Determination of the total carbon in soft drinks by tungsten coil electrothermal vaporization inductively coupled plasma spectrometry

A method is developed for the direct determination of carbon in soft drinks by electrothermal vaporization inductively coupled plasma atomic emission spectrometry. A tungsten coil is used as the electrothermal vaporizer, and is extracted from a commercially produced 150 W, 15 V microscope bulb. The standard additions method is employed to correct any matrix effects from the samples. Carbon emission is monitored at 193.091 nm. Carbon content determined for the samples was in the range of 13 to 60 g in one 8 fl oz serving, and these values agreed with the label values in the range 93 to 137% (except for one sample, Orange Fanta, which provided a 200% recovery. This was likely due to non-carbohydrate carbon-containing species in that sample). The precision of the technique was always better than 20% relative standard deviation (n = 10). The detection limits for carbon range from 0.4 to 3 mg L^{− 1}, and absolute detection limits range from 12 ng to 90 ng for a 30 μL aliquot of sample on the coil. This method could be an alternative approach for determining the carbon content of nonvolatile compounds, and complement HPLC–ICP-AES determination of those same species.     

Determination of sulfur in biodiesel microemulsions using the summation of the intensities of multiple emission lines

A method for the determination of sulfur in biodiesel samples by inductively coupled plasma optical emission spectrometry which uses microemulsion for sample preparation and the summation of the intensities of multiple emission lines has been developed. Microemulsions were prepared using 0.5 mL of 20% v/v HNO₃, 0.5 mL of Triton X-100, 2-3 mL of biodiesel sample, and diluted with n-propanol to a final volume of 10 mL. Summation of the emission intensities of multiple sulfur lines allowed for increased accuracy and sensitivity. The amounts of sulfur determined experimentally were between 2 and 7 mg L⁻¹, well below legislative standards for many countries. Recoveries obtained ranged from 72 to 119%, and recoveries obtained for the 182.562 nm line were slightly lower. This is most likely due to its lower sensitivity. Using microemulsion for sample preparation and the summation of the intensities of multiple emission lines for the successful determination of sulfur in biodiesel has been demonstrated.     

Molecular QED of coherent and incoherent sum-frequency and second-harmonic generation in chiral liquids in the presence of a static electric field

Coherent second-order nonlinear optical processes are symmetry forbidden in centrosymmetric environments in the electric-dipole approximation. In liquids that contain chiral molecules, however, and which therefore lack mirror image symmetry, coherent sum-frequency generation is possible, whereas second-harmonic generation remains forbidden. Here we apply the theory of molecular quantum electrodynamics to the calculation of the matrix element, transition rate, and integrated signal intensity for sum-frequency and second-harmonic generation taking place in a chiral liquid in the presence and absence of a static electric field, to examine which coherent and incoherent processes exist in the electric-dipole approximation in liquids. Third- and fourth-order time-dependent perturbation theory is employed in combination with single-sided Feynman diagrams to evaluate two contributions arising from static field-free and field-induced processes. It is found that, in addition to the coherent term, an incoherent process exists for sum-frequency generation in liquids. Surprisingly, in the case of dc-field-induced second-harmonic generation, the incoherent contribution is found to always vanish for isotropic chiral liquids even though hyper-Rayleigh second-harmonic generation and electric-field-induced second-harmonic generation are both independently symmetry allowed in any liquid.     

The vanishing of a higher codimension analogue of Hochster’s theta invariant

We study H. Dao’s invariant ${\eta_c^R}$ of pairs of modules defined over a complete intersection ring R of codimension c having an isolated singularity. Our main result is that ${\eta_c^R}$ vanishes for all pairs of modules when R is a graded complete intersection ring of codimension c > 1 having an isolated singularity. A consequence of this result is that all pairs of modules over such a ring are c-Tor-rigid.     

An optimal bound for inverses of triangular matrices with monotone entries

This article provides a new bound for 1-norms of inverses of positive triangular matrices with monotonic column entries. The main theorem refines a recent inequality established in Vecchio and Mallik [Bounds on the inverses of non-negative lower triangular Toeplitz matrices with monotonicity properties, Linear Multilinear Alg., 55 (2007), pp. 365–379]. The results are shown to be in a sense best possible under the given constraints.     

Simultaneous determination of Cr,Ga, In and V in soil and water samples by tungsten coil atomic emission spectrometry

Tungsten coil atomic emission spectrometry is employed for the simultaneous determination of Cr, Ga, In, and V. Both V and In are detected by this technique for the first time. The atomizer is a simple, inexpensive tungsten filament extracted from a mass-produced, commercially-available 150 W, 15 V microscope bulb. A 25 µl sample aliquot is placed directly on the coil and a small constant-current power source is used to carefully dry, ash and atomize the sample. Analytical signals are detected with a Czerny-Turner spectrograph and a charge coupled device detector. Multiple emission lines from all 4 elements are monitored simultaneously in a 54 nm spectral window. Concentration limits of detection are in the µg l^− 1 range for all elements, and the absolute limits of detection are 0.2, 2, 0.5, and 10 ng for Cr, Ga, In, and V, respectively. Even lower values may be obtained by combining the signals for the multiple emission lines of a single element. The method precision is typically better than 5.0% relative standard deviation, and sometimes as good as 0.95% (Ga). Standard reference materials of soil and water are used to check the method accuracy. After a simple acid extraction, the values determined by the method presented no significant difference from the reported values at the 95% confidence level.