Marjorie Marcourt

Philippe Cassagnau

René Fulchiron
email: rene.fulchiron@univ-lyon1.fr

Dimitri Rousseaux

Olivier Lhost

Simon Karam

A

Keywords: Nanocomposites, Carbon Nanotubes, Extensional Viscoelasticity, Electrical conductivity, Modeling

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Introduction

The addition of Carbon Nanotubes is a promising solution for the achievement of Conductive Polymer Composites (CPC). Owing to their large aspect ratio, only a small amount of fillers can turn an insulating polymer matrix to a composite with moderate electrical properties [START_REF] Kirkpatrick | Percolation and conduction[END_REF][START_REF] Bauhofer | A review and analysis of electrical percolation in carbon nanotube polymer composites[END_REF][START_REF] Pang | Conductive polymer composites with segregated structures[END_REF]. The preferred and reliable method for the filler incorporation is the melt mixing and more precisely the masterbatch dilution that can lead to suitable filler dispersion and distribution within the matrix [START_REF] Mcnally | Polymer-carbon nanotube composites: Preparation, Properties and Applications[END_REF]. Leaving apart all the parameters that must be taken into account (mixing duration, shear rates, filler functionalization) the generation of CPC with suitable electrical properties relies on the formation of a homogeneous network made of small aggregates, disentangled amounts of CNTs and individual CNTs [START_REF] Alig | Establishment, morphology and properties of carbon nanotube networks in polymer melts[END_REF][START_REF] Moreira | Aggregation of Carbon Nanotubes in Semi-dilute Suspension[END_REF][START_REF] Pegel | Dispersion, agglomeration, and network formation of multiwalled carbon nanotubes in polycarbonate melts[END_REF].

The use of rheological analysis combined with conductivity monitoring has paved the way for the comprehension of the filler network behavior in molten composites under both quiescent and small shear strain [START_REF] Obrzut | Shear-induced conductor-insulator transition in melt-mixed polypropylene-carbon nanotube dispersions[END_REF]. Indeed, the "dynamic percolation" [START_REF] Alig | Establishment, morphology and properties of carbon nanotube networks in polymer melts[END_REF][START_REF] Kharchenko | Flow-induced properties of nanotube-filled polymer materials[END_REF][START_REF] Martin | Formation of percolating networks in multi-wall carbon nanotube epoxy composites[END_REF][START_REF] Ma | Experimental observation on the flow-induced assembly of carbon nanotube suspensions to form helical bands[END_REF][START_REF] Sandler | Percolation in multi-wall carbon nanotube-epoxy composites: influence of processing parameters, nanotube aspect ratio and electric fields on the bulk conductivity[END_REF][START_REF] Kovacs | Two percolation thresholds in carbon nanotube epoxy composites[END_REF] and the conductor/insulator transition [START_REF] Alig | Conductivity spectroscopy on melt processed polypropylene multiwalled carbon nanotube composites: Recovery after shear and crystallization[END_REF][START_REF] Bauhofer | Shear-controlled electrical conductivity of carbon nanotubes network suspended in low and high molecular weight liquids[END_REF] have been brought to light. Those two specific mechanisms illustrate the huge capacity of the filler structure to evolve. The network buildup has been explained by Alig et al. [START_REF] Alig | Establishment, morphology and properties of carbon nanotube networks in polymer melts[END_REF] as the combination between strong dispersive interactions between nanotubes and depletion interactions between the diffusion of isolated CNTs that is made possible if the polymer viscosity is sufficiently low. The network destruction is more complex and is intimately linked to the filler network structure. In fact, it has been observed that under shear deformation at large shear rates [START_REF] Villmow | Influence of injection molding parameters on the electrical resistivity of polycarbonate filled with multiwalled carbon nanotubes[END_REF] or under extensional deformation [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF], the agglomerates are stretched and orient in the deformation direction. The aggregates network morphology changes in response to strains and, more precisely, its response is linked to its initial morphology [START_REF] Bauhofer | Shear-controlled electrical conductivity of carbon nanotubes network suspended in low and high molecular weight liquids[END_REF][START_REF] Skipa | Shear-stimulated formation of carbon nanotube networks in polymer melts[END_REF][START_REF] Skipa | Influence of shear deformation on carbon nanotube networks in polycarbonate melts: interplay between build-up and destruction of agglomerates[END_REF]. Similarly to highly filled materials whose flow behavior depends on the filler network structure, the electrical properties of CPC are also intimately linked to the filler network structure. The structural evolution of highly filled material has been widely investigated and is well described by a kinetic equation introduced by Barnes [20] for heterogeneous materials [START_REF] Chen | Characteristic of flocculated silica dispersion[END_REF][START_REF] Coussot | Rheology of concentrated dispersal systems in a low molecular weight matrix[END_REF][START_REF] Kee | Flow properties of time dependent food stuffs[END_REF][START_REF] Quemada | Rheology of concentrated dispersed systems and minimum energy dissipation principle. I Viscosity-concentration relationship[END_REF][START_REF] Yziquel | Non-linear viscoelastic behavior of fumed silica suspensions[END_REF][START_REF] Leonov | On the rheology of filled polymers[END_REF] as:

𝑑𝜉 𝑑𝑡 = 𝑎(1 -𝜉) 𝑏 + 𝑐𝜉𝛾̇𝑑 Equation 1
where ξ is a structural parameter that describes the filler agglomeration state: ξ = 1 the agglomeration state in the network is maximum and entirely efficient and ξ = 0 the network is fully broken. The constants a, b, c and d are linked to the material. The first term describes the network reinforcement and the second depending on the sign of c illustrates the shearinduced agglomeration or the shear-induced destruction. For instance, Leonov et al. [START_REF] Leonov | On the rheology of filled polymers[END_REF] argued that the breakup depends on the second invariant of the rate of deformation 𝐼𝐼 𝛾̇.

The conductivity variation due to the CNT network evolution has been first described by Alig et al. [START_REF] Alig | Establishment, morphology and properties of carbon nanotube networks in polymer melts[END_REF][START_REF] Alig | Conductivity spectroscopy on melt processed polypropylene multiwalled carbon nanotube composites: Recovery after shear and crystallization[END_REF]. They combined a kinetic equation which takes into account the evolution of the agglomerates fraction contributing to the conduction (𝜑 𝑒𝑓𝑓 ), with a percolation law to associate the network structure to the electrical properties of the composite.

𝑑𝜑 𝑒𝑓𝑓 𝑑𝑡 = 𝑘 0 (𝜑 -𝜑 𝑒𝑓𝑓 ) 𝑛 + 𝑘 1 (𝜑 -𝜑 𝑒𝑓𝑓 ) -𝑘 2 𝜑 𝑒𝑓𝑓 Equation 2
where 𝜑 is the filler total fraction, considering that, at equilibrium (when 𝑡 → ∞) all the CNTs contribute to the conductive network, 𝜑 𝑒𝑓𝑓 is the volume fraction of conductive agglomerates 𝑘 0 , 𝑘 1 and 𝑘 2 are the kinetic coefficients for respectively quiescent agglomeration, shear-stimulated agglomeration and shear-stimulated destruction process.

It must be noticed that 𝑘 1 and 𝑘 2 depend on the shear rate 𝛾. Alig et al. argued first that the network building was a second order mechanism (n=2) considering the agglomeration process as a clustering mechanism where two non-conductive particles stick together to create an electrically conductor agglomerate. Later, Skipa and coworkers [START_REF] Skipa | Shear-stimulated formation of carbon nanotube networks in polymer melts[END_REF][START_REF] Skipa | Influence of shear deformation on carbon nanotube networks in polycarbonate melts: interplay between build-up and destruction of agglomerates[END_REF] have shown that the value of n equal to 1 leads also to relevant results. Then, the solution of the kinetic equation is introduced into the percolation law that describes the macroscopic behavior of the composite. This model well describes the different conductivity evolutions observed under shear deformation at small shear rates. For instance, it can describe the interplay between build-up and destruction when the conductivity curve merges to a steady value [START_REF] Bauhofer | A review and analysis of electrical percolation in carbon nanotube polymer composites[END_REF][START_REF] Skipa | Influence of shear deformation on carbon nanotube networks in polycarbonate melts: interplay between build-up and destruction of agglomerates[END_REF]. The evolution of 𝑘 0 remained unexplained even if the authors highlighted the influence of the temperature on the conductivity recovery. In addition, Alig and coworkers [START_REF] Alig | Destruction and formation of a carbon nanotube network in polymer melts: Rheology and conductivity spectroscopy[END_REF] have observed large difference between the reaction rate 𝑘 0 for conductivity recovery experiments of comparable specimens. Surprisingly, for a shear-induced agglomeration that led to an increase of conductivity greater than six decades, they observed that the sum of the structuring parameter was very close to the breaking parameter. Moreover, they have proposed a destruction rate that depends on the shear rate (see Equation 2) [START_REF] Skipa | Shear-stimulated formation of carbon nanotube networks in polymer melts[END_REF][START_REF] Skipa | Influence of shear deformation on carbon nanotube networks in polycarbonate melts: interplay between build-up and destruction of agglomerates[END_REF] but did not deduce an obvious relation from the fitted parameters.

In this paper, a new approach to describe the destruction mechanism, especially for extensional strain, will be introduced and applied to the composites on the basis of conductivity measurements during extensional deformation.

Material and Methods

The CNTs are the NC7000 supplied by Nanocyl, a Belgian company. They are characterized by a diameter d around 9.5 nm and a mean length of 1.5 µm. The matrix used is a polystyrene (PS) with a melt flow index of 2.4 supplied by Total. The composites were melt mixed using a masterbatch dilution strategy and were supplied by Total as pellets. The concentration of CNTs in the initial masterbatch was of 15wt%. It was then dry blended with pure PS to reach the desired filler concentration before extrusion. From the supplied pellets, the specimens were compression molded at 200°C. A pressure of 20 bars was applied to the mold for 10 minutes. Then, the pressure was increased to 200 bars in 10 minutes and held during 5 min. Then, the specimen was cooled down to room temperature.

Electrical properties analysis has been conducted on compression molded samples that have been additionally submitted to a quiescent treatment at 200°C for around 20 min. This supplementary thermal treatment enables the filler network to recover an equilibrium state in which most of the CNTs take part to the electrical conduction. Indeed, just after the compression molding, this state is not obtained. The good contact between the electrodes and the specimen was ensured using a colloidal silver paste. Owing to a Keithley 237 power supply, a 10 volt Direct Current (DC) is delivered and the current passing through the sample is measured. The volume conductivity is then deduced using the specimen geometry as:

𝜎 = 𝐿.𝐼 𝑆.𝑈 Equation 3
with U the applied voltage, I the measured current, L and S respectively the specimen length and section. From these experiments, the percolation law linking the conductivity to the effective CNT's fraction was determined on specimens that have been annealed [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF]:

𝜎 = 𝜎 0 (𝜑 𝑒𝑓𝑓 -𝜑 𝑐 ) 𝛽 Equation 4
with 𝜑 𝑒𝑓𝑓 (≥ 𝜑 𝑐 ), the effective volume fraction of CNTs which contribute to the conduction and 𝜑 𝑐 the percolation threshold. It must be added that, since the samples have been annealed, the efficient fraction (𝜑 𝑒𝑓𝑓 ) of CNTs has been e assimilated to the total fraction (𝜑) to determine the parameters of this law. The obtained exponent 𝛽 is 2.2 with a percolation threshold 𝜑 𝑐 at 0.19 vol% and a pre-factor 𝜎 0 of 630 S.cm -1 .

Extensional experiments were carried out with a Extensional Viscosity Fixture EVF (TA Instruments) mounted on the ARES rheometer (TA Instruments). The set-up was modified in order to measure the specimen conductivity during the extensional test. This specific set-up has already been detailed in an earlier work [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF]. In some cases, the measurements have been carried out on samples directly after their compression molding without the annealing treatment. By this way, the structuring mechanism is not fully accomplished at the beginning of the experiment so that it can be caught during the measurements.

The differential equations which do not have an analytical solution were numerically resolved using the software Scilab (open source software published by Scilab Enterprises S.A.S). All the fitted parameters presented in this work were obtained by the means of a non-linear least squares regression method.

Description of the proposed model

Network structuring

The CNT network is made of aggregates that are connected together by individual CNTs or highly disentangled group of CNTs that constitute junctions between aggregates. Thermal diffusion triggers the formation of junctions and hence the filler network reinforcement [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF].

The structuring rate depends on the difference from the equilibrium state in a manner analogous to the model of Skipa et al. Even if we have been very cautious of the specimen's preparation, it remains possible that the initial state can slightly vary. The difference will be observed for specific specimens and will be detailed later in this work. The effective filler fraction that takes part to the conductivity is considered as the structural variable. Hence, the network structuring kinetics is given by:

𝑑𝜑 𝑒𝑓𝑓 𝑑𝑡 | 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑖𝑛𝑔 = 𝑘 𝑏𝑢𝑖𝑙𝑑 (𝜑 -𝜑 𝑒𝑓𝑓 ) Equation 5
where 𝜑 𝑒𝑓𝑓 is the filler that belongs to the percolated network; 𝜑 is the total filler concentration in the specimen and consequently, the upper limit of 𝜑 𝑒𝑓𝑓 . It can be pointed out that ξ appearing in Equation 1 would be 𝜑 𝑒𝑓𝑓 / 𝜑 in our notation. The parameter 𝑘 𝑏𝑢𝑖𝑙𝑑 has the dimension of the inverse time. The aggregation and the formation of connections can only be disrupted by deformation. Indeed, the theoretical energy required to counter the strong attractive forces between CNTs is around 1000kBT (T is the temperature and kB is the Boltzmann's constant) [START_REF] Huang | Dispersion of Carbon Nanotubes: Mixing, Sonication, Stabilization and Composite Properties[END_REF]. The structuring mechanism is pretty complex and embraces different mechanism at different scale but for states relatively close to the equilibrium, Equation 5 is acceptable. The filler network can be seen as a 3D structure made of CNTs. All the CNTs can be considered as equivalent sites for the binding of isolated CNTs or small aggregates. It can be added that, taken alone, Equation 5 has an analytical solution which asymptotically tends to 𝜑.

𝜑 𝑒𝑓𝑓 = 𝜑 + (𝜑 0 -𝜑) exp(-𝑘 𝑏𝑢𝑖𝑙𝑑 𝑡) Equation 6
where 𝜑 0 is the initial effective filler concentration which is different from 𝜑 when the material is not initially at equilibrium.

Network breakup

In our previous work, from Scanning Electron Microscopy, it has been shown that the aggregates and CNTs of an initially isotropic filler network orientate under extensional deformation [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF]. Thus, it can be considered that, the network is first stretched and then, the CNTs are strained apart from each other as shown in Figure 1.

Figure 1: Evolution of the filler network under extensional deformation

The first step does not induce major conductivity evolution as the orientation does not or very slightly impact of connections within the network [START_REF] Chang | Effects of uniaxial and biaxial orientation on fiber percolation in conductive polymer composites[END_REF][START_REF] Du | Effect of nanotube alignment on percolation conductivity in carbon nanotube/polymer composites[END_REF]. Thus, it can be assumed that extensional strains do not induce any increase of the number of connections.

Depending on the experimental conditions, this stage can take more or less time. However, when the CNTs are fully extended, the deformation will progressively pull apart the CNTs and the aggregates from each other. The number of connections will progressively decrease and so will the conductivity.

In Figure 1, the number of connections that are represented by the grey circles does not vary in early stage but dramatically decreases when the CNTs are fully extended. In that sense, it will be considered that the filler network is broken for a given limiting Hencky strain and that it is still efficient for a strain lower than this limit. From a mathematical viewpoint and avoiding any discontinuity which could provide numerical difficulties, the network breakup can be expressed using a simple decreasing sigmoid:

𝜑 𝑒𝑓𝑓 = 𝜑𝑒 -(𝑘 𝑏𝑟𝑒𝑎𝑘 𝜀 2 ) Equation 7
where 𝑘 𝑏𝑟𝑒𝑎𝑘 is the adimensional breaking parameter. It can be pointed that the exponent of the strain in Equation 7 could have been left as an adjustable parameter. However, the suitability of the value of 2 will be shown further.

For extensional measurements, where 𝜀 = 𝜀ṫ, the time derivative of equation 7 leads to

𝑑𝜑 𝑒𝑓𝑓 𝑑𝑡 | 𝑑𝑒𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 = -2𝑘 𝑏𝑟𝑒𝑎𝑘 𝜀̇2 𝜑 𝑒𝑓𝑓 𝑡 Equation 8
It can be added that, a priori, the breaking parameter 𝑘 𝑏𝑟𝑒𝑎𝑘 may be dependent on the extensional rate. This will be discussed further.

As a whole, the evolution of the CNTs that belongs to the percolated network (𝜑 𝑒𝑓𝑓 ) is the sum of the building (Equation 5) and destruction (Equation 8) parts.

𝑑𝜑 𝑒𝑓𝑓 𝑑𝑡 = 𝑘 𝑏𝑢𝑖𝑙𝑑 (𝜑 -𝜑 𝑒𝑓𝑓 ) -2𝑘 𝑏𝑟𝑒𝑎𝑘 𝜀̇2 𝜑 𝑒𝑓𝑓 𝑡 Equation 9
This differential equation was numerically solved using the Ordinary Differential Equation solver of the software Scilab. The solution of Equation 9 was then inserted into the percolation law (Equation 4) to obtain the conductivity as a function of time.

The initial effective filler concentration 𝜑 0 is also determined by means of the percolation law, simply adjusting 𝜑 0 to calculate the initial conductivity (if the material is not initially at equilibrium). Then, using a nonlinear least square regression algorithm, the two parameters 𝑘 𝑏𝑢𝑖𝑙𝑑 and 𝑘 𝑏𝑟𝑒𝑎𝑘 were fitted to the experimental data.

Results and Discussion

Validation of the model for one CNT content

In our previous work [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF], we have shown that the conductivity variation of CPC under extensional deformation can be linked to the Weissenberg number expressed as:

𝑊 𝑖 = 𝜆 𝑤 . 𝜀̇ Equation 10
where 𝜆 𝑤 is the characteristic time taken as the weight average relaxation time of the pure matrix deduced from a N modes Maxwell model [START_REF] Bird | Dynamics of polymeric liquids[END_REF] applied on the master curve of the pure matrix [START_REF] Ferry | Viscoelastic properties of polymers[END_REF]. For low Wi, there is a strong competition between the network restructuring and breakup. However, at large Wi, the destruction is predominant and from this point all the curves merge to the same maximal deformation that is when the specimen become electrically insulating. Without going into details, the choice of the weight average relaxation time among different possible averaging has been guided by the fact that it more reflects the polymer viscoelastic behavior because it contains the effect of both the average molar mass and the molar mass distribution.

Figure 2 shows, on a linear scale, the measured and calculated conductivities for low Wi.

First, it can be observed that the proposed model well describes the strong competition between network structuring and breakup that is characterized by the maximum of conductivity in Figure 2. Obviously this type of maximum is present only if the sample is not initially at equilibrium as a consequence of its preparation process (𝜑 0 < 𝜑). In this respect, it can be mentioned that this effect of a relaxation was already shown [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF] by recording the conductivity increase after cessation of elongation. For comparison, the conductivity calculated using the model proposed by Skipa et al [START_REF] Skipa | Shear-stimulated formation of carbon nanotube networks in polymer melts[END_REF][START_REF] Skipa | Influence of shear deformation on carbon nanotube networks in polycarbonate melts: interplay between build-up and destruction of agglomerates[END_REF] and applied to extensional strain is also shown in Figure 2. On this point, it must be recalled that this model has been initially tested only for shearing deformation. However, for extensional deformation, no structuring network induced by the strain has been observed contrary to shear deformation. Indeed, an insulating material will remain insulating under extensional deformation whereas under shear the conductivity can somehow increase [START_REF] Moreira | Aggregation of Carbon Nanotubes in Semi-dilute Suspension[END_REF]. In the present calculation, the parameter 𝑘 1 ′ which represents the kinetic factor for the network building is the sum 𝑘 0 and 𝑘 1 (see Equation 1) and 𝑘 2 is the factor governing the network strain-induced breakup. Indeed, the calculated result is inevitably monotonic so that a conductivity growth followed by a decrease cannot be predicted. Moreover, it must be mentioned that, if 𝑘 1 ′ had not been imposed to 0, the model prediction would tend to a non-zero steady conductivity value for high deformations contrary to the experiment. It can be added that this conductivity maximum observed in Figure 2 that illustrates the briefly predominance of the building mechanism could have been predicted using the model revision proposed by Skipa et al. [START_REF] Skipa | Influence of shear deformation on carbon nanotube networks in polycarbonate melts: interplay between build-up and destruction of agglomerates[END_REF] 0.0 0.5 where different CNTs populations have been considered (each of them being governed by specific kinetic parameters). However, that would have induced an increase of the adjustable parameters number. Consequently, the authors concluded that the solution of the regression is not unique and it is hard to give a physical meaning to all the set of parameters. First, the breaking and building parameters have been determined for a large number of experimental data that cover low and medium Wi. In those specific conditions there is a strong competition between network building and breaking so reliable values of 𝑘 𝑏𝑢𝑖𝑙𝑑 and 𝑘 𝑏𝑟𝑒𝑎𝑘 can be determined. From these calculations, it turned out that the obtained values for the breaking parameter (𝑘 𝑏𝑟𝑒𝑎𝑘 ) were practically independent of the temperature and of the extensional rate. This result will be discussed further.

Conversely, for very large Wi, that is for large extensional rates and low temperatures, it was not possible to adjust the structuring parameter because the structuring mechanism was not noticeable in the measured conductivity. In that specific case, only the breaking parameter has been determined. Nevertheless, at moderate and large Wi, (see Figure 4)

there is also a good description of the conductivity variation.

Concerning the structuring parameter (𝑘 𝑏𝑢𝑖𝑙𝑑 ), an obvious dependence of the obtained values with the temperature was observed whereas they appeared independent of the extensional rate. Moreover, other results that are not detailed in this paper show that this structuring parameter is independent of the filler concentration. This corroborates the assumption that the building mechanism is mainly driven by the polymer mobility in the matrix.

This analysis is summarized in Figure 5 where the variation of the building parameter 𝑘 𝑏𝑢𝑖𝑙𝑑 is displayed as a function of the inverse of the weight average relaxation time w.

which directly depends on the temperature. The variation of w was deduced from the Williams Landel Ferry equation [START_REF] Ferry | Viscoelastic properties of polymers[END_REF]. The details of the rheological behavior of the used PS matrix are given in Reference [START_REF] Marcourt | An original combined method for electrical conductivity measurement of polymer composites under extensional deformation[END_REF]. The correlation is very clearly shown in Figure 5 indicating that the building mechanism is controlled by the molecular mobility of the polymer. Indeed, when the viscosity of the polymer decreases, the structuring mechanisms that are composed of diffusion of single CNTs and agglomeration of close aggregates are enhanced. On the other hand for a frozen polymer (𝜆 𝑤 → ∞), the network cannot be rebuilt anymore (𝑘 𝑏𝑢𝑖𝑙𝑑 → 0). Here, a linear dependence between the building parameter and the inverse of the characteristic time of the polymer is obtained. Hence, for the following and for experiments at low temperatures (140°C and 160°C) where the structuring parameter could not be directly fitted on the measured conductivity, it has been calculated from the relation displayed in Figure 5. This important result shows that the polymer dynamics drives the network structuring.

Thus, the building parameter can be obtained from the relaxation time of the pure matrix and the Williams Landel Ferry coefficients for a given temperature. Consequently, Equation 9can be rewritten:

𝑑𝜑 𝑒𝑓𝑓 𝑑𝑡 = 𝛼 𝜆 𝑤-𝑇 𝑟𝑒𝑓 𝑎 𝑇 (𝜑 -𝜑 𝑒𝑓𝑓 ) -2𝑘 𝑏𝑟𝑒𝑎𝑘 𝜀̇2𝜑 𝑒𝑓𝑓 𝑡 Equation 11
where 𝛼 and 𝑘 𝑏𝑟𝑒𝑎𝑘 are dimensionless constants that depends on the material (𝛼 is characteristic of the matrix and 𝑘 𝑏𝑟𝑒𝑎𝑘 characteristic of the filler network).

0.41

As regards the breaking parameter 𝑘 𝑏𝑟𝑒𝑎𝑘 , the obtained values are summarized in Figure 6 where they are plotted versus the extensional rate. As it was already mentioned, the breaking parameter appears independent of the extensional rate. In this regard, it can be pointed out that this independence is consistent with the approach of Leonov [START_REF] Leonov | On the rheology of filled polymers[END_REF] who considered a breaking mechanism dependent on the squared deformation rate as it appears in the second member of Equation 11(in the model of Leonov, this comes from the second invariant of the shear rate tensor). Then, from all these results, Equation 11 will be used in the following with constant values of 𝛼 and 𝑘 𝑏𝑟𝑒𝑎𝑘 , respectively set to 0.41 and 1.3.

Figure 6:

Breaking parameter versus the extensional rate.

Generalization to other CNT contents

The domain of validity of the model proposed in the present work has been tested on materials with different filler concentrations in the range between 0.38 vol% and 1.9 vol% of CNT in PS and at different extensional rates. Here, for sake of simplification, it is assumed that the filler dispersion quality is comparable for the different tested concentrations.

However, it must be conceded that this assumption is questionable especially for large filler concentrations where there is a larger population of big agglomerates and at very low filler concentrations (lower than 0.5vol%) where the fillers are more dispersed and consequently, the structuring mechanism are quite limited. k break (s -1 )

1.3

In a previous work, the Hencky strain where the specimen conductivity reaches 10 -6 S/cm (εσ) has been arbitrarily considered as the transition between conducting and insulating behaviors. This limiting value is again considered here to characterize the composites behavior under different extensional conditions. Figure 7 displays experimental and calculated data obtained at 0.1 s -1 and 160, 180, 200 and 210 °C. The experimental data are chosen to cover low and large Wi values. For the calculated data, an initial efficient concentration 𝜑 0 of CNTs that belongs to the percolated network has been set to 95% of the total filler concentration 𝜑. This value corresponds to the initial measured value of conductivity and this illustrates the fact that the specimen is not totally at equilibrium at the beginning of the measurement.

At large Wi, (see Figure 7a and 7b) the model correctly predicts the evolution of εσ for different filler concentrations and extensional conditions. Figure 7c and 7d display εσ for close Wi values but obtained in different extensional conditions. At Wi = 0.4 there is a very good prediction of the model. However, at Wi = 0.2, the prediction of the model is acceptable, except for large concentrations (higher than 1.2 vol%). In those cases, the maximal deformation is overestimated and even predicts εσ that are larger than the specimen deformation at break. Indeed, under extensional deformation, the specimens break approximately after a Hencky strain of 4, however, from a Hencky strain of 3.5, the specimen becomes very thin and the homogeneity of the strain in the sample may not be ensured anymore. Consequently, the structuring mechanism may be disrupted while it is still considered in the model. Hence, at low temperatures, the building parameter is small so that it does not impact the prediction. However, at higher temperature (for instance 210°C) the structuring factor is quite important and leads to an overestimation of the εσ. With the decrease of Wi, the material can undergo larger deformation before becoming electrically insulating (from Wi = 1). This transition from large to low Wi can be well observed in Figure 8.

Conclusion

In this work, a new model for the description of the conductivity variation of Conductive Polymer Composites under extensional deformation has been proposed and tested for large ranges of CNTs concentrations and extensional rates. First of all, the proposed model gives the possibility to describe the conductive to insulating transition for experimental conditions that cover a large range of Wi values. Indeed, it well describes the conductivity variation when the destruction is predominant but also when there is a strong competition between structuring and destruction of the network. We have also observed that the structuring mechanism only depends on the temperature and, more precisely, it is directly linked to the weight average relaxation time of the pure matrix. This means that the effect of the temperature on the building parameter can be determined using the Williams Landel Ferry equation applied to the polymer matrix. Hence, the temperature effect is solely in the structuring mechanism. Moreover, the breaking mechanism has been considered directly dependent of the deformation and it turned out that it was independent of the temperature and of the extensional rate. In some cases, the model overestimates the limit of the material. It occurs when the structuring parameter is quite large. After large deformation, the network structuring cannot be considered anymore as efficient as it would for an isotropic filler network.

This model presents a large domain of validity and gives the possibility to predict the limit of the composite under extensional deformation. We assume that the building and breaking parameters are linked to the type of CNTs and the dispersion state of the CNTs within the polymer matrix. In addition, this model can be extended to different kinds of composites. For example, it can be successfully applied to specimens made of High Impact Polystyrene matrix filled with CNT. Moreover, the model might be generalized to take into account other types of deformation such as planar flow or even shear.

List of figures and tables

Figure 2 :

 2 Figure 2: Conductivity variation as a function of the Hencky strain for material PS/MWCNT

Figure 2

 2 Figure 2 shows the model of Skipa et al. fails at describing the experimental data.

Figure 3 and

 3 Figure 3 and Figure 4 display the conductivity variation of PS/MWCNT (0.79 vol %) under

Figure 3 :

 3 Figure 3: Conductivity as a function of the Hencky strain of PS/MWCNT (0.79 vol%) for low

Figure 4 :

 4 Figure 4: Conductivity as a function of the Hencky strain of PS/MWCT (0.79 vol%) for large

Figure 5 :

 5 Figure 5: Structuring parameter versus the inverse of the weight average relaxation time of

Figure 7 :

 7 Figure 7: Maximal deformation before conductive/insulating transition for PS filled with CNT

Figure 8 :

 8 Figure 8: Model prediction of the maximal Hencky strain before conductive/insulating

Figure 1 :Figure 2 :

 12 Figure 1: Evolution of the filler network under extensional deformation

Figure 3 :

 3 Figure 3: Conductivity as a function of the Hencky strain of PS/MWCNT (0.79 vol%) for low

Figure 4 :

 4 Figure 4: Conductivity as a function of the Hencky strain of PS/MWCT (0.79 vol%) for large

Figure 5 :

 5 Figure 5: Structuring parameter versus the inverse of the weight average relaxation time of

Figure 6 :

 6 Figure 6: Breaking parameter versus the extensional rate.

Figure 7 :

 7 Figure 7: Maximal deformation before conductive/insulating transition for PS filled with CNT

Figure 8 :

 8 Figure 8: Model prediction of the maximal Hencky strain before conductive/insulating

Acknowledgements

This work was funded by the French National Association for Research and Technology and the company Total (CIFRE convention N°2014/0672). The authors kindly thank doctor G.

Seytre and technician L. Cavetier for helping setting-up the home made EVF system and engineer and laboratory technician Eddi Scandino for the generation of the different composites.


domain: sdv spi

text:
Marwen Moussa

Ivan Tojo

Cédric Andrianirina

Florent Plessis

Sandra Allais

Effect of

Marwen Moussa *1 , Tojo Ivan Andrianirina 2 , Cédric Plessis 3 , Florent Allais 2 & Sandra Domenek 3

Effect of incorporating cellulose nanocrystals on the mechanical, thermal, morphological and transport properties of nanocomposite poly(vinyl alcohol) membranes Context § Bioethanol dehydration using pervaporation process is considered as more flexible, cleaner and requiring less energy than azeotropic distillation and molecular sieves [1]. § During the last decade, considerable efforts have been put in the development of innovative membranes in the quest of better chemical, hydrothermal and mechanical stability and optimized perm-selectivity perfomances [2]. § With the increasing drive towards the valorization of environmentally friendly biopolymers, the use of cellulose nanocrystals (CNC) as nanosized reinforcements in PVA has attracted considerable attention to replace the traditional mineral fillers and take advantage of the large specific surface area and interesting mechanical properties of CNC [3,4].

Membrane preparation:

z= membrane thickness The total fluxes obtained for PVA and PVA/CNC membranes were quite the same (9.5 10 -6 kg.m -2 .s -1 ) and compare well with commercial PVA membranes.

D i = diffusion coefficient S i = sorption coefficient

Conclusion & Prospects

CNC allow for increase of mechanical stability of PHV membranes Optimization of CNC/PVA permeability and long term stability by adapting CNC content Reactive CNC surface allows for surface grafting to obtain higher compatibility Pervaporation experiments:

• Trials using permeation cell: performed using a laboratory-scale unit in static mode; feed temperature= 60°C; PVA and PVA-CNC membranes (flat area of 34.21 cm²).

• Pilot plant trials: performed using a pilot unit; feed flow rate= 100 kg.h -1 ; feed temperature= 60°C; permeate pressure= 300 Pa.

PVA and PVA-CNC membranes (flat area of 170 cm²). • S MetOH < S EtOH even though MetOH is more hydrophilic than EtOH.

• S EtOH was the lowest at 3% CNC: this loading level is close to the percolation threshold.

• At 15% loading level, CNC aggregates would limit the sorption capacity. .Pa -1

)

  p i,p = partial pressure of component i in the permeate side p j,f = partial pressure of component j in the feed side P i = permeance t= permeation time i )=total (partial) flux m= permeate weight A= membrane surface area To study the characteristics of dense nanocomposite membranes based on PVA and CNC according to the sorption-diffusion mechanism. Different techniques were used : thermogravimetric analysis, differential scanning calorimetry, morphological and mechanical analyses, sorption and pervaporation experiments. PVA membranes with CNC loading levels between 3 and 30% w/w were successfully prepared. Average thickness was about 35±5 µm. DSC results showed that CNC loading did not change Tg (about 55°C) and crystallinity degree (about 40%) TGA analysis data show: • CNC were decomposed prior to the PVA • Thermal decomposition of PVA/CNC membranes shifted towards lower temperature Tensile properties: CNC loading improves the mechanical resistance PVA membranes with 15% CNC proved to be stable during pilot plant trials.

( 1 )

 1 UMR 782 GMPA, INRA-AgroParisTech, 1 avenue Lucien Brétignières, F-78850 Thiverval-Grignon, France (2) Chaire ABI -AgroParisTech , 247 rue Paul Vaillant Couturier, F-51100 Reims, France (3) UMR 1145 GéNiAl, INRA-AgroParisTech, 1 rue des Olympiades, F-91744 Massy, France

•

  Using the UNI ISO 527-3 standard CNC loading (% w/w) CNC loading (% w/w) Young modulus (MPa) Tensile strenght (MPa) weight (%) Membrane permeability decreased at 3% CNC for EtOH but remained constant for MetOH Diffusion coefficient data show: • Higher values for MetOH than for EtOH. Indeed, methanol has smaller molecular size. • For both EtOH and MetOH, D decreased with the increase of CNC loading: à tortuosity effect Sorption coefficient data show: • Higher values for EtOH than for MetOH except at 3% CNC loading level.

[ 1 ]

 1 Kaminski W., Marszalek J., Ciolkowska A. 2008. Chem. Eng. J. 135: 95-102 [2] Wee S. L., Tye C. T. and Bhatia S. 2010. Sep. Purif. Technol. 71:192-199 [3] Flynn, E.; Keane, D.; Tabari, P.; Morris, M. (2013). Sep. Purif. Technol., 118: 73-80. [4] Mohanty, A. K.; Drzal, L. T.; Misra, M. (2003). Polym. Mat. Sci. Eng. J., 88: 60-61.MW (g.mol -1


Nohade Nasrallah

Muneer M Alshater
email: muneermaher@gmail.com

Hazem A Marashdeh
email: hazem.marashdeh@adu.ac.ae

Osama F Atayah
email: dr.osamaatayah@gmail.com

Corporate Governance through the lens of "Corporate Governance: An International Review-CGIR": A Three Decade Retrospective Analysis

Keywords: The analysis is beneficial for the scientific community, CG institutes, corporations, universities, scholars, and governmental entities Corporate Governance, Corporate Governance: An International Review, Bibliometric, Scientometric

Research Findings/Insights: Using 1,112 documents from the Scopus database over 1993-2021, we found that CGIR has established itself as a prominent journal in the field of corporate governance (CG) by extensively contributing to the exploration and maturation of its concepts and theories. The study identifies four main clusters: CG and Executives' compensation schemes, CG and performance, CG key stakeholders, and CG pillars. CGIR is recommended to have further studies about CG topics in small and medium enterprises and developing countries.

Theoretical/Academic Implications:

We gather 1,112 documents over 1993-2021 and apply bibliometric techniques encompassing bibliographic coupling, keyword analysis, and content analysis using R-Studio and VOSviewer. It is also worth investigating CG topics in conjunction with the rise of ESG publications from regional, national, and global perspectives.

INTRODUCTION

The concept of corporate governance (CG) remains controversial, and its nexus draws concerns and prompts deep investigation. Analyzing CG evolution and its semantic discourse serves to understand its major strands. Systemic perturbations, economic disturbance, and financial turmoil might explicate CG regulatory substance and institutional status as it is "the system by which companies are directed and controlled" (Cadbury, 1992:15). This system is the composite of "ownership, boards, incentives, company law, and other mechanisms" (Thomsen, 2008:15).

Historically, the CG concept is impregnated by the work of Berle and Means (1932) when the separation of ownership and control arises as a coercive solution to mitigate agency problems. This view was opposed by fragmented ownership-control that led to self-interest managers acting for their own sake at the corporate expense. The problem was then decomposed to analyze the anatomy of the board of directors (BOD). To align their interests with the owners, companies should design mechanisms and incentives [START_REF] Shleifer | A survey of corporate governance[END_REF] that are attuned to the national institutional, cultural, and regulatory infrastructures [START_REF] Aguilera | The cross-national diversity of corporate governance: Dimensions and determinants[END_REF].

To factor CG focus from the traditional shareholder to a broader stakeholder focus with intrinsic value, the topic spreads to converge with managerial and legal issues [START_REF] Aguilera | Global corporate governance: On the relevance of firms' ownership structure[END_REF]. In some studies, the national systems highlight the importance of common versus civil law systems as determinants of variation in the quality of CG systems [START_REF] Fainshmidt | Varieties of institutional systems: A contextual taxonomy of understudied countries[END_REF]. Recently, the surge of artificial intelligence and other emerging technologies pinpoints the preponderance of automating board-level decision-making [START_REF] Hilb | Toward artificial governance? The role of artificial intelligence in shaping the future of corporate governance[END_REF].

Notwithstanding, CG is constitutive and reflective of broader socio-political and historical contexts, its repercussions swing between two main views: whether stronger corporate and financial regulations impose costly constraints on managerial actions or whether such chains Electronic copy available at: https://ssrn.com/abstract=4182574 [START_REF] Porter | Creating shared value[END_REF] are worthy of constraining managers from tunneling out [START_REF] Johnson | Tunneling[END_REF] or misallocating the firm's wealth. In this sense, BOD's roles stem under three interrelated aspects: supervisor, co-creator, and supporter [START_REF] Cossin | How strategic is your board? MIT Sloan Management Review Sloanselect Collection[END_REF]. CG should be designed to focus on corporations' long-term intrinsic corporate value and evade short-term financial engineering that aims to meet the numbers for executive compensation purposes [START_REF] Grove | Evolution of corporate governance towards intrinsic value[END_REF].

All the above phases have deeply marked CG field and their transcendental linkage is worth commenting. Intrisincally, the analysis and assessment of the journal venues and authors' productivity are still a major sticking point in the academic and scientific communities. The diversity and multitude of used metrics are contested and skeptically perceived. Whether the metric is mathematically and statistically proven or commercially biased for reputational purposes, the process engenders confusion and ambiguity. Concurrently, this trend is confronted with the digital transformation and social media that shift the analysis towards more digital metrics that can retrace blogs, comments, and feedback and mainly constitute an informal way to draw about the visibility and likability of scholar activities [START_REF] Ortega | To be or not to be on Twitter, and its relationship with the tweeting and citation of research papers[END_REF].

In the present paper, we attempt to understand CG evolution from the lenses of an exclusive CG outlet: the journal of Corporate Governance: An International Review (CGIR). We extend the study of [START_REF] Durisin | Maturation of corporate governance research, 1993-2007: An assessment[END_REF] that has assessed CG research evolution based on the analysis of the intellectual basis of 527 CGIR documents and 539 extracted from 15 important outlets. They found that CG reached maturation as a discipline. Yet, methodological approach and empirical grounding should be promoted to enable studying CG from the global perspective. Thus, we invigorate a blend of conventional and novel mediums to outline a comprehensive and wealthy database of 1,112 publications. CGIR's inaugural in 1993 demarcates CG's burgeoning era after the Cadbury report in 1992. Recently, the journal embarked on digital social media like "Twitter" to post important scholarly production messages in a distinctive approach, whereby new publications, announcements, discussions, and feedback are gathered. Thus, we investigate the following research questions: (RQ1) What is CGIR publications and citations trend over the last 29 years ? (RQ2) What are CGIR's most-cited papers? (RQ3) Who are the most productive and influential authors, institutions, and countries? (RQ4) What are CGIR thematic patterns? (RQ5) Which topics reveal to be persistent, hot, or cold?

We apply bibliometric analysis to synthesize the scattered large body of data, structure them based on specific algorithms, and extract valuable findings. To our knowledge, no prior bibliometric studies were conducted for CGIR. However, thanks to the emergence of scientific databases such as Scopus and Web of Science, we were able to extract significant data to pursue a complete analysis. In addition, powerful software such as Visualization of Similarities VOS and Biblioshiny package (R-studio) permits objectively performing the quantitative analysis [START_REF] Van Eck | Software survey: VOSviewer, a computer program for bibliometric mapping[END_REF] and helps in drawing the lines for qualitative analysis. Accordingly, the present research provides a comprehensive review and contributes to understand CG theories and concepts. It serves to (1) elaborate on CGIR major theoretical and empirical contributions, (2) identify top and most influential scholars in terms of journals, countries, and affiliations, (3) describe co-authorship relations and collaboration status and highlight their preponderance to curb citation trends, and (4) pinpoint CGIR motivational strategies to expand its visibility further.

Results indicate that the United Kingdom and the United States are the top contributors with 267 and 223 documents, respectively, and 9,960 and 9,305 citations, respectively. The top cited paper is the study of [START_REF] Erhardt | Board of director diversity and firm financial performance[END_REF] titled "Board of director diversity and firm financial performance" with 795 citations. Moreover, the conceptual structure map concludes to four clusters: CG and Executives' compensation schemes, corporate governance and performance, corporate governance key stakeholders, and corporate governance pillars.

The organization of this paper is as follows. Section 2 introduces the study's methodology, while section 3 reports the results, divided into three major parts (publication analysis, citation analysis, and network analysis). Section 4 provides the content analysis of each cluster. Finally, section 5 concludes with a summary of findings.

DATA AND METHODS

In this study, we collect the data of CGIR from the Scopus database from 1993 to 2021.

These documents consist of 824 articles, 96 conference papers, 91 reviews, 90 editorials, 7 notes, 3 errata, and 1 letter. We apply bibliometric analysis, which stems from a citation-based research approach. According to [START_REF] Pritchard | Statistical bibliography or bibliometrics[END_REF], this method assesses scientific publications using statistics and mathematics. Statistical results can provide meaningful insights into the research works published in a specific journal and the research domains covered [START_REF] Alshater | Journal of Sustainable Finance and Investment: A bibliometric analysis[END_REF][START_REF] Baker | Twenty-five years of the Journal of Corporate Finance: A scientometric analysis[END_REF]Dhiaf, Atayah, Nasrallah, & Frederic, 2021;[START_REF] Hassan | Twenty-nine years of the Journal of International Review of Economics and Finance: A scientometric overview (1992-2020)[END_REF][START_REF] Nasrallah | Intellectual Structure of Knowledge Management: A Bibliometric Analysis of the Journal of Information and Knowledge Management[END_REF]. Through the use of bibliographic information and by the use of dedicated software, both performance analysis and scientific mapping can be conducted [START_REF] Donthu | How to conduct a bibliometric analysis: An overview and guidelines[END_REF]. The performance analysis reveals the influential aspects of the literature, such as the most relevant and impactful documents, authors, sources, institutions, and countries. While scientific mapping produces visual interrelations between scientific actors, studies apply keyword co-occurrences, coauthorships, and co-citations. Recently, the bibliometric approach has been combined with content analysis to provide a deeper insight into the content explored, revealing the clusters of the most discussed topics in the studied literature. We perform a conceptual structure map based on the terms in the documents' titles and abstracts and follow Porter's stemming algorithm using R-studio and the natural language processing (NLP).

RESULTS

First, we start by providing a summary about CGIR and then move to discuss our main descriptive analysis. CGIR is published by John Wiley & Sons Ltd, UK. Its current editors are Konstantinos Stathopoulos, from the University of Manchester, UK, and Till Talaulicar, from the University of Erfurt, Germany. Grounded by an interdisciplinary research vector in accounting, economics, finance, law, management, sociology, and political science, CGIR harvested 38,966 citations up to this study cutoff date (Mid October -2021). Its impact factor is 3.396, and its 5year impact factor is 6.309. It has an H-index of 104 based on SCImago Journal Rank (SJR), which implies that at least 104 articles have been cited at least 104 times. The best quartile for this journal is Q1. It is indexed in almost all the major databases, including Scopus and Web of Science. Also, it enjoys strong rankings in both the Australian Business Dean Council (ABDC) and the Association of Business Schools (ABS) lists. CGIR is ranked "A" in the ABDC's 2021 journal (ABDC ranking has four categories: A*(highest), A, B, C (lowest)) and rated "3" in the ABS's Academic Journal Guide (AJG) in 2021 (ABS ranking has five categories: 4* (highest), 4, 3, 2, 1(lowest)).

In the next section, we will discuss CGIR yearly productivity in terms of publications and citations. We will also present results related to top authors, affiliations, and countries, and conclude with the network analysis.

Distribution of Publications and Citations

Figure 1 illustrates the annual productivity of the journal. CGIR experiences a strong start by publishing 45 articles in its inaugural year which implies the appetite to investigate CG topics and shed light on its interrelated facets. Notably, the performance and productivity of the journal in terms of publications can be divided into three periods. The first period (1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003) witnesses a strong start with an average of 28.9 documents per year. The second period (2004)(2005)(2006)(2007)(2008)(2009) depicts a sharp increase in publications with an average of 59.7 documents per year. Notably, 2007 stands as the most productive year for the journal, with 108 published documents distributed in five issues. Finally, the third period (2010-2021) represents a steady-state for the journal, with an average of 34.7 published documents per year.

Figure 1 CGIR Yearly Productivity Previous studies argue that the influence of a journal in the scientific community is measured by its citations [START_REF] Tsay | Citation analysis of Ted Nelson's works and his influence on hypertext concept[END_REF][START_REF] Svensson | SSCI and its impact factors: a "prisoner's dilemma[END_REF]. Table 1 presents the total citations over with 38,966 citations and 35.04 average citations per document. Remarkably, the highest number of publications and citations (5721) is depicted in 2007. In general, 88.68% of the 11 11 10 4 5 5 9 7 5 5 8 13 9 6 9 6 9 6 6 7 8 4 5 5 5 5 7 4 4 10 9 9 7 2 4 6 6 6 5 6 14 18 6 Electronic copy available at: https://ssrn.com/abstract=4182574

CGIR published documents are cited. This provides clear evidence of the influence of published topics on the scientific community. However, 2003 was the most influential year in terms of average citation per cited document (80.2), followed by 2009 (77.4). In addition, 76 documents out of 996 cited ones (7.63%) were awarded more than 100 times, 154 documents (15.46%) between 50-100 times, 472 documents (47.40%) between 10-49 times, and 294 documents (29.51%) between 1-9 times. Given that recent publications need time to accrue, we notice the decline in citations for the last three years, 2019, 2020, and 2021. On the other hand, the collaboration index (CI) represents the degree of collaboration among authors and was first derived by [START_REF] Lawani | Some bibliometric correlates of quality in scientific research[END_REF]. This index represents the average number of authors per article. It is calculated as the total number of authors divided by the total multi-authored articles published during a specific period. The CI for the CGIR over 1993-2021 is 1.85, implying a low collaboration among authors though several previous studies argue for enhancing scholars' technical and scientific collaboration [START_REF] Ding | Scientific collaboration and endorsement: Network analysis of coauthorship and citation networks[END_REF][START_REF] Koseoglu | Mapping the institutional collaboration network of strategic management research: 1980-2014[END_REF][START_REF] Finardi | Scientific collaboration framework of BRICS countries: an analysis of international coauthorship[END_REF]. ). In terms of the composite impact of the m-index, the results show that Praveen Kumar is ranked first with an m-index of 1.111 (above the average of 1), followed by Zattoni with 0.652. The United Kingdom and the United States headed the list from the countryside with remarkable publications of 267 and 223 documents, respectively. Both countries have earned the highest citations of 9,960 and 9,305 citations, respectively. Australia ranked third with 94 published documents and 5,785 citations. The significant contributions by authors from different countries around the world reflect the prestigious position of the CGIR in the scientific community.

It is worth commenting that the Cadbury, with the promulgation of its novel code of best practice and its innovative "comply or explain" enforcement scheme, has many global ramifications. The governance code movement has swept from the U.K. all over the world and this is attributed primarily to the distinctive brand of corporate governance reform pioneered by the Cadbury Committee. Here, Total number of publications, Total citations, h-index, g-index, m-index, Citation per publication, and Year of start = the starting year of publication. The h-index for an author indicates the h number of his/her publications cited at least h times. The m-index aims to weigh the period of academic endeavor to reduce the bias in favor of scientists with longer careers. It is measured by dividing the h-index by the number of years of publication. The g-index (g) accounts for the g number of highly cited publications receiving at least g 2 citations.

Figure 2 we apply Lotka's law. This law predicts the relative frequency distribution of the author's

Electronic copy available at: https://ssrn.com/abstract=4182574

productivity. The generalized form of Lotka's law is an inverse square function, where the minority of authors publish most publications. Table 3 shows that out of 1270 authors (81.3%) published one document, 187 authors (12%) two documents, and 3 authors (0.002%) published more than 10 documents. Interestingly, all groups have contributed less than expected based on Lotka's law. Lotka law states that the number of authors making "n" contributions is about 1/n 2 of those making one contribution. The deviation of the observed function from the predicted inverse square function acts as a metric for the inequality in productivity of the field

Citation Structure

Citation analysis is one of the most significant tools used to understand the journal's qualitative influence and contribution to the academic literature [START_REF] Uysal | Business ethics research with an accounting focus: A bibliometric analysis from 1988 to 2007[END_REF]. To have a broader and thorough insight into the citation structure of CGIR, a citation analysis was carried out over 1993-2021. Figure 3 shows that CGIR harvested 38,966 citations with a peak citation over 2002-2007, highlighting the highest citation growth rate. This is attributed to the appetite to describe CG topics and the global tendency to focus on CG effects in the context of the worldwide economy.

Between 2008 and 2016, CGIR experienced steady growth, while the last four years ended with the lowest citation growth, a fact ubiquitous across academic journals due to the time-specific nature of citations which induce that recent publications need time to accrue [START_REF] Baker | Twenty-five years of the Journal of Corporate Finance: A scientometric analysis[END_REF].

Electronic copy available at: https://ssrn.com/abstract=4182574 Electronic copy available at: https://ssrn.com/abstract=4182574

implying the total citations received considering the whole bibliographic database, and Normalized

Citations, a ratio of total actual count of citing items to the expected citation rate for documents with the same year of publication.

The most cited paper is the study of [START_REF] Erhardt | Board of director diversity and firm financial performance[END_REF] Electronic copy available at: https://ssrn.com/abstract=4182574

In terms of the most frequently cited journals, Table 5 shows the top 10 journals that CGIR cited over 1993-2021. The most cited source is the journal of financial economics with 3301 citations, followed by CGIR itself with 3065 citations. All these journals are rated A* in ABDC, Quartile 1 (Q1) and are leading journals in their fields, reflecting the high level of quality sources referred to CGIR publications.

Network Analysis (Mapping)

The network analysis relies on themes and keywords grounded by the fact that frequent coappearance of words in different documents indicates similarity and commonality in underlying subjects [START_REF] Callon | _From translations to problematic networks an introduction to co-word analysis[END_REF]. We use VOSviewer to develop mapping and network analyses based on two different factors: the number and power strength between the variables [START_REF] Van Eck | Software survey: VOSviewer, a computer program for bibliometric mapping[END_REF]. This analysis reveals which keywords are often jointly mentioned by authors and thus demonstrates the patterns and trends in a particular knowledge base [START_REF] Callon | _From translations to problematic networks an introduction to co-word analysis[END_REF][START_REF] Ravikumar | Mapping the intellectual structure of scientometrics: A co-word analysis of the journal scientometrics (2005-2010[END_REF]. We identify 1692 keywords out of 1,112 documents which show a high proportion of common words (1.52 words/document). This low ratio indicates CGIR exclusivity and concentration on CG themes.

We then shortlist keywords that appeared at least 5 times and present their co-occurrence cartography in Figure 4. Obviously, the biggest node is the red one titled "Corporate Governance," followed by three other nodes green, blue, and purple. The red cluster shows the substantive investigation in CG main theory and the board role such as "Agency theory", "Boards of directors", "Board structure", and "Board effectiveness". The green node focuses on "Boards of directors" with an emphasis on the importance of "Ownership structure" and "Family firms". The blue node evokes the close connection between CG and Corporate Social Responsibility (CSR) themes. This group encompasses key terms such as "Regulation", "Directors", "Power", "Diversity", "Performance" and "Shareholder activism". The purple cluster emphasizes CGIR international wingspan to publish CG from a country perspective. The related keywords in this group are "Institutional theory", "Corporate governance codes", "Shareholder value", "Board of director mechanism", "Business groups", "Board policy issues", "United Kingdom", "Japan" and "Italy".

To gain more insights, we draw on the historical trend of the keywords' patterns by time (Figure 5). It reflects CGIR main published topics over the last 16 years (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020)(2021). Keywords co-occurrence is now schematized through a smart color grading tool where the darks color represents the oldest keywords till gradually reflecting on recent trends highlighted in light colors.

The objective of the analysis is to orient readers to know about CGIR research theme trends (persistent, cold, and hot). Early research (dark blue) tackled CG ubiquitous components "Governance", "Directors", "Power", "Regulation", and "Shareholders" while the recent ones (light yellow) shifted scholars' interests towards "Family ownership", "Family firms" and "Resource dependency theory", "Corporate governance codes", "Ownership mechanisms", and "Boards of directors mechanisms". From a country standpoint, Figure 6 showcases the voluminous contribution of the United Kingdom (UK) to CGIR productivity followed by the United States of America (USA). Yet, the USA is placed at the centre of almost all geographical networks. For instance, the UK is mainly collaborating with the USA, Japan, Switzerland, Austria, Hong Kong, South Korea, Canada, and Denmark. At the same time, the USA has strong authorship collaborations with the UK, China, Germany, South Korea, Spain, Hong Kong, Canada, and Taiwan. Australia is also collaborating with China, the USA, and New Zealand. This normative indicator signals network diversity behind CGIR productivity and its broad spectrum of research.

CONTENT ANALYSIS

The content analysis serves to extract concepts into fewer content-related themes, revealing clusters that share the same meaning to attain condensed and broad representation for a particular knowledge domain [START_REF] Krippendorff | Emerging trends in content analysis[END_REF]. Researchers are nowadays able to gather scattered data, refine it, and adequately analyze it due to new technologies [START_REF] Stemler | Emerging trends in content analysis[END_REF]. In the below section, three analyses were generated to consolidate our previous findings and shed light on specific arrays of CGIR productivity: three-field plot analysis, trend and keywords analysis, and conceptual structure and discussion.

Three-Field Plot Analysis

The three-field plot shows the relationship between the author's keywords (research contents = middle field), authors affiliates (intellectual roots = rightfield), and the top authors' countries (left field). On the country level, Figure 7 shows that the UK, USA, Australia, China, Italy, Spain, Canada, Germany, Netherland, and Belgium have thoroughly focused on "Governance" themes. In addition, related CG themes like the "Agency theory" and "Boards of directors" have attracted many countries. In contrast, many universities have enriched the set of CG diversified topics, such as Copenhagen Business School, University of Groningen, and Bocconi University.

Trend and Keywords Analysis

To understand CGIR thematic structure thoroughly, we apply a trend analysis that captures similar themes and repetitive keywords based on 1,692 keywords extracted from 1,112 documents.

We aim to discover CGIR persistent trends and elaborate on the consolidated efforts to publish CG topics exclusively. Accordingly, we notice that the keyword "Corporate governance" is the most frequent (572) times, followed by "Board of directors" (82) times, "Agency theory" (56) times, the "Board Composition" (43), "Firm performance" (37), "China" (32), "Ownership

Electronic copy available at: https://ssrn.com/abstract=4182574

structure" (30), "Corporate social responsibility" (29), and "family firms" (22). Furthermore, the recent publication trend is schematized in Figure 8 for 1996-2021. The "Agency theory" depicts a bell shape with a peak in 2008. On another note, though the "Board of directors" was persistently investigated, it lost its attractiveness in 2015 and after that reverted to be the most popular CG theme.

Figure 8: CGIR Keyword Trends (1996-2021)

Conceptual Structure and Discussion

In this part, we perform a conceptual structure map based on the terms in the documents' titles and abstracts. We first paid attention to excluding editorials and manuscripts with no abstracts or keywords. Next, we rely on 668 documents and follow Porter's stemming algorithm using Rstudio and natural language processing (NLP). We thus identify four clusters as depicted in Figure 9. The first (purple) cluster mainly tackles "CG and Executives' compensation schemes" from the left. The second (blue) cluster is related to "Corporate governance and performance" While the Electronic copy available at: https://ssrn.com/abstract=4182574 third (red) cluster is "Corporate governance key stakeholders" the last (green) cluster concerns "Corporate governance pillars". In this latter instance, it was found that minority shareholders' interests cannot be protected even in the presence of independent directors and external governance mechanisms [START_REF] Huyghebaert | Expropriation of Minority Investors in Chinese Listed Firms: The Role of Internal and External Corporate Governance Mechanisms[END_REF]. The cluster covers a set of rich manuscripts that explores CG facets and main characteristics from contextual, geographical frameworks [START_REF] Carlsson | Swedish corporate governance and value creation: Owners still in the driver's seat[END_REF][START_REF] Kim | The proportion and social capital of outside directors and their impacts on firm value: Evidence from Korea[END_REF][START_REF] Muramiya | How cross-shareholding influences financial reporting: Evidence from Japan[END_REF][START_REF] Ngo | Do OECD-type governance principles have economic value for Vietnamese firms at IPO? Corporate Governance[END_REF]). In addition, many studies covered ownership and control structure [START_REF] Arslan | Ownership and control structure as determinants of corporate debt maturity: A panel study of an emerging market[END_REF][START_REF] Brennan | Boards of directors and firm performance: Is there an expectations gap? Corporate Governance[END_REF][START_REF] Lopatta | International Evidence on the Relationship between Insider and Bank Ownership and CSR Performance[END_REF]; boards composition [START_REF] Yoshikawa | How do board ties affect the adoption of new practices? The effects of managerial interest and hierarchical power[END_REF] and other CG areas. Nevertheless, the bulk of the first cluster publications was dedicated to investigating the effect of CG on CEO and top executives compensation schemes [START_REF] Sun | Rewarding poor performance: Why do boards of directors increase new options in response to CEO underwater options? Corporate Governance[END_REF][START_REF] Siming | Orders of Merit and CEO Compensation: Evidence from a Natural Experiment[END_REF][START_REF] Cho | The use of nonfinancial performance measures in CEO bonus compensation[END_REF][START_REF] Jiang | Chairperson collectivism and the compensation gap between managers and employees: Evidence from China[END_REF][START_REF] He | Managerial Labor Market during Institutional Transition: A study of CEO compensation and voluntary turnover[END_REF][START_REF] Mukherjee | Can Benford's Law explain CEO pay? Corporate Governance[END_REF].

Electronic copy available at: https://ssrn.com/abstract=4182574 governance" in all clusters, the "Agency theory (34)" gained the highest attraction in this group followed by "Shareholder value (15)", "Board composition (11)", "non-executive directors (11)"

and "Institutional theory (10)". Looking at the keyword trend evolution in Figure 11 (right side), we notice that most topics were persistently investigated. The "Agency theory" was heavily studied in almost all publications but varied yearly. The "Institutional theory" was also discovered but to a lower extent. Topics such as "Shareholder activism" and "shareholders value" have regained attraction in the last 3 years. This cluster encompasses manuscripts that have extensively investigated CG effects on companies' performance from different areas and CG principles and characteristics. For example, some papers have tackled the analysis in the context of large public companies [START_REF] Perrini | Does ownership structure affect performance? Evidence from the Italian market[END_REF][START_REF] Chen | The link between board composition and corporate diversification in Australian corporations[END_REF][START_REF] Solomon | Corporate governance in Taiwan: Empirical evidence from Taiwanese company directors[END_REF], family-controlled firms [START_REF] Van Essen | The Resilient Family Firm: Stakeholder Outcomes and Institutional Effects[END_REF][START_REF] Minichilli | Weathering the Storm: Family Ownership, Governance, and Performance Through the Financial and Economic Crisis[END_REF], and financial institutions [START_REF] Hackethal | Banks and German corporate governance: On the way to a capital market-based system? Corporate Governance[END_REF][START_REF] Kaymak | East meets west? Board characteristics in an emerging market: Evidence from Turkish banks[END_REF][START_REF] Yeh | Committee Independence and Financial Institution Performance during the 2007-08 Credit Crunch: Evidence from a Multi-country Study[END_REF]. Another stream of research provided a systematic review for CG prior literature [START_REF] Farah | Corporate governance in the Middle East and North Africa: A systematic review of current trends and opportunities for future research[END_REF], cross-regional studies [START_REF] Wu | State control, legal investor protection, and ownership concentration: Evidence from China[END_REF], CSR [START_REF] Frynas | Corporate social responsibility and international development: Critical assessment[END_REF][START_REF] Mackenzie | Boards, incentives and corporate social responsibility: The case for a change of emphasis[END_REF], CG codes and regulation [START_REF] Béthoux | What codes of conduct tell us: Corporate social responsibility and the nature of the multinational corporation[END_REF][START_REF] Bondy | Multinational corporation codes of conduct: Governance tools for corporate social responsibility? Corporate Governance[END_REF], women on boards [START_REF] Gabaldon | Searching for Women on Boards: An Analysis from the Supply and Demand Perspective[END_REF], environmental reporting [START_REF] Gibson | Corporate governance and environmental reporting: An Australian study[END_REF][START_REF] Ni | Climate risk and corporate tax avoidance: International evidence[END_REF], risk-taking [START_REF] Mishra | Multiple large shareholders and corporate risk taking: Evidence from East Asia[END_REF] financial reporting and earning management [START_REF] Hamm | Corporate venture capital, disclosure, and financial reporting[END_REF], and on country wealth and income inequality [START_REF] Brou | Corporate governance and wealth and income inequality[END_REF]. From another perspective, the three top-cited publications of the cluster are "Does the presence of institutional investors influence accruals management? Evidence from Australia" [START_REF] Hsu | Does the presence of institutional investors influence accruals management? Evidence from Australia[END_REF], "Do controlling shareholders enhance corporate value?" [START_REF] Yeh | Do controlling shareholders enhance corporate value? Corporate Governance[END_REF], and "A family member or professional management? the choice of a CEO and its impact on performance" [START_REF] Lin | A family member or professional management? the choice of a CEO and its impact on performance[END_REF] with 80 citations each. The second topcited manuscript (78 citations ) is "Continuity and change in corporate governance: Comparing Germany and Japan " [START_REF] Jackson | Continuity and change in corporate governance: Comparing Germany and Japan[END_REF].

Lin & Hu (2007) explore the type, role, and performance of CEO in family firms. The results show that firms with low requirements in managerial skills and a high potential for expropriation are more likely to choose a CEO from the controlling family (nepotism). [START_REF] Hsu | Does the presence of institutional investors influence accruals management? Evidence from Australia[END_REF] examine the effects of both short-and long-term oriented institutional ownership on the extent of earnings management examine. They find that transient institutions are associated with upward accruals management. In contrast, long-term-oriented institutions constrain such upward accruals management for portfolio firms that have strong incentives to do so (specifically, firms

Electronic copy available at: https://ssrn.com/abstract=4182574

with non-discretionary earnings below prior-year earnings). [START_REF] Yeh | Do controlling shareholders enhance corporate value? Corporate Governance[END_REF] explores the effect of shareholders' control and ownership on corporate valuation, emphasizing voting rights in Taiwanese listed companies. He finds that the corporate value is higher when the largest shareholder owns more cash flow rights (ownership). If the cash flow rights owned by the largest shareholder are greater than the median, the positive incentive effect will restrain the negative entrenchment effect. 17)", "Family firms ( 14)", "Stakeholders ( 14)", and "Institutional investors ( 14)". Figure 12 (right side) shows that apart from the extensive and persistent investigation of the topic "Corporate governance," "Board of directors" was steadily explored and has gained a relative attraction in the last 3 years. The top-cited three papers in this cluster are "Where is independent director efficacy?" with 78 citations [START_REF] Luan | Where is independent director efficacy? Corporate Governance[END_REF], "Agency relations within the family business system: An exploratory approach" with 72 citations [START_REF] Den Berghe | Agency relations within the family business system: An exploratory approach[END_REF], and "Compare and contrast: Perspectives on board committees" with 71 citations [START_REF] Spira | Compare and contrast: Perspectives on board committees[END_REF]. [START_REF] Luan | Where is independent director efficacy? Corporate Governance[END_REF] test the impact of independent outside director assignment on a firm's performance in Taiwanese companies. After controlling for a firm's past performance, they find that independent outside director appointments have a significantly positive impact on a firm's performance. In contrast, outperforming firms may have better performance but not significantly when assigning outside directors due to their absorptive capacity. Den [START_REF] Den Berghe | Agency relations within the family business system: An exploratory approach[END_REF] provide various definitions for the family firm and characterize it by agency relations within and between the family system, ownership system, and the business system. [START_REF] Spira | Compare and contrast: Perspectives on board committees[END_REF] tackle the establishment of board sub-committees as an efficient CG mechanism where specific tasks are delegated from the main board to a smaller group to harness the contribution of non-executive directors. Based on the Cadbury committee proposals to focus on audit committees and the Greenbury study group to advocate remuneration committees, the study performs interviews with participants in the audit and remuneration committees. This paper identifies significant differences in the orientation and operation of these committees that may lead to unacknowledged pressures on non-executive directors. This cluster is titled "Corporate governance pillars" and includes 41 documents where notably the following keywords appeared most frequently: "Governance (11)", "Accountability (8)", "Directors and Board of directors ( 11)", and "Board composition (5)". The word dynamics diagram in Figure 13 (right side) reaffirms the persistent popularity of CG topics in addition to specific concentration on some related pillars. The "Board composition" was well explored throughout the period, but its exploration dropped in 2010 and regained its place in the last three years (2019-2021). The "Board diversity" gained attraction in the previous 7 years (2015)(2016)(2017)(2018)(2019)(2020)(2021).

The top-cited articles in this cluster are "Women on corporate boards in Italy: The role of family connections" [START_REF] Bianco | Women on Corporate Boards in Italy: The Role of Family Connections[END_REF] with 72 citations, "Board diversity:

Beginning to unpeel the onion" [START_REF] Hillman | Board Diversity: Beginning to Unpeel the Onion[END_REF] CGIR published 1,112 documents and harvested 38,966 citations. Notably, the performance and productivity of the journal can be divided into three periods. The first period (1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003) witnesses a strong start with an average of 28.9 documents per year. The second period (2004)(2005)(2006)(2007)(2008)(2009) depicts a sharp increase in publications with an average of 59.7 documents per year. Notably, 2007 stands as the most productive year for the journal, with 108 published documents distributed in five issues. Finally, the third period (2010-2021) represents a steady-state for the journal, with an average of 34.7 published documents per year.

CGIR has an impact factor of 3.396 and an H-index of 104. Alessandro Zattoni, affiliated with LUISS University in Italy, is the top author with 37 publications. The most cited paper is the study of [START_REF] Erhardt | Board of director diversity and firm financial performance[END_REF] titled "Board of director diversity and firm financial performance" with 795 citations. In terms of publications and citations, the United Kingdom and the United States are the top countries with 267 and 223 documents, respectively, and 9960 and 9305 citations, respectively. Moreover, the trend analysis of CGIR is based on a total of 1,692 keywords. We perform a conceptual structure map based on the terms in the documents' titles and abstracts. We identify four clusters: the first (purple) cluster mainly tackles "CG and Executives' compensation schemes," the second (blue) cluster is related to "Corporate governance and performance," the third (red) cluster is "Corporate governance key stakeholders," and the last (green) cluster concerns "Corporate governance pillars"

We face some limitations while conducting our analysis. First, the study provides a broad overview of CGIR and is not a substitute for a systematic review. Second, the data collection is limited to the Scopus database, which might constitute a selection bias regarding other sources.

Third, we fail to account for new tools such as "Altmetrics" to account for comments and reviews on the Social Web.

In conclusion, the study draws on CGIR's ability to maintain its position and sustain the main competition. Therefore, we encourage further studies about CG topics in small and medium enterprises and developing countries. It is also worth investigating CG topics in conjunction with the rise of ESG publications from regional, national, and global perspectives.

Electronic copy available at: https://ssrn.com/abstract=4182574

  Figure2shows the top authors productivity yearly productivity over 1993-2021. The top

Figure 2 :

 2 Figure 2: Top Authors Productivity During the Period (1993-2021)

Figure 3 :

 3 Figure 3: CGIR Citation Pattern (1993-2021)To emphasize, a higher number of citations for a published document display a higher

  titled "Board of director diversity and firm financial performance." It harvested the highest number of citations since the inauguration of the journal in 1993. The main aim of the study was to shed light on how board characteristics in terms of racial and gender diversity influence firm performance. The authors discussed the relationship between the percentage of females plus ethnic minorities on the board and the return on assets and equity for a sample of US firms (1993-1998). According to LC, the article was cited 22 times internally in CGIR, while the GC shows that the article was globally cited 769 times in other journals. The second top-cited article is authored by Carter, D'Souza, Simkins & Simpson (2010) titled "The gender and ethnic diversity of US boards and board committees and firm financial performance." This article was cited 9 times in CGIR while 642 times by other journals. The paper examines the relationship between the number of women directors, the number of ethnic minority directors on the board, important board committees, and financial performance measured as return on assets and Tobin's Q. The results show no significant relationship between the gender or ethnic diversity of the board and financial performance for a sample of major US corporations (Carter, D'Souza, Simkins & Simpson, 2010).The third most cited article is authored by Terjesen, Sealy & Singh (2009), titled "Women directors on corporate boards: A review and research agenda." The article studies the gender diversity-firm outcome relationships; it examines how gender diversity on corporate boards influences corporate governance outcomes, impacting performance. The article was cited 26 times CGIR and 616 times in other journals. Notably, the three most cited articles discussed the same topic related to gender diversity and firm performance.

Figure

  Figure 4: Authors' Keyword Cartography

Figure 7 :

 7 Figure 7: Contributors' Diversification

Figure 9 :

 9 Figure 9: Conceptual Structure Map

Figure 10 :

 10 Figure 10: World Cloud and Topic Trend -Cluster 1: CG and Executives' Compensation Schemes

Figure 11 :

 11 Figure 11: World Cloud and Topic Trend -Cluster 2: Corporate Governance and Performance

Figure 12 :

 12 Figure 12: World Cloud and Topic Trend -Cluster 3: Corporate Governance Key Stakeholders

  with 68 citations, and "Do board processes influence director and board performance? Statutory and performance implications"[START_REF] Ingley | Do board processes influence director and board performance? Statutory and performance implications[END_REF] with 65 citations.[START_REF] Bianco | Women on Corporate Boards in Italy: The Role of Family Connections[END_REF] tackled the subject of female representation on Italian corporate boards before introducing gender quota legislation in 2012. Findings indicate that in most gender-diverse boards, at least one woman has a family connection to the controlling shareholder. While the presence of non-family-affiliated women is familiar on the boards of companies that are widely held, have younger and more educated boards, a higher proportion of independent directors, and a smaller number of interlocked directors.[START_REF] Hillman | Board Diversity: Beginning to Unpeel the Onion[END_REF] explores the different layers of boardroom diversity to answer CG ambiguous and unexplored areas. Finally,[START_REF] Ingley | Do board processes influence director and board performance? Statutory and performance implications[END_REF] evaluate the directors' perceptions of the current contribution of fellow board members to different aspects of governance practice based on a survey study with 3,000 directors. They illustrate the strategic orientation of the board, highlighting the extent to which individual directors and the board as a whole can influence key outcomes and, thereby, their governance contribution.

Figure 13 :

 13 Figure 13: World Cloud and Topic Trend -Cluster 4: Corporate Governance Pillars

TABLE 1 : CGIR Citation Structure (1993-2021) Year Total Publicati on Number of Cited Publication Percent of cited Publication Total Citations Average Citations per Publication Average Citations per Cited Publication Publications with citations > 100 50 -99 10 -49 1-9

 1

	45	25	55.56%	125	2.8	5.0	0	0	5	20
	39	23	58.97%	376	9.6	16.3	1	1	4	17
	37	19	51.35%	179	4.8	9.4	0	0	7	12
	20	17	85.00%	355	17.8	20.9	0	2	6	9
	19	17	89.47%	598	31.5	35.2	2	0	9	6
	19	18	94.74%	751	39.5	41.7	2	0	12	4
	28	25	89.29%	599	21.4	24.0	1	2	15	7
	29	28	96.55%	757	26.1	27.0	0	3	18	7
	26	26	100.00%	940	36.2	36.2	2	4	13	7
	26	24	92.31%	695	26.7	29.0	0	2	16	6
	30	29	96.67%	2326	77.5	80.2	3	7	16	3
	53	48	90.57%	2550	48.1	53.1	7	11	23	7
	69	68	98.55%	3187	46.2	46.9	3	26	32	7
	47	45	95.74%	2280	48.5	50.7	6	5	24	10
	113	111	98.23%	5721	50.6	51.5	14	22	58	17
	46	46	100.00%	2663	57.9	57.9	6	13	15	12
	50	50	100.00%	3872	77.4	77.4	11	13	21	5
	40	39	97.50%	2352	58.8	60.3	4	5	26	4
	41	41	100.00%	1517	37.0	37.0	4	8	18	11

Electronic copy available at: https://ssrn.com/abstract=4182574

Top Authors, Affiliations, and Countries

The top authors in CGIR in terms of the number of publications during the period

(1993- 2021)

are presented in Table

2

. Remarkably, Alessandro Zattoni, affiliated with LUISS University in Italy, stands top author in CGIR with 37 publications, followed by Praveen Kumar, affiliated with the University of Houston, USA, with 26 publications. The third leading author is William Judge, affiliated with Old Dominion University, USA, with 22 publications. Zattoni earned the highest citations (1164) and highest h-index (15), indicating that 15 of his articles were cited at least 15 times over 1993-2021. The g-index reveals that 34 of Zattoni articles were cited at least 1156 times (34 2

TABLE 2 : Top CGIR Authors (1993-2021) -Publication

 2

	Order	Author	Total Publication	Total Citations	h_index g_index m_index	Year of start	Average Citations per Publication
	1	ZATTONI A	37	1164	15	34	0.65		31.46
	2	KUMAR P	26	282	10	15	1.11		10.85
	3	JUDGE W	22	283	8	16	0.44		12.86
	4	MALLIN C	19	469	12	19	0.48		24.68
	5	TURNBULL S	10	326	7	10	0.25		32.60
	6	TAYLOR B	8	95	6	8	0.21		11.88
	7	WRIGHT M	8	170	6	8	0.23		21.25
	8	BOYD BK	7	156	5	7	0.19		22.29
	9	KIEL GC	7	1068	7	7	0.37		152.57
	10	MINICHILLI A	7	290	6	7	0.40		41.43
	11	MONKS RAG	7	56	5	7	0.18		8.00
	12	AGUILERA RV	6	643	5	6	0.31		107.17
	13	CLARKE T	6	150	5	6	0.17		25.00
	14	HUSE M	6	976	6	6	0.40		162.67
	15	LI S	6	335	5	6	0.39		55.83
	16	NICHOLSON GJ	6	910	6	6	0.32		151.67
	17	SOLOMON A	6	174	6	6	0.26		29.00
	18	VAN EES H	6	372	5	6	0.33		62.00
	19	DEAKIN S	5	212	5	5	0.28		42.40
	20	FILATOTCHEV I	5	171	5	5	0.39		34.20

Notes: This table reports the top authors of CGIR.

TABLE 3 : Lotka's Law for CGIR Publications

 3

	No. of Published Documents	N. of Authors	Proportion of Authors	Proportion based on Lotka Law	Deviation
	1	1270	81.3%	-	-
	2	187	12.0%	19.20%	-7.20%
	3	52	3.3%	8.53%	-5.23%
	4	17	1.1%	4.80%	-3.70%
	5	15	1.0%	3.07%	-2.07%
	6	7	0.4%	2.13%	-1.73%
	7	4	0.3%	1.57%	-1.27%
	8	2	0.001	1.20%	-1.199%
	10	3	0.002	0.95%	-0.948%
	22	1	0.001	0.77%	-0.769%
	24	1	0.001	0.06%	0.059%

Table 4 : Most Cited Documents

 4

	No	Authors	Title	Year	Local Citation	Global Citation	Normalized Local Citations	Normalized Global Citations
	1	Erhardt, N.L., Werbel J.D., Shrader C.B.	Board of director diversity and firm financial performance	2003	26		6.61	9.92
		Carter D.A., D'Souza	The gender and ethnic diversity of US boards
	2	F., Simkins B.J.,	and board committees and firm financial	2010	9		2.20	10.92
		Simpson W.G.	performance
	3	Terjesen S., Sealy R., Singh V.	Women directors on corporate boards: A review and research agenda	2009	26		4.36	7.95
	4	Rose C.	Does female board representation influence firm performance? The Danish evidence	2007	8		3.14	8.87
	5	Kiel G.C., Nicholson G.J.	Board composition and corporate performance: contrasting theories of corporate governance How the Australian experience informs	2003	14		3.56	5.62
	6	Nielsen S., Huse M.	The contribution of women on boards of directors: Going beyond the surface	2010	8		1.95	7.11
	7	Barako D.G., Hancock P., Izan H.Y.	Factors influencing voluntary corporate disclosure by Kenyan companies	2006	6		2.94	8.08
	8	Jackling B., Johl S.	Board structure and firm performance: Evidence from India's top companies	2009	10		1.68	4.89
	9	Jamali D., Safieddine A.M., Rabbath M.	Corporate governance and corporate social responsibility synergies and interrelationships	2008	8		2.30	6.24
			Are socially responsible managers really
	10	Prior D., Surroca J., Tribó J.A.	ethical? Exploring the relationship between earnings management and corporate social	2008	11		3.16	5.82
			responsibility
	11	Muth M.M., Donaldson L.	Stewardship Theory and Board Structure: A contingency approach	1998	19		5.73	7.59
	12	Kang H., Cheng M., Gray S.J.	Corporate governance and board composition: Diversity and independence of Australian boards	2007	16		6.28	5.85
	13	Aguilera R.V., Williams C.A., Conley J.M., Rupp D.E.	Corporate governance and social responsibility: A comparative analysis of the UK and the US.	2006	14		6.85	6.02
	14	De Andres P., Azofra V., Lopez F.	Corporate boards in OECD countries: Size, composition, functioning and effectiveness	2005	10		3.15	5.91
	15	Aguilera R.V., Cuervo-Cazurra A.	Codes of good governance	2009	17		2.85	3.01
	16	Van der Walt N., Ingley C.	Board dynamics and the influence of diversity of directors professional background, gender, and ethnic	2003	10		2.54	2.90
	17	Ding Y., Zhang H., Zhang J.	Private vs state ownership and earnings companies management: Evidence from Chinese listed	2007	8		3.14	4.38
	18	Arora P., Dharwadkar R.	Corporate governance and corporate social attainment discrepancy and organization slack responsibility (CSR): The moderating roles of	2011	6		1.91	5.89
		Pugliese A., Bezemer
	19	P.-J., Zattoni A., Huse M., Van Den Bosch	Boards of directors' contribution to strategy: A literature review and research agenda	2009	17		2.85	2.80
		F.A.J., Volberda H.W.
	20	Nicholson G.J., Kiel G.C.	Can directors impact performance? A case-governance based test of three theories of corporate	2007	14		5.49	4.23
		Total			257	7789

Local Citations; are citations received by a selected article internally to your collection. Global Citations; are citations received by a chosen article all over the world. Normalized Local Citations; is calculated by dividing the actual count of local citing items by the expected citation rate for documents with the same year of publication. Normalized Global Citations; is calculated by dividing the actual count of global citing items by the expected citation rate for documents with the same year of publication

TABLE 5 : Most Frequently Cited Journals in CGIR During the Period (1993-2021)

 5

	No.	Sources	Articles	Quartile	ABDC
	1	Journal of financial economics	3,301	1	A*
	2	Corporate governance: an international review	3,065	1	A
	3	Journal of finance	2,165	1	A*
	4	Strategic management journal	1,880	1	A*
	5	Academy of management journal	1,730	1	A*
	6	Academy of management review	1,159	1	A*
	7	Administrative science quarterly	1,055	1	A*
	8	Journal of corporate finance	916	1	A*
	9	Journal of management	782	1	A*
	10	Journal of accounting and economics	771	1	A*

The Australian Business Dean Council ABDC's 2021 journal (ABDC ranking has four categories: A*(highest), A, B, C (lowest)) and rated "3" in the ABS's Academic Journal Guide (AJG) in 2021.

Electronic copy available at: https://ssrn.com/abstract=4182574


Hajar Faraj

Nadège Follain

Giana Almeida

Alain Guinault

Matthieu Gervais

Cyrille Sollogoub
email: cyrille.sollogoub@lecnam.net

Sandra Domenek
email: domenek@agroparistech.frhajarfarajhajar.faraj@agroparistech.fr

Development of nanocellulose-based high gas barrier composites for packaging

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

INTRODUCTION

In situ physical aging by Differential Scanning Calorimetry

Polylactide (PLA) presents the advantage of being a biodegradable and renewable polyester with overall good mechanical properties, which makes it an interesting substitute for classical nonrenewable polymers. However, PLA has limited gas barrier characteristics, property of greatest importance for packaging applications. Cellulose Nanocrystals (CNC) is known for it's high crystallinity, as well as the ability to form percolation networks in polymeric matrices, which was proven in previous studies, to be both beneficial for barrier and mechanical properties [1,2].

In this work, nanocellulose-based composites were prepared via solvent casting. The effects of unmodified and modified nanocellulose particles on the relaxation and barrier properties of PLA were investigated. The adhesion between the matrix and the filler was enhanced after chemical modification, as well as the barrier properties to oxygen (for high contents).

PLA/CNC nanocomposite

CONCLUSIONS

  Fig. 4. i) Time-lag plot for oxygen permeation ii) Relative diffusivity for PLA, and PLA/CNC-based composites, Nielsen model included (1967)

Fig. 2 .Fig. 1 .Fig. 3 .

 213 Fig.2. SEM micrographs of PLA and PLA/Nanocellulose-based composites (Aglm for agglomerated and Nano for nano-dispersed)

{x=8 ; y= 17} Lauric Acid

	Neat PLA	142	1592	1.21	2.1	2.54
	PLA/5% CNC	161	1611	1.17	2.63	3.08
	PLA 10% CNC	192	1644	0.5	3.7	1.85
	PLA/5% CNC-g-Lauric Acid	182	2641	1.04	2.13	2.21
	PLA/10% CNC-g-Lauric Acid	230	4496	1.18	1.96	2.31
	PLA/30% CNC-g-Lauric Acid	88	1334	1.85	0.96	1.78

.Pa -1 )


Liana Stoll

Alessandro De

Oliveira Rios

Sandra Domenek

POLYLACTIDE FILMS WITH INCREASED OPTICAL BARRIER PROPERTIES THROUGH THE USE OF BIXIN

d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

0% 0.01% 0.05% 0.10% 1.0%

Films production

-Bixin was extracted from annatto seeds (Bixa orellana) with dichloromethane.

-Bixin extracts were added to PLA solution (7%w/w in dichloromethane) in order to achieve different bixin concentrations (w/w):

-Solutions were poured into Teflon plates and dried at ambient temperature for 48h.

-Films were peeled and thermo-pressed (160 °C, 6 min) to remove the residual solvent.

POLYLACTIDE FILMS WITH INCREASED OPTICAL BARRIER PROPERTIES THROUGH THE USE OF BIXIN

Materials and Methods

Conclusion

Acknowledgments: This study is part of a collaborative research project between AgroParisTech and the Federal University of Rio Grande do Sul (UFRGS), funded by PDSE-CAPES, CNPq (process number 400056/2016-0) andFAPERGS (process number 17/2551-0000911-8).

Results and Discussion

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Liana Stoll, Alessandro de Oliveira Rios; Sandra Domenek

The use of carotenoids as yellow-red colorants for polymeric materials represents a sustainable way of obtaining colored packaging. The introduction of bixin, a carotenoid with coloring and antioxidant properties, could be used to increase the barrier properties of poly(lactide) (PLA) films, turning the biodegradable polymer more suitable to protect light-and oxygen-sensitive food products. The present study aimed to evaluate the influence of bixin on the optical and oxygen barrier properties of PLA films. The thermal properties of films were also evaluated.

Films oxygen permeability was determined in a GDP-C permeameter (25 °C). The permeability (P) was calculated by multiplying the measured oxygen transmission rate by the sample thickness (measured with a micrometer on 9 points).

The diffusion (D) and sorption (S) coefficients were calculated with the help of the time-lag (t lag ) method.

Films crystallinity degree (χ) and glass transition temperature (T g ) were analyzed using a Q100 DSC.

Films characterization

The optical barrier properties were measured by placing the films in quartz test cells. Samples were scanned from 200 to 800 nm in a UV-Vis spectrophotometer. ü The presence of bixin reduced the light transmission of PLA films (Figure 2): the higher the concentration of bixin, the higher the films' barrier to ultraviolet (200-300 nm) and visible light (300-800 nm). The conjugated double bonds in bixin molecular structure serve as chromophore moieties, being responsible for its light absorption capacity.

χ (%) [m 3 m m -2 Pa -1 s -1 ] [m 2 s -1 ] [m 3 m -3 Pa -1 ] (°C) (
ü Bixin did not affect the oxygen solubility, diffusivity and permeability of the films, neither their thermal properties, given by Tg and crystallinity degree (χ) (Table 1).

P1-66

Figure 2 .

 2 Figure 2. Light transmittance (%) from 200 to 800 nm through PLA films

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Contact

Sandra Domenek: sandra.domenek@agroparistech.fr Liana Stoll: lianastoll@hotmail.com JRU 1145 Food Processing and Engineering between INRA and AgroParisTech, Group "Interactions between Materials and Media in Contact", 1 avenue des Olympiades,

Table 1 -

 1 Oxygen barrier and thermal properties of with bixin.

	%)

Figure 1. PLA films produced with different bixin concentrations (0 -1%)