Sébastien Tétin

Benjamin Caillard

Francis Ménil

Hélène Debéda

Claude Lucat

Claude Pellet

Isabelle Dufour
email: isabelle.dufour@ims-bordeaux.fr

Modeling and performance of uncoated microcantilever-based chemical sensors

INTRODUCTION

During the last decade, the use of resonant microcantilevers has involved a significant advance in the field of chemical sensors [START_REF] Sepaniak | Microcantilever transducers: a new approach in sensor technology[END_REF][START_REF] Goeders | Microcantilevers: sensing chemical interactions via mechanical motion[END_REF]. For this type of sensor the standard use is based on depositing a sensitive coating (usually a polymer or inorganic porous material) on a silicon microcantilever. Then, the specific sorption of the target gas by the sensitive coating modifies the mass of the microstructure and consequently its resonant frequency [START_REF] Sepaniak | Microcantilever transducers: a new approach in sensor technology[END_REF][START_REF] Goeders | Microcantilevers: sensing chemical interactions via mechanical motion[END_REF].

An alternative way to use a vibrating silicon microcantilever, without a sensitive coating, as a chemical sensor is proposed here. Using the fact that the resonant frequency of a microcantilever depends on the density and viscosity of the surrounding medium, it is possible to determine the concentration of a gas in a binary mixture.

In the first part of this paper, the analytical expression of the resonant frequency shift due to a modification of either the density or the viscosity of the fluid is presented. Then examples of measurements in binary gas mixtures (He/N 2 and CO 2 /N 2 ) are shown. In the last part, the measurements are compared to the analytical modeling results and the performance of such chemical microsensors is examined and compared to that of classical coated microcantilever-based chemical sensors.

II. ANALYTICAL EXPRESSION FOR THE FREQUENCY SHIFT

When a microcantilever vibrates in a viscous fluid (gas or liquid), the fluid offers resistance to the motion.

The fluid loading on the beam includes an inertial force, proportional to the beam acceleration, and a viscous or dissipative force that is proportional to the microcantilever velocity [START_REF] Blom | Dependance of the quality factor of micromachined silicon beam resonators on pressure and geometry[END_REF][START_REF] Hosaka | Damping characteristics of beam-shaped micro-oscillators[END_REF][START_REF] Sader | Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope[END_REF]. These fluid effects influence the dynamic response of the beam, in particular, the resonant frequency f r [START_REF] Sader | Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope[END_REF]:

 0 2 2 1 1 1 2 1 r f f Q Lg m     
Here f 0 is the undamped natural frequency of the microcantilever in vacuum, Q is the quality factor of the cantilever/fluid system (depending on the losses), g 2 is a fluid-dependent inertia parameter (defined later), and m is the microcantilever mass.

The classical result for the natural frequency f 0 in vacuum is [START_REF] Blevins | Formulas for natural frequency and mode shape[END_REF] 

2 0 0 2 2 E I L f L m        
with  0 = 1.875 corresponding to the fundamental flexural mode, L the cantilever length, E the Young modulus and I the moment of inertia of the microcantilever cross section about the axis of bending, given by 3 12 I bh  , with b and h the width and the thickness of the microcantilever.

The quality factor Q of a microcantilever sensor in a fluid environment depends on the system energy losses.

In general, these losses may be intrinsic (thermoelastic losses, clamping losses, bulk internal friction other than thermoelastic dissipation, etc.) [START_REF] Yasumura | Quality factors in micron-and submicron-thick cantilevers[END_REF][START_REF] Lochon | A microcantilever chemical sensors optimization by taking into account losses[END_REF] or due to the surrounding medium (viscous losses). In the case of gas chemical sensors, the surrounding medium is typically a gas at atmospheric pressure. In our case (no coating), the losses due to viscous damping in the fluid are dominant [START_REF] Blom | Dependance of the quality factor of micromachined silicon beam resonators on pressure and geometry[END_REF], and the results of Sader [START_REF] Sader | Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope[END_REF] are applicable. Using the current notation, Sader's expression for the quality factor Q may be written as

 2 0 1 2 1 / / Lg m Q f Lg m     
where g 1 and g 2 are the fluid-dependent viscosity and inertia parameters, given explicitly by:

   2 2 f r 1 i r b f g f 2          2 f 2 r r b g f 4     
where  f is the fluid mass density,  is the fluid viscosity, and r Γ and i Γ are the real and imaginary parts of the (dimensionless) "hydrodynamic function": [START_REF] Maali | Hydrodynamics of oscillating atomic force microscopy cantilevers in viscous fluids[END_REF] and  the length representing the thickness of the thin viscous layer surrounding the microcantilever in which the velocity has dropped by a factor of 1/e=0.37, which can be expressed by

 r Γ 1 2 a a b       i Γ 2 1 2 b b b b            
 f r f         
Considering small variations of fluid density and fluid viscosity it is possible to obtain the analytical expression of the resonant frequency shift due to these fluid property variations. Using equations 1-8, the resonant frequency shift can be approximated with a first-order approximation:

 2 1 1 8 2 f f r r f d df a d a b f h                     
where  is the density of the microcantilever. This analytical expression relates the relative resonant frequency shift to the mass density and viscosity of the fluid and also to the microcantilever geometrical parameters.

Remarks concerning the assumptions:

All the previous equations (1-9) are considered valid provided that [START_REF] Sader | Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope[END_REF]:

 The amplitude of vibration is much smaller than the microcantilever thickness; thus, there is no nonlinear term in the differential equation governing the microcantilever vibration.

 The microcantilever length is sufficiently larger than both its width and its thickness. In this case the equation for the microcantilever vibration is a one-dimensional beam equation.

 The fluid can be assumed to be incompressible. For this, the wavelength of vibration must exceed both the dominant length scale in the flow, b, and the amplitude of vibration. Moreover, in a gas phase medium, the assumption of incompressibility should be supplemented by the condition that the dominant length scale in the flow, b, is sufficiently greater than the mean free path of the gas.

In this paper, all of these assumptions are verified. In fact, the microcantilever geometry satisfies L > b and L >> h. Moreover, all the gases are used at atmospheric pressure and the microcantilever geometry is in the micrometer range consequently gases can be considered incompressible fluids. Different groups [START_REF] Maali | Hydrodynamics of oscillating atomic force microscopy cantilevers in viscous fluids[END_REF][START_REF] Boskovic | Rheological measurements using microcantilevers[END_REF] have already verified experimentally the equations 1-8 in the case of vibrations of microcantilevers in pure gases or air (mixture) at atmospheric pressure.

In the following section, the aim is to present some experimental data to demonstrate that this resonant frequency shift can be measured in the case of binary mixtures of varying concentrations.

III. MEASUREMENT OF THE FREQUENCY SHIFT

To verify if equation 9 can be used for gas detection, measurements have been made for two binary gas mixtures: helium in nitrogen and carbon dioxide in nitrogen in order to have one case with a smaller mass density than pure nitrogen and the other with a higher mass density.

A. Microcantilevers, Actuation, Vibration Measurements

The microcantilevers have been fabricated by ESIEE group (Paris, France, www.esiee.fr) using silicon technologies (Fig. 1).

The excitation of the microcantilever is made by electromagnetic actuation. The excitation arises due to the interaction between a magnetic field created by a magnet placed close to the chip and an electrical current passing through a conducting strip placed on the microcantilever. The Laplace electromagnetic force induces the structural motion. In order to detect the microcantilever oscillation, semiconductor strain gauges (boron-doped piezoresistors) are fabricated during the process. They are arranged in a half Wheatstone bridge configuration: a first gauge is located where the strains are maximum (the clamped-end of the beam) and the other is on the rigid substrate (Fig. 1). The way to measure the resonant frequency shift is to actuate the microcantilever at a fixed frequency close to the resonant frequency, and to read out the piezoresistive signal phase. When the resonant frequency shifts, the phase of the microcantilever signal is modified. Near the resonant frequency the phase is almost a linear function of the frequency; thus, the measurement of the phase shift at a fixed frequency allows one to determine the resonant frequency shift.

The microcantilevers are placed in a gas chamber (total volume: 500 µl) under a controlled gas flow (100 to 1000cm 3 /min). Gas streams containing binary mixtures of the desired species (helium or carbon dioxide) and nitrogen are fed to the chamber using bottles of gas and a set of mass-flow controllers.

Fig. 2 shows examples of resonant frequency shift measurements for various helium concentrations in nitrogen (2%, 1.5%, 1% and 0.5%) in the case of two microcantilever geometries among the five geometries studied. Based on the gas concentrations in the gas bottles (5% of helium in nitrogen and pure nitrogen) and the characteristics of the mass flow controllers, the flow rate required to generate the desired concentration mixture These measurements show that in the presence of helium, the resonant frequency increases. This phenomenon is almost linear with the helium concentration and is reversible. Overshoots can be observed at each gas concentration, because of the mass flow controller command. The lower concentration step (0.5%) gives a resonant frequency shift much higher than the frequency noise. This means that these types of microcantilevers could measure much smaller helium concentrations (limit of detection will be discussed in section IV). The amplitude of the resonant frequency shift depends on the microcantilever geometrical parameters.

D. Measurements for a Carbon Dioxyde/Nitrogen Mixture

The same experiments have been carried out with various carbon dioxide concentrations in nitrogen (1%, 2%, 3%, 4%) with a 1000cm 3 /min gas flow (this higher gas flow is due to the fact that in this case both gas bottles are with pure gases). Examples of resonant frequency shift measurements are presented in Fig. 3 for two different microcantilever geometries. measurements exhibit reversibility, and the smallest output signal in the experiments is much higher than the noise. In addition, quasi-linearity is observed.

IV. DISCUSSION

The aim of this section is to compare the expected resonant frequency shifts (based on equation 9 of section II,) to the experimentally measured shifts presented in section III.

A. Density and Viscosity of a Binary Mixture

First, in order to apply the theoretical equation it is necessary to know the mass density and viscosity of a binary mixture.

Using the definition of the mass density, in the case of a binary mixture it can be expressed as a function of the mass densities of each component:

   1 1 1 2 1 f x x             with 1  and 2
 the mass densities of gas 1 and gas 2, respectively, and 1

x the volume fraction of gas 1.

Contrary to the case of mass density, the viscosity of a binary mixture is not easy to obtain using the viscosity definition. An approximate expression for the viscosity of gas mixtures was derived by Sutherland in 1895. It is based on a simple mean-free-path model and, for a binary gas mixture, is given by [START_REF] Sutherland | The viscosity of mixed gases[END_REF]     

1 2 1 1 1 1 12 1 1 21 1 1 1 x x x x x x               with 1
 and 2  being the viscosities of gas 1 and gas 2, respectively.

Concerning the expressions for 12  and 21  , many attempts to predict these parameters have been made.

Wilkes [START_REF] Wilke | A viscosity equation for gas mistures[END_REF] derived the following expressions:

 2 1 2 1 2 1 4 1 1 2 12 2 2 1 8 1 1 M M M M                                          2 1 2 1 2 1 4 2 2 1 21 1 1 2 8 1 1 M M M M                                        
where 1 M and 2 M are the molar masses of the gases.

The average deviation between calculated and experimental data for thirteen mixtures involving different gases (CO2, O2, CO, H2, CH4, N2, etc.) is 1.9% [START_REF] Wilke | A viscosity equation for gas mistures[END_REF]. Brokwak [START_REF] Brokaw | Predicting transport properties of dilute gases[END_REF] gave other more complicated expressions resulting in almost the same numerical results: for 280 mixtures involving 25 gas pairs (including He/N2 and CO2/N2), the average error when comparing with experimental data is 0.7% [START_REF] Brokaw | Predicting transport properties of dilute gases[END_REF]. Both of these methods use only the viscosity and molecular mass of the two pure components.

B. Case of He/N 2 and CO 2 /N 2 Mixtures

Considering that helium, carbon dioxide and nitrogen are perfect gases, their mass densities can be calculated for a temperature of 25 C  and a pressure of 1000hPa . For these temperature and pressure conditions, the mass density of nitrogen, helium and carbon dioxide are, respectively, The viscosities of the gases also depend on the temperature:

 6 2 (2,2)* 2.6693 10 MT       
with M the molar mass (g.mol -1 ), T the temperature (K),  a length for the expression of the interaction potential (Å) and (2,2) In the modeling of the resonant frequency shift (equation 9) there are two terms: one due to the mass density variation and the other due to the viscosity variation. In order to understand the relative influence of the two effects, both terms have been calculated for various microcantilever geometries (Table II). The numerical results are presented in Table III for 1% concentration of helium or carbon dioxide. The numerical results presented in Table III show that, for the considered geometries, the term due to viscosity variation is negligible compared to that due to mass density variation. (The ratio of the terms is between 10 and 300). As a result, equation 9 can be simplified for the present application to

 1 8 f r r d df a b f h           
As expected from the modeling, the measured resonant frequency (Figs. 23) increases in the case of helium because of the decreasing mass density of the surrounding medium, whereas it decreases in the case of carbon dioxide because of increasing mass density.

In order to accurately compare equation 17 with measurements made with the five studied microcantilever geometries (Table II), linear regression has been performed on the experimental data to obtain numerical values of the slope of the relative resonant frequency shift versus the mass density of the gas (Fig. 4). The comparison of the slopes based on modeling and measurement is shown in Fig. 5. A very good agreement is observed between measurements and analytical modeling for the various microcantilever geometries and gas concentrations (Fig. 5).

D. Limit of Detection

The validity of equation 17 has been demonstrated, which means that this equation can be used to determine optimal values of the microcantilever geometric parameters and the associated performance of such microsensors.

For a given gas mixture, the relative resonant frequency shift increases with the width-to-thickness ratio of the microcantilever. Wide, thin microcantilevers will thus be preferred. This dimensional choice is confirmed by Fig. 4: the slope increases with the ratio b/h. For the five tested microcantilevers the most sensitive is #5 and the least sensitive is #1.

For the tested microcantilevers the resonant frequency is between 4kHz and 50kHz. Considering the experimental limit of frequency measurement of 10mHz, it is possible using equations 10 and 17 to estimate the limit of detection in both cases of helium/nitrogen and carbon dioxide/nitrogen mixtures (Table IV).

Figure 1 .

 1 Figure 1. Silicon microcantilever with electromagnetic actuation and piezoresistive measurement: (a) photograph. (b) electrical connection diagram: connection plots 2-3-4 represent piezoresistors and connection plots 1-5 denote the conducting path for electromagnetic actuation

(a few percent) is 100cm 3 Figure 2 .

 32 Figure 2. Example of resonant frequency shift measurement (drift removed) for different helium concentrations in nitrogen (2%, 1.5%, 1% and 0.5%) for two different microcantilever geometries: (a) L=6mm, b=200µm, h=109µm (b) L=1mm, b=600µm, h=19µm

Figure 3 .

 3 Figure 3. Example of resonant frequency shift measurement (drift removed) for different carbon dioxide concentrations in nitrogen (1%, 2%, 3% and 4%) for two different microcantilever geometries:. (a) L=6mm, b=200µm, h=109µm (b) L=1mm, b=600µm, h=19µm

Figure 4 .Figure 5 .

 45 Figure 4. Relative resonant frequency shifts for the five microcantilever geometries in the cases of He/N 2 and CO 2 /Ne mixtures of different concentrations. Linear regression has been made on the experiemental data (discrete markers)

  Boltzmann constant and  the energy in the action potential (J).Using equations 14-16 and the numerical values of the different parameters for each gas, the viscosities at

	where is the 25 C 23 1 1.380662 10 k J K     for nitrogen, helium and carbon dioxide are, respectively,		N	2		17.8		. Pa s	,		H	e		19.9		. Pa s	,
		2 CO		14.8		. Pa s	.
		Using equations 10-11, it is possible to calculate the mass density and viscosity of the binary mixtures for
	different concentrations of carbon dioxide or helium. The results of the relative variations are summarized in
	Table I.
								(2,2)*		1.1614	  * T	0.1487 		0.5249	e		0.7732	T	*		2.1618 e		2.4378 T	*	
		with the normalized temperature * T defined by
														T	*		kT 		    

*  the double normalized collision integral for the Lennard-Jones potential:

TABLE I .

 I RELATIVE VARIATION OF DENSITY AND VISCOSITY

	He or CO 2	He/N 2 Mixture f d  d f  	CO 2 /N 2 Mixture f d  d f  
	0.1 %	-0.0857 %	0.0144 %	0.0571 %	-0.0222 %
	1 %	-0.857 %	0.144 %	0.571 %	-0.222 %
	C. Experiment/Modeling Comparison

TABLE II .

 II

	beam	Length L (µm)	Width b (µm)	Thickness h (µm)
	3	2000	1000	112
	4	6000	1000	115
	5	1000	600	19
		MICROCANTILEVER GEOMETRIES
	beam	Length L (µm)	Width b (µm)	Thickness h (µm)
	1	6000	200	109
	2	2000	200	57

TABLE IV .

 IV Compared to classical resonant microcantilever-based chemical sensors with sensitive coating, the uncoated microsensors studies herein have smaller response times because there is no diffusion time in the response. The

		LIMIT OF DETECTION
	beam	He limit of detection mg/m 3 (ppmV)	CO 2 limit of detection mg/m 3 (ppmV)
	1	1210 (7562)	20287 (11461)
	2	134 (840)	2254 (1273)
	3	27 (168)	451 (255)
	4	242 (1512)	4057 (2292)
	5	11 (70)	188 (106)
		V. CONCLUSION

lack of the sensitive coating leads to a more reliable and reversible behavior because there is no significant absorption and desorption phenomenon. The results of this study demonstrate that uncoated microsensors may serve as viable devices for detection of specific concentrations of one gas in a binary mixture. The sensitivity and resolution of such sensors will be larger for those cases in which the difference between the mass densities of the two gases is higher.

ACKNOWLEDGMENT

This work has been supported by the EADS Foundation.


Frédéric Lochon
email: lochon@ixl.fr

Ludivine Fadel

Isabelle Dufour

Dominique Rebière

Jacques Pistré

SILICON MADE RESONANT MICROCANTILEVER: DEPENDENCE OF THE CHEMICAL SENSING PERFORMANCES ON THE SENSITIVE COATING THICKNESS

Keywords: Microcantilever sensor, resonant frequency, sensitive layer thickness

A gas sensor based on the use of a resonating microcantilever has been realized by using a polymer sensitive coating. From the theoretical study of the microcantilever sensitivity, it has been deduced that the sensitivity is enhanced when the resonant frequency or the sensitive coating thickness are increased. The sensitive coating thickness influence has then been verified experimentally by using PEUT (polyetherurethane) as sensitive coating for ethanol detection. From these measurements, some drawbacks are shown: the coating thickness increase leads to a sensor response time increase and a frequency noise increase which worsens the limit of detection. Conclusions are then made about the sensitive coating optimization depending on application constraint considerations.

I Introduction

Resonant microcantilevers are used for more than 10 years as chemical sensors [START_REF] Lange | Complementary metal oxide semiconductor cantilever arrays on a single chip: mass-sensitive detection of volatile organic compounds[END_REF][START_REF] Betts | Selectivity of chemical sensors based on micro-cantilevers coated with thin polymer films[END_REF][START_REF] Battiston | A chemical sensor based on a microfabricated cantilever array with simultaneous resonance-frequency and bending read-out[END_REF][START_REF] Sepaniak | Microcantilever transducers: a new approach in sensor technology[END_REF][START_REF] Datskos | Micro and nanocantilever sensors, Encyclopedia of nanoscience and nanotechnology[END_REF][START_REF] Thaysen | Polymer-based stress sensor with integrated readout[END_REF][START_REF] Zhou | Zeolitemodified microcantilever gas sensor for indoor air quality control[END_REF][START_REF] Abadal | Electromechanical model of a resonating nano-cantilever-based sensor for high-resolution and high-sensitivity mass detection[END_REF][START_REF] Raiteri | Micromechanical cantilever-based biosensors[END_REF][START_REF] Berger | Transduction principles and integration of chemical sensors into a micromechanical array device[END_REF].

Indeed, because microcantilevers are very sensitive mass sensors, it is possible to detect small variations of sensitive layer mass by depositing a sensitive layer at the microcantilever surface. The sorption of gas molecules into the sensitive coating makes then possible their detection. Thus, by knowing the sensitivity of the microcantilever, it is possible to estimate the gas concentration by measuring the resonant frequency shift.

Preprint This paper presents some results obtained with our special shaped microcantilevers combined with a polymer sensitive coating for ethanol detection. The influence of the sensitive coating thickness is detailed theoretically and confirmed by the presented experiments.

II Used microcantilevers

In opposition to classical parallelepiped-shaped microcantilevers, this paper presents results obtained with non-parallelepiped-shaped microcantilevers combined with a PEUT (polyetherurethane) sensitive layer (Figure 1).

The microcantilevers are composed of two parts: the arm and the plate. The arm corresponds to the part which links the substrate to the plate. For sensitivity reasons, all the realized microcantilevers have a plate larger than the arm, as the modification of resonant frequency is more important when a mass is added at the microcantilever free-end. The studied microcantilever dimensions are:

s.b 1 b 1 L 1 L 1 /n h 2 h 1

Sensitive coating Microcantilever

 L 1 =1.5mm, n=1.5, b 1 =200µm, s=5, h 1 =85µm (resonating at 22.770kHz).

 L 1 =2mm, n=2, b 1 =400µm, s=2.5, h 1 =89µm (resonating at 17.780kHz).

III Modeling

As it will be shown later in the paper, the resonant frequency is a key parameter to design a sensor with a good sensitivity, since the sensitivity of resonant microcantilever sensors is directly proportional to the resonant frequency (section 3.2

Resonant frequency without coating

By using the Rayleigh's method which consists in equaling the kinetic energy and the potential energy, a good approximation of the resonant frequency can be calculated by knowing a realistic expression of the microcantilever deflection.

It is then possible to express the approximate resonant frequency of an homogeneous nonparallelepiped shaped microcantilever [START_REF] Dufour | Resonant microcantilever type chemical sensors: analytical modeling in view of optimization[END_REF]:

1 1 2 1 1 1 2 h E f L     (1)
where:

1  is a rational fraction of s and n (n is the ratio of the total length of the structure to the plate length, and s is the ratio of the plate width to the arm width, see Figure 1), 1

 the microcantilever mass density, 1 Ê the microcantilever effective Young modulus, 1 h the thickness, and 1 L the length of the microcantilever.

The expressions found by using the Rayleigh's method are valid for a microcantilever resonating in vacuum. In our case, since the microcantilever resonates in air, a slight modification of the resonant frequency appears due to losses and fluid inertia.

This modification is usually negligible because the quality factor (linked to the losses) of the used microcantilevers is relatively high (at least better than 100).

Resonant frequency with coating

Analytical expression

When a layer is deposited on top of a microcantilever, its resonant frequency is modified for two reasons: the added mass tends to decrease the frequency (see section 2.2) while the Young modulus of the layer tends to increase the frequency (see section 2.3).

Using the Rayleigh's method, the microcantilever resonant frequency with a sensitive coating deposited can be expressed [START_REF] Timoshenko | Strength of materials[END_REF]:  is the deposited layer mass density, 2 h is the deposited layer thickness and 2 Ê is the deposited layer effective Young modulus.

    4 2 4 2 2 2 1 1 2 2 1 2 1 2 1 1 2 2 2 1 1 1 1 2 2 1 1 2 2 ˆˆˆ2 2 3 2 1 1 ˆ2 h E h E h h E E h h h h f L h h h E h E            (2)
From the resonant frequency expression (2), two terms can be extracted:  The mass effect term:

1 1 2 2 1 G h h     (3)
 The Young modulus dependent term:

  4 2 4 2 2 2 1 1 2 2 1 2 1 2 1 1 2 2 1 1 2 2 ˆˆˆ2 2 3 2 ˆĥ E h E h h E E h h h h Y h E h E       (4)

Mass effect

The term G clearly shows the influence of the material masses: when the mass densities increase, the resonant frequency decreases or when the thicknesses increase (i.e. the mass increases), the resonant frequency decreases.

Thus, using light materials will allow high resonant frequencies and an increased sensitivity (see section 3.2).

Young modulus effect

The term Y can also be expressed:

  2 3 3 1 1 1 4 6 4 ˆ1 Y Eh            (5)
With

2 1 ˆÊ E   and 2 1 h h   .
From equation ( 5), it can be seen that Y has a minimum value of 3 Gas sensor response

Gas sorption

The sorption of gas molecules into the sensitive coating is expressed as a modification of the coating mass density. This modification depends on the affinity of the coating for the adsorbed gas and on the gas concentration in the surrounding medium.

The modified mass density of the coating is expressed:

2 2
( )

g g C K C     (6)
where 2

 is the mass density of the coating without adsorbed molecules, K is the partition coefficient (defined as the ratio between the gas concentration in the coating and the gas concentration in the surrounding medium) and g C is the gas concentration in the surrounding medium.

The resulting resonant frequency is then expressed:

    2 3 1 1 2 1 1 1 2 ˆ1 4 6 4 2 1 g h E f L K C                     (7)

Gas sensitivity

For small variations of the resonant frequency, the gas sensitivity g C S is defined as:

0             g g C g C f S C (8)
Then, substituting [START_REF] Zhou | Zeolitemodified microcantilever gas sensor for indoor air quality control[END_REF] in [START_REF] Abadal | Electromechanical model of a resonating nano-cantilever-based sensor for high-resolution and high-sensitivity mass detection[END_REF] gives:

    2 0 1 1 2 2 2      g g C C Kh S f h h (9)
Using ( 9) and [START_REF] Zhou | Zeolitemodified microcantilever gas sensor for indoor air quality control[END_REF], it is possible to demonstrate that a theoretical optimum coating thickness exists for very low sensitive coating Young modulus [START_REF] Lochon | An alternative solution to improve sensitivity of resonant microcantilever chemical sensors: comparison between using high-order modes and reducing dimensions[END_REF]. This optimal thickness can be expressed as a function of the cantilever thickness and the mass densities of the cantilever and

For higher sensitive coating Young modulus, no optimal coating thickness exists since the sensitivity is always increased when increasing the sensitive coating thickness.

IV Experimental results

Test bench

The actuation of the microcantilever at its resonant frequency is done with an electronic device which permits the microcantilever oscillation. This frequency is then measured by an HP53131 (frequency counter) and sent to a PC (Figure 2).

Mass effect

The modeling process about mass effect has been verified by depositing the sensitive layer on the microcantilever top surface. Because the chosen sensitive material (PEUT) has a very low Young modulus ( 2 6.9

E MPa 
) compared to the cantilever material (silicon 1 130

E GPa  ),
the ratio sensitive coating Young modulus to cantilever material Young modulus is very low

( 5 5 e   
). Thus, the sensitive coating Young modulus cannot modify the resonant frequency and thus any modification of the resonant frequency is only due to an added mass.

To verify the dependence of the resonant frequency upon an added mass, the resonant frequency of a cantilever has been measured in oscillator configuration (Figure 2) during the sensitive coating deposition.

Preprint The deposition is performed with a spray coating device which allows reproducible and uniform sprays. The spray coater, which has been characterized, deposits a constant sensitive coating thickness per pulverization depending on multiple parameters (viscosity of the solution, pulverization pressure, …). Thus, the deposited sensitive coating thickness has to be determined a posteriori using (2) with 2

1

E E  : 2 0 1 1 2 2 2 1 f h h f           (11)
where 0 f is the resonant frequency without coating.

Figure 3 shows the modification of the resonant frequency during the spray and the estimated deposited coating thickness using (11):

Gas detection

To verify the sensitivity of the sensor, a microcantilever with its associated sensitive coating is inserted in a gas-line and is exposed to different ethanol concentrations (Figure 4). As shown in Figure 5 and as predicted theoretically, the sensitivity increases when the coating thickness increases. In order to compare these measurements with the theoretical expression ( 9), the measured normalized frequency shift and theoretical normalized frequency shift, using the partition coefficient of the literature (K=950) [START_REF] Lange | CMOS cantilever sensor systems Atomic-Force-Microscopy and Gas Sensing Applications[END_REF], have been plotted (Figure 6). The reason of the discrepancy for the first point has not been clearly identified but a surface interaction between the gas and the coating may explain this phenomenon: since the area in contact with the gas is approximately the same whatever the coating thickness is, a gas quantity trapped close to the surface would increase the sensitivity for thin sensitive coatings.

Table 1 shows the partition coefficient which is calculated from (9) using the estimated coating thickness, the measured resonant frequency with the deposited coating and the measured frequency shift for an exposition to 5.2% of ethanol.

The obtained values are in good accordance to the literature excepted when the coating is 1µm thick. This difference may be explained by surface interactions as said previously. This can be explained by the response time of the chamber. Indeed, the chamber is, naturally, filled progressively and its response time has to be taken into account. If the chamber response time is greater than the sensor response time, then the observed response time is mainly due to the chamber.

In fact, in our case for coating thicknesses up to 4 µm, the observed response time is due to the chamber while for the 21 µm thick coating the adsorption time affect the observed response time.

Preprint The increased response time for the 21 µm thick coating clearly shows that the increase in sensitivity (Figure 5) can be achieved to the detriment of the response time (Figure 7).

Limit of detection

The limit of detection (L.O.D.), calculated from the measured sensor sensitivity g C S and the measured frequency noise noise f  , is represented in Table 2

: 3 . . . g noise C f L O D S  
It can be seen that, the frequency noise and the sensitivity increase when the sensitive coating thickness increases. Because the frequency noise does not increase in the same way as the sensitivity, the limit of detection is minimal, and thus optimal, for a sensitive coating thickness between 1 µm and 21 µm. The existence of an optimum coating thickness also demonstrates that the coating thickness has to be chosen carefully to avoid large response times and to allow an optimized sensor response.

V Conclusion

The sensitive coating influence upon sensitivity, response time and limit of detection has been shown and the presence of an optimal sensitive coating thickness has been observed.

The sensor, using a 4 µm thick PEUT sensitive coating, has been able to detect ethanol with a sensitivity of about 0.29 mHz/ppm with a frequency noise of about 2 mHz.

The selectivity of the device has not been studied, but similar results could also be achieved when detecting other gases since the PEUT is sensitive to most volatile organic compounds (VOCs).

From the measurements, conclusions have been done about the sensitive coating influence upon sensitivity, response time and limit of detection. Theses conclusions raise issues about the optimization of the sensitive coating thickness.

Because the determination of the exact value of the optimal sensitive coating thickness would require much more experimental work, it could be interesting to characterize precisely the frequency noise. This characterization requires the theoretical determination of the viscoelastic losses that occurs in the sensitive coating.

More generally, a theoretical study on the losses in resonant microcantilever sensors will significantly help the designers in reducing the frequency noise and thus adapting the microcantilever geometries and enhancing the limit of detection.

Preprint

Figure 1 :

 1 Figure 1: A microcantilever and its sensitive coating

Figure 2 :

 2 Figure 2: Microcantilevers resonant frequency measurement setup

Figure 3 :

 3 Figure 3: Resonant frequency and estimated coating thickness versus deposition time

Figure 4 :

 4 Figure 4: Frequency shift (drift removed) for a microcantilever resonating at 16.9kHz with a sensitive coating thickness of 21 µm, exposed to ethanol at different concentrations

Figure 5 :

 5 Figure 5: Frequency shift (absolute value) for different coating thickesses for a microcantilever exposed to 5.2% of ethanol

Figure 6 :

 6 Figure 6: Normalized frequency shift (ratio frequency shift to coating thickness) versus coating thickness for a microcantilever exposed to 5.2% of ethanol

  Preprint -Materials Science & Engineering C, Vol 26/2-3, 2006, pp. 348-353. (doi: 10.1016/j.msec.2005.10.079)

Figure 7 :

 7 Figure 7: Normalized frequency shift versus time for different coating thicknesses

  Preprint -Materials Science & Engineering C, Vol 26/2-3, 2006, pp. 348-353. (doi: 10.1016/j.msec.2005.10.079)

  -Materials Science & Engineering C, Vol 26/2-3, 2006, pp. 348-353. (doi: 10.1016/j.msec.2005.10.079)

  ).

	Preprint -Materials Science & Engineering C, Vol 26/2-3, 2006, pp. 348-353. (doi:
	10.1016/j.msec.2005.10.079)

  -Materials Science & Engineering C, Vol 26/2-3, 2006, pp. 348-353. (doi: 10.1016/j.msec.2005.10.079)

Table 1 :

 1 Deduced partition coefficient for each coating thicknessesThe responses of cantilevers exposed to 5.2% of ethanol with different coating thicknesses have been normalized and are presented in Figure7. From this figure, one thing can be noticed: the response time is approximately the same for thin coatings and is bigger for the 21 µm thick coating.

	Coating	Frequency shift	Resonant	Deduced partition coefficient
	thickness (µm)	(Hz)	frequency (Hz)	(as defined in section III.3.1)
	1	-5.21	17758	1220
	2	-8.03	17699	951
	4	-15.3	17614	920
	21	-76.3	16907	987
	4 Response time

  -Materials Science & Engineering C, Vol 26/2-3, 2006, pp. 348-353. (doi: 10.1016/j.msec.2005.10.079)

		1,2
		1
	Normalized frequency shift	0,2 0,4 0,6 0,8			1 microns 2 microns 4 microns 21 microns
		0
	-50	50	150	250	350
		-0,2
			Time (s)

Table 2 :

 2 Limit of detection of ethanol for a microcantilever resonating at 17.7 kHz

	Sensitive coating thickness	1 µm	4 µm	21 µm
	Sensitivity (mHz/ppm)	0.1	0.29	1.5
	Frequency noise (Hz)	0.001	0.002	0.015
	Estimated limit of detection (ppm)	30	20.4	30

  -Materials Science & Engineering C, Vol 26/2-3, 2006, pp. 348-353. (doi: 10.1016/j.msec.2005.10.079)

ACKNOWLEDGEMENTS

This work was sponsored in part by the French Agency for Environment and Energy Management (ADEME) and the "Région Aquitaine".

The authors wish to thank Jean-Luc Lachaud and Serge Destor for their help in the design of the spray coating device, and Olivier Français and Patrick Sangouard for the microcantilever fabrication.


Frédéric Lochon
email: lochon@ixl.fr

Isabelle Dufour

Dominique Rebière

A MICROCANTILEVER CHEMICAL SENSORS OPTIMIZATION BY TAKING INTO ACCOUNT LOSSES

Keywords: Microcantilever, chemical sensor, quality factor, losses, aspect ratio

The current trend in increasing microcantilever resonant frequencies leads to relatively low quality factors for microcantilevers resonating in a gas medium. In order to increase the quality factor of such high-frequency microcantilevers, an approach that takes into account the different types of losses is provided to specify appropriate values of microcantilever aspect ratios (length-to-thickness, width-tothickness). Conventional values of aspect ratios result in low quality factors, while those proposed here lead to slightly higher values of quality factor.

Introduction

In order to design a very sensitive microcantilever-based chemical sensor, it is required to use highfrequency devices. Indeed, the sensitivity of such sensors is proportional to the resonant frequency. Moreover, to achieve a minimal limit of detection, high quality factors are preferable because they (a) increase the sharpness of the resonance peak and, thus, the frequency shift measurement accuracy, and (b) result in lower short-term noise in oscillator configurations. A theoretical approach is proposed to show the importance of taking into account different losses when designing a microcantilever-based sensor. The importance of increasing the resonant frequency is first presented and the four dominant losses that occur in a viscous medium are then detailed and analytical forms of equivalent quality factors are given. The relevance of taking into account each loss is detailed and illustrated. Then, the existence of an optimum quality factor for a given microcantilever length is illustrated and optimum aspect ratios (length to width, length to thickness) are presented. A discussion then follows which compares conventional aspect ratios with fully optimum and nearly optimum aspect ratios. A conclusion is then made about the proposed aspect ratio expressions.

Theoretical study

Assumptions

This study is limited to uniform parallelepiped shaped microcantilevers with a negligible sensitive coating Young's modulus. The microcantilever vibration amplitude is considered far smaller than any dimension to neglect non linear effects.

Sensor sensitivity

The resonant frequency n f of a parallelepiped shaped microcantilever with a sensitive coating deposited on its top (Figure 1) is given by [START_REF] Blevins | Formulas for natural frequency and mode shape[END_REF]:

          2 3 11 11 1 2 2 1 43 n n Eh f Lh h (1)
where n

 is a parameter depending on the mode order, 1

L is the microcantilever length, 1 Ê is the effective microcantilever Young's modulus, 1 h and 2 h are the microcantilever and sensitive coating thicknesses respectively, and 1

 and 2

 are the microcantilever and sensitive coating mass densities respectively.

From equation (1) it can be seen that the resonant frequency is inversely proportional to the dimensions if we do a geometric contraction by keeping constant the aspect ratios (length to thickness: 11 Lh, length to width 11 Lb, coating thickness to cantilever thickness 21 hh ).

The sensitivity S of a sensor exposed to a gas concentration g C is given by: 12 1 2

n n g f r Sf K Cr     (2)
where n f  is the frequency shift due to gas sorption, K the partition coefficient of the sensitive coating -gas couple and 21 rh h  .

Thus, high resonant frequency devices will have high sensitivity. But in order to have a low limit of detection, a high sensitivity is not sufficient: the noise has to be taken into account.

About losses

The quality factor, a key parameter for the accuracy of the measurement, expresses the losses influence: low-loss microcantilevers will have a high quality factor.

For most microcantilevers resonating in vacuum, the quality factor is determined by thermoelastic losses and support losses. But when used in air, these cantilevers can have a much lower quality factor because of the viscous losses due to the surrounding fluid and because an acoustic radiation may occur for wide cantilevers [START_REF] Lange | Complementary metal oxide semiconductor cantilever arrays on a single chip: mass-sensitive detection of volatile organic compounds[END_REF].

To evaluate the global quality factor, each loss is first studied separately. Then the global quality factor is calculated using:

12 11 1 1 ... global n QQ Q Q   (3)
This approach is fully valid for low loss microcantilevers and thus it can be applied to determine how to minimize losses.

Viscous losses

When vibrating in a fluid, a microcantilever is perturbed by viscosity and mass density of the environment. A general theoretical model describing viscous losses has been established by Sader [START_REF] Sader | Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope[END_REF].

For microcantilevers with a rectangular cross section, the equivalent quality factor associated with viscous losses can be analytically expressed:

11 01 4 () () rn viscous in h b Q        (4)
where n  is the resonant pulsation, 0  is the density of the fluid, and r  and i  are the real and imaginary components of the hydrodynamic function () n   of the microcantilever.

Sader has also proposed an approximate analytical expression of the hydrodynamic function for a wide range of Reynolds number [START_REF] Sader | Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope[END_REF].

Using equation ( 4), it can be seen that viscous losses are important for high values of 11 Lh or for very narrow microcantilevers.

Support losses

To obtain equation [START_REF] Blevins | Formulas for natural frequency and mode shape[END_REF], it has been supposed an infinitely rigid support. In fact, the vibration of the microcantilever produces a mechanical work on the support. This mechanical work generates an elastic wave into the support. The generated wave power is lost by propagation.

Hao et al. have proposed an analytical approach to quantify these losses [START_REF] Hao | An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations[END_REF]. The associated equivalent quality factor for a silicon based microcantilever is given by:

  3 1 support 2 1 1 3.97 nn L Q h      (5)
with:

sin( ) sinh( ) cos( ) cosh( )

nn n nn         (6)
It can be seen from equation ( 5) that support losses are important for low values of 11 Lh.

Acoustic losses

The vibration of the microcantilever in the fluid creates an acoustic pressure which propagates into the fluid. The evaluation of this acoustic radiation in the case of a microcantilever with a rectangular cross section is not trivial. By approximating the rectangular cross section with an elliptical cross section, Blake has obtained an approximate expression for the radiated power [START_REF] Blake | The radiation from free-free beams in air and in water[END_REF]:

4 2 3 00 01 0 0 () sin ( cos ) 512 ck b PU k d           (7)
where 0 c is the speed of sound in the fluid, 00 kc   is the wavenumber in the fluid and ()

U  is
given by: 1 0 () ()

L jx UU x e d x        (8) with () Ux 
the microcantilever velocity along the z axis at pulsation  .

To calculate the microcantilever velocity we can approximate the microcantilever mode shape in presence of low losses to the microcantilever mode shape without losses. It then comes:

  , n nn Uj w x     (9)
with:

  (, ) nv a c wx A x   ( 10
)
where A is the oscillation amplitude and

  vac x 
the mode shape of the microcantilever given by:

                           11 1 1
cos( ) cosh( ) cos cosh sinh sin sin( ) sinh( ) The equivalent quality factor associated with acoustic radiation can be calculated using [START_REF] Hao | An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations[END_REF]:

nn n n n n vac nn x xx x x LL L L       (
2 cantilever rad radiated W Q W   (15)
with:

 

1 22 12 0 1 , 2 L cantilever n n x Ww x d x      (16)
where

  12 1 1 1 2 2 bh h   
is the linear mass of the microcantilever with the sensitive coating.

Using equations ( 9) to ( 16), it then comes:

By using numerical calculations of (17) it can be seen that acoustic radiation becomes important for wide microcantilevers and for "acoustically long microcantilevers". The term "acoustically long microcantilevers" refers to cantilevers for which the structural wavelength (L 1 / n ) is comparable to the acoustic wavelength (

0 2 k   
) in the fluid.

Thermoelastic losses

Thermoelastic losses are caused by the microcantilever material heating due to vibration.

p thermo C Q ET           (18)
with:

1 1 1 2 np C h     ( 19
)
where

1 p C , 1
 , T ,  , are the heat capacity, the thermal expansion coefficient, the temperature, and the thermal conductivity of the microcantilever material, respectively, and n  is the microcantilever resonant pulsation.

From equation (18) it can be seen that thermoelastic losses are maximum for 2.2246  

. At this maximum loss, the thermoelastic quality factor for a silicon made microcantilever at room temperature is bigger than 10 4 .

Discussion on the total quality factor

The combination of all the losses shows that no general trend can be given to minimize all losses at the same time: an optimum value should exists. In fact, when combining the losses, it comes that optimal aspect ratios can be found for a given length (Figure 2). Indeed, the thickness can be adjusted to equilibrate viscous losses and support losses (Figure 3), while the width can be adjusted to equilibrate viscous losses and acoustic losses (Figure 4).

Because of the approximations in the evaluation of the quality factor associated with acoustic losses and because of the analytical expression forms, no exact analytical equations can be given to choose the aspect ratios ( 11Lh, 11 Lb). However, by determining the optimal width and thickness for a given microcantilever length, it is possible to observe that using 11 20 Lh and 11 3 Lb is a simple rule to obtain an almost optimal quality factor.

From figure 2, it can be seen that using conventional aspect ratios (

 11 50 Lh ,  11 10

Lb

) implies that viscous losses are dominant and thus sufficient to calculate the quality factor. But in that case, the quality factor can be much lower while the resonant frequency remains low because of a high 11 Lh ratio. A comparison between different aspect ratios is made in table 1.

It can be seen that, even if the proposed aspect ratios are not fully optimal, they allow to increase significantly both the quality factor and the resonant frequency compared to conventional aspect ratios.

Moreover, approximate relationships between the length and optimal width and thickness can be found in order to have even higher quality factors and resonant frequencies. With a numerical resolution (as presented in Figure 2 for one length), the optimum width (Figure 5) and thickness (Figure 6) have been obtained for microcantilever lengths between 10 µm and 1 mm. Using these optimum dimensions, two fitted expressions are proposed to obtain more precise ratios. The fitted expressions for the ratio length to optimum width (20) and length to optimum thickness (21), plotted on figures 5 and 6, are given by: The fitted expressions (20) and ( 21) should be used with care because they have been established for lengths only from 10 µm to 1 mm. Moreover, as said previously, the actual quality factor may be different due to approximations in the calculation of the acoustic losses.

Conclusion

The method, which takes into account all loses in microcantilever, presented here can help choosing microcantilever dimensions to increase the sensitivity, because of a frequency increase, and to reduce the limit of detection, because of a quality factor optimization. The aspect ratios can be chosen by using a simple rule ( 11 20 Lh , 11 3 Lb ), to obtain a nearly optimum quality factor, or by using the fitted expressions (20) and ( 21), to obtain a fully optimum quality factor. In both the nearly optimum and fully optimum cases, the resonant frequency, which is linked to the sensitivity, the quality factor, which impacts the limit of detection, and the top surface ( 11 , Lb), which is usually used for coating deposition and/or movement detection, are all increased. Such optimized microcantilever could be very interesting in terms of performance. This work has not taken into account losses that can occur in the sensitive coating (for example viscoelastic losses when using polymers as sensitive coatings). These aspect ratios can be significantly modified when using high loss sensitive coating (thick viscoelastic materials). However, if analytical expressions can be found for these losses, a similar work may be conducted to possibly find new aspect ratios. These proposed aspect ratios are no longer valid in water, but similar work can be done since the equations can be applied on any fluid as long as viscosity and mass density are known.

  The radiated energy during one period is given by: Preprint -Sensors and Actuators B, Vol 118, 2006, pp. 292-296. (doi: 10.1016/j.snb.2006.04.034).

Figure 1 :

 1 Figure 1: Geometry of the microcantilever and its sensitive coating

Figure 5 :

 5 Figure 5: Ratio length to optimum width for different microcantilever lengths (calculated values and fitted model)

Figure 6 :

 6 Figure 6: Ratio length to optimum thickness for different microcantilever lengths (calculated values and fitted model)

Table 1 :

 1 Comparison between different aspect ratios for 3 microcantilever lengths

	Length	Aspect ratio	Width	Thickness	Ratio length	Ratio length	Quality	Resonant
	(µm)	type	(µm)	(µm)	to width	to thickness	factor	frequency (kHz)
		Optimum	6.6	1	1.515	10	641	12000
	10	Proposed	3.33	0.5	3	20	300	6100
		Conventional	1	0.2	10	50	44.9	2400
		Optimum	37	7.7	2.703	12.99	1290	960
	100	Proposed	33.33	5	3	20	968	620
		Conventional	10	2	10	50	219	240
		Optimum	260	65	3.846	15.38	2460	78
	1000	Proposed	333.33	50	3	20	2160	62
		Conventional	100	20	10	50	813	24

ACKNOWLEDGEMENTS

This work was sponsored in part by the French Agency for Environment and Energy Management (ADEME) and the "Région Aquitaine".


When building borders aims at increasing the efficiency of railways: the creation of the French track owner (mid-1990s -mid-2000s) Arnaud Passalacqua (Université Paris Diderot, France)

T 2 M 2013 conference in Kouvola/St. Petersburg

As a member of the European Union, France has been constrained to deeply reform its railway system, after the adoption of the famous directive 91/440, in 1991. This text imposed to build an accounting border between the activity of transport and the management of the infrastructure and opened the way to various national solutions adopted by the members.

The French reform was decided in 1997, after 2 years of social and political tensions. The historical national operator, the SNCF 1 lost its monopoly in the field of railways with the creation of RFF 2 , a public agency which became the owner of the rail track and was also given the colossal railway debt of about € 2012 26 billions. By the way, France decided to go further than the requirement of the European directive and adopted an odd structure for the sector of railways. However, despite the creation of this new agency, the border with the historical operator is not so tight. The main factor of porosity has been inscribed in the law itself: the SNCF has been given a monopoly on the maintenance of the existing network, under the responsibility of RFF.

This paper proposes to discuss the nature of the border that has been then implemented between the SNCF and RFF and to understand the reasons behind the choices that were made in a very specific socio-political context. If on the European level, the long-term aim was to enable an open access to new railway operators in order to reduce costs and prices, this idea was not so clear in the national context, where the problem of the debt was much more important and the right-wing government did not want to get involved in a new strike after a very long conflict in November-December 1995.

The border reflects these various factors. It is first a financial separation, between both structures but also between the world of railways and the budget of the French State, constrained, at that time, to rigorous criterion imposed by the Maastricht treaty.

Of course it is also a physical border mainly between the infrastructure and the stations which have been kept by the SNCF. These physical aspects of the new border were not the easiest to define and were only solved about 10 years after the reform. The slowness of the process produced a new kind of no-man's lands, a typical figure of border problems: unused rail lands had to wait for a clarification before they could be reused for other urban purposes.

The border is also a cultural one. Since the reform, the SNCF has been engaged into a movement of deep change. The former values of technical leadership and public utility have been progressively combined with new values, such as commercial attitude and on-line modernity. For its part, RFF has tried to build a new culture besides the old culture of railway workers, based on the diversity of its increasing staff composed of civil servants, railway workers and private sector employees.

Finally, this border has also a temporal dimension. One of the main points was to change lots of practices in the world of railway, particularly on the profitability of investments and the national management of local transport services.

This paper is based on oral archives already collected and new investigations on the specific problem of 1 Société nationale des chemins de fer français.

2 Réseau ferré de France.

the ownership sharing between the SNCF and RFF3 .

1 The 1997 reform of French railways 1.1 A traumatic situation for French railways

In 1995, France lived one of the most important strikes of the XX th century. The right-wing government, led by Prime Minister Alain Juppé, under the rule of recently elected President Jacques Chirac, proposed a controverted reform of pensions. After decades of growth, the ageing of babyboomers imposed to revise the social system organized after World War II. But the propositions made by the government faced a hard opposition of the main left-wings trade unions, particularly the idea of increasing the working period from 37.5 years to 40 years for civil servants and employees enjoying a special pension regime, such as railway workers. They quickly became the main icons of the demonstrations and strikes that blocked the country in November-December 1995.

This specific situation can be explained by the tensions that were already to observe between the State and the monopolistic railway company, the SNCF. Negotiations on a planning document for the 1996-2000 period were hard, with the perspective of cost reductions and possible line closures. Rumours about these projects were published by various newspapers and quickly denounced by opponents.

The solidarity that seemed to support the strike despite its major impacts on the French economy and the daily life led the government to reduce its ambitions and eventually to renounce to the planning document. The president of the SNCF was constrained to resign. Trade unions could enjoy a major victory, despite their rivalry and the differences between their positions.

The most surprising point is that this traumatic situation led, two years after, to the major reform of French railways after that of 1937, which had given birth to the SNCF. The convergence of various reasons behind the highly visible 1995 strike explains this quick change.

1.2 A convergence of reasons behind a reform First, after the strike, the new president of the SNCF, Loïk Le Floch Prigent, deliberately impulsed a new dynamics in this old State-owned company, by shaking the old habits. He decided to revise the organization and to renew the staff, with a specific focus on customers, incomes and profitability, which were new concepts in such a company. On the internal point of view he opened new paths for social dialogue between the management and the employees. Le Floch Prigent was eventually constrained to resign after only 6 months, because of his involvement in a financial scandal, when he was head of the oil company Elf-Aquitaine. But his successor, Louis Gallois, followed the main lines of his policy.

Le Floch Prigent had understood that the 1995 strike revealed a disease of the company. Beside the problems of social dialogue and the fall of traffic due to the economic crisis of the 1990s, the main difficulty faced by the SNCF was its increasing debt. The historical railway debt had been recently increased by the high-speed train program decided by the State and realized and operated by the company. New high-speed lines had been expensive and public authorities had mainly let the SNCF pay for their building and operation, whereas the decision processes were more complex. Last point, the maintenance of the network was underestimated by the State so that the SNCF registered a deficit on this central activity. For the suburban transport, the company was also in doubt because of the unexpectedly high cost of the Eole project, a new regional train under Paris. The railway debt was about 46 billion € 2012 , with 41 billion € 2012 directly inscribed in the balance of the SNCF.

The faith in high-speed had probably to be rethought because of this economic failure. 20 years of railway development were to revise and what had been considered a major success of the French railways appeared as a drawback of the system. The only positive dynamics in the mid-1990s was the development of regional trains outside the Paris area : regional authorities appeared as potential financial partners in this activity of the company.

Two external constraints were also taken into consideration by actors. First the 91/440 directive of the European Union. This important text imposed to distinguish the accounting of the railway operation and the accounting of the network operation within every national frame. The historical railway operators had to reorganize themselves in order to be conformed to this prescription. Different solutions were invented by countries, but in the middle of the 1990s, only half of the State-members had done such a reform. For instance, Germany had chosen to create a holding, DB AG, with the two activities, the operation for the different DB subsidiaries and the network management for DB Netz. By the way, the German State had taken the burden of the German railway debt, a transfer which was allowed by the 91/440 directive. France had not engaged in such a process yet but was expected to do so by the authorities in Brussels.

The other external constraint was due to the implications of the Maastricht treaty of 1992: in order to be integrated to the project of common currency, every State-member had to follow rigorous economic criterion on its national budget. The national debt could not exceed 60% of the gross national product. France was exactly around this limit and the national debt was then a critical point in the national policy. The French State could not take the railway debt on its own budget.

A reform despite the government and then applied by its opponents

Before explaining what has been the reform itself, a focus has to be made on the actors themselves. It is striking to consider that the most important reform of French railways of the second half of the XX th century has been done more or less against all implied actors. First, the Prime Minister did not want to have any problems with the world of railways, after the traumatic strike of 1995. He did not want to be implied in any railway considerations any more. The Minister of Planning, Transport, Housing and Tourism, Bernard Pons, was an old-school gaulliste, likely to consider Brussels as a threat to the national independence. A friend of Chirac, he was not looking for a big reform in order to guarantee his political career. For the transport affairs, he had decided to let Anne-Marie Idrac, his Secretary of State, work alone. With a strong technical background in town planning and transport policy and being new in the political landscape, Idrac was the only member of the government likely to be interested in the field of railways.

The political opposition was composed of various forces, after the historical defeats of the socialist party in 1993 and 1995. On the field of transport and after the 1995 strike, the communist party was particularly active and enjoyed a high visibility, with the figure of an ex-railway worker, Jean-Claude Gayssot, representative of a Parisian working-class suburb. The proximity with the CGT4 , the important left-wing trade union, explained that Gayssot could enjoy a self-confidence in railway matters, thanks to the victory obtained mainly by the CGT over the government during the 1995 conflict. During the discussion of the reform project, Gayssot was the main opponent with a strong discourse.

The surprise came when Chirac decided to change the assembly of representatives and when the leftwing coalition won the election, with Gayssot as new Minister of Planning, Transport and Housing.

Being in charge of the sector of railways and after 18 months of opposition to the reform that the previous government had nearly not really implemented before the elections, Gayssot seemed to be able to go back to the old system. But, another surprise was that his political line was eventually to lightly adapt the reform by keeping its main principles: he let the reform find its place in the sector of railways, in apparent contradiction to his previous discourses.

Despite the wind of change produced by Le Floch Prigent, few of the SNCF managers were in favour of a reform that seemed to reduce the fields of action of the company, by giving the network to a new authority, and to prepare the opening of railway markets to new operators, whereas the SNCF was not perceived as a competitive company.

In this context, only few people were strong support of a reform. Mainly Claude Martinand, a State engineer with a left-wing political background. After the 1995 strike, in order to reflect on the longterm future of railways, Martinand was asked by the government to write a report, that finally gave birth to a draft law. Himself and the few people around him were sufficiently persuasive in order to convince Idrac and her staff to begin a reform of railways. And then Pons, that is to say Chirac. The reform was finally adopted in February 1997. The new State agency RFF was created with a double burden: the major part of the railway debt and the railway network. By the way, the reform mainly consisted in building borders.

2 Building borders in a unified world

A border for the French State

On the financial question, the reform was conceived as a border between the world of railways and the French State. Things had historically been really confused on that point. The first century of railways had been dominated by private companies operating lines built within a national frame adopted in 1842. In a context of economic crisis, a left-wing government decided of the nationalisation of railways with the creation of the SNCF in 1937. Since then, railways had been a public concern. The SNCF had developed a specific relationship with the State, particularly on financial questions. The State gave a yearly contribution to the budget of the operator and could guide the investments, but let the SNCF manage the railway debt. Since 1937, a long-established process of imbrications had developed.

The 1997 reform had the ambition to change the rules, by defining new borders. The first one distinguishes the State and the world of railways: by transferring the debt to a new agency, RFF, the State did not take it itself. By the way, the criterion imposed by Maastricht could be respected, even if this agency is a public one. To do so, the rule imposed that RFF had to find 50% of its resources out of the State subventions. Conceived as a mainly independent entity, RFF was not really the State any more. That is why the reform created a railway toll system: operators would pay in order to use the network held by RFF. And the monopolistic -at that time -SNCF would finance the resources of RFF. The fact that the State owned 100 % of the SNCF and that, finally, public entities paid to others in order to comply with the Maastricht obligations did not appear as a patch-up job but was considered a good preparation for the opening of successive railway markets, due to happen within the next years. A first border is here clearly to notice.

Another one implied the State: the reform imposed to RFF to guarantee any investment with a minimal profitability. Whereas the previous investments made by the SNCF under the rule of the State, particularly in high-speed lines, were hardly profitable, and that the State had finally to face the financial problem, the 1997 reform imposed a new border which intended to preserve the State from any new deficit linked to railway investments.

A porous border inscribed in law

Another problem of border was to define the link between RFF and the SNCF. A first point was a consequence of the idea of railway toll: the SNCF would have to pay an annual toll for using the network. But the system had to find another factor in order to preserve an equilibrium. The idea inscribed in the 1997 law was to keep the SNCF manage the maintenance of the railway network, even if the operator was not its owner any more. RFF would pay the historical operator in order to keep its own network in good condition. Almost for the existing network; for new lines, RFF would have the choice of the organization of maintenance. With such a system, the SNCF could be paid for that work and financial flows between RFF and SNCF could be more or less in equilibrium. In other words, the border defined by the law was very porous and both actors were still intrinsically linked.

A border between past and present

With the spatial borders addressed in the last part of the paper, the last important kind of border introduced by the reform is a temporal border. 1997 is conceived as the beginning of a new era, with new rules in the world of railways. By such a construction, the French State admitted that the previous situation was problematic and agreed to clear it, in the limits of its own possibility, imposed by Maastricht. The new system, based on the existence of a new agency in charge of the most important part of the debt, intended to be also a new birth for the historical operator. With deep changes in the management, the SNCF was also confronted to a new landscape, where the problem of the debt was replaced by the arrival of new competitors.

3 Questions of borders 3.1 Borders to promote mobility: an efficient paradox?

The creation of these various borders had various purposes but the most visible one was the compliance with the 91/440 directive of the European Union. Among the goals of the European Commission, the opening of railway markets to competition has progressively become the most important, with successive decisions concerning the different markets (international rail traffic, freight traffic, passengers traffic) during the 2000s years. The harmonization of driving licenses and the right of passengers and the definition of a global interoperability policy supported the creation of European railway markets with multiple operators, with more or less success.

In the French frame, the borders between RFF and the SNCF was supposed to be a guarantee of the equity between operators. RFF acted as a promoter of new operators, by selling them the best railway slots, particularly on the freight market. The border was more than a neutral line, it was also a political tool. Despite this configuration, the opening of the freight was eventually limited. In this competition, the SNCF also used its own weapons, such as the pressure that such an operator could apply on disseminated industrial customers. The general context of a decreasing market also explains the modest role played by new operators.

This example shows that the border between the SNCF and RFF must be seen as a highly sensitive zone. This is clearly confirmed when considering the spatial dimension of the border.

3.2 Ownership sharing after the reform : 10 years of tensions for sovereignty Ownership sharing between both entity has been a major problem during the 10 first years of their cohabitation. The 1997 law and the following decrees had addressed the important question of the ownership of railway territories. The network itself has been given to RFF, as the new owner of the tracks. The question of stations, depots or housings was more complex. For instance, the SNCF did not want to loose its huge number of housings, an important tool for providing interesting conditions to the railway workers. The importance of stations was crucial for the historical operator, but also for the new agency, in a foreseeable context of opening to new operators.

The law decided that the SNCF should keep the stations and its housings, RFF being the owner of the platforms, except for those perpendicular to the tracks, and the accesses to the platforms. The depots were also kept by the SNCF, which was a major advantage in the competition to come.

These theoretical distinctions had to be analysed more precisely and that explains the difficulties of the operation of ownership sharing. First, the SNCF did not exactly know its own estate. Some ownership problems had not been solved since the merger of the previous private companies in 1937. Being its own insurance company, the SNCF had not a real pressure on that point. The poor knowledge of the estate was a first problem in the sharing. But, of course, the company knew most of its territories and buildings and managed to give to RFF the most problematic assets and to keep the most interesting ones. A national commission for ownership sharing was created in 1998 in order to prepare decisions on the thousands of cases discussed. Its work lasted till 2006 and the government finally imposed to RFF and the SNCF to find definitive agreements. The stakes were enhanced by the fact that an important part of the discussed estates were strategic surfaces in urban centres. Local authorities generally wanted to have new projects on these territories that were no more of use for the railway services, but the ownership problems delayed any operations. In a context of promotion of urban density, particularly around stations, this situation was unbearable for other actors. Borders had to be well defined.

Cultural borders: toward an increased porosity of the French world of railway

The last border addressed by the 1997 reform may be the most important in the long term: the cultural evolution of the world of railways. Whereas the reform has generally built new borders, on the cultural point of view, its effects will probably abolish an old established border between the world of railway and the rest of the world. The iconic figures of railwaymen working with steam engines and the very specific conditions of work generally applied by railway companies, combined with strong internal links due to the structure of network characterizing this industry, explain the historical coherence and even a feeling of self-sufficiency of this industry. In the French frame as in many others, the constitution of a national monopolistic operator strengthened this feeling. So that even the State, which was supposed to control the activity and the financial results of the company, was often not really able to access to the data: the weight of the SNCF contributed to the existence of a State within the State.

The 1997 reform has slightly changed the situation, by breaking the monopoly of the SNCF not on railway operation but in the world of railways. RFF, as a new railway agency, has built another pole, even if its staff is still about 1% of the staff of the SNCF. But, RFF has chosen to recruit people of different origins and not only railway workers. At the beginning of the agency, the staff was divided between three kind of workers: railway workers coming from the SNCF, civil servants and employees of private companies. Some of the railway workers had probably been sent by the SNCF in order to have a look at the new structure, but most of them decided to join RFF in order to make possible projects that they could not achieve within the SNCF. Civil servants had generally a strong experience in the field of railways or transport, but found in RFF a way to have a new weight in the negotiations with the historical operator. And people coming from private companies were important for new activities organized by RFF, such as the management of the debt, which required specific knowledge in finance, and the management of real estate, with an important activity of selling and negotiations on urban projects.

As a result, the world of railway after the 1997 reform presents a renewed figure which is far more plural than it used to be and which leads to an increased porosity with other worlds, as those of finance or real estate development. It has to be noticed that the SNCF has evolved in a similar way with renewed relationships with customers or local authorities. If this movement had partially begun before 1997 -with the development of regional trains for instance -the reform has clearly strengthened this dynamics.

Conclusion

As a result, the 1997 reform of French railway can be considered as a creation of many new borders, even if on the cultural aspects, the erasing of borders appears as its main effect. After 15 years, it has to be noticed that the world of railways has deeply changed. Whether railway service is better or not is a highly complex point, but the diversity of actors implied in railway management and projects has been increasing. First, with RFF and the railway regulation authority (ARAF5 ). Then with new operators, mainly on the freight market. Last with new kinds of contracts in the development of the network, such as the public-private partnership for the new Tours-Bordeaux high-speed line, which allows a private company to build and operate a national railway line, the first out of the public sphere since 1937. A sign of the long-term dynamics opened by the 1997 law.

This paper is an English working version with a new perspective of a French paper: Passalacqua (A.), "La réforme ferroviaire française de 1997 : une histoire à rebondissements pour un scénario original", Revue d'histoire des chemins de fer, forthcoming. Precise references are given in the original version. For any question, please send an e-mail to arnaud.passalacqua@m4x.org.

Confédération générale du travail.

Autorité de régulation des activités ferroviaires.