SAPPHIRE DIELECTRIC RESONATORS FOR

MICROFLUIDIC COMPOSITIONAL ANALYSIS

A. Porch*, A. Masood, A.J. Naylon, A. Sulaimalebbe and D.A. Barrow
School of Engineering, Cardiff University, 1-5 The Parade, Newport Road, Cardiff CF24 3AA, U.K.

ABSTRACT
Cylindrical sapphire dielectric resonators (SDRs) have been developed for in-situ analysis of solvent composition
within microfluidic ducts. The SDRs operate in the TE011 mode, chosen such that its microwave electric field is parallel to
a circular duct milled into the sapphire. This results in very little depolarization of the electric field, giving very sensitive
dielectric characterization of the fluid within the duct. A miniaturized SDR operating at 22.7 GHz has a fluid sample vol-
ume of ~56 nl and has been demonstrated to have volumetric detection limits of ~3 ppm of acetonitrile in toluene and ~6
ppm of water in acetonitrile.

KEYWORDS: Microwave resonator, dielectric properties, solvent composition

INTRODUCTION
The ability to interrogate precisely the composition of liquid mixtures by non-contact techniques in both static and
flow situations (including extreme environments) is highly desirable for a variety of industrial, analytical and quality con-
trol procedures. In this context, microwave resonators have the useful dual roles of (a) sensitive characterization of the
dielectric polarization and loss of a sample for small applied electric fields, and (b) efficient volumetric heating of the
same sample (if its dielectric loss is large enough to permit heating) for high microwave input powers. Heating will not be
considered in detail here, but the design considerations of suitable resonators for both materials characterization and effi-
cient heating of the same sample are identical (i.e. if it can be detected, it can also be heated).
Here, sapphire dielectric resonators (SDRs) are described for ultra-sensitive dielectric measurements of microfluids.
Previously, we have demonstrated miniaturized, distributed (i.e. hairpin) resonators [1] and also lumped element (i.e. split
ring) resonators [2] for the successful in-situ analysis of a microcapillary containing a mixture of polar solvents. Whis-
pering gallery mode SDRs have also been described but with low fluid filling factors within the resonator [3]. The use of
the split ring resonator was found to increase significantly the measurement sensitivity due to decreased resonator vol-
ume, but it (and the hairpin resonator) suffered from the large depolarization of the applied electric of the liquid samples.
The SDRs described here have high quality (Q) factors (e.g. 40000 at 5.3 GHz) owing to the low loss tangent of single
crystal sapphire. The TE011 mode resonant mode is chosen to provide a divergence-free electric field E which is parallel
to any circular duct, resulting in unambiguous, ultra-sensitive compositional analysis of highly-polar solvents since the E-
field is not reduced by polarization. Test solutions are toluene:acetonitrile (i.e. high difference in polarity), and acetoni-
trile: water (more challenging since both are highly polar).

THEORY
If a dielectric sample (liquid or otherwise) is inserted into the electric field (of magnitude E0) of a resonator there will
be a decrease of its quality factor (Q) and decrease of resonant frequency due to the sample’s dielectric loss and polariza-
tion, respectively. These changes can be expressed using resonator perturbation analysis in the following form

⎛1⎞ Im(α ) Δf 0 Re(α )

Δ⎜⎜ ⎟⎟ ≈ − (1) ≈− (2)
⎝ ⎠
Q Veff f0 2Veff

where f0 is the unperturbed resonant frequency, α is the sample’s electric polarizability (defined by the induced electric
dipole moment p = αε0E0) and Veff is the effective volume occupied by the electric field energy (which scales roughly
with the resonator volume). Hence, conditions for both highly sensitive characterization and extreme, highly localised,
volumetric heating of a dielectric sample are achieved within a resonator that has (a) suitable orientation of the electric
field relative to the sample to maximise its dipole moment, and (b) miniaturised volume for electric energy storage.
Figure 1 shows an idealized, thin, cylindrical liquid column subject to an applied electric field. In case (a) the sample
has low polarizability (defined as αa per unit length) since the internal electric field is reduced by the polarization charges
developed on the curved surface of the liquid column, especially if the relative permittivity ε of the liquid is large, as will
be the case for polar solvents. In case (b) the internal electric field differs little from the applied field and results in
maximum polarizability (αb), and hence maximum measurement sensitivity. The ratio of the two is approximately

α b ε(ε + 1) ε
≈ ≈ (ε >> 1) (3)
α a 2(ε − 1) 2

For water at low frequencies, ε ≈ 80 so that αb/αa ≈ 41, and for acetonitrile (MeCN) ε ≈ 37 so that αb/αa ≈ 20. Hence,
these factors can be large and so can provide major enhancements in measurement sensitivity (and sample heating).

978-0-9798064-3-8/µTAS 2010/$20©2010 CBMS 2011 14th International Conference on

Miniaturized Systems for Chemistry and Life Sciences
3 - 7 October 2010, Groningen, The Netherlands
 Figure 1: S ample geometries leading to depolarization (a), and negligible depolarization ((b) and (c)).

EXPERIMENTAL DETAILS
Unfortunately, case (b) in Figure 1 is hard to achieve in a microwave resonator without increasing the resonator’s ef-
fective volume, thus offsetting the sensitivity gains obtained by sample orientation (from Equations (1) and (2)). An ele-
gant solution for microfluidic ducts is shown in case (c), where the duct follows a circular path. This follows the circular
electric field lines in a TE011 cylindrical SDR, so the applied electric field is always parallel to the surface of the duct, re-
sulting in maximum polarization. The high relative permittivity of the dielectric material of the resonator (for sapphire ε ≈
9.4 in its basal plane) results in a small effective volume ∝ ε1/2, so the gains in measurement sensitivity are two-fold.
A schematic diagram of the SDR with a milled, circular microfluidic channel is shown in Figure 2. The microwave
couplings (not shown) are via identical, loop-terminated RG405 coaxial cables and the transmitted power |S21|2 is meas-
ured in the frequency domain using an Agilent PNA-X network analyzer. The SDRs used here are variants of the split-
post resonator used for characterizing sheet samples [4]. In the TE011 mode the two resonator halves behave as one since
the E-field in the gap region is parallel to the dielectric interfaces. The resulting electric energy density has been com-
puted (using FEM) and is shown in Figure 3. Two prototype SDR sensors have been developed: one operates at 5.3 GHz
with a pair of sapphire pucks each of radius 10 mm and length 5 mm, another at 22.7 GHz with pucks of radius 2.25 mm
and length 1.0 mm. The 5.3 GHz SDR contains a circular Teflon AF microcapillary (ID 250 μm, OD 500 μm), supported
within a Teflon AF carrier slotted into a 1 mm gap between the pucks. The 22.7 GHz SDR has circular microfluidic chan-
nel of diameter 3 mm, width 100 μm and depth 60 μm, ablated with a 157 nm excimer laser into one of the pucks at the
position of the maximum E-field. The pucks were bonded together using a 1.2 μm thick spin-coated film of Teflon AF
1600, and fused silica microcapillaries (ID 100 μm, OD 160 μm) were used to interface with the microchannels.

RESULTS
Experimental results are shown in Figures 4 and 5 for the miniaturized (i.e. 22.7 GHz) SDR containing a solution of
acetonitrile (highly polar) in toluene (relatively non-polar). The resonant frequency decreases and the 3 dB bandwidth
(i.e. f0/Q) increases as the % volume of acetonitrile increases due to increased polarity. Such monotonic variations are ex-
pected theoretically when the E-field is not depolarized, giving unambiguous compositional analysis. This should be com-
pared with our earlier data [1],[2], where delpolarization effects result in multi-valued compositional analysis based on
microwave loss. The fluid volume in the miniaturized SDR is 56 nl and the sensitivity (resonant frequency shift) is ≈ 80
Hz decrease for a 1 ppm increase in acetonitrile (Table 1). The smallest measurable change of ≈200 Hz using the PNA-X
network analyzer sets a detection limit of ≈ 3 ppm of acetonitrile in toluene, i.e. absolute detection volume of just 0.6 pl.

Sapphire disks ∅
4.5 mm × 1 mm Sapphire
disk

Channel
500 μm

Micrograph of lower disk PTFE

Support

Circular channel Epoxy seal Fused silica

∅ 3 mm × 60 μm microcapillary 0 Electric field magnitude Max
1.2 μm Teflon AF
× 100 μm bonding layer

Figure 2: Configuration of the miniaturized sapphire Figure 3: Finite element simulation showing the distribu-
disk resonator (SDR) with laser-ablated microchannels. In- tion of electric field within the miniaturized sapphire dielec-
set: micrograph of the fabricated lower sapphire disk. tric resonator. The channels are positioned precisely in the
region of maximum E-field.

2012
 1000 21.74

900

Resonant Frequency (GHz)

21.72
800
Quality Factor

21.70
700

600 21.68

500
21.66
400
21.64
300

200 21.62
0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100

% Acetonitrile % Acetonitrile
Figure 3: Variation of Q factor with % vol. of acetoni- Figure 4: The resonant frequency shift with % vol. of ace-
trile (MeCN) in toluene for the 22.7GHz miniaturized SDR. tonitrile (MeCN) in toluene for the 22.7GHz miniaturized
The Q factor of the empty SDR is around 21000. SDR.

Table 1: Summary of the key parameters of the two sapphire dielectric resonators (SDRs) used in this study

Quality factor Active fluid Sensitivity* Sensitivity*

(empty) Volume MeCN:toluene MeCN:water

SDR 40 000 2.31 μl 10 Hz ≈ 6 Hz

@ 5.3 GHz
Miniaturized SDR 21 000 0.056 μl 81 Hz 37 Hz
@ 22.7 GHz
* “Sensitivity” is the magnitude of the frequency shift for a 1 ppm increase in MeCN concentration.

CONCLUSIONS
The properties of the sapphire dielectric resonators described here afford high sensitivity in the analysis of polar/non-
polar fluid mixtures, enabling applications from on-column HPLC mobile phase diagnosis and solvent QA to petrochemi-
cal industrial applications such as oil drilling, geo-prospecting and QC. The robust and resilient nature of the resonator
structures and the non-invasive principle of the technique allow for operation in extreme environments (temperature,
pressure, pH etc) and with optically opaque fluid matrices. The measurements are fast (sampling rates > 100 Hz are pos-
sible) and have been made ultra-sensitive by a combination of (a) suitable orientation of the microwave electric field rela-
tive to the sample, and (b) miniaturised resonator volume. Detection limits of around 3 ppm (by volume) of acetonitrile in
toluene and around 6 ppm of water in acetonitrile have been measured. Future work will involve the development port-
able, cost-effective, yet high performance instrumentation architecture as an alternative to the vector network analyzer.

ACKNOWLEDGEMENTS
We thank Dr. Oliver Castell and Dr. Chris Allender, of the School of Pharmacy at Cardiff University, for help with
the experiments and useful discussions.

REFERENCES
[1] R. Göritz, A. Masood, O. Castell, D. A. Barrow, C. Allender and A. Porch, “Microwave Compositional Analysis of
Solvent Matrices in Microcapillary Manifold Systems”, The Proceedings of MicroTAS 2007 Conference, Paris,
pp.1689-1691, October 2007.
[2] A. Masood, O. Castell, D. A. Barrow, C. Allender and A. Porch, “Split Ring Resonator Technique for Composi-
tional Analysis of Solvents in Microcapillary Systems”, The Proceedings of MicroTAS 2008 Conference, San
Diego, pp.1636-1638, October 2008.
[3] E.N. Shaforost et al., “High sensitivity microwave characterization of organic molecule solutions of nanoliter vol-
ume,” Applied Physics Letters, vol. 94, Mar. 2009, pp. 112901-3.
[4] J. Krupka, “Frequency domain complex permittivity measurements at microwave frequencies,” Measurement Sci-
ence and Technology, vol. 17, 2006, pp. R55-R70.

CONTACT
*Adrian Porch, tel: + 44-(0)-2920-875954; PorchA@cf.ac.uk

2013