Pádraig Kirwan

Extendibility of homogeneous polynomials on Banach spaces

We study the n-homogeneous polynomials on a Banach space X that can be extended to any space containing X. We show that there is an upper bound on the norm of the extension. We construct a predual for the space of all extendible n-homogeneous polynomials on X and we characterize the extendible 2-homogeneous polynomials on X when X is a Hilbert space, an L1-space or an L∞-space.

A comparison of polymeric materials as pre-concentrating media for use with ATR/FTIR sensing

Polymer-modified ATR-FTIR spectroscopy was investigated to determine its potential suitability for use as an analytical methodology for process stream analysis. The process stream under investigation contains toluene, tetrahydrofuran, ethanol, and acetonitrile in an aqueous matrix. Four polymers, Teflon® AF2400, poly(acrylonitrile-co-butadiene) (PAB), polydimethylsiloxane (PDMS), and poly(styrene-co-butadiene) (PSB), were chosen for study based on partition coefficients measured using a novel automated GC technique. Polymer suitability as pre-concentration media was assessed utilizing analyte/polymer diffusion coefficient data, equilibrium absorbance values, water ingress, and polymer plasticization. PAB displayed the fastest sensing times and enhanced sensitivities. Teflon® AF2400 demonstrated a low water absorption and a low degree of plasticization. Other factors affecting the diffusion rate of analytes were also investigated including molecular size, shape and analyte concentration. This research demonstrated that the choice of pre-concentrating medium is not a trivial issue, being dictated by a combination of sensitivity constraints as well as polymer robustness in real sample matrices.

A study of the factors affecting the diffusion of chlorinated hydrocarbons into polyisobutylene and polyethylene-co-propylene for evanescent wave sensing

Abstract Two polymers, polyisobutylene (PIB) and polyethylene-co-propylene (60% ethylene) (E/Pco), have been considered as preconcentration media for the detection of chlorinated compounds using mid-IR evanescent wave spectroscopy. In order to optimize and predict sensor response factors affecting the diffusion of analytes into the polymer films has been examined using a silver halide sensing fiber coupled to a FTIR spectrometer. A Fickian diffusion model was used to quantify the diffusion process. The diffusion model calculated a diffusion coefficient based on such parameters as refractive index of the polymer cladding and light guiding core, the polymer cladding thickness and the principal analyte wavelength of detection. The diffusion of analyte isomers was investigated. The diffusion of chlorinated benzene isomers was employed to determine whether the position of chlorines on the ring effects diffusion. Physical steric and molecular size effects were found to dominate the diffusion of these compounds. Solution composition was a fundamental issue in sensor design. The polarity of the sample stream was another diffusion determinant. The polarity of the matrix solution was altered by the addition of organic solvents. Rate of diffusion was seen to increase with decreasing matrix polarity. E/Pco was found to be less susceptible to polarity modification. The results obtained can be employed as a basis for the selection of a polymer for particular industrial applications and also as a means of improving the speed of sensor response.

Determination of Hydrocarbons Using Sapphire Fibers Coated with Poly(dimethylsiloxane)

A poly(dimethylsiloxane) (PDMS) coated sapphire fiber has been investigated as a sensor for hydrocarbons (HCs) in the mid-infrared region around 3000 cm−1. In order to optimize and predict sensor response, the diffusion behavior of the analytes into the PDMS preconcentration medium has been examined. A diffusion model based on Fickian diffusion was used to quantify diffusion. The model incorporated such factors as film thickness, refractive index of the polymer and the fiber core, and principal wavelength at which the analyte absorbs. A range of hydrocarbons, from hexane to pentadecane, was analyzed at 2930 cm−1 using both fiber-coupled Fourier transform infrared spectroscopy and a modular prototype system. Diffusion coefficients were determined for these compounds and diffusion behavior examined and related to factors such as analyte polarity and molecular size. The diffusion coefficients were found to range from 6.41 × 10−11 ± 5 × 10−12 to 5.25 × 10−11 ± 9 × 10−13 cm2 s−1 for hexane and pentadecane into a 2.9 μm PDMS film, respectively. The diffusion model was also used to examine the effect of changing system parameters such as film thickness in order to characterize sensor response.

The development of novel organically modified sol-gel media for use with ATR/FTIR sensing.

The ability to prepare and develop novel pre-concentration media by the sol-gel process, and their integration with mid-infrared transparent waveguides has been demonstrated. This research approach resulted in a mid-infrared sensing methodology in which the properties (porosity, functionality, polarity, etc.) of the recognition layer could be tailored by variation of the sol-gel precursors and processing conditions. Cross-linker type and concentration notably influenced p-xylene absorption and diffusion rate. Unreacted silanol groups appeared to be the dominant factor in the hydrophobicity of sol-gel layers. Variation of sol-gel precursors and thermal treatment altered both film cross-link density and polarity, as demonstrated by variation in the rate of analyte diffusion and equilibrium analyte concentration. The use of a novel 1 : 1 PTMOS : DPDMS material as pre-concentration medium in this analytical sensing approach was validated through the determination of p-nitrochlorobenzene in an aqueous environment. The response demonstrated linearity between 0-30 mg L(-1) with a correlation coefficient of 0.989 and a limit of detection of 0.7 mg L(-1). Sensing times for p-nitrochlorobenzene were also reduced from several hours to 24 minutes, without loss of measurement accuracy or sensitivity, by a 10 degrees C increase in the sensing temperature and the use of a predictive Fickian model previously developed by this research group.

Investigation into polymer-diffusant interactions using ATR-FTIR spectroscopy

Abstract Using a polymer coated attenuated total reflectance (ATR) waveguide and Fourier transform infrared (FTIR) spectroscopy, interactions between penetrants and a Teflon ® AF2400 polymer matrix were observed. The AF2400 membrane was coated onto the measuring surface of a ZnSe crystal, concentrating the target diffusant(s) within, and excluding interfering water from, the information region of the standing infrared evanescent wave. The Fickian diffusion of small molecular species into the AF2400 polymer membrane was followed through observation of distinct penetrant infrared absorption bands. During the analysis of a number of analytes (e.g. toluene, chlorobenzene (MCB), tetrachloroethylene (TeCE)), infrared bands caused by the action of penetrants within the AF2400 polymer matrix were observed. These bands may be attributed to the altering of original polymer infrared bands caused by optical or molecular (e.g. plasticisation) effects. The nature of the observed ‘interaction bands’ were investigated. Through monitoring of the interaction bands an increase in the detection sensitivity was observed for the examination of toluene solutions, indicating the potential of the penetrant/polymer interaction as a novel ‘smart’ enrichment technique for polymer-modified FTIR sensing.

Measurement of the Rates of Diffusion of Halomethanes into Polymer Films Using ATR-FTIR Spectroscopy

Polymer-modified attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectroscopy and FEWS (fibre-optic evanescent wave) spectroscopy have been very successful to date for sensitive detection of organic pollutants in water utilising the mid-infrared (MIR) region of the electromagnetic spectrum (4000-400 cm−1). This sensing approach involves the use of different polymer films for preconcentration with optimisation of the sensor related to the rate of diffusion of solvent molecules into these polymer films. Compounds such as chloroform, bromoform, bromodichloromethane and dibromochloromethane which are collectively referred to as trihalomethanes (THMs) were analysed in this work. A gaseous phase experimental design was used and from experimental data the rate of diffusion of each of the halomethanes was quantified based on a Fickian type diffusion model. Individual diffusion coefficient values were found to be in the range 3.38 E-10 ± 0.01 E-10 to 4.72 E-08 ± 0.42 E-08 cm2 s−1. Multicomponent effects were observed for mixtures of compounds diffusing into polyisobutylene and ethylene-propylene copolymer.

Complexification of Multilinear Mappings and Polynomials

We study various methods of complexifying real normed spaces. We see how the notions of duality and complexification are interchangeable. We obtain estimates for the norms of complexified multilinear mappings and polynomials. We see how polynomials can be complexified without reference to the associated multilinear mappings.