Joulia Salloum

Romain Léger

Hussein Chebbo

Loïc Daridon

Patrick Ienny

A new methodology for the mechanical behavior analysis of PVC and recycled PET foams: Finite element model updating using mechanical field measurements

Keywords: FEMU method, PVC foam, recycled PET foam, Sandwich composite materials, intrinsic properties

This paper aims to characterize the intrinsic mechanical behavior of an eco-friendly foam core used in sandwich materials dedicated to the maritime sector. A thorough understanding of intrinsic properties is essential for accurate dimensional structure characterization. The model setup is based on the choice of materials that meet the criteria of sustainable development, mechanical performance, and durability to promote ecological practices in the nautical industry. Experimental tests, instrumented by a digital image correlation technique, were carried out on two types of foams: polyvinyl chloride (PVC), which is the reference foam traditionally used in marine applications, and recycled polyethylene terephthalate (rPET), the substitute foam. The sample sizes recommended by compression test standards often lead to complex stress states that do not allow direct determination of the foam's intrinsic mechanical properties. Therefore, a finite element model updating method was required to identify the anisotropic elastic behavior of these two types of foams.

Introduction

Like most materials used for structures, sandwich materials are no exception to the current trend to replace traditional components with more eco-friendly counterparts. The difficulty in this substitution often comes from the inferior mechanical properties of the substitute materials, which calls into question the dimensioning of structures. The research project herein aims to define simple rules for designing sandwich materials based on eco-friendly materials for applications in the nautical field. The design is therefore based on the choice of environmentally friendly materials that can offer similar mechanical properties compared with traditional sandwich materials. In this paper, the core material is the one that will be studied. As such, polymer foams are often used as the core material of the sandwich structure.

Commercially available polymeric foams for structural applications are polyvinyl chloride (PVC) foams, polyurethane (PU) foams, and polyethylene terephthalate (PET) foams.

Polymer foams belong to the class known as solid foams, which are versatile materials [START_REF] Testouri | Highly structured polymer foams from liquid foam templates using millifluidic lab-on-a-chip techniques[END_REF].

They are also called cellular materials, where their porous solid structure comprises pores or cells filled with a gaseous phase [START_REF] Pérez-Tamarit | Multi-scale tomographic analysis of polymeric foams: A detailed study of the cellular structure[END_REF]. Polymeric foams, being thermoplastic materials, can be manufactured by different manufacturing processes: injection foaming, extrusion foaming, and gelation [START_REF] Dabo | Ad-hoc modeling of closed-cell foam microstructures for structure-properties relationships[END_REF]. All these foam manufacturing processes are carried out using the same steps to create their cellular structure. Generally, the compressive strength of polymeric foams is higher than their tensile strength (4)(5)(6) [START_REF] Rizov | Elastic-plastic response of structural foams subjected to localized static loads[END_REF] because their cellular structure is better suited to withstand compressive rather than tensile forces. Accordingly, in most cases, polymeric foams are mainly loaded in compression. In the case of this loading mode, the homogeneous equivalent macroscopic mechanical behavior can be described by three main stages [START_REF] Youssef | Finite element modelling of the actual structure of cellular materials determined by X-ray tomography[END_REF]: an initial linear elastic domain characterized by an equivalent elastic stiffness modulus and an equivalent transverse contraction coefficient, a plateau domain that can be described phenomenologically by yield stress and strain hardening slope, and finally, a densification domain, where the material exhibits volume type behavior. Francisco et al. [START_REF] Francisco | Study of an Anisotropic Polymeric Cellular Material Under Compression Loading[END_REF] studied the mechanical behavior of closed-cell PVC foam under compressive loading. They observed that heterogeneity and anisotropy greatly influence the mechanical response of this material studied under different directions of compressive loading. For example, the yield stress and the compressive modulus are higher in the thickness or longitudinal direction of the foam (out-of-plane) than that in the transverse direction (in-plane). Luong et al. [START_REF] Luong | Compressive properties of closed-cell polyvinyl chloride foams at low and high strain rates: Experimental investigation and critical review of state of the art[END_REF] studied the compressive properties of closed-cell PVC foam for different densities. As a result of their work, the density of the foam influences the force values at the peak and the plateau after the elastic part: foams with higher density offer better mechanical properties. Viana and Carlsson [START_REF] Viana | Mechanical Properties and Fracture Characterization of Cross-Linked PVC Foams[END_REF] concluded that cross-linked PVC foams with different densities have an almost isotropic behavior. This result was based on a study conducted by the authors to determine the mechanical properties (stress-strain response) and the fracture behavior of these materials.

The study mainly consisted of tensile tests and a comparison of the stiffness modulus obtained along the two longitudinal and transverse directions. Volnei Tita et al. [START_REF] Tita | Experimental analyses of the poly(vinyl chloride) foams' mechanical anisotropic behavior[END_REF] studied the anisotropic mechanical behavior of polyvinyl chloride (PVC) foams with a density of 60 kg/m 3 (Divinycell H60). This study discussed the challenges of assessing the mechanical properties of foams due to their anisotropy and heterogeneity [START_REF] Espadas-Escalante | Anisotropic compressive properties of multiwall carbon nanotube/polyurethane foams[END_REF], [START_REF] Hamilton | Evaluation of the anisotropic mechanical properties of reinforced polyurethane foams[END_REF]. It was shown through experimental analysis how the foam's microstructure affects its mechanical behavior using both compression and tensile in two material directions, longitudinal and transverse. It was shown that the studied foam was transversely isotropic. However, the mechanical properties can vary significantly depending on the loading direction and the testing method, whereas the material's microstructure also affects the phenomenological response, failure mechanisms, and hardening curves. Many research articles have discussed collecting or estimating material properties for cellular materials, particularly for compression loading, using standardized methods [START_REF] Viana | Mechanical Properties and Fracture Characterization of Cross-Linked PVC Foams[END_REF], [START_REF] Juntikka | Shear characterization of sandwich core materials using fourpoint bending[END_REF]. Much work has been done to study the mechanical behavior of polymeric foams, either on their experimental or numerical mechanical characteristics, such as the work of ( 5),( 7),( 16), ( 17), [START_REF] Tita | Numerical simulation of anisotropic polymeric foams[END_REF], [START_REF] Bilkhu | Material Modeling of Structural Foams in Finite Element Analysis Using Compressive Uniaxial and Triaxial Data[END_REF]. However, none of these studies have led to the determination of the intrinsic parameters of the foams. Standardized tests concerning foams, mainly sandwiches, do not make it possible to directly identify intrinsic properties due to the geometry of the samples. These tests are most often conducted under multiaxial stress conditions due to the thin thickness of the foams, and the boundary conditions used in these tests are often not designed to ensure being in a homogeneous stress state. As a result, the data used by ship designers is approximative and, therefore, leads to oversized structures. As a viable solution, interpreting these tests requires numerical finite element modeling. This paper aims to determine, by a finite element model updating (FEMU) method (20)(21) [START_REF] Ienny | Dissipative behaviour analysis of reprocessed polyethylene terephthalate using digital image correlation and updated finite element analysis[END_REF], the intrinsic elastic parameters of two types of foams: a regular PVC and a rPET, both having a density of 80 kg/m 3 , in order to study the potential substitution of the former with the latter, thus providing a more environmentally friendly and sustainable alternative.

Materials and methods

PVC and recycled PET foams

Two types of foams, a polyvinyl chloride (PVC) foam of commercial name "AIREX C70" and a recycled polyethylene terephthalate (rPET) foam of commercial name "ArmaForm Core" were studied in this paper. The PVC foam represents the reference material to be substituted by the rPET foam. Both are closed-cell foams with the same 80 kg/m 3 density. A summary of their different characteristics, taken from their technical sheets, is given in Table 1. These two foams are in the form of large rectangular plates having a thickness of 15 mm. The large sheets of rigid closed-cell foams were cut using a mechanical saw to prepare the specimens. However, these do not correspond to simple uniaxial compression tests but to triaxial compressions tests that do not directly lead to determining the intrinsic properties of the foams studied herein. In addition, it is essential to consider the representativity of the volume occupied relative to the pore size. If the specimen is too small compared to the pore size in the foam, it may result in a large dispersion in the compression measurements. Therefore, scanning electron microscopy (SEM) was used to verify the pore size in both foams. It helped to ensure that the specimen dimensions were appropriate for the pore size, and accordingly, The pore size of the rPET foam was observed to be larger than that of PVC. Indeed, for both foams, the average area of the pores was calculated using ImageJ software, and the results are displayed in Figure 2 along the three normal directions, , , and , representing length, width, and thickness or height of the foam, respectively. The dimensions of the chosen specimens for compression tests were deemed sufficient compared to the pores' size, thus ensuring that the experimental test results would be representative and accurate. As an additional observation, the pore size isotropy observed for PVC does not seem to be obtained for rPET. Based on these explanations, multiaxial compression tests were carried out on 15x15x15 mm 3 cubic specimens along two directions: the axis (in the thickness) and the axis, as shown in Figure 3 (i). The correspondent apparent stiffness modulus and the apparent transverse contraction coefficients are obtained in both directions. These tests confirm the transverse isotropy assumption discussed in the literature ( 12), as they cannot determine the foam's intrinsic elastic properties. In addition, to complete the triaxial stress conditions, the transverse dimension of 15 mm was extended to 30 mm and then 60 mm. However, a uniaxial compression test can still be performed on the foam along the or axis direction by sectioning the specimen to have a length greater than two times the width, and the thickness, respectively, thus enabling a uniaxial stress state along this direction. Accordingly, specimens of 15x40x15 mm 3 were cut to carry out uniaxial compression tests along the axis direction (Figure 3 (ii)). It is worth noting that no uniaxial compression tests along the axis direction were made. The rationale behind this decision will be explained later in this paper.

Figure 3: (i) Triaxial compression test along the and axis, (ii)Uniaxial compression test along the axis (F1 and F2 indicates faces observed with cameras).

Shear tests on foams

Shear tests were carried out on the two types of foams based on ISO 1922:2018 standards. To be able to perform these shear tests using the MTS Criterion C45.105 machine, the samples were prepared by bonding four steel sheets, each having dimensions of 100x40x5 mm 3 , with foam parts on both sides, as shown in

FEMU method

In the case of a sample with a width greater than its height undergoing a compression test, the stress state cannot be considered uniaxial compression. Instead, it is a multiaxial stress state, also known as a large compression test, which requires a numerical model to determine the intrinsic mechanical characteristics of the sample material. So, in this study, the FEMU method is used to identify the intrinsic elastic parameters of PVC and rPET foams based on the experimental data. This method updates the finite element model by adjusting its parameters until its resulting force response matches the experimental values. As such, the force response was used to achieve the minimization process, and the displacement values were used to define the boundary conditions. The model was created on Abaqus from a Python code with imposed different boundary conditions. A minimizing algorithm existing in Matlab called "fmincon" was used to recalibrate the model on Abaqus by comparing the calculated numerical values with the experimental measurements. Additionally, input parameters needed for this adjusting method are the specimen's dimensions, material properties (density and elastic parameters), and mesh size, while output parameters are only the adjusted elastic parameters. Further details on this method, including boundary conditions, are presented later in the Numerical elastic model section of the article. The element type used in Abaqus® is 3 degrees of freedom (DOF) hexahedral linear element.

Experimental results

Reproducibility of tests

Multiple tests were carried out to obtain reproducible results precisely by following standardized protocols and using calibrated equipment to conduct the different experimental tests to ensure the findings were valid and reliable. The findings' reproducibility was confirmed by replicating the experiments ten times. The graphs displayed in Figures 5 (i Although this paper primarily focuses on the elastic behavior of the foam, the yield stress is also an intrinsic quantity widely used in the design basis of components and structures. The experimental measurements of the apparent yield stress obtained are about 1.37 MPa and 0.78 MPa for PVC and rPET foams, respectively, meaning that substituting PVC with rPET would lead to an oversizing of the structure. Although the study of the collapsed part of the foam is not yet made, this observation could shed light on the differences in mechanical behavior between the two foams. Therefore, further research is needed to fully understand the mechanical behavior properties of both foams.

Triaxial compression tests

Considering that the foams studied in this paper have a thickness of 15 mm, compression tests were conducted on different sets of specimen dimensions. Three sets were tested in the thickness direction ( axis): a -15x15x15 mm 3 , b -30x30x15 mm 3 , and c -60x60x15 mm 3 .

Compression tests in the thickness (longitudinal) direction allow obtaining the apparent stiffness modulus . Ten samples were tested for each set of specimen dimensions (a-b-c).

Before proceeding to the analysis of the results, it is necessary to gain insight into the strain field calculations in material testing, whether a real and non-homogeneous strain field needs to be calculated or, in contrast, an averaged strain field is sufficient, i.e., "local approach" or "global approach" respectively. As such, the strain profile is plotted following compression tests on the three specimen sets (a-b-c), hence, ensuring that measurements are consistent and accurate and confirming a homogeneous strain field. An example of the different strain profiles, extracted from the elastic behavior zone, is shown in Figures 6 (i), (ii), and (iii), corresponding respectively for the specimen sets a, b, and c. Based on the obtained strain profiles for both foams, it can be demonstrated that the strain field is homogeneous. The magnification factor here is about 75 µm/pixel, and about 2 mm was removed from the borders while plotting the graphs to avoid edge effects. For the same material, the obtained apparent elastic modulus increased for each set of dimensions (a-b-c), as shown in Table 2.

This modulus is obtained through linear regression in the linear elastic part of the stress-strain curve by calculating its slope. As such, the slope of the linear elastic part between the strain values of about -0.0125 and -0.001 is highlighted in Figure 7. This difference in results depending on specimens' size, coming from the stresses' multiaxial nature, confirms that the standardized compression tests do not lead to identifying the foam's intrinsic characteristics. These apparent parameters will be used to initialize the identification procedure of the parameters by the FEMU method. Accordingly, compression tests were conducted along the axis direction (in the thickness) and along the axis direction on the cubic specimens (a-15x15x15 mm 3 ). These compression tests resulted in obtaining, in both directions, the apparent elastic modulus, which corresponds to the slope of the linear part of the stress-strain curve in the longitudinal direction. In contrast, the apparent transverse contraction coefficient ( or ) is, in absolute value, the ratio of the transverse strain measured in the direction perpendicular to the axis of solicitation on the longitudinal strain. Figure 7 shows an example of the longitudinal and transversal stress-strain curves of the compression test along the axis direction.

Figure 7: Stress-strain curves (calculation by the "global approach") of compression test in axis direction on PVC specimen (set a-15x15x15 mm 3 ).

Table 3 represents the different experimental apparent results obtained from the compression tests conducted following longitudinal and transversal directions on the set -a-of specimens. Following the compression tests conducted by subjecting the sample to longitudinal and transversal loading, the stress-strain curves obtained from the two adjacent faces (F1 and F2, as in Figure 3) of the specimen were plotted and compared, as shown in Figure 8. It was found that the transversal strain curves and , for both foams PVC and rPET, were almost superimposed, indicating that it can be considered an identical strain behavior whatever the transverse direction. This observation is consistent with the assumption of transverse isotropy where ( , ) represents the transverse isotropy plane. After this observation, a morphological study of the two types of foams was conducted.

Several morphological parameters were measured using both SEM and X-ray tomography techniques, such as the average pore area, the average circularity of pores, the pore count per area, and the ligament thickness. For instance, X-ray tomography was carried out on specimens of 6x6x6 mm 3 with a resolution of 3.89 for a total of 1390 obtained slices. The acceleration voltage and beam current of the X-ray tube were 50 kV and 115 μA, respectively. It is worth noting that all the obtained slices are normal to the direction. To obtain slices normal to the and directions, a reconstruction of the model using the ImageJ software was performed, followed by cross-sectional sections normal to the and directions. The average pore area was presented in the Materials and methods section of this article in Figure 2 to justify the choice of specimens' dimensions. In contrast, the other parameters are displayed in Figures 9 (i), (ii), and (iii) below. Following these morphological results, each parameter has an equal value in both normal directions, and , which differs from the value observed in the normal direction for both foams. Accordingly, this indicates that the two faces following normal directions, and , are morphologically identical. Therefore, these results confirm the previous result that both foams, PVC and rPET, have a transverse isotropic morphology along the normal direction. Consequently, the experimental compression tests and the morphological study results provide evidence for the validity of the transverse isotropy (along the axis) hypothesis in the tested foams herein.

Uniaxial compression tests

As previously discussed, the specimens can be cut along the or axis direction, allowing a uniaxial compression test to be performed. Since transverse isotropy along the axis has been validated, a uniaxial compression test along the and directions theoretically yields identical results. Accordingly, specimens of 15x40x15 mm 3 were cut to perform uniaxial compression tests along the axis direction (Figure 3 (ii)). It can be considered that the parameters obtained from these tests are intrinsic since the specimen is in a state of uniaxial stress, and therefore, there is no need to perform the FEMU method in this case. However, these parameters will be used to verify and validate the finite element model used to adjust the other elastic parameters. Table 4 represents the intrinsic elastic parameters measured.

Shear tests

Shear tests in the ( , ) plane were conducted on the two foams to identify the shear modulus . Using the DIC technique [START_REF] Ienny | Dissipative behaviour analysis of reprocessed polyethylene terephthalate using digital image correlation and updated finite element analysis[END_REF], was calculated for four observed faces (F1, F2 F3 and F4), resulting in an average value of about 24 MPa with a standard deviation of 1.6

MPa. This modulus is calculated using the formula (1), corresponding to half the slope of the linear part of the stress-strain curve in shear, in which and represent the shear stress and strain, respectively.

(

) 1
The shear tests carried out in this plane identified as an intrinsic elastic parameter, as the strain evolution profile, shown on the graph in Figure 10, is constant all over the specimen.

Therefore, the use of the FEMU method to adjust the shear modulus for this test is not needed. Since this shear test allowed determining an intrinsic property, other shear tests were also conducted but in the ( , ) plane, being the transverse isotropy plane. Once the intrinsic value of the shear modulus is determined, the Poisson's ratio can be calculated knowing that = , as the ( , ) is the transverse isotropy plane, and using the formula as follows:

(

The shear moduli and are shown in Table 5, as well as the Poisson's ratio . For the two foams, the Poisson's ratios resulting from shear tests (Table 5) and resulting from uniaxial compression tests along the axis direction (table 4) are equivalent.

Numerical elastic model

As mentioned earlier, based on the literature, PVC foams are transversely isotropic.

Accordingly, using this hypothesis, the compliance matrix of an elastic transversely isotropic material is given in the matrix form as written in the following linear elasticity relation:

(

The equation 4 below is obtained using Voigt notation:

The notations 1, 2, and 3 correspond respectively to the , , and axes. Knowing that for a transversely isotropic material where ( , ) is the isotropy plane: ;

;

. The determination of the compliance matrix is done by determining five elastic coefficients, or , , , , and . Based on this transversely isotropic hypothesis and given that the experiments determined four intrinsic elastic parameters, , , , and , the remaining elastic parameter is . The latter cannot be determined experimentally due to the limitations of the uniaxial compression theory, as previously explained in this paper. Therefore, a finite element model updating method was employed to determine this parameter by defining the material as a transversely isotropic where ( , ) is the isotropy plane.

Model dimensions and boundary conditions

A numerical method has been implemented to identify the intrinsic elastic parameters, experimentally established but considered apparent rather than intrinsic. A finite element model, as shown in Figure 11, was created on Abaqus, where two symmetries about ( , ) and ( , ) were applied. Displacements were applied to the boundaries according to the experiments. In other words, the imposed boundary conditions correspond to a state of triaxial compression, allowing the description of the compression tests carried out. The displacement along the axis on the top face of the sample generates the compressive force, whereas, on the bottom face, the displacement along the axis is blocked. On the other hand, a displacement on each of the two lateral faces was imposed to ensure a stress state identical to that obtained by performing the experimental test. These displacements are found following the calculation of the transverse strains by the image correlation method. The displacement applied on the face of normal , , and was calculated from the global strain , , and , respectively, and the width of the sample in this direction. Accordingly, these displacements are calculated as follows:

(5); ( 6);

Furthermore, this model has been linked to Matlab through Python to manage its input parameters easily. It will be explained in detail in the following section.

Optimization loop

To organize the recalibration method, an interface on Matlab was created. It was linked to the Python code by defining the input parameters in this interface (specimen's dimensions, mesh size, material properties, etc.). Moreover, a loop was also created in which the error between the experimental results and the numerical ones is calculated. This error is minimized after implementing it with the suitable other parameters in the minimizing function in Matlab. Once the minimal residual value is reached, the loop stops, and the intrinsic elastic parameters are obtained. These optimized parameters correspond to the minimal error possible. Although certain parameters have been identified intrinsically through experiments, they are also identified using this FEMU method. This identification enables the comparison between the values obtained both numerically and experimentally.

This method is a generalized approach for performing a finite element model updating method (FEMU) based on minimizing the error between the experimentally obtained results and numerical results for each set of input parameters. In this article, the materials under consideration are PVC and rPET foams. Since both foams present a homogeneous strain field, as shown in Figures 6 (i), (ii), and (iii), the FEMU method was used with a fixed single-element mesh parameter.

Numerical calculations

A sensitivity matrix for the adjusted elastic parameters was calculated. It was found that Young's moduli and are the influential parameters, as opposed to Poisson's coefficients and . The results of the sensibility matrix are shown in Table 6. The different compression tests along the longitudinal direction for the three sets of specimen dimensions (a, b, and c) and along the transverse direction were modeled to adjust the different elastic parameters. This adjustment requires calculating an average total error in force of these four tests simulated in parallel. As mentioned earlier, these numerical tests are conducted using displacement boundary conditions established from measured strain fields, and the average total error in force is thus the average of the force errors of the different compression tests in both directions. These force errors are calculated by summing the errors across all time points, where at each point on the curve, the numerical value is compared to the experimental value, and the resulting error is squared. The sum of all these squared errors yields the total error for each set of specimen dimensions. The error resulting from the compression test in the transverse direction was assigned a weight of 3, as only one set of specimen dimensions was tested in this direction, and the sensibility value of the modulus is about one-third of . Consequently, the average total error is calculated using the formula [START_REF] Youssef | Finite element modelling of the actual structure of cellular materials determined by X-ray tomography[END_REF].

Whereas represents the average total error, , , and correspond to the squared errors resulting from the longitudinal compression test on the sets of specimen dimensions a, b, and c, respectively. Moreover, is the squared error resulting from the compression test in the transverse direction. The adjusted parameters are displayed in Table 7, while an example of the total error evolution and the stress-strain curves are shown on graphs (i) and (ii), respectively, of Figure 12.

Analysis and discussions

Based on the graph (ii) of Figure 12, the green curve with the triangle pattern is drawn numerically using the apparent parameters found experimentally as input properties, while the blue curve with the dash pattern is drawn directly using the experimental values. On the other hand, the red curve with the square pattern is the one plotted using the adjusted parameters. The values in Table 7 correspond to the red curve in Figure 12. Since Poisson's coefficients were not found influential, their values displayed in Table 7 are not representative. This result is due to the fact that the FEMU method herein was realized based on adjusting force values. For instance, when this FEMU is performed based on displacement values, the Poisson's coefficients become influential, and their numerical values will therefore be representative [START_REF] Ienny | Identification from measurements of mechanical fields by finite element model updating strategies[END_REF]. But these two coefficients were already calculated, and their values were found intrinsic, as explained in the Triaxial compression tests and Uniaxial compression tests sections, as well as Young's Modulus . The latter validates the reliability of this adjusting method by comparing its intrinsic experimental value to the numerical adjusted one obtained. Experimentally, has a value of about 48.5 MPa with a standard deviation of 3.5 MPa and about 46.7 MPa with a standard deviation of 2.2 MPa for the faces F1 and F2, respectively, of the PVC specimens (Table 4). By comparing the numerical adjusted value of 48.1 MPa to the ones obtained experimentally and considering the standard deviation, obtained from both methods is found equal. By doing the same for the rPET foam, both the numerically and experimentally obtained are identical. This result allowed the validation and verification of the FEMU used herein. Hence, the value of Young's modulus is intrinsic and is equal to 74.4 MPa and 42.9 MPa for the PVC and rPET foams, respectively, while both are smaller than the values measured experimentally for the three sets of specimens' dimensions (a-b-c). This finding is logical and acceptable as the experimental properties are apparent. Thus, the experimental measurements are often subject to uncertainties and errors, leading to overestimation in the calculation of the material parameters. As such, the FEMU method tries to minimize the impact of such issues on the calibration process, resulting in smaller and more accurate adjusted values. On the other hand, the FEMU method relies on adjusting the parameters until the predicted response of the model matches the experimental measurements, assuming the model accurately represents the material's behavior. However, as the model may not be able to capture all the physical properties, the FEMU method results in smaller values of the parameters. Upon examination of the datasheets and the adjusted parameters, it was observed that the values in the datasheets are consistently higher than the adjusted values for both foams. These observations were consistent with the suggestions mentioned above that the standardized tests seem to precisely assume that the sample is in a uniaxial state of stress and thus calculate the various elastic parameters using the formulas of a uniaxial compression test. Since, in this study herein, the compression is not uniaxial, the consequent datasheet values obtained from these standardized tests contribute to an overestimation of the parameters.

Conclusions

This study identified the intrinsic elastic behavior of two polymer foams used as core materials for sandwich structures. This research was conducted based on an original method combining several experimental or numerical approaches. Digital image correlation (DIC)

technique was applied to determine the different strain values of each specimen for the different tests carried out. Accordingly, the experimental part led to determining some intrinsic parameters of the foam. Nevertheless, some parameters obtained are considered apparent due to the multiaxial state of stress found experimentally. These apparent properties, as well as morphological parameters, were used to validate the transverse isotropy behavior of the two foams PVC and rPET. After confirming this hypothesis, the study was completed by a FE model on Abaqus linked to a minimization function on Matlab, which resulted in identifying the intrinsic values of the other parameters. Moreover, the reliability of this method was tested by comparing one of its resulting parameters to the corresponding one from the uniaxial compression test conducted experimentally. A good correlation was found between numerical calculations and experimental results. This study will be complemented with a plastic characterization to establish the overall homogenized behavior of the foam.

  the compression tests conducted would represent the foam's properties. SEM visualizations at the same magnification along the thickness direction of PVC and rPET foams are represented in Figures 1 (i) and (ii).

Figure 1 :

 1 Figure 1: SEM results -(i) PVC foam, (ii) rPET foam.

Figure 2 :

 2 Figure 2: SEM results -Average pore area for PVC and rPET foams.

Figure 4 .

 4 A bio epoxy resin (SR InfuGreen 810 from the company Sicomin®) was used as a bonding agent. The test was conducted by applying a displacement on one side of the specimen and fixing the other. The crosshead speed was set to 10 mm/min. Images of the sample were taken during the test using the same setup as the one described in the Compression tests on foam section. The DIC technique was used to obtain the strain field and to calculate the corresponding shear modulus. Shear tests in two different planes, ( , ) and ( , ), were conducted on the two types of foam. For the tests in the ( , ) plane, four foam specimens measuring 40x40x15 mm 3 were prepared. In contrast, for the shear tests in the ( , ) plane, eight foam specimens measuring 15x40x15 mm 3 were cut due to the limitation of 15 mm in the direction. Figure4illustrates the setup of the bonded foam parts on the steel plates.

Figure 4 :

 4 Figure 4: (i) Shear test in ( , ) plane, (ii) Shear test in ( , ) plane.

  ) and (ii) below show an example of the reproducibility of the force-displacement curves for ten specimens (15x15x15 mm 3 ) for each foam (PVC and rPET) under compression loading. This result also confirms the choice of a test geometry representative of the material's morphology (REV).

Figure 5 :

 5 Figure 5: Force-displacement curves for 10 specimens (15x15x15 mm 3 ) -(i) PVC, (ii) rPET.

Figure 6 :

 6 Figure 6: Strain profiles obtained by the "local approach" -(i) set a, (ii), set b, (iii) set c.

Figure 8 :

 8 Figure 8: Stress-strain curves for triaxial compression test along axis -PVC and rPET,

Figure 9 :

 9 Figure 9: X-ray tomography and SEM results -(i) Pore count/36 mm 2 (ii) Average circularity

Figure 10 :

 10 Figure 10: Shear specimen and strain profile ( , ).

Figure 11 :

 11 Figure 11: FE model and boundary conditions.

Figure 12 :

 12 Figure 12: (i) Total error evolution, (ii) Stress-strain evolution for the set b of PVC

Table 1 :

 1 PVC and rPET foams' mechanical characteristics taken from supplier data sheets.

			Compression properties	Shear properties
	Foam	Density [kg/m 3 ]	Standardized test	Compressive Modulus [MPa]	Standardized test	Shear Modulus [MPa]
	PVC	80	DIN 53421 (superseded by ISO 844:2021) (23)	Average: 104 Minimum: 80	ASTM C393 (24)	Average: 30 Minimum: 24
	rPET	80	ISO 844:2021 (23) 57	ISO 1922:2018 (25)

. Compression tests on foams

	of conducting compression tests on such small specimens and the size of the representative
	elementary volume (REV) of the morphology of these foams. Consequently, compression
	Based on ISO 844:2021 standard, the compression tests were performed using a MTS tests were conducted on larger samples, as ultimately recommended in the standards.
	Criterion C45.105 machine equipped with a 1 kN load cell and instrumented by two CCD
	cameras to get the 2D full-field deformation measurements of the front and lateral faces of
	each specimen by digital image correlation technique. The cameras (SVS-Vistek
	svs2150XTLGEC model) equipped with 55 mm / F2.8 telecentric lens (Computar REC-M55
	model) were positioned in front of these faces to record images of resolution 1920 x 1080
	(pixel size 75 µm) at a sampling rate of 5 fps. The compression was carried out by applying a
	displacement on the top face of the specimen. The crosshead speed was set for each specimen
	to obtain a strain rate of 1.1 x 10 -2 s -1 . The evaluation of the in-plane strain tensors on each
	observed face of the sample by DIC technique was performed with a home-developed
	software called 'CinEMA' (22) which enabled the calculation of the different apparent elastic
	modulus and transverse contraction coefficients. The evaluation of the strain tensor at the
	sample surface is based on local least-squares adjustment, using a linear fit of the
	displacement field around the considered point contained in the suitable gauge length. Two
	gauge lengths have been defined depending on whether an average deformation (global
	approach) or a deformation profile (local approach) is measured over the entire surface of the
	sample. While the deformation profiles, analyzed by DIC, are associated with a 2 mm (30
	pixels) gauge length, the stress-strain curves are associated with a 14 mm (187 pixels) gauge
	length. The nominal stress is defined as the ratio between the uniaxial force recorded by the
	test equipment and the initial cross-sectional area of the sample. Sample dimensions are
	essential in such a study. The foam sheets used in this paper have a thickness of 15 mm, so to
	conduct a uniaxial compression test, specimen dimensions should have had a width less than
	or equal to half of its thickness, i.e., 7.5 mm. These tests are not feasible given the complexity

Table 2 :

 2 Experimental results -Stiffness apparent modulus .

			Apparent elastic modulus	[MPa]
		a-15x15x15 mm 3	b-30x30x15 mm 3	c-60x60x15 mm 3
	PVC	76.5	79.02	92.6
	Standard deviation	2.81	4.68	3.08
	rPET	40.6	45.6	53.6
	Standard deviation	6.03	9.05	6.79

Table 3 :

 3 Experimental elastic apparent properties of PVC and rPET foams (15x15x15 mm 3 ).

		[MPa]	[MPa]
	PVC	50.1	76.5	0.35	0.19
	Standard deviation	5.22	2.81	0.02	0.04
	rPET	19.7	40.6	0.35	0.15
	Standard deviation	5.9	6.03	0.07	0.07

Table 4 :

 4 Experimental intrinsic results of uniaxial compression along -axis.

			F1		F2
		[MPa]		[MPa]
	PVC	48.5	0.18	46.7	0.36
	Standard deviation	3.5	0.03	2.2	0.03
	rPET	18.9	0.16	15.1	0.21
	Standard deviation	4.2	0.02	3.8	0.05

Table 5 :

 5 Experimental intrinsic results of shear tests in ( , ) and ( , ) planes.

		[MPa]	[MPa]
	PVC	27	17.3	0.39
	Standard deviation	2.3	0.2	-
	rPET	12.2	8.02	0.18
	Standard deviation	1.7	1.04	-

Table 6 :

 6 Sensibility matrix for = 5%.

	Sensibility [%]	22.4	0.13	69.5	0.01

Table 7 :

 7 Numerical optimized elastic parameters.

		[MPa]		[MPa]
	PVC	48.1	0.18	74.4	0.36
	rPET	19.1	0.15	42.9	0.32

Acknowledgment

The authors would like to acknowledge the support provided by the Occitanie region in France and the WINDELO company for this project.


Benjamin Théron

Valentin Vaillant-Coindard

Cédric Balan

Yoann Rousselin

Jérôme Bayardon

Raluca Malacea-Kabbara

Pierre Le Gendre

Raluca Malacea Kabbara

Al and Zn phenoxy-amidine complexes for lactide ROP catalysis

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Phenoxy-imines (often abbreviated as FI) are among the most versatile ligands in coordination chemistry 1 and their complexes have found applications in many fields ranging from catalysis 2 to pharmacology, 3 molecular magnets, 4 or sensors. 5 Their ease of access and modularity allow to fine-tune the properties of the corresponding complexes according to the targeted application and thus to access very efficient systems. A more drastic modification of the FI ligand skeleton by replacing either the imine or the phenoxy group by another moiety has also led to extremely efficient systems, 6 sometimes even more efficient than the parent FI complexes. In this context, we have recently described a new variant of FI ligands that are phenoxy-amidines (FA type A, Fig. 1) and demonstrated their coordination ability. 7 One drawback, however, of A ligands is that the amidine function in the proligands (i.e. phenol-amidine AH) has a trans configuration that is not suitable for metal chelation, but it isomerizes upon coordination with the metal. This isomerization is slightly penalizing at the thermodynamic level and can lead to a more complicated coordination chemistry than expected. To address this problem, we have designed a phenoxy-amidine ligands (B) where the amidine function is oriented differently by being grafted through the nitrogen via a methylene spacer to the aryloxy unit. 8 We have shown that these ligands can form chelate complexes with Zn(II) and Al(III) while preserving the more thermodynamically favourable transconfiguration of the amidine. To further improve the scope of the FA ligand family, we envisaged a 3rd generation of FA ligands (C) for which the amidine function is directly linked to the aryloxy part through the nitrogen atom. Such ligands will form 5-rather than 6-membered metallacycles, which as previously shown by Chen and co-workers in FI series, can enhance the accessibility to the metal and improve catalytic activity. 9,[START_REF] Yasuhiko | FI ligands giving rise to 5-membered metallacycles have been used in olefin polymerization[END_REF] Removing the methylene linker between the aryloxy and the amidine fragments will also restore the conjugated character of the ligand. In olefin polymerization catalysis, it has been shown that the π-conjugated character of the FI ligands confers some "electronic flexibility" to the chelated metal active species, and this contributes to the good catalytic performance. 11 Moreover, the conjugated imine and aryloxy moieties generally produce a rigid, nearly planar chelated ring that helps control the coordination sphere around the metal and is certainly of importance in stereocontrolled processes. 2b One should also note, despite this is beyond the scope of this study, that the conjugated character of FI is a necessary Fig. 1 The different generations of phenoxy-amidine ligands condition for these ligands and their complexes to exhibit interesting photophysical properties for applications in sensors, organic electronics, etc. Herein, we present the synthesis of FA ligands of type C and their coordination chemistry toward Zn and Al. Schiff base Al and Zn complexes have been extensively studied as catalysts for the ring-opening polymerization (ROP) of cyclic (di)esters, such as lactide, to give biodegradable polymers. 2c,12 Therefore, we chose this benchmark reaction to test the efficiency of FA complexes.

Results and discussion

Synthesis of the proligands L1H-L6H.

The proligand L1H was readily prepared by adapting the procedure previously reported by Hofmann by reacting 2aminophenol and N,N-dimethylformamide dimethyl acetal for 10' at 50°C under microwave irradiation (Scheme 1, path a). 13 L2H was obtained through the ring opening of benzoxazole by pyrrolidine under solvent-free condition as described by Chang (Scheme 1, path c). 14 We have previously shown that the type-B FA ligands incorporating a phenyl group on the amidinecarbon (R = Ph) performs better regarding ROP control. 8 Attempts to synthesize analogous FA type-C ligands by reacting 2-aminophenol with the chloroiminium chloride generated from N,N-dimethylbenzamide and oxalyl chloride led to 2phenylbenzoxazole. We hypothesized that the phenol-amidine forms in these conditions but undergoes intramolecular cyclisation, as observed with the type-B FA ligand, although it was much slower in the latter case. 8 Likewise, reaction targeting a priori more robust FA ligand, with a larger t Bu group on the amidine-carbon and piperidine NR'2 moiety, also resulted in a cyclization product. On the contrary, reaction of 2-aminophenol with the chloroiminium chlorides prepared from 2methylbenzamide or 1-naphthylamide derivatives led to the phenol-amidine proligands L3H-L5H (Scheme 1, path b). Phenoxy-imines bearing an additional amine functionality have been used by Darensbourg,15 Shaver, 16 Lin, 17 Mehrkhodavandi, 18 Jones, 19 Mazzeo 20 and others to get highly active Zn-based catalysts in ROP of lactide. An analogous potentially tridentate FA ligand (L6H) with a pendant -(CH2)2NMe2 arm has been synthesized in one step and with 60% yield using the same strategy as for L2H, via the ring opening of benzoxazole by N,N,N'-trimethylethylenediamine. Suitable crystals for X-ray diffraction studies were obtained for the proligands L1H, L3H-L5H. ORTEP views are represented on Fig. 2. The amidine moieties in the four proligands exhibit a trans configuration, sp 2 character for the N2 nitrogen atom (ΣαN2 ≈ 360°) and a periplanar conformation (θ ≈ 0°) (Table 1). The conjugated character of the amidine group is also reflected by the ΔCN parameters (ΔCN = d(C-N) -d(C=N)) which are in the range 0.043 (16) to 0.052(2) Å. 21 The amidine plane is tilted by 126.4(1)≤|ψ|≤169.9(6)° with respect to the hydroxyaryl plane, and in the case of L3H-L5H, is almost orthogonal to the tolyl or naphthyl ring (80.0(9)° ≤|α|≤117.34(15)°). In addition, intermolecular H-bonds are observed in the solid state structures of L1H, L3H and L4H between the phenolic protons Scheme 1 Synthesis of L1H-L6H proligands. and the amidine-N atoms of two neighbored molecules oriented in a complementary pairing. The 1 H NMR spectra of L1H-L5H show only one isomer in solution which we assume to be the trans-isomer based on solid state structures. The other noticeable point is the number and shape of the NR'R" signal(s) in the 1 H NMR spectra of the proligands L1H-L2H versus those of L3H-L5H. The NMe2 group in L1H gives a broadened singlet at δ = 3.04 ppm (Δν½ = 10.93 Hz) whereas this signal in L3H is split into two sharper singlets at δ = 3.25 ppm (Δν½ = 6.86 Hz) and 2.75 ppm (Δν½ = 6.80 Hz). Similarly, the pyrrolidine protons appear as two broad signals in L2H whereas they give five well resolved multiplets in L4H and L5H. This discrepancy can be attributed to the presence of the aryl substituent on the amidine-carbon in L3H-L5H which impedes the rotation of the C-NR'R" amidine bond and make them non fluxional on the NMR time scale. The 1 H NMR spectrum of L6H in CD2Cl2 shows broad resonances for the methyl protons and two sets of broad signals for both the ethylene and formamidine protons. This observation could be explained by the presence of two rotamers resulting from the presence of two different substituents on the amidine moiety (NR'R") and from the restricted rotation of the amidine bond. Noteworthy, this spectrum becomes simpler in MeOD with only the splitting of the signal due to the methylene attached to the amidine group suggesting a faster interconversion of rotamers in this solvent. 22 Synthesis of the FA-Al complexes.

The proligands L1H-L6H were further reacted with one equivalent of AlMe3 in THF at room temperature for 2 hours (Scheme 2). The mono-ligated complexes thus formed were found to undergo redistribution, which prevented their isolation in pure form except in the case of 1a. Suitable crystals for X-Ray diffraction analysis were obtained for complex 1a and an ORTEP view is presented on Fig. 3. 1a exhibits a dimeric structure bridged by the O atoms of the aryloxy ligands and thus differs from previously reported 6-membered ring aluminum FA complexes that crystallize in monomeric form. 8 Other noticeable features are the relatively small O-Al-N angle (79.64( 4 Fig. 3 View of complex 1a (ORTEP, 50% probability ellipsoids; H atoms are omitted for clarity). For relevant bond distances and angles, see Table 2. gave rise to the formation of the bis-ligated complexes 1b-4b and 6b in 70-91% yields (Scheme 2). The complex obtained from L5H could not be isolated in an analytically pure form.

Alcoholysis reaction was conducted with 1b using one equiv. of i PrOH and afforded the alkoxy Al complex 1b'. The structure of complexes 1b-3b and 1b' were determined by X-Ray diffraction analysis (Fig. 4 & 5). Based on geometry indexes the geometries of 1b and 1b' can be best described as trigonal bipyramids (τ5(1b) = 0.69, τ5(1b') = 0.76) and those of 2b and 3b as intermediates between trigonal bipyramids and square pyramidal geometries (τ5(2b) = 0.51, τ5(3b) = 0.40). 23 Continuous shape measure values, 24 confirm the trigonal bipyramidal geometries for 1b and 1b' and

N2 C10 C8 C7 N1 C2 C1 O1 Al1 O1_$1 C11 Al1_$1 N1_$1 N2_$1
better match the trigonal bipyramidal geometries for 2b and 3b (See Table S95 in SI). The Al-Cmethyl distances (comprised between 1.970(2) and 1.980(2) Å) and Al-O distances (1.791(6) to 1.80(1) Å) are within the range of analogous FI complexes. 24 The Al-N distances (comprised between 2.07(3) to 2.163(10) Å) are within the longer ones described. The NR'2 moieties are slightly tilted relative to the amidine plane (6.9(2)°<|θ|<15.45(0.21)°), which itself deviates from the aryloxy plane (145. 42(3)°<|ψ|<156.8(1.2)°). In case of 3b, the bis-ligated complex can exist in the form of three pairs of enantiomers due to both atropisomer axial chirality, generated by the restricted rotation of Csp 2 -Csp 2 bond of the aryl moiety, and the chirality at metal (Fig. 5). The ORTEP view of 3b shows a disorder related to the position, either up or down, of one of the two methyl-tolyl groups, corresponding to the presence of two atropisomers in 3/1 ratio in the crystal (Fig. 5). 1 H NMR spectra of complexes 1b, 2b and 6b show diagnostic signals for the formamidine and Al-Me protons in the range 7.97-7.70 and -0.77--0.79 ppm, respectively. The bis-ligated complexes are chiral-at-metal which is reflected in the 1 H NMR spectrum of 1b' by the presence of two doublets for the diastereotopic isopropyl-methyl groups. VT-NMR experiment was conducted on 1b' (Fig. 6). When the temperature is raised, the signals of the isopropyl-methyl groups broaden and merge at 348(2.5) K (69.5(5) kJ.mol -1 ) consistent with the nonpersistence of the chiral structure. Within the same range of temperatures, one can also observe the coalescence of the NMe2 signals (Tc = 343(2.5) K, ΔG ‡ = 64.6(5) kJ mol -1 ) due to rotation about the amidine bond. The 1 H NMR spectrum of 3b in deuterated toluene at room temperature is more complicated and shows 3 sets of signals (Fig. 6), overlapping for some of them, and corresponding to the 3 possible enantiomeric pairs (Fig. 5). A progressive simplification of the Fig. 4 Views of complexes 1b, 1b', and 2b (ORTEP, 50% probability ellipsoids; H atoms are omitted for clarity). For relevant bond distances and angles, see Table 2. Fig. 5 Top: ORTEP view of complex 3b where both atropisomers are highlighted (disordered parts: 76%/24%). Thermal ellipsoids are drawn at 25% probability level. Disordered solvents and hydrogen atoms are omitted for clarity). Bottom: Representation of the three possible pairs of enantiomers for complex 3b. For relevant bond distances and angles, see Table 2. spectra was observed by raising up the temperature that we interpret as being due initially to the loss of the chirality at Al(Tc * = 308(5) K for the signal at 2.46 ppm, ΔG ‡ = 66(1) kJ mol -1 )and then to a free rotation of the NMe2 fragment around the amidine bond (Tc ** = 346.5(3.5) K, ΔG ‡ = 64.6(0.6) kJ mol -1 ). VT NMR experiment conducted on 3b in deuterated pyridine from 258 K to 383 K shows first a similar evolution, then the o-tolylmethyl signals broaden and approach coalescence at 383K (Tc *** >383 K, ΔG ‡ >82 kJ mol -1 ) (See SI, Fig S52 ). Noteworthy, complex 4b shows similar NMR behaviour than 3b. The nonpersistence of the chirality at the metal might be explained by decoordination-recoordination process, which was found to occur below 298 K in bis-ligated AlMe(FI)2 complexes. 25 Synthesis of the FA-Zn complexes.

Zn complexes were obtained via an alkane elimination route similar to that in Al series starting from ZnEt2 precursor and the proligand either in 1:1 or 2:1 ratio (Scheme 3). The heteroleptic complexes have a propensity for redistribution in solution which prevented in some cases their isolation in pure form. In fact, only complexes 1c, 2c, 5c and 6c have been isolated. The hetero-and homoleptic complexes were obtained in 40% to 93% yields and were characterized by NMR ( 1 H, 13 C, COSY, HSQC, HMBC), elemental analysis and for some of them X-ray diffraction. In the solid state, the heteroleptic complexes have a dimeric phenoxy-bridged structure and the homoleptic complexes have a spiro structure with the two FA ligands connected to the Zn atom in a C2 symmetric fashion. All the complexes adopt a distorted tetrahedral geometry around the Zn metal ion according to the geometry index τ4' ranging between 0.70 and 0.79 (Fig 7 and8). 26 In complexes 6c and 6d, the additional ethylene dimethyl 3. a : D = mean distance in between Zn atom and the aryloxy plane, b : θ (C8N2C7N1) and ψ (C7N1C1C2), c : the mean values of the two independent molecules are reported.

DOSY NMR experiment conducted on complex 1c shows that the dimeric structure is maintained in CD2Cl2 but not in deuterated pyridine as shown by the rather good fit between the hydrodynamic radii (rH), calculated from the diffusion coefficients measured in both solvents, and those estimated (r'H) from the solid state structure of the complex (CD2Cl2, 298 K, D = 11.5 x 10 -10 m 2 .s -1 , rH = 4.59 Å, r'H(dimer) = 4.46 Å / Pyridine-D, 298 K, Ð = 6.6 x 10 -10 m 2 .s -1 , rH = 3.76 Å, r'H(monomer) = 3.54 Å) (See SI, Fig S113 -S114). 1 H NMR spectra of complexes 1d and 2d show a split of the signals of the NR2 group due to more hindered motion about the amidine bond in the homoleptic complexes. NMR spectra of complexes 3d-5d in solution at room temperature were rather difficult to interpret due to the presence of several stereoisomers. NMR studies at variable temperatures were carried out for each of these complexes, showing a progressive simplification of the spectra when the temperature was raised up to 383 K (Fig. 9). Given the profile of the spectra, similar to those observed in Al series, we interpret this evolution as being due initially to the loss of chirality at Zn (Tc* = 303(5) K), then to the rotation of the NR'2 fragment around the amidine bond (Tc** = 323(5) K) and finally to the rotation around the Csp 2 -Csp 2 bond of the aryl fragment on the amidine carbon (Tc*** > 383 K). Interestingly, similar values were estimated from Eyring equation for the energy barriers for the epimerization at Zn and Al as for example in complexes 3b and 3d (pyridine-D, ΔG ‡ = 65(1) kJ mol -1 ). The 1 H NMR spectrum of complex 6d in CD2Cl2 shows sharp singlet at δ = 2.22 ppm (Δν½ = 3.92 Hz) for the NMe2 protons, and thus no diastereotopic splitting, indicating a bidentate rather than tridentate coordination mode of the FA ligands in solution.

ROP of Lactide.

The Al complexes were evaluated toward the ROP of rac-LA in toluene at 90 °C in the presence of isopropanol (Table 4). The dimeric complex 1a converted 94% of monomer, but the GPC analysis showed a bimodal profile, a large molecular weight distribution and a much smaller Mn than expected. For comparison, a previously reported 6-membered-ring (FA)Al complex, Al(Me)2(OC6H4(2-(CH2-N=C(H)NMe2))), gave similar performances ([LA]:[cat]:BnOH] = 100:1:1, toluene, 70 °C, 24 h, conv. 89% , Mnexp = 3500, Ð = 2.17). 8 The monomeric complexes 1b-6b showed slightly lower activities than 1a, but yielded PLAs with narrower dispersities and higher number average molecular weights. These Mn values remain, however, smaller than theoretically predicted, except in the case of 6b. Complex 1b' gave comparable ROP performance to the two components system 1b/ i PrOH and provided PLA chains terminated with isopropoxy end groups providing evidence that a coordinationinsertion mechanism is operating in these conditions (See SI, Fig. S116). Homonuclear decoupled 1 H NMR analysis showed slight isotactic bias in PLA produced from rac-LA using FA-Al complexes. In comparison with previous reports, the activities of 1b-6b (TOF = 3-4 h -1 ) are lower than that reported for an analogous pentacoordinated (FI)2AlMe complex (TOF = 12 h -1 ) reported by Milione in similar polymerization conditions. 25 The performances of the Zn complexes for the ROP in solution of rac-LA are reported in Table 5. Three FI-Zn complexes 7d, 28 8c, 17a and 8d 19 with and without an additional pendant amine arm, were synthesized for comparative purposes (Fig. 10). The polymerization of rac-LA (100 equiv.) have been conducted for 2 hours at 20-30 °C in CH2Cl2 and in the presence of i PrOH as coinitiator. Under these conditions, only the hetero-and homoleptic complexes 6c, 6d and 8c derived from FA and FI ligands with a pendant amine arm, led to high monomer conversions. SEC analysis of the resulting PLA showed chains with narrow dispersities and Mn values that match well with those predicted theoretically on the basis of monomer-catalyst ratio and conversion. Other heteroleptic complexes 1c, 2c and 5c produced also chain-length controlled and narrowly disperse PLA but with lower conversions (36-54%). These results differ from those obtained previously with 6-membered ring Zn (FA) complexes ([(OC6H4(2-(CH2-N=C(R)NR'2))Zn(Et)]2), which gave higher monomer conversions but broader dispersities, except for the FA ligand, which incorporates a phenyl group and a pyrrolidine on the amidine moiety. Heteroleptic FA Zn complexes thus appear to follow a trend opposite to that of FI complexes, for which five-membered ring systems show higher activity in ROP of ε-caprolactone than the six-membered ring Zn complexes. 27 The homoleptic complexes 1d-5d showed no activity for the ROP of rac-LA at 30 °C in the presence of i PrOH.

Complex 7d showed no activity at 30 °C in CH2Cl2 while 8d provided PLA with 52 % conversion after 2 h. Consistent with previous works in the literature, 20 these results highlight the crucial role of the additional amine arm for FI ligands and this generation of FA ligands in homoleptic Zn complexes to obtain an active ROP catalyst in solution. With regard to tacticity, it should be noted that FA-Zn complexes differ from their Al counterparts in producing PLA with a heterotactic rather than isotactic bias. Kinetic data for complexes 6c and 6d are gathered on Fig. 11 and show pseudo first order consumption of LA vs time with a higher rate constant for the heteroleptic complex (kapp = 0.030 ± 0.007 min -1 ) than for the homoleptic ones (kapp = . Left: First-order logarithmic plot for the polymerization of rac-LA at 25°C in CH2Cl2 using 6c (•) and 6d ( ▪ ) with i PrOH as initiators (100:1:1). Right: Mn and PDI against conversion associated with the kinetic studies of 6c (•) and 6d ( ▪ ) with i PrOH. 0.018 ± 0.003 min -1 ). A linear relationship between Mn values and the percentage of conversion of LA was also observed for both complexes and agree with well-controlled ROP processes. MALDI-TOF analysis of short PLA chains obtained after a short reaction time (40') using 6c and 6d in the presence of i PrOH as a co-initiator showed isopropoxy-terminated chains with a peak spacing of 144 Da and no intercalated peak due to secondary transesterification reactions. Nevertheless, a propensity for transesterification was observed for both complexes at higher monomer conversions (See SI, Fig. S117-S120). The zinc complexes were then tested under solvent-free conditions, which has the advantage of being closer to industrial PLA production conditions (Table 6). The four heteroleptic FA Zn complexes 1c, 2c, 5c and 6c, in combination with BnOH, yielded PLA after 10 min at 130°C with high conversions, moderate molecular weight control and broad molecular weight distributions (Ð = 1.85-3.15). Further reaction carried out with complex 6c and stopped after only 2 min led to a lower conversion but similar dispersity, ruling out the hypothesis that the lack of polymerization control was due to side transesterification reactions occurring at the end of the ROP process. Noteworthy, the heteroleptic FI Zn complex 8c showed similar performance in these conditions. The homoleptic complexes 1d-6d were all active for the ROP of rac-LA in bulk conditions at 130 °C. Complexes 1d and 2d with formamidinebased FA ligands were less active than complexes 3d-5d featuring an aryl substituent on the amidine carbon. Complex 6d, with two pendant amine arms, led to the highest activity. SEC analysis showed much narrower molecular weight distributions for the PLA chains obtained with the homoleptic Zn complexes than with the heteroleptic ones, but Mn values lower than predicted. Tests carried out in parallel with the homoleptic FI Zn complexes 7d and 8d, previously reported by Jones, show that the FA and FI Zn homoleptic complexes give similar performance. The most active initiator 6d was next tested in transfer chain conditions at lower catalyst loading ([LA]:[6d]:[BnOH] = 1000:1:10). Under these conditions, 6d afforded narrow disperse PLA chains with predictable Mn values and almost complete conversions of LA after 5 min at 130°C and after 2 min at 180°C.

Conclusions

In conclusion, the synthesis of FA ligands featuring a trisubstituted amidine N-linked to an aryloxy moiety is described. This new generation of FA ligands was found suitable to form chelate complexes with Al and Zn metal ions. Alkane metathesis route from the phenol-amidine proligand and aluminum or zinc alkyls was used and led to mono-ligated and bis-ligated complexes. The latter exhibit fluxional behaviour in solution, attributed to the hemilability of the FA ligand and the rotation around the C-NR'2 and C-Ar bonds of the amidine moiety. ROP catalytic tests of rac-LA in solution show that both Al and Zn complexes featuring FA ligands with a pendant amine arm perform best, following a similar trend to the parent FI complexes. On the other hand, the use of this new generation of FA ligands that form a 5-membered metallacycle rather than a 6-membered metallacycle did not contribute to improved ROP catalytic activities, contrary to what was previously observed in the FI series. However, these third-generation FA complexes are still quite competitive with their FI counterparts. Lastly, the homoleptic Zn complexes were successfully employed for ROP of rac-LA under free-solvent condition at 130-180°C and using BnOH as co-initiator. The best complex was again found to be complex 6d incorporating a pendant amine arm on the FA ligands, although the gap with other complexes was less significant in these harsher conditions.

Experimental

General consideration.

All reactions, except when indicated, were carried out under an atmosphere of argon using conventional Schlenk techniques and Ar glovebox. DCM, diethyl ether, THF, toluene, and pentane were dried using a MBRAUN SPS 800. HSQC and HMBC). Nomenclature: the positions of carbon and hydrogen atoms in FA ligands were labelled according to Fig. 12. The proligand L2H was synthesized according to previously reported procedure. 14 The synthesis of 7d 28 is described in SI (S59).

Synthesis of N'-(2-hydroxyphenyl)-N,N-dimethylformamidine L1H.

5 mL dichloromethane solution containing 250 mg (2.3 mmol) of 2-aminophenol and 274 mg (2.3 mmol, 1 equiv.) of DMF-DMA was heated in a microwave synthesis reactor for 10 minutes at 50 °C. The solvent was removed under vacuum to give L1H as an orange powder (358 mg, 95% yield). 1 H NMR (400 MHz, CD2Cl2, 298 K): δ (ppm) = 7.77 (s, 1H, H7), 6.91 (dd, J = 7.7, 1.5 Hz, 1H, H6), 6.90-6.84 (m, 1H, H4), 6.82 (dd, J = 7.9, 1.6 Hz, 1H, H3), 6.75 (td, J = 7.5, 1.7 Hz, 1H, H5), 3.04 (broad s (Δν½ = 10.9 Hz), 6H, NMe2). {

Synthesis of N'-(2-hydroxyphenyl)-N,N-pyrrolidinylformamidine L2H.

150 mg of benzoxazole (1.26 mmol, 1 equiv.) was totally dissolved in 210 µL of pyrrolidine (2 equiv.). We stirred at room temperature during 15 minutes. Then, the homogenous solution was dried under vacuum and to afford a white powder (235 mg, yield 98%). 1

Synthesis of N'-(2-hydroxyphenyl)-N,N-dimethyl-2methylbenzamidine L3H.

Under argon, 1.4 g (8.6 mmol) of 2-methylbenzamide was dissolved into 40 mL of dried toluene. 3.7 mL (43 mmol, 5 equiv.) of oxalyl chloride was then slowly added at 0°C. The solution was then allowed to reach r.t. and heated at 60°C overnight. Volatiles were evaporated and the crude whitish powder was washed with 3x30 mL of dried Et2O. The resulting chloroiminium chloride was solubilized again in 90 mL of dried CH2Cl2. 6 mL (43 mmol, 5 equiv.) of triethylamine were added and the mixture was cooled to 0°C. 938 mg (8.6 mmol, 1 equiv.) of 2-aminophenol were added and the solution was allowed to reach r.t. and stirred for 1 h. The volatiles were evaporated and the residue was taken back into 90 mL of diethyl ether. A 1M solution of HCl in diethyl ether was added until pH = 1 and the amidinium salt was then filtrated under vacuum. The solid was suspended into 30 mL of CH2Cl2 and aqueous NH3 was added until pH = 9-10. The solution was dried over MgSO4 and evaporated under vacuum. The crude product was purified by column chromatography on alumina using CH2Cl2 first, and then a 50/1 CH2Cl2/MeOH mixture, affording L3H as a pale orange solid (940 mg, 43% yield). 1

Synthesis of N'-(2-hydroxyphenyl)-N,N-pyrrolidinyl-2methylbenzamidine L4H.

1.65 g (8.7 mmol) of N,N-pyrrolidinyl-2-methylbenzamide were charged in a Schlenk tube and solubilized in 40 mL of dried toluene. 3.2 mL (37.4 mmol, 4.3 equiv.) of oxalyl chloride were added at 0°C. The solution was allowed to reach r.t. and then heated at 60°C overnight. After cooling the reaction mixture to r.t., 40 mL of dried diethyl ether were added and solvents were removed by filtrating cannula. The white solid was further washed twice with 40 mL of dried diethyl ether and then dried under vacuum for 5 h. The chloroiminium chloride intermediate was taken back in 80 mL of dried dichloromethane. 6.1 mL (43.5 mmol, 5 equiv.) of triethylamine and 949 mg (8.7 mmol, 1 equiv.) of 2-aminophenol were successively added at 0°C. The mixture was allowed to reach r.t. and stirred for 1.5 h before being hydrolyzed by 80 mL of distilled water. The product was extracted with dichloromethane and the organic phase was dried over MgSO4, before being evaporated under vacuum. The crude product was purified by column chromatography on alumina, using a 50/1 CH2Cl2/MeOH mixture as the eluent, affording L4H (1.6 g, 67% yield). 1 H NMR (600 MHz, CD2Cl2, 298 K): δ(ppm) = 7.27 (td, J = 7.5, 1.5 Hz, 1H, H4'), 7.23-7.17 (overlapping signals, 2H, H3' + H5'), 7.15 (dd, J = 7.5, 1.5 Hz, 1H, H6'), 6.74 (dd, J = 7.9, 1.5 Hz, 1H, H3), 6.66 (td, J = 7.6, 1.5 Hz, 1H, H4), 6.31 (td, J = 7.7, 1.5 Hz, 1H, H5), 6.03 (dd, J = 7.9, 1.5 Hz, 1H, H6), 3.73 (t, J = 7.0 Hz, 2H, Pyrr.), 3. 14-3.08 (m, 1H, Pyrr.)

Synthesis of N'-(2-hydroxyphenyl)-N,N-pyrrolidinyl-1naphthylamidine L5H.

This compound was prepared similarly to L4H starting with N,Npyrrolidinyl-1-naphthylamide (2.2 g, 11 mmol). L5H was isolated as an orange solid (1.9 g, 59% yield). 1

Fig. 2

 2 Fig.2Views of L1H, L3H-L5H (ORTEP, 50% probability ellipsoids; disorder is omitted for clarity) ) and definition of torsion angles θ, ψ and α. For relevant bond distances and angles, see Table1.

  Scheme 2 Synthesis of the FA-Al complexes.

Fig. 6

 6 Fig. 6 Top left: stacked 1 H NMR spectra (400 MHz, toluene-D8) of complex 1b' from 273 K to 353 K. Only the region from 0.7 to 3.6 ppm is shown. Top right: stacked 1 H NMR spectra (600 MHz, toluene-D8) of complex 3b from 298 K to 350 K. Only the region from 1.6 to 3.6 ppm is shown. Bottom: Dynamic behaviour of 1b' and 3b (loss of the chirality at Al (Tc*), rotation of the NMe2 fragment around the amidine bond (Tc**)).

Fig. 7 Fig. 8

 78 Fig.7Views of complexes 1c, 5c, 6c (ORTEP, 50% probability ellipsoids; H atoms are omitted for clarity). For relevant bond distances and angles, see Table3.

Fig. 9 .

 9 Fig. 9 . Stacked 1 H NMR spectra (400 MHz, Pyr-D5) of complex 3d from 238 K to 383 K. Only the region from 2.2 to 3.2 ppm is shown. Exchange broadening and coalescence due to loss of the chirality at Zn (Tc*), the rotation of the NMe2 fragment around the amidine bond (Tc**) and the rotation around the Csp 2 -Csp 2 bond of the aryl fragment on the amidine carbon (Tc***).

Fig. 10

 10 Fig. 10 homo-and heteroleptic FI-Zn complexes 7d, 28 8c 17a and 8d 19 synthesized for comparative purposes.

Fig. 11

 11 Fig.11. Left: First-order logarithmic plot for the polymerization of rac-LA at 25°C in CH2Cl2 using 6c (•) and 6d ( ▪ ) with i PrOH as initiators (100:1:1). Right: Mn and PDI against conversion associated with the kinetic studies of 6c (•) and 6d ( ▪ ) with i PrOH.

Table

  .

Table 1

 1 Relevant bond distances (Å) and angles (°) in the proligands.

		C7-N1	C7-N2	ΣαN2	θ a	ψ b	α c
	L1H	1.290(3) 1.335(3)	359.6(6) 5.0(3) -143.1(2)	-
	L3H	1.304(2) 1.356(2)	357.8(4) 7.0(2) -128.4(1) -116.88(15)
	L4H 1.305(16) 1.348(8) 359.9(1.7) 0.8(9) 169.9(6)	80.0(9)
	L5H	1.298(2) 1.342(2) 360.0(1.8) 1.8(2) -126.4(1)	117.34(15)

a : θ (C8N2C7N1), b : ψ (C7N1C1C2), c : α (N1C7C1'C2')

Table 2

 2 Relevant bond distances (Å) and angles (°) in the aluminum complexes.

C7-N1 C7-N2 Al-Me Al-O1 Al-N1 τ5 O1AlN1 θ a ψ b 1a

	1.309(2) 1.326(2)	1.977(3)	1.851(1) 2.174(1)	0.47 79.64(4)	6.9(2)	-150.99(12)
	1b c 1.318(4) 1.324(5)	1.980(2)	1.80(1) 2.14(3)	0.69 84.3(2.3)	9.3(2.8)	-156.8(1.2)
	1b' c 1.312(4) 1.321(1)	-	1.791(6) 2.07(3)	0.76 86.1(3.4) -7.7(1.0)	151.2(5.0)
	2b c 1.310(2) 1.322(4)	1.973(2)	1.797(2) 2.121(1)	0.51 82.36(9) -14.2(1.8) 155.9(1.2)
	3b c 1.320(1) 1.340(4)	1.970(2)	1.795(2) 2.163(10)	0.40 81.54(17) -15.45(0.21) 145.42(3)
	a : θ (C8N2C7N1), b : ψ (C7N1C1C2), c : the mean values of the two independent
	molecules are reported.

Table 3

 3 Relevant bond distances (Å) and angles (°) in Zn compounds.

		C7-N1	C7-N2	Zn-Et	Zn-O1	Zn-N1	τ4'	D a	O1ZnN1	θ b	ψ b
	1c	1.304(4)	1.328(4)	1.970(3)	2.064(2)	2.089(2)	0.71	0.730(3)	80.41(9)	1.3(5)	-151.4(4)
	5c c	1.307(12)	1.344(12)	1.985(9)	2.047(6)	2.082(7)	0.74	0.80(1)	89.2(11.6)	8.4(14)	-137.4(9)
	6c c	1.302(2)	1.330(2)	1.978(1)	2.065(6)	2.071(1)	0.70	0.635(1)	91.4(14.9)	3.7(2)	-152.8(1)
	1d	1.306(2)	1.323(2)	-	1.934(1)	2.024(1)	0.75	0.002(2)	86.49(5)	0.4(3)	174.5(1)
	2d c	1.309(3)	1.321(1)	-	1.942(3)	2.009(6)	0.72	0.131(2)	86.76(7)	-2.3(2.1)	177.4(1.2)
	3d	1.316(3)	1.339(3)		1.919(1)	2.042(2)	0.77	0.425(2)	86.24(7)	-5.80(3)	142.0(2)
	4d c	1.325(1)	1.333(4)		1.925(3)	2.047(3)	0.79	0.433(80)	86.30(19)	-5.9(1.8)	146.8(7.8)
	6d c	1.307(3)	1.329(1)		1.936(2)	2.012(7)	0.75	0.026(11)	86.9(3)	-3.3(6)	171.8(4.6)

Table 4

 4 ROP of rac-lactide mediated by FA-Al complexes. a

	Entry	Cat. Conv. (%) b Mntheo c	Mnexp d	Ð	Pm e
	1	1a	94	13 600	5 400	3.19 f	0.56
	2	1b	87	12 300	8 500	1.22	0.61
	3	1b' g	85	12 200	9 600	1.38	0.64
	4	2b	80	11 400	7 700	1.20	0.56
	5	3b	87	12 600	8 800	1.30	0.60
	6	4b	83	11 900	6 100	1.31	0.55
	7	6b	85	12 300	11 300	1.36	0.57

a Polymerization conditions: [rac-LA]0 = 1 M, 100 equiv. of rac-LA, 1 equiv. of i PrOH and 1 equiv. of metal catalyst, toluene, 90 °C, 24 h. b Monomer conversion. c Calculated using Mn,theo = [rac-LA]0/[catalyst]0 × MLA × conversion.

d

Measured by GPC in THF (45 ˚C) using PS standards and corrected by applying the appropriate correcting factor (0.58). e Determined from the methine region of the HD 1 H NMR spectrum. f GPC chromatogram presents bimodal profile. g Reaction performed in the absence of i PrOH.

Table 5

 5 ROP of rac-lactide mediated by FA-Zn and FI-Zn complexes. a

	Entry	Cat.	T (°C)	Conv. (%) b	Mntheo c Mnexp d	Ð	Pr e
	1	1c	20	49	7 100	6 400	1.11	0.77
	2	2c	20	54	7 800	6 800	1.08	0.74
	3	5c	20	36	5 200	4 500	1.08	0.62
	4	6c	20	90	13 000 10 900	1.13	0.57
	5	8c	20	93	13 400 11 500	1.04	0.65
	6	1d-5d	30	0	-	-	-	-
	7	6d	30	86	12 400 11 200	1.11	0.62
	8	7d	30	0	-	-	-	-
	9	8d	30	52	7 500	5 800	1.05	n.d.

a Polymerization conditions: [rac-LA]0 = 1 M, 100 equiv. of rac-LA, 1 equiv. of i PrOH and 1 equiv. of metal catalyst, CH2Cl2, 2 h. b Monomer conversion. c Calculated using Mn,theo = [rac-LA]0/[catalyst]0 × MLA × conversion. d Measured by GPC in THF (45 ˚C) using PS standards and corrected by applying the appropriate correcting factor (0.58). e Determined from the methine region of the HD 1 H NMR spectrum (See SI, Fig.

S115

).

Table 6

 6 ROP of rac-lactide mediated in bulk conditions by FA-Zn and FI-Zn complexes. a .

	Entry	Cat.	Ratio	T (°C)	T (min)	Conv. (%) b	Mntheo c	Mnexp d	Ð	Pr e
	1	1c	[300:1:1]	130	10	82	35 000	28 200	2.82	0.61
	2	2c	[300:1:1]	130	10	96	41 500	24 800	2.38	0.57
	3	5c	[300:1:1]	130	10	94	40 600	17 900	1.85	0.56
	4	6c	[300:1:1]	130	10	95	41 100	30 900	3.15	0.55
	5	6c	[300:1:1]	130	2	73	31 600	39 800	2.72	0.53
	6	8c	[300:1:1]	130	2	74	32 000	25 100	3.02	0.59
	7	1d	[300:1:1]	130	30	73	31 600	16 100	1.17	0.71
	8	2d	[300:1:1]	130	30	43	18 600	9 500	1.08	0.70
	9	3d	[300:1:1]	130	2	44	19 000	12 800	1.09	0.58
	10	4d	[300:1:1]	130	2	42	18 200	10 900	1.17	0.57
	11	5d	[300:1:1]	130	2	58	24 900	9 900	1.15	0.62
	12	6d	[300:1:1]	130	2	65	28 100	14 800	1.21	0.53
	13	6d	[1000:1:10]	130	5	95	13 700	9 600	1.18	0.57
	14	6d	[1000:1:10]	180	2	93	13 400	13 200	1.47	n.d.
	15	7d	[300:1:1]	130	2	48	20 800	14 800	1.12	0.61
	16	8d	[300:1:1]	130	2	42	18 200	8 700	1.07	0.59

a Polymerization conditions: free-solvent conditions, Ratio = [number of equiv. of rac-LA: number of equiv. of metal catalyst : number of equiv.of BnOH]. b Monomer conversion. c Calculated using Mn,theo = [rac-LA]0/[catalyst]0 × MLA × conversion. d Measured by GPC in THF (45 ˚C) using PS standards and corrected by applying the appropriate correcting factor (0.58). e Determined from the methine region of the HD

1 H NMR spectrum.

  , 14.51. HR-MS (ESI-pos): calcd for [C11H15N2O] + [M + H] + : calcd 191.11798. Found 191.11710. Δ = -4.134 ppm.

	H NMR (400 MHz, CD2Cl2, 298 K): δ(ppm) =
	8.02 (s, 1H, H7), 6.92 (m, 1H, H6), 6.86 (m, 1H, H4), 6.81 (m, 1H,
	H3), 6.74 (m, 1H, H5), 3.53 (s, 4H, Pyrr.), 1.96 (s, 4H, Pyrr.). Data
	in agreement with literature. { 1 H} 13 C NMR (101 MHz, CD2Cl2,
	298 K): δ(ppm) = 150.70 (C2), 149.80 (C7), 138.15 (C1), 123.46
	(C4), 120.01 (C6), 115.40 (C5), 113.29 (C3), 49.33 (Pyrr.), 45.80
	(Pyrr.

),

25.63

(Pyrr.), 25.08 (Pyrr.)

. Elemental Analysis: calcd for C11H14N2O: C, 69.45;

H, 7.42; N, 14.73. Found: C, 69.67; H, 7.56; N

  , 2.99-2.94 (m, 1H, Pyrr.), 2.12 (s, 3H, o-CH3), 2.05-1.98 (m, 2H, Pyrr.), 1.92-1.80 (m, 2H, Pyrr.). { 1 H} 13 C NMR (150 MHz, CD2Cl2, 298 K): δ(ppm) = 159.48 (C7), 150.70 (C2), 136.68 (C1), 135.52 (C1'), 135.22 (C2'), 130.70 (C3'), 129.24 (C4'), 128.09 (C6'), 126.38 (C5'), 122.61 (C4), 120.16 (C6), 119.03 (C5), 112.72 (C3), 48.69 (Pyrr.), 47.36 (Pyrr.), 26.24 (Pyrr.), 25.18 (Pyrr.), 19.21 (o-CH3). Elemental Analysis: calcd for (C18H20N2O)100(CH2Cl2)2 : C, 76.73; H, 7.16; N, 9.93. Found: C, 76.35; H, 7.12; N, 10.10. HR-MS (ESI-pos): calcd for [C18H21N2O] + [M + H] + : 281.16484. Found: 281.16397. Δ = -3.094 ppm.

  H NMR (600 MHz, CD2Cl2, 298 K): δ(ppm) = 7.92-7.85 (overlapping signals, 2H, H5' + H8'),7.84-7.79 (m, 1H, H3'), 7.56-7.49 (overlapping signals, 2H, H4' + H6'), 7.45 (dd, J = 8.3, 7.0 Hz, 1H, H9'), 7.30 (dd, J = 7.0, 1.2 Hz, 1H, H10'), 6.70 (dd, J = 7.9, 1.5Hz, 1H, H3), 6.56 (td, J = 7.7, 1.5 Hz, 1H, H4), 6.10 (td, J = 7.7, 1.5 Hz, 1H, H5), 5.88 (dd, J = 7.9, 1.5 Hz, 1H, H6), 3.93-3.82 (m, 2H, Pyrr.), 3.08-3.00 (m, 1H, Pyrr.), 2.92-2.86 (m, 1H, Pyrr.), 2.08-2.01 (m, 2H, Pyrr.),1.88-1.75 (m, 2H, Pyrr.). { 1 H} 13 C NMR (150 MHz, CD2Cl2, 298 K): Pyrr.), 47.67(Pyrr.), 26.21 (Pyrr.), 25.18 (Pyrr.). Elemental Analysis: calcd for (C21H20N2O)100(CH2Cl2)5 : C, 78.85;H, 6.32; N, 8.74. Found: C, 78.41; H, 6.40; N, 8.90. HR-MS (ESI-pos): calcd for [C21H21N2O] + [M + H] + : 317.16484. Found: 317.16510. Δ = -0.820 ppm. 299.3 mg of benzoxazole (2.4 mmol) were placed in an Eppendorf, and 0.62 mL (490.5 mg, 4.8 mmol, 2 equiv.) of N,N,N'-trimethylethylenediamine was added. The mixture was stirred at 60 °C for 2 h. The crude product was then purified by column chromatography on alumina column with a 10/1 DCM/MeOH mixture to afford 316 mg of L6H (60% yield).

	δ(ppm) =
	158.74 (C7), 150.53 (C2), 136.93 (C1), 133.77 (C1'/C7'), 133.65
	(C1'/C7'), 130.55 (C2'), 129.47 (C5'/C8'), 128.99 (C5'/C8'),
	127.63 (C4'/C6'), 126.77 (C10'), 126.08 (C4' /C6'), 125.72 (C9'),
	125.08 (C3'), 122.64 (C4), 120.00 (C6), 118.95 (C5), 112.74 (C3),
	48.52 (Synthesis of L6H.
	1 H
	NMR (400 MHz, MeOD, 298 K): δ(ppm) = 7.76 (s, 1H, H7), 6.93-
	6.80 (overlapping signals, 2 H, H4 + H6), 6.80-6.68 (overlapping
	signals, 2H, H3 + H5), 3.61 (overlapping signals, 2H, H9), 3.04
	(broad signal, 3H, H8), 2.56 (broad signals, 2H, H10), 2.30 (broad
	signals, 6 H, H11 + H12). {

1

H} 13 C NMR (100.6 MHz, MeOD, 298 K): δ(ppm) = 155.78 (C7), 151.42 (C2), 139.34 (C1), 124.54 (C4/C6), 120.82 (C3/C5), 120.00 (C4/C6), 115.18 (C3/C5), 58.35 (C10), 52.12 (C9), 45.67 (C11 + C12), 33.08 (C8). Elemental

Acknowledgements

We thank Dr Quentin Bonnin and Ms Marie-José Penouilh-Suzette (PACSMUB) for technical assistance with NMR spectroscopy and MALDI-ToF analysis. Prof. Jean-Pierre Couvercelle and Mr Sylvain Quillard are warmly thanked for their assistance in GPC measurements. Financial support from Ministère de l'Enseignement Supérieur et de la Recherche, the Centre National de la Recherche Scientifique (CNRS), ANR (MORFAL, ANR-22-CE07-0011), are gratefully acknowledged.

Synthesis of 6b

This compound was prepared similarly to 1b using L6H ligand (221 mg, 1 mmol). Complex 6b was isolated as a whitish powder (220 mg, 70% yield). 1 H NMR (400 MHz,298 K): δ(ppm) = 7.81 (s, 2H, H7), 6.79-6.69 (overlapping signals, 4H, H4 + H6), 6.53 (d, J = 7.7 Hz, 2H, H3), 6.43 (t, J = 7.5 Hz, 2H, H5), 3.56-3.37 (overlapping signals, 10H, H8 + H9), 2.68-2.47 (overlapping signals, 4H, H10), 2.26 (s, 12H, H11 + H12), -0.77 (s, 3H, AlMe). { 1 H} 13 C NMR (101 MHz, THF-d8, 298K): δ(ppm) = 157.07 (C7), 156.86(C2), 140.43 (C1), 124.76 (C4/C6), 116.29 (C5), 115.76 (C3), 115.51 (C4/C6), 58.39 (C10), 54.03 (C8/C9), 45.70 (C11+C12), 36.87 (C8/C9), -4.71 (AlMe). Elemental Analysis: calcd for (C25H39AlN6O2)100(C2H6OSi)15: C, 61.55; H, 8.15; N, 17.02. Found: C, 61.40; H, 8.18; N, 16.52.

Synthesis of 1b'.

In a glovebox, 147 mg (0.4 mmol) of 1b were suspended in 4 mL of toluene. 30.6 µL of isopropanol (24.04 mg, 0.4 mmol, 1 equiv.) were then added with a microsyringe and the mixture was heated at 100 °C for 2 h. Cooling the solution to r.t. allowed the product to precipitate as a white solid which was filtrated and then dried under vacuum, affording 1b' (100 mg, 61% yield). 1 H NMR (600 MHz,CD2Cl2,298 K): δ(ppm) = 7.75 (s, 2H, H7), 6.90 (t, J = 7.2 Hz, 2H, H4), 6.85 (d, J = 7.8 Hz, 2H, H6), 6.68 (d, J = 7.6 Hz, 2H, H3), 6.62 (t, J = 7.6 Hz, 2H, H5), 3.93 (m, 1H, OCH(CH3)2), 3.44 (s (Δν½ = 13.0 Hz), 6H, NMe2), 3.24 (s (Δν½ = 13.0 Hz), 6H, NMe2), 0.98 (d, J = 5.8 Hz, 3H, OCH(CH3)2), 0.76 (d, J = 5.5 Hz, 3H, OCH(CH3)2). { 1 H} 13 C NMR (150 MHz, CD2Cl2, 298 K): δ(ppm) = 156.21 (C7), 155.60 (C2), 139.14 (C1), 125.12 (C4), 117.00 (C5), 115.49 (C3), 114.89 (C6), 63.28 (OCH(CH3)2), 43.49 (NMe2), 38.59 (NMe2), 27.57 (OCH(CH3)2), 27.39 (OCH(CH3)2). Elemental Analysis: calcd for C21H29AlN4O3: C, 61. 15; H, 7.09; N, 13.58. Found: C, 61.16; H, 6.98; N, 13.41.

Synthesis of 1c.

In a glovebox, 133 mg (0.8 mmol) of L1H were solubilized in 5 mL of dried THF. 0.8 mL (0.8 mmol, 1 equiv.) of a 1 M solution of ZnEt2 in hexane was added and the mixture was stirred at r.t. for 2 h. The volatiles were evaporated under vacuum and the solid obtained was washed with 4 mL of pentane before being dried under vacuum affording 1c as a whitish powder (131 mg, 62% yield). 1 H NMR (400 MHz, pyridine-d5, 298 K): δ(ppm) = 7.97 (s, 1H, H7), 7.34 (dd, J = 7.9, 1.5 Hz, 1H, H3), 7.23 (m, 1H, H4), 7.11 (dd, J = 7.7, 1.7 Hz, 1H, H6), 6.65 (td, J = 7.5, 1.6 Hz, 1H, H5), 2.93 (broad s (Δν½ = 23.2 Hz), 6H, NMe2), 1.62 (t, J = 8.1 Hz, 3H, ZnCH2CH3), 0.69 (q, J = 8. 1 Hz, 2H, ZnCH2CH3). { 1 H} 13 C NMR (101 MHz, pyridine-d5, 298 K): δ(ppm) = 164.38 (C2), 155.92 (C7), 139.20 (C1), 126.74 (C4), 118.63 (C3), 117.29 (C6), 113.39 (C5), 41.46 (extracted from HSQC, NMe2), 36.74 (extracted from HSQC, NMe2), 14.43 (ZnCH2CH3), 0.24 (ZnCH2CH3). Elemental Analysis: calcd for C11H16ZnN2O: C, 51. 28; H, 6.26; N, 10.87. Found: C, 50.03; H, 6.58; N, 10.38.

Synthesis of 2c.

This compound was prepared similarly to 1c using L2H ligand (100 mg, 0.53 mmol). Complex 2c was isolated as a whitish solid powder (114 mg, 76% yield). 1 H NMR (400 MHz,298 K): δ(ppm) = 8.26 (s, 1H, H7), 7.35 (dd, J = 7.9, 1.5 Hz, 1H, H3), 7.29-7.15 (m, 2H, H4 + H6), 6.67 (m, 1H, H5), 3.48 (broad (Δν½ = 113.4 Hz), 4H, Pyrr.), 1.83-1.52 (overlapping signals, 7H, Pyrr. + ZnCH2CH3), 0.74 (q, J = 8. 1 Hz, 2H, ZnCH2CH3). { 1 H} 13 C NMR (151 MHz,298 K): δ(ppm) = 164.55 (C2),152.41 (C7),139.04 (C1),126.63 (C4/C6),118.79 (C3),116.70 (C4/C6),113.28 (C5),25.38 (Pyrr.),14.52 (ZnCH2CH3),0.42 (ZnCH2CH3). Elemental Analysis: calcd for C13H18ZnN2O: C, 55.04; H, 6.40; N, 9.88. Found: C, 54.80; H, 6.10; N, 9.65.

Synthesis of 5c.

This compound was prepared similarly to 1c using L5H ligand (316 mg, 1 mmol). Complex 5c was isolated as a whitish solid powder (384 mg, 93% yield). 1

Synthesis of 6c.

In a glovebox, 221 mg (1 mmol, 1equiv.) of the corresponding amidine proligand was dissolved in 10 mL of dried THF. 1 mL (1 mmol, 1equiv.) of a 1M solution of ZnEt2 in hexanes was then added and the resulting mixture was stirred at r.t for 2h. The solvent was then evaporated and the whitish powder was dried under vacuum (220 mg, yield 70%). 1

Synthesis of 1d.

In a glovebox, 354 mg (2.2 mmol) of L1H was dissolved in 10 mL of dried THF. 1.1 mL (1.1 mmol, 0.5 equiv.) of a 1M solution of ZnEt2 in hexane was then added and the resulting mixture was stirred at r.t. for 2 h. After having evaporated the solvents, the residue was washed with 6 mL of pentane and dried under vacuum affording 1d as a whitish powder (343 mg, 80% yield). 1 H NMR (500 MHz, CD2Cl2, 298 K): δ(ppm) = 7.95 (s, 2H, H7), 6.90 (overlapping signals, 4H, Ar), 6.75 (d, J = 7.9 Hz, 2H, Ar), 6.46 (t, J = 7.5 Hz, 2H, Ar), 3.13 (s (Δν½ = 7.6 Hz), 6H, NMe2), 2.91 (s (Δν½ = 7.5 Hz), 6H, NMe2). { 1 H} 13 C NMR (125 MHz, CD2Cl2, 298 K): δ(ppm) (selected signals) = 155.31 (C7), 126.19 (Ar), 118. 16 (Ar), 115.47 (Ar), 114.22 (Ar), 42.90 (CH3, NMe2), 35.79 (CH3, NMe2). Quaternary carbons not seen. Very few soluble, not enough for HMBC experiment. Elemental Analysis: calcd for C18H22ZnN4O2: C, 55. 18; H, 5.66; N, 14.30. Found: C, 55.22; H, 5.97; N, 13.95.

Synthesis of 2d.

This compound was prepared similarly to 1d using L2H ligand (380 mg, 2 mmol). Complex 2d was isolated as a whitish solid powder (175 mg, 40% yield). 1 H NMR (500 MHz, CD2Cl2, 298 K): δ (ppm) = 8.23 (2H, s, H7), 6.95 (dd, J = 7.9, 1.6 Hz, 2H, H3), 6.90 (td, J = 7.6, 1.6 Hz, 2H, H4), 6.74 (dd, J = 8.0, 1.5 Hz, 2H, H6), 6.45 (td, J = 7.5, 1.5 Hz, 2H, H5), 3.62 (m, 4H, Pyrr.), 3.37 (m, 4H, Pyrr.), 1.84 (m, 4H, Pyrr.), 1.73 (m, 4H, Pyrr.). { 1 H} 13 C NMR (125 MHz, CD2Cl2, 298 K): δ (ppm) = 160.68 (C2), 151.43 (C7), 136.12 (C1), 125.87 (C4), 118.26 (C6), 114.66 (C3), 114.01 (C5), 51.52 (Pyrr.), 45.63 (Pyrr.), 25.35 (Pyrr.), 24.94 (Pyrr.).Elemental Analysis: calcd for C22H26N4O2Zn: C, 59.53; H, 5.90; N, 12.62. Found: C, 59.58; H, 5.35; N, 12.45.

Synthesis of 3d.

This compound was prepared similarly to 1d using L3H ligand (254 mg, 1 mmol). Complex 3d was isolated as a yellowish solid powder (133 mg, 46% yield). 1 H NMR (400 MHz, pyridine-d5, 378 K): δ(ppm) = 7.52 (broad signal (Δν½ = 18.2 Hz), 2H, Ar), 7.21 (m overlapping with residual Pyr. signals, 2H, Ar), 7.04 (m, 2H, Ar), 6.94 (t, J = 7.5 Hz, 2H, Ar), 6.58 (d, J = 7.6 Hz 2H, Ar), 6.35 (t, J = 7.3 Hz, 2H, Ar), 3.05 (broad signal (Δν½ = 7.8 Hz), 12H, NMe2), 2.53 (broad signal overlapping with signal at 2.46, 3H, o-CH3), 2.46 (broad signal overlapping with signal at 2.53, 3H, o-CH3). { 1 H} 13 C NMR (101 MHz, pyridine-d5, 378 K): δ(ppm) = 166. 95, 161.73, 138.50, 137.98, 137.06, 129.92 (x2), 128.70, 125.09, 123.83, 122.16, 116.96, 112.20, 38.38, 18.90. Elemental Analysis: calcd for C32H34N4O2Zn: C, 67.19; H, 5.99; N, 9.79. Found: C, 66.55; H, 6.13; N, 9.68.

Synthesis of 4d.

This compound was prepared similarly to 1d using L4H ligand (280 mg, 1 mmol). Complex 4d was isolated as a yellowish solid powder (174 mg, 55% yield). 1 H NMR (400 MHz,383 K): δ(ppm) = 7.52 (broad (Δν½ = 17.9 Hz), 2H), 7.30-7.11 (overlapping signals with residual Pyr, 6H), 7.07 (d, J = 7.6 Hz, 2H), 6.93 (t, J = 7.6 Hz, 2H), 6.66 (d, J = 6.6 Hz, 2H), 6.35 (m, 2H), 3.85-3.30 (m, 8H, Pyrr.), 2.49 (broad singlet, (Δν½ = 14.8 Hz), 6H, o-CH3), 1.80 (broad (Δν½ = 13.7 Hz), 8H, Pyrr.). { 1 H} 13 C NMR (101 MHz, pyridine-d5, 383 K): δ(ppm) = 164. 48, 162.09, 137.43, 136.33, 130.53, 129.49, 129.12, 125.54, 124.42, 122.35, 117.25, 112.61, 48.73, 24.89, 19.10. One C not seen probably overlapping with other signals. Elemental Analysis: calcd for C36H38N4O2Zn: C, 69. 28; H, 6.14; N, 8.98. Found: C, 69.25; H, 5.68; N, 9.32.

Synthesis of 5d.

This compound was prepared similarly to 1d using L5H ligand (316 mg, 1 mmol). Complex 5d was isolated as a yellowish solid powder (160 mg, 45% yield). 1 H NMR (400 MHz,383 K): δ(ppm) = 8.52 (broad (Δν½ = 57.0 Hz), 2H), 7.96-7.78 (overlapping signals, 6H), 7.70-7.59 (m, Pyr.-d5 + 2H), 7.52 (t, J = 7.6 Hz, 2H), 7.43 (broad (Δν½ = 24.0 Hz), 2H), 6.99 (d, J = 7.8 Hz, 2H), 6.81 (t, J = 7.6 Hz, 2H), 6.72 (d, J = 7.6 Hz, 2H), 6.13 (t, J = 7.4 Hz, 2H), 3.85-3.40 (m, 8H, Pyrr.), 1.81 (broad (Δν½ = 16.7 Hz), 8H, Pyrr.). { 1 H} 13 C NMR (101 MHz, pyridine-d5, 383 K): δ(ppm) = 163. 81, 162.05, 138.68, 133.66, 133.57, 131.49, 129.48, 128.59, 127.69, 127.30, 126.05, 125.28, 124.38, 121.78, 117.27, 112.51, 48.77 (CH2, Pyrr.), 24.92 (CH2, Pyrr.). One C not seen probably overlapping with other signals. Elemental Analysis: calcd for C42H38ZnN4O2: C, 72.46; H, 5.50; N, 8.05. Found: C, 72.16; H, 5.42; N, 8.25.

Synthesis of 6d.

This compound was prepared similarly to 1d using L6H ligand (221.3 mg, 1 mmol). Complex 6d was isolated as a whitish solid powder (151 mg, 60% yield). 1 H NMR (500 MHz, CD2Cl2, 298 K): δ (ppm) = 7.97 (2H, s, H7), 6.95-6.82 (overlapping signals, 4H, H4 + H6), 6.74 (d, J = 7.7 Hz, 2H, H3), 6.45 (t, J = 7.4, Hz, 2H, H5), 3.37 (broad signal, 4H, H9), 2.93 (s, 6H, H8), 2.41 (broad signal, 4H, H10), 2.21 (m, 12H, H11 + H12). { 1 H} 13 C NMR (125 MHz, CD2Cl2, 298 K): δ (ppm) = 160.82 (C2), 155.62 (C7), 136.57 (C1), 126.06 (C4/C6), 118.03 (C3), 115.60 (C4/C6), 114.11 (C5), 57.52 (C10), 53.62 (C9), 45.72 (C11 + C12), 34.27 (C8). Elemental Analysis: calcd for (C24H36N6O2Zn)100(C2H6SiO)30: C, 55.94; H, 7.21; N, 15.91. Found: C, 55.26; H, 7.14; N, 15.56.

Author Contributions

This project was conceived by JB, RMK and PLG. All experiments were performed by BT, VVC, CB, JB and RMK. X-ray diffraction studies were performed by YR. The manuscript was written by PLG. All authors have given approval to the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.