Anthony Robert

Jean-Marc Zaccardi

Cécilia Dul

Ahmed Guerouani

Jordan Rudloff

Numerical Study of Auto-Ignition Propagation Modes in TRF-Air Mixtures: Towards a Better Understanding of Abnormal Combustion in Spark-Ignition Engines

Keywords: Auto-ignition, Deflagration, Detonation, Fuel Reactivity, LES

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Introduction

Two main abnormal combustions can be observed in modern spark-ignition engines: knock and low speed pre-ignition. Knock has been observed for the first time in 1882 by Sir Dugald Clerk who described it as a "persistent and troublesome enemy" [1] while the first observations of low-speed pre-ignition (LSPI) date back to the beginning of years 2000 [START_REF] Prochazka | Internationales Wiener Motorensymposium[END_REF]. However, in both cases, the triggering and the development of the abnormal combustion process rely on the auto-ignition characteristics of the air/fuel mixture. In order to control these abnormal phenomena, it is necessary not only to better understand how and when an auto-ignition can be triggered by "hot spots", but also how it will propagate inside the combustion chamber since the auto-ignition intensity and the potential resulting engine damages are linked to both aspects. Different approaches such as the Livengood-Wu integral can be used to predict the autoignition temporal onset. However, advanced tools and methodologies are still being developed to better understand and predict the auto-ignition propagation modes. The original theory regarding the auto-ignition propagation mode was provided by Zeldovich [START_REF] Zeldovich | [END_REF] and then developed more recently by Bradley and co-workers at Leeds University to analyze auto-ignition processes during CAI combustion [START_REF] Bradley | SAE Technical Paper[END_REF], during knocking combustion [START_REF] Bradley | SAE Technical Paper[END_REF], and lately during LSPI [START_REF] Kalghatgi | [END_REF]. Their auto-ignition calculations for 50%H 2 -50%CO-air mixtures allowed to highlight and to analyze the different propagation modes in various conditions. A specific classification diagram based on two dimensionless parameters has then been defined. Since then, this so-called "detonation peninsula" has been used for the analysis of both experimental occurrences of autoignition [7] and numerical results [8][9]. The recent studies of knocking combustion and LSPI require however to consider fuels whose auto-ignition characteristics are very different from those of H 2 -CO. Results obtained with n-heptane-air and isooctane-air mixtures have been recently illustrated by Bates et al. [10] but not fully compared to the original results from Gu et al. [11]. More recently, Chen et al. have thoroughly analyzed several simulation results obtained with n-heptane-air mixtures, by considering non-uniform mixture compositions, or even cool spots within the NTC region [12]. These results have highlighted the different auto-ignition propagation modes but the characteristics of n-heptane-air mixtures have not been compared to those of H 2 -CO-air or TRF-air mixtures, and the detonation peninsula location has not been compared to that defined by Gu et al. [11]. This article aims at confirming the relevancy of the original detonation peninsula when considering realistic fuels used in modern gasoline engines. Similar simulations as those performed by Bradley et al. are reported in this article but the novelty lies in the use of a TRF surrogate fuel featuring very different auto-ignition characteristic time scales as those of H 2 -CO. The first section introduces the main features of the original theory allowing to characterize the auto-ignition propagation mode. The second section introduces the numerical procedure used to reproduce the different auto-ignition propagation modes. The third section focuses then on the fuel reactivity. It discusses the expected impacts on the shape and location of the detonation peninsula when considering the auto-ignition characteristic time scales and diffusion properties of a realistic complex fuel. The fourth and fifth sections finally presents the 1D numerical setup and the simulation results obtained with various hot spots and thermodynamic conditions.

Theoretical background

Auto-ignition in Spark Ignition (SI) engines appears randomly in time during the engine cycle, after the spark in the case of knocking combustion, or before in the case of LSPI.

Regarding its location, auto-ignition is triggered in reactive centers resulting from mixture heterogeneities inside the combustion chamber. These heterogeneities can be linked to higher temperatures, to the local mixture composition featuring an increased reactivity (local fuel/air and dilution ratios), or even to external perturbations like solid particles or oil droplets. It is usually assumed, however, that reactive auto-ignition centers correspond to temperature gradients within the mixture, that is why these are often called "hot spots". Two kinds of waves are generated when auto-ignition is triggered: a reaction wave associated with the chemical propagation of the reactive front and a pressure wave initiated by the thermal explosion of the hot spot at the very beginning of auto-ignition. If the local overpressure generated at the moment of auto-ignition is strong enough to provide a critically short auto-ignition delay time in the surrounding mixture, the reactive front and the pressure wave may couple and form a detonation wave, which propagates throughout the mixture. Both waves are intrinsically linked, since the compression of the mixture close to the hot spot contributes to an increase in reactivity and propagates autoignition. Zeldovich [START_REF] Zeldovich | [END_REF] showed that a one-dimensional thermal hot spot characterized by its radius and by its temperature gradient between its center and the surrounding mixture can lead to four kinds of auto-ignition propagation modes. The first case corresponds to a supersonic auto-ignition with a reaction wave propagating ahead of the pressure wave. In Zeldovich's classification thermal explosions represent a limit case of supersonic autoignition with an infinite propagation speed of the reactive front. The second one corresponds to the stationary detonation for which the shock wave compresses the unburned gas ahead of it, thereby supporting and reinforcing the chemical reaction. The pressure and the reaction waves have thus the same speed which is theoretically the Chapman-Jouguet speed. Both waves continuously interact and amplify each other, resulting in high local pressure levels. Finally, the third and the fourth modes concern subsonic auto-ignition propagations, one with the reaction wave faster than the laminar flame speed and the other with the reaction wave slower, so that normal flame propagation driven by the laminar flame speed occurs. The different flame propagation modes issued from auto-ignition are widely discussed in literature [START_REF] Bradley | SAE Technical Paper[END_REF][START_REF] Bradley | SAE Technical Paper[END_REF][START_REF] Kalghatgi | [END_REF][7][8][9][10][11][12]. This original theory has then been further developed and applied to the analysis of autoignition in internal combustion engines by D. Bradley and his co-workers at the University of Leeds [START_REF] Bradley | SAE Technical Paper[END_REF][START_REF] Bradley | SAE Technical Paper[END_REF][START_REF] Kalghatgi | [END_REF]11]. A specific numerical methodology has been developed to determine the auto-ignition propagation mode around a one-dimensional thermal hot spot characterized by its radius r 0 and by its temperature gradient between its center and the surrounding mixture ∂T⁄∂r. Two dimensionless parameters (ε,ξ) were defined depending on the hot spot characteristics and on the surrounding fresh gas mixture properties (pressure, temperature, fuel/air equivalence ratio, dilution ratio).

ξ describes the coupling between the acoustic wave propagating at the speed of sound a, and the reaction wave propagation at the speed u a . It can be written as a dimensionless temperature gradient considering the temperature gradient between the center of the hotspot and the surrounding mixture, and the auto-ignition delay τ i (Eq. 1).

Eq. 1 = = = ⋅ ξ can also be written as a dimensionless temperature gradient by defining a critical hot spot temperature gradient (Eq. 2) for which the chemical resonance between the pressure wave and the reaction front occurs.

Eq. 2

= ⋅ with = ⋅
Theoretically, detonation is achieved as soon as the reaction and pressure waves propagate at the same speed (ξ = 1, [13]). However, because of species and thermal diffusion during the induction period, a developing detonation is not stringently restricted to this critical value ξ = 1. In fact, depending on the reactivity, a wider range of initial conditions can lead to a developing detonation. Thus, an upper limit ξ u and a lower limit ξ l have been introduced to classify the different propagation modes and to define a socalled detonation peninsula.

The second dimensionless parameter ε compares the characteristic chemical time scale given by the excitation time τ e , and the acoustic time scale given by ⁄ (Eq. 3). By quantifying the rate at which the auto-ignition chemical energy is released into the acoustic wave, ε measures the hot spot reactivity.

Eq. 3 = ⁄ It must be noted that ε and ξ are determined as a function of initial conditions (before chemical reactions start). Usually, characteristics of the fresh gas needed to determine ξ and ε can be directly known (pressure, fuel/air ratio) or derived (temperature and dilution) from experimental data or simulations. However, the thermal hot spot properties (radius and temperature gradient) must be assumed.

Lots of recent studies used this detonation peninsula to analyze experimental and numerical occurrences of knock and LSPI in highly charged SI engines. Based on this classification diagram, it has been shown that a developing detonation mode may appear under extreme conditions. It is therefore essential to validate the location of this peninsula.

Numerical procedure

The first step to estimate ε and ξ in our 1D calculations consists in calculating the autoignition characteristic time scales (τ i ,τ e ) of fuel-air mixtures by performing chemical kinetics calculations. The auto-ignition delay time τ i is defined as the time needed to increase the mixture temperature by 400K compared to the initial conditions. The excitation time τ e is the time required for the heat release rate to rise from 5% to its maximal value. This characteristic time being of the order of µs, a high temporal resolution is required for the post-processing to guarantee accurate calculations.

Involving a complex chemical mechanism in numerical codes to solve chemistry of realistic fuels requires computing thousands of species and reactions, and is too CPU time consuming as the objective of this work is to analyze a large number of operating conditions to precisely define the detonation peninsula. The tabulated model TKI-LES model [14] has thus been chosen to simulate auto-ignition as previous studies have already shown its ability to catch such phenomenon [15]. This model is based on a look- It is important to notice that even if this fuel can include up to 10% of volume fraction of ethanol, its RON remains around 95. A fuel surrogate and a kinetic mechanism including ethanol have been previously used by the authors to study the auto-ignition propagation modes [7]. These first investigations had been performed for E5 and E10 fuels and the comparison of the auto-ignition characteristic time scales τ i and τ e had not shown any significant difference.

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Based on the conclusions of [7], a Toluene Reference Fuel (TRF) surrogate has been defined with 42.8% isooctane, 13.7% n-heptane and 43.5% toluene [16].The choice of this specific TRF without ethanol is due to the surrogate definition methodology used by the authors [16]. Surrogate is defined to achieve similar characteristics as the reference fuel in terms of RON, MON, LHV and composition. In these works, the objective is to well represent the fuel auto-ignition characteristics so weighting to the RON and MON targets that is 10-times greater than those allocated to the fuel composition. In addition, the fuel oxygen-to-carbon ratio impacts the lower heating value and the fuel-air stoichiometric ratio, but to a much lesser extent the auto-ignition properties. The TRF surrogate can thus be considered as a good representative of a 95 RON E10 fuel in terms of auto-ignition properties. This preliminary study aims at analyzing the fuel impact on critical (ε,ξ) values and on the potential modification of the location of the original detonation peninsula. Fig. 1 compares the auto-ignition delay times and excitation times calculated for TRF-air mixtures to those obtained for 50%H 2 -50%CO-air mixtures. The comparison has been focused on temperatures below 1100 K at which auto-ignition usually occur in SI engines (either during knocking combustion or LSPI).

The critical temperature gradients leading to ξ = 1 for both fuels have first been compared to know if the required theoretical conditions for detonation are similar or not (Eq. 2). Fig. 1 (a) shows that the critical temperature gradients can be much higher for TRF-air mixtures than for H 2 -CO-air mixtures below 1100 K. A hot spot having a critical temperature gradient when considering H 2 -CO-air mixtures is thus not critical when considering TRF-air mixtures. At 50 bar and 1100 K for example, a critical temperature gradient of around 2.73 K/mm is obtained for 50%H 2 -50%CO-air mixtures but in the case of TRF-air mixtures this temperature gradient would lead to ξ ≈ 0.50 (the critical temperature gradient for TRF-air mixtures being around 5.44 K/mm). In this case, the dangerous detonation propagation mode should thus be avoided in favor of a supersonic deflagration mode. For a given temperature gradient at the hot spot, these two fuels will thus lead to very different ξ values. More generally, depending on the mixture's properties and on the chosen temperature gradient around the hot spot, a modification of the vertical position of the detonation peninsula can therefore be expected when considering TRF-air mixtures. This comparative analysis is performed here by considering that the two fuels only differ in their auto-ignition delay times τ i . However, the induction period is particularly essential to determine the auto-ignition propagation mode because of the mixture's homogenization around the hot spot during this period. Indeed, mixtures leading to long auto-ignition delay times, and those characterized by strong species and thermal diffusion properties around the hot spot will then allow the mixture to well homogenize before auto-ignition is triggered. As a consequence, the critical ξ values defining the limits between developing detonation and deflagrations might change when considering different fuels. By comparing the two fuels, it is also observed that excitation times of 50%H 2 -50%COair mixtures are ten to twenty times lower than those of TRF-air mixtures below 1100 K (see Fig. 1 (b)). Usually, in order to calculate ε, r 0 values between 1 and 5 mm are chosen as representative values for turbulent flow length scales and heterogeneities in SI engines. However, since excitation times of TRF-air mixtures are much higher than those of H 2 -CO-air mixtures, it is necessary to assume very large hot spot radii r 0 for TRF-air mixtures in order to reach the same ε values with both fuels. For example, considering H 2 -CO-air mixtures at 50 bar and 1100 K, a hot spot radius of 1.2 mm can lead to ε ≈ 10 (which can be considered as a meaningful limit value defining the steep transition between subsonic deflagration and detonation for ξ varying from 10 to 40 [START_REF] Bradley | SAE Technical Paper[END_REF]). In the same conditions, a radius of around 15 mm is needed to reach the same ε with TRF-air mixtures, which is not relevant to analyze auto-ignition in SI engines. Based on the computed τ e values, it has been found that reasonable hot spot radii below 10 mm can lead to ε ≈ 10 only at very high temperature and pressure levels. Consequently, if this analysis methodology based on a single thermal hot spot is considered and if the original detonation peninsula can be used for TRF-air mixtures, then the use of this peninsula should be limited to ε ≈ 10 (accordingly with recently reported analyses of LSPI events [10]).

The second important conclusion from this comparative analysis is that it is essential to calculate τ e as precisely as possible. Indeed, as a function of the assumptions used to define the hot spot, the accuracy of the chemical kinetics calculations greatly influence the location of the points in the detonation diagram (as it has been shown in [7] by comparing two chemical schemes).

Numerical set-up

To analyze auto-ignition behavior, one dimensional calculations are performed using the AVBP code [17]. The computational domain is presented in Fig. 2. A grid convergence has been achieved using cells down to 6 µm and the final mesh used for all calculations owns 3600 cells for a length of 180 mm, which corresponds to cells of 50 µm.

To mimic the hot spot, a linear temperature gradient is initialized on the left part of the domain with a defined amplitude and radius. Fig. 3 illustrates this simplified configuration for the general case where T 0 is chosen outside of the NTC region where τ i increases as T decreases.

Fig. 3: Initial hot spot definition.

A "symmetry" boundary condition is used at the center of the hot spot (left part of the domain) and a constant pressure boundary condition is defined at the outlet.

Regarding the initial conditions, the domain is fueled using a stoichiometric mixture without any dilution. All the calculations presented here are performed with an initial pressure P 0 of 50 bar and an initial temperature T 0 of 1100 K. This initial temperature corresponds to high temperature reactions and is higher than the classical fresh gases temperature that can be achieved in SI engines when auto-ignition is triggered (whether during classical knocking combustion or LSPI). However, this initial temperature condition has been chosen here to compare the obtained results with those already available in the literature [9][11]. Realistic operating conditions corresponding to knocking combustion or LSPI would rather lead to initial temperature conditions in the range of 700 to 900 K.

It must be noted that the reactivity and coupling parameters (ε, ξ) are defined using the initial conditions of the domain. Referring to the original works of Gu and Bradley, the reference initial temperature at r = r 0 /2 is used to determine τ i and τ e , then used to calculate ε and ξ. The choice of the reference temperature location has a significant impact on the calculation of (ε, ξ) values. Fig. 4 shows the variations of these parameters as a function of the temperature increase at the center of the hot spot ∆T 0 , for three hypotheses: when the reference temperature is taken at the outer limit of the hot spot (assumption n°1, r = r 0 ), at the middle of the hot spot (assumption n°2, r = r 0 /2), and at the center of the hot spot (assumption n°3, r = 0). For the highest ∆T 0 , the estimation of the two parameters varies a lot for the same initial conditions, meaning that the position on the detonation peninsula can be totally different.

For example, Table 1 summarizes the ε and ξ values obtained by considering these three different assumptions for the same hot spot configuration with a temperature increase ∆T 0 of 100 K. The impact on ε is rather limited but the impact on ξ values is really significant. For these conditions, a subsonic deflagration can clearly be expected according to assumption n°1, but assumption n°3 would indicate a developing detonation.

Table 1: Impact of the reference temperature on (ε, ξ) values for ∆T 0 = 100 K (r 0 = 12.1 mm, P 0 = 50 bar, T 0 = 1100 K, φ = 1, no dilution).

Assumption ε ξ

1: T @ r = r 0 7.0 15.7 2: T @ r = r 0 /2 7.6 8.9 3: T @ r = 0 8.1 5.3

For the fuel sensitivity analysis conducted here, a proper comparison with the original detonation peninsula provided by Gu and Bradley can only be achieved if a similar assumption is made regarding the choice of the reference temperature. The estimation of (ε, ξ) at r = r 0 /2 is used for the following cases.

Results

A large number of hot spot configurations are simulated in order to ascertain the relevancy of the original detonation peninsula when considering a realistic commercial fuel. The methodology consists in defining values for ε and ξ, and then to deduce the initial characteristics of the hot spot. Based on Eq. 3, the initial radius r 0 of the hot spot is given by Eq. 4.

Eq. 4 = ⋅ ⋅ whereas the initial temperature gradient is obtained based on Eq. 1 with Eq. 5.

Eq. 5 = !⋅

Several hundreds of calculations have been performed for ε and ξ respectively ranging from 1 to 17, and from 1 to 38 for both parameters. This large number of calculations have been performed in order to define as precisely as possible the location of the transition zone between deflagration and developing detonation.

To illustrate the potential of such numerical simulations, five different cases are first analyzed. Their assumed positions in the original detonation diagram are presented in 5. The first objective is to determine whether the assumed (ε,ξ) values for these five cases lead to case A in the subsonic deflagration zone, cases B and C at the limit of the detonation peninsula, case D in detonation zone and case E in the supersonic deflagration zone. Cases B and C correspond not only to a transition zone between the deflagration and the developing detonation, but also to operating conditions representative of those in which auto-ignition can occur in spark-ignition engines [START_REF] Kalghatgi | [END_REF]7,15]. On the contrary, no realistic engine operating conditions should lead to case E. However, this case is shown here to demonstrate that our numerical methodology and tools can reproduce the different propagation modes. Fig. 5: Position of analyzed conditions in the original detonation peninsula [START_REF] Bradley | SAE Technical Paper[END_REF].

The characteristic parameters for the corresponding hot spots are summarized in Table 2. In the following sections, the auto-ignition propagation modes are analyzed for these five different cases.

Case A, ε = 3.1, ξ = 16

According to the original detonation diagram obtained with H 2 -CO-air mixtures, case A should correspond to a subsonic deflagration mode. Results obtained with the TRF-air mixture confirm this propagation mode as it can be seen in Fig. 6 with the pressure and temperature profiles given for different timings up to t = 0.190 ms (τ i = 0.286 ms for the considered operating conditions). The pressure wave is distinctly propagating much faster than the reaction wave since the temperature increase in the computational domain is obviously slower than the pressure increase. The pressure wave intensity remains also quite limited, the maximal pressure being of the order of 63 bar. In those conditions, the deflagration propagation mode is well reproduced by the 1D calculations performed with the TRF. Case B, ε = 7.9, ξ = 10.7

Considering the original detonation peninsula, the case B should be located close to the transition zone between the subsonic deflagration and developing detonation modes. Indeed, it must be mentioned that the limit between these two modes is not clearly defined by a single line, and that a transition zone exists since it takes some time for the pressure and the reaction waves to couple.

Results obtained with the TRF-air mixture are illustrated in Fig. 7 for different timings up to t = 0.11 ms (τ i = 0.286 ms). Fig. 7: Hot spot auto-ignition for case B (r 0 = 12.2 mm, ∆T 0 = 131.8 K, ε = 7.9, ξ = 10.7, P 0 = 50 bar, T 0 = 1100 K, φ = 1, τ i = 0.286 ms). Time sequence from 0.03 ms up to 0.11 ms.

The analysis of the auto-ignition development shows that the pressure front is steeper than in the case A, and that the pressure wave is still propagating ahead of the reaction wave. This case corresponds thus once again to a subsonic deflagration even if both pressure and reaction waves propagate faster outside the hot spot (r 0 = 12.2 mm) in comparison with the case A. In addition, the pressure wave intensity is higher than for the case A, the maximal pressure being of the order of 85 bar. Indeed, an amplification of the pressure wave is observed here which points out a more intense auto-ignition reaction and an interaction between the pressure and the reaction waves. These various intensities in the subsonic deflagration regime can explain the various knocking intensities that can be experimentally observed. Indeed, the difference between light and moderate knocking cycles might not be due different auto-ignition propagation modes (deflagration or detonation) but more simply to subsonic deflagrations having different intensities.

A sharp peak pressure also appears at t = 0.105 ms, which points out the beginning of the transition towards a thermal explosion as it will be shown later with the analysis of the reaction wave speed. At this point, the calculations performed with TRF-air mixtures still confirm the location of the original detonation peninsula.

Case C, ε = 11.1, ξ = 8.7

According to the original detonation peninsula, case C should be located as well in the transition zone between the subsonic deflagration and the developing detonation mode.

The auto-ignition process illustrated in Fig. 8 shows that the coupling between the pressure and reaction waves tends to establish itself, but these waves are still not perfectly synchronized. The pressure increase within the hot spot is higher than for cases A and B thanks to the spatial proximity of the pressure and reaction fronts but the conditions required for a detonation are still not met. However, the pressure front becomes much steeper as soon as the reaction exits the hot spot (r 0 = 15.7 mm). In this case C, the pressure wave intensity is much higher than for case B with a maximal pressure of around 220 bar.

The results for t > 0.085 ms are not shown here because no real coupling of the pressure and reaction waves can be observed before they reach the end of the computational domain. The comparative analysis of cases B and C shows that the increased reactivity achieved with the larger hot spot radius allows to confirm the location of the transition zone between the subsonic deflagration and the developing detonation modes even when using a Toluene Reference Fuel.

Case D, ε = 16.9, ξ = 5.4

The last case D (see Fig. 9) allows to observe a gradual coupling of the pressure and reaction waves after they exit the hot spot (r 0 = 22.7 mm). This coupling is still not perfect as the pressure wave is still increasing at t = 0.06 ms meaning that the detonation regime is not fully established.

Fig. 9: Hot spot auto-ignition for case D (r 0 = 22.7 mm, ∆T 0 = 245.2 K, ε = 16.9, ξ = 5.4, P 0 = 50 bar, T 0 = 1100 K, φ = 1, τ i = 0.286 ms). Time sequence from 0.01 ms up to 0.06 ms.

However, the temperature and pressure fronts are very steep and propagate at the same speed. As a consequence, the pressure and reaction wave reinforce themselves and the pressure peaks reach extreme values above 250 bar. Much higher pressure levels above 350 bar can be reached in some cases even when considering small heterogeneities in terms of amplitude and radius, namely in the lower left toe of the detonation peninsula (ε lower than 10, ξ lower than 5).

This case D is quite extreme since it requires the use of a large hot spot to enhance the mixture's reactivity (r 0 = 22.7 mm). This radius is much too large to be representative of realistic mixture heterogeneities in SI engines and, accordingly, these (ε, ξ) values have not been reported so far as being representative of auto-ignitions observed in SI engines (see Fig. 5).

The results obtained here with case D show first that the simulation methodology is capable of catching such a detonation phenomenon, and also confirm once again that the developing detonation mode that can be forecasted with the original peninsula is confirmed when using a Toluene Reference Fuel.

Case E, ε = 5, ξ = 1

Case E is a specific case study that is detailed here to show that the calculation methodology can reproduce all the possible propagation modes. Low ε and ξ values are considered for this example, but these operating conditions are clearly out of scope for the analysis of realistic knocking and LSPI events (see Fig. 5).

Fig. 10: Hot spot auto-ignition for case E (r 0 = 8.7 mm, ∆T 0 = 4.7 K, ε = 5, ξ = 1, P 0 = 50 bar, T 0 = 1100 K, φ = 1, τ i = 0.286 ms). Time sequence from 0.270 ms up to 0.290 ms.

Pressure and temperature profiles shown in Fig. 10 focus on the very last stages of the calculation, starting at t = 0.270 ms up to t = 0.290 ms. The auto-ignition reaction rate is also plotted in the lower part of Fig. 10 to better highlight the reaction wave propagation. During this short period of time, a transition from a supersonic deflagration to a thermal explosion can be observed. Up to t = 0.282 ms, the reaction wave propagates slightly faster than the pressure wave and also that no sharp pressure peaks can be observed contrary to a developing detonation case. The maximal pressure levels rise up to 200 bar, which is higher than for subsonic deflagration but still lower than for developing detonations.

Then, from t = 0.282 ms, the reaction rate becomes homogeneous in the unburned gases zone and a thermal explosion takes place. Because of this homogeneous reaction, the pressure levels are increased but not as high as in the case of developing detonations (see Fig. 9). Surprisingly, Fig. 10 shows that no thermal explosion is observed at t = 0.286 ms which corresponds to the expected auto-ignition delay time τ i at 50 bar and 1100 K. This can be explained by the local auto-ignition delay time that is slightly increased by around 4 µs close to the outlet of the computational domain because of the static pressure imposed as outlet boundary condition. Consequently, the thermal explosion is not observed at t = τ i = 0.286 ms but just after t = 0.290 ms (not shown here).

To clarify the different propagation modes, Fig. 11 shows the reaction wave speed for the five different cases. These reaction wave speeds are plotted along the computational domain as a function of the hot spot radii that were used for the calculations. The reaction wave speed for case A remains very low around 100 m/s until it reaches r/r 0 ≈ 1.7 (with r 0 = 5.2 mm for case A). At that point, the reaction wave speed is sharply increasing because of the homogeneous auto-ignition in the whole domain which corresponds to the final transition towards a thermal explosion [START_REF] Zeldovich | [END_REF][START_REF] Bradley | SAE Technical Paper[END_REF]. A similar process can be observed for case B with a reaction wave speed around 370 m/s up to r/r 0 ≈ 1.8. In this case, the thermal explosion occurs thus when the reaction wave is propagating beyond a distance from the center of the hot spot of around 20 mm. For cases C and D, the reaction wave speeds increase as the coupling with the pressure wave is establishing. The reaction speed is thus getting closer and closer to the theoretical Chapman-Jouguet detonation speed above 1500 m/s. The computational domain is not long enough to reach a perfect coupling between the pressure and the reaction waves. It is, however, already way too long compared to the characteristic size of the unburned gases zone in SI engines. Consequently, if it is difficult to achieve a perfect coupling in those very favorable conditions combining a long computational domain and a high mixture's reactivity (T 0 = 1100 K), obtaining a stabilized detonation in SI engines will be even more questionable. Finally, a fast reaction wave can be observed for case E. the reaction wave speed is already higher than 1000 m/s at the beginning of combustion for r/r 0 < 1. Then, as shown by Fig. 11, a thermal explosion occurs as soon as the reaction wave propagates beyond x ≈ 15 mm (r/r 0 > 1.5).

Detonation peninsula for TRF-air mixtures

Given the large amount of calculations carried out, an automated post-processing has been set up to quickly identify the auto-ignition propagation modes for all the simulated (ε, ξ) values. However, this detection process is not straightforward and requires to define two main criteria.

The first criterion indicates if the pressure wave and reaction wave fronts are coupled or not. The second criterion indicates how far from the hot spot center, or how long after the beginning of auto-ignition the identification of the propagation mode should be performed. Indeed, even a simple subsonic deflagration can be allowed to degenerate into a thermal explosion (as shown for example by cases A and B in Fig. 11). It is therefore essential to decide on the nature of the propagation mode before this thermal explosion is triggered. In other more complex cases, it is even possible to observe a complete evolution of the propagation mode from a subsonic deflagration to a developing detonation which, depending on the conditions, may stabilize for some time, or quickly degenerate into a supersonic deflagration or a thermal explosion [11]. The second criterion allows to face these various situations by defining the spatial position where the identification of the auto-ignition propagation mode is performed when the pressure and reaction waves arrive at this position. Several post-processing variants have been tested and others are still being evaluated, with the objective of identifying the propagation mode in an automatic but above all robust way. It must can be noted that the definition of precise limits for the peninsula is not always required or even necessarily possible because various transition phenomena can occur. Fig. 12 shows the original detonation peninsula (black lines) [START_REF] Bradley | SAE Technical Paper[END_REF], the entire domain that could be investigated with TRF-air mixtures (blue region) and the limits (red dot lines) obtained with those new 1D calculations. For these results, the post-processing procedure is based upon the analysis of the relative position and velocity of the reaction and pressure waves. The analysis is carried out at the moment when the reaction wave reaches r = r 0 , just before the reaction begins its propagation into a perfectly homogeneous mixture. Theoretically, the detonation mode is reached when the positions and speeds of the reaction and pressure fronts perfectly coincide. However, a tolerance of 10% is used here on speed and position in order to take into account transition phenomena during which pressure and reaction fronts chase each other. The criteria used to differentiate the main modes of propagation are summarized in Table 3 as a function of the reaction and pressure wave speeds and positions (respectively noted here u a , x a , a, x p ). The first observation is that the region described with our TRF is much limited compared to the one obtained with a H 2 -CO fuel. Indeed, the parameter ε depends on τ e (Eq. 3)

which varies a few when changing the temperature of the hot spot (Fig. 1, bottom).

Looking at parameter ξ, Eq. 2 points out that it is linked to the critical temperature gradient, and Fig. 1 confirms a strong variation when temperature increases. The behavior of the critical temperature gradient between the two fuels is different, and explains the maximal low values of ξ reached at high values of ε.

This new peninsula obtained with TRF-air mixtures is close to the original one which shows that the auto-ignition propagation mode can be well predicted by the two dimensionless parameters ε and ξ even if the auto-ignition characteristic time scales τ i and τ e are very different for both fuels.

In these works, a particular attention has been paid to the definition of the transition zone between subsonic deflagration and developing detonation for the operating conditions representative of those in which auto-ignition can occur in spark-ignition engines (see Fig. 5). Fig. 12 shows that this transition occurs somewhere in between cases B and C characterized by hot spot radii of 12.2 and 15.7 mm respectively. It has to be kept in mind that there is no clear demarcation line between deflagration and developing detonation that is why case C is considered as a detonation case by our automatic post-processing methodology in Fig. 12, while the detailed analysis reported in Fig. 8 shows that the detonation is not really established even if the conditions are favorable. As mentioned above, high hot spot radii higher than that of case C (r 0 = 15.7 mm) are required to reach the developing detonation mode because of the high excitation times values of TRF-air mixtures in comparison with those of H 2 -CO-air mixtures (see Fig. 1). However, these radii being much higher than the turbulent flow and heterogeneities characteristic length scales in SI engines, it can be argued whether a developing detonation could really be observed in realistic engine operating conditions with a standard gasoline fuel.

Conclusions

A numerical procedure has been set up to simulate the propagation of auto-ignition originating from a one-dimensional thermal hot spot. By combining chemical kinetics calculations and the TKI-LES model, all the possible propagation modes can be reproduced and the original detonation peninsula originally defined for 50%H 2 -50%CO can be almost reproduced with a TRF surrogate representative of a realistic gasoline fuel. These works confirm thus that the propagation modes can be well defined by the two dimensionless parameters (ε, ξ) when studying auto-ignition in SI engines running on gasoline fuel. It has also been shown that the use of the detonation peninsula should be limited to ε ≈ 10. Indeed, the excitation times of TRF-air mixtures being much higher than those of H 2 -CO-air mixtures, higher values of ε should not be reached when assuming relevant hot spot radii for the analysis auto-ignition in SI engines. It should be noted, however, that this methodology is based on the assumption of a single hot spot, while multiple hot spots interacting with each other should be considered for the analysis of realistic engine conditions.

The current activities focus now on the automated post-processing methodology in order to accurately complete the definition of the new peninsula for TRF-air mixtures. Even if different criteria can be used to determine the auto-ignition propagation mode, it is important to note that the definition of exact boundaries between the different propagation modes is not required because of the assumptions made for the hot spot radius and temperature gradient. Additional works are also needed to confirm the peninsula's location when varying the mixture's characteristics according to realistic local conditions in SI engines (notably the fresh gases temperature, the fuel/air and dilution ratios). These new results will be published in an upcoming publication in 2018.

The combination of a reliable peninsula and 3D CFD engine calculations will then allow to study more precisely the impacts of mixture's heterogeneities and of the interactions between hot spots and the combustion chamber walls. The better understanding of autoignition propagation modes will thus allow to optimize future highly efficient internal combustion engines concepts mixing controlled flame propagation and auto-ignition processes such as Spark-Assisted Compression Ignition.

Fig. 1 :

 1 Fig. 1: Critical temperature gradients (a) and excitation times (b) computed for 50%H 2 -50%CO-air and TRF-air mixtures at 50 bar (stoichiometric conditions, no dilution).

Fig. 2 :

 2 Fig. 2: Calculation domain.

Fig. 4 :

 4 Fig. 4: Impact of the reference temperature on ε (top) and ξ (bottom) values as a function of ∆T 0 at the center of the hot spot (r 0 = 12.1 mm, P 0 = 50 bar, T 0 = 1100 K, φ = 1, no dilution).

Fig. 6 :

 6 Fig.6: Hot spot auto-ignition for case A (r 0 = 5.2 mm, ∆T 0 = 56.2 K, ε = 3.1, ξ = 16, P 0 = 50 bar, T 0 = 1100 K, φ = 1, τ i = 0.286 ms). Time sequence from 0.14 ms up to 0.190 ms.

Fig. 8 :

 8 Fig. 8: Hot spot auto-ignition for case C (r 0 = 15.7 mm, ∆T 0 = 169.6 K, ε = 11.1, ξ = 8.7, P 0 = 50 bar, T 0 = 1100 K, φ = 1, τ i = 0.286 ms). Time sequence from 0.030 ms up to 0.085 ms.

Fig. 11 :

 11 Fig. 11: Reaction front wave speed.

Fig. 12 :

 12 Fig. 12: Detonation peninsula calculated for TRF-air mixtures (P 0 = 50 bar, T 0 = 1100 K, φ = 1, no dilution).

  table of τ i and τ e , obtained using a priori calculations for a surrogate fuel in homogeneous reactors and considering the LLNL kinetic mechanism with 1388 species and 5935 reactions. The chemical computations are first performed with an in-house code named CLOE (based on the Senkin solver), and the resulting auto-ignition characteristic time scales (τ i ,τ e ) are then tabulated for different pressure and temperature levels. The values of τ i and τ e are just read in the table during the 1D calculations.

	Fuel reactivity

Contrary to previous studies of Bradley et al. which are based on H 2 -CO-air mixtures, this work focuses on the study of a complex fuel, namely the European standard fuel E10.

Table 2 :

 2 Hot spots characteristics for the five cases.

	Case A	3.1	16	r 0 [mm] 5.2	"K/mm& 10.8
	B	7.9	10.7	12.2	10.8
	C	11.1	8.7	15.7	10.8
	D	16.9	5.4	22.7	10.8
	E	5	1	8.7	0.54

Table 3 :

 3 Identification criteria for auto-ignition propagation modes.

		Reaction front speed	Reaction front position
		u a	x a
	Developing detonation	0.9*a < u a < 1.1*a	0.9*x p < x a < 1.1*x p
	Subsonic deflagration	u a ≤ 0.9*a	x a ≤ 0.9*x p
	Supersonic deflagration	u a ≥ 1.1*a	x a ≥ 1.1*x p

ACKNOWLEDGEMENTS

The authors would like to thank M. Matrat, A. Dulbecco, C. Angelberger and O. Colin for their support and comments.

FUNDING

The authors received no financial support for the research reported in this article.


Aliou Mbodji

Gabin Gbabode

Morgane Sanselme

Nicolas Couvrat

Michel Leeman

Valérie Dupray
email: valerie.dupray@univ-rouen.fr

Richard M Kellogg

Gérard Coquerel

Family of Conglomerate-Forming Systems Composed of Chlocyphos and Alkyl-amine. Assessment of Their Resolution Performances by Using Various Modes of Preferential Crystallization

published or not. The documents may come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Chlocyphos is the trivial name of a member of a family of phosphoric acids designed and introduced in 1985 by ten Hoeve and Wynberg [START_REF] Hoeve | The Design of Resolving Agents: Chiral Cyclic Phosphoric Acids[END_REF] . The enantiomers of chlocyphos are of great interest as several cyclic phosphoric acids, including phencyphos and anicyphos, are used as effective resolving agents in preparing optically pure amines [START_REF] Nieuwenhuijzen | Resolutions with Families of Resolving Agents: Principles and Practice[END_REF][START_REF] Dalmolen | Synthesis and Application of New Chiral Amines in Dutch Resolution: Family Behaviour in Nucleation Inhibition[END_REF] (ephedrine, valine etc). Diastereomeric salt formation process [START_REF] Van Der Haest | Towards a rational design for resolving agents. Part V: Substituent effects in the resolution of ephedrine using a series of cyclic phosphoric acids[END_REF] is often used to resolve these phosphoric acids but this method sometimes fails due for example to the formation of an oil, a gel or a solid solution 5 . Furthermore, this method does not always fit with industrial needs (i.e. low cost, high enantiomeric excess and high productivity). An attractive alternative method is to perform preferential crystallization [START_REF] Coquerel | Topics in Current Chemistry (Novel Optical Resolution Technologies)[END_REF] (PC) which could be in favorable cases a reliable and inexpensive process to resolve the racemic mixture into its enantiomers. PC consists in isolating pure enantiomers by alternating crystallization with no need for addition of any chiral agent. PC does not alter the global molecular symmetry of the system. However, it requires that the racemic mixture crystallizes in an equimolar mixture of enantiopure crystals (i.e a stable conglomerate). Leeman [START_REF] Leeman | The Resolution of 2-Hydroxy-5,5-dimethyl-4-phenyl-1,3,2dioxaphosphorinan 2-Oxide (phencyphos) by Preferential Crystallization[END_REF] and co-workers have reported the resolution by PC of a compound from the same family of phosphoric acids: Phencyphos. Indeed, Phencyphos monohydrate crystallizes as a conglomerate and its resolution by PC was successful. It is thus logical to apply this method of entrainment to the resolution of chlocyphos. Racemic chlocyphos crystallizes, as will be shown further, as a racemic compound. Thus, to achieve a resolution by PC, chlocyphos derivatives (salt or co-crystal) that exhibit a full chiral discrimination in the solid state (e.g. conglomerate forming system) must be found. Moreover, these derivatives must not display epitaxial behavior and/or other complications that can frustrate a resolution by PC [START_REF] Gervais | Oscillating Crystallization in Solution between (+)-and (-)-5-Ethyl-5methylhydantoin under the Influence of Stirring[END_REF] .

In the following, we report the search for conglomerate forming systems among a series of more than twenty salts formed by combining chlocyphos (a strong acid) with strong bases or alkyl amines in 1:1 ratio. The pre-screening involves first: Second Harmonic Generation [START_REF] Kurtz | A powder technique for the Evaluation of Nonlinear Optical Materials[END_REF] (SHG), a non-linear optical method, to preselect the non-centrosymmetric crystallized phases. For SHG active racemic mixture, both pure enantiomer and racemic samples were submitted to additional characterizations such as DSC and X -ray powder diffraction. Crystal structures of the salts were determined by SC-XRD. These revealed a high tendency of chlocyphos alkyl amine salts to crystallize as conglomerates with similar crystal packing arrangements. PC through its different modes [10][START_REF] Wacharine-Antar | Resolution of ((±)-Imeglimin-2,4-dichlorophenylacetate Methanol Solvate by Preferential Crystallization[END_REF] (SIPC, AS3PC and ASPreCISE) was performed at small scale and the results are discussed.

EXPERIMENTAL SECTION a. Materials and chlocyphos salt formation

Racemic mixture and pure enantiomers of chlocyphos in powder form were kindly provided by Syncom BV with a purity grade better than 99%. Strong bases (KOH, NaOH), amines, methanol, ethanol, isopropyl alcohol were purchased from Sigma-Aldrich and used without further purifications.

Scheme 1: Developed formula of chlocyphos (* indicates the stereogenic center)

Chlocyphos salts were obtained from acid-base reactions by addition of one equivalent of pure base and one equivalent of chlocyphos (racemic and enantiopure) in a polar solvent (e.g. methanol, ethanol or isopropyl alcohol) in a container placed in a thermostatic bath (T = 30 °C) under magnetic stirring to ensure complete dissolution. Solutions were kept at room temperature during crystallization, the crystals were collected, dried at ambient temperature and analyzed. Single crystals were also grown in methanol solution by slow evaporation method (vials sealed with pierced paraffin film) at room temperature and atmospheric pressure for crystal structure determination.

b. Second Harmonic Generation (SHG)

When a high-power laser (in our experimental set-up a Q-switched pulsed laser with a wavelength of 1064 nm which delivers 300 mJ pulses of 5 ns duration) interacts with a noncentrosymmetric material, it could give rise to a new wave at half of the fundamental wavelength (i.e 532 nm). This nonlinear optical process is called Second Harmonic Generation and is observable only for non-centrosymmetric crystals. In a conglomerate, molecules compulsorily organize in chiral crystalline structures (thus non-centrosymmetric). Conversely, racemic crystals are prone to adopt centrosymmetric crystalline structures. Herein, the SHG signal generated by the crystalline powder samples placed in wells (diffused light) was collected into an optical fiber (0.5 mm of core diameter), directed onto the entrance slit of a spectrometer (Ocean Optics) and recorded through the boxcar integrator. According to Kurtz and Perry's SHG powder method [START_REF] Kurtz | A powder technique for the Evaluation of Nonlinear Optical Materials[END_REF] , the SHG signal intensities of the samples were compared to that of a reference compound (αquartz, 45 μm average size).

c. Differential Scanning Calorimetry (DSC)

DSC analyses were performed on a DSC 204F1 Netzsch operating under a constant flow of helium. For these experiments, ca. 8.0 ± 0.1 mg of sample was heated in sealed aluminum pans from 20 °C to 350 °C using a heating rate of 5 °C/ min. Data obtained were analyzed using the Netzsch Proteus Thermal Analysis Software.

d. X-ray Powder Diffraction (XRPD)

XRPD measurements were carried out on a D8 Discover diffractometer (Bruker analytical X-ray Systems) with Bragg-Brentano geometry, in θ/θ reflection mode. The instrument was equipped with a copper anticathode (40 kV, 40 mA, Kα radiation: 1.5418 Å), and a lynx eye linear detector. The diffraction patterns were collected by steps of 0.04 ° (in 2-theta) over the angular range 3-30°, with a counting time of 4 seconds per step.

e. Single Crystal X-Ray Diffraction (SC-XRD)

The chosen crystal was stuck on a glass fiber and mounted on the full three-circle goniometer of a Bruker SMART APEX diffractometer with a CCD area detector. The cell parameters and the orientation matrix of the crystal were preliminarily determined by SMART Software [START_REF]SMART for WNT/2000 Smart software reference manual[END_REF] . Data integration and global cell refinement were performed with SAINT Software. Intensities were corrected for Lorentz, polarization, decay and absorption effects (SAINT and SADABS Softwares) and reduced to F O [START_REF][END_REF] . The program package WinGX 14 was used for space group determination, structure solution and refinement. The standard space group was determined from systematic extinctions and relative F O 13 of equivalent reflections. The structure was solved by direct methods [START_REF] Altomare | Completion and refinement of crystal structures with SIR92[END_REF] . Anisotropic displacement parameters were refined for all non-hydrogen atoms. All hydrogen atoms were located from subsequent difference Fourier syntheses and placed with geometrical constraints (SHELXL [START_REF] Sheldrick | SHELXL: High-resolution refinement[END_REF] ).

f. Solubility measurements

The solubility of each conglomerate was measured in different solvents using the classical evaporation method. A suspension of the conglomerate was prepared in the chosen solvent at a given temperature and let under stirring during several hours. Then the suspension was filtered, and the saturated solution was weighed and then evaporated in a ventilated oven at 50 °C. The solubility is calculated by dividing the mass of the recovered powder by the mass of the saturated solution. Hereafter, each reported value of the solubility is the mean value of three measurements and is expressed in weight percent (wt%).

g. Resolution by Preferential Crystallization (PC)

PC consists in alternating a stereoselective crystallization of the two enantiomers out of a racemic mixture. Its precise mechanism and full details on the method have been given by Collet et al [START_REF] Collet | Optical resolution by direct crystallization of enantiomer mixtures[END_REF] and by Coquerel [START_REF] Coquerel | Topics in Current Chemistry (Novel Optical Resolution Technologies)[END_REF] . Depending on the chlocyphos derivative studied, the resolution was carried out using one or several of the three different variants of the PC described hereafter. That is: Seeded Isothermal Preferential Crystallization (SIPC), Auto Seeded Polythermic Programmed Preferential Crystallization (AS3PC) and Auto-Seeded Preferential Crystallization Induced by Solvent Evaporation (ASPreCISE). Experiments were performed at 10 ml or 25 ml scales.

Seeded Isothermal Preferential Crystallization (SIPC mode)

A 60 ml screw cap vial was used as a batch crystallizer. The temperature was controlled via a cryo-thermostat and the stirring was ensured with a magnetic bar (15 mm) at about 500 rpm. An initial amount of racemic mixture (m ± ) was totally dissolved in the chosen solvent at initial temperature (T I ) slightly higher than the temperature of dissolution of the total amount of racemic mixture (T L ) to obtain an undersaturated racemic solution. The racemic solution was then cooled to the filtration temperature (T F ), temperature in which the racemic mixture became supersaturated but should not crystallize within several hours (metastable zone). Thus, a small amount of pure enantiomer (m seeds ) was added to the solution so that the initial enantiomeric excess (ee) of the resulting suspension was in the range 5-10%. The suspension was maintained at T F during an optimized time to reach growth of the desire enantiomer without promoting the crystallization of the unwanted enantiomer. The crystals (m crops ) were then isolated by filtration. The mother liquor was collected and reused after addition of a mass of racemic mixture equivalent to the mass of the harvested solid. Then, when possible, alternating crystallizations of R and S were performed.

Auto Seeded Polythermic Programmed Preferential Crystallization (AS3PC mode)

Experiments performed in the AS3PC mode were carried out with similar equipment as for SIPC.

Starting with a mass of racemic mixture (m±) and an appropriate amount of solvent, a saturated solution of racemic mixture was formed at the initial temperature T L (temperature of dissolution of the total amount of racemic mixture). A small amount of pure enantiomer (m seeds ) was then added to reach an ee in the range 5-10%. The suspension was heated to T B defined as ½ (T Homo + T L ) where T Homo stands for the temperature of homogenization (temperature of dissolution of the solute composed of the racemic mixture plus the enantiomer in excess). The suspension was subsequently cooled down to T F during a temperature versus time ramp to promote secondary nucleation and growth of the desired enantiomer. The following steps (harvest by filtration and recycling of the mother liquor) are identical to the SIPC experiments.

Auto-Seeded Preferential Crystallization Induced by Solvent Evaporation (ASPreCISE)

In this particular mode the metastable zones depend on the solvent evaporation rate. Solvent evaporation can be stimulated by distillation of the solvent under reduced pressure or by means of an inert gas stripping (e.g., nitrogen). The experimental process was performed in a 100 ml three-neck flask (supplied neck for N 2 gas, one neck for solvent evaporation and one neck for filtration) and temperature was accurately controlled by a cryo-thermostat. A small amount of pure enantiomer (seeded crystals) was added to the racemic saturated solution so that the initial enantiomeric excess was adjusted to circa 8%. Nitrogen gas was bubbled in the suspension to promote solvent evaporation. Volume variation from the initial volume was recorded versus time. The slurry was filtered off before primary nucleation of the unwanted enantiomer.

h. Polarimetric measurements

The enantiomeric purities of the crops were determined by polarimetric measurements performed with a Jasco-P2000 and an Anton Paar-MCP5100 polarimeters (10 mg of powder dissolved in 2 ml of solvent, λ = 546 nm, T = 20 °C, tube length equal to L = 10 cm).

RESULTS AND DISCUSSION

a. Characterization of chlocyphos free acid

A full characterization of the racemic and pure enantiomer of chlocyphos free acid was performed prior considering derivatives.

The DSC analyses performed on chlocyphos display a single endothermic event at 219.5 °C (onset) for the racemic mixture and 232.2 °C (onset) for S-enantiomer samples corresponding to their respective onset melting point. Before completion of the fusion, a sharp exothermic phenomenon appears, interpreted as chemical degradation (Figure 1). At the end of the DSC analysis performed on the chlocyphos for both racemic mixture and S enantiomer, there is a mass loss (circa 42%) compared to the mass before the measurement. The crucible content turned to be burned (dark residual). Hence, the chlocyphos likely degraded after the melt. No other extra thermal event corresponding to a polymorph, eutectoid, peritectoid or a solvate has been observed for the starting compounds. The absence of a significant SHG signal emitted by the crystallized racemic chlocyphos and the numerous differences in the XRPD patterns of racemic (black) and S enantiomer (red) samples in Figure 2 indicate that the racemic chlocyphos most likely crystallizes as a centrosymmetric racemic compound. Crystal structure determination from single crystal data of the racemic sample confirms this statement. Indeed, the crystal structure of chlocyphos samples were solved at room temperature in the triclinic centrosymmetric P-1 space group for the racemic sample and in the chiral space group P2 1 for the S-enantiomer. Their crystallographic parameters are also reported in Table 1.

b. Chlocyphos salt derivatives

As chlocyphos crystallizes as a racemic compound, experiments were pursued to find derivatives crystallizing as conglomerates (i.e. suitable for resolution by PC). The applied method consisted in: (i) performing SHG tests on the various salts of the racemic mixture to preselect the noncentrosymmetric crystallizing phases and (ii) conducting further investigations on these preselected compounds (such as DSC, XRPD, SC-XRD) to establish if the crystallized racemic mixture is not only non-centrosymmetric but also chiral (conglomerate). This is a robust method avoiding waste of time and material [START_REF] Galland | Spotting conglomerates by second harmonic generation[END_REF] . First trials involved strong bases such as sodium hydroxide, potassium hydroxide or ammonium hydroxide but none of these derivatives gave positive SHG response whatever the solvent used for the crystallization of the salt (methanol, ethanol or isopropyl alcohol). These salts were thus discarded. Conversely other trials with alkyl amines led to several positive SHG responses highlighted the corresponding salts as potential conglomerates (see Table 2). Thus, the study was focused on this family of compounds. c. Identification of conglomerates In the amine family tested (ten different bases) only three derivatives did not give a significant positive SHG signal (methylamine, tert-butylamine and tert-pentylamine) whereas the seven others gave SHG signal ranging from low to medium intensities (From 4 (1) to 54 (3) %). It is important to mention that SHG signal is considered as negligible (negative response) when its intensity is less than 1% of the signal of the reference sample (quartz powder with a 45 µm mean crystal size).

(i) Ethylammonium chlocyphos salt

Ethylammonium chlocyphos salt gave a positive but relatively weak SHG signal. Similar XRPD patterns between racemic and enantiomer salts were obtained at room temperature although with small angular shifts detected at 10 ° and in the range 26-30 ° in 2θ (Figure 3). DSC analyses performed on the salts showed an endothermic event at 238.5 °C (onset for racemic ethylammonium chlocyphos salt) and an endothermic event at 190.4 °C before the onset melting occurred at circa 274.6 °C (for S-ethylammonium chlocyphos salt) (supporting information, figure S1). TGA-MS measurement coupled to a DSC was performed to check whether the first endothermic event could correspond to desolvation, but the results showed that the thermal event did not correspond to any loss of solvent molecules (in accordance with the crystal structure of Sethylammonium chlocyphos salt obtained from SC-XRD; non-reported data). Numerous attempts to grow single crystals of sufficient size and quality of ethylammonium chlocyphos salt from the racemic mixture failed. However, the close similarity of the X-ray powder diffraction patterns of S enantiomer and the racemic mixture, yet with some peak shifts, strongly suggest that the racemic mixture crystallizes as a conglomerate but with partial solid solutions close to the enantiomer.

(ii) Propylammonium chlocyphos salt

In the case of the propylammonium chlocyphos salt, XRPD patterns for racemic and Senantiomer samples are totally different. Nevertheless, single crystals were obtained from ethanol solution from which the crystal structure of one racemic form was determined by SC-XRD and revealed a chiral P2 1 crystal arrangement. However, the calculated XRPD pattern of the racemic salt does not match with the XRPD pattern obtained from the bulk powder sample (experimental racemic) (supporting information, figure S2 and Table S1). XRPD measurements at different temperatures were performed on the racemic salt but the obtained XRPD patterns at 140 °C, 150 °C and 160 °C although different, were also different than the calculated racemic XRPD pattern.

Those results point out the existence of several crystalline forms (polymorphs or hydrated/solvated forms or racemic compound) for propylammonium chlocyphos racemic mixture salt. These various forms of propylammonium chlocyphos salt were highlighted by the DSC analyses performed on the racemic and S salts. DSC analyses of each salt display at least two endothermic events at 154.7 °C and 182.5 °C (onset melting point) for racemic salt and at 197.3 °C and 223.1 °C (onset melting point) for S-propylammonium chlocyphos salt corresponded to their polymorphic transition temperatures and melting points respectively (see supporting information, Figure S3).

The phase behaviour of propylammonium chlocyphos is rather complex. Additional thermal events can be observed for both the racemic compound and pure enantiomer (see supporting information, Figure S3) which seems in agreement with the various solid forms revealed by XRPD. Further studies must be carried out to understand more the phase behaviour of this particular derivative. However, the crystal structure determined from SC-XRD data, unambiguously proves the presence of a conglomerate among the different possible forms. Moreover, this crystal structure shows extensive analogies with those found for the longer alkyl amine salts (see below and compare table S1 and table 3).

(iii) Butylammonium, isobutylammonium, pentylammonium, hexylammonium and cyclohexylammonium chlocyphos salts

For every salt which gave a positive SHG response, XRPD patterns of racemic and pure enantiomer samples were found to be identical (i.e. perfectly superimposable) as reported in Figure 4. DSC analyses for each salt derivative revealed that the difference between melting point of racemic mixture and pure enantiomer samples ranges between 25-35 °C which is a common feature between a conglomerate forming system and its pure enantiomers [START_REF] Collet | Optical resolution by direct crystallization of enantiomer mixtures[END_REF] . The 'conglomerate like' thermal behavior of these salt derivatives was confirmed by determination of the calculated eutectic temperature by using Schroeder-Van Laar equation [START_REF] Schroder | Über die Abhängigkeit der Löslichkeit eines festen[END_REF][START_REF] Van Laar | Die Schmelz-oder Erstarrnngskurven bei binären Systemen, wenn die feste Phase ein Gemisch (amorphe feste Lösung oder Mischkristalle) der beiden Komponenten ist[END_REF] . DSC curves for each conglomerate are displayed in the supporting information, figure S4.

Based on the results obtained from SHG pre-screening, XRPD and DSC measurements, we can conclude that butylammonium, isobutylammonium, pentylammonium, hexylammonium and cyclohexylammonium chlocyphos salts are likely to form a family of conglomerate forming systems. Their crystal structures have been determined by SC-XRD from racemic mixture. The crystallographic data are summarized in table 3. As expected every crystal phase correspond to a chiral space group. For each salt, the calculated XRPD and experimental XRPD patterns match (see the reported supporting information, figure S5) which means that the single crystals are representative of the bulk sample and confirm the conglomerate forming system. However, several Flack 21 parameters are not close to zero and cast some doubts about the enantiomeric purity of these phases. For instance, for pentylammonium chlocyphos salt, the Flack parameter is 0.52 (16) and raises the possibility of epitaxy between R and S enantiomers or even multi-epitaxy. Moreover, racemic pentylammonium chlocyphos salt could crystallize as a metastable racemic compound.

d. Crystal structures description and trend of conglomerate formation

The asymmetric unit is always composed by two entities: one deprotonated chlocyphos molecule and one protonated amine molecule as represented in figure 5 for isobutylammonium chlocyphos salt. Inside the asymmetric unit, strong interactions are established by ionic-hydrogen bonds (table 4) between the oxygen atom O (2) of anionic chlocyphos and the protonated amine N (1) of the amine molecule (figure 5) and are wrapped around a 2 1 screw axis and led to molecular bond chains spreading along a or b direction (figure 6). Every ammonium moiety is connected to three chlocyphos anions: two are consecutive and form a single row (along b axis) and the third one (along a axis) connects to the adjacent row leading to double row periodic bond chains which build the crystal packing of isobutylammonium chlocyphos salt (figure 7). These periodic bond chains are stacked along c direction and the cohesions are ensured by Van der Waals interactions between amine chains and π-π interactions between neighboring chlocyphos benzyl rings. The other chlocyphos conglomerate derivatives (with the P2 1 space group) have similar crystal packing (see Table 3 and the representations of their crystal packing in the supporting information, figure S6). The crystal structures clearly show similarities for all conglomerate derivatives regardless their space groups P2 1 or P2 1 2 1 2 1 . The unit cell dimensions are closely related: a, b and c parameters remain close for butylammonium, isobutylammonium and cyclohexylammonium chloycphos salts which crystallize in the same space group P2 1 . Similar observations can be noted for the unit cell parameters (a, b and c) of the space group P2 1 2 1 2 1 for pentylammonium and hexylammonium chlocyphos salts. The hydrogen bond networks involving the hetero-atoms and in the molecular ribbon along a or b axes are identical. These characteristics lead to the same pattern of periodic bond chains and thus a clear homogeneity among the member of that family. The greater thermal displacement factors (see Table 5) for the atoms located at the end of the butyl alkyl moiety prompted us to successfully test other amines with longer chains. This resulted in spotting additional systems with full chiral discrimination in the solid state. It is as if the room for the butyl chain in the crystal exceeds the volume of that alkyl moiety. Through this study, we show that derivatives of chlocyphos alkyl amines also constitute a family of conglomerates analogously to the derivatives of 5-aryl-5-alkyl hydantoins and 4-aryl-triazotyl ketones as reported in the literature. [START_REF] Tauvel | Structural studies of several solvated potassium salts of tenatoprazole crystallizing as conglomerates[END_REF][START_REF] Viedma | Crystallization of chiral molecules. Handbook of crystal growth (Eds II); Fundamentals[END_REF] .

It is also worth noting that the difference in the SHG intensity leads to differentiate two groups in this family. A group of chlocyphos conglomerate derivatives (propylamine, butylamine, isobutylamine and cyclohexylamine) having a medium SHG intensity (≥ 20%) crystallizing in the polar P2 1 chiral space group. Another group of chlocyphos conglomerate derivatives formed with long alkyl chain (pentylamine and hexylamine), having a low SHG intensity (∼10%) and crystallizing in the non-polar P2 1 2 1 2 1 orthorhombic chiral space group. Polar space groups enhance the hyperpolarizability of the structure thus, for very similar molecules and packings, there is a good correlation between the SHG intensity and the class of non-centrosymmetric space group: polar and non-polar.

e. Resolution by preferential crystallization

Once the conglomerate nature of the racemic chlocyphos salts had been established, the efficiency of their chiral separation by PC was evaluated. It is indeed important to mention that, even if spotting a conglomerate is a prerequisite to the resolution of a chiral mixture by PC, several phenomena can prevent a productive entrainment effect [START_REF] Gonella | Spotting a conglomerate is just halfway to achieving a preparative resolution by preferential crystallization Org[END_REF] .

It is common in the literature to consider that a PC process gives a productive and strong entrainment, if a yield better than 20%, a purity of the crude crops better than 90% ee without any purification and a final enantiomeric excess of the mother liquor better than 10% ee can be reached [START_REF] Pasteur | Transformation des acides tartriques en acide racémique-Découverte de l'acide tartrique inactif. Nouvelle méthode de séparation de l'acide racémique en acides tartriques droit et gauche[END_REF] . In the following, the yield is defined as: with:

-m pure , the mass of pure enantiomer equal to the product of the mass of the crude crops and the optical purity (O.P) (m pure = m crops x O.P) -m seeds, the mass of seeded crystals -m (±) , the initial mass of racemic mixture invested.

The strategy adopted was as follows: SIPC was run first systematically to test the entrainment effect for each derivative. If the performances were good, AS3PC was then attempted at larger scale (25 ml). Alternative variants such as AsPreCISE were adopted if SIPC did not work.

(i) Resolution of butylammonium chlocyphos salt The difficulty to find an efficient process for the chiral resolution by PC was illustrated by preliminary tests performed in the classical SIPC mode on the salt formed with butylamine. Indeed, experiments led to very poor yield and low enantiomeric excess (non-reported data). As the first attempts to resolve butylammonium chlocyphos salt with SIPC mode have been unsuccessful, trials to work in the AS3PC mode were not undertaken for this salt. Preference was given to a resolution via the ASPreCISE mode. ASPreCISE was chosen as an alternative mode to perform the entrainment because of its capability to overcome the low variation of the solubility of the salt versus temperature 26 illustrated by Figure 8. After solubility studies, a non-azeotropic mixture of acetone/ethanol (90/10 v%) was chosen at 10 ml scale experiments at 20 °C. The solubility of the racemic salt at 20 °C was found to be 4.80 wt% in the solvent mixture (acetone/ethanol). The corresponding results are listed in Table 6. Six batches were independently performed in identical conditions except for the duration. Only single runs were tested and show a drop of the enantiomeric excess after 25 minutes. Even with these restrictions, after optimizing the duration of the run, a high enantiomeric excess was obtained (mean value circa 94. 8% ee) without washing nor recrystallization. Nevertheless, the yield (9.55%) as well as the final enantiomeric excess of the mother liquor (ee f = 7. 5% ee) did not reach the expected yield values (20% and 10% ee respectively). (ii) Resolution of isobutylammonium chlocyphos salt The variation of racemic mixture solubility in ethanol solution versus temperature was determined (see Figure 9). The solubility in ethanol at 20°C is 7.07 wt%. This condition was chosen to perform SIPC mode at 25 ml scale. At the end of each single run the temperature of filtration was adjusted at 5 °C in SIPC mode.

The mean value of the optical purity of the final product without any purification was 88% ee and a poor overall yield was obtained (circa 6.8%). The experimental conditions and results are summarized in the supporting information, Table S3. As SIPC, AS3PC mode was performed at 25 ml scale while considering the solubility of the racemic salt at 35 °C to be 9.5 wt% as shown in Figure 9. The amount of seed crystals added to enrich the saturated racemic solution with initial ee was fixed at 5% of the initial mass of the racemic mixture. The initial conditions and results of AS3PC of isobutylammonium chlocyphos salt are summarized in Table 7. AS3PC mode improved the PC performances when compared to SIPC (i.e. reduced experimental time, mean enantiomeric excess of 95% ee and mean yield of 9.3%). Even if the solubilities at which the two process were performed (7.07 wt% at 20 °C for SIPC and 9.5 wt% at 35 °C for AS3PC modes) were different, the target yield (20%) could not be reached in both modes despite a large temperature window (T B = 36 °C and T F =5 °C) for the auto-seeded process.

(iii) Resolution of hexylammonium chlocyphos salt

To evaluate the performances of PC on hexylammonium chlocyphosate, two modes (SIPC and AS3PC) were applied at 25 ml scale in isopropyl alcohol (the solubility at 20 °C is 10.62 wt%. see Figure 10). All experimental batches were carried out with the same amount of compound (2.335 g per batch) and suspension was prepared at 5 °C for SIPC experiments (50 mg of seeds) and at 25 °C for AS3PC experiments (90 mg of seeds). An in-situ focused beam reflectance measurement (FBRM-Mettler Toledo) particle counter has been also used to monitor the course of the auto-seeded process by measuring the particle number of chord lengths per unit time (particles of diameter 10µm). Seven batches were performed by alternating the crystallization of R and S enantiomers and the results are collected in Table 8. FBRM data (supporting information, Figure S7) highlighted a small variation of the particle number counts during the process for the performed batches (high enantiomeric excess, circa 96.9% ee) except for batch B 2 in which large number of small particles (circa 230 counts) were generated. It indicates the presence of the counter enantiomer particles which reduced sharply the optical purity down to circa 70% ee. AS3PC mode versus SIPC mode applied to the hexylammonium derivative improved the resolution in terms of experimental time (23 minutes to 37.8 minutes), enantiomeric excess (87.67% ee to 75.03% ee) and yield (4.4% to 3.3%) (see Table 8 and Table S3). The auto-seeded polythermal programmed preferential crystallization has proven its superiority to the classical isothermal process [START_REF] Wacharine-Antar | Resolution of ((±)-Imeglimin-2,4-dichlorophenylacetate Methanol Solvate by Preferential Crystallization[END_REF][START_REF] Courvoisier | Influence of the Process on the Mechanisms and the Performances of the Preferential Crystallization: Example with (±)-5-(4-Bromophenyl)-5-methylhydantoin[END_REF] but reaching a high yield remains still challenging for these derivatives.

(iv) Resolution of cyclohexylammonium chlocyphos salt For cyclohexylammonium chlocyphos salt, only AS3PC mode was applied. The solubility variation in methanol versus temperature is reported on Figure 11. The entrainment was performed at 40 °C with a corresponding solubility of 6.14 wt%. The initial conditions and results of twelve alternated PC batches are reported in Table 9 Pure enantiomers (circa 2.0 g) of cyclohexylammonium chlocyphos salt were collected with very high purity without any purification. Note that the last two batches were used for sampling to monitor the evolution of the rotatory power of the mother liquor and that led to a decrease of the optical purity and the yield. The obtained results have proven that a successful entrainment via AS3PC mode was performed with a high enantiomeric excess (circa 92% ee, mean value) and a The PC performances of these conglomerates have been assessed via three modes SIPC, AS3PC and ASPreCISE and the results highlight the limitations of the process at 25 ml scale (Table 10). The best entrainment (AS3PC mode) to resolve the racemic mixture was achieved with cyclohexylammonium chlocyphos salt. f. Parameters limiting the PC performances of chlocyphos derivatives. Several difficulties can be encountered when preferential crystallization is used to separate racemates. One or several of the following reasons are suspected to cause the severe limitation of the PC performances for this family of conglomerates:

(i)
high value of Flack parameter Because a metastable racemic phase has been spotted at room temperature and the high value of the absolute structure parameter (Flack parameter = 0.52 ( 16)) of its conglomerate forming system, it was intentionally decided to not perform the chiral resolution of the pentylammonium chlocyphos salt. In fact, comparisons between Flack parameters and the performances of PC for these conglomerates suggest possible epitaxies and then possible multi-epitaxy or alternated growth between the two enantiomers (table 10). Crystals of one enantiomer could grow on the surface of the other and lead to lamellar particles [START_REF] Kislyi | Racemic estrone methyl ether is the lamellar conglomerate[END_REF][START_REF] Green | Lamellar Twinning Explains the Nearly Racemic Composition of Chiral, Single Crystals of Hexahelicene[END_REF] with R-S alternation despite the existence of a stable conglomerate. Epitaxial racemic conglomerate [START_REF] Gervais | Oscillating Crystallization in Solution between (+)-and (-)-5-Ethyl-5methylhydantoin under the Influence of Stirring[END_REF][START_REF] Kaptein | Attrition-enhanced deracemization of an amino acid derivative that forms an epitaxial racemic conglomerate[END_REF][START_REF] Van Enckevort | On the Crystallization of Epitaxial Racemic Conglomerates[END_REF][START_REF] Zbaida | A Cyclic Continuous Process for Converting Conglomerates into Optically Pure Enantiomers by Crystallization and Dissolution with the Assistance of `Tailor-made[END_REF][START_REF] Davey | The chiral purity of a triazolylketone crystallized from racemic solution[END_REF][START_REF] Th | Polymorphism and Migratory Chiral Resolution of the Free Base of Venlafaxine. A Remarkable Topotactical Solid State Transition from a Racemate to a Racemic Conglomerate[END_REF][START_REF] Toyokura | Crystal growth of L-SCMC seeds in a DL-SCMC solution of pH 0.5. CGOM3[END_REF] hamper the entrainment and lead to low yield.

(ii)

Evidence of multi-epitaxy To verify this possible epitaxy hypothesis, a single crystal grown from the racemic mixture of isobutylammonium chlocyphos salt was soaked in a saturated solution of S-isobutylammonium chlocyphos salt for 30 minutes according to a well-established procedure [START_REF] Gervais | Oscillating Crystallization in Solution between (+)-and (-)-5-Ethyl-5methylhydantoin under the Influence of Stirring[END_REF][START_REF] Toyokura | Crystal growth of L-SCMC seeds in a DL-SCMC solution of pH 0.5. CGOM3[END_REF][START_REF] Beilles | Preferential crystallization and comparative crystal growth study between pure enantiomer and racemic mixture of a chiral molecule: 5-ethyl-5-methylhydantoin[END_REF] , but no partial dissolution of the immersed crystal was observed by optical microscopy. The α ratio < 2 (α = molar solubility of the racemic mixture (9.92 x 10 -3 mol. L -1 ) / molar solubility of the pure enantiomer (5.12 x 10 -3 mol. L -1 ) is not favorable for that type of demonstration.

To study the possible existence of the multi-epitaxy of isobutylammonium chlocyphos salt, we analyzed by SHG (Second Harmonic Generation) technique. Several mixtures with different enantiomeric excesses (0-100%) were prepared in two different manners:

-physical mixtures of R and S, -recrystallized mixtures of R and S in ethanol by slow evaporation. In order to homogenize the particle size distribution, these powder samples were gently ground by using mortar and pestle. The SHG intensities were normalized by using α-quartz (40 μm average size). The analyses show that the SHG intensity remains constant for the physical mixture whatever the enantiomeric excess. By contrast, the recrystallized samples show a maximum intensity for the racemic composition (Figure 12). The difference between the SHG efficiency of the physical mixture and the recrystallized mixture for a same enantiomeric composition correspond to the existence of microstructures between R and S crystals. It means that the dissolved enantiomer is likely to nucleate on the crystal of the opposite handedness during the crystal growth in the medium [START_REF] Simon | Enhanced second harmonic generation from an organic self-assembled eutectic binary mixture: A case study with 3-nitrobenzoic and 3,5-dinitrobenzoic acids[END_REF] . This phenomenon induces the creation of a bidimensional interface between these two crystals of opposite chirality and the resulting solid is not enantiomerically pure. This phenomenon is known as multi-epitaxy. Therefore, this structural behavior leads to poorly enriched solid and could limit the PC performances.

(iii) The problem of insufficient solubility variation over temperature

The temperature dependence of the racemic mixture solubility has also a strong influence on the yield and obviously should be taken into account to analyze the PC performances of these salts.

For these conglomerates, the slope of the solubility versus temperature is low (see Figures 8; 9; 10 and 11) and thus, consistent with a poor productivity. PC could also be limited by other several parameters (uncontrolled heteronucleation of the antipode or presence of a metastable racemic compound). However, the XRPD analyses of the crops did not reveal any metastable racemic compound. The low productivity might also come from kinetics (i.e: the stereoselective crystallization is very slow). In this case, the nucleation of the dissolved enantiomer occurs before a significant amount of the desired enantiomer has been crystallized. This limitation is, for instance, consistent with the results in AS3PC mode for hexylammonium chlocyphos salt. Indeed, for an initial racemic mixture mass of 2.335 g, we collect less than 0.25 g for a volume of 25 ml. Hence, several features converge to justify a limited entrainment effect within this series of stable conglomerates.

CONCLUSION

Through this study, we have demonstrated that chlocyphos, a stable racemic compound (space group: P-1), forms with alky amine family a series of stable conglomerates. The SHG prescreening technique pointed out seven salts as potential conglomerates. Their crystal structure, determined by SC-XRD, revealed among them, five derivatives as true conglomerates in a large domain of temperature (i.e. room temperature to fusion). Interestingly, the salt with the smallest cation (ethylammonium chlocyphos salt) is likely to crystallize as a conglomerate with partial solid solutions. This study features an interesting propensity between chlocyphos and alkyl amines to form a family of conglomerates with close analogy between their crystal packings. There is a pocket in which various alkyl amine chains can fit in and, these packings are flexible enough to adapt. Preferential crystallization is demonstrated to be feasible, but every derivative tested lead to a limited entrainment effect (enantiomeric excess of the mother liquor at the end of the entrainment (ee f ) does not exceed 10% ee). Consistently one can observe that: (i) several Flack parameters of crystals grown in racemic mixtures cast some doubts on the ability of those crystals to grow without epitaxy or heterochiral nucleation. This hypothesis is reinforced by the I(SHG) versus ee. law of recrystallized samples; (ii) some metastable racemic compounds have been spotted which indicate that the energetic differences between the homochiral and the heterochiral interactions in the solid state are small; (iii) under moderate supersaturation the kinetics of stereoselective crystal growth is rather slow and for a high supersaturation there is a complete loss of stereoselectivity. The homogeneity in the PC performances for the members of this family confirms a trend that has been observed on the few systematic studies among other families of conglomerate forming systems. Nevertheless, more investigations are necessary on homogeneous series of conglomerates to propose that early statement as a rule.

Figure 1 :

 1 Figure 1: DSC curves of racemic (black) and S (red) chlocyphos

Figure 2 :

 2 Figure 2: XRPD patterns of racemic (black) and S (red) chlocyphos

Figure 3 :

 3 Figure 3: XRPD patterns of racemic (red) and S (black) ethylammonium chlocyphos salt (arrows point the shifted peaks in left and right hands)

Figure 4 :

 4 Figure 4: From bottom to top: XRPD patterns of racemic (1) and R (2) butylammonium, racemic (3) and R (4) isobutylammonium, racemic (5) and R (6) pentylammonium, racemic (7) and R (8) hexylammonium, racemic (9) and R (10) cyclohexylammonium chlocyphos salts

Figure 5 :Table 4 :

 54 Figure 5: Asymmetric unit of racemic isobutylammonium chlocyphos salt, in thermal ellipsoidal representation with labeled atoms (pink dashed line represents the ionic hydrogen bond)

Figure 6 :Figure 7 :

 67 Figure 6: Periodic bond chains (PBC) around the 2 1 screw axis formed by the ionic hydrogen bonds of (i) isobutylammonium, (ii) pentylammonium, (iii) hexylammonium and (iv) cyclohexylammonium chlocyphos salts

Figure 8 :

 8 Figure 8: Solubility curve of racemic mixture butylammonium chlocyphos salt in isopropyl alcohol Table 6: Initial conditions and results of ASPreCISE mode at 10 ml scale for butylammonium chlocyphos salt

  m ± (g) m Ac/EtOH (g) m seeds (g) / ee (%) T F (°C) 0.398 9.70 0.032 / +100 20 N° Time(min) m total (g) m crops (g) OP (%) m pure (g) Yield (%) ee f (

Figure 9 :

 9 Figure 9: Solubility curve of racemic mixture isobutylammonium chlocyphos salt in ethanol

Figure 10 :

 10 Figure 10: Solubility curve of racemic mixture hexylammonium chlocyphos salt in isopropyl alcohol

Figure 11 : 9 :

 119 Figure 11: Solubility curve of racemic mixture cyclohexylammonium chlocyphos salt in methanol

Figure 12 :

 12 Figure 12: SHG efficiency normalized with α Quartz (40 μm average size) of physical mixture (black) and recrystallized mixtures with different enantiomeric excess (red) of isobutylammonium chlocyphos salt

Table 1 : Crystallographic data of chlocyphos

 1

		Racemic chlocyphos	S-chlocyphos
	CSD number	1912257	1912259
	Chemical Formula	[C 11 H 14 ClO 4 P]
	Molecular Weight / g.mol -1	276.64
	Temperature (K)	300
	Crystal System	Triclinic	Monoclinic
	Space Group	P-1	P2 1
	Z, Z' (asymmetric units per unit cell)	2, 1	4, 1
	a / Å	6.879 (3)	7.968 (1)
	b / Å	9.415 (4)	7.234 (1)
	c / Å	9.826 (4)	11.143 (2)
	 / °	82.597 (7)	90.00
	 / °	76.805 (6)	105.590 (3)
	 / °	80.685 (6)	90.00
	V / Å 3	608.6 (4)	618.8 (2)
	Nb reflexions unique / I>2I	2424 / 1956	2470 / 2279
	Final R1 / wR2 (I>2I)	0.0452 / 0.1135	0.0349 /0.0863
	Final R1 /wR2 (all data)	0.0565 / 0.1197	0.0383/ 0.0888
	Absolute structure (Flack) parameter	NA	-0.03 (7)

Table 2 : Salt formation and corresponding SHG responses

 2

	Acide	Amines	SHG	SHG Intensity
			signal	(% of the signal
				of reference
				quartz sample)
		Methylamine	-	0.1 (2)
		Ethylamine	+	4 (1)
		Propylamine	+	24 (1)
		Butylamine	+	20 (2)
	Chlocyphos	Isobutylamine Tert-butylamine	+ -	54 (3) 0.1 (1)
		Pentylamine	+	10 (2)
		Tert-pentylamine	-	0.2 (1)
		Hexylamine	+	10 (1)
		Cyclohexylamine	+	34 (2)

(values in brackets are uncertainties)

Table 3 : Crystallographic data of the conglomerate derivatives Chlocyphos Butylamine Isobutylamine Pentylamine Hexylamine Cyclohexylamine

 3

	Chem. Formula	[C 11 H 13 ClO 4 P] [C 4 H 12 N]	[C 11 H 13 ClO 4 P] [C 5 H 14 N]	[C 11 H 13 ClO 4 P] [C 6 H 16 N]	[C 11 H 13 ClO 4 P] [C 6 H 14 N]
	CSD number	1912254	1912255	1912258	1912271	1912256
	MW / g.mol -1	349.78	363.81	377.83	375.82
	Temperature (K)			300
	Crystal System	Monoclinic	Orthorhombic	Monoclinic
	Space Group	P2 1 (n°4)	P2 1 2 1 2 1 (n°19)	P2 1 (n°4)
	Z, Z'	2, 1		4, 1	2, 1
	a / Å	11.282 (1)	11.436 (1)	7.0043 (6)	7.1595 (5)	11.355 (1)
	b / Å	6.515 (7)	6.432 (8)	16.476 (1)	16.6398 (11)	6.5917 (7)
	c / Å	12.958 (1)	12.819 (2)	17.303 (1)	17.3695 (12)	13.076 (1)
	 / °	98.767 (2)	104.407 (2)	90	90	97.120 (2)
	V/ Å 3	941.4 (1)	913.3 (2)	1996.9 (3)	2069.3 (2)	971.2 (1)
	Nb reflexions unique / I>2I	3513 / 2561	3297 / 2640	3809 / 2338	4206 / 3202	3933 / 3257
	Final R1 / wR2 (I>2I)	0.0517 / 0.1109 0.0496 / 0.1110 0.0689 / 0.1523 0.0585/ 0.1430 0.0462 / 0.0942
	Final R1 /wR2 (all data)	0.0735 / 0.1264 0.0649 / 0.1247 0.1142 / 0.1781 0.0781 / 0.1561 0.0570 / 0.1007
	Absolute structure (Flack) parameter	-0.17 (10)	0.29 (9)	0.52 (16)	0.15 (14)	0.30 (1)

Table 5 : Isotropic displacement parameters of chlocyphos alky amines (U (eq) is defined as one third of the trace of the orthogonalized Uij tensor, bolded values are double of the value of the first carbon atom linked to the nitrogen atom)

 5

	Isotropic displacement	Butylamine Isobutylamine Pentylamine Hexylamine Cyclohexylamine
	U(eq) (Å 2 x 10 3 )
	C(1A)	104 (2)	62 (1)	103 (2)	116 (2)	47 (1)
	C(2A)	142 (3)	76 (2)	121 (3)	212 (5)	75 (1)
	C(3A)	250 (7)	179 (5)	174 (4)	331 (10)	99 (2)
	C(4A)	307 (10)	134 (3)	151 (3)	170 (3)	95 (2)
	C(5A)	-	-	207 (6)	219 (5)	81 (1)
	C(6A)	-	-	-	187 (4)	66 (1)

Table 7 : Initial conditions and results of AS3PC mode for isobutylammonium chlocyphos salt at 25 ml scale

 7

			m ± (g) m EtOH (g) m seeds (g) / ee (%) T B (°C) T F (°C)
			2.075 19.72	0.104 / -100	36	5
	N° Time(min) m total (g) m crops (g) OP (%) m pure (g) Yield (%) ee f (% ee)
	A 1	35	2.179	0.349 -60.10 0.210	5.11	4.82
	A 2	33	0.349	0.340 +57.80	0.196	9.44	4.51
	A 3	31	0.340	0.264 -86.24 0.138	6.65	3.22

Table 8 : Initial conditions and results of AS3PC mode for hexylammonium chlocyphos salt at 25 ml scale

 8

	Calculation: Mean value = runs (A+B i +C i )/7 (i =1;2;3)

  .

		m ± (g) m IPA (g) m seeds (g) / ee (%) T B (°C) T F (°C)
		2.335 19.65	0.09 / ±100	25	5
	N° Time(min) m total (g) m crops (g) OP (%) m pure (g) Yield (%) ee f (% ee)
	A	23	2.425 0.240 -96.87	0.232	6.08	4.73
	B 1	23	2.425 0.212 -85.94	0.182	3.94	3.75
	B 2	23	0.212 0.177 +70.78 0.125	5.35	2.60
	B 3	23	0.177 0.074 -99.23 0.073 3.21	1.54
	C 1	23	2.425 0.213	-85.10 0.181 3.90	3.73
	C 2	23	0.213 0.143 +96.87 0.138	5.91	2.87
	C 3	23	0.143 0.081 -78.91	0.064	2.74	1.35
	Mean 23	1.146 0.163 ± 87.67 0.142 4.4	2.9

  moderate yield (circa 10.92%, mean value), the best achieved among the derivatives considered for the resolution by PC.

				399	0.261	-83.50	0.218	8.88	7.76
	A 2	40	0.261	0.200	+97.97	0.196 15.13	7.03
	A 3	40	0.200	0.194	-95.68	0.186 14.36	6.70
	A 4	40	0.194	0.149	+100.0	0.149 11.50	5.44
	A 5	40	0.149	0.125	-100.0	0.125	9.65	4.60
	A 6	40	0.125	0.124	+92.38	0.114	8.80	4.21
	B 1		40	1.399	0.195	-100.0	0.195	7.02	7.00
	B 2		40	0.195	0.215	+77.92	0.167 12.89	6.06
	B 3		40	0.215	0.177	-100.0	0.177 13.67	6.39
	B 4 B 5 B 6	* *	40 40 30	0.177 0.198 0.153	0.198 0.153 0.094	+83.76 -92.38 +78.68	0.166 12.82 0.141 10.89 0.074 5.71	6.02 5.16 2.78
	Mean 40	0.389	0.174	±91.85	0.159 10.9	5.7

Table 10 : summary of the entrainment performances

 10

	Chlocyphos salt	PC mode	Mean OP	Mean Yield	Mean ee f	Absolute structure
			(% ee)	(%)	(% ee)	(Flack) parameter
	Butylamine	ASPreCISE	94.8	9.5	7.5	-0.17 (10)
	Isobutylamine	SIPC / AS3PC	88.5 / 94.6	6.8 / 9.3	3.4 / 5.0	0.29 (9)
	Hexylamine	SIPC / AS3PC	75.0 / 87.6	3.3 / 4.4	2.6 / 2.9	0.15 (14)
	Cyclohexylamine	AS3PC	91.8	10.9	5.8	0.30 (1)

ACKNOWLEDGMENT

Dr Thomas Vetter and ESR Ghufran ur Rehman (Laboratory CCAPPE-University of Manchester, UK) are thanked for their support for the FBRM studies. This research received funding as part of the CORE project (October 2016 -September 2020) from the Horizon 2020 Research and Innovation Programme of the European Union under Marie Sklodowska-Curie Grant Agreement No. 722456 CORE ITN.

ASSOCIATED CONTENT Supporting Information Available

For Table of Contents Use Only

Family of conglomerate forming systems composed of chlocyphos and alkyl-amine. Assessment of their resolution performances by using various modes of preferential crystallization.

Aliou Mbodji 1 , Gabin Gbabode 1 , Morgane Sanselme 1 , Nicolas Couvrat 1 , Michel Leeman 2 , Valérie Dupray* 1 , Richard M. Kellogg 2 and Gérard Coquerel [START_REF] Hoeve | The Design of Resolving Agents: Chiral Cyclic Phosphoric Acids[END_REF] 1 Normandie Univ, UNIROUEN, SMS, 76000 Rouen, France 2 Syncom BV, Kadijk 3, 9747 AT Groningen, The Netherlands valerie.dupray@univ-rouen.fr

Table of Contents Synopsis

A family of salts formed with Chlocyphos and various alkyl amines crystallizing as conglomerate was evidenced. Preferential crystallization through its various modes has been successfully developed for these conglomerates prior to find a suitable one for the resolution at laboratory scale and eventually at larger scale.

Table of Contents Graphics