Dr Nicolas Besnard

Dr Aurélien Etiemble

Dr Thierry Douillard

Dr Olivier Dubrunfaut

Dr Pierre Tran-Van

Dr Laurent Gautier

Sylvain Franger

Jean-Claude Badot

Dr Eric Maire

Dr Bernard Lestriez
email: bernard.lestriez@cnrs-imn.fr

Jean-Claude Badot

Prof S Franger

Dr J.-C Badot

Multiscale Morphological and Electrical Characterization of Charge Transport Limitations to the Power Performance of Positive Electrode Blends for Lithium-Ion Batteries

Keywords: lithium-ion batteries, composite electrodes: ionic and electronic wirings, 3D geometry, power performance

come

Introduction

Lithium-based batteries (LIB) have higher energy density and cycle life compared to other battery systems. [1] The demand for LIB with higher gravimetric and volumetric energy density is growing to extend the operation hours of mobile information technology (IT) devices, the driving mileages of all-electric vehicles, and due to the rapidly increasing integration of renewable energy into the global energy scheme. [2,3] This way, optimizing cell designs and electrode engineering is now well identified as being a (or even more the) main issue by both industrial and academic bodies. [2,3,4,5,6] Indeed, in commercial batteries, practical electrodes must be made thin to show acceptable power. As a result, 50% of batteries weight and volume are non electroactive materials. Consequently, LIB for Electrical Vehicles (EV) are locked on a trade-off between energy (autonomy) and power (charge rate).

Although industrial-grade active materials such as Graphite, LiFePO4 (LFP) or LiNi1/3Mn1/3Co1/3O2 (NMC) are intrinsically capable of very fast lithium (de)insertion, [7,8,9] several factors limit their rate (power) performance when formulated as thick electrodes. [10,11,12,13,14,15,16] These factors, which affect the rate of lithium and electron supplies to the active mass, also called the ionic and electronic wirings, depend on the architecture (nanoand microstructure) of the electrode through the interfacial areas, materials connectivity, and the transport length scales.

Novel opportunity for progressing in this direction and explore relationships between electrode architecture and electrochemical performance is implementation of X-ray computed tomography (XRCT) [17,18,19,20,21,22,23,24,25,26] and focused ion beam in combination with scanning electron microscopy (FIB-SEM) [27,28,29,30,31] techniques to characterize and quantify the 3D architecture of composite electrodes. XRCT is non-destructive technique that allows probing large volumes covering the entire electrode thickness, which is necessary for reliable analysis. However, one disadvantage of XRCT is the difficulty of distinguishing the carbon additive and the binder mixture from the pore space due to the small particle size and the low X-ray absorbance of the carbon and binder mixture. FIB-SEM is destructive but has the ability to provide 3D imaging at high enough spatial resolution. The combination of XRCT and FIB-SEM is then method of choice for exhaustive multi-scale description of electrode 3D geometry. [32,33] XRCT and FIB-SEM thus enable to extensively analyze a number of geometric parameters (volume fraction, surface area, particle size distribution, tortuosity…), which is of great potential to rationally design and optimize the formulation and the processing of composite electrodes. In particular, tortuosity, which is identified as critical parameter with respect to ionic transport, has been exhaustively studied with respect to its calculation method and the influence of particles shape and orientation, and electrode inhomogenities. [22,24,25,30,34] Comparatively, factors that play on the electrons transport and distribution to the active mass have been much less considered. [35] Moreover and surprisingly, attempts to correlate quantified 3D geometries with measured electrochemical power performance [19] or electrical transport properties [36] of same real electrodes remain rare or modest. In general, reconstructed geometries are used to calculate effective transport properties and make assumptions about the main limitations to rate performance. Intensive work is now undetaken to use reconstructed 3D geometries for smarter electrochemical modelling than the state-ofthe-art modelling based on idealized microstructures, [37,38,39,40] but still with very little or even no confrontation with measured electrochemical performance. Although significantly improved by considering the spatial distribution of the different phases, the efficiency of this approach remains nevertheless controversial as several of the models parameters remain assumed (for example the electrical conductivity of the electrode materials and the charge transfer reaction factors) and the influence of the inter-connectivity between the CB/binder network and the active mass is generally not considered. Moreover very long simulation times are required.

In this work, exhaustive characterizations of 3D geometries of NMC, LFP, and NMC/LFP blended electrodes are undertaken for rational interpretation of their measured electrical properties and electrochemical performance. Blending different active materials is an approach intensively followed by automotive battery suppliers intended to optimize the battery performance with respect to the automotive operating requirements. Motivations are to achieve a more balanced performance compared to what is possible with any individual compound, and to minimize the shortcomings of the parent materials. [ 41] It has been reported that the blending of NMC with LFP may improve the thermal stability and the electrochemical performance in terms of discharge capacity, cycle stability, and rate capability. [42] The pulse power capability of Lithium-and manganese-rich transition metal layered-oxides (LMR-NMCs) at low State-of-Charge (SoC) is also improved by incorporating a modest quantity of LFP. Very few works on blended positive electrodes paid attention, however, to the influence of the electrode engineering on electrochemical behavior. [43,44,45]

Results

Electrode morphology

Due to space limitation the experimental section is given in Supporting Information (SI), which is divided in several sections: materials (SI1), tomography observations (SI2), morphological quantifications (SI3), electrical measurements (SI4), electrochemical measurements (SI5). Table 1 gives the electrodes composition, average porosity and thickness. 3D geometry quantitative analysis was performed from X-ray and FIB/SEM tomography reconstructions following a set of previously developed methods. [22,26,35,46] Additional information about this set of electrodes can be found in previous papers that analyze the homogeneity of the samples [47,48] Here we focus on morphological parameters that have been found the more relevant for interpretation of the electrical properties and the electrochemical performance. FIB-SEM reconstructions of electrodes A (NMC), F (NMC/LFP), H (NMC/LFP) and J (LFP) are shown in Figure 1. Morphological parameters extracted from these analyses are reported in Table 1, and Figure 2 and3.

Connectivity of the different materials and phases

In electrode A (NMC), the packing of the large spherical NMC particles (about 10µm in size) determines micrometric porous interstices (Figure 1a-b). The PVdF binder and carbon black (CB) particles are coagulated together. This mixture forms micrometer thick strands spreading throughout the electrode gluing the NMC particles and partially filling the pores. The intra-connectivity 1 of this CB+PVdF mixture reaches 77%. The inter-connectivity2 between NMC and CB+PVdF represents only 13% of the NMC surface and 8% for the CB+PVdF mixture, the rest of their surface being exposed to porosity (Figure 2f). Thus, 87% of the NMC surface should be in contact with the electrolyte when it fills the porosity after battery assembly. The pores are large, between ten nanometers and about 1600nm with a median pores size at ~400nm (Figure 3a), and well-connected (100% intra-connectivity).

In electrodes J (LFP), the packing of the nanometric LFP particles, some of them being aggregated in clusters of particles of a few micrometers, determines well-connected pores of size between ten nanometers and about 800nm with a median pores size at ~100nm (Figure 3a). The surface fraction of LFP in contact with electrolyte should be high (LFP/porosity inter-connectivity is 90%, Figure 2e). However, the CB+PVdF mixture is scattered within the network of LFP particles and does not percolate (CB+PVdF intraconnectivity is only 25%, Table 1). This is expected given the particle size ratio of LFP and CB particles close to unity. [49] The blended NMC/LFP electrodes (F and H) have morphologies that resemble to the LFP electrode but with NMC particles distributed inside. Indeed, the strands of CB+PVdF mixture and the pores (Figure 3a) exhibit a nanometric range of size. Moreover, LFP and CB+PVdF mixture appear well mixed. As a matter of fact, the CB+PVdF mixture has about one-third of its specific surface in contact with LFP for both electrodes (Figure 2f). This homogeneous intermixing of these components may be related to some attractive interactions between the CB and the carbon coated LFP particles in the electrode slurry, as well as between the PVdF chains and the carbonaceous surfaces, [50] and to a repulsive interaction between PVdF and oxygen rich NMC surface. [51] The nanometric strands of CB+PVdF, are much well intra-connected through the network of LFP particles than in J, with values of 88% and 92% for F and H, respectively (Table 1), because the CB+PVdF mixture is excluded from the volume occupied by NMC and is thus more concentrated in the LFP/CB+PVdF mixture than in J. However, as a consequence of the LFP/CB+PVdF intermixing, only 2.6% of the NMC surface is connected with the CB+PVdF phase in H, which is 5 times less than in A, although both samples have same CB+PVdF contents (8wt%). Increasing this content to 12wt% in F allows increasing the NMC inter-connectivity with CB+PVdF to 8%. The interconnectivity of the LFP phase with the CB+PVdF mixture is also lower in H (13%) compared to F (23%), for same reason. If 15-17% of the NMC surface is in contact with the LFP phase in the two electrodes, it represents however a very small specific surface area fraction of LFP (<1%) (Figure 2e-f). Pores are well-connected in both NMC/LFP electrodes (100% intraconnectivity, Table 1). Pores size (Figure 3a) is included between a few ten nanometers up to about 800nm with a median pores size at ~130nm in electrode F. It is lower in H due to the bench-top hydraulic densification.

Tortuosity of the porosity

Physically, pore tortuosity is defined as the ratio of the actual distance travelled by the species per unit length of the medium. It is a measure for the elongation of a transport path due to the twisty structure of the pores imposed by the presence of the solid electrode matter.

It influences the liquid phase transport of electrolyte species, as expressed in the relationship of the intrinsic diffusion coefficient D0 in a non-tortuous path and the effective one Deff [52,53]

T D D D eff    0 2 0   (1)
where ε is the porosity, τ the tortuosity and T the tortuosity factor. Note that T is often confused to τ in the literature. The well-known Bruggeman relationship is often used to relate the tortuosity to the porosity: [24,34,52,53]

𝑇 = 𝜏 2 = 𝛾𝜀 1-𝛼 (2)
where α (Bruggeman coefficient) and γ are constants. It is generally assumed that γ=1 and α=1.5 in battery models. However, higher γ and/or α values have been obtained from experimental and simulation methods. Comparison of the tortuosity factors determined in previous investigations shows a large dispersion, even considering same electrode materials, and it appears that the method used to quantify the tortuosity has a major influence. As a rule, higher tortuosity factors are obtained by solving diffusion equation through finite element simulation, [18,21,23,25] porosimetry [52] or electrochemical measurements, [53] while lower values are determined by geometrical calculations. [17,22,23,28,54] In the case of electrodes with at least two populations of widely different sizes, the contributions of both the tortuosity of coarse and fine architectures have to be considered. The electrode tortuosity factor can be expressed as [55]

𝑇 𝑡 = 𝑇 ∘ 𝑇 𝜐 ( 3
)
where T0 is the microscale tortuosity factor of the electrode layer and T is the nanoscale tortuosity factor. This expression takes into account the "amplifying effect of the microporosity on the macroporous backbone". [55] In this paper, the tortuosity factor has been investigated by geometrical calculation but following a directional distance map propagation method, [54] which provides good-agreement with the effective diffusion-based tortuosity values. [22] Moreover, this method provides a more complete description of the tortuosity distribution as spatial distribution map. T0 has been estimated from X-ray tomography reconstructions by considering the deviations imposed by NMC particles only for propagation through the electrode; and T has been calculated for the pores distinguished by FIB-SEM tomography (Table 1). Bruggeman coefficient αt was then calculated by the combination of equations 2 and 3 (see detailed calculation in SI3 and values in Table 1) for being used in appreciation of electrochemical performance (see below equation 6).

In electrode A (NMC), microscopic tortuosity factor (Table 1) is estimated at 1.22.

Average nanoscale tortuosity factor is estimated at 2.10, which gives a Bruggeman coefficient of 1.35 to characterize the electrode at this scale. Tortuosity is however strongly dependent on the initial seed plane and the labelled trajectories direction, due to the anisotropic pore morphology (Table S1). However, some key morphological features can be identified looking at profile of the nanoscale tortuosity factor through the electrode thickness (Figure 3b, with initial starting plane close to electrode surface), and associated 2D cartography (Figure 3c).

Firstly, labelled trajectories followed through the pores have to pass around the large NMC particles, which results in high local tortuosities (T > 2). Secondly, the CB+PVdF mixture clusters induce a large range of pore size (Figure 3a), which leads to important tortuosity heterogeneities in agreement with previous works. [30,31,33b,36] The large cavities favour low tortuosity (T = 1.2-1.5), while tiny pores within the CB+PVDF mixture or at the interface between NMC particles and CB+PVdF mixture are characterized by high tortuosity (T = 1.7-2.5). Using equations 2 and 3, a mean Bruggeman coefficient of 1.54 is estimated as characteristic of the whole electrode, which takes into account the contribution of the coarse and fine structures. In electrode J (LFP), tortuosity is low (T = 1.25, Table 1) and rather homogenous (Figure 3b andf). Such values obtained by geometrical calculation appear lower than the one estimated in previous investigations of LFP electrodes, [23,28,53] which may be due to the geometrical calculation that tends to provide low tortuosity values [54,56,57], but also to the spherical shape and narrow size distribution of the LFP particles studied here. [24] The CB+PVdF cluster observed on the bottom right however induces local tortuosity heterogeneity due to its larger size than LFP particles and low porosity. A mean Bruggeman coefficient of 1.20 is estimated as characteristic of this electrode. For NMC/LFP blends, the contribution of the tortuosity factor of coarse and fine structures has to be considered. In as-received NMC/LFP electrode F, nanoscale pores tortuosity factor is constant through the thickness (Figure 3b). The 2D representation (Figure 3d) shows rather homogeneous tortuosity in the nanometric pores, scattered in the LFP/CB+PVdF mixture, while variations with higher values are observed around the NMC secondary particle. A mean Bruggeman coefficient of 1.34 is estimated as characteristic of the whole electrode. For the super-calendered NMC/LFP electrode H, the nanoscale tortuosity factor is slightly higher than the as-received NMC/LFP electrode F (Figure 3b). In addition, the 2D representations (Figure 3e) show more heterogeneities. However, direct comparison between F and H shall take into account the fact that they have different additives contents. As in electrodes A and F, higher tortuosity is observed at the junctions between the mixture of nanometric LFP particles with CB+PVdF mixture and the micrometric NMC particles. The cracking of the latter during the bench-top hydraulic pressing of H leads to the formation of interstices between the NMC grains, which also locally highly increase tortuosity. Compared to F, there are also tortuosity heterogeneities in the nanoscale pores, which may be associated with the decreases of the pore size and pathways number due to super-calendering. A Bruggeman coefficient of 1.30 is estimated as characteristic of the whole electrode. In summary, NMC and NMC/LFP electrodes architectures are characterized by geometrical Bruggeman coefficient of about 1.53 to 1.35 with respect to their pores tortuosity, which is a higher value than 1.2 found for the LFP electrode. This difference is due to the mismatch between the micrometric NMC and the nanometric CB or LFP particle sizes that induces detrimental large deviations for ionic paths in the corresponding electrodes.

Electrical properties

Real part of the complex conductivity, ', as a function of the frequency is shown in ) allowed to extract several well defined electrical properties (Table 1): the contact resistance, RC, between the electrode layer and the aluminum current collector and the electronic conductivity of the electrode layer, dc, which is first discussed.

Conductivity of NMC electrodes A and B (8 to 10.7S.m -1 , Table 1) is much higher than the NMC powder (4.9.10 -4 S.m -1 for pressed pellet), due to the CB addition and percolation in the electrode. The temperature independence of dc is characteristic of metallike electrical behavior (activation energy  0eV in Table 1), which shows that the CB+PVdF mixture percolates and short-circuits the less conductive NMC particles in the electrode. This behavior is related to the high intra-connectivity of the CB+PVdF mixture (77%) quantified from FIB/SEM images. The behavior of LFP electrodes J and K is more complex.

Decomposition of the high frequency part of the electrical spectra gives two conductivities.

First one, in the 10 6 -10 7 Hz frequency range, is the electronic conductivity of the electrode layer, dc, with values of 0.31 and 0.60S.m -1 and activation energy of 0.07eV that are close to the values obtained for pressed pellet of LFP powder (0.26S.m -1 and 0.09eV). This comparison confirms that the CB+PVdF mixture does not percolate, in agreement with low intra-connectivity of only 25% in the case of J as determined from FIB/SEM reconstructions.

The electrical conductivity in LFP electrodes J and K is mainly insured by the intraconnectivity of LFP particles and thus by the carbon coating percolation. [60] The signature of isolated CB+PVdF clusters is however seen at very high frequency (see SI4) with a second conductivity value of 4.1 and 6.3S.m -1 (in J and K) showing no dependence with the temperature (activation energy  0eV, Table 1). Increasing the CB content in the NMC electrode (B) does not bring significant change to dc (Table 1), likely because the CB+PVdF mixture percolation is already achieved in A. Contrarily, increasing the CB content in the LFP electrode (L) brings significant improvements to the electrical properties (Table 1 and Figure 4b), likely reflecting an improvement in the CB+PVdF intra-connectivity.

Similarly, the NMC/LFP electrodes H and F show electrical properties typical of percolated CB+PVdF network (see SI4), which is also well in agreement with high intraconnectivity of the CB+PVdF mixture (~90%). The NMC/LFP electrode H and the NMC electrode A have the same CB amount (in wt% and in v%, Table 1) and good intraconnectivity of the CB+PVdF mixture, which is however higher for H compared to A, e.g. 92 vs. 77% (Table 1). Nevertheless, the electrode film conductivity is lower for H, e.g. 3.4 vs 8.0S.m -1 . Such a result could be due to the larger size of the CB+PVdF mixture strands in NMC electrode (A) that form thicker (although less numerous) conducting paths than in NMC/LFP electrode H, possibly because the occurrence of resistive defects interrupting the current paths is more likely to happen in network with thinner strands. NMC/LFP electrode F has a higher CB content than H, e.g. 5.8 vs 3.9v%, and shows thus higher electrode conductivity, e.g. 8.1 vs 3.4S.m -1 . However it is interesting to note that the CB+PVdF mixture strands have same thickness in both electrodes. This way, the higher conductivity in F could be attributed to more numerous conducting paths, due to higher CB+PVdF mixture content, than in H.

A novel parameter to qualify the contact at the current collector/electrode interface is introduced. The contact resistance is given as Rc = RCR + Rf, where RCR is the constriction resistance and Rf is the resistance of the oxide film present at the extreme surface of the aluminum foil. [ 62 ,63] Rf is not expected to vary with the electrode composition. The constriction resistance RCR is expected to vary as

RCR  1/(dc) ( 4
)
where dc is the electrode mixture conductivity and  is the areal density of contact points at the collector/electrode interface. Comparison of J and K or of G and H, illustrates the influence of super-calendering. In the case of LFP electrodes, it can be seen that the electrode mixture as well as the isolated CB clusters conductivity slightly increase from 0.305 to 0.601S.m -1 and from 4.1 to 6.3S.m -1 , respectively, but the contact resistance significantly decreases from 36 to 0.8.cm² from J and K, which can be attributed to an increase of  (from 9.2 to 208 a.u.) (Table 1). For the NMC/LFP electrode G, as for LFP electrode J and K, two conductivities were extracted; the electrode mixture conductivity at lower frequency and some isolated CB+PVdF clusters at higher frequency, suggesting that percolation of the CB+PVdF mixture was hardly achieved.

However, super-calendering this electrode to form H resulted in the disappearance of the signature of isolated CB+PVdF clusters. Nevertheless, the electrode conductivity only slightly increases from 2.4 to 3.4S.m -1 , but the contact resistance significantly decreases from 7.5 to 0.64.cm² from G and H, which can be attributed to an increase of  (from 5.6 to 45.5 a.u.)

(Table 1).

Electrochemical measurements

Typical discharge curves of NMC electrodes (A and B), LFP (J and K) and NMC/LFP (F, G and H) at various C-rates and surface capacities of 2.6mAh.cm -2 are shown in Figure 5a-c. Considering the best electrode A, NMC delivered a reversible discharge capacity of 158mAh.g -1 at C/20 and 95mAh.g -1 at 2C. In electrode J, LFP delivered a low capacity, which can be attributed to the very high contact resistance for this sample (Table 1) that results in strong polarization even at very low rate. [63] Super-calendering J (to form K) results however in discharge capacity of 157mAh.g -1 at C/20 and 46mAh.g -1 at 2C. It is generally assumed that carbon-coated LFP is capable of sustaining high-rate discharge currents. [41,42] The degree of polarization is however larger and the discharge capacity lower in K (LFP) than in A (NMC), although both have same weight fraction of CB+PVdF mixture. This under performance of LFP in K can be attributed to the lack of intra-connectivity of the CB+PVdF mixture that results in low conductivity of the electrode and thus poor electronic wiring of the active mass. Such a behavior might appear in contradiction with the high intrinsic electronic conductivity of the LFP powder (0.26S.m -1 for a pellet, SI4). But recent works suggest the electronic conductivity within the carbon coating is likely hindered when LFP is wetted by the electrolyte, as a consequence of interactions between lithium ions and electrons within the carbon coating. [ 65 ] This is confirmed in SI5 (Figure S7c,d the transport of lithium specie inside the solid active particles. [73] The electronic wiring of the active mass affects (i) through the contact resistance at the electrode/current collector interface [63,75] and the electrical resistance of the CB network, and (ii) through the areal density of contact points or contact surface area between the active particles and the CB network. [76, 77,78,79,80,81]. The ionic wiring of the active mass affects (i) through the electrical resistance of the pores network, [72,73] and (ii) through the accessibility of the liquid electrolyte to the active mass surface (which can be covered by poorly ionic conductor material such as the binder or some liquid electrolyte degradation species). [82,83] Influence of the electrode parameters on the rate performance is conveniently assessed through a time constant, k (in hours), [69, 70,84,85] which is obtained from the relationship between the discharge capacity Q (in mAh.g -1 ) and the specific discharge current I (in mA.g - 1 ):

Q = Q0 -kI ( 5
)
where Q0 is the discharge capacity extrapolated to very low current. k is the capacity loss coefficient with respect to I. k1 and k2 can be defined below and above C*, respectively. Their variations with the temperature were studied in the case of electrode A and K (see Figure S6d). If k2 is determined by lithium ion diffusion kinetics into the electrode porosity, then it is expected to scale inversely with the effective diffusion coefficient of lithium ions inside the electrode, Deff, given by Equation (1). [69,70] In a limited temperature range, the diffusion variation with the temperature can be expressed by Arrhenius equation that gives: [86] ln (1/k) = ln(1/k0) -EA/kBT (6) with Ea the activation energy (in eV), kB (= 1,381.10 -23 J.K -1 ) the Boltzmann constant, T (K) the temperature, and k0 the prefactor. Above C* a good linear fit of equation ( 3) yields an Ea value of 0.13eV in the case of electrode A and 0.16eV for K, close to the value for diffusion in the free electrolyte (0.15-0.16eV), [65] while for charge transfer process values of 0.28 and 0.45eV are reported for NMC and LFP, respectively. [ 87 , 88 ] Thus, the temperature dependences of the electrodes time constants k2 clearly establish that the main limitations of the rate performance is diffusion within the electrolyte into the electrode porosity above C*.

The activation energy of k1 was also found equal to 0.28eV in the case of electrode A, suggesting that the rate performance below C* is rather dominated by the electrode resistance, itself being affected by the charge transfer process. Discussion about the discharge rate performance of all these electrodes is now divided in two parts, first below C* and then above C*.

In the case of NMC electrodes (Figure 5a andd), A displays better performance than B, although A has slightly lower mixture conductivity (8.0 vs. 11.8 S.m -1 ) and slightly higher contact resistance (0.08 vs. 0.07 and 0.03.cm²). Because B has higher CB+PVdF volume fraction, it can be assumed that the inter-connectivity of NMC with the CB+PVdF mixture is better in B than in A, i.e. higher than 13%. On the other hand, the access of the liquid electrolyte to the NMC particles must be reduced in B compared to A (NMC/electrolyte interconnectivity value lower than 87%). Thus, below C*, the lower rate performance of B is likely due to poorer ionic wiring of the active mass due to the surface covering of the NMC particles by the CB+PVdF phase limiting the liquid electrolyte access and hindering lithium insertion, as shown by the larger polarization and lower capacity. [80,83] In NMC/LFP electrodes, due to higher amount of CB+PVdF mixture in F (16.4v.%)

than in H (11.0v.%), both the NMC and LFP active particles are better contacted to this electronic conducting phase, as seen in the inter-connectivity values (Figure 3d ande), 8 and 3% for NMC/CB+PVdF, and 23 and 13% for LFP/CB+PVdF, in F and H, respectively. But, on the other hand, the access to the electrolyte is decreased, from 80 to 77% for NMC and from 86.2 to 76.3% for LFP, in H and F, respectively. Figure 5b ande in the rate performance can be attributed to improved electronic wiring of the active mass as a consequence of higher inter-connectivity with the CB+PVdF mixture in F. [35] According to M. Gaberscek model, Relectrode should scale inversely with the inter-connectivity between the active mass and the CB network if the main limitation comes from step (ii), i.e. charge incorporation of both ionic and electronic species. Looking at the voltage profiles (Figure 5b)

or the capacity delivered by each material (QNMC and QLFP, Figure 5e,f), one can see that the drop of capacity in H compared to F is largely due to malfunctioning of NMC. This observation shows that there is a critical NMC/CB+LFP inter-connectivity value for NMC to well-perform, situated between 3% (F) and 8% (H). Interestingly, G displays nearly similar rate performance than H (Figure 5b), although G has a 10 times higher contact resistance with the current collector than H, 7.5 and 0.64.cm², respectively. Such a difference in contact resistance is clearly seen in the higher polarization of G compared to H (Figure 5b), especially for the higher C-rates. The same discharge capacity for G and H, which is lower than F, shows however that the inter-connectivity with the CB+PVdF mixture is the governing factor that determines the rate performance up to C*. The comparison of the behavior of the NMC and LFP materials in the mixed and the unmixed electrodes is delicate matter, in particular because the true current felt by one active matter (in mA per g of NMC or LFP) varies between 1 or 2 times the total current applied to the electrode (in mA per g of NMC+LFP). A comparison of the whole set of electrodes is however feasible above C* using the discharge front model. [68,71] Considering that only lithium diffusion limitations determine the rate performance, the degree of discharge (DoD), defined as the capacity discharged at the considered rate, QC-rate, and expressed in percentage of the capacity discharged at low rate, is given by [71]

1 𝐷𝑜𝐷 = 𝑄 𝐶/20 𝑄 𝐶-𝑟𝑎𝑡𝑒 = 𝐿 2 ×(𝐶 𝑠𝑚𝑎𝑥,𝑁𝑀𝐶 ×%𝑣 𝑁𝑀𝐶 +𝐶 𝑠𝑚𝑎𝑥,𝐿𝐹𝑃 ×%𝑣 𝐿𝐹𝑃 )•(1-𝑡 + ) 𝜀•𝐶 0 •𝐷 𝑒𝑓𝑓 • 𝐶-𝑟𝑎𝑡𝑒 3600 (7)
with L (cm) the electrode thickness, Csmax (mol.cm -3 ) the maximal concentration of inserted species inside the active material, %vAM the volumetric fraction of the active material in the electrode, t + the cation transport number in the electrolyte (0.41 for Li + in LP30 [89] ), ε (%) the porosity of the electrode, C0 the electrolyte concentration (1.10 3 mol.cm -3 ) and Deff (cm².s -1 )

the effective diffusion coefficient of the lithium ions through the electrolyte filling the electrode porosity. Equation ( 7) takes into account the length of the paths the lithium ions must diffuse through the electrode to reach the active mass (depends on L²), their kinetics of diffusion (Deff that depends through Equations ( 1) and (2) on D0, 2.45.10 6 cm².s -1 for solvated Li + in LP30, [89] ,  and ) the mismatch between the maximal concentration of lithium species that could be inserted in the active mass (Csmax) and the concentration of lithium species in the electrolyte contained in the electrode porosity (C0, ). The maximal concentration of inserted species inside the active material is defined as:

𝐶 𝑠𝑚𝑎𝑥 = 𝜌•∆𝑥 𝑚𝑎𝑥 𝑀 (8)
with  (g.cm -3 ) the AM density (4.6g.cm -3 for NMC and 3.6g.cm -3 for LFP), Δxmax the maximum reversible insertion degree of the AM (0.61 for NMC and 0.92 for LFP) and M (g.mol -1 ) the AM molecular weight (96.46g.mol -1 for NMC and 157.76g.mol -1 for LFP). It gives values of 29.1.10 -3 mol.cm -3 for NMC and 21.0.10 -3 mol.cm -3 for LFP.

The discharge capacity at the 2C-rate (thus above C*) predicted by the discharge front model, Qmodel, was calculated with Eq. 7, Deff being calculated with Eq. 1 and 2, using mean values of the porosity (Table 1), Bruggeman coefficient (determined from tomography measurements, t (Table 1), and leaving  = 1. We considered that the LFP super-calendered K and the as-received J electrodes are characterized by the same Bruggeman coefficient, as this value appears to be characteristic of the spherical shape of the LFP particles. Moreover, both electrodes have same CB+PVdF content. Similarly, we considered that the NMC/LFP electrodes G and H have same Bruggeman coefficients. Measured and calculated values are compared in (Figure 6a-b). Very good agreement is found for A (NMC) and F (NMC/LFP) electrodes, which confirms that the discharge front model can be a convenient tool to estimate the rate performance of composite electrodes, as already shown. [68,71] However calculated values are significantly higher than measured ones for G and H (NMC/LFP), J and K (LFP)

electrodes. As the model considers only lithium diffusion limitations, the discrepancy observed for G, H, J and K electrodes must root in other limitations among which the electronic wiring limitations (contact resistance, electrical conductivity of the electrode, interconnectivity with CB+PVdF network). Indeed, J and K have low electronic conductivity values, 0.3 and 0.6S.m -1 , respectively, due to lack of CB+PVdF intra-connectivity (25% in J, Table 1). Additionally, J has huge contact resistance, 36.cm -2 . G and H have higher electronic conductivity values, 2.4 and 3.4S.m -1 , respectively, due to very good CB+PVdF intra-connectivity (92% in H, Table 1). However, the poor NMC/CB+PVdF interconnectivity (3%, Figure 3d) negatively affect the rate performance likely because of large polarization, as seen in Figure 5b, due to high electrode resistance. Moreover, G has large contact resistance, 7.5.cm -2 , which increases even more the polarization. Comparatively, F has higher electronic conductivity value, 8.0S.m -1 , respectively, due to very good CB+PVdF intraconnectivity (92% in H, Table 1) and low contact resistance, 1.0.cm -2 . Furthermore, the better NMC/CB+PVdF inter-connectivity (8%, Figure 3d) seems to be good enough for this electrode to show only lithium diffusion limitations in power performance. From the architecture and formulation point of view, one can say that in this electrode the electronic wiring of the active mass is fairly well designed. Same conclusion can be drawn for electrode A.

In complement, In Figure 6c-d the capacity losses at 2C-rate (expressed in percentage of the discharge capacity measured at very low rate, Eq. 9, or calculated with the discharge front model, Eq. 7) is decomposed into the diffusion and the electronic wiring contributions.

The former considers the drop in capacity that is expected based on the Li + diffusion limitation, which is predicted by the discharge front model (Eq. 10). × 100 (10) The electronic wiring contribution is simply the difference between the total and the diffusion losses. These plots rationalize the efficiency of the different electrode architectures by discriminating the two main types of limitations. Finally, this approach allows comparing the electrode designs. For example, knowing that electrodes A and F show only lithium diffusion limitations in rate performance, one can interpret with relevancy the higher discharge capacity of A compared to F, 100 and 81mAh.g -1 at 2C-rate, respectively. Looking at the set of equations written above, one can realize that the higher thickness and lower porosity in F detrimentally affect its performance. On the other hand, the performance of A could have been even better with a smaller Bruggeman coefficient. However, its large value is associated with the large size of the NMC particles that form large obstacle to bypass by the ion flux and by the presence of the tortuous CB+PVdF clusters. Interestingly, small capacity loss would be expected for the other electrodes (J, K, G and H) if only there were only lithium diffusion limitations. Their performance is clearly plagued by poor electronic wiring, which emphasizes the critical role of the conductive additive selection and of the electrodes processing to minimize this limitation. Same trends are observed at 3C-rate (Figure S11), but the contribution of the lithium diffusion limitations becomes more important.

𝑇𝑜𝑡𝑎𝑙 𝑙𝑜𝑠𝑠𝑒𝑠 (%) =

Conclusion

Combination of X-ray and FIB-SEM tomography techniques with BDS, together with the use of the electrochemical discharge front model, allow establishing unambiguous relationships between electrode 3D geometry, electrical properties and electrochemical performance. Moreover, quantitative assessment of the contributions of the electronic and ionic wiring limitations to power performance is achieved for the first time. Below a critical regime C*, between 1C and 1.5C, the discharge capacity depends on the electrode resistance that is determined by the contact resistance at the electrode/collector interface, the percolation of the CB+PVdF mixture, the contact surface area between the active particles and this mixture, and also with the electrolyte. Above C*, for electrodes with suitable electronic wiring, the discharge capacity is determined by the limitations opposed to lithium diffusion into the electrode pores tortuosity. The latter contribution can be satisfactorily estimated by using the discharge front model and a Bruggeman coefficient calculated from the product of the micro-and nano-scale geometrical tortuosity factors. The large NMC particle size, compared to the pores and/or LFP particles, favors the CB+PVdF mixture percolation but also higher pores tortuosity. The small LFP particles disfavor CB+PVdF percolation but favor lower pores tortuosity.

For

Figure 4a, b

 b Figure 4a,b for various electrodes A and B (NMC); F, G and H (NMC/LFP); J, K and L (LFP). The study of the temperature dependence and the analysis of Nyquist plots (see SI and also methodology in previous works [58,59,60,61]) allowed to extract several well defined

[ 64 ]

 64 RC and dc are plotted in Figure4cfor selected electrodes having close CB content of 3.5-4.2%v. dc regularly increases in the following order K (LFP), G (NMC/LFP), H (NMC/LFP) and A (NMC), in agreement with the CB volumic ratio in the mixture. However, RC does not follow this regular variation, as it displays maximum values for the G. The quantity 1/( RC) that should be proportional to  is plotted in Figure4dto relate RC and the different electrode morphologies. Low RC of electrode K (LFP) and further increase of RC with the decrease of LFP and the proportional increase of NMC contents in G can be attributed to the numerous contact points that the LFP particles can make at the surface of the current collector in addition to CB ones.[63] As the LFP nanoparticles content are progressively replaced by micrometric NMC particles, the areal density of contact points at the interface naturally decreases and thus RC increases. At highest NMC contents (in A), dramatic decrease of RC and increase of  can be explained by an accumulated layer of CB+PVdF, due to a processed induced rheological migration phenomenon.[48]

)

  where are compared the performance of electrodes K and L (but with surface capacities of 1.8mAh.cm-2 ). In L the CB content of 4.5wt% allows to achieve high electrode conductivity and much better rate performance. For NMC/LFP electrodes the discharge curves occur in two steps showing the electrochemical signature of both active materials, the distinct plateau of LFP appearing after the sloppy voltage decline of NMC. Best electrode F delivered reversible discharge capacity of 159mAh.g -1 at C/20 and 82mAh.g -1 at 2C, which represents an intermediate behavior between NMC and LFP (A and K) electrodes. Furthermore, discharge capacity as a function of the C-rate is shown in Figure5d-f. For NMC/LFP electrodes, the capacity delivered by each material (QNMC and QLFP) to the total discharge capacity at a given rate was determined from charges measured at the slow C/5 rate followed by a floating period (Q = QNMC + QLFP + Qfloating) see FigureS9b. The capacity Qfloating recovered during the floating period is significant in the case of electrode H as a consequence of large polarization in charge even at C/5 rate.A critical discharge rate, C*, is observed (marked by an arrow), except for electrode J.It appears as an elbow where the slope of the discharge curve markedly increases. Also known as maximum working rate,[66] C* identifies two different limitation regimes. Above C*, it is now well accepted that rate performance is controlled by the lithium ion diffusion resistance within the electrolyte in the electrode porosity[66,67,68,69,70,71,72]. The large mismatch between the lithium concentration in the electrolyte and the active material concentration in the electrode, and the limited lithium ion diffusion kinetics into the electrolyte lead to the depletion of lithium ions inside the electrode porosity at some point, and a brutal decrease in cell voltage that ends the discharge. Below C*, it is considered that the electrode resistance, Relectrode, is the limiting factor.[16,69b,73,74] It gathers several contributions reflecting several steps: (i) the transport of electrons and ions from their "reservoirs" to the active particles, (ii) the charge incorporation reaction which involves the transfer of both charged species from the outside into the interior of active particles and (iii)

  ,f clearly show the better performance of F below C*. Noteworthy, F and H have nearly the same contact resistance with the current collector, i.e. 1.0 and 0.64 .cm², respectively. Thus the difference

Figure 1

 1 Figure 1 2D and 3D FIB/SEM reconstructed views of (a-b) A (NMC), (c-d) F (NMC/LFP), (e-f) H (NMC/LFP) and (g-h) J (LFP) electrodes. NMC particles are red, LFP particles are green, the CB+PVdF mixture is blue and the porosity is white.

Figure 2 3D

 2 Figure 2 3D FIB/SEM reconstructed views of the NMC particles with the NMC surface area in contact with LFP (green zone), CB+PVdF mixture (blue zone) and porosity (grey zone) for (a) A (NMC, (b) F (NMC/LFP) and (c) H (NMC/LFP).Interconnectivity between the different materials/phases given as the specific surface area of (d) NMC, (e) LFP and (f) CB+PVdF mixture in contact with the other materials/phases for electrodes A, F, H and J.

Figure 3 (

 3 Figure 3 (a) Pore size distribution; (b) Tortuosity factor through electrodes thickness (ydirection); 2D pores tortuosity factor Tv representation for (c) A (NMC), (d) F (NMC/LFP), (e) H (NMC/LFP) and (f) J (LFP) electrodes. The side close to the electrode surface is in all cases at the bottom of the 2D maps.

Figure 4

 4 Figure 4 Real part of the complex conductivity as function of the frequency for (a) A (NMC) and F, G, and H (NMC/LFP); and (b) J, K, and L (LFP) electrodes. (c) Contact resistance and electrode conductivity; and (d) calculated value of areal density of contacts at the electrode/current collector interface for K, G, H and A.

Figure 5

 5 Figure 5 Potential vs. specific capacity curves at three C-rates (C/20, C and 2C) for (a) A, B (NMC); (b) F, G, and H (NMC/LFP); (c) J, K (LFP) electrodes. Discharge capacity as function of the C-rate for (a) A, B (NMC) and J, K (LFP); (e) F (NMC/LFP); (f) H (NMC/LFP) electrodes. The arrows mark the critical discharge rate, C*. For NMC/LFP electrodes, the capacity delivered by each active material is also plotted in (e) and (f).

Figure 6

 6 Figure 6Comparison between the measured and calculated (Eq. 7) discharge capacity at 2C-rate for (a) A (NMC), J and K (LFP); (b) F, G and H (NMC/LFP) electrodes. Capacity loss at 2C-rate (Eq. 9-10) decomposed into the diffusion and electronic wiring contributions for (c) A (NMC), J and K (LFP); (d) F, G and H (NMC/LFP) electrodes.

  Figure 1 A A

  LFP electrode at 3wt% of CB, the CB+PVdF mixture does not percolate as it is scattered among LFP particles, which results in very poor rate performance. Contrarily, in NMC electrode, the CB+PVdF mixture percolates and contacts 13% of the NMC particles surface area, leaving 87% of it accessible to the liquid electrolyte. It results low electrode resistance below C* and rate performance mostly determined above C* by the limitations opposed to lithium diffusion into the electrode pores tortuosity. Increasing at 4.5wt% the CB content allows the CB+PVdF mixture percolation in LFP electrode, reaching a target value of more than 3S.m -1 for dc, which restores satisfactory rate performance below and above C*.Contrarily, rate performance is degraded in NMC electrode as a consequence of insufficient access of the liquid electrolyte to the surface of NMC particles, which slows down the charge

	transfer process.
	In NMC/LFP electrode, at 3wt% of CB, the CB+PVdF mixture percolates, despite its
	scattering among LFP particles, because of higher CB+PVdF to LFP ratio than in LFP
	electrode with same CB content. However, NMC particles are starved from electrons as less
	than 3% of their surface area is contacted by the CB+PVdF mixture. It results poor rate
	performance. Increasing CB content at 4.5wt% allows retrieving enough electronic wiring of
	the NMC particles, 8% of their surface area being contacted by the CB+PVdF mixture, and
	also better electronic wiring of the LFP ones. It results low electrode resistance and rate
	performance above C* mostly determined by the limitations opposed to lithium diffusion into
	the electrode pores tortuosity. Then, a value between 3 and 8% of NMC inter-connectivity
	with CB+PVdF can be targeted for optimum charge transfer process.
	The measurement by BDS of the contact resistance at the electrode/collector interface
	showed the influence of this parameter and of calendering on electrochemical performance.
	Discussing only electrodes with percolation of the CB+PVdF mixture, insufficient
	calendering can lead to high contact resistance with significant effect on electrode
	polarization, as a consequence of low areal density of contact points. A value of 1 Ohm.cm -2

can be targeted for negligible influence of the contact resistance on electrochemical performance.

Table captions Table 1

 captions1 Composition, porosity and thickness (without aluminum collector) of NMC,

	LFP and blended NMC/LFP electrodes. Morphological parameters evaluated
	from X-Ray and FIB/SEM tomography reconstructions and electrical
	properties measured by Broadband Dielelectric Spectroscopy. All electrodes
	have a loading of 2.6 mAh.cm -2 , except J', K' and L' (1.8 mAh.cm -2 ). "n.m."
	means "not-measured"

Table 1 NMC/LFP Compaction C Content (w.%)/(v%) Porosity (vol. %) Thickness (µm) Intra- connectivity (%) Tortuosity factors and Bruggeman coefficient Electrical Properties: contact resistance, areal density of contact points, electrode conductivity (electrode and eventually isolated CB+PVdF clusters), activation energy

 1

			NMC LFP PVdF CB		Micrometer XCT	NMC LFP CB+PVdF Pores	To (micro) Tυ (nano) t	RC (.cm²)  (a.u.)	dc (S/m) -Ea (eV) isolated CB+PVdF (S/m) -Ea (eV)
	A	100/0 As-received	92/54.2 0 5/7.6 3/4.2	34	69 73	99.8 -100 77	1.22 1.54 2.10	0.08 152	8.0 -~0
	B	100/0 As-received	88/52.2 0 7.5/11.5 4.5/6.3	30	73 81	99.4 n.m. n.m. n.m.	1.14 n.m. n.m.	0.07 139	10.7 -n.m.
	F	50/50 As-received	44/24.0 44/30.6 7.5/10.6 4.5/5.8	29	77 78	13.6 100 100 88	1.06 1.34 1.38	1.0 12	8.1 -n.m.
	G	50/50 As-received	46/24.0 46/30.6 5/6.7 3/3.7	35	77 77	15.0 n.m. n.m. n.m.	1.06 n.m. n.m.	7.5 5.6	2.4 -n.m. 8.1 -n.m.
	H	50/50 Super calendered	46/25.5 46/32.5 5/7.1 3/3.9	31	71 73	16.3 100 100 92	1.06 1.30 1.42	0.64 45	3.4 -n.m.
	J	0/100 As-received	0 92/53.9 5/5.9 3/3.2	37	88 95	-100 25 100	1.00 1.25 1.20	36.6 9	0.3 -0.07 4.1 -~0
	J'	0/100 As-received	0 92/53.9 5/5.9 3/3.2	37	61 n.m.	-n.m. n.m. n.m.	1.00 n.m. n.m.	3.8 61	0.4 -n.m. 5.3 -n.m.
	K	0/100 Super calendered	0 92/59.8 5/6.6 3/3.6	30	78 80	-n.m. n.m. n.m.	1.00 n.m. n.m.	0.8 208	0.6 -0.06 6.3 -~0
	K'	0/100 Super calendered	0 92/59.8 5/6.6 3/3.6	30	57 n.m.	-n.m. n.m. n.m.	1.00 n.m. n.m.	0.4 369	0.7 -n.m. 7.8 -n.m.
	L'	0/100 Super calendered	0 88/54.5 7.5/9.4 4.5/5.1	31	59 n.m.	-n.m. n.m. n.m.	1.00 n.m. n.m.	0.29 107	3.3 -n.m.

The intra-connectivity is quantified as the volume fraction of the most voluminous cluster of one material/phase in the analyzed volume; a value of 100% meaning all voxels of this material/phase being part of a same unique network.

The inter-connectivity was characterized by identifying the common outlines of the different materials/phases and quantifying the specific surface area fraction of each material/phase in contact with another material/phase.

Acknowledgements

Financial funding from the ANR program no. ANR-15-CE05-0001-01 is acknowledged. The authors would like to acknowledge IMD (Institut de la Mobilité Durable -Sustainable Mobility Institute) and the network METSA (Microscopie Electronique et Sonde Atomique) for financial support. Thanks are also due to the CLYM (Centre Lyonnais de Microscopie: www.clym.fr) supported by the CNRS, the "Grand Lyon" and the Rhône-Alpes Region for use of the Zeiss NVision40 FIB/SEM. This work was made possible by the facilities provided by Swiss Light Sources (Paul Scherrer Institut) and the technical support from the staff of the TOMCAT beamline.

Received: ((will be filled in by the editorial staff))

Revised: ((will be filled in by the editorial staff))

Published online: ((will be filled in by the editorial staff))

All these results are relevant for battery technology because they were obtained for electrodes relevant for the industry in terms of composition, surface capacity, and manufacturing process. This work opens new prospects for rational electrode design, which is critical to build higher energy and power density batteries, in particular of EV application.

Searching for critical inter-connectivity values between the active particles and the electronic and ionic networks, as a function of materials parameters (particles intrinsic conductivity, size and shape) to achieve low electrode resistance looks very interesting.

Experimental section

Experimental section is given in Supporting Information (SI) due to space limitation.

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.


Fatma Slaimi
email: fatma.slaimi@univ-amu.fr

Sana Sellami
email: sana.sellami@univ-amu.fr

Omar Boucelma
email: omar.boucelma@univ-amu.fr

Ahlem Ben Hassine
email: ahlembh@gmail.com

Leveraging Track Relationships for Web Service Recommendation

Keywords: Service Recommendation, Web service, multi-Graph, Association rules, track relationship I

Existing Web services recommendation approaches are based on usage statistics or QoS properties, leaving aside the evolution of the services' ecosystem. These approaches do not always capture new or more recent users' preferences resulting in recommendations with possibly obsolete or less relevant services. In this paper, we describe a novel Web services recommendation approach where the services' ecosystem is represented as a heterogeneous multi-graph, and edges may have different semantics. The recommendation process relies on data mining techniques to suggest services "of interest" to a user.

INTRODUCTION

Recommendation Systems (RS for short) have proved useful to exploit Web consumer behavior in order to recommend an item of interest to a client e.g., a product, a document or a book to cite a few. During the last decade, several Web service recommenders have been proposed in the literature [START_REF] Manikrao | Dynamic Selection of Web Services with Recommendation System[END_REF] [START_REF] Zheng | QoS-Aware Web Service Recommendation by Collaborative Filtering[END_REF][START_REF] Cao | Hybrid Collaborative Filtering algorithm for bidirectional Web service recommendation[END_REF]. Most of those systems are based on both similarities between previously used services, and the assessments of the Quality-of-Service (QoS) combined with collaborative filtering (CF) [START_REF] Breese | Empirical Analysis of Predictive Algorithms for Collaborative Filtering[END_REF]. These approaches rely on static data and hence cannot deal with a continuously evolving Web services ecosystem, which is composed of services, service providers, Mashups and (users) developers. In such eco-system, services can be updated, deleted making the whole ecosystem prone to obsolescence. In addition, most of those services do not provide QoS metadata.

Other approaches consider the exploitation of trusted relationships between services and users or between users themselves [START_REF] Eirinaki | A trust-aware system for personalized user recommendations in social networks[END_REF][START_REF] Deng | Social network-based service recommendation with trust enhancement[END_REF][START_REF] Deng | Trust-based Service Recommendation in Social Network[END_REF]. Trust relationships are established on the basis of similar service invocations or by similar evaluations of Web services by different users. However, in other settings, e.g. a social network, a user might be interested by a service recommended by a friend rather than by other users, even if these users have provided same rankings for a service, or did invoke the same service. In addition, users' information feedback is often missing and user interests may change over time. Random evaluations provided by spam users may be another limitation for these recommendation systems.

Now that the big picture is drawn, why would it be worthy to extend/improve/develop recommendation approaches in the Web services ecosystem?

In this paper, we describe WSR-Track, a novel service recommendation system where (1) the service ecosystem is represented as a heterogeneous multi-graph, (2) nodes represent users (resp. services), and edges represent either trust relationships between users, or usage relationships between a user and a service, and (3) nodes and edges properties are integrated in the service discovery process. Trust relationships are expressed by means of ProgrammableWeb1 tracks. Usage relationships represent a service invocation. The recommendation process takes into account relationships, user records and preferences, invocations, watchlists and mashups.

The rest of the paper is organized as follows; related work is presented in Section 2 and Section 3 describes the WSR-Track recommendation system. Section 4 discusses experimental results and Section 5 concludes the paper.

II. RELATED WORK

Most of Web services RS proposed in the literature are based on Collaborative Filtering or CF [START_REF] Breese | Empirical Analysis of Predictive Algorithms for Collaborative Filtering[END_REF] [START_REF] Su | A survey of collaborative filtering techniques[END_REF]. A CF system proceeds as follows: (1) a user expresses his preferences by rating items. These ratings are considered as user preferences ; (2) the system matches some user ratings against other users' ratings and detects users with the most "similar" preferences; (3) the system recommends the highly-rated items for a user that are not forcibly rated by him. These systems are based on the idea that users with similar rates may have similar interests.

Other approaches were devoted to the use of QoS, ratings and relationships among Web services end-users [START_REF] Zhu | A Privacy-Preserving QoS Prediction Framework for Web Service Recommendation[END_REF].

Both approaches are reviewed below.

A. QoS Aware approaches

QoS properties are often expressed by means of performance indicators such as price, response time, availability, accuracy, etc. Many researches on Web service selection, recommendation and composition use QoS in order to improve the performance of their systems [START_REF] Wang | An Improved Artificial Bee ColonyApproach to QoS-Aware Service Selection[END_REF]. Generally, RS combine QoS evaluations with CF to recommend services [START_REF] Zhu | A Privacy-Preserving QoS Prediction Framework for Web Service Recommendation[END_REF][10] and users [START_REF] Cao | Hybrid Collaborative Filtering algorithm for bidirectional Web service recommendation[END_REF].

In [START_REF] Zhu | A Privacy-Preserving QoS Prediction Framework for Web Service Recommendation[END_REF], the recommendation approach makes use of the QoS ratings given by a user to predict QoS evaluations of other services that she never used.

In [START_REF] Deng | Trust-based Service Recommendation in Social Network[END_REF], authors consider when the user is interested in the QoS evaluations of other users, they will be considered as trustful ones. Similarity between users is expressed as an (Euclidean) distance. First, authors choose a set of services to recommend, and then calculate the degree of user confidence in these services by taking into consideration his preferences in term of services' categories.

In [START_REF] Manikrao | Dynamic Selection of Web Services with Recommendation System[END_REF], a recommendation system with semantic matching is described. The approach is based on CF and users' feedbacks, and helps a user to select a Web service from a list of similar ones. When a user invokes a service, he is asked to evaluate it. But in most cases, users do not provide explicit ratings [START_REF] Claypool | Implicit interest indicators[END_REF].

Xi et al. [START_REF] Chen | RegionKNN: A Scalable Hybrid Collaborative Filtering Algorithm for Personalized Web Service Recommendation[END_REF] studied the impact of user's location in the prediction of QoS. They proposed a novel approach where users are hierarchically grouped according to their location and their QoS evaluations. Consequently, users from the same region are considered as similar. Given a user, the system searches similar users in the same location (region) instead of exploring the set of all users. However, belonging to the same region does not necessary mean having the same preferences.

Authors in [START_REF] Jiang | An Effective Web Service Recommendation Method Based on Personalized Collaborative Filtering[END_REF] consider the impact of personalization of Web service items when computing the degree of similarity between users. That is, more popular services or services with more stable QoS should contribute less to user similarity measurement. Zhang et al. [START_REF] Zhang | Collaborative Filtering Based Service Ranking Using Invocation Histories[END_REF] propose to combine users QoS experiences, environment and user input (query) to predict Web services QoS values. But the environment and the user-input can hardly represent user's opinions/tastes.

B. Trust based approaches

The number of available services and users is increasing and so, some fake feedbacks of malicious users may be introduced as inputs to the RS: as a result, this may affect the quality of recommended services. This issue has been addressed in [2] [4-5] [7] [12-14] [22-23], where authors proposed trust-enhanced recommendation methods. Based on trust relations, trust-based approaches refer only to ratings given by trusted users.

SoCo [START_REF] Maaradji | Social-Based Web Services Discovery and Composition for Step-by-Step Mashup Completion[END_REF] is a Web service recommendation framework based on social networks analysis. SoCo enables the discovery and the composition process by transforming the interactions between users and services into a social network interactions among users represented as a graph. This graph links users according to their common interests; it describes their profiles including their preferences and their previous system usages. Services preferred by trusted workers are recommended.

The work of Deng.et al. [START_REF] Deng | Social network-based service recommendation with trust enhancement[END_REF] is based on the analysis of social networks' contents and users' relationships. Authors propose a Web service recommendation system based on trust relationships that are established either i) explicitly when a user specifies his/her list of trustful connections, from the beginning, or ii) implicitly when the same QoS evaluation is given by two different users. TSR [START_REF] Deng | Social network-based service recommendation with trust enhancement[END_REF] the service recommendation algorithm proposed is based on trusts and calculates the similarity between users via their assessments of public services. TSR also calculates the confidence of the user in a service. This confidence depends on the assessments of similar users. The most confident Web services are recommended.

In [START_REF] Zhang | Web Service Recommendation Based on Watchlist via Temporal and Tag Preference Fusion[END_REF], authors exploit the implicit users' ratings to build a CF-based RS that takes advantages of the user WatchList and preferences in terms of tags. The idea is to transform implicit evaluations into explicit ones to improve the recommendation accuracy. Empirical experiments based on ProgrammableWeb show that compared to CF, the recommendation system (with time preference and tags) provides results that are more accurate and more precise.

As mentioned above, most of RS inputs are users' relationships and similarities among users. In our work, the similarity between users is based on the following assumptions: 1) user A tracks user B, this means that A have similar interests as B in terms of Web services; 2) users tracking a user in common may have similar interests.

Moreover, unlike existing approaches which consider explicit user evaluations of services and QoS rating, we propose to exploit explicit users' relations, established via the track function to detect their services preferences. This information is obtained from their previous tracks. We assume the existence of track relations in ProgrammableWeb that play the role of explicit trust relationships. We can identify the most trusted users and then exploit their (track) records to recommend Web services. This simplifies the work needed to detect trust relations based on similar invocations or evaluations and minimizes the risk of using inconsistent information from spam users.

III. WSR-TRACK RECOMMENDATION SYSTEM

WSR-Track, the system we propose, consists of two main components:

-Graph generation process: Builds a heterogeneous multi-graph where the nodes represent users (resp.

services) and the edges illustrate track relationships among these users and between users and services. -Web services recommendation process: Provides the most adequate Web services for a target user based on his/her history and his/her tracked relations.

In the following we will detail both processes.

A. Graph generation process

The process builds a heterogeneous users/services multigraph by means of ProgrammableWeb track functions. A user can track (follow) either: Web services, mashups, searches or others users (see Figure 1). Hence, in following a user on ProgrammableWeb, one may infer Web services and mashups of interest. Based on these tracking functions, we can connect users and services with track relationships. Users (resp. services) represent the nodes while the track relations are the edges. We refer to this graph as the (users/services') track graph (TG) (cf. Definition 1). Since a user may track Web services and mashups, or create mashups, her/his history is defined by means of her/his followees or the mashups she/he created.

B. Web services recommendation process

The output of this process is the recommendation of a set of relevant Web services to a target user based on his/her history and his/her tracked relations. This process is divided in two steps: i) The first step retrieves data from the track graph by exploiting the users' relationships; ii) The second step merges this data with other information such as the user's history and the quality of services (popularity, usage, etc.) to select the most relevant services.

The first step, considered as a mining step, involves two actions:

• Neighborhoods detection, which consists of detecting user's neighbors in the track users graph to extract theirs recent histories, i.e. previous Web services usages.

• Association rules generation, based on Apriori [START_REF] Piatetsky-Shapiro | Discovery, analysis, and presentation of strong rules[END_REF] to mine "valid" association rules. These rules express correlation amongst used services. The second step, called recommendation step, consists of exploiting these association rules to select relevant Web services and to rank them according to their usage/popularity. In the following, more details will be given for the above mentioned steps.

1) Knowledge mining This step includes mainly two actions: neighborhood detection and association rules generation. a) Neighborhood Detection The recommendation system takes into account relations between users in order to recommend services. If a user u i follows a user u j , it means that u i is interested in services/mashups of u j . Therefore, we recommend services to a user u i , based on the history of his/her neighbors in the track graph (TG).

Once the list of neighbors is obtained from the TG, it is filtered in order to acquire the k most similar users. The similarity between users is measured according to the number of common services in their previous usages. Users deploying several common services may have similar interests and could be considered as similar. The similarity between two users u i and u j is measured using the following function [START_REF] Eirinaki | A trust-aware system for personalized user recommendations in social networks[END_REF].

Sim (u i ,u j )= | ⋂| | | | (1)
Where Hu i and Hu j are the recent histories of users u i and u j respectively.

b) Association rules generation Association rules (AR) (cf. definition 2) are useful for analyzing and predicting users' behaviors. They play an important role in data analysis, product clustering, product recommendation, etc.

In order to determine the most used and the closest Web services to a user u i , we will integrate the association rules mining method [START_REF] Piatetsky-Shapiro | Discovery, analysis, and presentation of strong rules[END_REF] into our approach. This method aims at discovering the relations of interest between two or more items. The idea is to find frequent items, associations, correlations, or causal structures from a data collection.

For sake of readability, we recall the definition of the main concepts used in the paper. [START_REF] Piatetsky-Shapiro | Discovery, analysis, and presentation of strong rules[END_REF]. Given: (1) a list of items I, and (2) a set of transactions T where each transaction T is composed of a set of items (T ⊆ I), the goal is to find all association rules that express correlation between the presence of an item with the presence of a set of items.

Definition 2. Association rules

For each association rule R i : X, Y Z, we apply two metrics which are the support(R i ) and the confidence(R i ). The support is used to measure the quantity of population concerned by this rule while the confidence is used to evaluate its statistical significance.

Since our recommendation process should only rely on significant and "valid" associations rules, two thresholds, minsupport and minconfidence, will be used respectively for the support and the confidence of each rule. Hence, each association rule R i with support(R i ) ≥ minsupport and confidence(R i ) ≥ minconfidence is extracted, while other associations will be ignored.

These two thresholds are given by the user according to the nature, type of the underlying data, and the objective of the analysis.

The association rules generation consists of two steps: i) frequent itemsets deduction, and ii) AR mining using Apriori [START_REF] Piatetsky-Shapiro | Discovery, analysis, and presentation of strong rules[END_REF]. As a first step, we define a frequent itemset with a minimum support ≥minsupport. All the items of an association rule should be included in the generated itemset i.e., if {AB} a frequent itemset then {A} and {B} are both frequent itemsets.

In a second step, we will apply Apriori on the obtained frequent itemsets. This algorithm uses breadth-first search and a tree data structure to extract candidate itemsets efficiently. It generates candidate itemsets of length k from the itemsets of length k -1. Then it prunes the candidates that have an infrequent subpattern. It determines all frequent itemsets among the candidates set of itemsets and generates the association rules. Most confident rules will be applied to recommend services for users.

The confidence of each rule R i : S 1 S 2 is measured as follows:

Confidence

(R i ) = , (2)
Where S 1 and S 2 are two Web services, and {S 1, S 2 } a frequent itemset that contains S 1 and S 2 , while {S 1 } is the frequent itemset containing only S 1.

Figure 3. Example of association rules generation

Figure 3 describes the main steps for generating an association rule. Given four users' previous transactions, with a minsupport set to 50% and a minconfidence set to 100%, Apriori generated a valid association rule R 1 : Twitter facebook.

2) Recommendation

The recommendation process (cf. Algorithm 1.) is based on the previously generated association rules. These rules are built up on frequent itemsets of services used by the target user and by his/her neighbors. To recommend a Web service, we need first to process these rules and then to rank them.

a) Association rules Processing Starting from the list of valid rules being generated, a set of candidate Web services to recommend will be selected. This set contains services involved in the consequences of each rule satisfying a friendship condition. A rule is considered to be friendship if and only if it encloses in its antecedents at least one service already used by the target user.

b) Ranking

The final step in the recommendation process consists on ranking the resulted services based on their popularity scores (cf. definition 3). Definition 3. Popularity. The popularity of a service (Pops) denotes the number of previously recorded usages this service has been involved in. A popular service will have a high popularity.

IV. EVALUATIONS

The main goal of our experimentations is to evaluate the user's satisfaction with recommended services. These recommendations are made based on the tracks relationships between users (resp. services).

Our experiments have been conducted on a real-world dataset. We used Tanagra platform 2 for the generation of Association rules, java with SQL Server 2005. We used a dual Core cpu@2.20G PC with 4G RAM, under Windows 7.

A. Dataset

Firstly we give a description of our dataset. The experimental dataset comes from the public Web service registry where Web services, mashups, member profiles can be searched 2 http://eric.univ-lyon2.fr/~ricco/tanagra/ through its own services. All the data are stored in a database of SQL Server 2005 and released as public dataset file on the Internet 3 .

From the all open data, we selected 1000 users who have more than 1 service in their histories of tracks, and 3138 services (include APIs and mashups) are involved by these users. Our dataset is divided into two parts: a testing set covers 20% of most recent published services in the history of each user, and the remaining 80% is a training set.

B. Evaluation metrics

To evaluate the performance and the effectiveness of our recommendation approach, several statistic metrics measures have been applied. Let's note that PR is the set of pertinent recommended services, R the set of recommended services and P the set of pertinent services.

1) Precision

Recommendation precision refers to a ratio of correctly predicted (satisfying user) services to the number of all recommended services. Precision=

| | | |
(3)

2) Recall

Recall refers to the ratio of correctly predicted services to the number of all the services satisfying the user in the testing set.

Recall=

| | | | (4)
The recall and precision are standard metrics to discuss the relevance of the recommended services according to the user's satisfaction.

3) RMSE The Root Mean Squared Error (RMSE) is used in evaluating accuracy of predicted rating (r s ). Let r s = 1 if s ∊ P 0 else .

RMSE=$

∑ ( & ' ,'
)

(
Where N is the number of recommended services.

4) Hit-rank

The hit-rank [START_REF] Deshpande | Item-based top-n recommendation algorithms[END_REF] metric is considered to take into account the ranks of returned services.

ℎ*+ --./0 = 2 * |4| ∑ ∑ 5 6 57 ∈9 [START_REF] Zhang | Web Service Recommendation Based on Watchlist via Temporal and Tag Preference Fusion[END_REF] Where h is the number of relevant services occurring at the positions p 1 ,p 2 , …,p h within the recommendation list; m is the total number of the users and L is the length of the recommendation list (|L| = 10).

Hence, services that occur earlier in the top-10 list are weighted higher than the services that occur later in the list. In order to ensure that our results are not sensitive to the particular training test partitioning of each dataset, we performed 10 different runs for each of the experiments, each time using a different random partitioning into training and test sets.

C. Experimental Setup

Our proposed system is mainly based on the Apriori where the number of generated rules depends on the values of both support and confidence parameters. In order to find the "best" parameters values for WSR-Track performance evaluation, we set the support and confidence configurations as follow: • Support: The number of generated association rules is inversely proportional to the support values, e.g. support=0.5 means that for a service to be considered as common, it must be used by 50% of the neighbors of the user. The higher is the support value, the more relevant rules will be generated. According to our experiments, all the support values beyond 0.6 can generate no more than one or two rules. For example, Apriori generates 200 association rules with a minimum support of 0.3. For the below experiments, we set the support value at 0.5. • Confidence : The number of generated rules is inversely to the confidence values (Figure 4). For our experiments we set the value of the support at 0.5 and the confidence value at 0.9. We used a sample of 30 randomly selected users among 1000 initially selected ones, having 1-30 services in their histories. Each test is repeated 5 times to ensure that results do not depend on the used dataset.

D. Experimental results

Four groups of experiments were conducted to evaluate the performance of WSR-Track system. The first one intends to find out the impact of the neighborhood sizes on both precision and recall. The second one assesses the impact of the number of tracked services in users' histories. The third group evaluates the effect of service popularity and the last one compares our system to other recommendation approaches.

1) Neighborhood size effect

To assess the impact of the target user's neighborhood size on the performance of our system and the precision of the generated recommendations, we randomly selected 30 users that tracked between 1 and 30 services. We repeated our tests using different neighborhood size [START_REF] Eirinaki | A trust-aware system for personalized user recommendations in social networks[END_REF]200] by an interval of 10. As illustrated in Figure 5 and Figure 6, the number of neighbors affects the recommendations accuracy in terms of precision, RMSE and recall. When the neighborhood cardinality size increases, the recommendations provided by our system are more precise and the error rate decreases. For example, more than 60% of recommended services are relevant for a user with 20 neighbors, while this number exceeds 80% of recommended services per 30 neighbors. It was observed that when the number of neighbors is less than 20, the precision value decreases. This result can be vindicated by the fact that with a high number of neighbors, Apriori mines several association rules leading to the improvement of the performance of the recommendation process. Thus, neighborhoods' size may have a positive influence on the recommended services precision. We can conclude that users need to follow at least 20 users in order to get relevant recommended services. Figure 7 shows that the neighborhood size brings a significant positive impact on the hit-rank metric values.

From this, we concluded that we obtain more accurate Web services between the top-10 returned services of recommendation lists when the neighborhoods' sizes increase. 2) Histories size effect We evaluated the effect of the users' histories size on the performance of our system. Figure 8 illustrates the precision and the recall values while varying the size of users' histories. It can be noticed that the variation of precision values is less important from 20 neighbors; therefore we can conclude that, users have to follow at least 20 users to get better recommended services.

3) Service popularity effect

We evaluated the impact of service's popularity on our recommendation system performance. Service's popularity is measured by its number of occurrences in the neighbors' histories.

For each user u, we identified the 5 most popular services in his/her neighborhood. We evaluated his satisfaction when he/she receives these services as recommendations. Figure 9 shows that a user's satisfaction increases when the recommended service is a popular one for his neighborhood. We conclude that the popularity of the service may have a great effect on the quality of recommendations.

4) Comparaison with others recommendations approaches

We compared the proposed approach WSR-Track with known recommendation approaches in the literature using the librec framework 4 namely, i)TrustSVD [START_REF] Guo | Trustsvd: Collaborative filtering with both the explicit and implicit influence of user trust and of item ratings[END_REF] which is a trust-based matrix factorization technique recommendation system that analyzes the social trust data from real-world data sets. This approach considers both explicit and implicit ratings to recommend; ii) Association Rules [START_REF] Piatetsky-Shapiro | Discovery, analysis, and presentation of strong rules[END_REF](AR) which only applies association rules in order to recommend services and (iii) Recommendation of popular services which is the applied strategy by ProgrammableWeb. It recommends the most popular services on the basis of use in mashups. The most popular service is the most used in mashups.

Figure 10. Comparaison with other recommendations approaches

We fixed the neighborhood size to 20 neighbors and the users' histories size to 30. As illustrated in Figure 10, our recommendation algorithm, which is based on Track relationships, provides the best accuracy values compared to others approaches. TrustSVD that is the closest to our system gives good precision values due to the inclusion of trust relations between users and services. But as all rating based approaches, it is not able to recommend services in the lack of rating values or invocation histories. Unlike TrustSVD, our approach provides good results even when users do not have services in their histories. Furthermore, one may notice that Popular, which is the ProgrammableWeb approach, returns the lowest results compared to TrustSVD and WSR-Track. This is due to the fact that Popular does not take into account users' interests and recommends the same services to all users. The results are not personalized.

To summarize, in our recommender system, the relations between users are established offline (track users graph) and updated periodically. Compared to existing CF methods for service recommendation, ours performs better in most cases.

The neighborhood size and the histories size affect positively the accuracy of our approach.

V. CONCLUSION Web service recommendation is still a challenging research issue due to the proliferation of available Web services in a dynamic environment and a variety of user needs. In this paper, we propose a graph-based recommendation method, which takes into account both users' history of service invocation as well as relationships among users (resp. services) based on track relations extracted from a subset of ProgrammableWeb services. We define a heterogeneous multi-graph of users and services that is exploited as follows: detection of neighbors, association rules generation and finally service recommendation. Experimental results show that our approach recommends more new Web services to the users.

Although using graphs to model the Web services ecosystem is not a new idea, from our perspective, this work is a first step towards building a real graph database, along the line of the Linked Data initiative. In future work, we plan to weight edges in using similarity values between users based on their profiles in order to detect the most similar tracked users. We will improve our approach in taking into account users that have no tracking relationships and we will address the cold start problem as well.

Figure 1 .

 1 Figure 1. Users/services' track graph Definition 1. Track Graph. TG=<V,E> is an oriented heterogeneous multi-graph where V = {v 1 , v 2 , …, v m } is a set of m registered users and services, and E={(v i ,v j )| user v i tracks user v j and/or user v i tracks service v j } is the set of oriented relations.Since a user may track Web services and mashups, or create mashups, her/his history is defined by means of her/his followees or the mashups she/he created.

Figure 2

 2 Figure 2 illustrates the main steps of WSR-Track recommendation system.

Figure 2 .

 2 Figure 2. WSR-Track Recommendation Processes

Figure 4 .

 4 Figure 4. Variation of the number of generated rules according to the confidence (support=0.5)

Figure 5 .Figure 6 .

 56 Figure 5. Impact of neighborhood' size

Figure 7 .

 7 Figure 7. Impact of neighborhood size (hit-rank)

Figure 8 .

 8 Figure 8. History' size impact

Figure 9 .

 9 Figure 9. Service popularity effects on Precision and Recall

  4 http://www.librec.net/

http://www.programmableweb.com/

http://www.lsis.org/sellamis/Projects.html#WeS-ReG