Samuel Marre

Arnaud Erriguible

Arturo Perdomo

François Cansell

Frederic Marias

Cyril Aymonier
email: aymonier@icmcb-bordeaux.cnrs.fr.

Francois Cansell

Kinetically controlled formation of supported nanoparticles in low temperature supercritical media for the development of advanced nanostructured materials

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Progress in nanotechnology toward the fabrication of nanodevices now requires the assembly of materials at length scaling from a few nanometers up to thousands of nanometers. This concept allows the development of advanced nanostructured materials, which have attracted wide interest in view of the new properties that can be developed, taking advantage of the association of several materials at the nanometer scale (quantum confinement or high surface to volume ratio). 1 In this purpose, more and more studies are nowadays focused on the control of materials properties via modification of their surface. [START_REF] Rieter | [END_REF] A particularly interesting challenge stands in combining properties of materials at different scales (from bulk properties down to size-dependent properties) via the deposition of nano-objects with controlled size and shape on surfaces of bulk materials (supported nanoparticles). These supported nanoparticles can present tremendous interests for catalytic applications for example. 3 Such structures can be obtained from conventional dry methods 4 or wet chemistries. 5 However, these processes generally require either high temperature syntheses or posttreatments like purification and drying steps, without ensuring good control on size and size distributions of the obtained nanomaterials. As an alternative, chemistry in supercritical fluids (SCFs) is of great interest as these media have unique tuneable properties intermediate between gas and liquid, which can be adjusted continuously by modulating temperature and/or pressure. 6 Supercritical fluids have been successfully used to deposit either organic [7][8][9][10][11] or inorganic 12-16 materials. For example, high quality metallic films were deposited using supercritical fluid chemical deposition (SFCD) either on planar substrates, 17 particles, 14 or inside nanoporous templates. 18 The formation of surface nanostructures is achieved through the chemical transformation of metal-organic precursors in supercritical mixtures. The main interest of supercritical fluids is that high nucleation rates can be reached, compared with liquid phase syntheses, leading to narrow size distribution nanoparticles. 19 Previous works have been reported on supported nanoparticles synthesis like gold, 20 platinum, 21 ruthenium, 22 or copper ones. 13 Authors have previously described a thermodynamic way to achieve control of the size. 21,23 Depending on the conditions in use, it is possible to tune the amount of metal-organic precursors adsorbed onto the surface of carbon nanotubes, or carbon aerogels, prior to their reduction. The transformation of this absorbed precursor by different ways (chemical reduction in a supercritical fluid with a reducing agent, chemical reduction with pure hydrogen at elevated temperature, thermal reduction in a supercritical fluid, thermal decomposition in an inert atmosphere, or chemical conversion with hydrogen or air at atmospheric pressure) is conducive to the formation of size controlled nanoparticles.

Another way to control the size of the deposited nano-objects includes controlling the kinetics of the precursor transformation. To achieve such a precise control, one can play not only on several operating parameters like temperature and residence time but also on the composition of reacting media. In the case of SFCD, supercritical CO 2 (scCO 2 ) is generally used as the main solvent, due to its low critical coordinates (T c ) 31.1 °C, P c ) 7.38 MPa). Most of the time, a cosolvent is added in order to improve the solubility of the precursor as well as to increase the overall density of the supercritical mixture. The nature of this cosolvent can strongly influence the kinetics of the metalorganic precursor transformation, as already shown in chemical vapor deposition processes. Indeed, it was reported that the use of alcohol cosolvents for reducing copper hexafluoroacetylacetonate hydrate Cu(hfac) 2 • H 2 O with hydrogen 24,25 allows dramatic increases of the copper deposition rate.

In supercritical media, this effect was reported for the addition of ethanol (EtOH), allowing decreasing the decomposition temperature of roughly 30 °C. 26 In addition, other papers highlight that the use of hydrogen, added to this mixture as reducing agent, allows a softer chemical reaction, limiting the contamination of the deposited material by organic byproducts from the precursor. 27 We also demonstrated in a previous study that the reduction of Cu(hfac) 2 • H 2 O in a supercritical CO 2 / isopropanol/H 2 mixture in presence of silica spheres could lead to the formation of supported copper nanoparticles at relatively low temperature, with the size being controlled by tuning temperature and/or residence time, 13 demonstrating that the knowledge of the reaction kinetics is a key parameter.

On the basis of these considerations, this paper presents a kinetic way for controlling the size of supported metal nanoparticles. Starting from the literature results in vapor phase and in connection with the surface decoration process of silica spheres with nanoparticles, we have investigated the reduction kinetics of Cu(hfac) 2 • H 2 O with H 2 in supercritical CO 2 -alcohol media, successively using methanol (MeOH), ethanol (EtOH), and isopropanol (iPrOH). The kinetics were determined for low temperatures in the range 100-150 °C and residence time up to 120 min, at pressures ranging from 20 to 22 MPa. We report also in this paper for the first time on a model to predict the size of supported metal nanoparticles as a function of residence time and temperature.

Experimental Section

The reduction kinetics of Cu(hfac) 2 • H 2 O with H 2 in supercritical CO 2 /alcohol mixtures were determined by proportioning the remaining precursor after the reaction took place in a high pressure/high temperature experimental setup reported in Figure 1.

In a typical experiment, a high pressure high temperature stirred reactor of 50 cm 3 (1, Figure 1) is first loaded with an alcohol solution containing the precursor (0.05 mmol of Cu(hfac) 2 • H 2 O in 0.05 mol of alcohol). It is thereafter pressurized with hydrogen (0.05 mol) and CO 2 (0.8 mol), using a feeding system composed of a chiller and a high pressure pump. The final molar composition of the reaction medium is CO 2 / alcohol ) 95/5 (initial pressure is 9 MPa at T ) 25 °C). The mixture is stirred and heated to the desired conditions (100 °C < T < 150 °C) using an external heating element surrounding the reactor (2, Figure 1). A pressure sensor and a thermocouple, placed inside the reactor, allow following the experimental conditions. After a given residence time, the reactor is depressurized and the alcohol solution containing the remaining precursor is recovered for proportioning using UV-visible spectroscopy (Cary 1C UV-visible spectrophotometer apparatus). Cu(hfac) 2 • H 2 O, methanol, ethanol, and isopropanol were purchased from Aldrich. CO 2 and H 2 were purchased from Air liquide and used as received.

The supercritical coordinates of the CO 2 /alcohol mixtures versus the molar percentage of CO 2 were estimated by the equation of state (EoS) of Peng-Robinson (Figure 2). One can see that in the studied conditions (i.e., mixtures CO 2 /alcohol: 95/5 molar, 100 °C < T < 150 °C and 20 MPa < P < 22 MPa), all three mixtures are under supercritical conditions.

The addition of H 2 can modify the critical coordinates of the system. 28 Taking into account these considerations, we have checked visually that the ternary mixtures CO 2 /alcohol/H 2 were supercritical in the studied conditions by running experiments in a sapphire high pressure/high temperature reactor.

Preliminary UV-visible measurements were realized for each alcohol in order to determine the characteristic absorption band allowing following the precursor's concentration. As an example, Figure 3 presents UV-visible spectrum of Cu(hfac) 2 • H 2 O in isopropanol for λ ranging from 210 to 360 nm after a chemical reduction was performed at 150 °C at different residence times. The two bands are attributed to ligand (π, π*) transitions (λ ) 307 nm with a shoulder at λ ) 325 nm) and charge transfer between the ligand and the metallic center (λ ) 227 nm), respectively. 29 By using a master curve verifying the Beer-Lambert's law, the concentrations were determined.

Several tests were performed with the different systems by varying the temperature (100-150 °C) and the residence time (0-120 min) in order to determine the reduction kinetics. The synthesis of silica-supported copper nanoparticles was performed for temperatures ranging from 100 to 125 °C by adding silica spheres in the reaction media. The mean sizes of the obtained copper nanoparticles were measured from TEM pictures. All of these data were integrated in a model developed to predict the evolution of the size of metal nanoparticles in the surface nanostructuration process.

Results and Discussion

Reduction Kinetics of Cu(hfac) 2 • H 2 O with H 2 in CO 2 /

Alcohol Supercritical Media. From a general point of view, the reduction of Cu(hfac) 2 • H 2 O to metal copper can be written as Since both alcohol and H 2 are in large excess compared with the precursor (molar ratio ) 10 3 ), the order of the reaction with respect to these reactants is 0. The kinetics of disappearance of Cu(hfac) 2 • H 2 O is given by eq 2:

where k 0 is a constant, R is the perfect gas constant (8,314

J • K -1 • mol -1
), E a is the activation energy of the reaction (in J • mol -1 ) and k app is the appearing kinetic constant. From this equation, the k app were determined at different temperatures. The proportioning of the precursor at the end of the experiment allows determining the conversion rate, defined as:

The conversion rates obtained within the framework of the study are reported in Figure 4.

These results were treated assuming a first order with respect to the precursor concentration. By integrating eq 2, we obtain Replacing the concentrations ratio by the conversion rate, it gives For each temperature and each alcohol cosolvent, Ln(1 -CR) was plotted as a function of the residence time (Figure 5).

These plots give straight lines, confirming the assumption of a first order reaction. The slopes correspond to the values of the rate constants, k app , the values of which are presented in Table 1.

Depending on the alcohol used as cosolvent, the values of the rate constant can be tuned in the range 2 • 10 -4 min -1 -3.2 • 10 -2 min -1 for low temperature ranging from 100 to 150 °C.

Using the obtained values of k app , we can determine the activation energy of the reaction E a , for each alcohol, by plotting the Napierian logarithm of k app as a function of (1000)/(RT) (Figure 6).

The activation energy required to reduce Cu(hfac) 2 • H 2 O is lower when MeOH is used as cosolvent (69 kJ • mol -1 ) compared with EtOH or iPrOH (80 kJ • mol -1 and 104 kJ • mol -1 , respectively; Figure 6), showing that the nature of the alcohol strongly influences the value of the kinetics constant. First, the use of MeOH as cosolvent leads to larger values of k app than EtOH or iPrOH (Table 1). One can also notice that the use of isopropanol, despite the low obtained kinetics (10 -4 min -1 < k app < 10 -2 min -1 ), allows tuning the value of the kinetics constant over 2 orders of magnitude by adjusting the temperature in the range 100-150 °C, allowing obtaining a precise control over the reduction of Cu(hfac

) 2 • H 2 O.
The variations of the copper deposition rate as a function of the alcohol used to assist the reduction of the precursor (iPrOH, EtOH, or MeOH) were reported equally in the case of the vapor phase processes. However, iPrOH leads to higher deposition rate than MeOH or EtOH. 30 The authors assume that this behavior is due to the pK a value of these alcohols in water (pK a iPrOH ) 17.1, pK a EtOH ) 15.8, pK a MeOH ) 15.3), which depends directly on the ability of the alcohol to liberate a hydrogen atom and to assist the reduction. However, it has been shown that the tert-butanol, which should be even more efficient than the iPrOH, does not lead to higher copper deposition rate, since it is not able to complex the precursor, due to steric hindrance. Thus, according to these results, two main parameters have to be taken into account to choose the more efficient alcohol to assist the reduction of Cu(hfac) 2 • H 2 O. First, the alcohol has to be able to complex the precursor (sterically compatible). Then, the easier it is for the alcohol to liberate a hydrogen atom, the more efficient it will be to assist the reduction.

Cu(hfac) 2 • H 2 O + H 2 + R-OH f Cu (0) +H 2 O + 2 H-hfac + R-OH (1) d[Cu(hfac) 2 • H 2 O] dt ) -k 0 exp ( -E a RT ) • [Cu(hfac) 2 • H 2 O] a with k app ) -k 0 exp ( -E a RT ) (2) conversion rate (CR) ) 1 - [Cu(hfac) 2 • H 2 O] t [Cu(hfac) 2 • H 2 O] t)0 (3) Ln([Cu(hfac) 2 • H 2 O]) ) Ln([Cu(hfac) 2 • H 2 O] t)0 ) -k app • t (4) Ln(1 -CR) ) -k app • t ( 5
)
These results and considerations are in contradiction with the kinetics that have been obtained in this study, using supercritical CO 2 /alcohol mixtures. Thus, the reduction mechanisms proposed for the vapor phase reduction of Cu(hfac) 2 • H 2 O by H 2 in presence of an alcohol are not valid anymore in supercritical media, mostly due to the presence of CO 2 . To explain this behavior, it is required to study the interaction that can be developed inside the reaction media, in particular due to the presence of CO 2 molecules that constitute the main solvent. IR spectroscopy studies that were realized for supercritical CO 2 / EtOH mixtures have shown that the alcohol molecules can interact with the CO 2 molecules. 31 Acceptor/donor bonds are created between the oxygen atom of the alcohol (which owns a negative charge: δ -) and the carbon atom of the CO 2 molecule (which owns a positive charge: δ + ), as shown in Figure 7.

This mechanism was observed for all of the three alcohols studied in this work (MeOH, EtOH, and iPrOH). The complex that is mainly formed in our conditions (molar ratio CO 2 /alcohol 95/5) is made of one CO 2 molecule for one alcohol molecule; however, some alcohol dimers have also been observed. [START_REF] Fulton | Supercritical fluid engineering science: Fundamental and applications[END_REF] This complexation leads to a modification of the alcohol reactivity. First, it induces a steric hindrance surrounding the alcohol function, which will vary depending on the nature of the alcohol, so that it might not complex the copper precursor in the same way. Then, the charge distribution around the oxygen atom will vary inducing a modification of the hydrogen lability. These two phenomena can explain the different behaviors observed in vapor phase deposition and in supercritical fluid chemical deposition.

Starting from these results, we have chosen to use CO 2 /iPrOH supercritical mixtures to decorate the surface of silica spheres with copper nanoparticles by reducing Cu(hfac

) 2 • H 2 O with H 2 .
This choice is supported by the fact that iPrOH, as a cosolvent, allows tuning the value of the kinetics constant over 2 orders of magnitude by adjusting the temperature in the range 100-150 °C. This mastering of the kinetics allows controlling precisely the nucleation rate, which is an important parameter for the design of supported nanostructures.

Synthesis of Silica Spheres Decorated with Copper

Nanoparticles at Low Temperature. On the basis of the results obtained from the kinetics measurements, silica spheres (170 and 550 nm in diameter) dispersed in the reactive media were decorated by copper nanoparticles by reducing Cu(hfac) 2 • H 2 0 with H 2 in supercritical CO 2 /iPrOH mixtures molar) by varying temperature and residence time.

Figure 8a presents a typical TEM picture of silica@nanoCu nanocomposite. The copper nanoparticles have a conventional spherical shape corresponding to the minimization of the surface energy and form a monolayer on the surface of the silica spheres (Figure 8b).

In order to quantify the influence of the reduction kinetics of the precursor on the eventual size of the supported nanoparticles, copper nanoparticles were deposited on 170 nm silica particles (for better visualization), and their sizes were measured from TEM pictures by manual counting (Figure 8c). The change in size for the silica spheres does not affect the sizes of the copper nanoparticles; however, lower rates of coverage of the surface were observed because of higher available specific surface area for the smaller silica spheres. The results and experimental conditions are summarized in Table 2. The fluid properties were estimated either using the Reichenberg correlation, which is known to be valid for the high pressure fluids (for viscosity) or using the EoS of Peng-Robinson (for the density).

By tuning temperature (100-125 °C) and/or residence time (60-120 min), we are able to tune the size of the copper nanoparticles (d avg ) from 5 to 17 nm, as shown in Table 2. As an example, Figure 9a-c shows the effect of temperature on the size of copper nanoparticles synthesized at R t ) 120 min, T ) 100, 115, and 125 °C, respectively.

The evolution of d avg as a function of R t and T for the obtained copper nanoparticles can be directly linked to the values of the kinetics constants, showing a kinetically controlled formation of the supported nanoparticles.

According to these experimental results, we have developed a model to describe the surface decoration of materials by metal nanoparticles.

Modeling of the Deposition Process. The Bimodal

Model. In a general way, the evolution of a particle size distribution can be described by a partial differential equation named the aerosol general dynamic equation. [START_REF] Frieldlander | Dust, and Haze[END_REF] This equation is used for simultaneous aerosol nucleation, condensation, coalescence, and coagulation. Different methods are usually used to solve this kind of equation. First, the sectional method, with either fixed or moved sections [START_REF] Hounslow | [END_REF] is very efficient but the computational time is important. Then, the method of moments, 35 assuming that the shape of the distribution is log-normal or monodisperse, allows simplifying the partial differential equation into a set of ordinary differential equations preserving the most important information about the process and for a computational time much shorter than the sectional methods. A simple monodisperse model derived from the moment method 36 has been proposed to predict particle size distribution. The phenomena taken into account for the growth of particles were coalescence and aggregation. The results fit well with those obtained by the rigorous sectional method. This model was successfully applied to material synthesis in high temperature gases, 37 as well as to the synthesis of metal nanoparticles in supercritical fluids with instantaneous precursor decomposition. 38 However, for nonsimultaneous precursor decomposition, as discussed in this paper, this monodisperse model leads to erroneous results for the particle size distribution.

In this context, we have used a bimodal model 39 to predict the evolution of the mean size of the supported copper nanoparticles as a function of R t and T. This model takes into account the coalescence and the aggregation mechanisms and is well suited in the case of very low precursor decomposition rates. The bimodal model is in very good agreement with the complete sectional model and requires the same level of computation time that the simple monodisperse model. This model is composed of two discrete monodisperse modes used to represent the particle size distribution: a size fixed nucleation mode (mode 1) and a moving accumulation mode (mode 2; Figure 10). The size fixed nucleation mode accounts for the introduction of newly generated particles (i.e., the generation of nuclei due to the precursor decomposition), and the moving The governing equation for N 1 is given by where β 11 and β 12 represent respectively the intramode coagulation kernel in mode 1 and the intermode coagulation kernel between modes 1 and 2. The rate of particle formation I, depending on precursor's reduction kinetics, is calculated by the relation with N a the Avogadro number, m p and M p the mass of the precursor and the molar mass of the precursor, respectively, and k app the constant kinetic estimated in the previous section.

In the same way, the evolution of N 2 and V 2 is given by the following equations:

where β 22 represents the intramode coagulation in mode 2.

The particle surface area concentration of mode 2 A 2 increases by intermode coagulation and decreases by intramode coagulation in mode 1 and by coalescence (third term on the righthand side), so the evolution of A 2 is given by where τ f is the characteristic sintering time and a 2s is the surface area of the completely fused (spherical) aggregate consisting of 2 particles. Note that only the particles in mode 2 are affected by coalescence; indeed, the particles in mode 1 are assumed to be spherical with a constant volume V 0 .

Definition of Parameters. For each aggregate in modes 1 and 2, the volume and surface area are described by the relations

1 dt ) - 1 2 β 11 N 1 2 ( r r -1 ) -β 12 N 1 N 2 + I (6) I ) N a m p M p k app exp(-k app t) ( 7
)
dN 2 dt ) - 1 2 β 11 N 1 2 ( 1 r -1 ) -1 2 β 22 N 2 N 2 ( 8
)
dV 2 dt ) - 1 2 β 11 N 1 2 ( r r -1 ) V 0 + β 12 N 1 N 2 V 0 (9) dA 2 dt ) - 1 2 β 11 N 1 2 ( r r -1 ) a 0 + β 12 N 1 N 2 a 0 -1 τ f (A 2 -N 2 a 2s ) (10) V 2 ) N 2 V 2 , A 2 ) N 2 a 2 ( 11
)
accumulation mode characterizes the particle growth by coagulation and coalescence. The model allows the description of the particle size evolution by the variation of four variables: the nuclei volume concentration of mode 1 N 1 , the particle volume concentration of mode 2 N 2 , the volumetric concentration of the aggregates V 2 , and the particle surface area concentration of mode 2 A 2 . In the model, the average volume of mode 2 is r times larger than V 0 , and r increases following the growth of aggregate particles by coagulation and coalescence. The volume of the nuclei in mode 1 V 0 is assumed to be constant and fixed to the volume of a copper atom. The obtaining of the following set of eqs 6-9 is detailed elsewhere. 38 with V 0 and a 0 the fixed volume and surface area of the monomer, respectively. V 2 and a 2 are the volume and surface area of the aggregate, respectively.

The primary particle size d p2 and the number of primary particles n p2 in an aggregate are defined by

The surface area of the completely fused (spherical) aggregate a 2s consisting of two particles is calculated by Coagulation Kernel. For the calculation of the coagulation kernel in mode 2, the collision diameter d c2 is preferred to the primary particle diameter d p2 in order to take into account the fractal-like aggregates (i.e., nonspherical aggregates). The collisions radius is defined by 40 with D f the fractal dimension. The value of the fractal dimension is generally fixed to 1.8 for cluster-cluster aggregation in the free molecule and continuum regime. 21,41 The collision radius in mode 1 is the particle diameter (d c1 ) d p1 ).

The collisions diameter is used to replace the solid sphere radius in the Fuchs interpolation expression for Brownian coagulation in the free molecule and continuum regimes. [START_REF] Seinfeld | Atmospheric Chemistry and Physics of Air Pollution[END_REF] So, the collision frequency is given by the relation where the particle diffusion coefficient D i is calculated from the Stokes-Einstein expression with a Cunningham slip correction factor: [START_REF] Phillips | [END_REF] with the Knudsen number Kn i as the ratio of the mean free path in the fluid λ g over the particle radius diameter d pi defined by where F f , μ f , and M f are respectively the density, the viscosity, and the molar mass of the fluid.

The mean particle speed c 12 and the transition parameter g 12 are given by where l i is the particle mean free path defined by, Characteristic Sintering Time. The characteristic coalescence time is an important parameter. For nanomaterials, the coalescence process is highly influenced by the particle size and the temperature. As discussed elsewhere, [START_REF] Johannessen | Synthesis of nano-particles in flames[END_REF] the dominant coalescence mechanism which prevails for nanoparticles seems to be the surface diffusion. The coalescence time for surface diffusion can be estimated by [START_REF] Lehtinen | Theoretical studies on aerosol agglomeration processes[END_REF] with where D s is the surface diffusion coefficient, σ is the surface tension, and δ is the surface layer thickness. Unfortunately, the estimation of the physical parameters, for the range of nanomaterials, is very difficult.

Another approach is to use the experimental data with the simulation in order to adjust the coalescence parameters. We propose to define the characteristic coalescence time by the expression

The pre-exponential term k 0 and the activation energy E a were estimated previously 38 for copper materials synthesis considering an instantaneous decomposition of the precursor: Simulation. The model was compared to the experimental results concerning the formation of metal copper particles on the surface of silica spheres in supercritical CO 2 /iPrOH mixture (90/5 molar ratio; from Table 2). Additional data concerning copper (i.e., M(Cu(hfac) 2 • H 2 O ) 495.6 g • mol -1 , M(Cu) ) 63.5 g • mol -1 , F(Cu) ) 8.9 g • mL -1 , diameter of a copper atom ) 2.8 Å) were obtained from literature to make the calculation. The resolution of the system (eqs 6-9) is achieved with the RADAU5 subroutine (Implicit Runge-Kutta method of order 5), developed by Hairer, [START_REF] Hairer | Springer Series in Comput. Mathematics[END_REF] which is particularly well-suited for the stiff problem.

V 1 ) N 1 V 0 , A 1 ) N 1 a 0 (12) d p2 ) 6V 2 A 2 (13) n p2 ) 6V 2 πd p2 3 ( 14
)
a 2s ) π2 2/3 d p 2 ( 15
)
d c2 ) d p2 ( V 2 V p2 ) 1/D f ) d p2 (n p2 ) 1/D f ) 3V 2 a 2 ( a 2 3 36πV 2 2 ) 1/D f (16) β ij ) 2π(D i + D j )(d ci + d cj ) [ d ci + d cj d ci + d cj + 2g ij + 8(D i + D j ) c ij (d ci + d cj ) ] -1 (
) D i ) k b T 3πμ f d ci [ 5 + 4Kn i + 6Kn i 2 + 18Kn i 3 5 -Kn i + (8 + π)Kn i 2 ] for i ) 1,2 17
Kn i ) 2λ f d ci ) 2 d ci ( π F f πM f 2RT ) for i ) 1,2 (19) c 12 ) (c 1 2 + c 2 2 ) 1/2 c i ) 8k b T πF p V i for i ) 1, 2 (18)
g 12 ) (g 1 2 + g 2 2 ) 1/2 g i ) 1 3d ci l i [(d ci + l i ) 3 -(d ci 2 + l 2 ) 3/2 ] -d ci for i ) 1, 2 (20)
l i ) 8D i πc i (22) τ ) r p 4 b(T) (23) b(T) ) 225δD s σM F p RT (24) τ ) k 0 r p 4 T T 0 exp ( E a R ( 1 T - 1 T 0 )) (21)
Figure 11 represents the evolution of the primary copper particle size as a function of residence time and temperature.

A good agreement is obtained between experimental and calculated primary particle size for the model including both the coalescence and the aggregation mechanisms taken into account. The proposed mechanism for the silica sphere decoration process (i.e., homogeneous nucleation followed by heterogeneous growth) is confirmed in the studied conditions. However, it might not be suitable anymore for unexplored conditions, in particular, for temperatures above 150-175 °C, where there is a competition between two decomposition processes of the precursor (reduction by H 2 /alcohol and thermolysis). This would indeed change the decomposition kinetics and thus the parameters of the model.

In the studied conditions, the first mode (homogeneous nucleation in the reaction media) is the limiting step of the process, which control the number of nuclei released in the reaction media. Since this is directly dependent on the precursor transformation kinetics, these model results clearly show the surface decoration of materials is a kinetically controlled process.

Conclusion

We have demonstrated the alcohol-assisted decoration of silica spheres by copper nanoparticles with a kinetic control of the copper nanoparticle size. This is achieved at low temperature (100-125 °C) using isopropanol as cosolvent, which allows tuning the reduction kinetics of the precursor over 2 orders of magnitude (k ) 2.2 • 10 -4 min -1 -1.1 • 10 -2 min -1 ) compared with using methanol or ethanol. A bimodal model was used to predict the size of the obtained copper nanoparticles. This takes into account both the introduction of newly generated nuclei from the precursor decomposition and the particle growth on the surface of the silica spheres by coagulation and coalescence. This model, developed for low temperature decomposition of the precursor, fits well with the experimental data obtained and can be applied to other kinds of material nanostructurations. This work demonstrates a new way for controling the size of supported nanoparticles, which is an important parameter for applications like catalysis, where the specific surface is a critical factor.

Figure 1 .

 1 Figure 1. Experimental setup: (1) high pressure/high temperature stirred reactor, (2) heating element.

Figure 2 .

 2 Figure 2. Evolution of the critical coordinates of CO 2 /alcohol mixtures as a function of the molar percentage of CO 2 obtained with the PHOPHY software, using the EoS of Peng-Robinson.

Figure 3 .

 3 Figure 3. UV-visible absorption spectrum of Cu(hfac) 2 • H 2 O in isopropanol after reduction at 150 °C for residence times ranging from 0 to 120 min.

Figure 4 .

 4 Figure 4. Conversion rates (CR, in %) of Cu(hfac) 2 • H 2 O, obtained for the different tests using methanol, ethanol, or isopropanol as cosolvent. Note that CR was not determined for iPrOH at T ) 100 °C, R t ) 30 and 60 min, due to very low values.

Figure 5 .

 5 Figure 5. Ln(1 -CR) as a function of the residence time for the reductions performed using successively methanol, ethanol, and isopropanol as cosolvent at different temperatures.

Figure 6 .

 6 Figure 6. Evolution of the Napierian logarithm of k app as a function of 1000/RT and deduced value of the activation energy for each of the three alcohols.

Figure 7 .

 7 Figure 7. Representation of the donor-acceptor interaction between a CO 2 and an ethanol molecule.

Figure 8 .

 8 Figure 8. (a) TEM pictures of a 500 nm silica sphere decorated by copper nanoparticles using the reduction of Cu(hfac) 2 • H 2 O with H 2 in supercritical CO 2 /iPrOH media. (b) Enlargement of a. (c) TEM pictures of a 170 nm silica sphere decorated by copper nanoparticles.

TABLE 2 :

 2 Experimental Conditions and Mean Diameter of the Copper Nanoparticles Measured from TEM Pictures μ f c ) 3.33.10 -5 Pa • s 120 9 ( 5 F f d ) 525 kg • m -3 μ f ) 3.49.10 -5 Pa • s 120 16 ( 6 F f ) 498 kg • m -3 μ f ) 3.5.10 -5 Pa • s 120 17 ( 5 F f ) 460 kg • m -3 a R t is the residence time. b m precursor is the weigth of Cu(hfac) 2 • H 2 0 introduced in the reaction media. c μ f is the viscosity of the media. d F f is the density of the media.

Figure 9 .

 9 Figure 9. Silica particles decorated with copper nanoparticles at R t ) 120 min and T ) 100 °C (a), T ) 115 °C (b), and T ) 125 °C (c).

Figure 10 .

 10 Figure 10. Schematic representation of the two modes of the bimodal model developed to predict the size of supported nanoparticles.

  dN

k 0 ) 11 ( 5 •

 115 10 31 m -4 s E a ) 20 ( 5 kJ • mol -1

Figure 11 .

 11 Figure 11. Evolution of copper primary particle size versus residence time.

TABLE 1 : Kinetics Constants of the Reduction of Cu(hfac) 2 • H 2 O with H 2 in Supercritical CO 2 /Alcohol Media at Different Temperatures

 1

		MeOH	EtOH	iPrOH
	100	2.2 ( 0.1	1.1 ( 0.3	0.2 ( 0.1
	120	11 ( 0.8	4 ( 0.2	2.1 ( 0.1
	130	15 ( 0.7	6.5 ( 0.5	3.1 ( 0.1
	150	31 ( 1	2 4( 0.6	11 ( 0.4

T(°C)

k app (10 -3 • min -1 )

Acknowledgment. Financial support from the French National Research Agency (ANR) is gratefully acknowledged (Project NANO4F). ICMCB is a member of the PILA network for high research and technological resources in multidisciplinary actions. The authors also want to thank Dr. Ryan Hartman for the interest he had shown in this work.


Christophe Jarry

François Osiurak

David Delafuys

Valérie Chauviré

Frédérique Etcharry-Bouyx

Didier Le Gall
email: dilegall@chu-angers.fr

Apraxia of tool use: more evidence for the technical reasoning hypothesis

Keywords: Apraxia of tool use, Mechanical problem-solving, Semantic memory, Executive planning, Technical reasoning

come   L'archive ouverte pluridisciplinaire

Introduction

First observations of tool use impairment were provided by Steinthal's (1871) study of an aphasic patient with deficits in the manipulation of everyday tools (see [START_REF] Goldenberg | Apraxia and beyond: Life and work of Hugo Liepmann[END_REF].

A few decades later, [START_REF] Liepmann | Drei aufsatze aus dem apraxiegebiet[END_REF][START_REF] Liepmann | [END_REF] shaped the concept of apraxia, a disorder of skilled movement that cannot be attributed to an elementary sensorimotor deficit or to aphasia (De Renzi, 1989). Liepmann proposed that tool use is supported by the creation of a visual or acoustic image of the action (i.e., movement formulae) in the posterior brain regions. He proposed the term ideational apraxia to describe patients who had difficulties in generating movement formulae. Later, De Renzi and Luchelli (1988) specified that ideational apraxia cognitive processes have been propose to account for tool use impairment. We propose to review these processes on the basis of three hypotheses: the semantic memory hypothesis, the executive planning hypothesis and the technical reasoning hypothesis. gesture engrams) and (2) tool function [START_REF] Buxbaum | Ideomotor Apraxia: A call to action[END_REF][START_REF] Buxbaum | Cognitive representations of hand posture in ideomotor apraxia[END_REF][START_REF] Buxbaum | Left inferior parietal representations for skilled hand-object interactions: Evidence from stroke and corticobasal degeneration[END_REF] contain the features of gestures which are invariant and critical for distinguishing a given gesture from others. For a hammering movement, for example, a broad oscillation from the particularly on pantomime production and recognition, manipulation knowledge and tool use (mis-selection of objects, object misuse, object omissions, sequence errors). Besides gesture engrams, the human brain would also contain semantic information about the familiar function of tools [START_REF] Cubelli | Cognition in action: Testing a model of limb apraxia[END_REF][START_REF] Renzi | Ideational apraxia[END_REF][START_REF] Ochipa | Conduction apraxia[END_REF][START_REF] Rothi | A cognitive neuropsychological model of limb praxis[END_REF][START_REF] Roy | Common considerations in the study of limb, verbal and oral apraxia[END_REF]. This conceptual knowledge supports representation about tool associations (matching object to recipient) and about purposes of the actions (matching object for shared purposes) [START_REF] Hodges | The role of knowledge in object use: Evidence from semantic dementia[END_REF]. There are divergent views on the functional subdivisions of semantic memory but all previous research concurs in assuming that specific tools are associated with specific actions [START_REF] Goldenberg | The neural basis of tool use[END_REF].

The semantic memory hypothesis has however been subject to criticism on theoretical as well as empirical grounds in recent years. For instance, [START_REF] Osiurak | Re-examining the gesture engram hypothesis: New perspectives on apraxia of tool use[END_REF] claimed that the role of gesture engrams in tool use remains unclear, notably if it is assumed that tool use is supported by a direct route from vision to action [START_REF] Humphreys | Objects, affordances, action[END_REF][START_REF] Yoon | Modelling direct perceptual constraints on action selection: The naming and action model[END_REF]. More importantly, [START_REF] Osiurak | Re-examining the gesture engram hypothesis: New perspectives on apraxia of tool use[END_REF] emphasized that evidence for the existence of gesture engrams is weak, if not absent. Likewise, many studies have demonstrated that semantic knowledge is neither necessary nor sufficient to support tool use [START_REF] Buxbaum | The role of memory in object use[END_REF][START_REF] Hodges | The role of knowledge in object use: Evidence from semantic dementia[END_REF]Osiurak et al., 2008;[START_REF] Silveri | Semantic memory in object use[END_REF]. It has also been suggested that semantic knowledge about tool function may be mainly involved in situations in which contextual information is lacking as would be the case, for example in situations in which a tool is presented in the absence of contextual cues (Osiurak et al., 2008). Nevertheless, even if semantic knowledge could help people to determine the usage of tools, this kind of information would not be involved in utilization per se [START_REF] Osiurak | Re-examining the gesture engram hypothesis: New perspectives on apraxia of tool use[END_REF]. Finally, the semantic memory hypothesis cannot account for everyday use, which generally requires carrying out unusual manipulations and uses of unfamiliar tools [START_REF] Goldenberg | The neural basis of tool use[END_REF].

Second, the executive planning hypothesis, inspired by [START_REF] Luria | Les fonctions corticales sup[END_REF] suggests that dysexecutive syndrome has a negative impact on everyday tool use. [START_REF] Luria | Les fonctions corticales sup[END_REF] proposed the term "frontal apraxia" to describe a breakdown in sequential organization of behavior.

Patients with this type of apraxia do not show classical ideational apraxia in that usual actions are performed perfectly, but disturbances arise in natural actions requiring a preformed plan and the maintenance of goals [START_REF] Poeck | Ideational apraxia[END_REF][START_REF] Schwartz | Cognitive theory and the study of everyday action disorders after brain damage[END_REF][START_REF] Schwartz | Analysis of disorder of everyday action[END_REF]Goldenberg et al., independent fro concerns familiar activities involved in daily life. [START_REF] Goldenberg | The impact of dysexecutive syndrome on use of tools and technical devices[END_REF] pointed out that dysexecutive syndrome is specifically associated with multi-step actions impairment which is step actions and tests solved by pre-planning (novel tools, Tower Of London) in LBD patients. These works indicate that pre-planning would play a role in certain situations involving tool use but is probably not a unitary concept.

Finally, the technical reasoning hypothesis (Gagnepain, 1990;[START_REF] Gall | Des apraxies aux atechnies: Propositions pour une ergologie clinique[END_REF][START_REF] Osiurak | Unusual use of objects after unilateral brain damage: The technical reasoning model[END_REF][START_REF] Osiurak | Grasping the affordances, understanding the reasoning: Toward a dialectical theory of human tool use[END_REF]; for a somewhat similar view, see [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF][START_REF] Goldenberg | The neural basis of tool use[END_REF] suggests that technical efficacy is always relative, not absolute, because technical reality does not correspond to physical reality [START_REF] Osiurak | Grasping the affordances, understanding the reasoning: Toward a dialectical theory of human tool use[END_REF]. For over, the same physical material does not always provide the technical property suitable for an intended action. For example, the lead of a pencil is friable when applied to paper but not to leather. Thus, the inability to use tools may reflect difficulties in identifying (distinction) and unifying (sequenciation) the technical means (dense, permeable, resistant, etc.) relevant for a given technical end (cutting, engraving, etc.). Technical means and ends are abstract principles which are not linked with any tool representation but are reconstructed de novo depending on each situation. In case of impairment, difficulties would mostly affect technical means or technical ends. So, technical reasoning would be involved in any situation requiring the use and the selection of tools: use of familiar tools in either conventional or unusual ways as well as mechanical Problem-Solving. Furthermore, this hypothesis predicts that patients with impaired technical reasoning would exhibit difficulties with single tool use or single associations between tool and object upon which the tool is to be used and also in situations in which a great number of tools is given. Consistent with this, patients with ideational apraxia can be perplexed, commit mislocation errors or engage in uncertain explorations when asked to perform multiple object use tests [START_REF] Renzi | Ideational apraxia[END_REF][START_REF] Rushworth | The left hemisphere and the selection of learned actions[END_REF].

There is a substantial amount of empirical support for the technical reasoning hypothesis. We recently observed that LBD patients with difficulties in using familiar tools were markedly impaired when asked to use familiar tools in an unusual way [START_REF] Osiurak | Unusual use of objects after unilateral brain damage: The technical reasoning model[END_REF]. Several studies have found a strong association in LBD patients between the capacity to use familiar tools and mechanical Problem-Solving skills [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF]; see also [START_REF] Goldenberg | The neural basis of tool use[END_REF][START_REF] Hartmann | It takes the whole brain to make a cup of coffee: The neuropsychology of naturalistic actions involving technical devices[END_REF][START_REF] Silveri | Semantic memory in object use[END_REF]. Moreover, [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF] demonstrated that left brain lesions especially disrupt the capacity to select novel tools to solve mechanical problems. It has also been shown that patients with dysexecutive syndrome do not fail to perform mechanical Problem-Solving tests or to pantomime object use and that novel tool use was not affected by dysexecutive syndrome [START_REF] Goldenberg | The impact of dysexecutive syndrome on use of tools and technical devices[END_REF]. These findings indicate that executive functions might not be involved in situations in which people are asked to solve problems with unfamiliar tools [START_REF] Goldenberg | The impact of dysexecutive syndrome on use of tools and technical devices[END_REF][START_REF] Hartmann | It takes the whole brain to make a cup of coffee: The neuropsychology of naturalistic actions involving technical devices[END_REF][START_REF] Rumiati | A form of ideational apraxia as a delective deficit of contention scheduling[END_REF][START_REF] Rushworth | The left hemisphere and the selection of learned actions[END_REF]. Nevertheless, the mechanical problem-solving test developed by [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF] from which most of the results discussed above have been obtained, does not require a sequence of actions to solve the problem. These authors also developed the Treasure Box test, consisting of three boxes with lids that can be opened after manipulation of several locks. Premature opening of one lock could block the opening of another lock, so each stage depended on the previous one. Although these boxes required a sequence of mechanical actions to be solved, the solution could be found by trial and error.

Pre-planning was not necessary, which left open the issue of this ability's involvement in mechanical problem-solving.

The present research is designed to clearly distinguish these three hypotheses. We assessed 16 patients with left brain-damage (LBD) and aphasia and 19 healthy controls with a large apraxia battery examining semantic memory, executive planning and technical reasoning. Participants were asked to perform tasks typically studied in apraxia research (Pantomime of Tool Use, Single Tool Use), semantic memory tests (Functional and Categorical Associations and Recognition of tool utilization gestures) and a multiple-step executive function test (Tower Of London;[START_REF] Shallice | Specific impairments of planning[END_REF]. Above all, we proposed original tests requiring the actual use of familiar tools (Tool-Object Pairs) and the use of novel tools (Sequential Mechanical Problem-Solving). Like the novel tool test developed by [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF], we proposed two conditions for both tests (Tool-Object Pairs and Sequential Mechanical Problem-Solving). In the Choice condition subjects had to select among several tools the relevant one to perform the task. In the No-Choice condition, only the relevant tool was given.

Different theoretical elements allow us to make different predictions about the expected deficits according to each hypothesis (Table 1) and about the possible interactions between tasks. The memory hypothesis assumes that people acquire knowledge about manipulation and function of tools with which they had prior experience. Thus, gesture engrams and functional knowledge should be necessary to ensure the selection and the use of familiar tools but not when people have to solve sequential mechanical problems or carry out tests requiring executive functions. So, the semantic memory hypothesis allows us to expect associations between semantic memory (Recognition of tool utilization gestures and Functionnal and Categorical Associations) and familiar tool use (Tool-Object Pairs).

However, the semantic memory hypothesis does not predict any association between semantic memory and novel tool use (Sequential Mechanical Problem-Solving). Moreover, this hypothesis does not predict any association between the performance in Tool-Object Pairs and that in Sequential Mechanical Problem-Solving. The same is true of the executive planning hypothesis which is also insufficient for the prediction of any such association (Tool-Object Pairs and Sequential Mechanical Problem-Solving). In contrast, given that executive functions are supposed to enable people to deal with novelty and planning problems, the executive planning hypothesis predicts a strong association between performance in Sequential Mechanical Problem-Solving and the Tower Of London. Finally, the technical reasoning hypothesis suggests that the ability to reason about technical means and ends is involved in any situation requiring the use of tools. Therefore, there should be a strong association between the performance in Tool-Object Pairs and in Sequential Mechanical Problem-Solving. However, no association is predicted between performance in these two tests and that in the Tower Of London. Of particular interest is that only the technical reasoning hypothesis predicts association between familiar tool use (Tool-Object Pairs) and novel tool use (Sequential Mechanical Problem-Solving) independently of executive planning and semantic memory abilities.

- -----------------------------Table 1 about here - ------------------------------2. Method

Participants

Patients were admitted to the neurological department of the Angers University Hospital for a first unilateral cerebral vascular accident with hemiparesis and aphasia. Clinical which were collected primarily for clinical purposes and using different scanners, did not allow us to apply modern neuroimaging analyses. The p classified by an experienced neurologist (VC) according to relatively general anatomical criteria. Patients had a preliminary interview with a neuropsychologist (CJ) or speech therapists (DD) to examine language and vigilance. Linguistic capacities were tested with comprehensive and expressive exercises (e.g., naming, repetition, speech comprehension, global in 1, Broca in 5, Wernicke in 4, amnesic in 2, subcortical in 2 and non-classifiable in 2.

LBD subjects were included only if their behaviour unequivocally indicated comprehension r visuo-explorative behaviour. Our control group was composed of nineteen volunteer participants recruited from senior citizens' community associations around Angers.

Preliminary screening with the Mini Mental State Examination [START_REF] Folstein | Mini-mental state: A practical method for grading the cognitive state of patients for the clinician[END_REF] attested to their cognitive efficiency (mean score 29/30, range 26-30).

All participants were right-handed, and had no previous history of neurological or psychiatric illnesses. Informed consent was obtained from all participants or their relatives, and the study was conducted in accordance with the Declaration of Helsinki. Demographic and clinical data are displayed in Table 2. All participants used their left hand in order to prevent any effect due to motor or sensory impairment in the LBD group. There were no significant differences with respect to age and gender distribution between patients and control subjects. The mean educational level was somewhat higher for patients than for controls [t (33) = 1.8, p = .012].

- -----------------------------Table 2 about here -------------------------------

Pantomime of Tool Use

This test consisted of ten tools (key, corkscrew, screwdriver, match, light bulb, scissors, bread-knife, bottle-opener, hammer, pitcher, electrical plug, saw) that the examiner presented one at a time on a

Participants were asked to pantomime the use of each tool. Testing was preceded by two practice items (key and corkscrew) for which a correct pantomime was demonstrated if participants did not produce it themselves [START_REF] Hartmann | It takes the whole brain to make a cup of coffee: The neuropsychology of naturalistic actions involving technical devices[END_REF]. The time limit was set to 1 minute for each item. The performance was videotaped and rated on a 3-point scale [START_REF] Osiurak | Unusual use of objects after unilateral brain damage: The technical reasoning model[END_REF]. Two points were given if the expected action was directly achieved within the time limit. One point was given if the participant performed the action with errors (content or spatiotemporal). No points were given when the action was completely unrecognizable (maximum = 20 for each condition).

Single Tool Use

The same tools mentioned above were presented once again on the "vertical tool panel". Participants were required to grasp, one at time, each object and to demonstrate the movement involved in its typical use. Practice items were the same as in Pantomime of Tool

Use. The procedure of data recording and analysis was the same as described in the previous paragraph (maximum = 20 for each condition).

Tool-Object Pairs

This test consists of the same 10 familiar tools and the corresponding objects upon which they can be used (padlock, bottle sealed with a cork, screw in a wooden board, candle, bulb socket, sheet of paper, piece of bread, bottle sealed with a cap, nail in a wooden board, glass, electrical socket and a piece of wood). These objects were adapted to enable a onehanded performance (Figure 1).

Participants first performed tasks in the Choice condition and then in the No-Choice One object at time was placed on the table, between the participants and the upon which it was to be used and then to demonstrate the action typically made with the tool used on the object. In the No-Choice condition only the tool associated with the object was ne object at a time was placed on the table and subjects were asked to do what is typically done with the presented tools and objects. Two tools (key and corkscrew) were used as practice items, that is, subjects were helped to select the tool as well as to carry out the correct action, if necessary. The performance was videotaped and rated on a 3-point scale (0, 1, 2; [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF][START_REF] Osiurak | Unusual use of objects after unilateral brain damage: The technical reasoning model[END_REF]. For both conditions, two points were given if the expected action was directly achieved with the appropriate tool within the time limit. One point was given if the participant performed the action within the time limit after unsuccessful trials. No points were given when the action was not successfully achieved (maximum = 20 for each condition). The time limit was set to 1 minute for each item.

------------------------------Figure 1 about here ------------------------------

Sequential Mechanical Problem-Solving

This test was inspired by a series of studies by Goldenberg and colleagues [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF][START_REF] Goldenberg | The impact of dysexecutive syndrome on use of tools and technical devices[END_REF][START_REF] Hartmann | It takes the whole brain to make a cup of coffee: The neuropsychology of naturalistic actions involving technical devices[END_REF] in which function from structure. In this test, participants are asked to select (among a collection of three novel tools) the one tool that is best suited for taking up a cylinder. Nevertheless, as mentioned above, this test consists of mechanical problems that do not require a sequence of actions to be solved. Therefore, we specifically designed the Sequential Mechanical Problem-Solving based on two major principles. The first is that a sequence of several actions is required to solve the problem. The second is that trial-and-error strategies are insufficient for successful performance.

We constructed three different transparent boxes. A little blue wooden cube or a little blue wooden bead (the targets) was stuck inside each one (Figure 2). The aim of this test was to extract the target out from the box. For each box, different actions were required to do so.

The test was adapted to enable a one-handed performance. For Box A, participants had to remove the lid with their hand, and then lift the target up with a hook that they had to create by folding a metal rod. For Box B, participants had to insert an appropriate rod in the Box C, participants had to first use a rigid rod to make a lever and thus lift the mobile compartment that was located inside the box. This first action permitted to bring the target (a blue wooden bead) to the entrance of the box. Then, participants could carry out the second action of using a rod to extract the target out from the box. Problems could not be resolved by using only the hands, lucky movements, trial-and-error strategies or by choosing randomly among the rods. For each problem, one particular rod was the most effective. It was the only one presented in the No-Choice condition. Each rod involved different grips and numbers of movements but most of them proposed in the Choice condition were completely useless 1 . Thus, in the Choice condition some controls and some LBD patients did not resolve the problems with the most effective rods. Nevertheless, we accepted their performance when the target was finally extracted from the box.

For each item, participants were initially invited to observe carefully each side of the box. Then, the position of the target was ostensibly shown to subjects. A target similar to the target stuck inside the box was also presented to subjects to ascertain that they identified the target to be extracted. Participants were then asked to bring the target out from the box with the available rod(s), without lifting the boxes.

All participants performed first the Choice condition and then the No-Choice condition. In the Choice condition, the 16 rods were presented simultaneously on the table on the left of the subjects. The physical properties of the rods were manipulated so that: Half of the rods were made in metal and half of wood; half have a right angle and half do not; half half short; and half was rigid and half flexible. In the No-Choice condition, only the supposedly more efficient rod was given to participants to solve the problem. The time limit was 3 minutes for each box in each condition and the performance was videotaped. A 4-point scale was employed in the two conditions. Three points were given if the target was extracted within the time limit, independently of the rod that was used. Two points were given if the target was moved inside the box. One point was given if the target was touched by one of the rods. If none of these criteria were fulfilled, no points were given. The maximum score for each condition was 9.

- -----------------------------Figure 2 about here ------------------------------

Tower Of London

This test was proposed to assess the ability to solve multiple step problems involving minimal mechanical constraints. It was selected to minimize the effects of language skills.

The test involved two identical devices (the participant's device and the examine that consisted of three sticks and three wooden beads. The examiner presented a specific configuration of beads and asked the participant to replicate the configuration on his own device. We employed a revised version of the classical Tower Of London [START_REF] Berg | The Tower of London spatial problem-solving task: Enhancing clinical and research implementation[END_REF][START_REF] Shallice | Specific impairments of planning[END_REF]. There were two examples and six problems with a range from 2 to 7 moves. Examples were used to ascertain that participants understood the rules: only one bead can be moved at time, by using only one hand; one bead could be placed on the smallest stick, and only two on the middle stick; a bead cannot be moved if the two others were not placed on the sticks. The time limit for each item was 2 minutes. Performance was rated on a 4-point scale according to the number of movements (see Table 3). The maximum score was 18.

- -----------------------------Table 3 about here -------------------------------

Semantic knowledge of manipulation and tool function

Two tests were proposed to assess semantic memory. The first explored manner-of-use knowledge. The second explored functional and associative object knowledge.

Recognition of tool utilization gestures

This test consisted of twelve sets of four photographs. In each set, one photograph depicted the correct use of the tool, whereas the remaining three photographs showed the tool incorrectly oriented, inappropriately held or dangerously held. The tools shown on the photographs were the same that had already been pantomimed and demonstrated. Testing was preceded by two practice items for which feedback on correctness was given. One point was credited for each correct response given in 30 sec, totalling 10 points.

Functional and Categorical Associations

Four images with different single objects were presented below the picture of a tool (target stimulus: key, corkscrew, screwdriver, match, light bulb, scissors, bread-knife, bottle opener, hammer, pitcher, electrical plug, saw). Subjects were asked to select one out of four objects that best matched the target stimulus. Two subtests were assigned in order to evaluate either "functional" or "categorical" associations [START_REF] Goldenberg | The neural basis of tool use[END_REF]. In the subtest "functional associations", the target stimulus (e.g. saw) and the correct response (e.g. piece of wood) were functionally associated. the correct response (e.g., a saw, an axe) could be used for the same purpose. Each subtest was preceded by two practice trials (key and corkscrew) for which feedback on correctness was given. A score of 1 point was given if the correct response was given in 30 sec, totalling a score of 20 possible points for both conditions.

Statistics

Because of unequal group sizes and partly unequal variances, non-parametric tests were preferred. Between-group comparisons were performed with the Mann-Whitney U-test.

Wilcoxon signed-rank tests were used for within-group comparisons and Spearman rank order correlations were used to study relationships between variables. To further explore the correlational structure of test results in LBD patients, the correlation matrix of all experimental tests was subjected to multidimensional scaling using the ALSCAL procedure.

We also carried out stepwise regression analyses to determine contribution of semantic memory and technical reasoning in familiar object use. Results were considered significant at -level of p < .05.

Results

Effects of demographics variables in the control group and the patient group

In the control group, Spearman rank order correlations revealed negative correlations between age and performances on Tool-Object Pairs (Choice condition, rho = -.67, p = .002;

No-Choice condition, rho = -.58, p = .009) and Recognition of tool utilization gestures (rho = -.50, p = .029). Associations were also found between education level and the No-Choice condition of Tool-Object Pairs (rho = .54, p = .017) and Recognition of tool utilization gestures (rho = .56, p = .013). Correlations between demographic participant variables and Sequential Mechanical Problem-Solving, Pantomime of Tool Use, Single Tool Use and Tower Of London did not reach statistical significance. No significant correlations were found between global cognitive efficiency (MMSE) and any of the experimental tasks.

In LBD patients, no significant correlations were found between demographics and any of the experimental tasks.

Comparisons between groups

Table 4 displays Differences between groups were also found in the Tower Of London (z = 2.19, p = .029), Functional and Categorical Associations (z = 2.70, p = .007). However LBD patients did not significantly differ from controls on Recognition of tool utilization gestures (z = 0.67, p = .501).

- -----------------------------Table 4 about here -------------------------------

Correlations between test results in control group

Results

few associations between experimental tasks in the control group. A significant association was found between Pantomime of Tool Use and Single Tool Use (rho = .55, p < .05). Tower Of London was correlated with Tool-Object Pairs, Choice condition (rho = .49, p < .05) and No-Choice condition (rho = .80, p < .001) and with Recognition of tool utilization gestures (rho = .51, p < .05).

- -----------------------------Table 5 about here -------------------------------

Correlations between test results in LBD patients

Results are presented in Table 6. Spearman rank order correlations revealed a strong association between Pantomime of Tool Use, Single Tool Use, Tool-Object Pairs and Sequential Mechanical Problem-Solving (all rho > .66, all p < .004). Thus, Tool-Object Pairs and Sequential Mechanical Problem-Solving were associated (see Figure 3 ------------------------------Table 6 about here -------------------------------------------------------------Figure 3 about here ------------------------------ - -----------------------------Figure 4 about here - -----------------------------

Discussion

This study proposed to explore the relationships between technical reasoning, semantic knowledge and executive planning in tool use in LBD patients. Our primary interest was the technical reasoning hypothesis which only predict associations between familiar tool use (Tool-Object Pairs) and novel tool use (Sequential Mechanical Problem-Solving).

The main results can be summed up as follows. First, we obtained high correlations between all tasks involving tools. Second, we found no association between Tool-Object Pairs, Sequential Mechanical Problem-Solving, and the Tower Of London. Finally, we found associations between the ability to use tools and knowledge of tool function (Functional and Categorical Associations) but not with knowledge of tool manipulation (Recognition of tool utilization gestures).

A core mechanism ?

The technical reasoning hypothesis suggests that technical reasoning supports the use of tools in any kind of tool use situation. The key finding of this study is the strong association, in LBD patients, between all tasks involving tools in all conditions. Indeed, our results show that LBD patients were impaired in the use and selection of tools both in Tool-Object Pairs and Sequential Mechanical Problem-Solving. These findings corroborate results observed with the Novel Tool Test that have shown that novel tool selection is impaired in LBD patients [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF][START_REF] Goldenberg | The neural basis of tool use[END_REF][START_REF] Hartmann | It takes the whole brain to make a cup of coffee: The neuropsychology of naturalistic actions involving technical devices[END_REF]. These findings are also consistent with previous correlations between usual and unusual use of tools [START_REF] Osiurak | Unusual use of objects after unilateral brain damage: The technical reasoning model[END_REF] in LBD patients. The originality of this study lies nevertheless in the demonstration that LBD patients are impaired for tool selection whether or not they are already familiar with the tool. This is consistent with previous studies showing that LBD patients with apraxia can be perplexed or engage in uncertain explorations when requested to carry out multiple tool use tests [START_REF] Renzi | Ideational apraxia[END_REF][START_REF] Rushworth | The left hemisphere and the selection of learned actions[END_REF] as well as recent studies on Alzheimer patients indicating that distractor tools have an impact on everyday actions [START_REF] Giovannetti | Target-related distractors disrupt object selection in everyday action: Evidence from participants with dementia[END_REF]. However, the Choice condition and No-Choice conditions are strongly associated in both tasks (Tool-Object Pairs and Sequential Mechanical Problem-Solving). This result corroborates the results of De Renzi and Luchelli (1988) concerning the high correlation between a multiple object test and a single object test, suggesting that tool use impairment in LBD patients is not completely dependent on the number of tools presented or the number of steps necessary to complete an action (see also [START_REF] Hartmann | It takes the whole brain to make a cup of coffee: The neuropsychology of naturalistic actions involving technical devices[END_REF]. Tool use impairments can effectively appear after frontal lobe lesions, or be a consequence of right brain damage or diffuse brain damage [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF][START_REF] Hartmann | It takes the whole brain to make a cup of coffee: The neuropsychology of naturalistic actions involving technical devices[END_REF][START_REF] Schwartz | Naturalistic action production following right hemisphere stroke[END_REF]. In those cases, they are certainly due to visuo-spatial or attentionnal disturbances. We suggest that our results support the view that LBD lesions affect a specific technical reasoning mechanism that operates in every situation requiring the use of a tool. However, to confirm whether our findings are specific to patients with left brain damage, our method will have to be replicated with left and right brain damaged patients.

Action planning

The executive planning hypothesis suggests that dysexecutive syndrome impacts negatively on everyday tool use, especially in natural actions requiring a preformed plan and the maintenance of goals. The Tool-Object Pairs task does not require a sequence of actions to be achieved. However, the Sequential Mechanical Problem-Solving task does require such a sequence. Difficulties in dealing with novelty and planning problems are also one of the main signs of dysexecutive syndrome. Therefore, in line with the executive planning hypothesis a strong association could be predicted between performance in the Sequential Mechanical Problem-Solving task and in Tower Of London. Our results nevertheless did not corroborate this prediction since no association was found between these two tests. Previous studies had already shown that performance in the Novel Tool Test [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF][START_REF] Goldenberg | The neural basis of tool use[END_REF][START_REF] Hartmann | It takes the whole brain to make a cup of coffee: The neuropsychology of naturalistic actions involving technical devices[END_REF] can be impaired independently of frontal lobe lesions or dysexective syndrome. Nevertheless, the originality of the present study is to demonstrate that when patients are faced to a sequence of mechanical actions, the role played by executive planning is still minimal.

In sum, executive planning is involved in situations requiring the creation of a mental plan such as in the Tower Of London, but not in situations requiring a sequence of mechanical principles to be achieved. The absence of correlation between Sequential Mechanical Problem-Solving and Tower Of London again supports the technical reasoning hypothesis and strengthens the conclusions of [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF] that the ability to solve mechanical problems is an ability to perform a non-routine task, which nevertheless does not depend on executive functions (see also [START_REF] Goldenberg | The impact of dysexecutive syndrome on use of tools and technical devices[END_REF]. Morover, in our study, one patient with frontal lesion (LBD 10) exhibited a deficit in Sequential Mechanical Problem-Solving without deficit in Tower Of London. Anatomo-clinical explorations will be needed to confirm this dissociation between executive planning and mechanical planning in frontal lesions.

Action representation

As discussed above, the memory hypothesis assumes that knowledge of tool manipulation (gestures engrams) and knowledge of tool functions (semantic memory) support skilled tool use [START_REF] Buxbaum | Ideomotor Apraxia: A call to action[END_REF][START_REF] Buxbaum | Cognitive representations of hand posture in ideomotor apraxia[END_REF][START_REF] Buxbaum | Left inferior parietal representations for skilled hand-object interactions: Evidence from stroke and corticobasal degeneration[END_REF][START_REF] Heilman | Two forms of ideomotor apraxia[END_REF][START_REF] Rothi | A cognitive neuropsychological model of limb praxis[END_REF][START_REF] Sirigu | A selective impairement of hand posture for object utilization in apraxia[END_REF]. Central to the memory hypothesis is the idea that people acquire knowledge about manipulation and functions of tools with which they had prior experience, so that gesture engrams and semantic memory should be particularly useful when people have to use familiar tools, but not when they have to use novel tools to solve mechanical problems.

Our results indicate that both Tool-Object Pairs and Sequential Mechanical Problem-Solving are correlated with Functional and Categorical Associations but not with Recognition of tool utilization gestures. First, these results support dissociation between knowledge of object function and knowledge of object manipulation (Buxbaum et al. 2002). Second, dissociations between tool use impairments (familiar and novel, Choice and No-Choice conditions) and knowledge about tool manipulation provide a new argument against gestures engrams.

Interactions between technical reasoning and functional knowledge

The technical reasoning hypothesis assumes that technical reasoning supports the use of tool independently of executive planning and semantic memory abilities. Our results partially confirm the technical reasoning hypothesis. Indeed, Functional and Categorical Associations are surprisingly associated with Sequential and Mechanical Problem-Solving.

Regression analyses demonstrated that Sequential Mechanical Problem-Solving and Functional and, to a lesser degree, Categorical Associations both contribute to performance on Tool-Object Pairs. These findings are in line with previous studies [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF][START_REF] Randerath | From pantomime to actual use: How affordances can facilitate actual tool-use[END_REF][START_REF] Osiurak | Re-examining the gesture engram hypothesis: New perspectives on apraxia of tool use[END_REF] demonstrating the involvement of both, semantic memory and technical reasoning in actual use of familiar tools. One possible explanation for the association between technical reasoning and memory related processes (functional knowledge) in the use of familiar and novel tools is that humans first try to operate with familiar solutions they have encountered from previous experience.

Functional and categorical knowledge could potentially be recruited in order to find solutions based on similarity with previous experience. That might sometimes be useful especially for single steps, when the end of the action is clear or very similar to previous experience. However, technical reasoning is necessary when the solution is less predefined, for example when participants also have to select one out of several presented tools to complete the action or to determine what steps are needed to achieve the goal. In those cases, real time analysis of mechanical relationships between possible technical means and possible technical ends is needed and potentially related to previous experience (memory related processes). In this framework, semantic memory might, at least in part, guide the behavior of patients by allowing them to select the usual tool corresponding to a given object. But, as our results indicated, even if this interpretation still implies a minimal role of semantic memory, this kind of knowledge would be far from necessary, since LBD patients also failed the No-Choice condition in which a tool was directly presented with the corresponding object on which it was to be used. Thus, the following hypothesis can be formulated: when technical reasoning is strongly deficient, functional knowledge is not sufficient to support tool selection and tool manipulation because the purpose of the action cannot be identified. depend on left parietal lobe integrity because of their demands on categorical apprehension of relationships between imitation of postures and Sequential Mechanical Problem-Solving and to re-examine the issue of the dorsal stream (see also [START_REF] Buxbaum | Ideomotor Apraxia: A call to action[END_REF] in light of the technical reasoning hypothesis.

Finally, the correlation between Pantomime of Tool Use and Sequential Mechanical

Problem-Solving is equally noteworthy. Pantomime of tool use is a classical test in clinical neuropsychology traditionally associated with semantic memory [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF]. [START_REF] Goldenberg | Defective pantomime of object use in left brain damage: apraxia or asymbolia ?[END_REF] demonstrated that it is not a specific task due to its correlation with a variety of other verbal and non-verbal tasks dependent on left hemisphere function.

According to this, we suggest that technical reasoning can play a role in pantomime of tool use even if tools are not physically present. Moreover, our results are in line with results of [START_REF] Goldenberg | Tool use and mechanical Problem-Solving in apraxia[END_REF] showing a correlation between pantomime of tool use and novel tool selection.

Conclusion

In sum, all tasks involving tools are strongly associated in LBD patients. The ability to solve sequential mechanical problems does not depend on executive planning. Also, familiar and novel tool use are associated with knowledge about object function but not with knowledge about tool manipulation. Our findings provide new evidence for the theory that although human tool use may involve conceptual knowledge, it is likely to be supported primarily by technical reasoning. It is noteworthy that somewhat similar proposals have already been formulated in other fields of psychology. For instance, Penn et al. (2008) suggested that unlike non-human primates, including those primates known to be tool users in the wild, humans are able to reinterpret the physical world in terms of abstract principles and that this ability could be the basis for human tool use. Studies in developmental psychology also demonstrate that tool use and innovation are independent from acquired conceptual knowledge and executive functioning (Beck et al. 2011;[START_REF] Defeyter | Acquiring and understanding of design: Evidence from -Solving[END_REF]. The present results therefore encourage us to continue in this direction and to incorporate data from comparative or developmental psychology in the study of technical reasoning.

Footnote 1

Example for the box C: instead of making lever, some subjects in the Choice condition unfolded the long metal rod (Figure 2) in order to bring the target to the entrance of the box. This action was impossible in the No-Choice condition since only a rigid rod was given.

Regardless of whether subjects made lever or unfolded the long metal rod, two actions were nevertheless necessary to extract the target (bringing the target to the entrance of the box and bringing out the target from the entrance of the box).

  the results of experimental tests for the control group and for LBD patients. LBD patients scored significantly lower than controls on all tests involving tool use (Pantomime of Tool Use: z = 3.26, p = .001; Single Tool Use: z = 3.03, p = .002; Tool-Object Pairs (Choice condition): z = 3.55, p < .001; Tool-Object Pairs (No-Choice condition): z = 2.88, p = .004; Sequential Mechanical Problem-Solving (Choice condition): z = 3.43, p = .001; Sequential Mechanical Problem-Solving (No-Choice condition): z = 2.68, p = .007).

  ) in both conditions (Choice and No-Choice). Furthermore, the two conditions (Choice and No-Choice) of Tool-Object Pairs and Sequential Mechanical Problem-Solving were associated in both tests. Significant association (all rho > .55, all p < .028) was found between Functional and Categorical Associations and Pantomime of Tool Use, Single Tool Use and Tool-Object Pairs (Choice condition and No-Choice condition). Functional and Categorical Associations were also correlated with Sequential Mechanical Problem-Solving for Choice condition (rho = .82, p < .001) and No-Choice condition (rho = .74, p < .001). Furthermore, conceptual knowledge of object manipulation (Recognition of tool utilization gestures) showed few associations with tasks involving tool use. Only correlation between Single Tool Use and Recognition of tool utilization gestures reached statistical significance (rho = .57, p = .021). Performance on the Tower Of London was not correlated with any of the other variables.

  correlations are represented by smaller distances between the respective data points. The distances correspond to the rank order of the correlations but not necessarily to their absolute values. There is a clear separation between Recognition of tool utilization gestures and Tower Of London and the other experimental tasks. Tool Object Pairs in the Choice condition is strongly associated with Sequential Mechanical Problem-Solving in the No-Choice condition. Functional and Categorical Association occupy an intermediate position with equal distance of Tool Object Pairs, No-Choice condition and Sequential Mechanical Problem-Solving in the Choice condition.

-

  In order to investigate which of the correlated variables explained a significant amount of variance in familiar tool use, we carried out a forward regression analysis. Tool-Object Pairs in the Choice condition were used as the dependant variables, and the predictor variables were the score on Pantomime of Tool Use, Sequential Mechanical Problem-Solving (Choice and No-Choice condition) and Functional and Categorical Associations (Tool-Object Pairs in the No-Choice condition and Single Tool Use were excluded because their apparent predictive power could be the result of their similarity with the dependant variable). The analysis showed that the scores on Sequential Mechanical Problem-Solving in the No-Choice condition contributed significantly to the Tool-Object Pairs index in the Choice condition, accounting for 72.2% (p < .0001) of this factor's variance. The association of Sequential Mechanical Problem-Solving in the No-Choice condition and the Functional and Categorical Associations contributed together to the Tool-Object Pairs index in the Choice condition, accounting for 78.4% (p < .0001) of the variance.

Table 2

 2 Demographical and clinical data.Table 3 Tower Of London scoring system. Table 4 Results of experimental tests in controls and LBD patients.

	LBD (n = 16)	Control (n = 19)	LBD vs. control

* p < .05

Table 5

 5 Correlations between tests results (Spearman Rho) in control group.

	FCA
	STU TOP C TOP NC SMPS C SMPS NC TOL Reco

Table 6

 6 Correlations between tests results (Spearman Rho) in LBD patients.

	FCA
	STU TOP C TOP NC SMPS C SMPS NC TOL Reco

= .98) which is displayed in Fig.4. Higher

Acknowledgments

We thank to our colleague Dr Sharman Levinson for improving English.