Gaëlle Charrier

Antoine Desrues

Céline Barchasz
email: celine.barchasz@cea.fr

Jocelyne Leroy

Renaud Cornut

Bruno Jousselme

Stéphane Campidelli
email: stephane.campidelli@cea.fr

Covalently functionalized carbon nanotubes as stable cathode materials of lithium/organic batteries

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

Introduction

Li-ion batteries are among the most widespread electrochemical energy storage systems. Many portable electronic devices are equipped with these types of batteries, because of their attractive properties: relatively high volumetric energy densities, high operating voltage, good cyclability and low self-discharge. [1][2][3][4] The principle underlying the operation of Li-ion batteries is based on the insertion/deintercalation of Li + into host materials at the anode and cathode. Their energy density is mainly restricted by the specic capacities of these intercalation materials. Today, the performances of Li-ion batteries seem to have reached intrinsic limits (about 250 W h kg À1 ), 3,[5][6][7][8] while costs are still high. As a consequence, research efforts looking for new solutions with higher storage capacity, lower cost, and targeting electric vehicle requirements are ongoing. Li/organic batteries have recently attracted much attention due to the high theoretical specic capacity of organic materials, their low molecular weight, potential low cost and recyclability. [9][10][11][12] At the end of the 90s, research studies on Li/organic batteries started to emerge. Several studies have been devoted to the study of conducting polymers (polyacetylene, polyaniline.) used as positive electrode materials. 10,[13][14][15][16][17][18] Recently, quinones have been identied as attractive materials as they present a characteristic two-electron transfer process accompanied by the capture of two Li ions. [19][20][21][22][23][24][25] They can be integrated as positive electrode materials with good electrochemical reversibility and high storage capacities (theoretical values up to 450-500 mA h g quinone

À1

). 10 Specically, interesting results were obtained recently with anthraquinone either in the monomeric or polymeric forms. [26][27][28][29][30][31][32][33] Yet, several problems have to be solved before commercialization of such systems. First, quinone derivatives and organic molecules in general are poorly conducting. This problem can be partially solved, for instance by the addition of carbon black or metallic additives into the electrode composition in order to improve the conductivity of the electrodes. Besides, an important drawback of the Li-organic batteries arises from the signicant solubility of the molecules in classical organic electrolytes of the batteries, 27,34,35 leading to important losses of the active material from the cathode aer few charge/discharge cycles. A crucial issue is then to nd a way to limit the dissolution of the active material by, for example, anchoring it at the positive electrode and then preserving the system from self-discharge and capacity fading.

In this work, we report the covalent functionalization of multiwalled carbon nanotubes (MWNTs) with an anthraquinone derivative and test the resulting material as a positive electrode in Li-organic batteries. To this end, 2-aminoanthraquinone is transformed into the corresponding diazonium salt and graed to the surface of the MWNTs via the chemical reduction of the diazonium function. 36 For the last 15 years, carbon nanotubes have attracted tremendous attention in the domains of energy production and storage because of their chemical and electrical properties which allow the fabrication of highly conductive and high specic surface area electrodes. [37][38][39][40] Carbon nanotubes have been regularly used in lithium batteries to enhance the electronic conductivity of the materials and to improve the cyclability of the devices. 40,41 Here carbon nanotubes are used as positive electrode materials in lithium organic batteries to ensure the electronic conductivity of the electrode and act as a support for the covalent immobilization of the active material. Charge/discharge tests are then realized on puried and MWNTs graed with the anthraquinone and on MWNTs simply mixed with the anthraquinone, i.e. without covalent graing. The results highlight the fundamental importance of the covalent graing of the MWNTs. Indeed, the anthraquinone molecules remain anchored to the electrodes and the systems remain stable over prolonged cycling and present a promising specic capacity in the range of 110 mA h g electrode

À1

(for a maximal capacity of 260 mA h g À1 for anthraquinone alone, i.e. without carbonaceous additives).

Materials and methods

Characterization techniques

IR spectra were recorded on a Bruker alpha FT-IR spectrometer. XPS: a Kratos Analytical Axis Ultra DLD using an Al Ka source monochromatized at 1486.6 eV was employed. A hemispherical analyzer working at a pass energy of 160 eV was used for the global spectra, and the sole core levels were recorded at 20 eV. Raman spectra were recorded on a Horiba Jobin-Yvon LabRAM ARAMIS with excitation at 532 nm. UV-Vis-NIR absorption spectra were recorded on a Perkin Elmer Lambda 900 UV/VIS/NIR Spectrometer. Electrochemical measurements: preliminary tests were realized before cell assembly on a PGZ301 VoltaLab potentiostat using a classical three-electrode device with Ag/AgNO 3 as the reference electrode and glassy carbon as the counter electrode. The working electrode was composed either of puried MWNTs, functionalized MWNTs or glassy carbon. The electrolyte used was LiClO 4 0.1 M in acetonitrile. Aer coin cell assembly, the electrochemical tests were monitored with an Arbin® battery cycler (at 5 or 50 mA g electrode À1 between 1.5 and 3.5 V vs. Li + /Li).

Purication of carbon nanotubes

Commercial grade multi-walled carbon nanotubes (NC3100™) were purchased from Nanocyl. They were rst puried by an oxidative treatment as follows: 42 MWNTs (100 mg) were dispersed into 35% nitric acid (300 mL) by sonication for 30 minutes. The mixture was reuxed for 8 hours at 110 C. The nanotubes were then vacuum ltered through a 0.45 mm PTFE membrane and washed with deionized water. They were redispersed in NaOH 2 M by sonication for another 30 minutes before being vacuum ltered, washed with deionized water, with HCl 1 M, then water again and nally rinsed with acetone and diethyl ether.

Synthesis of the diazo-anthraquinone 1 43,44 2-Aminoanthraquinone (1 g, 4.5 mmol) was reacted for 1 hour with one equivalent of NOBF 4 (0.52 g, 4.5 mmol) in dry dichloromethane at 0 C. The solvent was vacuum removed and the product was dried under vacuum. The crude diazonium salt was stored at À20 C and used as it is.

Functionalization of the nanotubes 2

Puried MWNTs (10 mg) were dispersed in N-methylpyrrolidone by sonication for 30 minutes. The diazonium salt (275 mg, 1 equivalent per carbon) and a spatula tip of iron powder were then added. The solution was stirred for 12 hours at room temperature. The nanotubes were then vacuum ltered through a 0.45 mm PTFE membrane and washed with HCl 1 M and with deionized water. This functionalization procedure was repeated twice. Self-standing electrodes were obtained aer ltration (16 mm diameter, 2 mg) and were integrated as positive electrodes in coin cells.

Electrode cell assembly

The coin cells were assembled in an argon-lled glove-box using CR2032 casing. 45 Lithium metal foil was used as a negative electrode and Celgard 2400® as a separator. Either puried or functionalized nanotubes were used as self-standing positive electrode materials. A non-woven Viledon® separator (polyolenbased) layer was also added between the positive electrode and the Celgard® layer as an electrolyte reservoir. 150 mL of electrolyte were added into the coin cells before sealing. The electrolyte was composed of lithium bis(triuoromethanesulfonyl)imide (LiTFSI, 99.95%, Aldrich) 1 M dissolved in 50/50 tetraethylene glycol dimethyl ether (TEGDME, stored on molecular sieves, 99%, Aldrich)/1,3-dioxolane (DIOX, anhydrous, 99.8%, Aldrich). The measurements were reproduced on 5 cells fabricated with puried or functionalized MWNTs.

Results and discussion, experimental

The synthesis of the diazonium salt corresponding to the 2-aminoanthraquinone and the functionalization of MWNTs are shown in Scheme 1. The diazonium derivative 1 was characterized by IR spectroscopy. A signal around 2300 cm À1 corresponding to the "N^N + " function appears aer the reaction, indicating the formation of the diazonium salt (see Fig. S1 †). Anthraquinone diazonium salts were then mixed with MWNTs in the presence of iron powder acting as a reducing agent to decompose the diazonium into the radical of anthraquinone that can react on the nanotube surfaces. 36 Qualitative and quantitative analyses were performed before and aer the functionalization step by means of XPS. Fig. 1a andc show the surveys obtained respectively for puried and functionalized MWNTs. The total carbon and oxygen amounts were obtained by dividing the relevant peak integrated areas of well-dened C1s and O1s core level spectra by the appropriate bulk sensitivity factors. For puried MWNTs, the quantity of oxygen is about 5%, due to the formation of oxidized surface terminations such as "C]O" or "COOH" aer the purication process in nitric acid.

Fig. 1b andd show the decompositions of the C1s energy level signals for the puried MWNTs and functionalized MWNTs 2. Five Gaussian-Lorentzian curves were attributed to the various carbon atoms (Csp 2 , Csp 3 , C-O and C]O) present at the surface of the samples. 42,46 Aer the graing reaction, an important increase (up to 13%) of the quantity of oxygen in the functionalized nanotube materials was observed and was attributed to the presence of anthraquinone molecules. SEM images were recorded for puried and graed MWNTs, and they are presented in Fig. 2. Aer the two functionalization steps, the nanotubes are embedded in a thick coating of anthraquinone polymer, conrming the XPS results. The nanotube functionalization was also characterized by absorption and Raman spectroscopy (Fig. S2 †). Aer functionalization with anthraquinone, the D-band, characteristic of the disorder in the sp 2 structure of the nanotube, increased signicantly. However, no specic feature of the anthraquinone was observed. Absorption spectra show featureless decay typical of MWNTs.

The electrochemical activity of the puried and functionalized materials was tested using a classical three-electrode device with a silver reference electrode and glassy carbon as the counter electrode in acetonitrile using LiClO 4 as the supporting electrolyte. 47 First, the puried MWNT sample was used as a working electrode and cyclic voltammetry measurements were recorded (Fig. 3 black curve). No electrochemical activity was detected. In a second time, glassy carbon was used as a working electrode and the cyclic voltammetry of the anthraquinone was performed in solution (Fig. 3 blue curve). A reversible 2-electron reduction peak is observed at À1.10 V with reoxidation at À0.95 V vs. Ag/AgNO 3 . Finally, MWNT/anthraquinone derivatives 2 were tested as a working electrode. The cyclic voltammogram exhibited similar reduction and oxidation peaks at À1.10 and À0.70 V vs. Ag/AgNO 3 , respectively (Fig. 3 red curve). The peaks were attributed to the reduction and reoxidation of the quinone groups, conrming the presence of anthraquinone on the nanotube surfaces and the efficiency of the functionalization method.

Puried and functionalized MWNTs were integrated into coin cells and tested as positive electrode materials in Li/organic cells; charge/discharge proles at 5 mA g electrode À1 are presented in .

For the MWNT-anthraquinone 2 positive electrode materials, a gravimetric energy density close to 240 W h kg electrode À1 can be extrapolated from the average potential and the specic capacity which is competitive with other Li/Organic cathode materials. 10 Remarkably, the functionalized MWNTs 2 show an excellent stability as 98% of the initial capacity is retained aer 50 cycles (Fig. 4c). Prolonged cycling performed at 50 mA g electrode À1 showed that 80% of the initial capacity is retained aer 500 cycles (Fig. 4d), with very limited evolution aer the 100 th cycle.

To highlight the crucial role of the covalent linkage between the nanotubes and the active molecules, MWNTs were simply mixed with anthraquinone and tested in coin cells. A solution of anthraquinone was drop-cast on MWNT electrodes; the resulting mixture contained 50 wt% of anthraquinone which would give a maximal capacity of 130 mA h g electrode À1 . Aer integration as a positive electrode material in a coin cell, discharge/ charge tests were realized (see Fig. 4c and S4 †). Specic capacities of ca. 25 mA h g electrode À1 were obtained. This value is higher than the value obtained for the puried carbon nanotubes (5 mA h g electrode À1 ). Surprisingly, we did not observe a progressive loss of the capacity from 130 to 25 mA h g electrode

À1

during the rst cycles. We believe that the anthraquinone dissolves rapidly in the electrolyte and reacts with the lithium metal electrode, between coin cell fabrication and its electrochemical characterization. This proves that the covalent bonding of the active materials to the nanotubes is of primary importance both for the specic capacity and for the stability of the system. Post-mortem tests supported these conclusions: cells were disassembled aer prolonged cycling and in the case of MWNT/anthraquinone covalently graed 2 no brown coloration of the electrolyte was observed, indicating that the active material does not dissolve during cycling. Covalent bonding of the electroactive molecule to the MWNTs thus solves the principal issues described in the literature for Li/organic systems. 10,34 In order to improve the storage capacity of these materials based on anthraquinone, we tried to reduce the ratio of carbon nanotubes/active molecules. Arc-discharge SWNTs (Carbon Solutions, Inc) and graphene obtained by exfoliation of graphite (NanoIntegris, PureSheet MONO™) were functionalized and tested in coin cells but both materials gave poor results due to the alteration of the conductive sp 2 network during graing and also because of the small particle sizes of exfoliated graphene. An alternative is to use double-walled carbon nanotubes; the proportion of carbon vs. electroactive groups would thus be reduced while conserving the electronic properties of the systems thanks to the presence of non-graed inner walls.

Conclusions

A new positive electrode material for Li/organic batteries has been developed by the covalent graing of electroactive molecules (anthraquinone) to carbon nanotubes. This new material has been integrated into lithium batteries and discharge/charge tests were performed. Our system presents an excellent stability over prolonged cycling, as 98% of the specic capacity is retained aer 50 cycles. This method provides a simple and efficient solution to the issue of the dissolution of the active material in the electrolyte, a well-known problematical phenomenon for Li/organic cells. The storage capacity (equal to 110 mA h g electrode À1 in the present work) can be improved by reducing the ratio between the carbonaceous material and the active functions, or by the use of electroactive molecules exhibiting higher theoretical capacities (e.g. naphthoquinone instead of anthraquinone). Optimization is This journal is © The Royal Society of Chemistry 2016 in progress to obtain the thickest coating as possible, while preserving good charge and mass transport properties. The method developed in this work can be applied for other metals acting as negative electrode materials such as Na and Zn.

Fig. 4a andScheme 1

 1 Fig. 4a and b and S3. † These results show a large increase of the discharge capacity for functionalized nanotubes 2 compared to

Fig. 1 Fig. 2

 12 Fig. 1 XPS surveys of the purified (a) and functionalized MWNTs 2 (c); decomposition of the C1s peaks for purified (b) and functionalized MWNTs 2 (d); the peak at 290 eV comes from the PTFE filtration membrane.

Fig. 3

 3 Fig. 3 Cyclic voltammetry for MWNTs (black line), glassy carbon with anthraquinone in solution (blue line), and MWNT/anthraquinone 2 (red line) in acetonitrile with 0.1 M LiClO 4 as the supporting electrolyte.

Fig. 4

 4 Fig. 4 (a) Charge/discharge profiles as a function of time for purified MWNTs (black) and MWNT/anthraquinone 2 (red) used as a positive electrode material in a Li/organic accumulator (2 mg samples, 5 mA g electrode À1 applied). (b) Discharge curves for purified MWNTs (black) and MWNT/anthraquinone 2 (red) as a function of the capacity. (c) Capacity retention of samples with purified MWNTs (black), MWNTs mixed with the anthraquinone molecule (blue) and MWNT/anthraquinone 2 (red) used as a positive electrode material. (d) Capacity retention over 500 cycles of a sample of MWNT/anthraquinone 2 used as a positive electrode material (50 mA g electrode À1 applied).

Acknowledgements

The authors acknowledge the "Programme Transversal Nanosciences" and the NTE program from CEA (Project Naturalis) for nancial support. The authors would also like to graciously thank Dr Fannie Alloin and Prof. Jean-Claude Leprêtre (LEPMI) for fruitful discussion and collaboration.


Sylvain Petit

Julien Robert

Solene Guitteny

Pierre Bonville

Claudia Decorse

Jacques Ollivier

Hannu Mutka

Michel J P Gingras

Isabelle Mirebeau

Solène Guitteny

Order by Disorder and Energetic Selection of the Ground State in the XY Pyrochlore Antiferromagnet Er2Ti2O7. An Inelastic Neutron Scattering Study

Keywords: number(s): 75, 10, Jm

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Geometrically frustrated magnetism is a forefront research topic within condensed matter physics, as testified by the wealth of exotic phenomena discovered over the past years [START_REF]Introduction to Frustrated Magnetism[END_REF][START_REF] Gardner | [END_REF][3]. For instance, the problem of an XY antiferromagnet on the pyrochlore lattice (the celebrated lattice of corner-sharing tetrahedra) has been considered with much interest since this model displays an extensive classical degeneracy [4,5] along with classical and quantum order by disorder (ObD) effects [4][5][6][7][8][9][10][11][12][13]. The elegant concept of ObD [14,15] is a cornerstone of ordering in frustrated condensed matter systems. ObD comes into play by selecting a ground state, either because fluctuations away from this particular configuration allow for a relative gain of entropy compared to other classically degenerate states, or because quantum mechanical zero point fluctuations define a minimum in the total energy.

Until now, the number of confirmed examples for ObD in real materials have remained scarce [16]. For ObD to be an efficient selection mechanism, the classical groundstate degeneracy must be extremely robust and the minimal theoretical model not openly subject to additional terms that would spoil the accidental emerging symmetry and lift the degeneracy. Recently, the XY pyrochlore antiferromagnet Er 2 Ti 2 O 7 has been proposed as a candidate that satisfies these conditions in a rather compelling way [7][8][9][10]. Given the unique position of Er 2 Ti 2 O 7 among frustrated quantum magnets, it is of foremost importance to scrutinize the soundness of this proposal.

The crystal electric field (CEF) acting on the Kramers Er 3+ ion is responsible for a strong XY-like anisotropy, with easy magnetic planes perpendicular to the local 111 ternary axes [START_REF] Gardner | [END_REF]13]. Combined with antiferromagnetic interactions, an extensive classical degeneracy is expected [4][5][6]13]. Despite this degeneracy, Er 2 Ti 2 O 7 undergoes a second-order phase transition towards an antiferromagnetic noncollinear k = 0 Néel phase at T N = 1.2 K [13,[17][18][19]. In this configuration, denoted ψ 2 and depicted in Fig. 1(a), the magnetic moments are perpendicular to the 111 axes [13,20] and make a zero net magnetic moment per tetrahedron.

A theory based on a Hamiltonian written in terms of interacting pseudospins 1/2, each describing the single-ion CEF ground doublet, along with four anisotropic nearestneighbor exchange parameters (J ±± ,J ± ,J z± ,J zz ), has been proposed for Er 2 Ti 2 O 7 [8]. For the set of parameters determined by inelastic neutron scattering (INS) experiments in a large applied magnetic field [8,21], the theory [8] predicts a quantum ObD selection of ψ 2 , on the basis of a linear spin wave calculation [6][7][8][9], as well as thermal ObD at T c , also selecting ψ 2 [10]. Another consequence of ObD in Er 2 Ti 2 O 7 is the opening of a spin gap, previously inferred from EPR experiments [22] as well as from deviation of the T 3 law in specific-heat measurements [23], and very recently confirmed from INS measurements [24]. However, while the spin gap is a necessary consequence, it is not a definitive proof of this scenario: whatever the mechanism, a spin gap is expected since the ordered ψ 2 ground state breaks a global discrete symmetry [6].

In this work, we follow a different route and consider an anisotropic bilinear exchange Hamiltonian written for the Er 3+ moments along with the CEF contribution (henceforth referred to as model A). As shown in Ref. [25], an energetic selection of the ψ 2 state is possible for a specific range of anisotropic exchange parameters, owing to magnetocrystalline effects described by the CEF (see also Ref. [26]). We model the spin excitation spectra within this CEF-induced energetic selection scenario. The comparison with new INS data allows one to determine a new set of anisotropic exchange parameters. These are compatible with those determined from in-field INS experiments [8] and based on the pseudospin 1/2 Hamiltonian (referred to as model B), from which quantum [7][8][9] and thermal (at T N ) ObD [10] is predicted. Both approaches lead to a spin gap of the correct order of magnitude. However, in model A, the spin gap results strictly from the admixing of the CEF levels via the mean field [25]. Our results revive the debate regarding the ordering mechanism in pyrochlore antiferromagnets and illustrate that the argument of quantum ObD being the chief governing mechanism causing ψ 2 ordering in Er 2 Ti 2 O 7 is not definitive. More generally, they emphasize the limitations of the projection onto the pseudospin 1/2 subspace (shift from model A to model B) with solely bilinear anisotropic spin-spin coupling in describing even qualitatively the physics of highly frustrated rare-earth pyrochlores.

CEF energetic selection mechanism (model A). This approach considers a mean-field anisotropic bilinear exchange

Hamiltonian written for the Er 3+ moments J i at sites i of the pyrochlore lattice (see Refs. [25,26]). It also contains explicitly the CEF contribution, H CEF :

H = H CEF + 1 2 i,j J i • K i,j • J j , (1)
where

H CEF = n,m B nm O nm is written in terms of O nm
Stevens operators [START_REF] Wybourne | Spectroscopic Properties of Rare Earths[END_REF][START_REF] Jensen | Rare Earth Magnetism[END_REF]. The B nm have been determined to fit a number of experiments, including the intensities and positions of the crystal-field levels, as well as the susceptibility [START_REF] Cao | [END_REF][START_REF]The crystal field is modeled by the following coefficients: B 20 = 616 K, B 40 = 2850 K, B 43 = 795 K, B 60 = 858 K, B 43 = -494 K, B 66 = 980 K[END_REF][START_REF][END_REF]. In the following, those values are considered as fixed parameters. K i,j denotes an anisotropic coupling tensor, defined in the ( a, b, c) frame attached to the Er 3+ -Er 3+ bonds [START_REF][END_REF][START_REF] Malkin | [END_REF]. It is described by 3 symmetric parameters, K a,b,c , and an antisymmetric exchange constant (Dzyaloshinskii-Moriya like), K 4 [START_REF][END_REF].

In this model, the molecular field induces an admixture between the ground and excited CEF levels, leading to an effective magnetic anisotropy. This point is best evinced by considering the problem of an Er 3+ ion in a local magnetic field h i : 1(b) shows the ground-state energy of H computed as a function of θ and φ (in the local basis) for a field h = 1 T, which is the actual order of magnitude of the molecular field in Er 2 Ti 2 O 7 (see below). Minima along the sixfold directions of the CEF, slightly tilted away from the XY plane perpendicular to the local [111] direction, are clearly observed. As shown in Fig. 1(c), the tilt grows as h 2 but remains less that 1 • for realistic values of h. The potential well in the vicinity of the minima can be approximated by a highly anisotropic harmonic potential whose curvature along θ (denoted by C θ ) is far steeper than along φ (denoted by C φ ). The average curvature, given by C θ C φ [START_REF] Jensen | Rare Earth Magnetism[END_REF], is approximately 3×10 -2 K at h = 1 T, a value about the same order of magnitude as the one emerging from zero-point fluctuations (quantum ObD) [8].

H = H CEF + g J μ B h i • J i . Figure
Returning to model A, Eq. ( 1), this effective anisotropy combined with appropriate exchange parameters stabilizes the ψ 2 state (note that other phases, namely a canted ferromagnet as well as the antiferromagnetic Palmer and Chalker state can also be stabilized depending on the values of K a.b.c.4 [11,26]). Here, the moment direction at each of the 4 sites of a primitive tetrahedron basis is given by (x,x,y),(-x,-x,y),(-x,x,-y),(x,-x,-y) with y ≈ 2x (in the cubic frame). Note that this is allowed by symmetry for the ψ 2 state, but not for the other component (ψ 3 ) of the 5 two-dimensional representation [33].

The dynamical structure factor S( Q,ω) that exposes the spin dynamics is modeled by a random phase approximation (RPA) calculation (see Refs. [START_REF] Jensen | Rare Earth Magnetism[END_REF]34] and the Supplemental Material [START_REF][END_REF]). For the relevant set of K a,b,c,4 parameters (see below), numerical calculations show the opening of a spin gap RPA G ≈ 15 μeV at Brillouin zone centers. To emphasize explicitly the influence of the CEF levels in causing this gap, calculations have been performed for B nm parameters multiplied by a renormalization coefficient η. This has the effect of rescaling all CEF energy gaps by η. In these calculations, the exchange coupling remains fixed, so that the molecular field and the Néel temperature are essentially unchanged, but the effective magnetic anisotropy inherited by admixing of the ground CEF doublet with excited CEF states decreases with increasing η. S( Q,ω) is also globally unchanged, yet the spin gap gradually decreases and tends to zero for large η. Numerical calculations show that C θ ∼ h while C φ ∼ h 5 /η 4 . Ultimately, as η → ∞, the U (1) classical ground-state degeneracy within the Hilbert space strictly composed of a direct product of single-ion CEF ground doublets is recovered [see Fig. 1(f)]. In that limit, quantum [7][8][9] and thermal [10] ObD would become the sole mechanism able to lift the accidental degeneracy.

Comparison with experiments. To determine the K a,b,c,4 couplings, the INS data were fitted to the calculated S( Q,ω) within the RPA. The neutron measurements were performed on a large Er 2 Ti 2 O 7 single crystal grown with the floating-zone technique. The crystal was inserted in a copper sample holder and attached on the cold finger of a dilution fridge, allowing one to cool the sample down to 50 mK. Data were collected on the IN5 time-of-flight instrument (ILL) which combines high flux with position-sensitive detectors allowing for singlecrystal spectroscopy. Measurements were carried out with an incident neutron wavelength of 6 Å in zero field and under an applied magnetic field of 1.5 and 2.5 T along [1,-1,0]. The spin excitation spectra measured along the high-symmetry directions of the cubic unit cell at 50 mK are shown in Fig. 2. These results compare well with prior measurements (see Ref. [21] and the Supplemental Material of Ref. [8]). Because of the magnetic ψ 2 domains, the identification of the expected four different spin wave branches is not straightforward. This means that the inelastic peaks in Fig. 2 contain several modes within the experimental resolution. This is evidenced in the high-resolution setup, using a wavelength of 8.5 Å. The highly Gaussian (nearly triangular) profile of the resolution line inherent to the counterrotating disk choppers instrument, which yields an energy resolution of about 20 μeV, reveals two acoustic-like modes originating from different magnetic domains (see Supplemental Material). Using the same high-resolution setup, the zero-field data confirm the opening of a spin gap at zone centers: as shown in Fig. 2(c), the energy resolution permits us to discriminate between the inelastic scattering and the strong Bragg intensity at the Q = (111) position. Above the elastic line, the neutron intensity first shows a dip and then a peak, a behavior that is typical of a spin gap. Fitting the data through a Lorentzian profile convoluted with the resolution function [see blue line in Fig. 2(c)] yields exp G ≈ 43 μeV. This value compares very well with previous estimates [22][23][24].

To determine the exchange parameters, we calculate S( Q,ω) assuming an equal population of the six ψ 2 magnetic domains. On the basis of exhaustive calculations as a function of the parameters K a,b,c,4 in zero and applied magnetic field, the INS data were fitted by matching the location of the maximum INS intensity in several directions. A good agreement is found for the following values:

K a ∼ 0.003 ± 0.005 K, K b ∼ 0.075 ± 0.005 K, K c ∼ 0.034 ± 0.005 K, K 4 ∼ 0 ± 0.005 K. ( 2
)
Many others sets that capture independently the magnetization or the excitation spectrum can be found but the present determination provides values that capture all these experimental data [START_REF][END_REF]. With these exchange parameters, the spin gap is evaluated with the RPA at RPA G ≈ 15 μeV, a value smaller than exp G , but of the correct order of magnitude. Discussion. It is instructive to compare our results [Eq. ( 2)] with those found using the pseudospin 1/2 approach (model B) [8]. The corresponding anisotropic exchange Hamiltonian is described in detail in Ref. [8] and is based on the anisotropic couplings (J ±± ,J ± ,J z± ,J zz ) acting between pseudospin 1/2 components written in their local basis. The calculation of the dynamical structure factor for this model was performed within the Holstein-Primakov approximation, using the SPINWAVE software developed at the LLB [35]. Following the same fitting procedure as above, a set of parameters is obtained which largely confirm the results of Ref. [8] (see Table I). The most striking point is that models A and B lead to very similar S( Q,ω). This is due to the fact that both models adopt a predominant effective Hamiltonian with bilinear couplings in terms of pseudospin 1/2 operators when projected in the CEF ground doublet [36]. Specifically, there is a relationship [26] between the two sets of anisotropic exchange couplings based on the g ⊥ and g z Landé factors deduced from the groundstate doublet wave functions [START_REF][END_REF]. Table I, which allows us to compare K a,b,c,4 transformed in the (J ±± ,J ± ,J z± ,J zz ) language with the values determined from model B and from Ref. [8], shows that the sets of values are similar whether determined from either model. Further, owing to the ObD mechanism, model B leads to a spin gap G = 21 μeV [8], a value of the same order of magnitude as the one ( RPA G = 15 μeV) obtained in model A.

While the maps in Fig. 2 demonstrate an overall agreement with experiment, some discrepancies are observed nonetheless, which equally affect models A and B. The most important difference concerns the acoustic-like mode stemming from (0,0,2), which seems to disperse continuously up to 0.45 meV in the neutron data. Within the experimental uncertainty, there is no gap opening when this branch crosses the optical one [see the arrows in Fig. 2(a), left and right columns of the H = 0 panel]. Such a gap opening occurs in the calculations, separating the acoustic branch from a higher energy optical branch. Furthermore, both models predict two well-separated modes at the zone centers Q = (1,1,1), (2,2,0), and (0,0,2) at about 0.45 and 0.5 meV, whereas a single one is observed in experiment [middle column of the H = 0 panel in Fig. 2(a)]. More elaborate models are probably necessary to explain these features, taking into account the long-range part of the dipolar interaction or more complex coupling terms than bilinear ones.

Reference [24] reports the evolution of the spin wave gap as a function of temperature, and ascertains that it varies as the square of the ψ 2 order parameter. The gap calculated in the framework of model A shows instead a linear evolution with the order parameter [see Fig. 2(d)]. The difference between the linear and squared order variations is most pronounced in a narrow temperature range spanning T N to 0.6×T N . Unfortunately, in this temperature range, we believe that the experimental uncertainty in Ref. [24] is too large to allow one to discriminate between the two behaviors. Further experiments are planned to shed light on this issue.

Conclusion.

To conclude, the present study shows that the molecular field induced admixture between CEF levels generates an effective magnetic anisotropy as a plausible mechanism [25] for an energetic selection of the ψ 2 state. The proposed model captures a number of key features of the inelastic neutron scattering data, including the opening of a spin gap. Its order of magnitude shows that the proposed mechanism appears as efficient as the ObD scenario, questioning the completeness of the projected pseudospin 1/2 model [7][8][9][10] as a minimal model of Er 2 Ti 2 O 7 . Our study raises the question of whether cooperating quantum [7][8][9] and thermal [10] order by disorder is the sole or even the principal mechanism for the selection of ψ 2 in this material, and whether its advocacy as a rare example of ObD [7][8][9][10]12] will stand the test of time. On a more positive note, it seems plausible that quantum fluctuations and anisotropy induced by CEF admixing cooperate to select ψ 2 in Er 2 Ti 2 O 7 . Conversely, one might ask whether their competition might be responsible in part for some of the perplexing properties of Er 2 Sn 2 O 7 [26].

FIG. 1 .

 1 FIG. 1. (Color online) (a) Sketch of the ψ 2 magnetic configuration. (b) Illustration of the energetic selection by molecular field induced magnetocrystalline anisotropy: the ground-state energy of Hamiltonian H computed for h = 1 T shows minima along the axes φ = 0,60,120,180 degrees, however slightly tilted out of the XY plane (θ o = 90). (c) shows the corresponding tilt angle as a function of h. (d) and (e) show respectively the curvature along θ and φ of the potential wells as a function of the magnetic field h. (f) shows the evolution of the spin gap as a function of the renormalization η of the Stevens coefficients B nm (see text).

FIG. 2 .

 2 FIG. 2. (Color online) IN5 time of flight spectra taken at 50 mK with an incident wavelength of 6 Å along various directions, in zero field (a) or under a magnetic field of 2.5 T applied along the (1,-1,0) direction (b). S(Q,ω) is shown for the RPA (model A) and spin half (model B), taking into account equipopulated ψ 2 domains, as described in the main text. The global agreement is evident but the arrows point out specific Q regions showing the limits of the two models. (c) INS raw data recorded with an incident wavelength of 8.5 Å at Q = (111) and T = 50 mK showing the spin gap (blue line) at 43 μeV. (d) Evolution of the spin gap and of the magnetic moment in model A as a function of temperature. The saturated moment is 3.7 μ B while T N = 2.1 K (at the mean-field level).

TABLE I .

 I Anisotropic exchange parameters. Units are in 10 -2 meV. Positive values correspond to AF interactions.

	Coupling	Model A	Model B	Ref. [8]
	J ±±	6.1 (±0.1)	4.3 (±0.1)	4.2 (±0.5)
	J ±	7.8 (±0.1)	6.0 (±0.1)	6.5 (±0.75)
	J z±	1.2 (±0.1)	-1.5 (±0.1)	-0.88 (±1.5)
	J zz	-1.2 (±0.1)	-2.2 (±0.1)	-2.5 (±1.8)

Acknowledgments. We acknowledge E. Lhotel, L. Jaubert, and P. McClarty for many useful discussions, as well as F. Damay for a careful reading of the manuscript. We also thank S. Turc (cryogeny group at ILL) for his technical help while setting up the magnet and the dilution fridge. Research at the Perimeter Institute for Theoretical Physics is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation.


Bernard Yannou
email: bernard.yannou@ecp.fr

François Cluzel

Romain Farel

Capturing the relevant

Keywords: Radical Innovation Design, RID methodology, front end of innovation, need seeker innovation, value bucket, dependency structure modeling, usage driven innovation, pain driven innovation

published or not. The documents may come

Introduction

The Dependency Structure Modelling Value Bucket (DSM-VB) is a tool integrated in our Radical Innovation Design (RID) methodology. RID is a structured process for exploring the front end of innovation in need seeker mode. Indeed, the problem setting stage starts with reframing an ideal need, comparable to a box inside which useful thinking is performed in addressing two domains: the domain of problems or pain points, and the domain of situations or usage scenarios. The two spaces -problems and usage scenariosare populated with real world situations. For this purpose, some modeling techniques such as causal graph representations and usage storyboarding are used. A first "ideal performances matrix" of the DSM-value-bucket tool allows problems to be crossed with usage scenarios to express in which usage situations people are subject to pains. Next, existing design solutions -commercial solutions or patents -are identified and their coverage of the two spaces is modeled. Here the DSM-VB tool represents the coverage effectiveness and efficiency of both problems and usage scenarios by two appropriate Yannou B., Cluzel F., Farel R., 2016. Capturing the relevant problems leading to pain and usage driven innovations: the DSM Value Bucket algorithm. Concurrent Engineering -Research And Applications (CERA). matrices: the Solution-Problem matrix and the Usage-Solution matrix. Multiplying both matrices calculates the likelihood for the existing solutions to satisfactorily answer any problem arising during one usage scenario. Subtracting this matrix from the "ideal performances matrix" results in a final "value buckets" matrix, highlighting which problem is worthy of being addressed in an innovation project. The last step of the RID problem setting stage is to select a subset of opportunistic value buckets to consider further in the problem solving stage, so as to ensure radical innovation on "blue ocean" -i.e. not yet explored -usage and problem situations. The DSM-VB tool has been successfully applied to more than 20 innovation projects in more than 15 companies over the past 3 years. In this paper, the DSM value bucket tool is illustrated in the search for radical innovations for a champion handitennis wheelchair. Two important value buckets are detected as crucial to improve the likelihood of victory. It is then shown that creativity workshops starting from these two value buckets lead to several convincing innovations. The DSM value bucket tool opens the possibility of automating radical usage-driven innovations along with systematic investigation and representation of problems or pain points and usage scenarios.

Exploring the front end of innovation

A lot of research has already been undertaken in design engineering for monitoring the design process of a new product. Quality Function Deployment (QFD) and the matrix flow approach of Nam Suh systematic design [START_REF] Suh | Axiomatic Design: Advances and Applications[END_REF] have been extensively used to organize the design process in a data driven manner, from needs to product and process parameters. For instance, a unified information and mapping paradigm for concurrent product/process design is proposed in [START_REF] Aungst | The Virtual Integrated Design Method[END_REF]. But such design methods do not particularly prompt practitioners to explore the causes of needs in different user contexts, and are not especially well-adapted to foster ideation at the time and place it is necessary. They provide frameworks to store data, but no strong frame for innovating. The tools proposed in TRIZ methodology [START_REF] Savransky | Engineering of creativity -Introduction to TRIZ Methodology of Inventive Problem Solving[END_REF] perform root-cause analyses, starting from existing perfectible products (not services) with apparent contradictions. But here, enduser contexts and markets (competitors, existing solutions) are quasi absent. TRIZ is adapted for a class of innovations as little is done to characterize the need opportunities especially in the light of what the other existing solutions are efficient or successful at. For these reasons, the authors also explored the literature in marketing and business administration about the front end of innovation. The front end of innovation is the earliest moment before entering a formal product development process where people try to discover and assess the relevance of innovation opportunities, sometimes called growth territories. Booz and Company stipulates that firms follow at least one of three innovation strategies: Need Seeker, Market Reader, or Technology Driver, depending on whether the focus is on the customer, the market or the technology. In their 2012 innovation report [START_REF] Jaruzelski | The Global Innovation 1000: Making Ideas Work[END_REF], they offer the following definitions:  Need Seekers, such as Apple (US), Dyson (UK) and Decathlon (France), "make a point of engaging customers directly to generate new ideas. They develop new products and services based on superior end-user understanding. Their goal: to seek out both articulated and unarticulated needs, and then to try to get their new products to market first."  Market Readers, such as Hyundai, Caterpillar and Loréal, "use a variety of means to generate ideas by closely monitoring their markets, customers, and competitors, focusing largely on creating value through incremental innovations to their products. This implies a more cautious approach, one that depends on being a "fast follower" in the marketplace."  Technology Drivers, "such as Google and Bosch, depend heavily on their internal technological capabilities to develop new products and services. They leverage their R&D investments to drive both breakthrough innovation and incremental change, in hopes of meeting the known and unknown needs of their customers via new technology." According to this study (see [START_REF] Jaruzelski | The Global Innovation 1000: Making Ideas Work[END_REF]), "following a Need Seekers strategy, although difficult, offers the greatest potential for superior performance in the long term. Fifty percent of respondents who defined their companies as Need Seekers said their companies were effective at both the ideation and conversion stages of innovation, compared with just 12 percent of Market Readers and 20 percent of Technology Drivers. These are the same companies, by and large, that consistently outperform financially." Being predominantly Need Seeker is not easy, and can be done in two ways:

-Using lead-users (see von Hippel [START_REF] Hippel | The age of the consumer-innovator[END_REF]), their insightful refreshing ideas and dreams and their testimonies on usage and pain points. This is the case of Decathlon in France for sports and outdoor equipment. -Having a visionary leader like Steve Jobs (Apple) or James Dyson (Dyson), company growth and the number of product references being limited by the imagination and controlling power of a single brain. There is thus a need for a methodology which investigates growth territories or strategic value niches that generate disruptive innovations beyond current customer expectations. This must be done in a cooperative, multidisciplinary and secure manner. After Motte et al [START_REF] Motte | The specificities of radical innovation[END_REF], it can be done thanks to adapted organization and special methodologies and processes. In terms of organization, Millier [START_REF] Millier | Marketing The Unknown: Developing Market Strategies For Technical Innovations[END_REF] insists on the necessity of managing antagonism and finding a balance between exploration and exploitation of new idea territories. Christensen [START_REF] Christensen | The Innovator's Solution: Creating and Sustaining Successful Growth[END_REF][START_REF] Christensen | The Innovator's Dilemma: The Revolutionary Book That Will Change the Way You Do Business HarperBusiness[END_REF] notes that for disruptive innovations to succeed, companies must not put too much emphasis on customers' current needs, and need to work on how to adopt new technologies or business models that will meet customers' unstated or future needs. In terms of methodology, Christensen [START_REF] Christensen | The Innovator's Solution: Creating and Sustaining Successful Growth[END_REF][START_REF] Christensen | The Innovator's Dilemma: The Revolutionary Book That Will Change the Way You Do Business HarperBusiness[END_REF] proposes the jobs-to-be-done concept, defined as "a framework which is a tool for evaluating the circumstances that arise in customers' lives. Customers rarely make buying decisions around what the "average" customer in their category may do -but they often buy things because they find themselves with a problem that they need to solve. With an understanding of the "job" for which customers find Yannou B., Cluzel F., Farel R., 2016. Capturing the relevant problems leading to pain and usage driven innovations: the DSM Value Bucket algorithm. Concurrent Engineering -Research And Applications (CERA).

themselves "hiring" a product or service, companies can more accurately develop and market products well-tailored to what customers are already trying to do." For this and other works on innovations, Clayton Christensen has been designated as the most influential management thinker in the world (see The Washington Post paper [START_REF] Mcgregor | The world's most influential management thinker?[END_REF]). Ulwick [START_REF] Ulwick | What Customers Want: Using Outcome-Driven Innovation to Create Breakthrough Products and Services McGraw-Hill[END_REF] has extended it in a principle of design-outcome segmentation instead of a conventional a priori customer segmentation. Another recent and popular method for designing a value offer along with its business model is the Business Model Canvas developed by Osterwalder and Pigneur [START_REF] Osterwalder | Business Model Generation[END_REF]. The authors recently refined the process of designing the value offer by designing the fit between a customer profile and a value map (see [START_REF] Osterwalder | Value Proposition Design[END_REF]). A customer profile is defined by three components: pains, gains and jobs (similar to the jobs-to-be-done mentioned above). A value map is made of pain alleviators, gain creators and job contributors. In the following, RID methodology puts the emphasis on pains needing alleviation. Inspired by these ideas, Yannou et al [START_REF] Yannou | Usage Coverage Model For Choice Modeling: Principles[END_REF] and He et al [START_REF] He | Choice Modeling for Usage Context-Based Design[END_REF] have adapted this user-centered perspective to model the market demand model in a design engineering platform through the representation of usage contexts. It is called the Usage Context Based Design (UCBD). Yannou et al [START_REF] Yannou | Set-based design by simulation of usage scenario coverage[END_REF] also proposed the Design by Usage Coverage Simulation principle for evaluating how much a new product or product family [START_REF] Wang | A Usage Coverage-Based Approach for Assessing Product Family Design[END_REF] may cover a number of characteristic usage scenarios . New coverage indicators have been developed. They show that innovative designs may be proved to be dominant i.e. ranked first because performing better, on a subspace of usage situations. These designs are then naturally in a "blue ocean" (after Kim and Mauborgne [START_REF] Kim | Blue ocean strategy -How to create uncontested market space and make the competition irrelevant[END_REF]) which is almost a guarantee of success when launching an innovative offer. A similar principle of satisfactory coverage of usage situations has been followed by Bekhradi et al in [START_REF] Bekhradi | Usefulness Simulation of Design Concepts[END_REF]. Indeed, in the context of fatal falls of elderly people, they simulate how much a product-service design concept can usefully cover most of fall situations while alleviating at best the consequent pains -deaths, lowering of life expectancy, loss of autonomy… -.

Examples of pain and usage driven designs

Let us illustrate how pain driven design processes may lead to successful innovative products. We took three recent innovations from Decathlon and Groupe SEB (France). Each time, let us start with unsatisfactory usage situations corresponding to a clear boundary of experience or needs. The first example is the need to learn how to ride a bike for children. Biking is a widespread leisure activity, and learning how to ride a bike for children corresponds to a widespread social practice. Observing the existing usage situations today, one may notice that the most common current practice is to start biking on a small bike with fixed or removable side wheels for added stability at any time, the pedals being fixed on the front wheel axle or linked to the back wheel by a transmission chain. When asking people what pains exist in different usage situations, they often fail to mention the main pains and always have trouble to quantifying them. However, simple observations of children and parents in public spaces suggest that:

-As soon as removable side-wheels are dismantled: o Children fall, cry, are wounded, and lose confidence. o Parents run after the child, in a bent position, they are anxious and sometimes fall themselves. -Learning with side-wheels takes a long time and does not teach equilibrium.

-In addition, traditional children's bikes around the world (see Figure 1.a) have uncomfortable brake handles articulated with the handlebar through a vertical rotational axis, resulting in a braking system that is both too bulky for children's small hands, and too difficult for a young child to activate. Most of the time, brakes do not deliver an effective service for children.

In 2013, Decathlon designed the Woony bike1 (see Figure 1.c) and protected it with 3 patents. They started from the idea that the most efficient manner to learn equilibrium is the old principle of draisin (see Figure 1.b). A lot of draisins are sold today, but Decathlon's innovation is to accustom children to a draisin and to add, as quickly as in 15 seconds, the two pedals and transmission chain instead of accustoming children to a full bike plus sidewheels. In doing so, a child who trusts his/her draisin may decide by him/herself to add the pedals once the equilibrium is acquired. The result gives immediate confidence with the draisin frame and instantaneous learning of how to pedal. In addition, one patent concerns hand brakes articulated with handles by a horizontal rotational axis, permitting a small hand aperture and weak efforts. What can we conclude from this example? First, that a need seeker oriented design company such as Decathlon starts its design process with observations of typical usage situations and tries to make explicit what people have difficulty expressing because such situations are so natural for them. Second, that it is also very unusual to qualify pains in terms of measurable pain indicators that may be turned into functional specifications. For example, the average number, or distribution of child falls during his/her apprenticeship, the number of parent races, the average number and seriousness of children's injuries, the average total time to learn how to ride a bike. Third, when important pains are detected, a root cause analysis must be systematically completed before starting to design, so as to understand deep pain causes such as, here, the lack of equilibrium when the side wheels are removed. The second example concerns the practice of snorkeling. After statistical investigation, the pain points turn out to be mask condensation, lack of natural inhaling (inhaling through the snorkel with open mouth provoking mouth and tongue dryness), a narrow vision, facial deformation provoked by mask pressure, low visibility of the diver from boats, global anxiety provoked by breathing through the mouth. A root cause analysis of the condensation phenomenon reveals that the air compartment inside a conventional mask, if not renewed, warms on contact with the face causing condensation on the cold surface of the glass or plastic mask. In addition, a lot of people do not try snorkeling despite a desire for underwater exploration due to claustrophobia or a first bad experience. In Blue Ocean Strategy methodology [START_REF] Kim | Blue ocean strategy -How to create uncontested market space and make the competition irrelevant[END_REF], understanding the motivations of these non-clients is a major strategy for innovation without the pressure of competition, because new market territories are always to be conquered. The solution to the whole set of pains has been found with the Decathlon Tribord Easybreath1 mask and snorkel set (see Figure 2.b). Two air compartments separate the eyes (up) and nose and mouth (down). They are separated by valves that allow air flow renewal of the upper eye compartment, forcing the expired hot and humid air out by another external exhaust circuit. Natural breathing by nose or mouth is thus enabled, the air flow from upper to lower compartment preventing the built-up of condensation (Figure 2.a). The product is described in users' blogs as amazing with, in addition, increased visibility and a comfortable sealing joint on the face. Following that maxim, Yannou et al [START_REF] Yannou | Observations from radical innovation projects considering the company context[END_REF] structured the RID process in two macro stages of problem setting (see Figure 4) and problem solving (see Figure 10). Radical Innovation Design® is a methodology for a number of reasons. It is based on structuring principles as well as a stage-and-gate process (see also [START_REF] Cooper | A process model for industrial new product development[END_REF][START_REF] Cooper | Stage-gate system: A new tool for managing new products[END_REF][START_REF] Cooper | Winning at new products: accelerating the process from idea to launch[END_REF]) which is highly detailed in the early problem setting following Cooper [START_REF] Cooper | Predevelopment activities determine new product success[END_REF].There is a list of 9 expected templated deliverables throughout the process. It makes use of two computerized tools, namely the DSM-Value-Bucket tool described in the present paper and the UNPC-monitor tool [START_REF] Yannou | The UNPC innovativeness set of indicators for idea or project selection and maturation in healthcare[END_REF]. We are pleased to report successful implementation in various company contexts since after more than 35 RID innovation projects with 25 companies, several innovations are in the process of being launched on the market.

The goal of RID methodology is to maximize the potential value creation within a legitimate design perimeter called ideal need. RID is a systematic exploration/exploitation process of value creation opportunities through a series of stages making the inventory of usage situations (or scenarios) and pain points (or problems) users may experience. RID uses simultaneously 3 perspectives:

-The perspective of an economist: design is considered as a probabilistic theory of value creation, -The perspective of an industrial designer: design starts with the know-how for observing users -their usages, pain points, needs…-and inventing new usages, -The perspective of a design engineer: knowing how to measure utilities to create, gather evidence and bring serious proofs of concept using the most suitable/appropriate technologies. Yannou et al showed in [START_REF] Yannou | Observations from radical innovation projects considering the company context[END_REF] that the more the design team completes the successive RID deliverables, especially in problem setting, the more likely the innovation outcome will be successfully launched on the market. To that aim, they use monitoring with four proofs to consolidate along the design process: Usefulness, Novelty, Profitability and Concept. This is the UNPC model described in [START_REF] Yannou | The UNPC innovativeness set of indicators for idea or project selection and maturation in healthcare[END_REF]. The problem setting starts with the reframing of the initial idea submitted by the innovation project initiator into an ideal need. Let us take the example of need seeker innovation on the wheelchair of a handitennis champion -an example free of confidentiality rights. It was the actual innovation project initiated by a 22-year old handicapped female student who is nearly ranked 30 th in the world, and who set the objective of winning in the Rio-2016 Paralympic Games. She came with the initial idea of "to develop the lightest possible handitennis wheelchair". Such a goal would have led to a carbon fiber high-tech wheelchair. But making the wheelchair lighter is not an objective in itself, so this was reframed into the following ideal need: "to achieve high-level performance for point in all game situations." This ideal need is a "box perimeter" inside which thorough investigation must be pursued. Contrary to most people on creativity, the authors do not believe that to "think outside the box" is the must, but it is more efficient to "think inside the box, providing the box is large enough and sufficiently well-defined." Continuing with the RID process, two domains (or worlds) are investigated concurrently within the ideal need perimeter (see Figure 4):

-The domain of problems. This consists of inventorying, quantifying and causally ordering the miscellaneous pain points, counter-performances, dissatisfactions, and needs, that users may experience. -The domain of situations. This consists of inventorying, qualifying and dimensioning the usage situations that users experience and in which problems occur with more or less intensity.

Yannou B., Cluzel F., Farel R., 2016. Capturing the relevant problems leading to pain and usage driven innovations:

the DSM Value Bucket algorithm. Concurrent Engineering -Research And Applications (CERA).

Once these two domains are populated with pains and usage situations, a series of matrices (see Figure 5) are built for systematizing detection and prioritization of value buckets worthy of further exploration in creativity sessions. These matrices are filled or computed in the so-called DSM-Value-Bucket algorithm.

Figure 4 The problem setting macro-stage of Radical Innovation Design® methodology

Defining the real world consists of building a causal graph (of problems) and a usage scenarios space of characteristic usage situations (see Figure 4). Next, as existing solutions may partially cover problems in usage situations, a covered causality graph and a covered usage scenario spaces are derived from the careful analysis of the conditions (usage scenarios) and of the effectiveness and efficiency of service delivery (problems/pain points more or less relieved). Next, in the final targeting stage of problem setting, a list of weighed value buckets is derived. This represents the combinations of important problems occurring during very characteristic (frequent) usage situations and for which few existing solutions exist or are really effective/efficient. From this list of value buckets, a perimeter of ambition is defined by the project team, including a) a subset of relevant value buckets, b) other (problems x usage-situations) currently covered by existing situations but that consumers consider as "must have", c) these previous choices being compatible between them and with the present offer portfolio and customer segmentation of the company (represented by "business logics" in Figure 4). This process of resulting in a list of prioritized value buckets is summarized in Figure 5.

Figure 5

The principle of the DSM Value Bucket tool for detecting and prioritizing value buckets worthwhile to further explore in creativity sessions. See also Figure 8 on the example of the handitennis wheelchair.

The problem setting stage for the handitennis wheelchair

The determination of value buckets has been partly automated by a matrix representation of dependencies between problems, usage situations and existing solutions and by handling of three matrices leading to the DSM-Value-Bucket tool. This approach and tool may be affiliated to Dependency Structure Modelling approaches [START_REF] Eppinger | Design Structure Matrix Methods and Applications[END_REF]. In Figure 6, the causal graph is represented as causal paths leading to a point loss problem and it is further graphically covered by four existing solutions. Here, some modeling techniques of causal graph representations are borrowed from the system dynamics practice (see for instance [START_REF] Schaffernicht | Causality and diagrams for system dynamics[END_REF]). For simplicity, we only retain 4 problems out of 16, namely: time loss (moving), injury of the racquet hand, loss of ball power and extended tiredness during the match. In Figure 7, a graphical tessellation of typical usage situations during a match is represented. Proximity of two usage situations means a high probability of time precedence (or in other cases, proximity of user types). For simplicity, we only retain 4 usage scenarios out of 8, namely: serve, shot while on the move, ball reception and starting to move to hit ball.

Yannou B., Cluzel F., Farel R., 2016. Capturing the relevant problems leading to pain and usage driven innovations: the DSM Value Bucket algorithm. Concurrent Engineering -Research And Applications (CERA).

Practically, a pre-screening of problems is undertaken and a first version of the causal graph of problems sketched. Next, the list of typical usage situations is established and, for each usage situation, an observation protocol is designed and followed to (a) get a deep understanding of the pains/problems possibly occurring in this usage situation, (b) measuring them (frequency, repeatability, importance, consequences) and (c) carrying out a root cause analysis. It goes far beyond the classical personas method storyboarding usage situations with weak rationale of situational representativity and no measurements of pain points. For instance, here, the serve situation was carefully studied: gestures were recorded and analyzed, ball speed was measured as well as service accuracy, ability to serve aces, and the double fault rate. In addition, it was observed that a back and forth translation as well as a rotational twist of the wheelchair occurred during the serve. This is obviously due to the translational freedom of the four wheels and the rotational freedom of the two caster wheels. An additional investigation in root causes led to experiment the advantages in blocking the four wheels during serve (+30% in ball speed) or of only blocking the rotation of caster wheels (+20% in ball speed).

Figure 6

The covered causality graph for the handitennis wheelchair issue (refer to Figure 4) Figure 7 The covered usage scenarios space for the handitennis wheelchair (refer to Figure 4)

The DSM Value Bucket algorithm

The determination of value buckets is automated by matrix representations of dependencies between problems, usage scenarios and existing solutions (see simplified Figure 5). Three matrices A, B and C are built along the problem setting stage of the RID process described in previous sections. The first matrix A (see Figure 8) expresses which problems occur during usage scenarios, the second (matrix B) how far existing solutions cover problems and the third (matrix C) to what degree existing solutions are useful in usage situations. Combining these three matrices results in a matrix E of value buckets: this indicates the combinations of important problems occurring during characteristic usage situations and for which few existing solutions are useful or efficient. Matrix A is named the "Ideal performances matrix" and links problems (columns) and usage scenarios (rows) with an intensity scale from 0 to 5 for expressing how much (or often) a problem occurs in a usage scenario. The intensity scale runs from 0=null; 1=weak; 2=moderate; 3=average; 4=important; to 5=very important. For instance (see Figure 8, matrix A):

-The racket hand injury mainly occurs when the player starts moving, pushing with her hand to propel the wheelchair, grasping the racket and the hand rim at the same time. -There is significant power loss during serve due to an uncontrolled twist of the wheelchair.

Yannou B., Cluzel F., Farel R., 2016. Capturing the relevant problems leading to pain and usage driven innovations:

the DSM Value Bucket algorithm. Concurrent Engineering -Research And Applications (CERA).

Matrix B is the "(solutions X problems) matrix" and expresses the relevance of an existing solution for a given problem with the same qualitative scale from null (0) to very important [START_REF] Hippel | The age of the consumer-innovator[END_REF]. For instance (see Figure 8, matrix B):

-The ergonomic hand rim is highly relevant for avoiding racket hand injury.

-The ergonomic hand rim also partly avoids time loss.

-Both the back posture system and the manual lever are good for relieving generalized tiredness.

Matrix C is the "(usages X solutions" matrix" and expresses the relevance of an existing solution in a given usage scenario with the same qualitative scale from null (0) to very important [START_REF] Hippel | The age of the consumer-innovator[END_REF]. For instance (see Figure 8, matrix C):

-The manual lever is very efficient during a start moving situation and moderately so during shot in move. -The back posture system is efficient during the serve situation. At this stage, an "Intrinsic Value Buckets matrix" D is computed as the subtraction between the "Ideal performances matrix" A expressing the importance of problems to solve in usage situations and the matrix multiplication C x B expressing the average relevance of existing solutions in (usage, problem) cases. Of course, this difference is normalized so that each number on both sides of the subtraction has a value between 0 and 1. Moreover, one introduces a "bucket filter" BF, a real number comprised between 0 and 1 (0.5 by default), to eliminate the least important (usage, problem) cases, following formula [START_REF] Suh | Axiomatic Design: Advances and Applications[END_REF].

IVB ij = Max (0, A ij Max kl (A kl ) -2 × 𝐵𝐹 × CB ij Max kl (CB kl ) ) (1)
Finally, the importance of problems (relatively to the ideal need) and the size of usage scenarios are assessed, again using the 0 to 5 intensity scale (see Figure 8, size and importance introduced in the surroundings of matrix D). The rationale for weighting problem importance and usage size must be captured. The RID framework encourages keeping the traceability of exploration/exploitation and decision-making. For instance, the logic for justifying problem importance may be: -Ball power loss and time loss moving should be significantly improved for the player. -Tiredness and hand injury are second order issues for the player. The rationale for justifying the size of usage scenarios may be the scenario frequency (comparing the number of times serving and shooting while in movement) and of its importance for winning a point (80% of serves in handitennis are winning points). Assessment of relative importance of problems and size of usage is based on designers' assessments. In practice, for both weight vectors to come up with, the authors advise to use any kind of pairwise comparison method for transforming multiple pairwise comparison matrices filled by decision makers -designers and/or experts -into a unique weighting vector which is further projected into a 0-5 scale (see for instance [START_REF] Limayem | Handling Imprecision in Pairwise Comparison -For Better Group Decisions in Weighting[END_REF][START_REF] Yannou | The COMPARE method for easy and fast specification and design selection by product pairwise comparisons[END_REF] or [START_REF] Saaty | Ranking by the eigenvector versus other methods in the analytical hierarchy process[END_REF]).

A final "Normalized value buckets matrix" E is computed to augment intrinsic value buckets with importance of problems and size of usage scenarios, following formula [START_REF] Aungst | The Virtual Integrated Design Method[END_REF].

NVB ij = IVB ij × size i × importance j
(2) The whole DSM Value Bucket process is summarized in Fig. 8. Table 1 shows the influence of the Bucket Filter for filtering more or less the value buckets while acting like heat maps. For instance, with a BF of 1.0, only two value buckets are highlighted whereas with a null BF, 12 value buckets are highlighted. The real values contained in the Normalized value buckets matrix have no practical meaning, no unit. This is a ratio scale, they may be relatively compared within a matrix of a given BF value.

Figure 8 The DSM Value Bucket data streaming and computation mechanics (refer also to simplified Figure 5) Two important value buckets were revealed for the handitennis wheelchair project; their matrix coordinates are (1,2) and (3,2) (see Figure 8). The designer team was asked to verbally interpret them and they came up with these natural justifications: -Value bucket #1 (1,2): The loss of power during serve is partly due to the (observed) wheelchair twist. -Value bucket #2 (3,2): The champion player is late into position for receiving the ball, and consequently she returns the ball with power loss; this is due to her right hand grasping the tennis racket and at the same time moving the wheel.

For brevity, these two revealed value buckets are chosen to compose the ambition perimeter. One major characteristic of Radical Innovation Design® is to have a two-stage ideation process (see Figure 9) and to straightforwardly initiate the problem solving stage with as many focused scenario creativity sessions as value buckets in the ambition perimeter. For each value bucket, a brainstorming is done, composed of a divergent and a convergent part. The selection of ideas in the convergent part and the monitoring of idea maturities are aided by the so-called UNPC monitor tool (see [START_REF] Yannou | The UNPC innovativeness set of indicators for idea or project selection and maturation in healthcare[END_REF] for more details). A set of four metrics is used to dynamically investigate the probability of ideas having high impacts on Usefulness, Novelty, Profitability and Concept (UNPC) and increase likelihood for the idea to be transformed into an innovation success on the market. Then ideas are combined into consistent scenarios. For each consistent scenario, a brainstorming is performed, resulting in one or several consistent design concepts. The problem solving macro-stage of Radical Innovation Design® methodology can be summarized by the process shown in Figure 10 which includes the two creativity sessions, a process that is comparable to that of problem setting in Figure 4. Applied to the handitennis wheelchair problem (see Figure 11):

-From value bucket #1 (1,2): 1 usage scenario has been finally selected leading in turn to one design concept. From value bucket #2 (3,2): 2 usage scenarios have been finally selected leading in turn to two design concepts. For Value Bucket #1, the preferred staging of usage scenario is that "The champion positions herself behind the baseline and prepares to serve. She activates a system for blocking the rotation of the two caster wheels. The serve does not provoke any twist but automatically releases the blocking system, allowing her to push the hand rims propelling her on the court." Such a usage scenario must be at this stage a kind of fairy tale, staging the situation with relieved pains and augmented performances -the essential values. The concept creativity provided several architectural designs. The one depicted in Figure 11 has been designed with a CAD tool and is based on the following principles: "The champion activates by a lever two yokes which slide and come in place on either side of the small front caster wheels. A pawl immobilizes the caster wheels during service. The serve generates a torque that deforms the yokes and releases them; they automatically slide up with a spring." For Value Bucket #2:

-The first preferred usage scenario is based on the following story: "Suddenly, the champion does not have the racket in hand anymore when it comes to seize the two hand rims of the chair. The racket disappears temporarily." -The second preferred usage scenario is based on the following story: "The champion is able at any time able to detach her right hand from the right hand rim and then to rest her hand holding the racket or positioning her racket for a shot while allowing the left hand to control both wheels accelerations and decelerations." This usage scenario led to a design concept of a two-rim system for the left-hand wheel, the outer rim controlling the right wheel via an axis between wheels. After verification, it seems that solution has already been patented.

Figure 11

Illustration of the two-stage ideation process (scenario creativity and concept creativity) starting from the two value buckets identified for the handitennis wheelchair

Conclusions

In this paper, we propose a method for structuring and automating the discovery of value buckets during the front end of need seeker innovations. The interest of need seeker innovations was first revealed by, amongst others, Christensen [START_REF] Christensen | The Innovator's Solution: Creating and Sustaining Successful Growth[END_REF][START_REF] Christensen | The Innovator's Dilemma: The Revolutionary Book That Will Change the Way You Do Business HarperBusiness[END_REF] and Ulwick [START_REF] Ulwick | What Customers Want: Using Outcome-Driven Innovation to Create Breakthrough Products and Services McGraw-Hill[END_REF], but these ideas had not been implemented into a design engineering process. RID methodology may be compared to well-known innovative design methodologies (see Table 2) like TRIZ, QFD or axiomatic design and design thinking. Compared to TRIZ, RID uses a causal graph to represent the problem structure, whereas comparable substancefields representations in TRIZ are used for representing imperfect solutions. In the same manner, QFD and axiomatic design may be used to represent the propagation of the voice of the customer into the product components and design parameters, but little is done to characterize problem opportunities, especially in the light of what the other existing solutions use to efficiently perform or "cover". Finally, RID demonstrates that there are other methods than the design thinking prototype-and-learn experimental loop, RID

Figure 1

 1 The children's bike: (a) traditional bike with fixed or removable side wheels (b) the 19 th century dandy horse or draisin (c) Decathlon Woony with adaptable pedal and transmission chain system

Figure 2

 2 Figure 2 Snorkeling solutions (a) Condensation and mouth breathing are common when practicing snorkeling (b) Decathlon Easybreath mask and snorkel set avoids condensation while permitting nose breathing and wide vision.The third example concerns the cooking and eating of French fries. The pains can easily be listed by reference to the traditional fryers which use open or sealed frying of potatoes in an oil reserve (see Figure3.a). These traditional fries are too fatty and unhealthy; the oil reserve must be changed regularly at the risk of intoxication; oil smells bad even with sealed fryers; fryers always present risks of fire, skin burns and child accidents (see Figure3.b). Groupe SEB invented Actifry fryer 1 (see Figure3.c) which demands only one spoon of oil per cook. A new heating principle has been developed along with a continuous move of fries. Healthy fries are now possible without bad smells, oil storage and burn risks.

Figure 3

 3 Figure 3 Cooking French fries (a) traditional fryers designed as oil reserves (b) pains are smelling, oil hygiene, risks of burns and fatty fries (c) Groupe SEB Actifry fryer needing as little as one spoon of oil

Figure 9

 9 Figure 9The two-stage ideation process starting from the value buckets included in the perimeter of ambition

Figure 10

 10 Figure 10 The problem solving macro-stage of Radical Innovation Design® methodology

Table 1

 1 Influence of the Bucket Filter on the Normalized value buckets matrix Yannou B., Cluzel F., Farel R., 2016. Capturing the relevant problems leading to pain and usage driven innovations: the DSM Value Bucket algorithm. Concurrent Engineering -Research And Applications (CERA).

			Time	Power	Tired	Hand
	BF = 0.0	E Serve	loss 0	loss 12	ness 5,4	injury 0
		Shot in move		0	9,6	7,2	0
		Ball receiving		8	12	9	4
		Start moving		3,2	2,4	3	2
			Time	Power	Tired	Hand
	BF = 0.25	E	loss	loss	ness	injury
		Serve		0	10,8 3,51	0
		Shot in move		0	5,12 1,92	0
		Ball receiving	5,2	9,2	5,85	2,9
		Start moving	1,44	0,88	1,5	1,12
			Time	Power	Tired	Hand
	BF = 0.5	E Serve	loss 0	loss 9,6	ness 1,62	injury 0
		Shot in move		0	0,64	0	0
		Ball receiving	2,2	6,2	2,7	1,8
		Start moving		0	0	0	0,22
			Time	Power	Tired	Hand
	BF = 0.75	E Serve	loss 0	loss 8,4	ness 0	injury 0
		Shot in move	0	0	0	0
		Ball receiving	0	3,4	0	0,7
		Start moving	0	0	0	0
			Time	Power	Tired	Hand
	BF = 1.0	E Serve	loss	0	loss 7,2	ness 0	injury 0
		Shot in move		0	0	0	0
		Ball receiving		0	0,4	0	0
		Start moving		0	0	0	0

See video on https://www.youtube.com/watch?v=prAj7K9_hE0

See video at https://www.youtube.com/watch?v=lwf3SOiKo2g#t=18

See https://www.youtube.com/watch?v=nvy6KYPld9k

Yannou B., Cluzel F., Farel R., 2016. Capturing the relevant problems leading to pain and usage driven innovations: the DSM Value Bucket algorithm. Concurrent Engineering -Research And Applications (CERA).

proposing a more systematic and set-based thinking manner to investigate usage and pain driven innovations. The DSM Value Bucket tool was designed three years ago and has already been applied successfully to more than 20 innovation projects with 15 private companies, as well as the "handitennis wheelchair project" presented in this paper (the authors have no nondisclosure agreement). The DSM-VB modeling process and algorithm is a core component of the Radical Innovation Design® methodology. Future research will validate the relevance of the most rated resulting value buckets in the light of effectively launching the corresponding disruptive products.