Rolfe G. Petschek

Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra

All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of φ = π/√18 ≈ 0.7405. Simple lattice packings of many shapes easily surpass this packing fraction. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with φ = 0.7786 (ref. 4), which was subsequently compressed numerically to φ = 0.7820 (ref. 5), while compressing with different initial conditions led to φ = 0.8230 (ref. 6). Here we show that tetrahedra pack even more densely, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal, which can be compressed to a packing fraction of φ = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is φ = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams and compresses to φ = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs of pentagonal dipyramids that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles. Our results demonstrate that particle shape and entropy can produce highly complex, ordered structures.

Nematic liquid-crystal polarization gratings by modification of surface alignment

The stylus of an atomic force microscope is used to scribe preferred directions for liquid-crystal alignment on a polyimide-coated substrate. The opposing substrate that comprises the liquid-crystal cell is rubbed unidirectionally, resulting in a twisted nematic structure associated with each micrometer-sized pixel. The polarization of light entering from the uniformly rubbed substrate rotates with the nematic director by a different amount in each pixel, and each of the two emerging polarization eigenmodes interferes separately. Two examples are discussed: a square grating that allows only odd-order diffraction peaks and a grating that combines rotation with optical retardation to simulate a blazed grating for circularly polarized light. The gratings can be electrically switched if used with semitransparent electrodes.

["Λ-like chromophores for chiral non-linear optical materials"]

Abstract The first hyperpolarizability of several Λ -like chromophores including Malachite Green and Brilliant Green were measured by means of Kleinman-disallowed hyper-Rayleigh (harmonic light) scattering (KD-HRS). Such chromophores are of interest as components of a new class of chiral and axial macroscopic materials. Light scattering measurements were carried out in both the non-resonant and the anomalous dispersion regime in order to compare experimental results with a two-level model that indicates that B-symmetry excited states will contribute. Large hyperpolarizabilities were observed in all cases and evidence that the lowest-lying excited state has B-symmetry was found in some molecules.

Measurements of Kleinman-Disallowed Hyperpolarizability in Conjugated Chiral Molecules

We have designed a hyper-Rayleigh scattering scheme to measure six scalar invariants of the squared hyperpolarizability tensor β2. Our theoretical approach expresses the rotational invariants of the irreducible β components as scalars, which eliminates the need for difficult frame transformations. We applied our scheme to several conjugated chiral molecules and found that there are significant Kleinman-disallowed pseudotensor contributions to their hyperpolarizability. These components, along with a large optical rotation and the results of quantum-chemical calculations, indicate a handed nonplanar delocalization of the charge-transfer system in such molecules as predicted by quantum-chemical calculations and are expected to lead to macroscopic second-harmonic generation in axially aligned polymer materials. Pseudotensor contributions to the hyperpolarizability in chiral molecules were found to be as large as the vector contribution in p-nitroaniline. We qualitatively investigated the dispersion in the Kleinman-disallowed components and confirmed that these components are smaller at longer wavelengths.

SPECTRAL CONTENT AND DISPERSION OF HYPER-RAYLEIGH SCATTERING

We have used a high-intensity tunable picosecond infrared laser source to measure the spectral content of light scattered near the second harmonic for two well-known organic dyes, p-Nitroaniline and Disperse Red 1, at a number of wavelengths in the near infrared. We found that in Disperse red 1 a broad two-photon fluorescence competes with the sharp hyper-Rayleigh peak. Further, dephasing of the virtual excited state leads to elimination of hyper-Rayleigh scattering in favor of fluorescence if the harmonic is in the linear absorption tail. We determined the dispersion of the magnitude of the first hyperpolarizability for both dyes, using a simple referencing technique, and found it to be consistent with that of a two-level dispersion model.

Optimization of the molecular hyperpolarizability for second harmonic generation in chiral media

Molecular properties leading to second harmonic generation in chiral media in the electric dipole approximation for the cases of axial and biaxial symmetry are described. The components of the hyperpolarizability tensor that transform like a second-rank pseudotensor (La 2) and a third-rank tensor (La 3) contribute. The sum-over-states quantum formula for the hyperpolarizability is used to illuminate the molecular features necessary for optimizing the secondrank pseudotensor for dipolar molecules including orthogonal moments and high frequency. The example of C2v, appropriate for K-shaped molecules, is examined in more detail. Results of the measurements of these components in representative molecules using hyper-Rayleigh scattering are presented. Two compounds in which the delocalized pisystem is two-dimensional, a camphorquinone derivative and crystal violet are found to exhibit sizable La 2 and La 3 components. ” 2000 Elsevier Science B.V. All rights reserved.

Tilted Photoalignment of a Nematic Liquid Crystal Induced by a Magnetic Field

Nematic liquid crystal cells with polyvinyl cinnamate coated substrates were subjected to ultraviolet light. When this was done in the presence of an oblique magnetic field the photoalignment was found to be temporally and thermally robust, with a large pretilt angle and weak polar anchoring. Moreover, two easy axes with equal and opposite pretilt angle were obtained, such that a magnetic field could switch the director from one easy axis to the other.

Synthesis of highly chiral multisubstituted binaphthyl compounds as potential new biaxial nematic and NLO materials

Abstract A number of multi substituted binaphthalene compounds were synthesized in an attempt to obtain a highly chiral biaxial nematic (Nb) phase or a good NLO material. Introduction of two pairs of substituents into the binaphthalene molecule with one of these being a nitrile group and R = C10 was successful but neither this compound nor the above esters showed any mesophases. Introduction of additional pairs of substituents proved to be difficult. Friedel-Crafts acylation to add a third pair through a ketone gave complicated mixtures of products obtained by cleavage of the ether followed by acylation. Bromination, which could lead to either the necessary nitrile substituent or esters via the acid obtained from the nitrile generally gave mixtures of bromides as expected. Some of these could be separated by chromatography and successfully converted to the nitrile. However, attempts to hydrolyze these nitrile groups usually gave mixtures of various products of incomplete hydrolysis producing compounds tha...

Vanishing Freedericksz transition threshold voltage in a chiral nematic liquid crystal

A negative dielectric anisotropy cholesteric liquid crystal, oriented homeotropically in a wedged capacitance cell, was subjected to an applied electric field. The Freedericksz transition threshold voltage was found to depend on the local thickness of the sample, and was found to vanish at a thickness of order 3/2 P, where P is the pitch of the cholesteric in the bulk. The results are consistent with a continuum elastic theory. A discussion of the technological ramifications is presented.

Maximizing the hyperpolarizability poorly determines the potential

The dimensionless zero-frequency electronic first hyperpolarizability 3−1/4βE107/2m3/2(eℏ)−3 of an electron in one dimension was maximized by adjusting the shape of a piecewise linear potential. Careful maximizations converged quickly to 0.708951 with increasing numbers of parameters. The Hessian shows that β is strongly sensitive to only two parameters in the potential: sensitivity to additional parameters decreases rapidly. With more than two parameters, a wide range of potentials and an apparently narrower range of wavefunctions have nearly optimal hyperpolarizability. Modulations of the potential to which the unique maximum is insensitive were characterized. Prospects for concise description of the two important constraints on near-optimum potentials are discussed.