Jean-David Peltier

Benoît Heinrich

Bertrand Donnio

Olivier Jeannin

Joëlle Rault-Berthelot

Emmanuel Jacques

Cyril Poriel

N-cyanoimine as electron-withdrawing functional group for Organic Semiconductors: Example of Dihydroindacenodithiophene positional isomers

Manipulating the frontier molecular orbitals by chemical design is one of the chief aspect in organic electronics. For an application in the field of n-type organic field-effect transistors (OFET), depressing the LUMO energy level is particularly important to ensure efficient charge injection. In this work, we report the incorporation of electron-withdrawing cyanoimine functional groups on the bridges of dihydroindacenodithiophene regioisomers. Cyanoimines are barely known in the field of organic electronics but herein have been found to be highly efficient to depress the LUMO energy level of an organic semiconductor and can thus be envisaged as an attractive alternative to widely known electron-withdrawing units such as dicyanovinylene. This work focusses on a detailed structure-property relationship study, including incorporation in n-type OFETs, of two dihydroindacenodithiophene regioisomers bearing two cyanoimine groups either in a syn-or an anti-configuration. As far as we know, this work is only the second example reported to date on Ncyanoimines incorporated in n-type OFETs and shows the potential of these functional groups in organic electronics.

Introduction

In the last decades, the development of organic electronics has increased the demand of new organic semiconductors (OSCs) adapted to their use in specific devices such as organic light-emitting diodes (OLED) 1, 2 using either fluorescent 3-5 or phosphorescent [6][7][8][9] emitting materials, organic photovoltaics (OPV) [10][11][START_REF]Solar Cells -New Approaches and Reviews[END_REF] or organic fieldeffect transistors (OFET). [START_REF] Gao | [END_REF][14][15][16][17] The fantastic development of this technology has been possible thanks to a strong synergy between physics and chemistry. The chemists have notably synthesized highly efficient OSCs which are the heart of the devices. The molecular construction of an OSC is often based on the association of a πconjugated fragment on which are attached functional groups to tune electronic/physical properties in order to fit with a precise device. Among the numerous OSCs designed, those based on bridged oligoarylenes and especially on "bridged ter-arylene" such as dihydroindenofluorenyl (IF) or dihydroindacenodithienyl (IDT) derivatives have been the subject of intense researches due to the high versatility of such extended cores. Indeed, IF-and IDT-based materials have found applications in the four main organic devices: OLED, [18][19][20][21][22] PhOLED, 7,[23][24][25] OPV [26][27][28][29][30] and OFETs. [31][32][33][34][35][36][37] The easy modulation of the electronic/physical properties of IF and IDT cores is at the origin of this versatility. Three main design techniques are generally used to tune their properties: (i) modification of the geometry by positional isomerism, (ii) substitution of the constituting aryl units, and (iii) bridges functionalization. Positional isomerism is surely the most original design strategy used in recent years to manipulate the properties of bridged oligoarylenes. 19,21,22,34,[38][39][40][41][42][43][44][45] It consists in modifying the linkages (to modify the electronic coupling between the three constituting aryl units) and/or the ring bridges arrangements (to modify the geometry of the molecules). Indeno[1,2-b]fluorene-6,12-dione 1,2-b-IF(=O) 2 46 (framed in green in chart 1) and s-indaceno[1,2-b:5,6-b′]dithiophene-4,9-dione para-IDT(=O) 2 34,39 (framed in green in chart 2) are the socalled para-anti isomers built on the association of three phenyl units in 1,2-b-IF(=O) 2 or one phenyl unit and two thienyl units in para-IDT(=O) 2 . These units are connected by a para linkage and the two ketone bridges are in an anti-configuration. Both platforms have been widely studied in the last fifteen years and will be discussed below. Their corresponding meta-syn isomers indeno[2,1-b]fluoren-10,11-dione (2,1-b-IF(=O) 2 ) 37 and s-indaceno[1,2-b:7,6-b′]dithiophene-4,6-dione (meta-IDT(=O) 2 ) 34,39 are the second generation of positional isomers, possessing a meta-linkage and a synconfiguration of the bridges (charts 1 and 2). Thanks to the low LUMO energy levels of these four platforms, many efficient electron-poor materials for n-type OFETs, the main topic of this work, have been constructed. However, para-syn isomers 1,2-b-IF(=O) 2 and para-IDT(=O) 2 have been far more studied than meta-syn isomers 2,1-b-IF(=O) 2 and meta-IDT(=O) 2 , see below.

A c c e p t e d m a n u s c r i t p t

The second design strategy is the classical substitution of the three constituting aryl units. In the IF-dione series, the disubstitution of the side phenyl rings of 1,2-b-IF(=O) 2 has widely been studied whereas it is almost absent for its regioisomer 2,1-b-IF(=O) 2 . 23,37,[47][48][49][50] Alkyl chains, 51 amines, 51 halogen atoms 32,52 or substituted thiophenes 53 ' 54 have been for example introduced in 1,2-b-IF(=O) 2 . Recently, Zhan et al have notably reported an 1,2-b-IF(=O) 2 based material possessing S-butyl side chains at C2 and C7 positions displaying an ambipolar character with very high hole and electron mobility µ FE (0.71 and 0.65 cm² V -1 s -1 resp.). 51 Poly-substitutions of the side phenyl units (1,2-b-IF(F 4 )(=O) 2, 32 1,2-b-IF(F 6 )(=O) 2, 32,55 1,2-b-IF(F 8 )(=O) 2 56 ) or of all the phenyl units (1,2-b-IF(I 2 )(F 8 )(=O) 2 , 56 1,2-b-IF(I 2 )(C 12 H 25 ) 4 (=O) 2 57 or 1,2b-IF(I 2 )(C 10 H 21 ) 4 (=O) 2 57 ) have also been described, leading in some cases to highly efficient materials with low LUMO energy level and high µ FE such as in 1,2-b-IF(F 6 )(=O) 2 (LUMO= -3.53 eV, µ E = 0.16 cm² V - 1 s -1 ). 32 Similarly, para-IDT(=O) 2 58,59 (framed in green chart 2) or from its isomer meta-IDT(=O) 2 , (which synthesis has not been reported so far) have followed similar design strategies. 34,39 Disubstitution at C2 and C7 of para-IDT(=O) 2 has been performed for example with ethyl, 60 hexyl 34,[60][61][62] or dodecyl 60 groups. If changing the alkyl groups has a weak impact on the electronic properties of the OSCs, the corresponding OFETs can exhibit drastically different transport characteristics such as shown by Zhang and co-workers. Indeed, electron mobilities decrease from 0.22 cm 2 V -1 s -1 for para-IDT(2,7didodecyl)(=O) 2 to 0.03 cm 2 V -1 s -1 for para-IDT(2,7-diethyl)(=O) 2 60 and to 0 cm 2 V -1 s -1 for para-IDT(2,7-dihexyl)(=O) 2 showing the chief role played by the side chains on the device performance. Alternatively, hexyl groups were also positioned at C3 and C8 of the IDT core (para-IDT(3,8-dihexyl)(=O) 2 ) in order to allow additional substitutions of the central core for example with alkyl chains (para-IDT(2,3,7,8-tetrahexyl)(=O) 2 ) or with thienyl units (para 63 Introduction of thienyl pending units allows to strongly decrease the oxidation potentials from 0.72 V for para-IDT(3,8-dihexyl)(=O) 2 to 0.36 V for para-IDT(3,8-dihexyl)(2,7-terthienyl)(=O) 2 due to the extension of the conjugation. 63 A similar strategy was also employed for DDPP-PhCO by introduction of two diketopyrrolopyrrole-thienyl fragments (chart 2). 33 As for IF series presented above, meta isomer meta-IDT(=O) 2 has been far less explored than para isomer and only 2,8-dihexyl-s-indaceno[1,2-b:7,6-b']dithiophene-4,6-dione(meta-IDT(2,8-dihexyl)-(=O) 2 ) has been reported. 34 The last strategy consists in modifying the bridges. Thanks to the ketone borne by the bridges, 1,2-b-IF(=O) 2 and para-IDT(=O) 2 (or their alkyl substituted analogues) are versatile platforms to introduce other functional groups at the bridges. Difluoromethylene bridges 64,65 in 1,2-b-IF(F 2 ) 2 derivatives (in orange chart 1) have for example been investigated but the most studied chemical modification to generate electron-poor materials is the incorporation of a dicyanovinylene unit 54,66 (see different substituted 1,2-b-IF(=C(CN) 2 ) 2 and para-IDT(=C(CN) 2 ) 2 coloured in blue in charts 1 and 2). The electron-withdrawing effect of dicyanovinylene bridges induces a strong lowering of the LUMO energy level (by more than 0.6 eV) compared to their corresponding diones 1,2-b-IF(=O) 2 /para-IDT(=O) 2 . 34,37 Often, this LUMO levels lowering leads to an important increase of the OFETs performance notably in term of electron mobility. 66,67 For example, para-IDT(=C(CN) 2 ) 2 displays interesting characteristics in n-channel OFET (µ FE = 7.1 × 10 -2 cm 2 V -1 s -1 , I Don /I Doff of 2.3 × 10 7 and subthreshold swing of 1.2 V/dec) 34 31,37 and meta-IDT(= C(CN) 2 ) 2 34 with their low LUMO level (-3.81 and -4.07 eV resp.) have been successfully used in n-channel OFETs and even incorporated in "pseudo-complementary metal oxide semiconductor" inverters. 37 Following these design approaches, very efficient dicyanovinylene-IF-based compounds incorporating thienyl rings, have been synthesized by the groups of Marks, Fachetti and Usta (nC12-TIFDMT, β-DD-TIFDMT, α,ω-2OD-TIFDMT, α,ω-2EH-TIFDMT) 66,68 reaching very high electron mobility (0.11 cm 2 V -1 s -1 for α,ω-2OD-TIFDMT 68 for example). These works have highlighted the importance of the position of the alkyl chains on the device performance. However, in the field of OFETs, the molecular diversity of the electron-withdrawing groups incorporated on the bridges of dihydroindenofluorene or dihydroindacenodithiophene fragments is very limited and even almost exclusively based on dicyanovinylenes and ketones. In 1983, a N-cyanoimine group, which is the association of a nitrile group to a sp 2 nitrogen atom has been introduced on the bridges of a structurally related dihydroindeno[2,1-a]indene. 69 In 1984, the potential of this unit as electron acceptor was envisaged. 70 However, only few examples have been reported to date (cyclohexadienes, 70 dihydroanthracene, 71,72 spiro[5,5]undecatetraene 73 benzodifuran 74 or benzodithienyl). [74][75][76] As far as we know, no precise structure-properties-device performance relationship study on this interesting functional group has been done and only one example of OFET is reported using thiophene-fused dicyanoquinonediimine. 76 The electronic and physical effects of Ncyanoimines on the bridges of π-conjugated systems are therefore rarely reported. The present work will focus on this feature and aim at exploiting the lack of efficient functional groups used to depress the LUMO energy level of bridged OSCs. We provide herein a detailed structureproperties-device performance relationship study including synthesis, physicochemical properties (electrochemistry, absorption spectroscopy, powder and single crystal X-ray diffraction, differential scanning calorimetry), molecular modelling (DFT and TD-DFT) and incorporation in n-type OFETs (using SU-8 as insulator and with selfassembled monolayer of 4-(dimethylamino)benzene thiol) of two IDT regioisomers possessing N-cyanoimines on the bridges namely para-IDT(=NCN) 2 and meta-IDT(=NCN) 2 (framed in red chart 2). In these examples, we notably show that N-cyanoimines display interesting packing characteristic, are thermally stable, and as efficient as dicyanovinylenes to depress the LUMO energy level of bridged OSCs and can be successfully introduced as active layer in n-type OFETs with low subthreshold swing.

-IDT(3,8- dihexyl)(2,7-dithienyl)(=O) 2 or para-IDT(3,8-dihexyl)(2,7-dioligo- thienyl)(=O) 2 ).

Results and discussion

Synthetic procedures

Scheme 1 Synthesis of para-IDT(=NCN) 2 (top) and meta-IDT(=NCN) 2 (bottom).

In materials science, a key feature for chemists consists in synthesizing target OSCs in a short and highly efficient manner and if possible by using common synthetic intermediates. Herein, para-IDT(=NCN) 2 and meta-IDT(=NCN) 2 were obtained from their corresponding diones para-IDT(=O) 2 and meta-IDT(=O) 2 synthesized at the gram scale from diester 1 or 2 as previously reported. 34 These diones are also central building blocks in the synthesis of dicyanovinylene analogues para-IDT(=C(CN) 2 ) 2 and meta-IDT(=C(CN) 2 ) 2 . 34 Thus, non-enolizing diones para-IDT(=O) 2 and meta-A c c e p t e d m a n u s c r i t p t IDT(=O) 2 react with N,N-bis-(trimethylsilyl)carbodiimide in the presence of titanium tetrachloride [70][71][72]76 to provide target para-IDT(=NCN) 2 and meta-IDT(=NCN) 2 as green-brown powders with good yields of 61 and 70 % respectively ( Scheme 1). These syntheses are short (4 steps), easy to perform and possess good overall yields of 20% and 32% for para-IDT(=NCN) 2 and meta-IDT(=NCN) 2 respectively. It is important to note that both compounds were more soluble in common organic solvents than their dicyanovinylene analogues para-IDT(=C(CN) 2 ) 2 and meta-IDT(=C(CN) 2 ) 2. 34 These compounds will be used herein as model compounds to evaluate the impact of the cyanoimine group on the properties.

Molecular conformation and self-assembling

Single crystals of para-IDT(=NCN) 2 and meta-IDT(=NCN) 2 were obtained from chloroform/methanol mixture (Figs. 12345).

Para-IDT(=NCN)

2 crystallized in the P-1 space group with one molecule per asymmetric unit (Fig. 1, top). The central parasubstituted IDT core (rings 1 to 5) has a length of 10.55 Å similar to those previously reported in literature for structurally related compounds. 39,77 Due to the para linkage, the central parasubstituted IDT core is almost flat with small dihedral angles of 0.15° between the two mean planes of the thienyl rings 1 and 5 and that of the central phenyl 3 (a distance of 0.026 Å between the two mean planes of the thienyl units, which are parallel, is measured). The distance between the two nitrogen atoms of the N-cyanoimine groups and the mean plane of the para-IDT core are for both measured at 0.03 Å for the nitrogen atom of the imine group and at 0.06 Å for the nitrogen atom of the cyano group showing that the cyanoimine groups are nearly in the mean plane of the para-IDT core. The planarity of the para-IDT core in para-IDT(=NCN) 2 is even more marked than that observed for identical para-IDT cores possessing different bridge functionalization. For a para-IDT core substituted on the bridges with tolyl units, 77 Wong and coworkers have indeed reported an angle of 2.68° between the two mean planes of the thienyl units and that of the central phenyl ring. Our groups have shown that para-IDT core may even be more deformed with rigid spiro-connected fluorene units in the bridges(angle of 3.39°). 39 This shows that the bridges can modify the planarity of the IDT cores by packing forces and/or intramolecular interactions. It should indeed be mentioned that cyano of the cyanoimine groups exclusively point toward the sides of the molecules due to intramolecular "short contacts" (corresponding to an interatomic distance inferior to the sum of the Van der Waals radii of the involved atoms) between the carbon atom of the cyano units and the carbon and hydrogen atoms in β position of the thienyl rings (Fig. 2, top). No intramolecular interaction is observed between the para-IDT core and the hexyl chains.

Meta-IDT(=NCN)

2 also crystallized in the P-1 space group with one molecule by asymmetric unit (Fig. 1,bottom). The central meta-IDT core of meta-IDT(=NCN) 2 (rings 1-5) has a length of 9.98 Å, which is shorter than that of para-IDT(=NCN) 2 (10.55 Å) due to the different linkage (para vs meta) of the central phenyl ring. A similar influence of the linkages has been previously shown with other bridged πconjugated systems such as dihydroindenofluorenes. 22,24,25 As observed for its para isomer, meta-IDT(=NCN) 2 is almost planar with very weak angles between the plane of phenyl ring 3 and those of each thienyl ring 1 and 5 (1.2 and 2° resp.). Note these angles are nevertheless higher than that measured for para-IDT(=NCN) 2 (0.15°, see above). Another deformation is observed in meta-IDT(=NCN) 2 with an angle of 3.41° detected between the mean plane of thienyl ring 1 and thienyl ring 5. This feature differs to what is observed in para-IDT(=NCN) 2 were the two thienyl rings are in two parallel planes. The distances between the two nitrogen atoms of the imine groups and the mean plane of the meta-IDT core are different for the two bridges (0.07 / 0.03 Å for the nitrogen atoms of the imine and 0.30 / 0.15 Å for the nitrogen atoms of the cyano groups). Thus, the imine groups are pointed out of the mean plane of the meta-IDT core on the same side of this plane and in opposite direction of the hexyl units. As for the para isomer, the terminal cyano groups point exclusively towards the sides of the molecule due to intramolecular interactions between the carbon atom of the cyano units and the carbon and hydrogen atoms in β position of the thienyl rings (Fig. 2, A c c e p t e d m a n u s c r i t p t bottom). Additionally, some intramolecular interactions are also observed between the meta-IDT core and its two hexyl chains that appear differently bent. One of the most important features is linked to the different supramolecular organizations of the two isomers, para-IDT(=NCN) 2 and meta-IDT(=NCN) 2 , described below. These structural features can be assigned to the different geometry of the two cores and the resulting position of the two imines, in an anti (para-IDT(=NCN) 2 ) or in a syn configuration (meta-IDT(=NCN) 2 ). Many intermolecular "short contacts" are detected in the packing diagram of both para-IDT(=NCN) 2 (Fig. 3) and meta-IDT(=NCN) 2 (Fig. 4). Interestingly, these intermolecular interactions appear to arise from different atoms for the two isomers, which explain the different packing diagrams discussed below. Some short contacts are particularly detected for the three atoms of the imine group clearly highlighting the importance of the bridge functionalities in the packing diagram. The exhaustive list of the short intermolecular distances is gathered in ESI.

One may additionally note that the inter-planar distance between two para-IDT cores and three stacked meta-IDT core are short: 3.41 Å in para-IDT(=NCN) 2 and 3.36 or 3.37 Å in meta-IDT(=NCN) 2 (Fig. 5).

In the light of Janiak's works, 78 detailed in ESI, centroid-centroid distances, vertical displacements and ring slippage angles between cofacial thienyl and phenyl rings (rings 1/1', 2/2' and 3/3' for para-IDT and rings 1/1', 2/2' and 3/3' or rings 1'/1'', 2'/2'' and 3'/3'' for meta-IDT cores) have been measured clearly highlighting strong intermolecular interactions (see values in ESI).

Molecular self-organization in the crystalline and mesomorphic states

Thermal behaviour. The two isomers were investigated by thermogravimetric analysis (TGA), differential scanning calorimetry (DSC) and small-and wide-angle X-ray scattering (S/WAXS). Both compounds start to degrade above 250 °C and possess high 5% weight temperatures T d (at around 364 and 365 °C respectively, for the para-and meta-isomer, see TGA traces in Electronic Supplementary Information (ESI) showing a high thermal stability of both compounds, even slightly higher than the one of para-and meta-IDT(=C(CN) 2 ) 2 34 (T d recorded around 349 and 352 °C resp.). As thermal stability is a key feature for Organic Electronics, TGA traces show that N-cyanoimine groups are appealing from this point of view.

Fig. 6. DSC traces of IDT(=NCN) 2 regioisomers (1st heating run (black) and cooling run (red) at 5°C/min, endotherm up); Cr: crystalline phase; Mes: meso phase.

As observed in DSC traces at the first heating curves presented in Fig. 6 (see the second heating curves in ESI), para-IDT(=NCN) 2 melts at 139 °C (∆H = 25 J/g), far above its isomer meta-IDT(=NCN) 2 (52°C, ∆H = 28 J/g) which indicates stronger cohesion of its crystalline selforganization. As a matter of fact, both compounds exhibit even lower melting temperatures than their diketone or dicyanovinylene analogues (around 170 °C for para-IDT(=O) 2 and para-IDT(=C(CN)

2 ) 2 34 ; around 145 °C for meta-IDT(=O) 2 and meta-IDT(=C(CN) 2 ) 2 ) 34 whereas cyanoimine groups like dicyanovinylenes, give rise to strong molecular association through dipolar interactions. This feature indeed explains that the positional long-range order persists for IDT(=NCN) 2 and IDT(=C(CN) 2 ) 2 derivatives above the melting temperature, within broad mesomorphic ranges extending to above 250°C. IDT(=O) 2 derivatives in contrast do not give rise to such strong dipolar association and directly melt to the isotropic liquid phase. The early melting of the crystalline structures of IDT(=NCN) 2 derivatives is therefore not a matter of molecular association strength, but likely of sterically constrained crystalline selfassembling. Molecular self-organization. The self-organization of both IDT(=NCN) 2 regioisomers was investigated by S/WAXS in crystalline and mesomorphic states (Fig. 7). Similarly to the previously reported IDT(=C(CN) 2 ) 2 , 34 all states consist in lamellar structures, defined by the alternation of layers of conjugated cores and aliphatic tails (Fig. 8). While the previous derivatives only crystallize into fine powdered solids unsuitable for single-crystal investigation, the single-crystal structures obtained for IDT(=NCN) 2 gives access to the detailed molecular self-assembling within lamellae and to the three dimensional structure formed by the superposition of lamellae.

- -------------------------------------------------------------------- In both isomeric structures, the core layers present a ribbon substructure emerging from the π-stacking of the lath-like fused-rings into columns that alternate with parallel strips of =NCN groups, selfassociated with dipolar interactions. The π-stacking distances perpendicular to the ring planes (hπ = 3.25-3.3 Å) are moreover similar, leading to equivalent compactness (para-IDT(=NCN) 2 : ρ = 1.305 g/cm 3 ; meta-IDT(=NCN) 2 : ρ = 1.298 g/cm 3 ). Yet, the arrangements in the lamellar plane are different, due to connection of =NCN groups on either both sides or identical side of the rigid core. Their connection on opposite sides in the para configuration authorizes unique core orientation and arrangement in a single-molecule a×b sublattice. In the meta configuration, the unsymmetrically substituted cores have to revert their orientation in the sublattice plane to allow their compact association into dipolar strips. This implies sublattice and thus cell doubling, which in this particular structure occurs in the direction of the rows of π-stacked molecules, through their alternated lateral orientation. As a result, substituents are equally distributed on both sides of rows and are engaged in symmetrical dipolar strips, maintaining the structure periodicity to a single row. In addition, if the dipolar association induces comparably large tilt angles of cores within layers in both structures (ψ = 44-45° for para; ψ = 40-41° for meta), the directions of tilt in the layer plane are turned for the two row configurations. The para IDT cores are tilted in the stacking direction (i.e. along a-axis), presumably because tilting in another direction would impact negatively on the dipolar association, as each molecule is engaged in two strips through the antiparallel alignment of the =NCN groups. The constraints on the tilt direction are released for the meta isomer, so that a different direction is effectively observed, affecting the area projected on the lamellar plane (stacking and ribbon periodicities for para: h stack = 4.896, d rib = 8.824 Å; for meta: h stack = 3.457, d rib = 9.827 Å). Finally, it should be mentioned that the molecular area A mol , ratio of molecular volume V mol and periodicity d, of para-IDT(=NCN) 2 (A mol = 40.29 Å 2 ; σ c = A mol ×cos(ψ) = 28-29 Å 2 ) exceeds the section of ca. 2×18.5 Å 2 for two crystallized chains 79 and that a compact intercalated monolayer of chains is effectively formed in this case, whereas this threshold is not reached for the meta isomer meta-IDT(=NCN) 2 (A mol = 34.90 Å 2 ; σ c = 26-27 Å 2 ) and chains accordingly arrange in strongly tilted double-layers (Table 1). 80 Table 1 Structural parameters of the triclinic structures adopted by meta-and para-IDT(NCN) 2 in the single crystal state at -123°C, in the crude powder at 20°C and in the mesophase at 190°C, whereas indexation of the room temperature pattern of paraisomer failed, presumably due to coexistence of several modifications: a, b, c, α, β, γ, V, Z and ρ are the parameters, volume, number of molecules per cell and density of the triclinic lattices; d 001 and Z L are the cell periodicity along the sequence of molecular layers and the number of involved layers; A and Z A are the area of the sublattice formed by the lateral arrangement of molecules and the number of involved molecules. same triclinic structure as in the single-crystal state, with only slight deviations of the lattice parameters due to thermal expansion (Table 1). The powder melts at low temperature to a pasty-like solid, identified to a mesophase with a high degree of positional order. The mesomorphic nature of this phase is indeed confirmed by the appearance in the S/WAXS patterns of the broad scattering signal h ch , corresponding to the molten chains, while the numerous sharp reflections (Fig. 7) indicate that the IDT(=NCN) 2 cores remain organized in a long-range correlated three-dimensional cell, throughout the molten chains layers. The cell geometry turned out to be triclinic, with an a×b sublattice close to that of the crystalline powder. Impressively, there is almost no variation of A mol between crystal and mesophase, suggesting that the internal structure of the core layers is hardly affected by the melting process (Table 2). The main alteration of the geometry, with respect to crystal, is an increase of the lamellar periodicity that follows the higher volume contribution of molten chains and the thermal expansion. The further structural change consists in the doubling of the lattice along c-axis, meaning that the cell now includes two laterally shifted lamellae. In contrast, the structure of para-IDT(=NCN) 2 in the powder crystalline state is obviously very different from that of its single-crystal structure, as deduced from the composition of the room-temperature S/WAXS pattern. Indexation trials failed, possibly because of the coexistence of several crystalline states. On heating, the crystalline powder melts to a highly ordered triclinic mesophase similar to that of the meta isomer, with in particular the same numbers of lamellae per cell and of molecules per sublattice, and quite comparable lattice parameters. The main difference between both regioisomers comes down to slightly less expanded lamellae for the para-isomer in the mesomorphic state and on the contrary to more expanded lamellae in the crystalline state, in relation with the formation of an intercalated aliphatic layer. This configuration is expectedly less cohesive than the bilayer of strongly tilted chains of the meta-isomer, which is presumably one main cause for its lower melting temperature.

Table 2. Geometrical parameters of the self-organization of meta-and para-IDT(=NCN) 2 in the single crystal state at -123°C, in the crude powder at 20°C and in the mesophase at 190°C, and comparison with meta-and para-IDT(=C(CN) 2 ) 2 : d = d 001 /Z L is the periodicity of the lamellae formed the alternation of IDT and aliphatic layers, V mol = V/Z is the molecular volume (values for meta-and para-IDT(=C(CN) 2 ) 2 are calculated using reference volume data), A mol = V mol /d is the molecular area, i.e. the average area covered by a molecule in the plane of the layers.

Finally, the use of cyanoimine groups instead of dicyanovinylene maintained the broad-range lamellar mesomorphism, with only a slightly higher lateral expansion of lamellae (Table 2). A major contribution to this higher A mol is obviously the tilted directions of cyanoimine groups that induce the tilting of the whole core, whereas dicyanovinylene groups are essentially orthogonal to the core axis. Beyond these details, the self-organization of the four compounds appears thus rather comparable.

Electrochemical properties.

Electrochemical studies of the two isomers were performed in Bu 4 NPF 6 0.2 M /CH 2 Cl 2 solutions at a concentration of 10 -3 M for meta-IDT(=NCN) 2 and of 0.5 × 10 -3 M for para-IDT(=NCN) 2 . The cyclic voltammetries (CVs) are presented in Fig. 9. All the peak potentials obtained from the CVs are summarized in Table 3. Both compounds present similar CVs with two reversible reduction waves between 0.0 and -1.0 V and one weakly reversible oxidation wave with a maximum around 1.46 V for para-IDT(=NCN) 2 and at 1.7 V for meta-IDT(=NCN) 2 . In oxidation, both compounds display an oxidation at higher potential values than those recorded for their structurally related analogues para-and meta-IDT(=C(CN 2 ) 2 ) 34 (Table 3). The onset oxidation potentials of the present cyanoimines based compounds are indeed shifted by 80 mV in the para-series (from 1.24 to 1.32 V) and by 160 mV in the meta-series (from 1.40 to 1.56 V) compared to their dicyanovinylene analogues. As this oxidation wave can be assigned to an electron transfer centred on the IDT core (see the electronic distribution of the HOMO, Fig. 10), the potential difference may be assigned to a stronger electron-withdrawing effect of the cyanoimine units compared to the dicyanovinylene units. Surprisingly, this effect does not significantly exist in reduction, as both isomers present a very similar onset reduction potential at ca -0.3 V (-0.27 V for para-IDT(=NCN) 2 ) and -0.33 V for meta-IDT(=NCN) 2 ). The electronic distribution of the LUMOs is identical for both isomers and centred on the two cyclopentadienyl-Ncyanoimine rings (Fig. 10). Since the side phenyl rings are not involved in the LUMO distribution, this feature explains why the onset reduction potentials are very similar for both isomers. From the onset oxidation and reduction potentials recorded at 1. The difference between the HOMO energy levels of para-and meta-IDT(=NCN) 2 is assigned to a disruption of the conjugation in the latter due to the meta connection between the phenyl and the thienyl rings and the resulting partial electronic decoupling (note that in the light of recent works, the π-conjugation is not completely interrupted by a meta linkage and has a different influence on singlet and triplet energies and on HOMO/LUMO energy levels 38 ). Indeed, in the case of meta-IDT(=NCN) 2 , there is a conjugation breaking in the middle of the central phenyl of the meta-IDT core (see electronic distribution of the HOMO Fig. 10, bottom) leading to a deeper HOMO level compare to its para isomer (-5.96 vs -5.72 eV). The energy difference between the two HOMO levels (0.16 eV) is similar to that calculated for the two IDT-dicyanovinylene (0.17 eV) confirming that the IDT core is at the origin of this feature and not the bridge functionalization.

Structure type T [°C] d [Å] Vmol [Å 3 ] Amol [Å 2 ]

meta-IDT(=NCN)2 para-IDT(=NCN)2

The electrochemical gaps of both para-IDT(=NCN) 2 and meta-IDT(=NCN) 2 are very short, 1.59 eV and 1.89 eV respectively and the difference between the two isomers is mainly assigned to the different HOMO energy (difference of 0.24 eV). In addition, one can note that the LUMO energies of para-and meta-IDT(=NCN) 2 are very similar to those of para-and meta-IDT(=C(CN 2 ) 2 ), indicating that the bridge functionalization by =C(CN) 2 or by =NCN leads to similar electronic effects on the LUMO energy. This is an important finding in this work, which shows the strong potential of cyanoimine groups to depress the LUMO level of a bridge ter-arylene. Thus, the gap of such bridged ter-arylene can be tuned either by positional isomerism (geometry) or by bridges functionalization, which both influence the HOMO energy without altering the LUMO energy. The trend observed for the electrochemical HOMO/LUMO energy levels is in accordance with that obtained from theoretical calculations (Fig. 10 and Table 3).

The HOMO of para-IDT(=NCN) 2 (Fig. 10, top) is dispersed on the IDT core with a delocalization over the whole IDT core and the HOMO of meta-IDT(=NCN) 2 (Fig. 10, bottom) presents a clear π-conjugation interruption at the two opposite carbon atoms of the central phenyl ring (nodal plane). This difference leads to a deepening of the calculated HOMO energy from the para-to the meta-isomer (-6.17 eV / -6.32 eV) due to the partial electronic decoupling occurring in the latter. The energy difference between the two HOMO levels (0.15 eV) is similar to that calculated for the two IDT-dicyanovinylene (0.17 eV) confirming that the IDT core is at the origin of this feature and not the bridge functionalization. In contrast the LUMO are mainly localized on the two cyclopentadienyl/cyanoimine cores (Fig. 10) with LUMO energies calculated at -3.95 and -3.89 eV for the paraand meta-isomer respectively. Both compounds present intense and well defined absorption bands between 300 and 550 nm (307, 322, 347(sh), 387 (sh) nm for para-IDT(=NCN) 2 and 315, 404, 478, 502 for meta-IDT(=NCN) 2 ) and very weak absorption bands at lower energy (Inset Fig. 11, maximum recorded at 711 nm for para-IDT(=NCN) 2 and at 599 nm for meta-IDT(=NCN) 2 ). These low energy bands were assigned to a HOMO/LUMO transition possessing a very weak oscillator strength (λ: 793 nm/f:0.0306 for para-IDT(=NCN) 2 (Fig. 10, top); λ: 704 nm / f:0.006 for meta-IDT(=NCN) 2 ) Fig. 10, bottom). The very weak oscillator strengths of this transition can be explained by the absence of significant overlap between the HOMO (located on the IDT core) and the LUMO (located on the cyclopentadienyl-cyanoimine ring). Therefore, this transition presents a strong charge-transfer character. Compared to the HOMO-LUMO transitions recorded for para-IDT(=C(CN) 2 ) 2 and meta-IDT(=C(CN) 2 ) 2 , 34 these transitions are shifted to lower wavelengths (from 743 to 711 nm in the para-series and from 630 to 599 nm in the meta-series). The blue shift of ca 30 nm from dicyanovinylenes to cyanoimines is consistent with a shorter π-conjugated pathway in the latters, which is caused by the bridges functionalization. From the onset of these low energy bands, the optical gaps of para-IDT(=NCN) 2 and meta-IDT(=NCN) 2 were respectively determined at 1.41 eV (λ onset =879 nm) and at 1.61 eV (λ onset = 770 nm) both being shorter than their dicyanovinylenes analogues (1.29 /1.57 eV for para-IDT(=C(CN) 2 ) 2 and meta-IDT(=C(CN) 2 ) 2 ). 34 In addition, the transition possessing the largest oscillator strength for both isomers (para-IDT(=NCN) 2 : λ = 321 nm, f = 1.6648 ; meta-IDT(=NCN) 2 : λ = 312 nm, f = 1.5283) involves a major contribution of HOMO/LUMO+2 with both molecular orbital located on the IDT core. This calculated transition are in accordance with the more intense absorption bands recorded at 322 nm for para-IDT(=NCN) 2 and at 315 nm for meta-IDT(=NCN) 2 .

In the solid state (thermally-evaporated thin film possessing a thickness of 40 nm, Fig. 11, bottom), the absorption spectra are red shifted compared to those recorded in solution. The onset absorption band recorded at 1016 nm for para-IDT(=NCN) 2 and at 856 nm for meta-IDT(=NCN) 2 provides a short ∆E opt of 1.22 and 1.45 eV respectively. The slight ∆E opt contraction from liquid to solid state, around 0.2 eV, results from strong packing in the solid state.

Organic field-effect transistors.

The last important step was to evaluate the impact of the electronwithdrawing N-cyanoimine groups in devices, herein OFETs. Both para-and meta-IDT(=NCN) 2 have been used as active layer in n-type channel OFETs possessing a bottom-gate bottom-contact (BG-BC) architecture (see device structure in SI). The fabrication process was the following: 150 nm thick aluminium layer was evaporated on a 5 × 5 cm 2 glass substrate and patterned by conventional photolithography. SU-8 2000.5 photoresist from Microchem was then spin coated to obtain a 400 nm thick layer. 50 nm thick gold layer was then thermally evaporated and patterned by photolithography. Finally, the OSCs were deposited by evaporation under vacuum as a 40 nm thick layer. This BG-BC structure in which the OSC is evaporated in the last process step, avoids any structural effect resulting from the following step.

Mobility μ FE , threshold voltage V TH , subthreshold swing SS and the on/off ratio of the drain current (I Don /I Doff ) presented I nwere extracted from the transfer characteristics in the linear and saturated regimes of a series of at least five OFETs of different dimensions (W = 4000 µm, L = 3 to 50 µm), fabricated during the same process to get a more precise insight on the reproducibility of the values (see Fig. 12). Table 4 reports the average values and the highest measured linear and saturated mobilities are presented between brackets.

In the first set of measurements, without thermal treatment of the devices after fabrication, one can note that devices using para-IDT(=NCN) 2 present better performances than those using meta-IDT(=NCN) 2 . The linear/saturated maximum µ FE values strongly increase from 6.7/5.4 ×10 -5 cm² V -1 s -1 to 0.81/1.4× 10 -3 cm² V -1 s -1 from meta-IDT(=NCN) 2 to para-IDT(=NCN) 2 . A similar difference between the two regioisomers has previously been detected in the dicyanovinylene series. 34 For both type of bridges, the para-IDT core is more efficient when incorporated in OFET than the meta-IDT core. This feature shows the importance of regioisomerism in the materials design for electronics. The second set of measurements was performed after annealing the devices at 80 °C during one hour. 34 Again, the linear/saturated maximum µ FE values are also higher for the devices using para-IDT(=NCN) 2 compared to those using meta-IDT(=NCN) 2 (0.58/1 ×10 -3 cm² V -1 s -1 vs 1.6/2.5×10 -6 cm² V -1 s -1 , resp.). However, annealing process seems to have two different effects on the devices. The first effect could be related to a better organisation in the insulator/OSC interface. Indeed, subthreshold slopes (SS) were strongly improved in both cases (reaching an interesting value of 1.3 for para-IDT(=NCN) 2 ) meaning that carrier accumulation in the active channel is favoured with the annealing process. This observation is also strengthened with the improvement of threshold voltage (V TH ) (from 14.9 to 13.5 V). Thus, defect density in the first layer of OSC has been decreased. 50 This effect could be linked to an increase of grain size. However, µ FE (generally improved when grain size increases) slightly decreases after annealing treatment. We have to notice that µ FE is extracted from the maximum of transconductance g m corresponding to a high gate-source voltage V GS . In both cases, drain current I D decreased when V GS increased (more easily visible in meta-IDT(=NCN) 2 -based OFET). This phenomenon could be linked to a high access resistance in the interface between drain/source and OSC.

Recently, we have shown that the covering of gold drain and source electrodes by self-assembled monolayer (SAM) of DABT (4-(dimethylamino)benzene thiol) can have a beneficial effect on the performance and stability of the resulting OFETs. 34,82 Devices with gold modified electrodes were fabricated using the same fabrication process as described above. After the thick gold layer was thermally evaporated and patterned by photolithography, the substrates were immersed in a 1.6 mg/mL acetone solution of DABT for 10 min at room temperature under dry-nitrogen atmosphere. Devices were then rinsed with acetone and OSCs were then evaporated in the last process step. Performances are presented in Fig. 13 and summarized in the Table 5.

In a first series of experiments in which the devices were tested without annealing, one can note that for para-IDT(=NCN) 2 , the linear/saturated µ FE values are more than doubled compared to the devices without DABT. This is therefore an efficient strategy to strongly increase the device performance. The maximum value, 3.8 × 10 -3 cm² V -1 s -1 , remains nevertheless moderate compare to the state of the art. [START_REF] Gao | [END_REF][14]83 Interestingly, this increase of the linear/saturated µ FE values is not observed for meta-IDT(=NCN) 2 based devices for which the mobilities remain roughly similar (Table 4) in both type of devices.

A second set of experiments were performed after annealing the devices for 1 hour at 80 °C. Despite a slight increase was observed for saturated µ FE of para-IDT(=NCN) 2 , 4.6×10 -3 cm² V -1 s -1 , the heating of the devices was deleterious for linear µ FE (Table 5). The same phenomenon observed without DABT could explain this deterioration. Indeed, with DABT, SS is significantly improved (from 3.7 V/dec to 1.4 V/dec for para-IDT(=NCN) 2 and from 15.1V/dec to 5.9 V/dec for meta-IDT(=NCN) 2 ). Channel creation is then improved with the annealing process but µ FE is limited with the dewetting process leading to an increase of access resistance.

As the two compounds possess similar electronic properties, it is clear that the difference in term of performance comes from a different molecular organisation in the bulk of meta-IDT(=NCN) 2 rendering the charge transport less efficient than in its isomer para-IDT(=NCN) 2 . Then, the annealing process has a positive effect with an increase of the OSC grain size but, because of a too thin layer, dewetting process between grains seems to appear and limits the drain current. This phenomenon has already been observed with C 60 . 81 As a matter of fact, both isomers self-assemble in the solid state in the same way, namely strips of stacked cores that alternate with cyanoimine groups, and the stacking distance is even equivalent (see above). However, the semiconducting performances of the para isomer are certainly enhanced by the superimposition of the cores along stacks, whereas the constraints from the arrangement of lateral groups make that successive meta-IDT cores are respectively shifted and turned. It should be mentioned that the introduction of DABT appears to lead to a weaker improvement of the devices performances for para-IDT(=NCN) 2 than for previously described para-IDT(=C(CN) 2 ) 2. 34 Tentatively, this is not an effect related to electrode / OSC interface, but from the insulating layer (SU-8/OSC interface). Additional experiments on device optimization and characterization need to be done in order to explain the different performances of the devices. At the present stage, differences of thin film morphology influencing OFET performances could not be checked, but are unlikely due to the identical composition and the similar way of self-assembling.

SCO V TH (V) V ON (V) SS (V/dec) I Don /I Doff Linear µ FE (µ FE maximum value) (cm² V -1 s -1 )

Conclusion

In this work, we report the use of electron-withdrawing fragments, namely N-cyanoimines incorporated on the bridges of indacenodithiophene regioisomers. In order to show the impact of the bridge substitution, the main physicochemical properties of these OSCs have been compared to those of their corresponding analogues para-IDT(=C(CN) 2 ) 2 and meta-IDT(=C(CN) 2 ) 2 , bearing the widely used dicyanovinylene units at their bridges. The four compounds were found to self-organize into lamellar structures, defined by the alternation of layers of conjugated cores and aliphatic tails. The cohesive molecular self-assembling promoted by the dipolar association of cyanoimine or dicyanovinylene groups resulted in the formation of three-dimensional lamellar mesophases that extend from above melting temperature to sample degradation. Compared to dicyanovinylene functionalities, the present cyanoimine groups induce a decrease of the HOMOs energy (from -5.64 eV to -5.72 eV in the para-series and from -5.80 to -5.96 eV in the meta-series and keep the LUMOs energy almost unaltered (from -4.10 eV to -4.13 eV in the para-series and -4.07 eV for both metaderivatives, values from electrochemical measurements). This shows that cyanoimines are very strong electron-withdrawing groups and as good as the famous dicyanovinylene fragments to depress the LUMO energy level of an OSC. This is a key feature in the design of future electron-poor materials. In addition, these fragments are also highly thermally stable, which is a key feature in Organic Electronics. Thanks to their low LUMO levels, both meta-IDT(=NCN) 2 and para-IDT(=NCN) 2 ) have been successfully used as active layer in n-type OFETs using as insulator an organic material, i.e. SU8 insulator and with gold electrodes modified by self-assembled monolayer of DABT.

As far as we know, the present work is the second example 76 reported to date of N-cyanoimines based OSC in n-type OFETs. Herein, higher OFET performances have been obtained. Para-IDT(=NCN) 2 based devices present higher linear/saturated fieldeffect mobilities than its regioisomer meta-IDT(=NCN) 2 . As a similar conclusion was drawn for their dicyanovinylenes analogues, 34 the para-IDT-core appears to be intrinsically more efficient in OFET than its meta isomer, and this finding for the =NCN bridges is explainable by the features of the molecular organization in the solid state. We believe that cyanoimines can present an alternative to widely known electron-withdrawing units such as dicyanovinylene, with induction of comparable semiconducting properties and of considerably improved solubility that facilitates the processing. They deserve to be tested with other π-conjugated systems to fully explore their potential. We are currently working in this direction.

A c c e p t e d m a n u s c r i t p t

  whereas its corresponding dione para-s t it u t io n & B r id g e F u n c t io n n a li z a t io n B r id g e F u n c t io n n a li z a t io n C 10 H 21 , C 12 H 25 R in g S u b s ti tu ti o n & B ri d g e F u n c ti o n n a liz a ti o n Chart 1. Electron-deficient DihydroIndenofluorenyl (IF) derivatives

  A c c e p t e d m a n u s c r i t p t IDT(=O) 2 not. Similarly, 2,1-b-IF(=C(CN) 2 ) 2

Fig. 1

 1 Fig. 1 Molecular structures from X-ray crystallography of para-IDT(=NCN) 2 (top) and meta-IDT(=NCN) 2 (bottom).

Fig. 2

 2 Fig.2 Intramolecular short-contacts in para-IDT(=NCN) 2 (top) and in meta-IDT(=NCN) 2 (bottom).

Fig. 3

 3 Fig. 3 Intermolecular interactions in para-IDT(=NCN) 2 .

Fig. 4

 4 Fig. 4 Intermolecular interactions in meta-IDT(=NCN) 2 .

Fig. 5

 5 Fig. 5 Arrangement of two or three molecules in the packing diagram of para-IDT(=NCN) 2 (top) and of meta-IDT(=NCN) 2 (bottom).

  Mes Cr para-IDT(=NCN) 2 Heat flow (W/g) Temperature (°C) A c c e p t e d m a n u s c r i t p t

Fig. 7 S

 7 Fig. 7 S/WAXS patterns of para-IDT(=NCN) 2 (left) and meta-IDT(=NCN) 2 (right) at room temperature in the pristine state (bottom, black), at 190 °C (middle, red) and then at room temperature after cooling (top, blue) ; h ch is the scattering signal from molten alkyl chains.

-Fig. 8

 8 Fig. 8 Views of the crystal structure of para-and meta-IDT(=NCN) 2 (top-bottom).

aaaa

  = 7.0293; b = 10.0818; c = 8.972(3) α = 81.078; β = 85.448; γ = 80.052 V = 1306.4 (Z = 2) = 4.8961; b = 8.3385; c = 16.1441 α = 91.827; β = 90.314; γ = 99.320 V = 650.0 (Z = 1) = 7.20(4); b = 10.22(0); c = 9.15(2) α = 81.6(7); β = 85.9(0); γ = 79.2(6) = 7.42(0); b = 10.05(0); c = 41.9(7) α = 82.5(2); β = 84.7(8); γ = 77.5(6) a = 7.34(3); b = 9.85(4); c = 43.9(6) α = 84.8(8); β = 83.9(6); γ = 76.7(4) V = 3072 (Z = 4) ρ = 1.104 d001 = 43.7 (ZL = 2) A = 70.3 (ZA = 2) Indexation of the room temperature S/WAXS patterns performed in the crystalline powder state of meta-IDT(=NCN) 2 demonstrated theA c c e p t e d m a n u s c r i t p t

Fig. 9 .

 9 Fig. 9. CV of para-IDT(=NCN) 2 (left) and meta-IDT(=NCN) 2 (right) (10 -3 M) recorded in CH 2 Cl 2 + Bu 4 NPF 6 0.2 M, sweep-rate 100 mV.s -1 . Platinum disk (Ø: 1mm) working electrode.

  32 and -0.27 V for para-IDT(=NCN) 2 and at 1.56 and -0.33 V for meta-IDT(=NCN) 2 , we determined the HOMO/LUMO energies of the two compounds at -5.72 / -4.13 eV for para-IDT(=NCN) 2 and at -5.96 / -4.07 eV for meta-IDT(=NCN) 2 . The LUMO are very deep (below -4 eV) and hence adapted to application in n-type OFETs (see below).

A c c e p t e d m a n u s c r i t p t

Fig. 10

 10 Fig. 10 Representation of the energy levels and the main molecular orbitals obtained by DFT (B3LYP/6-311+G(d,p)) involved in the electronic transitions of para-IDT(=NCN) 2 (top) and meta-IDT(=NCN) 2 (bottom) obtained by TD-DFT (B3LYP/6-311+G(d,p)) and shown with an isovalue of 0.04 [e bohr -3 ] 1/2 .

a

  vs SCE, b Calculated from onset oxidation/reduction potential. c ΔEel = HOMO-LUMO from electrochemical data. d hc/λ = 1239.84/λ (in nm) from absorption spectrum, λ being the low energy absorption band edge. UV-Vis absorption spectra. UV-vis absorption spectra recorded in THF are shown in Fig. 11, top.

Fig. 11

 11 Fig.11Absorption spectra of para-IDT(=NCN) 2 and meta-IDT(=NCN) 2 in THF (top) and in the solid state (bottom, thermally-evaporated thin film, thickness 40 nm). Inset: Focus on the 500-900 nm (top) or 600-1100 nm (bottom) portion of these spectra.

Fig. 12

 12 Fig. 12 Transfer characteristics of OFETs with para-IDT(=NCN) 2 (Top) and meta-IDT(=NCN) 2 (bottom), without annealing (left) or after annealing 1h at 80 °C (right)(V DS = 10 V).

Table 3 .

 3 Selected electronic properties of cyanoimines and dicyanovinylenes IDT derivatives.

Table 4 .

 4 Electrical properties of OFETs

Fig. 13. Transfer characteristics of OFETs with DABT using para-IDT(=NCN) 2 (Top) and meta-IDT(=NCN) 2 (bottom), without annealing (left) or after annealing 1h at 80 °C (right)(V DS = 10 V).

Table 5 .

 5 Electrical properties of DABT modified OFETs

Acknowledgements

We thanks the Region Bretagne and the Agence de l'Environnement et de la Maîtrise de l'Energie (ADEME) for a studentship (JDP), Dr Bruno Laffite (ADEME), the University of Rennes 1 for financial support (Action Incitative 2013), the IETR for financial support, the C.R.M.P.O (Rennes) for mass analysis. This work was granted access to the high performance computing resources of CINES (Montpellier, France) under allocation 2018-A0040805032 awarded by GENCI. BD and BH thank the CNRS and Université de Strasbourg (UNISTRA) for support.

Conflicts of interest

"There are no conflicts to declare".

Notes and references


Maud Marchal

Emmanuel Promayon

Jocelyne Troccaz

Simulating Complex Organ Interactions: Evaluation of a Soft Tissue Discrete Model

Computer assisted procedures play a key role in the improvement of surgical operations. The current techniques in simulation potentially lead to more accuracy, more safety and more predictability in the surgical room. Despite the important number of algorithms proposed for interactively modelling deformable objects such as soft human tissues, very few methods have attempted to simulate complex anatomical configurations. In this paper, we present a new approach for soft tissue modelling whose novelty is to integrate the interactions between a given soft organ and its surrounding organs. The proposed discrete model is compared to finite element method in order to quantify its performance and physical realism. The model is applied to the simulation of the prostatebladder set.

Introduction

The human body is a system of complex interactions between organs and tissues. These interactions are particularly intricate in the case of soft tissues. Actually soft tissues are undergoing deformations depending on their own physical characteristics and contiguous organs motions. Two main directions are taken to model human soft tissues: the biomechanical approach and the computational discrete approach [START_REF] Delingette | Towards realistic soft tissue modeling in medical simulation[END_REF].

The biomechanical approach is based on continuum mechanics. The most frequently used framework of this approach is the Finite Element Method (FEM) which offers the advantage of being based on a strong theoretical background. However researchers face two kinds of difficulties when applying this method to computer aided medical simulation: high computational cost and awkward construction and updating of complex anatomical environments where rigid, elastic and active structures are present and interact.

Computational discrete approaches, such as mass-spring networks, offer a simpler alternative to the construction of such complex structures and can be more easily modified to match changing structures in a particular simulation. While they are not computationally demanding, these approaches are difficult to control and assess.

For both methods, there are few examples for the integration of multiple dynamic interactions between soft organs and their environment. This study presents a new soft tissue modelling method based on a discrete approach that allows such interactions to take place. The method named Phymul is a volumetric evolution of a surface model developed by Promayon et al. [START_REF] Promayon | Physically-based model for simulating the human trunk respiration movements[END_REF]. It allows to model the objects with interior nodes. In addition, the method can integrate the incompressibility constraint for each component of the environment. It has been validated by comparisons with a finite element method as a "gold standard" of soft tissue modelling.

Our medical aim is to model the prostate and the surrounding organs and to simulate deformations in real time. Prostate cancer is the second leading cause of cancer deaths in men in several countries. The prostate is therefore subject to an increasing number of diagnostic and therapeutic procedures that are evaluated by physicians for potential improvements in care. Modelling the interactions between the prostate and its environment may allow more accurate procedures to be developed and accepted by urologists.

The paper is structured as follows. At first, the model and its operation are described. Then, comparisons with well-proven soft tissue modelling methods are presented. Finally the modelling of the prostate and its environment is introduced.

2 Phymul: a Volumetric Evolution for a Soft Tissue Modelling Method

In this section, a volumetric version of Phymul is presented. Phymul is a discrete model based on computer graphics modelling. The new proposed approach allows to define objects not only with surfacic nodes as in the original Phymul [START_REF] Promayon | Physically-based model for simulating the human trunk respiration movements[END_REF] but with interior nodes. The first paragraph presents the geometrical description of models with Phymul. Then, dynamics are described and finally, as soft tissue modelling is one of the major interest in our application, the specific modelling of elastic components is detailled.

Geometrical Description

Phymul allows building separated objects with their own properties and choosing the interactions between them. The components of our model are all derived from a main basis: a set of nodes describing the geometry of the object to model. Each node has a position, a neighbourhood and different properties depending on what kind of component it belongs to. The nodes can be placed by the user either on the surface or inside the component. A mass is assigned to each node in order to generate forces and dynamics. Moreover the user can choose to model each component with a surfacic description (only nodes on the surface) or with a volumetric description (nodes are present inside the component), depending on their physical properties.

Living structures are governed by three main kinds of components: rigid components to model skeleton, deformable components to model soft tissues and active deformable components to model muscles. The latter inherit deformable components properties. Components with different properties can be easily stitched together in Phymul. Fig. 1 shows different configurations: interactions between two elastic components or two rigid components and interactions between an elastic and a rigid component. (b) Border nodes of solid and elastic components are doubled but constrained to be in the same position, whatever the forces applied on them. The forces on elastic component can thus be transmitted to solid component (for example, a link between a bone and a muscle). (c) Solid components are linked together by an elastic component (for example, two bones linked by a ligament).

Elastic Component E2 Elastic component E1 Solid component S1 Elastic component E1 Solid component S2 Solid component S1 (a) Elastic-Elastic interaction (b) Solid-Elastic interaction (c) Solid-Solid interaction

Modelling Description

Besides the geometrical description, forces acting on each component and generating displacements and deformations have to be considered. Three kinds of forces can be used in the model: force fields (e.g. gravitation force), locally applied forces (e.g. forces generated by the user) and local shape memory forces to model deformable properties.

In addition to forces, constraints have to be implemented to model complex behaviours and to maintain some conditions such as non-penetrating volume. Phymul can deal with two kinds of constraints:

local constraints that are applied to a single node, for example to keep a node in a particular region of space global constraints that are applied to a set of nodes, for example to enforce an object volume constraint.

The algorithm considers constraints as non-quantified force components: their satisfaction is guaranteed by using a direct projection algorithm based on the gradient vector of the constraint function. Position constraints can be easily defined at each node. For example volume preservation can be satisfied with a simple algorithm whose basis is detailled in [START_REF] Promayon | Physically-based model for simulating the human trunk respiration movements[END_REF]. In this method, nodes belonging to the surface are distinguished from nodes located inside the component to model. The algorithm works with all types of polyhedra: the mesh used for the geometrical description does not interfer in the volume computation. Finally, to solve the system dynamics, at each time t, the forces on each node are summed and the equations of motion are integrated taking into account the local and global constraints. The discrete integration scheme used for the equation of motion is Newton-Cotes scheme.

Elastic Component

Soft tissue modelling being our aim, let focus on the elastic component of Phymul, and detail how the elasticity property is built and computed. The elastic property is the ability for an object component to come back to its original shape once deformed, independently of the global object position. The elasticity in Phymul is described using an original formulation that has better stability properties than mass-spring networks, as shown by Promayon et al. [START_REF] Promayon | Physically-based model for simulating the human trunk respiration movements[END_REF]. To model the elastic property of a node we define a local elasticity memory. The local shape memory force is generated on each node as follows: at each iteration, given the neighbour positions, we compute a shape ideal position: "an attraction node". Its position is ensured to locally minimize the deformation energy. When the node is at the shape nominal position, the local deformation and the shape memory force are both zero.

The difference between a mass-spring network and the local shape memory force is illustrated Fig. 2 with three nodes. Two nodes are fixed and a force is applied on the third node. With mass-spring system, the elasticity force is generated with two springs between the node and its neighbours. With the local shape memory, the elasticity force is represented by a spring between the node and its attraction node. The unique elasticity parameter of a given component is the stiffness of the spring on each node. Like mass-springs, local shape memory are easy to use for topological modifications. To compute the elastic property, a local shape coordinate system is defined on each node in order to find the shape ideal position whatever the object space orientation. Each node position is defined in the local coordinate system relatively to its neighbourhood at rest shape. During simulations, according to the neighbouring nodes position, a target position is computed for each node of an elastic component.

Comparisons with the Truth cube Data and FEM

New approaches of soft tissue modelling can be more easily experimented with phantoms than with complex tissue structures. The validation through these phantom studies are then considered to be applicable to various tissues using their own biomechanical properties.

In 2003 in a project named "Truth cube"1 , Kerdok et al. [START_REF] Kerdok | Truthcube : Establishing physical standards for real time soft tissue simulation[END_REF] validated their finite element deformation using the volumetric displacement data of 343 beads embedded in a silicone rubber cube and tracked by Computed Tomography. Material properties and geometry were known and boundary conditions had been carefully controlled while CT images were taken. Using this Truth cube data, we have been able to compare real data with both Phymul and the Finite Element Method.

A finite element model of the "Truth cube" has been built using commercial FE modelling software (ANSYS 8.0 software, Ansys Inc., Cannonsburg, PA). The material properties are isotropic and linear (with a Young Modulus of 14.9 kPa and a Poisson ratio of 0.499). The cube edge dimension is 8 cm and the mesh is made of 8-node solid hexahedral linear elements, as in the model used by Kerdok. Large deformations are employed. For Phymul, the mesh was the same as the FEM mesh. The nodes are linked to form hexahedra. Comparisons have been achieved for three compression levels of 5%, 12.5% and 18.25%. We focus on the distances between measured bead positions and those predicted by the two modelling methods. As measurement, we used the following formula with d the Euclidian distance:

d(realBeads position af terCompression, simulatedBeads position) d(realBeads position init, realBeads position af terCompression)

× 100

(1) to obtain a distance between real data and simulated date relative to the real beads displacement. The latest results are in mean:

for the 5% compression level (mean real displacement: 2.64 mm):

35.6% (Phymul) and 33.8% (Ansys), -for the 12.5% compression level (mean real displacement: 6.12 mm):

21.5% (Phymul) and 20.2% (Ansys), -for the 18.25% compression level (mean real displacement: 9.17 mm):

16.9% (Phymul) and 16.8% (Ansys).

FEM produces lower mean errors than our model. Nevertheless, distances are very small compared to global characteristics. More precisely differences between FEM and our model are less than 0.2 mm for 5% compression. Concerning the computational cost, our method presents like other discrete approaches the advantage to be linear in the number of nodes and so enables the building of complex models with as necessary nodes as needed. On a Pentium 4 2.4 GHz, it takes 0.017 ms per node for each iteration. The number of iterations depends on the integration scheme. The FEM time results obtained with Ansys cannot be directly compared with Phymul's values, since a single step computational cost cannot be determined. Indeed, simulation time strongly depends on the hypothesis (non-linearity for example).

Prostate Modelling in its Environment

After the validation with simple objects, more complex models containing several objects and better fitting to the prostate shape have been introduced. Modelling the prostate and its environment remains difficult because many factors are influencing prostate motion and deformation. Indeed, measurements of prostate position have demonstrated movements [START_REF] Melian | Variation in prostate position quantitation and implications for three-dimensional conformal treatement planning[END_REF] and deformations [START_REF] Forman | Evaluation of changes in the location and shape of the prostate and rectum during a seven week course of conformal radiotherapy[END_REF] of the organ mainly due to rectum and bladder filling and recently due to breathing [START_REF] Malone | Respiratory-induced prostate motion: quantification and characterization[END_REF] and patient position.

In this paper, our aim is to simulate the influence of an endorectal echographic probe on prostate shape in function of bladder filling. The model presented contains three components: the prostate, the bladder and the rectum. An anatomic view of the prostate and its environment during a biopsy is represented in Fig. 3. The prostate and the bladder are represented by two deformed spheres. Bladder shape is deformed under gravity and is described with surfacic nodes (like an envelope). Prostate has a volumetric description. The echographic probe inside the rectum is simulated by the applied forces with a cylinder shape. Proportional scales of all organs are respected. Bladder and prostate are stitched together with a limited number of nodes. Top node of the bladder is fixed for each simulation with a different bladder shape (see Fig. 3 b) simulating different bladder repletions. During simulations, a pressure equivalent to real applied forces for biopsy is applied inside the rectum upward to deform the prostate. After simulations with variations of bladder volume, it appears that the measured deformations correspond to those observed during surgical gestures. The prostate tends to deform more when the bladder is empty (10% of its height) than when the bladder is full (5% of its height). The simulated deformations match to experiment measurements performed during a biopsy or a brachytherapy.

Discussion and Conclusion

In this paper, Phymul model and first simulations have been validated with objects of simple geometry. The first validation is a comparison with the Truth cube data and a finite element method. Results show that our method is relatively close to the FEM in terms of accuracy. A second set of experiments concerning the external shape of the cube has also been performed. Results show that our method performs similarly to the FEM in predicting deformations. It is important to note that there are a lot of other measurements to compare modelling methods. The distance choosen in this paper, although emphasis on a particular aspect, seems to us to be more relevant to compare both the discrete model and FEM to real data. The difference, even for FEM, shows us that simplistic modelling of object can induce relatively large difference in deformations, even for simple real object such as Truth cube. In a future work it could be of major interest to classify comparison measurements.

The second validation is directly linked to the prostate application. The model presented here is very simplified but allows to demonstrate how more complex models can be defined with simplicity with our method. We currently extend the work to a more realistic prostate and environment in terms of shape.

The incorporation of physical parameters in the model is a key element of soft tissue modelling. Even if it is possible to measure these parameters in isolated tissue [START_REF] Fung | Mechanical Properties of Living Tissues[END_REF], their determination is still very difficult to perform in vivo, especially since these parameters are patient and pathology specific. In addition the complexity of tissue interactions makes it difficult to perform a backward validation process. Prostate properties are reported in few papers [START_REF] Krouskop | Elastic moduli of breast and prostate tissues under compression[END_REF]. Elastography has opened new possibilities to determine elasticity. Recently, Kemper et al. [START_REF] Kemper | Mr elastography of the prostate: initial in-vivo application[END_REF] published elasticity coefficients for the prostate. We have also performed another parallel study concerning the ability to translate FEM parameters (Young modulus for instance) in a local shape memory force. We plan to directly introduce Young modulus into Phymul through a force as a function of deformations. Future work will deal with modelling interactions with needles and ultrasound probe frequently used in biopsy or brachytherapy.

Finally in this paper, a new approach to soft tissue modelling, well-suited to model interactions between organs has been proposed. Our object-oriented based method allows modelling several organs simultaneously. Contacts and interactions between tissues can be described more easily than in FEM for example. Compared to other discrete methods, we can define constraints like incompressibility and express objects properties with more accuracy and stability. By incorporating the interactions with instruments and by modelling more realistic organs, we will also be able to model the prostate behaviour by taking into account not only the organ itself but also its environment.

Fig. 1 .

 1 Fig. 1. Interaction configurations: (a) Border nodes (bigger black nodes) of elastic components belong to one component but have neighbours in the other elastic component. (b) Border nodes of solid and elastic components are doubled but constrained to be in the same position, whatever the forces applied on them. The forces on elastic component can thus be transmitted to solid component (for example, a link between a bone and a muscle). (c) Solid components are linked together by an elastic component (for example, two bones linked by a ligament).

Fig. 2 .

 2 Fig. 2. Difference between mass-spring system and local memory shape

Fig. 3 .

 3 Fig. 3. Model of the prostate and different bladder filling

Fig. 4 .

 4 Fig. 4. Prostate and bladder in different states

Data are available: http://www.medicalsim.org/truthcube/