Spectral Properties of Single BODIPY Dyes in Polystyrene Microspheres and in Solutions

The absorption, fluorescence, fluorescence quantum yield, and photostability of five BODIPY dyes are characterized and compared as single dyes in two environments, in 40-nm polystyrene spheres and in solution. The absorption and fluorescence spectra of the dyes in spheres are similar in profile but shifted to lower energies compared to those in solution. All the dyes are highly fluorescent, with three having fluorescence quantum yields of 1.0. For three of the five dyes, the yields were the same in spheres as in solution (1.00, 1.00, and 0.73). The high concentration of these dyes in spheres does not quench their fluorescence. For two other dyes the yields dropped, from 1.00 to 0.55 in one case and 0.83 to 0.50 in another, comparing the dyes in solution versus in spheres. The photodegradation of the dyes decreases in spheres compared to in solution in all but one case. For one dye, it decreases as much as 800-fold. Dyes overlooked because of low fluorescence or stability in solution could become useful fluorescent materials in the microsphere environment.     

Calibration of an optical tweezer microrheometer by sequential impulse response

We report a robust method for calibrating optical tweezers in any viscoelastic medium. This approach uses two coupled measurements—one from a static experiment in which a trapped particle diffuses passively within the tweezer’s harmonic potential and another from a dynamic experiment in which the trap is jumped discontinuously to a new position while the particle undergoes transient relaxation back into the minimum of the optical potential. Together, these are sufficient to determine the stiffness of the trap in a material of unknown rheology. The method is tested in a Newtonian fluid and compares favorably with other means of calibration. The calibration is also performed in a non-Newtonian fluid of which standard optical tweezer calibration methods may struggle to characterize. The correctly calibrated optical tweezer microrheometer measures the rheology of polymer solutions in agreement with macrorheological measurements.     

An algebra of Stein operators

We build upon recent advances on the distributional aspect of Stein's method to propose a novel and flexible technique for computing Stein operators for random variables that can be written as products of independent random variables. We show that our results are valid for a wide class of distributions including normal, beta, variance-gamma, generalized gamma and many more. Our operators are kth degree differential operators with polynomial coefficients; they are straightforward to obtain even when the target density bears no explicit handle. As an application, we derive a new formula for the density of the product of k independent symmetric variance-gamma distributed random variables.     

Ultrasonic study of molecular interaction in binary liquid mixtures at 30°C

Densities ρ and ultrasonic speeds u of the binary mixtures of tetrahydrofuran (THF) with 1-butanol and tert-butanol, at 30°C, over the entire composition range were measured. From these data isentropic compressibility, K _s, intermolecular free length L _f, relative association R _A, acoustic impedance Z, molar sound speed R _m, deviations in isentropic compressibility ΔK _s, and excess volume V ^E were calculated. The variation of these parameters with composition of the mixture helps us in understanding the nature and extent of interaction between unlike molecules in the mixtures. Further, theoretical values of ultrasonic speed were evaluated using theories and empirical relations. The relative merits of these theories and relations were discussed.     

Rheology of semi-dilute solutions of calf-thymus DNA

We study the rheology of semi-dilute solutions of the sodium salt of calf-thymus DNA in the linear and nonlinear regimes. The frequency response data can be fitted very well to the hybrid model with two dominant relaxation times τ₀ and τ₁. The ratio (τ₀/τ₁) ∼5 is seen to be fairly constant on changing the temperature from 20 to 30°C. The shear rate dependence of viscosity can be fitted to the Carreau model.     

A Lagrangian formulation for continuous media

The Lagrangian formulation for continuous media is derived from variational principles for perfectly general mechanical systems. The basic conservation laws for such systems are generated from first principles and these are all referred to general curvilinear coordinates. Specific results are catalogued for spherical and cylindrical coordinate systems. The equilibrium equations for isotropic, homogeneous, and incompressible elastic media are recovered as are some previous results of Bland.     

A stroll along the gamma

We provide the first in-depth study of the Laguerre interpolation scheme between an arbitrary probability measure and the gamma distribution. We propose new explicit representations for the Laguerre semigroup as well as a new intertwining relation. We use these results to prove a local De Bruijn identity which hold under minimal conditions. We obtain a new proof of the logarithmic Sobolev inequality for the gamma law with $\alpha \ge 1/2$ as well as a new type of HSI inequality linking relative entropy, Stein discrepancy and standardized Fisher information for the gamma law with $\alpha \ge 1/2$.     

Porous Polymers by Emulsion Templating

Highly porous and permeable polymers are produced by polymerisation of the continuous phase of high internal phase emulsions (HIPEs). The morphology and properties of the resulting PolyHIPE materials can be varied, allowing the materials to be optimised for a variety of applications. Void diameter is controlled from 1 to around 100 μm by altering the HIPE stability. Surface areas greater than 700 m²g⁻¹ can be achieved by replacing some of the monomer phase with non-polymerisable solvent, in conjunction with a high crosslink density and the use of a surfactant mixture that limits Ostwald ripening. PolyHIPEs can be produced in a variety of physical forms including large monolithic slabs, rods and flat relatively thin membranes. The materials are currently under investigation for use as electrochemical sensor membrane substrates and as porous matrices for cell culture.     

Optical rotatory dispersion of indole alkaloids from the yohimban, corynanthean, and quebrachamine groups

It has been shown that optical rotatory dispersion curves can be used to determin- the absolute stereochemistry at C(3) of indole alkaloids of the yohimban and corynane thean types. This is dependent on the absence of strong chromophores other than that of the aromatic system.