Amit Sharma

Carine Julcour
email: carine.julcour@ensiacet.fr.

Ashutosh A Kelkar

Raj M Deshpande

Henri Delmas

Mass Transfer and Solubility of CO and H 2 in Ionic Liquid. Case of [Bmim][PF 6 ] with Gas-Inducing Stirrer Reactor

Since the past decade, ionic liquids have gained significant importance as alternative solvents for catalysis applications. Many of the reactions evaluated in ionic liquids employ gases as substrates, and therefore it is important to know their solubility and mass transfer characteristics. This work reports for the first time both the solubility and volumetric gas-liquid mass transfer coefficient k L a for hydrogen and carbon monoxide in 1-n-butyl-3-methylimidazolium hexafluorophosphate ([Bmim][PF 6 ]) at three temperatures (293, 323, and 373 K) in relevance to hydroformylation reaction. The experimental data on the volumetric gas-liquid mass transfer coefficient are described by a dimensionless correlation for the bench-scale stirred tanks with gas-inducing impeller. k L a values have also been evaluated for different [Bmim][PF 6 ]-decane emulsions at 373 K.

Introduction

Among many applications as solvents, ionic liquids are being viewed as alternative solvents to water, particularly in cases where water can interact with transition metal catalysts or substrates have very low solubility in water. [START_REF] Chauvin | A Novel Class of Versatile Solvents for Two-Phase Catalysis: Hydrogenation, Isomerization, and Hydroformylation of Alkenes Catalyzed by Rhodium Complexes in Liquid 1,3-Dialkylimidazolium Salts[END_REF][START_REF] Wasserscheid | Ionic LiquidssNew "Solutions" for Transition Metal Catalysis[END_REF][START_REF] Wasserscheid | Ionic Liquids in Synthesis[END_REF] This has led to research activities mainly on the development of new catalyst/ solvent systems for various reactions. However, there are limited reports addressing reaction engineering aspects: intrinsic kineticssneeding the concentration of the dissolved gases and organic substrates in the ionic catalytic phasesand evaluation of mass transfer limitations in such highly viscous media.

The aim of the joint NCL Pune and LGC Toulouse project is to approach these questions related to quantitative engineering of gas-liquid-liquid reactions with ionic liquids as it was yet investigated in usual aqueous biphasic catalysis at LGC by Hablot et al., [START_REF] Hablot | Gas-Liquid-Liquid Reaction using Water Soluble Catalyst[END_REF] Purwanto and Delmas, [START_REF] Purwanto | Gas-Liquid-Liquid Reaction Engineering: Hydroformylation of 1-Octene using a Water Soluble Rhodium Complex Catalyst[END_REF] Purwanto et al., 6 Desphande et al., [START_REF] Deshpande | Kinetics of Hydroformylation of 1-Octene Using [Rh(COD)Cl] 2 -TPPTS Complex Catalyst in a Two-Phase System in the Presence of a Cosolvent[END_REF] Lekhal et al., [START_REF] Lekhal | Mass Transfer Effects on Hydroformylation Catalyzed by a Water Soluble Complex[END_REF] and Jauregui-Haza et al. [START_REF] Jauregui-Haza | Multifactorial Analysis in the Study of Hydroformylation of Oct-1-ene Using Supported Aqueous Phase Catalysis[END_REF] There are recent reports on gas solubility in ionic liquids; [START_REF] Berger | Ionic Liquid-Phase Asymmetric Catalytic Hydrogenation: Hydrogen Concentration Effects on Enantioselectivity[END_REF][START_REF] Anthony | Solubilities and Thermodynamic Properties of Gases in the Ionic Liquid 1-n-Butyl-3methylimidazolium Hexafluorophosphate[END_REF] however, there are no investigations on the gas-liquid mass transfer in these media. This work especially deals with solubility and mass transfer of H 2 and CO in 1-n-butyl-3methylimidazolium hexafluorophosphate ([Bmim][PF 6 ]), the ionic liquid selected for biphasic hydroformylation kinetics. Solubility and mass transfer rates have been measured by pressure variations in a gas self-induced reactor.

State of the Art: Gas Solubility and Mass Transfer in Ionic Liquids

Over a decade ionic liquids (ILs) have sparked an increased collective interest of chemists and technologists for reaction chemistry, including catalytic reactions. The bulk of ionic liquid research has been focused on the use of ILs as solvents for a variety of reactions and only recently on their physicochemical properties.

Multiphase reaction systems are frequently encountered in chemical reaction engineering practice, and there are several industrially important applications, such as hydrogenation, hydroformylation, alkylation, ozonolysis, oxidation with molecular oxygen, ammonolysis, addition halogenation, etc., where it is desirable to have practically complete utilization of the solute gas. A gas-inducing stirred reactor is likely to provide better gas-liquid contact than other reactors with possibly lower power consumption. [START_REF] Joshi | Mass Transfer and Hydrodynamic Characteristics of Gas-Inducing Type of Agitated Contactors[END_REF] However, a clear understanding of gas solubility and mass transfer is important in understanding the reaction engineering aspects of any reaction.

Ionic liquids offer new opportunities for the development of improved biphasic systems.

In aqueous biphasic systems low reaction rates are usually obtained because of phase transfer limitations caused by low substrate solubility in the catalyst phase. On the other hand, ionic liquids are good solvents for a wide range of both organic and inorganic species without undesirable interactions with the metal center.

Thus, biphasic hydroformylation of higher olefins using rhodium-phosphine complexes in room-temperature ionic liquids (RTILs), like [Bmim][PF 6 ] or [Bmim][BF 4 ], has proved to be a very attractive alternative to current aqueous system. [START_REF] Chauvin | A Novel Class of Versatile Solvents for Two-Phase Catalysis: Hydrogenation, Isomerization, and Hydroformylation of Alkenes Catalyzed by Rhodium Complexes in Liquid 1,3-Dialkylimidazolium Salts[END_REF] Biphasic systems using ionic liquids to retain the homogeneous catalyst result in additional mass transfer steps but enable desired catalyst recycling via simple decantation. In particular, the modeling of reaction under such mass transfer limitations will require the knowledge of both gas-liquid equilibria and mass transfer coefficients (k L a). There are no available results on mass transfer effects in ionic liquid based biphasic catalysis. However, there are several reports on solubility of gases in ionic liquids. [START_REF] Berger | Ionic Liquid-Phase Asymmetric Catalytic Hydrogenation: Hydrogen Concentration Effects on Enantioselectivity[END_REF][START_REF] Anthony | Solubilities and Thermodynamic Properties of Gases in the Ionic Liquid 1-n-Butyl-3methylimidazolium Hexafluorophosphate[END_REF][START_REF] Dyson | Determination of Hydrogen Concentration in Ionic Liquids and the Effect (or Lack of) on Rates of Hydrogenation[END_REF][START_REF] Ohlin | Carbon Monoxide Solubility in Ionic Liquids: Determination, Prediction and Relevance to Hydroformylation[END_REF][START_REF] Kumelan | Solubility of CO in the Ionic Liquid[END_REF][START_REF] Kumelan | Solubility of H 2 in the Ionic Liquid[END_REF][START_REF] Jacquemin | Low-Pressure Solubilities and Thermodynamics of Solvation of Eight Gases in 1-Butyl-3-methylimidazolium Hexafluorophosphate[END_REF] Solubility of different gases (carbon dioxide, ethylene, ethane, methane, argon, oxygen, carbon monoxide, hydrogen, and nitrogen) in [Bmim] [PF 6 ] has been measured by Anthony et al., [START_REF] Anthony | Solubilities and Thermodynamic Properties of Gases in the Ionic Liquid 1-n-Butyl-3methylimidazolium Hexafluorophosphate[END_REF] but they have reported that the solubility of carbon monoxide, hydrogen, and nitrogen was below the detection limit of their apparatus. Kumelan [START_REF] Kumelan | Solubility of CO in the Ionic Liquid[END_REF] and hydrogen from 313 to 373 K. [START_REF] Kumelan | Solubility of H 2 in the Ionic Liquid[END_REF] The hydrogen solubility was found to increase with increase in temperature, whereas no significant temperature dependence was observed for CO solubility. Conversely Jacquemin et al. [START_REF] Jacquemin | Low-Pressure Solubilities and Thermodynamics of Solvation of Eight Gases in 1-Butyl-3-methylimidazolium Hexafluorophosphate[END_REF] have observed a maximum for hydrogen solubility in [Bmim][PF 6 ] around 310 K. The comparison of all data provided by those research groups, who have used different techniques and pressure ranges, exhibits a large scattering of gas solubility values for these low-soluble gases (with deviations up to nearly 200%). Thus, there is a necessity for the development of a robust and high-precision technique to evaluate thermodynamic properties.

In the present article, solubility and mass transfer coefficient of carbon monoxide and hydrogen are reported in [Bmim][PF 6 ]. k L a values have also been evaluated for [Bmim][PF 6 ]-decane mixtures, using different ratios of the two phases, in order to mimic biphasic reaction media. Measurements have been carried out in an autoclave reactor equipped with a self-gas-inducing agitator.

Experimental Section

Materials.

[Bmim][PF 6 ] was obtained from Solvionic with a purity of 99%. The specification for water content is <0.1% (measured at 0.03% according to Karl Fisher titration) and for halide content <0.005%. Thermogravimetry analysis (performed at 150 °C) shows about 0.15% of volatile com-pounds. From headspace gas chromatography/mass spectrometry (GC/MS) analysis, bromobutane (used for IL synthesis) is found as the major volatile impurity.

Decane, 99+ % purity, was supplied by Sigma-Aldrich. Carbon monoxide and hydrogen were purchased from Linde gas s.a.

Experimental Setup.

The schematic diagram of the experimental setup is shown in Figure 1. A 650 mL highpressure autoclave (flat bottom, internal diameter d R ) 8 × 10 -2 m) made of Hastelloy C276 was used for the measurements. The reactor was equipped with two symmetrical baffles (W/d R ) 0.049) and a six-bladed gas-inducing stirrer (d st ) 3.2 × 10 -2 m) with a variable speed up to 2000 rpm. The stirrer was mounted on a hollow shaft, with holes above the liquid surface.

When the gas-inducing impeller is rotating, the pressure behind the blades is reduced. Above a critical speed the gas is sucked through the holes of the hollow shaft to the holes in the impeller and dispersed into the liquid in small bubbles.

The liquid temperature, measured with a thermocouple, was set using an external heating jacket controlled by a PID. A highprecision pressure transducer (Keller PR33X, uncertainty of less than 0.015 bar) was used to measure pressure variations. Sensitivity of pressure gauges was increased once the pressure operation zone was selected. As only pressure differences were used, it could be considered that uncertainty was limited to the signal noise at constant pressure, i.e., 0.005 bar. Temperature was measured at (0.1 °C, whereas temperature control was achieved within (0.5 °C. Both temperature and pressure of the reactor were recorded online on a computer at a rate of 1-5 Hz.

Theoretical Background for the Experiments.

The experimental technique used to measure the solubility and hence Henry's constant involved batch absorption of a single gas at a given temperature and pressure and measuring of the total gas pressure variation corresponding to the dissolved gas amount in equilibrium with final pressure. Pressures up to 25 bar were used to ensure accuracy of pressure variation measurement.

Moreover in order to determine the gas-liquid mass transfer coefficient k L a, the dynamics of the pressure variation of the gas phase was recorded as the absorption proceeded. This technique was previously described [START_REF] Teramoto | Effects of Pressure on Liquid-Phase Mass Transfer Coefficients[END_REF][START_REF] Ledakowicz | Effect of Suspended Inert Solid Particles on Gas-Liquid Mass Transfer in Mechanically Agitated Contactors[END_REF][START_REF] Chaudhari | Gas-Liquid Mass Transfer in "Dead-End" Autoclave Reactor[END_REF] and known as the dynamic pressure step method. After the desired liquid temperature was reached, the reactor headspace was flushed with the gas solute and the liquid was saturated at low pressure (P 0 ) P atm ). Then the stirring was stopped and the gas solute pressure was rapidly increased in the reactor (to P m ). At t ) t 0 , the stirrer was started again and the pressure was recorded as a function of time until it remained constant (new equilibrium pressure P f ). Integration between t ) t 0 (P ) P m ) and t of the mass balances in gas and liquid phases (perfectly stirred) leads to A typical plot is shown in Figure 2: k L a value can be determined from the slope of the line. [START_REF] Zieverink | Gas-Liquid Mass Transfer in Benchscale Stirred Tanks-Fluid Properties and Critical Impeller Speed for Gas Induction[END_REF] The main question about this technique concerns the part of the pressure curve to be used as the stirrer speed cannot be instantaneously varied from zero to the desired speed. The best choice is to select the portion which best fits the exponential pressure variation. It corresponds to the linear variation of the logarithmic pressure difference ratio, from about 20% to 70% of the total pressure variation.

Results and Discussion

Physical Properties of [Bmim][PF 6 ]. All relevant physical properties of [Bmim][PF 6

] except diffusivity were measured between 293 and 373 K and are given in Table 1. Those data are found in good agreement with previously published values.

The density of [Bmim][PF 6 ] was determined using an oscillating U-tube densimeter (Anton Paar DMA 38) and was well described as a linearly decreasing function of temperature: where temperature T is in Kelvin.

Rheometer measurements (TA Instruments CSL2 500) showed that [Bmim][PF 6 ] has a Newtonian behavior. Its viscosity was measured at various temperatures, and data regression gave the following dependence with temperature:

The surface tension of [Bmim][PF 6 ] was experimentally determined using Wilhelmy plate method (GBX 3S tensiometer) and could be expressed as

The diffusivity of hydrogen and carbon monoxide in [Bmim][PF 6 ] was estimated using the correlation compiled by Morgan et al. [START_REF] Morgan | Diffusivities of Gases in Room-Temperature Ionic Liquids: Data and Correlations Obtained Using a Lag-Time Technique[END_REF] The authors have measured the diffusivity of carbon dioxide, ethylene, propylene, 1-butene, and 1,3-butadiene in six different ionic liquids, including [Bmim][PF 6 ], at 30 °C using a lag-time technique. They have found diffusivity values much greater than those predicted by Stokes-Einstein or Wilke-Chang equations (after fitting the solvent association coefficient to an unusual value of 0.15). So they have proposed the following correlation which accounts for the liquid molar volume (V 1 in cm 3 /mol) of the solute 1 at its atmospheric boiling point, the viscosity (in cP) and density (in g/mL) of imidazolium ionic liquid 2: with diffusivity D in m 2 /s. This correlation was used without further modification to estimate diffusivities in the investigated range of temperatures (293-373 K), and the corresponding values are reported in Table 2.

Solubility Studies.

The absorption of H 2 and CO into [Bmim][PF 6 ] was measured at three different temperaturess293, 323 and 373 Ksusing a high-precision pressure sensor. Before performing the solubility experiments, the free reactor volume (subtracting all fittings and stirrer volumes) was determined precisely by filling it with nitrogen from a known volume ballast and measuring pressure variations. The value obtained (615 ( 3 mL) was also verified by measuring the known Henry's constant for the N 2 -water system at room temperature. Several experiments were performed with H 2 -[Bmim][PF 6 ] and CO-[Bmim][PF 6 ] systems to check for the repeatability of the results (estimated at less than 5%). For all the experiments, the reactor was filled with 300 mL of [Bmim][PF 6 ].

Figure 3, parts a and b, shows the experimental data plotted as the mole fraction of the gas dissolved in the liquid phase versus the absolute pressure of the gas at different temperatures. As can be seen, the trend followed is linear, suggesting that Henry's law is applicable. The results of solubility in terms of Henry's constants (in bar) are listed in Table 3.

From the variations of Henry's constants as a function of temperature, the enthalpy of solvation of H 2 can be roughly estimated at 3.0 kJ/mol between 293 and 323 K and -0.60 kJ/ mol between 323 and 373 K, whereas for CO a constant value of -3.8 kJ/mol can be considered on the whole temperature range.

In accordance with previous studies, [START_REF] Kumelan | Solubility of CO in the Ionic Liquid[END_REF][START_REF] Kumelan | Solubility of H 2 in the Ionic Liquid[END_REF][START_REF] Jacquemin | Low-Pressure Solubilities and Thermodynamics of Solvation of Eight Gases in 1-Butyl-3-methylimidazolium Hexafluorophosphate[END_REF] solubility of CO was found larger than that of H 2 in the investigated range of temperatures. The trend as a function of temperature is consistent with that observed by Jacquemin et al. [START_REF] Jacquemin | Low-Pressure Solubilities and Thermodynamics of Solvation of Eight Gases in 1-Butyl-3-methylimidazolium Hexafluorophosphate[END_REF] (decrease of CO

( P m -P f P(t) -P f ) ) ( P m -P 0 P f -P 0 ) k L a(t -t 0 ) (1) F(kg/m 3 ) ) 1621.3 -0.85T (2)
µ(Pa•s) ) exp ( -14.945 + 4042.4 T ) (T in K) [START_REF] Wasserscheid | Ionic Liquids in Synthesis[END_REF] σ(N/m) ) (85.48 -0.135T) × 10 -3 (T in K) (4)

D ) 3.7 × 10 -7 1 µ 2 0.59(0.02 V j 1 (1.0(0.07) F 2 2.0(0.1 (5)
solubility with increasing temperature, maximum of solubility for H 2 in the investigated range); however, the temperature effect is much more significant for CO than H 2 .

As shown in Figure 4, the values measured in this study are in good agreement with those reported by Kumelan et al. [START_REF] Kumelan | Solubility of CO in the Ionic Liquid[END_REF][START_REF] Kumelan | Solubility of H 2 in the Ionic Liquid[END_REF] around room temperature (difference of about 10%), but the deviation becomes larger at higher temperatures (up to 30% for H 2 and 55% for CO at 373 K). Those authors have determined gas solubility over a large temperature range and for pressures up to about 9 MPa using volumetric measurements on a thermostatted high-pressure cylindrical view cell.

Jacquemin et al. [START_REF] Jacquemin | Low-Pressure Solubilities and Thermodynamics of Solvation of Eight Gases in 1-Butyl-3-methylimidazolium Hexafluorophosphate[END_REF] have also investigated the solubility of the two gases as a function of temperature, but near atmospheric pressure, using an isochoric saturation method. The Henry's constants they have reported are systematically lower when compared to the data of this work, with a mean deviation close to 100% both for H 2 and CO.

Berger et al. [START_REF] Berger | Ionic Liquid-Phase Asymmetric Catalytic Hydrogenation: Hydrogen Concentration Effects on Enantioselectivity[END_REF] and Dyson et al. [START_REF] Dyson | Determination of Hydrogen Concentration in Ionic Liquids and the Effect (or Lack of) on Rates of Hydrogenation[END_REF] have also measured the solubility of hydrogen in [Bmim][PF 6 ], but only at room temperature. The measurement technique of Berger et al. [START_REF] Berger | Ionic Liquid-Phase Asymmetric Catalytic Hydrogenation: Hydrogen Concentration Effects on Enantioselectivity[END_REF] is similar to the one used in the present work, but in a much lower volume reactor (10 mL of ionic liquid), whereas Dyson et al. [START_REF] Dyson | Determination of Hydrogen Concentration in Ionic Liquids and the Effect (or Lack of) on Rates of Hydrogenation[END_REF] have employed high-pressure 1 H NMR spectroscopy (at a pressure of 100 atm). According to their results, the numerical values of Henry's constant at room temperature were 5560 [START_REF] Berger | Ionic Liquid-Phase Asymmetric Catalytic Hydrogenation: Hydrogen Concentration Effects on Enantioselectivity[END_REF] and 6600 bar [START_REF] Dyson | Determination of Hydrogen Concentration in Ionic Liquids and the Effect (or Lack of) on Rates of Hydrogenation[END_REF] which are about 30% and 50% larger than the value obtained in this work, respectively.

Ohlin et al. [START_REF] Ohlin | Carbon Monoxide Solubility in Ionic Liquids: Determination, Prediction and Relevance to Hydroformylation[END_REF] have reported the solubility of carbon monoxide in several ionic liquids at 295 K using high-pressure [START_REF] Dyson | Determination of Hydrogen Concentration in Ionic Liquids and the Effect (or Lack of) on Rates of Hydrogenation[END_REF] C NMR spectroscopy. According to these authors the value of Henry's constant in [Bmim] [PF 6 ] at room temperature, 3270 bar, is about 50% higher than in this work.

As said previously, these discrepancies in the data reported by the different authors are probably due to the experimental techniques applied but maybe also to the impurities present in the samples of ionic liquids used by the different research groups.

Mass Transfer Studies. 4.3.1. [Bmim][PF 6 ]. 4.3.1.1. Critical Stirrer Speed and Gas Induction.

The critical impeller speed N cr at which the onset of gas induction occurs may be considered as the first step in the design of the reactor. Joshi and Sharma [START_REF] Joshi | Mass Transfer and Hydrodynamic Characteristics of Gas-Inducing Type of Agitated Contactors[END_REF] have proposed a correlation by measuring the critical impeller speed for pipe and flattened cylindrical impellers and have not found any dependence on liquid property:

According to the Bernoulli equation and based on the assumption of same velocity for the liquid and the paddle, K ) -1, whereas the experimental value of K lies in the range of -0.9 to -1.3.

Sawant and Joshi [START_REF] Sawant | Critical Impeller Speed for the Onset of Gas Induction in Gas-Inducing Types of Agitated Contactors[END_REF] have studied the effect of liquid viscosity (from 0.8 to 80 mPa • s) and found a slight dependence on viscosity, N cr 2 ∝ (µ/µ w ) 0.11 , resulting in the following equation (which corresponds to K ) -0.97):

More recently Poncin et al. [START_REF] Poncin | Hydrodynamics and Volumetric Gas-Liquid Mass Transfer Coefficient of a Stirred Vessel Equipped with a Gas-Inducing Impeller[END_REF] have found a weaker value of the exponent of (µ w /µ) in eq 7 (0.07).

Due to the large variation of [Bmim][PF 6 ] viscosity in the temperature range, the correlation of Sawant and Joshi [START_REF] Sawant | Critical Impeller Speed for the Onset of Gas Induction in Gas-Inducing Types of Agitated Contactors[END_REF] was used to calculate the critical stirrer speed, giving 670, 610, and 570 rpm for 293, 323, and 373 K, respectively.

The values calculated previously were found consistent with observations made using a glass beaker of nearly same diameter and heated from the bottom, but it was also seen that gas induction did not proceed the same way at different temperatures (cf. Figure 5). At 293 K, bubbles were not released continuously and most of the gas holdup was trapped around the stirrer blades (Figure 5a) over a large range of stirrer speed, whereas at 373 K gas was dispersed in the whole liquid (Figure 5c) in form of small bubbles above critical speed.

Gas-Liquid Mass Transfer.

Experiments were carried out to determine the gas-liquid mass transfer coefficient for hydrogen and carbon monoxide in [Bmim][PF 6 ]. They were performed at the same three temperatures, using the dynamic pressure step method discussed in section 3.3.

In Figure 6 the values of the volumetric mass transfer coefficient k L a are plotted versus the stirrer speed at the three temperatures. Each point is a mean of three to four measurements with standard deviation less than 10%.

k L a increases with increasing N (rotation speed) and also with temperature. The last effect is much higher than in usual aqueous solutions, probably due to a much higher decrease of viscosity with temperature in ionic liquids and due to the very peculiar change in gas dispersion as shown in Figure 5.

It is usually agreed that mass transfer can be nicely correlated as a function of power consumption. [START_REF] Zieverink | Gas-Liquid Mass Transfer in Benchscale Stirred Tanks-Fluid Properties and Critical Impeller Speed for Gas Induction[END_REF][START_REF] Poncin | Hydrodynamics and Volumetric Gas-Liquid Mass Transfer Coefficient of a Stirred Vessel Equipped with a Gas-Inducing Impeller[END_REF][START_REF] Dietrich | Raney-Nickel Catalyzed Hydrogenations: Gas-Liquid Mass Transfer in Gas-Induced Stirred Slurry Reactors[END_REF] An alternative approach when this parameter cannot be evaluated is to describe the effect of different operating parameters on k L a using a dimensionless correlation of the form Sh ) f(Re, Fr, Sc, We,...). The following paragraphs refer to such models.

Dietrich et al. [START_REF] Dietrich | Raney-Nickel Catalyzed Hydrogenations: Gas-Liquid Mass Transfer in Gas-Induced Stirred Slurry Reactors[END_REF] have measured the gas-liquid mass transfer in nonelectrolytic liquids (distilled water, ethanol, and reaction

N cr 2 d st 2 gH l ) - 2
π 2 K (6) N cr 2 d st 2 gH l ( µ w µ ) 0.11
) 0.21 (7) mixtures involved in adiponitrile hydrogenation) using a gasinducing stirrer of Rushton type and proposed the following correlation:

where a was found to be a function of the ratio between liquid height and tank diameter. As this equation does not account for the critical impeller speed N cr , it will fail near the onset of gas induction, and thus it is only suitable for stirrer speeds N . N cr .

Poncin et al. [START_REF] Poncin | Hydrodynamics and Volumetric Gas-Liquid Mass Transfer Coefficient of a Stirred Vessel Equipped with a Gas-Inducing Impeller[END_REF] have also characterized mass transfer performance of a gas-liquid stirred tank provided with a radial gasinducing turbine, and they have proposed an empirical correlation for an air-water system:

This correlation shows that k L a strongly increases with N above N cr ; the asymptotic value at high Fr does not correspond to usual stirring conditions.

Recently Zieverink et al. [START_REF] Zieverink | Gas-Liquid Mass Transfer in Benchscale Stirred Tanks-Fluid Properties and Critical Impeller Speed for Gas Induction[END_REF] have studied the gas-liquid mass transfer characteristics of a laboratory autoclave equipped with a gas-inducing Rushton stirrer using different organic liquids (sunflower oil, toluene, acetone, n-hexadecane) with a viscosity range from 0.4 to 60 mPa • s. After evaluating many dimensionless correlations, they have found that Sh ∝ Re b (Fr -Fr cr ) c Sc d best fitted their data. As the organic liquids used in their study were very similar in surface tension and density, they omitted the Weber number effect.

In the present work, the values of the volumetric gas-liquid mass transfer coefficient k L a for hydrogen and carbon monoxide in [Bmim][PF 6 ] obtained by dynamic absorption technique were modeled using different correlations based on Sh, Sc, Re, and (or) Fr as relevant dimensionless groups. Previous parametric study indeed underlined the influence of stirrer speed, viscosity (through temperature effect), and gas diffusivity (changing gas nature) on k L a.

All the selected model equations and fitted parameters with 95% confidence interval are listed in Table 4. Those parameters were optimized using Levenberg-Marquardt method (DataFit software) after linearization of the equations. To compare the quality of prediction of the different models, the root-meansquare value between the experimental and predicted k L a was calculated as Figure 7 presents the parity plots of predicted versus experimental values of mass transfer coefficients. Values at 800 rpm, close to critical speed and maybe too sensitive to any hydrodynamic disturbance, were excluded for the optimization but accounted for in the calculation of the criteria and the plot of parity diagrams.

In accordance with penetration theory models I to IV and VII set the exponent of Schmidt number to 0.5, whereas in equations V and VI it is let free in the fit. rms ) 1 a rms is the root-mean-square value between the experimental and predicted k L a, given as rms started by introducing critical impeller speed in critical Reynolds number. The rest of the equations, i.e., III and IV, follows the approach proposed by Zieverink et al. [START_REF] Zieverink | Gas-Liquid Mass Transfer in Benchscale Stirred Tanks-Fluid Properties and Critical Impeller Speed for Gas Induction[END_REF] and use a combination of Re and Fr, with one of the two factors corrected for the onset of gas induction. It could be argued that the soundest combination should involve the Reynolds number to account for the actual turbulence in the reactor and a modified Froude number, Fr -Fr cr , to account for the induced gas flow rate.

N ∑ i)1 N ( k L a i,exp -k L a i,calc k L a i,exp
) ((1/N)∑ i ) 1 N [(k L a i,exp -k L a i,calc )/(k L a i,exp )] 2 ) 1/2 .
Correlations giving Sh as a function of Sc 0.5 and Fr c (or (Fr -Fr cr ) c ) fail to predict the data over the temperature range as they underestimate the effect of viscosity. Letting the exponent of Sc free results thus for this parameter to negative values which have no physical significance. It was also observed by Zieverink et al. [START_REF] Zieverink | Gas-Liquid Mass Transfer in Benchscale Stirred Tanks-Fluid Properties and Critical Impeller Speed for Gas Induction[END_REF] when trying to correlate the k L a values obtained for different liquids.

If in equation III or IV no constraint is put on the Sc exponent, then the optimization leads again to unrealistic negative values for this parameter, along with very large confidence intervals, showing that too many free parameters are involved in fitting our data set.

From analysis of selected models ( Models III and IV using a combination of Re and Fr, with one of the two factors corrected for the onset of gas induction, lead to the lowest criteria, and no clear discrimination can be made in between the two models.

[Bmim][PF 6

]-Decane Mixtures. Finally the gas-liquid mass transfer coefficient was measured in [Bmim][PF 6 ]-decane mixtures at 373 K, using different volume ratios of the two phases, in order to mimic conditions of biphasic hydroformylation.

First it is noteworthy that mass transfer coefficients in ionic liquid phase are about 10 times smaller than in organic phase. As solubility (per volume) is of same order of magnitude this mass transfer limitation may become important even for moderately fast reactions.

In the reaction mixture, k L a increases when increasing decane volume fraction due also to lowering of emulsion viscosity. The larger increase was found around phase inversion (cf. Figure 8). These results are very important as possible industrial reaction will be carried out in such two-liquid-phase media where gas-liquid mass transfer is clearly better than in pure ionic liquid phase due to both the average viscosity reduction and to the very fast liquid-liquid mass transfer as compared to gas-liquid. [START_REF] Lekhal | Mass Transfer Effects on Hydroformylation Catalyzed by a Water Soluble Complex[END_REF][START_REF] Dumont | Mass Transfer Enhancement of Gas Absorption in Oil-in-Water Systems: A Review[END_REF] In this two-phase liquid system with ionic liquid as the dispersed phase, gas is fast transferred to the organic phase due to high k L a, then faster transferred to the ionic liquid phase due to much higher interfacial area, droplets being much smaller than gas bubbles.

Conclusion

The present work reports experimental results on the solubility of hydrogen and carbon monoxide in [Bmim][PF 6 ] at different temperatures and pressure up to 25 bar. [Bmim][PF 6 ] exhibits low syngas solubility (around 3 times lower than in decane at 373 K) which is not convenient for hydroformylation kinetics. Gas-liquid mass transfer coefficients were also measured in this ionic liquid, showing a very strong effect of both temperature and stirrer speed. Correlations were proposed using various dimensionless parameters including modified Reynolds or Froude numbers to account for the critical impeller speed. Best fit was obtained for models of the form Sh ∝ Re b (Fr -Fr cr ) c Sc 0.5 or Sh ∝ (Re -Re cr ) b Fr c Sc 0.5 . In [Bmim][PF 6 ]-decane mixtures, a large increase of k L a was found near phase inversion while increasing decane fraction. Thus, from an engineering point of view, biphasic hydroformylation using ionic liquids should be preferentially conducted with a continuous organic phase in order to reduce the effect of gas-liquid mass transfer limitations.

Figure 1 .

 1 Figure 1. Schematic diagram of the experimental setup.

Figure 2 .

 2 Figure 2. Graphical representation of eq 1 for the determination of gas-liquid mass transfer coefficient (H 2 , 1500 rpm, 20 °C).

Figure 3 .

 3 Figure 3. Solubility of H 2 (a) and CO (b) in [Bmim][PF 6 ] as a function of (equilibrium) pressure at 293 ([), 323 (gray filled square), and 373 K (∆).

Figure 4 .

 4 Figure 4. Ln H (Henry's constant) vs the inverse of temperature (K) for H 2 (a) and CO (b) in [Bmim][PF 6 ].

Figure 5 . 1 1

 51 Figure 5. Photographs of the gas dispersion (air) inside [Bmim][PF 6 ] at 1500 rpm: (a) 293 (b) 323, and (c) 373 K.

Figure 6 .

 6 Figure 6. Gas-liquid mass transfer coefficient (k L a) vs stirrer speed (rpm) for H 2 (a) and CO (b) in [Bmim][PF 6 ]: 293 ([), 323 (gray filled square), and 373 K (∆).

) 2 Relations

 2 I, V, and VII are based on usual Reynolds number (using the impeller speed N) and exclude critical impeller speed N cr from analysis. Conversely model equations II and VI take into account zero mass transfer when gas induction has not

Figure 7 .

 7 Figure 7. Comparison of calculated vs experimental k L a for the different model equations listed in Table 4: (a) model I, (b) model II, (c) model III, (d) model IV, (e) model V, (f) model VI, and (g) model VII.

Table 1 . Physical Properties of [Bmim][PF 6 ] Measured between 293 and 373 K a

 1

	temp (K)	density F (kg/m 3 )	viscosity µ (Pa • s)	surface tension σ (10 -3 N/m)
	293	1371 ( 1 (1368 (298 K)

b , 1360 (298 K) c ) 0.35 ( 0.02 (0.264 d , 0.286 e ) 45.8 ( 0.05 (47 b , 48.8 (298 K) c ) 313 1354 ( 1 (1350 b ) 0.12 ( 0.01 (0.107 d , 0.094 e ) 43.1 ( 0.1 f 323 1345 ( 1 (1339 b ) 41.9 ( 0.1 g 333 1337 ( 1 0.055 ( 0.003 (0.049 d , 0.040 e ) 353 0.030 ( 0.001 (0.024 d ) 368 0.021 ( 0.001 (0.015 d ) a Values in parentheses are literature data. b Ref 22. c Ref 23. d Ref 24. e Ref 25. f At 315 K. g At 320 K.

Table 2 . Diffusion Coefficients of H 2 and CO in [Bmim][PF 6 ], According to Morgan et al. (Ref 26)

 2

		diffusion coefficient	diffusion coefficient
	temp (K)	of H 2 (10 -10 m 2 /s)	of CO (10 -10 m 2 /s)
	293	2.2	1.8
	323	5.7	4.7
	373	12.9	10.5

Table 3 . Henry's Constants (bar) for H 2 and CO in [Bmim][PF 6 ]

 3

	temp (K)	Henry's constant H H2 (bar)	Henry's constant H CO (bar)
	293	(4.35 ( 0.12) × 10 3	(2.19 ( 0.04) × 10 3
	323	(3.89 ( 0.10) × 10 3	(2.66 ( 0.06) × 10 3
	373	(4.00 ( 0.09) × 10 3	(3.06 ( 0.06) × 10 3

Table 4 . Model Equations and Estimated Parameters for Gas-Liquid Mass Transfer with Gas-Inducing Stirrer (with 95% Confidence Intervals)

 4 Re cr ) b Sc 0.5 0.95 -1.290 ((0.404) 1.415 ((0.177) III Sh ) 10 a (Re -Re cr ) b Fr c Sc 0.5 0.44 -1.262 ((0.318) 1.354 ((0.145) 0.863 ((0.551) IV Sh ) 10 a Re b (Fr -Fr cr ) c Sc 0.5

		model eq	rms a	a	b	c	d
	I	Sh ) 10 a Re b Sc 0.5	2.59	-1.967 ((0.710)	1.503 ((0.275)
	II	Sh ) 10 0.44	-1.658 ((0.408)	1.388 ((0.157)	1.148 ((0.399)
	V	Sh ) 10 a Re b Sc d	0.95	-14.012 ((8.154)	3.612 ((1.441)		1.816 ((0.889)
	VI	Sh ) 10 a (Re -Re cr ) b Sc d	0.50	-4.742 ((3.189)	2.012 ((0.570)		0.919 ((0.384)
	VII	Sh ) 10 a Re b Sc 0.5 We 0.5	1.60	-3.140 ((0.561)	1.444 ((0.217)

a (Re -

Table 4 )

 4 , following conclusions can be brought about: • As expected, taking into account the critical stirrer speed through modified Reynolds number results in much lower rms criteria (0.95 for model II against 2.59 for model I, 0.50 for model VI against 0.95 for model V). • Letting Sc exponent free in models I and II (resulting in models V and VI, respectively) also decreases rms criteria but also leads to larger confidence intervals due to the huge influence of viscosity on k L a values (µ appears in both Sc and Re numbers). • Including the Weber number in eq I with a square root dependence, as proposed by Dietrich et al., 29 allows a better fitting of k L a values, but the criteria is still quite high. As only one ionic liquid was used, variation of surface tension in the operating range is maybe too low to accurately account for this parameter. It should be noted that the fitted exponent of Reynolds (1.44) is in good agreement with what obtained Dietrich et al.

  [START_REF] Dietrich | Raney-Nickel Catalyzed Hydrogenations: Gas-Liquid Mass Transfer in Gas-Induced Stirred Slurry Reactors[END_REF]

Acknowledgment

CEFIPRA, under the project 3305-2, is gratefully acknowledged for financial support.

g ) gravitational constant, m • s -2 t ) time, s D ) diffusivity of gas in ionic liquid, m 2 • s -1 Fr ) Froude number, N 2 d st 2 /(gH l ), dimensionless Fr cr ) critical Froude number, N cr 2 d st 2 /(gH l ), dimensionless H l ) liquid height above impeller, m H ) Henry's constant, bar k L a ) volumetric gas-liquid mass transfer coefficient (liquid-phase side), s -1 N ) stirrer speed, s -1 N cr ) critical stirrer speed, s -1 P ) pressure, bar P 0 ) equilibrium pressure after degassing the liquid, bar P atm ) atmospheric pressure, bar P m ) initial pressure (just before gas absorption), bar P f ) equilibrium final pressure (after gas absorption), bar Re ) Reynolds number, FNd


Fahima Rachedi

Dr Richard Guilet
email: richard.guilet@iut-tlse3.fr

Patrick Cognet

Josiane Tasselli

Antoine Marty

Pascal Dubreuil

Keywords: Catalytic oxidation, Microreactors, Waste air

Microreactor for Acetone Deep Oxidation over Platinum

A catalytic, silicon-based, microstructured reactor was developed for the catalytic oxidation of volatile organic compounds, with the aim of small-scale localized air treatment. The microreactor was based on the stacking of microstructured platelets, and the active catalyst phase, i.e., platinum, was deposited onto the walls of the microchannels by the thermal evaporation technique. The experimental setup allowed testing the efficiency of the catalytic microreactor. The deep oxidation of acetone (as a target compound) in air was carried out at increasing temperatures, resulting in ignition curves. Wide ranges of inlet acetone concentrations (500-8000 ppmv) and space velocities (18,700-201,000 h -1 ) were studied. Regarding acetone oxidation, the catalytic microreactor was found to exhibit high performances in terms of conversion, selectivity, and temperatures required to reach 50 and 95 % conversions.

Introduction

In recent years, microsystems such as heat exchangers or mixers have become of great interest for non-reactive processes. However, these microsystems have not yet offered all their industrial potentiality as microstructured reactors [1][2][3].

Typically, microreactors are microstructured devices featuring small channels in the range of micrometers. They can be constructed from microstructured plates enabling the fluid flow distribution over microchannels. Each microstructured platelet is typically made up of parallel microchannels with a width of the order of 50-500 lm and a width-to-depth ratio ranging from 1 to 100. As Kiwi-Minsker and Renken [4] underline in their review, microreactors offer very large surfaceto-volume ratios ranging from 10,000 to 50,000 m 2 /m 3 , while the specific surface in conventional laboratory and production vessels is usually 100 m 2 /m 3 and rarely exceeds 1000 m 2 /m 3 . The small dimension of the channels and the high surface-tovolume ratio ensure many properties of these devices and offer new possibilities for reaction pathways by achieving previously inaccessible residence times. They allow high heat and mass transfer and efficient fluid mixing [5,6] as well as high adaptabilities in terms of process design by numbering up of microstructured elements.

Regarding reaction processes, they enable a reduction of the time required to achieve complete conversion. Short residence times also reduce unexpected reactions of products and enhance the yield and selectivity. High heat transfer properties enable high control of temperature, facilitating isothermal processes, preventing hot-spot formation and avoiding thermal runaway, especially when the occurring reactions involve high exothermicity. Thus, microreactors can offer some advances in catalytic processes. Furthermore, due to the characteristic dimensions of the microchannels, microstructured devices enable a large decrease in the distance between the catalytic zone and the stream, with more efficient heat and mass exchange properties than for conventional packed-bed reactors. Catalytic microstructures and subsequent flow control allow a more secure manipulation of hazardous, inflammable and even explosive products, which is not possible in conventional reactors. Recently, the applications of microreactors to catalytic reactions were reviewed by Kiwi-Minsker and Renken [4]. Although the use of microreactors for catalytic reactions offers clear advantages, the authors conclude that the introduction of the solid catalyst remains a difficulty and that catalytic wall microreactors are more suitable. Moreover, Kolb and Hessel [7] give an overview of the work and research interests in the field of catalytic gas phase reactions. Many examples using various technologies are reported, such as oxidations, hydrogenations, dehydrogenations, dehydrations, and reforming processes. Among them, deep or partial catalytic oxidation is of great interest for many applications, including oxidation for air treatment.

Removal of air pollutants such as volatile organic compounds (VOC) is a major health and environmental concern. European directives indeed tend to regularly decrease the authorized pollutant emission levels. VOC include a wide variety of chemicals: aliphatic and aromatic hydrocarbons, halogenated hydrocarbons, aldehydes, ketones, alcohols, glycols, ethers, epoxides, phenols, etc. The three major sources of VOC are: power generation (20 %), vehicle emissions (40 %), and solvents for industrial purpose (27 %) [8]. They are commonly found in the atmosphere at a high level in all urban and industrial centers. They actively take part in the increase of the greenhouse effect, and a carcinogenic effect is also assigned to some of them [9,10]. The large variety of sources and compounds with different physical and chemical properties has led, over the years, to the development of a wide range of VOC treatment processes [11]: bioprocesses (biofilters), chemical processes (combustion, ozonation, photooxidation), and physical processes (condensation, adsorption, absorption). Actually, the main processes are adsorption-and/or combustionbased systems. The first is a non-destructive process and needs a subsequent treatment of the adsorbent, and the second process usually occurs at high temperatures (about 1200 °C) in order to avoid the formation and release of hazardous byproducts, such as dioxins, but produces high levels of nitrogen oxides (NO x ), which eventually requires further treatment [12].

In the last several years, catalytic oxidation has become an alternative destructive process of VOC that offers many advantages, such as high combustion efficiency and extremely low emissions of NO x and unburnt hydrocarbons. Compared to thermal combustion, the reaction occurs at lower temperatures, between 200 and 500 °C, which is of very great interest from energy, security and operation cost points of view. Regarding the catalyst performances, various catalytic materials, such as noble metals (Pt, Pd) and mixed oxides (V, Mn, Co, Cu, Cr), supported or not on oxides (e.g. alumina), have been shown to be efficient for VOC oxidation [13][START_REF] Henegan | Catalysis[END_REF][START_REF] Papaefthimiou | [END_REF]. Platinumbased catalysts are considered as being among the most active catalysts for VOC deep oxidation [16][17][18].

Although heterogeneous catalytic deep oxidation of VOC is a quite well-known process [19], its application to air treatment is nowadays limited to large-scale units. The major difficulty is often linked to the multiple pollution sources and subsequently the necessity of collecting all of the polluted effluents towards a large-scale treatment unit. In fact, much of the industrial air pollution comes from enclosed sources. Processes that could easily adapt and fit to various localized pollution sources, whatever the pollutants, the flow and the application, would be a great technological advance in air pollution treatment. In the field of small-scale localized air treatment, the main limitation is the inherent difficulty in designing and sizing the reactor for these applications.

Thus, catalytic microsystems could be implemented for the removal of volatile organic compounds in various industrial environments such as drying, painting, varnishing and drycleaning workshops. As mentioned above, they offer the advantage of being adaptable by numbering up of small units, and they consequently allow the design of appropriate catalytic processes whatever the scale and the effluent. Moreover, while the catalytic oxidation processes are generally carried out in a catalytic fixed-bed reactor with an inflammation risk of the catalytic bed because of hot-spot formation, microreactors offer new advances as they allow heat to be transferred or removed very easily and efficiently [20].

In this work, the performances of a silicon-based microstructured reactor for catalytic oxidation of acetone are presented. Acetone was chosen as a representative volatile organic compound because it is both a widespread VOC and one of the most difficult to oxidize [8]. The catalytic activity of the microreactor was tested for a wide range of inlet concentrations and various space velocities.

Microstructured Reactor

The experiments were carried out in a microreactor designed according to the characteristics of the reaction and based on the stacking of microstructured platelets. The core part of the reactor was composed of 12 stacked platelets (30 × 30 mm) held by screws in a cylindrical inner housing. The whole was embedded in a stainless-steel outer housing equipped with four electrical resistive cartridges allowing heating of the reactor (see Figs. 1,2).

One advantage of the proposed reactor is its modularity: The platelets were inserted in the inner housing recess and could be easily removed and replaced, allowing various configurations (microchannels geometry and/or platelets length) to be tested.

The platelets were fabricated from silicon wafers with 525 lm thickness: (i) Silicon is an interesting material in terms of heat transfer, with high conductibility allowing heat release from the reactor core; (ii) moreover, microtechnologies offer the possibility to structure the silicon material in surface and Each of the 12 platelets was made up of 29 parallel microchannels of 200 lm width, microstructured by the deep reactive ion etching (DRIE) technique according to the Bosch process, i.e. a cyclic repetition of an ion-assisted etching of the silicon substrate by an etching gas (SF 6 ) and a sidewall passivation using a polymer-producing gas (C 4 F 8 ) [21]. After a thermal oxidation step in order to recover the silicon surface by a thin oxide layer (0.1 lm), the active catalyst phase was deposited on the walls of the microchannels (see Fig. 3). The selected material, platinum (Pt), which is well known for its catalytic potentialities in gas phase reactions, was deposited by the thermal evaporation technique, allowing large-scale fabrication and good reproducibility of the catalyst layer thickness (about 130 nm). The mean roughness of the microchannel surface was evaluated by atomic force microscopy. After catalyst deposition, the roughness was about 10 nm.

Regarding the gas feed, the gas stream was introduced from the inlet tube to the platelets stack via a diffuser (a drilled plate distributor associated with a diffusion chamber).

Experimental

The main goal of the experiments was to determine the efficiency of the microreactor for VOC deep oxidation. The present work dealt with studying acetone conversion versus temperature for various inlet acetone concentrations and air flows. The experimental setup is shown in Fig. 4.

With a 10-mL glass syringe (Hamilton Gastight®) with PTFE plungers, liquid acetone (Chromosolv®, ≥99.9 %; Sigma Aldrich) was injected into an evaporation cell through a capillary tube, by using a syringe pump (PH 2000 Infusion) from Harvard Apparatus, which allowed getting the required low liquid flows (a few milliliters of acetone per hour).

The evaporation cell was fed with a gaseous stream composed of synthetic air (80 % N 2 , 20 % O 2 ) 5.6 from Linde Gas, controlled by mass flow meters (5850 TR Series Brooks®). The required acetone liquid flow was calculated according to the air flow to reach the desired concentration. Before being introduced into the microstructured reactor, the gaseous acetoneair mixture was formed in the evaporation cell at 200 °C; the evaporator was equipped with a heating resistor. A cylindrical grill and a capillary tube within the cell ensured the homogeneity of the gas flow at the inlet of the microreactor. A thermocouple at the outlet of the evaporator and a PID regulator allowed the temperature to be controlled. The microreactor was equipped with two thermocouples; one was placed in the stainless steel outer housing and the other one was placed just at the end of the platelets, which allowed the control of the reaction temperature.

The inlet and outlet of the microreactor were connected to an on-line gas phase chromatography (GPC) apparatus (CP3800) from Varian. The GPC system was equipped with both a thermal conductivity detector (TCD) and a flame ionization detector (FID), to enable the analysis of all gaseous components. Thus, the on-line analytical equipment allowed simultaneous monitoring of the VOC concentration at the inlet and outlet, and of the potential products of the reaction, such as H 2 , CO, CH 4 , CO 2 , C 2 H 4 as well as N 2 and O 2 . Before testing the activity of the catalytic microstructured platelets, the catalyst was activated in situ at 450 °C for 8 h under a constant air flow. After the first run, the temperature of the catalyst was maintained at 550 °C, the highest reaction temperature, for a few hours. The experimental assessment of catalytic activity was carried out by scanning the operating temperature and the gas flow as well as the VOC concentration. The ranges of the parameters are given in Tab. 2. Mass flow controllers were used to prepare the feed mixture. The VOC concentration range was established according to the authorized levels of pollutant emissions and the inlet air flow. The corresponding liquid feed rate was controlled by the syringe pump, and the VOC liquid flow was calculated assuming that the evaporation cell was efficient enough to vaporize all the liquid.

Before each run, the VOC inlet concentration was determined on-line by GC after the steady state was reached at the evaporator outlet. The inlet concentration deviation was considered acceptable when not exceeding 5 %. For a given concentration and a fixed gas flow, the operating temperature was increased from 200 to 500 °C by steps of 25 °C. For each temperature, the outlet stream was analyzed after the steady state was established. The experiments were conducted at atmospheric pressure. The ignition curves were constructed by following both VOC disappearance and CO 2 appearance.

Regarding the flow behavior within the microreactor, the mean residence time is the total volume of the microchannels divided by the total inlet gas flow rate, corrected to the operating temperature and pressure of the gas stream in the reactor. The inlet air flow rate was here metered with a mass flow controller set to standard conditions. For each experiment, the flow rate within the microreactor was corrected to the operating conditions assuming that the ideal gas law is valid. Thus, the mean residence time decreases by about 60 % when the temperature increases from 200 to 500 °C. With regard to the operating temperature used in this work, the mean residence times ranged from 7 to 120 ms. Moreover, the hourly space velocities were calculated to compare the experimental results. The hourly space velocity is indeed widely used in the catalysis literature and is commonly defined as the ratio of the gas feed volume flow rate (measured at standard temperature and pressure) over the catalyst volume or weight. In this paper, the gas hourly space velocity (GHSV; in h -1 ) was defined as the ratio of the total air inlet flow rate at standard conditions over the total volume of the microchannels. It is actually the inverse of the mean residence time. The GHSV ranged from about 18,700 to 201,000 h -1 .

Results and Discussion

The efficiency of the catalytic microreactor for acetone oxidation was studied by obtaining the light-off curves (conversion versus temperature). Experimental points were obtained by increasing the temperature. The reactivity of the system was both established according to the shape of the light-off curves and in terms of T 50 and T 95 , meaning the temperatures at which conversions reach 50 and 95 %, respectively. These parameters were obtained from the light-off curves.

Conversion Calculation

All experiments, whatever the operating parameters, allowed observing that CO 2 was the only reaction product detected. Actually, water was not measured. GPC allowed determining the acetone and carbon dioxide concentrations in the outlet stream, C out and C CO 2 , respectively. The acetone conversion was calculated by following both the VOC disappearance and the CO 2 appearance, and by using the mass balance in relation with the reaction scheme:

H 3 C-CO-CH 3 4O 2 → Pt 3CO 2 3H 2 O
The mass balance on acetone for the reaction, in terms of molar flow, gives:

F in F out F CO 2 =3 (2)
Since the microreactor could be considered as almost isothermal and since the VOC concentrations were very low in the gas stream, the total volume and molar flows were regarded as constant throughout the reactor. Thus, Eq. ( 1) was written in terms of concentrations as:

C in C out C CO 2 =3 (3)
From the measured inlet and outlet concentrations, acetone conversions were calculated according to both outlet acetone concentration (acetone disappearance) and outlet carbon dioxide concentration (CO 2 appearance), i.e. X /Acetone and X /CO 2 , respectively:

X =Acetone 1 À C out C av (4) X =CO 2 C CO 2 =3 C av ( 5
)
where C av was actually the average of the measured inlet acetone concentration. X /Acetone and X /CO 2 should be equal, according to the mass balance. However, as the inlet concentration could undergo variations according to the efficiency of the evaporator, and since the mass balance was verified, the inlet concentration, C in , was calculated using the mass balance (Eq. 3) for each oxidation temperature (experimental points). Thus, the acetone conversion was calculated from Eq. ( 6) avoiding the influence of the inlet concentration variation:

X C in À C out C in (6)

Ignition Curves

Figs. 5678show the conversion of acetone into CO 2 versus oxidation temperature at various inlet concentrations as a function of the space velocity ranging from 18,700 h -1 over 35,000 and 68,000 h -1 to 201,000 h -1 . The figures gather the results of the experiments with similar inlet concentrations. The concentrations given in the legend are the inlet target concentrations, whereas the ones indicated in brackets are the inlet acetone concentrations measured when steady state was established.

Regarding the highest concentration studied (see Fig. 5), acetone oxidation starts from 200 °C, and almost complete conversion (97 %) of acetone into CO 2 is obtained at 350 °C for the 18,700 h -1 space velocity. It must be repeated here that CO 2 and water were the only products formed under the experimental conditions used. No carbon monoxide was detected under any of the experimental conditions. Moreover, it is observed that higher space velocities lead to similar results, although the results tend to underline that the conversion decreases slightly when space velocity rises. The same behavior is observed in Figs. 6 and7 for 4000 and 2000 ppmv inlet concentration. However, in Fig. 7, one observes that the conversion at 350 °C does not exceed 85 and 50 % when the space velocities are 68,000 and 201,000 h -1 , respectively. For the lowest concentration, i.e. 500 ppmv, Fig. 8 displays similar results. Although acetone conversion increases obviously with temperature, it does not exceed 94 % even at 525 °C when GHSV = 68,000 h -1 . Nevertheless, one run (not represented here) at 35,000 h -1 for a nearby concentration, i.e. 615 ppmv, exhibits much higher conversions, more than 90 % at 325 °C and 98 % at 525 °C.

These results can also be compiled with other experiments in terms of temperatures required to reach 50 and 95 % conversions, i.e. T 50 and T 95 , respectively. It can be seen from Fig. 9 that the temperatures required for 50 % conversion do not much depend on the concentration, whatever the inlet concentration and for the two space velocities reported. Whatever the experimental conditions (i.e. concentration and space velocity), T 50 is near 270 °C, although a slight increase is observed when the space velocity increases: T 50 ranges from 260 °C at 18,700 h -1 to near 300 °C at 201,000 h -1 (see Fig. 10). Fig. 10 highlights the expected influence of the space velocity: Oxidation needs higher temperatures to be completed when the space velocity increases. Regarding the temperature required to reach 95 % conversion, Fig. 9 exhibits a different behavior according to space velocity. At 68,000 h -1 , T 95 is not only higher, but also does not depend on the inlet concentration. This could be explained with an apparent first-order pro-cess. However, T 95 obviously decreases at 35,000 h -1 with increasing concentration. This could arise from mass transfer limitations. Indeed, at 35,000 h -1 , the mean residence time is about twice higher than at 68,000 h -1 and a much lower T 95 is reasonably expected whatever the inlet concentration. Thus, a diffusion limitation could explain the higher T 95 observed for the lowest concentration. Further work is in progress to study the influence of the size (depth and width) of the microchannels on the conversion of acetone.

With regard to the literature on catalytic oxidation of acetone over platinum-based catalysts, our results are promising. Gil [17] found complete conversion of acetone at 352 °C using platinum on a clay-based support at a GHSV of about 34,000 h -1 . Regarding low concentrations, Burgos [22] performed oxidation of 225 ppmv acetone over a Pt/Al 2 O 3 /Al monolith at a GHSV of 3680 h -1 . According to the reported ignition curves, T 50 was about 210 °C and complete conversion was reached at 340 °C. These temperatures are obviously lower than those of Fig. 8, even at a lower inlet concentration. However, one must underline that the GHSV values of our study are more than ten times higher than the above-mentioned one. This fact is emphasized by the data obtained by Sharma [23]. The oxidation of acetone at 400 °C using a Pt-loaded hydrophobic catalyst did not yield more than 80 % conversion, with inlet concentrations ranging from 550 to 2350 ppmv and with GHSV values ranging from 3000 to 15,000 h -1 . Moreover, a comparison with the above-mentioned results must be considered with regard to the nature of the catalyst support. Although the catalyst is the same, Pt deposited by the thermal evaporation technique might exhibit a different activity than a Pt-catalyst supported on clay or alumina.

Effect of O 2 Concentration on Acetone Oxidation

In order to evaluate the effect of oxygen, experiments for a given stream flow and concentration were carried out at different oxygen concentrations in the inlet gas stream: 10 and 20 %. The 10 % concentration was obtained by mixing the air stream with a stream of helium (50 % in volume), maintaining the total gas flow rate. The experiments were conducted at 2000 ppmv and at a GHSV of 68,000 h -1 , and the light-off curves were achieved and are presented in Fig. 11. The acetone conversions are slightly higher when the oxygen concentration decreases. The difference is especially obvious between 225 and 300 °C, and T 50 decreases from 275 to 265 °C when the oxygen concentration decreases from 20 to 10 %.

Even if the negative effect of oxygen does not clearly appear from these two experiments, it is in accordance with the literature. Indeed, this effect is commonly observed when VOC catalytic oxidation is performed using a supported Pt catalyst. The catalytic oxidation of methyl-isobutyl-ketone over a Pt/zeolite catalyst exhibits maximum conversion with 8 % oxygen in the feed [24]. This was also reported by Papaefthimiou [START_REF] Papaefthimiou | [END_REF] for the oxidation of butanol with a Pt/c-Al 2 O 3 catalyst, and a kinetic study allowed determining a negative reaction order with respect to oxygen. Although a high oxygen concentration tends to inhibit the reaction, from a process point of view it is preferable to operate the VOC oxidation with air. A catalytic silicon-based microstructured reactor was designed for the treatment of VOC-containing air streams. The design was based on the stacking of silicon microstructured platelets with platinum as the active catalyst phase. The performance of the microreactor for catalytic oxidation of acetone was tested. Ignition curves were determined from acetone disappearance and carbon dioxide formation with increasing temperatures. Outlet stream analysis coupled with mass balance showed that no by-products were obtained. According to inlet acetone concentrations ranging from 500 to 8000 ppmv, the catalytic activity reached more than 95 % conversion, depending on the operating space velocity. The decrease of the inlet concentration and/or the rise of the space velocity resulted in a loss of efficiency, possibly due to diffusion limitations. Moreover, the determination of T 50 and T 95 , the temperatures required to reach 50 and 95 % conversion, respectively, highlighted, under the operating conditions, that T 50 did not much depend on the inlet concentration.

The results showed that the catalytic phase was very active for acetone deep oxidation. The effectiveness of the designed microreactor is promising. However, other relevant experiments should be carried out and added to prove the feasibility of the process and the real efficiency of the microsystem for catalytic oxidation of volatile organic compounds with the aim of small-scale localized air treatment. Investigations are in progress regarding the efficiency of the catalytic microreactor toward the degradation of other VOC.

The authors have declared no conflict of interest. [-] conversion of acetone calculated from carbon dioxide formation X /Acetone [-] conversion of acetone calculated from acetone disappearance

Symbols used

Figure 1 .Figure 2 .

 12 Figure 1. Explosion view of principal elements of the microreactor.

  depth. It is possible to obtain channels of various depths and widths in a reproducible way. In the present paper, only one set of platelets was used (see Tab. 1).

Figure 3 .Figure 4 .

 34 Figure 3. View (scanning electron microscopy) of microchannels obtained by DRIE after Pt deposition.

Figure 5 .

 5 Figure 5. Ignition curves for 8000 ppmv. () 68,000 h -1(8290 ppmv), (D) 35,000 h -1 (8547 ppmv), (᭜) 18,700 h -1 (7787 ppmv).

Figure 6 .

 6 Figure 6. Ignition curves for 4000 ppmv. () 68,000 h -1 (3947 ppmv), (D) 35,000 h -1 (3947 ppmv), (᭜) 18,700 h -1 (3865 ppmv).

Figure 7 .Figure 8 .

 78 Figure 7. Ignition curves for 2000 ppmv. (᭺) 201,000 h -1 (2225 ppmv), () 68,000 h -1 (2198 ppmv), (D) 35,000 h -1 (2213 ppmv).

Figure 9 .Figure 10 .

 910 Figure 9. Temperatures required for 50 and 95 % conversion (T 50 and T 95 ) versus inlet acetone concentration. 35,000 h -1 : (×) T 50 , ( ) T 95 ; 68,000 h -1 : (᭛) T 50 , (᭜) T 95 .

Figure 11 .

 11 Figure 11. Influence of O 2 concentration on ignition curves at 68,000 h -1 . (ᮀ) 10 % O 2 (2198 ppmv), (᭜) 20 % O 2 (2083 ppmv).

Table 1 .

 1 Characteristics of the microreactor.

	S channel [mm 2]	42
	V channel [mm 3]	3
	n	12
	N	300
	S tot [mm 2]	12,600
	V tot [mm 3]	900
	S/V [m 2 /m 3]	14,000

Table 2 .

 2 Operating parameters.

	Air flow range [NL/h]	16.8, 31.2, 61.2, 181.2
	Concentration range [ppmv]	500, 2000, 4000, 8000
	Temperature [°C]	200-550


Romain Delhem

Caroline Marty

Patterns of coining and constructions: the role of productivity

, which are processes used to coin new units based on analogy with an existing one. Unlike constructions, they cannot be considered systematically productive in synchrony. After providing measurement methods, we assess the productivity of three patterns (‧whelm, ‧licious and ‧holic). To do so, we carried out a statistical analysis using two web corpora. Unlike Kay, we show that the difference between constructions and patterns of coining is not so clear-cut, since patterns of coining may undergo constructionalization, and that qualitative aspects should be taken into account along with quantitative data when trying to assess the status of a wordformation pattern.

1.

Introduction

The notion of pattern of coining was first introduced by Fillmore during his lectures at the University of California, Berkeley [START_REF] Fillmore | Construction Grammar Lecture Notes[END_REF], and later developed by Kay at the Second International Conference on Construction Grammar [START_REF] Kay | Patterns of coining[END_REF]. The draft for the conference is the basis for [START_REF] Kay | The Limits of (Construction) Grammar[END_REF].

The notion of pattern of coining is closely related to that of construction. The latter is typically defined as a learned pairing of form and function (Goldberg 2019, 2); it is also entrenched (Bybee 2006, 715) and productive [START_REF] Fillmore | Regularity and Idiomaticity in Regular Constructions: The Case of Let Alone[END_REF]. Patterns of coining, on the other hand, lack full productivity (Kay 2013, 38) and should therefore not be considered constructions. Indeed, while redundant models of Construction Grammar posit that even partially productive patterns can be considered constructions, complete-inheritance models (of which Kay is a proponent) claim that constructions are necessarily fully productive.

Such approaches assume that a grammar (which is made up of a set of constructions) should only contain what is needed "to produce and understand all possible utterances of a given language and no more" (Kay 2013, 32, emphasis in the original).

Patterns of coining, on the other hand, "are neither necessary nor sufficient to produce or interpret any set of expressions of the language" (Kay 2013, 33). In other words, such patterns do license a certain number of expressions, but not systematically; it is therefore impossible to predict the grammaticality of an expression derived from a pattern of coining. In complete-inheritance models, full-fledged constructions and patterns of coining are both unpredictable form-meaning pairings, but they differ with regard to productivity. This notion, however, remains problematic because productivity is a matter of degree [START_REF] Baayen | Corpus Linguistics in Morphology: Morphological Productivity[END_REF].

In this squib, we seek to propose a detailed analysis of the notion of pattern of coining, and, more specifically, to see how it ties in with the notion of productivity. To do so, we first deal with productivity and how it can be measured. We then present the examples of patterns of coining given by [START_REF] Kay | The Limits of (Construction) Grammar[END_REF], as a well as two other patterns that potentially qualify for this categorization (the ‧licious pattern and the ‧holic pattern).

Measures of productivity will be given for each of them. Finally, we discuss the results by raising some questions about the relationship between patterns of coining and constructions in light of their degree of productivity.

Defining productivity

Linguistic productivity has received numerous definitions, mainly involving morphology. Schultink (1961, 113), for instance, defines productivity as "the possibility for language users to coin unintentionally and in principle unlimited number of new formations, by using the morphological procedure that lies behind the form-meaning correspondence of some known words". If such a procedure can readily be used to coin new words, then it can be deemed "available" to speakers (Plag 1999, 34), and it will be productive, in the sense that it will allow for the creation of new forms.

Productivity was thus first defined and measured for morphological patterns, but it was then expanded to encompass syntactic constructions (e.g. Perek 2018). To measure productivity, several methods have been proposed.

Token and type frequency measure the number of instances of the pattern attested and number of different lexemes attested in a given corpus, respectively. Since this paper focuses on word-formation patterns, we will only take into account type frequency.

Indeed, [START_REF] Bybee | Phonology and Language Use[END_REF] notes that the productivity of a morphological process is determined first and foremost by its type frequency. According to [START_REF] Pfänder | Experience Counts: Frequency Effects in Language[END_REF], token frequency can help account for entrenchment only, when type frequency may provide the basis for possible schema formation and generalization. Token frequency is of lesser importance here because what is at stake is not the number of times a type is used by speakers (i.e. its entrenchment), but the number of types that a

given word-formation process may yield (i.e. schema formation). We will therefore favor type frequency (or "realized productivity", Baayen 2009, 6).

These two measures are sometimes used to calculate type-token ratio (TTR), where a higher TTR indicates greater lexical diversity, and indirectly productivity. However, TTR can be problematic for comparisons, because its precision depends on corpus size.

Two measures specifically take into account hapax legomena (tokens that occur only once with some type):

▪ Expanding productivity (Baayen 2009, 7) is the proportion of hapax legomena of the pattern under study among the number of hapax legomena in the corpus.

▪ Potential productivity (Baayen 2009, 7-8) is the proportion of hapax legomena of the pattern among the total number of tokens of the pattern in the corpus.

Using expanding productivity implies having access to the total number of hapax legomena in the corpus, which is hard to obtain for very large corpora. For this reason, we will favor potential productivity.

For the rest of this squib, when measuring productivity, we will therefore use both type frequency and potential productivity, which both shed light on the availability of a word-formation process, but in different ways, as we will see.

3.

Kay's patterns of coining [START_REF] Kay | The Limits of (Construction) Grammar[END_REF] only gives two examples of patterns of coining. The first one is the verb underwhelm, which is the result of a process of reanalysis and analogy based on the preexisting verb overwhelm ⇔ 'X has a strong emotional effect on Y'.

The latter verb was first reanalyzed: its form was recognized as having two components (over + whelm) and one of these components was assigned part of the meaning of the verb. In that case, the part over was associated to the 'strong' part of the meaning in accordance with the conventional metaphor MORE IS UP (Lakoff & Johnson 1980, 15).

This part was then replaced with another semantically close element, in this case its direct antonym under, thus yielding the new verb underwhelm ⇔ 'X has a weak emotional effect on Y'.

So far this pattern of coining has not been very productive. We carried out a statistical analysis on the English Web Corpus 2015 (enTenTen15) to measure the type frequency and the potential productivity of the pattern. After sorting the results manually, we found 15 types and 229,782 tokens. Among these occurrences, 8 of them are hapax legomena. The potential productivity is therefore 0.003%, indicating very low productivity. We note that under is the only prepositional element that has been largely 1 attested in the prefix slot (6,668 tokens in the enTenTen15). Two other prepositions can exceptionally be encountered, but they do not appear in the enTenTen15:

(1)

Since the four prepositions above, over, under and below form a contrast set (Tyler & Evans 2003, 109), it is not surprising that the expressions abovewhelmed and below whelmed can be readily formed and understood in contrast with overwhelmed and underwhelmed. In that case, because of their semantic contrast, one would very probably interpret abovewhelmed as being more intense than overwhelmed, and below whelmed as more intense than underwhelmed.

The pattern [PREPOSITION‧whelm]V is clearly a pattern of coining, because the first slot could not be instantiated by just any preposition (*asidewhelmed, *inwhelmed); besides, if someone actually coined such an expression, it would not be instantly understandable and would probably require a definition. On the other hand, the occasional expressions abovewhelm and below whelm are instantly understandable because they are based on an analogy with two semantically close units.

We use the term preposition with the extended meaning given by Pullum & Huddleston (2002, 598-1 601). Under this terminology, preposition may head nominal elements, but also clausal elements (whereas traditional grammar would call them subordinating conjunctions); they may also have no complement (in which case they correspond to a number of traditional adverbs). 6 a. Are you abovewhelmed at work? Dutifully doing the day-to-day but stressed by the systematic strain of your routine?

b. I was ready to be below whelmed by this book since so many publications on language disappointed me in the past.

The second example of pattern of coining given by Kay is the sequence ‹ ADJECTIVE as NOUN › (e.g. cold as ice), which has mostly lost its comparative meaning to become non-compositional and acquire an intensive meaning ('very X'). From established instances of the sequence, speakers will generalize the pattern as ‹ ADJX as NY › ⇔ 'very X', where the noun is chosen because it denotes a class of entities that typically manifest the quality denoted by the adjective. The pattern is then opened to other adjectives, which in turn select nouns typically associated with the quality the adjective denotes.

According to Kay (2013, 38), ‹ ADJECTIVE as NOUN › is not a construction because its slots cannot be instantiated by any adjective or noun (*heavy as a truck); it therefore has limited productivity. Although this vision is somehow shared by [START_REF] Desagulier | A Lesson from Associative Learning: Asymmetry and Productivity in Multiple-Slot Constructions[END_REF], he

shows that the ‹ ADJECTIVE as NOUN › pattern actually has several productive subschemas (white as NOUN, ADJECTIVE as hell).

From the description of these two patterns of coining by Kay, we provide a tentative a generalization on how patterns of coining work:

(i) The basis of analogy is an established construction which is already part of the construct-i-con of a given language community.

(ii) This construction is reanalyzed: a speaker recognizes a link between part of the form of the construction and part of its meaning.

(iii) Through a process of analogy, one of the components of the reanalyzed construction can be replaced by another element which is formally or semantically close.

(iv) The pattern can be used in a limited way (low type or token frequency) insofar as the linguistic community does not recognize the validity of every potential production.

The different steps of the process can be summed up as follows:

Basis → Reanalysis → Analogy → Limited applicability

If one accepts the notion of pattern of coining, one still has to bear in mind that constructions and patterns of coining are different in nature: the former is a unit while the latter is a completely dynamic process. The unit ‧licious has been analyzed as a libfix by [START_REF] Norde | Nerdalicious scientainment. A network analysis of English libfixes[END_REF]. Libfixes are "'liberated' elements that originate from the reanalysis of existing words" according to [START_REF] Hamans | Contra de linguïstische preutsheid: Over -gate en andere libfixen[END_REF]. Based on this definition, the unit ‧holic could be analyzed as a libfix as well.

Productivity of other potential patterns of coining

Although

The •licious pattern can be found in words such as curvalicious or yummalicious. The use of ‧licious as a libfix became popular in the 2000s with the use of the newly-coined adjective bootylicious, in which ‧licious has been "liberated" from delicious and acquired the status of libfix. The unit ‧licious is added to a noun or an adjective to create a new adjective denoting a quality that is very pleasing to the senses (with the analogy delicious ⇔ 'very pleasant to the taste'). The pleasing experience stems directly from the referent of the base, which can denote inanimate entities (bookilicious), people (hubbylicicous) or body parts (bootylicious).

The ‧holic pattern is based on an analogy with the noun alcoholic ⇔ 'person addicted to alcohol'. Although it is morphologically complex (alcohol + ‧ic), in this sense it is noncompositional: the addiction component cannot be predicted from the affixation of an adjectivizing suffix to a given nominal base. The word was then probably reanalyzed, giving rise to the expression workaholic, whose appearance was traced back to 1947 by the Oxford English Dictionary. Nowadays, the slot in the pattern can be filled by any noun which denotes either a physical entity (e.g. cookieholic, dogaholic) or an activity (e.g. golfaholic, yogaholic); the coined noun serves to denote a person who is addicted to the referent of the first element of the pattern. Diachronic type frequency (Figure 1) shows that the •hood pattern is clearly above the other three, while the •whelm pattern is always very low. This would indicate that type frequency is indeed a good indicator for productivity. The •holic pattern and the •licious pattern saw their type frequency increase from the 1970s and the 1990s on, respectively.

Their type frequency is still nowhere near that of the •hood pattern, however.

Diachronic potential productivity (Figure 2) shows different results: the •hood pattern and the •whelm pattern are very stable over time, while the other two patterns end up being higher than the •hood pattern. This shows that the suffix •hood is used to coin words very regularly, while the •whelm pattern is regular in its unproductivity. On the other hand, there was a surge of interest for the other two patterns, indicated by the larger proportion of hapax legomena among all the tokens of these patterns.

A more synchronic analysis was carried out based on the data from the enTenTen15.

After sorting the results manually, we found 333,575 tokens and 2,519 types of ‧licious words. The potential productivity is 0.5%. As for ‧holic, there are 88,236 tokens and 1822 types, and its potential productivity is 0,01%. These scores can be considered as indicating high productivity, especially when comparing them to the scores for the ‧ whelm pattern, whose potential productivity is only 0.003%.

Discussion

The quantitative results shown in the previous section show that type frequency and potential productivity are two good indicators for productivity, but yield different results:

▪ Type frequency reflects to what extent a given pattern can be used to coin a large number of units;

▪ Potential productivity, used diachronically, indicates tendencies, i.e. whether a pattern is stable in coining new words (or not), or whether it shows significant variation, indicating a sudden (dis)interest for this pattern.

Although the •holic and the •licious patterns seem to behave similarly from a quantitative point of view, they differ in the way their meaning combines with the meaning of other units. The •holic pattern yields transparent combinations: given a noun with denotation X and the [NOUN•holic]N pattern, the resulting unit X•holic can be interpreted directly as 'person addicted to X'. The •licious pattern, on the other hand, is slightly more complex, as there appears to be several meanings attached to it. We singled out three main senses to the pattern.

▪ It can refer to a nice feeling stemming from the referent of the base, which is present in the situation. For example, bagelicious refers to the pleasant feeling one experiences as they eat a bagel (whose taste properties are the origin of the pleasurable sensation).

▪ It may denote a pleasant feeling that is related to the referent of the base, but not originating from an actualized experience. Someone can experience a summerlicious moment without it necessarily being summer when they speak:

the situation will just have properties usually associated with summer.

▪ Finally, the [ADJECTIVE•licious] subpattern may yield lexemes in which the libfix denotes high degree (e.g. fabilicious 'absolutely fabulous') or a conjunction of two qualities (e.g. frugalicious 'both frugal and delicious').

The status of a given linguistic unit (construction or pattern of coining) should therefore not be based solely on quantitative measures of productivity. Qualitative features like semantics must also be considered.

Indeed, in enTenTen15, the •licious patterns yields a greater number of types than the

•holic pattern (2,519 vs 1,822) and its potential productivity is higher (0.5% vs 0.01%).

However, from a qualitative point of view, the •holic pattern seems to coin units in a more stable, systematic way. The •licious pattern, on the other hand, yields lexemes which may not be as easily understandable: terriblicious could mean 'both terrible and delicious' or 'absolutely terrible'. Therefore, from a qualitative perspective, •holic appears to be a better candidate to constructional status. The fact that •licious has a higher potential productivity than •holic may be accounted for from a diachronic perspective: the former is more recent than the latter. vs 10,582). Therefore, the •holic pattern without its original lexeme is quantitatively more entrenched than the •licious pattern without its original lexeme.

To sum up, even though •licious does show higher productivity figures, it does not appear as diachronically stable and semantically coherent as •holic. In this regard, in spite of the purely quantitative data, the •holic pattern appears to be more likely to be categorized not as a pattern of coining, but as construction.

According to Kay, patterns that are not fully productive do not qualify as constructions.

Since productivity is a matter of degree and can change over time, something that was considered a mere pattern of coining can, as time goes by, come to be thought of as a construction. This may therefore be the case of the ‧holic pattern. This would mean that patterns of coining may have an optional final step consisting in the emergence of an independent construction. This step can thus be added to those already given in section 3:

This analysis also accounts for the fact that •licious has a higher potential productivity than •hood, which (v) If the pattern used to coin new expressions is used more frequently and with more elements, it may become a full-fledged construction which speakers can use independently, without relying on another existing construction to interpret it.

If we add this potential final step, the full evolution of a pattern of coining can be summed up as follows:

Basis → Reanalysis → Analogy → Limited applicability → Construction This means, conversely, that a given construction may be the end product of the evolution of a pattern of coining. In that case patterns of coining could constitute a kind of lexical constructionalization, where innovation through analogy may lead to the creation of a new form-meaning pairing. Therefore, a one-off utterance that was first assembled "on the fly" (Cappelle 2014) may well become part of the lexicon and even yield a fully productive morphological word formation process.

Conclusion

Within complete-inheritance models, the only relevant criterion to distinguish constructions from patterns of coining is productivity. If the slots of a given pattern can be filled systematically, then the pattern is a construction; if not, it is merely a pattern of coining. Productivity, however, is a matter of degree: some patterns (e.g. More qualitative criteria should also be considered. Some patterns yield transparent combinations (e.g. [NOUN•holic]N) while others are semantically more complex (e.g.

[X•licious]A). Because of this, the •holic pattern seems closer to constructional status than the •licious pattern, despite higher productivity indicators in the recent years for the latter.

Consequently, there seems to be a gradient between clearly unproductive patterns of coining, patterns of coining under constructionalization and fully constructionalized patterns of coining. Precisely because of the dynamic nature of language, completeinheritance models should take into account the fact that patterns of coining, in some cases, are transitions between nonce expressions and full-fledged constructions.

  Kay only gave two examples of patterns of coining, their characteristics can be applied to other patterns that enable speakers to coin new words through reanalysis and analogy. Two of these potential patterns are [X•licious]A and [NOUN•holic]powder and semi-sweet chocolate give this chocolicious ice cream extra flavor […]. (enTenTen15) b. Jorge is an avid golfer and travelholic who enjoys reading, problem solving, and history. (enTenTen15)

  The libfix status of •licious and •holic[START_REF] Hamans | Contra de linguïstische preutsheid: Over -gate en andere libfixen[END_REF] does not indicate whether [X•licious]A and [NOUN•holic]N are full-fledged constructions or patterns of coining, although libfixes and patterns of coining both rely on reanalysis. To determine this, one has to measure their productivity, since it is the basis of Kay's definition. We therefore calculated the type frequency and the potential productivity of these patterns from a diachronic point of view by relying on data from the COHA (Corpus of Historical American English). Two other patterns were used as reference points:▪ [PREPOSITION•whelm]v,which is a good candidate to the status of pattern of coining;▪ [NOUN•hood]N, which intuitively seems highly productive and which would certainly be deemed a construction.

Figure 1 .Figure 2 .

 12 Figure 1. Type frequency of several morphological pattern based on data from the COHA.

  [NOUN•holic]N) lie somewhere between established construction ([NOUN•hood]N) and patterns of coining ([PREPOSITION•whelm]v).

  It thus seems logical that it should yield a greater number of new, one-off formations in 2015 . 1%) for the •holic pattern. If we study token frequency numbers without delicious on the one hand and alcoholic on the other, •holic has a higher token frequency(13,119

	2
	Moreover, even if •licious has a greater number of tokens, among the 333,275 results,
	322,993 of them are delicious (96.8%), while there are only 75,117 alcoholic tokens
	(85,

is older and more stable over time.

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