CPU-based prediction with Self Organizing Map in Dynamic Cloud Data Centers

Nabila Djennane 1 , Meziane Yacoub 2 , Rachida Aoudjit 1* , and Samia Bouzefrane 2* 1 Lari Lab, UMMTO 1 djennanenabila@gmail.com 1 * aoudjit rachida@yahoo.com 2 Cedric Lab, CNAM 2 meziane.yacoub@cnam.fr 2 * samia.bouzefrane@cnam.fr Abstract-The major objective of resource management systems in the cloud environments is to assist providers in making consistent and cost-effective decisions related to the dynamic resource allocation. However, because of the demand changes of the applications and the exponential evolution of the cloud, the resource management systems are constantly called into question with regard to their ability to guarantee an effective resource provisioning. To tackle these challenges, the future demand prediction is a practical solution that has been adopted in the literature. The prediction has widely relied on the CPU utilization since it is considered as a leading cause of the Quality of Service (QoS) dropping. The successful application of artificial intelligence techniques in forecasting problems motivated us to use the Kohonen Self Organizing Maps (SOM) that tries to capture the gathered empirical CPU load time series in regular behaviors to perform an accurate forecast. The proposed solution is a two-step approach that first classifies the collected data and then predicts the future CPU load. The experimental results show that our proposed system outperforms other models reported in the literature. In addition, we proved that SOM known for its strength in classification is also effective for prediction.

Index Terms-Cloud Computing, Resources management, Load prediction, Times series, Clustering, Self organizing Map.

I. INTRODUCTION

Increasingly used by companies in all industries, cloud computing is considered as a revolutionary technology for the 21st century. Cloud computing is a general term used to describe the on-demand delivery of different resources and services over the Internet. It refers to the data storage and computation through the Internet on remote powerful servers rather than using local computers. Thanks to this type of services, companies do not need to invest in their own equipment. Basically, cloud computing refers to three service categories: Infrastructure as a Service (IaaS), Platform as a Service (PaaS) and Software as a Service (SaaS).

Cloud providers, such as Amazon Web Services (AWS), offer virtual server storage, but also Application Programming Interface (APIs) that allow the users to transfer their workloads to remote virtual machines. An IaaS can provide servers, networks, storage space within data centers. Once users have allocated storage capacity, they can start, stop or configure the VMs and storage as they wish. The infrastructure provided as virtual machines can be small, medium, large or very large to suit different needs. Therefore, the IaaS is scalable and flexible, and can be adapted to the workload. As a consequence, the IaaS becomes as one of the most dominant services offered by cloud providers nowadays.

Although cloud computing promises a revolution in the Information and Technology (IT) world, companies still face economic challenges that require an optimal resource management, due to the growing demand for resources and the dynamic nature of the cloud usage.

The cloud resource management is a complex process. To be effective, it must allocate an appropriate amount of resources based on the current demand for applications to meet the service level agreement (SLA) and minimize the waste of resources. Indeed, under-provisioning results in a violation of the SLAs and a poor quality of service (QoS). On the other hand, over-provising wastes energy and resources and even increases costs in terms of cooling and maintenance.

Various techniques such as load balancing and consolidation have been implemented to address the resource management problem. However, the use of these techniques without taking into account the ever-changing resource requirements of hosts can lead to disastrous problems. Therefore, forecasting the future behavior of the application based on specific aspects is the only practical and effective solution for good resource provisioning [START_REF] Amiri | Sur-vey on prediction models of applications for resources provisioning in cloud[END_REF] [2] [3] [START_REF] Liu | Workload forecasting based elastic resource management in edge cloud[END_REF]. Indeed, accurately predicting the future use of host resources allows to make intelligent management decisions.

CPU is one of the main causes of resource scarcity on the cloud hosts, since it is the most dynamic, reactive and ever fluctuating resource. It is intuitive that the CPU management is inefficient, which can be disastrous for applications if they are based on reactive methods like optimisation methods.

Hence, to optimize the use of CPU resource, monitoring its condition and behaviour and correcting the causes of failure with proactive methods are necessary. It is therefore essential to apply forecasting models to manage cloud resources. However, it is very difficult to accurately predict host utilization in a timely manner because of the very fast variation of the host utilization and the strong instability with many bursts.

The contribution of this paper attempts to meet this challenge by proposing a solution that addresses the abovementioned issues. Indeed, our proposed methodology aims at predicting the CPU resource of the next time slot based on historical data issued from previous slots. We resort to Self Organizing Map (SOM) algorithm known for its high capacity in clustering, which we use to its full potential. The time period for which forecasting provides critical information about future load is very important. Therefore, we introduce the sliding window technique which has proven its success in predicting long time series. Thus, to predict CPU load of the next time slot we variate the observation windows. For prediction, we also use SOM through a simple but efficient method. We illustrate the feasibility of our approach by using the PlanetLab dataset generated by the COmon project [5].

The remainder of this paper is structured as follows. In section II, we discuss the literature review. In section III, we motivate our choice and present the used algorithm. Section IV describes our proposed methodology by detailing each step. Section V highlights the conducted experiments and the performed results before concluding in Section VI.

II. RELATED WORK

To ensure a good QoS and to avoid resources wasting, we need to manage resources. However, the big issue is how to predict the future use of the host in real time as the workload varies with time. Predicting future use of hosts is essential for placing virtual machines on appropriate hosts or migrating virtual machines in advance from overloaded or underloaded hosts.

Numerous studies have been carried out on the prediction in cloud computing according to various objectives of the research: Prediction of the servers' load [START_REF] Toumi | Server load prediction using stream mining[END_REF], [START_REF] Di | Host load prediction in a Google compute cloud with a Bayesian model[END_REF], [START_REF] Gondhi | Prediction based energy efficient virtual machine consolidation in cloud computing[END_REF], [START_REF] Verma | Server workload analysis for power minimization using consolidation[END_REF], [START_REF] Song | Host load prediction with long short-term memory in cloud computing[END_REF], prediction of the VMs' load [START_REF] Jheng | A novel VM workload prediction using grey forecasting model in cloud data center[END_REF], [START_REF] Beloglazov | Managing overloaded hosts for dynamic consolidation of virtual machines in cloud data cen-ters under quality of service constraints[END_REF], prediction of the VM use [START_REF] Dabbagh | An energyefficient VM prediction and migration framework for overcommitted clouds[END_REF], [START_REF] Minarolli | Tackling uncertainty in long-term predictions for host overload and underload detection in cloud computing[END_REF], prediction of the host use [START_REF] Mason | Predicting host CPU utilization in the cloud using evolu-tionary neural networks[END_REF].

In the context of virtual machine migrations, various workload prediction techniques are used [START_REF] Gmach | Workload analysis and demand prediction of enterprise data center applications[END_REF], [START_REF] Roy | Efficient autoscal-ing in the cloud using predictive models for workload fore-casting[END_REF], [START_REF] Khan | Workload characterization and prediction in the cloud: a multiple time series approach[END_REF], [START_REF] Wu | Adaptive workload prediction of grid performance in confidence win-dows[END_REF], [START_REF] Chen | Self-adaptive resource allocation for cloud-based software services based on iterative QoS prediction model[END_REF].

The CPU load is one of the most studied indicator to forecast the data-center activity, as it is one of the leading causes of resource shortages on cloud hosts. Artificial Intelligence (AI) and Machine learning (ML) algorithms such as neural networks and linear regression have been widely applied in recent years to predict the CPU load.

Authors, in [START_REF] Dinda | Host load prediction using linear models[END_REF], used several prediction models to predict the execution times of tasks, based on the CPU load forecast. [START_REF] Duggan | Predicting host cpu utilization in cloud computing using recurrent neural networks[END_REF] used a recurrent neural network formed with the so-called back propagation algorithm to predict the CPU utilisation of a host on the Google Cluster trace data set.

Authors, in [START_REF] Beloglazov | Optimal online deter-ministic algorithms and adaptive heuristics for energy and performance efficient dynamic consolidation of virtual ma-chines in cloud data centers[END_REF], proposed the implementation of local regression, median absolute deviation, inter-quartile range and robust local regression methods to determine when servers may be over-utilized based on CPU usage.

To improve the performance of the VM placement algorithm proposed in [START_REF] Beloglazov | Optimal online deter-ministic algorithms and adaptive heuristics for energy and performance efficient dynamic consolidation of virtual ma-chines in cloud data centers[END_REF], Mason et al. [START_REF] Mason | Predicting host CPU utilization in the cloud using evolu-tionary neural networks[END_REF] proposed the evolutionary neural network approach to predict the host CPU utilization based on both one-step and multi-steps ahead.

Unlike the approach described by Song et al. [START_REF] Song | Host load prediction with long short-term memory in cloud computing[END_REF] who used the short term memory (LSTM) model in a recurrent neural network (RNN), Qazi and Aizenberg in [START_REF] Qazi | Cloud Datacenter Workload Prediction Using Complex-Valued Neural Networks[END_REF] proposed a prediction mechanism using MLMVN, which is a feed forward neural network using complex-valued neurons. The CPU usage of individual host machines for the 29 days was utilized for evaluation.

In order to propose a virtual machine consolidation approach, the Kernel Density Estimation technique is used in [START_REF] Mahdhi | A Prediction-based VM Consolidation Approach in IaaS Cloud Data Centers[END_REF] to estimate resource usage and predict future host's states. Using real web server request traces, Calheiros et al. [START_REF] Calheiros | Workload prediction using ARIMA model and its impact on cloud applications QOS[END_REF] proposed an auto-regressive integrated moving average (ARIMA) model that assesses the accuracy of future workload forecasting.

In [START_REF] Rahmanian | A learning automatabased ensemble resource usage prediction algo-rithm for cloud computing environment[END_REF], an LA-based ensemble prediction algorithm based on Learning Automata (LA) theory is proposed for CPU load prediction based on several VMs gathered from the dataset of the CoMon project. The proposed approach combines the prediction values of multiple prediction models. Each model is given a weight according to its performance. Then, an autonomic approach is used to determine how much accurate each prediction model is according to their predictions.

In [START_REF] Kumar | Workload prediction in cloud using artificial neural network and adaptive differential evolution[END_REF], the authors presented a workload prediction model using neural network and self adaptive differential evolution algorithm to learn the best suitable mutation strategy along with optimal crossover rate.

Sadeka et al., in [START_REF] Islam | Empirical prediction models for adaptive resource provisioning in the cloud[END_REF], proposed empirical prediction models for adaptive resource provisioning in cloud computing using neuronal network and linear regression. Their prediction method applied some strategies including sliding window. They also provided evaluation metrics for validating the technique such as MAPE and RMSE.

Salam Ismaeel et al.,[START_REF] Ismaeel | Using ELM Techniques to Predict Data Centre VM Requests[END_REF], proposed an ELM technique to predict data center VM requests based on historical data, that they combine with the clustering K-Means method. The authors presented these techniques in a small framework. They used data from real google traces.

In order to minimize energy cost and consumption in cloud data centers and to reduce the number of active physical servers on data centers, Fahimeh Farahnakian et al. in [START_REF] Farahnakian | Energy-Efficient Virtual Machines Consolidation in Cloud Data Centers Using Reinforcement Learning[END_REF], proposed a dynamic virtual machine consolidation based on k-nearest neighbor regression algorithm that predicts in each host the CPU usage. To achieve SLA violation and energy cost, they adopted four algorithms of [START_REF] Beloglazov | Optimal online deter-ministic algorithms and adaptive heuristics for energy and performance efficient dynamic consolidation of virtual ma-chines in cloud data centers[END_REF] that they combined with their proposed method k-nearest neighbor algorithm.

In [START_REF] Chen | An Adaptive Short-Term Prediction Algorithm for Resource Demands in Cloud Computing[END_REF], an adaptive short-term prediction strategy is proposed to adaptively select a precise short-term prediction method. The proposed approach works in three stages: preprocessing of abnormal data and replacement of outliers, adaptive selection to select a better prediction algorithm based on a dynamic threshold and finally an error adjustment by proposing an error adjustment factor for improve accuracy. The conducted experiments demonstrate the effectiveness of the proposed approach in terms of the prediction accuracy, however it suffers from a high time cost.

To address the challenge of allocating several requests to a VM, authors in [START_REF] Kaur | An intelligent regressive ensemble approach for predicting resource usage in cloud computing[END_REF] proposed A Regressive Ensemble Approach for Predicting (REAP) CPU usage of a scientific application. REAP predicts intelligently the CPU utilization by integrating Genetic Algorithm-based feature selection and CPU usage prediction techniques. The experimental results show that the proposed approach enhances the accuracy by 2% and reduces the execution time by 16.2% comparatively to the existing machine learning regression models.

The authors, in [START_REF] Qui | A deep leanrning Approach for VM Workload Prediction in the Cloud[END_REF], proposed a deep learning approach that they designed with a deep belief network (DBN) composed of multiple layered restricted boltzmann machines and a regression layer. They used the DBN to extract the high level features from data and regression layer for prediction. A MAPE error is calculated to evaluate the proposed method.

Salam Ismaeel et al, in [START_REF] Islam | Empirical prediction models for adaptive resource provisioning in the cloud[END_REF], proposed a survey of the most techniques and algorithms used in proactive dynamic VM consolidation. This study focuses on energy consumption.

The authors of [START_REF] Hishamf | An intelligent swarm based prediction approach for predicting cloud computing user resource need[END_REF] combined linear and non linear prediction models using ARIMA and SVR. ARIMA model is used to predict time series of linear attributes while SVR model is used to extract non linear attributes from the dataset they used. Both models used MAPE and RMSE to validate their methods.

The authors of [START_REF] Kumar | Scaled Conjugate Gradient Backpropagation based SLA Violation Prediction in Cloud Computing[END_REF] consider another important parameter for prediction that is the SLA. Since this parameter is critical for both the customer and the cloud provider, they use scaled conjugate gradient neural network to make predictions possible on SLA violations.

Cloud data centers contain hundreds of thousands of servers, which host millions of VMs of different sizes, types and applications. Hence, since server resources are strongly influenced by the VMs they host, it makes more sense to focus on VMs resource management rather than server management as in [START_REF] Toumi | Server load prediction using stream mining[END_REF] [7] [START_REF] Gondhi | Prediction based energy efficient virtual machine consolidation in cloud computing[END_REF].

The choice of a good data set that is representative of a real cloud computing environment is important. Authors of [START_REF] Mahdhi | A Prediction-based VM Consolidation Approach in IaaS Cloud Data Centers[END_REF] Our research work focuses on the data set of [5] like in [START_REF] Beloglazov | Optimal online deter-ministic algorithms and adaptive heuristics for energy and performance efficient dynamic consolidation of virtual ma-chines in cloud data centers[END_REF] [START_REF] Mason | Predicting host CPU utilization in the cloud using evolu-tionary neural networks[END_REF] [33] [START_REF] Islam | Empirical prediction models for adaptive resource provisioning in the cloud[END_REF]. The drawback of these works is that they did not exploit all the data. Some of them selected randomly some VMs while others selected randomly time intervals. This distorts the results in case of generalization.

In addition this data set is of time series type, which is an important point to take into account. The produced time series present a particular difficulty in predicting their future values. It is well known that the usual prediction methods already used in prediction problems have poor performance when used without first clustering the time series [START_REF] Barnston | Correspondence among the Correlation [root mean square error] and Heidke Verification Measures; Refinement of the Heidke Score[END_REF].

The fact that, the works cited above didn't resolve well the problem, motivates us to propose and focus in this paper on three important issues: data clustering, time series analysis and predicting the future CPU load.

III. THE SELF ORGANIZING MAP

Developed by Teuvo Kohonen, self-organized map (SOM) is a new method to represent neural networks and to perform automatic classification tasks. Unlike artificial neural networks, SOM is an unsupervised method. It is composed of simple elements (neurons) assembled into neural networks, whose the functioning is strongly influenced by the connection of the elements to each other. SOM is often used to analyze observed data whose the structure requires investigation.

A. PRINCIPLE OF SOM

SOM is a method that projects the space of observed data (of large dimensions) into a space of small dimensions such as 1, 2 or 3D, called MAP. The map is made up of a set of neurons connected to each other according to the notion of neighbourhood. Each neuron has fixed coordinates in the map space and coordinates adaptable on the space of the data called referential vectors, responsible for an area of this space.

This projection must respect the topology of the data. It is based on vector quantification methods that partition all available observations into similar groups using learning algorithms. These groups are characterized by their neighbourhood structures, which can be materialized using a discrete space called a "topological map". This space forms a small lattice on which neighbourhood structures are taken into consideration by the model. The choice of a topology depends on the nature of the problem.

The implementation of a topological map requires a distance δ on the topological space to define the notion of neighbourhood on the map. It is a discrete distance defined by the length of the shortest path connecting two neurons on the map. Thus, the order neighbourhood of a neuron can be defined as the set of neurons located at a distance d from the neuron.

The distances that link the neurons to each other allow to vary the relative influence of the different neurons which can be quantified by a K function. We often use a family of K T functions set to T , sometimes called activation functions to better control the size of the neighbourhood as in the following:

K T = K( δ T ) (1)
T is a parameter used to control the influence between neurons.

B. ALGORITHM OF SOM

Once the map topology and activation functions have been chosen, the reference vectors are obtained by learning from the data. The algorithm used to learn the map is described as in the following.

Step 0 : Initialization of the reference vectors W .

Step 1: At each iteration: As input of the map, an example of a selected learning X(n) is presented. The algorithm compares the example to all the reference vectors so that the winning neuron i is the one whose reference vector W i (n) is the closest to the input X(n) :

i * = argmin(d(W i (n), X(n))) (2)
Where i denotes in turn each neuron in the network and W i its referent vector.

We evaluate the neighbourhood of the winning neuron by the equation below:

K T i * (i) = K T (δ(i, i * )) (3)
Then, all neurons of the Map are updated for any i belonging to the neighbourhood of i * . The Map is more adapted by the fact that the neurons are neighbours of i * :

W i (n + 1) = W i (n) + α(t)K T i * (i)[X(n) -W i (n)] ( 4
)
where α is a learning parameter called learning step which decreases as a function of n, and is less than 1. It's also an important element because it allows to find a compromise between the convergence speed and the quality of the map unfolding.

Finally the stopping criterion of the algorithm is defined in several ways: number of iterations, difference between weight vectors, quantification error and so on.

Phases 1, 2 and 3 are called respectively as in the following: Competition: After selecting an example from the database, we look for the neuron that most closely resembles it. This neuron called "winning neuron" is often rated BMU (Best Matching Unit).

Cooperation: In this step, the neighbourhood of the winning neuron is determined. It refers to the region of the map that is the most active and closest, in terms of the distance used, to the observation. The size of the neighbourhood of the winning neuron is controlled by the learning radius.

Adaptation: The winning neuron is modified to look more like the example and then information about its neighbourhood is disseminated. This modification is done using the activation function which controls the influence of the winning neuron on its neighbourhood.

C. AUTOMATIC CLASSIFICATION WITH KOHONEN MAPS

Once a map is learned, we have the typical profiles of each neuron called codebooks. Two close neurons in the map are close standard profiles and a set of contiguous codebooks represent a particular profile in the data.

Codebooks are a data set on which a hierarchical classification can be applied to group similar neurons. The classification of a new element can be done as follows:

• Present the new element at the card entry.

• Identify the winning neuron, the one whose codebook is close to the new element. • Identify the cluster of the winning neuron.

IV. OUR PROPOSED APPROACH

In this section, we will highlight our methodology and describe our proposed model while depicting each component (see Fig. 1).

A. Methodology description

In the cloud computing, a data center is mainly made up of a set of virtualized servers. Services are offered to customers by allocating several heterogeneous virtual machines. The real loads of these virtual machines are often dynamic. Thus, the static allocation of resources is doomed either to waste, if it is based on a worst-case scenario estimate, or to performance degradation, if it is based on the average load. Thanks to the cloud computing model, resources can be allocated on demand and the sizing is adapted to load variation. However, resource variations, especially the CPU load of VMs are frequent and unpredictable, resulting in server overload, under-load or even inactivity. This results in degraded performance, wasted resources or violations of service level agreements (SLAs).

It appeared necessary to develop proactive methods for the management of virtual machines before it leads to under-consumption of resources on physical servers or overconsumption.

In order to make an acceptable solution that is able to predict future resources requirement in the cloud, we explored a number of existing prediction methods as proposed in the literature.

The first step of our proposed solution is to choose a representative data set from a real environment. Since the CPU resource is the most dynamic one on the servers, we choose the Planetlab data of CoMon project [5]. These data are gathered from a real workload of monitoring infrastructure. The CPU utilization data is obtained from more than one thousand VMs from servers located within more than 500 locations around the world. Data is collected every 5 minutes. So, our research problem relates to time-series analysis such as each VM is a time series data that consists of a sequence of N pairs (CP U i , t i ), where CP U i is the percentage of CP U utilisation at time t i .

The Self Organizing Map mainly adopted in our proposed system is one of the most common techniques used in clustering problem. However, in our work, we propose to use it not only for this purpose but also for prediction.

Moreover, to determine the best prediction on window, we incorporate the concept of sliding window, which forecasts future CPU resources using previous data in different observation windows sizes. Our proposed models are carried out using statistical metrics as discussed in the following sections. 2) Selection Once all the data are projected on Map and each neuron summarizes the VMs belonging to it with the same behavior, and in order to continue the next steps, we have chosen to select a subset of VMs from each neuron in order to obtain a sample of data of reduced size while keeping the heterogeneity of the whole set. In this way, our simulations for the prediction that is the purpose of our work will not be saturated. The data selection was made according to Algorithm 2. Each time we are interested in prediction problems using time series, the sliding window is requested, especially in the case of long series. Indeed, the prediction can only be made on a finite number of points. In our case, we have CPU loads as used by the VMs gathered every five minutes during 24 hours. Our data are therefore as follows : Because there is no rule to determine the appropriate size of the observation window for better prediction, we have decided to vary the window size in order to decide which one will be the right one as follows:

B. Our Proposed System Components

CP U t0 V M1 , CP U t1 V M1 , ..., CP U t k V M1 CP U t0 V M2 , CP U t1 V M2 , ..., CP U t k V M2 CP U t0 V M N , CP U t1 V M N , ..., CP U t k V M N N :
In Fig. 2, the size of the observation window is only used as an illustrative example. In our work, we considered two scenarios.

In the first one, we tried to predict the 7th value by using the previous 6 values, and in the second scenario, our aim was to predict the 13th using the previous 12 values. For each time series, i. e. for each VM, the values were predicted from 7 to 288 in the first scenario and from 13 to 288 in the second scenario, knowing that we cannot predict the values from 0 to 6 and from 0 to 12 because of scarce values. Therefore, we use the following:

• First Case:

The 6 values of each VM: From 0 to 6 to predict the 7th value From 1 to 7 to predict the 8th value From 2 to 8 to predict the 9th value . . . From 282 to 287 to predict the 288th value • Second Case:

The 12 values of each VM: From 0 to 12 to predict the 13th value From 1 to 13 to predict the 14th value From 2 to 14 to predict the 15th value . . . From 276 to 287 to predict the 288th value We note: XV M i,j the CPU measurement of V M i at time j (i=1,n) (j = 1, 288) Therefore, we create in each case two matrices : input matrix M Input and output matrix M Output written as follows:

• Case 01 : Observation Window = 6

M Input =     X V M1,1 X V M1,2 ... X V M1,6 X V M1,2 X V M1,3 ... X V M1,7 ... X V Mn,282 X V Mn,283 ... X V Mn,287     (1) M Output = X V M1,7 X V M1,8 ...X V Mn,288 (2)
• Case 02 : Observation Window = 12

M Input =     X V M1,1 X V M1,2 ... X V M1,12 X V M1,2 X V M1,3 ... X V M1,13 ... X V Mn,276 X V Mn,277 ... X V Mn,287     (3) M Output = X V M1,13 X V M1,14 ...X V Mn,288 (4)
The data of the input matrix in each case will be again learned using SOM to gather similar observations within the same neurons according to algorithm 3. Steps 6 to 10 of SOM-1 7 until Convergence; At the end of this step, we obtain two Maps from each case.

4) Splitting

To evaluate the quality of the obtained Maps, a strong similarity within the same neuron must be respected. Therefore, we compute the standard deviation of each neuron of Maps.

Then, we define a threshold that we have set at a fix value.

The two obtained Maps in the previous step will be splited into two Sub-Maps according to the defined threshold as in Algorithm 3. Algorithm 4: Spliting The MisClassified Data will be once again presented to SOM, in order to reclassify and better distribute them on the neurons and by the way reduce the standard deviation (See algorithm 5).

Algorithm 5: SOM-3 Steps 6 to 10 of SOM-1 7 until Convergence;

5) SOM-Prediction

As we introduced earlier, we applied our SOM-based algorithm for both clustering and prediction. We will explain here how to make the prediction possible using SOM.

We consider the final obtained SOM Map by the previous step.

Each map consists of a set of neurons and each neuron gathers a set of similar input observation windows. The goal of SOM-Predictor is to make prediction in each one of the neurons. Let Y i denote the set of M neurons corresponding to each Map Y i = {(y 1 , y 2 , ..., y M )}, and (where k=number of time slot) the subset of M input data mapped to neuron i. For each element of X n corresponds an observed output from M output . We note the set of outputs by

X n = {(x t0 1 , x
O n = {o 1 , o 2 , .., o n }.
The CPU load at time t k+1 for all observation window data belonging to the same neuron is then computed as follows: In this section, the efficiency of the proposed prediction system will be evaluated using a real world CPU load trace [5] described in Table 1. Our experiments are conducted under Matlab environment using SOM toolbox [START_REF] Vesanto | SOM toolbox for Matlab[END_REF].

P red(y i ) = n j=1 o j n (5)
First, we plot some VMs of the data set (Fig. 3) to show the diversity of types and variability during 24 hours (one measurement every five minutes). 4 shows the SOM Map obtained after projection with the data by PCA tool, while Fig. 5 is the SOM Map obtained after selecting some VMs to be used in the remaining steps. The two Maps obtained (Fig. 4 and Fig. 5) are not very different. This shows that the selected VMs summarize well the global data and therefore our selection method is efficient and the new obtained data set is homogeneous. The selection step is very important during the simulations. Indeed we have 11737*288 data. This number will increase considerably during sliding windows step that not only blocks our simulations but also creates redundancies of observation windows.

Fig. 6 and Fig. 7 correspond to the SOM Maps obtained after classification of the observations windows for the two different cases 6 and 12 respectively. These figures clearly show that the SOM Map is spread out over the data set, which proves that the Maps are well learned in such a way that they reach all points, even the remote ones.

In statistics, the standard deviation can be used to calculate the homogeneity of several populations on the same variable. It measures the dispersion of the values of a data set around the mean. If the data values are all similar and homogeneous, then the standard deviation will be small and close to zero. If the data values are highly variable, then the standard deviation will be large and greater than zero.

The standard deviation is computed for each neuron and displayed in Fig. 8 and Fig. 9 by the U-Matrix. As shown by these figures, the standard deviation varies between 0 and 13.5 when the slide window is equal to 6, and between 0 and 14.6 when the slide window is equal to 12. After several simulations, we define a threshold=2 which will be used to split the obtained SOM Maps into two parts: the well classified data and mis-classified data. We keep the neurons whose the standard deviation is less than the threshold while the dataset belonging to those whose the standard deviation is higher than the threshold will be learned again by the SOM algorithm in order to better reclassify them and to obtain two other maps in each case, that are better learned.

In order to illustrate the effectiveness of this work, the proposed SOM-predictor is compared with: Support Vector Machine (SVM) and MultiLayer Perceptron (MLP) [START_REF] Collobert | Links between Perceptrons, MLPs and SVMs[END_REF] models. To make this possible, we use the same selected data set and the same size for observation windows and prediction windows.

To conduct our evaluation and comparison, we have selected two methods as described below. Our choice was based on similar works of the literature:

• Root-Mean-Square Error (RMSE): is a frequently used measure of the difference between the values predicted by a model or an estimator and the values observed defined as follows:

RM SE = N i=1 ( Ŷi -Y i ) 2 N (6)
• Mean absolute percentage Error (MAPE): is a measure that indicates about the mean of the dispersion between predicted and observed values, with the linear model (absolute difference). Therefore, it's a convenient indicator for comparison. The formula is:

M AP E = 1 N N i=1 Ŷi -Y i Y i (7)
Table 2 and Table 3 show significant values and clearly highlight the chosen prediction method compared to SVM and MLP. RMSE and MAPE errors obtained with SOM are the smallest in the two cases where observation windows are equal to 6 and 12. However, for SOM, the size of observation window is clearly important such that the results of the errors show that the choice of a smaller observation window allows us to better predict.

In addition to the numerical values, we plot in figures Fig. 10 Fig. 11 some VMs such that the graphs of each figure show the observed values and the predicted ones by the three methods SOM, MLP and SVM for each VM. The figures show clearly that the lines of SOM follow the same variations of the observed ones. In the data center environment, the goal is not to predict the exact future CPU values but to predict the variation that can each VM take in time. The peaks of load that may occur are critical and have an important role in the consolidation of VMs, especially in their migration. Hence, through our experimentation, we have shown that SOM combined with the proposed methodology is quite robust to predict better, especially in critical cases unlike MLP and SVM which predict quite well but are weak in such cases.

In addition to our experiments, we present some VMs of the non-selected dataset to the SOM Map as shown in figure Fig. 12 (with observation window=6) to predict the future CPU load with the three predictor methods. The results are shown in graphs of Fig. 13 and Fig. 14 and prove that SOM predicts better than MLP and SOM. Our prediction method is quite simple but very efficient as shown by the obtained results and graphs compared to the two prediction methods SVM and MLP which are known for their robustness in regression prediction.

As a perspective, we plan to further test the proposed method by considering not only the CPU workload, but also different types of workloads (memory, storage, etc.) and investigate the correlation between them. We intend also to implement our method on a real platform for real-time decision making.

  [START_REF] Qazi | Cloud Datacenter Workload Prediction Using Complex-Valued Neural Networks[END_REF] [START_REF] Ismaeel | Using ELM Techniques to Predict Data Centre VM Requests[END_REF] [25][START_REF] Dinda | Host load prediction using linear models[END_REF] have worked on the data set of Google [40] that gathers the collected CPU and memory traces of web servers, while in [5] collected the percentage of CPU usage by several VMs hosted in different servers located in different regions of the world.

1 )

 1 Clustering: A general rule in the descriptive statistics consists in firstly observing and visualizing the data

Figure 1 : 1 1 6 Select V M ∈Xrandomly 7 find 8 Update the weight of the winner y * and its neighborhoods 9 y

 116789 Figure 1: Proposed System Model

Algorithm 2 : 5 foreach y i ∈ Y do 6 S[] ← allV M s ∈ y i 7

 2567 Selection 1 Input: a set of neurons Y = {y 1 , y 2 , .., y M } 2 begin; 3 Initialize i = 1 4 repeat SOrd[] ← Ord(S, desc) ; // Order S in Descending Order according to their radius error 8 SSelected[] ← take one out of 3 from SOrd[]

Figure 2 :

 2 Figure 2: Scheme of slide windows

Algorithm 3 :- 2 1

 32 SOMInput: M Input 2 Output: a set of neurons Y = {y 1 , y 2 , .., y M } 3 begin; 4 Initialize Y = {y 1 , y 2 , .., y M } randomly 5 repeat 6

1

  Input: Map,Threshold; 2 Output: MisClassifiedData[], WellClassifiedData; 3 foreach Neuron ∈ M ap do 4 if STD(Y)≤ T hreshold then 5 WellClassifiedData[] ← Data ∈ N euron

Figure 3 :

 3 Figure 3: CPU Load of different VMs during 24 hours with 5minutes interval showing the diversity of VMs types and their variations

Figure 4 :

 4 Figure 4: PCA projection of data and neurons after Classification of all VMs

Figure 6 :

 6 Figure 6: PCA projection of data and neurons after sliding window, Case: slide window=6

Figure 7 :

 7 Figure 7: PCA projection of data and neurons after sliding window, Case: slide window=12

Figure 8 :Slide

 8 Figure 8: UMatrix showing Standard deviation of each cluster, a: Case Slide Window=6, b: Case Slide Window=12

Figure 9 :Figure 10 :

 910 Figure 9: Observed and Predicted data for some VMs with the SOM, MLP and SVM methods, Case Slide Window=6

Figure 11 :Figure 12 :

 1112 Figure 11: Prediction protocol for coming data

Figure 13 :

 13 Figure 13: Observed and Predicted data for some VMs of not selected dataset using Slide Window=12

Table I :

 I Data DetailAs shown in Table1, we have 11737 VMs and each VM contains 288 CPU traces. An Input matrix of 11737*288 is presented to SOM to be classified. Fig.

	Day	Number of VMs
	2011/03/03	1052
	2011/03/06	889
	2011/03/09	1061
	2011/03/22	1516
	2011/03/25	1078
	2011/04/03	1463
	2011/04/09	1358
	2011/04/11	1233
	2011/04/12	1054
	2011/04/20	1033
	Total	11737

Table II :

 II RMSE ERRORs

		Slide Window=6 Slide Window=12
	SOM	0,2063	0,41985
	SVM	0,7329	1,17
	MLP	0,7577	1,19

Table III :

 III MAPE ERRORs

The problem consists then in using:• Case 01 : Observation Window = 6X V M1,1 X V M1,2 X V M1,3 X V M1,4 X V M1,5 X V M1,6 to predict X V M1,7 X V M1,2 X V M1,3 X V M1,4 X V M1,5 X V M1,6 X V M1,7 to predict X V M1,8 ... X V M1,282 X V M1,283 X V M1,284 X V M1,285 X V M1,286 X V M1,287 to predict X V M1,288 ... X V Mn,282 X V Mn,283 X V Mn,284X V Mn,285 X V Mn,286 X V Mn,287 to predict X V Mn,288• Case 02 : Observation Window = 12 X V M1,1 X V M1,2 X V M1,3 X V M1,4 X V M1,5 X V M1,6 X V M1,7 X V M1,8 X V M1,9 X V M1,10 X V M1,11 X V M1,12 to predict X V M1,13 X V M1,2 X V M1,3 X V M1,4 X V M1,5 X V M1,6 X V M1,7 X V M1,8 X V M1,9 X V M1,10 X V M1,11 X V M1,12 X V M1,13 to predict X V M1,14 ... X V M1,276 X V M1,277 X V M1,278 X V M1,279 X V M1,280 X V M1,281 X V M1,282 X V M1,283 X V M1,284 X V M1,285 X V M1,286X V M1,287 to predict X V M1,288 ... X V Mn,276 X V Mn,277 X V Mn,278 X V Mn,279 X V Mn,280 X V Mn,281 X V Mn,282 X V Mn,283 X V Mn,284 X V Mn,285 X V Mn,286 X V Mn,287 to predict X V Mn,288


A G Oshchepkov
email: oshchepkov@catalysis.ruelena.savinova@unistra.fr

G Braesch

G Rostamikia

A Bonnefont

M J Janik

M Chatenet

E R Savinova

Insights into the Borohydride Electrooxidation Reaction on Metallic Nickel from operando FTIRS, on-line DEMS and DFT

Keywords: Borohydride oxidation reaction, polycrystalline nickel electrode, Fourier Transform Infrared Spectroscopy, Differential Electrochemical Mass Spectrometry, Density Functional Theory calculations

Direct Borohydride Fuel Cells (DBFCs) are considered as promising power sources for portable and mobile applications. Their advantages are high theoretical energy density, and high theoretical cell voltage. Metallic Ni has recently emerged as a promising electrode material for DBFCs. In this work we combine electrochemical, operando Fourier-Transform infrared spectroscopy (FTIRS), and online differential electrochemical mass spectrometry (DEMS) measurements with density functional theory (DFT) calculations to advance the understanding of the borohydride oxidation reaction on Ni.

Introduction

Thanks to its high energy density, non-toxicity, facile storage and transportation, sodium borohydride (NaBH4) is considered as a promising carbon-free energy carrier. Direct Borohydride Fuel Cells (DBFCs), which utilize NaBH4 as a fuel, are considered as promising power sources for portable and mobile applications due to their high theoretical cell voltage, high theoretical number of transferred electrons [START_REF] Li | A new application of nickel-boron amorphous alloy nanoparticles: anode-catalyzed direct borohydride fuel cell[END_REF] and the ensuing high theoretical energy density. However, currently available platinum group metal (Pt, Pd)-based electrocatalysts do not allow one to take full advantage of the low standard potential of the borohydride oxidation reaction (BOR, Eq1 and Eq1*) due to the hydrogen evolution reaction competing with the BOR at potentials below 0 V vs RHE (HER, Eq2) and heterogeneous hydrolysis of BH4 -(Eq3) as well catalyzed by transition metals [START_REF] Olu | Evaluation of anode (electro)catalytic materials for the direct borohydride fuel cell: Methods and benchmarks[END_REF].

BH4 -+ 8 OH -⇄ BO2 -+ 6 H2O + 8 e - E 0 = -0.41 V vs RHE (Eq1) or BH4 -+ 8 OH -⇄ B(OH)4 -+ 4 H2O + 8 e - (Eq1*)

2 H 2 O + 2 e -⇄ 2 OH -+ H 2 E 0 = 0 V vs RHE (Eq2) BH4 -+ 2 H2O  BO2 -+ 4 H2 (Eq3)
Ni has been considered as a BOR catalyst by several groups (see e.g. Refs [START_REF] Dong | Electrooxidation mechanisms and discharge characteristics of borohydride on different catalytic metal surfaces[END_REF][START_REF] Geng | Ni-Pt/C as anode electrocatalyst for a direct borohydride fuel cell[END_REF][START_REF] Zhang | Nickel particles supported on multi-walled carbon nanotubes modified sponge for sodium borohydride electrooxidation[END_REF][START_REF] Santos | Nickel and Nickel-Cerium Alloy Anodes for Direct Borohydride Fuel Cells[END_REF][START_REF] Romanova | Electrochemical Oxidation of Borohydride-Ion on Nickel Electrode: a Study by the Method of IR-Spectroscopy[END_REF][START_REF] Zhang | Three-dimensional functionalized graphene networks modified Ni foam based gold electrode for sodium borohydride electrooxidation[END_REF][START_REF] Li | A new application of nickel-boron amorphous alloy nanoparticles: anode-catalyzed direct borohydride fuel cell[END_REF][START_REF] Ma | Facile fabrication of gold coated nickel nanoarrays and its excellent catalytic performance towards sodium borohydride electro-oxidation[END_REF][START_REF] Grinberg | Direct borohydride oxidation electrocatalysts based on Ni-Ru/C and Ni-Ru-F/C alloys[END_REF] and refs therein). However, the results were rather contradictory, some papers claiming high, the otherlow BOR activity of Ni. Recently we have demonstrated [START_REF] Oshchepkov | Nickel Metal Nanoparticles as Anode Electrocatalysts for Highly Efficient Direct Borohydride Fuel Cells[END_REF] that the BOR activity of Ni is strongly dependent on its surface state (metallic vs oxidized). Metallic Ni, with its low HER activity [START_REF] Oshchepkov | On the Influence of the Extent of Oxidation on the Kinetics of the Hydrogen Electrode Reactions on Polycrystalline Nickel[END_REF][START_REF] Oshchepkov | Nanostructured nickel nanoparticles supported on vulcan carbon as a highly active catalyst for the hydrogen oxidation reaction in alkaline media[END_REF], appeared to be an excellent BOR catalyst ensuring a low open-circuit potential (OCP) and enabling net BOR current below E = 0 V vs RHE. Density functional theory (DFT) calculations suggest that the high BOR activity at low potentials is due to a better balance in the adsorption energies of Had, OHad, and B-containing reactive intermediates, compared to Pt and Au surfaces. Indeed, BH4 - adsorption on Ni being weaker than on Pt, it limits surface blocking by BHad, but stronger than on Au, thus resulting in a faster BOR kinetics [START_REF] Oshchepkov | Nickel Metal Nanoparticles as Anode Electrocatalysts for Highly Efficient Direct Borohydride Fuel Cells[END_REF][START_REF] Olu | Anode Electrocatalysts for Direct Borohydride and Direct Ammonia Borane Fuel Cells[END_REF]. Later Braesch et al. [START_REF] Braesch | Nickel 3D Structures Enhanced by Electrodeposition of Nickel Nanoparticles as High Performance Anodes for Direct Borohydride Fuel Cells[END_REF][START_REF] Braesch | A high performance direct borohydride fuel cell using bipolar interfaces and noble metal-free Ni-based anodes[END_REF] have successfully demonstrated that DBFC anodes made from Ni enable higher power densities and cell voltages than equivalent DBFCs with Pt of Pd-based anodes. However, Ni-based anodes do not enable to completely valorize the BH4 -fuel, as only four electrons per BH4 -species are produced in the anode reaction, the other four being lost into H2 that escapes the cell. This could be ascribed to metallic Ni being poor hydrogen oxidation reaction (HOR) catalyst, a downside of its advantages.

The present contribution attempts to provide further insights into the mechanisms of the BOR at Ni surfaces. Applying operando Fourier-Transform Infrared spectroscopy (FTIRS) and online differential electrochemical mass spectrometry (DEMS), products and eventual intermediates of the BOR on Ni are detected; it will notably be shown that H2 has two origins: HER from cathodic reduction of the solvent -water, and catalytic decomposition/dissociative adsorption of the BH4 - species at the Ni surface. Supplement experimental data with the DFT calculations combined with these spectroscopic/metric evidences enable to shed light on the BOR mechanism on Ni.

Experimental and computational details

Materials. Two types of the Ni working electrodes (WE) were utilized in this work. Electrochemical (EC) and FTIRS measurements were performed with a polycrystalline Ni disk purchased from MaTeck (99.99%Ni, Ø5 mm for electrochemical and Ø10 mm for FTIRS). The top surface of the Ni disk (in what follows addressed as Nipoly) was thoroughly polished with an Al2O3 slurry with size of the granules from 1.0 down to 0.3 μm (Alfa Aesar) and then sonicated in ethanol (5 min.) and water (10 min.). For electrochemical and FTIRS measurements, the Nipoly rod or disk were fixed either in a holder or on top of a glass tube, respectively, and their lateral surface was sealed with a Teflon tape so that only the flat top surface of the electrode was accessible to the electrolyte. Prior to each measurement (i.e. acquisition of a cyclic voltammogram or a FTIR spectrum) the top surface of the Nipoly fixed in the holder was additionally polished with an Al2O3 slurry (0.3 μm, Alfa Aesar), rinsed with ultra-pure water (18.2 MΩ cm, TOC < 3 ppb, Arium H2OPRO-UV-T-TOC or PURELAB Chorus 1) and sonicated (for ca. 1 min) in ultra-pure water. Short polishing time and utilization of the Al2O3 granules with 0.3 μm size allow to fully remove Ni oxides from the surface and thus achieve high reproducibility of the measurements. Ni felt from Sorapec was used as an electrode in the DEMS cell. Prior to the measurements it was subjected to an acid etching following the procedure detailed in Ref [START_REF] Braesch | Nickel 3D Structures Enhanced by Electrodeposition of Nickel Nanoparticles as High Performance Anodes for Direct Borohydride Fuel Cells[END_REF] to remove Ni oxides/hydroxides from its surface, and pressed between a PTFE membrane and a current collector. Some complementary experiments were performed with an Au disk (Ø8 mm, MaTeck, 99.99%).

Electrochemical measurements. Electrochemical measurements were performed in 0.1 M NaOH electrolyte in a standard three-electrode cell (Pyrex glass) at room temperature 294  1 K using a Biologic SP-300 potentiostat. The electrolyte was prepared from NaOH solution (50% in water, Premium quality, Aldrich) and ultra-pure water. The counter electrode (Pt wire) and the reference electrode (Hg|HgO|0.1 M NaOH) compartments were connected with the working electrode chamber via a glass frit and a Luggin capillary, respectively. All electrode potentials reported in this paper are referred to the reversible hydrogen electrode (RHE). Prior to each experiment, the glassware was cleaned by soaking in a H2SO4:H2O2 (1:1 v/v) mixture and then thoroughly washed with ultra-pure water.

FTIRS measurements. Spectroelectrochemical measurements were performed at room temperature (298  2 K) under potentiostatic conditions using a Gamry Reference 600 potentiostat and a VERTEX 80v Brucker Fourier transform infrared spectrometer equipped with a MCT detector (N2-liquid temperature) using a ZnSe prism. Three-electrode glass cell with Pt foil as a counter electrode and either reversible hydrogen, RHE, or Hg/HgO (EHg/HgO = 0.928 V vs RHE) as a reference electrode was used for the measurements. The chamber was continuously purged with N2 in order to avoid any traces of CO2 from air which might affect the analysis. The spectra were collected in a double-sided acquisition mode between wavenumbers from 4000 to 700 cm -1 with a resolution of 4 cm -1 . In order to obtain a single-beam spectrum, 256 interferograms were co-added and then Fourier transformed. For every single measurement a background spectrum was obtained at the open-circuit potential (EOC varying from -0.29 to -0.23 V vs RHEin the presence of NaBH4) right before the start of the acquisition at a sample potential. In what follows all spectra are presented after subtraction of this background. In case of the spectra acquisition at the OCP as a function of time, the first spectrum was used as a background and subtracted from all the subsequent ones. Owing to this subtraction, negative-pointing peaks in the difference FTIR spectra indicate accumulation of the corresponding species in the thin layer trapped between the WE and the prism, while positive-pointing peaks reveal impoverishment of the thin layer in the respective species.

After immersion in the electrochemical cell and before the measurement of FTIR spectra, the Nipoly electrode (in a meniscus configuration) was conditioned in a N2-saturated 0.1 M NaOH or 0.1 M NaOD solution (prepared from 50% NaOH solution in H2O, premium quality, Aldrich; 40% NaOD solution D2O, 99.5% Alfa Aesar) by cycling between, first, -0.20 and 0.40 V, second, -0.06 and -0.40 V and, finally, -0.20 and 0.40 V vs RHE at a sweep rate (v) of 20 mV s -1 . The potential interval between -0.1 and 1.5 V vs RHE was used for conditioning the Au electrode. Then 2 M NaBH4/NaBD4 (dissolved in 0.1 M NaOH/NaOD) was added to the cell in order to achieve final concentration of 0.2 M NaBH4/NaBD4. A typical protocol of electrochemical measurements during an operando FTIR measurements consisted in 1) recording 3 scans between -0.20 and 0.30 V vs RHE, 2) applying potential equal to Eoc at which the Ni (Au) disk was pressed to the surface of the prism and a background spectrum was collected, 3) applying potential of interest (Ei = -0.25 -0.4 V vs RHE for Ni and Ei = -0.2 -1.5 V vs RHE for Au) at which a series of FTIR spectra (typically 11) was collected in order to see the dynamics of their evolution with time.

Reference solutions were prepared from NaBH4 (NaBD4), NH3BH3, H3BO3, NaBO2, B2O3 and Na2B4O7 (all of the highest quality available and purchased either from Aldrich (NaBH4 and NH3BH3) or Alfa Aesar) in 0.1 M NaOH (NaOD) or pure H2O (D2O, 99.8%, Alfa Aesar). Spectra of the reference compounds were acquired in FTIR-ATR configuration with a hemispherical ZnSe prism.

DEMS Measurements. DEMS measurements were performed in order to measure the amount of hydrogen generated at a metallic Ni electrode during the BOR. A specifically designed 3-electrode electrochemical cell, inspired by Refs. [START_REF] De Souza | The use of mass spectrometry in electrochemical measurements -The DEMS technique[END_REF][START_REF] De Souza | Electro-oxidation of ethanol on Pt, Rh, and PtRh electrodes. A study using DEMS and in-situ FTIR techniques[END_REF][START_REF] Bergamaski | Nanoparticle size effects on methanol electrochemical oxidation on carbon supported platinum catalysts[END_REF], was used where the WE was placed at the bottom of the cell against PTFE membranes in order to ensure the smallest delay between the production and detection of the gaseous species. A freshly prepared RHE and a glassy carbon plate were used respectively as a reference and a counter electrode. In order to have high surface area of metallic Ni, and thus ensure significant gas generation and high sensitivity of detection, the Ni disk was replaced by a Ni felt freshly etched in a mixture of strong acids (see Refs [START_REF] Braesch | Nickel 3D Structures Enhanced by Electrodeposition of Nickel Nanoparticles as High Performance Anodes for Direct Borohydride Fuel Cells[END_REF][START_REF] Grdeń | Surface science and electrochemical analysis of nickel foams[END_REF] for the etching procedure). The electrical contact was made by using a Ni ring (previously electrochemically oxidized to limit its BOR contribution) pressed against the felt and connected to a Ni wire (similarly oxidized). This wire was placed in a glass tube purged with Ar in order to minimize contact of the wire with the electrolyte. The WE being placed at the bottom of the cell, controlling mass-transport to its surface is not trivial. To partially solve this issue, the end of the glass tube was placed as close to the WE as possible. In this manner, the Ar bubbles could create some convection in the vicinity of the WE. Unfortunately, the mass-transport could not be precisely controlled and the measurements were not performed in standard "Levich conditions". The DEMS cell was cleaned and prepared similarly as the ones presented above.

Because the BOR at low potentials occurs in competition with the HER, the H2 generation at the Ni electrode could arise from either of the two reactions. In order to separate these two contributions and provide unambiguous information regarding the hydrogen source required for the understanding of the BOR mechanism, the sodium borohydride was replaced by sodium borodeuteride (NaBD4, 99% (isotopic), Alfa Aesar) and was dissolved in 1 M NaOH. In such a configuration, ionic currents corresponding to the three different masses could be detected by the mass spectrometer: Im/z=2 (corresponding to H2 originating from the HER), Im/z=4 (corresponding to D2 originating from the BOR), and Im/z=3 (corresponding to HD, originating from recombination of Had and Dad). In order to estimate the number of electrons valorized during the BOR, the cell must be calibrated. To do so a cell constant was determined from the m/z = 2 current measured while collecting cyclic voltammograms (CVs) in a supporting electrolyte. Fig. S1 shows the values of If and Im/z=2 as well as the cell constant K and the resulting equivalent faradaic current, IH2,eq, obtained by correcting the ionic current by the constant. Because this calibration procedure depends of the area of the Ni electrode, it was performed for each WE. Once the ionic currents are calibrated into the equivalent current, the number of electrons valorized during the BOR can be estimated (Eq4):

𝑛 = 8 𝐼 f 1 2 𝐼 HD + 𝐼 D 2 + 𝐼 f (Eq4) 𝑛 -number of electrons per BD4 -species If = Faradic current (mA) IHD = Calibrated ionic current of HD (mA) ID2 = Calibrated ionic current of D2 (mA)
DFT Calculations. All calculations were performed using the ab initio total energy and moleculardynamics Vienna ab initio simulation program (VASP) developed at the Institute for Material Physics at the University of Vienna [START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF][START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF]. The electronic structure was represented using the projector augmented wave method [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF][START_REF] Holzwarth | Comparison of the projector augmented-wave, pseudopotential, and linearized augmented-plane-wave formalisms for density-functional calculations of solids[END_REF], a plane wave basis set with a cut off energy of 450 eV, and the Perdew-Wang form of the generalized gradient approximation [START_REF] Perdew | Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation[END_REF]. A 5 x 5 x 1 Monkhorst-Pack k-point mesh was used for sampling the Brillouin zone and performing unrestricted (spin polarized) calculations. Harmonic vibrational modes were calculated and used for zero-point vibrational energy (ZPVE) corrections to the adsorbate energies. Transition states searches were performed using the climbing image nudged elastic band method (CI-NEB). A (111) surface was used to represent the nickel surface. The Ni(111) surface was modeled with a 4 layer slab with the two bottom layers constrained to nickel fcc lattice positions and the two top layers allowed to relax. A 3 x 3 surface cell was used. A surface coverage of 1 adsorbate molecule per 9 surface atoms was used to calculate the energetics on the reaction intermediates, unless otherwise specified. A vacuum region of 15 Å was inserted between the periodic surface slabs. Binding energies and reaction energies were calculated using the same approach as our prior work examining borohyride electrooxidation on other late transition metal surfaces [START_REF] Rostamikia | First principles mechanistic study of borohydride oxidation over the Pt(111) surface[END_REF].

Results and discussion

Electrochemistry

Fig. 1 shows CVs of a polished Nipoly rod in NaOH solutions in the absence and in the presence of NaBH4. The shape of the CV in the 0.1 M NaOH supporting electrolyte (Fig. 1a) confirms that the surface of the electrode is essentially metallic. Indeed, it has been demonstrated [START_REF] Oshchepkov | On the Influence of the Extent of Oxidation on the Kinetics of the Hydrogen Electrode Reactions on Polycrystalline Nickel[END_REF][START_REF] Oshchepkov | Exploring the Influence of the Nickel Oxide Species on the Kinetics of Hydrogen Electrode Reactions in Alkaline Media[END_REF] that presence of surface (hydr)oxides significantly modifies the shape of the CV of a Ni electrode (i.e. an additional anodic peak appears at E < 0.15 V vs RHE), the latter could thus serve as a fingerprint of the surface state. The fact that the electrode is in its metallic state, is critically important, as it ensures the high BOR activity. One may notice that the OCP of the Nipoly in 5 mM NaBH4 (Fig 1b) is equal to E = -0.257 V vs RHE, at higher NaBH4 concentrations lying between -0.25 < E < -0.28 V vs RHE (Fig. S2). These values are very similar to those observed for Ni nanoparticles electrodeposited on carbon, NiED/C (E = -0.235 V vs RHE in 5 mM NaBH4 + 1 M NaOH, see curve 3 in Fig. 1b replotted from our previous publication [START_REF] Oshchepkov | Nickel Metal Nanoparticles as Anode Electrocatalysts for Highly Efficient Direct Borohydride Fuel Cells[END_REF]). The OCP value of the Nipoly is significantly lower than that of either polycrystalline Pt (E ≈ 0 V vs RHE [START_REF] Olu | Influence of the concentration of borohydride towards hydrogen production and escape for borohydride oxidation reaction on Pt and Au electrodesexperimental modelling insights[END_REF]) or partially oxidized Ni (E = -0.152 V vs RHE [START_REF] Oshchepkov | Nickel Metal Nanoparticles as Anode Electrocatalysts for Highly Efficient Direct Borohydride Fuel Cells[END_REF]), which goes along with the higher HER activity of the latter [START_REF] Oshchepkov | Nanostructured nickel nanoparticles supported on vulcan carbon as a highly active catalyst for the hydrogen oxidation reaction in alkaline media[END_REF].

One might notice however different shapes of CVs for Nipoly and NiED/C in the presence of NaBH4. While for NiED/C, the faradaic current reached the mass-transport-limited value already at ca. E = -0.1 V vs RHE (for 5 mM NaBH4), no mass-transport-limited current was achieved for the Nipoly electrode. This difference may be explained by a lower number of the available surface sites on the Nipoly rod compared to that of the NiED/C electrode. The calculation of the electrochemically active surface area, ECSA, of Ni by integrating anodic peaks in CVs obtained in NaOH solution (Fig. 1a) and using 0.514 mC cm -2 conversion coefficient [START_REF] Machado | The hydrogen evolution reaction on nickel surfaces stabilized by H-absorption[END_REF] gives values of 0.26 ± 0.01 and 14 ± 1 cm 2 for Nipoly rod and the NiED/C electrode, respectively. This significantly smaller ECSA of the Nipoly electrode results in its higher surface coverage with the surface intermediates, in other words, higher surface 'poisoning'. Indeed, even if the surface 'poisoning' effect on Ni electrodes is much less pronounced than that on the Pt ones [START_REF] Olu | Influence of the concentration of borohydride towards hydrogen production and escape for borohydride oxidation reaction on Pt and Au electrodesexperimental modelling insights[END_REF][START_REF] Braesch | Borohydride oxidation reaction mechanisms and poisoning effects on Au, Pt and Pd bulk electrodes: From model (low) to direct borohydride fuel cell operating (high) concentrations[END_REF], it cannot be fully discarded. This surface poisoning manifests itself in the positive shift of the BOR currents with the BH4 -concentration seen in Fig. 1c as well as in the increase of the OCP value at high BH4 -concentration (Fig. S2).

Other conditions being equal, the extent of 'poisoning' is determined by the ratio between the concentration of BH4 -and the number of the adsorption sites on the electrode surface, and this applies both to Pt [START_REF] Olu | Insights into the potential dependence of the borohydride electrooxidation reaction mechanism on platinum nanoparticles supported on ordered carbon nanomaterials[END_REF] and to Ni [START_REF] Braesch | Nickel 3D Structures Enhanced by Electrodeposition of Nickel Nanoparticles as High Performance Anodes for Direct Borohydride Fuel Cells[END_REF] electrodes.

Fig. 1 here

Along with the number of the active sites and the BH4 -concentration, the anodic potential limit is a factor that strongly affects the BOR. CVs represented in panel (d) of Fig. 1 demonstrate that increasing the electrode potential beyond ca. 0.2 / 0.3 V vs RHE (depending on the BH4 - concentration) results in a current decrease down to a very low value. Comparison of CVs in the presence and in the absence of BH4 -indicates that this current decay at positive potentials is due to the surface α-Ni(OH)2 formation, the latter being inactive towards the BOR. Potential reversal from 0.4 V down to ca. 0.1 / 0.2 V vs RHE (depending on the BH4 -concentration) results in regeneration of the BOR currents, due to the electrochemical reduction of the electrode surface (cf.

Fig 1a).

It should be noted that further increase of the anodic potential limit leads to an irreversible loss of a significant part of the BOR activity [START_REF] Oshchepkov | Nickel Metal Nanoparticles as Anode Electrocatalysts for Highly Efficient Direct Borohydride Fuel Cells[END_REF], which can be explained by the resistance of the formed -Ni(OH)2/NiO/NiOOH towards electrochemical reduction at room temperature unless very high cathodic polarization is applied [START_REF] Ferreira | On the Electrochemical Reduction of β-Ni(OH)2 to Metallic Nickel[END_REF][START_REF] Hall | Nickel hydroxides and related materials: a review of their structures, synthesis and properties[END_REF].

Thus, electrochemical measurements confirm that BOR is catalyzed by Ni in the interval of low potentials (-0.25 < E < 0.4 V vs RHE), while on Pt anodic BOR currents can only be observed at E > 0 V vs RHE, because of the high activity of the latter in the HER.

FTIRS

Fig. 2 shows the temporal evolution of the FTIR spectra of a Nipoly disc in a 0.2 M NaBH4 + 0.1 M NaOH solution at two electrode potentials: EOC = -0.23 V vs RHE and E = 0.2 V vs RHE.

Because of the subtraction of the background spectrum, positive-pointing absorption peaks correspond to the species whose concentration decreases with time, while negative-pointing peaks correspond to those whose concentration increases with time. Consumption of BH4 -can be clearly observed already at the OCP (EOC = -0.23 V vs RHE) from the growth of the intensity of the stretching ( (B-H)) and bending ( (B-H)) modes of the B-H bond at 2260 and at 1100 cm -1 , respectively (cf. positive-pointing peaks in Fig. 2a). This is accompanied by the emergence of two negative-pointing absorption peaks, at 1080 cm -1 and at 960 cm -1 . At higher potential above 0 V vs RHE (as an example Fig. 2b shows data for E = 0.2 V vs RHE), the FTIR spectra change drastically: instead of the 1080 cm -1 and 960 cm -1 absorption bands, one may observe appearance of the bands at 1415, 1320, 1150 and 1030 cm -1 . Potential reversal to the OCP results in the resurgence of the absorption bands at 1150 and 960 cm -1 . The influence of the electrode potential on the in situ FTIR spectra can be clearly observed from Fig. 3a.

Fig. 2 here

Infra-red spectroscopy has been widely applied in the past for studies of boron compounds and their complex equilibria in aqueous solutions. Electrochemical BOR has been investigated with in situ FTIRS (in the external reflection configuration) on Pt [START_REF] Lima | Borohydride electrooxidation on Au and Pt electrodes[END_REF], Au [START_REF] Concha | In situ infrared (FTIR) study of the mechanism of the borohydride oxidation reaction[END_REF][START_REF] Concha | In situ infrared (FTIR) study of the borohydride oxidation reaction[END_REF], Cu-Ag [START_REF] Duan | Anodic behavior of carbon supported Cu@Ag core-shell nanocatalysts in direct borohydride fuel cells[END_REF][START_REF] Duan | Kinetics of sodium borohydride direct oxidation on carbon supported Cu-Ag bimetallic nanocatalysts[END_REF], Pd [START_REF] Grimmer | The electrooxidation of borohydride: A mechanistic study on palladium (Pd/C) applying RRDE, 11B-NMR and FTIR[END_REF] and Ni [START_REF] Romanova | Electrochemical Oxidation of Borohydride-Ion on Nickel Electrode: a Study by the Method of IR-Spectroscopy[END_REF], whereby some of the absorption bands observed in this work have also been documented. It should be noted however that the assignment of the absorption peaks is not unambiguous. This is due to the presence of numerous absorption bands with similar frequencies, which might correspond to vibrations of different bonds (B-H, B-O(H), B-O-B). Note also that borates in aqueous solutions are subject to complex acid-base and polymerization equilibria, resulting in pH and concentration dependence of the vibrational spectra. To help the assignment, in situ FTIRS measurements have been performed with NaBD4 in NaOD + D2O and NaOH + H2O. Furthermore, FTIR spectra were acquired for a series of H and D-substituted reference compounds. The spectra of reference compounds are shown in Fig. 4, while the assignment of the observed vibrations is provided in Table 1.

Fig. 3 here

Table 1 here

One may see that in situ FTIR spectra of the BOR on metallic Ni acquired at E < 0 V vs RHE closely resemble the reference spectrum of NaBO2 in NaOH, with its two broad absorption features at 1150 and 935 cm -1 . According to the literature data [START_REF] Peak | ATR-FTIR spectroscopic studies of boric acid adsorption on hydrous ferric oxide[END_REF], the observed spectral features are indicative of the presence of tetrahedral B(OH)4 -ions with 1150 and 935 cm -1 peaks corresponding to the asymmetric stretching of the B-OH and to the B-O-H bending. The 1150 cm -1 peak is very broad, which may be attributed to the formation of polyborates due to the tendency of metaborate to polymerize in aqueous solutions at concentrations above 50 mM [START_REF] Zhu | Structure of aqueous potassium metaborate solution[END_REF][START_REF] Li | Thermodynamic and Dynamic Modeling of the Boron Species in Aqueous Potassium Borate Solution[END_REF]. In NaOD + D2O, both peaks shift to lower frequencies (1030 and 835 cm -1 ). The red-shift of the two peaks upon H/D substitution suggests that the B-OH stretching not only involves elongation/contraction of the B-O bond but also displacement of H(D). Formation of B(OH)4 -(the final product of the BOR) at the Ni electrode already at EOC = -0.23 V vs RHE is remarkable, confirming the exceptional activity of metallic Ni for this reaction [START_REF] Oshchepkov | Nickel Metal Nanoparticles as Anode Electrocatalysts for Highly Efficient Direct Borohydride Fuel Cells[END_REF]. It is worth mentioning that the 1150 and 935 cm -1 vibrations have been observed in previous studies of the BOR on Pd, Pt and Au electrodes, but attributed to various reaction intermediates rather than to the BOR product.

Fig. 3 shows that increasing the electrode potential results in a gradual disappearance of the spectral features of tetrahedral B(OH)4 -. Instead, peaks at 1415 and 1155 cm -1 , characteristic of the C3v symmetry of B(OH)3, emerge, as confirmed by the reference spectra of H3BO3 and B2O3 solutions (Fig. 4). H/D substitution results in their red-shift to 1380 and 890 cm -1 , confirming that the former corresponds to the B-OH stretching, while the latter to the B-O-H bending vibration. Formation of B(OH)3 rather than B(OH)4 -at E > 0 V vs RHE can be attributed to the acid-base equilibrium (Eq5) established in the thin layer trapped between the surface of the Ni electrode and the ZnSe prism.

(B(OH)3 + 2H2O ⇌ [B(OH)4] -+ [H3O] + ; pKa = 8.9 -9.2 [START_REF] Lopalco | Boric Acid, a Lewis Acid With Unique and Unusual Properties: Formulation Implications[END_REF] (Eq5)

To verify this, spectra of boric acid in water (pH ≈ 5.5) and in NaOH of varied concentrations were acquired. Fig. 4d shows that, as the concentration of NaOH increases, peaks at 1415 and 1155 cm - 1 corresponding to the C3v symmetry of B(OH)3 gradually disappear, while peaks corresponding to tetrahedral symmetry of B(OH)4 -emerge. In 0.1 M NaOH one may also observe vibrational peak at 1320 cm -1 , which however disappears at higher NaOH concentrations. This behavior allows to attribute the latter peak to B-O-B vibrations in polymeric BxOyHz species. Indeed, it is known that the extent of polymerization of borates strongly depends on the pH. At high pH, solutions are dominated by B(OH)4 -species, at low pH by B(OH)3, while the concentration of di-, tri-, and tetramers is the highest at intermediate pH values (between 7 and 12) [START_REF] Graff | Complexation of Nickel Ions by Boric Acid or (Poly)borates[END_REF]. The peak at 1320 cm -1 was also detected during in situ FTIRS measurements at E > 0 V vs RHE both in NaOH + H2O and NaOD + D2O. The fact that H/D substitution does not lead to a red-shift of the 1320 cm -1 peak is in agreement with its assignment to the B-O-B bond vibrations. Thus, FTIRS data evidence formation of the B(OH)4 -on Ni starting from the OCP and its transformation into B(OH)3 and polyborates following changes in the interfacial pH when the conversion rate of BH4 -to its final product (that consumes OH -) increases. Note that at the OCP the interfacial pH does not change even at long reaction times (cf. Fig 2a ), since the OH -consumption of the anodic BOR (Eq.1/1*) is counterbalanced by the OH -formation of the cathodic HER (Eq.2). However, at potential values positive of the OCP the anodic current dominates, the OH -consumption of the anodic BOR resulting in an interfacial pH decrease. Such a behavior is accentuated by the high (equal to 2 in this work) NaBH4 to NaOH concentration ratio (dictated by the instability of the ZnSe prism at high NaOH concentration and by insufficient infra-red signal-to-noise ratio at low NaBH4 concentration), but may occur even in more concentrated NaOH, especially at longer reaction times.

The in situ FTIR spectra of this work do not provide any evidence regarding the formation of soluble BOR intermediates, such as BH3OH -suggested during the BOR on Pt and Au [START_REF] Pasqualeti | Borohydride electrooxidation on carbon-supported noble metal nanoparticles: Insights into hydrogen and hydroxyborane formation[END_REF]. The fact that dissolved intermediates are not observed indicates that they either do not desorb or rapidly readsorb and react on the electrode surface. It must also be noted that, according to the rotatingring disc studies of the BOR on Pt and Au [START_REF] Pasqualeti | Borohydride electrooxidation on carbon-supported noble metal nanoparticles: Insights into hydrogen and hydroxyborane formation[END_REF] the amount of BH3OH -species escaping the working electrode is small and thus might not be detectable by the FTIRS. Indeed, spectra acquired under similar conditions during the BOR on an Au disk electrode did not show any straightforward sign of the BH3OH -species either (Fig. S3).

Fig. 4 here

To provide complementary information regarding the vibrational signature of BH3OH -as well as the reactivity of Ni towards the latter, ammonia-borane (NH3BH3) oxidation was studied on the Ni disk using in situ FTIRS (Fig. 3d). It is known that NH3BH3 in water is subject to homogeneous hydrolysis which is believed to result in the formation of BH3OH -and NH4 + [START_REF] Molina Concha | In situ Fourier transform infrared spectroscopy and on-line differential electrochemical mass spectrometry study of the NH3BH3 oxidation reaction on gold electrodes[END_REF][START_REF] Nagle | Ammonia borane oxidation at gold microelectrodes in alkaline solutions[END_REF]. The latter are confirmed by the spectra of the NH3BH3 reference acquired in NaOH and NaOD electrolyte (Fig. 4), where the peak at 1175 cm -1 likely corresponds to the B-OH vibration in BH3OH -. The band is observed in the same spectral range as B-OH in B(OH)4 -, but the latter is much broader, which is not surprising considering the tendency of borates to polymerize. Fig. 3d indicates that NH3BH3 oxidation on Ni starts at even lower potentials than the BOR (EOC = -0.29 V vs RHE). In addition to the appearance of B-OH and B-O-B vibrations characteristic of the formation of B(OH)4 -, B(OH)3 and polyborates, as discussed above for the BOR on Ni, one may notice a negative pointing peak around 1175 cm -1 , which suggests disappearance of BH3OH -and its transformation in B(OH)4 -and B(OH)3 during the ammonia-borane oxidation.

If the accumulation of the BH3OH -intermediate during the BOR occurred in significant quantities, then its formation could also be detected thanks to B-H vibrations, which are quite different in BH4 -and BH3OH -species (Fig. 4). However, analysis of the FTIR spectra during the BOR does not show any sign of the BH3OH -formation either in the B-OH or B-H vibrational interval. It is the high activity of Ni towards BH3OH -oxidation which is likely to explain why this species could not be observed during the BOR on Ni. Thus, even if one cannot rule out formation of the BH3OH - intermediate during the BOR on Ni, its escape from the surface into the electrolyte is expected to be minor due to its fast oxidation on the Ni surface.

Finally, it is instructive to compare FTIR spectra during the NaBH4 and NaBD4 oxidation, when both are performed in NaOH + H2O (Fig. 3a and3c). Remarkable similarity of this set of spectra and absence of peaks corresponding to vibrations of either H-O-D or D-O-D suggest that neither D2O nor HOD is formed during the NaBD4 oxidation on Ni (cf. Eq1*), which is consistent with the low activity of metallic Ni in the HOR. We will come back to this issue in the next section, when discussing the differential electrochemical mass spectrometry (DEMS) data.

DEMS

DEMS measurements have been performed in order to detect eventual formation of hydrogen during the borohydride oxidation on Ni. NaBD4 was used instead of NaBH4 to differentiate between hydrogen formation from borohydride and water (especially for E < 0 V vs RHE). Fig. 5 shows faradaic and MS ionic currents (recalculated into the faradaic current using calibration procedure described in Section 2) during the BOR (only anodic sweeps are shown, for full cycles the reader should refer to Fig. S4) on an etched Ni felt acquired in a linear potential sweep and corresponding to the formation of H2, HD and D2. The noise visible in the MS currents results from bubbles blocked in the pores of the Ni felt electrode and released randomly. The OCP value observed in the DEMS cell was somewhat higher than in the electrochemical cell (cf. Fig. 1), especially at low NaBH4 concentration, which may be attributed to the presence of some (hydr)oxides on the surface of the Ni felt (since some oxidized patches might persist on the surface after the etching procedure).

Let us start the discussion with the analysis of the data in 50 mM NaBD4 (Figs. 5b,c,d). One may see that at E > 0 V vs RHE, the D2 evolution current closely matches the faradaic one, suggesting that the BOR on Ni occurs in an overall 4e -process. The other 4e -are released in the form of two D2 molecules per BD4 -species and thus are not valorized (Eq6):

BD4 -+ 4 OH - B(OH)4 -+ 2 D2 + 4 e - (Eq6)
This conclusion agrees with the FTIRS measurements (lack of vibrations characteristic of either D2O or HOD during the 0.2 M NaBD4 oxidation in 0.1 NaOH in H2O). The amount of HD detected at E > 0 V vs RHE in 50 mM NaBD4 is small confirming the above conclusion. At potentials below E = 0 V vs RHE, noticeable H2 evolution currents are detected, which correspond to the HER, the latter on Ni occurring through a Volmer (Eq7)-Heyrovsky (Eq8) mechanism [START_REF] Oshchepkov | On the Influence of the Extent of Oxidation on the Kinetics of the Hydrogen Electrode Reactions on Polycrystalline Nickel[END_REF][START_REF] Oshchepkov | Exploring the Influence of the Nickel Oxide Species on the Kinetics of Hydrogen Electrode Reactions in Alkaline Media[END_REF][START_REF] Oshchepkov | On the effect of temperature and surface oxidation on the kinetics of hydrogen electrode reactions on nickel in alkaline media[END_REF].

H2O + e -= Had + OH - (Eq7, Volmer step)

Had +H2O+ e -=H2 + OH - (Eq8, Heyrovsky step)

While Had formation via the Volmer step (Eq 7) occurs at potentials below E = 0 V vs RHE, it is likely to persist on the surface even at E > 0 V vs RHE due to its strong adsorption on metallic Ni [START_REF] Oshchepkov | Exploring the Influence of the Nickel Oxide Species on the Kinetics of Hydrogen Electrode Reactions in Alkaline Media[END_REF][START_REF] Santos | Hydrogen electrocatalysis on single crystals and on nanostructured electrodes[END_REF]. In the meantime, chemical recombination of hydrogen atoms (Tafel step, Eq9) is slow due to the strong adsorption of Had on the surface of metallic Ni.

Had + Had (Dad) = H2 (HD) (Eq9, Tafel step)

While at E > 0 V vs RHE and high BD4 -concentration (50 mM) the HD formation currents are significantly inferior of those corresponding to the D2 formation, this is not the case at E < 0 V vs RHE and low (5 mM) BD4 -concentration (Fig. 5a), whereby ID2 and IHD become comparable. Formation of HD during the BOR points to the likely B-D (B-H) bond dissociation on the Ni surface with formation of a Dad intermediate in this potential range. It should however be noted that Dad could also originate from D2 (released during the BD4 -oxidation) re-adsorption on Ni. As mentioned above, this HDad formation could only be observed either at low electrode potentials or low BD4 -concentration, suggesting that dissociation of BD4,ad on the surface of Ni is potentialactivated.

Fig. 5 here

Finally, the number of electrons n produced during the BOR was estimated (Eq4, see Experimental Section) using the DEMS data and plotted in Fig. 6. The estimation was made with and without consideration of the HD contribution to follow its impact. At high BD4 -concentration n is comprised between 4 and 5. Including the HD contribution in the calculation decreases the number of electrons by almost 1 at low potentials but has minor influence at E > 0.1 V vs RHE, as expected from the discussion above. It is interesting to note that, at low BD4 -concentration, n noticeably increases at E > 0.1 V vs RHE, that is in the potential interval where OH adsorption and Ni(OH)2 formation occur on the Ni surface. This may be attributed to the (i) potential-dependent rate of the Volmer step and (ii) its acceleration in the presence of (hydr)oxides on the Ni surface [START_REF] Oshchepkov | On the Influence of the Extent of Oxidation on the Kinetics of the Hydrogen Electrode Reactions on Polycrystalline Nickel[END_REF][START_REF] Oshchepkov | On the effect of temperature and surface oxidation on the kinetics of hydrogen electrode reactions on nickel in alkaline media[END_REF], both helping to better valorize D2 escaping during BD4 -oxidation. shows that all elementary oxidation steps are unfavorable. Based on the oxidation equilibrium potential (E = -0.41 V vs RHE), the overall oxidation of aqeuous borohydride to the final aqueous oxidation product would be uphill in energy 0.72 eV at E = -0.5 V vs RHE. The surface reaction is uphill by 2.19 eV at this potential, due to both favorable initial oxidative adsorption of borohydride and favorable desorption of the final B(OH)3 -product. This suggests an overpotential of ~0.3 V would be necessary to make the surface catalytic reaction favorable on Ni(111), in good agreement with the experimentally observed OCP.

Fig. 7 here

At E = 0 V vs RHE, all reaction intermediates are less stable than the final state B(OH)3 * adsorbate, and all oxidation steps are favorable or only slightly unfavorable. Presuming activation barriers correlate reasonably well with reaction energies, a significant oxidation current would be expected at E = 0 V vs RHE based on the DFT reaction energetics in good agreement with the experimental data. The preferred reaction path follows initial B-H dissociation from BH4*, followed by BH3-OH bond formation, successive B-H dissociation to BOH*, then final B-OH formations to the final product. Oxidation of BH3 * to BH2 * and BH3OH * is slightly endothermic (0.17 eV and 0.06 eV, respectively). Also, BOH* oxidation is slightly endothermic (0.17 eV) at 0 V vs RHE. At E = 0.5 V vs RHE, all reaction steps are downhill from BH4 * to the final surface product of B(OH)3 * suggesting fast surface kinetics were the Ni surface to remain stable in metallic form at this high oxidation potential (but in practice Ni is covered by OHad/-Ni(OH)2 above ca. E = 0.2 -0.25 V vs RHE, cf. Fig. 1a)

Table 2. here

Table 2 compares the desorption energies of closed-shell reaction intermediates with their surface oxidation elementary reaction energies at E = 0 V vs RHE. BH3, BH2OH and BH(OH)2 are stable gas phase species that could possibly desorb from the surface as partial oxidation intermediates. Desorption of all these species is significantly more exothermic than oxidation reaction energies, suggesting further oxidation would be preferential and partial oxidation intermediates would not be observed in the fluid phase. BH3* and BH2OH* bind strongly to the Ni(111) surface and are highly unlikely to desorb. BH(OH)2 binding is relatively strong and the desorption reaction is endothermic, though desorption and oxidation would be competitive closer to the borohydride oxidation equilibrium potential. The preference for complete oxidation of B-containing intermediates agrees with the lack of FTIR observation of partial oxidation products. Though the reaction energy diagrams in Fig. 7 treat BH4* oxidation as directly producing a proton and electron pair, the hydridic nature of the B-bound hydrogen suggests B-H dissociation would occur, first, through a chemical step to produce H* that could then subsequently oxidatively desorb (Volmer step, Eq7), or recombine with another H* to form H2 (Tafel step, Eq9). The activation barrier for this initial B-H dissociation is 0.18 eV (18.5 kJ mol -1 ), suggesting that the nickel can effectively break B-H bonds, and a high surface coverage of H* would be expected in the presence of borohydride solution at low potentials.

The competition between H* oxidative desorption (Volmer step) and hydrogen evolution (Tafel step) would be potential dependent, as evolution is a chemical process whereas oxidation is an elementary electrochemical step. Fig. 9 illustrates the effect of surface coverage on the energetics of hydrogen evolution and oxidation at Ni(111) surface. At 1/9 monolayer of hydrogen, the hydrogen evolution is unfavorable by 0.34 eV. H* oxidation is endothermic at potentials below at E = 0.34 V vs RHE. Such a low coverage of H* would not motivate oxidation or hydrogen evolution over most of the potential range of interest. The adsorption of H* is only slightly coverage dependent up to 1 ML, however, there is a step change in H* stability above 1 ML. Fig 9b shows that at 10/9 monolayer of hydrogen, the evolution reaction is exothermic (reaction energy equals -0.67 eV). Alternatively, the oxidation reaction is exothermic over the entire potential range of interest, and there will be a kinetic competition between H* oxidation and evolution. Above 0 V vs RHE, oxidation of H* becomes more favorable than the evolution reaction. Competition between the oxidation and evolution reactions dictates the Coulombic efficiency of borohydride oxidation. Note however that the above discussion is based on reaction energies (thermodynamic), not activation barriers (kinetics). Previous studies of the hydrogen electrode kinetics on Ni [START_REF] Oshchepkov | On the Influence of the Extent of Oxidation on the Kinetics of the Hydrogen Electrode Reactions on Polycrystalline Nickel[END_REF][START_REF] Oshchepkov | Nanostructured nickel nanoparticles supported on vulcan carbon as a highly active catalyst for the hydrogen oxidation reaction in alkaline media[END_REF][START_REF] Oshchepkov | Exploring the Influence of the Nickel Oxide Species on the Kinetics of Hydrogen Electrode Reactions in Alkaline Media[END_REF][START_REF] Oshchepkov | On the effect of temperature and surface oxidation on the kinetics of hydrogen electrode reactions on nickel in alkaline media[END_REF] suggest that the hydrogen oxidation on Ni follows a Heyrovsky-Volmer mechanism, with the Volmer step being rate-determining. A small contribution of the Tafel step cannot be excluded close to E = 0 V vs RHE, but as soon as the potential is increased, the Heyrovsky-Volmer mechanism is dominating. Hence, studies of the hydrogen electrode kinetics on Ni also support faster Volmer compared to the Tafel step above E = 0 V vs RHE.

Though the reaction energies presented in Fig. 9 would suggest H* oxidation will outcompete evolution as the potential is increased, we observe either no (cf. Fig. 6b) or weak (cf. Fig. 6a) increase in the oxidation efficiency at higher potentials experimentally. One of the possible explanations could be the influence of Had, BH4,ad and/or other B-containing adsorbates on the borohydride (and on the hydrogen) oxidation kinetics. We leave this dilemma as a topic for future study.

Fig. 9 here

If the fed reactant is BD4 -, the relative coverage of D* (from B-D dissociation) and H* (from the Volmer reaction) will be dictated by both potential and BD4 -concentration. We considered direct H2 (D2) evolution from BH4* (i.e., direct formation of H2 rather than formation of surface H*), and found an activation barrier of 1 eV (Fig. S5). This high barrier relative to B-H dissociation suggests the relative ratio of HD and D2 evolved is dictated by the relative coverage of H* and D*, and is in agreement with the experimental observation that higher BD4 -concentrations (which would produce higher D* coverages) decrease the fraction of HD formed. Finally, it should be emphasized that the kinetics of the B-H dissociation might be influenced by the potential, the interfacial electric field, and the orientation of the surrounding water and OH - [START_REF] Zhou | Dihydrogen Bonds in Aqueous NaBD4 Solution by Neutron and X-ray Diffraction[END_REF], the latter not considered within our DFT calculations.

Conclusions

Metallic Ni is highly active towards the BOR at low potentials (around or below 0 V vs RHE). However, BOR on Ni produces 4 instead of 8 e -in theory and is accompanied by H2 (D2 in case of BD4 -) formation, namely 2 D2 molecules per BD4 -species, as evidenced by the online DEMS.

Along with the electrode potential, the BOR kinetics is strongly affected by the ratio of BH4 - concentration and the number of sites available on the Ni electrode surface. While increase of the BH4 -concentration results in the surface poisoning by the reaction intermediates, this effect is much less pronounced on Ni compared to either Pt or Pd electrodes. Operando FTIRS provides evidence for the formation of the final BOR product, B(OH)4 -, at potentials as low as -0.23 V vs RHE, but no sign of soluble BOR intermediates in the whole potential interval studied (from -0.23 to 0.4 V vs RHE). The lack of FTIRS observation of partial oxidation products is corroborated by DFT calculations, the latter suggesting preference for complete oxidation of B-containing intermediates. In addition, the results of this work provide a warning regarding the interfacial pH change, which may occur in a thin layer upon infra-red spectroelectrochemical measurements in the external reflection configuration. In this work, such an interfacial pH change leads to a shift of the acid-based and polymerization equilibria resulting in the conversion of B(OH)4 -into B(OH)3 and polyborates.

According to the DFT calculations, BH4 adsorbs molecularly on Ni ). Ionic currents acquired in 50 mM NaBD4 were smoothed after the measurements using a 50% percentile filter method with a 10-points window.

Fig. 6 here 2 Fig. 7

 27 Fig.6 here

Fig. 8 hereFig. 8

 88 Fig. 8 here

FiguresFig. 1 .

 1 Figures

Fig. 2 .

 2 Fig. 2. In situ FTIR spectra of a polycrystalline Ni disk in 0.2 M NaBH4 + 0.1 M NaOH recorded as a function of time at given potential values, (a) E = -0.23 V vs RHE and (b) E = 0.2 V vs RHE.

Fig. 3 .

 3 Fig. 3. In situ FTIR spectra of a polycrystalline Ni disk in (a) 0.2 M NaBH4 + 0.1 M NaOH in H2O, (b) 0.2 M NaBD4 + 0.1 M NaOD in D2O, (c) 0.2 M NaBD4 + 0.1 M NaOH in H2O, (d) 0.2 M BH3NH3 + 0.1 M NaOH at different electrode potentials as specified in the plots.

Fig. 4 .

 4 Fig. 4. Infrared spectra recorded in ATR configuration for different reference solutions: 2 M NaBH4, 2 M NaBD4, 2 M NH3BH3, 2 M NaBO2, 0.2 M H3BO3, sat. B2O3 and saturated Na2B4O7 in either 0.1 M NaOH/NaOD or pure H2O/D2O.

Fig. 5 .

 5 Fig. 5. DEMS measurement of an etched Nifelt in Ar-saturated 1 M NaOH + (a) 5 mM or (b, c, d) 50 mM NaBD4, v = 10 mV s -1 .The ionic (H2, HD, D2) currents are recalculated into the faradic ones using the calibration constant determined independently (K = 2.197 10 10 ). Ionic currents acquired in 50 mM NaBD4 were smoothed after the measurements using a 50% percentile filter method with a 10-points window.

Fig. 6 .

 6 Fig. 6. Estimation of the number of electrons produced during the BOR on Ni in the anodic sweep in Ar-saturated 1 M NaOH + (a) 5mM and (b) 50 mM NaBD4. Calculation made with either the HD and D2 or D2 only contribution using Eq4. Red line denotes maximum number of electrons (8e -) which could be transferred during the BOR.

Fig 7 .

 7 Fig 7. Borohydride oxidation reaction energy diagrams for the Ni(111) surface at a) E = -0.5 V vs RHE, b) E = 0 V vs RHE, and c) E = 0.5 V vs RHE.

Fig. 8 .Fig. 9 .

 89 Fig. 8. DFT optimized a) initial, b) transition, and c) final states for dissociation of BH4* to BH3* and H* on the Ni(111) surface.

Acknowledgments

This work has been performed in the frame of the MobiDiC project, funded by the French National Research Agency (ANR, grant # ANR-16-CE05-0009-01), and RSF Project No. 18-73-00143, funded by the Russian Science Foundation.

Tables

 Table 1.Band frequencies recorded for the references solutions in the ATR-FTIR measurements