Mélissa Dali

Chloé Picq

Olivier Rossel

Pawel Maciejasz

Charles-Henri Malbert

David Guiraud

Comparison of the efficiency of chopped and non-rectangular electrical stimulus waveforms in activating small vagus nerve fibers

Keywords: Vagus nerve stimulation, obesity, neuromodulation, nerve modeling, burst waveforms, chopped pulses, compound action potential

Introduction

Vagus nerve stimulation (VNS) is a wellestablished technique successfully used to treat intractable epilepsy [START_REF] Degiorgio | Prospective long-term study of vagus nerve stimulation for the treatment of refractory seizures[END_REF][START_REF] Morris | Evidence-based guideline update: Vagus nerve stimulation for the treatment of epilepsy report of the guideline development subcommittee of the american academy of neurology[END_REF] and refractory depression [START_REF] Sackeim | Vagus nerve stimulation (vns TM ) for treatment-resistant depression: efficacy, side effects, and predictors of outcome[END_REF]4]. VNS is also a promising therapy in the treatment of cardiac disorders and morbid obesity [5,[START_REF] Guiraud | Vagus nerve stimulation: state of the art of stimulation and recording strategies to address autonomic function neuromodulation[END_REF][START_REF] Malbert | Effects of chronic abdominal vagal stimulation of small-diameter neurons on brain metabolism and food intake[END_REF][START_REF] Malbert | Obesityassociated alterations in glucose metabolism are reversed by chronic bilateral stimulation of the abdominal vagus nerve[END_REF][START_REF] Dali | Model based optimal multipolar stimulation without a priori knowledge of nerve structure: application to vagus nerve stimulation[END_REF]. However, contrary to most of VNS applications, weight reduction and/or insulin sensitivity improvement required the stimulation of both vagal trunks; a mandatory condition that cannot be achieved at the cervical level without significant cardiac side-effects some of which being life threatening [START_REF] Malbert | Effects of chronic abdominal vagal stimulation of small-diameter neurons on brain metabolism and food intake[END_REF]. As a consequence, most of the studies targeted obesity [START_REF] Krolczyk | Effects of continuous microchip (MC) vagal neuromodulation on gastrointestinal function in rats[END_REF] have used bilateral stimulation after the cardiac branches e.g. at the diaphragmatic level. At this level, the control of the gastric function requires the activation of small afferent nerve fibers, i.e. type B or C [START_REF] Mei | The composition of the vagus nerve of the cat[END_REF]. Thresholds for activation of Bfibers and C-fibers are respectively 2-3 and 10-100 times greater than the threshold of the large A-fibers (Aα, Aβ, Aγ) [START_REF] Castoro | Excitation properties of the right cervical vagus nerve in adult dogs[END_REF]. Membrane depolarization requires significant electrical charge injection on a fragile tissue over long periods, that may cause damages at the electrode-tissue interface level [START_REF] Merrill | Electrical stimulation of excitable tissue: design of efficacious and safe protocols[END_REF]. Therefore, charge reduction is mandatory. Optimizing the pulse shape (waveform) while reducing charge needed to activate small axons can reduce constraints on stimulator and preserve the tissues. Previous studies suggested that non-rectangular waveforms could activate fibers of the peripheral nervous system with less charge than rectangular ones: i) using ramp, exponential, gaussian but continuous waveforms [START_REF] Sahin | Non-rectangular waveforms for neural stimulation with practical electrodes[END_REF][START_REF] Jezernik | Charge and energy minimization in electrical/magnetic stimulation of nervous tissue[END_REF], ii) chopped waveforms [START_REF] Qing | Burst-Modulated Waveforms Optimize Electrical Stimuli for Charge Efficiency and Fiber Selectivity[END_REF][START_REF] Shepherd | Electrical stimulation of the auditory nerve: II. Effect of stimulus waveshape on single fibre response properties[END_REF][START_REF] Dali | Investigation of the efficiency of the shape of chopped pulses using earthworm model[END_REF] also named burstmodulated waveforms. Chopped waveforms seem promising especially for B and C fibers as it was shown that these fibers profoundly modulate the metabolism through the vagal projections in the brain [START_REF] Malbert | Effects of chronic abdominal vagal stimulation of small-diameter neurons on brain metabolism and food intake[END_REF]. Chopped waveforms are composed of n stimulating cathodic pulsons of T on duration separated by n-1 nonstimulating pulsons (high impedance phases) of T of f duration. The whole of pulsons are followed by an anodic phase to ensure charge balancing. P W tot is defined as the total duration of the cathodic phase whereas P W sum takes into account only the stimulating pulsons within the cathodic phase (Eq. 2). Note that for continuous pulse, P W tot = P W sum = P W .

Recently, chopped pulses were investigated in the context of VNS [START_REF] Qing | Burst-Modulated Waveforms Optimize Electrical Stimuli for Charge Efficiency and Fiber Selectivity[END_REF] and applied on left cervical vagus nerve of rats. They assessed the ability of chopped rectangular pulses to activate C-fibers and A-fibers compared to a rectangular continuous pulse. Both types of pulses have the same P W tot duration of 200µs. The number of pulsons varied (from 2 to 10), implying different values of T on and T of f , that is, different value of P W sum . Their results indicated that by maintaining 50% of C-fibers activated, chopped pulses required 45% less charge than the conventional rectangular pulse and produced 11% less Afibers activation. They found that rectangular pulse with short duration (40 µs) and chopped rectangular pulse -with short T on (20 µs) and short P W sum (40 µs) -required less charge to maintain the same level of C fibers activation than rectangular pulse with total duration of 200 µs. Malbert et al. [START_REF] Malbert | Effects of chronic abdominal vagal stimulation of small-diameter neurons on brain metabolism and food intake[END_REF] investigated the impact of pulson type stimulation on brain function during chronic VNS applied at the abdominal level on both vagal trunks. They compared one pulson configuration with a more classical single long lasting pulse and found that the pulson configuration was more effective than the single long lasting pulse either for triggering action potential on the afferent vagus or for activation of frontal brain cortices.

Chopped pulses were also investigated in the context of cochlear implant. Shepherd et al. [START_REF] Shepherd | Electrical stimulation of the auditory nerve: II. Effect of stimulus waveshape on single fibre response properties[END_REF] studied the response of single fiber of the auditory nerve, composed of myelinated fibers, to a variety of stimulus waveforms. Among them, biphasic chopped pulses with P W sum of 60 µs were compared to biphasic continuous rectangular pulse with P W duration of 60 µs (with or without interphase gap). Number of pulsons tested was 2, 3 and 6 with respective T on of 30 µs, 20 µs and 10 µs. T of f duration were adjusted so that P W tot duration was 120 µs. They found that rectangular continuous pulses with an interphase gap (60 µs) had lower activation thresholds than chopped pulses, whatever the number of pulsons is, and a rectangular pulse without an interphase gap had higher activation threshold (Fig. 8 in [START_REF] Shepherd | Electrical stimulation of the auditory nerve: II. Effect of stimulus waveshape on single fibre response properties[END_REF]).

We recently studied the charge efficiency of chopped pulses were in lumbricus terrestris [START_REF] Dali | Investigation of the efficiency of the shape of chopped pulses using earthworm model[END_REF] as a simplified model of peripheral nerve. The objective was to evaluate if nonrectangular chopped pulses such as quarter sine and ramp were more charge efficient than rectangular chopped pulse, varying stimulation duration parameters. The results indi-cated that non rectangular chopped pulses activated Medial Giant Fiber (MGF) and Lateral Giant Fiber (LGF) with less charge than rectangular chopped pulses. For the Medial Giant Fiber MGF (respectively LGF), the gain of charge was up to 33.9% (respectively 17.8%) using chopped ramp, and up to 22.8% (resp. 18.1%) using chopped quarter sine.

The studies of Qing et al., Malbert et al and Shepherd et al. suffer from limitations. They did not compare non-rectangular but continuous waveforms against chopped ones, and the comparison between the efficiency of chopped versus continuous waveforms is not straightforward. The main reasons are the interdependence of the stimulus strength and duration (the so-called strength duration curve) and the definition of the duration in order to make a fair comparison, i.e. considering P W tot or P W sum . Indeed the three last studies used P W tot but we hypothesize that a continuous waveform with the same amplitude and P W sum would be more efficient than the chopped one.

In order to better understand the impact of various waveforms on stimulation effectiveness, we have addressed this problem twofolds. We performed experiments in a complex model of the abdominal porcine vagus nerve, and we have completed our study with results of computer simulations. To further concentrate on waveform efficiency we focused on single unit activation instead of a whole nerve activation with recruitment. We thus compared the threshold of activation of a unique fiber against all the tested waveforms.

Method

Chopped pulses

The Fig. 1 shows the waveforms used in experimental studies and modeling. The pulses were biphasic asymmetric and chargebalanced. It consisted of a cathodic phase (continuous or chopped) followed by an anodic phase. The cathodic continuous pulses consisted of a rectangular shape (Fig. 1,A), a ramp (Fig. 1,B) or a quarter of a sine (quarter sine) (Fig. 1,C). The cathodic chopped pulses were composed of multiple pulsons with T on duration. Each pulson was separated by a non-stimulating pulson of T of f duration. The chopped pulses shape could be rectangular (Fig. 1, D), ramp (Fig. 1,E) or quarter sine (Fig. 1,F). In order to minimize the influence of anodic phase to avoid misleading interpretations, the charge balancing was performed at low current amplitude and long duration. The anodic phase was identical for all the tested waveforms and consisted of a continuous rectangular pulse of 2.8 ms duration. For all waveforms, the charge at the activation threshold was computed using the formula:

Q th = T on × n k=1 I th (k) (1)
Where I th (k) is the current amplitude of pulson k at the activation threshold and n the total number of stimulating pulsons. P W sum is computed as follows:

P W sum = T on × n (2)
P W tot is the total duration of the cathodic pulse:

P W tot = T on × n + T of f × (n -1) (3)
Note that for the rectangular pulse, n = 1 and T on = P W tot = P W sum = P W ; for the continuous ramp or quarter sine, P W tot = P W sum = P W, T of f = 0.

Experimental study on porcine model

Ethics statement

A preliminary experiment was performed on one anesthetized female pig to preselect waveforms and to reduce experimental load. The next experiments were carried out on 5 anesthetized female pigs (3 months old, Large White). The experimental procedure was conducted in accordance with the ethical standards of the European and French regulations (Agreements number R-2012-CHM-03 and 00341.01). The experiment consists in stimulating the vagus nerve bilaterally at the level of the thoracic crux while simultaneously recording afferent activity at the the cervical level (left vagus nerve) using the single fiber method [START_REF] Cuche | Desensitization of ileal vagal receptors by short-chain fatty acids in pigs., American journal of physiology[END_REF].

Surgical procedure

Intramuscular injection of ketamine (5 mg.kg -1 ) was used as a pre-anesthesia. Anesthesia was induced by inhalation of isoflurane (5 % v/v). Once anesthetized, pigs were intubated then artificially ventilated and the SpO 2 and SpCO 2 were constantly monitored. The first part of the experiment -electrodes implantation on vagus nerves, balloon insertion in the stomach and left cervical vagus nervewas done under isoflurane anesthesia. The second part -precise dissection of single fiber, recording and stimulation -was done under pentobarbital anesthesia. In order to inject pentobarbital (20 mg.kg.hr -1 , Sanofi), a venous cannula was inserted in the ear. Just before recording and until the end of the experiment, D-tubocurarine (0.2 mg.kg -1 , Sigma) was slowly injected (IV) every 2 hours in order to suppress motion artifacts. Body temperature was maintained at 38.5 ± 0.5 • C by a self-regulating heating cover placed under the animal. At the end of the experiment, pigs were euthanized by an injection of potassium chloride in the venous cannula in the ear.

Stimulating device implantation

The pig was placed in right lateral decubitus, at the level of the 8th intercostal space an incision was made to reach the mediastinal area. The vagal trunks were isolated as close as possible to the entrance of the diaphragm. Cuff electrodes (Axonic, Sophia Antipolis, France) were placed around the posterior and anterior vagus trunks and maintained by surgical staples placed on the Dacron covered cuffs. The electrodes had a diameter of 3±0.1 mm. They were made of two rows of two Pt-Ir 10 % contacts (4 in total), short-circuited together to form a bipolar-ring configuration. Surface area of a contact was: 7.56 mm 2 with length of 3 mm and width of 2.52 mm. The distance edge-toedge between the two rows was 7 mm. The experiment focused on the stimulation and recording of afferent gastric fibers. To be able to verify duodenal origin of the vagus neurons that were recorded, we inserted an inflatable balloon in the stomach of the pig. The insertion of the balloon was achieved while the pig was placed in dorsal decubitus. A midline laparotomy was performed and a balloon (15 cm long latex balloon with double-lumen catheter ID 3.5 mm for air/retrieval and ID 1.0 mm for pressure sensing) was inserted in the proximal duodenum. The stomach and abdomen were sutured and closed before dissection of the cervical nerve.

Afferent neurons recordings

Stimulation of vagal trunks induced evoked action potentials (APs) which were recorded on the left cervical vagus nerve. Spontaneous and evoked activities of the afferent vagal neurons were recorded using the procedure already described in [START_REF] Cuche | Desensitization of ileal vagal receptors by short-chain fatty acids in pigs., American journal of physiology[END_REF]. Briefly, the skin and cervical muscles surrounding the vagus nerve were attached to a metallic frame creating a pool filled with warmed paraffin oil. The nerve was then microdissected to isolate a bunch of few, possible just one, nerve fibers. The isolated fibers were placed on a recording electrode (tungsten, 50 µm, WPI USA), as shown in Fig. 2. The electrodes were connected to a home-made high impedance differential amplifier (gain 50,000, impedance 20 M Ω) associated with a specifically designed band pass filter (300-6000 Hz). The electroneurogram data (ENG) were digitized at 20 kHz using a custom-made software written under Labview 2011 (National Instruments. USA). Each time a bunch of fibers has been isolated, the balloon in the duodenum was inflated to verify the location of the receptive field of the axon under scrutiny. More precisely, we verified with the ENG whether the distension of the stomach produces APs in those fibers. The inflation procedure was computer controlled to maintain a 20 mmHg pressure within the balloon. If, during the inflation, we had no evoked AP at the cervical level, we changed the fiber to record until we found a duodenal one. Otherwise, we proceeded with the stimulation protocol.

Stimulation protocol

Stimulation was performed using an external AXIS stimulator (AXONIC, Sophia Antipolis, France). This stimulator is a simplified version of the one described in [START_REF] Andreu | Souquet, A distributed architecture for activating the peripheral nervous system[END_REF] limited to 4 channels but with higher amplitudes of intensity available (up to 30 mA, 20 V, 10 µA step). Before starting the stimulation protocol, the electrodes' impedance was estimated in order to determine maximal stimulus amplitude that could be delivered without exceeding stimulator's compliance voltage. The used stimulator was designed for humans so the method for impedance estima-tion is based on [START_REF] Guiraud | Original electronic design to perform epimysial and neural stimulation in paraplegia[END_REF]: the ratio of the potential drop and the delivered current at the end of 1 ms-long rectangular pulse of 0.5-1 mA amplitude. A stimulation sequencer was build to generate automatically a succession of stimulation patterns of varying shapes and amplitudes. The stimulation protocol was performed for each bunch of vagus gastric fibers found. One vagus nerve (anterior or posterior) was stimulated at a time. The protocol comprised different waveforms with different charges to be tested starting from the lowest to the highest to determine the fiber activation threshold. The initial amplitude for each waveform corresponded to a charge of 1.5 nC. Afterwards, the stimulus amplitude increased exponentially (10% increase rate) and for each amplitude, 6 pulses were generated at a frequency of 2 Hz. There was a pause of 1 s after each series of stimuli. In a preliminary study, all waveforms listed in Fig. 1 were tested, except chopped rectangular, eliminated as a result of experiments reported in [START_REF] Dali | Investigation of the efficiency of the shape of chopped pulses using earthworm model[END_REF]. At the outcome of this preliminary study, chopped ramp pulse was eliminated for next studies because few amplitudes could be tested before the maximal stimulus amplitude delivered by the stimulator was reached. For next studies, the protocol comprised 4 waveforms (Fig. 1) with the following characteristics:

• Continuous rectangular pulse, P W tot = 350 µs (Fig. 1,A)

• Continuous ramp pulse, P W tot = 350µs, composed of 14 Ton of 25 µs, no Toff (Fig. 1,B)

• Continuous quarter sine pulse , P W tot = 350µs, composed of 14 Ton of 25 µs , no Toff (Fig. 1,C)

• Chopped quarter sine pulse, P W tot = 1000µs, P W sum = 350µs composed of 14 Ton of 25 µs alternated with 13 Toff of 50 µs duration (Fig. 1, F)

• Chopped quarter sine pulse, P W tot = 325µs, P W sum = 125 µs composed of 5 Ton of 25 µs alternated with 4 Toff of 50 µs duration (Fig. 1,F)

The rectangular pulse was repeated twice (once at the beginning and once at the end) to check the reliability of the response of the neurons. This procedure was found necessary to assess the stability of the whole protocol from the cell response to the electrode positioning. The trial was rejected if the relative difference between the 2 obtained thresholds were above 10%. The procedure of isolating a bunch of fibers, verifying if they were of duodenal origin, and executing stimulation has been performed during each experiment. The number of iterations strongly depended on the time required to identify the fibers and were limited to the total duration allowed for the experiment i.e. less than 4 hours: the estimated survival time of the vagal afferent neurons once severed from their cell body in the nodose ganglia.

Data analysis

Evoked APs were processed using Matlab (Mathworks, USA). The recorded ENG were sorted and counted. For each fiber and waveform, the threshold for activation was determined. We defined a threshold stability criteria (T SC) as the minimal amplitude for which AP was evoked for at least 3 out of the 6 stimulus repetitions. When comparing 2 waveforms, n was the number of fibers that passed the common threshold stability criteria (CTSC) common to both waveforms and noted: n for CT SC. The charge at the activation threshold (Q th ) delivered by the stimulator was determined by the formula 1. Statistical analysis was performed on Q th data using R software (R Core Team, Austria). Data were tested for normality with the Shapiro-Wilk test. The comparison of Q th was first performed with a two way repeated measures ANOVA with factors animal and waveforms. Then, Q th obtained with the the different waveforms were compared two by two using the dependent t-test for paired samples, and the Wilcoxon signed rank test in case of non-parametric distribution. Only those pairs of thresholds obtained by two waveforms were analyzed, for which corresponding charge could be delivered during the experiment with both compared waveforms without exceeding the compliance voltage limit. A Bonferroni correction was applied for the multiples tests, the p-value presented included this correction. A significance level of 5% was chosen.

2.4. Modeling 2.4.1. Models of nerve and electrode, axon response to stimulation A volume conductor model for a nerve and cuff electrode coupled with a model of mammalian myelinated nerve fiber was used to study the recruitment mechanisms with the chopped and continuous pulses. The 3D nerve trunk surrounded by a bipolar cuff electrode was modeled using Comsol Multiphysics (COMSOL Inc, Burlington, MA). Modeling of nerve and electrode were previously described in [START_REF] Dali | Model based optimal multipolar stimulation without a priori knowledge of nerve structure: application to vagus nerve stimulation[END_REF][START_REF] Dali | Numerical simulation of multipolar configuration and prepulse technique to obtain spatially reverse recruitment order[END_REF]. The nerve model was composed of a fascicle diameter 2.7 mm surrounding the endoneurium. The fascicle was surrounded by a perineurium with a thickness equal to 3% of the fascicle diameter [START_REF] Grinberg | Fascicular perineurium thickness, size, and position affect model predictions of neural excitation[END_REF] and an epineurium (2.9 mm diameter). A physiological saline layer (50 µm thickness) was modeled between the Cuff electrode and the epineurium. The cuff electrode was modeled according to the same characteristics as described in the experimental section on porcine model (Sec. 2.2.3). A two part process was used to determine fiber activation. The first step was the computing of the step response of the potential fields through the volume conductor model -as a result of electrode stimulation -using COMSOL multiphysics. The second step was to determine the response of a myelinated nerve fiber to the field set up by the cuff electrode system (emission of an AP). Models of mammalian myelinated fibers with 71 Nodes of Ranvier (NoR) were implemented on Matlab (The MathWorks, Natick, Massachusetts). To be consistent with diameter of B-fibers, a 2 µm myelinated axon was modeled, located at 1 mm from the cathode. Two membrane dynamics were used: CRRSS model of a mammalian myelinated fiber at 37 • C [START_REF] Chiu | A quantitative description of membrane currents in rabbit myelinated nerve[END_REF][START_REF] Sweeney | Modeling of mammalian myelinated nerve for functional neuromuscular stimulation[END_REF] with perfect insulating myelin, and double cable MRG model [START_REF] Mcintyre | Modeling the excitability of mammalian nerve fibers: influence of afterpotentials on the recovery cycle[END_REF][START_REF] Mcintyre | Cellular effects of deep brain stimulation: modelbased analysis of activation and inhibition[END_REF] at 37 • C. The waveforms were modeled in the same way as the waveforms delivered by the stimulator: continuous quarter sine and the continuous ramp were modeled as n pulsons with identical T on duration without non-stimulating pulsons (T of f = 0 µs). We thus do not study the influence of the recovery phase and the interstim delay: the anodic phase was not included in simulations. The current threshold amplitude was determined using a dichotomy method. Activation was defined by the induction and propagation of APs along the NoR. Q th was computed using the formula 1.

Waveform study

The modeling study was performed to further extent the results obtained in-vivo. All waveforms listed in Fig. 1 were modeled with duration described in Table . 2 and Q computed. The main objective was to assess which waveforms were more charge-efficient compared to the conventional rectangular pulse. The analyzes were as follows:

• Continuous pulses at P W = 350 µs vs. continuous rectangular at P W = 350 µs.

• Chopped pulses at P W sum = 350 µs vs. continuous rectangular at P W = 350 µs.

• Chopped pulses at P W tot = 1000 µs vs. continuous rectangular at P W = 1000 µs.

• Chopped pulses at P W tot = 325 µs vs. continuous rectangular at P W = 350 µs.

Note that P W tot = 325 µs (instead of P W tot = 350 µs) for chopped pulse to stay consistent with experiments and technical constraints. The comparison between experimental results and simulations allows to assess the validity of the modeling in such conditions and thus to evaluate the validity of the extension to other waveforms that were not experimentally tested. For all the waveforms, we presented Q th normalized with respect to the charge at the activation threshold of the 350 µs continuous rectangular. A subsidiary question was to evaluate the most relevant duration (i.e. P W tot or P W sum ) in order to compare the chopped and the continuous pulses. As described in the method section, we stimulate the nerve distally and recorded dissected single afferent B fibers proximally. A total of 110 thresholds were determined during 5 experimental sessions. An example of recording, averaged over 6 trials, is shown on the Fig. 3. Stimulation artifact is visible at the beginning of the recording. 36 fibers out of 110 did not pass the TSC regardless of the waveform types. It was possible to distinguish nerve fibers between them owing to the delay between the onset of the stimulation and the evoked AP so the velocity was computed. Less than 5% of fibers with high velocities (greater than 40 m.s -1 ) were observed. The propagation velocity of these fibers corresponds to type Aβ myelinated neurons. The average propagation velocity of the remaining fibers was 7.54 m.s -1 ± 4.43m m.s -1 . It allows to identify these fibers to type B and further confirms that afferent gastric fibers includes some B fibers [START_REF] Mei | The composition of the vagus nerve of the cat[END_REF]. When testing the influence of factors on Q th ANOVA yielded significant change for both the waveforms type and the animal (two-way repeated measures ANOVA, p-value<<0.001). There was no interaction between animal and waveforms (two-way repeated measures ANOVA, p-value=0.33). Waveforms were then compared two by two using CT SC. Fig. 5 represents Q th at same P W sum for A: ramp vs. rectangular, B: quarter sine vs. rectangular, C: ramp vs. quarter sine, D: chopped quarter sine vs. rectangular. In the first step, the ramp and rectangular pulses were compared (Fig. 5,A). 49 fibers passed the CT SC. Statistical analysis showed that Q th for the ramp pulse was lower than for the rectangular pulse (t-test, p-value<<0.01). The mean gain of charge was 485 nC, corresponding to a saving of 19.0% with ramp compared to rectangular. In the second step, quarter sine and rectangular pulses were compared with n = 68 for CT SC, (Fig. 5,B). Results showed that Q th was significantly lower for quarter sine pulse than for the rectangular pulse (Wilcoxon test, p-value << 0.01). The mean charge reduction was 421 nC, corresponding to a saving of 14.5% with quarter sine compared to rectangular. Then, ramp and quarter sine pulses were analyzed with n = 47 for CT SC (Fig. 5,C). Statistical analysis showed that Q th for the ramp pulse was lower than Q th for the quarter sine pulse (t-test, p-value << 0.01). The mean charge reduction per fibers was 108 nC, corresponding to a saving of 4.2% with ramp compared to quarter sine. Afterwards, rectangular P W = 350 µs and chopped quarter sine P W tot = 1000 µs, P W sum = 350 µs were compared with n = 23 for CT SC (Fig. 5,D). Comparison was done at P W sum . Statistical analysis showed that Q th for the chopped quarter sine pulse was higher than for the rectangular pulse (ttest, p-value<<0.01). The mean increase was 825 nC, corresponding to an additional consumption of 33.6 % of the chopped quarter sine (P W tot = 1000 µs, P W sum = 350 µs) compared to the rectangular pulse. Finally, we compared chopped quarter sine P W tot = 325 µs, P W sum = 125 µs, with rectangular. This time, comparison was done at P W tot with few fibers: n = 5 for CT SC. The mean charge reduction with chopped quarter sine compared to rectangular was 156 nC (8.8% saving) but there was a doubt on the significance of the results. Indeed, Wilcoxon paired sample test showed a p-value corrected of 0.1 closed to the threshold of significance of 5%.

Results

Single fiber experiment on the porcine subjects

In summary, among the waveforms evaluated, the statistical analysis showed that the ramp was the most efficient to activate the duodenal neurons (lowest Q th ). Thresholds for quarter sine were close to the ramp (less 5% difference). The rectangular pulse was less efficient than the quarter sine and ramp pulses. At P W tot , The chopped quarter sine pulse was less efficient compared to the rectangular pulse but more efficient if P W sum was used instead.

Modeling 3.2.1. Chopped pulses and continuous pulses

Relative differences of Q th between nonrectangular waveforms and the common con- tinuous rectangular pulse are presented in Table . 1. First, we compared continuous non-rectangular waveforms to the continuous rectangular pulse. The results indicated that Q th was lower for the continuous quarter sine pulse (-23.2%) and the continuous ramp pulse (-30.1%), at the same stimulus duration. These results were qualitatively consistent with the study of Sahin et al. [START_REF] Sahin | Non-rectangular waveforms for neural stimulation with practical electrodes[END_REF]. Second, the chopped waveforms were compared to the continuous rectangular pulse using P W sum = 350 µs (i.e not taking into account the T of f ). The results indicated that the Q th was significantly higher for the chopped rectangular pulse (+ 128.3%), and also for the chopped ramp (+ 39.5%) and chopped quarter sine (+ 71.1%). Third, the chopped waveforms were compared to the continuous rectangular pulse using common P W tot = 350 µs (i.e taking into account the T of f ). Contrary to the previous results, Q th for the chopped rectangular pulse was lower (-18.5%) as well as chopped ramp (-45.8%) and chopped quarter sine (-35.7%). Fourth, the chopped waveforms were compared to the continuous rectangular pulse using common P W tot = 1000 µs. The same observation could be drawn than previously: Q th was lower for the chopped rectangular pulse (-20%) as well as chopped ramp (-51.1%) and chopped quarter sine (-40.0%).

Comparison between model and experimental data

The table 2 shows normalized Q th obtained by modeling and porcine experimentation. For the waveforms presented, Q th was normalized with respect to Q th required to activate with the continuous rectangular pulse with P W = 350 µs. For the porcine model, the normalized charge was computed for each waveform that passed the CTSC common with continuous rectangular pulse. Quantitatively the results were not comparable, both models used for simulations underestimated the activation thresholds. However, qualitatively, by comparing the chopped and continuous waveforms at the same P W sum , the modeling results corroborated the experimental observations. Indeed, continuous ramp pulse was the most efficient waveform, followed by the continuous quarter sine. Chopped pulses were the least efficient. On the contrary, by comparing waveforms at an equivalent P W tot (Table 2, P W tot = 325 µs and P W tot = 350 µs on the one hand; P W tot = 1000 µs on the other hand) chopped ramp and quarter sine (table 2, P W tot =325) were more efficient than continuous ramp and quarter sine waveforms (table 2, P W tot =350). Concerning the MRG dynamics, the normalized charge for continuous ramp and quarter sine pulses had the same magnitude as those obtained experimentally. The charge decrease was globally underestimated by the CRRSS dynamics. However, for both models, the decrease of charges was overestimated for the quarter sine pulse at P W sum = 350µs, P W sum = 1000µs compared to experimental results.

Discussion

Single fiber experiments on porcine model

Compared to the conventional rectangular pulse with P W = 350 µs, the continuous ramp pulse activated duodenal neurons with the lowest charge, followed by the continuous quarter sine pulse and the chopped quarter sine pulse P W sum = 125 µs, P W tot = 325 µs. The chopped quarter sine P W sum = 350 µs, P W tot = 1000 µs was the least efficient among the waveforms. Due to time constraints and technical limitations, only a subset of waveforms have been tested on porcine experiments. Therefore, we skipped those that were known to be less efficient than others (e.g. chopped rectangular, chopped ramp [START_REF] Dali | Investigation of the efficiency of the shape of chopped pulses using earthworm model[END_REF]). In our experiments a relatively low number of fibers were activated by chopped waveforms compared to continuous ones (Fig. 4). This was caused by the fact that the chopped waveforms compared to:

1. the corresponding continuous waveforms with the same P W tot , require slightly less charge to activate fibers (table 2), but much higher amplitudes to provide this charge 2. the corresponding continuous waveforms with the same P W sum , require 2 times the same charge to activate the fibers (table 2).

In consequence, in both cases the chopped waveforms were more often exceeding the stimulator compliance voltage before activating the fibers than the corresponding continuous waveforms. The continuous ramp pulse needs slightly less charge than the continuous quarter sine pulse (4.2%). However, for the same amount of injected charges and the same P W sum the maximum peak currents compared to the rectangular waveform are 2 times higher for a ramp and 1.57 times higher for a quart sine. Since the difference in Q th for those two waveforms is small, and because fewer fibers were activated with ramp compared to quarter sine (Fig. 4), the use of the quarter sine pulse rather than the ramp pulse seems more appropriated in a clinical context.

Modeling

The modeling study qualitatively confirmed the experimental results on the pig. Moreover, the results normalized to the classical rectangular continuous stimulus, were close between MRG dynamics and experimental data. It indicates that the MRG dynamics is a very appropriate candidate to study non rectangular pulses and in particular multi-pulsons that contains high dynamics, as only a scale factor may be needed to fit experiments and simulations. We thus demonstrated that MRG is able to predict axons' responses to stimulation using chopped waveforms whereas MRG's parameters from in-vivo were not measured in such conditions. The scale factor mainly comes from the fact that conductivities, extracted from different species and different experimental conditions, and the electrode positioning are not accurate enough. However it can be easily adjusted for a given experimental setup. CRRSS dynamics model is less indicated as results shows much more discrepancies even with a correcting scale factor. These results support the qualitative robustness of the active models, even for stimulation parameters for which they were not designed, i.e., a succession of pulsons on small myelinated fibers.

Our study proved that the models can thus be used to virtually investigate a large set of possible waveforms with a high confidence.

The only limitation is that the results should be compared against the classic rectangular pulse and not in an absolute manner. Note, however, an exception in the porcine study on chopped quarter sine P W sum = 125 µs, P W tot = 325 µs, where the models predicted a smaller Q th compared to the continuous ramp and continuous quarter sine pulses. This difference must be mitigated: for the chopped quarter sine P W sum = 125 µs, P W tot = 325 µs, the number of exploitable samples was small (6 fibers passed the stability threshold criteria), and a doubt remained concerning the statistical results. The order of magnitude is respected but the relative values between certain waveforms were so close that it is impossible to experimentally validate this result without a larger set of samples.

Chopped pulses relevance

The relevance of the comparison between chopped pulses and continuous pulses should be discussed. Indeed, two points of view face in the rare articles on the topic [START_REF] Qing | Burst-Modulated Waveforms Optimize Electrical Stimuli for Charge Efficiency and Fiber Selectivity[END_REF], [START_REF] Shepherd | Electrical stimulation of the auditory nerve: II. Effect of stimulus waveshape on single fibre response properties[END_REF]. Should we compare chopped and continuous pulses with the effective stimulation duration (P W sum ) or the total stimulation duration (P W tot )? The difficulty comes from the impossibility to uniquely define a stimulation duration, P W , and then an equivalent strength-duration curve. Comparison of chopped and continuous pulses at the same P W tot indicated that the Q th was smaller for the chopped pulses. However, for the same P W sum , i.e. when comparing the chopped waveforms with same continuous waveforms, but without pauses between the pulsons, the continuous waveforms were more efficient. Therefore, we can conclude that the short continuous pulses are the most efficient, this information being already known if we consider the classic strength-duration curves but not obvious when comparing chopped and unchopped waveforms with ambiguous conclusion as reported in previous studies.

Another question is raised by Qing et al. [START_REF] Qing | Burst-Modulated Waveforms Optimize Electrical Stimuli for Charge Efficiency and Fiber Selectivity[END_REF]: chopped pulses further discriminate fiber activation by favoring activation of C-fibers and limiting activation of large Afibers. They associated this observation with the mechanism of prepulses on large diameter fibers. This remark must be mitigated, given that the study by Grill and Mortimer [START_REF] Grill | Inversion of the current-distance relationship by transient depolarization[END_REF] suggested that there is a minimum duration for the prepulses to act on the reduction of excitability (i.e. an increase of the activation threshold). In the study of Grill and Mortimer, prepulses shorter than 200 µs produced an increase in excitability rather than a decrease. Moreover, adding an interpulse between the prepulse and the activation pulse (to be compared with the T of f duration) changes the effect on the excitability [START_REF] Van Den Honert | The response of the myelinated nerve fiber to short duration biphasic stimulating currents[END_REF]; this decreases as the duration of the interpulse increases. Instead, we can hypothesize that since the current needed for the activation of the C-fibers is 10 to 100 times greater than the current required to activate A-fibers, it is possible that the large diameter fibers reached their blocking threshold. Indeed, for high current values, virtual anodes [START_REF] Ungar | Generation of unidirectionally propagating action potentials us-ing a monopolar electrode cuff[END_REF] can be observed near the cathode, causing an hyperpolarization of the membrane and preventing the AP propagation. Contrary to the previous studies [START_REF] Qing | Burst-Modulated Waveforms Optimize Electrical Stimuli for Charge Efficiency and Fiber Selectivity[END_REF], [START_REF] Shepherd | Electrical stimulation of the auditory nerve: II. Effect of stimulus waveshape on single fibre response properties[END_REF], the anodic discharge was identical for all waveforms: a rectangular pulse of 2800 µs. This choice is justified in order to study only the influence of the cathodic phase of stimulation. We thus avoid introducing a confusing factor on the influence of the anodic phase which could distort the comparison between the waveforms. Besides, other consideration such as interpulse after the cathodic phase is not discussed neither studied in this paper and in the cited work on the chopped pulse, but should be considered for further optimization [START_REF] Maciejasz | Delaying discharge after the stimulus significantly decreases muscle activation thresholds with small impact on the selectivity: an in vivo study using time[END_REF][START_REF] Shepherd | Electrical stimulation of the auditory nerve: II. Effect of stimulus waveshape on single fibre response properties[END_REF]. It becomes very difficult to understand the contribution of each phenomenon to the final result; a great care should be taken when comparing the efficiency of different waveforms as the comparison is based on a non-unique definition of variables, in particular P W . Moreover, the dynamics of the membrane should be related to the timing of the chopped pulse to further understand and then maybe optimized the effect of these intra-pulse high frequency.

Conclusion

We have demonstrated in the experimental and modeling studies that it is possible to save charge injection with non-rectangular waveforms. Results are qualitatively similar between experiments and model prediction further increasing the interest of modeling prior to experimental work. It shows the qualitative robustness of the models even in the case of complex waveforms. The charge reduction depends on waveforms and whether the pulse is chopped or not. The efficiency of chopped waveforms relatively to continuous pulses should be reconsidered based on the way the active pulse duration is computed. However, our study leads to lower the interest of chopped pulse as a continuous waveform with an equivalent P W sum , is always more efficient. Among continuous waveforms, ramp is the most efficient, quarter sine is slightly less efficient and rectangular is much less efficient than those two waveforms. In the pig experiment, for the same current range, continuous quarter sine pulse activates more gastric nerve fibers than ramp waveform, and therefore is an attractive candidate for a long-term use in implanted devices. We showed that chopped pulse mechanisms on axon membrane must be further investigated to make a fair comparison with continuous pulse. Two-year outcome of vagus nerve stimulation (vns) for treatment of major depressive episodes., The Journal of clinical psychiatry 66 (9) (2005) 1097-1104.

Figure 1 :

 1 Figure1: Waveforms used during simulations and experiments. For pig experiments, the anodic phase was always rectangular pulse of 2800 µs duration and amplitude allowing obtaining the same charge as during the cathodic phase.D and E waveforms were tested through simulations.

Figure 2 :

 2 Figure 2: The transected cervical vagus nerve during recordings with the isolated bunch of fibers lying on the of the recording electrode. The diameter of the electrode was 50 µm.

Figure 3 :

 3 Figure 3: Example of recording of the amplified evoked potential (gain of the amplifier: 50,000). Continuous rectangular pulse with P W tot = 350 µs was used for stimulation.

Figure 4 :

 4 Figure 4: Percentage of gastric nerve fibers activated, as a function of their estimated propagation velocity.

Fig. 4

 4 Fig.4represents the percentage of fibers that passed TSC as a function of conduction velocity. This percentage was normalized to the total number of fibers recorded (110). Less than 5% of fibers with high velocities (greater than 40 m.s -1 ) were observed. The propagation velocity of these fibers corresponds to type Aβ myelinated neurons. The average propagation velocity of the remaining fibers was 7.54 m.s -1 ± 4.43m m.s -1 . It allows to identify these fibers to type B and

  vs chopped quart sin

Figure 5 :

 5 Figure 5: Comparison of Q th between waveforms in the pig experiments. A: Ramp P W = 350 µs vs rectangular P W = 350 µs, B: quarter sine P W = 350 µs vs rectangular P W = 350 µs, C: Ramp P W = 350 µs vs quarter sine P W = 350 µs, D: Rectangular P W = 350 µs vs chopped quarter sine P W sum = 350 µs, P W tot = 1000 µs.

Table 1 :

 1 Difference of Q th between simulated non-rectangular and rectangular waveforms for P W = 350µs and P W = 1000µs.

	Waveform	P W sum P W tot	Difference relative to the rectangular waveform. (%) Rectangular P W = 350 µs Rectangular P W = 1000 µs
	Ramp	350	350	-30.1	/
	quarter sine	350	350	-23.2	/
	Chopped rectangular 350	1000	128.3	-20.0
	Chopped ramp	350	1000	39.5	-51.1
	Chopped quarter sine 350	1000	71.1	-40.0
	Chopped rectangular 125	325	-18.5	/
	Chopped ramp	125	325	-45.8	/
	Chopped quarter sine 125	325	-35.7	/

Table 2 :

 2 Comparison of normalized Q th for chopped and continuous pulses. Units of P W tot , P W sum , T on and T of f are µs

	Waveform	Porc. exp.	Number of pulsons (T on )	P W tot P W sum T on	T of f	Normalized charge rect 350 µs (%)	Normalized charge rect 350 µs (%)	Normalized charge rect 350 µs
								CRRSS	MRG	porc. exp. (%)
								model	model
	Rectangular	Yes	1	350	350	350	0	100	100	100
	Rectangular	No	1	1000	1000	1000 0	285	205	/
	Ramp	Yes	14	350	350	25	0	70	85	84
	quarter sine	Yes	14	350	350	25	0	77	88	87
	Chopped rectangular No	14	1000	350	25	50	228	193	/
	Chopped ramp	No	14	1000	350	25	50	139	142	/
	Chopped quarter sine Yes	14	1000	350	25	50	171	154	134
	Chopped rectangular No	5	325	125	25	50	82	89	/
	Chopped ramp	No	5	325	125	25	50	54	74	/
	Chopped quarter sine Yes	5	325	125	25	50	64	79	91

Acknowledgment

MD, PM, CP, and DG drafted the manuscript and all co-authors revised the manuscript. CHM, PM, OR and DG designed the stimulation protocols. CHM designed and performed the surgical approach on porcine subjects. PM and CP acquired and pre-processed experimental data. CP, PM and MD performed statistical analyses.

MD and DG defined the numerical implementation of models and algorithms and processed the simulated data. This work was supported by the INTENSE project with a grant from BPI France within the Investments for the Future program in France.


Mostefa Boumediene

Boumediene Haddad
email: haddadboumediene@yahoo.com

Annalisa Paolone

Mokhtar Drai

Didier Villemin

Mustapha Rahmouni

Serge Bresson

Ouissam Abbas

Synthesis, thermal stability, vibrational spectra and conformational studies of novel dicationic meta-xylyl linked bis-1-methylimidazolium ionic liquids

Keywords: Meta-xylyl, bis-imidazolium, Thermal analysis, conformers, Raman measurements, DFT calculations

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

ABSTRACT

In recent years, dicationic ionic liquids have been subject of a strongly growing research effort for their interesting and important properties that suggest them to be potential candidate for many applications. Therefore, the knowledge about the synthesis, thermal stability, vibrational spectra and conformational behaviour of these compounds is an important subject of study. The objective of the work presented in this paper is to investigate the influence of the substituent relative meta-position of dicationic ionic liquids (ILs), namely meta-xylyl linked bis-1-methylimidazolium ILs, on thermal stability, vibrational spectra and conformational studies. In the first step, four new meta-xylyl linked bis-imidazolium [m-C6H4(CH2ImMe)2 + ] ionic liquid (ILs) containing the dichloride [Cl -]2, di(bis(trifluoromethylsulfonyl) Imide) [(CF3SO2)2N -]2, bis(tetrafluoroborate) [BF4 -]2 and bis (hexafluorophosphate) [PF6 -]2 anions were synthesized. The obtained dicationic ILs were characterized by 1 H-NMR, 13 C-NMR, 19 F-NMR, 31 P-NMR and FT-IR spectroscopy. Also, their thermal properties were determined and compared. The thermal behavior confirmed that [m-C6H4(CH2ImMe)2 + ] dicationic ILs containing [(CF3SO2)2N -]2 and [PF6 -]2 are more stable that the dichloride [Cl -]2, and bis(tetrafluoroborate) [BF4 -]2 dicationic ILs, and they show a good thermal stability up to 340°C which makes them suitable for thermal application. In the next step, a computational study of the conformers of [m-C6H4(CH2ImMe)2], by means of DFT calculations with the 6-31G** basis set and the B3LYP theory was performed. Additionally, vibrational spectroscopy studies were conducted by infrared (FTIR) and Raman (FT-Raman) spectroscopy on the four dicationic ILs, differing for their anions. Finally a computational investigation of the interactions between anions and cation is presented.

INTRODUCTION

One of the principal aims of modern chemistry is to design effective solvents that will be alternative to organic solvents, and that would not have the same disadvantages (e.g: high toxicity, high flammability and high vapor pressure) [START_REF] Reichardt | Solvents and solvent effects in organic chemistry[END_REF][START_REF] Cull | Room-temperature ionic liquids as replacements for organic solvents in multiphase bioprocess operations[END_REF]. Scientific researchers in this field have suggested several tracks for the discovery of a new class of solvents, less harmful and less volatile. One of them regards "ionic liquids", which have been developed in the last decade as new green solvents, more acceptable to the environment, with excellent physical and chemical properties [START_REF] Suarez | Synthesis and physical-chemical properties of ionic liquids based on 1-n-butyl-3-methylimidazolium cation[END_REF] that make them green substitutes more attractive compared to conventional organic solvents. They exhibit several exciting properties, such as their low melting points [START_REF]Ionic liquids in synthesis[END_REF], good solvation properties [START_REF] Anderson | Characterizing ionic liquids on the basis of multiple solvation interactions[END_REF], their very low vaporization voltages [START_REF] Poole | Chromatographic and spectroscopic methods for the determination of solvent properties of room temperature ionic liquids[END_REF], their thermal and chemical stabilities [START_REF] Haddad | Bis-methyl imidazolium methylidene bis (trifluoromethanesulfonyl) imide, crystal structure, thermal and dielectric studies[END_REF] and their high solubilities [START_REF] Huddleston | Room temperature ionic liquids as novel media for 'clean'liquid-liquid extraction[END_REF].

Concerning their structures, they are designable properties, determined by the molecular interactions between the ions [START_REF] Panja | Clusters of the Ionic Liquid 1-Hydroxyethyl-3-methylimidazolium Picrate: From Theoretical Prediction in the Gas Phase to Experimental Evidence in the Solid State[END_REF]. Therefore, unravelling the structureproperty relationships and finding universal correlations that can be utilized for a rational design is one of the main aim of the current research; in other words the coupled selected cations -anions can be adapted and adjusted to obtained ionic liquids with physicochemical properties desired for a specific application [START_REF] Merouani | Acoustic cavitation in 1-butyl-3methylimidazolium bis (triflluoromethyl-sulfonyl) imide based ionic liquid[END_REF]; among these adjustments, it is possible to functionalize the imidazole as precursor in the synthesis reactions for the production of new substituted ionic liquids with new properties [START_REF] Panja | Cluster formation through hydrogen bond bridges across chloride anions in a hydroxyl-functionalized ionic liquid[END_REF].

Recently, a new class of the ionic liquid family known as dicationic ionic liquids (ILs) has emerged as more effective and versatile compared to conventional monocationic ILs. Dicationic ionic liquids based on imidazolium [START_REF] Chae | Interesting phase behaviors and ion-conducting properties of dicationic N-alkylimidazolium tetrafluoroborate salts[END_REF], pyrrolidinium [START_REF] Anderson | Structure and properties of high stability geminal dicationic ionic liquids[END_REF], piperidinium [START_REF] Haddad | New dicationic piperidinium hexafluorophosphate ILs, synthesis, characterization and dielectric measurements[END_REF], and ammonium [START_REF] Zhang | Ionic liquids based on aliphatic tetraalkylammonium dications and TFSI anion as potential electrolytes[END_REF] cations represent the majority of the investigations in this field. A comparison between dicationic ILs and monocationic ILs, having a different length of grafted alkyl group was reported. [START_REF] Gurung | Optical Kerr effect spectroscopy of CS 2 in monocationic and dicationic ionic liquids: insights into the intermolecular interactions in ionic liquids[END_REF][START_REF] Montalbán | Ecotoxicity assessment of dicationic versus monocationic ionic liquids as a more environmentally friendly alternative[END_REF].

The dicationic ILs have been the subject of many experimental and theoretical studies because of their properties makes them attractive for applications in a variety of fields including organic synthesis, catalysis, electrochemistry, and separation.

They are thermally more stable, with higher viscosities, melting point, densities [START_REF] Payagala | Unsymmetrical dicationic ionic liquids: manipulation of physicochemical properties using specific structural architectures[END_REF][START_REF] Shirota | Comparison between dicationic and monocationic ionic liquids: liquid density, thermal properties, surface tension, and shear viscosity[END_REF],and have a greater d-spacing of the crystal structure than the monocationic ones [START_REF] Payagala | Unsymmetrical dicationic ionic liquids: manipulation of physicochemical properties using specific structural architectures[END_REF].

The recent years have seen a strongly growing research effort regarding the influence of substituents functionalized in ionic liquids on the physical and chemical properties. In general, substituents in ortho, meta or para-positions alter the conformations, equilibrium relationships, vibrational spectra, the molecular structure, interionic interactions and thermal properties of the substituted in functionalized ionic liquids.

Very recently, we have investigated the conformers of the cation and the anioncation hydrogen bonding in Para-xylyl linked bis-imidazolium ionic liquids by using IR and Raman spectroscopic studies with the help of DFT calculation [START_REF] Haddad | Para-xylyl bis-1-methylimidazolium bis (trifluoromethanesulfonyl) imide: Synthesis, crystal structure, thermal stability, vibrational studies[END_REF][START_REF] Haddad | Para-xylyl linked bis-imidazolium ionic liquids: A study of the conformers of the cation and of the anion-cation hydrogen bonding[END_REF].

The facile synthesis of the same dicationic ILs (bis-imidazolium group) followed by new substitution at the position meta for the cationic site can give rise to new dicationic ILs namely Meta-xylyl linked bis-imidazolium ionic liquids; however, to the best of our knowledge, the study of the thermal stability, vibrational spectra and conformational studies of these dicationic ILs are not covered yet by the literature.

In this study, four new dicationic ILs based on meta-xylyl linked bis-imidazolium pairing the dichloride, bis(hexafluorophosphate), bis(tetrafluoroborate) and di(bis (trifluoromethanesulfonyl) imide) anions were investigated by using spectroscopic and thermal analysis; the thermal stability of all these dicationic ILs and their decomposition process were investigated, with the aim to understand the relationship between the structure and properties.

MATERIALS, AND METHODS

The chemicals used in this study: 1-methyl-1H-imidazole (> 99%), [1,3-bis (chloromethyl) benzene], α, α′-dichloro-m-xylene (98%), potassium hexafluorophosphate (≥ 99%), lithium bis (trifluoromethylsulfonyl) Imide (99%), ammonium tetrafluoroborate (99.5 wt %), were purchased from Aldrich and used as received. Diethyl ether and N,N-dimethylformamide were purchased from Fluka.

Deionized H2O was obtained with a Millipore ion-exchange resin deionizer.

General procedure for the synthesis of dicationic ILs

The synthesis of 3,3'-dimethyl-1,1'-(1,3-phenylenedimethylene)-bis(1H-imidazolium) dichloride can be described as follows [START_REF] Haddad | Synthesis of palladium-bidentate complex and its application in Sonogashira and Suzuki coupling reactions[END_REF]. Briefly, The dicationic IL named [m-C6H4(CH2ImMe) + following the same procedure.

-[NH4 + BF4 -] (0.68g, 6.5 mmol) under microwave heating to give [m-C6H4 (CH2ImMe)

+ 2] [BF4 -] 2
The summary of the synthesis reactions is depicted in the following Scheme 1 and Scheme 2:

NMR characterization

The structures of synthesized dicationic ILs are confirmed by using 1 H, 13 C, 19 F and 31 P -NMR spectroscopy, in order to check the occurrence of the expected chemical reactions and confirm the absence of any impurities. 1 H-NMR (500 MHz), 13 C-NMR (125.75 MHz) and 19 F-NMR (470.62 MHz) spectra were recorded on a Bruker DRX 500 MHz spectrometer. Spectra were recorded in dimethylsulfoxide (DMSO-d6), using the DMSO residual peak as the 1 H internal reference (δ = 2.5 and 3.3), and the central peak of DMSO-d6 at δ = 39.5 as the 13 C reference. Chemical shifts (δ) are

given in ppm and referred to the internal solvent signal, namely TMS and CFCl3, respectively. All NMR spectra confirm that our dicationic ILs have been successfully synthesized and prove a good purity. The spectroscopic data are given below:

[m-C6H4 (CH2ImMe)

THERMAL ANALYSIS

Concomitant measurements of thermogravimetry (TGA) and differential thermal analysis (DTA) were performed by means of a Setaram Setsys Evolution 1200 TG System, with a fixed temperature rate of 5°C/min, in an argon flux of 60 ml/min. For each sample, an initial mass of ~20 mg was used.

VIBRATIONAL SPECTROSCOPY

Infrared spectroscopy data were acquired by attenuated total reflectance spectra on a Vertex 70-RAM II Bruker spectrometer (Bruker Analytical, Madison, WI) operating with a Golden Gate TM diamond ATR accessory (Specac Ltd., Slough, UK).

FTIR/ATR spectra [3500-600 cm -1 ] were collected with a nominal resolution of 1 cm - 1 by co-adding 64 scans for each spectrum. Only for the sample containing Cl -as anion, an additional spectrum was acquired in transmission mode by means of an Agilent Cary 660 with a resolution of 1 cm -1 in the frequency range between 4000 and 400 cm -1 , by dissolving the ionic salt in KBr in the proportion 1:100 in mass. The measurement was the mean of 100 scans. Prior of this measurement the sample was kept at 80°C for 48 hours in order to increase its crystallinity and remove hydration water.

FT-RAMAN spectra were acquired by means of a Vertex 70-RAM II Bruker FT-RAMAN spectrometer. This instrument is equipped with a Nd:YAG laser (yttrium aluminium garnetcrystal doped with triply ionized neodymium) with a wavelength of 1064 nm and a maximum power of 1.5 W. The measurement accessory is prealigned; only the Z-axis of the scattered light is adjusted to set the sample in the appropriate position regarding the focal point. The RAM II spectrometer is equipped with a liquid-nitrogen cooled Ge detector. FT-RAMAN spectra [3500-150 cm -1 ] were collected with 1 cm -1 nominal resolution by co-adding 128 scans for each spectrum at room temperature.

COMPUTATIONAL

The isolated cation (m-xylene) was investigated computationally by means of the Spartan software [START_REF] Shao | Advances in methods and algorithms in a modern quantum chemistry program package[END_REF][START_REF] Hehre | A guide to molecular mechanics and quantum chemical calculations[END_REF]. Concerning the anions their spectra are well known both from an experimental and computational point of view [25][START_REF] Vitucci | Infrared spectra of bis(trifluoromethanesulfonyl)imide based ionic liquids: Experiments and DFT simulations[END_REF]. After the optimization, we obtained many degenerate geometries, that were removed from the following procedures. The vibration frequencies and the infrared intensity and Raman activity of the optimized structures having an energy not higher than 5 kJ/mol from the lowest energy conformer were calculated by means of the Spartan software. Only 7 of them had all positive vibrational frequencies and can therefore, be considered as stable points of the potential energy surface. In order to compare the experimental infrared and Raman spectra with the calculated one, we constructed expected IR and Raman spectra summing Gaussian curves centered at each calculated vibration frequency, with an intensity proportional to the calculated one and a fixed line width of 10 cm -1 .

Moreover, the optimized geometry of the four ionic couples of m-xylene with 2 Cl -, 2 BF4 -, 2 PF6 -or 2 NTf2 -anions were obtained by DFT calculations using the 6-31G** basis set and the B3LYP theory.

RESULTS AND DISCUSSION

COMPUTATIONAL RESULTS

Table 1 reports the values of the four dihedral angles of the seven stable points of the potential energy surface (all vibrational frequencies are positive), after the optimization of geometries by means of DFT calculations using the 6-31G** basis set and the B3LYP theory. The two dihedrals C3C2C7N3 and C3C4C8N1 define the relative orientation of the two imidazolium rings, while the two dihedrals C4C8N1C15 and C2C7N3C13 describe the rotation of the imidazolium rings around its axis with respect to the xylene groups. In Table 1 also the values of the energy difference with respect to the lowest energy conformer are reported. [START_REF] Haddad | Para-xylyl bis-1-methylimidazolium bis (trifluoromethanesulfonyl) imide: Synthesis, crystal structure, thermal stability, vibrational studies[END_REF] and experimentally from X-Ray diffraction data [START_REF] Ibrahim | Synthesis and characterization of imidazolium salts bearing fluorinated anions[END_REF][START_REF] Willans | Bis (N-heterocyclic carbene) Dipalladium Complexes: Synthesis, Solid-State Conformational Studies and Solution Behaviour[END_REF] for the pxylene compounds. Additionally Table S1 of the Supplementing Information reports the calculated vibrational frequencies, their infrared intensities and the Raman activities, for all seven conformers.

C1-C2 C2-C7 C7-H7 C7-N3 N3-C10 N3-C13 C10-C11 C11-N4 C13- N4 N4-C20

THERMAL ANALYSIS

Decomposition studies are performed to investigate the influence that the structural parameters of anions have on the thermal degradation process of dicationic ILs, and to determine which ILs can be used in applications involving high temperatures [START_REF] Maton | Ionic liquid thermal stabilities: decomposition mechanisms and analysis tools[END_REF]. [NTf2] -. This trend indicates that the thermal stability of the dicationic ILs, therefore, depends on the anionic species, which have a significant impact on their thermal behavior, as observed in the imidazolium salts with these anions [START_REF] Zhou | Low-melting, low-viscous, hydrophobic ionic liquids: 1-alkyl (alkylether)-3-methylimidazolium perfluoroalkyltrifluoroborate[END_REF][START_REF] Fox | Flammability, thermal stability, and phase change characteristics of several trialkylimidazolium salts[END_REF]. the structure of anion is difficult, probably due to a large number of parameters such as ion size, shape, charge density, polarizability and flexibility of ions and planarity of molecular geometry. The lower thermal stability of the dichloride salt relative to those containing [BF4] -, [PF6] -and [NTf2] -, and his decomposition rate varied significantly during the pyrolysis, due to residual water. In addition to that, it is more nucleophilic than the larger fluoride containing anions and thus decompose by SN1 or SN2 nucleophilic decomposition [START_REF] Fox | Flammability, thermal stability, and phase change characteristics of several trialkylimidazolium salts[END_REF][START_REF] Awad | Thermal degradation studies of alkyl-imidazolium salts and their application in nanocomposites[END_REF]. The pyrolysis of the imidazolium based salts has been reported to proceed most likely via SN2 process, and therefore, change in the basicity and/or nucleophilicity of the anions is likely to bring about a change in the thermal stability of the ILs [START_REF] Macfarlane | Pyrrolidinium imides: a new family of molten salts and conductive plastic crystal phases[END_REF]. The results indicated that dicationic ILs containing

[NTf2] -shows slightly higher stability, they are less nucleophilic compared to the halides ones, which provides higher thermal stabilities compared to others dicationic ILs. This result may be attributed to the size of the [NTf2] -that is much larger and possesses higher polarizability than perfluorinated [PF6] -and [BF4] -ions. Moreover, the better flexibility and charge distribution of [NTf2] -tend to increase the interactions (attractive forces), and finally the molecular weight of the combination cation/anion.

It was reported that the melting point (Tm) of a compound is determined by the strength of its crystal lattice, which in turn is controlled by three main factors: intermolecular forces, molecular symmetry, and the conformational degrees of the freedom of a molecule [START_REF] Dearden | The QSAR prediction of melting point, a property of environmental relevance[END_REF][START_REF] Abramowitz | Melting point, boiling point, and symmetry[END_REF]. Increasing the size of the anion generally results in weaker coulombic interactions in the crystal lattice, poor packing of the ions, and a decrease in the melting temperatures (Tm: Cl, Br > PF6 > BF4 > NTf2) [START_REF] Holbrey | Physiochemical Properties of Ionic Liquids: Melting Points and Phase Diagrams in[END_REF]. The comparison of the Tm values of the dichloride salt with those containing the [BF4]

-, [PF6] -and [NTf2] -clearly shows the impact of the anion symmetry (see Table 3).

For the same cation, the salts with fluoro anions ([BF4] -… ) generally exhibit a lower melting point than those with higher symmetry [Cl] -, because this fluoro anions not only possesses chemical and electrochemical stability, but they also have low symmetry, high flexibility, and a weakly coordinating nature. These results suggest that packing efficiency of the salt could be disrupted by reducing the anion symmetry, thus lowering the melting point. 4. In the dicationic ILs with the BF4 anion the strong absorption lines centered around 761 and 1026 cm -1 are due to the anion; in the dicationic IL with PF6, the intense lines around 742 and 852 cm -1 are attributable to the vibrations of the anion [25]. Apart for these lines, the other absorption bands are common to the dicationic ILs and are therefore attributable to the vibrations of the common m-xylene cation. Their detailed attributions are reported in Table 4. Table 4. Observed FTIR/ATR bands and their assignment of the four dicationic ILs. (vw = very weak; w = weak; m = medium, s = strong; sh = shoulder; ν = Str = stretch; δ = deformation; bend = bending deformation; ω = wagging; ρ = rocking; ɤ = out-ofplane; s = symmetric; as = antisymmetric).

[m-C6H4 (CH2ImMe) Figure 5 reports a comparison in the frequency range between 720 and 400 cm -1 of the calculated infrared absorption spectra of the seven conformers of the cation and the experimentally measured spectrum of [m-C6H4 (CH2ImMe) 2][Cl] 2, that has no contribution coming from the anion. It is evident that all calculated lines should be displaced towards lower frequency multiplying them by a factor in the range 0.97-0.99. The strong experimental absorption line centered around 620 cm -1 is found computationally around 636 cm -1 in all conformers. The lines measured around 654 cm -1 and 698 cm -1 are obtained computationally around 665 and 707 cm -1 in Conf A and around 668 and 707 cm -1 in Conf B (the conformers with the lowest energies).

The experimental absorption around 681 cm -1 could be attributed to Conf E that is expected to show a line around 683 cm -1 from the DFT calculations. The lack of any experimental absorption band between 610 and 636 cm -1 suggests the occurrence of very limited concentrations of conformers B, C, F and G, that should present clear absorptions in this frequency range (after scaling).

RAMAN SPECTROSCOPY

Complementary to infrared absorption spectroscopy, Raman spectroscopy is a vibrational spectroscopy technique used in chemistry to identify molecules and study chemical bonding and intramolecular bonds.

In Figures 6, 7 and 8, we present a comparison between FT-Raman spectra of our four substituted dicationic ionic liquids (ILs) in the spectral ranges 1000-50, 1700-1000 and 3500-2700 cm -1 , respectively. Figure S1, reported in the Supplementing Information, shows a comparison of the FT-Raman bands [50-3500 cm -1 ] of the studied dicationic ionic liquids; their assignment is reported in the following with a discussion for each spectral region.

Region 1000-45 cm -1

In this region, the most characteristic modes were discussed in several zones. The In dichloride salt, we notice the presence of the following vibrational modes: 61, 90 and 190 cm -1 assigned to intermolecular interactions. The same observation for the two fluorinated dicationic ILs, with slight difference in the position of the peak, which depends on the strength of the anion -cation interaction.We note that the size of the anion adjacent imidazolium rings affected the vibrational behavior of the modes situated in this spectral zone. The larger the anion, the higher the wavenumbers of the intermolecular Raman modes: 61 and 90 cm -1 for Cl -against 69; 95 / 70; 99 and 72 cm -1 for, PF6 -, BF4 -, and [NTf2] -respectively. In the spectral zone [1000-200 cm - 1 ], the changes are more spectacular, as we observed very different vibrational modes between dicationic ionic liquids according to the paired anion. In the case of the [NTf2] -anion, the CF3 asymmetric and symmetric deformation contributes to the 571, 591 and 741 cm -1 bands respectively. In addition, other assignable modes of vibrations from the trans-[NTf2] -anion are: a SO2 rocking (313 and 326 cm -1 ), a SO2

wagging (399 and 404cm -1 ), a SO2 symmetric deformation (552 cm -1 ) and a SO2 symmetric bending (507 cm -1 ). As for the other anions, a great similarity is observed between the spectra relating to PF6 and BF4 anions especially at 471 cm -1 as reported by Talaty et al. [START_REF] Talaty | Raman and infrared spectra and ab initio calculations of C2-4MIM imidazolium hexafluorophosphate ionic liquids[END_REF] and 742 cm -1 concerning the stretching and scissoring modes of vibration with a clear difference in intensities. Further two modes are observed at 620 and 766 cm -1 , assigned to a bending, and symmetric stretching S-N-S respectively.

Moreover, in this zone, we showed the characteristic bands corresponding to all modes of the C-H bond (in the N-C(H)-N fragment) and the stretching vibrations of the N-heterocyclic ring that used before as the diagnostic bands in spectroscopic similar studies on molecules containing the imidazolium ring as investigated by Haddad et al. [START_REF] Panja | Clusters of the Ionic Liquid 1-Hydroxyethyl-3-methylimidazolium Picrate: From Theoretical Prediction in the Gas Phase to Experimental Evidence in the Solid State[END_REF][START_REF] Haddad | Para-xylyl bis-1-methylimidazolium bis (trifluoromethanesulfonyl) imide: Synthesis, crystal structure, thermal stability, vibrational studies[END_REF][START_REF] Haddad | Para-xylyl linked bis-imidazolium ionic liquids: A study of the conformers of the cation and of the anion-cation hydrogen bonding[END_REF][START_REF] Haddad | Effects of C (2) methylation on thermal behavior and interionic interactions in imidazolium-based ionic liquids with highly symmetric anions[END_REF] and by Kausteklis et al. [69]. The bending motions of these bonds (HCCH) have predominant contribution in the weak bands in the zone from 750 to 900 cm -1 .

Region 1700-1000 cm -1

At the beginning of this spectral region, (C-C) skeletal modes are shown in the range [1000-1200 cm -1 ], as intense band (symmetric stretching at 1005 cm -1 ).

According to literature [START_REF] Kiefer | Experimental vibrational study of imidazoliumbased ionic liquids: Raman and infrared spectra of 1-ethyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide and 1-ethyl-3-methylimidazolium ethylsulfate[END_REF][START_REF] Moschovi | Vibrational spectroscopic study of the protic ionic liquid 1-H-3-methylimidazolium bis (trifluoromethanesulfonyl) imide[END_REF][START_REF] Moumene | Vibrational spectroscopic study of ionic liquids: Comparison between monocationic and dicationic imidazolium ionic liquids[END_REF][START_REF] Drai | Synthesis, experimental and theoretical vibrational studies of 1-methyl and 1, 2dimethyl, 3-Propylimidazolium bis (trifluoromethanesulfonyl) imide[END_REF], all fundamental vibrations of the [NTf2] -anion are situated below 1400 cm -1 , then two SO2 antisymmetric stretching modes are expected between 1335 and 1352 cm -1 and the symmetric one, νs SO2 (1160 cm -1 ), with contributions from the νs CF3 symmetric stretching (intense polarized band at 1244 cm -1 ) [70]. In monocationic ionic liquids, the chloride was found in the plane of the ring, while BF4 is positioned over the ring and has short contacts not only with H-C (2), but also with a proton of the methyl group, as suggested by Katsyuba et al.

[58] thanks to the observation of the BF4 antisymmetric stretching mode of vibration (1025 cm -1 ). The spectral zone [1500-1400 cm -1 ] particularizes δ (CH2) bending [69]. The presence of the phenyl ring could be identifying also by C= C stretching bands in the spectral range [1650 -1500 cm -1 ], undoubtedly, the most characteristic vibration of the phenyl group is observed as a clear band around 1596 cm -1 for the fluorinated dicationic ILs, and 1610 cm -1 for the dichloride dicationic IL, that was assigned to ν (C=C).

Region 3500-2700 cm - This region namely C-H region, is characterized notably by the stretching vibrations of the C-H bonds occur in the range from 3000 to ~ 2700 cm -1 attributed to aliphatic C-H symmetric and asymmetric stretching modes, while the aromatic CH groups vibrate at higher frequency manifesting between 3200 and 3000 cm -1 . The band observed in the Raman spectrum near 2970 cm -1 can be assigned to a νas CH3 asymmetric stretching, as reported by Kausteklis et al. [69][70]. Moreover, the C-H stretching vibration bands of the aromatic phenyl ring, the methylene and the methyl group attached to the imidazolium ring appear in the Raman spectra at 3027, 3043, 6). In this region, the vibrational bands at higher wavenumbers can be referred to C(4,5)-H stretching modes, whereas those at lower wavenumbers can be assigned to the C(2)-H stretching modes. The optimized structures of the four ionic couples of m-xylene with 2 Cl -, 2 BF4 -, 2 PF6 -or 2 NTf2 -anions were obtained by DFT calculations using the 6-31G** basis set and the B3LYP theory. Different starting geometries were investigated. For all the four possible anions, the cation preserves its structure close to that found for conformer A, reported in Section 4.1 (see Figure 9). Moreover, in all cases the two anions prefer to reside both in the same half plane were the benzene ring is placed, in positions close to the imidazolium C13 and C15 carbon atoms (see Figure 2) and the attached H atoms. The only exception is observed in the case of the two Cl - anions, which prefer to displace toward the methylene groups with carbon atoms C7 and C8. In this case the distances between Cl and the hydrogen atoms of the imidazolium ring (H14, Figure 9), of the methyl group (H7) and of the benzene ring (H1) are 2.027, 2.521 and 2.861 Å, respectively. In the case of the BF4 anions the F2 and F1 atoms (figure 2) distance from H14 are 2.030 and 2.091 Å, while for PF6 the F1 and F2 distance from H14 increases to 2.046 and 2.105 Å. Finally in the case of NTf2, the closest oxygen atom has a distance of 1.929 Å from H14. In all cases the anions reside outside the planes defined by the imidazolium rings, with increasing distance for Cl, BF4, PF6 and NTf2. However, these results need to be compared to experimental structural data, that at present are not available, due to the lack of Xray diffraction data in the solids.

3065 cm -1 for [m-C6H4(CH2ImMe)2 + ][Cl -]2; 3071 cm -1 for [m-C6H4(CH2ImMe)2 + ][BF4 -]2; 3031, 3071 cm -1 for [m-C6H4(CH2ImMe)2 + ][PF6 -]2; 3022, 3075 cm -1 for [m- C6H4(CH2ImMe)2 + ][NTF4 -]2.

CONCLUSION

Four new substituted dicationic ionic liquids based on meta-xylyl linked bis-1methylimidazolium, combined with four anions, namely dichloride [Cl -]2, di(bis(trifluoromethylsulfonyl) Imide) [(CF3SO2)2N -]2, di(tetrafluoroborate) [BF4 -]2 and di(hexafluorophosphate) [PF6 -]2 were synthesized for the first 1 H, 13 C, 19 F and 31 P-NMR spectroscopies confirm the production of the desired ILs. Combined TGA/DTA measurements indicate that the thermal stability of the ILs is in the following order NTf2>PF6>BF4>Cl; the latter compound is highly hygroscopic. While the NTf2 based sample is liquid at room temperature, the other three samples are solid and the melting points are in the order NTf2<BF4<PF6<Cl. Moreover, the vibrational spectra of these ionic liquids were investigated by using FTIR and FT-RAMAN spectroscopies. Quantum chemical theory (at the DFT level) was used to calculate the possible conformers of the cation. Due to the complex structure of the cation seven conformers exists with a difference in energy of less than 5 kJ/mol. The comparison with the experimental IR spectrum suggests that at least three of them could be present in the samples. Finally a computational investigation of the interaction between anions and cation is presented.

Scheme 1 .

 1 Scheme 1. Synthetic route of dichloride salt [m-C6H4 (CH2ImMe) 2] Cl2, MW microwave.

Figure 1 . 1 H

 11 Figure 1. 1 H NMR (500 MHz) (a) and 13 C NMR (125.75 MHz) (b), spectra of [m-C6H4 (CH2ImMe) 2 + ][Cl -]2

Figure 2 .

 2 Figure 2. Schematics of the cation with labels identifying the atoms whose distances and angles are reported in Table1and schematics of the different anions.

Figure 3 .

 3 Figure 3. TGA and differential thermal analysis (DTA) thermographs for the synthesized dicationic ionic liquids (ILs).

Figure 3

 3 Figure3shows the decomposition profiles of the four dicationic ILs based on the [m-C6H4 (CH2ImMe)2] dication from room-temperature up to 800°C. The present dicationic ILs were found to be thermally stable in a wide range of temperature. As reported for most dicationic ILs, the dicationic IL containing [NTf2] -is more stable than those containing [PF6] -, [BF4] -and Cl -[START_REF] Ngo | Thermal properties of imidazolium ionic liquids[END_REF][START_REF] Clough | Thermal decomposition of carboxylate ionic liquids: trends and mechanisms[END_REF]. We observed that dichloride salt begins to decompose (lose 0.07mg ≈ 0.5% of its initial mass) at 83°C probably due to the water of hydratation; the real decomposition of this salt is revealed in the range 300-357 °C (lose of ≈ 72%), to reach the maximum level of loss (≈ 90%) at 800°C. The analogue salt containing BF4 anion loses the same amount compared to the halide salt, of its weight ≈ 0.5% at 190°C, but only 21% at 300°C, and reaches 84% of loss weight at 800°C. The two other salts containing [PF6] -and [NTf2] -have similar thermal behavior and are stable in a wider temperature range. The thermal stability of the salts generally increases in the order: halides < [BF4] -< [PF6] -<

Figure 4 .

 4 Figure 4. Comparison of the infrared absorption spectra of the four dicationic ILs.

Figure 4

 4 Figure 4 reports the infrared absorbance spectra of the four dicationic ILs synthesized in this study. Most of the absorption lines of the dicationic IL containing NTF2 as anion are due to the vibrations of the anion, as reported in Table4. In the

2 Figure 6 .

 26 Figure 6. Raman spectra of the four dicationic ILs in the frequency range 1000-45 cm -1 .

Figure 7 .

 7 Figure 7. Raman spectra of the four dicationic ILs in the frequency range 1700-1000 cm -1 .

2 Figure 8 .

 28 Figure 8. Raman spectra of the four dicationic ILs in the frequency range 3500 -2700 cm -1 .

Figure 9 .

 9 Figure 9. Schematics of the optimized structures of the four ILs with different anions (top-left: Cl; top-right: BF4; bottom-left: PF6; bottom-right: NTf2).

2 + ][Cl -]2: 1 H-NMR

	(DMSO-d6), δH ppm: 9.12 (s, 2H, NCHN), 7.69-7.67 (d, 4H, NCHCHN), 7.40-7.49 (m, 4H, C6H4), 5.41 (s, 4H, -CH2-), 3.85 (s, 6H, 2 × CH3). 13 C-NMR (DMSO-d6) δ ppm: 36.15, 51.96, 122.71, 124.46, 128.44, 129.08, 130.29, 135.86, 137.08

[m-C6H4 (CH2ImMe) 2 + ][BF4 -]2: 19 F-NMR (

	DMSO-d6) δF (ppm): -148.17 (s, BF4).
	[m-

C6H4 (CH2ImMe) 2 + ][PF6 -]2: 19 F-NMR

	(DMSO-d6) δ ppm: -69.63, -70.82. 31 P-NMR (DMSO-d6) δ ppm: -133.72, -137.27, -140.78, -144.30, -147.81, -151.19, 154.71(sept, PF6 -)
	[m-

C6H4 (CH2ImMe) 2 + ][NTf2 -]2: 19 F-NMR

	(DMSO-d6) δF (ppm): -79.36 (s, [NTF2 -]).

N N CH 3 H 9 H 7 H 8 C N N H 2 H 4 H 5 H 6

Table 1 .

 1 The label, the dihedral angles and the difference in relative energy with respect to the lowest energy one of the seven cation conformers.

	Label	Dihedral	Dihedral	Dihedral	Dihedral	Relative
		C3C2C7N3	C3C4C8N1	C2C7N3C13	C4C8N1C15	Energy
						(kJ/mol)
	A	-123.52	-123.99	-130.52	-131.32	0.00
	B	122.49	85.63	133.55	-145.72	3.45
	C	125.88	118.85	-45.82	133.75	3.61
	D	-121.84	-122.43	37.64	-129.76	3.70
	E	-143.20	136.94	-124.46	126.78	4.22
	F	-97.20	-119.24	-14.94	-132.60	4.60
	G	88.98	123.36	30.42	131.92	4.73

Table 2

 2 displays some significative distances and angles of the lowest energy conformer. Similar values are obtained also for the other conformers, except for the four dihedral angles reported in Table1. A comparison with experimental data is not possible because no study of the structure of meta-xylyl linked bis-1-

	methylimidazolium compounds is available. However, the presently calculated
	values of bond lengths and angles well compares with those obtained both
	computationally

Table 2 .

 2 Some significative distances and angles calculated for the lowest energy conformer of m-xylene. The labels of atoms refer to Figure 2.

distances (Å)

Table 3 .

 3 Thermal properties of synthesized dicationic ILs: melting point, Tm, and decomposition temperature, Td.

	Dicationic ILs	Physical State at 25 °C Tm (°C)	Td (°C)
	[m-C6H4 (CH2ImMe) 2][Cl] 2	Solid	196	357
	[m-C6H4 (CH2ImMe) 2][PF6] 2	Solid	150	476
	[m-C6H4 (CH2ImMe) 2][BF4] 2	Solid	136	407
	[m-C6H4 (CH2ImMe) 2][NTf2] 2	Liquid	--	491

6 H 4 (CH 2 ImMe) 2 ][NTf 2 ] 2 Wavenumber (cm -1 ) [m-C 6 H 4 (CH 2 ImMe) 2 ][PF 6 ] 2 Raman Intensity (a.u) [m-C 6 H 4 (CH 2 ImMe) 2 ][BF 4 ] 2 [m-C 6 H 4 (CH 2 ImMe) 2 ][Cl] 2 20

	1700 1600 1500	1400 1300	1200 1100 1000
	[m-C
	1700 1600 1500	1400 1300	1200 1100 1000
	1

  The C-H stretching of the imidazole ring are observed at

	3119, 3152 cm -1 for [m-C6H4(CH2ImMe)2 + ][Cl -]2, 3127, 3158, 3179 cm -1 for [m-
	C6H4(CH2ImMe)2 + ][PF6 -]2, 3135, 3158, 3179 cm -1 for [m-C6H4(CH2ImMe)2 + ][BF4 -]2, ,
	3134, 3153, 3178 cm -1 for [m-C6H4(CH2ImMe)2 + ][NTF2 -]2, (Figure

Table 5 .

 5 Observed FT-RAMAN bands and their assignment of 4 dicationic ILs at room temperature. (vw = Very weak; w = weak; m = medium, s = strong; sh = shoulder; ν = Str = stretch; δ = deformation; bend = bending deformation; ω = wagging; ρ = rocking; τ = torsion, s = symmetric; as = antisymmetric).

	[Cl] 2	[m-C6H4 (CH2ImMe) 2] [PF6] 2 [BF4] 2	[NTf2] 2	Vibrational assignment	Refs
					Range: 3500-2700 cm -1
		3179 (w)	3179 (w)	3178 (vw)	H-C-C-H asymmetric stretch , νas (H-C(4)), νas (H-C(5))	[44]/[45]/[55]/[69]/[70]

(w) 3158 (vw) 3158 (vw)

(vw) H-C-C-H asymmetric stretch

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support by The Ministry of Higher Education and Scientific Research (MESRS) of Algeria in PRFU project code: B00L01UN200120180002; also, Mostefa Boumediene would like to thank Doctor Guendouzi Abdelkrim, Head of the Department of Chemistry, Faculty of Sciences, University of Saïda, Algeria for their fruitful support, Moreover; Mostefa Boumediene would like to congratulate his supervisor Mr : HADDAD, who deserve the second place in the promotion of the rank of Professor related to 41st session of CUN results.

COMPUTATIONAL INVESTIGATION OF THE STRUCTURE ANIONS-CATION