Adrien Thirion
email: adrien.thirion@nanomade.com

Estelle Mazaleyrat

Blaise Mulliez

Francis Bony

Hélène Tap

Pulse: An unobtrusive vitals monitoring system based on innovative high sensitivity sensors

Keywords: Ballistocardiography, Heart Rate, Heart Rate Variability, Breath Frequency, Actigraphy, low-cost, strain sensor

Disorders with a transient signature (e.g., obstructive sleep apnea, drowsy driving, sudden infant death syndrome, or atrial fibrillation) are difficult to predict. The Pulse system, including a matrix of unobtrusive strain sensors, was designed to extract four different vital parameters: actigraphy, Breath Frequency (BF), Heart Rate (HR), and Heart Rate Variability (HRV). Thanks to the high sensitivity of the innovative Nanomade strain sensors, it shows good performances (accuracy around 98.5% for HR/HRV and up to 96% for BF) in regard with the state of the art. Moreover, these sensors can easily be integrated into different equipment, are adaptive and low-cost.

I. INTRODUCTION

The last decades have seen a significant evolution in medical diagnosis. Yet, some disorders remain difficult to predict due to their transient nature. Among the most critical ones, there are Obstructive Sleep Apnea (OSA) [START_REF] Benjafield | Estimation of the global prevalence and burden of obstructive sleep apnoea: a literature-based analysis[END_REF], drowsy driving [START_REF] Higgins | Asleep at the Wheel-The Road to Addressing Drowsy Driving[END_REF], sudden infant death syndrome [START_REF] Kinney | The Sudden Infant Death Syndrome[END_REF] and atrial fibrillation (the leading cause of embolic stroke worldwide) [START_REF] Furberg | Prevalence of atrial fibrillation in elderly subjects (the Cardiovascular Health Study)[END_REF]. These disorders are highly difficult to detect because affected persons show very few symptoms.

Yet, monitoring the following four vital parameters can substantially help diagnose these aforementioned conditions [START_REF] Liu | Identifying Obstructive Sleep Apnea by Exploiting Fine-Grained BCG Features Based on Event Phase Segmentation[END_REF]- [START_REF] Yu | Automatic Detection of Atrial Fibrillation from Ballistocardiogram (BCG) Using Wavelet Features and Machine Learning[END_REF] :

• the actigraphy that quantifies the subject movements;

• the respiratory rate or Breath Frequency (BF) that represents the number of breaths per minute; • the Heart Rate (HR) that is the average of time intervals between two heartbeats; • the Heart Rate Variability (HRV) that represents the variation of these intervals. HR and HRV can be contactless measured via BallistoCar-dioGraphy (BCG), a technique which evaluates the strains generated by the ejection of blood from the heart into the descending aorta [START_REF] Starr | Studies on the estimation of cardiac ouptut in man, and of abnormalities in cardiac function, from the heart's recoil and the blood's impacts; the ballistocardiogram[END_REF]. This technique also helps retrieving respiratory and body movement information. Since the early 2000's, several BCG sensor technologies (e.g. accelerometers, piezoelectric sensors, strain gauges) and signal processing techniques (e.g. peak detection, machine learning, autocorrelation) have been implemented. Among the sensor solutions found in the literature, some of these use low-cost but bulky and/or heterogeneous technologies that remain difficult to be incorporated into devices [START_REF] Laurino | Moving Auto-Correlation Window Approach for Heart Rate Estimation in Ballistocardiography Extracted by Mattress-Integrated Accelerometers[END_REF]- [START_REF] Albukhari | Bed-Embedded Heart and Respiration Rates Detection by Longitudinal Ballistocardiography and Pattern Recognition[END_REF]. On the opposite, others are based on easy to use yet costly sensors [START_REF] Vehkaoja | Correlation approach for the detection of the heartbeat intervals using force sensors placed under the bed posts[END_REF]- [START_REF] Pino | BCG algorithm for unobtrusive heart rate monitoring[END_REF].

This paper introduces an innovative, generic and unobtrusive vitals monitoring system, called Pulse. It relies on an adaptive, low-cost and high sensitivity strain gauges matrix that can easily be integrated into various types of equipment (e.g. bed, vehicle seat, wheel chair,...). An Analog Front-End (AFE) circuit and an embedded digital processing were developed according to the sensors physical characteristics, to determine HRV, actigraphy, BF and HR despite body motion artifact. The proposed system and the sensor technology are described in Section II. Then, the experimental setup is detailed in Section III. Next, the results are presented in Section IV while conclusion and perspectives are drawn in Section V.

II. SYSTEM SUMMARY

The system includes a strain sensors matrix and a dedicated circuit, as illustrated in Fig. 1. The strain sensors and the electronic front-end ensuring the signals conditioning until the analog-to-digital conversion, are detailed below. The digital signal processing, ensuring the vitals parameters extraction, were embedded in a dual-core micro-processor.

A. The Pulse sensor

The Pulse sensor used in the present study consists in 12 Nanomade strain sensors spread over an ultrathin flexible 14 cm x 19 cm surface, glued on a polycarbonate sheet, used as a strain-propagating medium (Fig. 2a).

Nanomade strain sensors were chosen for their sensitivity, flexibility, thinness and low cost: allowing the detection of very faint signals. In the present case, they present a gauge factor of 30, while commercial strain gauges typically present a strain factor of 2.

• The thinness and flexibility of Nanomade strain sensors (250 µm thick) provide seamless integration capability into beds and seats for BCG applications. • Nanomade strain sensors are low cost: for comparable dimensions, Nanomade strain sensors cost approximately 10 times less than commercial strain gauges. Nanomade strain sensors rely on the tunnel effect in Conductive Nanoparticle Assemblies (CNAs) [START_REF] Herrmann | Nanoparticle films as sensitive strain gauges[END_REF]- [START_REF] Sangeetha | Nanoparticle-Based Strain Gauges Fabricated by Convective Self Assembly: Strain Sensitivity and Hysteresis with Respect to Nanoparticle Sizes[END_REF]. A Nanomade strain sensor consists of proprietary CNAs containing ink deposited between interdigitated conductive (copper) electrodes on an insulating (polyimide) flexible substrate.

The strain sensors are squares of 5x5 mm 2 and are positioned to efficiently capture respiratory and cardiac signals via BCG: the sensor design consists in a 3x4 matrix with 5.5 cm spacing. This geometry allows to cover a broad spectrum of morphologies and offers versatility regarding integration (seamless and unobtrusive integration in beds, seats, etc).

The static sensor resistance R varies from 3 kΩ to 30 kΩ due to process variations. Upon compressive (resp. tensile) strain, the CNAs move closer to (resp. away from) each other, resulting in a decreased (resp. increased) sensor resistance (Fig. 2b). The resistance variations ∆R of all the strain sensors are monitored as they translate the deformations induced by respiratory and cardiac movements. The variation range for each parameter is detailled in Table I.

B. Analog Front-end circuit

The output sensors' signals are processed in the Analog Front End (AFE) circuit presented in Fig. 3. The 12 sensors are biased independently by a variable current source, to overcome the static resistance dispersion. Then, the signals are filtered by a first-order high-pass filter with a cut-off frequency of

III. EXPERIMENTAL SETUP

The Pulse system was seamlessly integrated in two different types of equipment.

First, the sensor is put in a economic plane seat between the stuffed tissue and the seat foam. the Pulse sensor is positioned in the seating area. It is the optimal sensor position in a seat, for two reasons:

• the BCG craniocaudal momentum (head-to-foot axis) is larger than the other translations [START_REF] Leonhardt | Unobtrusive Vital Sign Monitoring in Automotive Environments-A Review[END_REF],

• body motions are less important in the seating area. Then, the sensor is inserted in a standard medical bed between the memory foam and the elastic one. This position is the most straightforward technique to integrate the sensor even though signals are significantly attenuated due to the memory foam thickness (7cm). In a bed, contrary to a seat, the craniocaudal translation is more difficult to capture. Instead, the best bed-based BCG signal is a combination of dorsoventral (back-to-chest) and transversal (side-to-side) components. To maximize the BCG amplitude, the Pulse sensor is therefore positioned around the chest area [START_REF] Vehkaoja | Effects of sensor type and sensor location on signal quality in bed mounted ballistocardiographic heart rate and respiration monitoring[END_REF].

Eight healthy subjects were involved in this study, installed and asked to remain still for 10 min in three different conditions for HRV/HR results: sitting on a plane seat, lying on their back and on their side on a standard medical bed. A POLAR H10 ECG belt, attached to the subject by a chest strap, is used as reference.

To validate the BF measurement, the subjects had to breath following several rhythms given by a metronome: from very low rate (5 bpm) to hyperventilation (40 bpm). Thanks to the sensors sensitivity, the recorded signals' amplitude was high enough and reliable results were obtained.

IV. RESULTS AND DISCUSSION

The embedded software was developed to dynamically select, among the 12 sensors of the matrix, the one delivering the signal with the most useful information. Thanks to this feature, combined with the high sensitivity of the CNA-based sensors, the Pulse system is able to extract signals such as the

Paper

Correct cardiac peak detection accuracy Cathelain et al. [START_REF] Cathelain | Dynamic Time Warping for Heartbeat Detection in Ballistocardiography[END_REF] 95.6 % Albukhari et al. [START_REF] Albukhari | Bed-Embedded Heart and Respiration Rates Detection by Longitudinal Ballistocardiography and Pattern Recognition[END_REF] 83.9 % Lee et al. [START_REF] Lee | Physiological Signal Monitoring Bed for Infants Based on Load-Cell Sensors[END_REF] 73.8 % Bruser et al. [START_REF] Bruser | Adaptive Beat-to-Beat Heart Rate Estimation in Ballistocardiograms[END_REF] 95.9 % Pulse: medical Bed 97.8 % Pulse: plane seat 99.9 % ones presented in Fig. 4, from which vital parameters can be determined with accuracy.

The Pulse system cardiac accuracy is given in Table II regarding with the state of the art. It outperforms the others solutions found in the literature, with an accuracy up to 99.9%. The performances obtained on the airplane seat are slightly better than those achieved on the medical bed because the thick memory foam of the bed significantly attenuates the signals.

The Pulse system breathing average accuracy is 96.3% and can even reaches 99% for BF around 20 bpm. This is suitable for the targeted applications and similar to [START_REF] Peng | Detection of Sleep Biosignals Using an Intelligent Mattress Based on Piezoelectric Ceramic Sensors[END_REF]; others references do not quantify their accuracy.

V. CONCLUSION

The Pulse system, including a matrix of unobtrusive strain sensors, was designed to determine vitals. Thanks to the high sensitivity of the innovative Nanomade strain sensors, it shows good performances in regard with the state of the art. Moreover, these sensors can easily be integrated into different equipment (medical bed, plane seat), are adaptive and lowcost.

Yet, signals remain difficult to process in highly noisy environment (e.g. in a car). Furthermore, the relative pressure exerted by the person on each sensor could be computed to provide new features (e.g., person's position, fainting, pressure ulcer risk). As a perspective, a new AFE enhancing the SNR, allowing to combine information from separate sensor' matrices, a 32bits ADC improving the resolution and a dedicated algorithm, involving machine learning techniques should be considered to broaden application fields.

•Fig. 1 :

 1 Fig. 1: Architecture of the Pulse system.

Fig. 2 :

 2 Fig. 2: PULSE sensor stack-up and working principle. (a) Sensor stack-up. (b) Strain sensor working principle.

Fig. 3 :

 3 Fig. 3: AFE circuit duplicated for each sensor and then combined through the multiplexer.

Fig. 4 :

 4 Fig. 4: Cardiac (a) and Respiratory (b) amplitude versus time.

TABLE I

 I

: Resistance variation and frequency range for each vital parameter extracted.

TABLE II :

 II Pulse system cardiac accuracy, in regard with state of the art solutions.


Guillaume Raybaud

Morvan Ouisse

Julien Leng

Adrien Pelat

Jean-Philippe Groby

Vicent Romero-García

Rubén Picó

François Gautier

Control of bending wave reflection at beam terminations by thermally tunable subwavelength resonators

Keywords:

The perfect absorption of bending waves by thermally tunable subwavelength absorbers is analytically and experimentally demonstrated in this work for a reflection problem in beams. These absorbers are local resonators located at the end of a semi-infinite beam and consist of thin blades covered with a layer of Shape Memory Polymer (SMP), the stiffness and damping of which strongly depend on the temperature. The resonators therefore present both energy leakage from the absorbers to the beam and inherent losses thanks to the presence of the SMP. In particular, the situation in which the inherent losses balances the energy leakage is known as the critical coupling conditions and leads to the perfect absorption of the incident wave in the reflection problem. It is shown that these conditions can be simultaneously fulfilled for the different blades of the resonating system by tuning the temperature of the SMP and the geometry of the blades. The analytical results are based on the Impedance Matrix Method. The experimental validation highlights the possibility of achieving multi-frequency subwavelength absorption in the case of multi-blades configurations.

Introduction

In the last decades, a large number of solutions have been proposed for controlling vibrations in structural waveguides. The use of viscoelastic materials is a common and efficient solution to achieve damping over a wide frequency range [START_REF] David | of Viscoelastic Vibration Damping[END_REF][START_REF] Zhou | Research and applications of viscoelastic vibration damping materials: A review[END_REF]. In this case, the vibration damping results from heat dissipation obtained with the shear forces in the viscoelastic material. More efficiency in narrow frequency band can be achieved by using local resonators, such as Tuned Vibration Absorbers (TVAs) or Tuned Mass Dampers (TMDs) [START_REF] Sun | Passive, adaptive and active tuned vibration absorbers-a survey[END_REF]. These solutions are extensively covered in the literature and consist in trapping the wave energy inside the TVA at a target frequency [START_REF] Krenk | Tuned mass absorber on a flexible structure[END_REF][START_REF] Heng | Design of a tunable mass damper for mitigating vibrations in milling of cylindrical parts[END_REF][START_REF] Sun | Membrane-type resonator as an effective miniaturized tuned vibration mass damper[END_REF]. A wide variety of designs have been proposed in various contexts to reduce the vibration of target modes (civil engineering, machinery, rolling motion of ships, ship hull vibrations, aircraft vibrations, etc.) [START_REF] Pieter | Mechanical vibrations[END_REF]. Being often compact, TMDs can also be periodically arranged to decrease the vibrational response of structures by making use of destructive Bragg interferences at specific frequency ranges called bandgaps or stop bands [START_REF] Carcaterra | Transient energy exchange between a primary structure and a set of oscillators: Return time and apparent damping[END_REF][START_REF] Carcaterra | Trapping of vibration energy into a set of resonators: Theory and application to aerospace structures[END_REF][START_REF] Casalotti | Metamaterial beam with embedded nonlinear vibration absorbers[END_REF][START_REF] Billon | Design and experimental validation of a temperature-driven adaptive phononic crystal slab[END_REF][START_REF] Hu | Metamaterial beam with graded local resonators for broadband vibration suppression[END_REF].

In the case of a beam like structure, a local sub-wavelength resonator can be practically made by extending the beam with a very thin beam segment, called blade, the first mode frequency of which matches a targeted frequency of interest. The absorption by this kind of system has already been studied in the case of a reflection and transmission problem [START_REF] Leng | Limits of flexural wave absorption by open lossy resonators: reflection and transmission problems[END_REF]. Perfect absorption, or zero reflection, occurs when the inherent losses of the resonator exactly compensates the energy that leaks out through the interface between the resonator and the surrounding medium. This phenomenon is called critical coupling [START_REF] Leng | Limits of flexural wave absorption by open lossy resonators: reflection and transmission problems[END_REF][START_REF] Romero-Garcia | Use of complex frequency plane to design broadband and sub-wavelength absorbers[END_REF][START_REF] Groby | Use of slow sound to design perfect and broadband passive sound absorbing materials[END_REF].

One way to control the inherent losses in the system is to bond a thin layer of damping material to the resonator. However, fulfilling the critical coupling conditions requires to precisely adjust the inherent losses of the system, which is difficult in practice when using conventional damping materials. The damping properties of such materials do not depend only on the type of material used, but also on the way the material is bonded to the structure and on the ambient temperature. Practical conditions can therefore deviate from ideal analytical and numerical conditions. Moreover, the modification of the losses in the system implies to change the viscoelastic material which can also be arduous. The investigation of other methods to control more effectively the inherent losses of the resonators is therefore of great interest.

In this work, the possibility of tuning the subwavelength resonator properties by using temperature is investigated. To this end, we use a shape memory polymer (SMP) whose properties strongly depend on temperature. In particular, by increasing the temperature and reaching the glass transition temperature of the SMP, the SMP softens and becomes more dissipative. This particular temperature is localised in the transition state where the material changes from a glassy state to a rubbery state. We use tBA/PEGDMA which has been characterized in previous studies [START_REF] Butaud | Sandwich structures with tunable damping properties: On the use of shape memory polymer as viscoelastic core[END_REF] and for which it is possible to precisely adjust the damping of the system by thermal control [START_REF] Butaud | In-core heat distribution control for adaptive damping and stiffness tuning of composite structures[END_REF].

The objective of the paper is to demonstrate the possibility of controlling the reflection of the bending waves at the end of a beam by achieving perfect absorption at one or two a priori targeted frequencies. The use of local resonators (single or double blades) critically coupled by thermal control allows such control. This mechanical system constitutes a tunable absorber on given geometry specifications.

Three subwavelength absorber configurations are chosen and presented in Sec. 2. A model to compute the reflection coefficient is developed and used to evaluate the thermal and geometrical tuning in Sec. 3. Then, the experimental results compared to the analytical simulations are shown in Sec. 4. The reflection coefficient at 𝑥 = 0 is measured using a voice-coil source at x S about 1 cm from the free edge and 5 accelerometers 25 mm apart halfway between x S and 𝑥 = 0. The lenghts l i and l j denote the length of the blades. 𝐙 i and 𝐙 j denote the impedance matrices of the blades at 𝑥 = 0 + and 𝐙 k denotes the impedance matrix of the whole system at 𝑥 = 0 -.

Configuration of the subwavelength absorbers

The system under study is a structural waveguide subjected to bending waves and consists of an aluminium beam of regular cross section. Blade resonators are placed at the end of the beam. A layer of SMP of thickness h SMP = 2 mm is also placed on each blade. These resonators present therefore both inherent losses through the presence of the SMP layers, and energy leakage since the flexural field can propagate from the resonators to the waveguide through the interface connecting the 2 systems and vice-versa [START_REF] Leng | Limits of flexural wave absorption by open lossy resonators: reflection and transmission problems[END_REF][START_REF] Romero-Garcia | Use of complex frequency plane to design broadband and sub-wavelength absorbers[END_REF].

Three configurations are considered (see Fig. 1): a single-blade configuration (A) (see Fig. 1(a)) and two dual-blade configurations with detuned (B) (see Fig. 1(b)) or close (C) resonance frequencies (see Fig. 1(c)). These configurations are realized and photographed in Figs. 1(d), 1(e) and 1(f), respectively.

Analytical model of the reflection coefficient of the beam termination

The reflection coefficient is computed using the Impedance Matrix Method which is a convenient method for variable property waveguides [START_REF] Georgiev | Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect[END_REF][START_REF] Denis | Scattering effects induced by imperfections on an acoustic black hole placed at a structural waveguide termination[END_REF][START_REF] Raybaud | Zero reflections by a 1d acoustic black hole termination using thermally controlled damping[END_REF], adapted from an acoustic context [START_REF] Félix | Multimodal analysis of acoustic propagation in three-dimensional bends[END_REF]. In the case of blades covered with uniformly heated SMP, the properties of the termination do not depend on the 𝑥 axis outside the junction. The resolution is then more direct. The Transfer Matrix Method is an alternative method to reach the same result [START_REF] Mace | Wave reflection and transmission in beams[END_REF].

In the framework of Euler-Bernoulli model for beams in harmonic regime [START_REF] Geradin | Mechanical Vibrations: Theory and Application to Structural Dynamics[END_REF], the state vector 𝐗 T = [𝑤 𝜃 𝑄 𝑀] is composed of the displacement 𝑤, the slope 𝜃, the shear force 𝑄 and the bending moment 𝑀. The time convention is chosen to be 𝑒 -𝑗𝜔𝑡 . The governing equations can be written in the state-space as

𝜕𝐗 𝜕𝑥 = 𝐇𝐗, (1)
with

𝐇 = ⎡ ⎢ ⎢ ⎢ ⎣ 0 1 0 0 0 0 0 1∕𝐸 * (T)𝐼 -𝜌𝑆𝜔 2 0 0 0 0 0 -1 0 ⎤ ⎥ ⎥ ⎥ ⎦ = [ 𝐇 1 𝐇 2 𝐇 3 𝐇 4 ] . (2)
H is the transition matrix, which is a compact formulation of the Euler-Bernoulli model, where 𝜔 is the angular frequency, 𝜌 is the mass density, 𝑆 is the beam cross-sectional area and 𝐼 is the moment of inertia. 𝐸 * (T) = 𝐸(1 + 𝑗𝜂) is the local equivalent complex storage modulus describing the elastic (with the Young's modulus 𝐸) and viscous properties (with the loss factor 𝜂) of the sandwich beam compound by the aluminium and SMP layers at temperature T. The equivalent parameters of the multi-layer termination are computed in Eq. ( 2) using the Ross Ungar Kerwin mixing law [START_REF] Ross | Damping of plate flexural vibrations by means of viscoelastic laminae[END_REF] (see [START_REF] Denis | Measurement and modelling of the reflection coefficient of an acoustic black hole termination[END_REF]).The impedance matrix Z, which relates the kinematic and the force in 𝐗, can be expressed by solving the Riccati equation (see Eq. (A.4) in [START_REF] Georgiev | Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect[END_REF]):

𝜕𝐙 𝜕𝑥 = -𝐙𝐇 1 -𝑗𝜔𝐙𝐇 2 𝐙 + 𝐇 3 𝑗𝜔 + 𝐇 4 𝐙. ( 3
)
This equation is linear since it does not depend on the 𝑥 axis for 𝑥 < 0. It can therefore be directly solved from the free end condition at 𝑥 = l i to 𝑥 = 0 + for each blade i (with i = 0 , 1 , 2 or 3 ).

At the junction (see Fig. 1(g)), the continuity of displacement and slope, and the balance of forces and moments give the following system for one or multiple attached blades:

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 𝑤(0 -) = 𝑤(0 + ) 𝜃(0 -) = 𝜃(0 + ) 𝑄 𝑘 (0 -) = ∑ 𝑖 𝑄 𝑖 (0 + ) 𝑀 𝑘 (0 -) = ∑ 𝑖 𝑀 𝑖 (0 + ) . ( 4
)
In terms of impedance, these relations can be written in a compact way as a simple impedance addition considering two blades 𝑖 and 𝑗 (see Fig. 1(g)):

𝐙 k (0 -) = 𝐙 i (0 + ) + 𝐙 j (0 + ), (5)
where 𝐙 i (0 + ) and 𝐙 j (0 + ) are the impedances of the blades i et j before the junction and 𝐙 k (0 -) is the impedance of the full termination after the junction (see Fig. 1

(g)). The index k denotes the beam configuration (A), (B) or (C).

In order to calculate the reflection matrix R at 𝑥 = 0 -, the final step consists in switching from the state to the wave formalism, which leads to

𝐑 = [𝑗𝜔𝐙𝐄 2 -𝐄 4 ] -1 [𝐄 3 -𝑗𝜔𝐙𝐄 1 ], ( 6
)
where E is the matrix whose columns are the eigenvectors of -𝑗𝐇 (see Eqs. (A.5) to (A.10) in [START_REF] Georgiev | Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect[END_REF]). Although R is a matrix whose diagonal components describe the reflection of propagative and evanescent waves, the following sections will focus only on the far-field propagation (𝑥 → -∞). The component R 11 , which carries the energy and is frequency dependent, is therefore only considered and denoted R in the following. The modulus of R is plotted in Fig. 2(a) in the complex frequency plane for a nominal geometry. This nominal geometry is chosen to be a beam of thickness h = 10 mm extended by the blade 1 . The background color map corresponds to log|R| plotted in the complex frequency plane in the case where the system is quasi-conservative with the SMP at room temperature (20°C): at this temperature, the SMP is in a glassy state with a very small loss factor. One pole (yellow spot), for which |R| is singular, can be noticed as well as a zero (blue spot) at a specific complex frequency. The real part of the frequency associated to the pole and zero corresponds to the resonance frequency of the system, whereas the imaginary part corresponds to the amount of losses in the system. In the conservative case, these losses are directly the energy leakage propagating from the blade to the beam. As the time convention is 𝑒 -𝑗𝜔𝑡 , the frequency of the poles has a negative imaginary part. In a conservative case, the frequency of zeros and poles are complex due to the temporal invariance property of the scattering matrix. As a consequence, the position of the poles can be controlled by introducing losses into the system. If the losses exactly compensate the leakage, the zero is exactly located on the real frequency axis. This phenomenon is called the critical coupling [START_REF] Romero-Garcia | Use of complex frequency plane to design broadband and sub-wavelength absorbers[END_REF][START_REF] Groby | Use of slow sound to design perfect and broadband passive sound absorbing materials[END_REF].

The losses and the elastic properties are tuned using a heated layer of SMP. The intrinsic viscoelastic properties of this material are plotted as a function of the temperature and frequency on Fig. 3 [START_REF] Butaud | Sandwich structures with tunable damping properties: On the use of shape memory polymer as viscoelastic core[END_REF]. The Young modulus 𝐸 decreases in a monotonous way with the temperature and rapidly around 70°C at 100 Hz. This fast variation corresponds to the glass transition. The loss factor 𝜂 increases rapidly up to the glass transition to reach a high value of 2.5, then decreases.

Figures 2(b) and 2(c) show the effect of increasing the losses on the location of the zero in the complex frequency plane. The resulting |R| along the real frequency is also plotted in Fig. 2(d). Figure 2(b) corresponds to the system with losses (heated at 44°C). By increasing the losses, which corresponds to increasing the temperature from 44°C to 48°C then 51°C, the zero can be moved and aligned on the real frequency axis and thus reach the critical coupling (see Fig. 2(c)). Above that temperature, there is too much losses to achieve this goal.

Figure 2(a) depicts the variation of the zero position when the temperature and the geometry of the blade evolve. The white dashed line under the colored markers, the color of which refers to the temperature (see Fig. 2(e)) describes the evolution of the first zero when the temperature increases from 20 to 100°C for the nominal geometry. The shape of the trajectory is in accordance with the intrinsic temperature dependent properties of the SMP: the zero monotonously shifts to the low frequencies when the temperature rises and the losses increase until the glass transition state of the SMP and then decrease. It can be observed that two different temperatures result in locating the zero on the real frequency axis.

Figure 2(a) also shows two other parametric variations on the length l i and the thickness h i , see the inset Fig. 2(e). For each increment of the geometric variation, the same temperature variation is applied. The length variation is marked with a set of blue points of different shade. Each shade is an increment of l i . When l i increases, the trajectory moves towards the low frequencies by tightening. In a similar way, when the thickness of the beam h i decreases (set of red points), the trajectory moves towards the high frequencies and towards the positive imaginary frequencies.

This representation provides a deep understanding of the roles played by l i , h i and the temperature in the position of the zeros of R. It can be noticed that it is possible to locate a zero on the real frequency axis on a large frequency band by playing with these 3 parameters. By considering the same process for the zeros corresponding to the higher order modes, it is possible to locate a zero on the real frequency axis at very high frequencies. In addition, it is possible to reach very low frequencies by playing with other parameters such as the thickness of the uniform beam (i.e., single-blade (A)).

In the following, it is proposed to build a tool providing the operating temperature that leads to a perfect absorption at a target frequency and for a given resonator geometry. This tool is depicted in Fig. 4, in which a surface gathering all the configurations of length l i and thickness h i that lead to a perfect absorption at a given temperature T and frequency 𝑓 is represented. To obtain the surface in Fig. 4, the previous analysis is repeated by varying the temperature and the geometry of the blade. Then, all the configurations that give rise to a critical coupling are stored (i.e., the configurations where the zero is located on the real frequency axis). Finally, these data are organized in the form of a surface with l i , h i and T. The color scale indicates the frequency at which |R| = 0. This surface can be read as follows: for the nominal geometry l i = 15 mm and h i = 0.8 mm, the vertical line crosses the surface at two points M and N. This means that two critically coupled configurations are found, one at 51°C for 3.5 kHz (point M) and another at 80°C for 2.2 kHz (point N). Referring to Fig. 2(d), the trajectory of the zero intersects twice the real frequency axis at these points. The folding of this surface corresponds to the case where the top of the trajectory of the zero in Fig. 2(a) is to the real frequency axis.

Using this surface, it becomes possible to find the geometrical configurations of blade meeting the critical coupling conditions at the targeted frequencies and fixed temperature. In the case of a SMP temperature fixed at 80°C and targeted frequencies 𝑓 1 = 2.2 kHz, 𝑓 2 = 1.2 kHz and 𝑓 3 = 2 kHz, the configurations for which the critical coupling conditions are met correspond to the intersections of the white and black lines in Fig. 4, and denoted by the point N, P and Q. The geometry and temperature corresponding to these points are given in Tab. 1. The blade 0 has been subjected to the same analysis with a thinner uniform beam in order to reach lower frequencies.

Numerical and experimental application

The systems (A), (B), (C), represented in Figs. 1(a),(b),(c), are designed from the previous study. The single-blade (A) has a thickness h = 5 mm and is ended by the blade denoted 0 . The dual-blades are thicker, h B = h C = 10 mm, for manufacturing reasons, and are ended by the blades 1 and 2 for the configuration (B) and the blades 1 and 3 for the configuration (C). The length l i and the thickness h i of the blades, as well as the operating temperature T and the target frequency 𝑓 of each blades are detailed in the Tab. 1. The double-blade systems are therefore built from an analysis which considers each single-blade independently, without accounting for the coupling between blades. Figures 5(a), 5(b) and 5(c) show the variations of |R| in the complex frequency plane. The points noted k i denote the zeros of R of the system k induced by the blade i. For comparison, the points noted S i are the zeros of single-blade systems. The variations of R on the real frequency axis are shown in Figs. 5(d),(e),(f).

When the blades are designed for two frequencies that are far away from each other, the zeros of the dual-blade (B) almost correspond to the zeros of the two associated single-blades (see Fig. 5(b)). On the contrary, when the targeted frequencies are close to each other, the zeros of the dual-blade (C) no longer correspond to the zeros of the isolated single-blades (see Fig. 5(c)) and are thus no longer located on the real frequency axis. Both the frequencies and the amplitude of |R| are different (see Fig. 5(f)). This could be explained by a coupling effect between the two blades.

It can be noted, however, that it is possible to exactly reach zero at one of the two target frequencies by adjusting the temperature. Referring to the trajectory of the zero in Fig. 2(a), in order to locate C 1 on the real frequency axis, the temperature has to be lowered. Conversely, to locate C 3 on the real frequency axis, the temperature should be increased. Besides, it is possible to design a dual-blade system able to reach two critical couplings at close frequencies. This requires to account for the coupling between both blades in the parametric study, which is not addressed in this article. Although the perfect absorption at wide frequency range cannot be reached using this method, multi-blade systems are still relevant solutions for widening the damping frequency range of systems.

The three systems (A), (B) and (C) (see Figs. 1(d),(e),(f)) are manufactured in aluminum beams of length L ≈ 1 m by wirecut electrical discharge machining. The layer of SMP is glued to each blade with epoxy glue. The beam is hanged with elastic wires (Fig. 1(g)) to mimic free boundary conditions. To ensure the most uniform thermal field possible, the beam is placed in a thermal chamber for the time of the measurements. To verify the effective temperature, a thermal controler (RKC REX-D100 with a precision of 0.1°C) is used with the sensor located near the SMP layer. The temperature regulation has been observed to be stable within a 1°C interval. The measurements are performed with a temperature step varying between 5°C and 0.5°C depending on the change of the mechanical properties of the SMP (the 0.5°C step was used close to the target temperatures). All measurements are started 2 minutes after temperature stabilization so that the temperature can be considered as uniform in the sample. This procedure has been successfully proven in previous works [START_REF] Butaud | Sandwich structures with tunable damping properties: On the use of shape memory polymer as viscoelastic core[END_REF][START_REF] Billon | Design and experimental validation of a temperature-driven adaptive phononic crystal slab[END_REF][START_REF] Ouisse | Damping control for improvement of acoustic black hole effect[END_REF]. A voice-coil is used for the excitation to generate a white noise at 𝑥 = x S . The displacement field is measured at five positions x i (i ∈ [1 ∶ 5]) using accelerometers located between the excitation and the equipped end. Then, the contributions of the forward and backward propagating and evanescent waves amplitudes are identified using an inverse technique in order to estimate R [START_REF] Denis | Measurement and modelling of the reflection coefficient of an acoustic black hole termination[END_REF].

The analytical results are compared with the experimental measurements in Figs. 5(g) to 5(p) for different SMP temperatures. The critical couplings expected in practice are not reached exactly at the same temperature as in simulation. T Ref is used to refer to the temperature showing comparable numerical and experimental results. The 2). However, a good trend can be observed in Fig. 5, in which the red curves show the experimental results and the dashed black curves show the numerical results accounting for the machining geometry errors of the blades (about 0.01 mm). The slight temperature-dependence of the elastic parameters of the aluminum is also considered [START_REF] Stanford | Le module d'young de l'aluminium et de ses alliages en fonction de la température [the young's modulus of aluminium and its alloys as a function of temperature[END_REF]. The frequency offset can be explained by the thin layer of glue and the added mass of the accelerometers which are not taken into account in the model. It can also be explained by the slight difference between the experimental parameters of the SMP and those obtained from the empirical model [START_REF] Butaud | Sandwich structures with tunable damping properties: On the use of shape memory polymer as viscoelastic core[END_REF].

(g) (h) (i) (m) (o) (p) (j) (k) (l) (a) (b) (c) (d) (e) (f)
For system (A), the critical coupling is reached (see Fig. 5(j)). Around this reference temperature, it is clear that the trend is well captured experimentally (see Figs. 5(g),(m)). For system (B), the same conclusions as for (A) can be drawn. As expected, two critical couplings for two different frequencies are obtained (see Figs. 5(h),(k),(o)). For system (C), the same trends as in simulation are obtained (see Figs. 5(i),(l),(p)). The critical coupling can be reached on the first or the second drop by slightly decreasing or increasing the temperature. This is the case at 2.1 kHz for the second drop in Fig. 5(i). The drop at 1.1 kHz comes from a twisting mode.

Conclusion

The system proposed in this paper is a bending subwavelength resonator enhanced by thermal control. It provides a way to obtain a zero reflection at a target frequency by adjusting the length and thickness of a blade attached to a beam of given width and thickness. This blade is covered with a layer of SMP whose stiffness and damping properties depend on the temperature. It is a versatile system: if some parameters are constrained such as the geometry of the host beam or the thickness of the SMP layer, it is still possible to adjust the blade geometry to reach a target frequency. On the contrary, if the blade geometry is constrained, it is always possible to adapt the thickness of the SMP layer and play with the temperature.

In addition, we showed that it is possible to design a multi-resonant system by simply adding blade endings. The model presented is valid for more than two blades. It has been shown that these multiresonators are efficient in a homogeneous temperature environment as long as the blades are designed for this operating temperature. A nice way to improve the system would consist in designing a multiresonator where the temperature for each blade would be controlled independently. In this manner, it may be possible to achieve broadband perfect absorption, at least for some frequency ranges.

Figure 1 :

 1 Figure 1: (a) Schematic view of the single-blade (A). (b) Resp. dual-blade (B). (c) Resp. dual-blade (C). The geometry of the blades are reported in Tab. 1. h A = 5 mm, h B = h C = 10 mm and h SMP = 2 mm. (d) Photograph of single-blade (A) realised by wirecut electrical discharge machining. (e) Resp. dual-blade (B). (f) Resp. dual-blade (C). (g) Schematic view of the experiment set-up. The configurations (A), (B), (C), denoted k in a general case, are hung up in a thermal chamber.The reflection coefficient at 𝑥 = 0 is measured using a voice-coil source at x S about 1 cm from the free edge and 5 accelerometers 25 mm apart halfway between x S and 𝑥 = 0. The lenghts l i and l j denote the length of the blades. 𝐙 i and 𝐙 j denote the impedance matrices of the blades at 𝑥 = 0 + and 𝐙 k denotes the impedance matrix of the whole system at 𝑥 = 0 -.

Figure 2 :

 2 Figure 2: (a) Position of the zero under parametric variation. The variation of temperature is followed by the color marker and the dashed white trajectory. The blue (resp. red) markers correspond to the white trajectory with a variation of length (resp. thickness). The colormap corresponds to log|R| of the nominal configuration at 20°C. The black frame corresponds to the zoom of (b) and (c). (b) Complex frequency plane of log|R| (colormap) of the nominal configuration at 44°C. (c) Complex frequency plane of log|R| of the nominal configuration at 51°C. The white dashed line indicates the trajectory of the zero when the temperature increases. The markers corresponds to the position of the first zero at 44°C, 48°C and 51°C. (d) |R| as function of Re(f) for the 3 temperature configurations at 44°C, 48°C and 51°C corresponding to the markers of (c). (e) Caption block for the parametric variation.

Figure 3 :

 3 Figure 3: Temperature and frequency dependence of the Young's modulus 𝐸 and the loss factor 𝜂 of the shape memory polymer (tBA/PEGDMA) governed by the empirical formula in [16].

Figure 4 :

 4 Figure 4: Surface gathering all the configurations of length l i and thickness h i leading to a perfect absorption at operating temperature T. The absorption frequency is represented by the colormap. The points M and N are the two critical coupling configurations for a nominal geometry occurring at 51°C and 80°C. The white line represents a chosen temperature of 80°C and the black lines are the isolines of the target frequencies 𝑓 1 , 𝑓 2 and 𝑓 3 . The points M, P and Q denote the configurations from the temperature and frequency set point which corresponds to the intersection between the white and black lines.

Figure 5 :

 5 Figure 5: (a) log|R| in the complex frequency plane of the single-blade (A) at 85°C. The zero and pole are marked by the black circle and dot. The label A 0 names the zero induced by the blade 0 of the system (A). (d) |R| along the real frequency axis of the single-blade (A). (b) log|R| in the complex frequency plane of the dual-blade (B) at 80°C. The labels B 1 and B 2 denote the zeros induced by the blades 1 and 2 of the system (B). The color labels S 1 and S 2 , marked with color circles, denote the position of the zero induced by the blade 1 and 2 of a two single-blades. (e) |R| along the real frequency axis of the double-blade (B) in black. The dashed color lines correspond to |R| of the compared single-blades. (c) and (f) same as (b) and (e) for the dual-blade (C) involving the blades 1 and 3. (g) to (p) present the measured |R| in red solid lines of the systems (A) (first column: (g), (j) and (m)), (B) (second column: (h), (k) and (o)) and (C) (third column: (i), (l) and (p)), compared to the numerical |R| in black dashed lines computed accounting for the machining geometry. In lines (i.e., (j), (k) and (l)) are the resulted |R| for different operating temperature around T Ref , see Tab. 2.

Table 1

 1 Geometry, target frequency and operating temperature for each blade.

	Blade	0	1	2	3
	l i (mm)	20	15	18.8	15.5
	h i (mm) 0.3867	0.8	0.71	0.79
	𝑓 (Hz)	500	2200 1200 2000
	T (°C)	85	80	80	80

Table 2

 2 Numerical and experimental T Ref for the systems (A), (B) and (C).

	System	(A) (B) (C)
	T num Ref (°C)	85	80	80
	T exp Ref (°C)	95	90	88

guillaume.raybaud@univ-lemans.fr G. Raybaud et al.: Preprint submitted to Elsevier

Acknowledgments

The work has been founded by the Agence Nationale de la Recherche in the framework of the project eTNAA (ANR-17-CE08-0035-01, 2017-2021). This work also has been supported by the EIPHI Graduate school (contract "ANR-17-EURE-0002"). Jean-Philippe Groby and Vicent Romero-García acknowlegde the financial support of the ANR-RGC METARoom (ANR-18-CE08-0021) project and the project HYPERMETA funded under the program Étoiles Montantes of the Région Pays de la Loire.


Kishalay Bhar

Wenbin Guo

Mathieu Gonidec

Venkata Nikhil

Franc Perdih Surabhi Bhatt

Philippe Guionneau
email: philippe.guionneau@u-bordeaux.fr

Guillaume Chastanet
email: guillaume.chastanet@icmcb.cnrs.fr

Anuj K Sharma
email: anuj.sharma@curaj.ac.in

Franc Perdih

High temperature spin crossover behaviour of mononuclear bis-(thiocyanato)iron( ii ) complexes with judiciously designed bidentate N-donor Schiff bases with varying substituents

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

Introduction

Spin state switching [Low Spin (LS) ↔ High Spin (HS)] triggered by external perturbations (T, P, hυ) in spin crossover (SCO) [START_REF] Kahn | Spin-transition polymers: from molecular materials toward memory devices[END_REF][START_REF] Gütlich | Spin Crossover in Transition Metal Compounds I[END_REF][START_REF] Bousseksou | Switching of molecular spin states in inorganic complexes by temperature, pressure, magnetic field and light: towards molecular devices[END_REF] molecules leads to changes in magnetic moment, conductivity, dielectric constant and even colour of the material. This makes SCO materials suitable for applications as molecular switches or memories in information and sensor devices. [START_REF] Kahn | Spin-transition polymers: from molecular materials toward memory devices[END_REF][START_REF] Gamez | Iron Spin-Crossover compounds: from fundamental studies to practical applications[END_REF][START_REF] Lefter | Charge transport and electrical properties of spin crossover materials: towards nanoelectronic and spintronic devices[END_REF][START_REF] Kumar | Sublimable Spin-Crossover Complexes: From Spin-State Switching to Molecular Devices[END_REF][START_REF] Ridier | Unprecedented switching endurance affords for high-resolution surface temperature mapping using a spin-crossover film[END_REF][START_REF] Dayen | Room temperature optoelectronic device operating with spin crossover nanoparticles[END_REF] In general, transition metal complexes with electronic configurations 3d n (n = 4-7) in suitable octahedral coordination environments are known to exhibit SCO phenomenon. [START_REF] Kahn | Spin-transition polymers: from molecular materials toward memory devices[END_REF] Among them, iron(II) (3d [START_REF] Kumar | Sublimable Spin-Crossover Complexes: From Spin-State Switching to Molecular Devices[END_REF] ) SCO complexes are widely studied due to their remarkable change in magnetic and optical properties during the electronic transition from the diamagnetic (S = 0, t 2g [START_REF] Kumar | Sublimable Spin-Crossover Complexes: From Spin-State Switching to Molecular Devices[END_REF] , [START_REF] Kahn | Spin-transition polymers: from molecular materials toward memory devices[END_REF] A 1g ) LS state to the paramagnetic (S = 2, t 2g 4 e g 2 , [START_REF] Lefter | Charge transport and electrical properties of spin crossover materials: towards nanoelectronic and spintronic devices[END_REF] T 1g ) HS state. [START_REF] Kahn | Spin-transition polymers: from molecular materials toward memory devices[END_REF] In the solid state, the SCO behaviour of a molecule is primarily defined by two well-known parameters such as its transition temperature (T 1/2 ) and cooperativity.

The transition temperature (T 1/2 ), 1 defined as the temperature at which the ratio of HS and LS fractions are equal, depends upon coordinated ligand environment around the metal centre. It is evident that weak field ligand stabilising the HS state of metal ion results in low T 1/2 value. On contrary, a strong ligand field stabilises the LS state and the T 1/2 value shifts towards the higher temperature region. [START_REF] Zheng | Stabilization of the low-spin state in a mononuclear iron (II) complex and high-temperature cooperative spin crossover mediated by hydrogen bonding[END_REF] Thus to achieve spin transition near room temperature for SCO molecules, judiciously designed ligands frameworks that can stabilise the LS state are required. Properly designed Schiff bases [START_REF] Kumar | Spin-crossover in iron (II)-Schiff base complexes[END_REF] are well-suited for this purpose because of their ease of preparation and versatility in ligand framework, where the ligand field can be easily fine-tuned by smart variation of the amine and carbonyl components.

The cooperativity [START_REF] Nicolazzi | Thermodynamical aspects of the spin crossover phenomenon[END_REF][START_REF] Reeves | Mapping the cooperativity pathways in spin crossover complexes[END_REF][START_REF] Spiering | Elastic interaction in spin-crossover compounds[END_REF][START_REF] Enachescu | Elastic models, lattice dynamics and finite size effects in molecular spin crossover systems[END_REF] in SCO systems may be defined as how effectively the local change in spin state at the metal site is transmitted among the spin active metal ions via non-covalent and/or covalent bonds throughout the crystal lattice, in a multiscale description. [START_REF] Guionneau | Multiscale Approach of Spin Crossover Materials: A Concept Mixing Russian Dolls and Domino Effects[END_REF][START_REF] Guionneau | Crystallography and spin-crossover. A view of breathing materials[END_REF] The SCO behaviour of molecules is markedly varied from gradual to abrupt to hysteretic with the improvement of cooperative elastic interactions between the molecules. In literature SCO behaviours of cis-[Fe II (L) 2 (NCS) 2 ] complexes containing the bidentate N-donor ligands (L) are well documented. [START_REF] Guionneau | Spin Crossover in Transition Metal Compounds II[END_REF][START_REF] Tailleur | Thermal spincrossover with a large hysteresis spanning room temperature in a mononuclear complex[END_REF][START_REF] Tailleur | Using polymorphism to master the spin crossover mechanism in [Fe (PM-PeA) 2 (NCSe)[END_REF][START_REF] Guo | Unprecedented reverse volume expansion in spin-transition crystals[END_REF][START_REF] Létard | Wide Thermal Hysteresis for the Mononuclear Spin-Crossover Compound cis-Bis (thiocyanato) bis [N-(2 '-pyridylmethylene)-4-(phenylethynyl) anilino] iron (II)[END_REF][START_REF] Létard | Structural, magnetic, and photomagnetic studies of a mononuclear iron (II) derivative exhibiting an exceptionally abrupt spin transition. Light-induced thermal hysteresis phenomenon[END_REF][START_REF] Guionneau | Structural approach of the features of the spin crossover transition in iron (II) compounds[END_REF][START_REF] Létard | Structural, magnetic and photomagnetic study of the [Fe (PM-NEA) 2 (NCS) 2] spin crossover complex[END_REF][START_REF] Létard | Spin crossover properties of the [Fe (PM-BiA) 2 (NCS) 2] complex-Phases I and II[END_REF] In this regard, system to obtain spin crossover near or above room temperature region. In X-PPMA, a phenyl group is introduced in place of imine H of PM-L ligand to enhance the electronic conjugation in the ligand framework (Scheme 1) for effective stabilisation of LS state of iron(II). [START_REF] Zheng | Stabilization of the low-spin state in a mononuclear iron (II) complex and high-temperature cooperative spin crossover mediated by hydrogen bonding[END_REF] In addition, we have also varied the para-substituent of the aniline derivative from ClBrCH 3 to explore their effect on SCO behaviour. [START_REF] Wang | Ligand Substituent Effects on the Spin-Crossover Behaviors of Dinuclear Iron (II) Compounds[END_REF] Successfully, three new iron(II) complexes of type cis-[Fe(X-PPMA)

complexes
2 (NCS) 2 ]•H 2 O [4-X-N-(phenyl(pyridin-2-yl)methylene)aniline; X-PPMA; X = -Cl (1), -Br (2), -CH 3 ( 3

Results and discussion

Synthesis and characterization

Three new bidentate N-donor Schiff bases (Cl-PPMA, Br-PPMA and CH 3 -PPMA)

were synthesized by refluxing 1:1 molar ratio of 2-benzoylpyridine and the corresponding aniline derivative (4-chloroaniline, 4-bromoaniline and 4methylaniline) in methanol for 24 h. All the ligands were characterized by ESI-MS and 1 H-NMR spectroscopy (see experimental section). Complexes (1-3) were isolated in dark blue crystalline form by mixing 2:1 molar ratio of the respective Schiff bases and Fe(NCS) 2 (prepared in-situ see experimental section) in methanol under nitrogen atmosphere at room temperature. The composition of complexes (1-3) was ascertained by elemental analyses and spectroscopic studies (see experimental section). In the FTIR spectra, complexes 1-3 shows the characteristic bands of cis-oriented nitrogen bonded thiocyanate ν(C≡N) around 2100 and 2057 cm -1 and peaks of Schiff bases ν(C=N + C=C) in the range 1625-1470 cm -1 (see experimental section).

Room temperature characterizations

The spin state of iron(II) in 1-3 was determined through room temperature Mössbauer and crystallographic studies.

Room temperature Mössbauer studies on 1-3 reveal one doublet with relatively low values of quadrupole splitting (∆E Q < 1 mm/s) and isomer shift (δ < 0.5 mm/s) parameters (Table S1; Figure S1) which are attributed to the LS state ( 1 A 1g ) of iron(II). [START_REF] Gütlich | Spin crossover phenomena in Fe (ii) complexesDedicated to Professor FA Cotton on occasion of his 70th birthday[END_REF] The structural data for 1-3 at 293(2) K (1 RT , 2 RT and 3 RT ) reveals complexes 1-3 crystallize in tetragonal system with a chiral space group either P4 3 2 1 2 (1) or P4 1 2 1 2

(2 and 3) as a mixture of two possible enantiomers (Λ or Δ) in bulk sample. [START_REF] Suryadevara | Chiral Resolution of Spin-Crossover Active Iron (II)[2x2] Grid Complexes[END_REF][START_REF] Bartual-Murgui | Chiral and racemic spin crossover polymorphs in a family of mononuclear Iron (II) compounds[END_REF][START_REF] Ma | Homochiral versus racemic polymorphs of spin-crossover iron (ii) complexes with reversible LIESST effect[END_REF] 1-3 contain [Fe(X-PPMA) 2 (NCS) 2 ] molecular unit (X = Cl for 1, Br for 2 and CH 3 for 3) (Table S2). Electron density associated with disordered solvent molecules was removed by solvent mask. Therefore, the chemical formula and crystal data given in Table S2 do not take into account these solvent molecules. In each complex, the iron(II) centre is located on the two-fold rotation axis adopting a pseudo-octahedral geometry (Figure 1). The iron(II) centre is coordinated by two pyridine N atoms (N1 and N1 i ), two imine N atoms (N2 and N2 i ) of two bidentate Schiff bases (Cl-PPMA for 1, Br-PPMA for 2 and CH 3 -PPMA for 3) along with two cis-oriented thiocyanato N atoms (N3 and N3 i ) (symmetry code: (i) x, y, -z + 1). The equatorial plane is formed by two imine N atoms and two thiocyanato N atoms. The axial sites are occupied with two pyridine N atoms. The average Fe-N distances are 1.9669 Å for 1, 1.9703 Å for 2 and 1.9651 Å for 3 (Table S3), strongly suggesting a LS state of iron(II) in 1-3. The distortion around the iron(II) centre is calculated in terms of angle distortion parameters [START_REF] Guionneau | Multiscale Approach of Spin Crossover Materials: A Concept Mixing Russian Dolls and Domino Effects[END_REF][START_REF] Guionneau | Crystallography and spin-crossover. A view of breathing materials[END_REF][START_REF] Ketkaew | OctaDist: a tool for calculating distortion parameters in spin crossover and coordination complexes[END_REF] S4).

Variable temperature magnetic susceptibility studies of 1-3

Variable-temperature magnetic susceptibility measurements were carried out on crystalline samples between 10-500 K for 1 and 10-475 K for 2 and 3. The temperature dependent plots ( being the molar magnetic susceptibility, Regarding complex 3, the temperature dependent plot (Figure 4 combines SQUID and VSM measurements) shows that it exhibits a complete and noncooperative spin crossover above room temperature with strong irreversible features.

The value remains close to 0-0.2 cm 3 .K.mol -1 between 10-300 K suggesting LS state of iron(II) as evident from room temperature Mössbauer spectra and cooling) 200 K. Additionally, the original hydrated sample of complex 3 was heated in an oven at 480 K outside SQUID and then magnetic measurement was performed by cooling the sample from 300 K to 10 K. The cooling path is identical with the second cooling curve of the previous measurement. When a 830 nm light irradiation is applied at 10 K on a fresh sample, no photoswitching is observed, while after thermal treatment at 450 K, around 40% of conversion is recorded, witnessing the occurrence of the LIESST effect. [START_REF] Decurtins | Light-induced excited spin state trapping in a transition-metal complex: The hexa-1-propyltetrazoleiron (II) tetrafluoroborate spin-crossover system[END_REF] The photo-induced state can be erased upon warming at 0.5 K/min above 80 K, with a relaxation temperature T(LIESST) = 60 K. [START_REF] Chastanet | A critical review of the T (LIESST) temperature in spin crossover materials-What it is and what it is not[END_REF][START_REF] Létard | Critical temperature of the LIESST effect in iron (II) spin crossover compounds[END_REF] Mononuclear bis-(thiocyanato)iron(II) spin crossover complexes of formula [Fe(L) n (NCS) 2 ] generally exhibit the equilibrium temperature (T 1/2 ) below room temperature region. [START_REF] Guionneau | Spin Crossover in Transition Metal Compounds II[END_REF][START_REF] Tailleur | Thermal spincrossover with a large hysteresis spanning room temperature in a mononuclear complex[END_REF][START_REF] Tailleur | Using polymorphism to master the spin crossover mechanism in [Fe (PM-PeA) 2 (NCSe)[END_REF][START_REF] Guo | Unprecedented reverse volume expansion in spin-transition crystals[END_REF][START_REF] Létard | Wide Thermal Hysteresis for the Mononuclear Spin-Crossover Compound cis-Bis (thiocyanato) bis [N-(2 '-pyridylmethylene)-4-(phenylethynyl) anilino] iron (II)[END_REF][START_REF] Létard | Structural, magnetic, and photomagnetic studies of a mononuclear iron (II) derivative exhibiting an exceptionally abrupt spin transition. Light-induced thermal hysteresis phenomenon[END_REF][START_REF] Guionneau | Structural approach of the features of the spin crossover transition in iron (II) compounds[END_REF][START_REF] Létard | Structural, magnetic and photomagnetic study of the [Fe (PM-NEA) 2 (NCS) 2] spin crossover complex[END_REF][START_REF] Létard | Spin crossover properties of the [Fe (PM-BiA) 2 (NCS) 2] complex-Phases I and II[END_REF] The bidentate Schiff bases, PM-L (Scheme 1) containing pyridine-2-carboxyaldehyde and aniline derivatives are widely used in literature (Table 1, Sl. No 1-9). In X-PPMA, one phenyl group is introduced instead of the imine hydrogen of PM-L Schiff bases (Scheme 1). The presence of phenyl group enhances the conjugation in X-PPMA ligand system, strengthening the ligand field as compared to the other PM-L ligands, and stabilises the LS state of iron(II) up to 300 K. As a result, complexes 1-3 show temperature induced gradual spin crossover behaviour above 300 K (Table 1, Sl. No 10-12) with some irreversible features. While complexes 1 and 2 do not exhibit any photoswitching at low temperature, complex 3

does after warming at 450 K. According to the linear T(LIESST) vs T 1/2 relationship reported for the spin crossover complexes (T(LIESST) = T 0 -0.3T 1/2 ), [START_REF] Chastanet | A critical review of the T (LIESST) temperature in spin crossover materials-What it is and what it is not[END_REF][START_REF] Létard | Critical temperature of the LIESST effect in iron (II) spin crossover compounds[END_REF] An important feature of these new compounds is that they crystallize with solvent molecules, which is not the case for the other complexes and polymorphs. The loss of solvent might be at the origin of the irreversible behaviours recorded. Therefore, thermo-gravimetric analyses (TGA) and variable temperature X-ray studies were performed. [Fe(PM-PEA) 2 (NCSe) 2 ]-I [START_REF] Tailleur | Thermal spincrossover with a large hysteresis spanning room temperature in a mononuclear complex[END_REF] Hysteresis and reversible/T 1/2 ↓= 266 K, T 1/2 ↑= 307 K/ΔT = 41 K 3.

[Fe(PM-PEA) 2 (NCSe) 2 ]-II [START_REF] Tailleur | Using polymorphism to master the spin crossover mechanism in [Fe (PM-PeA) 2 (NCSe)[END_REF] Gradual and reversible/T 1/2 = 245 K 4.

[Fe(PM-BiA) 2 (NCS) 2 ]-II [START_REF] Létard | Structural, magnetic, and photomagnetic studies of a mononuclear iron (II) derivative exhibiting an exceptionally abrupt spin transition. Light-induced thermal hysteresis phenomenon[END_REF] Abrupt and reversible/T 1/2 ↓=168 K, T 1/2 ↑= 173 K/ΔT = 5 K 5.

[Fe(PM-BiA) 2 (NCS) 2 ]-I [START_REF] Létard | Spin crossover properties of the [Fe (PM-BiA) 2 (NCS) 2] complex-Phases I and II[END_REF] Gradual and reversible/T 1/2 = 198 K 6.

[Fe(PM-TeA) 2 (NCS) 2 ] [START_REF] Guionneau | Structural approach of the features of the spin crossover transition in iron (II) compounds[END_REF] Gradual and reversible/ T 1/2 ↓=186 K, T 1/2 ↑= 192K/ΔT = 6K 7.

[Fe(PM-AzA) 2 (NCS) 2 ] [START_REF] Guionneau | Structural approach of the features of the spin crossover transition in iron (II) compounds[END_REF] Gradual and reversible/ T 1/2 ↓=186 K, T 1/2 ↑= 192K/ΔT = 6K 8.

[Fe(PM-NEA) 2 (NCS) 2 ] [START_REF] Létard | Structural, magnetic and photomagnetic study of the [Fe (PM-NEA) 2 (NCS) 2] spin crossover complex[END_REF] Very gradual and reversible/T 1/2 = 204 K 9.

[Fe(PM-pBrA) [Fe(CH

Thermogravimetric analyses of 1-3

Thermogravimetric analyses (TGA) of complexes 1-3 were made between 30 and 800 °C in the static atmosphere of nitrogen to examine their thermal stabilities. TG curve (Figure S6)

indicates that complexes 1-3 are stable respectively up to 231 °C, 232 °C and 272 °C, and then decompose gradually up to 800 °C. Complexes 1 and 2 show a gradual weight loss (observed: 2.1%, calculated: 2.3% for 1; Figure S7; observed: 1.9%, calculated: 2.0% for 2;

Figure S8) in the temperature range 60-140 °C and 60-122 °C, respectively corresponding to a water molecule. However, for complex 3 the water molecule is released in two steps in the temperature range 72-177 °C and 177-203 °C (observed: 2.38% and calculated: 2.4%; Figure 5).

Figure 5 TGA plot and loss of water in complex 3.

Variable-temperature crystallographic studies of 1-3

To establish magneto-structural correlations, variable-temperature crystallographic data were collected for complexes 1-3. The crystal structures of 1 and 2 were determined at 150 K (1/2 150K ), 250 K (1/2 250K ), 300 K (1/2 300K ), 350 K (1/2 350K ), 400 K (1/2 400K ), 450 K (1/2 450K ) in warming mode. The complexes crystallise in tetragonal system with a chiral space group either P4 3 2 1 2 (for 1) or P4 1 2 1 2 (for 2) (Tables S4 andS5). The spin state of iron(II) is determined based on variable-temperature (150-450 K) structural evidences such as <Fe-N> bond length, bond length distortion () and bond angle distortion (, ) parameters (Tables S6 andS7). It is observed that iron(II) is in LS state between 150-300 K. A smooth spin conversion from LS to HS state occurs in 300-450 K temperature range in complexes 1 and 2. The evolutions of the coordination sphere parameters (Fe-N bond, , , ) as a function of temperature (150 K to 450 K) are plotted for 1 (Figure 6a) and 2 (Figure 6b). At 450 K, the HS conversion is 94% (for 1) and 87% (for 2) which is in good agreement with the observed magnetic data (2.8 cm 3 .K.mol -1 for 1: 93% HS and 2.7 cm 3 .K.mol -1 for 2:

90% HS). Each crystalline water molecule is connected to one coordination complex through weak O•••H-C hydrogen bonds (Figure 7a). Structural data as well as TG analyses clearly indicate that the crystalline water molecule present in the complexes is lost above 400 K (1) and 350 K (2). After de-hydration, a slight ligand motion in 1 and 2 is noticed between structures at 150 K and 450 K (Figures 6a and6b). Both the de-hydration and this ligand motion may explain the slight deviation in spin crossover behaviour in 1 and 2 between the first warming and the other thermal cycles, since it may alter the intermolecular interactions. ) in cooling mode after heating the crystal at 420 K. In all cases, the complex crystallises in tetragonal system with a chiral space group P4 1 2 1 2 (Table S8).

At 150 K and 250 K, the observed coordination sphere parameters (Fe-N bond, , , ) are in line with the LS state (Table 2). The coordination environment around iron(II) gradually changes from LS to HS (Table 2) state with increase in temperature from 250 K to 420 K. At 400 K and 420 K, the HS conversion is 72% and 81%, respectively for iron(II). This is in good agreement with the observed magnetic data (2.1 cm 3 .K.mol -1 at 400 K: 70% HS and 2.45 cm 3 .K.mol -1 at 420 K: 81% HS). When the crystal is cooled down to 90 K (3 90Kcooling ) after heating at 420 K, the LS state of iron(II) is recovered (Table 2). The crystal deteriorated rapidly above 420 K; it is not possible to follow the structural evolution in the temperature range 420-475 K compared to magnetic measurements. However, according to thermogravimetric analyses the water molecule is released in two steps between (i) 345-450K and (ii) 450-475K that probably causing the deviation in spin crossover behaviour in 3 at 450K and 475K. K and 500 K. On the contrary, complex 3 shows complete and non-cooperative spin crossover behaviour with some unusual irreversible features between 300 K and 475 K. For 3, the spin crossover is reversible and gradual in nature between 90 K (LS) and 400 K (72% HS) as is evident of crystallographic parameters. First deviation occurs at 450 K upon cooling. Upon further warming at 475 K the complex exhibits a HS state of iron(II) that is stable down to 300 K upon further cooling. Below this temperature, it converts gradually to LS state on cooling. The equilibrium temperatures for first warming (T 1/2 ↑) and second cooling (T 1/2 ↓) are 375 K and 200 K, respectively. The structural modification and reorganisation of intermolecular contacts as well as loss of water molecule in complexes 1-3 were monitored through variable-temperature crystallographic evidences between 150-450 K (1 and 2) and 90-420 K (3) and thermogravimetric analyses. It is worth mentioning that de-hydration at higher temperature in complexes 1 and 2 creates some minor irreversible ligand motion which may be responsible for slight deviation in spin crossover. On the other hand, the de-hydration at high temperature in complex 3 causes strong irreversibility in spin crossover behaviour.

Experimental

Materials and methods

Synthesis of Schiff bases

The Schiff bases were synthesized using the following procedure. To the dry methanol solution (25 mL) of 2-benzoylpyridine (0.366 g, 2 mmol), a stoichiometric amount of aniline derivatives [4-chloroaniline (0.254 g, 2 mmol) for Cl-PPMA, 4-bromoaniline (0.344 g, 2 mmol) for Br-PPMA and 4-methylaniline (0.214 g, 2 mmol) for CH 3 -PPMA] were added and refluxed for 24 h under nitrogen atmosphere. The yellowish brown solution was concentrated on a steam bath and dried in vacuo over CaCl 2 to get brown oil-like compound for subsequent use. However, all ligands were used for the preparation of iron(II) compound without further purification.

Synthesis of complexes 1-3

Complexes 1-3 were prepared following a reported method [START_REF] Létard | Wide Thermal Hysteresis for the Mononuclear Spin-Crossover Compound cis-Bis (thiocyanato) bis [N-(2 '-pyridylmethylene)-4-(phenylethynyl) anilino] iron (II)[END_REF][START_REF] Létard | Structural, magnetic, and photomagnetic studies of a mononuclear iron (II) derivative exhibiting an exceptionally abrupt spin transition. Light-induced thermal hysteresis phenomenon[END_REF] MLCT transitions = 530 (1.36 × 10 3 ) (shoulder) and 585 (2.24 × 10 3 ) (broad peak).

Single crystal X-ray data collection and refinements

Structure determination at room temperature

Single-crystal X-ray data for 1-3 were collected at 293(2) K using an Agilent

Technologies SuperNova Dual diffractometer equipped with an Atlas detector using radiation (λ = 0.71073 Å). The data were processed using CrysAlisPro. 35 The structures were solved by direct methods implemented in SHELXT [START_REF] Sheldrick | SHELXT-Integrated space-group and crystal-structure determination[END_REF] and refined by a full-matrix least-squares procedure based on F 2 with SHELXL2017. [START_REF] Sheldrick | Crystal structure refinement with SHELXL[END_REF] All the nonhydrogen atoms were refined anisotropically. Hydrogen atoms were readily located in difference Fourier maps and were subsequently treated as riding atoms in geometrically idealized positions with U iso (H) = kU eq (C), where k = 1.5 for methyl groups, which were permitted to rotate but not to tilt, and 1.2 for all other H atoms unless otherwise noted. The room temperature structures are denoted as 1 RT , 2 RT and 3 RT .

Structure determination at variable temperatures

For variable temperature structural studies, suitable single crystals for 1-3 were selected from magnetic samples. The X-ray diffraction data were collected on Bruker

  related to Schiff bases of pyridine-2-carboxaldehyde and para-substituted anilines [substituted-N-(2-pyridylmethylene)aniline; PM-L, L = phenyl, biphenyl, phenylethyne, phenylazo, naphthylethyne, Scheme 1] are particularly interesting as they exhibit a varied range of SCO behaviours (gradual → abrupt → hysteresis) albeit below room temperature. In such PM-L based complexes, the para-substituent of aniline plays an important role on the nature of the spin crossover. The cooperativity in this molecular system arises primarily due to hydrogen bonds (particularly S•••H-C contact) as well as π-π stacking and difference in the packing arrangements. 16, 18-20 In this endeavour, a new series of bidentate N-donor Schiff bases [4-X-N-(phenyl(pyridin-2-yl)methylene)-aniline; X-PPMA; X = -Cl, -Br, -CH 3 ; Scheme 1] have been synthesised using 2-benzoylpyridine and aniline derivatives (4chloroaniline, 4-bromoaniline and 4-methylaniline) for molecular cis-[Fe(L) 2 (NCS) 2 ]

); Scheme 1 ]Scheme 1

 11 Scheme 1 Structures of the reported PM-L ligands, newly synthesized X-PPMA Schiff bases and molecular cis-[Fe(X-PPMA) 2 (NCS) 2 ].H 2 O complexes.

Figure 1

 1 Figure 1 View of molecular structures of complexes (a) 1 (b) 2 and (c) 3 at room temperature.

Figures 2 and 3 )

 3 Figures2 and 3) show that complexes 1 and 2 undergo complete but non-cooperative spin crossover above room temperature. The observed value remains close to 0-0.2 cm 3 .K.mol -1 in the temperature range of 10-300 K clearly indicative of LS state of iron(II). This is consistent with room temperature Mössbauer spectra and crystallographic bond/angle distortion parameters. Upon further warming the samples, their values gradually increase and reach a maximum of 3.0 cm 3 .K.mol -1 at 500 K (1) and 475 K (2) expected for an iron(II) ion in its HS state. Upon cooling the samples down to 250 K, the value decrease again gradually to 0.2-0.3 cm 3 .K.mol - 1 with slight deviation for both 1 and 2 (Figures2 and 3). The average spin crossover temperature ( ) is found to be around 375 K for 1 and 380 K for 2. No photoswitching effect at 10 K is observed for these two compounds whatever the wavelength used between 405 and 980 nm.

Figure 2

 2 Figure 2 Temperature dependence of product for 1 recorded on the SQUID magnetometer (o) and VSM (green line first cycle and red line second cycle).

Figure 3

 3 Figure 3 Temperature dependence of

  crystallographic bond/angle distortion parameters. Upon first warming of the sample from 300-450 K, the value gradually increases until it reaches a maximum value of 3.0 cm

Figure 4

 4 Figure 4 Temperature dependence of product for 3 recorded on the SQUID magnetometer (o first warming, □ after 1h in an oven at 480 K) and VSM (green line first cycle, red line second cycle and black line third cycle). Behaviour of 3 after thermal treatment at 450 K (1h in an oven) under 830 nm light irradiation (Δ) and after ().

  these [Fe(L) n (NCS) 2 ] complexes are often lying on a T 0 = 120 K line. Complexes 1 and 2 are characterized by quite high T 1/2 (above 350 K) which supports the absence of LIESST effect on these complexes. Complex 3 after thermal treatment has a T 1/2 of 200 K which perfectly supports the observation of a T(LIESST) temperature of 60 K.

  3 -PPMA) 2 (NCS) 2 ].0.75H 2 O(3) Gradual and strongly irreversible/ T 1/2 ↑(1st warming) = 375 K and T 1/2 ↓(2nd cooling) ; PM-TeA = N-(2'-pyridylmethylene)-4-(aminoterphenyl); PM-AzA = N-(2'pyridylmethylene)-4-(phenylazo)aniline; PM-NEA = N-(2-pyridylmethylene)-4-(naphthalene-1-ethynyl)aniline; PM-pBrA = N-(2'-pyridylmethylene)-4-bromoaniline.

Figure 6 2 (

 62 Figure 6 Thermal evolution of coordination sphere parameters for (a) 1 and (b) 2 (lines are guides for the eyes).

Figure 7 2 .

 72 Figure 7 Superposition of the molecular structures at 450 K(red) and 150 K(blue) for (a) 1 and (b) 2.

Crystal packing in 1- 3 In the crystalline state of 1 - 3 ,

 313 individual molecules are connected to each other through weak (pyridine)C-H•••C(NCS) contacts involving two NCS moieties and two pyridine rings of two neighbouring molecules (Tables3-5) along crystallographic caxis forming an 1D-helical chain (Figure8). Further, these 1D-helical chains are linked through weak (NCS)S•••H-C(aniline) and weak intermolecular (aniline)C•••H-C(phenyl) interactions along ab-plane leading to a 3D-network structure (Figure8). It is found that iron(II) centres are in relatively close proximity along c-axis (intra-chain Fe-Fe distances) but in ab-plane iron(II) centres (inter-chain Fe-Fe distances) are widely separated. Moreover, the inclusion of large phenyl group in PPMA ligands leading the complexes to crystallise in tetragonal system with chiral space group either P4 3 2 1 2 (for 1) or P4 1 2 1 2 (for 2 and 3) in contrast to the complexes with PM-L ligands. Also, the supramolecular arrangement of 1D-helical chains diminishes the possibilities of π-π stacking as well as weakens major intermolecular contacts (NCS)S•••C(phenyl groups-Schiff base) as compared to the reported complexes of PM-L ligands. This crystal packing is primarily responsible for non-cooperative gradual spin crossover in complexes 1-3.

Figure 8 A 1 Table 3

 813 Figure 8 A view of Left: 1D-helical chain formed through (pyridine)C-H•••C(NCS) and Right: Crystal packing where adjacent 1D-helical chains are connected through primarily (NCS)S•••H-C(phenyl/aniline) and C-H•••C(aniline/phenyl) interactions in 1

  [START_REF] Bousseksou | Switching of molecular spin states in inorganic complexes by temperature, pressure, magnetic field and light: towards molecular devices[END_REF] .K.mol -1 at 450 K as expected for a HS iron(II) ion. Upon first cooling of the

	sample down to 250 K, the	product decreases more gradually following a
	different path and reaches a value of 1.8 cm 3 .K.mol -1 indicating 60% iron(II) ions in
	HS state. Upon second warming up to 475 K,	value increases to 3.1 cm 3 .K.mol -1
	following the first cooling path and upon second cooling	value remains same up
	to 300 K indicative of expected HS state of iron(II). With further decrease in
	temperature from 300-10 K,	value decreases to 0.38 cm 3 .K.mol -1 following a
	different path compared to first cooling. This value corresponds to around 10% HS
	state of iron(II) ions. This last curve is reversible upon further warming. The average
	spin crossover temperatures are around	(1 st warming) 375 K and	(2 nd

Table 1

 1 Spin crossover data for bis-(thiocyanato)iron(II) complexes with reported PM-L

	ligands 17-25 and complexes 1-3
	Sl. No. Complexes 1. [Fe(PM-PEA) 2 (NCS) 2 ] 21	SCO behaviour/T 1/2 /ΔT Hysteresis and reversible/T 1/2 ↓=194 K, T 1/2 ↑= 231
		K/ΔT = 42 K
	2.

Table 2

 2 Evolution of the relevant coordination sphere parameters for 3

		3 150K	3 250K	3 400K	3 420K	3 250Kcooling 3 90Kcooling
	Fe-N (Å)	1.9595(15) 1.958(3)	2.104(3)	2.116(4)	1.958(3)	1.956(3)
		1.9487(15)	1.948(3)	2.146(3)	2.177(4)	1.956(3)	1.949(3)
		1.9488(15)
		1.9553(17)	1.958(3)	2.047(5)	2.058(6)	1.956(3)	1.947(3)
		1.9552(17)
	<Fe-N> (Å) 1.954(2)	1.955(3)	2.099(4)	2.117(5)	1.957(3)	1.951(3)
	 (Å)	0.028	0.032	0.210	0.238	0.007	0.020
	 ()	39.1	39.9	65.9	68.8	40.4	39.0
	 ()	132	132	190	198	136	132
	V(FeN 6 ) Å 3 9.868	9.892	12.034	12.332	9.889	9.802
	Spin state	LS	LS	HS (72%) HS (81%) LS	LS

Table 4

 4 Reorganisation of inter-molecular contacts in 2

	Contact	2 150K	2 250K	2 300K	2 350K	2 400K	2 450K
	(pyridine)C-H•••C(NCS) 2.784 2.795 2.803 2.792 2.940 2.990
	Fe•••Fe(Intra-chain)	7.639 7.658 7.669 7.634 7.600 7.603
	(NCS)S•••H-C(aniline)	3.026 3.024 3.026 3.000 3.034 3.081
	C-H•••C(aniline/phenyl)	3.048 3.091 3.117 3.086 3.127 3.119
	Fe•••Fe(Inter-chain)	10.823 10.867 10.910 10.954 11.067 11.140

Table 5

 5 Reorganisation of inter-molecular contacts in 3

	Contact	3 150K	3 250K	3 400K	3 420K	3 250Kcooling 3 90Kcooling

4-Chloro-N-(phenyl(pyridin-2-yl)methylene)aniline (Cl-PPMA)

  Molecular formula C 18 H 13 BrN 2 (336.0262). Yield: 598 mg (88.77%); ESI-MS (in CH 3 OH): m/z = 337.0334 [Calcd. 337.0335 for (Br-PPMA+H) + ]. 1 H-NMR (δ/ppm,

	CDCl 3 ): 6.57 (2H), 7.23 (2H), 7.49 (3H), 7.60 (1H), 7.91 (1H), 8.06 (3H), 8.73 (1H).
	UV-Vis (λ max /nm in CH 3 OH; ε/M -1 cm -1 ): 247 (1.54 × 10 4 ), 346 (4.49 × 10 2 ).
	4-Methyl-N-(phenyl(pyridin-2-yl)methylene)aniline (CH 3 -PPMA)
	Molecular formula C 19 H 16 N 2 (272.1313). Yield: 491 mg (90.24%); ESI-MS (in
	CH 3 OH): m/z = 273.1389 [Calcd. 273.1386 for (CH 3 -PPMA+H) + ]. 1 H-NMR (δ/ppm,
	CDCl 3 ): 2.24 (3H), 6.61 (1H), 6.96 (1H), 7.49 (4H), 7.60 (1H), 7.91 (1H), 8.06 (4H),
	8.73 (1H). UV-Vis (λ max /nm in CH 3 OH; ε/M -1 cm -1 ): 261 (1.05 × 10 4 ), 346 (5.6 × 10 2 ).
	Molecular formula C 18 H 13 ClN 2 (292.0767). Yield: 505 mg (86.35%); ESI-MS (in
	CH 3 OH): m/z = 293.0847 [Calcd. 293.0840 for (Cl-PPMA +H) + ]. 1 H-NMR (δ/ppm,
	CDCl 3 ): 6.60 (2H), 7.10 (2H), 7.50 (3H), 7.60 (1H), 7.92 (1H), 8.06 (3H), 8.74 (1H).

UV-Vis (λ max /nm in CH 3 OH; ε/M -1 cm -1 ): 248 (1.21 × 10 4 ), 347 (1.75 × 10 2 ).

4-Bromo-N-(phenyl(pyridin-2-yl)methylene)aniline (Br-PPMA)

  Yield: 500 mg (64.47%); C 38 H 28 N 6 OS 2 Cl 2 Fe (775.54): calcd. C: 58.85, H: 3.64, N: 10.84, S: 8.27; found: 58.50, H: 3.45, N: 10.76, S: 8.72%. FTIR (KBr disc, cm -1 ): 3440, 3050, 2890, 2814, 2100, 2060, 1590, 1480, 1445, 1398, 1336, 1256, 1161, 1085, 1011, 841, 800, 739, 694, 640, 597, 519, 432, 403. UV-Vis (λ max /nm in CH 3 OH; ε/M - 1 cm -1 ): Cl-PPMA based π→π* transitions: 258 (2.01 × 10 4 ), 340 (4.13 × 10 3 ); MLCT transitions: 530 (7.26 × 10 2 ) (shoulder) and 585 (1.05 × 10 3 ) (broad peak). Yield: 480 mg (55.52%); C 38 H 28 N 6 OS 2 Br 2 Fe (864.45): calcd. C: 52.80, H: 3.26, N: 9.72, S: 7.42; found: C: 52.74, H: 3.25, N: 9.71, S: 7.78%. FTIR (KBr disc, cm -1 ): 3453, 3059, 2878, 2096, 2057, 1625, 1475, 1443, 1389, 1337, 1257, 1160, 1065, 996, 838, 800, 7.43, 695, 594, 513, 405. UV-Vis (λ max /nm in CH 3 OH; ε/M -1 cm -1 ): Br-PPMA based π→π* transitions = 258 (2.32 × 10 4 ), 340 (5.03 × 10 3 ); MLCT transitions = 530 (7.85 × 10 2 ) (shoulder) and 585 (1.42 × 10 3 ) (broad peak). Yield: 300 mg (41.08%); C 40 H 34 N 6 OS 2 Fe (730.21): calcd. C: 65.39, H: 4.66, N: 11.44, S: 8.73; found: C: 65.41, H: 4.54, N: 11.51, S: 9.05%. FTIR (KBr disc, cm -1 ): 3459, 3025, 2899, 2818, 2097, 2057, 1583, 1498, 1446, 1336, 1255, 1162, 1107, 1068, 1017, 983, 834, 797, 740, 692, 600, 537, 403. UV-Vis (λ max /nm in CH 3 OH; ε/M -1 cm -1 ): CH 3 -PPMA based π→π*/n→π* transitions = 272 (8.17 × 10 3 ), 340 (2.52 × 10 3 );

	[Fe(Br-PPMA) 2 (NCS) 2 ].H 2 O (2)
	[Fe(CH 3 -PPMA) 2 (NCS) 2 ].H 2 O (3)
	[Fe(Cl-PPMA) 2 (NCS) 2 ].H 2 O (1)

with little modification. Under nitrogen atmosphere, iron(II) perchlorate hexahydrate, Fe(ClO 4 ) 2 . 6H 2 O (0.254 g, 1 mmol) and potassium thiocyanate, KSCN, (0.194 g, 2 mmol) were dissolved in 15 mL freshly distilled methanol in presence of ascorbic acid to prevent the oxidation of iron(II). The colourless solution of Fe(NCS) 2 was separated from the white precipitate of potassium perchlorate by filtration, and added drop wise to a stoichiometric amount of Schiff base [Cl-PPMA (0.584 g, 2 mmol) for 1, Br-PPMA (0.674 g, 2 mmol) for 2 and CH 3 -PPMA (0.544 g, 2 mmol) for 3] taken in 10 mL distilled methanol. The resulting intense blue solution was filtered and kept for slow evaporation in inert atmosphere. After 3-4 days needle (for 1-3) shaped dark blue crystals were obtained. The crystalline compounds were collected by filtration and washed with cold methanol and dried under vacuum.

Acknowledgements

AKS acknowledges CSIR project grant (ref.: 01(3084)/21/EMR-II), SERB project grant (EMR/2016/001452) and DST-INSPIRE research grant (IFA-13, CH-97). KB is grateful to DST-SERB for NPDF research grant (PDF/2017/000929). VNR acknowledges Central University of Rajasthan, India for fellowship. FP is grateful for financial support from the Slovenian Research Agency (ARRS) through project P1-0175. We thank the EN-FIST Centre of Excellence, Ljubljana, Slovenia, for using SuperNova diffractometer for the data collections. Authors acknowledge the instrumental facilities through DST-FIST Grant (grant ref.: SR/FST/CSI-257/2014(c)) at Department of Chemistry, Central University of Rajasthan, India. The instrumental facilities at MNIT, Jaipur, India and STIC, Cochin, India are also gratefully acknowledged. The CNRS, University of Bordeaux and X-Ray facility service of the ICMCB are kindly acknowledged. The CNRS, the University of Bordeaux and the Région Aquitaine are also acknowledged as well the CSC and IDEX Bordeaux program for funding. Authors also thank Dr. V. Raghavendra Reddy, UGC-DAE Consortium for Scientific Research, Indore, India, for room temperature Mössbauer studies of complexes (1-3). The Central Instrumental Facilities (CIF) at Central University of Rajasthan for powder-XRD studies is gratefully acknowledged. Authors also acknowledge the valuable contribution of Late Dr. Sunil G. Naik to this work.

Notes and references ‡The supporting information contains Mössbauer spectral data, room temperature powder-XRD, room and variable temperature X-ray crystallographic data, thermogravimetric analyses for 1-3. §CCDC No: 1978235-1978237 for 1 RT -3 RT , 1979597, 1979599-1979600, 1979602, 1979604 and 2009216 for 1, 1979605, 1979607-1979609, 1979611, 2009217 for 2 and 1979617-1979618 and 1979620-1979623 for 3 contain the supplementary crystallographic data. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge

APEX-II with graphite monochromated radiation (λ = 0.7017 Å), equipped with CCD detectors and an Oxford instruments nitrogen cryo-stream. Structures were solved using a direct methods with Olex2. [START_REF] Dolomanov | OLEX2: a complete structure solution, refinement and analysis program[END_REF] Space group was checked by Platon software. [START_REF] Spek | Single-crystal structure validation with the program PLATON[END_REF] For 1 and 2, data were collected on the full sphere at 150 K (1 150K and 2 150K ) then at 250 K (1 250K and 2 250K ), 300 K (1 300K and 2 300K ), 350 K (1 350K and 2 350K ), 400 K (1 400K and 2 400K ) and 450 K (1 450K and 2 450K ) on a single crystal. Above 450 K the stability of crystal was lost. In 1 450K , there are some 'B level' errors, including large U(iso) of H (H2, H3, H4, H9), large flack X, low bond precision, small distance of C7--C12. For 3, data were first collected on full sphere at 150 K (3 150K ) then at 250 K (3 250K ), 400 K (3 400K ) and 420 K (3 420K ) on a single crystal. This crystal was then save apart. Another crystal was used to find out the stability. Above 420 K, the stability of the crystal was lost. So, after warming at 420 K, crystal structures were recorded at 250 K (3 250Kcooling ) and 90 K (3 90Kcooling ) using the first crystal. Electron density associated with disordered solvent molecules was removed by solvent mask.

Therefore, the chemical formula and crystal data given in Tables S5 andS8 do not take into account these solvent molecules.

Caution! A particular caution had to be taken for these X-ray diffraction data collections. All the compounds crystallize in a chiral space group and since both chiral forms of the crystals cannot be distinguished by a sole unit-cell check, a full data collection and structural determination is always needed to know the space group.

Consequently, all the temperature dependence should be made on the same crystal.

After checking the stability of the crystal for each compound a suitable single crystal was selected for X-ray diffraction to run the whole set of data collection. It also means that if one single-crystal breaks during a measurement the full process of the variable temperature study must be re-done on a new crystal. This time-consuming experimental protocol is the guarantee for reliable structural data.

Magnetic measurements

Magnetic measurements were performed using a MPMS 7XL SQUID Magnetometer from Quantum design, operating at 20 kOe of applied magnetic field, on 12.40 mg (for 1), 10.83 mg (for 2) and 11.24 mg (for 3) of samples prepared in a polypropylene bag.

The temperature was scanned from 10 K to 400 K at a sweeping rate of 3 K/min (for 1), in a settle mode (for 2) and 4 K/min (for 3). The photoswithcing was recorded directly into the SQUID magnetometer through an optical fibre placed close to the sample (6 cm). Irradiation is applied on a thin layer of compound and the relaxation temperature T(LIESST) is recorded according to the already reported protocol. [START_REF] Chastanet | A critical review of the T (LIESST) temperature in spin crossover materials-What it is and what it is not[END_REF][START_REF] Létard | Critical temperature of the LIESST effect in iron (II) spin crossover compounds[END_REF][START_REF] Chastanet | Light-induced excited spin-state trapping: a methodological approach[END_REF] Further, the magnetic data up to 500 K (for 1-3) were recorded using Microsense EZ7 Vibrating Sample Magnetometer with the 150-1000 K EV1-LNA temperature control option. Samples were weighed in aluminium capsules that were wrapped closed, and glued to a 3 mm  quartz rod with double-face scotch tape. The measurements were performed under 15 kOe magnetic field at a temperature sweeping rate of 5 K/min. Nitrogen gas flow was used for temperature control. The diamagnetic corrections were made using Pascal's constants. [START_REF] Bain | Diamagnetic corrections and Pascal's constants[END_REF] Let us note that compound 3 was recorded in the SQUID as a fresh sample and after 1h at 450 K in an oven.

Conflicts of interest

There are no conflicts to declare.