Numerical Modelling of Light Propagation for Development of Capillary Electrophoretic and Photochemical Detection Systems

Abstract

Capillary electrophoresis (CE) has been used for over 30 years as an efficient separation technique [1]. These separations are typically preformed using capillaries with internal diameter ranging from 2 μm to 200μm and as the diameter increases above 100μm, a reduction in separation performance is observed [2]. One of the main factors limiting the overall performance of CE separations is Joule heating associated with the passing of the electric current through resistive medium. The high surface-to-volume ratio in a smaller capillary diameter allows for efficient heat dissipation which is beneficial for compound separation, however, simultaneously this has a negative impact on the detection performance due to the corresponding reduction in analyte volume available for detection [3]. Historically when capillaries were first used for CE, they were coated with polyimide and presented excellent robustness but posed problems with optical detection as polyimide is highly absorbing below 550nm preventing optical detection in that spectral range. Such capillaries were striped of the coating to enable the optical detection in UV and low wavelength visible range. However, capillaries striped of their coating are brittle and can easily be damaged making usage often impractical. The introduction of the polytetrafluoroethylene (PTFE) coated capillaries allowed for optical detection within the UV range as well as across the entire visible spectrum. Although the PTFE coated capillaries are not as durable as the polyimide coated capillaries, they are significantly more robust than coatless ones and allow for easier deployment during typical daily laboratory routine. Absorbance photometry is a detection technique used to determine the concentration of target species in a liquid sample based on interaction between the probe light and species [4]. Typically it is a measurement of the light intensity with and without a sample placed in the light path. A scheme of light intensity measurement with the sample located for detection is presented in Figure 1. The sample transmittance, T, is defined as the ratio of the initial light intensity, I 0 , to the recorded light intensity, I 1 (Eq. 1). I 0 should be measured with the sample holding cuvette empty. This allows for reflections and potential absorption by the cuvette material to be taken into account during sample measurement. Sample absorbance, A, is measured as the negative log of the transmittance (Eq. 2). The cuvette length 𝑙 is known, as well as species molar absorptivity coefficient α, which is a specific characteristic of every species. Light attenuation along the light path is governed by Beer-Lambert’s law where c is molar concentration (Eq. 3) [5]. The method of calculating the actual optical path length is presented elsewhere [6]. Despite excellent performance in analyte separation, CE techniques still constitute a minority of the commercial applications due to detection limitations imposed by popular absorbance photometric detectors. Various developments in CE have occurred such as the development of UV-transparent capillaries which facilitated CE by making it possible to employ the commercially available detectors. In the past different approaches have also been employed to alter the geometry of the detection system in order to improve the detection performance for CE. These include the application of rectangular capillaries to reduce refraction effects on the cylindrical boundaries [2], multi-reflection cells for increased signal intensity [7], and development of Z-shaped flow cells with increased optical pathlength for analyte detection [8]. Some detectors were built employing these methods, but to date the majority of the commercially available absorbance based detectors work on the basis of a single passage of light through the sample contained in a capillary. To gain a better understanding of light propagation through capillaries and how to improve detection levels, the modelling of the light propagation through capillaries has been previously undertaken. Much of this work was limited to two-dimensional projections and two-layer models (no coating present) taking into account capillary material and inner cavity [9]. Previous numerical simulations of light propagation through capillaries have been reported as a tool for flow-cell design and have been limited to prediction of light path for these specific cases only [10]. The numerical problem of ray-tracing through a capillary is an excellent example where advantage can be taken of the ability to perform numerous calculations quickly on a computer to allow for ray paths, ray path overlaps, and resultant light intensities to be calculated. This book chapter presents a theoretical study on the light propagation through coated capillaries, focusing on PTFE-coated capillaries. These models can be used to increase the performance of absorbance photometric detection and for associated photochemical applications.