| Capillary electrophoresis (CE) is the workhorse of countless analytical laboratories and is used routinely in various industries including pharmaceutical, forensic and clinical applications. Basically, CE is a method for separating charged molecular species in a buffer-filled capillary by the application of an electric field; the analytes move from one end of the capillary to the detector at the other end at speeds determined by their charge, size and shape. Generally, in free solution CE uniformly charged polyelectrolytes (such as DNA) are free-draining, meaning that their speed is independent of their size. Hence, until recently, a gel or other sieving medium has been necessary for the separation of polyelectrolytes; however, modifying uniformly charged polymers on the molecular level, via conjugation to uncharged polymers, allows for separation in free solution CE. In this thesis, advancements to the theory of free solution electrophoresis of polyelectrolytes, in particular, to the theories for two new free solution electrophoresis methods relying on conjugation, are presented. The first method, called End Labelled Free Solution Electrophoresis (ELFSE), can be used to sequence DNA, a negatively charged polymer in solution. Two different means of improving the resolution of ELFSE are predicted, one based on the molecular end effect, the other based on using a controlled electro-osmotic flow. In addition, a theory for the segregation of the DNA and label coils in ELFSE is presented. The second method is called Free Solution Conjugate Electrophoresis (FSCE); it allows for characterization of a sample of neutral polymers differing in length. The relevant theory, developed herein, elucidates how to accurately determine the molar mass distribution of the sample through FSCE measurements. In addition, supporting theories are developed that clarify the correct equation for the diffusion coefficient of molecules undergoing free solution electrophoresis, as well as illustrate that under ideal conditions, a viscosity gradient within the capillary serves only to decrease resolution and hence can not be used to improve performance. These theoretical studies constitute the six articles presented in this thesis. In addition, a comprehensive review article covering the development of ELFSE over the last decade, the theoretical concepts used to predict the ultimate performance of ELFSE for DNA sequencing, and the technological advances that are needed to speed the development of competitive ELFSE-based sequencing and separation technologies, is given in Appendix A. The predicted improvement in ELFSE resolution based on the end effect theory was also proven experimentally; the article with these findings is provided in Appendix B. |
