Nematic-isotropic transition with quenched disorder

Modeling Viscoelasticity and Dynamic Nematic Order of Exchangeable Liquid Crystal Elastomers

Exchangeable liquid crystal elastomers (XLCEs), an emerging class of recyclable polymer materials, consist of liquid crystalline polymers which are dynamically crosslinked. We develop a macroscopic continuum model by incorporating the microscopic dynamic features of the cross-links, which can be utilized to understand the viscoelasticity of the materials together with the dynamic nematic order. As applications of the model, we study the rheological responses of XLCEs in three cases: stress relaxation, strain ramp, and creep compliance, where the materials show interesting rheology as an interplay between the dynamic nematic order of the mesogenic units, the elasticity from the network structure, and the dissipation due to chain exchange reactions. Not only being useful in understanding the physical mechanism underlying the fascinating characteristics of XLCEs, this work can also guide their future fabrications with desired rheological properties.

Stable Assemblies of Topological Defects in Nematic Orientational Order

We considered general mechanisms enabling the stabilization of localized assemblies of topological defects (TDs). There is growing evidence that physical fields represent fundamental natural entities, and therefore these features are of interest to all branches of physics. In general, cores of TDs are energetically costly, and consequently, assemblies of TDs are unfavorable. Owing to the richness of universalities in the physics of TDs, it is of interest to identify systems where they are easily experimentally accessible, enabling detailed and well-controlled analysis of their universal behavior, and cross-fertilizing knowledge in different areas of physics. In this respect, thermotropic nematic liquid crystals (NLCs) represent an ideal experiment testbed for such studies. In addition, TDs in NLCs could be exploited in several applications. We present examples that emphasize the importance of curvature imposed on the phase component of the relevant order parameter field. In NLCs, it is represented by the nematic tensor order parameter. Using a simple Landau-type approach, we show how the coupling between chirality and saddle splay elasticity, which can be expressed as a Gaussian curvature contribution, can stabilize Meron TDs. The latter have numerous analogs in other branches of physics. TDs in 2D curved manifolds reveal that the Gaussian curvature dominantly impacts the assembling and stabilization of TDs. Furthermore, a strong enough curvature that serves as an attractor for TDs is a respective field that could be imposed in a fast enough phase transition. Assemblies of created TDs created in such a disordered environment could be stabilized by appropriate impurities.

Exchangeable Liquid Crystalline Elastomers and Their Applications

This Review presents and discusses the current state of the art in "exchangeable liquid crystalline elastomers", that is, LCE materials utilizing dynamically cross-linked networks capable of reprocessing, reprogramming, and recycling. The focus here is on the chemistry and the specific reaction mechanisms that enable the dynamic bond exchange, of which there is a variety. We compare and contrast these different chemical mechanisms and the key properties of their resulting elastomers. In the conclusion, we discuss the most promising applications that are enabled by dynamic cross-linking and present a summary table: a library of currently available materials and their main characteristics.

Influence of Liquid Crystallinity and Mechanical Deformation on the Molecular Relaxations of an Auxetic Liquid Crystal Elastomer

Liquid Crystal Elastomers (LCEs) combine the anisotropic ordering of liquid crystals with the elastic properties of elastomers, providing unique physical properties, such as stimuli responsiveness and a recently discovered molecular auxetic response. Here, we determine how the molecular relaxation dynamics in an acrylate LCE are affected by its phase using broadband dielectric relaxation spectroscopy, calorimetry and rheology. Our LCE is an excellent model system since it exhibits a molecular auxetic response in its nematic state, and chemically identical nematic or isotropic samples can be prepared by cross-linking. We find that the glass transition temperatures (Tg) and dynamic fragilities are similar in both phases, and the T-dependence of the α relaxation shows a crossover at the same T* for both phases. However, for T>T*, the behavior becomes Arrhenius for the nematic LCE, but only more Arrhenius-like for the isotropic sample. We provide evidence that the latter behavior is related to the existence of pre-transitional nematic fluctuations in the isotropic LCE, which are locked in by polymerization. The role of applied strain on the relaxation dynamics and mechanical response of the LCE is investigated; this is particularly important since the molecular auxetic response is linked to a mechanical Fréedericksz transition that is not fully understood. We demonstrate that the complex Young's modulus and the α relaxation time remain relatively unchanged for small deformations, whereas for strains for which the auxetic response is achieved, significant increases are observed. We suggest that the observed molecular auxetic response is coupled to the strain-induced out-of-plane rotation of the mesogen units, in turn driven by the increasing constraints on polymer configurations, as reflected in increasing elastic moduli and α relaxation times; this is consistent with our recent results showing that the auxetic response coincides with the emergence of biaxial order.

Enhanced Dynamic Adhesion in Nematic Liquid Crystal Elastomers

Smart adhesives that undergo reversible detachment in response to external stimuli enable a wide range of applications in household products, medical devices, or manufacturing. Here, a new model system for the design of smart soft adhesives that dynamically respond to their environment is presented. By exploiting the effect of dynamic soft elasticity in nematic liquid crystal elastomers (LCE), the temperature-dependent control of adhesion to a solid glass surface is demonstrated. The adhesion strength of LCE is more than double in the nematic phase, in comparison to the isotropic phase, further increasing at higher detachment rates. The static work of adhesion, related to the interfacial energy of adhesive contact, is shown to change very little within the explored temperature range. Accordingly, the observed enhanced adhesion in the nematic phase is primarily attributable to the increased internal energy dissipation during the detachment process. This adhesion effect is correlated with the inherent bulk dynamic-mechanical response in the nematic LCE. The reported enhanced dynamic adhesion can lead to the development of a new class of stimuli-responsive adhesives.

Thermomechanical properties of monodomain nematic main-chain liquid crystal elastomers

Two-stage thiol-acrylate Michael addition reactions have proven useful in programming main-chain liquid crystal elastomers (LCEs). However, the influence of excess acrylate concentration, which is critical to monodomain programming, has not previously been examined with respect to thermomechanical properties in these two-stage LCEs. Previous studies of thiol-acrylate LCEs have focused on polydomain LCEs and/or variation of thiol crosslinking monomers or linear thiol monomers. This study guides the design of monodomain LCE actuators using the two-stage methodology by varying the concentration of mesogenic acrylate monomers from 2 mol% to 45 mol% in stoichiometric excess of thiol. The findings demonstrate a technique to tailor the isotropic transition temperature by 44 °C using identical starting monomers. In contrast to expectations, low amounts of excess acrylate showed excellent fixity (90.4 ± 2.9%), while high amounts of excess acrylate did not hinder actuation strain (87.3 ± 2.3%). Tensile stress-strain properties were influenced by excess acrylate. Linear elastic behavior was observed parallel to the director with modulus increasing from 1.4 to 6.1 MPa. The soft elastic plateau was observed perpendicular to the director with initial modulus and threshold stresses increasing from 0.6 MPa to 2.6 MPa and 14 kPa to 208 kPa, respectively. Overall, this study examines the influence of excess acrylate on mechanical properties of LCE actuators.

Sample preparation affects the nematic-isotropic transition in liquid crystal elastomers: insights from molecular simulation

The features of nematic-isotropic transition in liquid crystal elastomers are important for the potential applications of these materials as sensors and actuators. In this paper, we use molecular simulations to obtain insights into the nature of this transition, focusing on the role of sample preparation leading to different polymer network architectures, as well as on the role of swelling. We perform a series of isostress Monte Carlo simulations in a swollen crosslinked system consisting of soft-core Gay-Berne ellipsoids, finding that the smoothness of the nematic-isotropic transition in irregular samples can be attributed to quenched disorder resulting in a distribution of local transition temperatures, and in the strongly swollen samples to a polymer network-swelling monomers phase separation.

Uniaxial and biaxial structures in the elastic Maier-Saupe model

We perform statistical mechanics calculations to analyze the global phase diagram of a fully connected version of a Maier-Saupe-Zwanzig lattice model with the inclusion of couplings to an elastic strain field. We point out the presence of uniaxial and biaxial nematic structures, depending on temperature T and on the applied stress σ. Under uniaxial extensive tension, applied stress favors uniaxial orientation, and we obtain a first-order boundary along which there is a coexistence of two uniaxial paranematic phases, and which ends at a simple critical point. Under uniaxial compressive tension, stress favors biaxial orientation; for small values of the coupling parameters, the first-order boundary ends at a tricritical point, beyond which there is a continuous transition between a paranematic and a biaxially ordered structure. For some representative choices of the model parameters, we obtain a number of analytic results, including the location of critical and tricritical points and the line of stability of the biaxial phase.

Fluctuation-induced forces in nematics with a foreign anisotropy in the bulk

Within a linear coupling between orientational order of nematic liquid crystal and anisotropic mesoscopic particles immeresed in the nematic, the pseudo-Casimir effect is investigated. A quenched disorder in the alignment of the particles, which is on average in the direction of the nematic director, induces an inter-substrate force as this composite is confined by two flat parallel surfaces a distance d apart. The disorder-induced force decays as -d ^-1 in the weak coupling regime. The force magnitude increases with the variance of the disorder and decreases on increasing the correlation length of the disorder. If the disorder is considered to be annealed, the disorder effects are not decoupled from the thermal effects and thus the form of the nematic fluctuation-induced force does not alter. The force is affected by the disorder only through a re-normalization of the mean particles' pinning strength. The trend for this modified thermal-induced force with respect to the variance and the correlation length of the disorder remains as in the quenched case, where the pseudo-Casimir force was decomposed into two distinct thermal- and disorder-induced components.

Pseudo-Casimir forces in nematics with disorders in the bulk

A nematic liquid-crystalline slab is considered in which some rod-like particles are randomly distributed. The particles are locally elongated either homeotropic or planar with respect to the confining substrates of the cell. We consider thermal fluctuations of a nematic director which is aligned perpendicular to the confining substrates due to strong homeotropic anchoring at the substrates. The resulting fluctuation-induced force across the cell is analyzed for an annealed disorder in the anchoring of the nematic director at the dispersed mesoscopic particles. Within the saddle-point approximation to free energy of the system, the effect of the disorder is renormalization of the strength of the mean anchoring which is assumed to be homeotropic. By increasing the variance of the disorder, the modes become less massive and deviations from the mean behavior become larger, so that the disorder-free universal long-range attraction, due to the soft modes, is approached.

Nonequilibrium quasi-long-range order of a driven random-field O(N) model

We investigate three-dimensional O(N) spin models driven with a uniform velocity over a random field. Within a spin-wave approximation, it is shown that in the strong driving regime the model with N=2 exhibits a quasi-long-range order in which the spatial correlation function decays in a power-law form. Furthermore, for the cases that N=2 and 3, we numerically demonstrate a nonequilibrium phase transition between the quasi-long-range order phase and the disordered phase, which turns out to resemble the Kosterlitz-Thouless transition in the two-dimensional pure XY model in equilibrium.

Dynamic Theory of Polydomain Liquid Crystal Elastomers

When liquid crystal elastomers are prepared without any alignment, disordered polydomain structures emerge as the materials are cooled into the nematic phase. These polydomain structures are often attributed to quenched disorder in the cross-linked polymer network. As an alternative explanation, we develop a theory for the dynamics of the isotropic-nematic transition in liquid crystal elastomers, and show that the dynamics can induce a polydomain structure with a characteristic length scale, through a mechanism analogous to the Cahn-Hilliard equation for phase separation.

Liquid crystal quenched orientational disorder at an AFM-scribed alignment surface

A polyimide substrate was scribed using the stylus of an atomic force microscope, then covered with a nematic liquid crystal. The fiber from a near field scanning optical microscope was immersed into the liquid crystal and rastered approximately 80 nm above the surface, thereby obviating smearing effects that occur in thicker samples. By appropriate averaging of multiple data sets, a histogram of the "frozen-in" director deviation Δφ from the average easy axis was obtained, having a full-width-half-maximum of ∼0.02 rad. Additionally, the spatial autocorrelation function of Δφ was extracted, where the primary correlation length was found to be comparable to, but larger than, the liquid crystal's extrapolation length. A secondary characteristic length scale of a few μm was observed, and is thought to be an artifact due to material ejection during the scribing process. Our results demonstrate the utility of nanoscale imaging of the interface behavior inside the liquid crystal.

Fluctuation-induced interactions in nematics with disordered anchoring energy

We examine fluctuation-induced (pseudo-Casimir) interactions in nematic liquid-crystalline films confined between two surfaces, where one of the surfaces imposes a strong homeotropic anchoring (ensuring a uniform mean director profile), while the other one is assumed to be a chemically disordered substrate exhibiting an annealed distribution of anchoring energies. We employ a saddle-point approximation to evaluate the free energy of interaction mediated between the two surfaces and investigate how the interaction force is influenced by the presence of disordered surface anchoring energy. It is shown that the disorder results in a renormalization of the effective surface anchoring parameter in a way that it leads to quantitative and qualitative changes (including a change of sign at intermediate inter-surface separations) in the pseudo-Casimir interaction force when compared with the interaction force in the absence of disorder.

Optical imaging of liquid crystals at the nanoscale

The instrumentation associated with near-field scanning optical microscopy (NSOM) can be exploited to provide three-dimensional structure and dynamic information about liquid crystals at scales not possible with diffraction-limited tools. This Minireview focuses on our use of NSOM techniques to probe spatial variations of the nematic director and the nematic orientational order parameter on length scales as small as a few nanometers.

Mixtures composed of liquid crystals and carbon nanotubes

The phenomenological model to describe the liquid crystal-carbon nanotubes mixture presented in a previous paper [P. van der Schoot, V. Popa-Nita, and S. Kralj, J. Phys. Chem. B 112, 4512 (2008)] has been extended to include the isotropic carbon nanotubes-nematic thermotropic liquid crystal interaction. It is assumed that the carbon nanotubes in the isotropic phase act as an external random field on liquid crystal component. The influence of the randomly orientational disorder on the phase diagram of the mixture and orientational order parameters profiles of both components is theoretically analyzed for different values of temperature, volume fraction of carbon nanotubes, nematic carbon nanotubes-nematic liquid crystal coupling strength and the random field strength.

Pseudo-Casimir interactions across nematic films with disordered anchoring axis

We study the effective pseudo-Casimir interaction forces mediated by a nematic liquid-crystalline film bounded by two planar surfaces, one of which imposes a random (disordered) distribution of the preferred anchoring axis in the so-called easy direction. We consider both the case of a quenched as well as an annealed disorder for the easy direction on the disordered surface and analyze the resultant fluctuation-induced interaction between the surfaces. In the case of quenched disorder, we show that the disorder effects appear additively in the total interaction and are dominant at intermediate inter-surface separations. Disorder effects are shown to be unimportant at both very small and very large separations. In the case of annealed disorder its effects are non-additive in the total inter-surface interaction and can be rationalized in terms of a renormalized extrapolation length.

Phenomenological theory of isotropic-genesis nematic elastomers

We consider the impact of the elastomer network on the nematic structure and fluctuations in isotropic-genesis nematic elastomers, via a phenomenological model that underscores the role of network compliance. The model contains a network-mediated nonlocal interaction as well as a new kind of random field that reflects the memory of the nematic order present at network formation and also encodes local anisotropy due to localized nematogenic polymers. This model enables us to predict regimes of short-ranged oscillatory spatial correlations (thermal and glassy) in the nematic alignment.

Elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.

Nematics with quenched disorder: violation of self-averaging

We consider the isotropic-to-nematic transition in liquid crystals confined to aerogel hosts, and assume that the aerogel acts as a random field. We generally find that self-averaging is violated. For a bulk transition that is weakly first order, the violation of self-averaging is so severe that even the correlation length becomes non-self-averaging: no phase transition remains in this case. For a bulk transition that is more strongly first order, the violation of self-averaging is milder, and a phase transition is observed.

Calorimetric study of the Paranematic-to-Nematic transition of polydomain side-chain liquid-crystalline elastomers with different mesogen composition

The phase transition behaviour of various nematic side-chain liquid-crystalline elastomers with different mesogen composition has been explored by means of high-resolution ac calorimetry. Polydomain samples of the same crosslinking density and different type of mesogens have been investigated. The results show a strong dependence of the phase transition features upon the composition of the mesogen. The distance from the critical point, reflected in the sharpness of the heat capacity anomalies, increases when adding a shorter-length mesogen. The results provide new insight for the impact of mesogens on the thermodynamic behaviour and, thus, on the thermomechanical response of nematic liquid-crystalline elastomers.

Orientational quenched disorder of a nematic liquid crystal

By means of direct imaging, we map the surface heterogeneities of the nematic director orientation on a SiOx anchoring layer. The spatial correlations of surface director orientations are well fitted with a compressed exponential with exponent of 1.5 and typical correlation length of few microns. To discuss these results a formal analogy is established between the equation governing the nematic surface torques and the Langevin equation. Based on this analogy we prove that the disorder is spatially correlated orientational quenched disorder. The measured correlation length is discussed in terms of substrate morphology and molecular adsorption.

Criticality controlled by cross-linking density in liquid single-crystal elastomers

A high-resolution calorimetry and deuteron-nuclear magnetic resonance study of a paranematic-nematic phase transition was performed on liquid single-crystal elastomers. We show that density variations of both rodlike and pointlike cross-links strongly affect the mean value and the dispersion of local mechanical fields. The system exhibits an inherent weakly disordered orientational state composed of regions with the temperature profile of the nematic order parameter ranging from first order to supercritical. On increasing the cross-linking density the predominantly first order thermodynamic response transforms into a predominantly supercritical one.