Jean-François Nicaud

Denis Bouhineau

Christian Varlet

Anh Nguyen-Xuan

Towards a product for teaching formal algebra

This paper describes a research work whose objective is to help students to learn algebra with a computer. Firstly, we summarise the theoretical foundations and we describe a prototype devoted to the factoring problem. With this prototype, the student solves problems without making the calculations. The student can also observe the system solving a problem and providing explanations. Secondly, we summarise several experiments we carried out with students and we describe the results we got. Last, we present our new objective that consists of making a product that will be available for all students and teachers.

Introduction

From 1987 to 1997, the APLUSIX team worked in the field of Artificial Intelligence in Education, in the domain of formal algebra, with four research objectives : [START_REF] Anderson | The Architecture of Cognition[END_REF] to develop ILEs (Interactive Learning Environments) that can help students to learn formal algebra, [START_REF] Beeson | Design Principles of Mathpert: Software to support education in algebra and calculus[END_REF] to build theoretical foundations for designing such systems, [START_REF] Bundy | Using Meta-level Inference for Selective Application of Multiple Rewriting Rule Sets in Algebraic Manipulation[END_REF] to do experiments on the systems with students, (4) to analyse how students learn using these systems. We focused on the factorisation problem for developing a full prototype that we experimented with students. Considering that our system was useful for students and that very few ILEs in algebra were available as products (actually the only one we know is MATPERT [START_REF] Beeson | Design Principles of Mathpert: Software to support education in algebra and calculus[END_REF]), we decided, at the beginning of 1998, to add a new objective to the preceding ones: to make a product, i.e., a system available for all the students and teachers, and we began to work in that direction. Products are generally the objective of companies, not of university researchers. In our domain we think that it is very difficult for a company to create a complex system and to make enough money with it. That is why we decided to make a product ourselves.

In this paper, we summarise the theoretical foundations for designing ILEs in algebra, we describe the last prototype we experimented with students, we summarise the main experiments we conducted and the results we got. Last, we indicate the current state of development of the product and the future work.

Modelling human reasoning in formal algebra for building ILEs

We consider domains of knowledge in which problems are solved by transforming algebraic expressions. Examples of such problems are factorisation, equation solving, calculus of primitives. Problems can come directly from mathematics or from various domains (geometry, physic, biology, etc.) where algebra appears as a framework for representing objects and as a tool for solving problems. This domain of knowledge and problems can be called cognitive formal algebra: the formal feature comes from the restriction to problems that are solved by transforming algebraic expressions, the cognitive feature comes from the restriction to humanlike reasoning.

Analysis of human reasoning

We consider features of cognitive formal algebra that can be observed at transformation level from the behaviour of students and teachers. 1) The basic mechanism consists of replacing a sub-expression with an expression, using what we call a transformation rule. For example, x 2 -1 can be replaced by (x+1)(x-1) in 3(x 2 -1)+(x+1)(2x+1), providing 3(x+1)(x-1)+(x+1)(2x+1). 2) Many transformation rules come from identities (e.g., A 2 -B 2 = (A+B)(A-B)).

3) Transformation rules are matched to sub-expressions. 4) Matching can use expression-concepts (concepts from expressions). For example, matching A 2 -B 2 to 4x 2 -1 is not simple because neither does 4x 2 have the form A 2 , nor 1 the form B 2 . Human matching uses a concept of square: as 4 is the square of 2, 4x 2 is the square of 2x, so that it matches the square of A. 5) Matching can be made modulo a numerical factor. For example, AB+AC matches (2x-4)(x+1)+(3x-6)(2x-1). Human matching uses a concept of matching modulo a numerical factor: x-2 is recognised in 2x-4 (modulo 2) and in 3x-6 (modulo 3). 6) When they have been used frequently, transformation rules have a compiled form [START_REF] Anderson | The Architecture of Cognition[END_REF]. For example, the rule AB+AC -> (A+B)(A-B) becomes search a common factor. 7) Some transformation rules are based on a process, e.g., the discriminant. 8) Rule-concepts (concepts from transformation rules) are used. For example, the transformations of (

x-2)[2(x+1)]+(x-2)[3(2x-1)] into (x-2)[2(x+1)+ 3(2x-1)
] and of 4x 2 -1 into (2x+1)(2x-1) are called factorisations. 9) There is an important concept of reduction. Reduction rules have generally the highest priority for any problem type. 10) There are well identified problem types (e.g., factorisation, equation solving), however the characterisation of solved forms is not precise and is sometimes teacher dependant. 11) Reduction and cleaning up take a important place in solved forms.

The observation of students and teachers shows that some problem types have no strategic difficulties. At any given time, there is only one thing to do. In fact, there are always many applicable transformations. The only thing to do is the result of specialised knowledge combi-ning transformation and strategic features, which is another aspect of compiled knowledge [START_REF] Anderson | The Architecture of Cognition[END_REF]. Sometimes, this lack of strategic difficulties is the result of a strong limitation of the domain, like when, at some level, factorisation problems are limited to expressions that match an identity so that they are solved just by applying the identity and reducing the result. For domains with strategic difficulties, it is sometimes necessary to backtrack to a previous step in order to try another path (see figure 1). This means that the solving process must be considered in a heuristic search framework [START_REF] Pearl | Heuristics[END_REF] and that knowledge is necessary for deciding when to backtrack, where to backtrack and what rule to choose.

Modelling human reasoning

We have built a general model of human reasoning in formal algebra for building ILEs, the MCA model (Model based on Compiled knowledge for Algebra), and a particular model of the factorisation domain for building the APLUSIX system. These models implement the features of the above analysis. In the general model, there are a heuristic search framework, a theory of expressions, expression-concepts, matching-concepts, rule-concepts, plans, subproblems. For details, see [START_REF] Nicaud | Modélisation en EIAO, les modèles d'APLUSIX[END_REF]. In the particular model for factoring polynomials:

1) There is no plan and no sub-problem because the domain is not complex enough 1 . 2) Three expression-concepts have been defined: monomial, factor, square. For example, the concept of monomial has three slots: coefficient, variable and degree. Each of the following expressions: 4, -4, x, -x, 4x, -4x, x n , -x n , 4x n , -4x n are monomials, and a unique transformation rule is able to calculate the sum of two monomials of the same degree.

3) The matching-concept modulo a constant factor is used, in particular for matching factors. 4) Four main rule-concepts have been defined: strong-factoring, strong-expansion, strongreduction, elementary. For example, factoring out a monomial is strong-factoring and factoring out a constant is elementary.

We have stated the following strategic principle [START_REF] Gélis | Elements of a theory of algebra for ILEs[END_REF]: For factoring polynomials, use in priority strong-factoring and strong-reduction. This principle is important for choosing the rule to apply, for deciding when to backtrack and for providing help to the student.

A few models have been built by authors of ILEs for algebra. PRESS [START_REF] Bundy | Using Meta-level Inference for Selective Application of Multiple Rewriting Rule Sets in Algebraic Manipulation[END_REF] has rule-concepts and uses these concepts for choosing the rule to solve equations. But PRESS has no expression-concept. In MATHPERT [START_REF] Beeson | Design Principles of Mathpert: Software to support education in algebra and calculus[END_REF], the essential object is the operator. Operators are chosen with the help of indicators. There is not expression-concept and no real rule-concept. DISSOLVE [START_REF] Oliver | DISSOLVE: An Algebra Expert for an ITS[END_REF] has expression-concepts, in particular the factor concept, but no rule-concept. These three systems do not use a heuristic search framework.

The APLUSIX prototype

From 1987 to 1997, the APLUSIX system evolved. Some functionalities were modified or added, other were suppressed when they seamed to be useless. The last version is described here. The system was mainly used at an intermediate level, and sometimes at a low level. It was particularised for some features for these levels. In both levels, the use of the discriminant was not known by the students.The system provides the learner with two interaction modes, an observation mode, in which the student observes the system solving a problem, and an action mode, in which the student solves a problem. Moreover, the system may be used in a free way, the student choosing the parameters and the problems, or in a directed way, parameters and problems being described in automata. 1 Plans and sub-problems are implemented for another domain in another prototype.

The observation mode

In the observation mode, APLUSIX uses reference knowledge to solve a problem, step by step, generating and displaying a search tree. For many problems, at the considered level, the search tree consists of a unique branch. However, a two branch tree is sometimes obtained (figure 1). Each step is described using the rule or the rule-concept applied. The rule itself is used for factorisation (the rules under study) otherwise the rule-concept is used. At each step, the learner can ask for explanations about the matching. In this case, the system provides details in a temporary window, for example:

3x-1 is a commun factor in (4- 12x)(x-7)-x(9x-3) because (4-12x)(2x-7)=-4(3x-1)(x-7) and -(-2x-7)(9x-3)=-3x(3x-1)
In previous prototypes, explanations about the strategies were available for the students. They have been abandoned because experiments show that they were useless at this level. They will be available for other levels in the future.

The action mode

In the action mode, the learner solves problems. At each step, (s)he chooses an action in a menu. The action is either a rule (for factorisations) or a rule-concept (figure 2). After that, an action window is opened for selecting the concerned sub-expression. For factorisations, the student has in addition to indicate the matching (figure 3). The request of the student is then analysed by the system. When it is correct, the system calculates and displays the result. When it is not, a message is displayed. At any time, it is possible to go back to a previous step by clicking on this step. In this mode, the student can ask for help using the menu (figure 2). In the action mode, the student is freed from calculations and calculation errors. In the action window (figure 3), the input of expressions is controlled and syntax errors are indicated as soon as they occur. The selection of sub-expressions is simplified: the first click selects a monomial, at each other clicks, the minimal sub-expression including all the clicks is selected. Experiments have proved the interest of this mode. It allows the student to focus on the matching and on the strategy so that (s)he can solve more difficult problems. Of course, we do not consider this mode as the unique one to use. It is a complement to the traditional paper/pencil mode.

The analysis function. This function analyses the student's request. Its role is to decide whether the request is correct or not. When the request is correct, it is applied, otherwise feedback is provided. The analysis function does not use the reference solver because there are correct transformations that are not envisaged by the reference solver. For example, factor out x+2 from (4x+8)(x-1)-(2x+4)(3x-2) is a correct request that is not generated by the reference solver which generates factor out 2x+4 from (4x+8)(x-1)-(2x+4)(3x-2). The analysis is performed by production rules.

The help function. In the last version, the help function suggests one or two actions among the more promising ones that have not yet been applied. Sometimes, it suggests backtracking. In the first version, the help function was different (we did not want to tell the student what to do): we suggested the possible transformations in the selected step, so that the student had to think to decide which one to choose. This method did not work. Some students followed the first suggestion every time, others did not use the help because there were too many things to read.

Parameters

Parameters determine the behaviour of the system. In the free mode, the student can change their values. In the directed mode, they are set by an automaton. Some of these parameters are: -expand-and-reduce: when it is true, the menu includes an expand-and-reduce action allowing expansion and reduction in one step of first order polynomials like 2(x-3)-3(x+1).

-a2+2ab+b2-U: when it is true the identity a 2 +2ab+b 2 can be used by the student with a value of b such as -2, otherwise, the a 2 -2ab+b 2 identity is required with b equal to 2.

-help: when the value is true, the action mode allows the student to ask for help.

-delay-help: indicates, when help is true, the delay before giving the student access to help.

-step-by-step: when the value is true, the student is not allowed to perform complex matching for factoring out a polynomial (e.g., for factoring out x-4 from (x-4)(x+1)-(2x-8)(3x-1), (s)he has first to transform 2x-8 in 2(x-4)).

Automata

An automaton is a list of linked problems in a file. Each problem is described by a name, an expression, an optional modification of the parameters and optional links. For example : says to factor the expression 9-4x 2 +(2x-1)(2x+3) in the given context. When this problem is finished, the link indicates the next problem.

Experiments with the APLUSIX prototype

From 1987 to 1997, we carried out several experiments. The first showed that a wide majority of the students like to work with APLUSIX (as they told us) and learned with the system (this was attested by a pre-test and a post-test). In this section, we summarise the major experiments we carried out during this period.

Two experiments done in 1990 and 1991

Two pilot experiments were carried out in 1990 and 1991 the objectives of which were, first, to evaluate the user friendliness of the interface, and, second, to determine the degree of difficulty of the different types of matching modulo a numerical factor, and the way perceptual factors may interfere with the recognition of an expression.

The data gathered from these pilot studies led to an important improvement of the interface, particularly in the way the student has to tell the system how to match an expression to a transformation rule. For instance, in the first prototype, when the student wanted to apply the rule A 2 -B 2 -> (A+B)(A-B) to the sub-expression 4x 2 -9, (s)he had just to designate the sub-expression and the rule. In the improved interface, the student must designate the sub-expression, the rule and, in addition, the values of A and B. In this way, the student is more active, and it is possible to evaluate the degree of the student's matching knowledge. For instance, a student may recognise that the expression 4x 2 -9 matches the rule A 2 -B 2 , and that the values of A and B are, respectively, 2x and 3; but (s)he may not recognise that the expression 4(3x-2) 2 -9 matches the same rule (with the correct values for A and B).

Hand analysis of the protocols showed that the matching of an expression to a rule can be more or less difficult, depending on the necessity of implicitly factoring out numerical factors, to obtain an expression that can be directly matched to the rule. This result led us to define the notion of "visibility": an expression is totally "visible" when it matches directly a rule.

An experiment realised in 1992

A controlled experiment on learning to solve factorisation problems with the action mode, was carried out in 1992 with a new version APLUSIX/V0-M2. The student can ask for advice when (s)he do not know how to proceed. When (s)he makes a mistake, the system gives the student a comment about the mistake, an "error message".

This experiment comprised three phases. The first two phases concerned the acquisition of matching skills based on the rule factoring out and second order identities. In the third phase, the problems were more complex, they can be solved in different ways, and for some of them, the students must choose between different promising rules. A wrong choice may lead to an impasse. Forty-six secondary school students (14-16 years-old) participated in the experiment. Each student spent four forty-five minutes sessions with the system.

A program was developed to diagnose the student's state of matching knowledge during the learning process [START_REF] Nguyen-Xuan | Automatic diagnosis of the student's knowledge state in the learning of algebraic problem solving[END_REF]. The program distinguishes between 17 categories of matching, the categories being defined by five types of basic visibility of matching. To evaluate the student's matching knowledge, the method used consists of sequentially increasing or decreasing a student's matching score for a category of matching knowledge. The score for a category of matching knowledge is increased every time (s)he performs correctly and without help a transformation involving this category.

The individual protocols were given to the program to calculate the evolution of the students' score during the learning experiment. The results showed that the notion of visibility we defined was relevant: the less an expression is visible in regard to a given transformation rule, the more it is difficult to be mastered.

A hand analysis of the protocols showed three important points. Firstly, the majority of students learned to backtrack, something they did not do in a paper-and-pencil situation. The search tree presented in the display may have played the role of a reification [START_REF] Conlon | PathFinder: A Programming Tool for Search Based Problem Solving[END_REF][START_REF] Singley | The reification of Goal Structure in a Calculus Tutor: Effects on Problem-Solving Performance[END_REF] that helped foster the concept of a search space.

Secondly, observing the way in which matching knowledge was acquired led us to differentiate between two different styles of learning which we have termed the conceptual based learning style and the experiential based learning style. We hypothesise that these styles of learning are related to the depth of the student's conceptual knowledge of algebra. The student who learned in an experimental way progressed slowly and did not generalise his (her) matching ability immediately from one expression to another : (s)he may have acquired his (her) matching skill solely by establishing a relation of surface similarity between the structures of symbols representing an abstract rule and the structure of symbols representing an algebraic expression. Conversely, students whose progress was based on a deeper understanding of the concepts of square and of factor had less difficulty in quickly generalising their matching ability over expressions that had different surface features.

Thirdly, we have observed that the matching knowledge about the identities was more stable than the matching knowledge about the factor out rule. We hypothesised that this result was related to the way the error messages and the prompts were formulated by the system. In the case of identities, the prompts were general, the system told the student to apply an identity to an expression, but it did not tell the student what were the values of A and B to type in. So that the student still had something to do by him(her)self: find the correct values of A and B. The error messages were, on the contrary, very precise. Indeed, in the case where the student wanted to match an expression E to an identity, and the expression cannot match, the error message was "this expression is not a difference of two squares". When the student gave an erroneous value of A and/or B for an identity, the system's error message indicated clearly in which way it was an error, by saying, for instance, "With the values of A and B you gave, A 2 -2AB+B 2 = x 2 -8x+16 and not x 2 -4x+4." So that the student can understand why his (her) action was erroneous.

By contrast to the case of identities, in the case of factoring out a (numerical, monomial, or binomial) factor from an expression, the error messages were laconic, and the prompts too precise. For any error in applying the factor out rule, the error message was always the same : "it is not possible to factor out [expression designated as A] from [selected expression]." So that there was no hint about the reason of the error. The prompt concerning the application of the factor out rule was, on the contrary, too precise. Consider the student who asks for help at the problem state (4-12x)(2x-7)-(-2x-7)(9x-3). Among the possible actions is the application of the factor out rule. The prompt was: "factor out 3x-1 from (4-12x)(2x-7)-(-2x-7)(9x-3)." So that the student did not have anything to do except to copy exactly the prompt.

An experiment carried out in 1994

An experiment was conducted in May 1994 [START_REF] Nguyen-Xuan | Effects of feedback on learning to match algebraic rules to expressions with an intelligent learning environment[END_REF], with 12 students of the same age. The objective of this experiment was to test the hypothesis that less detailed prompts about the application of the factor out rule, and more detailed comments about the errors in applying this rule would result in an improved learning of this rule, and would also provide more useful data for the analysis of the learning process. The learning situation was identical to that of the preceding experiment. The prompts relating to the identities were not modified. The prompts for the factor out rule were more general. Consider the student who asks for help at the problem state (3x+6)(3-2x)-(2x+3)(-8-4x). The prompt was formulated more laconically "factor out a common factor from (3x+6)(3-2x)-(2x+3)(-8-4x)." So that the student still had to find out by him(her)self the common factor of the expression. The comments on errors differentiate two cases, and the formulation of the comments was more precise about the origin of the error. (i) If the student gives a value of A (a numeral, a monomial or a binomial) that is not a common factor, the system picks out the terms that do not have A as a factor. (ii) If the student wants to factor out a numeral, a monomial or a binomial from a product (for example "factor out 3 from (3x+6)(3-3x)") the system says: "I cannot do what you asked, because common factor applies only to sums." The results showed that the improvement in the matching knowledge about the factor out rule was statistically significantly better for the subjects in this learning experiment than in the previous one.

An experiment carried out in 1997

The previous experiments used only the action mode. A learning experiment was then conducted in 1997 in which we compared four groups of 20 students. The 80 students were selected by a pre-test in order to obtain four groups that did not differ in their factorisation problem solving ability: low level and high level students were eliminated from the experiment. The 80 students were randomly assigned to one of the four groups in a 2 by 2 factorial plan: two learning contexts (the learning-with-examples context and the learningjust-by-solving context), and presence or absence of help/explanation from the system. These results suggest that, concerning the matching knowledge, learning by action is more effective than learning by observation [START_REF] Nguyen-Xuan | Learning to match algebraic rules by solving problems and by studying examples with an ILE[END_REF].

Conclusion, current state and future work

Conclusion

A priori, scientific research does not have the role of realising products, with the industrial and commercial meaning of this term. As an explanation of that situation, we could say that the development of prototypes is sufficient and satisfactory enough to validate a theory, or to allow experiments. This was the way we worked during the last decade.

From 1987 to 1997, the various prototypes built up for APLUSIX filled these two objectives: (1) the approach adopted and the problem-solving model (the MCA model cited in section 2.2) made it possible indeed to analyse, model and help algebraic manipulation done by students during problem-solving activities in pre-algebra; (2) experiments led to the refinement of the models and trying to answer general questions about learning theories.

But, since the beginning of 1998, the APLUSIX team has decided to design a new version of APLUSIX which will not be a prototype but a product. The work considered for this purpose must tackle constraints of several kinds, which give an explanation of our motivation: 1) constraint of openness: we want to continue the research on the modelling of the cognitive processes of problem-solving and the research on the modelling of the learning processes; 2) constraints of availability: we want to give a general tool (APLUSIX) to teachers and researchers in psychology and didactics to take part in the research (this introduces one of the major characteristics of a product: to be available for all); 3) constraint of quality (design): we want to allow the use and the realisation of experiments on a large scale (feedback is waited for), which introduces other characteristics of a product: robustness, ergonomics; 4) constraints of adaptability and parametrisation: we want to develop the scope of APLUSIX, development in terms of the variety of possible activities (factorisation, equation solving calculus of primitives, etc.) and in terms of available school levels. The parametrisation is intended to allow the product to adapt its functions according to the desired use.

The terms openness, availability, quality, parameterisation summarise our objectives. Some of them are clearly the attributes one can hope in a product. The others relate to the research aspect that APLUSIX will continue to have.

From prototype to product: rewriting rules for the knowledge base

The flexibility offered by a prototype is not conceivable for a product under the same conditions. If one can imagine modifying a prototype to carry out such or such experiment or such adjustment, that is not easily conceivable with a product. Each modification would mean a new version of the product to maintain and commercialise. And yet we want to have the same flexibility with the future product as with the preceding prototypes. In order to obtain such flexibility, we have changed the framework.

One major change is: the product that we are realising is constructed over one knowledge base which is partly external. This part of the knowledge base will be represented by a set of rewriting rules written in a natural form. The knowledge base will be accessible to an advanced user (teacher or experimenter). If one occults the aspects related to the robustness, the availability and maintenance, the choice for a definition of the knowledge base, independent and accessible, is a major difference between the preceding prototypes and the product to come. We count on this major characteristic of the next APLUSIX to ensure the openness and the parametrisation of the product we want to design.

The development of the elements characteristic of the external knowledge base of APLUSIX was based on the preceding experiments and the study of the preceding prototypes. In particular, the study of the preceding prototypes emphasised a set of parameters and a set of knowledge in algebra used, implicitly or not: -parameters of environment (visibility of rules, availability of help and diagnostic) -parameters for the application of rewriting rules (search for sub-expressions, conceptual matching, matching modulo a coefficient) -grouping of rewriting rules in semantic groups (factorisation, reduction, development, etc.) -establishment of a hierarchy in the application of rewriting rules. This set of parameters will be defined in the knowledge base. Algebraic knowledge contained in the preceding prototypes was expressed in a compiled form. In the same way, the matching mechanisms specific to algebra were compiled (matching of sub-expressions, conceptual matching, matching modulo a factor). Sometimes these mechanisms were badly distinguished from the rest of the code. From a general point of view, this knowledge was static. They evolved only with the change of the prototype. Furthermore, this knowledge was not accessible in extenso to non-specialists. However a mathematical form, was diffused [START_REF] Nicaud | Modélisation en EIAO, les modèles d'APLUSIX[END_REF]. It is this form which was used as a starting point for writing the knowledge base of the future product. For example, in [START_REF] Nicaud | Modélisation en EIAO, les modèles d'APLUSIX[END_REF] three rules like the following expressed factorisation by a common factor:

If E is of the form A1+... +An with n>= 2 and each Ai admits the factor U with degree pi and Q is a canonical integer ranging between 1 and the minimum of pi and for any i, U with the degree Q is a factor of Ai with cofactor Ci then replace E by Uq(C1+... +Cn)

The equivalent formulation that we wish to obtain is the following much more natural one: a*b+a*c -> a*(b+c). The use of this rule is not straightforward. It is done using a complex matching mechanism which takes into account the concepts seen in 2.1.

Note: If the definition of the rules is opened, the matching mechanism is closed. It is compiled and comprises non trivial mathematical knowledge (associativity, commutativity, identity elements, etc.). However this mechanism is dependent on parameters. These parameters can be changed by program, and defined a priori in the knowledge base for each occurrence of a rewriting rule in one group.

Figure 1 :

 1 Figure 1: A two branch tree generated by the system.

Figure 3 :

 3 Figure 2The action menu

  mode action) (expand-and-reduce yes) (help yes) (delay-help 5) (commute no) (a2+2ab+b2-U no) (do-one-step no) (step-by-step no)) ((or (> nb-aide 0) (eq erreur factor-out-error) abandon) 1d1) (t 1b))

A product soon

The current state of the work is the following: (1) strategic aspects of the problem-solving are designed, (2) display/selection of algebraic expressions are realised, (3) creation ex nihilo of algebraic and the strategic elements have been initialised, (4) a plain algorithm for matching terms with rewriting rules (with matching of sub-expressions modulo associativity and commutativity) is already obtained, (5) an advanced matching algorithm (with conceptual matching, matching modulo a factor) is nearly achieved. A first version of the final product, with more or less the same functionalities as APLUSIX-M0-V2, is planned for the end of 1999. Other versions, with a developed scope are planned for 2000. Our current platform for the work is Windows 95 and Object Oriented Pascal Delphi.


Lucas Fonseca
email: lucasfonseca@lara.unb.br

Antônio Bó

David Guiraud

Benjamin Navarro

Anthony Gélis

Christine Azevedo-Coste

Investigating Upper Limb Movement Classification on Users with Tetraplegia as a Possible Neuroprosthesis Interface

Spinal cord injury (SCI), stroke and other nervous system conditions can result in partial or total paralysis of individual's limbs. Numerous technologies have been proposed to assist neurorehabilitation or movement restoration, e.g. robotics or neuroprosthesis. However, individuals with tetraplegia often find difficult to pilot these devices. We developed a system based on a single inertial measurement unit located on the upper limb that is able to classify performed movements using principal component analysis. We analyzed three calibration algorithms: unsupervised learning, supervised learning and adaptive learning. Eight participants with tetraplegia (C4-C7) piloted three different postures in a robotic hand. We achieved 89% accuracy using the supervised learning algorithm. Through offline simulation, we found accuracies of 76% on the unsupervised learning, and 88% on the adaptive one.

I. INTRODUCTION

Diseases and lesions of the nervous system can have dramatic consequences for patients. Cases like stroke or spinal cord injury (SCI) can cause partial or complete paralysis of limbs. In the worst cases, individuals lose not only lower limbs motor capabilities, usually relying on a wheelchair for locomotion, but also upper limb motion [START_REF] Popovic | Control of Movement for the Physically Disabled[END_REF].

Numerous technologies have been proposed as solutions for upper limbs disabilities, such as functional electrical stimulation (FES) [START_REF] Hart | A comparison between control methods for implanted FES hand-grasp systems[END_REF], and robotic devices [START_REF] Lotte | Wireless intraoral tongue control of an assistive robotic arm for individuals with tetraplegia[END_REF]. However users with tetraplegia often face challenges on controlling these devices. Relative success has been achieved by either simple interfaces [START_REF] Lobo-Prat | Non-invasive control interfaces for intention detection in active movement-assistive devices[END_REF] or invasive brain-computer interfaces [START_REF] Wodlinger | Ten-dimensional anthropomorphic arm control in a human brain-machine interface: difficulties, solutions, and limitations[END_REF]. Whenever the user still has some controllable upper limb motor capability, it is possible to use that to control a device [START_REF] Peckham | Efficacy of an implanted neuroprosthesis for restoring hand grasp in tetraplegia: A multicenter study[END_REF]. The challenge is then to identify the intended movement performed by the user. Electromyography (EMG) has been considered [START_REF] Peckham | Efficacy of an implanted neuroprosthesis for restoring hand grasp in tetraplegia: A multicenter study[END_REF], [START_REF] Tigra | A novel EMG interface for individuals with tetraplegia to pilot robot hand grasping[END_REF], however muscular activitybased control presents some issues like the need for one sensor per muscle. Also, the presence of co-contraction makes it difficult to contract individual muscles and, when FES is present, the stimulation artifacts in the EMG signal have to be considered. Instead of muscle activity, movements can be used as inputs. In [START_REF] Sarcevic | Wireless Sensor Network based movement classification using wrist-mounted 9DOF sensor boards[END_REF], postures performed by healthy subjects were classified using a method based on Linear Discriminant Analysis and 2 9-DOF (degrees of freedom) inertial measurement units (IMUs). Additionally, [START_REF] Merad | Pre-clinical evaluation of a natural prosthetic elbow control strategy using residual limb motion and a model of healthy inter-joint coordinations[END_REF] used multiple IMUs and a radial basis function network based regression algorithm to control an elbow prosthesis with residual upper limb movement on amputees. Recently, on [START_REF] Elias B Thorp | Upper Body-Based Power Wheelchair Control Interface for Individuals With Tetraplegia[END_REF], three subjects with tetraplegia controlled a powered wheelchair using residual shoulder movement. The method in [START_REF] Elias B Thorp | Upper Body-Based Power Wheelchair Control Interface for Individuals With Tetraplegia[END_REF] is based on Principal Component Analysis (PCA) and 4 IMUs.

In this work we propose a system capable of associating shoulder movements to three commands on a robotic hand. It is based on a single IMU with only accelerometer and gyroscope. For that, we developed three classifiers based on PCA. Eight subjects with tetraplegia piloted the robotic hand postures with one classifier, and the other two were later evaluated through simulation.

II. SUBJECTS AND METHODS

Eight patients with tetraplegia were selected at Propara Neurological Rehabilitation Center in Montpellier, France. They had SCI levels C4-C7, American Spinal Injury Association impairment scale A or B and stable medical condition. They were males between 18 and 65 (39±15) years old, and had lesion chronocity higher than 6 months (14±17 years). The protocol was approved by a national ethical committee (CPP 2016-A00711-50) and subjects provided informed consent prior to their participation. They had limited hand movement, but could perform controlled shoulder movement.

For validation purposes we used the Shadow Dexterous Hand (Shadow Robot Company, London, UK), a robotic hand that can reproduce human movements with great fidelity. We set up two different postures on it: in opened position (fingers fully extended); and in closed position (fingers fully flexed) in a grasping attitude. We also configured a rest position (semi-flexed fingers).

One IMU (Hikob© Fox, Villeurbanne, France) was positioned either on the subject's upper arm or shoulder depending on their ability to execute two distinct movements in a reproducible manner. The IMU communicated wirelessly with a a computer at approximately 50 Hz. It sent 3-axis accelerometer and 3-axis gyroscope data. No magnetometer was used in order to simulate a scenario where low processing power and power consumption are issues, e.g. if it were implanted.

Subjects faced the robotic hand so they could see it react to their movements. The set-up is illustrated on Fig. 1, where the robotic hand is in the closed position.

Two movements were calibrated and associated to two commands to control the robotic hand. Since there are three different positions to be controlled by two movements, the finite state machine depicted on Fig. 2 was employed. Each command had to correctly classify the user's movement to activate the desired posture -robotic hand opened or closed -from the rest position. When in one of these two postures, any movement triggered the rest position.

The experimental protocol consisted of a calibration and a validation phase. On the calibration phase, we asked users to repeatedly perform up to four movements during 10 seconds each. These could be any repeatable and distinct movement, like moving the shoulder up or forward, and returning it to the initial position. On the validation phase we asked them to pilot the robotic hand. Each posture was comprised of two movements: one starting on the rest position, which had to be correctly classified by the system, and one back to the rest position, which had only to be detected, but not classified (see Fig. 2). Each of the two postures (open/close) was executed 5 times in a random order following our instructions.

We developed three algorithms: unsupervised learning, supervised learning, and unsupervised adaptive learning. The unsupervised learning algorithm collected data from the IMU during the calibration phase and derivated it to remove the steady state component and to ignore initial angular positions. Thresholds were then calculated according to Eq. 1.

T = max dX dt 2 (1)
where vector X features the raw sensor measurements and vector T is the threshold vector. An overlaying moving window of 1 second was defined. Whenever its center value was greater than a threshold, a movement was detected and characterized as a 6-dimension point based on the Root Mean Square (RMS) of each of the 6 axis. A PCA is then applied to these points and the two first principal components are used to find two movement centroids based on the mean 2-dimensions coordinates of all points. After that the system calculates the centroids and points on all possible combination of two movements. It then proposes the best combination based on the highest score s, defined by Eq. 2.

s = d 1,2 σ 1 + σ 2 (2)
where d 1,2 is the distance between the two centroids, and σ i is the standard deviation of the distance of all points of movement i to that movement centroid. After calibration, the system could start classifying new movements associating the new PCA calculated 2dimensional point to the closest centroid, and activating the appropriate robotic hand command.

On the supervised learning algorithm the user performed the previously calibrated movements and watched the robotic hand reaction. We then observed the PCA graphical representations of these points in real time. If the new points seemed to appear far from the initially calibrated ones, we recalibrated the system with them, and without the old ones. It was also possible to arbitrarily choose each centroid location on the 2-dimensional space. With these tools we were able to manually tune the learning process until the users felt they had good control over the robotic hand.

On the adaptive learning algorithm, this process of improving the calibration is automated. After every new movement during the validation phase, the system is recalibrated using the new point, removing the oldest one.

Note that, differently from the supervised learning system, the other two are completely automatic. The three systems are summarized in Fig. 3. Users performed the experiments with the supervised learning algorithm. All data was recorded to later simulate the two other algorithms.

III. RESULTS

The average performance achieved experimentally with the supervised algorithm and through simulation with the other two is shown on Table I. Results were calculated as the percentage of correctly classified commands. Note how the unsupervised had inferior results (76%) when compared to the supervised (89%) and adaptive (88%). Additionally, the adaptive learning algorithm would have the best performance were it not for patient p1.

After the initial calibration phase, it was possible to analyze its results on a graphic that represents the two main components of the PCA. Fig. 4 shows an example of one experiment.

The adaptive learning algorithm was simulated with points from the validation phase. Fig 5 shows the performance obtained along all steps of the learning process. Note how the performance seems to further improve after the seventh point.

IV. DISCUSSION

We developed a system capable of classifying two shoulder movements performed by persons with tetraplegia with 89% accuracy. Even though the performance achieved by [START_REF] Sarcevic | Wireless Sensor Network based movement classification using wrist-mounted 9DOF sensor boards[END_REF] (96%) was greater, tests were done only on able-bodied subjects. Both [START_REF] Radmand | On the Suitability of Integrating Accelerometry Data with Electromyography Signals for Resolving the Effect of Changes in Limb Position during Dynamic Limb Movement[END_REF] and [START_REF] Krasoulis | Improved prosthetic hand control with concurrent use of myoelectric and inertial measurements[END_REF] used multiple IMUs and EMG, with many more features than this work, to classify upper limb movement with LDA, the latter achieving results close to 80% on a 6 classes scenario. It is expected users with tetraplegia to have lower dexterity than healthy subjects, but our results indicate that, given more training for both users and system, better results are achievable. Furthermore, in comparison to the EMG approach, our system is capable of classifying multiple movements with a single IMU.

During the calibration phase, graphical visualizations as presented on Fig. 4 helped to assess the supervision process and manually tune the calibration. This, therefore, was a subjective process. Still, we were able to tune the system so the supervised learning algorithm presented the best results, while the unsupervised learning method presented the worst, highlighting the importance of the supervision on learning tasks with low informations level.

It was clear the difference in subject attitude and performance between the calibration (no feedback) and the validation (visual feedback from the robotic hand) phases. It was not unusual for them to change the movements then. When that happened, if no supervision was allowed, we would see results as the one shown on Fig. 6. That explains some of the bad performances, as subject p5's on the unsupervised algorithm. Nevertheless, these are also the cases when the adaptive learning performs best because it is capable of forgetting those initial trials and "focus" only on the recent ones. Note how p5's performance improves both on the supervised and adaptive algorithms. Were the adaptive algorithm working on real time, we expect its performance would improve in a similar manner as depicted on Fig. 5. Still, visual feedback representing a deeper functioning of the system and user's performance may be beneficial [START_REF] Elias B Thorp | Upper Body-Based Power Wheelchair Control Interface for Individuals With Tetraplegia[END_REF].

Observing Fig. 5, we can see the performance only improves after many new points are considered for learning. It possibly happens because the system still recalls the original, outdated points. As soon as the new points become a majority, their cumulative weight overcomes the old ones. It is also important to note that the adaptive learning system is fully automated, which can be an advantage on real world scenarios, when a user would possibly calibrate and operate it without specialized assistance. Since only the supervised learning system was tested by the subjects, and not the adaptive, such scenarios are yet to be evaluated.

Although no subject had cognitive impairments, some of them presented difficulties on operating the system. Most of them had never seen a robotic hand, and none was ever able to control one. In deed, novel technologies and control interfaces may initially be hard to use [START_REF] Elias B Thorp | Upper Body-Based Power Wheelchair Control Interface for Individuals With Tetraplegia[END_REF]. As a result, sometimes they lost focus on the task, and performed careless movements. That was particularly true for subject p6. Once again, in this case, we can see a slight improvement when using the adaptive learning system, highlighting the importance of the algorithm adaptability, either supervised or not.

In a larger clinical trial, our system should be adapted to control a more functional neuroprosthesis, e.g. FES on forearm to control grasping. The current finite state machine requires every posture to return to the rest position before performing a new one, which was useful for the algorithm evaluation, but is not practical. In addition, triggering the predefined movements works well for complex tasks as grasping, but lacks fine control like proportional force or hand opening range. This, too, could be addressed with residual shoulder movement [START_REF] Elias B Thorp | Upper Body-Based Power Wheelchair Control Interface for Individuals With Tetraplegia[END_REF], and could even be integrated in a larger finite state machine. Nevertheless, the simple setup of a single commercial IMU and flexible, quick learning algorithm provide easy adaptation and scalability.

V. CONCLUSION Complex neuroprosthesis can be controlled by residual movement in users with tetraplegia. We developed a system capable of classifying different shoulder movements using a single wireless IMU with only accelerometer and gyroscope. We found that results close to 90% could be achieved either by a supervised system or by a unsupervised adaptive system with minimum user training. Regardless of the approach, the calibration process is simple and fast. To the extend of our knowledge, this is the first work to perform movement classification experiments where subjects with tetraplegia controlled a robotic hand. Future works include longer training and sessions with functional daily life activities.

Figure 1 .

 1 Figure 1. Experimental set-up.

Figure 2 .

 2 Figure 2. Finite state machine used to control the robotic hand depending on the classified movement performed.

Figure 3 .

 3 Figure 3. Learning processes block diagram.

Figure 4 .

 4 Figure 4. Supervised learning and classification for subject p8. The two axis represent the two principal components. Squares represent the movements used for learning and the asterisks the movements classified by the system. C1 and C2 are the centroids for movements 1 and 2, respectively. The circles, for visualization purposes only, represent three standard deviations of the euclidean distance of the squares to their centroids.

Figure 5 .

 5 Figure 5. Adaptive learning algorithm process. The average best result was achieved when learning from 9 points. For comparison purposes, the red dashed line indicate the unsupervised learning system performance, and the yellow dashed line represent the supervised learning system performance.

Figure 6 .

 6 Figure 6. Unsupervised learning system test for subject p5. Note how almost all movements were classified as Movement 1, and they were significantly different than those initially calibrated (square points).

Table I MEAN

 I PERFORMANCE RESULT ON THE RANDOM 10 MOVEMENTS SEQUENCE TEST. THE SUPERVISED LEARNING SYSTEM SCORES WERE OBTAINED FROM TESTS WITH THE SUBJECTS, WHILE THE OTHER TWO WERE SIMULATED.

	Subject		Performance [%]
		Supervised Unsupervised Adaptive
	p1	90	70	60
	p2	100	100	100
	p3	90	50	90
	p4	70	70	70
	p5	100	60	100
	p6	70	70	80
	p7	90	90	100
	p8	100	100	100
	Average	89	76	88

This work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil, and by the LabEx NUMEV incorporated into the I-Site (Montpellier, France).


Bruna Rego De Vasconcelos

Lulu Zhao

Patrick Sharrock

Ange Nzihou

Doan Pham
email: doan.phamminh@mines-albi.fr

Bruna Rêgo De Vasconcelos

Catalytic transformation of carbon dioxide and methane into syngas over ruthenium and platinum supported hydroxyapatites

Keywords:

come

Introduction

Synthesis gas, or syngas, is a gas mixture containing mainly carbon monoxide (CO) and hydrogen (H 2 ). Commercialized firstly in 1800s by the London Gas, Light, and Coke Company, syngas has nowadays several applications for illuminating cities, providing heat and power, fueling vehicles through both direct use with gas engine, and conversion to liquid fuels, as well as for obtaining chemicals or intermediates by different chemical or biological transformation processes [START_REF] Coolcock | A review of cleaning technologies for biomass-derived syngas[END_REF][START_REF] Kundiyana | Syngas fermentation in a 100-L pilot scale fermentor: design and process considerations[END_REF]. By catalytic way, syngas can be converted into other platform molecules or final products such as methanol, ethanol, aldehydes, waxes, diesel, olefins, gasoline, electricity, etc. [START_REF] Coolcock | A review of cleaning technologies for biomass-derived syngas[END_REF][START_REF] Richardson | A short overview on purification and conditioning of syngas produced by biomass gasification: catalytic strategies, process intensification and new concepts[END_REF].

Syngas can be obtained from the gasification of coal, wood, agricultural and forestry residues, and biomass-containing wastes [START_REF] Atikah | Assessing the gasification performance of biomass: a review on biomass gasification process conditions, optimization and economic evaluation[END_REF]. Gasification process takes place at high temperature (up to about 1000 • C), using different atmospheres of vapor, carbon dioxide, nitrogen, oxygen, or mixture of these components. Gas product of this process needs to be purified by suitable technologies as a function of its use [START_REF] Abdoulmoumine | A review on biomass gasification syngas cleanup[END_REF].

Syngas can also be obtained from the reforming of light hydrocarbons such as methane. Different oxidants can be used, in particular oxygen and carbon dioxide. Thus, catalytic partial oxidation of methane to syngas using molecular oxygen can be selectively carried out over highly dispersed nickel supported ceria (Ni/CeO 2 ), according to Eq. (1) [START_REF] Zhu | Catalytic partial oxidation of methane to synthesis gas over Ni-CeO2[END_REF]. Both the conversion of methane and the selectivity into CO reached more than 90% above 650 • C for a mixture having the molar ratio of methane to oxygen equal to 2. Previously, Choudhary et al. showed that Co/MgO catalyzed selectively the oxidation of methane by molecular oxygen into syngas with 75% of methane conversion and 90-91% of CO and H 2 selectivity at 700 • C [START_REF] Choudhary | Low-temperature selective oxidation of methane to carbon monoxide and hydrogen over cobalt-MgO catalysts[END_REF].

CH 4 + 1/2O 2 → CO + 2H 2 H • 298 = -36 kJ mol -1
(1)

CH 4 + CO 2 → 2CO + 2H 2 H • 298 = 247 kJ mol -1 (2)
Using CO 2 as oxidant, methane can also be reformed into syngas by catalytic way, according to Eq. [START_REF] Kundiyana | Syngas fermentation in a 100-L pilot scale fermentor: design and process considerations[END_REF]. Nickel-based catalysts seemed to be the most appropriate for this reaction. Boukha et al. showed that an equimolar mixture of CH 4 and CO 2 was quasitotally converted at high temperature (650-800 • C) with high selectivity into syngas over nickel supported on phosphate-based supports [START_REF] Boukha | Methane dry reforming on Ni loaded hydroxyapatite and fluoroapatite[END_REF]. High performance of nickel supported on alumina and alumina-aluminum phosphate was also obtained at the temperature range of 750-800 • C for this catalytic process [START_REF] Pelletier | Stable nickel catalysts with alumina-aluminum phosphate supports for partial oxidation and carbon dioxide reforming of methane[END_REF]. Nickel-based catalysts supported on other supports such as ceria-zirconia, zeo- lite, manganese oxide, silica, magnesium oxide, carbon nanotube, mixture of zirconia-silica oxides, hydrotalcite, Mo 2 C, etc. were generally found to be active for the conversion of CO 2 /CH 4 mixture at high temperatures, and with high selectivity in syngas product [START_REF] Awa | Tunable ceria-zirconia support for nickel-cobalt catalyst in the enhancement of methane dry reforming with carbon dioxide[END_REF][START_REF] Wang | A comparison study on methane dry reforming with carbon dioxide over LaNiO3 perovskite catalysts supported on mesoporous SBA-15, MCM-41 and silica carrier[END_REF][START_REF] Littlewood | Ni0.05Mn0.95O catalysts for the dry reforming of methane[END_REF][START_REF] Ren | High-performance Ni-SiO2 for pressurized carbon dioxide reforming of methane[END_REF][START_REF] Zanganeh | Preparation of nanocrystalline NiO-MgO solid solution powders as catalyst for methane reforming with carbon dioxide: effect of preparation conditions[END_REF][START_REF] Ma | Effect of catalytic site position: nickel nanocatalyst selectively loaded inside or outside carbon nanotubes for methane dry reforming[END_REF][START_REF] Liu | Methane reforming with carbon dioxide over a Ni/ZiO2-SiO2 catalyst: influence of pretreatment gas atmospheres[END_REF][START_REF] Serrano-Lotina | Influence of the operating parameters over dry reforming of methane to syngas[END_REF][START_REF] González | Dry reforming of methane on Ni-Mg-Al nano-spheroid oxide catalysts prepared by the sol-gel method from hydrotalcite-like precursors[END_REF][START_REF] Shi | Ni-modified Mo2C catalysts for methane dry reforming[END_REF]. Other active metals such as cobalt, copper, ruthenium, and rhodium were also studied in the reforming of methane by carbon dioxide, which showed high catalytic performances [START_REF] Rahemi | Non-thermal plasma assisted synthesis and physicochemical characterizations of Co and Cu doped Ni/Al2O3 nanocatalysts used for dry reforming of methane[END_REF][START_REF] Homsi | A highly reactive and stable Ru/Co6-xMgxAl2 catalyst for hydrogen production via methane steam reforming[END_REF][START_REF] Ghelamallah | Impact of barium and lanthanum incorporation to supported Pt and Rh on ␣-Al2O3 in the dry reforming of methane[END_REF].

Syngas formation from catalytic conversion of a mixture of methane and carbon dioxide seems to be pertinent from point of view of the sustainable development concept. In fact, methane and carbon dioxide are the two main components of biogas and natural gas. This process offers new valorizations of biogas and natural gas including the transformation of carbon dioxide into useful products. However, to the best of our knowledge, this catalytic process has not been developed at large industrial scale yet. This may be related to the fact that the reaction of methane with carbon dioxide into syngas is highly endothermic (Eq. ( 2)). In fact, the C O bond energy in carbon dioxide molecule is 724 kJ mol -1 [START_REF] Chandra | Comprehensive Inorganic Chemistry[END_REF], so the transformation of this molecule must be activated. High temperature, typically in the range of 650-950 • C, is needed for getting high catalytic conversion of methane and carbon dioxide into syngas. This temperature range leads to high energy consumption, and also to the deactivation of catalyst. The deactivation is principally due to coke deposition from side reactions such as methane cracking, reverse water-gas-shift, as well as to the sintering of both active phase and catalyst support. For example, using TEM analysis, Tsyganok et al. highlighted coke deposition on the surface of a nickel-based catalyst [START_REF] Tsyganok | Mg-Al layered double hydroxide intercalated with [Ni(edta)]2-chelate as a precursor for an efficient catalyst of methane reforming with carbon dioxide[END_REF]. This deposition could reach up to 9.9 wt.%. Most of the larger nickel particles (15-35 nm) were encapsulated with graphitic layers. High energy consumption and catalytic deactivation appear as the main drawbacks of the dry reforming of methane for industrial scale-up.

This work is devoted to the synthesis of hydroxyapatite supported ruthenium or platinum catalysts, and to the investigation of their catalytic performance in the transformation of methane and carbon dioxide into syngas. Ruthenium and platinum are well known as active phases in different catalytic reactions, in particular for reforming processes. Hydroxyapatite is chosen as support material by its thermal stability, and also by its possible high specific surface area, and its basicity properties [START_REF] Pham Minh | Thermal behavior of apatitic calcium phosphates synthesized from calcium carbonate and orthophosphoric acid or potassium dihydrogen orthophosphate[END_REF]. The formation of ruthenium and platinum particles on HAP surface using different synthesis methods, and the reactivity of the prepared ruthenium and platinum catalysts are discussed. We have been also successful in the quantification of water formed during the dry reforming of methane process. To the best of our knowledge, the quantification of water has never been previously reported in the literature for this process. This allows establishing correctly the mass balance of the process since it was formed at a non-negligible amount in this reaction.

Materials and methods

Catalyst preparation

Hydroxyapatite powder was synthesized by the conventional precipitation method using orthophosphoric acid and calcium The deposition of ruthenium and platinum on HAP support was carried out by three methods using RuCl 3 and K 2 PtCl 4 as metal precursors (Aldrich, p.a. grade): Incipient wetness impregnation (IWI), cationic exchange (CEX), and excess liquid phase impregnation (LIM) [START_REF] Pham Minh | Degradation of olive oil mill effluents by catalytic wet air oxidation: 2-oxidation of p-hydroxyphenylacetic and p-hydroxybenzoic acids over Pt and Ru supported catalysts[END_REF]. IWI preparation was performed with both ruthenium and platinum (Table 1), because this method is simple and generally efficient for the deposition of well-dispersed metal particles for catalytic application. An aqueous solution of metal precursor was added drop-by-drop to HAP support in order to wet perfectly the powder without excess of the liquid phase. The concentration of the metals was calculated to reach the desired metals contents in the final solids. The mixture was dried at room temperature until the complete elimination of water (checked by infra-red measurement). CEX method was used for the preparation of ruthenium according to previous works, wherein ruthenium particle in the range of 3.0-5.5 nm were obtained [START_REF] Peeters | Alcohol amination with heterogeneous ruthenium hydroxyapatite catalysts[END_REF][START_REF] Akbayrak | Hydroxyapatite supported ruthenium(0) nanoparticles catalyst in hydrolytic dehydrogenation of ammonia borane: insight to the nanoparticles formation and hydrogen evolution kinetics[END_REF]. HAP powder was added to a diluted aqueous solution of RuCl 3 at room temperature under stirring (500 rpm) for 4 h. Then the suspension was filtered using 0.45 m filter-paper, and the solid was dried at room temperature up to the complete removal of residual water. LIM preparation was used for the deposition of platinum. This method was previously found as the most efficient for the dispersion of Pt on TiO 2 support [START_REF] Pham Minh | Degradation of olive oil mill effluents by catalytic wet air oxidation: 2-oxidation of p-hydroxyphenylacetic and p-hydroxybenzoic acids over Pt and Ru supported catalysts[END_REF]. HAP support was added into an aqueous solution of K 2 PtCl 4 under stirring for 24 h at room temperature in order to insert platinum species on the surface of the support. Then, platinum precursor was reduced by formaldehyde in KOH medium. The solid was recovered by filtration and dried at room temperature up to the complete elimination of residual water. For IWI and CEX methods, dried solids were calcined at 400 • C under air atmosphere. For LIM method, the dried catalyst was directly used for catalytic test, without further thermal treatment. Table 1 summarized the prepared catalysts.

Catalyst characterizations

Elemental analysis for the determination of metal loadings was carried out using ICP-AES method (HORIBA Jobin Yvon Ultima 2) after a mineralisation step. Specific surface area of solids was determined by BET method (Micrometrics Gemini Vacprep 061). Infra-red (FTIR) spectrum was recorded using a Shimadzu FTIR 8400S spectrometer. X-ray diffraction (XRD) was performed with a Phillips Panalytical X'pert Pro MPD diffractometer. The morphological and textural surface of the solid products was observed by scanning electron microscope (SEM) using a Philips XL30 ESEM apparatus (FEI Company), and by transmission electron microscope (TEM) using a FEG JEOL JEM 2100F equipped with a HAADF detector. This TEM apparatus is coupled with an EDS BRUKER which is equipped with a SDD detector (SDD of 127 eV resolution). Carbon content due to the deposition of carbonaceous species on the used catalyst was evaluated by CHNS analyzer (CE instruments, NA2100 series).

Catalytic test

The reaction of methane with carbon dioxide was carried out using either a U-sharp quartz reactor or a stainless steel fixed-bed reactor. Details of these reactors will be presented later. Catalytic test was carried out using gas mixture containing 20 vol.% of CH 4 , 20 vol.% of CO 2 and 60 vol.% of N 2 . The mixture of gas products from the outlet of the reactor were analysed by a micro-chromatograph analyser (Agilent 3000 GC) which allowed determining the volume percentage of each gas in this mixture.

Results and discussion

Elemental analysis

ICP-AES was performed for the determination of Ru and Pt contents of the dried or calcined catalysts (Table 2). High deposition yields (79-90%) were observed for both the metals by different deposition methods. The loss was probably due to the fixation of the metals on flask walls during the preparation.

Specific surface area (S BET )

Specific surface area measurement was performed with the initial HAP support and the calcined catalysts (Table 3). HAP support had the specific surface area of 60 m 2 g -1 . As expected, the deposition of Ru and Pt (<1 wt.%) did not significantly modify its specific surface area.

SEM and TEM

Fig. 1 presents SEM and TEM images of Ru/HAP IWI, or HAP supported ruthenium catalyst which was prepared by IWI method and calcined at 400 • C. At micrometric scale (Fig. 1(A) and (B)), individual particles (yellow arrows) and agglomerates of these individual particles (yellow circle) could be observed, thanks to the difference of contrast between Ru-based compounds and the elements present in HAP support. At nanometric scale, Ru particles could be more easily observed. Their particle size varied from some nm to hundreds of nm (pink arrows, Fig. 1(D)). Ru particles did not have the expected spherical shape. On the other hand, irregular shape and rod shape were usually observed. Well-defined particles such as rod shape are generally formed by crystalline growth in solution with the presence of surfactant. In our case, no additional surfactant was used. So, understanding the formation of these well-defined Ru particles still needs scrutiny.

SEM and TEM images of Ru/HAP CEX are presented in Fig. 2. The results were similar compared to those in Fig. 1 for Ru/HAP IWI, with the formation of both individual Ru particles and agglomerates of these individual particles (SEM images, Fig. 2(A) and (B)). At nanometric scale, Ru-based particles of irregular shape or rod shape were also observed. The formation of Ru-based particles indicates that crystallization or agglomeration of Ru-based compounds took place when HAP particles were set in contact with RuCl 3 solution, and the expected cationic exchange between Ru 3+ and Ca 2+ did not happen or only partially occurred.

In contact with chloride anions, hydroxyl groups of apatitic structure can be partially replaced by chloride anions to form This result suggests that anionic exchange between chloride (Cl -) and hydroxyl (OH -) anions might also take place but the sensibility of the EDX analysis was not enough for the detection of chlorine resulting from this exchange. Further analysis such as secondary ion mass spectrometry (SIMS) may be useful to highlight this anionic exchange. Also, the calcination of the catalyst at 400 • C under air atmosphere did not allow the complete removal of chlorine from the catalytic solids.

Fig. 4 shows imaging of chemical elements present in Ru/HAP CEX. Rod and irregular Ru-based particles on the surface of HAP support could be observed. As observed previously for Ru/HAP IWI, Fig. 4 highlighted also the association of chlorine with ruthenium. As communicated above, ionic exchange between ruthenium species and calcium species, and between chloride and hydroxyl groups seemed to not happen. Fig. 5 shows SEM and TEM images of Pt supported HAP catalyst, prepared by excess liquid phase impregnation (Pt/HAP LIM). Pt-based particles and agglomerates were observed either at micrometric (Fig. 5 (A)) or nanometric (Fig. 5(B),(C) and (D)) scale. The size of Pt-based particles varied from some nm to hundreds of nm. Imaging analysis confirmed the presence of platinum particles at nanoscale (Fig. 6).

SEM and TEM images of Pt/HAP IWI are presented in Fig. 7. In contrast with previous catalysts, Pt-based particles of this catalyst could not be visible by SEM analysis suggesting the absence of particles or agglomerates at micrometric scale (Fig. 7(A)). At higher magnifications (Fig. 7(B) and (C)), TEM analysis highlighted the formation of Pt particles with particle size varying from less than 1 nm up to about 25 nm (pink arrows).

TG

The results of TG analysis of the initial HAP support, and the catalysts after calcinations are presented in Fig. 8. HAP support had different weight losses in the temperature range investigated, which correspond to the removal of surface moisture (around 100 • C), to the dehydration of hydrogenophoshate groups, and to the continuous dehydration of hydroxyl groups in the apatitic structure of HAP [START_REF] Lebugle | Effect of structure and composition on the thermal decomposition of calcium phosphates (Ca/P = 1.33)[END_REF][START_REF] Lazic | The effect of temperature on the properties of hydroxyapatite precipitated from calcium hydroxide and phosphoric acid[END_REF]. For Ru and Pt supported catalysts, the dehydration was less important up to 370 • C, because they were already calcined at 400 • C. Above 370 • C, they had the similar behavior compared to the initial HAP support.

FTIR and XRD

FTIR spectra of the initial HAP support and the calcined catalysts can be found in Fig. 9. Characteristic peaks of phosphate (1076, 1038, 960, 603, and 559 cm -1 ) and hydroxyl (633 cm -1 ) groups were found for HAP support [START_REF] Pham Minh | Carbonate-containing apatite (CAP) synthesis under moderate conditions starting from calcium carbonate and orthophosphoric acid[END_REF]. As expected, FTIR spectra of the calcined Ru and Pt catalysts did not have any significant difference compared to that of HAP support.

Fig. 10 shows XRD patterns of the initial HAP support and the calcined catalysts. HAP showed low crystallinity, which is generally observed for hydroxyapatite synthesized at moderate temperature (80 • C). For the calcined Ru and Pt catalysts, the calcination at 400 • C increased the crystallinity of HAP support. No crystalline phase of Ru-and Pt-based component was observed, because of their low contents in the prepared catalysts (<1 wt.%). According to the results of TEM-EDS analysis, either XRD or FTIR analyses did not reveal the presence of chloroapatite in the final prepared catalysts.

Comparative catalytic study

The first catalytic tests for comparing various catalysts prepared in this work were performed in a U-shape quartz reactor (Fig. 11). In the literature, the use of this reactor configuration is largely reported for bi-phasic gas-solid catalytic test. At laboratory scale, most work related to the transformation of methane and carbon dioxide into syngas was carried out with the U-shape quartz reactor [START_REF] Zhu | Catalytic partial oxidation of methane to synthesis gas over Ni-CeO2[END_REF][START_REF] Boukha | Methane dry reforming on Ni loaded hydroxyapatite and fluoroapatite[END_REF][START_REF] Awa | Tunable ceria-zirconia support for nickel-cobalt catalyst in the enhancement of methane dry reforming with carbon dioxide[END_REF][START_REF] Littlewood | Ni0.05Mn0.95O catalysts for the dry reforming of methane[END_REF][START_REF] Zanganeh | Preparation of nanocrystalline NiO-MgO solid solution powders as catalyst for methane reforming with carbon dioxide: effect of preparation conditions[END_REF][START_REF] Ma | Effect of catalytic site position: nickel nanocatalyst selectively loaded inside or outside carbon nanotubes for methane dry reforming[END_REF][START_REF] Liu | Methane reforming with carbon dioxide over a Ni/ZiO2-SiO2 catalyst: influence of pretreatment gas atmospheres[END_REF][START_REF] González | Dry reforming of methane on Ni-Mg-Al nano-spheroid oxide catalysts prepared by the sol-gel method from hydrotalcite-like precursors[END_REF][START_REF] Rahemi | Non-thermal plasma assisted synthesis and physicochemical characterizations of Co and Cu doped Ni/Al2O3 nanocatalysts used for dry reforming of methane[END_REF][START_REF] Tsyganok | Mg-Al layered double hydroxide intercalated with [Ni(edta)]2-chelate as a precursor for an efficient catalyst of methane reforming with carbon dioxide[END_REF][START_REF] Sun | CO2 reforming of CH4 over xerogel Ni-Ti and Ni-Ti-Al catalysts[END_REF]. For a given catalytic test, 500 mg of catalyst was introduced into the reactor. Then, it was heated by a vertical furnace to 400 • C at the rate of 20 • C min -1 under N 2 flux (70 N mL min -1 ). At this temperature, the reaction was started by feeding the reactor with the mixture of gas reactants (20 vol.% of CH 4 , 20 vol.% of CO 2 and 60 vol.% of N 2 ) at the flow rate of 70 N mL min -1 . The reaction was kept at this temperature for 1 h and gas product of the reaction was analyzed by an Agilent 3000 - GC. Then, the reaction temperature was changed to 500 • C at the heating rate of 20 • C min -1 , and was kept at this temperature for 1 h, under the flux of reactants. Gas product of the reaction was also analyzed by -GC. This procedure was repeated for 600 and 700 • C. Catalytic tests using successively-increased temperature programs were already reported by Baktash et al. [START_REF] Baktash | Alumina coated nickel nanoparticles as a highly active catalyst for dry reforming of methane[END_REF].

The initial HAP support had negligible catalytic activity under the reaction conditions used (result not showed). For Ru and Pt catalysts summarized in Table 1, the results obtained are shown in Fig. 12 for the evolution of the concentration of CH 4 and CO 2 . For all four catalysts, the concentration of CH 4 was always slightly higher than that of CO 2 , in the final gas product mixture. It may be due to the reverse water-gas-shift reaction, where CO 2 reacts with H 2 to form CO and H 2 O, as shown in Eq. ( 4) [START_REF] Shi | Ni-modified Mo2C catalysts for methane dry reforming[END_REF]. Ru catalysts were found active within the temperature range investigated (400-700 • C). But the deactivation seemed to be important. The reactivity of Ru/HAP IWI slowed down strongly within the first three hours of time-onstream when the reaction was kept at 500-700 • C. For Ru/HAP CEX, it partially lost its reactivity between 600 and 700 • C (decrease of H 2 and CO production at 700 • C). This was probably due to the formation of carbonaceous deposits on the surface of the catalysts, as illustrated in Fig. 13. Carbonaceous species covered the surface of Ru catalyst, leading to the reduction of available active sites and so causing the catalytic deactivation. This carbon deposition must be due to side reactions of the process, including the Boudouard reaction (Eq. ( 5)), and the methane cracking (Eq. ( 6)).

CH 4 + CO 2 → 2CO + 2H 2 H • 298 = 247 kJ mol -1
(3)

CO 2 + H 2 → CO + H 2 O H • 298 = 41 kJ mol -1 (4) 2CO → C + CO 2 H • 298 = -172 kJ mol -1 (5) CH 4 → C + 2H 2 H • 298 = 75 kJ mol -1 (6)
As expected, CO and H 2 were found to be the main gas products of the reaction. No other peak was detected from the mixture of gas products of the reaction by -GC analysis. In all cases, the concentration of CO was systematically higher than that of H 2 . As explained above, the water-gas-shift reaction must happen (Eq. ( 4)), taking into account the fact that the concentration of CO 2 was always smaller than that of CH 4 in the final gas products. Platinum catalysts were found active in this reaction. Pt/HAP IWI was much more active than Pt/HAP LIM. This seemed to be in coherence with SEM and TEM analyses. In fact, Pt particles present in Pt/HAP IWI (Fig. 7) were more dispersed than those present in Pt/HAP LIM (Fig. 5). This means that Pt is more available when prepared by IWI method compared to LIM method. For Pt/HAP IWI, at 700 • C, the concentrations of CH 4 and CO 2 remaining in the gas product mixture were around 6 and 9%, respectively, for the reaction time of 5 h at this temperature.

Isothermal test

The U-shape quartz reactor above has advantage to be simply designed and fabricated. However, powder catalyst cannot be really immobilized under gas stream. Consequently, when gas flow rates accidentally increase, catalyst bed becomes fluidized and can get out the reactor. The risk of preferential gas passage may also be present. Thus, a stainless steel fixed-bed reactor was designed and fabricated for isothermal catalytic test. Fig. 14 shows the scheme of this reactor.

The same reactants mixture was used for the isothermal catalytic test. The catalyst bed was now fixed between two beds of inert alumina. The reaction temperature was controlled by a thermocouple, set at the center of the catalyst bed. At the outlet of the reactor, a gas counter was used for measuring the total gas flow rate. From this last one and the concentration of each gas, analyzed by -GC, the molar flow rate of each gas at the outlet of the reactor (Q i , mol h -1 ) could be obtained. The conversion and the selectivity of the reaction were thus calculated as follows:

X CH4 , % = Q E CH4 -Q O CH4 Q E CH4 × 100 (7) X CO2 , % = Q E CO2 -Q O CO2 Q E CO2 × 100 (8) Sel CO , % = Q O Oxygen Q T Oxygen × 100 (9) Sel H2 , % = Q O Hydrogen Q T Hydrogen × 100 (10)
where: X CH4 and X CO2 : conversion of CH 4 and CO 2 , respectively; Q E CH4 and Q O CH4 : molar flow rate of CH 4 (mol h -1 ) at the inlet and outlet of the reactor; Q E CO2 and Q O CO2 : molar flow rate of CO 2 (mol h -1 ) at the inlet and outlet of the reactor; Sel CO and Sel H2 : selectivity of the reaction in CO and H 2 , respectively; Q E Oxygen and Q O Oxygen : atomic flow rate of oxygen (mol h -1 ) at the inlet (under CO 2 form) and outlet (under CO form) of the reactor; Q E Hydrogen and Q O Hydrogen : atomic flow rate of hydrogen (mol h -1 ) at the inlet (under CH 4 form) and outlet (under H 2 form) of the reactor.

The major problem of this catalytic process is the deactivation due to carbon deposition. This deposition is favored by decreasing reaction temperature [START_REF] Pakhare | A review of dry (CO2) reforming of methane over noble metal catalysts[END_REF]. So, the isothermal catalytic test was carried out at 700 • C. Pt/HAP IWI was selected for this test because it appeared as the most performant catalyst from Fig. 12. The catalyst was heated under nitrogen (70 N mL min -1 ) up to 700 • C. At this temperature, the reactor was fed with the mixture of reactants containing 20 vol.% of CH 4 , 20 vol.% of CO 2 and 60 vol.% of N 2 (70 N mL min -1 ) for starting the catalytic test. Fig. 15(A) simply reports the composition of gas at the outlet of the reactor obtained by -GC. These results confirmed those obtained with the U-shape quartz reactor (Fig. 12 for Pt/HAP IWI catalyst at 700 • C). The remaining concentration of CH 4 and CO 2 at the outlet of the reactor was about 7-9 and 6-7% within the first hours of reaction, respectively. These correspond to the conversion of CH 4 and CO 2 close to 50 and 67%, respectively (Fig. 15(B)). The catalyst reached the stability after only the first ten hours of time-on-stream. The initial deactivation could be attributed to the carbonaceous deposition, as shown by SEM analysis (Fig. 16). Crystallites of HAP support were slightly covered by amorphous carbonaceous species. But Pt particles, with high contrast, could be observed (yellow arrows, Fig. 16), signifying that they could still be accessible for the catalytic reaction. This last one explains the stability of the catalyst after the first ten hours of time-on-stream.

Along the reaction, the conversion of CO 2 was higher compared to that of CH 4 . It has been usually reported in the literature, as recently reviewed by Usman et al. [START_REF] Usman | Dry reforming of methane: influence of process parameters -a review[END_REF], and could be explained by the reverse water-gas-shift reaction (Eq. ( 4)). This reaction is generally favorable at the temperature range of 400-800 • C [START_REF] Pham Minh | Carbonate-containing apatite (CAP) synthesis under moderate conditions starting from calcium carbonate and orthophosphoric acid[END_REF]. Table 4 shows some results reported in the literature on the conversion of CH 4 and CO 2 at 700 • C and ambient pressure over noble metalbased catalysts. Under the similar reaction conditions, the catalytic activity of platinum supported on HAP support (this work) could be compared with that of noble metal-based catalysts, prepared on other supports. According to TEM results in Fig. 7, the catalytic performance of our Pt/HAP IWI can still be improved by limiting the formation of large Pt particles.

The selectivity reached around 87% into CO and around 70-80% into H 2 (Fig. 15(C)). This confirms the results obtained with the Ushape quartz reactor above (Fig. 12(C) and (D) for Pt/HAP IWI at 700 • C). Previously, we supposed that side reactions took place, in particular the water-gas-shift reaction (Eq. ( 4)). Fig. 15(C) enhances this hypothesis, wherein the selectivity in H 2 was smaller than the selectivity in CO, and the conversion of CO 2 was higher than that of CH 4 . Using a water trap at the outlet of reactor (Fig. 14), which contains fine particles of silica-gel, water was well identified and quantified as by-product of the reaction. The increase of water selectivity with the decrease of hydrogen selectivity confirmed that water-gas-shift took place. Note that water analysis has never been reported for this process. The formation of water was discussed by Pintar's research team [START_REF] Awa | Tunable ceria-zirconia support for nickel-cobalt catalyst in the enhancement of methane dry reforming with carbon dioxide[END_REF][START_REF] Aw | Strategies to enhance dry reforming of methane: synthesis of ceria-zirconia/nickel-cobalt catalysts by freeze-drying and NO calcination[END_REF][START_REF] Djinovic | Biogas to syngas conversion without carbonaceous deposits via the dry reforming reaction using transition metal catalysts[END_REF] but any details were given on how it has been done.

From the flow rate and the composition of the outlet gas measured along the reaction, the matter balance for all the elements of the reaction could be established (Fig. 17). Hydrogen balance was done with water, hydrogen and methane. Oxygen balance was performed with water, carbon monoxide and carbon dioxide. Carbon balance was obtained with methane, carbon monoxide and carbon dioxide. Note that coke deposition was not included into the carbon balance because it could not be correctly measured during the catalytic test. For a given element (A), the matter balance was calculated as follow:

Abalance = A inlet A outlet
with A: C, O or H; A inlet : flux of element A fed into the reactor (mmol/h); A outlet : flux of element A quantified from the outlet gas (mmol/h).

For both O and H, the matter balance was buckled with the values close to unit along the reaction time. So, if there are other by-products which have not been detected by the -GC used, their concentration must be negligible. For C, despite the exclusion of carbonaceous deposition, the carbon balance was relatively buckled, meaning that the main components of the outlet gas were carbon monoxide and unreacted methane and carbon dioxide.

Conclusions

Using hydroxyapatite (HAP) as support, Ru and Pt supported catalysts were prepared by different methods and were investigated in the catalytic transformation of CH 4 and CO 2 to syngas. For both metals, catalysts prepared by incipient wetness impregnation (IWI) were found to be the most efficient. Ru-based catalysts were quickly deactivated in this reaction, because of coke deposition. On the other hand, Pt/HAP IWI catalysts were found to be active and stable for a long reaction time of 50 h of time-on-stream, under the reaction conditions used.

Water was experimentally identified and quantified as a byproduct of the reaction. Further work would be focused on the continuous quantification of this water, which may help for identifying the presence of side reactions. The influence of the basicity of HAP support, as well as the dispersion of active metal (Pt) on the catalytic performance will be also subject of future work.

Fig. 1 .

 1 Fig. 1. SEM (A, B) and TEM (C, D, E) images of Ru/HAP IWI; yellow and pink arrows: Ru-based particles; yellow circle: Ru-based agglomerate. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 2 .

 2 Fig. 2. SEM (A, B) and TEM (C, D) images of Ru/HAP CEX; yellow and pink arrows: Ru-based particles; yellow circle: Ru-based agglomerate. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3 .

 3 Fig. 3. Imaging of ruthenium, calcium, phosphorus, and chlorine present in Ru/HAP IWI; (A): TEM image with imaging analysis zone (green rectangle); B to E: imaging of phosphorus, ruthenium, calcium, and chlorine, respectively; (F): image treatment of phosphorus (blue), calcium (red) and ruthenium (sky-blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

Fig. 4 .

 4 Fig. 4. Imaging of ruthenium, calcium, phosphorus, and chlorine present in Ru/HAP CEX; (A): TEM image for mapping; B to E: mapping of phosphorus, ruthenium, calcium, and chlorine, respectively; (F): image treatment of phosphorus (red), calcium (blue) and ruthenium (sky-blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

Fig. 5 .

 5 Fig. 5. SEM (A, B) and TEM (C, D) images of Pt/HAP LIM; yellow and pink arrows: Pt-based particles; yellow circle: Pt-based agglomerate. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6 .

 6 Fig. 6. Imaging of platinum, calcium, and phosphorus present in Pt/HAP LIM; (A): TEM image for mapping; B to D: mapping of calcium, phosphorus, and platinum, respectively; (E): image treatment of calcium (red), phosphorus (green) and platinum (turquoise). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

Fig. 7 .

 7 Fig. 7. SEM (A) and TEM (B, C) images of Pt/HAP IWI; pink arrows: Pt-based particles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 8 .

 8 Fig. 8. TG analysis of the initial HAP support and different catalysts.

Fig. 9 .

 9 Fig. 9. FTIR spectra of the initial HAP support and the prepared Ru-and Pt-based catalysts.

Fig. 10 .Fig. 11 .

 1011 Fig. 10. XRD patterns of the initial HAP support and the prepared Ru-and Pt-based catalysts.

Fig. 12 .Fig. 13 .

 1213 Fig. 12. Evolution of the concentration of methane (A), carbon dioxide (B), carbon monoxide (C) and hydrogen (D) in the final reaction product over Ru and Pt supported catalysts at 400-700 • C and atmospheric pressure using U-shape quartz reactor; 500 mg of catalyst; inlet gas flow rate: 70 N mL min -1 of 20%CO2-20%CH4-60%N2.

Fig. 14 .

 14 Fig. 14. Scheme of the stainless steel fixed-bed reactor. Reactants: mixture of 20 vol.% of CH4, 20 vol.% of CO2 and 60 vol.% of N2; MCF: mass flow controller; limit pressure: 30 bar; internal diameter: 8 mm; total length of the reactor: 30 cm; homogeneous temperature zone: 8 cm at the center of the reactor.

Fig. 15 .

 15 Fig.[START_REF] Ma | Effect of catalytic site position: nickel nanocatalyst selectively loaded inside or outside carbon nanotubes for methane dry reforming[END_REF]. Catalytic performance of Pt/HAP IWI at 700 • C; 500 mg of catalyst; inlet gas flow rate: 70 N mL min -1 ; (A): outlet gas composition; (B) conversion of CH4 and CO2, and (C): selectivity in H2 and CO calculated from the total gas flow rate and the concentration of gas at the outlet of the reactor.

Fig. 16 .

 16 Fig. 16. Example of SEM image of Pt/HAP IWI after 7 h of catalytic test.

Fig. 17 .

 17 Fig. 17. Matter balance of the reaction.

Table 1

 1 Catalysts prepared in this work.

	Catalyst	Metal deposition	Pre-treatment
	Pt/HAP IWI	Incipient wetness impregnation	Air calcination at 400 • C
	Pt/HAP LIM	Liquid impregnation	Drying only at 105 • C
	Ru/HAP IWI	Incipient wetness impregnation	Air calcination at 400 • C
	Ru/HAP CEX	Cationic exchange	Air calcination at 400 • C
	hydroxide. Briefly, orthophosphoric acid (85 wt.% in water, p.a.) was
	progressively added to an aqueous suspension of calcium hydrox-
	ide. The final molar ratio of calcium to phosphorus was fixed at
	1.67. The reaction mixture was kept at 80 • C for 2 h under stir-
	ring (500 rpm). Then, the precipitate of hydroxyapatite was filtered,
	rinsed with water and dried overnight at 105 • C. This powder was
	thereafter called HAP.

Table 2

 2 Ruthenium and platinum contents determined by ICP-AES analysis.

	Pt/HAP IWI	0.73	0.92
	Pt/HAP LIM	0.80	0.92
	Ru/HAP IWI	0.66	0.80
	Ru/HAP CEX	0.72	0.80

Catalyst

Pt or Ru (wt.%), ICP-AES Pt or Ru (wt.%), theoretical value

Table 3

 3 Specific surface area of the initial HAP support and of the calcined catalysts.

	Catalyst	SBET, m 2 g -1
	Initial HAP support	60
	Pt/HAP IWI	59
	Pt/HAP LIM	60
	Ru/HAP IWI	57
	Ru/HAP CEX	56

Table 4

 4 Reactivity of noble metal-based catalysts at 700 • C and ambient pressure for the conversion of methane and carbon dioxide into syngas.

	Metal and its	Support	Catalyst weight,	Inlet gas	Inlet gas flow	CH4 conv., %	CO2 conv., %	Time-on-stream, h	Refs.
	content (wt.%)		mg	composition, vol.%	rate (N mL min -1 )
	1%Pd	Al2O3	100	25%CH4, 25%CO2 diluted in He	4	≈59	≈52	3	[36]
						≈44	≈37	6
	1%Pt	MgO-Al2O3	50	33%CH4, 33%CO2	x	81	72	6	[37]
				diluted in N2
		ZrO2-Al2O3				86	70
		CeO2-Al2O3				90	78
	1%Ru	ZrO2-Al2O3				50	85
		MgO-Al2O3				50	37
	1%Pt	La2O3	500	10%CH4, 10%CO2 diluted in Ar	83	≈78	x	x	[38]
		Al2O3				≈86
	0.5%Rh	La2O3 Al2O3				≈90 ≈90
	1%Pt	ZrO2	100	50%CH4, 50%CO2	26	79	86	4	[39]
	0.7%Pt	HAP	500	20%CH4, 20%CO2
				diluted in N2

Acknowledgments

The authors gratefully acknowledge colleagues at RAPSODEE Center for technical help.