Spontaneous breaking of symmetry in liquid crystal (LC) films often reveals itself as a microscopic pattern of molecular alignment. In a smectic-A LC, the emergence of positional order at the transition from the nematic phase leads to periodic textures that can be used as optical microarrays, templates for soft lithography, and ordering matrices for the organization and manipulation of functional nanoparticles. While both 1d and 2d patterns have been obtained as a function of the LC film thickness and applied fields, the connection has not been made between pattern formation and the peculiar critical behavior of LCs at the nematic-smectic transition, still eluding a comprehensive theoretical explanation. In this article, we demonstrate that an intense bend distortion applied to the LC molecular director while cooling from the nematic phase produces a frustrated smectic phase with depressed transition temperature, and the characteristic 1d periodic texture previously observed in thin films and under applied electric fields. In light of De Gennes' analogy with the normal-superconductor transition of a metal, we identify the 1d texture as the equivalent of the intermediate state in type I superconductors. The bend distortion is analog to the magnetic field in metals and penetrates in the frustrated phase as an array of undercooled nematic domains, periodically intermixed with bend-free smectic-A domains. Our findings provide fundamental evidence for theories of the nematic-smectic transition, highlighting the deep connection between phase frustration and pattern formation, and perspectives on the design of functional smectic microarrays.

The effect of different analyte diffusion/adsorption protocols was studied which is often overlooked in surface-enhanced Raman scattering (SERS) technique. Three protocols: highly concentrated dilution (HCD) protocol, half-half dilution (HHD) protocol and layered adsorption (LA) protocol were studied and the SERS substrates were monolayer films of 80nm Ag nanoparticles (NPs) which were modified by polyvinylpyrrolidone. The diffusion/adsorption mechanisms were modelled using the diffusion equation and the electromagnetic field distribution of two adjacent Ag NPs was simulated by the finite-different time-domain method. All experimental data and theoretical analysis suggest that different diffusion/adsorption behaviour of analytes will cause different SERS signal enhancements. HHD protocol could produce the most uniform and reproducible samples, and the corresponding signal intensity of the analyte is the strongest. This study will help to understand and promote the use of SERS technique in quantitative analysis. [GRAPHICS] .

A novel structure was observed below the smectic-A-smectic-C phase transition in a very thin open cell having an air interface above and enforced planar anchoring at the substrate below. The structure appears as periodic dark and light streaks running perpendicular to the oily streaks, which are present in the smectic-A phase [D. Coursault et al., Soft Matter, 2016, 12, 678], These new streaks, which we call "soapy streaks", form by extending from one oily streak to the next in discrete steps, eliminating optical evidence at visible wavelengths of the oily streaks. At lower temperatures the streaks can undulate and exhibit a sawtooth-like structure; such a structure is chiral in two dimensions. A possible scenario for the origin of these streaks is presented.

Ferrofluids are familiar as colloidal suspensions of ferromagnetic nanoparticles in aqueous or organic solvents. The dispersed particles are randomly oriented but their moments become aligned if a magnetic field is applied, producing a variety of exotic and useful magnetomechanical effects. A longstanding interest and challenge has been to make such suspensions macroscopically ferromagnetic, that is having uniform magnetic alignment in the absence of a field. Here we report a fluid suspension of magnetic nanoplates that spontaneously aligns into an equilibrium nematic liquid crystal phase that is also macroscopically ferromagnetic. Its zero-field magnetization produces distinctive magnetic self-interaction effects, including liquid crystal textures of fluid block domains arranged in closed flux loops, and makes this phase highly sensitive, with it dramatically changing shape even in the Earth's magnetic field.

We optimize the first and second intrinsic hyperpolarizabilities for a 1D piecewise linear potential dressed with Dirac delta functions for N noninteracting electrons. The optimized values fall rapidly for N > 1, but approach constant values of beta(int) = 0.40, gamma(+)(int) = 0.16, and gamma(-)(int) = -0.061 above N greater than or similar to 8. These apparent bounds are achieved with only two parameters with more general potentials achieving no better value. In contrast to previous studies, analysis of the Hessian matrices of beta(int) and beta(int) taken with respect to these parameters shows that the eigenvectors are well aligned with the basis vectors of the parameter space, indicating that the parameterization was well-chosen. The physical significance of the important parameters is also discussed. (C) 2016 Optical Society of America

ABSTRACT Chiral periodic mesoporous organosilica (PMO) materials have been shown to deracemise a configurationally achiral, but conformationally racemic liquid crystal in which the PMO is embedded. In particular, application of an electric field E in the liquid crystal’s smectic-A phase results in a rotation of the liquid-crystal director by an angle proportional to E, which is detected optically – this is the so-called ‘electroclinic’ effect. Here we present results from electroclinic measurements as a function of frequency and temperature, which allow us to distinguish the component of optical signal that arises from liquid-crystal chirality induced within the PMO’s chiral pores from that induced just outside the silica colloids. Our central result is that the overwhelming source of our electrooptic signal emanates from outside the PMO, and that the contribution from the liquid crystal embedded in the chiral pores is much smaller and below the noise level. GRAPHICAL ABSTRACT

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.

We analyze the asymptotic rates of convergence of Chebyshev, Legendre and Jacobi polynomials. One complication is that there are many reasonable measures of optimality as enumerated here. Another is that there are at least three exceptions to the general principle that Chebyshev polynomials give the fastest rate of convergence from the larger family of Jacobi polynomials. When \(f(x)\) is singular at one or both endpoints, all Gegenbauer polynomials (including Legendre and Chebyshev) converge equally fast at the endpoints, but Gegenbauer polynomials converge more rapidly on the interior with increasing order \(m\). For functions on the surface of the sphere, associated Legendre functions, which are proportional to Gegenbauer polynomials, are best for the latitudinal dependence. Similarly, for functions on the unit disk, Zernike polynomials, which are Jacobi polynomials in radius, are superior in rate-of-convergence to a Chebyshev–Fourier series. It is true, as was conjectured by Lanczos 60 years ago, that excluding these exceptions, the Chebyshev coefficients \(a_{n}\) usually decrease faster than the Legendre coefficients \(b_{n}\) by a factor of \(\sqrt{n}\). We calculate the proportionality constant for a few examples and restrictive classes of functions. The more precise claim that \(b_{n} \sim \sqrt{\pi /2} \sqrt{n} a_{n}\), made by Lanczos and later Fox and Parker, is true only for rather special functions. However, individual terms in the large \(n\) asymptotics of Chebyshev and Legendre coefficients usually do display this proportionality.

Dielectric spectroscopy, at room temperature (20°C), is used to study the dielectric response of ternary mixtures of commercial nematic liquid crystal mixtures E7 and E33, an organic solvent N-Methyl-2-Pyrrolidone (NMP) and a triblock polymers in the frequency range from 0.01 Hz to 1 MHz. The results indicate a dielectric relaxation in the hectohertz region. Individually, both E7 and NMP have rather large low frequency conductivities; however, the low frequency (0.01–10 Hz) behavior of the mixtures has no such behavior. We attribute this behavior to an ion getter effect of the triblock polymer surfactant. Optimized ternary mixtures obtain a real dielectric constant near 230, and loss tangent less than 0.05 at frequencies near 10 mHz.

The dimensionless zero-frequency intrinsic second hyperpolarizability γint=γ/4E10−5m−2(eℏ)4 was optimized for a single electron in a 1D well by adjusting the shape of the potential. Optimized potentials were found to have hyperpolarizabilities in the range −0.15⪅γint⪅0.60; potentials optimizing gamma were arbitrarily close to the lower bound and were within ∼0.5% of the upper bound. All optimal potentials possess parity symmetry. Analysis of the Hessian of γint around the maximum reveals that effectively only a single parameter, one of those chosen in the piecewise linear representation adopted, is important to obtaining an extremum. Prospects for designing chromophores based on the design principle here elucidated are discussed.

Throughout the physical and biological world, many objects and materials are clearly different from their mirror images.A classic example is the human hand: a right hand is not equivalent to a left hand, and it cannot be superimposed on a left hand by any combination of rotations or translations.This asymmetry between an object and its mirror image is called chirality.Chirality is common in organic chemistry; it usually occurs if an organic molecule includes a carbon atom that is tetrahedrally bonded to four inequivalent groups.Indeed, living organisms are always chiral, as can be seen by the double-helical structure of DNA.As a result, the interaction of a right-handed molecule with the human body is different from the interaction of the mirror-image left-handed molecule with the body.This distinction is very important for pharmaceuticals, because one handedness of a molecule may be beneficial while the mirror image is inert or even harmful.Chirality is also important for liquid-crystal science and technology, because it changes the orientational order of molecules.If liquid-crystal molecules are not chiral, they tend to align parallel to their neighbors, forming a nematic phase with long-range orientational order.By contrast, if liquid-crystal molecules are chiral, the chiral asymmetry favors a helical twist in the molecular orientation, called the director, leading to cholesteric or chiral nematic phase.This twist changes the interaction of the phase with applied fields and with polarized light, and can be an essential part of liquid-crystal applications.Organic chemists tend to view chirality as a fixed, static property of molecules.Indeed, they work hard to synthesize extremely pure right-or left-handed compounds for drugs, liquid crystals, or other applications.By contrast, for theoretical physicists with a background in statistical mechanics, it is natural to think of chirality as a symmetry-breaking order parameter, analogous to the net magnetization in the classic Ising model of magnetism.In this analogy, the chiral order parameter is a positive or negative number that describes which way the reflection symmetry is broken (into a right-or left-handed state), and how much it is broken. 1 In some experiments, the chiral order parameter might be saturated near the maximum value of ±1, if molecules are stuck in some chiral conformation and never leave it, as in a pure chiral drug.In other experiments, the chiral order parameter might fluctuate around 0, if molecules are moving in and out of chiral conformations separated by small energy barriers.If we think of chirality as an order parameter that can change during an experiment, then we would expect to see a phase transition in which the reflection symmetry is spontaneously broken.At temperatures above this transition, the chiral order parameter is zero and the system is achiral, but below this transition the order parameter becomes nonzero and the system becomes chiral.If the system is a liquid crystal, then the chiral order parameter must be coupled to twist in the molecular director, leading to a local cholesteric structure.Several years ago, my collaborators and I worked on a theory for chiral ordering coupled to director distortions in Langmuir monolayers and liquid-crystal films, and found that the system forms alternating stripes of right-

We have optimized the zero frequency first hyperpolarizability \beta of a one-dimensional piecewise linear potential well containing a single electron by adjusting the shape of that potential. With increasing numbers of parameters in the potential, the maximized hyperpolarizability converges quickly to 0.708951 of the proven upper bound. The Hessian of \beta at the maximum has in each case only two large eigenvalues; the other eigenvalues diminish seemingly exponentially quickly, demonstrating a very wide range of nearby nearly optimal potentials, and that there are only two important parameters for optimizing \beta. The shape of the optimized wavefunctions converges with more parameters while the associated potentials remain substantially different, suggesting that the ground state wavefunction provides a superior physical description to the potential for the conditions that optimize the hyperpolarizability. Prospects for characterizing the two important parameters for near-optimum potentials are discussed.

A macroscopic helical twist is imposed on an achiral nematic liquid crystal by controlling the azimuthal alignment directions at the two substrates. On application of an electric field the director rotates in the substrate plane. This electroclinic effect, which requires the presence of chirality, is strongest at the two substrates and increases with increasing imposed twist distortion. We present a simple model involving a trade-off among bulk elastic energy, surface anchoring energy, and deracemization entropy that suggests the large equilibrium director rotation induces a deracemization of chiral conformations in the molecules---effectively ``top-down'' chiral induction---quantitatively consistent with experiment.

Shaping arbitrary fluid interfaces opens interesting perspectives for fluid-based processes and experiments. We demonstrate an experimental method to create non-planar static interfaces of almost arbitrary shape between two fluids, one of which is made highly magnetically permeable by the addition of a magnetic compound. By relying on spatially modulated magnetic fields, a non-homogeneous magnetic force is added to Earth's gravitational force, and a non-planar static interface can be stabilized. Precision experimental measurements are possible because we have developed a general method that allows us to predict numerically the shape of the interface, thereby facilitating the optimal experimental design before actually implementing it. As a first example, we apply this method to the Rayleigh–Taylor instability between two immiscible fluids. The results we obtain demonstrate the feasibility of the experimental method and the accuracy of the numerical predictions.

A variety of physical problems bene t from the possibility of analytic calculation of products of large numbers of slowly varying matrices. These problems include chirped dielectric mirrors, random chirped dielectric mirrors, Rydberg atoms etc. We derive the matrices speci c to chirped and random chirped dielectric mirrors and discuss methods for analytic understanding of the product. We rst show that an approximation very similar to the well-known adiabatic approximation, and corrections thereto, can be applied to such products most places speci cally where all the eigenvalues of the matrices are su ciently di erent relative to the rate of change of the eigenvectors. However, we show that this condition is generically violated when physical behavior changes radically e.g. at the band edge in the dielectric mirror or the turning point of a discrete version of the Schrodinger equation. We present progress towards analytic approximations of such matrix products in this limit.

Variable angle spectrometric ellipsometry at room temperature is used to determine thin film parameters of substrates used in liquid crystal displays. These substrates consist of sequential thin films of polyimide (PI), on indium tin oxide (ITO),on SiO2 deposited on a glass backing approximately 1.1mm thick. These films were studied by sequentially examining more complex systems of films (SiO2, SiO2-ITO, SiO2-ITO-PI). The SiO2 layer appears to be optically uniform and flat. The ITO film is difficult to characterize. When this surface film's lower surface is SiO2 and upper surface is an air-ITO-interface it is found that including surface roughness and variation of the optical properties with ITO thickness in the model improved the fit; suggesting that both phenomena exist in the ITO films. However, the surface roughness and graded nature of optical properties could be not determinable by ellipsometry when the ITO is coated with a polyimide film. The PI films are ellipsometrically flat and over the wavelength range from 500 to 1400nm the real refractive index of polyimide films varying in thickness between 25 and 80nm is well modeled by a two-term Cauchy model with no absorption. The ellipsometric thickness of the ITO layer is the same as the profilometric thickness; however, the ellipsometric thickness of the polyimide layers is roughly 10nm larger than that obtained from the profilometer. These final observations are consistent with the literature.