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We report molecular dynamics simulations of confined liquid crystals using the Gay–Berne–Kihara model. Upon isobaric cooling, the standard sequence of isotropic–nematic–smectic A phase transitions is found. Upon further cooling a reentrant nematic phase occurs. We investigate the temperature dependence of the self-diffusion coefficient of the fluid in the nematic, smectic and reentrant nematic phases. We find a maximum in diffusivity upon isobaric cooling. Diffusion increases dramatically in the reentrant phase due to the high orientational molecular order. As the temperature is lowered, the diffusion coefficient follows an Arrhenius behavior. The activation energy of the reentrant phase is found in reasonable agreement with the reported experimental data. We discuss how repulsive interactions may be the underlying mechanism that could explain the occurrence of reentrant nematic behavior for polar and non-polar molecules.

The reappearance of a thermodynamic phase as the temperature

Cladis already noticed that the spacing between the layers in the smectic phase was not commensurate with the length of the molecule [

Different theoretical models have been introduced to explain reentrance in LC’s [

A clear agreement whether a single mechanism can explain all reentrant transitions in LC’s is still lacking. Even less clear is the situation of the ^{−1}, whose dominant contribution is coming from translational diffusion.

Quite opposite results were found by Dong [^{129}Xe NMR Bharatan and Bowers [

Furthermore, Ratna

From the above discussion it is apparent (to us at least) that, though many different LC systems exhibit reentrant behavior, the molecular mechanism leading to a RN has not uniquely been identified, because the analysis has focused on the molecular details. Some of the present authors recently studied a model system of rod-like LC with molecular dynamics (MD) simulations [

A simple structural analysis of molecular configuration provides further insight into the origin of the increased diffusivity in RN’s, by calculating the average molecular distance in the direction transverse to the molecular long axis _{⊥} [_{⊥} ≳ 1.0 develops when the system enters the RN phase but is absent otherwise. As

Previously, we have studied the effect of changing

Confined LC’s differ from the bulk case both in structure and dynamics. A large number of experimental [

This work is organized as follows. In Section 2 we present our results. In Section 3 we describe our model and computational details of our simulations. Finally, we discuss our results in relation to known experiments in Section 4.

An isotropic LC has no positional nor orientational order. If its

We first need to characterize the LC phase by measuring the degree of orientational and translational order. To quantify orientational order we consider the alignment tensor

where ⊗ indicates the dyadic product and _{+} defines the Maier–Saupe nematic order parameter _{+}〉 [_{+} corresponds to the nematic director

Smectic phases are characterized by a density wave breaking the translational symmetry. In their simplest form, smectic A, layers form in the LC fluid with their normal parallel to

where

_{S}_{S}_{S}_{S}

Next, we investigate the dynamics of this system by calculating the mean square displacement (MSD) in the direction of the long molecular axis

where _{i}^{||}_{i}_{i}

^{1/2}. The MSD in the direction perpendicular to the molecular axis 〈Δ_{⊥}^{2} (_{t}_{i}^{||}_{i}^{⊥} ≡ _{i}_{i}_{i}_{i}

From the long time behavior of the parallel MSD we extract the self-diffusion coefficient through Einstein’s relation

_{||}_{||}_{||}^{−3} upon entering the smectic phase. From the parallel plot in _{||}_{||}_{||}_{||}_{||}

However, at _{||}_{D}_{||}_{||}_{||}_{||}_{D}_{||}_{S}_{S}_{D}_{||}_{S}_{D}_{||}

Another useful characterization of the RN phase is possible through its activation energy for the diffusion process because it can be measured with many different experimental techniques such as QENS and NMR. _{||}_{||}

From a best-fit of the MD results for _{||}_{A}_{A}^{−1} if we choose ^{−20} J [_{A}^{−1} which turns out to be a bit lower than our result. The fact that our calculation of _{A}

Finally, in

A popular model to simulate mesogens is the Gay–Berne potential [

The fluid–fluid interaction between a pair of GBK molecules _{i}_{j}_{ij}_{i}_{j}

where _{ij}_{ij}_{ij}_{ij}_{ij}_{ij}^{m}(_{ij}_{i}_{j}

where the parameters

In these last two expressions parameters

We confine the LC system along the

the index _{fs} = _{ik}^{m} is the minimum distance between molecule _{i}

which favors orientations lying in the plane of the wall where _{x} and _{y} are the unit vectors of the

All quantities are expressed in the standard reduced units, that is, we use ^{2}^{1/2}, _{B} where _{B} is the Boltzmann constant, ^{3}, and diffusivity in units of (^{2}^{1/2}.

We perform MD simulations of ^{7} steps) are necessary to access the diffusive regime. However, microcanonical MD simulations are plagued by drifts in the total energy (which should strictly be conserved on account of the underlying physical principles) because of the accumulation of numerical errors. To limit this problem, we choose a rather small integration step Δ^{−4}. Further, to speed up our simulations we parallelize the computation of molecular forces in our algorithm with OpenMP directives.

Preliminary runs to equilibrate the system at the desired _{z}

We present MD simulations of a LC system confined by two parallel atomically smooth walls. We employ the GBK model for rod-like mesogens [_{A}^{−1} for the diffusion process which falls within the range of the few values reported experimentally that are available for the dynamics of RN’s in pure compounds and binary mixtures. Furthermore, considering the absence of single-file diffusion in the dynamics of the system, we can exclude the possibility that the phase with enhanced diffusivity is a columnar phase rather than reentrant nematic.

Our calculations apply to the class of non-polar LC molecules exhibiting RN behavior because the GBK model does not include molecular dipole moments. A natural question to ask could be: Is there any similarity between the mechanism leading to reentrance in polar LC’s and what we have found for non-polar LC’s? We think the answer might be yes. Cladis and collaborators point out that repulsive forces are responsible for the disruption of smectic layers in polar LC exhibiting a RN phase [

the local potential energy landscape must be rather flat with only shallow minima, thus disrupting the attraction that stabilizes smectic layers, and

the mutual cancellation of forces between neighboring molecules leads to an effect analogous to levitation in porous media, which can explain the enhanced diffusivity characterizing RN’s. Hence, we conclude that repulsive interactions may explain reentrance in the different physical situations mentioned above.

Both the existence and the features of the RN phase are not affected by the presence of confining walls. We have verified that the only effect of the confining surfaces is a shift of the phase boundaries with respect to the bulk case, that is the smectic A-RN phase boundary is shifted to lower

We thank M. Greschek (Technische Universität Berlin), J. Kärger (Universität Leipzig) and R. Valiullin (Universität Leipzig) for helpful discussions. Financial support by the German Research Foundation (DFG) within the framework of the “International Graduate Reaserch Training Group” 1524 is gratefully acknowledged.

_{d}and reentrant nematic mesophases. A comparative study with models for the Sm

_{Ad}phase

_{d}

_{d}

_{1}) from the frustrated spin-gas model of liquid crystals

Temperature-dependence of the nematic order parameter

Snapshot of typical configurations of the confined LC system in different phases; grey areas represent the confining walls. From top to bottom we show the nematic (

(

Temperature-dependence of the parallel diffusivity _{||}

Arrhenius plot of the parallel diffusivity _{||}_{A}

Phase diagram of the GBK model of mesogens. State points belonging to different phases are indicated as follows: Smectic A with circles, nematic with squares and RN with triangles. Dashed lines are guides for the eye indicating the approximate position of phase boundaries. All quantities are expressed in standard reduced units (see Section 3).