R Khalil

A Dudka

D Galayko

P Basset

HIGH-VOLTAGE LOW POWER ANALOGUE-TO-DIGITAL CONVERSION FOR ADAPTIVE ARCHITECTURES OF CAPACITIVE VIBRATION ENERGY HARVESTERS

Keywords: Energy harvesting, successive approximation ADC, VHDL-AMS, calibration, MEMS

This paper presents a design and modeling of a block allowing converting a high voltage into a digital code which is used in a smart adaptive conditioning circuit to calibrate an electrostatic harvester for vibration energy. A smart energy management in the harvester is needed to achieve an optimal conversion of the vibration energy. This block is achieved with a successive approximation analogue-to-digital converter (SA ADC) and a voltage divider to reduce the voltage applied on the ADC. The design is done in Austrian Microsystem CMOS035HV technology. This study is validated by VHDL-AMS/ELDO modeling for the harvester, the divider and the harvester.

INTRODUCTION

The energy capacity, as well as lifetime of the existing sources is limited, and alternative energy sources are needed. Extracting the power from the ambient energy sources such as light, temperature gradients, and mechanical vibration is therefore a subject of research. The energy harvesting source converts the mechanical energy to electrical energy using an electrostatic transducer, which operates as a variable capacitor implemented in a MEMS technology. The harvester needs a smart control to achieve optimal electromechanical conversion of the vibration energy. This control requires some measurements of high voltages (10-50 V) and should consume low power. Thus, a low power ADC must be used. Power saving can be achieved in ADC through the selection of a suitable low-power ADC. The successive approximation ADC is known as one of the best candidates in terms of low-power [START_REF] Michael | An ultra low-energy adc for smart dust[END_REF]. In this paper, we explain how we use the SA ADC and the voltage divider in the harvester conditioning circuit.

HARVESTER OPERATION

An electrostatic energy harvester consists of a mechanical resonator, an electromechanical transducer (based on MEMS technology) [START_REF] Basset | A batchfabricated and electret-free silicon electrostatic vibration energy harvester[END_REF] and an electrical conditioning circuit managing the operation of the transducer and providing an interface with the load [START_REF] Dudka | Vhdl-ams modeling of adaptive electrostatic harvester of vibration energy with dual-output dc-dc converter[END_REF] as shown in Fig. 1. One of the possible architecture of conditioning circuit, initially proposed by Yen [START_REF] Yen | A variablecapacitance vibration-to-electric energy harvester[END_REF], is composed of two main parts: a charge pump and a flyback circuit controlled by a switch SW (Fig. 1). The charge pump circuit transfers electrical charges from a large initially pre-charged capacitor C res toward a small temporary storage C store with the use of variable transducer capacitor Cvar. The energy for this charge pumping comes from the mechanical domain through the variations of the transducer capacitor. During the pumping, the converted energy is stored in the C store capacitor, the C store voltage U store increases and C res voltage U res decreases very slightly (since C res >> C store ). Fig. 3 shows that the energy conversion is maximal for a particular range (U 1 , U 2 ) of U store [START_REF] Dudka | Vhdl-ams modeling of adaptive electrostatic harvester of vibration energy with dual-output dc-dc converter[END_REF] and when U store reaches the upper border of this range U 2 , a part of the charges of C store must be returned to C res , so to put U store at the low limit U 1 of this range. This is performed by the inductive flyback circuit. Topologically, the flyback circuit is similar to a Buck DC/DC converter, but with an output voltage U res needed to be pulled up as efficiently as possible using the energy of C store . As soon as U store reaches U 2 , the switch SW is set on by external control blocks and C store starts to discharge on C res through the inductor. When U store is reduced to U 1 , the switch becomes off and the inductor discharges on C res through the diode D3. After this, a new charge pump operation cycle starts. From theoretical investigation [START_REF] Galayko | Mechanical/electrical power-aware impedance matching for design of capacitive vibration energy harvester[END_REF] U 1 and U 2 parameters are calculated as:

) ( 1 . 0 max 1 res store res U U U U - + = (1) ) ( 6 . 0 max 2 res store res U U U U - + =
Here, U store max is the saturation voltage of the charge pump given by [START_REF] Yen | A variablecapacitance vibration-to-electric energy harvester[END_REF]: where C max and C min are the maximal and minimal values which takes the transducer capacitance. From eq. ( 2), U store max depends on the ratio between C max and C min that are, in turn, related to the resonator vibration parameters such as frequency and amplitude, which usually vary in the time. Consequently, U store max voltage is not a fixed value and moreover cannot be measured directly since during charge pumping U store never reaches the saturation [START_REF] Dudka | Vhdl-ams modeling of adaptive electrostatic harvester of vibration energy with dual-output dc-dc converter[END_REF]. However, that U store max can be measured in an ad-hoc calibration cycle, which repeats periodically (much more rarely then a charge pump+flyback cycle).

res store U C C U min max max = (2)
In order to calculate U 1 and U 2 during the system calibration, we need to measure U store max and U res (High Voltage). Consequently, to interface analog voltages with the digital electric circuit, we need to use a voltage divider and an analog-to-digital converter. Vibration energy harvesters provide low values of powers (tens microwatts), hence, the conditioning electronics, including ADC, should consume as few as possible. In this work, we demonstrate the design of a very low power consumption successive approximation ADC.

SUCCESSIVE APROXIMATION ADC ARCHITECUTRE

In Fig. 2, we can see how different parts of the successive approximation ADC are connected. In our topology, the signal is sampled in the first clock cycle and is converted in the next N clock cycles, where N is the number of bits. The sample and hold operation is achieved with the use of the digital to analogue converter (DAC), when it is set in"sampling" mode. The DAC, allowing to achieve the successive approximation of the input voltage value, contains an array of binary weighted capacitors whose topology can be reconfigured by switches. The DAC output is connected to the negative input terminal of the comparator as it is shown in Fig. 4, while the common mode voltage U cm is connected to the positive input terminal and the comparator output is connected to the control unit. The control unit represents the successive approximation register (SAR) that controls the DAC switches allowing to switch capacitors terminals to the three reference voltages: the supply voltage U dd , the common mode voltage U cm = U dd /2 and the ground gnd. It generates the output digital word representing the digitally approximated input voltage. This ADC uses 2 digital clocks F start to sample the signal and F clock internal clock that equals to (N+1).F start . This architecture was described in details in [START_REF] Allam | Systematic design of a successive approximation analog-to-digital converter[END_REF].

Successive approximation ADC modes

The conversion of the ADC is achieved in 3 different modes. In the first half of the first clock cycle, the input signal is connected to the bottom plates of the DAC capacitors while the upper plates are connected to U cm , this is the sampling mode and corresponds to the configuration shown in Fig. 4. In the second half of the first clock cycle, all the bottom plates are connected to U cm , this is the inversion mode. After the first cycle, the control unit checks the comparator output (comp_out). If it is high, it connects the largest capacitor bottom plate to U dd , if it is low; the control unit connects the largest capacitor bottom plate to gnd. This mode is called charge redistribution mode. The same is repeated with all capacitors in the array, in N clock cycles. At i th clock cycle, the output of the comparator corresponds to i th bit of the output ADC word. This bit value is saved by the control unit and after the end of the charge redistribution mode; the digital output of the control unit is equal to the digitally approximated input voltage. In Fig. 5, we can see how the voltage of the In our system, we use 8-bit SA ADC with sampling frequency F start =277.8 Hz, i.e one sample every 3.6ms, F clock =2.5 KHz and 2.5 V supply voltage.

VOLTAGE DIVIDER CIRCUIT

In present work the division factor of divider is 20, since the maximal value for U store is limited by 50V and the voltage supplied by the ADC is 2.5V. The proposed divider consists of 2 resistors connecting in series, 2 switches and an output capacitor as shown in Fig. 6. At every sample, resistors divide U store by 20, and the divided voltage is stored in the capacitor C div , so that the successive approximation ADC can sample this value. The clock used in the divider (CLK_DIV) has the same sampling frequency but with the smaller pulse width to decrease the power consumption.

The relation between U store and the divider output U out_div can be calculated based on equation:

CALIBRATION OF THE HARVESTER USING SUCCESSIVE APPROXIMATION ADC

In this section, the whole system is connected; the divider circuit is interface between the harvester and the ADC, the ADC output bits are connected to the flyback control switch as shown in Fig. 7. The flyback control enables the ADC during the calibration mode and disables it in normal mode.

The calibration cycle starts with putting U 1 to a very low value (zero), so that C store voltage becomes equal to C res voltage. During 20 ms U store remains at the U res value, which gives to the ADC enough time to measure it. After that, the flyback switch control orders the charge pumping to start, and U store starts to increase, up to the saturation. During this charge pumping, the voltage U store is measured with 3.6 ms sampling step. The goal of this measurement is to detect the U store max value.

The digital values corresponding to the neighboring samples of U store are compared, and when there are 2 consecutive steps have the same value, their value is considered as measured U store max (it means that U min mentioned equals to the ADC resolution). At the end of the calibration cycle the flyback switch control block turns off the ADC and U 1 as well as U 2 are calculated. Then, the normal mode (periodic charge pump+flyback cycles) starts till the next calibration cycle begin as it is shown in Fig. 8.

MODELATION RESULTS

In this paper, we present simulation results which demonstrate the harvester operation with ADC during almost 11 seconds. Here, calibration cycles repeat every 900 ms, such a low interval is chosen in order to reduce the modeling time, in reality the calibration phase should be less frequent (tens of seconds) to reduce the power consumed. In the top part of the Fig. 9, U store is plotted together with the measured U store voltage. We can see that during the calibration cycle there is a good matching between them because of the good resolution of the ADC. In the bottom part of the Fig. 9, the real U res is plotted with the measured U res voltage. The increase in the real U res value is explained by the accumulation of the energy of the system (i.e., a normal harvester operation). As we see, U res is measured only once during the calibration cycle. In the normal operation mode between calibration cycles ADC is deactivated by the signal off1. The measured U store max value is reset to 0 and the equivalent U res is saved until the next calibration cycle.

CONCLUSION

In this paper, we presented the architecture design and modeling of the electrostatic vibration energy harvester with a successive approximation ADC and a voltage divider. The use of such ADC in energy harvester application is suitable for low power consumption. The whole system of the harvester including the SA ADC is simulated with VHDL-AMS/ELDO mixed model using the cadence environment. Simulation results of the harvester with the use of 8-bit SA ADC demonstrate a good matching between U store and the measured from ADC U store mes during the calibration cycle. The estimated power consumption of the ADC is around 1.25µW for one step conversion. The comparator is the dominating block in power consumption of ADC with the used sampling frequency and 8-bit resolution, whereas the DAC has much less contribution.

Fig. 1 :

 1 Fig. 1: Conditioning circuit of the vibration harvester.

Fig. 2 :

 2 Fig. 2: Successive approximation ADC architecture.

Fig. 4 :

 4 Fig. 4: Sampling mode in successive approximation ADC with 4 bits (given for example).

Fig. 3 :

 3 Fig. 3: Operation of the harvester with basic conditioning circuit architecture.

Fig. 5 :

 5 Fig. 5: 8-bit successive approximation ADC operation.

  Hence, from eq. (3) we have R 1 = 19R 2 . The time of charging C div is determined by:

  The presented voltage divider circuit is designed in CMOS 0.35µm high voltage technology of Austrian Microsystem (AMS035HV).

Fig. 6 :

 6 Fig. 6: Voltage divider circuit interfacing the harvester with the ADC

Fig. 8 :

 8 Fig. 8: Calibration cycle of the harveste.r


Zsuzsanna ; Marton

Ludovic Chaput

Guillaume Pierre

Marianne Graber
email: mgraber@univ-lr.fr

Prof M Graber

Lipase hydration state in the gas phase: Sorption isotherm measurements and inverse gas chromatography

Keywords: Water, Lipase, Adsorption, Inverse Gas Chromatography, Solid/Gas Biocatalysis Water, Lipase, Adsorption, Inverse Gas Chromatography, Solid/Gas Biocatalysis IGC, Inverse Gas Chromatography a W, water thermodynamic activity, CALB, Candida antarctica Lipase B, BET, Brunauer-

Introduction

Contrary to expectations that enzymes are only active in aqueous solutions, enzyme activity in almost anhydrous media was demonstrated in the 1930s and has been extensively explored for the last decades [START_REF] Bell | Biocatalyst behaviour in low-water systems[END_REF][START_REF] Dordick | Principles and selected applications of non-aqueous enzymology[END_REF]. These media include among others organic liquid, supercritical fluids, solvent-free, ionic liquids and gas phase systems.

These non-conventional almost anhydrous reaction media possess great advantages over classical aqueous ones, such as shifting of thermodynamic equilibrium in favor of synthesis over hydrolysis and allowing easier recovery of products. However a small amount of water is required for catalytic action of enzyme, as some residual bound water are absolutely essential for maintaining the enzyme active conformational state and for promoting flexibility of enzyme, by acting as a lubricant [START_REF] Helms | Protein Dynamics Tightly Connected to the Dynamics of Surrounding and Internal Water Molecules[END_REF][START_REF] Trodler | Modeling structure and flexibility of Candida antarctica lipase B in organic solvents[END_REF].

The quantity of required water varies depending on each individual case. The optimal amount depends on several parameters, including, polarity of enzyme active site, solvent hydrophobicity, substrate and reaction conditions. In any case, the activity, stability and specificity of enzymes in non-conventional media are greatly affected by the level of water present in the medium.

The best way to quantify the availability of water to the biocatalyst in non-conventional media is to use the parameter "thermodynamic water activity" (a W ), which describes the effect of mass action of water on the equilibrium and is therefore a better measure of the effect of water than the water content [START_REF] Halling | Biocatalysis in low-water media: understanding effects of reaction conditions[END_REF].

Many studies were performed in organic solvents at varying a W . Nevertheless, the influence of water on biocatalysis, remains unclear and needs to be further elucidated. In particular, no general trend has been found for the dependence of selectivity, especially enantioselectivity, on a W [START_REF] Jonsson | Thermodynamic and kinetic aspects on water vs. organic solvent as reaction media in the enzyme-catalysed reduction of ketones[END_REF][START_REF] Persson | Factors Governing the Activity of Lyophilised and Immobilised Lipase Preparations in Organic Solvents[END_REF]. For several years, we have been working with continuous gas phase reactors for performing enzymatic reactions. In this type of reaction medium, a solid packed enzymatic sample is percolated by a carrier gas, which simultaneously carries gaseous substrates to the enzyme and removes gaseous products. In this system the a W in the reaction medium can be perfectly controlled and fixed independently of the other reaction medium components, by incorporating water in the inlet gas at the correct molar fraction. If the gas phase is assumed as ideal, a W is then obtained by dividing the partial pressure of water by its saturation pressure at the operating temperature. In case of organic media however, the calculation of a W requires the knowledge of activity coefficients, whose estimation is far from being straightforward.

The solid/gas reactor is therefore a powerful tool for studying accurately the sole influence of a W on biocatalysis [8,9].

The effect of a W on different types of reactions catalyzed by lipase B from Candida antarctica has been studied extensively in our laboratory, by using solid/gas reactor. It was observed that water had a very complex role, and could simultaneously act as a lubricant, by change in enzyme flexibility and increase of enzyme activity, as a competitive and enantioselective inhibitor, as a competitive substrate, and by interacting with all reactants, free enzyme, transition state and products, like solvent molecules do in liquid media [10-13].

In our different studies performed in solid/gas reactors, all these different effects of water have been assessed as a function of a W in the reaction medium, but could not be relied to real hydration state of the enzyme. This is unfortunate as such knowledge is essential to gain a fundamental understanding on the effect of water on enzyme catalysis. At which a W protein charged groups are they likely to be surrounded by clusters of water molecules? Above which a W is a water monolayer retained on the enzyme surface, surrounding both charged and polar groups of the enzyme? Above which a W has the substrate to displace water molecules adsorbed to the enzyme to interact with it? The answer to this last question is not only dependent on a W level allowing water monolayer formation, but also on the ability of substrate to compete with water for adsorption on the immobilized enzyme.

In the following study, we are trying to answer all these questions, by studying adsorption of both gaseous water and substrates on enzyme, thanks to adsorption isotherm measurements and the use of Inverse Gas Chromatography (IGC), which is a dynamic and very accurate vapor adsorption technique, allowing accurate characterization of surface properties [START_REF] Greene | The determination of heats of adsorption by gas-solid chromatography[END_REF][START_REF] Kiselev | Gas-chromatographic determination of adsorption and specific surface for solids[END_REF][START_REF] Gray | A gas chromatographic method for the study of sorption on polymers[END_REF].

In IGC the roles of stationary (solid) and mobile (carrier gas and vapor probe molecule) phases are inverted from traditional analytical Gas Chromatography (GC). Indeed, in GC, a standard column is used to separate and characterize several vapor molecules, whereas in IGC, known vapor probe molecules are injected into a column packed with the solid sample under investigation, which is immobilized CALB in our case, and whose surface characterization is performed.

There have been very few experimental studies addressing both water and substrates adsorption on enzymes [START_REF] Dimoula | Substrates and water adsorption phenomena in a gas/solid enzymatic reactor[END_REF][START_REF] Hidaka | Gaseous ethanol oxidation by immobilized enzyme in a packed bed reactor[END_REF], although these adsorption phenomena might be a way to better elucidate enzyme kinetics and specificity. Recently we have studied molecular mechanism of hydration of free, deglycosylated, and desalted pure CALB in the gas phase.

We showed that hydration occurs in two phases. For water activities below 0.5, water initially binds to well-defined water-binding sites at the protein surface and then above 0.5, gradually a spanning water network is formed [START_REF] Branco | Molecular mechanism of the hydration of Candida antarctica lipase B in gas phase: water adsorption isotherms and molecular dynamics simulations[END_REF].

Nevertheless these results cannot be directly used to explain the reaction kinetics we measured in solid/gas reactor, for which we had to use an immobilized CALB preparation on silanized Chromosorb. Indeed, this porous diatomite support allows a uniform carrier gas and probe vapour flow through the enzymatic fix bed, and a better access of gas to the enzyme surface. Moreover, it avoids large pressure drop across the column containing the enzyme sample. In the present paper, we show adsorption studies performed with the same immobilized enzymatic sample, in order to be able to overlay these adsorption phenomena and CALBcatalyzed reaction kinetics in continuous solid/gas reactors.

Materials and methods

Enzyme and chemicals

Candida antarctica lipase B was a lyophilized preparation (Chirazyme L2) kindly supplied by Roche Industrie (Penzberg, Germany). All probes used in IGC experiments were of the highest purity (99% minimum) and checked by gas chromatography before use.

Adsorption of lipase onto a solid support

CALB adsorption was performed onto 60-80 mesh Chromosorb P AW DMCS, (Acid Washed DiMethylChloroSilanized; Varian, France), as previously described [START_REF] Léonard | Enantioselective acylation of R-2pentanol in a solid/gas reactor catalysed by lipase B from Candida antarctica[END_REF], by using 30 mg of lyophilized Chirazyme L2 per 6 g of support.

Measurement of biocatalyst water adsorption isotherm

Water adsorption isotherm of Chromosorb alone and with immobilized lipase were measured at 25°C by using a DVS Advantage automated moisture sorption analyzer (Surface Measurement Systems Ltd., London, UK) between 0 and 95% relative humidity. The samples were initially dried for 10 h at 25°C under totally dried flowing air in the DVS moisture sorption analyzer to obtain the starting dry sample mass. The required humidity is generated by mixing dry and water saturated vapor gas flows in the correct proportions using two mass flow controllers and one vapor humidifier. The instrument was run with a dm/dt (m, mass; t, time) set at 0.002% min -1 to reach the equilibrium. This means that the relative humidity will remain constant until the mass variation falls consistently below this threshold. Once this condition has been reached, the relative humidity of the system will be raised or lowered to the next level.

The water adsorption curve was modeled using the Brunauer-Emmet-Teller (BET) [START_REF] Brunauer | Adsorption of gases in multimolecular layers[END_REF] gas adsorption equation (Eq 1).

C m C a C m m a a w w w × - × + × = × - 0 0 ) 1 ( 1 ) 1 ( ( 1
)
where m is the mass of bound water (in mg per mg of dry enzyme), m 0 is the monolayer water coverage, a W the water activity and C a constant. From the linear regression of the plot of

m a a w w × -) 1 (
versus a W , the theoretical monolayer water coverage can be calculated:

I S m + = 1 0
, where S is the slope and I the y-intercept [START_REF] Costantino | Determining the water sorption monolayer of lyophilized pharmaceutical proteins[END_REF].

Inverse Gas Chromatography (IGC) measurements

Theory of IGC

IGC consists in measuring the retention times of vapor probes of known properties in a column packed with the solid material of interest, which is immobilized CALB in our case.

The retention time of these probes is related to the affinity of the probes for the support.

Measuring how this retention time changes as a function of probe molecule chemistry, column temperature and ambient relative humidity, allows obtaining a wide range of physical properties of the solid under investigation.

In the present study, IGC was operated in the infinite dilution regime, which means that a very small amount of vapor probe was injected into the carrier gas stream through the column, leading to a very low surface coverage by the adsorbates. The retention volume of the probe is thus independent of its concentration and the result is a linear adsorption isotherm, which can be described by Henry's Law. The specific retention volume V G of vapor probes, normalized to a temperature of 273.15K and 1g of supported enzyme was calculated using Eq 2, where t (min) is the retention time of the probe, t 0 (min) is the dead-time obtained with methane, F (mL.min -1 ) the carrier gas flow rate, m (g) the mass of immobilized CALB and T (K) the temperature of the column. The James and Martin compressibility factor, j, was calculated using Eq 3, where P i and P 0 are the inlet and outlet pressures, respectively.

T F m t t j V G 15 . 273 . ) ( . 0 × - = (2) 1 ) / ( 1 ) / ( . 2 3 3 0 2 0 - - = P P P P j i i (3)
The specific retention volume V G of vapor probes is related to the variation of the free energy of adsorption ∆G ads in the following way:

C V T R G G ads + × × - = ∆ ) ln (
where C is a constant depending on the choice of a reference state of the adsorbed probe and also on the total area of the solid accessible to the probe.

∆G ads takes into account two kinds of interactions: dispersive interactions (corresponding to

London forces) and specific interactions, which consists mostly out of Lewis acid-base contributions.

sp ads d ads ads G G G ∆ + ∆ = ∆
To obtain the dispersive as well as the specific parts of ∆G ads , different apolar and polar vapor phase probe molecules are respectively injected and their specific retention volume V G determined.

In case of apolar probes, like alkanes, which can only interact by dispersive interactions, V G is related to

d ads G ∆
by Eq 4 :

F o r P e e r R e v i e w ' ) ( ) ( 2 ln 2 1 2 1 C a N C V RT G d L d S G d ads + - = + - = ∆ γ γ (4)
Where N is the Avogadro constant, R the gas constant, a the probe surface area, (Figure 1). In the present study, the specific free enthalpy of adsorption and the dispersive component of the surface energy of supported enzyme were calculated using the constants given in Table 1.

The enthalpic part of

S T H T G ∆ - ∆ = ∆ / / (5)
These

sp ads H ∆
values can then be converted into acid-base parameters if acid-base concepts are applied, which were developed by several authors, including Gutmann [START_REF] Gutman | Donor-Acceptor approach to Molecular Interactions[END_REF]. The Gutmann approach involves a simple four-parameter equation, with an acid and base term for each amphoteric polar probe according to Eq 6: K A is the acceptor (acid) number and K B is the donor (base) number of the solid surface. DN and * AN are the donor and acceptor numbers of the amphoteric vapor probe molecules, which are available from literature [START_REF] Mukhopadhyay | Review: Aspects of acid-base interactions and use of inverse gas chromatography[END_REF] and given in Table 1.

* AN K DN K H B A sp ads × + × = ∆ (6)
K A and
( ) R H T p st v ∆ - =         ∂ ∂ 1 ln
, giving the differential isosteric heat of adsorption ∆H st , by plotting ln p versus 1/T, applied to chromatographic data at infinite dilution, which are necessarily isosteric (constant adsorbate coverage of zero) [START_REF] Condor | Physicochemical Measurement by Gas Chromatography[END_REF][START_REF] Kiselev | Gas Adsorption Chromatography[END_REF].

C RT H T V ads G + ∆ - = / ) / ln( (7)

Conditions for IGC measurements

Experiments were performed using an SMS-IGC2000 apparatus (Surface Measurement Systems Ltd., London, U.K.), allowing fully automated determination of interactions of ten different gas probe molecules with solid column packing material under investigation (Chromosorb alone or with immobilized CALB in our case), under a wide range of humidity and temperature conditions. A complete explanation of the design of this apparatus can be found in reference [START_REF] Newell | The use of inverse phase gas chromatography to study the change of surface energy of amorphous lactose as a function of relative humidity and the processes of collapse and crystallisation[END_REF].

For each IGC experiment, DMCS treated 4 mm ID glass column packed with 500 mg of support alone or immobilized CALB was used. Before measurements, column packed was pre-conditioned for 10 hours at the initial temperature and a w studied. To obtain the dispersive as well as the specific surface energies, different polar and non-polar vapor phase probe molecules were injected and their specific retention volume V G determined.

250 µL of each probe were injected with p/p° was fixed to 0.025, where p and p° being respectively equal to partial pressure of probe in the gas and saturated vapour pressure of probe, calculated by assuming an ideal gas type behavior by p°(T)=e (-∆Hvap/RT) , at temperatures comprised between 313 and 338K and a W ranging from 0 to 0.4. The carrier gas (helium) flow rate was 10 mL/min. All measures of retention time were triplicated.

To determine the enthalpies of adsorption (∆H ads ) of pentan-2-ol and hexan-3-ol on immobilized CALB, 250 µL of pentan-2-ol or hexan-3-ol at p/p° = 0.05 were injected at varying temperature: between 308 and 324K for 0 < a w < 0.15 and between 314 and 322K for higher a w values with pentan-2-ol; between 314 and 322 for all a W values with hexan-3-ol.

Results

Water adsorption by immobilized CALB, studied by water adsorption isotherm

Water adsorption experiments were carried out with both silanized Chromosorb support alone and the same support with immobilized CALB (Figure 2). Although the ratio of enzyme CALB to support was only 1/200 (m/m), the presence of enzyme on the support induced significant changes: Support alone presented a slight uptake of water in the total range of a W , with an overall uptake of around 0.15% mass increase at a W = 0.9. Support with immobilized enzyme adsorption isotherm showed an uptake of water between 2 and 3 higher than support alone, in the first part of the curve (a W 0 to 0.35) and a water sorption exponential and much higher for a W values above 0.35, reaching 0.92% mass increase at a W = 0.9.

The water adsorption isotherm shape of Chromosorb with immobilized CALB differs from the sigmoid shape of curves obtained with CALB alone [START_REF] Branco | Molecular mechanism of the hydration of Candida antarctica lipase B in gas phase: water adsorption isotherms and molecular dynamics simulations[END_REF], and more generally with isolated proteins [START_REF] Lee | Effect of water activity on enzyme hydratation and enzyme reaction rate in organic solvents[END_REF], which can be modeled by the BET equation. The BET model assumes the gradual recovery of surface by homogenous layers, characterized by a constant C, associated to the energy of hydration of the surface. It allows in particular revealing the formation of a water monolayer and its weight, and the occurrence of free water for higher a w [START_REF] Dimoula | Substrates and water adsorption phenomena in a gas/solid enzymatic reactor[END_REF]. Yet, BET model is considered as a good mathematical tool to characterize the water adsorption isotherm and to determine the size of the monolayer for proteins, and this for a w up to 0.4. Beyond this value, the BET model is known to gradually sweep from experimental observations [START_REF] Brunauer | Adsorption of gases in multimolecular layers[END_REF].

In our case, the curve which presents a W /((1+a W )m) as a function of a W (Figure 3) does not fit the BET model. This assumption is highlighted at a w = 0.2, where the curve displays a break point whereas a linear curve is expected for enzymes following the BET model [START_REF] Branco | Molecular mechanism of the hydration of Candida antarctica lipase B in gas phase: water adsorption isotherms and molecular dynamics simulations[END_REF].

These results suggest that Chromosorb support prevents the possibility to evaluate the CALB hydration with BET model. The water adsorption isotherm we obtained, resembles type III isotherm, according to IUPAC classification proposed by Brunauer, Deming and Teller [START_REF] Brunauer | On a theory on the Van der Waals adsorption of gases[END_REF].

This uncommon isotherm suggests that interactions between water and solid are very low, which is actually the case with silanized Chromosorb of hydrophobic nature.

Thus, we used an alternative method, i. e. IGC, to analyze the feature of CALB adsorbed on support. IGC allows determining many parameters of solid surface, such as dispersive and specific surface energy. By following the evolution of these parameters with varying a W , the hydration state of CALB can be estimated indirectly.

Determination of a W allowing saturation of water binding sites on immobilized CALB, by studying surface properties of immobilized lipase by IGC

The saturation of water binding sites at the surface of immobilized enzyme CALB, when increasing a W , can be estimated by determining the surface properties, like propensity to adsorb apolar molecules or surface Lewis acid-base properties, as a function of a W . These investigations can be performed by IGC, which has become a widely used technique to characterize the surface properties of solid organic compounds like natural fibers [START_REF] Heng | Methods to Determine Surface Energies of Natural Fibres: A Review[END_REF] and food materials [START_REF] Zhou | Effects of flavor compound chemical structure and environmental relative humidity on the binding of volatile flavor compounds to dehydrated soy protein isolates[END_REF].

Influence of a W on the adsorption of apolar molecules on immobilized CALB

Figure 4 presents the evolution of the specific retention volumes V G of five apolar probes nundecane (C11), n-decane (C10), n-nonane (C9), n-octane (C8) and n-heptane (C7) with the a W of the carrier gas, through the column filled with immobilized CALB, at 313K. For the longest alkanes, n-undecane and n-decane, it appears that the retention volumes decrease and then reach a plateau near a W = 0.2. This same observation has been reported by Comte et al.

on glass beads for a W ≥ 0.15, and was interpreted as coverage of the surface of the support by water molecules [START_REF] Comte | Surface properties of low specific surface powders using inverse gas chromatography[END_REF].

Indeed water molecules progressively hide interaction sites from alkane probes and their retention time decrease. When the specific retention volume becomes constant it may be assumed that the surface of the immobilized CALB is covered by a layer of water molecules.

Then the alkane probes adsorb on a film of water rather than on supported CALB.

The value of d S γ for the immobilized enzyme followed the same trend with increasing humidity (Table 2), thus confirming the hypothesis of water coverage of the surface at this water activity level.

Influence of a W on the adsorption of polar molecules

The use of polar probes allows evaluation of Lewis acid-base interactions between these probes and a solid support. First, the acid-base character of the immobilization support alone, silanized Chromosorb, was determined by IGC at a W = 0. Monopolar probes were used: Moreover, the Lewis basicity and acidity of the support with the immobilized CALB were determined in the same conditions with both monopolar probes. It was found that support with the enzyme and buffer salts has an acidic character even more pronounced than the Chromosorb alone: the immobilized CALB affinity for 1,4-dioxane is higher (

sp ads G ∆ = 12.4
kJ/mol.mg) and its affinity for chloroform even lower ( sp ads G ∆ = 2.1 kJ/mol.mg). These variations cannot be attributed to the immobilization buffer salts (pH 7.5), they are probably due to the presence of the enzyme. We assume that amino acids rather basic nature, such as arginine, lysine and histidine, are in contact with the support (including residual silanol groups) and become thus hidden. As a result, only the amino acid with acidic side chain may interact with the polar probes, resulting in a decrease in basicity.

To determine the effect of a W on Lewis constants for the immobilized CALB, In accordance with the result obtained with monopolar acidic and basic probes, the supported enzyme presented a higher Lewis acidity constant K A than Lewis basicity constant K B .

Determination of competitive adsorption of substrates and water at the surface of immobilized lipase by IGC

In our experiments with enzymes in gas phase, different polar substrates were used, including primary or secondary alcohols. These compounds may compete with water for adsorption sites on the immobilized enzyme. A way to investigate this competition is to measure the enthalpy of adsorption (∆H ads ) of polar substrates, on immobilized enzyme at different a W .

This parameter is a direct measure of the strength of interaction between substrate and supported enzyme and the evolution of this parameter with a W can be ascribed as site blocking by water in a competitive adsorption situation. The influence of a W on ∆H ads of pentan-2-ol and hexan-3-ol on immobilized CALB is shown on figure 7.

First, it can be observed that on the total range of a W studied, for both pentan-2-ol and hexan-3-ol adsorption, |∆H ads | values are higher than the enthalpy of condensation, being respectively equal to -52.6 kJ/mol and -43.4 kJ/mol. This implies that the enthalpies of adsorption are not only due to the heat of condensation of the compound onto the solid, but also to physic-chemical interactions between compound and immobilized enzyme.

Secondly, it appears that the enthalpy of adsorption of pentan-2-ol and hexan-3-ol vary in two stages with a W . In the first stage, |∆H ads | decreases rapidly with increasing a W . In the second stage, it continues to decrease but with a very low slope. This stabilisation of the |∆H ads | values corresponds to a decrease of alcohol retention times, and to their lower variation with temperature. This could be attributed to the coverage of the immobilized lipase by adsorbed water molecules, which hides binding sites from alcohols, in a competitive adsorption situation. The a W corresponding to the breaking point between these two parts of the adsorption curve decreases from 0.2 to 0.1, when changing from pentan-2-ol to hexan-3-ol.

Relation between hydration state and CALB activity and selectivity

The IGC study allows finding some correlation between CALB catalytic activity at different a W in gas phase, and water status (strongly or weakly bound). In our solid/gas enzymatic reactor experiments, the optimal a W with respect to alcoholysis reaction was found to be in range 0.05 to 0.1 [START_REF] Bousquet-Dubouch | Alcoholysis catalyzed by Candida antarctica lipase B in a gas/solid system obeys a Ping Pong Bi Bi mechanism with competitive inhibition by the alcohol substrate and water[END_REF]. This corresponds to a water activity level at which only stronger adsorptive interactions with water occurs, and polar groups of immobilized enzyme are not totally covered by water. This high catalytic activity of CALB at very low a W was also observed by other authors in liquid media [START_REF] Valivety | Lipases from different sources vary widely in dependence of catalytic activity on water activity[END_REF]. It could be assigned to the ability of the dehydrated enzyme to keep essential water molecules in its structure by tight bonding. For many other enzymes, it was shown that they begin to regain their catalytic activity at hydration levels comprised between 0.12 and 0.2 mg H 2 O/mg protein, corresponding to a W values much higher than 0.1 [START_REF]Protein-Solvent Interaction[END_REF].

In our solid/gas experiments, we have extensively studied the ability of CALB to resolve racemic mixtures of secondary alcohols, and found that the influence of a W on CALB enantioselectivity was very significant. For example in case of the CALB-catalyzed resolution of pentan-2-ol or hexan-3-ol, through the esterification with methyl propanoate, the enantiomeric ratio (E value) varied respectively from 101 and 67 at a W close to 0, to a maximum of 320 around a W = 0.2 and 120 at a W = 0.1 [12,13]. Above these optimal a W values for enantioselectovity, E values decreased for both secondary alcohols.

As far as pentan-2-ol is concerned, the point a W = 0.2 appears as a "turning point" where the CALB enantioselectivity towards this alcohol starts to decrease with increasing a W . We have shown that the point a W = 0.2 corresponds also to a breaking point for the enthalpy of adsorption of pentan-2-ol on immobilized CALB. Then above a W 0.2, water molecules that were trapped at the enzyme have to leave in order to make room for the adsorption of alcohol, and then gain motional freedom. It can be suggested that above this point, water acts more as a "solvent", with high entropic effects, than as an enantioselective inhibitor, through very specific steric effects, as it was shown for very low a W values [12]. This can also be connected to the large entropic term seen for enantioselectivity at high water activity. As CALB enantioselectivity is disfavoured by entropy, the result is a decrease of E with a W , for a W > 0.2, and an increase of E at low a W where water predominantly acts through steric effects, by binding in the stereospecificity pocket.

Concerning hexan-3-ol, enantioselectivity starts to decrease at a lower a W value equal to 0.1, than for pentan-2-ol [13]. This gap between pentan-2-ol and hexan-3-ol for "a W turning point" may be explained by the bigger size and less polar character of hexan-ol, for which difficulty in gaining access to non-wetted part of the surface of the immobilized biocatalyst is higher.

Indeed the change in a W dependence for enantioselectivity coincides with that of the stabilization for the enthalpy of adsorption of hexan-3-ol on immobilized CALB.

Concluding remarks

We have shown that water adsorption and IGC studies can be used successfully to monitor hydration state of immobilized CALB, and also to investigate the adsorption of substrates in a competitive situation with water. As the conditions used for these studies resemble the ones of the continuous enzymatic solid/gas reactor, in which we have extensively studied activity and selectivity of CALB, it was possible to link adsorption results with particular effects of water on enzyme properties. As a result, this study allows a further insight into the complex and as yet not fully understood role of water on biocatalysis.

  the probe surface energy, d S γ the dispersive component of the solid, and C' a constant. If a series of alkanes is injected, d S γ can be derived from the slope of the alkane line in a plot of RTlnV G versus probe molecules are also injected, then specific interactions can be measured. The experimental points for the polar probe molecules are located above the alkane line in the surface energy plot. The vertical distance between each point and the alkane straight line represents the specific contribution of the interaction, which is expressed as the specific free energy sp ads G ∆

  calculated by performing the experiment at different temperatures, and calculating the slope of the plot T

  dioxane, being respectively Lewis acid and basic probes, in order to obtain respectively a measure of the Lewis basicity and acidity of the support. It needs to be emphasized that sp ads G ∆ values measured are not intrinsic properties of the support but depend on the properties of the adsorbate as well. Nevertheless results allowed to conclude that the support presented predominantly an acidic or electron-accepting character, as it presented a much higher affinity for 1,4-dioxane ( /mol/mg). This could be attributed to the presence of residual silanol groups at the surface of the support after silanization treatment.

Figure 1 :

 1 Figure 1: Determination by IGC of the dispersive component of the surface energy of the

Figure 2 :

 2 Figure 2: Water adsorption isotherm at 298K of Chromosorb alone (∆) and with immobilized

Figure 3 :

 3 Figure 3: BET plot for water adsorption at 298K on immobilized Candida antarctica lipase B

Figure 4 :

 4 Figure 4: Evolution of specific retention volume V G of apolar molecules with a W on

Figure 5 :

 5 Figure 5: Variation of specific free energy of adsorption of ethanol (◊), acetonitrile (∆) and

Figure 6 :Figure 7 :

 67 Figure 6: Determination of enthalpy of adsorption of ethanol (◊), acetonitrile (∆) and ethyl

Figure 1 :Figure 2 :

 12 Figure 1: Determination by IGC of the dispersive component of the surface energy of the solid (immobilized CALB) and the specific free energy of adsorption of polar probes with the solid. 120x80mm (600 x 600 DPI)

Figure 3 :Figure 4 :Figure 5 :Figure 6 :

 3456 Figure 3: BET plot for water adsorption at 298K on immobilized Candida antarctica lipase B (5mg of lyophilized Chirazyme L2 per gram of Chromosorb). 120x80mm (600 x 600 DPI)

Figure 7 :

 7 Figure 7: Evolution of enthalpy of adsorption of pentan-2-ol (∆) (results from [13]) and hexan-3-ol (♦) on immobilized CALB as a function of water activity. 120x80mm (600 x 600 DPI)

  al. for the adsorption of gaseous probes on mineral solids[START_REF] Comte | Surface properties of low specific surface powders using inverse gas chromatography[END_REF]. This evolution was interpreted as a progressive coverage of the surface by water molecules until polar sites were saturated. K A acceptor (acidity) and K B the donor (basicity) properties of the immobilized CALB, were evaluated. The Lewis acidity (K A ) and basicity (K B ) constants decrease when a W increase (Table2), following the same trend as

	The enthalpic part of	sp ads G ∆	,	H ∆	sp ads	, was calculated for each of these probes by performing
	these experiments at different temperatures for each a W . Figure 6 shows an example of the
	curves obtained for a W =0.2, between 313 and 338K.
	Then, from the donor or acceptor character of electron of injected probes and from
	∆	H	sp ads	F o r values, sp ads G ∆	values. These results indicate that water
							P
							e
							e r
							R
							e
							v i e
							w
							sp ads G ∆	of
	different polar amphoteric probes (ethanol, acetonitrile and ethyl acetate) were determined at
	different humidity. Results obtained at 313K are shown on Figure 5. It appears that values of
	sp ads G ∆	for the different probes strongly decrease when increasing a W from 0 to 0.1 and then

stabilize. Such a drop in the specific free energy of sorption with increasing a W at low humidity level, followed by a stabilisation at higher a W level, has been observed by Comte et molecules are able to progressively mask polar surface groups of immobilized enzyme and that these groups are completely covered by water at a W equal to 0.1.

Table 1 :

 1 Characteristics of n-alkane and polar probes used in IGC: molecule surface area (a),

	This work was supported by the French Ministry of National Education, Higher Education
	and Research and the French National Agency for Research ANR (Program "Chimie et
	Prcédés pour le Développement Durable"). Dr Majid Naderi (Surface Measurement Systems
	Ltd., London, U.K.) is thanked for water adsorption isotherm measurements of Chromosorb
	alone and with immobilized lipase.

alcohols. J. Mol. Catal. B: Enzym., 2009, 59, 90-95.

Table 2 :

 2 Evolution of the dispersive component of surface energy, d

	S γ , at 313K and acid-base

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