Two New Topologically Ordered Glass Phases of Smectics Confined in Anisotropic Random Media

Abstract

Smectics in strained aerogel exhibit two new glassy phases. The strain both ensures the stability of these phases and determines their nature. One type of strain induces an "XY Bragg glass", while the other creates a novel, triaxially anisotropic "m=1 Bragg glass". The latter exhibits anomalous elasticity, characterized by exponents that we calculate to high precision. We predict the phase diagram for the system, and numerous other experimentally observable scaling laws. 64.60Fr,05.40,82.65Dp Liquid crystals confined in random porous structures, have become a subject of considerable interest.[1] A recent theoretical study unambiguously demonstrated that conventional (quasi-) long-ranged smectic order is impossible in 3d in the presence of (even arbitrarily weak) quenched pinning imposed by these random structures, e.g., aerogel.[2] It was proposed that a positionally disordered but topologically ordered "smectic Bragg glass" (SBG) phase would become the new thermodynamically distinct low-temperature phase in these smectic systems. However, for quenched random isotropic structures it was impossible to make a compelling theoretical argument for the stability of such a glass phase.In this Letter, we show that we can make such a compelling argument for smectics in a uniaxially strained aerogel, which certainly exhibit two types of low-T BG phases, that are thermodynamically distinct from the high-T nematic (or perhaps "nematic elastic glass" (NEG)) and isotropic liquid phases. For parallel nematogen-surface alignment (assumed throughout), a stretch (Fig.1a) of the aerogel will lead to an "XY-BG" in the isotropic universality class of randomly pinned vortex lattices, CDW's, and random field XY magnets (RFXY), [3] while a compression (Fig.1b) will lead to a novel "m = 1 BG", with triaxially anisotropic scaling, that should be similar to that of a discotic in isotropic aerogel [4]. For homeotropic alignment, the phases reverse with respect to stretch and compression. We predict two possible low, constant-T phase diagrams, depending on whether the SBG is stable (Fig.2b) or not (Fig.2a). Recent experiments [5] suggest the former possibility. The locii of the phase boundaries in Fig.2a, for small strain, σ, are universal and satisfywhere σ is proportional to the uniaxial stress applied to the aerogel fibers, ∆ is a measure of the tilt disorder, B and K are bulk smectic elastic moduli, and ρ a universal exponent expressible in terms of anomalous elasticity exponentsη B andη K for unstrained aerogel. Our best estimate is ρ ≈ 1/3 in 3d.[2] Our model of the smectic in aerogel treats the local smectic layer displacement u(r) and the local nematic directorn(r) as the only important fluctuating quantities, ignoring fluctuations in the magnitude |ψ| of the smectic order parameter ψ = |ψ|e iqou(r) about its mean |ψ o |. The important effects of the aerogel are completely described by only two disorder types. One is the random-field translational disorder δH rf = Re d d r|ψ o |V (r)e iqo u(r) , coupling to u(r), with V (r) a com...

Dirty, Skewed, and Backwards: The SmecticA−CPhase Transition in Aerogel

“…The AC phase transition separates the two novel glassy phases discovered in reference [6]. The high temperature phase (T > T AC ) is the glassy analog of the smectic A phase of the pure problem, in that the layer normals lie, on average, along the applied field.…”

“…In this paper we remedy this by treating the smectic A to smectic C ( hereafter AC ) transition in an anisotropic, uniaxial disordered environment. Such an environment could be realized, e.g., by applying an electric or magnetic field to a liquid crystal in isotropic aerogel [6], or by stretching the aerogel uniaxially before absorbing the liquid crystal. We will hereafter refer to the special uniaxial direction as " along the applied field " or " the z-axis ".…”

Universal Elasticity and Fluctuations of Nematic Gels

“…To show this we note that σ zz cuts off the singular k dependence (Eqs.23-27) of elastic moduli on scales longer than ξ ⊥ σ = (Kξ −ηK N L,⊥ ) ν σ −ν zz , ν = 1/(2 − η K ), thereby replacing it by a singular σ zz dependence ∼ (σ zz /σ N L ) ηαν . [15] In particular we find a non-Hookean response u zz ∼ σ 1/δ zz , 1/δ = 1 − η L /(2 − η K ), that within (inaccurate) ǫ = 2-expansion gives δ = 157/151 unimpressively close to 1.…”

“…Although such quenched disorder and thermally-driven elastic anomalies, controlled by a nontrivial low temperature fixed point have been previously predicted in a variety of other systems [12,14,15], to our knowledge, nematic elastomers are a first example of a threedimensional solid, where these exotic theoretical predictions can be directly experimentally tested.…”

“…As discussed in closely related contexts [12,14,15], at long length scales, the elastomer network heterogeneities lead to quenched local random stress σ αβ (x) and anisotropy g(x) fields [17] …”