Amanullah Yasin
email: amanullah.yasin@univ-nantes.fr

Philippe Leray
email: philippe.leray@univ-nantes.fr

Local Skeleton Discovery for Incremental Bayesian Network Structure Learning

Keywords: Statistical learning, Incremental learning, Data mining, Data stream, Bayesian network structure learning

Nowadays there are a huge number of applications produce the immense amount of data in the form of a data stream, which needs real time analysis. Sensor networks, real-time surveillance and telecommunication systems are the examples of such applications. The real time analysis of the data stream leads to a number of computational and mining challenges. In this scenario new data arrives continuously and an efficient learning algorithm must be able to improve its learning accuracy by incorporating the time and memory constraints. This paper addresses the problem of incremental Bayesian network structure learning for high dimensional domains. The local skeleton discovery methods for Bayesian network structure learning are outperforming to deal with such domains. Here we transformed the local discovery algorithm Max-Min Parents and Childrens (MMPC) into an incremental fashion. We learned a set of candidate-parent-children for each variable by using incremental hill-climbing. The reduced search space saves a lot of computations and reduces the complexity. Our algorithm is then illustrated with a toy example.

I. INTRODUCTION

Many sources produce data continuously like customer click streams, telephone call records, large sets of web pages, multimedia, scientific data and sets of retail chain transactions etc. Such type of data is called data stream so, it is a real time and continuous ordered sequence of items, which are not feasible to store nor possible to control the order [START_REF] Golab | Issues in data stream management[END_REF].

Data stream mining means extracting useful information or knowledge structures from continuous data. It becomes the key technique to analyze and understand the nature of the incoming data. Typical data mining tasks, including association mining, classification, and clustering, helps to find interesting patterns, regularities, and anomalies in the data. However traditional data mining techniques cannot directly apply to data streams. This is because most of them require multiple scans of data to extract the information, which is unrealistic for data stream. More importantly the characteristics of the data stream may change over time and the evolving pattern needs to be captured [START_REF] Gama | Knowledge Discovery from Data Streams[END_REF]. Furthermore, we also need to consider the problem of resource allocation in mining data streams. Due to the large volume and the high speed of streaming data, mining algorithms must cope with the effects of a system overload.

Thus how to achieve optimum results under various resource constraints becomes a challenging task.

Bayesian network (BN) is a graphical representation for joint probability distribution among a set of random variables. It has been used in many applications like medical diagnosis and financial forecasting. It represents by directed acyclic graphs (DAG), where nodes of the DAG represent the random variables and the arcs of the DAG are represents the direct influence of one variable to the other. The intensity of the influence between the variables is defined by the conditional probability. To find the best structure of the BN, which describes the data is called structure learning.

BN structure learning is proved to be a NP-Hard problem [START_REF] Chickering | Learning bayesian networks is NP-complete[END_REF], it motivated to use of heuristic search methods to solve it. Many heuristics have been proposed in the literature, it can be classify in three categories for Bayesian Network (BN) structure learning:

• Score and search based methods are search over the space of all possible Bayesian networks in an attempt to find the network with a maximum score. Unfortunately, in such methods the search space is super-exponential in the number of random variables. It is very hard to compare all the structures specially in high dimensional domains [START_REF] Chickering | Learning bayesian networks: Search methods and experimental results[END_REF]. Therefore, score-based methods are theoretically intractable despite the quality of the search heuristic in use. • Constraint based methods, the main idea behind these types of methods is to exploit the independence semantics of the graph. They construct the graphical structure called "patterns" using statistical tests or information theoretic measures [START_REF] Spirtes | ser. Adaptive Computation and Machine Learning Series[END_REF]. Later using different assumptions they direct the edges to get a directed acyclic graph (DAG). Its performance is limited with small conditioning set and criticized for complex structures. • Local Search methods first search for the conditional independence relationships among the variables on a dataset and construct a local structure around a target variable i.e. Parent-Children (PC) or Markov Blanket (MB), using different heuristics like IAMB [START_REF] Tsamardinos | Algorithms for Large Scale Markov Blanket Discovery[END_REF], MMPC [START_REF] Tsamardinos | Time and sample efficient discovery of Markov blankets and direct causal relations[END_REF], MBOR [START_REF] Rodrigues De Morais | A novel scalable and data efficient feature subset selection algorithm[END_REF] and then they use another heuristic to learn the full BN structure. For instance MMHC [START_REF] Tsamardinos | The max-min hillclimbing bayesian network structure learning algorithm[END_REF] combines MMPC and greedy search approaches.

Applying BN structure learning in high dimensional domains e.g. biological or social networks, faces the problem of high dimensionality. These domains produce data sets with tens or hundreds of thousands of variables. The recent Max-Min Hill-Climbing algorithm (MMHC) [START_REF] Tsamardinos | The max-min hillclimbing bayesian network structure learning algorithm[END_REF] has been proposed to solve high dimensionality problem and it outperforms on a wider range of network structures. MMHC combines, both the local search and the score-and-search based approaches. In the first phase, it learns the possible skeleton of the network using the local discovery Max-Min Parent Children (MMPC) algorithm. While in the second phase, it orients the determined edges using the greedy hill-climbing search. Algorithms using local discovery for skeleton identification performs better than other leading non-hybrid structure learning algorithms in high dimensional domains [START_REF] Tsamardinos | The max-min hillclimbing bayesian network structure learning algorithm[END_REF] Here we will focus on Local Search which is most scalable method. In this paper, we present an incremental local skeleton learning algorithm (iMMPC) to identify the set of candidate parent children (CPC) of a target variable in any BN which faithfully the distribution of data. We applied incremental hill climbing method to find a set of CPCs for a target variable and observed that it saves a considerable amount of computing time.

This paper is organized as follows: first we discussed the previous work already done in the field of incremental learning and data stream mining in the section [sec:Related-Work]. In section [sec:Backgroun] we recall the basics of the heuristics used in our proposed method. In section [sec:iMMPC-Approach] we present our incremental Local Search approach iMMPC. In section [sec:Toy-Example] we explained our method with an example. Finally we conclude in section [sec:Conclusion-and-Perspectives] with some proposals for future research.

II. PREVIOUS WORK

In the field of incremental Bayesian Network Structure learning, some works proposed to iteratively revise the structure of a Bayesian network. It can be classified in two categories, approaches deal with the stationary domains and nonstationary domains. Algorithms which deal with stationary domains consider the data is drawn from single underlying distribution, which will not change with the passage of time. The models are also not very different when they evaluated with respect to similar data sets [START_REF] Alcobé | Incremental hill-climbing search applied to bayesian network structure learning[END_REF]. On the other hand, algorithms deal with non-stationary domains consider the underlying distribution of data may change with time so, drift or shift change may occur. Furthermore, we can divide these domains with respect to BN structure learning methods.

Buntine's [START_REF] Buntine | Theory refinement on bayesian networks[END_REF] proposes a batch algorithm that uses the score-and-search based Bayesian approach, later he proposes some rules to convert it into an incremental algorithm. He considered two conditions, if there is time constraint for incremental or online learning then it updates the posterior probabilities only of the parent structure. Otherwise both structure and parameters will be updated.

Lam and Bacchus's [START_REF] Lam | Using new data to refine a bayesian network[END_REF] approach is also an extension of their batch algorithm and based on Minimal Description Length (MDL) principle. The idea is to first learn both partial network structure from the new data and existing network using the MDL learning method and then update the global old structure by using the newly learned partial structure.

Friedman and Goldszmidt [START_REF] Friedman | Sequential update of bayesian network structure[END_REF] proposes three different approaches, first naive approach, where previously seen data is stored and then a batch learning procedure is called for each new example. Second approach based on Maximum Aposteriori Probability (MAP). Third approach called incremental. In this approach, a set of network candidates is maintained, which called the frontier of the search process. And at the arrival of new examples, it updates the stored information. Later it runs the search process to verify if any network in the frontier seems more appropriate than a current model.

Alcobe [START_REF] Alcobé | An incremental algorithm for tree-shaped bayesian network learning[END_REF] adopted Chow and Liu [START_REF] Chow | Approximating discrete probability distributions with dependence trees[END_REF] tree structure algorithm and proposed a heuristic ACO (Arches in Correct Order) to trigger the updating process when data invalidates the current structure. It rebuilds the network structure from the branch which is found to be invalidated. Later he proposed two heuristics to change a batch Hill-climbing search into an incremental one. Section III-B will describe more deeply these heuristics.

All above approaches deal with the stationary domains and use the scoring methods to learn BN structure incrementally.

A recent work in this field done by Nielsen and Nielsen [START_REF] Nielsen | Adapting bayes network structures to non-stationary domains[END_REF] considers the non-stationary domains where a concept shift may occur. This approach consists of two mechanisms, first monitoring and detecting when and where the model should be changed and second relearning and using a local search strategy integrating the parts of the model that conflict with the observations.

As a conclusion we see that most of the algorithms use the scoring methods and treat the incremental process in different ways for stationary domains. Score based methods are not scalable for data stream mining, the judicious choice for handling a great number of variables is a local search approach. It's why we take advantages of local search approaches and proposed iMMPC algorithm: a scalable incremental method for stationary domains with high dimensionality, in section IV.

III. BACKGROUND

A. MMPC(T): Local Search approach for BN Structure Learning

The MMPC(T) algorithm discovers the set of CPC (candidate parent-children, without distinguishing among both) for a target variable T. It is a combination of M M P C(T ) algorithm and additional correction for symmetric test.

Algorithm M M P C(T ) (cf. Algo. 1) has also two phases. In forward phase it adds variables in CPC for a target variable T and in backward phase it removes the false positives. The pivotal part of the MMPC algorithm is the forward phase of M M P C(T ) algorithm. This phase starts from the empty set of CPC(T) for a target variable T, then sequentially adds the variables in CPC which have strong direct dependencies.

Function min(Assoc) used to measure the association between two variables given CPC, it is zero if these two variables are independent conditionally any subset of CPC. So variables having zero associations given any subset of already calculated CPC, can never enter in CPC(T). This function estimates the strength of association by using any measure of association Assoc like χ 2 , mutual information (MI) or G 2 . Further "MaxMinHeuristic" [START_REF] Tsamardinos | The max-min hillclimbing bayesian network structure learning algorithm[END_REF] selects the variables which maximize the min(Assoc) with target variable T conditioned to the subset of the currently estimated CPC. Forward phase stops when all remaining variables are independent of the target variable T given any subset of CPC. In the category of score based methods, here we are discussing the Alcobe [START_REF] Alcobé | Incremental hill-climbing search applied to bayesian network structure learning[END_REF] approach. In his approach, he proposed two heuristics to change a batch Hill-climbing search (HCS) into an incremental algorithm. We will first describe the usual non incremental HCS and then introduce Alcobe's heuristics.

1) Hill Climbing Search : HCS (cf. Algo. 2) methods traverse the search space called neighborhood by examining only possible local changes at each step and applying the one that maximizes the scoring function. The neighborhood of a model M consists of all models which can be built using the operators op and argument pairs A, where the operator can be Add Edge, Delete Edge or Reverse Edge. A scoring function f (M, D) is used to measure the quality of the model. Search path or traverse path is a sequence of operators and argument pairs added on each step to obtain a final model M f , in other words, it is a sequence of intermediate models.

Definition 1. (Search Path) Let M 0 be an initial model, op be an operator and A be an argument pair. Then the final modelM f , is the model with highest score to the neighborhood, obtained by a hill-climbing search algorithm as:

M f = op n (...(op 2 , (op 1 , A 1 ), A 2 ), ..., A n )

So search path is the sequence of operators and argument pairs

O op = {(op 1 , A 1 ) , (op 2 , A 2 ) , . . . (op n , A n )} used to build M f .
Models in a search path are in increasing quality score order.

f (M 0 , D) < f (M 1 , D) < f (M 2 , D) • • • < f (M f , D)
M i = ∅ Repeat oldScore = f (M i , D) i++ M i = op(M i-1 , A i ) \** where op(Mi-1, Ai)= arg max (op k , A)∈Gn f op k (Mi-1, Ai), D **\ Until oldScore ≥ f (M i , D) Return M i
2) Incremental Hill Climbing Search (iHCS): In iHCS (cf. Algo. 3) Alcobe discussed two main problems: firstly, when and which part needs to update, secondly to calculate and store sufficient statistics. At each iteration, it repeats the search path by traversing the reduced DAG space. He proposed two heuristics "Traversal Operators in Correct Order" (TOCO) and "Reduced search space" (RSS). It is assumed that data is sampled from same distribution. The search space is also supposed not to change too much when few data are added in current dataset or new data slightly change the underlying distribution so, the scoring function imagined being a continuous over the space of datasets.

First heuristic verifies the learned model and its search path for new data. If the new data alter the leaning (search) path then it is worth to update an already learned model. Second heuristic applies when TOCO found the path is not valid so, it is necessary to revise the current structure. At each step of the search path, it stores the k models in a set B having the score closer to the best one. The set B reduces the search space by avoiding to explore those parts of the space where low quality models were found during former search steps.

IV. INCREMENTAL MMPC(T) APPROACH

Now we can present our local search algorithm iMMPC(T) for stationary domains. As already discussed the pivotal part of the MMPC(T) algorithm is the forward phase of a M M P C(T ) algorithm. In this phase variables enter incrementally in the set of CPC(T).

M ini = (op j , A j ) i = 0 M = M ini \** RSS **\ Repeat oldScore = f (M i , D) i++ M i = op(M i-1 , A i ) \** where op(Mi-1, Ai)= arg max (op m , A)∈B i f (op m (Mi-1, Ai), D) **\ if (M i =M f inal ) then Recalculate B k Endif Until oldScore ≥ f (M i , D)
Forward phase of the M M P C(T ) algorithm as a HCS:: First of all, let's demonstrate the forward phase of the M M P C(T ) algorithm can be transformed into a Hill Climbing search using a specific search space (set of models). The idea of M M P C(T ) (forward phase) is also the same as HCS, stepwise it generates a model by improving the quality function on each step. In M M P C(T ) a model can be defined as: Definition 2. (Model) Let T be a target variable and CPC is a set of candidate parent-children of T, without distinguishing among both parent and children variables. Then model M is an undirected graph which is defined by variables V = T ∪ CP C and edges E = {< T, x >, ∀ x ∈ CP C}.

To measure the quality of a model, we define a scoring function as: Operator also defined as: Definition 4. (Operator) Let T is a target variable. Operator can be defined by AddU ndirectedEdge(T, X) which corresponds to add X to the set of CPC(T).

Mutual Information (MI) has the property that M I(X, Y ∪ W ) ≥ M I(X, Y ) means MI always increasing by including additional variables. Furthermore, following property of conditional mutual information justify our choice of MI [START_REF] De Campos | A scoring function for learning bayesian networks based on mutual information and conditional independence tests[END_REF]:

Conditional mutual information between X and Y given a set of variables Z defined as:

M I(X, Y ∪W | Z) = M I(X, Y | Z)+M I(X, W | Z ∪Y ) (1)
If Z is an empty set and Mutual Information (MI) used to measure the strength of the Assoc (Assoc = MI) then equation 1 can be written as:

Assoc(T, CP C ∪X) = Assoc(T, CP C)+Assoc(T, X | CP C)
So to maximize f (M, D) it needs to maximize Assoc(T, X | CP C) and it is the "MaxMinHeuristic" of the MMPC(T) algorithm. At each step M M P C(T ) algorithm searches within the neighborhood to improve the quality function and select the best model. This neighborhood space over the models obtained by applying the one operator AddUndirectedEdge(T, X).

With the above three definitions, we can easily describe the forward phase of theM M P C(T ) algorithm works as hill climbing search.

A. Our Proposal of Incremental MMPC(T)

After showing the HCS behavior of theM M P C(T ) algorithm (forward phase) we are able to adapt TOCO and RSS heuristics of Alcobe approach (Algo. 3) with model M , scoring function f and operator as previously defined. Our Initial model M 0 corresponds to an empty set of CPC (M 0 ={T }). Incremental MMPC(T) starts from an initial model M 0 and then searches in the neighborhood to find the best one. This iterative process continues until all remaining variables find the weak dependencies. So the search path in iMMPC is a sequence of the variables added in the set of CPC(T) incrementally. Each step of the search path can be called intermediate model and for each intermediate model (or search step) we store the k neighboring models having the association value very close to the best one, as a set B where k is a user input value, greater the value of k guarantees more significant model.

On the arrival of new data iMMPC(T) first verify the previously learned path and define the initial model M i from which the search will be resumed. If the initial model is a best model then it will continue to improve an existing model in the light of a set B (set of best arguments) to introduce new variables in the final model, otherwise it will recalculate the set of best arguments. We maintain the set B in descending order. Relearning process limits the search space by using the set B.

Backward phase of M M P C has no concern as calculations of Assoc remains the same in iMMPC.

V. TOY EXAMPLE Now we are providing a simple example for the better understanding of an incremental M M P C(T) algorithm. The The data fed to the algorithm is sampled from the distribution of the original graph and we are interested in identifying CP C(X6).

We are going to present two cases correspond to the two columns in figure 1. In the first one we handle data D and other is to handle data D ∪ D . First case will start by searching the whole neighborhood space and storing the reduced search space (with k = 4) B. In second case the incremental algorithm will reduce the search space by using reduced search space B. So it starts from an initial model M 0 which contains an only target variable and empty set of CPC. In the first iteration, it generates the neighborhood by applying the operator AddU ndirectedEdge(M 0 , X) and then calculate the association between X6 and each of the seven other variables. Suppose the maximum value is obtained for X4 variable, and f (M 0 ) < f (M 1 ), so X4 is added in the CP C(T ). At this step, we store the four best variables which have the association value closest to the maximum one so, for instance set B0 = {X4, X3, X7, X2}.

Next iteration starts from a model M 1 and repeats the same process. Suppose the maximum association value found by applying the AddU ndirectedEdge(M 0 , X3) operator and f (M 2 ) > f (M 1 ), so X3 is added in the CP C (T ). We store the four best variables which have the association value closest to the maximum one so, set B1 = {X3, X7, X2, X5}. And the same in third iteration where X7 is added in the list of CPC, also the set of the best operator is stored as B2.

Now we cannot proceed because there is no other model having the maximum value greater than f (M 2 ). In other words we can say that the remaining variables have the zero association with the target variable given any subset of CPC.

On the arrival of new data D , our algorithm will relearn the model for data D ∪ D . Again it starts from the initial model and generates the neighborhood by applying the AddU ndirectedEdge(M 0 , X) operator for only those variables which are stored in the set of best arguments found in the previous learning process. So here the search space reduced for only four models. Again supposed the variable X4 has a maximum association value so, it added in the list of CPC(T). Here we also the search path, if the search path is not in the same sequence then we need to recalculate the set of best operators.

The complexity of our algorithm if we consider the above the best case then at first time forward phase needs 3(n -2) comparisons and for next incremental stage it requires only 3k comparisons. In average case if new data changes then the complexity will be O(2k + n). For the worst case when the distribution of the entire data is changed or model learning process starts from scratch then it needs maximum comparisons O(3n).

This simple example illustrates the interest of our incremental approach. In high dimension, k n and lot of Assoc computations are saved.

VI. CONCLUSION AND PERSPECTIVES

In this paper, we have proposed an incremental version of local search Max-Min Parent-children algorithm of Bayesian Network structure learning. We applied incremental hill climbing approach to discover the set of CPC of a target T. We store the most strong dependencies as a set of best arguments. It reduces the search space for new data by considering only the strong dependencies. This approach improves the performance of the algorithm systematically and reducing the complexity significantly.

In the further, we plan to carry out more systematic experimentation on real datasets to confirm the interest of applying TOCO and RSS heuristics in CPC discovery and then extend this work by incrementally identifying the whole structure. We also plan to apply optimize measuring by storing sufficient statistics. Furthermore, dealing with non-stationary domains by handling shift or drift detection.

Algorithm 1 M

 1 M P C (T ) Require: target variable data D; threshold θ Output: a set of Candidate Parent and Children (CPC) of T \** Forward Phase: MaxMinHeuristic **\ CP C = ∅ Repeat < F, assocF > = max x∈X CP C (min S⊆CP C Assoc (x; T | S)) if assocF = 0 then Add (CP C, F ) Endif Until CPC has not changed \** Backward Phase: **\ For all X ∈CPC if ∃S⊆ CP C, s.t. Assoc (X; T | S) < θ then Remove (CP C, X) Endif Return CPC B. Incremental Adaption of Score Based BN Structure Learning

Algorithm 2

 2 Hill Climbing Search (HCS) Require: Data D; scoring function f (M, D); a set of operators OP = {op 1 , . . . , op k } Output: DAG: a model M of high quality i = 0

Algorithm 3

 3 Incremental Hill Climbing Search (iHCS) Require: data D; scoring functionf (M, D), a set of operators OP = {op 1 , . . . , op m } and B i is a set of k best operators and argument pairs for model M i Output: DAG: a model M of high quality \** TOCO **\ Verify previous search path: After evaluation of scoring function f over new data D ∪ D , let (op j , A j ) be a last pair where the new data agree with previously learned search path.

Definition 3 .

 3 (Quality Measuring) Let D be a dataset with a faithful distribution P and M is a model. The quality of model M can be measured by a function f (M, D), where f (M, D) = M I(T, CP C) and its value increases when good variables are added to CPC.

Figure 1 .

 1 Figure 1. Toy example

ACKNOWLEDGMENT

We would like to thank the Higher Education Commission (HEC) of Pakistan and the KOD team of Polytech Nantes, France for supporting this research.


G C Arteaga

M A Del Valle

M Antilén

M Romero

A Ramos

L Hernández

M C Arévalo

E Pastor

G Louarn

Nucleation and Growth Mechanism of Electro-synthesized Poly(pyrrole) on Steel

Keywords: pyrrole, polypyrrole, nucleation and growth mechanism, n-doping, p-doping

Polypyrrole was electro-synthetized by potentiodynamic and potentiostatic methods on AISI 316 stainless steel (SS) using lithium perchlorate as supporting electrolyte and acetonitrile as solvent to obtain the respective polymeric coating. One of the most relevant characteristics of this polymer is that its voltammetric response showed the presence of reversible p-and n-doping/undoping processes. Moreover, nucleation and growth mechanisms (NGM) were established by i/t transients deconvolution recorded during the potentiostatic electro-polymerization. It was found that the overall process mechanism involved two contributions, namely an instantaneous nucleation with two-dimensional growth (IN2D) and a three-dimensional progressive nucleation with diffusion-controlled growth (PN3Ddif The nuclei shape predicted by these NGMs are consistent with the respective morphologies obtained by SEM and AFM, which validates, once more, the proposed electro-polymerization model and the predictions from the NGM morphology of the respective electro-deposited polymer. In short, a correlation between the structure of the starting unit, doping and morphology of the electro-deposited polymer was established. At the same time conditions for the electro-obtention of this widely studied polymer were optimized, but this time on SS, a cheap electrodic substrate that makes its potential application more feasible.

INTRODUCTION

Poly(pyrrole), Ppy, has been one of the most studied conducting polymers and used in different applications, the most relevant being fuel cells, materials for artificial muscles, as heavy metals extractor, carbon nanotubes fabrication, counter electrode for solar cells coating. Besides, often used as a biosensor and gas sensor, anti-electrostatic coating, solid electrolytic capacitor, electrochromic windows, displays, polymer batteries, electronic devices, functional membranes, etc. [1][2][3][4][5][6][7][8][START_REF] Skotheim | Handbook of Conducting Polymers[END_REF][START_REF] Skotheim | Handbook of Conducting Polymers, Vols. I and II[END_REF][START_REF] Del Valle | [END_REF][12][13][14].

In the last century, Ppy was one of polymers with more publications, mainly due to the aforementioned applications. The purpose of the current work was to accomplish and contribute to the understanding of Ppy nucleation and growth mechanism on SS, because derivatives from this monomer have been previously studied on this substrate [15] and have been analyzed and characterized. However, py has not been studied under these conditions, which is essential not only for the sake of comparison, but also because offers a cheap and affordable working medium and electrode.

Electro-synthesis will enable in situ characterization using potentiodynamic (cyclic voltammetry, CV) and potentiostatic techniques that will lead to establish, respectively, the doping/undoping processes and the nucleation and growth mechanism (NGM). The latter will be correlated with morphological results, to be performed by scanning electron microscopy (SEM) and atomic force microscopy (AFM), to verify if the NGM allows predicting morphology, as already established in other cases [16][17][18][19][20][21][22][23][24][25]. Besides, a correlation between morphology and starting unit structure and with their macroscopic properties, e.g. conductivity and type of doping, will be searched for.

EXPERIMENTAL

All aqueous solutions were prepared with freshly deionized water on a Heal Force (Smart Series) deionizer. All measurements were performed at room temperature (20 °C) under high purity argon atmosphere in three-compartment anchor-type electrochemical cells. The working electrode was a 0.07 cm 2 geometric area AISI 316 steel disc (SS). The counter electrode was a platinum wire coil of large geometric area. Ag/AgCl in tetramethylammonium chloride solution, its potential adjusted to that of a saturated calomel electrode, SCE, was utilized [39] as reference electrode. Unless otherwise stated, all potentials quoted in the current work are referred to this electrode at room temperature.

Py (Aldrich, 98%) electro-oxidation on SS was optimized in cell assemblies under the abovementioned conditions. The electro-polymerization was carried out using successive potentiodynamic scans (CV), potential scan rate 50 mV•s -1 and within different potential windows. Solutions having different monomer concentrations and various supporting electrolytes were employed.

Thus, after numerous trials, optimal conditions that enabled working with the four proposed starting units were as follows. 0.01 mol•L -1 monomer solution in 0.1 mol•L -1 lithium perchlorate (LiClO 4 99%, Aldrich) supporting electrolyte in 99.8% acetonitrile (CH 3 CN, Aldrich) as solvent, the latter being suitable for working within the -0.6 and 1.5 V window.

From these results, the potentiostatic method (PM) was tried. The optimum potential to preparer the SS/Ppy electrode in this medium was 1.36 V. According to the specific goal, electrolysis time ranged between 1 and 30 min.

In each case, to optimize the conditions to be employed, the stable electrochemical response of the modified electrode in a solution containing just supporting electrolyte was determined. This enabled the respective p-doping/undoping and n-doping/undoping processes to be analyzed in order to find the amount of charge involved and, especially, the most reversible response.

All electrochemical measurements (polymerization and characterization) were performed on an Autolab PGSAT 20 potentiostat. Furthermore, to observe the morphology of each polymeric deposit, analyses were conducted using SEM on a JEOL, Model 6300F, Scanning Electron Microscope. Then, to detail the morphology and topography of the polymer, AFM measurements were made on a Digital Instruments Nanoscope Multi-Mode AFM-2 at the University of La Laguna, Spain. Finally, to complement the characterization Fourier Transform Infrared -Attenuated Total Reflectance (ATR) spectroscopy measurements were accomplished on an IFS 66/S BRUKER spectrometer, and Raman spectroscopy measurements were carried out on a Bruker RF S100 spectrometer (excitation wavelength 1064 nm).

RESULTS AND DISCUSSION

The voltammetric profile in Fig. 1 depicts py electrochemical oxidation after 50 successive CV cycles, under the experimental conditions (concentration, supporting electrolyte) and within the optimum working window set forth herein. Current increase between consecutive cycles is an evidence of polymer growth, along with the clear presence of p-(between 0.0 and 1.0 V) and ndoping/undoping (between 0.0 and -0.6 V) processes.

Besides of evidencing the n-doping/undoping processes, these profiles allow establishing the nucleation and growth region, around 1.5 V. The optimum working potential for the potentiostatic method should thus be searched for in this region, Fig. 2. In Fig. 2, the i-t transients evidences that, under the other experimental conditions used here, 1.36 V is the most suitable potential for py potentiostatic electro-polymerization. Table 1 shows the respective negative (E cat ) and positive (E an ) limits within which this phenomenon takes place and the corresponding n-doping/undoping charges that revealed the process is fully reversible, since the cathodic/anodic charge quotients obtained for the electrochemical response (Fig. 3A) are very close to one. Table 1. n-doping (n-Q d ) and n-undoping (n-Q u ) charge of electro-synthesized polymers on SS within the respective negative cat ) and positive (E an ) potential limits.

1.200 V 1.250 V 1.300 V 1.310 V 1.320 V 1.360 V 1.380 V 1.400 V
Polymer E cat (V) E an (V) n-Q d (C) n-Q u (C) n-Q d : Q u Ppy -0.6 0.2 8.6•10 -6 8.5•10 -6 1.00
At the same time the respective charges calculated for p-doping/undoping indicated the process was fully reversible under the electro-synthesis conditions set forth herein, see Table 2.

Table 2. p-doping (p-Q d ) and p-undoping (p-Q u ) charge of polymers synthesized on SS electrodes

within the respective limits of negative (E cat ) and positive (E an ) potential.

Polymer E cat (V) E an (V) p-Q d (C) p-Q u (C) p-Q d : Q u Ppy -0.3 1.2 5.20•10 -4 5.21•10 -4 0.99
Optimum conditions, established by voltammetric characterization, were utilized to conduct the potentiostatic electro-polymerization. The same SS electrodes were employed in solutions similar to those already described as optimal, at a potential close to the anodic switching potential of each monomer. I-t transients shown as example in Fig. 4 indicated that when working under potentiostatic conditions in the NG region, a general behavior pattern exists that can be describe considering, firstly, that after the sudden initial current rise and subsequent exponential drop, ascribable to monomer oxidation, the current increases once more as nucleation, that gives rise to deposit growth (induction time ), takes place as a function of such growth [27,28].

Thus, as seen in other cases [29][30][START_REF] Horwood | Instrumental Methods in Electrochemistry[END_REF][START_REF] Turcu | [END_REF][33][34][35][36], it was observed that at potentials lower than the optimal one, the induction time,  is very high, while at higher potentials is very low and erratic with a total lack of reproducibility and, consequently, the generated film would be undergoing over-oxidation. On this basis, the most suitable potential for each of the studied monomers, when potentiostatic deposition was the technique of choice, are shown in Table 3.

Figure 4 shows time-current transients deconvolution, recorded during the potentiostatic preparation under the selected optimum conditions, in order to determine the respective NGM, as described in similar studies [20,22,[28][29][30][START_REF] Horwood | Instrumental Methods in Electrochemistry[END_REF][START_REF] Turcu | [END_REF][33][34][35][36]. The equations describing the contributions that enabled deconvoluting the obtained transients, corresponding to the respective NGM, were instantaneous nucleation with two-dimensional growth (IN2D) and progressive nucleation with diffusion-controlled three-dimensional growth (PN3D dif ) [START_REF] Horwood | Instrumental Methods in Electrochemistry[END_REF]:

  2 2 t P 1 e 1 P i    (1)   2 t 4 P 3 2 / 1 e 1 P t i     (2)
The first contribution corresponds to equal-size nuclei (instantaneous nucleation) with a cylinder-shaped growth (two-dimensionally, parallel to the electrode), while the second consists of nuclei that appear and grow as a function of electrolysis time, parallel and normal to the electrode, hemisphere-shaped. Consequently, morphology consistent with this NGM prediction would be expected for these deposits. Nevertheless, it is worth noting that this mechanism is different from previous reports related to pyrrole derivatives on steel under the same conditions [15]. This fact would be, as expected, an evidence of monomer structure effect.

Parameters of equations ( 1) and ( 2) are displayed in Table 3, where M is the monomer molar mass, k is the growth parallel to the electrode rate constant, n is the number of electrons involved, F is the Faraday constant, h is the height of the monolayer, N 0 is the number of active surface sites, t is the time, ρ is the film density, C is the monomer bulk concentration, D is the diffusion coefficient, A dif and N dif are the nucleation rate constant in the steady state and the number of nuclei formed under diffusion control, respectively [25][26][27][28][29][30][START_REF] Horwood | Instrumental Methods in Electrochemistry[END_REF][START_REF] Turcu | [END_REF][33][34][35][36]. P 1 , P 2 , P 3 , and P 4 values obtained by transient deconvolution (Fig. 4) that allowed accurate simulation of the experimental transients, are summarized in Table 4.

Table 3. Expressions for the parameters of equations ( 1) and ( 2).

Parameter

Expression P 1 P 2 P 3 P 4 Table 4. Numerical values of the parameters of equations ( 1) and (2) (Table 3) appropriate to deconvolute i/t transients recorded on SS (Fig. 4).

Polymer E (V) P 1 (A•cm) P 2 (ms -2 ) P 3 (mA•cm -2 •s 1/2 ) P 4 (ms -2 ) r 2 Ppy 1.36 1.10 0.18 0.07 0.15 0.9915

Values in Table 4 highlight, first, that r close to unity indicates a clear correlation between experimental and simulated transients and, consequently, the obtained NGM would be reliable. Besides, Fig. 4 shows that the profiles obtained by deconvolution or the sum of the curves calculated from the respective deconvolution equations (using the constants of Table 4) coincide almost exactly with the experimentally recorded transient.

Subsequently, to determine deposit morphology and particularly to validate the simulations leading to NGM determination, SEM was utilized to characterize the coating, Fig. 5A.

The micrograph in Fig. 5A allows ensuring that the morphology obtained for the deposit corroborates what was predicted from NGM, since semispheres with irregular size can be observed, consistent with a progressive nucleation mechanism.

To verify the morphological prediction from the NGM, the AFM technique was employed. The result that corroborates the prediction is depicted in Fig. 5B: two contributions are observed for Ppy, consistent with the NGM that presents two kinds of nuclei, with growth at different rates, causing a quite uneven surface. To round out the characterization and verify the NGM prediction, measurements were conducted by ATR and RAMAN spectroscopy. Figure 6 shows the ATR spectrum, where the bands are clearly assigned as follows: 3538 cm -1 ; C-NH stretching vibration corresponding to the pyrrole ring; 1630 cm -1 assigned to ring-deformation vibrations of pyrrole NH; 1207 cm -1 , refers to C-N stretching vibrations of the py ring; 1443 cm -1 C=C, are assigned to stretching vibration of the py ring, and 1040 and 925 cm -1 corresponding to =C-H of the ring plane.

Thus, the assignment of these bands confirmed in situ interaction between electrode substrate (SS in this case) and polymer matrix, Ppy, [37-39].

Finally, measurements were conducted using Raman spectroscopy that corroborated the polymer obtention, Fig. 8, since it is possible to identify the following bands: 1545 cm -1, corresponding to the C α =C β asymmetric stretching; 1423 cm -1 , assigned to the C α =C β. symmetric stretching; 1370 cm -1 the C β =C β ring stretching; 1247 cm -1 ascribed to C α = C α' stretching (inter-ring); 1224 cm -1 assigned to the C α -N stretching, and 1110 cm -1 assigned to C-H [39-41]. NGM deconvolution of Ppy on steel, exhibited many differences with respect to pyrrole derivatives previously reported (3,4-ethylenedioxypyrrole (PEDOP) and 3,4 propylenedioxypyrrole (PRODOP)) [15], wherein the following contributions predominate: instantaneous nucleation with three-dimensional growth under charge-transfer control (IN3D ct ), however, a second contribution also exists, corresponding to a three-dimensional progressive nucleation under diffusion-controlled growth (PN3D dif ), the latter contribution also occurs for Ppy under the same electro-synthesis conditions, indicating that the first contribution is governed by epoxi-alkyl chains for pyrrole derivatives. So, these results clearly demonstrated that the substituent chains govern the IN3D ct contribution.

Ppy ATR and RAMAN characterization revealed, from signals assignment, that its conformational structure is flat. In addition as, unlike its derivatives (PEDOP and PPRODOP), Ppy lacks of substituents allowed its structure to be worked out this way.

CONCLUSIONS

Ppy was obtained on steel under the found optimum working conditions, exhibiting both n-and p-doping/undoping processes Although the second charging process always presented greater charge than the first, both are practically reversible with regard to the respective charges involved.

Besides of characterization of p-and n-doping/undoping processes, that allow proposing and choosing the most appropriate starting unit, depending on the use in mind for the polymeric deposit, Ppy experimental transients were simulated. Two contributions to the overall process were found, one involving an instantaneous nucleation with two-dimensional growth (IN2D) and a second corresponding to a three-dimensional progressive nucleation with diffusion-controlled growth (PN3D dif ). The value of r very close to 1 for all simulations must be highlighted. Furthermore, the morphology associated with these NGMs correlates exactly with those experimentally determined by SEM and AFM. This allows shorter path for the choice of the starting unit and the experimental design to prepare the modified electrode according to their potential use.

Figure 1 .

 1 Figure 1. Voltammetric profile of 0.01 mol•L -1 py + 0.1 mol•L -1 LiClO 4 in CH 3 CN, during the electropolymerization on a 0.07 cm 2 SS disc (v = 50 mV•s -1 ), by successive potentiodynamic cycles (number of cycles on the respective curve).

Figure 2 .

 2 Figure 2. i-t transients recorded during py electro-polymerization by potentiostatic method (E showed in the insert). Interface: SS/0.01 py + 0.1 mol•L -1 LiClO 4 , CH 3 CN.

Figure 3 .

 3 Figure 3. SS/Ppy electrode response: A) n-doping/undoping potential region; B) p-doping/undoping potential region.

Figure 4 .

 4 Figure 4. i-t transients deconvolution recorded for py at SS under the optimal working conditions.

Figure 5 .

 5 Figure 5. Images: A) SEM of Ppy on SS. B) AFM of Ppy on SS.

Figure 6 .

 6 Figure 6. Ppy ATR spectrum.

Figure 7 .

 7 Figure 7. Ppy Raman spectrum.

ACKNOWLEDGMENTS

The authors thank CONICYT financial support through grants FONDECYT 1100055, and Ecos-Conicyt C09E02. GC Arteaga thanks CONICYT Scholarship 2009, Folio 57090049.


This work deals with a new sol-gel route named complex sol-gel process ͑CSGP͒ based on a very strong complexing agent ͑ascorbic acid͒ to synthesize gel precursors of Li 1.1 V 3 O 8 . Results show that original morphologies are stabilized for anhydrous samples prepared by annealing these gels at low temperature. They lead to either high capacity and unexpected excellent cyclability, or atypical lithium insertion behavior.

Lithium vanadium oxide, Li 1+␣ V 3 O 8 ͑␣ Ϸ 0.1-0.2͒, has been intensively studied for the past 20 years for its attractive electrochemical properties. Indeed, it provides a fair energy density and a good capacity retention. Li 1+␣ V 3 O 8 could be prepared by several routes. One interesting synthesis technique consisted in the annealing at temperatures higher than 300°C of a gel precursor obtained from the reaction of V 2 O 5 and LiOH•H 2 O at 50°C under N 2 . [1][2][3] Such a technique allows for obtaining a sample with an initial specific capacity close to theory but with a poor cyclability. [3][4][5] In a previous work, 4 cyclability was found to be dependent on morphology of the grains. Such results incited us to search for new synthesis routes leading to unusual morphologies with the aim to increase cyclability of lowtemperature prepared samples.

The goal of this work was to evaluate the interest of the new variant sol-gel route named complex sol-gel process ͑CSGP͒ developed by Deptula et al. 6 to synthesize gel precursors of Li 1.1 V 3 O 8 . The main feature in this process is the use of a very strong complexing agent ͑ascorbic acid, ASC͒ for the sol preparation. Such procedure was successfully applied to the synthesis of Li x Mn 2 O 4±␦ spinels, 6,[START_REF] Deptuła | 2nd International Symposium on New Materials for Fuel Cell and Modern Battery Systems[END_REF] LiNi x Co 1-x O 2 layered oxides, [START_REF] Deptuła | [END_REF]9 and composite TiO 2 -LiCoO 2 . 10 We present here results of synthesis, characterization, and lithium insertion behavior of Li 1.1 V 3 O 8 samples prepared by annealing CSGP gels at low temperature. Results show unusual morphologies leading to excellent cycling behavior, as well as an original Li insertion behavior.

Experimental

A flowchart of the preparation procedure is shown in Fig. 1. Commercial NH 4 VO 3 was dissolved at 80°C in water and immediately introduced into the reservoir of a Rotavapor equipment ͑Büchi, Switzerland͒ after addition of ascorbic acid ͑ASC͒. Concentrated LiOH was then slowly added into the reservoir. A chemical treatment of the sample with concentrated HNO 3 and H 2 O 2 ͑1m Lo f each reagents on1gofpowder͒ was also applied in order to remove traces of ASC in the sample. The obtained slurry was then dried at 105°C for 24 h. The sample is noted as ASCR 105 .

The previous process was repeated once without addition of ASC ͑sample noted noASC 105 ͒ and once without chemical treatment ͑sample noted ASC 105 ͒, everything else being the same. All samples were heat-treated at 400°C for 6 h before electrochemical studies ͑obtained samples are noted ASCR 400 , noASC 400 , and ASC 400 , re-spectively͒.

For the sake of comparison, another sample prepared by the standard sol gel route ͑V 2 O 5 + LiOH,H 2 O͒ and annealed at 400°C, noted SG 400 , was also investigated.

All thermal treatments were performed in an air-ambientprogrammed Carbolite furnace type CSF 1200. Thermogravimetric analysis ͑TGA͒, Fourier transform infrared spectroscopy ͑FTIR͒ in the attenuated total reflectance ͑AT R ͒ mode and FT-Raman measurements were performed on a Setaram TG-DSC 111, a Bruker Vertex 70, and a Bruker RFS 100 ͑ = 1064 nm͒, respectively.

X-ray diffraction ͑XRD͒ data were collected ͑ CuK␣ ͒ with a ⍜/2⍜ Bruker D5000 diffractometer mounted with a linear MOX-TEK detector.

Scanning electron microscopy ͑SEM͒ images were obtained from a GEOL 6400 microscope. Electrochemical measurements were achieved with a Mac-Pile controller using two-electrode Swagelok-type cells. The composite electrode was coated on an Al disk from a mix of 85% of Li 1.1 V 3 O 8 , 10% of C Super P, and 5% of polyvinylidene fluoride ͑PVDF͒. Ethylene carbonate:dimethyl carbonate ͑EC:DMC͒͑2:1͒ + 1 M LiPF 6 ͑from Merck͒ was used as the electrolyte. Galvanostatic cycling was performed using a current that corresponds to the insertion-desinsertion of 1 Li within 2.5 h and 1 Li within 5 h per formula unit, respectively ͑ϳ60 mA/g, ϳ0.3 mA/cm 2 ͒ in the range 3.7 to 2 V.

Results and Discussion

TGA measurements ͑10 K/min͒ show that all samples are waterfree above 350 to 450°C. ASC 105 is the only sample that presents an increasing weight above 500°C, which can be attributed to oxidation of V IV species. The weight increase roughly corresponds to oxidation of all V IV to V V with the addition of near to 1.5 atoms of oxygen per formula unit, leading to Li 1.1 V 3 O 8 . It means that only the ASC 105 sample contains mainly V IV species.

Infrared measurements show typical V=O, V-O-V, and Li-O-V vibrations of vanadium oxide compounds for samples fired at 400°C and do not show any trace of remaining carbonates coming from thermal decomposition of the organic-based precursor. Raman spectra did not show any carbon traces in the 400°C samples. These results indicate that all 400°C samples are organic and carbon-free. Figure 2 presents XRD patterns of these four samples. As deduced from Rietveld refinement, unit cell parameters for Li 1.1 V 3 O 8 are similar for all samples and ASCR 400 shows a strong preferred orientation owing to the platelet-like shape of the grains ͑see below͒. Note also that all samples prepared from heat-treatment of Li 1.1 V 3 O 8 gels prepared using CSGP method show traces of ␤-Li 0.3 V 2 O 5 ͑ ͒ 11 ͑5w t%f o rA S C 400 , roughly 2 wt % for noASC 400 , and a negligible amount for ASCR 400 ͒. ASCR 400 contains in addition traces of V 2 O 5 ͑ * ͒.

The SEM study is summarized on Fig. 3. The phase impurities detected by XRD were not seen as separated grains in the SEM images of corresponding samples. noASC 400 sample displays a morphology close to that observed for standard Li 1.1 V 3 O 8 SG 400 , whereas the ASC 400 sample shows large ͑about 30 m͒ porous polycrystalline grains and the ASCR 400 sample is made of large ͑about 3 ϫ 6 m͒ well-crystallized platelets. Such morphologies have never been observed before for low-temperature Li 1.1 V 3 O 8 to our knowledge, as submicrometer size agglomerates of needle-like grains are obtained using standard synthesis procedures. 4 It should z E-mail: Dominique.Guyomard@cnrs-imn.fr be concluded then, that our CSGP routes, including the chemical treatment that lead to the ASCR sample, are very efficient in providing new morphologies of Li 1.1 V 3 O 8 . Consequences are now discussed in respect to electrochemical performance.

Figure 4 shows the capacity retention on cycling of the four samples. Although initial capacity of SG 400 ,A S C 400 , and ASCR 400 are similar and close to 245 mAh/g, the capacity retention of the two latter looks much better, especially for ASC 400 ͑capacity loss ϳ Ͻ0.3%/cycle͒, than that of standard SG 400 . Good cycling behaviors ͑capacity loss Ͻ0.5%/cycle͒ of low temperature Li 1.1 V 3 O 8 samples have been obtained using either very specific experimental conditions ͑50 wt % of graphite in the positive electrode mixture, 12 potentiostatic equilibration upon each oxidation, 13 ͒ or pillaring molecules. 14,15 It should also be noted that, to our best knowledge, other works where the active material has been prepared at 400°C or lower and tested under similar experimental conditions to those reported here show a poorer capacity retention ͑loss Ͼ 1.5%͒ on cycling. 4,16 In this respect, our recent results show that this poor capacity retention was confirmed irrespective of the liquid electrolyte ͑solvents and salts͒, the cell type that was used ͑Swagelok, button, or coffee bags͒ or the positive electrode preparation procedure including the very promising one proposed by Guy et al. 17 Moreover, we observe that the capacity retention is strongly improved upon increasing the cycling discharge rate by a factor 2.5 ͑as in Ref. 18͒ or more or by using solid electrolyte poly͑ethylene oxide͒. 19 For these reasons we believe that the capacity retention of Li 1.1 V 3 O 8 mainly depends on side reactions ͑or their consequences͒ such as the formation of an inorganic-organic layer on the surface of the grains that occurs on cycling with liquid electrolytes. 19 On this basis the larger grains for ASCR 400 and especially the specific mor-phology for ASC obtained at low temperature open interesting prospects for optimizing the cycling properties of this compound without strong capacity loss. 4 This effect was also observed recently by Gao et al. 20 who obtained a higher initial capacity ͑350 mAh/g͒, although the capacity loss was larger ͑ϳ1.5%/cycle͒.

Very surprisingly, the noASC 400 sample presents a very low initial capacity, although it has a similar grain size as standard SG 400 . Such behavior was reproducible. It has not been obtained previously to our knowledge and is totally unexpected. The incremental capacity curves vs voltage on the first cycle are shown on Fig. 5 for each sample. No peaks related to V 2 O 5 are observed for sample ASCR 400 showing that V 2 O 5 content in the sample is low. Note that in the case of ASC 400 the reduced phase ␤-Li 0.3 V 2 O 5 is active and responsible for the small peaks observed at roughly 3.45 and 3.65 V on oxidation. 21 One main difference between noASC 400 and other samples is the very low amplitude of the 2.6 V process as well as the absence of that at 2.2 V in the former. The process at 2.6 V appears in other samples as a single or a double peak in the 2.4-2.5 V range on the first discharge, and a single peak at 2.7 V on the first charge. This electrochemical process is related to the phase transformation between Li ϳ3 V 3 O 8 and Li 4 V 3 O 8 22 and corresponds roughly to 90 mAh/g. The low amplitude of the phase transformation has been confirmed by XRD of a noASC 400 sample at the end of the first discharge and accounts for the low capacity recovered on discharge. Such phenomenon has never been observed yet on various Li 1.1 V 3 O 8 samples studied in our laboratory and is very surprising. Further work on thorough characterization of noASC 400 sample is under way in order to assess the origin of the absence of this phase transformation.

Conclusions

The preparation of anhydrous Li 1.1 V 3 O 8 through the original CSGP process and variants gives rise to unexpected Li insertion behavior.

One sample shows atypical Li insertion process with no Li ϳ3 V 3 O 8 to Li 4 V 3 O 8 phase transformation. It is detrimental to the delivered capacity, but it opens new and interesting issues in the field of the basic understanding of Li 1.1 V 3 O 8 Li insertion behavior. Further work is needed in order to assess the origin of the absence of the phase transformation. Some samples display improved cycling behavior compared to standard low temperature Li 1.1 V 3 O 8 , which seems related to their unusual morphology. Such a finding leads to new directions for optimizing the cycling properties of these compounds. Especially, variations around the routes investigated here appear as extremely promising for preparation of even better performing samples.

A

  . Deptuła, a M. Dubarry, b A. Noret, b J. Gaubicher, b T. Olczak, a W. Łada, a and D. Guyomard b,z a Institute of Nuclear Chemistry and Technology, 03-195 Warsaw, Poland b Institut des Matériaux Jean Rouxel, 44322 Nantes cedex 3, France

Figure 1 .

 1 Figure 1. Flowchart for preparation of Li 1.1 V 3 O 8 gels using CSGP method.

Figure 2 .

 2 Figure 2. XRD patterns of ͑a͒ noASC 400 , ͑b͒ ASC 400 , ͑c͒ ASCR 400 , and ͑d͒ SG 400 samples. Lines that corresponds to ␤-Li 0.3 V 2 O 5 and V 2 O 5 are noted ͑ ͒ and ͑*͒, respectively.

Figure 3 .

 3 Figure 3. SEM pictures of ͑a͒ noASC 400 , ͑b͒ ASC 400 , ͑c͒ ASCR 400 ,a n d͑d͒ SG 400 samples.

Figure 4 .

 4 Figure 4. Variation of specific capacity recorded during galvanostatic cycling for ͑a͒ noASC 400 , ͑b͒ ASC 400 , ͑c͒ ASCR 400 , and ͑d͒ SG 400 .

Figure 5 .

 5 Figure 5. Incremental capacity vs voltage curves, obtained from galvanostatic cycling data for ͑a͒ noASC 400 , ͑b͒ ASC 400 , ͑c͒ ASCR 400 , and ͑d͒ SG 400 samples.

Acknowlegments

The authors are grateful to R. Mancini and C. R. Casaccia ͑Italian Agency for the New Technologies, Environmental-ENEA, Rome, Italy͒ for FTIR analysis and interpretation. This work was done with the financial support of CNRS and region Pays de la Loire.

Institut des Matériaux Jean Rouxel assisted in meeting the publication costs of this article.