Interpolation properties associated with the second order abstract Cauchy problem

Summary LetA be a closed linear operator on a Banach spaceX. In this work we present some interpolation and extrapolation results for the well posed abstract Cauchy problem of second order; namely, if the second order abstract Cauchy problem is exponentially well posed onD(A ^{k + 1} ),k N thenA is sandwiched by cosine function generators.     

Instability of hexane-acetonitrile mobile phases used for the chromatographic analysis of triacylglycerides

Comprehensive 2-D LC is an emerging separation technique that has seen a rapid increase in applications in the last decade. The technique has been applied for the separation of numerous complex mixtures including triacylglycerides (TAG). Determination of TAG in food products such as rice, palm, and canola oils have been previously described and the technique of choice utilizes a silver-modified silica column with hexane-ACN as the mobile phase. Repeated retention time inconsistencies were experienced in our studies when this mobile phase was applied to the separation of natural and synthetic mixtures containing TAG. The present report summarizes a study performed to determine the relative stability of ACN, propionitrile (PCN), and butyronitrile (BCN) at concentrations ranging from 0.43 to 2.8% in hexane and heptane. The data obtained suggest that unless evaporative loss of the mobile phase is prevented, TAG retention time irreproducibility can be significant when using mobile-phase mixtures prepared with ACN or PCN. BCN should be used as the solvent modifier in cases where evaporation cannot be prevented.     

Development of a comprehensive multidimensional liquid chromatography system with tandem mass spectrometry detection for detailed characterization of recombinant proteins

A multidimensional comprehensive liquid-phase separation system (2DLC) coupled on-line to an electrospray-ionization time-of-flight (ESI-TOF) mass spectrometer (MS) was used to resolve structural alterations and/or post-translational modifications for detailed protein characterization. The system described in this work consists of cation-exchange chromatography in the first dimension and reversed-phase chromatography in the second dimension. A unique spiked gradient was employed in the first dimension to enhance recovery of peptides. This combination of separation followed by MS detection offered the advantages of unique selectivity and high efficiency of the separation methods combined with the mass specificity and sensitivity of MS. During the course of this study it was determined that altered or modified peptides were shown to be better resolved than during a one-dimensional separation. The 2DLC/ESI methodology allowed for a comprehensive evaluation of post-translational modifications and chemical reactions of recombinant proteins, providing a meaningful evaluation of product quality that was not possible with other current analytical approaches. In addition, the system can be used to provide sequence coverage of complex proteins.     

Nanoparticle-based one-dimensional photonic crystals

Herein we present a fast, reliable method for building nanoparticle-based 1D photonic crystals in which a periodic modulation of the refractive index is built by alternating different types of nanoparticles and by controlling the level of porosity of each layer. The versatility of the method is further confirmed by building up optically doped photonic crystals in which the opening of transmission windows due to the creation of defect states in the gap is demonstrated. The potential of this new type of structure as a sensing material is illustrated by analyzing the specific color changes induced by the infiltration of solvents of different refractive indexes.     

Controlled epoxidation of poly(styrene‐b‐isoprene‐b‐styrene) block copolymer for the development of nanostructured epoxy thermosets

To be used as templates for nanostructured thermosets, a commercial poly(styrene‐b‐isoprene‐b‐styrene) (SIS) block copolymer (BCP) was epoxidized by three different epoxidation procedures. An exhaustive analysis of methodologies using metal catalyzed/hydrogen peroxide, dimethyldioxirane (DMDO), and meta‐chloroperbenzoic acid (m‐CPBA) was performed to obtain reactive BCPs. The DMDO approach was the best strategy to obtain highly epoxidized SIS BCP (85 mol %) without formation of side products. Careful control in BCP epoxidation by metal catalyzed/hydrogen peroxide and m‐CPBA approaches led to a maximum epoxidation degree (ED) of approximately 60 mol % without the formation of side products. The ED by metal catalyzed/hydrogen peroxide strategy could be further increased to 69 mol %, but a significant amount of crosslinking, ring opening, and polymer chain scission reactions were detected by spectroscopic and chromatographic techniques. The miscibility of epoxidized BCPs with diglycidyl ether of bisphenol‐A epoxy system before and after curing was analyzed to develop nanostructured epoxy thermosets. For ED higher than 69 mol %, BCPs were miscible, while those with lower ED presented macrophase separation. Highly epoxidized BCPs obtained by the DMDO methodology were successfully used to obtain ordered nanodomains inside the epoxy matrix, as determined by atomic force microscopy. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Determination of short-chain branching content in polyethylene by pyrolysis comprehensive multidimensional gas chromatography using low thermal mass column technology

A research effort was undertaken to utilize the pyrolysis process to create fragments of polyethylene that could be indicative of branching, and allow quantitiation of said short-chain branches by pyrolysis comprehensive 2-D GC (Py-GC x GC). Several strategies for sample introduction and pyrolysis such as the in-column pyrolysis device and the programmed temperature vaporizer (PTV) were studied. The chromatographic separations were executed using low-thermal mass (LTM) comprehensive 2-D GC (GC x GC). A series of polyethylene-co-hexene samples were analyzed and a linear correlation of 1-hexene content with branching peak ratio was found. Correlation coefficients were determined as 0.97 for the measurements performed.     

Direct measurement of part-per-billion levels of dimethyl sulfoxide in water by gas chromatography with stacked injection and chemiluminescence detection

Dimethyl sulfoxide (DMSO) is a chemical of industrial significance with many important applications. DMSO is used as an industrial solvent, in drug delivery and healthcare applications, among others. Analysis of DMSO in water typically involves extensive sample preparation, enrichment, and derivatization to improve solute detectability. A novel gas chromatographic procedure has been developed for the direct measurement of trace levels of DMSO in an aqueous matrix, such as potable water. The technology utilizes stacked injection techniques for in-column solute enrichment, a precolumn to enhance solute focusing effects, and sulfur chemiluminescence detection for matrix suppression and sensitivity. A detection limit of 2 parts per billion (ppb) (v/v) of DMSO in water was attained. Relative precision of less than 7% at the concentration of 10 ppb (v/v) of DMSO was demonstrated. A correlation coefficient of 0.9988 was obtained over a range of 2 ppb (v/v) to 100 ppb (v/v). No detectable carry-over was found at the 5 ppb (v/v) level whereas less than 4% carry-over was observed at the 100 ppb (v/v) level. Various sample storage media including glass, polyethylene, and polycarbonate were also studied to minimize solute loss. Recoveries greater than 84% were achieved with all storage media tested. The method was found to be reliable and simple to implement.     

Gas chromatography with state-of-the-art micromachined differential mobility detection: operation and industrial applications

Ion mobility spectrometry (IMS) has potential analytical applications in very diverse fields such as chemical, petrochemical, environmental, and, more recently, in drug, chemical warfare agent, and explosives detection. Commercially available IMS instruments are based on time-of-flight (TOF) mass spectrometry. IMS is inherently suitable for field operation as it uses relatively simple microfluidic devices and operates at atmospheric pressure. It is portable, highly sensitive with tunable selectivity, yet can be produced at relatively low cost. Key limitations of this analytical detection technique are low duty cycle, ion cluster formation, short linear dynamic range, and restriction to only positive or negative ion collection in a single analysis. Microelectromechanical system, radio frequency modulated IMS (MEMS RF-IMS), also known as differential mobility spectrometry, has recently been developed and commercialized. The technology is based on IMS, and MEMS RF-IMS offers substantially better performance. In this study, the strengths and limitations of the recently introduced differential mobility detector when used with gas chromatography in trace analyses are discussed and illustrated with applications of industrial significance.     

Quantifying hepatic fibrosis using a biexponential model of diffusion weighted imaging in ex vivo liver specimens

The purpose of this study was to evaluate the non-Gaussian behavior of diffusion related signal decay of the ex vivo murine liver tissues from a dietary model of hepatic fibrosis. To this end, a biexponential formalism was used to model high b-value diffusion imaging (up to 3500 s/mm²), the findings of which were correlated with liver histopathology and compared to a simple monoexponential model. The presence of a major, fast diffusing component and a minor, slow diffusing component was demonstrated. With increasing hepatic fibrosis, the fractional contribution of the fast diffusing component decreased, as did the diffusion coefficient of the fast diffusing component. Strong correlation between the degrees of liver fibrosis and a two-predictor regression model incorporating parameters of the biexponential model was found. Using Akaike's Information Criterion analyses, the biexponential model resulted in an improved fit of the high b-value diffusion data when compared to the monoexponential model.