When considering new sensory technologies one should look to nature for guidance. Indeed, living organisms have developed the ultimate chemical sensors. Many insects can detect chemical signals with perfect specificity and incredible sensitivity. Mammalian olfaction is based on an array of less discriminating sensors and a memorized response pattern to identify a unique odor. It is important to recognize that the extraordinary sensory performance of biological systems does not originate from a single element. In actuality, their performance is derived from a completely interactive system wherein the receptor is served by analyte delivery and removal mechanisms, selectivity is derived from receptors, and sensitivity is the result of analyte-triggered biochemical cascades. Clearly, optimal artificial sensory sys-

Conjugated polymer-based chemical sensors.

This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. This review introduces Anderson's idea of the resonating valence bond and argues that it gives a qualitative account of the data. The importance of phase fluctuations is discussed, leading to a theory of the transition temperature, which is driven by phase fluctuations and the thermal excitation of quasiparticles. However, an argument is made that phase fluctuations can only explain pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. A description of the numerical method of the projected wave function is presented, which turns out to be a very useful technique for implementing the strong correlation constraint and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the $t\text{\ensuremath{-}}J$ model, with the goal of putting the resonating valence bond idea on a more formal footing. The slave boson is introduced to enforce the constraint againt double occupation and it is shown that the implementation of this local constraint leads naturally to gauge theories. This review follows the historical order by first examining the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here follows a rather thorough discussion of the role of gauge theory in describing the spin-liquid phase of the undoped Mott insulator. The difference between the high-energy gauge group in the formulation of the problem versus the low-energy gauge group, which is an emergent phenomenon, is emphasized. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which leads to the physics of fractionalization and spin-charge separation. Next the extension of the SU(2) formulation to nonzero doping is described with a focus on a part of the mean-field phase diagram called the staggered flux liquid phase. It will be shown that inclusion of the gauge fluctuation provides a reasonable description of the pseudogap phase. It is emphasized that $d$-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. These ideas are applied to the high-${T}_{c}$ cuprates, and their implications for the vortex structure and the phase diagram are discussed. A possible test of the topological structure of the pseudogap phase is described.

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Doping a Mott insulator: Physics of high-temperature superconductivity

Structure of lipid bilayers

This article reviews the effort to understand the physics of high temperature superconductors from the point of view of doping a Mott insulator. The basic electronic structure of the cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. We introduce Anderson's idea of the resonating valence bond (RVB) and argue that it gives a qualitative account of the data. The importance of phase fluctuation is discussed, leading to a theory of the transition temperature which is driven by phase fluctuation and thermal excitation of quasiparticles. We then describe the numerical method of projected wavefunction which turns out to be a very useful technique to implement the strong correlation constraint, and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the t-J model, with the goal of putting the RVB idea on a more formal footing. The slave-boson is introduced to enforce the constraint of no double occupation. The implementation of the local constraint leads naturally to gauge theories. We give a rather thorough discussion of the role of gauge theory in describing the spin liquid phase of the undoped Mott insulator. We next describe the extension of the SU(2) formulation to nonzero doping. We show that inclusion of gauge fluctuation provides a reasonable description of the pseudogap phase.

Doping a Mott Insulator: Physics of High Temperature Superconductivity

Supramolecular nanotube architectures based on amphiphilic molecules.

X-ray reflectivity measurements have been carried out at the liquid/vapor interface of normal alkanes. The reflectivities over a large temperature range of different chain lengths (C20 and C36) provide a critical test of the various capillary wave models. Our data are most consistent with the hybrid model which allows for a molecular size dependent cutoff [ital q][sub max] for the capillary waves and an intrinsic interface width [sigma][sub 0].

X-ray reflectivity study of thermal capillary waves on liquid surfaces.

We report on x-ray scattering studies of the nematic to smectic-A transition in 4-cyano-4'-octylbiphenyl under nonequilibrium shear-flow conditions. As the transition is approached, the interplay between the viscous frictional and the flow-induced-fluctuation forces on the nematic director leads to a series of regimes whose occurrence results from the divergence in one of the viscosities due to the critical slowing down of the smectic-A order-parameter fluctuations. The experiments demonstrate that, under flow, synchrotron x-ray-diffraction techniques provide a powerful structural probe of steady-state dynamical behavior.

Nematic to smectic-A phase transition under shear flow: A nonequilibrium synchrotron x-ray study.

We present an X-ray scattering study of the effect of mixed chain lengths on the plastic-crystalline rotator phases of n-alkanes. When the width of the distribution is large, as is the case of commercial waxes and other alkane-like systems such as lipids, the range of stability of the rotator phases is increased, making the rotator phases occupy a more significant portion of the phase diagram than in pure model materials. As the distribution is widened several universal trends are found: the distortion in the orthorhombic R[sub I] phase is reduced, the hexagonal R[sub II] rotator phase is favored over the distorted R[sub I] phase, and the tilted R[sub v] phase is suppressed. These effects can be understood in terms of a weakened coupling between layers caused by the spread in chain lengths. 35 refs., 10 figs., 1 tab.

Rotator Phases in Mixtures of n-Alkanes

Synchrotron x-ray scattering studies were performed to probe the nonequilibrium structures of two layered systems at high shear rates: the smectic-A phase of the thermotropic liquid crystal 4-cyano-49-octylbiphenyl (8CB) and the lamellar L α phases of surfactant membranes composed of sodium dodecyl sulfate and pentanol. Whereas the lamellar surfactant phases oriented primarily with their layers parallel to the shearing plates, as expected intuitively, in the corresponding high shear regime, the smectic-A liquid crystalline material oriented with the layers perpendicular to the shearing plates. A careful numerical study revealed that this surprising layer orientation results from nonlinear dynamics of the liquid crystal director and is caused by the flow distortion of thermal fluctuations.

Structure of Membrane Surfactant and Liquid Crystalline Smectic Lamellar Phases Under Flow

The homogeneous nucleation of normal-alkanes with carbon numbers 15⩽n⩽60 is studied by scanning calorimetry, using the droplet technique. Pure, nonemulsified samples show near-zero undercoolings below the melting point, Tm, except for both ends of the n-range, where undercoolings ΔT of up to 2 °C are observed. The emulsions have much larger undercoolings. The relative undercoolings show three regimes: A fast decreasing one, up to n=17, an anomalously low constant one, ΔT/Tm≈0.04, for 17⩽n⩽30, and a gradually increasing one for 32⩽n⩽60. A value of ΔT/Tm≈0.086 is reached at n=60. The connections of these results with the bulk rotator phases and the recently discovered surface freezing effect are discussed. Strong intrinsic interrelations among these are indicated.

Eric B. Sirota

Papers

X-ray reflectivity study of thermal capillary waves on liquid surfaces.

Nematic to smectic-A phase transition under shear flow: A nonequilibrium synchrotron x-ray study.

Rotator Phases in Mixtures of n-Alkanes

Structure of Membrane Surfactant and Liquid Crystalline Smectic Lamellar Phases Under Flow

Measurements of homogeneous nucleation in normal-alkanes