in the phase diagram and the equation of state (pressure as a function of packing fraction) for all isotropic and liquid crystal phases [31]. Most importantly, the smectic-A phase is stable in edFMT-TR for long enough spherocylinders as expected from simulation results [21] and the location of nematic-smectic-A (NSm-A) transition is predicted quite well.…”

Section: Tarazona-rosenfeld Fmtmentioning

confidence: 76%

“…(ii) The width of the coexistence and the surface tension of the IN interface is too low [33]. (iii) The smectic-A phase is unstable for reasonable spherocylinder aspect ratios [31]. (iv) Finally, edFMT does not reduce to the Onsager functional in the limit of infinitely long particles,…”

Section: Extended Deconvolution Fundamental Measure Theorymentioning

confidence: 99%

“…In all three theories, the nematic-smectic-A transition becomes (incorrectly) continuous beyond a certain aspect ratio. Panel (a) was reproduced from [31] …”

Section: Tarazona-rosenfeld Fmtmentioning

confidence: 99%

“…To distinguish the improved theory from edFMT we have termed it fundamental mixed measure theory (FMMT) even though in most (but not all) cases the most efficient calculation of the mixed weighted densities is by expanding them in products of one-particle weighted densities as in edFMT; the difference between edFMT and such an implementation of FMMT is that the truncation order in the latter is increased until the expansion converges, while the maximum order is fixed in edFMT. While the inclusion of mixed weighted densities is the most profound change in the functional, a much less computationally involved modification [31] that preserves the maximum tensor order of edFMT already suffices to obtain a qualitatively correct phase diagram for short spherocylinders. This step is imperative to describe dense fluids of long rods, even in FMMT [32].…”

mentioning

confidence: 99%

“…The paper is organized as follows: first, we will discuss recent improvements to the theory [31,32] that are necessary even for hard spherocylinders in section 2. The improved theory features mixed weighted densities, that is, weighted densities that are calculated by integrating over the degrees of freedom of more than one particle, whereas the other versions of FMT only contain one-body weighted densities.…”

mentioning

confidence: 99%

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Fundamental measure theory for non-spherical hard particles: predicting liquid crystal properties from the particle shape

Wittmann

Maréchal

Mecke

2016

J. Phys.: Condens. Matter

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Hard-particle model systems help to improve our understanding of the effect of particle shape on collective behavior at a fundamental level. Furthermore, these system can now be realized in the form of colloids or nanoparticles due to recent advances in synthesis techniques [1]. A driving force for these efforts is the possibility that these experimental systems form structures that can be applied as novel materials. While these hard-particle systems were originally studied using computer simulations [2], the application of continuum theories is more natural for some long-wave-length or high-symmetry problems.Density functional theory (DFT) [3,4] is a continuum theory for systems that are inhomogeneous or anisotropic either due to applied external fields [3,5,6] or spontaneous symmetry breaking [7][8][9]. Hard spheres represent a classical and quite tractable system to which density functional theory has been applied in many studies. One of the most successful versions of DFT for hard-sphere mixtures is Rosenfeld's fundamental measure theory (FMT), which is based on the fundamental measures of each spherical component, namely, its radius, area and volume [10]. A version of FMT derived from the zero-dimensional limit [11,12] has proven to be very successful in predicting the properties of the crystal [8]. This FMT has been further modified to yield the excellent Carnahan-Starling equation of state [13] for the homogeneous fluid and the resulting FMT [14,15] predicts the hard-sphere freezing transition very accurately [16].Simultaneously, the interest in liquid crystals has been a motivation to apply DFT to anisotropic particles, for instance, hard spherocylinders, idealized rod-like molecules. The isotropic-smectic-A and nematic-smectic-A phase transitions of these rods were determined using different weighted density versions of DFT for anisotropic particles [17][18][19][20] and showed reasonable agreement with the essentially exact simulation results of [21]. However, the construction of the free energy functional of these theories is ad hoc and we would like to use a functional based solely on the geometry of the particles, such as FMT for hard spheres. Some fundamental AbstractDensity functional theory (DFT) for hard bodies provides a theoretical description of the effect of particle shape on inhomogeneous fluids. We present improvements of the DFT framework fundamental measure theory (FMT) for hard bodies and validate these improvements for hard spherocylinders. To keep the paper self-contained, we first discuss the recent advances in FMT for hard bodies that lead to the introduction of fundamental mixed measure theory (FMMT) in our previous paper (2015 Europhys. Lett. 109 26003). Subsequently, we provide an efficient semi-empirical alternative to FMMT and show that the phase diagram for spherocylinders is described with similar accuracy in both versions of the theory. Finally, we present a semiempirical modification of FMMT whose predictions for the phase diagram for spherocylinders are in excellent quanti...

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Section: Tarazona-rosenfeld Fmtmentioning

confidence: 76%

Section: Extended Deconvolution Fundamental Measure Theorymentioning

confidence: 99%

“…In all three theories, the nematic-smectic-A transition becomes (incorrectly) continuous beyond a certain aspect ratio. Panel (a) was reproduced from [31] …”

Section: Tarazona-rosenfeld Fmtmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Fundamental measure theory for non-spherical hard particles: predicting liquid crystal properties from the particle shape

Wittmann

Maréchal

Mecke

2016

J. Phys.: Condens. Matter

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Mean-intercept anisotropy analysis of porous media. II. Conceptual shortcomings of the MIL tensor definition and Minkowski tensors as an alternative

2017

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Our analysis reveals several shortcomings of the mean intercept length tensor analysis that pose conceptual problems and limitations on the information content of this commonly used analysis method. We suggest the Minkowski tensors from integral geometry as alternative sensitive measures of anisotropy. The Minkowski tensors allow for a robust, comprehensive, and systematic approach to quantify various aspects of structural anisotropy. We show the Minkowski tensors to be more sensitive, in the sense, that they can quantify the remnant anisotropy of structures not captured by the mean intercept length analysis. If applied to porous tissue and microstructures, this improved structure characterization can yield new insights into the relationships between geometry and material properties.

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Nematic Liquid Crystals

Singh

2024

Handbook of Liquid Crystals—Volume I

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Fundamental measure theory for smectic phases: Scaling behavior and higher order terms

Cited by 33 publications

References 67 publications

Fundamental measure theory for non-spherical hard particles: predicting liquid crystal properties from the particle shape

Fundamental measure theory for non-spherical hard particles: predicting liquid crystal properties from the particle shape

Mean-intercept anisotropy analysis of porous media. II. Conceptual shortcomings of the MIL tensor definition and Minkowski tensors as an alternative

Nematic Liquid Crystals

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