> MIXING REACTIONS BY
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> TEMPERATURE GRADIENT FOCUSING

### CROSS-REFERENCE TO RELATED APPLICATIONS

1.  This application is a continuation‑in‑part of U.S. Patent
    Application No. 10/197,331 filed on July 18, 2002 which claims
    benefit of the filing date of both co‑pending Provisional Patent
    Application No. 60/307,691, filed on July 25, 2001, and 60/323,404,
    filed on September 19, 2001 and this application claims benefit of
    the filing date of co‑pending Provisional Patent Application
    No. 60/588,237 filed on July 15, 2004.

### STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

2.  This invention was made by employees of the United States Government
    and may be manufactured and used by or for the Government for
    governmental purposes without the payment of any royalties.

### FIELD OF THE INVENTION

3.  The present invention relates to a method for electrokinetic
    focusing of materials in a fluid, and in particular, methods for
    electro-focusing materials in fluidic devices using electric field
    gradients.

### BACKGROUND OF THE INVENTION

4.  Over the past decade a great deal of research has been focused on
    the development of technology related to micro-total-analytical
    systems. This technology is based on the concept of a series of
    microfluidic channels also known as microchannels for the movement,
    separation, reaction, and/or detection of various materials such as
    chemicals; biological compounds such as amino acids, proteins, and
    DNA; or cells or colloidal particles.

5.  One disadvantage with prior microfluidic devices and methods is that
    there is frequently a mismatch between the extremely small
    quantities of sample material used for analysis and the often much
    larger quantities needed for loading the sample into the
    microfluidic device and transporting the sample to the point of
    analysis. For example, a typical analysis sample may be around one
    nanoliter or less of a liquid containing one or materials that is
    injected into a separation channel and then separated
    electrokinetically as it moves down the channel to a detection
    region. However, the channels used to transport the sample materials
    to the injection point are typically also filled with the sample,
    thus increasing the required amount of the sample by a factor of 100
    or more. In addition, the sample is typically loaded onto the
    microfluidic device into a reservoir from a pipette so that in all,
    approximately 99.9% of the sample is discarded as waste.

6.  One general way of addressing the problem of requiring a large
    sample for analysis is to use any one of a number of focusing
    techniques. In the context of this disclosure, "focusing" refers to
    methods for manipulating the velocity of a material and thereby
    causing it to move towards a position at which the velocity is zero.
    At the zero velocity position the material will accumulate and
    increase in concentration, i.e., it will become focused. In
    addition, the location of the zero velocity position is often
    dependent upon some characteristic of the material or molecule being
    focused, so that different materials are focused at different
    positions, and can thereby be separated.

7.  In this context, focusing is to be distinguished from stacking,
    which is a related class of methods. Stacking involves moving
    materials through a velocity gradient (which is often transient) so
    that the materials accumulate along the velocity gradient. However
    with stacking, there is no point where the material velocity is
    zero. Hence, in stacking methods the maximum degree to which
    material concentration can be increased is theoretically limited to
    the ratio of the velocities on the fast and slow sides of the
    velocity gradient. In contrast, for focusing at a zero velocity
    position, there is no theoretical limit to the concentration factor.

8.  Prior focusing methods include isoelectric focusing; electromobility
    focusing; counteracting chromatographic electrophoresis; temperature
    gradient focusing, disclosed in U.S. Patent Application Publication
    No. 2003/0019752, herein incorporated by reference; and most
    recently, chiral temperature gradient focusing, disclosed in
    co‑pending U.S. Patent Application No. 10/**\[P07526US04/RFH\]**,
    herein incorporated by reference; and micellar affinity gradient
    focusing, disclosed in U.S. Patent Application Publication
    No. 2004/0206626, herein incorporated by reference. With the
    exception of the recently described micellar affinity gradient
    focusing method, the focusing methods all separate different
    materials based upon their electrophoretic properties, e.g.,
    mobility in the case of electromobility focusing and temperature
    gradient focusing, and the isoelectric point in the case of
    isoelectric focusing.

9.  Electric field gradient or electromobility focusing is one technique
    which can be used to concentrate samples at a given position within
    a microfluidic device before the analysis step. Further, the
    electric field gradient can be used to concentrate the entire sample
    at the beginning of the separation channel so that very little of
    the sample would be wasted.

10. Electric field gradient focusing is accomplished by the application
    of an electric field gradient within a microchannel. In response to
    the electric field gradient, there is a corresponding gradient in
    the electrophoretic velocity of any ionic material within the
    microchannel. The total velocity of the material is the sum of its
    electrophoretic velocity and the bulk fluid velocity. If these two
    components of the velocity are in opposite directions, they can be
    balanced so that the material will have zero total velocity.

11. When there is a gradient in the electrophoretic velocity, the
    balance between bulk and electrokinetic velocities can occur at a
    single position along the microchannel and therefore can result in
    focusing of the material at that position. Typically, the electric
    field gradient used in focusing is generated by the external
    manipulation of the electric field in the middle of the microchannel
    through the use of conducting wires, salt bridges, porous membranes,
    or other structures that will pass electric current but will
    restrict the flow of bulk fluid and the materials that are to be
    focused.

12. Several recent developments with regard to focusing methods in
    microfluidics, and in particular, the use of electric field
    gradients, have been made. A description of related methods of
    focusing can be found in C. F. Ivory, W. S. Koegler, R. L. Greenlee,
    and V. Surdigio, Abstracts of Papers of the American Chemical
    Society 207, 177-BTEC (1994); C. F. Ivory, Separation Science and
    Technology 35, 1777 (2000); Z. Huang and C. F. Ivory, Analytical
    Chemistry 71, 1628 (1999); W. S. Koegler and C. F. Ivory, Journal of
    Chromatography a 726, 229 (1996); and P. H. Ofarrell, Science 227,
    1586 (1985), all of which are hereby incorporated by reference.

13. To illustrate the basic principles disclosed in these publications,
    reference is made to Figure 1(a) which depicts a length of
    fluid-filled microchannel of constant cross-sectional area with an
    electrode, denoted 4, in the middle, and two further electrodes at
    each end, denoted 3 and 5, so that the voltages V~1~, V~3~ at the
    ends and the voltage V~2~ at the middle of the channel can be
    controlled. A single negatively charged material to be focused is
    present in a fluid that is provided to the microchannel. The
    electrical connection, represented as electrode 4, can be
    accomplished with a simple metal wire as depicted in Figure 1(a), or
    through a more complicated structure consisting of additional fluid
    channels and porous membrane structures or salt bridges.

14. The electric field in the section 1, i.e., the channel between
    electrodes 3 and 4 is
    $E_{1} = (V_{2} - V_{1}\frac{)}{(}\frac{l}{2})$ and the electric
    field in section 2, i.e., between electrodes 4 and 5, is
    $E_{2} = (V_{3} - V_{2}\frac{)}{(}\frac{l}{2})$, where V~1~, V~2~,
    and V~3~ are the voltages applied to the three electrodes 3, 4, and
    5, and $l$ is the length of the microchannel. If *E~1~* differs from
    *E~2~* as shown in Figure 1(b), the electrophoretic velocity of the
    material in the channel, $u_{\text{EP}}$, will be different in
    section 1 than in section 2. If an overall bulk fluid velocity,
    $u_{B}$ \<0, is applied, e.g., either electro-osmotic or
    pressure-driven, the bulk fluid velocity must be the same, due to
    continuity, in all parts of the microchannel. The total velocity of
    the material, *u~T~* = *u~B~* + *u~EP~*, will then be the sum of the
    electrophoretic and bulk velocities, which can differ in section 1
    from section 2.

15. The use of the microchannel device of Figure 1(a) for focusing of
    the material is illustrated in Figure 2 where
    $u_{T,1} > 0 > u_{T,2}$, so that the material moves into the middle
    from both directions and is thus focused in the middle of the
    channel near electrode 4.

16. One major drawback to electric field gradient focusing is that the
    microchannel device tends to be difficult to construct and that it
    requires the control of voltage on an additional electrode, e.g. 4
    of Figure 1(a), which is used to apply the electric field gradient.
    In addition, if electrodes are used to generate electric field
    gradients, unwanted chemical products will be generated
    electrochemically at the fluid‑electrode interface. If the electric
    field gradient is produced through the use of a salt bridge or
    membrane, the electrochemical products can be avoided, however only
    materials that cannot pass through the membrane or salt bridge can
    be focused.

17. Two additional methods for concentrating a sample include sample
    stacking and field amplified sample injection in which a sample is
    concentrated as the sample crosses a boundary between low and high
    conductivity fluids. These methods can achieve preconcentration
    factors of 100 to 1000-fold although these methods require multiple
    fluids. Sweeping is yet another concentration method which is
    capable of a very high degree of sample concentration (e.g., up to
    5000-fold), but is useful only for small hydrophoic molecules with a
    high affinity for a mobile micellar phase.

18. An additional technique for concentrating an ionic material includes
    isoelectric focusing. Isoelectric focusing is commonly used for the
    concentration and separation of proteins and involves the focusing
    of materials at their respective isoelectric points along a pH
    gradient.

19. Two examples of recent isoelectric focusing techniques are provided
    by U.S. Patent Nos. 3,664,939 to Luner et al. and 5,759,370 to
    Pawliszyn. Both references relate to isoelectric focusing with pH
    gradients that are created by the application of a temperature
    gradient. Isoelectric focusing uses a pH gradient to focus materials
    and in particular proteins, at positions along the pH gradient where
    the local pH is equal to the isoelectric points of the materials.
    The isoelectric point is the pH at which the material has zero
    electrophoretic mobility, i.e., approximately zero charge. pH
    gradients for isoelectric focusing are typically generated using
    ampholyte mixtures or immobilized ampholytes in gels. The two above
    referenced patents are included here as examples of prior art uses
    of temperature gradients for focusing. It is, however, very unusual
    for isoelectric focusing to be done with a pH gradient generated
    using a temperature gradient.

20. One disadvantage of isoelectric focusing is that it is limited in
    application because it can only be used with materials having an
    accessible isoelectric point such as proteins and peptides.
    Additionally, the concentration to which a protein can be focused
    with isoelectric focusing is severely limited due to the low
    solubility of most proteins at their isoelectric points.

BRIEF SUMMARY OF THE INVENTION

21. Broadly speaking, the present invention involves temperature
    gradient focusing, in conjunction with the concept that a molecular
    species or other material in a fluid can be focused and thereby
    spatially localized, e.g., as a focused band, and then allowed to
    interact or mix with another molecular species or material that is
    carried by a bulk fluid flow or electrophoresis through the focused
    band of the first material. If the interaction, binding, or reaction
    of the two materials produces a third material, that third material
    can then also be focused on the temperature gradient. Detection of
    the focused band of the third material, which is the product of the
    interaction or reaction of the first two materials, signals that the
    interaction has occurred. If the product of the interaction is a
    duplex of the first two materials, further manipulations can then be
    used to determine the strength of the binding of that duplex by
    measuring its melting curve and melting temperature.

22. In the context of this disclosure, "duplex" refers to a pair of two
    different molecular species or other subject materials that are
    bound together through specific or non-specific interactions,
    including biochemical, physiological, and/or pharmaceutical
    interactions. Examples of types of molecules or materials that would
    typically be involved in duplex formation include: proteins, nucleic
    acids, glycoproteins, carbohydrates, hormones, pharmaceuticals,
    antibodies, and aptamers. Specific examples of duplex forming pairs
    include: DNA/DNA, DNA/PNA, DNA/RNA, RNA/PNA, antibody/antigen,
    antibody/hapten, nucleic acid aptamer/protein, drug molecule/drug
    target molecule, enzyme/substrate, enzyme/inhibitor,
    enzyme/cofactor, binding protein/substrate, carrier
    protein/substrate, lectin/carbohydrate, receptor/hormone,
    receptor/effector, ligand/cell surface receptor, virus/ligand, etc.

23. Temperature gradient focusing is conducted using a method and device
    for concentrating and separating materials in a fluid within fluid
    conduits which include channels, microchannels, and capillary tubes.
    The concentration is achieved by balancing the electrophoretic
    velocity of a material against the bulk flow of fluid in the
    presence of a temperature gradient. Using an appropriate fluid, the
    temperature gradient can generate a corresponding gradient in the
    electrophoretic velocity of the material so that the electrophoretic
    and bulk velocities sum to zero at a given position and the material
    will be focused at that position.

24. 

25. 

26. 

27. 

28. 

29. One aspect of the present invention concerns a method for analyzing
    the interaction between a first material and a second material in a
    fluid. The interaction gives rise to a third material. The method
    includes the steps of introducing a first material into a fluid and
    applying an electric field to the fluid thereby causing the first
    material to move electrophoretically with an electrophoretic
    velocity. A temperature grading is established in the fluid having a
    significant component substantially aligned with the electrophoretic
    motion of the first material, thereby generating a gradient in the
    electrophoretic velocity of the first material. A flow is produced
    in the fluid having a significant component substantially aligned
    with a direction opposite a direction of the electrophoretic motion
    of the first material. The magnitudes of the electric field,
    temperature gradient and the flow are such that the first material
    will accumulate or be focused at a first position along the
    temperature gradient. A second material is introduced to the fluid
    so that the second material moves through the first position,
    thereby interacting with the first material to form a third
    material. The third material of the interaction is focused at a
    position along the temperature gradient.

30. In accordance with another aspect of the present invention, a method
    is provided for determining the melting temperature of a duplex of a
    first molecular species and a second molecular species in a fluid.
    The method includes mixing a first molecular species and a second
    molecular species in a fluid to form a sample solution containing a
    duplex. An electric field is applied to the fluid thereby causing
    the duplex to move electrophoretically with an electrophoretic
    velocity. A temperature gradient is established in the fluid having
    a significant component substantially aligned with the
    electrophoretic motion of the duplex, thereby generating a gradient
    of the electrophoretic velocity of the duplex. A flow is produced in
    the fluid having a significant component substantially aligned in a
    direction opposite a direction of the electrophoretic motion of the
    duplex wherein magnitudes of electric field temperature gradient and
    flow are such that the duplex will accumulate or be focused at a
    position along the temperature gradient. A local temperature around
    the first position is at a first temperature. A focused band of the
    duplex is detected at the first position thereby determining an
    amount of the duplex in the focused band at the first temperature.
    At least one of the electric field, temperature gradient and the
    flow are progressively changed so that a local temperature around
    the focused band becomes progressive different than the first
    temperature. The amount of the duplex is monitored in the focused
    band. The amount of the duplex is compared in the focused band at
    each progressively different temperature thereby determining the
    melting temperature of the duplex.

31. In accordance with yet another aspect of the present invention, a
    method is provided for using a temperature gradient focusing device
    to determine the melting temperature of duplex of a first molecular
    species and a second molecular species in a fluid. The temperature
    gradient focusing device has a temperature gradient. The method
    includes mixing a first molecular species and a second molecular
    species in a fluid to form a sample solution containing a duplex.
    The sample solution is introduced into the temperature gradient
    focusing device. The operational parameters are adjusted in the
    temperature gradient focusing device so that the duplex is focused
    at a position along the temperature gradient. A local temperature
    around the first position is at a first temperature. The focused
    band of the duplex is detected at the first position thereby
    determining the amount of the duplex in the focused band at the
    first temperature. Progressively, the operational parameters are
    changed so that the local temperature around the focused band
    becomes progressively different than the first temperature. The
    amount of the duplex is monitored in the focused band and the amount
    of the duplex in the focused band is compared at each progressively
    different temperature thereby determining the melting temperature of
    the duplex.

32. One advantage or feature of the present invention is provided by a
    technique that allows for simultaneous concentration and separation
    in a manner similar to isoelectric focusing but which is adoptable
    for use with any charged material and is not limited to materials
    for a specific isoelectric point or range of isoelectric points.
    Further, the temperature gradient focusing of the present invention
    can be used to achieve higher degrees of sample concentration, e.g.,
    more than 10,000 fold concentration of a dilute material, when
    compared with any prior single sample preconcentration method.

33. A further feature of the present invention is that the
    electrophoretic velocity gradient is formed within the channel or
    capillary in response to the temperature gradient without the need
    for externally manipulated voltages or complicated and difficult to
    fabricate semi-permeable structures.

34. Further features and advantages of the present invention will be set
    forth in, or apparent from, the detailed description of preferred
    embodiments thereof which follows.

### BRIEF DESCRIPTION OF THE DRAWINGS 

35. The invention will now be described in detail with respect to
    preferred embodiments with reference to the accompanying drawings,
    wherein:

36. Figure 1(a) is a schematic depicting a prior art microchannel device
    which provides for electric field gradient and Figure 1(b) is a plot
    of the electric field versus distance (x) along the microchannel of
    Figure 1(a);

37. Figure 2 is a plot of velocity versus distance along the
    microchannel of Figure 1(a);

38. Figure 3(a) is a schematic illustration of temperature gradient
    focusing and fluid conduit in the form of a microchannel in
    accordance with the present invention, Figure 3(b) depicts
    temperature distribution along the microchannel of Figure 3(a), and
    Figure 3(c) is a plot of the function
    $f(T) = \frac{\sigma(\text{20}) \cdot \eta(\text{20})}{\sigma(T) \cdot \eta(T)}$
    plotted as a function of the distance along the microchannel of
    Figure 3(a), where σ(T) is the temperature dependent conductivity,
    σ~0~ is a constant, and η(T) is the temperature dependent viscosity,
    and Figure 3(d) is a plot depicting velocity as a function of
    distance along the microchannel;

39. Figure 4(a) is a schematic illustration of a microchannel for
    temperature gradient focusing created by Joule heating according to
    another embodiment of the present invention, Figure 4(b) depicts the
    temperature profile along a length of the microchannel of Figure
    4(a), Figure 4(c) is a plot of the function,
    $f(T) = \frac{\sigma(\text{20}) \cdot \eta(\text{20})}{\sigma(T) \cdot \eta(T)}$,
    plotted as a function of the distance along the microchannel of
    Figure 4(a), and Figure 4(d) is a plot showing electrophoretic
    velocity, bulk velocity, and total velocity vs. distance along the
    microchannel of Figure 4(a);

40. Figure 5 is a schematic drawing of a fluidic device according to
    further embodiment of the present invention;

41. Figure 6 is a schematic drawing of a capillary fluidic device
    according to an alternate embodiment of the present invention;

42. Figure 7(a) is a schematic drawing depicting a mixing reaction by
    temperature gradient focusing prior to the addition of the second
    material, and Figure 7(b) is a schematic drawing of the mixing
    reaction of Figure 7(a) after the addition of second material in
    accordance with the present invention; \[move F1 slightly to the
    right in Figure 7(a), and draw F1 at the same position in (a) and
    (b), and put F2 to the left of F1 in (b)\]

43. 

44. Figure 8 is a plot relating intensity versus distance along a
    temperature gradient prior to the addition of the second material
    (top panel) and after the addition of the second material (bottom
    panel); and

45. Figure 9 is a plot depicting fluorescence intensity plotted as a
    function of position along a separation conduit in accordance with
    one embodiment of the temperature gradient focusing method of the
    present invention.

### DETAILED DESCRIPTION OF THE INVENTION

46. A material can be focused in a fluid conduit such as a channel or
    capillary when its total velocity is in opposite directions in
    different portions of the conduit, so that the material will move
    into the middle of the conduit and stop at a position where its
    velocity is zero. One way of accomplishing this is to cause the
    material to move with an electrophoretic velocity that varies along
    the length of the conduit. This can be accomplished by producing an
    electrophoretic velocity gradient along the conduit. If an
    electrophoretic velocity gradient is established, but the
    electrophoretic velocity is still in the same direction along the
    entire length of the conduit, a counter‑balancing bulk flow can be
    applied to the fluid in the conduit, driven either by
    electroosmosis, pressure gradients, or both, so that the total
    velocity of the material, i.e., the vector sum of the bulk flow
    velocity and electrophoretic velocity of the material is equal to
    zero at some position along the conduit.

47. Temperature gradient focusing is a method for focusing materials
    that produces the required material electrophoretic velocity
    gradient through the application of a temperature gradient. In
    temperature gradient focusing, a fluid with a temperature dependent
    ionic strength is typically used to give an electrophoretic velocity
    that is temperature dependent. Then the electrophoretic velocity of
    the material can be altered in different portions of the conduit or
    capillary simply by heating or cooling different portions of the
    conduit. The application of a temperature gradient then results in
    an electrophoretic velocity gradient, which, with a counteracting
    bulk flow, can be used for focusing. It should be noted that, in
    contrast to electric field gradient focusing where the electric
    field gradient is applied using a combination of electrodes and
    membranes, using temperature gradient focusing of the present
    invention, the necessary electric field gradient is produced by the
    application of a temperature gradient. With temperature gradient
    focusing, different materials are focused at different positions and
    thereby separated based upon differences in their electrophoretic
    mobilities.

48. In the method of the present invention, temperature gradient
    focusing is used to first focus one material in a fluid, after which
    a second material is introduced to the system and allowed to move so
    that it passes through the focused band of the first material and
    allowed to interact with it. If the interaction produces a third
    material, that third material can then also be focused on the
    temperature gradient (assuming that it is charged and that it has
    the same sign of charge as the first material). Detection of the
    focused band of the third material, which is the product of the
    interaction or reaction of the first two materials, signals that the
    interaction has occurred. If the product of the interaction is a
    duplex of the first two materials (or of some parts of the first two
    materials), further manipulations can then be used to determine the
    strength of the binding of that duplex by measuring its melting
    curve and melting temperature.

49. The types of fluids that would typically be used include ionic
    aqueous solutions, ionic non-aqueous solutions, aqueous buffer
    solutions, and mixtures of aqueous and non-aqueous solutions. The
    types of materials that could be analyzed using this method include
    any pair of materials in which at least one of the materials is
    charged when dispersed or dissolved in the fluid used. Specific
    examples of materials that could be analyzed for their interactions
    using this method include single stranded DNA, single stranded PNA,
    single stranded DNA covalently bound to a 'drag tag', nucleic acid
    aptamers, antibodies, molecules with molecular weight less than 500
    amu, amino acids, peptides, proteins, cytokines, nucleic acids,
    cells, colloidal particles, bacterial particles, and viral
    particles.

50. Further description of the present invention will now be made with
    reference to the drawings, and in particular to Figure 3(a), where a
    fluid-filled microchannel 10 includes electrode connections 12, 14
    at each end one of which is connected to a high voltage source such
    as an electrical power supply and the other of which is electrically
    grounded. The velocity of a material in the microchannel 10 is given
    by the sum of its electrophoretic velocity, u~EP~, and the bulk
    velocity, u~B~, of the fluid:

$u_{T} = u_{\text{EP}} + u_{B}$.

51. If there is a gradient in the electrophoretic velocity, the bulk
    velocity can be adjusted so that the total velocity is equal to zero
    at a single point along the microchannel 10, and the material will
    be focused at a position around that point. The electrophoretic
    velocity of a material in the microchannel 10 is given by the
    product of the electric field, E, and the electrophoretic mobility
    of the material: $u_{\text{EP}} = E \cdot \mu_{\text{EP}}$.

52. A temperature gradient is applied along the length of the channel as
    shown in Figure 3(b). This results in corresponding gradients in
    both the electric field E and the electrophoretic mobility μ~EP~.

53. The electric field in the microchannel 10 is given by:

$E = \frac{I}{A \cdot \sigma}$,

where *I* is the electric current running through the microchannel 10,
*A* is the channel cross-sectional area of the microchannel 10, and *σ*
is the conductivity of the fluid. Since the conductivity of the fluid is
most often temperature-dependent, the electric field is also most often
temperature-dependent. Here, constant current is presumed because the
current running through any given section of the microchannel 10 will be
the same for all parts of the microchannel, whereas the voltage drop
across a portion of the microchannel 10 and the electric field in the
microchannel 10 will depend on the temperature of that portion. One
skilled in the art will readily appreciate that the present temperature
gradient focusing differs from electric field gradient focusing in that
in electric field gradient focusing, the velocity gradient that is used
for focusing results from a gradient in the electric field imposed by
the addition or subtraction of current from a point or points within the
microchannel.

54. Using microchannel 10, it is possible to manipulate the conductivity
    of the fluid by changing the temperature. Consequently, it is
    possible to produce electric field gradients in microfluidic
    devices, such as microchannel 10, through the application of a
    temperature gradient.

55. At fixed current density, the electric field in microchannel 10 is
    inversely proportional to the conductivity of the fluid in the
    microchannel. Most often, the primary temperature dependence of the
    conductivity is due to the variation of the fluid viscosity with
    temperature, so it can be written as
    *σ* = *σ*~0~·*η*(20)/(*η*(*T*)·*f*(*T*)), where σ is the
    conductivity, σ~0~ is a constant, η(T) is the temperature dependent
    viscosity, and $f(T)$ is a dimensionless function that accounts for
    any other temperature dependence. Similarly, the temperature
    dependence of the electric field is given by *E* =
    *E*~0~·*η*(*T*)·*f*(*T*)/*η*(20), where E is the electric field and
    E~0~ is a constant.

56. For the types of fluids most commonly used microfluidic analysis,
    e.g., aqueous buffers, the function $f(T)$ is constant or only
    weakly dependent on temperature. However, it can be non-constant,
    i.e., variable, if, for example, the ionic strength of the fluid is
    temperature dependent. Advantageously, the fluids of the present
    invention are characterized by a non-constant $f(T)$.

57. The electrophoretic mobility of a material in the fluid is also
    dependent on the viscosity, and so can be written as
    *μ~EP~* = *μ*~0~·*η*(20)/(*η*(*T*)·*f~EP~*(*T*)), where $\mu_{0}$
    and *f~EP~*(*T*) are defined in analogy to σ~0~ and $f(T)$ where,
    for most materials, *f~EP~*(*T*) will be constant. The
    electrophoretic velocity of the material can then be written as
    *u~EP~* = *E*~0~·*μ*~0~·*f*(*T*)/*f~EP~*(*T*). It should be noted
    that if $f(T)$ and *f~EP~*(*T*) have the same temperature
    dependence, e.g., they are both constant, then *u~EP~* will not be
    temperature dependent, and an electric field gradient produced in
    this way can not be used for focusing.

58. If, on the other hand, $f(T)$ and *f~EP~*(*T*) do not have the same
    temperature dependence, then temperature gradients will result in
    gradients in the electrophoretic velocity, which can be used for
    focusing as described above.

59. One skilled in the art will readily appreciate a major advantage of
    this present method over some other methods of preconcentration is
    that the concentrations of the background ions (those ions that are
    included in the fluid to provide a temperature-dependent ionic
    strength) are completely unaffected by the focusing. This results
    from the fact that if the background ions are considered as
    materials to be focused, then, by definition, *f~EP~*(*T*) = $f(T)$
    and there is no gradient in the electrophoretic velocities of the
    background ions.

60. Most commonly this technique would be implemented with a fluid
    characterized by a strongly temperature dependent $f(T)$ and with
    materials characterized by a constant or nearly constant
    *f~EP~*(*T*). However, the present temperature gradient focusing can
    also be implemented in a system in which $f(T)$ is constant and
    *f~EP~*(*T*) is not, or in which both $f(T)$ and *f~EP~*(*T*) are
    non-constant, but differ in their temperature dependence. One type
    of fluid that would have a temperature dependent *f(T)*, and could
    therefore be used for temperature gradient focusing, would be a
    fluid with a temperature dependent ionic strength.

61. One preferred fluid system is composed of 0.9 mol/L
    Tris(hydroxymethyl)aminomethane and 0.9 mol/L boric acid in water
    (0.9 M Tris-borate buffer), with an expected pH of about 8.7 (at
    room temperature). From measurements of the conductivity of the 0.9
    M Tris-borate buffer and the known viscosity of water, the function
    $f(T)$ for 0.9 M Tris-borate buffer was determined to vary from 1 at
    20ºC to 0.77 at 70ºC.

62. The counterbalancing bulk flow can be applied electroosmotically if
    the electro-osmotic mobility does not differ too much from the
    electrophoretic mobility of the material to be focused. If the
    electro-osmotic mobility is written as
    *μ~EO~* = *μ~EO~*^0^·*η*(20)/*η*(*T*), then by adjusting the ratio
    of the lengths of the hot and cold channels, (assuming
    *f~EP~*(*T*) = constant) focusing can be achieved if
    *f*(*cold*)/*f*(*hot*) \< ‑*μ*~0~/*μ~EO~*^0^ \< *f*(*hot*)/*f*(*cold*),
    where $f(\text{hot}) > f(\text{cold})$ (If
    $f(\text{hot}) < f(\text{cold})$, then the inequalities have the
    opposite sign). If x is the fraction of the total channel length
    that is hot, then focusing will occur if:
    *x*·*f*(*hot*)/*f*(*cold*) + (1 ‑ *x*) \< ‑*μ*~0~/*μ~EO~*^0^ \<
    *x* + (1 ‑ *x*)·*f*(*cold*)/*f*(*hot*), where
    $f(\text{hot}) > f(\text{cold})$. By adjusting x, it is then
    possible to tune the range of material mobilities that are focused.
    In many cases, the electrophoretic and electroosmotic mobilities
    will not be so well balanced, and therefore although the bulk
    velocity will be largely due to electroosmosis, it must also be
    adjusted using an externally applied pressure gradient.

63. It should be noted that temperature gradient focusing can also be
    implemented in microchannels or other fluid conduits of non-constant
    cross-section. The final results are essentially unchanged, since in
    most instances, the dependence on the cross-sectional area of the
    channel cancels out in the equations. As a result, it is possible to
    generate the temperature gradient using Joule heating within the
    microchannel. This would serve to simplify the design and operation
    of a microfluidic device using this technique even further, since
    the focusing and the temperature gradient could be produced using
    the same voltage source and pair of electrodes as illustrated in
    Figure 4(a).

64. Microchannel 20 shown schematically in Figure 4(a), has electrodes,
    22, 24, and two sections, sections 26, 28, of different
    cross-sectional area. Section 26 has a cross-sectional area of 27
    and section 28 has a cross-sectional area of 29. The electrical
    resistance per unit length of each section is given by:
    $R_{i} = \frac{1}{(}\sigma \cdot A_{i})$, where σ is the
    conductivity of the fluid in the microchannel 20. When a current,
    *I*, is passed through the microchannel 20, the power per unit
    length dissipated through Joule heating in each section will be:
    $P_{i} = I^{2} \cdot R_{i} = \frac{I^{2}}{(}\sigma \cdot A_{i})$. In
    general, the resulting temperature in section 28 will be higher than
    that in section 26, as shown in Figure 4(b): $T_{2} > T_{1}$. The
    electric field in each section of the microchannel 20 is given by
    the current multiplied by the resistance per unit length:
    *E~i~* = *I*·*R~i~* = *I*/(*σ*·*A~i~*) = *I*·*η*(*T~i~*)·*f*(*T~i~*)/(*σ*~0~·*h*(20)·*A~i~*).

65. The electrophoretic velocity of a material in each section of the
    channel is: *u~EP~^i^* =
    *μ*~0~·*f*(*T~i~*)·*I*/(*σ*~0~·*f~EP~*(*T*)·*A~i~*). If a bulk flow
    velocity is applied along the channel, it will not be the same in
    each section, but will instead be given by *u~B~^i^* =
    *u~B~*^0^/*A~i~*, where, *u~B~*^0^ is a constant. The ratio of the
    electrophoretic velocity to the bulk velocity is then given by:
    *u~i~^ratio^* = *μ*~0~·*f*(*T~i~*)·*I*/(*σ*~0~·*f~EP~*(*T*)·*u~B~*^0^) ≡ *u~0~^ratio^*·*f*(*T~i~*)/*f~EP~*(*T*)
    via adjusting *u~B~*^0^ so that
    $\left| u_{1}^{\text{ratio}} \right| > 1 > \left| u_{2}^{\text{ratio}} \right|$
    as shown in Figure 4(d), which can result in focusing. Because the
    ratio of the electrophoretic velocity to the bulk velocity does not
    depend on the cross‑sectional areas of the two sections, the same
    considerations as above apply if bulk flow is applied
    electroosmotically.

66. Joule heating may be used to generate the temperature gradient in
    the microchannel device of Figure 4(a). The following is a
    non-limiting example demonstrating Joule heating of a microchannel
    of the type shown in Figure 4 (a).

67. The microchannel used for this demonstration was similar to the one
    shown schematically in Figure 4(a). The width, i.e., cross sectional
    area 29, of the narrow channel, i.e., section 28, was about 70 μm,
    and the width of the wide section, i.e., section 26, cross sectional
    area 27 was about 350 μm. The length of the tapered portion of the
    channel was about 500 μm. The depth of all portions of the channel
    was about 30 μm. The total length of the microchannel was about 2
    cm, with the length of the section 28 divided by the total length, x
    ≅ 0.8. Access to each end of the microchannel was provided by a 3 mm
    hole through the lid piece of the microchannel.

68. The fluid used was 0.9 M Tris-borate buffer. The material to be
    concentrated was the carboxyfluorescein. An 8 μmol/L solution of
    carboxyfluorescein in the 0.9 M Tris-borate buffer was prepared.
    Detection of the carboxyfluorescein was performed using a
    fluorescence microscope and CCD cameras. Simultaneous color and
    grayscale images were obtained.

69. To demonstrate gradient focusing using Joule heating, the
    microchannel was filled with the caboxyfluorescein solution and 1900
    V was applied along its length using a high voltage power supply and
    platinum electrodes, with the positive voltage V~2~ applied to the
    narrow end via electrode 22, and the wide end held at ground at
    electrode 24.

70. After 6 min., the carboxyfluorescein was highly concentrated at the
    junction between sections 26 and 28 of the microchannel 20. The
    concentration factor achieved by using this example was typically
    about 100-fold per minute.

71. Referring now to Figure 5, in order to have better control of the
    temperature gradient, experiments were done using three temperature
    zones, two cold zones provided by cooling copper blocks 53a, 53b
    covering much of the ends of the microchannel 50, and one hot zone
    provided by heated copper block 52. The microchannel 50 was made out
    of thin (125 μm) sheets of poly(carbonate) substrate 51, which were
    pressed onto the copper blocks 52, 53a, 53b. Thermal contact between
    the poly(carbonate) and the copper blocks was insured using a
    thermally conductive adhesive 56. The copper blocks 52, 53a, 53b
    were arranged so that there was a 1 mm gap 58 between the heated
    copper block 52 and the cooling copper block 53a and a 2 mm gap 59
    between heated copper block 52 and the cooling copper block 53b.

72. Microchannel 50 also includes electrodes 55, 54, fluid
    reservoirs 57, and a narrow hot zone 50a near the middle of the
    microchannel 50. The heated copper block 52 was heated using a small
    high-power resistor embedded into the copper and its temperature was
    regulated using a PID temperature controller (Omega Engineering Inc,
    Stamford, CT). To regulate the temperature of the cold zones, ¼ inch
    diameter holes were drilled through the cooling copper blocks 53a,
    53b and cold water from a thermostatted bath (Neslab, Portsmouth,
    NH) was passed through them.

73. Thin polycarbonate microchannel chips, i.e. substrate 51 was
    attached to the copper blocks 52, 53a, 53b using thermally
    conductive adhesive 56 in the form of transfer tape (3M). The
    substrate 51 was pressed against the copper blocks 52, 53a, 53b from
    above with 3 mm thick PDMS (Sylgard 184, Dow Corning, Midland, MI)
    gaskets 60 and a 2 mm thick acrylic (Acrylite OP-4, Cyro Industries,
    Mt. Arlington, NJ)) top plate 61, which was secured to the outer
    copper clocks using nylon screws (not shown).

74. During temperature gradient focusing, a voltage potential is applied
    to electrode 55 and electrode 54 is set to ground using a high
    voltage power supply. In most cases, the electrophoretic and
    electroosmotic mobilities are not sufficiently balanced, so that an
    externally applied pressure gradient must be applied to microchannel
    50 to allow microchannel 50 to provide focusing and separation of
    different types of materials: small dye molecules, amino acids,
    proteins, DNA, colloidal particles, and cells. There are many
    possible means for applying the necessary pressure gradient,
    including the use of pneumatic pressure controllers, and adjusting
    the volume of fluid contained in the reservoirs 57 to take advantage
    of gravitational and/or capillary (surface tension-driven) forces.

75. The microchannel 50 may be formed by imprinting with a micro
    machined silicon template and then sealed with a similar material
    according to the method disclosed in Ross, D.; Gaitan, M.; Locascio,
    L.E., *Analytical Chemistry* 2001, 73, 4117-23, herein incorporated
    by reference.

76. The copper block arrangement was also used to determine the degree
    of focusing that could ultimately be reached with temperature
    gradient focusing. Beginning with a 8 nM solution of Oregon Green
    488 carboxylic acid in 0.9 M Tris-borate, 100 min of focusing
    resulted in a focused plug of Oregon Green 488 carboxylic acid with
    a peak concentration over 80 μM -- a greater than 10000-fold
    increase in concentration.

77. It will become readily apparent to one of ordinary skill in the art
    that the present method provides for use in numerous applications.
    For example, temperature gradient focusing could be used as a
    preconcentration step before an analysis or separation or as a
    simultaneous concentration and separation technique. In addition,
    temperature gradient focusing could be used for preparative scale
    separation of different materials or different enantiomers if the
    focused material or materials are collected after focusing.

78. In addition, temperature gradient focusing may be used with any
    charged material and not just small molecules. For example, the
    materials may include larger molecules such as proteins and DNA, or
    even particles and cells. In addition, the present method can be
    adapted for use to sort particles or cells by electrophoretic
    mobility.

79. In one separation mode, the bulk velocity could be ramped over time
    to scan focused sample peaks past a fixed detector, e.g. the
    detector shown in Figure 5. This would produce results similar to
    capillary electrophoresis but the widths of the sample peaks would
    be determined by the applied gradients and the peak heights would be
    determined by how long a given peak was in the focusing "window". If
    the ramp speed were halved, the peak heights would all be doubled,
    so that the ramp rate could be chosen dependent on the concentration
    limit of detection necessary. Alternatively, the focusing window
    could remain fixed and a scanning or imaging detector could be used
    to locate the separate peaks.

80. In a further embodiment, the method may be adapted for a system
    where temperature dependence is due to something other than the
    ionic strength. An example is a system having *f(T)* constant but
    *f~EP~(T)* not constant, or variable. One way to accomplish this
    would be to use a fluid with a temperature dependent pH. In such a
    system, this embodiment of the present invention is similar to
    isoelectric focusing schemes. However, the present invention differs
    from isoelectric focusing in that, in the present system, an
    opposing fluid flow is applied so that materials are focused at a pH
    other than their isoelectric points.

81. When using any of the embodiments of the present method, operating
    parameters which include voltage, bulk flow rate, and temperature of
    the different zones may be held constant with time or varied with
    time to affect the position and width of focused sample peaks.
    Varying of parameters may be accomplished using any of a number of
    methods which include the methods previously described above in
    which the focused sample peaks are scanned past a fixed detector.

82. Advantageously, in order to achieve the fastest accumulation of
    material in the focused peak, the highest possible voltage should be
    used. However, a higher applied voltage requires a faster bulk flow
    which can result in greater dispersion, i.e., wider focused peaks,
    which is disadvantageous for separation and for achieving
    pre-concentration of a sample to a high concentration in a very
    narrow peak. Therefore, a high voltage and fast bulk flow could be
    used for the initial accumulation of material into a relatively
    broad peak, and the voltage flow and flow rate could then be reduced
    to the values which give the narrowest peaks. Further, temperature
    gradients could be turned on and off to first concentrate the sample
    and then release the focused peak and allow it to flow on down the
    channel. Further, the temperature gradient can be adjusted to be
    linear or nonlinear, and the temperature gradient may be monotonic
    or non-monotonic. Thus, operating parameters may be adjusted to
    achieve the desired results.

83. While the previously disclosed embodiments are directed to a
    microchannel or microfluidic device, the present method may be
    adapted for incorporation for use with substantially larger channels
    which may include millimeter and centimeter if not larger in
    dimension which should now be apparent to one of ordinary skill in
    the art. Because temperature gradient focusing uses low conductivity
    fluids, one can adapt the present method for use in much larger
    scale geometries than the micron-sized channels and capillaries
    described in detail herein.

84. Further, the previously described method can be adapted for use in
    modified capillary fluidic systems known to one of ordinary skill in
    the art. Figure 6 depicts a capillary fluidic system having a
    capillary tube 70 spanning between two fluid reservoirs 77. Two
    temperature blocks, denoted as heated block 72 and cooling block 73
    are located along the length of the capillary tube 70 to provide a
    desired temperature gradient in the capillary tube 70.
    Alternatively, temperature blocks being both cooling, both heated,
    both at ambient temperature, or any combination, thereof, may be
    substituted to provide the desired temperature gradient.

85. The fluid reservoirs 77 contain a fluid with temperature dependent
    ionic strength. Electrodes 74, 75 are connected at one end to a
    power supply and on the other end, are in contact with the fluid in
    the reservoirs 77. The power supply applies a driving voltage
    through the capillary tube 70. A source of bulk flow is driven
    either by electro-osmosis with the applied driving voltage, by a
    pressure gradient applied, e.g. by a pump, or a combination of the
    two. Detector 80 is used to detect materials present in the fluid.

86. The temperature gradient focusing technique of the present invention
    can be used for mixing reactions and for monitoring and/or detecting
    the interactions between different materials such as interacting
    molecular species. In one form of mixing reactions/interactions, a
    material is first focused using temperature gradient focusing as
    described above with regard to the prior embodiments. Subsequently,
    a second material is introduced into the fluid conduit and a product
    of the interaction of the two materials can be focused on the same
    temperature gradient and detected. The materials and/or their
    interaction products can be detected in accordance with conventional
    detection methods known to one of ordinary skill in the art as well
    as in accordance with previously described detection methods.

87. Referring now to Figures 7(a) and 7(b), mixing reactions in
    accordance with the present invention can be conducted using a fluid
    conduit such as microchannel 710 which comprises a hot zone and a
    cold zone produced by heated block 718 and cooled block 720,
    respectively. This creates a temperature gradient in the fluid 716
    which contains a first material to be separated or focused. An
    electric field is established in the fluid 716 by applying a voltage
    potential to a high voltage electrode 712 so that the voltage
    between terminal 712 and a grounding electrode 714 causes the first
    material to move electrophoretically. The voltage is most commonly
    applied by an electrical power supply 726.

88. As with the prior embodiments, a temperature gradient is established
    along the length of the microchannel 710 which has a significant
    component substantially aligned with the electric field to thereby
    generate a gradient of the electrophoretic velocity of the first
    material. The gradient of electrophoretic velocity of the first
    material can be established by the fluid 716 having an ionic
    strength or pH which is temperature dependent as described above.

89. A bulk flow is produced in the fluid 716 due to electroosmosis
    resulting from the applied voltage and adjusted via pressure
    controller 728 to have a significant component substantially aligned
    in the direction opposite of the direction of the electrophoretic
    migration of the first material so that the total velocity of the
    first material is equal to zero at a position along the microchannel
    and a focused band of material F~1~ will form at that position. The
    bulk flow is established in a similar manner to that described with
    regard to the prior embodiments.

90. Next, a second material is introduced into the fluid so as to move
    through the now focused first material band F~1~, and to interact
    with the first material. The second material can be introduced to
    either end of the microchannel, depending on whether it has an
    electrophoretic mobility that is less than or greater than that of
    the first material. If the electrophoretic mobility of the second
    material is less than that of the first material, or if the second
    material is of the opposite charge than the first material, then the
    second material should be introduced into the end of the channel
    where the bulk fluid flow predominantly determines the direction of
    motion of the first material. More specifically, if a fluid with a
    temperature-dependent ionic strength is used, the second material
    should be introduced into the high ionic strength end. If, on the
    other hand, the second material has an electrophoretic mobility that
    is greater than that of the first material, assuming that they have
    the same sign of charge, it should be introduced into the end of the
    channel where the electrophoretic motion dominates or the low ionic
    strength end.

91. After the second material is introduced, if hybridization, binding,
    or other interaction or chemical reaction of the two materials
    occurs, the product of that interaction, i.e., a third material,
    will be focused at a second position and a second band F~2~ will be
    observed as depicted in Figure 7(b).

92. Preferably, the position of the second band F~2~ will be different
    than the position of the first band F~1~, due to a difference in
    electrophoretic mobility.

93. In a non‑limiting example of this method, this method can be used to
    observe the interaction of single strand DNA with another nucleic
    acid. In this example, the first material is negatively charged
    single stranded (ss) DNA which is labeled for observation within the
    microchannel 710, and the second material is a peptide nucleic acid
    (PNA) which is introduced into the microchannel 710. First, the
    ssDNA is focused as a single band F1. Then, the neutral PNA is
    introduced into the microchannel 710. The PNA is carried by the bulk
    flow of the fluid through the stationary, focused band of single
    strand DNA at location F1.

94. The ssDNA and PNA are allowed to interact with each other. If the
    PNA and ssDNA hybridize, the hybrid duplex will focus at a different
    spatial location within microchannel 710 because of its different
    electrophoretic mobility and as a result a second band, F~2,~ is
    observed. If the PNA is not complimentary to the focused ssDNA, the
    two will not hybridize with one another and the neutral PNA will
    remain unfocused. In such an instance, a second band will not be
    observed and the result will be the same as shown in Figure 7(a).

95. The following non‑limiting example is included to provide further
    understanding of the present mixing reaction method using
    temperature gradient focusing. The ssDNA was fluorescently labeled
    on the 5' end while the PNA probes contained a fluorescence label on
    the N‑Terminus. The labels were fluorescein for DNA (green emission)
    and TAMRA for PNA (orange emission). Using a VHS tape and frame
    grabbing software, the hybridization of a perfect complement PNA
    probe to ssDNA was recorded. The experiment was performed in a 30 μm
    I.D. fused silica capillary, 10 cm long. The capillary was
    mechanically and thermally anchored to two copper blocks at
    different temperatures to create a temperature gradient along a 2 mm
    section approximately midway along the length of the capillary. A
    temperature gradient from 10°C to 80°C was applied. The fluid used
    was 0.1 mol/L Tris(hydroxymethyl)aminomethane, 0.1 mol/L phenol in
    water (0.1 M Tris-phenol buffer). A voltage of +3000 V was applied
    to the 10°C end of the capillary and the 80°C end was electrically
    grounded. Figure 8 is the line profile monitoring the fluorescence
    emission from the PNA/DNA duplex that resulted from the mixing and
    the unreacted ssDNA. In Figure 8, the top panel is a plot depicting
    a line profile before the introduction of PNA into the bulk flow and
    the bottom panel is a plot depicting a line profile 20 minutes after
    the introduction of PNA into the bulk flow. The single peak in the
    top panel is the ssDNA after 10 minutes of focusing from an initial
    concentration of 0.4 μm. The bottom panel shows two peaks
    corresponding to the PNA/DNA duplex and free ssDNA.

96. Additional experiments were performed with different ssDNA sequences
    that included perfect matches and perfect mismatches to a PNA probe
    sequence. The mismatched sequences did not hybridize and a new
    fluorescent band was not observed.

97. In an alternative measurement using temperature gradient focusing,
    the interactions between two materials are observable as a function
    of spatial position within a temperature gradient. For example, this
    method can be used to study duplex matching by first mixing together
    the two materials and allowing the two to hybridize to form a
    duplex. Subsequently, the hybridized sample is then focused along
    the cold side of the microchannel 710. The bulk flow is then
    adjusted so that the duplex moves towards the hot side of the fluid
    conduit. The duplex can be detected along the temperature gradient
    and the melting temperature of the duplex can be measured by
    detecting the change in intensity of the duplex peak as it is moved
    towards the hot end of the gradient. When the duplex reaches a
    position along the gradient where the local temperature is equal to
    the melting temperature of the duplex, the two materials forming the
    duplex will come apart and move away from the focused duplex band,
    and the duplex band will consequently decrease in intensity.

98. The following non‑limiting example is provided to give a better
    understanding of how the interaction between two materials can be
    observed using temperature gradient focusing. In this example, a
    fluorescence melting profile of a PNA/DNA duplex that contained a
    single base pair mismatch (SBPM) was studied. The temperature
    gradient focusing separation was performed in a 30 μm I.D. fused
    silica capillary, 3 cm long. The capillary was mechanically and
    thermally anchored to two copper blocks at different temperatures to
    create a temperature gradient along a 2 mm section approximately
    midway along the length of the capillary. A temperature gradient
    from 20°C to 80°C was applied. The fluid used was 0.1 mol/L
    Tris(hydroxymethyl)aminomethane, 0.1 mol/L phenol in water (0.1 M
    Tris-phenol buffer). A solution of equal amounts of the PNA and DNA
    was prepared in the 0.1 M Tris-phenol buffer and introduced into the
    capillary via a fluid reservoir on the 20°C end of the capillary. A
    voltage of +2000 V was applied to the 20°C end of the capillary and
    the 80°C end was electrically grounded. The pressure applied to the
    80°C end of the capillary was adjusted to control the bulk flow rate
    so that the PNA/DNA duplex was first focused on the 20°C end of the
    2 mm gradient section. The bulk flow was then progressively adjusted
    so that focused duplex band was moved spatially from the 20°C end to
    the 80°C end of the 2 mm gradient section. A plot of the measured
    fluorescence intensity as a function of distance along the gradient
    section is shown in Figure 9 with the 20°C on the right side of the
    graph and the 80°C end on the left side of the graph. The green
    channel emission (circles) corresponds to free ssDNA while the red
    channel emission (squares) corresponds to the PNA/DNA duplex that
    contains a single base pair mismatch. The melting temperature can be
    identified as the temperature at the position where the red channel
    curve has decreased to about half its initial intensity
    (approximately 800 μm in Figure 9). Additional experiments compared
    the results obtained with a single base pair mismatch with those
    obtained when the DNA and PNA sequences were perfectly matched.
    After measuring the temperature inside the capillary to determine
    the temperature at each position along the capillary, a 7°C
    difference was observed in the melting temperature between the
    perfect match and the single base pair mismatch. This result is
    comparable to results obtained with conventional UV absorbance-based
    melting curve experiments.

99. The two examples described above can be combined in an assay to
    first determine if there is a hybridization or binding interaction
    between two materials, and then if a hybridization event occurs,
    further testing of the melting temperature of the duplex can be
    performed by scanning the focused duplex through the temperature
    gradient and monitoring the signal as a function of position. The
    assay involves focusing ssDNA on the cold side of the gradient, and
    then flowing the PNA through the sample. If a hybridization event
    occurs, the resulting focused duplex peak can be concentrated on the
    cold side of the gradient to a desired concentration before
    sequentially scanning through the temperature gradient by changing
    the bulk flow so the duplex will move from cold to hot side of the
    gradient. The melting temperature can be determined from data such
    as the melting curve shown in Figure 9. Comparisons of different
    melting curves and melting temperatures can then be used to
    determine the degree of mismatch (perfect match, single base pair
    mismatch, etc.) of the DNA and PNA sequences.

100. In another form of a mixing reaction/interaction using temperature
     gradient focusing, the PNA material can be replace with a second
     single stranded DNA material that has been covalently or otherwise
     bound to a 'drag tag' or a molecule with an electrophoretic
     mobility that is less than that of the single stranded DNA by
     modifying the teaching of Vreeland, W. N., Meagher, R. J. &
     Barron, A. E. (2002) *Analytical Chemistry* **74,** 4328-4333.
     Normally, there is only a very small difference in the
     electrophoretic mobility of single stranded and double stranded
     DNA. Consequently, it would be difficult to resolve the focused
     bands corresponding to the free single stranded DNA and the DNA/DNA
     duplex. Drag tags would therefore be used to reduce the
     electrophoretic mobility of the second single stranded DNA so that
     the drag-tag-DNA/DNA duplex would focus at a different position
     than the first single stranded DNA, so that both could be
     independently detected.

101. The present mixing reactions/interactions temperature gradient
     focusing can also be used to study enzyme/substrate interactions.
     For example, an enzyme could be initially focused within the
     separation conduit. The substrate could then be added to the bulk
     flow. The appearance of a focused product would signify that the
     enzyme/substrate reaction had occurred. Alternatively, the
     substrate could be focused first and subsequently introduce the
     enzyme into the bulk flow.

102. The present temperature gradient focusing methods for mixing
     reactions/interactions can be combined by selecting various aspects
     of the previously described methods. For example, nucleic
     acid‑protein interactions or those that involve drug‑target binding
     events can be analyzed using the present method. The only
     requirement is that at least one of the two input materials can be
     focused using temperature gradient focusing.

103. It will now be apparent to one of ordinary skill in the art that
     the present mixing reaction using temperature gradient focusing
     provides the ability to the concentrate targets prior to the assay
     reaction, with no theoretical limit to the concentration factor.
     This leads to assays with improved detection limits. This is in
     contrast to prior methods of concentrating a target which is
     difficult in affinity based capillary electrophoresis assays and
     typically involves a pre‑concentration step.

104. Another advantage of the present method is the ability to mix
     constituents within a microfluidic geometry that does not require
     complex channel geometries or channel modifications. Because of the
     low Reynold's number in microfluidic devices, mixing two fluid
     streams together by diffusion alone can require unacceptably long
     channel lengths. One way to overcome this is to introduce
     geometries that facilitate mixing such as serpentine channels or
     slanted wells ablated into channels. With temperature gradient
     focusing, the focusing mechanism isolates one of the species to be
     mixed in a unique spatial location while the second species is
     allowed to flow through the focused band by bulk flow (or by a
     combination of bulk flow and electrophoretic motion if the second
     species is charged). This allows for mixing to occur over small
     length scales, e.g. 50‑200 μm defined by the length of the focused
     band. In addition, the labeling for detection, e.g. target or probe
     is simplified because only one needs to be labeled since the
     product of the target and probe focuses in a unique location.

105. A further advantage of processing PNA/DNA duplexes through a
     temperature gradient, e.g., determining melting temperatures of
     duplexes, is that the present method requires much lower
     concentration samples. A conventional UV absorbance-based melting
     temperature measurement typically requires μM levels of DNA samples
     while temperature gradient focusing only requires nM to pM levels,
     an improvement of 3‑6 orders of magnitude.

106. In addition, the present temperature gradient focusing‑based
     analysis can also be performed faster than the conventional UV
     absorbance-based melting temperature measurement, e.g., 5 min
     compared to 60 min as initially demonstrated. In addition to
     melting curves of PNA/DNA duplexes, the scanning temperature
     gradient focusing can be used for any temperature dependent assay,
     e.g. polymer precipitation reactions.

107. One of ordinary skill in the art now will readily appreciate that
     the present temperature gradient focusing differs from prior art
     methods such as sample stacking and isotachophoresis. In both
     cases, samples are focused or concentrated as a result of gradients
     in their electrophoretic velocities. In sample stacking and
     isotachophoresis, the velocity gradients are generated at the
     interfaces between solutions of different composition, and the
     position at which the concentration or focusing occurs is not
     stationary, but moves along with the electroosmotic flow in the
     channel or capillary. In contrast to both sample stacking and
     isotachophoresis, the velocity gradients that produce material
     focusing in the present temperature gradient focusing result from
     applied temperature gradients.

108. Further, one skilled in the art will recognized that the present
     temperature gradient focusing differs from isoelectric focusing
     techniques such as those disclosed in U.S. Patent Nos. 3,664,939
     and 5,759,370. Unlike isoelectric focusing techniques in which the
     pH gradient is established by using a fluid system that has a
     temperature dependent pH, the present temperature gradient focusing
     typically utilizes a fluid that has a temperature dependent ionic
     strength. When a temperature gradient and a voltage are applied to
     a microchannel, the ionic strength gradient of the fluid gives rise
     to a velocity gradient, which is used for focusing. As a result, a
     material present in the fluid is focused at a position where the
     material\'s total velocity, i.e., the sum of the electrophoretic
     velocity of the material and the bulk velocity of the fluid is
     zero. Therefore, in the present temperature gradient focusing, the
     pH and the isoelectric point of the material are typically not
     critical. In the embodiment of the present invention that utilizes
     fluids with a temperature-dependent pH, and thereby uses a
     thermally generated pH gradient for focusing, a bulk fluid flow is
     applied so that rather than focusing at its isoelectric point as in
     isoelectric focusing, a material will focus at a position along the
     pH gradient where the local pH is unequal to the isoelectric point
     of the material.

109. It will now be apparent to one of ordinary skill in the art that
     the present temperature gradient focusing method provides numerous
     advantages over prior methods. The present method is simpler to
     implement as no imbedded electrodes or salt bridges are necessary.
     In addition, like isoelectric focusing, temperature gradient
     focusing can be used to both concentrate and separate materials,
     but without the disadvantages associated with isoelectric focusing.

110. A further advantage of the present invention is provided in that
     only a single, continuous fluid system is required. Solid phase
     extraction and related preconcentration methods of the prior art
     require multiple fluids where one fluid is used to carry the
     material to the preconcentrator and a second fluid is used to
     release the material from the preconcentrator. Further examples of
     multiple fluid systems include sample stacking, field amplified
     injection, iosotachophoresis, and sweeping.

111. Further, the present temperature gradient focusing provides
     enhanced concentration when compared with the prior art of other
     single preconcentration methods.

112. Although the invention has been described above in relation to
     preferred embodiments thereof, it will be understood by those
     skilled in the art that variations and modifications can be
     effected in these preferred embodiments without departing from the
     scope and spirit of the invention.

What is claimed is:

1\. A method for analyzing the interaction between a first material and
a second material in a fluid, said interaction giving rise to a third
material, said method comprising the steps of:

introducing a first material to a fluid;

applying an electric field to said fluid thereby causing said first
material to move electrophoretically with an electrophoretic velocity;

establishing a temperature gradient in said fluid having a significant
component substantially aligned with the electrophoretic motion of said
first material, thereby generating a gradient of the electrophoretic
velocity of said first material;

producing a flow of said fluid having a significant component
substantially aligned in a direction opposite a direction of the
electrophoretic motion of said first material;

wherein magnitudes of said electric field, said temperature gradient,
and said flow are such that said first material will accumulate or be
focused at a first position along said temperature gradient; and

introducing a second material to said fluid so that said second material
moves through said first position, thereby interacting with said first
material to form a third material;

whereby said third material of said interaction is then focused at a
second position along said temperature gradient.

2\. The method of claim 1, wherein an ionic strength of said fluid is
temperature dependent and said temperature gradient establishes a
gradient in the ionic strength of said fluid.

3\. The method of claim 2, wherein:

said first material is a first single stranded DNA molecule and said
second material is selected from the group consisting of a second single
stranded DNA molecule, a single stranded PNA molecule, and a third
single stranded DNA molecule covalently bound to a molecular species
having an electrophoretic mobility substantially different from the
electrophoretic mobility of said first single stranded DNA molecule; and

said third material is a duplex of said first material and said second
material.

4\. The method of claim 2, wherein said first material is selected from
the group consisting of nucleic acid aptamers and antibodies, and said
second material is selected from the group consisting of amino acids,
peptides, proteins, cytokines, nucleic acids, cells, colloidal
particles, bacterial particles, and viral particles.

5\. The method of claim 2, wherein said first material is selected from
the group consisting of amino acids, peptides, proteins, cytokines,
nucleic acids, cells, colloidal particles, bacterial particles, and
viral particles, and said second material is selected from the group
consisting of nucleic acid aptamers and antibodies.

6\. The method of claim 2, wherein said first material is a substrate,
said second material is an enzyme, and said third material is the
product of a reaction between said enzyme and said substrate.

7\. The method of claim 2, wherein said first material is an enzyme,
said second material is a substrate, and said third material is the
product of a reaction between said enzyme and said substrate.

8\. The method of claim 2, wherein said first material and said second
material together produce a chemical reaction to form said third
material.

9\. The method of claim 2, wherein said first material is a drug and
said second material is a target molecular species, and said third
material is a complex of said drug and said target molecular species.

10\. The method of claim 2, wherein said first material is a first
protein and said second material is a second protein and said third
material is a complex of said first protein and said second protein.

11\. The method of claim 2, wherein said first material and said second
material are both fluorescently labeled for detection along the
temperature gradient.

12\. The method of claim 2, wherein said fluid is selected from the
group consisting of ionic aqueous solutions, ionic non-aqueous
solutions, aqueous buffer solutions, and mixtures of aqueous and
non-aqueous solutions.

13\. The method of claim 2, wherein said electric field is applied using
a set of components comprising an electrical power supply and two or
more electrodes contacting said fluid.

14\. The method of claim 2, wherein said step of establishing a
temperature gradient comprises applying an electric current to said
fluid to produce said temperature gradient by Joule heating.

15\. The method of claim 2, wherein said step of establishing a
temperature gradient comprises supplying thermal energy to said fluid
via a heated block.

16\. The method of claim 2, wherein said step of establishing a
temperature gradient comprises removing thermal energy from said fluid
via a cooled block.

17\. The method of claim 2, wherein said flow is generated by
electroosmosis.

18\. The method of claim 2, wherein said flow is generated by pressure
gradients.

19\. The method of claim 2, wherein said flow is generated by a
combination of electroosmosis and pressure gradients.

20\. The method of claim 2, wherein said step of applying an electric
field, said step of establishing a temperature gradient, and said step
of producing a bulk flow are comprised of using an electrical power
supply to apply a voltage to said fluid, and wherein the electric field
provided by said electrical power supply causes the electrophoretic
motion of said first material, a flow of electric current in said fluid
thereby generating said temperature gradient by Joule heating, and
electroosmosis of said fluid thereby producing said flow of said fluid.

21\. The method of claim 2, wherein said step of applying an electric
field and said step of producing a bulk flow comprise using an
electrical power supply to apply a voltage to said fluid, and wherein
the electric field provided by said electrical power supply causes the
electrophoretic motion of said first material, and electroosmosis of
said fluid thereby producing said flow of said fluid.

22\. The method of claim 2, wherein said third material is a duplex of
said first material and said second material, and the magnitude of said
flow is initially adjusted so that a local temperature at said second
position is a first temperature; and

further comprising the steps of:

detecting a focused band of said duplex at said second position, thereby
determining an amount of said duplex in said focused band at said first
temperature;

changing at least one of the group consisting of said electric field,
said temperature gradient, and said flow so that a local temperature
around said focused band of said duplex is at a second temperature;

detecting the focused band of said duplex at said second temperature,
thereby determining an amount of said duplex in said focused band at
said second temperature; and

comparing the amount of said duplex in said focused band at said first
temperature to the amount of said duplex in said focused band at said
second temperature,

thereby determining if said interaction is different at said first
temperature and said second temperature.

23\. The method of claim 2, wherein said third material is a duplex of
said first material and said second material, said duplex having a
characteristic melting temperature, and the magnitude of said flow is
initially adjusted so that a local temperature at said second position
is a first temperature; and

further comprising the steps of:

detecting a focused band of said duplex at said second position, thereby
determining an amount of said duplex in said focused band at said first
temperature;

progressively changing at least one of the group consisting of said
electric field, said temperature gradient, and said flow so that the
local temperature around said focused band becomes progressively
different than said first temperature;

monitoring the amount of said duplex in said focused band; and

comparing the amount of said duplex in said focused band at each
progressively different temperature,

thereby determining the melting temperature.

24\. The method of claim 2, wherein said first material is selected from
the group consisting of single stranded DNA, single stranded PNA, single
stranded DNA covalently bound to a molecular species having an
electrophoretic mobility substantially different from the
electrophoretic mobility of single stranded DNA, nucleic acid aptamers,
antibodies, molecules with molecular weight less than 500 amu, amino
acids, peptides, proteins, cytokines, nucleic acids, lectins, and
carbohydrates; and said second material is selected from the group
consisting of single stranded DNA, single stranded PNA, single stranded
DNA covalently bound to a molecular species having an electrophoretic
mobility substantially different from the electrophoretic mobility of
single stranded DNA, nucleic acid aptamers, antibodies, molecules with
molecular weight less than 500 amu, amino acids, peptides, proteins,
cytokines, nucleic acids, lectins, and carbohydrates.

25\. A method for determining the melting temperature of a duplex of a
first molecular species and a second molecular species in a fluid, said
method comprising the steps of:

mixing a first molecular species and a second molecular species in a
fluid to form a sample solution containing a duplex;

applying an electric field to said fluid thereby causing said duplex to
move electrophoretically with an electrophoretic velocity;

establishing a temperature gradient in said fluid having a significant
component substantially aligned with the electrophoretic motion of said
duplex, thereby generating a gradient of the electrophoretic velocity of
said duplex;

producing a flow of said fluid having a significant component
substantially aligned in a direction opposite a direction of said
electrophoretic motion of said duplex;

wherein magnitudes of said electric field, said temperature gradient,
and said flow are such that said duplex will accumulate or be focused at
a first position along said temperature gradient, a local temperature
around said first position being at a first temperature;

detecting a focused band of said duplex at said first position, thereby
determining an amount of said duplex in said focused band at said first
temperature;

progressively changing at least one of the group consisting of said
electric field, said temperature gradient, and said flow, so that a
local temperature around said focused band becomes progressively
different than said first temperature;

monitoring the amount of said duplex in said focused band; and

comparing the amount of said duplex in said focused band at each
progressively different temperature,

thereby determining the melting temperature of the duplex.

26\. The method of claim 25, wherein an ionic strength of said fluid is
temperature dependent and said temperature gradient establishes a
gradient in the ionic strength of said fluid.

27\. The method of claim 26, wherein said first molecular species is
selected from the group consisting of single stranded DNA, single
stranded PNA, single stranded DNA covalently bound to a molecular
species having an electrophoretic mobility substantially different from
the electrophoretic mobility of single stranded DNA, nucleic acid
aptamers, antibodies, molecules with molecular weight less than 500 amu,
amino acids, peptides, proteins, cytokines, nucleic acids, lectins, and
carbohydrates; and said second molecular species is selected from the
group consisting of single stranded DNA, single stranded PNA, single
stranded DNA covalently bound to a molecular species having an
electrophoretic mobility substantially different from the
electrophoretic mobility of single stranded DNA, nucleic acid aptamers,
antibodies, molecules with molecular weight less than 500 amu, amino
acids, peptides, proteins, cytokines, nucleic acids, lectins, and
carbohydrates.

28\. A method for using a temperature gradient focusing device to
determine the melting temperature of a duplex of a first molecular
species and a second molecular species in a fluid, said temperature
gradient focusing device having a temperature gradient, said method
comprising the steps of:

mixing a first molecular species and a second molecular species in a
fluid to form a sample solution containing a duplex;

introducing said sample solution into said temperature gradient focusing
device;

adjusting operational parameters of said temperature gradient focusing
device so that said duplex is focused at a first position along said
temperature gradient, a local temperature around said first position
being at a first temperature;

detecting the focused band of said duplex at said first position,
thereby determining the amount of said duplex in said focused band at
said first temperature;

progressively changing said operational parameters so that the local
temperature around said focused band becomes progressively different
than said first temperature;

monitoring the amount of said duplex in said focused band; and

comparing the amount of said duplex in said focused band at each
progressively different temperature,

thereby determining the melting temperature of the duplex.

29\. The method of claim 28, wherein said first molecular species is
selected from the group consisting of single stranded DNA, single
stranded PNA, single stranded DNA covalently bound to a molecular
species having an electrophoretic mobility substantially different from
the electrophoretic mobility of single stranded DNA, nucleic acid
aptamers, antibodies, molecules with molecular weight less than 500 amu,
amino acids, peptides, proteins, cytokines, and nucleic acids; and said
second molecular species is selected from the group consisting of single
stranded DNA, single stranded PNA, single stranded DNA covalently bound
to a molecular species having an electrophoretic mobility substantially
different from the electrophoretic mobility of single stranded DNA,
nucleic acid aptamers, antibodies, molecules with molecular weight less
than 500 amu, amino acids, peptides, proteins, cytokines, and nucleic
acids.

## ABSTRACT OF THE DISCLOSURE

A method is provided for observing mixing interactions and reactions of
two materials in a fluid. The method in one form provides for
concentrating by balancing electrophoretic velocities of a material
against the bulk flow of fluid in the presence of a temperature
gradient. Using an appropriate fluid, the temperature gradient can
generate a corresponding gradient in the electrophoretic velocity of the
material so that the electrophoretic and bulk velocities sum to zero at
a unique position and the material will be focused at that position. A
second material can then be introduced into the fluid and allowed to
move through and interact with the focused band of the first material.
Products of the interaction can then be detected as they are focused at
a different position along the gradient. The method can be adapted to
study the temperature dependence of the molecular interaction.