(1)Gravimetric sensors “Quartz Crystal Microbalance&rdquo
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(2) Direct detection (bio)sensors I I I I. No sample preparation: continuous monitoring + time resolution (kinetic) Surface immobilization of receptor molecules: multiple measurement steps are possible Sensitivity defined by mass to physical measurement conversion efficiency Selectivity defined by affinity of the surface functionalization to the targeted compound, rejecting unwanted interference (antibody) I Improved signal to noise ratio by using evanescent wave (rejects bulk noise and keep only close-to-surface signal) I Detection limit determined by system noise level (detection limit=noise/sensitivity) = complete system (electronics, fluidics ...). detection layer (organic, bio) organic interface (metallic interface) inorganic transducer (glass, quartz) 2 / 29.
(3) Quartz crystal resonator basics Examples of direction detection sensors: Surface Plasmon Resonance, (optical) waveguide sensors, vibrating cantilever, electrochemical enzyme sensors. I Quartz crystal resonator: piezoelectric substrate confining an acoustic wave I Boundary conditions: half-wavelength confined between parallel (plano-plano) or curved (plano-convex) sides of a quartz plate I Odd overtones are confined in the same boundary conditions. A. I Resonance frequency determined by plate thickness and shear wave velocity: 3340 m/s in AT-cut quartz (temperature compensated) I Application: f = 5 MHz requires t = λ/2 = c/(2f ) = 334 µm. t N=1,. 3,. 5 3 / 29.
(4) Quartz crystal resonator basics Examples of direction detection sensors: Surface Plasmon Resonance, (optical) waveguide sensors, vibrating cantilever, electrochemical enzyme sensors. I Quartz crystal resonator: piezoelectric substrate confining an acoustic wave I Boundary conditions: half-wavelength confined between parallel (plano-plano) or curved (plano-convex) sides of a quartz plate I Odd overtones are confined in the same boundary conditions I Resonance frequency determined by plate thickness and shear wave velocity: 3340 m/s in AT-cut quartz (temperature compensated) I Application: f = 5 MHz requires t = λ/2 = c/(2f ) = 334 µm 4 / 29.
(5) Butterworth-Van Dyke electromechanical model I Butterworth-VanDyke model 1 2 3 : RLC series branch represents damped spring-mass (“motional branch”) I Electrodes separated by a dielectric define a parallel capacitance Mechanical M ẍ + hẋ + kx = F h (damping) M (mass) k (stiffness) x (displacement) ẋ (velocity) √ Q = h1 kM q k ω0 = M. Electrical L1 q̈ + R1 q̇ + q/C1 = U R1 (resistance) L1 (inductance) 1/C1 (capacitance) q (electrical charge) i = dq/dt q (current) Q=. 1 R. L C. R1 L1 C1. k C0 M h. ω0 = √ 1. L1 C1. 1 S.. Butterworth, On electrically-maintained vibrations, Proc. Phys. Soc. (London), 27 410–424 (1914) Van Dyke The electric network equivalent of a piezoelectric resonator, Phys. Rev 25 (6) 895 (1925) 3 D.W. Dye, The piezo-electric quartz resonator and its equivalent electrical circuit, Proc. Phys. Soc. (London) 38 (1) 399 (1925) 2 K.S.. 5 / 29.
(6) Butterworth-Van Dyke electromechanical model I Butterworth-VanDyke model 1 2 3 : RLC series branch represents damped spring-mass (“motional branch”) I Electrodes separated by a dielectric define a parallel capacitance Mechanical M ẍ + hẋ + kx = F h (damping) M (mass) k (stiffness) x (displacement) ẋ (velocity) √ Q = h1 kM q k ω0 = M. Electrical L1 q̈ + R1 q̇ + q/C1 = U R1 (resistance) L1 (inductance) 1/C1 (capacitance) q (electrical charge) i = dq/dt q (current) Q=. L C. 1 R. ω0 = √ 1. L1 C1. 1 S.. Butterworth, On electrically-maintained vibrations, Proc. Phys. Soc. (London), 27 410–424 (1914) Van Dyke The electric network equivalent of a piezoelectric resonator, Phys. Rev 25 (6) 895 (1925) 3 D.W. Dye, The piezo-electric quartz resonator and its equivalent electrical circuit, Proc. Phys. Soc. (London) 38 (1) 399 (1925) 2 K.S.. 6 / 29.
(7) Butterworth-Van Dyke electromechanical model I Butterworth-VanDyke model 1 2 3 : RLC series branch represents damped spring-mass (“motional branch”) I Electrodes separated by a dielectric define a parallel capacitance 12/ 3/ 2016 8:45:34 AM 1311.6010K42- 103899-La. Trc1. Y11 Real 10 mS/ Ref 30 mS Cal Off. Mem4[Trc1]. Y11 Real 10 mS/ Ref 30 mS. 0.08 0.07 0.06. C1 R1. M1. 0.05. L1. C0. 0.04 0.03 30 mS. 1 M1 M2 M3 M1 M2 M3. 9.996900 MHz 9.996562 MHz 9.997233 MHz 9.996900 MHz 9.996739 MHz 9.997069 MHz. 20.081 mS 10.004 mS 10.005 mS 50.356 mS 19.987 mS 19.948 mS. M M 2 M 13. 0.02. M2M3. 0.01 0 -0.01 -0.02. Ch1 Start 9.99 MHz Trc3. Pwr -10 dBm Bw 100 Hz. Y11 Phase 50°/ Ref 0° Cal Off. Mem5[Trc3]. Stop 10.02 MHz. Y11 Phase 50°/ Ref 0°. 250. 2. Antiresonance: new concept introduced by the parallel capacitance. M1 10.014586 MHz 29.84 °. 200 150 100. M1. 50. 0°0 -50 -100 -150 -200 -250. Ch1 Start 9.99 MHz. Pwr -10 dBm Bw 100 Hz. Stop 10.02 MHz. 7 / 29.
(8) QCM sensitivity. 4. dt I QCM is claimed to detect “mass” bound to the sensor surface A I Definition of the sensitivity: S = dff · dm 0 I Allows for comparing a wide range of acoustic transducers, from kHz to GHz and nanometric to macroscopic df A df f 1 I Sauerbrey (1959) : dtt = dff = dλ λ ⇒ S = f · Aρdt = f ρdf ·t = ρ·t. t. t: QCM thickness, ρ = 2.643 g.cm−3 : quartz density, dm = A · ρ · dt: adsorbed mass over area A Assumption: perturbation (dt t) of a layer with same properties than quartz (ρL = ρ) Numerical application: 5 MHz QCM exhibits S = 11 cm2 /g 4 G.. Sauerbrey, Verwendung von Schwingquarzen zur Wägung dünner Schichten und zur Mikrowägung, Zeitschrift für Physik A Hadrons and Nuclei, 155 (2), 206–222 (1959) 8 / 29.
(9) Detection limit I I I I I. the smallest quantity that can be detected using the sensor e.g. 3σ with σ the measurement fluctuation (noise) includes all sources of noise: electronics, fluidics, digitization detection limit=noise/sensitivity long term drift=low noise correlated noise: baseline stabilization prior to running a measurement (double layer stabilization, temperature stabilization) I Typical resolution: 1 Hz at 5 MHz=0.2 ppm ⇒ dm = 18 ng/cm2 A I Protein film: ρprotein = 1.4 g/cm3 and 5 nm thick ⇒ 700 ng/cm2 I ⇒2.5% surface coverage by proteins can be detected with QCM. I. J.-M Friedt, K. H. Choi, L. Francis and A. Campitelli, Simultaneous Atomic Force Microscope and Quartz Crystal Microbalance measurements: interactions and displacement field of a QCM, Japanese J. Appl. Phys., 41 (6A), 2002, 3974-3977. 9 / 29.
(10) Displacement and acceleration I F~ = m · ~a I static displacement: A0 = C × V = 2 pm/V since C = 1.4 · 10−12 m/V I dynamic displacement5 if Q = 1000 : A = A0 × Q = 2 nm/V I x = A sin(ωt) ⇒ v = A · ω(ωt) ⇒ |~a| ≤ A · ω 2 I f = 5 MHz: |a| = 2 · 10−9 × (2π × 5 · 106 ) = 2 · 106 m/s2. Excellent gravimetric sensitivity linked to the huge acceleration on the sensor surface. 5 J.-M Friedt, K. H. Choi, L. Francis, A. Campitelli, Simultaneous Atomic Force Microscope and Quartz Crystal Microbalance measurements: interactions and displacement field of a QCM, Jap. J. of Appl. Phys. 41 (6A) pp.3974-3977 (2002) 10 / 29.
(11) Dissipation measurement (QCM-D) I I I I. Frequency related to “mass” (acoustic wave confinement boundary condition variation) Dissipation = Q −1 related to viscous losses Viscous losses related to the conformation of the molecules B. Kasemo in Göteborg: creation of Q-Sense 6 (using aliasing !). R. Richter & al, Pathways of Lipid Vesicle Deposition on Solid Surfaces: A Combined QCM-D and AFM Study, Bio. J. 85 3035–3047 (2003). 6 M. Rodahl, F. Höök, A. Krozer, P. Brzezinski, B. Kasemo, Quartz crystal microbalance setup for frequency and Q-factor measurements in gaseous and liquid environments, Rev. Sci. Instrum. 66 (7) 3924–3930 (1995). 11 / 29.
(12) Shear wave penetration depth I I I I. Newtonian fluid: constant stress-strain relation defines the viscosity Fluids characterized by dynamic (shear) viscosity η: dragged by the shear wave 7 Exponentially decaying displacement q with depth (6= propagative pressure wave) η A(z) = A(0) exp(−z/δ) with δ = ρω. I Considering the dynamic viscosity of water η = 1 cP, and ρ = 1 g.cm−3 , then r z 10−2 δ= cm = 180 nm 2π × 5 · 106. A vibrating surface. 7 K.K Kanazawa & J.G. Gordon, The oscillation frequency of a quartz resonator in contact with liquid, Analytica Chimica Acta 175 99–105 (1985). 12 / 29.
(13) Measurement examples: electrochemical deposition I Reversible thin film deposition controlled electrically I Examples: Cu ↔ Cu 2+ + 2e − or Ag ↔ Ag + + e −. Ag. Cu Rigid layer ⇒ ∆fn /n ∝ √ ∆mlayer (low damping) Viscous layer ⇒ ∆fn / n ∝ {∆mliquid , ∆mlayer } (high damping) 13 / 29.
(14) Measurement examples: globular proteins I I I I. surface chemistry: hydrophobic thiol on gold S-layer protein forms a crystal on a hydrophobic surface (reversible) little/no variation of the quality factory (damping) simultaneous optical measurement: thickness and density of the layer. Globular proteins ∼ thin rigid film: valid approximations for both acoustic (mass effect) and optics ⇒ conditions applied during BIAcore’s radiolabelling calibration 8 8 J.-M Friedt, L. Francis, G. Reekmans, R. De Palma, A. Campitelli and U.B. Sleytr, Simultaneous surface acoustic wave and surface plasmon resonance measurements: electrodeposition and biological interactions monitoring, J. of Appl. Phys., 95 (4), 2004, 1677-1680. 14 / 29.
(15) Measurement examples: fibrillar proteins I Globular proteins (S-layer, IgG, IgE, BSA ...) are short and spread on the surface (5-10 nm) as a rigid layer I Fibrillar proteins (collagen, fibrinogen) extend deep in the buffer solution, equivalent to a thick layer full of solvent ⇒ strong contribution of viscosity. I rigid interaction: ∆fN ∝ N √ I viscous interaction: ∆fN ∝ N I Large damping variation and √ ∆fN /N scaling as N as opposed to constant: signatures of viscous interactions. 30 µg/ml collagen. 15 / 29.
(16) Measurement conclusions ⇒ optics underestimates the adsorbed mass (lower optical index than expected). Analyte (bulk concentration, µg/ml). collagen (30µg/ml) collagen (300µg/ml) fibrinogen (46µg/ml) fibrinogen (460µg/ml). √ ∆fn / n (Hz) QCM. 2 − 12. ?. ?-1000. NO. 50. 4.7 ± 0.7 1.0 ± 0.1. 75 ± 15 100. NO NO. 45=900 8=160. 3-5 0.2-0.5. ± ± ± ±. 1000 1200 110±5 NO. NO NO 55±5' 1110 100=1700. 100 >120 4-10 8-10. d (nm) SAW/SPR. 560±20 135±15 1750±150 2100±200 750±100 1500±500. 16.0 ± 3.0 19.0 ± 3.0 6.0 ± 1.5 13.0 ± 2.0. 25 35 50 50. Cu S-layer CTAB. x (%) SAW/SPR. surface density (ng/cm2 ). 15 10 10 10. ∆fn /n (Hz) QCM. ∆D (×10−6 ) QCM. 16 / 29.
(17) Measurement conclusions ⇒ acoustics overestimates the adsorbed mass (bound solvent to the organic layer). Analyte (bulk concentration, µg/ml). collagen (30µg/ml) collagen (300µg/ml) fibrinogen (46µg/ml) fibrinogen (460µg/ml). √ ∆fn / n (Hz) QCM. 2 − 12. ?. ?-1000. NO. 50. 4.7 ± 0.7 1.0 ± 0.1. 75 ± 15 100. NO NO. 45=900 8=160. 3-5 0.2-0.5. ± ± ± ±. 1000 1200 110±5 NO. NO NO 55±5' 1110 100=1700. 100 >120 4-10 8-10. d (nm) SAW/SPR. 560±20 135±15 1750±150 2100±200 750±100 1500±500. 16.0 ± 3.0 19.0 ± 3.0 6.0 ± 1.5 13.0 ± 2.0. 25 35 50 50. Cu S-layer CTAB. x (%) SAW/SPR. surface density (ng/cm2 ). 15 10 10 10. ∆fn /n (Hz) QCM. ∆D (×10−6 ) QCM. 17 / 29.
(18) Sensitivity mapping & packaging Scanning Electrochemical Microscope mapping of a QCM gravimetric sensitivity. 9. I strongest sensitivity at center of electrode I sensitivity vanishes on the surrounding of the resonator I the higher the overtone, the better the energy confinement over the electrode I O-ring around the sensor will not impact the acoustic wave. 9 A.C. Hillier & M.D Ward, Scanning electrochemical mass sensitivity mapping of the quartz crystal microbalance in liquid media, Anal. Chem. 64 (21) 2539–2554 (1992). 18 / 29.
(19) Beyond the bulk acoustic resonator: FBAR A 1 dm I S = dff · dm = ρ·t ⇒ dff = ρ·A·t = dm m with m the mass of the resonator I increasing S requires shrinking m and hence t I thin Film Bulk Acoustic Resonator: replace bulk acoustic resonator with piezoelectric film on a membrane I but rising S associated with rising f0 .... I ... and oscillator noise rises with f0 , degrading the detection limit I ⇒ is the detection limit improved on a FBAR architecture ?. Challenge of generating shear wave on a thin piezoelectric film deposited using a vapor method (C-axis normal to the growth plane). 19 / 29.
(20) Beyond the bulk acoustic resonator: SAW. I Another strategy for reducing the mass of the vibrating element: confine the acoustic wave to the surface I SAW: Surface Acoustic Wave devices I Rayleigh wave boundary conditions only met at the free surface ... I ... but Rayleigh waves exhibit out-of-plane component radiating as pressure waves in fluids. I Shear wave can be confined on a surface if a slow guiding layer is deposited on the surface (cf optical fiber) I Love-mode SAW devices exhibit high sensitivity and compatibility with liquid media I Love mode SAW sensors extensively used as bio-sensors. Example: N-isopropyl acrylamide (N-IPAAM) is a polymer whose conformation (hydrophilic v.s hydrophobic) changes with temperature 20 / 29.
(21) Beyond the bulk acoustic resonator: SAW I Another strategy for reducing the mass of the vibrating element: confine the acoustic wave to the surface I SAW: Surface Acoustic Wave devices I Rayleigh wave boundary conditions only met at the free surface ... I ... but Rayleigh waves exhibit out-of-plane component radiating as pressure waves in fluids. I Shear wave can be confined on a surface if a slow guiding layer is deposited on the surface (cf optical fiber) I Love-mode SAW devices exhibit high sensitivity and compatibility with liquid media I Love mode SAW sensors extensively used as bio-sensors. Example: N-isopropyl acrylamide (N-IPAAM) is a polymer whose conformation (hydrophilic v.s hydrophobic) changes with temperature 21 / 29.
(22) Measurement example I From SAW: phase and magnitude measurements I From SPR: optical thickness → exploit the viscous dissipation of the propagating acoustic wave SAW A (dB). −21. NIPAAM (N-isopropyl acrylamide) Thermocouple. x. LASER 670 nm. 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1. 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1. 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1. 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1. 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1. 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1. 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1. 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1. 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1. Liquid cell. Notice this is very difficult to reproGuiding layers duce with QCM Piezoelectric substrate (bottom side of sensor in contact Coupling prism with prism). Output IDT. SAWΔ φ (◦ ). Input IDT. 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1. −22 −22.5 −23 20. SPR Δ θ (m◦ ). z. 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1. −21.5. 25. 30. 35. 40. 45. −30 20. 25. 30. 35. 40. 45. 1200 1000 800 600 400 200 0 −200 20. 25. 30. 35. 40. 0 −10 −20. Temperature (◦ C). 45 22 / 29.
(23) Measurement example I From SAW: phase and magnitude measurements I From SPR: optical thickness → exploit the viscous dissipation of the propagating acoustic wave. 38.9. 34.7. 28.2. Cycle 3 (23.9 °C − 40.4 °C − 23.5 °C). 0 22.9. 900. 4. 600. 3. 300. 2 23.9. 32.5. 39.6. 35.2. 28.8. 0 23.5. 300. 6. 31.2. 41. 36.2. 29.4. Cycle 4 (23.5 °C − 43.4 °C − 26.1 °C). 0 23.9. 1200. 5. 900. 4. 600. 3. 300. 2 23.5. 34. 42.8. 38.8. 31.7. 0 26.1. L. Francis, J.-M. Friedt, C. Zhou, P. Bertrand In situ evaluation of density, viscosity and thickness of adsorbed soft layers by combined surface acoustic wave and surface plasmon resonance, Anal. Chem. 2006; 78 (12) (2006), pp. 4200-4209. PNIPAAm layer content (%). 3. °. 600. 2 22.9. 1200. 5. 900. 4. 10. 2. 34.9 °C ↓. 681. 501. 5. ° 30.8 C ↓ 146. 25 °C. 0. 20. 146. 25. 30. 35. 40. 45. Layer thickness (nm). 50. 55. 60. 4. 34.9 °C ↓ 3.5. 3. Viscosity (cP). 6. 30.5. 5. SPR Δθ (m ). 300. 1200. °. 3. Cycle 2 (22.9 °C − 41.2 °C − 23.9 °C). SPR Δθ (m ). 600. SPR Δθ (m°) SAW ΔA/Δφ (dB/rad). 900. 4. 6. SPR Δθ (m°) SAW ΔA/Δφ (dB/rad). SAW ΔA/Δφ (dB/rad). 5. 2 22.4. SAW ΔA/Δφ (dB/rad). 1200. 90. 1. Cycle 1 (22.4 °C − 39.1 °C − 22.9 °C). 35.1 °C ↑. 50. 6. 15. 2.5. 35.1 °C ↑. 2. 30.8 °C ↓. 1.5. 1 20. 25 °C 25. 30. 35. 40. 45. Layer thickness (nm). 50. 55. 60. 23 / 29.
(24) Device characterization I I I I I. Typical frequency: 150 MHz Acoustic wave velocity: shear wave on quartz 5060 m/s λ = c/f = 33 µm two-electrodes separated by a 50% gap: 8 µm-wide electodes fluidic confinement challenge: water over the electrodes induces a capacitive short circuit ⇒ wall with wavelength width over the acoustic path to confine the liquid. 24 / 29.
(25) -20. Electronics. I Two approaches: oscillator and frequency counter (closed loop), or frequency sweep and phase/magnitude measurement (open loop). Amplitude (dB). I Detection limit determined by sensitivity and reader electronics noise. D. Rabus, J.-M. Friedt & al., A high sensitivity open loop electronics for gravimetric acoustic wave-based sensors, IEEE Trans. UFFC 60 (6), 1219–1226 (2013). -40 -45 -50. 154 156 158 Frequency (MHz). 160. device device device device. 150. (D: distance between. I observe ϕ at fixed frequency and variations of v induces variation τ and hence ϕ. -35. 200. Phase (degree). =. 2π Dv. -30. 152. I Network analyzer will always provide some characteristics, if only of a failing sensor dϕ df. 1 2 3 4. -55. I Oscillator Barkhausen conditions are difficult to meet in strongy varying environments (losses). I ϕ = 2π · f · τ = 2π · f · D/v ⇒ IDTs). device device device device. -25. 100. 1 2 3 4. 50 0 -50. -100 -150 -200. 154. 156 158 Frequency (MHz). 160 25 / 29.
(26) Electronics. 10. Magnitude. I Detection limit determined by sensitivity and reader electronics noise. Phase. I Two approaches: oscillator and frequency counter (closed loop), or frequency sweep and phase/magnitude measurement (open loop). AD9954. I ϕ = 2π · f · τ = 2π · f · D/v ⇒ IDTs). dϕ df. = 2π Dv (D: distance between. I observe ϕ at fixed frequency and variations of v induces variation τ and hence ϕ. 1 0 1 0. AD8367. Gain controller. SYPD−2. Magnitude Phase. AD9954. Source. I Oscillator Barkhausen conditions are difficult to meet in strongy varying environments (losses) I Network analyzer will always provide some characteristics, if only of a failing sensor. ADuC7026 A A D Controller D C C SPI. SAW sensors. AD8367. phase detector. SYPD−2. low noise amplifier. low noise amplifier. 1 0 1 0. 10 P.. Durdaut, M. Höft, J.-M. Friedt, E. Rubiola, Equivalence of Open-Loop and Closed-Loop Operation of SAW Resonators and Delay Lines, MDPI Sensors (2019) 26 / 29.
(27) Ongoing project Replace passive glass slides in optical systems with active SAW transducers. 11. Replace the low permittivity quartz with high permittivity, strongly coupled lithium tantalate ⇒ solve the fluidic handling by solving the capacitive short circuit issue ? 11 J.-M. Friedt, L. Francis, Combined surface acoustic wave and surface plasmon resonance measurement of collagen and fibrinogen layers, Sensing and Bio-sensing Research, 2016 27 / 29.
(28) Ongoing project Lithium tantalate substrate: high permittivity (εr ' 40) substrate propagating a shear wave ⇒ no need for fluidic confinement ! 5 lar1 echo3-echo1 lar2 echo3-echo1. 0. lar1 echo2-echo1. phase difference (deg). lar2 echo2-echo1. -5 -10 -15 -20 -25 -30 -35. 0. 500. 1000. 1500. 2000. time (s). Non-specific binding of proteins from powder milk (' 500 µg/ml). 28 / 29.
(29) Conclusion I The quartz crystal resonator: much more than a “microbalance” I direct detection system for probing thin film properties, including mass (density× thickness) and viscosity I Readily accessible substrates (cf. electronics quartz resonators) for experimenting I Opportunity to use radiofrequency electronics design skills I Ability to measure sub-100 ng.cm−2 masses: even used on satellites to assess outgassing Applicability to practical point of care biosensors? 14. 12 13. !. TODO I Experiment by yourself15 : jmfriedt.free.fr/QCM_BUP.pdf I Tuning fork for gas sensing: QEPAS (Quartz Enhanced Photo-Acoustic Spectroscopy) 12 R. Naumann, W. Moore, D. Nisen, W. Russell & P. Tashbar, Quartz crystal microbalance contamination monitors on Skylab: A quick look analysis (1973) 13 B.E. Wood & al., Review of Midcourse Space Experiment (MSX) satellite quartz crystal microbalance contamination results after 7 years in space, Proc. 9th Intl Symp. on Materials in a Space Environment (2003) 14 T. Leı̈chlé, L. Nicu & T. Alava, MEMS Biosensors and COVID-19: Missed Opportunity 15 J.-M. Friedt, Introduction à la microbalance à quartz : aspects théoriques et expérimentaux, Bulletin de l’Union des Physiciens n.852 (March 2003), pp.429-440 29 / 29.
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