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Toroidal electrokinetic separation techniques are based on separation tracks with toroidal layouts. These techniques can produce analytical and preparative separations with unprecedented high resolutions and peak capacities. Runs are performed in a closed loop with a quasi-continuous circulating mode of migration until the desired resolutions are achieved. They are different to the commonly used open layouts, where runs are always limited in either space (with an inlet and an outlet) or time (with a start and a finish line) and either electroosmosis or a pressure driven counter-flow must be applied to increase the resolving power. Toroidal layouts allow much more freedom in the use of the operating conditions, as will be described and compared in the following chapters.

Electrokinetic phenomena is a class of phenomena that includes electrophoresis, electroosmosis, streaming current and potential, surface conductivity, dielectric dispersion, and electroacoustics. The phenomena occur in liquid solutions (some of them can also occur in gels) containing electrolytes, and are intimately related to the theory of electromagnetism and classical fluid dynamics. However, they are distinct from electrochemistry related phenomena as they focus on the transport of charged and uncharged entities instead of on the chemical reactions, which involve the movement of electrical charges between electrodes and electrolytes.

The application of static or alternating electric fields to liquid solutions promotes the analytical and preparative separation of charged and uncharged entities, ranging from mono-atomic to macroscopic particles. This has led to the development of dozens of techniques that are indistinctly called electrophoretic, electromigration, electromigrative, electrodriven, or electrokinetic separation techniques. Luckily, all of them have the same acronym: ESTs! However, the term electrophoretic seems to be too specific, as it only refers to one of the electrokinetic phenomena. The term electromigration became commonly used in microelectronics to denote the phenomenon of atom displacement in solid conductors caused by the flow of electrons (the term “displacement of atoms by the electron wind” is commonly used in this field). Therefore, this word does not appropriately describe the separation techniques discussed here. The terms electrodriven and electromigrative are, perhaps, too broad to be used to refer to these separation techniques. In conclusion, the term electrokinetic separation techniques seems to be the most precise name for these techniques, and will hereafter be taken as their official name, as it undoubtedly specifies the set of phenomena used in the separations.

The categorization of the dozens of electrokinetic separation techniques (ESTs) is highly necessary as they have important theoretical and practical differences. Consequently, the categorization of these techniques into three levels is proposed as it produces a simple and practical nomenclature. This categorization begins with the first level: the layout of the separation path, which can be either open (O) or toroidal (T) in shape (as previously described).

The second level of categorization is the platform where the ESTs are performed. Capillary (C), microchip (M) and slab (S) platforms are the most common. Flexible fused-silica microtubes, popularly known as capillaries, are already widely used to achieve high separation efficiencies in the open layout and are also starting to be used in the toroidal layout. Cylindrical capillaries are the most frequently used, but square and rectangular capillaries are also available. In the case of microchips, microchannels are etched onto slides of polymeric materials, glasses, fused silica (amorphous), and quartz (crystalline). They show great promise for the development of novel, multifunctional microstructures. The use of 3D printing allows an even larger number of techniques to be performed on this platform, both for basic research and an uncountable number of applications. The slab platform is normally made of a slab of gel, cellulose acetate, nylon membrane, or another porous substance. These macroscopic supports always have an anti-convective effect that prevents the sample from spreading due to convection. In addition, they usually play additional, well established, roles in the separation mechanisms.

The third and lowest level of categorization is the separation mode. This refers to the underlying molecular mechanism used to promote the separation of the analytes of interest, both among themselves and from any undesired sample interferant. The modes include affinity electrophoresis (AE), electrochromatography (EC), end-labeled free-solution electrophoresis (ELFSE), free-solution electrophoresis (FSE), isoelectric focusing (IEF), isotachophoresis (ITP), microemulsion electrokinetic chromatography (MEEKC), micellar electrokinetic chromatography (MEKC), and sieving electrophoresis (SE), to mention only a few. It is interesting to note that this nomenclature is currently normally used for the separation modes, as a result of the recommendations made by IUPAC.

When combining these three levels of categorization to accurately name, produce an acrynom, and describe an EST, the following intuitive rules are proposed: (1) the first word represents the first level of categorization; either open (O) or toroidal (T). (2) The second word specifies the platform: capillary (C), microchip (M), or slab (S). (3) The last word specifies the separation mode. A summary of the ESTs covered in this book is given in alphabetical order in the following table using this proposed nomenclature.

Layout	Platform	Separation mode
(1) Open	(1) Capillary	(1) Affinity electrophoresis
(2) Toroidal	(2) Microchip	(2) Electrochromatography
	(3) Slab	(3) End-labeled free-solution electrophoresis
		(4) Free-solution electrophoresis
		(5) Isoelectric focusing
		(6) Isotachophoresis
		(7) Microemulsion electrokinetic chromatography
		(8) Micellar electrokinetic chromatography
		(9) Sieving electrophoresis

The full names and acronyms of these 54 combinations are presented in Appendix A. However, the feasibility of some of these techniques is not obvious. For instance, running the isotachophoresis mode in the toroidal layout may be difficult because the leading and terminating electrolytes must be exchanged before each high voltage rotation (see Chapter 6).

Free flow electrophoresis (FFE) is a special layout mainly used for preparative separations in special macro- and microchip platforms (shallow two-dimensional chambers). Many separation modes can be performed in this setup. The sample is continuously fed as a narrow streak into the stream of the separation medium and an electric field is orthogonally applied to this flow direction, driving the components of interest to specific collection points of the outlet. This is also discussed in Appendix A.

It must be remembered that, for some applications, gel slabs can be used for at least two purposes; merely as an anticonvective agent (to prevent band spreading) and/or as a sieving agent. In the latter case a high rate of analyte collisions against the polymer net is observed and plays a fundamental role in the separations. All of these techniques and their respective underlying phenomena are discussed in relation to the open and toroidal layouts throughout this book.

Electrophoresis and electroosmosis are the most commonly used phenomena that drive separations in the ESTs. Moreover, a large quantity of additional basic phenomena can be directly observed and studied in the many ESTs. Some examples of these additional phenomena include fluid flow, analyte adsorption, phase partitioning, and the degree of acid–base ionization, as well as the interactions of ion–ion, ion–molecule, target–ligand, antibody–antigen, and many others. Moreover, the quantity of phenomena that can be mathematically modeled using well established theories is remarkable. Most of these phenomena can be modeled from first principles, without the need to add empirical or ad hoc parameters. Even so, as in all areas of science, there are a few experimental observations for which good models do not currently exist, and some of them even lack an adequate theory. It is an interesting field for developing models, testing theories, making predictions, and testing hypotheses involving quantifiable predictions and measurements. Finally, but no less importantly, the resulting separation techniques have an impressive number of applications within diverse fields such as clinical analysis, pharmaceutical analysis, genetic analysis, food analysis, environmental analysis, and proteome analysis, to mention only a few.

The present book is written in such a way as to – hopefully – make it an interesting read for experts in the field as well as for users of these technologies, non-specialists, and students. The whole book is richly illustrated and presents a large number of very useful equations showing the relationships between important operational parameters and other fundamental variables. These are important tools for both readers who are interested in the theories of the field and those who are interested in the practical applications of the ESTs. Mathematical deductions are shown only in the appendices because the intent is not to bother readers who are not very familiar with mathematical methods. Students interested in becoming familiar with the modeling of the electrokinetic phenomena are encouraged to read these appendixes.

In Chapter 1 the fundamental concepts and definitions related to liquids that may contain a background electrolyte are reviewed, paying specific attention to their applications to the ESTs. Phenomena and definitions studied in this chapter include the relative permittivity of water, dissolution, solvation, dissociation, ionization, Gibbs free energy, ionization constants, both -pH and p-pH diagrams, the Henderson–Hasselbalch equation, and the buffer capacity of aqueous solutions.

Chapter 2 is dedicated to the fundamentals of ESTs. This includes the electrophoresis of single molecules, ionic limiting mobility, bands, peaks, zones, isoelectric points, both turbulent and laminar flow, electroosmosis, suppression of electroosmosis, the Joule effect, heat dissipation, temperature profiles, molecular diffusion, band broadening, sample stacking, band compression, and the separation modes.

The focus of Chapter 3 is the open (common) electrophoresis layout. The relationships between independent variables (or users' operational parameters) and the performance indicators are given for this type of layout (open). Examples of such performance indicators are: number of theoretical plates, number of theoretical plates per unit time squared, plate height, resolution, resolution per unit time, peak capacity, band capacity, and both peak and band capacity per unit time.

In Chapter 4 the toroidal layouts of the three platforms (capillary, microchip, and slab) are presented in detail. The microholes (capillary), microconnections (microchip), and connections (slab) that function as the hydrodynamic and electrical communication between the toroid's internal lumen and the external environment (reservoirs and electrodes) are examined in detail. The concept of the passive and active modes of operation are also presented. Active modes are used to prevent the bands from leaking out of the toroids and into the reservoirs.

Chapter 5 gives a summary of the performance indicators presented in Chapters 3 and 4. Tables comparing the performance indicators as functions of the operational parameters are shown in this chapter. The performance indicators of the open and toroidal layout are contrasted and the pros and cons of each layout are examined.

The high voltage setups used in the open and toroidal layouts are discussed in Chapter 6. One important aspect that differentiates the toroidal layout from the open layout is the way the high voltages are connected and operated. Conventional positive and/or negative high voltage modules can be used; however their output must be quickly redistributed (rotated) in a cyclic manner to keep the set of bands running until the desired resolutions are achieved. This is performed using high voltage distributors and the pros and cons of each are shown using didactic illustrations.

Heat removal and temperature control in both open and toroidal layouts are presented in Chapter 7. In addition to the side effects of the temperature gradients on band dispersion, many unexploited potentials and advantages of a rational cooling design are presented and discussed for all platforms (capillary, microchip, and slab). This is examined with the aid of dozens of figures and a solid theoretical basis.

Most of the detectors that are compatible with the open layout are also compatible with the toroidal layout. They are presented in Chapter 8, which also includes the following detection systems: absorption, contactless conductivity, fluorescence, thermal lens, and mass spectrometry. Many advantages of fluorogenic and labeling reactions in both the open and toroidal layouts are presented. In addition, the use of these reactions to increase the detection limits, performance indicators, and separation selectivities is also discussed.

In Chapter 9 a few examples of the applications of the toroidal layout are presented. These include the analyses of amino acids, stereoisomers, and isotopomers, among others. The potential of toroidal electrophoresis to obtain separation efficiencies of over one hundred million theoretical plates is shown and discussed. This is the only chapter that omits the open layout, as it would be almost impossible to present all of its applications (across all platforms and separation modes) in a single book.

Important mathematical deductions pertaining to the ESTs are made in the appendixes. These deductions have been left for the appendixes to make the main text more fluidic and light.