LIST OF SYMBOLS

a.................................................................................................................................... radius

b...................................................................................................................... channel breadth

c.......................................................................................................................... concentration

c₀................................................................................................................ initial concentration

d................................................................................................................................ diameter

d_i......................................................................................................... steric inversion diameter

e....................................................................................................................... electron charge

f.......................................................................................... friction coefficient or friction factor

g_x.............................................................................................................. gravity in x-direction

h................................................................................................... gridline spacing in x-direction

i.................................................................................................................................... current

i.................................................................................................... gridline number in x-direction

j................................................................................................... gridline number in y-direction

k.............................................................................................................. Boltzmann’s constant

k................................................................................................... gridline spacing in y-direction

l................................................................................................. induced sample layer thickness

m............................................................................................. number of gridlines in x-direction

n............................................................................................. number of gridlines in y-direction

n_i⁰........................................................ initial number of active ions per volume (number density)

p................................................................................................................................. pressure

s............................................................................................................................ scale factor

t........................................................................................................................................ time

t_m.............................................................................................................. membrane thickness

t_r......................................................................................................................... retention time

t₀................................................................................................................................ void time

u, u_x................................................................................................. flow velocity in x-direction

v.................................................................................................................................. velocity

v_y...................................................................................................... flow velocity in y-direction

ávñ........................................................................................................... average flow velocity

ávñ_zone...................................................................... average flow velocity for a zone of particles

w......................................................................................................... plate separation distance

w_z..................................................................................................... flow velocity in z-direction

w_1/2..................................................................................................... peak width at half height

x................................................................................................................. coordinate direction

x_DL.......................................................................................................... double layer thickness

y................................................................................................................. coordinate direction

z.................................................................................................................................... charge

z................................................................................................................. coordinate direction

A.......................................................................................... distance from origin to peak elution

C........................................................................................................................... capacitance

C_B................................................................................................................... bulk capacitance

C_DL.................................................................................................... double layer capacitance

C_p............................................................................................................ specific heat capacity

D............................................................................................................... diffusion coefficient

D_h................................................................................................................ hydraulic diameter

E.............................................................................................................. electric field strength

E_eff.............................................................................................. effective electric field strength

E_y.................................................................................................................. Young’s modulus

H............................................................................................................................ plate height

H_D....................................................................................... diffusion contribution to plate height

H_i.................................................................................. instrumental contribution to plate height

H_n............................................................................... nonequilibrium contribution to plate height

H_p..................................................................... sample polydispersity contribution to plate height

J_D............................................................................................................... flux due to diffusion

J_F.................................................................................................... flux due to the applied field

K....................................................................................................................................... gain

L........................................................................................................................ channel length

L_e...................................................................................................................... entrance length

N.................................................................................................................... number of plates

P.................................................................................................................................... power

Q...................................................................................................................... thermal energy

Q.................................................................................................................... volume flow rate

R......................................................................................................................... retention ratio

.............................................................................................. average value of retention ratio

R_B....................................................................................................... bulk electrical resistance

R_e............................................................................................................... electrical resistance

Re................................................................................................................ Reynolds’ number

R_h................................................................................................... hydraulic Reynolds’ number

R_s.............................................................................................................................. resolution

S’.............................................................................................................. applied field strength

S_d.............................................................................................................. size selectivity index

T........................................................................................................................... temperature

U.......................................................................................................................... drift velocity

V_e....................................................................................................................... elution volume

V₀.......................................................................................................................... void volume

V.................................................................................................................................. voltage

V_eff.................................................................................................................. effective voltage

Z............................................................................................................................. impedance

Z_T..................................................................................................................... total impedance

a............................................................................................................................ aspect ratio

b................................................................................................. membrane deflection constant

g.............................................................................................................. steric transition factor

e............................................................................................................................. permittivity

e_{DL.............................................................................................................................}permittivity of the double layer

e_{r......................................................................................................................................................}relative permittivity

e₀....................................................................................................... permittivity of free space

f................................................................................................................... field susceptibility

z.......................................................................................................................... zeta-potential

h................................................................................................................................ viscosity

h₀....................................................................................................................... initial viscosity

k.......................................................................................................................... Debye length

l......................................................................................... nondimensional retention parameter

m........................................................................................................... electrophoretic mobility

r_B........................................................................................................ bulk electrical resistivity

r_e................................................................................................................ electrical resistivity

r_m................................................................................................................................. density

s.................................................................................................................. standard deviation

....................................................................... average standard deviation along the time axis

t.......................................................................................................................... time constant

............................................................................................................................. frequency

CHAPTER 1

INTRODUCTION

Collecting biological samples for diagnosis or other analysis, sending them off to a lab, and then waiting for hours, days, or even weeks for results is a typical scenario for doctors, patients, and other scientists in health care, chemical analysis, environmental monitoring and other fields. Typically, medical and chemical analyses must be performed in dedicated labs because the analysis systems are bulky, slow, expensive, delicate, and often complex. There is a great demand for speeding up these analysis systems and moving them to the location where the results are needed. A host of researchers are working in these fields and struggling to develop systems that are portable, robust, efficient, capable of multidimensional analysis, and inexpensive or even disposable. Systems of this type would allow doctors to quickly diagnose problems, allowing much faster treatment. Field researchers could perform required tests on site much more quickly and efficiently. The possibility even exists for “home” tests usable by inexperienced operators. These systems will not be possible, though, without the development of small, inexpensive, high-speed, high-resolution analysis systems. One technique that has the potential to contribute significantly towards the goal of realizing a total microanalysis system is electrical field- flow fractionation (ElFFF).

Scope of Work

In this dissertation, microfabrication technologies are employed to develop a miniaturized Electrical Field- Flow Fractionation (m-ElFFF) system for chemical analysis and separation of biological molecules. The theory, scaling effects, and motivation behind the development of the m-ElFFF system are elucidated along with the fabrication of the miniaturized system. The system is characterized concerning its separation and analysis abilities and compared to macroscale electrical field- flow fractionation (ElFFF) systems. An electrical detection system is integrated into the m-ElFFF separation channel and characterized for its detection capabilities using both resistance and impedance methods. The ability of the miniaturized system to separate biologically relevant particles is demonstrated using polystyrene particles with adsorbed proteins and cellular homogenate. The potential for the m-ElFFF system is reviewed and suggestions for future work in this area are enumerated.

This work is part of a greater project to develop a complete micro-analysis system including integrated injection, separation, detection, measurement, and signal analysis systems. This work serves as proof-of-concept for the greater work involving a commercially available miniaturized electrical field- flow fractionation system and demonstrates the abilities of the system regarding biomedical applications. Additionally, this study demonstrates the efficacy of miniaturizing field- flow fractionation (FFF) systems and provides a springboard for further work involving other FFF systems.

Bioinstrumentation

Field-flow fractionation is a small subset of techniques within the broad field of bioinstrumentation. Bioinstrumentation includes all instrumentation and techniques used for collection, manipulation, analysis and characterization of biological tissues, products, molecules, cells, and activities. This field includes such diverse interests as imaging, biosensors, instruments for measurement of biopotentials, needle design, photodetectors, pressure and flow measurement, and heat transfer in tissues. A number of books covering bioinstrumentation and its diverse fields have been published and are available for the interested reader [[1],[2]]. Active areas in the field of bioinstrumentation and of great interest in this work are bioanalysis systems, bioseparations [[3]], or as they are more generally called, chromatography systems. Field- flow fractionation is an important technique in the broader areas of chromatography and biochemical analysis.

Chromatography

Chromatography refers to a variety of techniques used to separate biological and chemical mixtures into their component parts. Chromatography systems can be used either to separate and determine the component parts of a mixture or to purify specific components of a mixture. Numerous separation methods exist for purification of both small molecules and larger complexes of molecules such as organelles and cells. Liquid and gas chromatography are perhaps the most basic types of chromatography and rely on differential interactions between the material being separated and the walls or surface of the chambers through which the mixture is carried. In liquid and gas chromatography, there is a mobile phase consisting of the material being separated, a carrier, and a stationary phase consisting of a reactant on the walls (a coating or surface condition) or other surface around or through which the mobile phase passes. Gas chromatography is typically performed for chemical analysis rather than purification purposes, while liquid chromatography can be used to provide not only analytical information, but also can be used for large scale chemical purification. Molecular separations are usually done in high yields using liquid chromatography. Common modes for such separations include ion-exchange, normal phase, reverse phase, gel permeation, affinity, and hydrophobic. Other chromatographic techniques such as electrophoresis, which requires a gel, separate samples due to differences in molecule size and charge [[4]]. This family of electrophoresis techniques is similar to gas and liquid chromatography in that interactions with the gel cause the separation of the particles, but there is no carrier material for the particles being separated, rather they are driven using electric fields or other forces. Cells and organelles are frequently separated using centrifugation, which separates based on the buoyant mass of the cell. Free-flow electrophoresis, which utilizes an electric field across a curtain of flowing carrier between two closely spaced vertical plates, allows for continuous sample injection, but requires discretization of the detection and collection systems and is limited by distortion in the fluid stream caused by the parabolic flow profile [[5]]. All of these methods have advantages in specific applications, but also have characteristic limitations. Chemical separation systems may denature proteins and electrophoresis systems often require very high field strengths. Another method of separating molecules, cells, and other mixtures is then needed for applications in which these limitations preclude the use of these systems. Field-flow fractionation is the solution for some applications.

Field- Flow Fractionation

Field- flow fractionation (FFF) was first described in the mid-60s by J. Calvin Giddings. FFF is a class of separation techniques that rely on a field perpendicular to the direction of separation to induce a migration of particles injected into the system. A wide variety of fields have been used in FFF systems with the most common FFF subtypes being flow (fFFF) [[6]-,[7],[8],[9],[10],[11],[12],[13]], thermal (TFFF) [14-23[14]], sedimentation (SdFFF) [24-33[24]], steric (SFFF) [34-40[34],[35],[36],[37],[38],[39],[40]], and electrical (ElFFF). Other subtypes of FFF that are of interest include gravitational (GFFF) [41-48[41],[42],[43],[44],[45],[46],[47],[48]], dielectrophoretic (dep-FFF) [49-52[49],[50],[51],[52]], cyclical [[53]], and magnetic (MFFF) [54-57[54],[55],[56],[57]] FFF. Combinations of these fields as well as variations on the basic design are commonplace.

Although the same types of fields are used in FFF systems as in the direct field methods, there is no longer a requirement of resolution in the direction of the field, so field strengths can be lower and run times shorter. In addition to these advantages, FFF systems are elution methods and allow the collection of fractions during a separation. Since the theory for FFF systems is well-developed, the elution volumes for a given sample can be directly related to a physical parameter of the sample, such as electrophoretic mobility in the case of electrical FFF [1].

Electrical Field-Flow Fractionation

The first electrical field-flow fractionation (ElFFF) system built in 1972 used a flexible-membrane-bounded channel with electrodes outside the membranes [[58]]. It was able to separate proteins, but ran into a variety of problems. Work continued for the next few years on a variety of flexible [[59]] and rigid [[60]] membrane channels, but the experimental results deviated significantly from theory and there was difficulty in fabricating systems that would generate significant field strengths and reach their theoretical potential. During the next 20 years, only sporadic reports of attempts at ElFFF surfaced including a system that used annular porous glass channels [[61]], a thermal-electrical system [[62]], and some FFF variants such as continuous split-flow (SPLITT) separations [[63]] and electropolarization chromatography (ElFFF in hollow fibers) [64-68[64],[65].[66],[67],[68]]. None of these methods reached their anticipated potential and were eventually abandoned. In the meantime, the other FFF methods were developed and began to rise to prominence as powerful separation and analytical techniques. In 1993 an ElFFF system in which the channel walls also served as the electrodes was introduced [[69]]. The system was found to be excellent for the separation of colloids and other suspensions, but limited with respect to proteins. This system revived interest in ElFFF and the analytical possibilities that electric fields provide. Shortly after the announcement of this system, several groups began active work in the area of ElFFF and demonstrated its analytical value with respect to sugars [[70]], polymer particles [[71],[72]], colloids [[73]], colloidal adsorption complexes [[74]], and other chemicals [[75]]. In addition, work has been done on the mechanism of separation and retention in ElFFF systems [[76],[77]].

ElFFF, as mentioned previously, is not a direct‑field separation technique, but rather relies on an electric field perpendicular to the direction of separation (perpendicular to flow direction) to perform the separation function as shown in Figure 1. The separations are performed in a low‑viscosity liquid (typically an aqueous carrier solution) which is pumped through the separation channel. The ElFFF process is based on controlling the relative velocity of particles by forcing particles towards the wall of the channel. Particles with high charge density or “z‑potential” will pack more closely to the wall while particles of lower z‑potential will form a more diffuse cloud that extends further into the flow stream; see Figure 2. Since the flow in the channel is laminar and easily characterized, i.e. parabolic, the particles will flow through the channel at particular rates based on z‑potential and particle size. Since the particle size is easily determined using other techniques, the effect of the ElFFF process is to separate particles by z‑potential. Thus ElFFF also has the potential to directly measure z‑potentials and the electrophoretic mobility of particles. z‑potentials are discussed in further detail in Chapter 2.

Figure 1. Diagram of operation of ElFFF system showing input and output ports, application of electric field, parabolic flow profile, and relative channel dimensions.

ElFFF has all the advantages of FFF systems, such as being an elution method which allows collection of fractions, plus additional ones such as the ability to perform separations on cells, large molecules, colloids, emulsions, and delicate structures such as liposomes: separations that may be difficult or impossible to perform in other separation systems [69]. ElFFF separations can be performed on particles in either the “as is” condition or following surface modification with biological molecules. Applications of ElFFF systems include cell and organelle separations, separation and analysis of bacteria and viruses, characterization of emulsions, liposomes, and other particulate vehicles, diagnostic tests for specific molecules in colloidal suspensions, quick and accurate separations of macromolecules, environmental water monitoring, tests for sample contamination, and research involving z‑potentials. ElFFF systems also find application as sample pretreatment systems by performing an initial separation on a sample that is later collected for further testing by another analysis system.

Figure 2. Representation of theoretical operation and mode of particle retention and separation in ElFFF channels. The balance between electrical forces and diffusion determines the average distance of a particle from the wall, and the flow profile determines the rate at which the particle cloud moves along the channel. Less compressed particle fields move ahead of more compressed fields due to the parabolic velocity profile.

Some of the special advantages of ElFFF systems include low power and voltage requirements. The voltage in ElFFF systems seldom exceeds three volts with power consumption measured in milliwatts or less. Thus the system could easily be made portable and allow for regular field measurements not possible with other systems. This prospect is particularly exciting considering the potential for environmental monitoring and soil analysis mentioned previously. ElFFF theory also suggests that miniaturization of the system will improve the resolution and separation capabilities of the system by increasing the effective field realized in the channel.

Micromachining

Micromachining technologies, or the use of lithographic and other precision fabrication techniques, have grown out of the semiconductor and integrated circuit fabrication industries. The first techniques that came to be known as micromachining were developed in the late 60s and early 70s, but did not begin to be extensively used until the mid-to-late 1980s. Owing to their origins, most micromachining techniques and equipment are similar or identical to those used in the mature integrated circuit industry. Thus, texts dealing with fabrication of integrated circuits are also generally relevant to microfabrication [[78],[79]]. As with integrated circuit fabrication, micromachining techniques generally revolve around the use of photolithography to produce devices on the micrometer and nanometer scale. These technologies typically involve semiconductor materials, most notably silicon, as the base substrates with glass another often-used substrate. Metals, insulators, and plastics are often deposited or applied to the substrate to help develop the microscale devices.

Micromachining technologies can be broken down into two basic categories. The first category is bulk micromachining, which involves the removal of material from the base substrate by etching or other means. Bulk micromachining techniques include KOH etching of silicon (more broadly wet etching) and reactive ion etching (RIE) of silicon using CF₄or other gases (dry etching) as examples. The second broad category of micromachining is surface micromachining, or the addition of material or processing above the substrate. In surface micromachining the substrate serves only as a base upon which to build and generally is not otherwise involved in the device. Surface micromachining is dominated by the use of thin film techniques such as the growth of oxides and nitrides on silicon, the deposition of metals using sputtering or electron beam evaporation, the application of polymers using spin-on techniques, and the etching of these materials using both wet and dry etching as with bulk micromachining. Electroplating and micromolding techniques would also fall under surface micromachining.

Other important micromachining techniques include the bonding of multiple substrates and the use of sacrificial processes such as the so-called dissolved wafer process. Several “macro-machining” techniques, such as electrical discharge machining (EDM) [[80],[81],[82]] and injection molding [[83],[84]], have also been scaled into the micromachining domain and are known as precision machining. New techniques are being developed regularly, and there is a broad spectrum of techniques with specific applications that are not in general use. While many of these techniques are of potential interest, there are far too many possible micromachining techniques to discuss here. A number of texts, though, have surveyed the range of micromachining techniques and describe in more detail the most common techniques as well as those techniques seen less frequently [[85]-[86],[87],[88],[89],[90],[91]].

Micromachining technologies have been used not only to miniaturize existing transducers, but also to enable the development of products that would have been impossible using conventional techniques. Devices ranging from gyroscopes to diffraction gratings to components of jet engines have successfully been fabricated and miniaturized using micromachining. The first commercially relevant micromachined structures were developed in the early 1980s and included manifold pressure sensors for cars and disposable blood pressure sensors for medical use. Currently, accelerometers, pressure sensors, and ink-jet print heads are the most common commercially available microfabricated devices. Micromachining has also been used to develop improved microfluidic, magnetic, thermal, optical, and mechanical transducers.

Of special interest in this work is the application of micromachining technologies to the development of improved chemical and biological transducers. Micromachining technologies have been used in the development of chemical and biological devices such as glucose sensors and electronic noses, neural recording arrays, microneedles and micropipettes for precise dosing and sample handling, and DNA amplification (PCR) systems. Micromachining technologies have also been applied with great success to chemical and biological analysis systems; one area of which is chromatography systems.

Microfabricated Chromatography Systems

Great progress has been made in the fabrication of micro-scale analysis systems in the last few years. For example, dozens of groups have produced a number of microfabricated electrophoresis type systems [[92]-[93][108]] as well as micromachined free-flow electrophoresis systems [[109],[110]]. Other liquid chromatography [[111],[112]], gas chromatography [[113]-[114],[115],[116],[117],[118],[119]], and hybrid [[120],[121]] systems have been built using micromachining technologies. Numerous other publications show there are significant advantages to be found in micromachining separation systems including increased resolution, reduced separation times, smaller sample sizes, and increased parallelism of analysis. Micromachining technologies have also been recently applied to FFF systems. Micromachined thermal [[122]], electrical [[123]], and dielectrophoretic [[124]] FFF systems have been reported. As with other miniaturized chromatography systems, the abilities and performance of ElFFF systems change dramatically when miniaturized.

Although microfabricated analysis systems are interesting themselves, most researchers are using microfabrication in an attempt to completely integrate all the components of the analysis system onto one chip. These micro-Total-Analysis-Systems (m-TAS) could include sample handling systems, detection systems, amplification systems (such as PCR [[125]-[126],[127],[128]]), pumps, valves, mixers, and other flow devices, as well as signal processing electronics. Several of these systems could be combined to develop the so-called “Lab-on-a-chip” that would be able to analyze multiple samples quickly, with high accuracy, and most likely in a completely portable system. Even though no one has yet realized the goal of a micro-Total Analysis System, several groups are working on the project and making significant progress.

Biochemical Analysis System Detectors

A critical component of any biochemical analysis system, especially a m-TAS system, is the detector. Many of the recent advances in chromatography and other chemical analysis systems can be tied directly to improvements in detection systems. The analysis systems these detectors work with are used to study all kinds of chemicals and biological molecules and to screen these particles for efficacy in various medical applications. Thus, detection systems must also be versatile with the ability to detect a wide range of particle types. Some of the systems that require detection components include the chromatography and analysis systems mentioned previously and the various biomedical devices that use proteins, DNA, antibodies, cells, and other biological particulates (such as PCR). Of critical importance to all of these techniques is the detection, monitoring, and transduction methods used to collect, observe, and interpret the signals, separation, or reaction generated by the device. Almost every method for energy transduction has been used to measure and observe signals in these various devices including optical, electrical, mechanical, thermal, chemical, magnetic, and others. Each of the chromatographic types has developed its own particular detection methods that work best for it. For example, gas chromatographs often use thermal conductivity detectors since gases vary widely in thermal conductivity or flame ionization detectors which burn the gases as they exit the column, but both are typically unsuitable for liquid applications. For liquid applications, which are of more interest to this work, one of four detection methods are used for almost all detection applications: the UV detector, the fluorescence detector, the refractive index detector, and the electrical conductivity detector [[129]].

UV, fluorescence, and refractive index detectors are all optical detection techniques and can be considered as a group. UV detection systems provide the most popular detection method and can operate in a number of different configurations. Most UV systems measure absorption, extinction, or light scattering between 180 and 350 nm by generating a constant beam of UV light and then measuring the transmitted light using a photo-electric cell. Fluorescence detectors are considered the most sensitive and work by exciting a “fluorescent” molecule at one wavelength that then emits light at a longer wavelength. While many particles of detection interest are fluorescent, the majority of molecules that are of interest must be derivatized to become fluorescent which can occasionally influence the separation itself. Fluorescence detection must also be done in low light levels to minimize background noise. Refractive index detectors are the least sensitive in general, and most susceptible to noise and slight variations in ambient conditions. In general refractive index detectors work by measuring the change in angle of a beam of light passed through the sample caused by a change in the refractive index. There are several different methods for accomplishing this measurement, each with its own advantages and disadvantages.

The optical techniques generally used with chromatography systems are the most popular, but they have several disadvantages. They are generally very bulky, expensive, complex, and often require modification of the sample being detected in order to perform measurements. They are also very sensitive to physical movement and require considerable maintenance. Although UV extinction and light scattering techniques are quite robust and allow for a variety of sample types, they are also expensive and bulky. For large-scale labs with fixed laboratory equipment, these detection techniques provide high sensitivity and are well characterized and developed, but for use with portable equipment, and especially for use with the new crop of microscale analysis systems, more compatible, low-cost detection methods will need to be developed and tested.

The conductivity detector is the least specific detector in that it measures a bulk property of the solution rather than detecting a specific particle or chemical. The bulk property, conductivity in this case, can be modified significantly by the presence of analyte. The first conductivity chromatography detector was developed in 1951 [[130]] and significant improvements have been made in conductivity detectors in the intervening years including reductions in volume to as little as 0.1 mL [[131]]. Conductivity detectors typically consist of two electrodes separated by a small distance in which the sample being probed can be placed. The electrode geometry can vary as needed and dozens of designs have been presented [[132]]. The detector can be either used a stand-alone device or used in a Wheatstone bridge to amplify the signal. Advantages of conductivity detectors include being simple, reliable, and accurate as well as inexpensive.

Electrochemical detectors are also used regularly in chromatography and vary from conductivity detectors in that they respond only to substances that are reducible or oxidizable. Thus, they are species specific and measure only the electron flow that is generated at the electrode surface. The electrochemical detector consists of three electrodes, the working electrode (where the reaction takes place), the auxiliary electrode, and the reference electrode (which compensates for changes in the carrier conductivity). The configuration and geometry of the electrodes varies widely and is often application specific. The signal generated at the working electrode is proportional to the concentration of analyte passing through the detector since the reacting species is constantly being consumed and must diffuse to the surface of the electrode to continue the reaction. Electrochemical sensors with extremely small detection volumes have also been developed [[133],[134]]. Sensitivity in electrochemical detectors also rivals that of fluorescence-based systems for some analytes. Electrochemical detectors share several advantages with conductivity detectors such as simplicity, accuracy, reliability, and low cost.

Another system, which is not typically used as a detection system but may have great value in a microfabricated system, is electrical impedance spectroscopy (EIS). EIS is an electrical method similar to conductivity detection and electrochemical detection that scans the detection volume with an electrical frequency sweep, typically between 10 kHz and 10 MHZ [[135]]. The advantage of this system is that it can detect a wider range of particles and the resulting spectroscopic data can be used for particle size and type determination, in addition to the typical concentration measurement. With a single pair of electrodes, a type of two-dimensional image can be constructed that can also be used for sample characterization. Even more exciting is the possibility of using multiple electrodes to perform what is called electrical impedance tomography (EIT), an electrical impedance imaging technique [[136],[137]]. EIT usually requires a circle of 16 or 32 electrodes to approximate the spatial distribution of the impedance [[138]-[139],[140],[141]]. EIT works by passing a small current through individual pairs of electrodes and measuring the voltage generated. Sequential measurements using multiplexers and inverse algorithms are then used to reconstruct the image. Thus, EIT systems have a significant disadvantage in that they require extensive signal processing electronics and software. EIT may also be somewhat slow relative to other detection systems. The potential advantage, though, is that detection and spectroscopic determinations can be combined into one system, making for an extremely powerful detection system.

Integrated and Off-Chip Detectors

For a practical total analysis system, one must integrate sample handling, data processing, and data acquisition. Unfortunately, most current micromachined systems still rely on off-chip components to perform the bulk of the detection and signal processing duties, whether or not the actual detection takes place on-chip or off-chip. These detection systems are generally the same ones used for the corresponding macro-analysis system with slight modifications for working on the smaller microscale systems. For example, in all of the microfabricated electrophoresis systems referenced earlier, bulky fluorescence detection systems were used. In many other systems, after processing the sample using the microscale device, the sample is moved off-chip for analysis. Moving the sample off-chip, though, can be very detrimental in terms of resolution for chromatography systems [[142]], and measurement quality for other systems. The relatively large size of most detectors also limits the possibilities for parallel channel processing. There is a great need for a simple on-column detector for use with these micromachined analysis systems.

Several groups have proposed designs for detectors compatible with microscale devices, but only a few groups have actually succeeded in miniaturizing detection systems, all of which are electrically based systems rather than optically based. Several groups have demonstrated microfabricated thermal conductivity sensors for gas chromatography [113,[143]]. Two groups have demonstrated a microfabricated conductivity detector and its application to detection in electrophoresis systems [[144]-[145],[146]], though not on microfabricated electrophoresis systems. A microfabricated electrochemical detection system was reportedly used on a microfabricated liquid chromatography system, but data on the detector has not been published [112]. While the system was not used for chromatographic detection, a microfabricated EIS system has been demonstrated [[147],[148]] that could be converted into a detection system.

There are several inherent advantages of using microfabrication techniques to fabricate on-chip detectors. The first is that the primary goal of almost all detectors is to minimize detection volume, connections, and their associated dispersion effects, which compromise the separation just performed. Second, micromachining is very compatible with VLSI and other semiconductor optical techniques, so a laser or other optical detectors may be available on-chip soon. In fact the excellent optical qualities of silicon have already been harnessed in one system to develop an optical detector cell with external light sources and detectors [[149]]. Conversely, the trend in microscale analysis systems is away from silicon and towards glass and plastics which are less expensive (and potentially disposable), so many of the current detectors which rely on the semiconductor properties of silicon will not be applicable to the rising generation of devices unless specific steps are taken to integrate them after channel fabrication.

Considering the work that has already been done and the future direction of microfabricated analysis systems, it appears that electrical detection systems are the simplest to fabricate on the microscale as well as the most reliable. Therefore, in this work, a low-power detector capable of being used as a conductivity detector or an impedance spectroscopy based detection system is developed, designed, and characterized for use with microfabricated bioanalysis systems.

Chapter Outlines

Following this introduction, Chapter 2 will examine the theory behind ElFFF and scaling effects that are expected to be encountered as the ElFFF system is miniaturized. Chapter 3 will examine the requirements for fabrication of a miniaturized ElFFF system, describe the fabrication of the miniaturized system, and report the results of system fabrication. Chapter 4 will examine the function of the miniaturized ElFFF system and investigate the operating parameters, abilities, and scaling effects in the miniaturized ElFFF system. Chapter 5 will describe the design, fabrication, and testing of an integrated electrical detector using both resistance and impedance spectroscopy modes. Chapter 6 will describe application of the complete system to separation and analysis of biologically relevant particles. Chapter 7 will summarize the findings of this dissertation and suggest future efforts related to this work.

CHAPTER 2

THEORY AND SCALING EFFECTS

“There is no compelling fundamental reason …to reduce the thickness of FFF channels [[150]].” This quote from the father of FFF systems, J. Calvin Giddings, has directed FFF instrumentation research away from miniaturization for the last several years. While the statement appears to be true for most types of FFF systems, there are compelling reasons for miniaturizing both ElFFF and TFFF systems. By comparing the differences in theory between general FFF systems and ElFFF systems, a better understanding for why there are “compelling fundamental reasons” specifically for miniaturization of ElFFF systems is obtained. Additionally, a close look at scaling in FFF and ElFFF systems in particular identifies other potential advantages and disadvantages from miniaturization.

Introduction

Although not all FFF systems benefit significantly from miniaturization, there are a number of advantages common to all chromatography systems when miniaturization is considered. One of the key interests in miniaturization consists of the opportunity for total-analysis-systems (TAS) that combine sample handling, analysis, detection, and signal processing on one chip. It is anticipated that combining all of these functions on one chip will shorten analysis time and make the systems relatively portable so that critical analyses can be performed in the field or at bedside. If these total-analysis systems can be produced at low cost, the systems could also be disposable eliminating the need for cleaning or for handling hazardous material. As mentioned previously, there has been significant progress made in miniaturizing some of the components of a total-analysis-system, and some progress has been made in integrating these components, though significant work remains to be accomplished before a true micro-total-analysis-system (m-TAS) is completed.

The main component of most total-analysis-systems is a chromatography system, and most chromatography systems naturally gain advantages from miniaturization. Some of these advantages include: reduced plate heights or increased resolution, reduced analysis times, increased parallelism of analysis, reduced sample size, reduced system size, and reduced power consumption. Additionally, when microfabrication technologies are used to miniaturize the chromatography systems, additional advantages are accrued such as: the potential for batch fabrication and the associated reduction in production costs, the possibility for integrated electronics, signal processing, and particle detection, and improved manufacturing precision. Most of the performance gains associated with miniaturized chromatography systems are connected to two phenomena. First, the field strength for a given system increases as the system is miniaturized. Thus a higher field is available to drive the separation over a shorter distance which reduces analysis times and time-dependent plate height contributions. Second, the smaller channel dimensions reduce spatially related contributions to plate height and the resolution improves again.

The advantages for general FFF systems are not as far ranging as for most chromatography systems since the field strengths in FFF systems are generally not improved by miniaturization. Therefore, for many FFF subtypes, there is only minimal benefit from miniaturization. For ElFFF and TFFF, though, field strengths do improve with miniaturization and most of the advantages associated with general chromatography systems can also be claimed by these systems.

Since ElFFF systems are the focus of this work, the focus will be on advantages specific to this system. ElFFF systems, as mentioned gain from miniaturization and microfabrication all of the advantages associated with miniaturization of general chromatography systems such as: shorter analysis times, improved resolution, reduced sample size requirements, reduced power consumption, reduced fabrication costs, potential for integrated electronics, signal processing, and detection, reduced system size, and the increased parallelism of analysis. ElFFF has additional advantages that may not be similar to those of other systems such as: reduced time constants, reduced solvent consumption, reduced steric transition point, and reduced relaxation and equilibration times. Miniaturization of ElFFF systems improves the ability of the system to analyze smaller particles, but reduces the systems capabilities for larger particles.

A miniaturized ElFFF system would be available to provide analysis in a number of different fields and for a range of applications. Some of the applications for which a miniaturized ElFFF system would be ideal include those for which macro ElFFF systems are already employed. The main application of ElFFF systems to date has been for the characterization of polymers [69,71,72] and colloids [73,74]. ElFFF has also been used to characterize sugars [70] and clays [[151]]. Since interest in ElFFF has just recently been revived, the full range of applications is just beginning to be explored. When fully developed, ElFFF is expected to have similar applications to other FFF systems, but perform separations using a different mechanism and provide unique information regarding the samples being analyzed. Of specific interest is the application of ElFFF systems to biological analysis. Other FFF systems have been used to analyze and characterize such diverse biological materials as cells [48,[152]-[153],[154],[155]], bacteria [[156]-[157],[158]], viruses [[159],[160]], proteins [[161],[162],[163],-[164]], DNA [[165],[166]], starches [[167],[168],-[169]], lipid emulsions [[170]-[171],[172],[173]], liposomes [[174]], micelles [[175]], and vesicles [[176],[177]]. Other potential biological and medical applications include studies of DNA and protein adsorption on surfaces, analysis of drug delivery vehicles such as vesicles, micelles, emulsions, and liposomes, organelle separation and characterization, and diagnostic tests (separation of viruses and bacteria). ElFFF systems are not limited to biological applications, but are also available for particle analysis in a growing list of fields. A relatively well-developed field is environmental water monitoring where ElFFF has been applied with some success [151], as well as other FFF systems [[178]-[179],[180],[181]]. Other applications for ElFFF systems are being discovered on a regular basis and may include relatively unrelated fields such as archeology [[182]]. ElFFF is likely to prove valuable as a sample pretreatment system. Used in this manner, it would provide an initial separation that would then be collected for analysis in another system. ElFFF systems are also expected to be valuable in z-potential research. The list of applications for ElFFF systems is expected to continue to grow.

Even though the applications for ElFFF are significant and increasing, the power of current ElFFF systems is limited. In order for ElFFF to reach its full potential and prove successful in the areas mentioned previously, more powerful ElFFF systems will need to be developed. Miniaturization of the ElFFF system appears to be one route for development of an improved ElFFF system. To fully understand whether or not miniaturization would improve the system, a close look at both general FFF theory and ElFFF theory is required, along with the scaling effects in these systems.

General FFF Theory

In general, the theory behind general FFF systems is well developed [[183]-[184],[185],[186]]. The ElFFF channel, as shown in Figure 1, is a thin channel of rectangular cross-section with an aspect ratio (the ratio of width to height) over 80 (as needed to closely approximate two infinite, parallel plates [[187],[188]]). All FFF channels are of a similar design except that the applied field varies between FFF subtypes. Flow between parallel plates separated by small distances is laminar for the flow velocities of interest and is described by

(1))

where v is the flow velocity at a distance y from one of the plates, h is the viscosity of the fluid, w is the plate separation, and dp/dx is the pressure gradient along the flow axis. As the parabolic distribution given in equation 1 implies, the fluid velocity at the surface of the plates is zero while at a maximum in the center of the channel. Thus, if a particle or group of particles were to maintain an average distance y different from another particle or group of particles, their velocities through the channel would be different and they would exit the channel at distinct times.

Retention

Retention theory involves an understanding of what causes disparate particles to be retained at different levels and at different rates. In FFF, an applied field is used to control the average velocity of the particles in the channel by controlling the average distance an exponentially distributed cloud of particles protrudes into the flow stream with respect to the top and bottom surfaces of the channel. If the field is applied as shown in Figure 1, particles that are more susceptible to the field will reside closer to the wall of the channel than particles with less susceptibility. The particle cloud for the more susceptible particles protrudes less into the flow stream and therefore has a lower velocity than particles in the middle of the stream. The difference in average velocity produces the separation.

This conceptual view is quantified using equations 2 through 10 and is demonstrated graphically in Figure 2. The flux of particles towards the walls of the channel caused by the applied field will be opposed by dispersive effects in the channel such as diffusion. The dispersive flux is given by

, (2))

where c(y) is the concentration of the particles as a function of the distance of the particles from the wall, y, J_D is the flux of the particles, and D is the diffusivity. The diffusivity, D, can be calculated using the modified Einstein equation

, (3))

where k is the Boltzman constant, T is the absolute temperature, and d is the particle diameter. The applied field will cause a flux of particles, J_F_, towards the wall. This flux is governed by the equation

, (4))

where U, the drift velocity, is dependent on the applied field strength as shown by

, (5))

where S’ is the applied field strength, f is the field susceptibility of the particles and f is the sample friction coefficient. Therefore, the average thickness of the particle field will be determined by a balance between dispersive and electric forces. At equilibrium, the flux due to diffusion and the flux due to the applied field are equal

. (6))

Therefore, the following relationship can be derived

. (7))

Solving equation 7 for the concentration distribution produces

. (8))

Equation 8 shows that the concentration distribution of particles is exponential with the ratio between D and U as the parameter that defines the spatial distribution of the particle cloud. The ratio D/U therefore gives a relative measure of the thickness of this particle field. The ratio between diffusivity and drift velocity gives a length, commonly assigned the symbol l, as given by

. (9))

A dimensionless number, l, characterizes the separation in the channel and corresponds to a ratio between the two lengths l and w, as given by

. (10))

This retention parameter, l, can be related to the retention ratio, R. R is defined as the average particle cloud velocity, ávñ_zone, along the channel compared to the average carrier velocity

. (11))

The relationship between R and l, and the governing equation for FFF systems, is given by [183]

. (12))

At high retention levels (as l, l and R approach zero), the bracketed portion of equation 12 approaches one (coth(1/2l) approaches one as l goes to zero), so equation 12 is typically approximated using the simpler expression

. (13))

Since most FFF systems are operated under high retention, equation 13 is generally a reasonable approximation and is much more convenient for analysis of FFF systems.

Experimentally, R is found either by dividing the time required for one channel volume to move through the channel, t₀, by the time required to elute the particles of interest, t_r (retention time), or by dividing the void volume, V₀ (one channel volume or the volume required to pass an unretained sample), by the volume required to elute the particles of interest, V_e, as shown in

. (14))

The value of miniaturization on retention in FFF systems is highly dependent on the system subtype. As can be seen from equation 10, retention is an inverse function of channel height. Thus, as the channel height goes down, the value of the retention ratio goes up indicating a loss of retention. Generally, the goal of most FFF instruments is to increase retention, as reducing retention can easily be accomplished by reducing the field strength. Thus, for general systems, miniaturization will actually prove a disadvantage. The only possible offset to this disadvantage occurs when the field strength in the system is also a function of channel height, as is the case with ElFFF and TFFF systems. Specific effects regarding the effects of miniaturization on retention will be discussed in the section on scaling effects later in this chapter.

Plate Heights

Particle clouds in FFF systems are not generally limited to the volume into which they were initially injected, but tend to become dispersed across volume elements by mixing, diffusion, and other forces. As these particles spread in the volume and time dimensions, they can begin to overlap and cause a loss of separation efficiency. Thus, this spreading and loss of information must be limited to produce the best separations possible. The level of separation efficiency generated by a particular instrument can be quantified using the plate theory of chromatography. In plate theory, the length of a separation column can be broken down into N theoretical plates of height H as given by

. (15))

The plate height, H, is a measure of variance (s²) that has been created by the separation system while the band of particles being separated moves through the channel. N therefore becomes a measure of the separation efficiency of the system and indicates the number of times a certain separation distance is accomplished in a channel. H can be closely approximated by the ratio of variance to the length of the channel, L, [4] as shown by

. (16))

The total plate height can be thought of as the sum of several contributing factors. One group of factors, known as instrumental factors, H_i, can be minimized by good instrument design and operation procedures. These factors include the structure of the instrument (wall roughness, section connections, etc), sample plug length, and factors related to extra-column devices such as detectors and tubing. Once the instrumental factors have been minimized, the largest contributor to band broadening will be the nonequilibrium effects, H_n. These nonequilibrium effects are caused by the inherent distribution of the sample over a number of volume elements and slow movement of particles between volume elements. A third group of factors, H_p, is related to the polydispersity, or variation, in the sample being tested or separated. The fourth factor, H_D, is caused by the diffusion of particles in the system. Thus, the plate height, H, can be found as the sum of these factors as given in

. (17))

The terms H_p and H_D are bracketed in this equation since they are not related to system parameters or are small enough to be neglected and can be ignored for optimization of FFF systems. H_p, while it can be significant, is related only to the sample being tested and does not depend on any of the system parameters, and H_D, while it becomes more significant as the channel heights drop, is still insignificant at the channel heights of interest to this work as will be shown later in this chapter. Thus, for the purposes of this work, the plate height will be approximated by

. (18))

In FFF, the nonequilibrium component of plate height, H_n, is heavily dependent on the channel dimensions and the flow rate [183] as given by

. (19))

The function c(l) is generally represented by

. (20))

As retention increases, R and l decrease, and H_n becomes progressively smaller due to the highly compact bands. In this case the function c(l) closely approaches 24l³ [4] and H_n can be found using

. (21))

Since l is a function of both w and D, it is then reasonable to further simplify equation 21 by replacing l with equation 10 and then rearranging terms to arrive at

. (22))

Equation 22 is a critical equation for understanding of the value of miniaturization on FFF systems. Even a cursory examination of the equation indicates that reducing w will actually increase plate heights or in effect lessen the efficiency of the system unless U is somehow a function of w as well. Thus, it would seem that there is no motivation for miniaturization of the system and that miniaturization would be pointless and of little use other than for the convenience of a smaller package. This appears to be the case for several of the FFF subtypes. For example, in sedimentation FFF, there is no relationship between field strength and channel thickness and therefore no apparent rationale for miniaturizing the system. A similar result is obtained for flow FFF. For electrical and thermal FFF, though, the applied field strength is dependent upon the channel thickness assuming a constant or limited applied voltage or temperature difference. Thus, there is potential for improvement in plate heights using miniaturization for both electrical and thermal FFF systems. The exact improvements will be examined when the theory specific to electrical FFF systems is discussed.

Experimentally, band broadening and plate heights, H, can be measured and estimates of H_n and H_ican be made. This is done by measuring the width of a sample peak at half height, w_½, and the elution volume of the peak, A, as shown in Figure 3. The number of plates, N, can then be calculated using [[189]]

. (23))

The plate height, H, can then be calculated using the defining equation for the plate theory given in equation 15. Using equation 21 to estimate the nonequilibrium band broadening effects, a plot of plate height, H, versus flow velocity, <v>, can be made. Since the dominant plate height term is directly related to flow velocity as given in equation 21, the plot of plate height should increase linearly with flow rate. Since the instrumental band broadening is assumed constant, the intercept of this plot at zero flow velocity is the instrumental band broadening, H_i. Figure 4 shows how a plot of this type would be constructed and read. In FFF systems, the instrumental band broadening is typically characterized by injecting an unretained sample (typically acetone) into the FFF system and measuring the plate height as shown in Figure 3 for a series of flow velocities. The plate height is found using a limiting version of equation 19

Figure 3. Diagram of elution peak showing the important measurements that are made to determine the plate height in the channel. A is the elution time, w_1/2 is the width to the sample peak at half height. The measurements can be made on either a time or volume axis.

. (24))

As can be seen from equation 24, c(l) goes to 1/105 for acetone and other unretained samples [187].

As mentioned previously, diffusion can also play a role in increasing plate heights and contributes to the overall plate height. The equation for the contribution of diffusion to plate heights in FFF systems is

. (25))

Figure 4. Sample plate height measurement showing how the nonequilibrium plate height contribution, H_n, and the instrumental plate height, H_i, can be found experimentally.

Equation 25 is a ratio between the diffusion and the average flow velocity in the channel. Thus, diffusion is only significant in plate height measurements when the flow velocity becomes very small and longitudinal diffusion is able to cause a significant spreading of the injected sample. Typically, diffusion coefficients for particles of interest in FFF systems are never greater than about 1 ´ 10^-5 cm²/s and are usually several orders of magnitude less. Typical flow velocities are usually about 0.1 cm/s and rarely less than 0.01 cm/s. Thus, plate height contributions due to diffusion are typically measured in microns. Instrumental and nonequilibrium plate heights, though, are typically measured in millimeters making the contribution of diffusion negligible unless flow velocities fall unnaturally low. It is possible, though, that for a miniaturized system in which the instrumental plate height has been significantly reduced, the diffusive component of plate heights may become significant.

Resolution

The resolution of a chromatography system, R_s, is a measure of the relative separation efficiency of the system. The resolution can be measured experimentally by comparing the width of two particle peaks with their separation distance. An example of what various resolutions might look like is given in Figure 5. Mathematically, a resolution equal to 1 is defined as two peaks separated by 4s. On a time axis the equation for resolution is given by

(26))

where Dt_r is the difference in retention times, and is the average variance of the sample peaks on the time axis. The retention time, t_r, and the difference in retention times, Dt_r, can be related to the retention ratio and other parameters using the equations

(27))

and

, (28))

where is the average value of the retention ratio, R, and DR is the difference between the two R values. The variance, s_t, can be related to the number of plates, N, using

(29))

Figure 5. A sketch of how various resolution values appear experimentally. A resolution of one occurs when the two sample peaks are separated by 4s. Other resolution values are found using ratios compared to this standard.

Using equations 28 and 29, equation 26 can be related to parameters in the FFF system by

. (30))

Combining equations 15 and 22, we arrive at an expression for N

. (31))

By replacing N in equation 30 with equation 31, an equation for resolution using FFF system parameters can be derived

. (32))

Replacing DR /R with Dd/d we arrive at

. (33))

Examination of equation 33 reveals that for any FFF system, the resolution of the system is proportional the square root of channel height. Thus, a reduction in channel height would not be expected to improve resolution in any FFF system. Additionally, if the entire system is miniaturized, then the length would also be reduced, further reducing the resolution in the system. Thus, miniaturization does not appear practical or reasonable from a resolution standpoint, as several researchers have pointed out [76,150]. There are other areas where miniaturization may be advantageous, though, and some of these advantages have been mentioned previously and others will be discussed later. One other consideration when examining equation 33 is that for some systems (thermal and electrical), U is dependent on the channel height and additional gains may be possible in resolution for those systems. Further investigation of this possibility will be performed in the ElFFF theory section.

It should be mentioned here that a slightly different approach to resolution in FFF systems has been taken here than in some papers published on the subject. For example,

(34))

is the beginning equation for resolution as reported in an earlier publication [4]. In this equation, S_d is the size selectivity index for the system and d is the average diameter of the particles being compared. Replacing H in equation 34 with equation 22 and rearranging terms, we arrive at

. (35))

Note that equation 35 is identical to equation 33 except for the addition of the size selectivity term. In some FFF systems, S_d can be a very important parameter, while in others, S_d is close to 1 and of little importance to estimates of resolution or retention.

Other FFF Considerations

Steric Transition Point

One important effect that is encountered in FFF systems is the steric transition point where particle elution times begin to reverse once the radius of the particles being separated exceeds the layer thickness. In normal FFF modes, smaller particles will elute ahead of larger particles. However, beyond the steric transition point, this elution order will be reversed and larger particles elute ahead of smaller particles. Conceptually this transition occurs because the particles begin to exceed the layer thickness, l, of the particle cloud and can no longer circulate randomly in the particle cloud. In effect, the particles become pressed against the surface of the FFF channel and are separated strictly by particle diameter rather than a balance between size and susceptibility to the applied field. Larger particles, which naturally protrude farther into the flow stream and into the higher velocity flow areas, are swept along more quickly and exit the channel earlier than smaller particles that do not protrude into the flow stream as much, as shown in Figure 6. The steric transition point is then a measure of the amount of zone compaction and the effective field that operates in the channel. A knowledge of the location of the steric transition point can be extremely helpful, not only because it is necessary to avoid confusion when interpreting retention and separation data, but also because steric separations can often be done at very high flow rates and with very high resolution.

Figure 6. Representation of how average layer thickness determines elution order. For normal mode retention, particle elution time is determined by average layer thickness. For large particles being retained in a steric mode, the elution time is determined solely by the diameter of the particle. The representation also shows how steric and normal mode separations could be confused if not adequately understood.

The steric transition point is directly related to the layer thickness and, by association, the characteristic length, l. Since the steric transition point depends on the distribution of the particle cloud, it might be expected that miniaturization of the system will impact the steric transition point. If this idea is correct, then by miniaturizing FFF systems it may be possible to move the steric transition point to lower particle sizes and make high speed steric mode separations possible on even relatively small particles.

The steric inversion diameter, d_i, can be found using

(36))

where g is a dimensionless number of order unity used for complications originating from wall repulsion and other effects [[190]]. Observation of equation 36, though, indicates that for general FFF systems, there is no effect from channel height on the steric transition point. The only parameter that determines the steric inversion point is the sample drift velocity, which is a function only of the applied field for most systems and not sensitive to channel dimensions. As with other effects in FFF, though, some FFF subtypes show that U is sensitive to the channel height and that there is potential for the steric inversion point to be adjusted by adjusting channel dimensions in these systems. Adjustment of the steric transition point using channel heights may be especially valuable for systems in which the magnitude of the applied field is limited.

Stop Flow

After the sample to be analyzed is injected into an FFF system, time is required for particles to migrate toward the channel walls and establish an equilibrium position under the influence of the applied field. The establishment of equilibrium in the channel is not instantaneous and requires a relaxation time, t_e, equal to the time required for a particle to migrate from one electrode to the other in the presence of the applied field. If the drift velocity, U, is constant, the relaxation time will be found using

. (37))

To permit sample equilibration in FFF systems, it is customary to allow for a period of stop flow in which the particles are encouraged to migrate under the influence of the applied field to an equilibrium position. If this stop flow time is not practiced, high velocity flow lines are able to overly influence the migration of particles through the channel and cause peak fronting and losses in resolution, especially for small particles which tend to elute shortly after the void peak. In the case of these small particles, the elution peak tends to blend in with the void peak and can even be entirely lost in it if an insufficient stop flow time is allowed. For most FFF systems, stop flow times of at least 5 minutes are practiced and the stop flow time is often much longer. It is clear from equation 37 that reductions in channel height or miniaturization of FFF systems would have a positive effect on equilibration times and could significantly reduce or even eliminate the need for stop flow. This reduction in equilibration time would be even more significant for the FFF subtypes in which the drift velocity, U, is also a function of the channel height, w, such as ElFFF and TFFF.

Edge Effects

One concern common to all FFF systems is that the parabolic flow profile, so useful in the y-direction where it is used to perform the separation function in FFF, might also exist in the transverse (z) direction of the channel. A parabolic distribution in this direction would serve to increase band broadening and reduce the resolution of FFF systems. A high aspect ratio channel is required to reduce this effect. Other researchers have reported that aspect ratios over 100 closely approximate two parallel plates and generate flow profiles in which the effect of this transverse parabolic flow profile is minimized [187]. To verify this claim, a numerical model of the two-dimensional flow through a low aspect ratio channel was created and analyzed using the software program Matlab. The Gauss-Seidel iterative method with successive over-relaxation (SOR) was used to solve the partial differential equations defining the flow in the channel. The code for the simulation and a detailed explanation of the method used in the simulation is included in Appendix A. Figure 7 shows two of the simulated flows. The first flow is for a relatively low aspect ratio channel (Figure 7a) and shows the parabolic flow pattern in both the y and z directions. Figure 7b shows the flow in a simulated channel with an aspect ratio of 200. Note that the transverse parabolic flow profile is completely annihilated and that only the y-direction parabola survives. Thus, at very low aspect ratios, there is little danger of a transverse (z-direction) parabolic flow skewing the results or increasing peak broadening, and edge effects are minimized. There is only a slight disruption of this approximation at the edges. The infinite parallel plate approximation can be improved by increasing the aspect ratio and optimizing the edge surface using precise manufacturing processes. Micromachining is ideal for both increasing the aspect ratio and creating precise, smooth sidewalls.

ElFFF Theory

The theory related specifically to ElFFF systems is also firmly established, but not as well demonstrated, and some of the effects peculiar to ElFFF have not been adequately described in the theory. An understanding of the theory behind ElFFF and some of its unique variations is critical in understanding the operation and applications of ElFFF systems and in determining the possible advantages and difficulties to be created by miniaturizing the system. Several of the parameters of an ElFFF system are expected to change with the channel height including plate height, steric transition point, the time for samples to equilibrate in the channel, electrical time constants, and effective fields in the channel.

As mentioned previously, several researchers have discussed miniaturization of FFF systems and arrived at the conclusion that the advantages of miniaturization are limited and there is little real benefit in terms of efficiency or resolution [150]. The reasons for most of these claims revolve around the results presented earlier regarding lack of improved resolution when miniaturizing general FFF systems. Additionally, it is generally much easier and much more

(a)

(b)

Figure 7. Numerically calculated two-dimensional flow profiles. The magnitude in the z-direction is not important and can be normalized for any channel. a) Flow profile for an aspect ratio of 5. b) Flow profile for aspect ratio of 200. Notice the nearly perfect one-dimensional flow profile with virtually no edge effects.

practical to increase the field strength in the system to increase the separation efficiency rather than to fabricate a new instrument. As Giddings also points out, the dimension of true importance here is the particle cloud thickness, l, which can be adjusted by varying the field strength and is not explicitly dependent on any geometric dimensions. For some systems, though, it is not possible or practical to increase the applied field strength indefinitely. Would miniaturization be valuable in these systems? In some FFF subtypes, the field strength is dependent on the plate separation distance. Could miniaturization be valuable for these FFF subtypes? Considering that the evidence seems to point squarely against miniaturization, some may ask why it is being considered. All of these questions will be answered in this section.