Fanny Castéran

Dr Ruben Ibanez

Dr Clara Argerich

Prof Karim Delage

Francisco Chinesta

Philippe Cassagnau
email: philippe.cassagnau@univ-lyon1.fr

Prof. F Chinesta

Application of Machine Learning Tools for the Improvement of Reactive Extrusion Simulation

Keywords: artificial engineering, experimental data, machine learning, polymer processing, reactive extrusion

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Introduction

Reactive extrusion is known to be an efficient and economical way of reactive processing of thermoplastic polymers. Corotating and counter-rotating twin-screw extrusion in particular are widely used for bulk polymerization, chemical modification of polymers and reactive compatibilization of polymer blends.

Whereas polymer synthesis and post synthesis modifications were originally exclusively carried out in batch mixers, some valuable features of extrusion process make it an advantageous alternative for some of these reactions. As a matter of fact, aside from being fast and continuous, this process makes possible to perform polymerizations or chemical reactions without any organic solvent (environment-friendly). It is also an efficient way to devolatilization, which can be useful to remove volatile organic compounds (VOC) such as monomers or reaction byproducts. Moreover, the adaptability of the screw design helps the formulation of complex materials. The screw profile can indeed be specifically designed for each formulation and define different areas of feeding, kneading, shearing, or conveying, depending on the expected final properties of the material. [1] As reported in the literature, all these features have been widely exploited through a large number of chemical reactions and polymer systems studied. [2][3][4][5][START_REF] Beyer | Reactive extrusion: Principles and applications[END_REF] However, some disadvantages of using the extruder as a reactor must be considered: While because of the additional complexity of reactive extrusion, most simulations of reactive extrusion are based on simplified steady state 1D models. It however involves coupling with several submodels to obtain constitutive equations (viscosity, chemical kinetics, mass and temperature transfers…), which is not trivial and takes time. [10] Yet, despite many researches and published papers, there is a lack of describing complex polymer formulations such as reactive extrusion systems.

In these circumstances and given the progress made today in artificial intelligence tools dealing with small amounts of data, it seems interesting to try developing models based on data to reinforce possible weaknesses in existing physical models, to enrich the models when we are confident in the data collected, or even to improve the data when they present a large variability. Finally, the aim of this work is to combine the logic of physical models with the accuracy of machine learning techniques to describe the reactive extrusion of a complex system. This reactive system is based on the in situ reaction of a reactive polyethylene oligomer with a triamine or a sorbitol while dispersing in a polypropylene (PP) matrix.

Experimental Section

In this work, reactive systems that are model systems, but also complex were chosen to study, in order to justify the use of artificial intelligence methods. The chosen systems consist of dispersing a polymer network resulting in the in situ reaction of a polyethylene oligomer grafted with maleic anhydride and a triamine or a sorbitol in a PP matrix. The reactions were performed by a one-step reactive extrusion process. Several process parameters were tested in order to analyze their influence on the final materials. The processes were also simulated thanks to the software LUDOVIC, whose results have then been compared with the experiments. Finally, machine learning techniques were employed in order to improve the simulation by bringing a correction to its outputs.

Materials

In the present study, a system previously developed in lab in the framework of Ph.D. thesis was used. [11] Actually, the reaction between a linear polyethylene oligomer grafted with maleic anhydride derivates (Ceramer 1608, Baker Hughes) and a trifuctional polyetheramine oligomer (Jeffamine T-403, Huntsman) was studied. The reaction results in a crosslinked network with an equilibrium storage modulus value similar to synthetic rubbers (Ge ≈ 2 × 10 6 Pa). The objective of the present paper was to perform in situ this reaction in a PP matrix by reactive extrusion. A similar system was also studied by replacing the triamine with a Sorbitol (D(-)-Sorbitol, VWR Chemicals).

The PP used in this work was an isotactic homopolymer (PPH7060, Total). It has a melting temperature of 165 °C and a density of 0.905 g cm -3 . Its melt flow index was 12 g/10 min (230 °C, 2.16 kg), which corresponds to a zero shear viscosity of 3.10 3 Pa s (T = 180 °C).

The Ceramer 1608 from Baker Hughes used in this study was a solid at room temperature. It has a melting point of 75 °C and a zero shear viscosity of η 0 = 2 Pa s (T = 180 °C). The technical datasheet provided by the supplier specified an acid value of 154 mg KOH/g and a saponification value of 215 mg KOH/g. The datasheet also specified that the maleic anhydride derivates used for the functionalization of Ceramer 1608 were not only maleic anhydride but also mono-isopropyl maleate (Z and E isomers) and maleic acid (Z and E isomers). For simplification purposes, maleic anhydride will be considered as the only maleic anhydride derivate of this functionalized oligomer.

The Jeffamine T-403 trifunctional polyetheramine oligomer from Huntsman was liquid at room temperature. It has a density of 0.978 g cm -3 with a zero shear viscosity of η 0 = 0.07 Pa s (25 °C), a molar mass of 400 g mol -1 , and a amine hydrogen equivalent weight of 81 g eq -1 according to its technical datasheet.

The Sorbitol was conditioned as a white solid powder. The chemical structures of the reactants are presented in Table 1.

The amount of functional groups in the oligomers has been determined from the acid and saponification values in the case of the Ceramer 1608 and from the amine hydrogen equivalent weight in the case of Jeffamine T-403. In the case of Sorbitol, only the two primary alcohol functions were considered.

The reagent ratios of the two systems were determined assuming near stoichiometry. The ratio in weight of Ceramer 1608 against Jeffamine T-403 was set at 75/25, and the one of Ceramer 1608 against Sorbitol was set at 85/15.

The reaction mechanisms are shown in Figure 1. The reaction between the Ceramer and the triamine involved a reaction between the maleic anhydride groups of the Ceramer and the amine groups of the Jeffamine, yielding a cyclic imide moiety along with water as a by-product. As for as the reaction between the Ceramer and the Sorbitol, the maleic anhydride cycle was opened, forming an ester function and a carboxylic acid function. These reactive systems were quite complex due to their chemistry and the solubility of the reagents, and it was therefore difficult to transcribe the real conditions in a simulation such as LUDOVIC in terms of, for example, network formation (reaction conversion) as a function of time and temperature. This was where data science and machine learning become interesting to use to improve existing simulations.

Process

The chemical extrusion was carried out in one single step with a co-rotating twin-screw extruder (Leistritz ZSE18, L/D = 60, D = 18 mm). The PP pellets and Ceramer were introduced together at the entrance by a hopper, the Sorbitol was introduced at the same spot with a powder feeder, and the Jeffamine was added once passed the melting zone at bloc 3 by means of a HPLC pump. A vent was placed over the second last bloc in order to remove the gases generated during the process. The final materials were cooled by air at the die exit of the extruder and then pelleted. All the experiments were carried out at 200 °C with the first blocs at lower temperature to minimize clogging effects at the inlet. The temperature and screw profiles used for all the experiments are described in Figure 2.

The formulations with the system Ceramer/Jeffamine dispersed in PP were carried out as specified in Table 2, with screw rotation speeds from N = 200 to 1000 rpm and exit flow rate from  w = 3 to 20 kg h -1 . Two formulations were tested for this system with φ = 15 wt% and φ = 30 wt% of dispersed phase. Concerning the system Ceramer/Sorbitol, it was dispersed at φ = 20 wt% in PP for different processing conditions: screw rotation speeds of N = 300 and 800 rpm, and exit flow rates of w  = 5 kg h -1 and w  = 10 kg h -1 .

Temperature and pressure were measured at the die entrance. However, the thermocouple used inside the die did not measure the true temperature at the core of the material but the temperature on the sides, thus influenced by the die temperature. Some temperatures were then measured at the exit by means of a manual thermocouple. The experiments performed are summarized in Table 2.

Characterizations

Tensile-test pieces (5A) were injected with a Babyplast injection press at 200 °C and 90 bar. Young modulus was determined by tensile test with a speed of 1 mm min -1 and stress at yield, elongation at break, and stress at break were measured with a tensile speed of 50 mm min -1 .

Morphologies were characterized by scanning electronic microscopy (SEM) with ZEISS MERLIN COMPACT VP. The samples were prepared from the injected tensile-test pieces (5A). They were then fractured in liquid nitrogen and metallized with 10 µm of a copper coating.

The kinetics of the chemical reaction leading to the formation of a chemical network was studied from rheological studies using an Ares-G2 strain controller rheometer using a geometry of parallel plates of 25 mm diameter and a gap of 1 mm spacing. The variation over time of the rheological behavior of the premixed reactants were thus measured, under an angular frequency of 1 rad s -1 at 140 and 180 °C under nitrogen. The Ceramer and the Jeffamine were premixed in an internal mixer at T = 110 °C and 50 rpm for 2 min. The Ceramer and the Sorbitol were first premixed at T = 140 °C, N = 300 rpm, and for a w  = 3 kg h -1 flow rate in the extruder previously described. They were then mixed in an internal mixer at T = 140 °C and N = 60 rpm for 5 min to extract the gases that formed bubbles inside the material and may alter the measures.

The viscoelastic behavior of the materials was studied with frequency sweep measurements using plate geometry of 8 mm diameter and 1 mm gap. A frequency sweep was applied from 100 to 0.01 rad s -1 under a strain of 2% (linear regime). These tests were performed on the resulting samples of the kinetics measurements.

Modeling and Machine Learning

Simulation

The LUDOVIC simulation software that we used here has been developed to simulate the flow along a screw profile corresponding to industrial reality. It was also important to be executable on a personal computer without needing excessive computation time or power. To meet these expectations, LUDOVIC uses a global model describing the total flow by linking local 1D models. Various singular strategies and simplifications have therefore been used to achieve sufficient precision despite the 1D considerations described below.

It is commonly admitted in these process conditions that the material melting occurs rapidly after reaching the first restrictive element. Consequently, this phenomenon is by default assumed instantaneous in the simulation. Meanwhile, it is possible for the user to import a specific melting model.

Concerning then the melt conveying section, two main different elements have to be considered and require distinct methodologies: the screw elements and the kneading discs (left and right-handed). The screw elements are often treated in 1D or 2D using a model flattening out the screw channel with a sliding barrel moving at the top. Yet, the strategy employed in this software uses a different 1D model following cylindrical coordinates along an eight-shaped pattern representing the screw channel. The channel section is considered to be rectangular and perpendicular to the screw flights with a constant width and Stokes equations are solved in this section. The kneading discs are also usually simulated using 2D approaches but a 1D approach is necessary to ease the calculations. Based on previous studies, only the peripheral flow in the θ-direction around a disc is thus considered. The representations of both these elements are schematized in Figure 3.

In these configurations, the flow is locally calculated as Newtonian and isothermal. It is however expressed following Newtonian flow equations that include a specific viscosity that is a function of the shear rate and the temperature. This viscosity can be then defined apart and follow specific rheological models such as power law, Carreau-Yasuda or Casson. The mean viscosity in channel direction and the mean temperature can be then calculated. A 1D approach is used to define the temperature. As the screws in a twin-screw extruder are not totally filled, the filling ratio is unknown. Consequently, the calculation has to follow an iterative procedure: The die temperature is randomly defined, and the simulation is run backward the flow, from the die until the feeding section. If the final pressure and temperature do not match the expected inlet ones, the exit temperature is adjusted, and the calculations are reiterated until the match with the inlet conditions. The exact equations and methods used in the simulation have been fully detailed by Vergnes et al. in their article. [9] Despite all these drastic simplifications, LUDOVIC software has been validated by numerous experiments and compared with 3D simulations. [12,8] It has also been widely used since its creation in various extrusion domains, such as polymer blends, in situ nanocomposites, extrusion cooking of cereal-based products, and more recently, glass and plant fibers break during compounding. [13][14][START_REF] Valle | Advances in food extrusion technology[END_REF][START_REF] Ville | [END_REF][17] For this study, the screw profile, extruder and die dimensions as well as barrel temperature were defined to correspond to our experiments. With respect to the material properties, since the software does not consider a dispersed phase, we assumed that the rheological behavior of the formulation is only determined by the matrix. As PP is the matrix, the simulation has been run considering one unique PP phase. The physical properties of this phase were defined from the experiments of Fel et al. who obtained good results using LUDOVIC to simulate twin-screw extrusion of the same PP as the one we used. [18] A Carreau-Yasuda law was thus applied using the following equation:

1 0 1  T T a m a η η λ γ ( ) ( ) ( ) ( ) = + - (1)
where η 0 is the zero shear viscosity, λ is the relaxation time,  γ is the shear rate, a and m are specific parameters. The values of these parameters and the thermal properties are summarized in Table 3.

Finally, the heat transfer coefficient between the polymer and the die have been fixed at 50 W m -2 K -1 and the one between the polymer and the barrel was of 350 W m -2 K -1 , which corresponds to values used in similar simulations. [9,19]

Machine Learning Techniques

In the past, science was based on the extraction of models, these being simply the causal relation linking causes (inputs) and responses (outputs). This (intelligent) extraction or discovery was performed by smart (and trained) human minds from the data provided by the direct observation of the reality or from engineered experimental tests. Then, with the discovered, derived, or postulated model, predictions were performed, leading to the validation or rejection of these models.

Thus, physics-based models, often in the form of partial differential equations, were manipulated by using numerical techniques, with the help of powerful computers. However, sometimes models are not available, or they are not accurate enough. In that case, the most natural route consists of extracting the model from the available data (a number of inputs and their associated outputs). When data is abundant and the time of response is not a constraint, deep-learning could constitute the best alternative. However, some industrial applications are subjected to: i) scarce data and ii) necessity of learning on-the-fly under stringent real-time constraints. There is no free lunch: to compensate the lack of data some extra-knowledge must be incorporated during the model extraction (discovery).

In what follows, we will consider that data and perform efficient regressions for correlating the chosen inputs with the selected outputs. To account the just mentioned difficulty associated with the necessity of proceeding in the low-data limit, we will consider two techniques that the authors proposed recently: i) a sparse collocated parametric separated representation, called sPGD, and ii) a regression based on the construction of goal-oriented non-Euclidean metrics able to compare data, that is calculating the distance between data. The last technique was called Code2Vect. [20,21] Both techniques are revisited and summarized as follows.

Sparse Regression -sPGD

Linear regression is the simplest way of linearly relating input parameters with output quantities of interest. For illustrating the procedure (for additional details the interested reader can refer to Ibanez et al. ( 2018)) we consider a given output (u) expected depending on the two input parameters p and q, that is, u(p,q). The simplest regression, as previously indicated consists in the linear relation presented in Equation (2).

, u p q a b p c q

( )= + × + × (2)
If three data is available, that is, the output u 1 related to the inputs p 1 and q 1 ; the output u 2 related to p 2 and q 2 , and finally u 3 associated with p 3 and q 3 , one could calculate the three coefficients (a, b, and c) in Equation (2). Ea [J mol -1 ] 40 000

However, very probably the parametric dependence u(p,q) is nonlinear, and with no more data, calculating richer regressions seems out of reach. Here a solution exists, the sPGD instead of considering the simple approximation given by (2), considers

, U p q P p Q p ( ) ( ) ( ) = × (3)
that being both functions P(p) and Q(q) unknown defines a nonlinear problem, to be calculated in the solution procedure.

In that case one proceeds by linearizing, that is, by assuming Q(q) given and looks for P(p). Thus, for computing P(p) the three available data enables an approximation richer that the linear previously considered. Then, from the just computed P(p) one looks to update Q(q) again with three available data. Thus, P(p) and Q(q) could be approximated using a quadratic approximation, leading to richer nonlinear approximations. The solution compactness is enforced by maximizing sparsity.

As soon as functions P(p) and Q(q) are calculated, the output U in Equation ( 3) can be easily and quickly calculated for any value of the inputs p and q.

Code2Vect

Classification and regression could be facilitated if the outputs difference, for example, |u 1u 2 |, scales with the data distance, for example, ,

p p q q   --. If the difference of the output scales with the distance between the data-points, as soon as a new data comes, its associated output could be calculated by interpolating the ones at the neighbor data-points.

However, sometimes two data points can be very close while the associated outputs differ considerably. In that case, in Argerich et al. (2019) it was proposed mapping the data point into a reduced space, for example, (p i ,q i ) into z i , such that the distance |z iz j | scales with |u iu j |. [21] Thus, classification and regression become almost trivial in the z-space. The mapping that transform (p,q) into z can be viewed as the construction of a non-Euclidian metric, and was detailed in Argerich et al. (2019).

Model-Data Hybridization

Sometimes one measures data, for example, u exp (p,q), that differs from a model prediction based on existing knowledge or physics, that provides u mod (p,q). When both differ significantly the model prediction cannot be employed anymore without incurring risks. Two valuable gateways consist in:

• Elaborating more accurate models. However, this route implies time and effort. • Elaborate a model of the measured data, that is a regression for expressing the dependence between u exp and the parameters, in our example, p and q. This pragmatic alternative is confronted to the necessity of having enough data for constructing the regression by using for example one of the techniques previously described (sPGD and Code2Vect).

An appealing alternative route consists in assuming that the measures are expressed from the model and its intrinsic deviation, that is, u exp (p,q) = u mod (p,q) + C(p,q), where C refers to the correction. By assuming that if the model is a reasonably good approximation of the real system, the correction is much less rich that the data itself, the construction of C(p,q) will require much less data for the same degree of accuracy. Thus, the available data, even if not so big, suffices for creating the regression as discussed before. This is the rationale behind the co-called Hybrid-Twin paradigm, as described in ref. [22].

Results and Discussion

Kinetics Study

A study of the reactions kinetics of the two reactive systems has been performed according to the rheological method described in the experimental part. As shown in Figure 4, the reaction between Ceramer and Jeffamine is clearly faster than the reaction with the Sorbitol at any temperature, even if the Ceramer has been premixed longer with the Sorbitol than with the Jeffamine. The final shear storage moduli of these systems are both above 3.10 6 Pa, with higher values for the Ceramer/Jeffamine system. The viscoelasticity studies are present in Figure 5, they reveal that these reactive systems behave like solids at these temperatures (G′ ≫ G″, tan(δ) ≈ 10 -2 ) so that we can assume that they form a high-density crosslinked network.

With such systems with a fast kinetics, it is difficult to obtain a relevant kinetic model, and the mixing conditions in the extruder are not well known for these systems. At higher temperatures such as our processing conditions, the reactions are even faster, and for the Ceramer/Jeffamine system, the reaction occurs before the dispersion in the matrix. The viscosity ratio between the reactive system and the PP matrix is then advantageous for a dispersion in the PP, but as showed later, this results in a coarse morphology. However, the Ceramer/Sorbitol has a slower kinetics that allows a lubrication phenomenon leading paradoxically to a better morphology.

Morphologies

The high reactivity of the dispersed Ceramer/Jeffamine system can be an advantage in reactive extrusion process because of the short residence times (between 15 and 90 s in the present study), however it can also affect the quality of the dispersion. Actually, the SEM analysis reveals large and deformed nodules (about 10 µm). This phenomenon can be explained by a fast reaction occurring before the system reaches a good dispersion in the matrix. Consequently, solid networks are created and avoid better dispersion afterward.

No real difference in the morphologies can be clearly noticed with the variations of process conditions. The SEM analysis also pointed out a lack of affinity between the matrix and the nodules as we could observe their detachment from the matrix. This lack of affinity can also be a notable factor explaining the shape of the nodules.

The Figure 6 presents images obtained with the samples that have been processed at  w = 10 kg h -1 and N = 600 rpm for 15% and 30% of dispersed phase.

The SEM observation performed on the Ceramer/Sorbitol system highlight the same lack of affinity between the different phases. However as expected, the nodules obtained are more spherical with a better dispersion with a characteristic size of 1 µm. No significant differences in morphologies can be linked to process variations. Therefore, the slower reaction seems to have improved the shape and size of the nodules. But it is worth noting that the dispersion of nodule sizes is quite large, maybe due to not optimized process conditions (screw profile with insufficient shear rate for instance). Figure 7 presents images obtained with the samples that have been processed at w  = 10 and 5 kg h -1 with N = 300 rpm.

Mechanical Tests

To measure the impact of the oligomer network dispersion in the PP matrix, tensile tests have been performed on samples differing by their amount of dispersed phase (φ) and the processing conditions (flow rate (  w ) and screw rotation speed (N)). For comparison, these tests have also been performed on the raw PP used in the formulation processed in the same conditions than the other formulations. Young modulus (E), yield stress (σ y ), and strain at break (ε b ) obtained are reported in Table 4.

First, it appears that the addition of a dispersed phase seems to alter the mechanical properties. This could be explained by the poor compatibility between the PP phase and the PE-based dispersions. Actually, this kind of blends generally requires a compatibilization between both phases to obtain improved mechanical properties.

Then, by studying the influence of process parameters, it seems that a high flow rate of 10 kg h -1 results in a lower Young's modulus and a higher elongation at break than lower flow rates. Such conditions induce a high shear rate which could induce a degradation of the PP matrix explaining these results. Regarding the screw speed, this parameter seems to have much more influence on the Ceramer 1608/Sorbitol system than on the Ceramer 1608/Jeffamine T-403 system. The main parameter influenced by the rotation speed is the residence time, and although this parameter has an influence on the final reaction speed of the Ceramer 1608/Sorbitol system, it has no influence on that of the Ceramer 1608/ Jeffamine T-403 system because the reaction time is shorter than the residence time and the material therefore stops changing. 4. Mechanical properties of blends processed at different screw rotation speeds (N), different exit flow rates ( w  ) and for different amounts of dispersed phase (φ).

Material

φ [%]  w [kg h -1 ] N [rpm] E [MPa] σ y [MPa] ε b [%] Raw extruded

Results: LUDOVIC versus Experiments

Remember that we used the hypothesis that the rheological behavior of the compound material depends only on the properties of the matrix. The simulation has thus been run considering only one single PP phase in the extruder, implying no differences between the different formulations studied. Figure 8 shows, for the system Ceramer/Jeffamine, the comparison between simulation outputs and experimental data. It is worth noting that the 1D global model of Ludovic software model fits well the experiments (around 20% of maximum error) despite the numerous simplifications and hypothesis implied in this simulation. However, some inaccuracies can be noticed, particularly at high flow rates. The previously mentioned problem of the extruder thermocouple appears clearly in the plot of the temperatures. The temperatures measured manually are more relevant, but they do not perfectly match between the experiments and the model. It can however be explained by the inaccuracy of the experimental data that have been performed with a manual thermocouple at the exit of the extruder, and it is particularly tricky to obtain the exact core temperature of the material this way. Finally, even if the results of the simulation can be enough for most engineering studies, they also can be improved, and machine learning can be a solution to bring this additional accuracy. Similar comparison between LUDOVIC's results and experimental data for the system Ceramer/Sorbitol is shown in Figure 9. As said earlier, the simulation considers a single PP phase. The same simulation values have thus been used for this comparison. For this system, the simulation seems to fit less the experiments and to over predict the results. Therefore, it appears that the dispersed phase has finally a significant influence on the behavior of the material. Actually, as it can be seen in Figure 3, this reaction is slower and as the viscosities of the reactants are significantly lower than the viscosity of the PP (viscosity ratio of 7.10 -4 between the Ceramer and the PP), we can assume that the reactive system has a lubricant effect on processing condition before creating a dispersed phase of sufficiently high viscosity to be dispersed in the PP matrix. This phenomenon has been described by Cassagnau et al. for various reactive systems. [23] Consequently, we cannot approximate the viscosity of the material as the viscosity of the matrix anymore, but as a lower apparent viscosity (lubricant effect), at least at the early stage of mixing. Finally, it appears that classical modeling simulations are not perfectly adapted to describe polymer blends, especially low viscosity ratio blends.

Machine Learning

In this section, the numerical results associated to the previous section are presented and discussed. The section is structured as follows: the first part addresses the data sets and the employed numerical algorithms. Then, the results associated with a full data-driven regression and a hybrid-twin solution will be exposed. Finally, some conclusions will be drawn.

Problem Statement

Data is coming from two different sources. From one hand, data coming from the Ludovic simulation software, that will be called simulation data. On the other hand, data coming from experimental measures will be referred as experimental data. Both data sets have the same four outputs to be predicted namely, torque, pressure, engine power, and exit temperature. Simulation data has two inputs: flow rate and rotation speed, whereas experimental data, other than the two previous inputs, includes an extra input parameter, the dispersed phase. This last parameter was not considered in the model because of the Ludovic model limitations.

In the following, each of the four outputs will have a ground truth and an approximate model. The basic truth for torque, pressure, and engine power are the experimental measurements, while the approximate model consists of the simulation data. On the contrary, Ludovic software is able to give a more accurate exit temperature measurement since it can extract the temperature at the middle of the die section. Contrarily, the temperature sensor is located on the die wall where the temperature significantly differs from the actual temperature. For that reason, we will consider that the simulation temperature dataset contains the ground truth whereas the experimental measures define the approximate model.

The experimental dataset contains 47 samples (or measurements). The same 47 samples were replicated from simulation (Ludovic). The main goal is to have a regression model which is able to infer the outputs for any point in the parametric space. For that purpose, the initial data set is split into 38 points to construct the regression (training) and 9 points to check the prediction accuracy (test).

As previously reported, we have used two different regression techniques, the sPGD and the Code2Vect -C2V.

Finally, we will compare two different approaches:

• The first, which will be called full data-driven, creates a regression directly on the ground truth. • The second, which will be called hybrid-twin, involves a regression of the difference between the ground truth and the approximate model. By doing that, a certain amount of the correlations already present in the approximate model were described and therefore, the regression of the deviation is expected to be more linear.

Full Data-Driven Regression

As mentioned above, the first approach considers a direct regression on the ground truth without considering the effect of the approximate model. Figure 10 shows the sPGD regression results for the 4 outputs using a full data-driven modeling. The accuracy of the regression is quite acceptable, as the real quantity of interest follows the same tendency than the estimated one. The exit temperature presents less deviation than the other three quantities, due to the fact that the ground truth for the temperature is the simulation In what follows the computed predictions obtained by the regression for the data used in the regression construction (referred in Figure 9-and the next Figures-as "Inside Training") and those that were not considered in the training (referred in Figure 9 as "Outside Training") are compared with the collected data.

Figure 11 shows the Code2Vect regression results in the full data-driven case. As it can be seen, the results are again acceptable. It can be noticed that C2V generates a model that predicts very well in the training points (blue points), however, in some cases the errors in the test dataset (black points) are higher compared with the sPGD results.

Table 5 reports the relative errors for the full data-driven case. The relative error has been normalized with respect to the mean value of each quantity of interest, respectively. As it can be clearly seen, the C2V presents less error in the training-set in comparison with the sPGD technique. However, when considering the test-set, the sPGD seems globally more accurate.

Hybrid-Twin Regression

The second approach consists of subtracting the approximate model to the ground truth. A regression is applied to that deviation. By doing so, we expect that certain correlations will be already explained by the approximate model facilitating the regression construction and its performances. Thus, the model of the deviation is expected to be easier to capture than the full data-driven route.

Figure 12 shows the estimation of the four outputs when using the hybrid-twin procedure using the sPGD regression to model the deviation. As it can be appreciated, the hybrid-twin methodology behaves slightly better in the training-set. When considering the test-set, the hybrid-twin methodology is on the same level of accuracy than the full data-driven approach.

Figure 13 reports similar results when using the C2V for modeling the deviation. As it can be appreciated, C2V model predicts very accurately within the training set. When considering the test set, C2V behaves better than sPGD for the engine power and torque.

Table 6 reports a relative error for both C2V and sPGD techniques. As it can be seen, C2V for the torque and sPGD for engine power, perform better than the full data-driven approach. It is also important to highlight that the exit temperature is harder to predict than the full data-driven case. This issue can be explained by the fact that the measured and the computed temperatures do not correspond, one is the bulk material and the other is measured near the die wall.

Conclusion

The aim of this work was to use machine learning tools combined with a simulation software, based on physical models, to obtain accurate predictions of a complex system with few experimental data. The framework of the present study is the reactive extrusion process for the in situ synthesis of a crosslinked dispersed phase. This dispersed phase is based on the reaction between a maleic anhydride functionalized PE oligomer phase with either a triamine or a diol. Viscoelasticity measurements proved that these reactive systems lead to high-density crosslinked networks (Ge ≈ 3 × 10 6 Pa). Kinetics studies showed that the reactivity of the first system (Amine based reactions) is really fast (<10 s at these processing temperatures) which prevents a good dispersion (coarse morphology) in PP during the extrusion process. The kinetics of the second system (sorbitol-based reaction) being slower, the resulting morphology is finer but a lubricant effect was observed. Finally, in both cases morphologies revealed a lack of affinity between the phases, causing poor properties of the final materials. The twin-screw extrusion 1D software Ludovic was used to model the experiments and it appeared that classical modeling simulations are in some cases not perfectly adapted to describe polymer blends, especially low viscosity ratio blends. Machine learning methods were then applied to these results in order to improve the predictions. The amount of data being limited (47 samples here), two different regression techniques dealing with low data were experimented: sPGD and Code2Vect (C2V), following two different strategies. The first one, called "full data-driven," creates a regression directly on the ground truth (basically experimental data), and the second one, called "hybrid-twin", involves a regression of the difference between the ground truth and the approximate model (Ludovic software data) that can be seen as a correction of the model. As a result, both strategies and both techniques succeed to bring acceptable predictions of the experiments despite few data. Differences between the two regression techniques are however noticeable depending on the predicted parameter. The hybrid-twin strategy seems also to give slightly better results than the full data-driven one. Moreover, the hybrid-twin strategy has the advantage to predict precisely a complex process whether considering physical phenomenon and theories from the model. It thus combines the logic of physical models with the accuracy of machine learning techniques in low data conditions.

Figure 1 .

 1 Figure 1. A) Reaction between Ceramer 1608 and Jeffamine T-403 oligomers; B) Reaction between Ceramer 1608 and Sorbitol.

Figure 2 .

 2 Figure 2. Scheme of the screw configuration used in the study.

Figure 3 .

 3 Figure3. Geometries of a screw element (the C-shaped chamber) and a bilobal kneading disc.[9]

Figure 4 .

 4 Figure 4. Variation of the absolute complex viscosity versus time for the two reactive systems at the temperature T = 140 and 180 °C; ω = 1 rad s -1 .

Figure 5 .

 5 Figure 5. Variation of storage modulus G′ and loss modulus G″ versus frequency of the two systems at T = 200 °C.

Figure 6 .

 6 Figure 6. SEM images obtained from the observation of Ceramer/Jeffamine system dispersed in PP; processed at  w = 10 kg h -1 and N = 600 rpm for

Figure 7 .

 7 Figure 7. SEM images of Ceramer/Sorbitol system dispersed in PP. Processing conditions w  = 10 kg h -1 for C) and at w  = 5 kg h -1 for D) with N = 300 rpm. Magnitude: x5000; Power: 5 kV.

Figure 8 .

 8 Figure 8. Plots of temperature, engine power, pressure, and torque obtained by the simulation versus parameters obtained experimentally under different processing conditions. The dotted lines show the correlations between experimental and simulation datas. Reactive system: Ceramer/ Jeffamine phase dispersed in PP. * T extruder: Temperature measured from extruder thermocouple, T manual: Temperature measured in the bulk polymer at the die exit.

Figure 9 .

 9 Figure 9. Plots of engine power, pressure, and torque obtained by the simulation versus these parameters obtained experimentally at different flow rates and screw rotation speeds. The dotted lines show the correlations between experimental and simulation datas. Reactive system: Ceramer/Sorbitol system dispersed in PP.

Figure 10 .

 10 Figure 10. sPGD full data-driven results for engine power (top left), exit pressure (top right), exit temperature (bottom left), and torque (bottom right).

Figure 11 .

 11 Figure 11. C2V full data-driven results for engine power (top left), exit pressure (top right), exit temperature (bottom left), and torque (bottom right).

  dataset, where the use of a deterministic model avoids dispersion.

Figure 12 .

 12 Figure 12. sPGD hybrid-twin results for engine power (top left), exit pressure (top right), exit temperature (bottom left), and torque (bottom right).

Table 1 .

 1 Chemical structures of the reactants constituting the reactive systems.

	Name		Structure			Supplier
	Ceramer 1608	O	O	O	O R	OH	Baker Hughes
			O			O
		C H 3	n	m		p CH 3
			(m +n +p = 50,
			R = H or iPr)
	Jeffamine			CH 3		Huntsman
	T-403
		CH 3		O	CH 3 NH 2 y
	N H 2		O H 3 C x	O		NH 2 z
			(x +y +z = 5 -6)
	(D)-Sorbitol			OH	OH	VWR Chemicals
		O H
			OH	OH

Table 2 .

 2 Formulations and processing conditions for the different reactive blends. Exit flow rate w  [kg h -1 ]

	System studied	% Dispersed phase φ		Rotation speed N [rpm]
	75/25	15%	3	200 to 1000
	Ceramer 1608	(12% Ceramer 1608;	5	200 to 1000
	Jeffamine T-403 +	3% Jeffamine T-403)	8	300 to 1000
	PPH7060		10	600 and 1000
			15	600 and 1000
			20	1000
		30%	3	150 to 600
		(23% Ceramer 1608; 7% Jeffamine T-403)	5	600 and 1000
			8	600 and 1000
			10	600 and 1000
	85/15	20%	5	300 and 800
	Ceramer 1608	(17% Ceramer 1608;	10	300 and 800
	Sorbitol	3% Sorbitol)
	+
	PPH7060

Table 3 .

 3 PP thermal properties and Carreau-Yasuda parameters used in the simulation.

	Thermal properties	Solid state	Liquid state	Carreau-Yasuda
				parameters
	Heat capacity [J kg -1 K -1 ]	2500	2500	η 0 [Pa s]	1 000
	Density [kg m -3 ]	900	750	λ [s]	0.4
	Thermal conductivity	0.33	0.33	a	0.21
	[W mK -1 ]
	Melting temperature [°C]	165		m	0.6
	Melting enthalpy [kJ kg -1 ]		209	T ref [°C]	200

Table 5 .

 5 Relative error for the full data-driven modeling.

	Error DD %	Engine power Exit pressure	Torque	Exit temperature
	sPGD train	12.6	7.2	14.0	0.4
	C2V train	2.4	1.6	1.3	0.0
	sPGD test	14.9	6.5	8.8	0.6
	C2V test	8.0	12.7	13.7	0.9

Acknowledgements

This research was funded by the French ANR through the DataBEST project.

Conflict of Interest

The authors declare no conflict of interest.


Bogdan Iorga

Philippe Savignac
email: savignac@poly.polytechnique.fr

Controlled Reactivity of Phosphonates by Temporary Silicon Connection

Keywords: phosphonate carbanion, Peterson reaction, silicon, halogenation, alkylations 1

In this review a summary of the different syntheses of trimethylsilylphosphonates is given. Their chemical reactivity in the light of their synthetic utility leading to numerous types of functionalized phosphonates is described. The material is presented according to the role played by the trimethylsilyl group. 1 Introduction 2 General Methods for the Synthesis of a-Silylated Phosphonates A. Michaelis-Arbuzov Route B. Michaelis-Becker Route C. Kinnear-Perren Route D

Introduction

a-Silylated phosphonates have been known since 1956 1 but their common use as reagents in phosphorus chemistry has become important only in recent years. [2][3][4][START_REF] Colvin | Silicon Reagents In Organic Synthesis[END_REF][START_REF] Ager | [END_REF][7] The first participation of the trimethylsilyl group in phosphonates chemistry was reported in 1972, 8 as an extension of the Peterson reaction, and the use of trimethylsilyl as protecting group appeared in 1988. 9 Undoubtedly, the presence of trimethylsilyl on the a-carbon atom to phosphorus has opened a research area giving rise to new synthetic developments and applications for phosphonates chemistry. Trimethylsilyl has the ability to stabilize and modify the reactivity of the adjacent carbanions and, consequently, their reactivity does not parallel that of other functional phosphonates. The easy connection of the trimethylsilyl group at the a-carbon atom combined with a ready disconnection as trimethylsilanolate or trimethylsilylheteroatom have contributed to confer a-silylated phosphonates upon a role of intermediates to control the reactivity of phosphonate carbanions. For a number of years we have been engaged in a program to develop novel and efficient routes for the synthesis of phosphonates. In this area, a-silylated phosphonates appear as reagents of significant synthetic importance for the preparation of functionalized phosphonates. The overall operation involving a-silylated phosphonates is depicted in Scheme 1. In this review, the types of reaction they undergo, with an emphasis on their synthetic utility, and various methods of preparation are summarized. Scheme 1.

2

General Method for the Synthesis of a-Silylated Phosphonates A. Michaelis-Abuzov Route Several chloromethylsilanes have been used as silylmethylphosphonate precursors, although few of them have received utility in organic synthesis. The diethyl 1-(trimethylsilyl)methylphosphonate 3 (R = Et), the most useful reagent, was first prepared in 56.5 % yield by refluxing for 68.5 h at 100-185°C a mixture of triethyl phosphite 1 and (chloromethyl)trimethylsilane 2 (Scheme 2). 1 Reduction of reaction time lowers significantly the yield. 10 Replacement of triethyl phosphite by trimethyl phosphite, to prepare the corresponding dimethyl ester, has little effect on the yield, which is comparable to the previous one (64.5 %). 11 By contrast, the use of (bromomethyl)trimethylsilane in reaction with triethyl phosphite decreases dramatically the yield which brings down at 25 %. 12 In further examples, essentially chloromethylsilanes bearing different group (Et, Ph) on the silicon atom have been used for the preparation of the corresponding silylmethylphosphonates in yields ranging from 44 to 75 %. 13,14 One example of conversion of chloromethyl-to iodomethylsilanes followed by Michaelis-Arbuzov reaction has also been reported. 15

Scheme 2.

Surprisingly, secondary a-silylated bromides were reactive, but the reactions require severe conditions (3-12 h at 170-200°C). Thus by the Michaelis-Arbuzov rearrangement of triethyl phosphite with (a-bromobenzyl)trimethyl-and (a-bromobenzyl)triethylsilanes, the corresponding diethyl (trimethyl)-and (triethylsilyl)benzylphosphonates were obtained in 56 and 24 % yields, respectively. 16

B. Michaelis-Becker Route

(Halogenomethyl)trimethylsilanes 2 (X = Cl, Br) undergo typical Michaelis-Becker reaction with a variety of dialkylphosphites 4 to give dialkyl 1-(trimethylsilyl)methylphosphonates 3 in modest yields (23-38 %) (Scheme 3). 11,12,17,18 This method, being not economical in terms of yields, has only limited utility and has never been developed.

Scheme 3.

C. Kinnear-Perren Route

The 1-(trimethylsilyl)methylphosphonic dichloride 5 has been prepared on large scale but in modest yield (31 %) by reaction between (chloromethyl)trimethylsilane 2 (X = Cl), phosphorus trichloride and aluminium trichloride followed by hydrolysis with a limited amount of water. Although this procedure give moderate yields, the large number of phosphonic diesters 3 subsequently prepared in fair to good yields (40-71 %) by alcoholysis of 5 is compensatory (Scheme 4). 19,20 Scheme 4.

1-(Trimethylsilyl)methylphosphonic dichloride 5 has also been prepared with a yield roughly comparable to the previous one (22.5 %) by reaction of tetramethylsilane with a large excess of phosphorus trichloride in the presence of oxygen. 21

D. Carbanionic Route

Unquestionably, the most attractive procedure for the preparation of dialkyl 1-(trimethylsilyl)methylphosphonates is the carbanionic route. The obvious difficulties resulting from transmetallation reactions which attend the execution of carbanionic reactions involving activated methylene groups have led to the development of ingenious procedures based on the trapping of 1-lithioalkylphosphonate anions with chlorosilanes in the presence of LDA. For example, the addition at -70°C of trimethylchlorosilane (TMSCl) (1 eq.) to a solution of dialkyl 1-lithioalkylphosphonates prepared from dialkyl alkylphosphonates (1 eq.) 6 and LDA (2 eq.) produces after work-up the dialkyl 1-(trimethylsilyl)alkylphosphonates 8 in 75-90 % yields of isolated product (Scheme 5), via the quantitative and clean generation of the stable intermediates, substituted dialkyl 1-lithio-1-(trimethylsilyl)methylphosphonates 7. 22,23 By varying the reactants, dialkyl methyl-, alkyl-, halogenomethyl-or benzylphosphonates 6, a number of dialkyl 1-(trimethylsilyl)phosphonates 8 may be easily obtained, thus extending significantly the scope and synthetic utility of the carbanionic route. 24,25 This expeditious and versatile technique has largely supplanted the previously reported carbanionic approaches. For example, addition of an excess of dimethyl 1-lithiomethylphosphonate, generated with n-BuLi (1 eq.), to a cooled THF solution of TMSCl, or addition of TMSCl in excess to a cooled solution of dimethyl 1-lithiomethylphosphonate resulted in the two cases in low yields (27-31 %) of dimethyl 1-(trimethylsilyl)methylphosphonate 8 (R = Me, R 1 = H). 26,27 Scheme 5.

The synthetic advantages of the carbanionic route are evident. Compared with the Michaelis-Arbuzov and Michaelis-Becker routes involving (chloromethyl)trimethylsilane, an expensive reagent, the carbanionic route uses TMSCl, an inexpensive and readily accessible starting material. Similarly, all the phosphonates are commercially available or accessible on laboratory scale. In addition, the carbanionic route leads to the lithiated a-silylphosphonate intermediates which may be directly used for further transformations. This method of generating carbanions 7 by proton-metal exchange reaction from a-substituted dialkyl methylphosphonates 6 is complemented by the halogen-metal exchange reaction from dialkyl trichloromethylphosphonate. Compared with the carbanionic route using lithiophosphonates, the use of cuprophosphonates provides another synthetic access to dialkyl 1-(trimethylsilyl)alkylphosphonates 8, but not so attractive. 28,29 3

Reactions of a-Silylated Phosphonates A. Trimethylsilylmethyl as Masked Carbanion

Several groups have demonstrated that desilylation of organosilanes containing a C-SiMe3 moiety initiated by means of fluoride ion (CsF, KF or TBAF) is an effective way for the transfer of carbanions to electrophilic centers. Some examples involving the fluoride-induced formation of a-phosphonylated carbanions from 1-(trimethylsilyl)methylphosphonates containing a fragile C-Si bond have been described. Cleavage of the carbon-silicon bond under these conditions offers the advantages of neutral conditions and contributes to better yields from sensitive substrates than those obtained under basic conditions. This procedure, appearing operationally simpler and cleaner than traditional protocols, has been applied to the preparation of alkenes 26,30 and 1-alkenylphosphonates 31 by Horner-Wadsworth-Emmons (H-W-E) and Peterson reactions, respectively. When dimethyl 1-(trimethylsilyl)benzylphosphonate was treated with benzaldehyde in the presence of fluoride ion sources (CsF, KF, TBAF), stilbene and dimethyl benzylphosphonate, a protodesilylation product, were produced. The best result of stilbene (85 %) was obtained upon heating in THF for 1 day with freshly dried CsF. Use of MeCN gave a similar result, whereas in toluene the reaction became very slow. KF was less effective even in the presence of 18-crown-6. TBAF was efficient at room temperature, however, the modest yield seems to be due to the difficulty in drying or the existence of acidic hydrogen, easily transmetallated by the resulting carbanion. When CsF or KF were used, only the E-stilbene was obtained, while TBAF afforded a mixture of E-and Z-stilbene in a 90/10 ratio. The formation of dimethyl benzylphosphonate seems to be due to the protonation by water which still remained in the system, and the yield of the olefin becomes water dependent. In the case of reactions with isobutyraldehyde, the corresponding olefins were obtained in low yield (35 %) as a E+Z mixture (70/30). By contrast, cinnamaldehyde gave stereochemically pure E,E-1,4-diphenyl-1,3-butadiene in 67 % yield. 26,30 Several variations on the reaction between diethyl 1-(trimethylsilyl)methylphosphonate 3 (R = Et) and aromatic aldehydes have been reported by solvent-free techniques in a domestic oven. At room temperature in the presence of dried CsF, unsupported or supported on magnesium oxide, the O-silylated diethyl 2-hydroxy-2-arylethylphosphonates were produced selectively in 60-80% yields of isolated product. The hygroscopic nature of CsF can complicate the reaction and under non-anhydrous conditions, with non-dried CsF for example, formation of diethyl arylvinylphosphonates is observed. 32

Generation

B. Trimethylsilyl as Directing Group

In 1968 Peterson made the important discovery that the anions resulting from lithiation of (methylthio)methyltrimethylsilane and (trimethylsilyl)methyldiphenylphosphine sulfide reacted with benzophenone to afford b-oxidosilanes which decompose to give olefins by loss of Me3SiOLi. This olefination reaction resulting in functionally substituted alkenes has been extended to phosphonates and can be considered as an alternative to the H-W-E reaction. 35 The reaction has been investigated with dialkyl 1-(trimethylsilyl)alkylphosphonates Despite a large number of investigations, a systematic study of the Peterson reaction including solvent, temperature, additives, nature and size of the a-substituents is lacking. Although the reported reactions have not all been effected under the same experimental conditions, it is possible to consider the nature of the carbonyl compounds (aldehydes or ketones) and of the group attached to the a-carbon atom (H, 8,22,25 alkyl, 8,22,23,37 OR, 38 SR, 39,40 NR 2 2, 41 F, [42][43][44][45][46] Cl 9 ) as experimental variables which affect the stereoselectivity. However, since aldehydes have been more systematically used than ketones, the comparison is best limited to this class of carbonyl compounds. Thus, the reaction of dialkyl 1-(trimethylsilyl)methylphosphonates 3 with aromatic aldehydes favours the E isomer (cis P(O)/H relationship) while aliphatic aldehydes give a mixture of the E and Z isomers in approximately equal amounts. 8,22,25 Similarly, the presence of a fluorine atom at the a-carbon atom promotes the E isomer with aromatic aldehydes and a mixture of E and Z isomers with aliphatic aldehydes. [42][43][44][45][46] With a chlorine substituent, the two isomers are formed in approximately equal amounts. 9 Introduction of an alkyl group (Me, Et, n-Pr, n-Pent, neo-Pent) at the a-carbon atom leads predominantly to the Z isomer (trans P(O)/H relationship) with aromatic aldehydes whilst a mixture of E and Z isomers is produced with aliphatic aldehydes. 8,22,23,37 The presence of a NR 2 2 group at the a-carbon atom strongly favours Z-configured products with both aromatic and aliphatic aldehydes. 41 Introduction of a SMe group at the a-carbon atom leads exclusively to the E isomer (trans P(O)/H relationship) with aromatic aldehydes and predominantly to the same isomer with aliphatic ones. PROGCOMP ENRfu 40

Figure 1.

For lithiated allylic phosphonates, the substitution pattern about the carbon skeleton affects the regioselectivity of the initial silylation as well as the reactivity of the resulting silylated anion. PROGCOMP ENRfu 47 In the case of a-silylated allylic phosphonates, the trimethylsilyl group has been shown to be useful both as directing and protecting group to control the regioselectivity of the system. For example, the lithiated diethyl allylphosphonate reacts with TMSCl to give diethyl 1-(trimethylsilyl)allylphosphonate in 47 % yield. It has been shown that the 1-sodio-1-(trimethylsilyl)allylphosphonate reacts with paraformaldehyde on heating in THF to give a mixture of 2-trimethylsilyl-1,3-butadiene (H-W-E reaction, 36 %) and 2-diethoxyphosphonyl-1,3-butadiene (Peterson reaction, 12 %). By contrast, the corresponding lithiated anion reacts with paraformaldehyde in hexane at low temperature to give only the Peterson product in 32 % yield. PROGCOMP ENRfu 48,49 Additionally, treatment of diethyl crotylphosphonate 16 at low temperature with LDA (3 eq.) followed by addition of TMSCl provide exclusively the -silylated crotylphosphonate anion 17. By virtue of the trimethylsilyl group, this anion reacts with ethyl formate in the -position to give 18. On acidic hydrolysis, the desilylated diethyl (2E)-3-formyl-2-butenylphosphonate 19 was isolated in 78 % yield (Scheme 9). PROGCOMP ENRfu 50

Scheme 9.

By contrast, the a-silylated carbanion generated from diethyl prenylphosphonate, on reaction with alkyl formates, behaves as a Peterson reagent leading to 1-Z-2-diethoxyphosphonyl-1alkoxy-3-methylpenta-1,3-dienes in high yields (72-92 %). 51 The presence of the two methyl groups at the g-position determines the a-regioselectivity of this anion towards the alkyl formates and favours the fast decomposition of the hindered kinetic erythro-adduct, leading to the Z enol ether, after a Peterson syn-elimination of the oxophilic silylated moiety. 51 The reaction of lithiated 1-(trimethylsilyl)cinnamyl-, prenyl-and crotylphosphonates with aldehydes was also studied. The cinnamyl derivative undergoes Peterson reaction with aromatic or aliphatic aldehydes to give phosphonodienes in high yield and with high stereoselectivity. Thus, with aromatic aldehydes almost stereomerically pure E,Ephosphonodienes were obtained, whereas predominantly Z,E-phosphonodienes resulted from reaction with aliphatic aldehydes. In contrast, the prenyl derivative undergoes a strict gregioselectivity in its reaction with aromatic aldehydes leading to phosphonolactones and to a mixture of phosphonolactones (major product) and Z,E-phosphonodienes (minor product) on reaction with aliphatic aldehydes. 52 Decomposition at low temperature of the adduct 14 to 1-alkenylphosphonates 15 can be avoided by trapping the b-oxidosilanes 14 in situ at -90°C with an excess of TMSCl. For example, treatment of the diethyl 1-lithio-1-(trimethylsilyl)alkylphosphonate 7 (R = Et) with ethyl formate followed by addition of TMSCl (1.5 eq.) provided the mixed acetal 20 as the major product. While there are some difficulties encountered in the hydrolysis of enol ethers, the mixed acetals 20 may be easily and completely hydrolyzed in few minutes at room temperature with diluted HCl, via the sensitive silylated enol ethers 21, to give the a-substituted formylphosphonates 22 as a mixture of aldehyde and enol forms. The silylated enol ethers 21 can be used advantageously in place of the traditional enol ethers, thus offering an efficient approach to the synthesis of diethyl 1-formylalkylphosphonates 22 (Scheme 10). 53 More recently, another example involving the intermediacy of phosphorylated sulfines has been reported. Treatment of diethyl allenylphosphonates 30 with LDA at low temperature followed by reaction with TMSCl leads to the desired a-silylated allenylphosphonate 31. This very unstable compound is directly added to a solution of R 2 -Li (R = Me, n-Bu, s-Bu) (1 eq.) in THF at -78°C to give the a-phosphonylated carbanions 32. When the anions 32 were allowed to react with an excess of sulfur dioxide and the resulting sulfines 33 stirred overnight, only poor yields of diethyl 2-thienylphosphonates 34 (12-25 %), contaminated with the protonated form of 32, were obtained. The separation of these two compounds proved to be problematic (Scheme 13). 56 The major disadvantage of the method is the incomplete reaction of 32 with sulfur dioxide.

Scheme 13.

a-Silylvinylphosphonates have proved to be effective precursors of more elaborated phosphonates by Friedel-Crafts-type reactions (Scheme 14). 57 Thus, a-silylated phosphonoketene dithioacetals 36 react with acid chlorides to produce a-acetylated phosphonoketene dithioacetals 37. In the case of acyclic dithioacetals 35 (R 3 = Et), the asilylated intermediates 36 were prepared in fair yields by addition of LiTMP to a mixture of 35 and TMSCl at -78°C, in order to prevent elimination of a thiolate anion. Replacement of acyclic dithioacetal in 35 by a cyclic dithioacetal (R 3 -R 3 = (CH2)2) provided, in the same experimental conditions, a better yield of a-silylated phosphonoketene cyclic dithioacetals 36 (81 %). Reaction of cyclic dithioacetals 35 (R 3 -R 3 = (CH2)2) with a mixture of acid chlorides (2 eq.) and

AlCl3 (2 eq.) in CH2Cl2 at 0°C for 1-3 h gives a-acylated phosphonoketene dithioacetals 37 in satisfactory yields (68-89 %). A comparative study between silylated 36 and unsilylated 35 phosphonoketenes dithioacetals has demonstrated that the a-trimethylsilyl substituent was essential to increase reaction rate and yields. 57 Scheme 14.

C. Trimethylsilyl as Protecting Group

In the carbanionic route, lithiated phosphonates 38 on reaction with electrophiles having electron withdrawing group (EWG-X) produce new species 40 containing a more acidic methylene group. Consequently, the initially formed carbanion 38 undergoes a facile transprotonation by the new species 40 to produce a substituted lithiated carbanion 39 which can in turn undergo further reactions. The resulting crude product is unavoidably a complex mixture of expected 40, starting 6 and undesired phosphonates which cannot be usefully separated (Scheme 15). 43 These disadvantages are overcome when a proton of the methylene group is replaced with a trimethylsilyl group which stabilizes the adjacent carbanion and control its reaction with electrophiles. Removal of the trimethylsilyl group as trimethylsilanolate or fluorotrimethylsilane results in formation of functionally substituted phosphonates. Each of the steps of this reaction sequence may be conveniently executed in one pot without the isolation of intermediates.

Scheme 15.

Together with these innovations, the use of a-silylated phosphonate carbanions has become one of the most useful and general method available for the synthesis of pure diethyl amonohalogenoalkylphosphonates 44 in high yields. Two different procedures may be employed for the obtention of a-monohalogenomethylphosphonates, one by nucleophilic phosphonohalogenomethylation of substrates (Scheme 16), 9,[58][59][60][61][62][63] the other by electrophilic halogenation of phosphonates (Scheme 17). [64][65][66] The former, using trihalogenomethylphosphonates as starting materials, has been developed for fluorine and chlorine substituents, whereas the latter, which appears to be fairly general, has greater synthetic utility and has been employed for the four halogens.

Scheme 16.

Diethyl trihalogenomethylphosphonates 41 were submited to a double halogen-metal reaction with n-BuLi in the presence of TMSCl to give the diethyl 1-lithio-1-halogeno-1-(trimethylsilyl)methylphosphonates 42. Under these conditions, the resulting stable carbanions 42 undergo safely alkylation reactions leading to trisubstituted phosphonates 43. Owing to the presence of activating atoms (F, Cl), the C-Si bond is very sensitive and the trimethylsilyl group easily eliminated with EtOLi in EtOH to produce the substituted a-monofluoroor amonochloroalkylphosphonates 44 in high yields and free of byproducts (Scheme 16). 9,[58][59][60]63 Scheme 17.

In the second approach, the substituted diethyl 1-lithio-1-(trimethylsilyl)methylphosphonates 7 (R = Et) result from a double proton-metal exchange from the corresponding phosphonates 6 (R = Et) with LDA in the presence of TMSCl. At low temperature, these carbanions undergo halogenation at carbon with commercial electrophilic halogenating reagents: Nfluorobenzenesulfonimide (NFBS), hexachloroethane, dibromotetrachloroethane or dibromotetrafluoroethane and iodine to give cleanly the quantitative formation of the halogenated derivatives 43. After removal of the trimethylsilyl group with EtOLi in EtOH, the diethyl a-monohalogenoalkylphosphonates 44 are isolated in pure form and practically quantitative yields (Scheme 17). [64][65][66] The electrophilic halogenation can be coupled with the phosphate-phosphonate transformation to provide a convenient one-pot procedure applicable for the construction of amonohalogenoalkylphosphonates 44 bearing widely varied alkyl appendages R 1 (Scheme 18). 66 Thus, the addition of alkyllithiums, R 1 Li, to triethyl phosphate 45 proceeds as expected to give the intermediate diethyl 1-lithioalkylphosphonate 38 (R = Et) which was subjected to sequential silylation and halogenation to afford the monohalogenated derivatives 44 in 85-97 % yields after desilylation. The overall result is that prior nucleophilic substitution of triethyl phosphate with alkyllithiums constitutes a route to diethyl a-monohalogenoalkylphosphonates 44. 66 The principle of protection of a proton of the methylene group by the trimethylsilyl has been applied to the preparation of functionalized tetraethyl methylenediphosphonates. 67 The extension of this work provides an efficient method for the incorporation of deuterium into phosphonates 51. 68,69 Deuteriolysis with heavy water of functionalized dialkyl 1-lithio-1-(trimethylsilyl)methylphosphonates 7 (R = Et) followed by desilylation with LiOD generated in situ was effected with a number of compounds 50 containing a variety of functional groups R 1 including alkyl, aryl, heteroaryl, thioalkyl, thioaryl, halogen, phosphoryl, etc... Incorporation of deuterium and chemical yields are good to excellent, and the reaction conditions are mild enough to preserve functionality at phosphorus (Scheme 20). 68,69 Scheme 20.

Another illustration of the advantages of trimethylsilylphosphonate reagents is provided by the transformations involving the readily available diethyl 1-(trimethylsilyl)vinylphosphonate 52. 37,70 This one has been found to be a valuable reagent for the facile conversion of vinylphosphonates into alkyl-, 37 alkenyl-, 37 b-keto-70 and b-amidophosphonates 70 in high yields. Owing to the trimethylsilyl group, which activates the vinylphosphonates towards the nucleophilic addition of organometallic reagents by virtue of its polarizing effect, Grignard reagents R 2 MgX, as well as alkyllithiums R 2 Li, add to the double bond at low temperature to give stable carbanions 53. They undergo a variety of reactions with electrophiles as alkyl halides, 37 acid chlorides, 70 carbonyl compounds 37 and isocyanates 70 to form functionalized diethyl 1-(trimethylsilyl)alkylphosphonates 54. All the intermediates 54 are successfully protodesilylated by TBAF in moist THF in near quantitative yields to give the functionalized phosphonates 55 (Scheme 21).

Scheme 21.

Recently it has been reported that the presence of TMSCl significantly enhances the rate of the conjugate nucleophilic addition of cuprates (R 2 2CuLi with R = Me, n-Bu, s-Bu, Ph) to 1alkenylphosphonates. The study has shown that the rate of nucleophilic addition of dimethylcuprate to diethyl 1-propenylphosphonates 56 was at least ten times faster at -78°C in the presence of TMSCl than in its absence. A typical reaction between cuprate and 1alkenylphosphonate in the presence of TMSCl was complete in half an hour at -78°C whereas only traces of diethyl 3-methylbutylphosphonate 57 were observed after three hours in the absence of this reagent. A common by-product of the additions to diethyl vinylphosphonates was the a-silylated phosphonate 58 whose formation occurs subsequent to the nucleophilic addition (Scheme 22). 71

Scheme 22.

Other applications of 1-(trimethylsilyl)methylphosphonates include the reaction with bielectrophilic reagents for the preparation of three-, four-, five-and six-membered cycloalkylphosphonates 61. 72 The diethyl trichloromethylphosphonate 23 is particularly well suited to this approach and the exchange of the three halogen atoms with n-BuLi followed by sequential addition of TMSCl and w-dibromoalkanes 59 results in the formation of a series of silylated cycloalkylphosphonates 60. The C-Si bond not being activated by the presence of an electron withdrawing group, the trimethylsilyl group of 60 was removed by the use of moist TBAF in THF solution (Scheme 23). 72 The same principle has been applied to the synthesis of phosphonates bearing two symmetrical or unsymmetrical, saturated or unsaturated, alkyl groups on the a-carbon atom. 73

6 .

 6 Scheme 6.

8 ,

 8 Scheme 8.

Scheme 10 . 11 .

 1011 Scheme 10.

Scheme 18 .

 18 Scheme 18.

Scheme 23 .

 23 Scheme 23.

C]-2,2-difluoroethene 13. In search of a 14 C-radiolabelled form of 1,1-difluoroethene, the fluoride ion-induced desilylation has been accomplished using diethyl 1,1-difluoro-1-(trimethylsilyl)methylphosphonate 11 and commercial [ 14 C]-formaldehyde in the presence of catalytic amount of anhydrous CsF (Scheme 7). The key intermediate 12 undergoes a H-W-E

Acknowledgments

We are grateful to ATO-FINA for financial support to B. I., to M. Multan from the Ecole Polytechnique (BCX) for assistance in collecting the literature and the Centre National de la Recherche Scientifique (CNRS).


A Facile and High Yielding Synthesis of Symmetrical and Unsymmetrical Diarylalkynes Using Diethyl Dichloromethylphosphonate as Precursor

Virginie Mouriès, Rachel Waschbüsch, John Carran, and Philippe Savignac

Hétéroéléments et Coordination, URA CNRS 1499, DCPH, Ecole Polytechnique, 91128 Palaiseau Cedex. Fax +33 1 69 33 39 90; e-mail dcph@poly.polytechnique.fr

The reaction, under internal quench conditions, of diethyl dichloromethylphosphonate and symmetrical or unsymmetrical diarylketones in the presence of n-BuLi, leads to the corresponding symmetrical or unsymmetrical diarylalkynes via a Fritsch-Buttenberg-Wiechell rearrangement in a simple, high yielding, onepot reaction.

We recently reported an efficient synthesis of dichloromethylphosphonate (1) 1 which is known as a useful precursor for the preparation of dichloroalkenes from carbonyl compounds on large scale. [2][3][4][5] As a component of another project we required preparative access to symmetrical or unsymmetrical diarylalkynes for [4+2] cycloaddition reactions. There are several methods reported in the literature [START_REF] Furber | Comprehensive Org. Funct. Group Transf[END_REF] for the synthesis of these type of alkynes and we will just mention the more relevant one. Diarylalkynes are currently prepared via an oxidative coupling between aryl or substituted arylhalides and cuprous acetylides in pyridine [START_REF] Castro | [END_REF][8][9] or with terminal alkynes catalyzed by palladium at elevated temperatures. 10,11 In the presence of cuprous iodide, the palladium-catalysed reaction proceeds under mild conditions and gives the diarylalkynes in good yield. 12 This methodology has been widely used in the preparation of a variety of functionalised diarylalkynes. [11][12][13][14][15][16] Another approach uses the formation of diarylalkenes obtained by a Wittig-Horner reaction from arylmethylphosphonate esters and the corresponding aldehydes. After bromination of the alkenes and an elimination, effected with a base, the diarylalkynes are isolated. A recent preparation of dipyridylalkynes uses this process. 17 In the same way, 1-chloro-1-arylmethylphosphonate has been introduced as an efficient reagent for the synthesis of phenylpyridylalkynes. 18,19 It is known that alkynes can equally be obtained through the Fritsch-Buttenberg-Wiechell rearrangement (1894) with 1,1dibromoalkenes as starting materials. [20][21][22] The reaction proceeds through the formation of an alkylidene carbene intermediate produced by an α-elimination of the 1,1-dibromoalkene O (EtO) 2 P Cl H Cl (Scheme 1). However, as recently reported, the reaction is frequently non-specific, giving mixtures of compounds. [23][24][25]

Scheme 1

We wish to report the generation of symmetrical and unsymmetrical diarylalkynes in a onepot synthesis from 1 and symmetrical or unsymmetrical diarylketones in a Fritsch-Buttenberg-Wiechell rearrangement (Scheme 2). As previously described in our synthesis of chloroalkynes and terminal alkynes 1 we use internal quench conditions. Simultaneous addition of 1 and the prospective ketone (2) to LiHMDS in THF solution at low temperatures leads to a phosphorylated carbanion which is only present for a short duration before it reacts with the ketone (2) to give the non-isolated gem-dichloroalkene (3). These conditions thus eliminate the possibility of decomposition of the phosphorylated carbanion to unwanted products. The reactions are easily monitored by 31 P NMR spectroscopy as on warming to room temperature the end of the first stage of the reaction is signalled by a single lithiophosphate peak ( 31 P NMR δ (THF) +0.4 ppm). Next, the reaction medium is cooled to -60°C and two equivalents of n-BuLi are added followed by slow (40 min) warming to 0°C. This procedure gives the carbene (4) which rearranges to give the required products (5). Occasionaly the reaction mixture is observed to have a brown colouration but this does not affect the result of the experiment. Neutral hydrolysis followed by ethereal extraction and subsequent drying, filtration and evaporation leads to a crude product which is practically free from impurities as observed by 1 H and 13 C NMR spectroscopy. Filtration of a hexane solution of the alkyne through a silica plug gives the pure title compounds, in cases where the alkyne is not soluble in this solvent then trituration with hexane yields the pure product. We first attempted the reaction using benzophenone and obtained a 95% yield of diphenylalkyne 5a on preparative scale, free of any side products. The success achieved in the Fritsch-Buttenberg-Wiechell rearrangement of 1 with benzophenone prompted us to investigate the reaction of 1 with a large variety of symmetrical and unsymmetrical diarylketones and to study the scope and limitations of the procedure. All the ketones used are commercially available or prepared according to known methods.

R 1 R 2 X X B - R 1 R 2 R 2 R 1 R 1 ,R 2 ≠ H Scheme 2
It was of interest to explore the effect of the steric bulk of the ketone in the reaction. This was demonstrated by experiments with three ketones of decreasing steric bulk. Thus, 2,2',4,4',6,6'-hexamethylbenzophenone and 2,4,6-trimethylbenzophenone do not react at all however 2,2'-dimethylbenzophenone reacts completely to give the corresponding alkyne 5d in good yield.

We verified that treatment of 3 with excess of n-BuLi (2 eq.) was necessary in the second step of the reaction to form the acetylenes 5. In the presence of only one equivalent of n-BuLi, this reacts at first with the HMDS present from the first step to reform LiHMDS in preference to a halogen exchange reaction, despite the presence of the two chlorine atoms. The gemdichloroalkenes can be recovered in quantitative yield in this case. We also established that at low temperature, the second step of the reaction involving the halogen-metal exchange is fast whereas the formation of carbene is slow. Performing the reaction using benzophenone as ketone we obtained gem-dichloroolefin 3 as usual, then addition of n-BuLi (2 eq.) gives, after 45 min at -80°C, a 60 : 40 ratio of vinyl (6) to acetylenic product (5a) after ethanolysis. With 4,4'-dichlorobenzophenone addition of n-BuLi gives, after 5 min at -85°C, a 87 : 13 ratio (vinyl to acetylenic). Finally, after the addition of n-BuLi we maintained the temperature at -90°C for 5 min before ethanolysis and obtained, after normal workup, the gem-diarylmonochloroolefins 6 (in 50 / 50 E+Z mixture in the case of 5f) described in Table 2 as the sole products. Thus the formation of the carbene intermediate 4 is a slow process which occurs at temperatures higher than -80°C. This experimental evidence is also aided by the observation that at -90°C after n-BuLi addition, the reaction mixture remains colourless. In conclusion we have presented in this paper a useful method for the preparation of symmetrical or unsymmetrical diarylalkynes 5. This facile, one-pot reaction starting from the versatile reagent 1 works well with a wide range of diaromatic ketones and a variety of substituents are tolerated under the reaction conditions. The simplicity of the experimental procedure, and the high yields obtained make this approach attractive. With a small variation in reaction conditions a variety of monochloroolefins 6 have been prepared.

Scheme 3

(i) (ii) R 1 R 2 Cl H 6 f 4-MePh Ph i 4-MeO-Ph 4-MeO-Ph j 4-Cl-Ph 4-Cl-Ph 6 R 1 R 2 LiHMDS 2 R 1 R 2 O -78°C to r.t. 1 +
for singlet, doublet, triplet, quadruplet and multiplet respectively. Organic solvents were purified by standard procedures. THF was distilled under an inert atmosphere from purple solutions of sodium-benzophenone ketyl.

The synthesis of all compounds was carried out under dry nitrogen.

Synthesis of diarylalkynes 5; General procedure:

n-BuLi (14 ml of 1.6M solution in hexane, 22 mmol) is added to THF (20 ml) and cooled to -78 °C. A solution of HMDS (3.90 g; 24 mmol) in THF (20 ml) is then slowly added at this temperature via a dropping funnel. The reaction mixture is then allowed to slowly warm to 0°C before once again cooling to -78 °C. A mixture of diethyl dichloromethylphosphonate (4.42 g; 22 mmol) and the diaryl ketone (20 mmol) in THF (50 ml) is then slowly added to the reaction mixture maintaining the temperature at -78 °C. Stirring is continued at this temperature for 10 min. and then the reaction is allowed to warm to 0°C over a period of 30 min. The reaction mixture is cooled to -60 °C and n-BuLi (29 ml, 46 mmol) is added. The brownish reaction mixture is then left to warm to 0 °C over a period of 30 min. H 2 O (20 ml) is then added to the reaction mixture with rapid stirring and the mixture is extracted with diethyl ether (3 x 30 ml) and the ethereal extractions are washed with H 2 O (2x20ml) then with 2M HCl (3 x 5 ml) before drying (MgSO 4 ), filtration and evaporation to yield the crude title compounds. These can be purified further by filtration through a silica plug using hexane as eluent or trituration with dry hexane or column chromatography .

Synthesis of gem-diarylchloroolefins 6; General procedure:

As above except that the second addition of 2 equiv. of n-BuLi is carried out at -90 °C and the reaction mixture is kept at this temperature for 5 min before ethanol (10 ml) is added at -90 °C. The reaction is then worked up as above.

  NMR spectra were recorded on a Bruker AC 200 spectrometer operating at 200 MHz for proton, 50.3 MHz for carbon and 81.01 MHz for phosphorus. 31 P downfield shifts (δ) are expressed with a positive sign, in ppm, relative to external 85% H 3 PO 4 in H 2 O. 1 H and 13 C chemical shifts (δ) are reported in ppm relative to CDCl 3 as internal standard. Coupling constants (J ) are given in Hz. The following abbreviations are used: s, d, t, q, m

Table 1 .

 1 Alkynes 5

	Product ref.	Yield (%)	mp (°C)	1 H NMR (250 MHz, CDCl 3 ): δ, J (Hz)	13 C NMR (250 MHz, CDCl 3 ): δ	m/z (FAB) M +
	5a 8	95	(m, 2H, Ar-H). 57-59 7.3-7.4 (m, 3H, Ar-H), 7.42-7.6	C), 129.00 (Ar-C), 132.28 (Ar-C) 90.04 (∫C), 123.91 (Ar-C), 128.93 (Ar-	178
	5b 26	89	oil	(m, 3H, Ar-H), 7.42-7.55 (m, 2.68 (s, 3H, Ar-CH 3 ), 7.23-7.4	123.63 (Ar-C), 124.15 (Ar-C), 126.21 21.3 (CH 3 ), 89.04 (∫C), 94.05 (∫C),	192
				3H, Ar-H), 7.61-7.73 (m, 3H,	(Ar-C), 128.76 (Ar-C), 128.94 (Ar-C),
				Ar-H)	130.07 (Ar-C), 132.1 (Ar-C), 132.43
					(Ar-C), 140.71 (Ar-C)

Table 2 .

 2 Chloroolefins 6

	Product Ref.	Yield (%)	mp (°C)	1 H NMR (250 MHz, CDCl 3 ): δ, J (Hz)	13 C NMR (250 MHz, CDCl 3 ): δ	m/z (FAB) M +
	6f 36	84	oil	2.4 (s, 3H, ArCH