Dielectric spectroscopy

Dielectric spectroscopy is another example of electronic detection. As opposed to capacitance cytometry, which measures capacitance at a 1 kHz frequency, dielectric spectroscopy measures permittivity as a function of frequency (from 40 Hz to 50 GHz). This direct, nondestructive, and sensitive technique can probe a system at various length scales, from centimeters to microns, with sample volumes as small as femtoliters. It, thus, provides information about the species present and the chemical environment.

In the past, a variety of research groups have applied dielectric spec-troscopy across an extremely broad range of frequencies: from millihertz to tens of gigahertz. Interpreting the results of these experiments, however, has proved far from trivial. One reason for this is the number of physical processes which contribute to dielectric measurements in fluid samples. Table 36.1 below gives a partial illustration of the diverse interwoven phenomena involved.

Despite this complexity, many of the different contributions to permittivity data are well understood. For example, a simple screening theory after Cole and Cole19 define general features in the dielectric spectra, all relating to polarization relaxations. These features are generally classified as a-, p-, or g- dispersions. a-dispersion is the permittivity enhancement by rearrangements of small ions, including screening at the fluid interface. p-dispersion arises from distortions of cellular membranes and macromolecules. g-disper-sion is due to rotations and deformations of small, polar molecules or groups (frequently, the solvent). Access to a broad frequency range is imperative with biological samples, due to their chemical diversity.20 21 In solution with total ionic strengths = 0.1 M, a-dispersion extends up to = 1 GHz, while p-dispersions extend from = 1 kHz22 up to the relaxational modes of macro-molecules in the infrared (THz) and beyond.

Dielectric spectra from a-, p-, and g-dispersions have a common form2324: at low frequencies, the polarization is able to closely follow the applied electric

PDMS microfluidic mold

PDMS microfluidic mold

Coplanar Glass' End-launch waveguide substrate SMA adaptor

(Ti/Au metal lines)

Figure 36.6 CPW device, showing the Ti/Au wave guide (not to scale) and microfluidic sample containment. Across the central portion, the inner line width is 40 ^m, outer line widths 380 ^m, and the inner-outer separation is 7 ^m. Total substrate length is 34 mm. (From Facer, G.R., Notterman, D.A., and Sohn, L.L., Appl. Phys. Lett., 78, 996-998, 2001. With permission.

Coplanar Glass' End-launch waveguide substrate SMA adaptor

(Ti/Au metal lines)

Figure 36.6 CPW device, showing the Ti/Au wave guide (not to scale) and microfluidic sample containment. Across the central portion, the inner line width is 40 ^m, outer line widths 380 ^m, and the inner-outer separation is 7 ^m. Total substrate length is 34 mm. (From Facer, G.R., Notterman, D.A., and Sohn, L.L., Appl. Phys. Lett., 78, 996-998, 2001. With permission.

field (relative permittivity e = elf); at high frequencies, applied excitations oscillate too fast for the charges to response (e = eHF). Generally, eLF >>eHF.

We have developed a coplanar waveguide (CPW) on chip which allows us to perform dielectric spectroscopy on samples confined to a microfluidic channel or well across nearly nine orders of magnitude in frequency, from 40~Hz to 26.5~GHz.6 Because coupling to the sample is capacitive, our CPWs allow measurements from DC to microwave frequencies, without the need for surface functionalization or chemical binding.25 A wide range of species can, therefore, be analyzed rapidly and directly. An added feature of our CPW is that its planar geometry allows for straightforward integration with microfluidic devices.5,26,27 Below, we discuss the fabrication of the CPW devices, and the low frequency to microwave spectra we have obtained for biomolecular solutions and cell suspensions.

A schematic diagram of our CPW devices is shown in Figure 36.6. They are symmetric metal transmission lines comprised of a 40-^m-wide central strip bordered by two grounded 380-^m-wide conductors. Each metal region is an evaporated Ti/Au 50 A/500 A base topped with an electrodeposited gold layer (total Au thickness 1~^m). The substrate is glass, and connection is via end-launch SMA adaptors. Capacitive coupling to the fluid is achieved by encapsulating the metal lines in 1000 A of PECVD -grown silicon nitride. Silicone poly(dimethylsiloxane), PDMS, confines the fluid.

At frequencies below 100 MHz, the relative permittivity is obtained from the impedance Z via e = 1/jw Z Co, where Co is the capacitance through the sample volume when empty and is typically ~10 fF. Z data are obtained with a Hewlett-Packard 4294A impedance analyzer (excitation amplitude 500~mV). We have confirmed that the data are free of nonlinear conductive effects. Microwave data (= 45 MHz) are phase-sensitive transmission and reflection coefficients (S-parameters) at the adaptors, obtained with a Hewlett-Packard 8510C vector network analyzer.

We have examined a variety of samples, including solutions of hemoglobin (derived from washed and lysed human red blood cells) and live E.

Figure 36.7 Relative permittivity data: real (a) and imaginary (b) components. Solid traces are from hemoglobin (100 mg/mL), dashed traces for Tris buffer (1 mM, pH 8), and dotted curves are Cole-Cole calculations as per Equation (36.1). (From Facer, G.R., Notterman, D.A., and Sohn, L.L., Appl. Phys. Lett, 78, 996-998, 2001. With permission.)

Figure 36.7 Relative permittivity data: real (a) and imaginary (b) components. Solid traces are from hemoglobin (100 mg/mL), dashed traces for Tris buffer (1 mM, pH 8), and dotted curves are Cole-Cole calculations as per Equation (36.1). (From Facer, G.R., Notterman, D.A., and Sohn, L.L., Appl. Phys. Lett, 78, 996-998, 2001. With permission.)

coli suspensions. The concentration of hemoglobin is 100 mg/mL in 0.25~M Tris buffer (pH 8), and that of DNA is 500 mg/mL, in 10~mM Tris and 1~mM EDTA (pH 8) buffer. E. coli aresuspended in 85% 0.1 M CaCl2/15% glycerol. For our measurements, we employed molded microfluidic channels and simpler enclosed wells. Results are consistent (within a scaling factor for the fluid -CPW overlap length) for sample volumes ranging from = 3 pL to = 2 0 mL. For the following discussions, we present data from capped 10 mL wells.

Figure 36.7 shows e from 40 Hz to 110 MHz, for hemoglobin, dilute Tris buffer (concentration 1 mM, pH 8), and a Cole-Cole19 model calculation relating e to the angular frequency w.

Here eLF - eHF is the dielectric increment, t is a characteristic time constant, a = 1 defines the sharpness of the transition, and oLP is the DC conductivity. For the calculation in Figure 36.7, eLF - eHF = 1340, t = 1.70 ^s, a = 0.91, and oLF = 40 nS. A small series resistance (90W) is included in the model to fit high-frequency loss within the CPW.

0 5 10 15 20 25 Frequency (GHz)

0 5 10 15 20 25 Frequency (GHz)

Frequency (GHz)

Frequency (GHz)

Figure 36.8 Microwave transmission data. (a) Raw data, for the cases of no sample (dotted) and a 100-^g/mL hemoglobin solution (solid). (b) Normalized data (using the respective buffers) for 100 ^g/mL hemoglobin (solid trace) and 500-^g/mL phage l-DNA (dashed), showing the difference in their microwave response. (c) Solid trace is the (buffer-normalized) response of E. coli, and the dotted trace is that of the Tris buffer from the hemoglobin solution (normalized using deionized H2O). (From Facer, G.R., Notterman, D.A., and Sohn, L.L., Appl. Phys. Lett, 78, 996-998, 2001. With permission.)

Frequency (GHz)

Figure 36.8 Microwave transmission data. (a) Raw data, for the cases of no sample (dotted) and a 100-^g/mL hemoglobin solution (solid). (b) Normalized data (using the respective buffers) for 100 ^g/mL hemoglobin (solid trace) and 500-^g/mL phage l-DNA (dashed), showing the difference in their microwave response. (c) Solid trace is the (buffer-normalized) response of E. coli, and the dotted trace is that of the Tris buffer from the hemoglobin solution (normalized using deionized H2O). (From Facer, G.R., Notterman, D.A., and Sohn, L.L., Appl. Phys. Lett, 78, 996-998, 2001. With permission.)

The spectra in Figure 36.7 show two features. First, the dielectric increment of the high-frequency transition is a constant of the measurement geometry. Second, and in contrast, the eLF to eHF transition frequency is directly proportional to the total ionic strength of the solution. As shown, the dispersion model Equation 36.1 describes the data well.

Figure 36.8 shows transmission data from 45~MHz to 26.5~GHz. In Figure 36.8a, raw transmission and reflection are shown for two control cases: a dry sample setup and deionized water. Figures 36.8b and 36.8c contain transmission data sets for hemoglobin, DNA, and live E. coli which have been normalized with respect to their corresponding buffers. Figure 36.8c also shows (dotted trace) transmission data from the buffer used for hemoglobin measurements, normalized using deionized water data. This, in particular, demonstrates that even at high salt concentrations (0.25~M Tris-HCl), the microwave effects of buffer salts are limited to a monotonic decrease in transmission below 10~GHz.

Three descriptive notes should be made regarding the data. First, periodic peak and trough features (such as those marked by arrows in Figure 36.8b) are interference effects due to reflections at the SMA adaptors and the fluid itself. Second, the SMA adaptors impose the high-frequency cutoff at 26.5~GHz. Finally, reproducibility of the microwave data has been verified for three CPW devices, using several successive fluidic assemblies on each. Only the interference structure changes slightly from device to device.

The most striking aspect of the microwave data is that the transmission through the hemoglobin and bacteria specimens is higher than that through their respective buffer samples. In addition, the response due to 100 ^g/mL of hemoglobin is far stronger than that for DNA even though the DNA is more concentrated (500 ^g/mL). Furthermore, the hemoglobin exhibits increased transmission across a frequency range from <100 MHz to 25 GHz, which is unique among the samples measured to date (by contrast, the onset of increased transmission in the bacteria data is at ~1 GHz). The increases in transmission are not correlated to any change in reflection, indicating that there is a decrease in power dissipation within the sample. Finally, the breadth of the response implies no resonant process is at play (as is also the case for the E. coli data). We must, therefore, conclude that the increased transmission represents an increase in the transparency of the medium to microwaves, i.e., that these specimens are better dielectrics than water alone at this frequency. The fact that this frequency range coincides with the g-dispersion transition in water (implying high dissipation) is most likely a contributing factor to the success of detection.

Other samples measured, for which data are not shown here (G. R. Facer, D. A. Notterman, and L. L. Sohn, unpublished), include collagen, bovine serum albumin, and ribonucleic acid solutions. These macromolecule solutions exhibit behavior highly similar to that of the DNA in Figure 36.8b (i.e., with the 10-20 GHz interference features present) and not to that of the buffer solution. This raises the possibility that the strength and shape of the interference features are more sensitive to the presence of macromolecules and their counterion clouds than just to simple salts. Again, it is reasonable to conclude that this frequency range is significant due to the g-dispersion of water. The reason for the strength of transmission enhancement by hemoglobin, compared to that by nucleic acids or other proteins, is yet to be confirmed, but we hypothesize that it associated with the activity of the central heme complex.

In summary, we have developed CPW devices which allow us to perform dielectric spectroscopy on small volumes of biological samples confined with a microfluidic channel or well. These devices yield permittivity spectra across an exceptionally broad range of frequencies: from 40 Hz to 26.5 GHz thus far. Neither chemical treatment nor surface activation is required. By combining transmission line design with robust thin-film insulation, sensitivity to sample properties can be achieved in low- and high-frequency regimes within a single device.

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