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Ultraviolet Resonant Raman Enhancements in the Detection of ...

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as <strong>the</strong> <strong>in</strong>ternal standard. For solids, <strong>the</strong> <strong>in</strong>troduction <strong>of</strong> an <strong>in</strong>ternal standard is more<br />

difficult s<strong>in</strong>ce heterogeneities <strong>in</strong> terms <strong>of</strong> particle sizes and distribution are present. This<br />

results <strong>in</strong> irreproducible measurements and large error especially when one considers that<br />

<strong>the</strong> typical laser beam spot size is on <strong>the</strong> order <strong>of</strong> tens <strong>of</strong> microns <strong>in</strong> diameter.<br />

The effects <strong>of</strong> laser attenuation and self-absorption <strong>of</strong> <strong>the</strong> <strong>Raman</strong> signal were<br />

derived <strong>in</strong> <strong>the</strong> Methods section. The laser penetration depth and return <strong>Raman</strong> signal are<br />

functions <strong>of</strong> <strong>the</strong> optical (absorption and scatter<strong>in</strong>g coefficients) and physical (particle size<br />

and sample thickness) properties <strong>of</strong> <strong>the</strong> sample. The wavelength dependent laser<br />

penetration depths, evaluated us<strong>in</strong>g <strong>the</strong> <strong>in</strong>tegral <strong>in</strong>side Equation 5.14, are shown <strong>in</strong> figure<br />

27 for 2,4,6-TNT and PETN. S<strong>in</strong>ce <strong>the</strong> wavelength <strong>of</strong> <strong>the</strong> <strong>Raman</strong> signal <strong>of</strong> <strong>the</strong> analyte<br />

varies with <strong>the</strong> excitation wavelength, <strong>the</strong> value <strong>of</strong> <strong>the</strong> molar absorptivity, , at each<br />

desired excitation wavelength must first be determ<strong>in</strong>ed. Note: The biggest unknown<br />

material property, and <strong>the</strong> one most difficult to characterize, is <strong>the</strong> light scatter<strong>in</strong>g<br />

coefficient, which was not <strong>in</strong>cluded <strong>in</strong> <strong>the</strong> model <strong>of</strong> Equation 5.14. It is recognized that<br />

future model improvements should <strong>in</strong>clude <strong>the</strong> scatter<strong>in</strong>g coefficient.<br />

Figure 27. Calculated penetration depth <strong>of</strong> <strong>the</strong> UV <strong>Raman</strong> signal for <strong>the</strong> phenyl r<strong>in</strong>g<br />

stretch <strong>of</strong> 2,4,6-TNT (left) and symmetric NO2 stretch <strong>of</strong> PETN (right).<br />

From Figure 27, it is clear that <strong>the</strong> deep-UV excited <strong>Raman</strong> scatter<strong>in</strong>g from<br />

explosives will come from very near <strong>the</strong> sample surface. In general, UV excitation<br />

provides a higher <strong>Raman</strong> cross section for a sample, because <strong>of</strong> <strong>the</strong> dependence <strong>of</strong> <strong>the</strong><br />

59

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