Nina Girard-Perier

Fanny Gaston

Nathalie Dupuy

R A Sylvain

Marque

Lucie Delaunay

Samuel Dorey
email: samuel.dorey@sartorius.com

Study of the mechanical behavior of gamma-irradiated single-use bag seals

Keywords:

To protect from the external environment the solutions stored in the single use plastic bags used in the biopharmaceutical industry, perfect sealing of the bag is necessary to maintain confinement integrity. These single use plastic bags are manufactured from two different multilayer films, an EVA (ethyl vinyl acetate)/EVOH (ethyl vinyl alcohol)/EVA film and a PE (polyethylene)/EVOH/PE film. The EVA or PE contact layer provides chemical biocompatibility with the bag content (biological solution, food, etc.) in contact with the plastic while the EVOH layer provides oxygen barrier properties. Our first objective was to study the impact of the gamma irradiation dose (from 0 kGy to 270 kGy) on the mechanical tensile behavior of the seals. Our second objective was to evaluate the impact of the location of the seals on their tensile properties. The study showed that the seals are never impacted during tensile testing: this evaluation reveals that in fine cracking of the film occurs before any modification of the seal. Its function of closure and content protection from the external environment is fully achieved, whatever the gamma irradiation dose and the seal location. Only the multilayer film on both sides of the seal is altered after 100 % elongation strain. The EVA/EVOH/EVA and the PE/EVOH/PE multilayer films showed no degradation for a y-irradiation dose up to 115 kGy whereas they were altered at 270 kGy. The seals at different locations on the EVA bag showed different film mechanical behaviors, in correlation with the orientation of the polymer film extrusion process.

Introduction

Plastic bags used in the biopharmaceutical and food industries are designed for the preparation and storage of biopharmaceutical solutions and foods, among other things. To protect their content from the external environment, these bags must be hermetically closed, meaning they must not present any opening affording contact between the solution with gas or microorganisms and they must prevent any loss of the substance they contain [START_REF] Brown | Laser welding of thin polymer films to container substrates for aseptic packaging[END_REF][START_REF] Hron | Application of design of experiments to welding process of food packaging[END_REF]. To satisfy these criteria, plastic bags are composed of appropriate multilayer polymer films such as polyethylene/ethyl vinyl alcohol/ polyethylene (PE/EVOH/PE) or ethyl vinyl acetate/ethyl vinyl alcohol /ethyl vinyl acetate (EVA/EVOH/EVA) providing sealing and gas barrier properties [START_REF] Dorey | Generation of O 2 -Permeation Barrier during the Gamma-Irradiation of Polyethylene/Ethylene-Vinyl Alcohol/Polyethylene Multilayer Film[END_REF][START_REF] Dorey | Effect of gamma irradiation on the oxygen barrier properties in ethyl-vinyl acetate/ethylene-vinyl alcohol/ethyl-vinyl acetate multilayer film[END_REF].

The technique used in the packaging industry to seal two plastic films is the direct bonding technique [START_REF] Amanat | Welding methods for joining thermoplastic polymers for the hermetic enclosure of medical devices[END_REF]. The main advantage of direct bonding is that no other material or adhesive is used to join the films. Direct bonding principle consists in, in a first step, heating the polymer (close to its melting temperature) at the interface, which provokes an inter-diffusion of the polymer chains and, in a second step, cooling the polymer to allow seal consolidation [START_REF] Amanat | Welding methods for joining thermoplastic polymers for the hermetic enclosure of medical devices[END_REF].

Depending on the type of heat generation, the direct bonding techniques can be classified as: thermal bonding, friction bonding and electromagnetic bonding [START_REF] Stokes | Joining methods for plastics and plastic composites: An overview[END_REF]. With the increase in new materials and components and in the aim of covering a large panel of applications, complementary techniques have been developed besides these three direct bonding techniques [START_REF] Stokes | Joining methods for plastics and plastic composites: An overview[END_REF]. Indeed, the thermal bonding techniques are classified as hot gas sealing, extrusion sealing, hot-tool (hot-plate) sealing, and infrared heating. The friction sealing techniques are classified as spin sealing, angular vibration sealing, orbital sealing, vibration sealing, and ultrasonic sealing. Finally, the electromagnetic bonding techniques are subdivided as resistance sealing, induction sealing, high frequency sealing, and microwave heating [START_REF] Stokes | Joining methods for plastics and plastic composites: An overview[END_REF]. In this study, to seal two multilayer films and form a single-use bag, two main techniques are used: the hot tool sealing and the high frequency sealing. The hot tool sealing technique makes it possible to melt the polymer between two plates previously subjected to Joule heating. The sealing is performed during the cooling under pressure. For the high frequency sealing, a high frequency generator causes a discharge between two cold electrodes holding the polymers to join. The fusion is produced by induction (REYNE, 2020).

In the biopharmaceutical industry, to ensure the function of closure and non-contamination from the external environment, the sealing must fulfill several parameters taken as guidelines from the standards (ASTM D882, 2012;ASTM F2097, 2008ASTM F2097, 2008;ISO 15747, 2018). The film/film seal must show no bubble, water ingress, channel, or fold, and its width must be constant. The bag must present the same parameters as the film/film seal, showing no leak or pressure decay (ISO 15747, 2018).

After their manufacturing, biopharmaceutical bags are sterilized by ionizing radiation (mainly by gamma rays) to reach the Sterility Assurance Level (S.A.L) target and prevent the presence of microorganisms inside the bags. It is well known that polymers can be modified under gamma irradiation. Irradiation causes the formation of radical species, leading, in the presence of other organic compounds to the formation of unsaturated compounds and carboxylic acids (Gaston et al., 2016a(Gaston et al., , 2016b)). The pH of water stored in biopharmaceutical bags may decrease, this acidification being due to the formation of carboxylic acids, such as ethanoic acid [START_REF] Dorey | XPS analysis of PE and EVA samples irradiated at different γ-doses[END_REF][START_REF] Manso | Influence of pH and temperature variations on vapor phase action of an antifungal food packaging against five mold strains[END_REF][START_REF] Yoshida | Chitosan biobased and intelligent films: Monitoring pH variations[END_REF]. Also, irradiation can cause polymers to change color [START_REF] Gaston | Monitoring of the discoloration on γ-irradiated PE and EVA films to evaluate antioxidant stability[END_REF] because of changes in the color of the antioxidants present in the polymer recipe. A number of studies have been published dealing with the seal mechanical properties in the aim to achieve the best possible optimization of the sealing process [START_REF] Küçükrendeci | The investigation of suitable welding parameters in polypropylene sheets joined with friction stir welding[END_REF][START_REF] Mehrpouya | An artificial neural network model for laser transmission welding of biodegradable polyethylene terephthalate/polyethylene vinyl acetate (PET/PEVA) blends[END_REF]. However, very few studies deal with the impact of gamma irradiation on plastic seals [START_REF] Wang | Enhanced sheetsheet welding and interfacial wettability of 3D graphene networks as radiation protection in gamma-irradiated epoxy composites[END_REF] and even fewer report on the mechanical behavior of gamma irradiated seals (B.G. [START_REF] Porto | Gamma radiation effects in packaging for sterilization of health products and their constituents paper and plastic film[END_REF].

The aim of our study was to investigate the seal resistance during handling by studying the seal mechanical tensile behavior after sterilization by gamma irradiation. The seals were qualified with optimized parameter settings prior to irradiation. To do so, tensile tests were performed on the seals of two lots of PE/EVOH/PE bags and EVA/ EVOH/EVA bags, for different gamma irradiation doses (0, 30, 50, 115 and 270 kGy) and for different seal locations in the EVA and the PE bags. Seal mechanical resistance results were analyzed and discussed using the chemometric technique of Principal Component Analysis (PCA), and the benchmark method for data analysis [START_REF] Esbensen | Multivariate data analysis: In practice / an introduction to multivariate data analysis and experimental design[END_REF][START_REF] Kumar | Chemometrics tools used in analytical chemistry: An overview[END_REF][START_REF] Martens | Multivariate calibration[END_REF].

Material & methods

Samples

The two types of single-use plastic bags investigated were made of two different multilayer films (Fig. 1): an EVA film, composed of one layer of ethylene vinyl alcohol (EVOH) sandwiched between two layers of ethylene vinyl acetate (EVA) (total thickness ~360 μm) and a PE film, composed of one layer of ethylene vinyl alcohol (EVOH) sandwiched between two layers of polyethylene (PE) (total thickness ~400 μm). To evaluate any lot effect, two different lots were studied. For the multilayer film extrusion process, two directions were taken into account as per ISO527 (ISO 527-1, 2019): machine direction (MD), along the direction of the polymers chains during the extrusion process, and transversal direction (TD), perpendicular to MD.

Gamma irradiation

EVA bags and PE bags were wrapped in PE-packaging and irradiated at room temperature by a 60 Co gamma source. This 60 Co gamma source provides a dose rate of 10 ± 3 kGy/h -as given by Synergy Health Marseille (France) -affording doses of 30 (± 1), 50 (± 1), 115 (± 2) and 270 (± 5) kGy. The targeted dose was obtained after several cycles of kGy.

Sealing

EVA bag manufacturing

The EVA bag (Fig. 2a) were manufactured using the high frequency sealing technique (electromagnetic bonding). Two lots (corresponding to two different sizes of bag, 4 L and 50 L) as well as three bags from each lot, irradiated at five different gamma doses (0, 30, 50, 115 and kGy), were investigated. Five different seal locations were selected, locations 3 and 4 being selected to study sealing at the corners.

PE bags manufacturing

The PE pre-made bags (Fig. 2b) were manufactured using the hottool (hot-plate) sealing technique (thermal bonding). Two lots, corresponding to different sizes of bag, 200 L and 100 L) as well as two bags from each lot, irradiated at five different gamma doses (0, 30, 50, and 270 kGy), were investigated. Sixteen different seal locations were selected. Only the longitudinal seals were studied here (orange lines).

Tensile tests

The mechanical properties of irradiated and non-irradiated seals were measured using a universal testing machine, Zwick Z005. The specimens were cut according to ASTM F88/F88 M (ASTM F0088, 2015) (150 mm length, 15 mm width). More details are provided in a previous article [START_REF] Dorey | Generation of O 2 -Permeation Barrier during the Gamma-Irradiation of Polyethylene/Ethylene-Vinyl Alcohol/Polyethylene Multilayer Film[END_REF]. Seal strength is expressed in N per a 15 mm width specimen (N/15 mm).

The different sample locations were selected in order to study the mechanical resistance of the seal all over the bag. For the EVA bags, five samples were cut corresponding to five different seal locations, as shown in Fig. 2a. As for the PE bags, 16 samples were cut corresponding to different seal locations, as shown in Fig. 2b.

Principal component analysis and software

PCA is a multivariable technique used to reduce a larger set of variables to a smaller set of variables called "principal components" [START_REF] Martens | Multivariate calibration[END_REF]. The principal components represent the highest variances in the original variable matrix. All computations were performed using the Unscrambler x 10.5 software. the mechanical test. This means that only the film part is broken by the strain applied (Fig. 3). As observed in Fig. 3b-d, the seal shows no opening or tear and no delamination takes place. Once the interpenetration of the polymer chains has occurred, the seal then keeps its function of sealing, whatever the gamma irradiation dose and the seal location. The film/film sealing was performed with optimized parameter settings prior to irradiation and no defects, such as bubbles, infiltrations, channels, or folds, were visually observed after gamma irradiation and before tensile testing. The seal width remained constant after the gamma irradiation treatment.

EVA bags

The strength-strain curves for the sealing performed on the EVA bags are displayed in Fig. 4. There are two different groups of curves, depending on the seal location. The curves at the top of the figure represent seals 1,3 and 4, while the curves at the bottom of the figure represent seals 2 and 5. For a thorough study, PCA was performed on the six characteristic points of all EVA strain strength curves (Fig. 5a andb). This PCA analysis provides a quantitative discussion about the variability of each factor and highlights any inter-dependence between parameters (i.e., Ultimate Tensile Strength (UTS), Y1 Strength, Y1 Strain, Y2 Strength, Y2 Strain).

Fig. 5a shows the correlation between the six characteristic points of the tensile curve. On the one hand, Y1 Strength, Y2 Strength and Ultimate Elongation are correlated. UTS, Y1 Strain and Y2 strain are correlated. On the other hand, Y1 Strength, Y2 Strength and Ultimate Elongation are anti-correlated with UTS, Y1 Strain and Y2 strain. Indeed, these two groups are both in the same hemisphere but in different quadrants. The start of the plastic deformation (Y1) is linked to the break. In Fig. 5b, the first and second components account for 78 % of the variance. The first component, which represents 54 % of the total variance, is linked to the seal location. Seals 1,3 and 4, in blue, green and grey, respectively, are separated from seals 2 and 5, in red and dark red (Fig. 5b). This observation indicates that seals 1,3 and 4 have a different mechanical behavior from seals 2 and 5, as shown in Fig. 4. Seals 1,3 and 4 display an earlier rupture, a higher UTS and a lower ultimate elongation value. The Y1 Strength and Strain and Y2 Strain values are the same for both groups whereas the Y2 Strength is higher for seals 1,3 and 4 than for seals 2 and 5.

The separation of these two groups is accounted for by the direction of the film extrusion. Seals 1,3 and 4 exhibit the same mechanical behavior as the EVA/EVOH/EVA multilayer film, when they are analyzed in Machine Direction (MD) mode (the direction of the polymers chains) and seals 2 and 5 exhibit the same the same mechanical behavior as the multilayer film when analyzed in Transversal Direction (TD) mode (perpendicular to the polymers chains) [START_REF] Dorey | Effect of gamma irradiation on the oxygen barrier properties in ethyl-vinyl acetate/ethylene-vinyl alcohol/ethyl-vinyl acetate multilayer film[END_REF].

The EVA bag seals thus have the same mechanical behavior as the EVA/EVOH/EVA multilayer film, depending on the direction in which the seals are analyzed. However, tensile results for the EVA/EVOH/EVA multilayer film along the machine direction reveal a lower ultimate tensile strength at break. This observation confirms once again that the seal part is not damaged during the tensile test.

PCA is performed on seals 1,3 and 4 (Fig. 6a and Fig. 6b) and on seals 2 and 5 (Fig. 6c and Fig. 6d), as Fig. 4 shows different UTS and ultimate elongations according to the gamma dose within these two groups.

As for seals 1, 3 and 4 (Fig. 6a), the UTS, Ultimate Elongation, Y2 Strength, Y2 Strain are correlated and observed along PC1. Y1 Strength and Y1 Strain are correlated between them (and not correlated with the others) and observed along PC2. The influence of gamma irradiation is represented along PC1 (Fig. 6b). Gamma irradiation is correlated with UTS. The 270 kGy samples (green points) are away from the 115 kGy, kGy, 30 kGy and 0 kGy samples (red, brown, grey and blue points, respectively.) For the bags irradiated at doses higher than 115 kGy, the seals break earlier (low UTS and Ultimate Elongation) than with lower irradiation doses.

For seals 2 and 5, PCA is performed, showed in Fig. 6c and Fig. 6d. The correlations between parameters are different in this case from those obtained for seals 1,3 and 4. These differences observed with the correlation loadings of both groups of seal locations (Fig. 6a andc) confirm once more the different seal mechanical behaviors according to the seal location and according to the polymer chain orientation. In this case, UTS, Ultimate Elongation, Y2 Strength and Y1 Strength are observed along PC1. UTS and ultimate elongation on the one hand and Y2 Strength and Y1 Strength on the other hand are anticorrelated. Y1 Strain and Y2 Strain are non-correlated and observed along PC2. The influence of gamma irradiation is represented along PC1 (Fig. 6d).

The same observations are obtained for seals 1,3 and 4 vs 2 and 5; for bags irradiated at doses higher than 115 kGy, the seals break earlier (low UTS and Ultimate Elongation) than with lower doses. Moreover, Y2 strength and Y1 strength increase with the gamma dose.

Fig. 7a represents UTS as a function of the gamma dose. As observed before in Fig. 4, the UTS values for seals 1, 3 and 4 are higher than those for seals 2 and 5. For non-sterile, 30 kGy, 50 kGy and 115 kGy irradiated bags, seals 1, 3 and 4 have a UTS ~ 40 % higher than seals 2 and 5. This value is lower for the 270 kGy dose with a difference of ~25 %.

For seals located at positions 2 and 5 (black square), the UTS increases slightly from 0 kGy to 30 kGy (~10 %), seems to reach a plateau from 50 kGy to 115 kGy (~45 N), and decreases from 115 kGy to kGy (~20 %) to reach 38 N. As for seals 1,3 and 4 (red spheres), the UTS shows the same increase from 0 kGy to 30 kGy and reaches the same plateau for 30, 50 and 115 kGy, whereas the decrease is more significant from 115 kGy to 270 kGy (~37 %). In conclusion, the UTS, and therefore the mechanical behavior, is significantly affected for seals irradiated at doses higher than 115 kGy. This represents the film behavior after ionizing radiation. This is explained by the fact that with gamma irradiation the chains are less flexible and they will then start to break, because of a lower tensile strength [START_REF] Dorey | Generation of O 2 -Permeation Barrier during the Gamma-Irradiation of Polyethylene/Ethylene-Vinyl Alcohol/Polyethylene Multilayer Film[END_REF][START_REF] Dorey | Effect of gamma irradiation on the oxygen barrier properties in ethyl-vinyl acetate/ethylene-vinyl alcohol/ethyl-vinyl acetate multilayer film[END_REF].

Fig. 7b shows the ultimate elongation (or elongation at break). The same tendency is observed for the two seal types (2 and 5 vs 1, 3 and 4): the ultimate elongation would be maximal at 30 kGy and remain constant in the range 50-115 kGy.

The resistance strength of the film in contact with the seal is lowered by 35 % for the TD mode (corresponding to seals 2 and 5) and 58 % for the MD mode (seals 1, 3 and 4). For Ultimate Elongation, the film in contact with the seal shows values ~35 % lower (for both types of seal, i. e., 2,5 and 1,3,4.) [START_REF] Dorey | Effect of gamma irradiation on the oxygen barrier properties in ethyl-vinyl acetate/ethylene-vinyl alcohol/ethyl-vinyl acetate multilayer film[END_REF].

PE bags

The PE bag seals are all oriented in the same direction, as strainstrength curves constitute one single group (Fig. 8). Similarly to what happens for EVA seals, the strain applied to PE seals impacts only the PE film and not the seal itself (Fig. 3).

In Fig. 9, PCA is performed on the six characteristic mechanical values (described in Fig. 8) of the PE seal tensile curve. Fig. 9c shows that UTS and ultimate elongation are correlated and UTS is observed along PC2. Importantly, the ultimate elongation in this case is not so significant, as it is placed close to the center in the model (Fig. 9c); the farther the position in the model, the higher the significance. UTS and ultimate elongation are non-correlated with Y1 and Y2 strain. Moreover, there is a minor anti-correlation percentage between UTS/ultimate elongation and Y1/Y2 strength. Y1 and Y2 strength are observed along PC1.

Fig. 9a represents the score plots with seal locations and it shows no influence of the seal location on the seal mechanical behavior, as data points are not tightly close. Indeed, the seals in that pre-made bag configuration are along the machine direction, which corresponds presently to the multilayer film extrusion orientation and the seal samples are all cut out along the film transversal direction. This would also mean that performing film/film sealing on another film direction would lead to homogeneous behavior even though the tensile property values could be different to the ones observed in that study. Fig. 9b represents the score plots with gamma doses. For doses 0-30-50-115 kGy, gamma irradiation is represented along PC2. Indeed, the 0 kGy points (in blue) are at the bottom of Fig. 9b, whereas the 115 kGy points (in red) are at the top. This observation is accounted for by the fact that the film in contact with the seal and irradiated at 115 kGy has a lower UTS (and therefore will break earlier) than the non-sterile film seal. Surprisingly, seals irradiated at 270 kGy are observed along PC1 (in green, on the right). Correlating that observation with Fig. 9c, the film in contact with the seal and irradiated at 270 kGy has a higher Y1 and Y2 strength than the 0-115 kGy film seal. Also, they have the same UTS value as the seal irradiated at 115 kGy. Fig. 10 confirms these first observations. Fig. 10a represents the UTS as a function of the gamma dose. The UTS decreases from 71 N (0 kGy) to 61 N (270 kGy), which represents a drop of 14 %. The decrease in UTS values with gamma irradiation was also observed by B.G. Porto et al. (B.G. Porto et al., 2018). Indeed, they noticed a 2-9 % decrease depending on the seal location, of the sealing resistance of the packaging (paper and plastic film) used for the sterilization of health products. The decrease in the mechanical resistance with the gamma dose has also been observed for the same multilayer film PE/EVOH/PE [START_REF] Dorey | Generation of O 2 -Permeation Barrier during the Gamma-Irradiation of Polyethylene/Ethylene-Vinyl Alcohol/Polyethylene Multilayer Film[END_REF]. However, in that study, the UTS values for the film alone (i.e., not in contact with the seal) were ~30 % higher than for the film investigated in the current study. The ultimate elongation values for the film alone (not in contact with the seal) are between 20 and 40 % higher. This could be explained by the fact that the thickness of the film in contact with the seal is reduced compared with that of the film alone. Indeed, the pressure applied during sealing induces outflow, which reduces the film thickness.

Whatever the seal location and the irradiation dose, the mechanical tensile tests clearly show that there is no weakening of the seals and thus no loss of bag integrity is expected.

Fig. 10b shows the ultimate elongation as a function of the gamma dose. The tall error bars confirm that this parameter close to the model center in Fig. 9c does not significantly evolve with increasing gamma irradiation doses.

Conclusion

The tensile behavior of the seals of EVA or PE single use bags sterilized by gamma irradiation has been investigated. Different seal locations for EVA bags and for PE pre-made bags have been selected. This evaluation reveals that in fine the film shears before any modification of the seal. The mechanical behavior of the seals may depend on their location on the bags and is directly linked to the film extrusion direction. For the EVA bags, the rupture of the part of the film in contact with the seal is observed at lower strain and higher strength than those made perpendicular to the film extrusion direction. For the PE bags, the tested seal locations along one direction show no difference as for the seal tensile behavior.

The influence of the gamma irradiation has likewise been studied. Although at 270 kGy the tensile properties of the film are significantly altered, with a decrease in the film resistance, they remain unchanged at the doses required in the biopharmaceutical industry (ISO 11137-1, 2006) (i.e., ≥25-~45 kGy). No bag features showed changes up to 115 kGy.

For both kinds of bags, the seals are never impacted during the tensile test, whatever the gamma irradiation dose and the seal location. At the end of the tensile test, the seals show no opening, no delamination and no tear. No bubble or channel is generated. The seal key features are entirely preserved, whatever the seal location and the gamma irradiation dose: the bag integrity is maintained, and the bag content is thus protected from the external environment. The work presented here demonstrates the seal resistance during the handling of the bag after sterilization by gamma irradiation.

Funding sources

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

CRediT authorship contribution statement

Fig. 1 .

 1 Fig. 1. Example of PE bag.

Fig. 3 .

 3 Fig. 3. Example of one of EVA seals before the beginning of the tensile test (a) seal after the end of the tensile test. The seal was not impacted by the test (no opening, no break), only the film was broken (b). Optical microscope pictures of the EVA bag seal (c) and PE bag seal (d).

Fig. 4 .

 4 Fig. 4. Strength-strain curves for each seal location (1-5) and each gamma dose (0-270 kGy) for the EVA bags. Colors according to gamma doses.

Fig. 5 .

 5 Fig. 5. PCA performed on the six characteristic points of each tensile curve for the EVA bags obtained for the 2 lots and all the gamma doses. a) Score plots with seal locations. b) Correlation loading (ellipses represent, from outside to inside, 75 % and 100 % of the correlation).

Fig. 6 .

 6 Fig. 6. PCA performed on the six characteristic points of each tensile curve for the EVA bags obtained for 2 lots, all gamma doses. a) Correlation loadings for seals 1,3 and 4. b)) Score plots with gamma doses for seals 1, 3 and 4. c) Correlation loadings for seals 2 and 5. b) Score plots with gamma doses for seals 2 and 5.

Fig. 7 .

 7 Fig. 7. Ultimate tensile strength (UTS) for seals 2 and 5 (black squares) and seals 1, 3 and 4 (red spheres) -left and Ultimate elongation for seals 2 and 5 (black squares) and seals 1, 3 and 4 (red spheres) -right. The average of all the bag lots is represented for each gamma irradiation dose.

Fig. 8 .

 8 Fig. 8. Strength-strain curves for each seal location (1-16) and each gamma dose (0-270 kGy) for the PE bags. Colors according to gamma doses.

Fig. 9 .

 9 Fig. 9. PCA performed on the six characteristic points of each tensile curve for the PE bags obtained for 2 lots and all gamma doses. a) Score plots with seal locations. b) Score plots with gamma doses. c) Correlation loadings (ellipses represent 75 % and 100 % of the correlation).

Fig. 10 .

 10 Fig. 10. Ultimate tensile strength (UTS)-a) and ultimate elongationb). The average of all bag lots is represented for each gamma irradiation dose.

Acknowledgments

We thank Sartorius Stedim FMT S.A.Sfor the financial support of this work.


Fabien Martinez -Em

Ken Peattie

Faith in the future: On a mission to integrate sustainability into management theory and practice

Keywords: Corporate sustainability, missionaries, believers, syncretism, management paradigms, analogical reasoning

) capacity to open themselves to 'external' idea systems and viewpoints. The type of relationships that are developed amongst and between themselves is alleged to critically shape a firm's sustainability performance. The article ends with an outline of implications for the future of corporate sustainability theory, referring to theories and concepts recently developed in the field (i.e., organisational and institutional logics multiplicity, paradox perspective).

Introduction -Sustainability -The 21 st century business challenge

In the field of corporate social responsibility (CSR), one of the most significant developments has been the recognition of the need to challenge the ideological assumptions of capitalism [START_REF] Kazmi | Is corporate social responsibility a new spirit of capitalism?[END_REF] and make business practice more harmoniously aligned with 'sustainability' goals, reflecting society's concern for fostering progress towards combined social equity, ecological integrity and economic prosperity [START_REF] Bansal | Evolving sustainability: a longitudinal study of corporate sustainable development[END_REF].

Corporate sustainability (henceforth CS) is recognised both as an explicit and distinct (although closely related) topic for management scholarship [START_REF] Montiel | Corporate social responsibility and corporate sustainability[END_REF] and as the ultimate stage of CSR development within a firm [START_REF] Kolk | The social responsibility of international business: From ethics and the environment to CSR and sustainable development[END_REF][START_REF] Maon | Organizational stages and cultural phases: A critical review and a consolidative model of corporate social responsibility development[END_REF].

Changes to products, technologies, regulations and business school syllabi, and the emergence of organizations such as the World Business Council for Sustainable Development, or of sustainability management positions, targets and strategies amongst leading companies, can all be offered as evidence that business is changing to address the sustainability challenge. These however largely represent the adoption of the trappings of sustainability thinking rather than its substance. As noted by Valente (2010, p. 40), 'despite the growing consensus among scholars and managers on the need for paradigmatic change [towards 'sustaincentrism'], there is little sign within the academic, practitioner, and public policy domains that such a shift is taking hold [...] A continual stream of evidence reveals devastating business practices that catastrophically undermine social and ecological integrity'.

An early and influential framing of how sustainability challenges management thinking comes from [START_REF] Gladwin | Shifting paradigms for sustainable development: Implications for management theory and research[END_REF]. They attribute the lack of progress towards sustainability to the clash between two management paradigms: the existing, dominant 'technocentric' paradigm and its comparatively new and radically opposing challenger: 'ecocentrism'. These two represent alienated and opposing poles with neither https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 capable of truly integrating human society and culture with nature. [START_REF] Gladwin | Shifting paradigms for sustainable development: Implications for management theory and research[END_REF] see hope in the emergence of a new alternative 'sustaincentric' management paradigm that emphasises the inextricable links between socio-economic activities and our natural systems.

Despite its potential however, sustaincentrism remains a category -an 'ism'that falls short of explaining the processes that will help management research and practice bridge the gap between business and sustainability. It has been largely side-lined by CSR research and criticised as an ambiguously defined concept that risks the co-option of ethics by business concerns [START_REF] Valente | Theorizing firm adoption of sustaincentrism[END_REF]. Furthermore, the pursuit of a sustaincentric approach to business is not facilitated by 'conventional' management theories that tend to promote the status quo in management thinking. Sustaincentrism may represent a path by which business and sustainability can become reconciled, but it seems to remain tantalisingly out of reach for management practitioners and theorists. Gladwin et al. (1995, p. 889) argue that 'significant contributions toward understanding ecologically and socially sustainable economies, societies, and organizations, however, will arise only from new fundamentals, new languages and new lenses'. This paper aims to extend our understanding of how sustainability might be better integrated into management thinking (theory and practice) by applying the lens of syncretism. As an element of cultural studies, syncretism is most closely associated with religious studies, and with efforts to reconcile or integrate opposing principles and practices when more than one belief system (or faith) come together [START_REF] Lambropoulos | Syncretism as mixture and as method[END_REF][START_REF] Lindenfeld | Indigenous encounters with Christian Missionaries in China and West Africa, 1800-1920: A comparative study[END_REF]. In an influential examination into how companies adopt and integrate CSR into their strategies, culture and operations, [START_REF] Berger | Mainstreaming corporate social responsibility[END_REF] identify a syncretic approach as one of three types of CSR 'mainstreaming' (the others being a business case based or a social values led approach). Beyond this however, the potential relevance of syncretism for CSR and CS contexts, has not been seriously considered as a theory of reconciling paradigms (Martinez, https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 [START_REF] Martinez | Achieving greener growth: a business perspective for proactive commitment[END_REF]. Also, although Berger et al. (2007, p. 38) highlight the potential importance of 'syncretic stewardship' to achieve greater CSR (and by implication CS) they do not say much about the processes (and their participants) through which it can be achieved.

One emerging approach to the pursuit of CS is a paradox perspective [START_REF] Hahn | Cognitive frames in corporate sustainability: Managerial sensemaking with paradoxical and business case frames[END_REF][START_REF] Wray-Bliss | Redeeming organisational soul[END_REF] that seeks to accommodate potentially conflicting economic, environmental, and social concerns. The paradox perspective, and its critique of the notion of a 'win-win' resolution of the business case, seeks to move beyond an emphasis on business logic towards an emphasis on values and identities. Hahn et al. (2018, p. 237) argue that 'accommodating conflicting personal and organizational identities and values around sustainability can foster change for sustainability.' They echo [START_REF] Fiss | The symbolic management of strategic change: Sensegiving via framing and dThe symbolic management of strategic change: Sensegiving via framing and decouplingecoupling[END_REF] in explaining that 'the coexistence of conflicting identities and values within the organization can drive cognitive organizational reorientation.' What remains unclear are the processes that govern how such conflicting identities and values interact to maintain or transcend the sustainability paradox, rather than seeking to resolve or reject it. To understand them, there may be benefits in following [START_REF] Frederick | Moving to CSR: What to pack for the trip[END_REF] advice, and looking beyond the conventional CSR literature to studies from religious and cultural disciplines. Some scholars observe that the economic paradigm that dominates management fields has proved impervious to sustainability pressures [START_REF] Starik | Toward a theory of sustainability management: Uncovering and integrating the nearly obvious[END_REF][START_REF] Swanson | Embedding CSR into corporate culture: Challenging the executive mind[END_REF] and therefore resembles a religious faith in being intractable, enduring and resistant to change [START_REF] Baird | Category formation and the history of religions[END_REF]. This creates the potential for cultural and religious studies to inform our understanding of how actors of the corporate world meet the sustainability challenge, since it represents not just a battle of competing business logics, but a battle between technocentric and ecocentric 'faiths'. A further clue to the potential relevance of religious perspectives comes in the semantics of the CS debate. Language denoting an idea system as faith-based, https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 such as 'doctrine', 'dogma' or 'creed' tends to be used by proponents of one faith when talking about the other [START_REF] Martinez | On the role of faith in sustainability management: A conceptual model and research agenda[END_REF]. Leading thinkers on each side are referred to as 'gurus', and each side appears to believe they are the ones led by logic and evidence, whilst the other is driven by dogma. Maon et al. (2010: 31) describe top management's support in their final seventh 'tranformative' level of CS orientated CSR as 'devotion' whilst Gladwin et al. (1995: 896) refer to sustainability 'believers'. These references have not been extensively echoed in CS research thereafter, despite their relevance to aspects of CS (cultural change, faithing processes) that remain largely understudied. In a similar vein, some 'Human Relations' authors (e.g., [START_REF] Berkelaar | Bait and switch or double-edged sword? The (sometimes) failed promises of calling[END_REF][START_REF] Kim | How do callings relate to job performance? The role of organizational commitment and ideological contract fulfillment[END_REF] have explored how people at work have recourse to vocational callings (secular or sacred) to make sense of, and add meaning to, their work place. While this can be inferred to reflect a certain level of interest in understanding how business agents relate to faith (in a way that may affect corporate behaviour), there is a shortage of scholarly work that has attempted to explicitly extend this phenomenon to the context of CSR or CS. This article examines syncretism, an established concept in the study of religious change and faithing processes, in terms of its potential to bring believers back in the study of corporate sustainability phenomena in ways that contribute to a paradigmatic shift towards sustaincentrism We align with a stream of scholarly contributions advocating for a social constructionist trend in management theory (e.g., [START_REF] Drucker | Managing in the next society[END_REF][START_REF] Fuller | Constructing futures: A social constructionist perspective on foresight methodology[END_REF][START_REF] Hamel | The future of management[END_REF][START_REF] Mcdonald | It's time for management version 2.0: Six forces redefining the future of modern management[END_REF]. The main objective is to articulate how a diverse range of actors in the corporate context relate to their beliefs about capitalism, firms and sustainability. According to [START_REF] Lambropoulos | Syncretism as mixture and as method[END_REF], syncretism is a model of integration that embraces conflicting expectations, allowing for cultural change to be driven by competing faiths. We propose that this 'model' can prove relevant and useful in CS fields as an alternative to conventional approaches that rarely seem to rise above a win-win appeal to https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 logic when tackling the tensions and paradoxes that characterise the links between economic, environmental and social sustainability concerns.

Authors such as [START_REF] Patel | Multiparadigmatic studies of culture: Needs, challenges, and recommendations for management scholars[END_REF][START_REF] Bhalla | A multiparadigmatic perspective of strategy: A case study of an ethnic family firm[END_REF] argue that multiple paradigms exist and interact within businesses, shaping their cultures and behaviours, implying that the processes of interaction between paradigms are important for our understanding of some key aspects of change processes that are at work within organizations. In this article, we explore how elements from different paradigms interact in business to form a syncretic field within which diverse processes of adaptation, integration and perhaps disintegration operate.

Unpacking the construct of syncretism

To explore the potential of syncretism to better understand and progress the processes through which greater CS can be achieved, this paper adopts an approach to theorising known as analogical reasoning [START_REF] Cornelissen | Moving forward: Developing theoretical contributions in management studies[END_REF]. It involves constructing analogical relations between phenomena that have no antecedents of theoretically and empirically established correspondences [START_REF] Wilbers | Post-festum and heuristic analogies[END_REF].

Analogical reasoning in management studies has provided influential theories in various domains (e.g., [START_REF] Clemente | Public opinion as a source of deinstitutionalization: A "spiral of silence" approach[END_REF], perhaps most notably in relation to the behavioural theory of the firm by drawing analogies between the human mind and digital computers [START_REF] Cornelissen | Moving forward: Developing theoretical contributions in management studies[END_REF]. In this article, we produce a conceptual representation of the source domain (i.e., 'syncretism'), reviewing its key vocabulary, base assumptions, and causal structure, and transpose it to the target domain (i.e., CS). From the religious and cultural literature, we import the key constructs of syncretism (including its antecedents and outcomes) and create an integrated framework explaining how elements from diverse belief systems can co-exist and interact in the business environment to form a https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 'syncretic field' where a firm's readiness to engage in sustainability may be understood and influenced.

Syncretism 'refers to the cultural mixture of diverse beliefs and practices within a specific socio-historical frame; to the congruity of dissent within such a frame, despite differences of opinion, [and] to the forging together of disparate, often incompatible, elements from different systems' (Lambropoulos, 2001: 225). It has been used across disciplines including anthropology, linguistics, psychology, theology, and political theory [START_REF] Baron | Syncretism and ideology: Latin New York Salsa musicians[END_REF][START_REF] Lambropoulos | Syncretism as mixture and as method[END_REF] and applied to a variety of institutional spheres of cultures in contact, including organizations [START_REF] Baron | Syncretism and ideology: Latin New York Salsa musicians[END_REF][START_REF] Lambropoulos | Syncretism as mixture and as method[END_REF], to provide theoretical foundations for new models of social change and/or benefits of a syncretic approach.

Although most work on syncretism focuses on the fusion of religious forms and beliefs [START_REF] Lindenfeld | Indigenous encounters with Christian Missionaries in China and West Africa, 1800-1920: A comparative study[END_REF][START_REF] Wagner | Pattern and process in ritual syncretism: the case of peyotism among the navajo[END_REF], it re-emerged as a theoretical framework in social theory during the 1990s to explore the dynamics of institutional and cultural transformations relating to globalization, transnational nationalism and diaspora communities [START_REF] Lindenfeld | Indigenous encounters with Christian Missionaries in China and West Africa, 1800-1920: A comparative study[END_REF][START_REF] Stewart | Syncretism and its synonyms: reflections on cultural mixture[END_REF]. Syncretic theory sees collective social constructions (such as belief systems, religions, cultures and institutions) as porous and 'composed of an indeterminate number of features which are decomposable and combinable' (Berk & Galvan, 2009, p. 545).

Consequently they are open to intermixture and the borrowing of concepts and symbols whilst interpenetrating, hybridizing or blending with each other [START_REF] Stewart | Syncretism and its synonyms: reflections on cultural mixture[END_REF].

Corporations are social constructions within which a permanent struggle for meaning takes place between multiple institutional logics [START_REF] Besharov | Multiple institutional logics in organizations: Explaining their varied nature and implications[END_REF]. Marquis and Lounsbury (2007, p. 799) define these institutional logics as the 'broad cultural beliefs and rules that structure cognition and fundamentally shape decision-making and action in a field'.

Such cultural beliefs and rules will include elements that shape a corporation's commitment to sustainability (e.g., [START_REF] Pache | Inside the hybrid organization: Selective coupling as a response to competing institutional logics[END_REF][START_REF] Swanson | Toward an integrative theory of business and society: a research strategy for corporate social performance[END_REF]. The equivalent to institutional https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 logics in cultural and religious studies of syncretism is the notion of 'idea systems' (e.g., [START_REF] Laibelman | Going against the flow: An exercise in ethical syncretism[END_REF][START_REF] Stewart | Syncretism and its synonyms: reflections on cultural mixture[END_REF][START_REF] Wagner | Pattern and process in ritual syncretism: the case of peyotism among the navajo[END_REF]. In this article, we seek to transpose to the field of business what can be understood about the way in which elements of idea systems (used interchangeably with the notion of 'belief systems' in this article) interact in a syncretic field to shape pro-sustainability paradigmatic change.

Cultural and religious studies identify that individuals, including religious leaders and worshippers, will vary in the intensity with which they relate to idea systems; may adopt different roles in relation to the key ideas; and may actively accept and/or contest encountered 'foreign' elements (e.g., [START_REF] Hesselgrave | Syncretism: Mission and missionary induced?[END_REF][START_REF] Hiebert | Syncretism and Social Paradigms[END_REF][START_REF] Mcgavran | Understanding Church growth[END_REF][START_REF] Meyer | If you are a Devil, you are a Witch and, if you are a Witch, you are a Devil": the integration of "pagan" ideas into the conceptual universe of Ewe Christians in Southeastern Ghana[END_REF][START_REF] Meyer | Beyond syncretism: translation and diabolization in the appropriation of Protestantism in Africa[END_REF][START_REF] Sanneh | Translating the message: The missionary impact on culture[END_REF][START_REF] Van Rheenen | Syncretism and contextualization: The Church on a journey defining itself[END_REF]. To understand these phenomena, a useful distinction in the syncretism literature exists between the roles of 'missionaries' who preach a faith, and the role of 'believers' who are preached to. [START_REF] Hesselgrave | Syncretism: Mission and missionary induced?[END_REF] emphasises that 'missionaries' are mainly concerned with the active diffusion of their faith in ways that either transcend cultural barriers or integrate with local idea systems. In the transcending function, missionaries are conservative, dedicating their lives to proselytizing and/or performing religious functions and duties to persuade individuals to join their 'cult' [START_REF] Mcgavran | Understanding Church growth[END_REF]. They view their beliefs as the unique truth that must be preserved and taught. Elements that are external to this cult are alienated, ignored or rejected, resulting in a tendency to impose a single idea system while neglecting other (less powerful) idea systems. For example, critical African intellectuals observe how the influence of 'Western' missionaries on certain local churches created tensions with local communities perceived as overly submissive to Western cultural imperialism [START_REF] Meyer | Beyond syncretism: translation and diabolization in the appropriation of Protestantism in Africa[END_REF]. When https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 missionaries act as purely conservative agents of faith, they may be led to underestimate the importance of local social and cultural contexts, limiting their success.

The role of missionaries

An alternative approach is to preach the faith in more explorative ways that demonstrate respect for local customary beliefs and practices, allowing for constructive dialogue [START_REF] Hiebert | Syncretism and Social Paradigms[END_REF] and allowing existing relations of dominancesuch as that of 'Western cultural imperialism'to be moderated [START_REF] Sanneh | Translating the message: The missionary impact on culture[END_REF]. The practice of exploration notably helped some Christian missionaries accommodate and innovate by moving beyond literal Bible translations and adapting key ideas to the reality and power of local cultural systems (including their languages and other sign systems, patterns of behaviour, rituals, myths, beliefs and worldviews) [START_REF] Hiebert | Syncretism and Social Paradigms[END_REF]. Explorative Christian missionaries are inclined to value local converts for their particular cultural agency, whereas conservative missionaries perceive them as cultural clients of elements of a dominant idea system such as those rooted in Western cultural traditions [START_REF] Sanneh | Translating the message: The missionary impact on culture[END_REF].

Consistent with the idea of Wray-Bliss (2018) that corporations are governed through the values and beliefs of their leaders, we propose that the business environment is also constituted in terms of conservative and explorative missionaries that potentially influence a firm's sustainability performance. We would view exploratory 'missionary' characteristics as compatible with the development of a stakeholder-oriented management culture that engages business and social actors in relationships of mutual sympathy and empowerment and facilitates inter-cultural exchange. Missionary exploration can however be impeded by the tendency of missionaries to over-emphasise the outer layers of culture (i.e. the behaviours, institutions, beliefs and values that are most apparent and immediate), rather than the inner core comprising a worldview, cosmology, ideology and basic belief system [START_REF] Hesselgrave | Syncretism: Mission and missionary induced?[END_REF]. A missionary's target group can therefore attempt to reassert its 'culture core' and seek separation from the idea system promoted by the missionary. https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440

Resistance to the CS message can in turn explain some of the tensions that can arise between the firm and its stakeholders, and between the firm and CS, such as when manager missionaries are viewed internally as too close to external stakeholder interests [START_REF] Carollo | Activists in a suit': Paradoxes and metaphors in sustainability managers' identity work[END_REF]. [START_REF] Wheeler | Paradoxes and dilemmas for stakeholder responsive firms in the extractive sector: Lessons from the case of Shell and the Ogoni[END_REF] report instances of firms failing both to replicate their corporate stakeholder-responsiveness at the local level, and to develop managerial capabilities at a sufficiently deep level throughout the firm (across business units) to yield benefits for both stakeholders and the business. This can be explained by a lack of explorative potential by business missionaries, and perhaps even by those (scholars and practitioners) who 'preach in favour' of a 'beyond profits' approach and stakeholder-oriented culture, but in practice are not able to establish a deeply rooted and far-reaching CS culture within their firms. We add that the potential for compatibility or incompatibility between 'competing' idea systems in business, and the syncretic dynamics that are at play, do not only depend on missionaries' intentions and actions. The literature on religious syncretism also emphasises the role of 'believers' (e.g., [START_REF] Hiebert | Syncretism and Social Paradigms[END_REF][START_REF] Meyer | Beyond syncretism: translation and diabolization in the appropriation of Protestantism in Africa[END_REF][START_REF] Sanneh | Translating the message: The missionary impact on culture[END_REF].

The role of believers

Believers are mainly concerned about developing their own relations to faith in ways that either preserve aspects of their cultural identities, or translate into obedience under a dominant idea system. Meyer (1994, p. 43) discusses the role of 'active agents' of faith, or in [START_REF] Sanneh | Translating the message: The missionary impact on culture[END_REF] words 'local converts', as a group of critical believers who strive to freely engage with elements from their own idea systems and from others. These believers may attempt to mould an idea system that threatens to dominate, infusing it with elements from their own idea system(s), so that it becomes integrated with their cultural identities. This explains the rise of African Christianism, as described by [START_REF] Meyer | Beyond syncretism: translation and diabolization in the appropriation of Protestantism in Africa[END_REF]. A number of African intellectuals and 'believers' strove to interpret the contents of the 'Christian message' through the prism of https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 their own cultural viewpoints, resulting in a local expression and application of Christian faith [START_REF] Van Rheenen | Syncretism and contextualization: The Church on a journey defining itself[END_REF].

In parallel to the existence of active agents of faith (or critical believers), diverse social and institutional logics governing the world of faith exist to promote obedience to dominant idea systems. One logic can be found in the representation of faith as 'revealed truth', one that is not framed by culture and is therefore inflexible and impervious to the infusion of elements from (foreign) cultural systems [START_REF] Sanneh | Translating the message: The missionary impact on culture[END_REF]. Another logic stems from positioning missionaries as authoritative agents of faith whose teachings and ideas must be adhered to and reproduced. Believers who accept these logics and embrace the dominant idea system as legitimate truth, may then come to critically evaluate beliefs, decisions and practices drawn from their own cultural contexts [START_REF] Hiebert | Syncretism and Social Paradigms[END_REF]. They can be referred to as client believers who are likely to accept the precepts of a dominant idea system as unique truth.

The role of believers in business has received little scholarly attention beyond ideas of using spirituality to 'improve' relations between people in the work place and developing a more sustainability-oriented worldview [START_REF] Cavanagh | Spirituality for managers: Context and critique[END_REF]. What seems to have been insufficiently scrutinised is the role played by 'disciples' of technocentrism in shaping the cultural systems of business organisations. Francis (1993, p. 322) discusses the existence of 'Cornucopian' believers amongst technocentrists who continue to support unsustainable levels of growth and resource exploitation because they believe that human will and ingenuity, combined with increasing technological expertise, can overcome future socioecological problems. A more moderate form of technocentrism, discussed by [START_REF] Turner | Sustainability: Principles and practice[END_REF], promotes resource conservationism and managerialism. The suggested existence of two distinct forms of technocentrism reflects the assumption that the level of commitment to technocentric faith may vary from person to person. The dominance of technocentric faith in https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 the corporate world [START_REF] Gladwin | Shifting paradigms for sustainable development: Implications for management theory and research[END_REF] means that this variability should not be neglected since it may determine the likelihood of technocentric believers acting either as critical agents of faith, or as clients of faith. We anticipate that critical technocentric believers are more likely to explore solutions to sustainability problems outside their own idea systems.

Examining the roles played by business missionaries (i.e., conservative or explorative) and business believers (i.e., critical or client) will likely add nuance to the interpretations made about a firm's capacity to shift from technocentrism towards sustaincentrism. In particular, the interactions between diverse agents of faith, with their own socially held expectations and ethical values [START_REF] Pullen | Ethics, embodiment and organizations[END_REF], may reveal the nature of the transcultural dynamics [START_REF] Hiebert | Anthropological reflections on missiological issues[END_REF] that shape the process of syncretism in business contexts. Novel combinations of elements from divergent idea systems can be produced as individuals attempt to identify common themes and correspondences between alternative paths, assess what elements among idea systems are compatible or incompatible, and in the latter case either select between alternative paths or creatively explore how divergences can be resolved [START_REF] Laibelman | Going against the flow: An exercise in ethical syncretism[END_REF][START_REF] Shaw | Introduction: problematizing syncretism[END_REF][START_REF] Stewart | Syncretism and its synonyms: reflections on cultural mixture[END_REF]. Berk and Galvan corroborate the idea that actors in any institutional contexts are likely to engage in syncretism by drawing 'on a wide variety of cultural and institutional resources to create novel combinations ' (2009, p. 544). Arguably, creativity is more likely to be found within explorative missionaries and critical believers who hold pluralist truth claims and redemptive relations to power. Others, with exclusivist truth claims and hierarchical relations to power, are inclined to perpetuate the status quo. The existence of divergent idea systems in the corporate context, combined with the varying capacity of missionaries and believers to engage with these systems (as synthesised in Table 1), provides for a certain level of complexity regarding the predictability of syncretic outcomes. https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440

[Insert Table 1 about here]

Implications for theory and research

The application of a syncretic perspective to the challenge of developing more prosustainability organizational environments has implications for future theorizing and research, particular in relation to the management of paradoxes and institutional logics.

Our perspective supports and expands growing theoretical and empirical literature exploring the role of agency in organizational logic multiplicity; in particular research in social welfare and multiple agency (e.g., [START_REF] Mitchell | Stakeholder agency and social welfare: Pluralism and decision making in the multi-objective corporation[END_REF], origins of hybridization (e.g., [START_REF] Busco | Sustaining multiple logics within hybrid organisations: Accounting, mediation and the search for innovation[END_REF][START_REF] Mangen | The challenge of sustaining organizational hybridity: The role of power and agency[END_REF] and embedded agency in paradoxes and institutional complexity (e.g., [START_REF] Delbridge | Inhabiting institutions: Critical realist refinements to understanding institutional complexity and change[END_REF][START_REF] Schildt | Organizational settlements: Theorizing how organizations respond to institutional complexity[END_REF]. These streams of literature bring actors and their values to the fore and challenge the dominant single-objective logic of management theory with its emphasis on identification of trade-offs and criteria for prioritizing logics. A shared finding of these papers and our framework is that most, if not all, organizations routinely and durably accommodate multiple logics [START_REF] Schildt | Organizational settlements: Theorizing how organizations respond to institutional complexity[END_REF][START_REF] Smets | Reinsurance trading in Lloyd's of London: Balancing conflicting-yet-complementary logics in practice[END_REF] and to some extent, all managers have a dual identity balancing private and public interest [START_REF] Rivera-Santos | Alliances between Firms and Non-profits: A multiple and behavioural agency approach[END_REF].

A recurrent theme that resonates with our propositions is that organizational actors are strongly reluctant to engage in trade-offs between logics (e.g., [START_REF] Mitchell | Stakeholder agency and social welfare: Pluralism and decision making in the multi-objective corporation[END_REF][START_REF] Schildt | Organizational settlements: Theorizing how organizations respond to institutional complexity[END_REF]. Instead, they creatively deploy multi-objective reasoning that focuses on the design of 'truces' accommodating seemingly irreconcilable logics [START_REF] Mitchell | Stakeholder agency and social welfare: Pluralism and decision making in the multi-objective corporation[END_REF].

Current research has only started to investigate the processes of negotiation between actors and mediation of logics leading to such truces [START_REF] Bishop | Becoming hybrid: The negotiated order on the front line of public-private partnerships[END_REF]. Such negotiations aim to preserve the distinction between logics while also exploiting the benefits of their https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 interdependence [START_REF] Smets | Reinsurance trading in Lloyd's of London: Balancing conflicting-yet-complementary logics in practice[END_REF]. Truces can combine, mediate or bridge elements of different logics [START_REF] Busco | Sustaining multiple logics within hybrid organisations: Accounting, mediation and the search for innovation[END_REF][START_REF] Delbridge | Inhabiting institutions: Critical realist refinements to understanding institutional complexity and change[END_REF] or preserve distinct logics [START_REF] Stadtler | Coopetition as a paradox: Integrative approaches in a multi-company, cross-sector partnership[END_REF]. However, extant literature observes that more research is needed to understand why and when one or another type of truce is negotiated [START_REF] Schildt | Organizational settlements: Theorizing how organizations respond to institutional complexity[END_REF] and to what extent the type of truce is decided by actors or dictated by structural factors [START_REF] Delbridge | Inhabiting institutions: Critical realist refinements to understanding institutional complexity and change[END_REF]. Our framework adds granularity to the analysis of the role of actors in multi-stakeholders' agency, explaining how differences between conservative and explorative missionaries and between critical and client believers result in different types of settlements between logics (that are framed as syncretic forms in this study).

The syncretic perspective complements in this sense research applying paradox perspectives to understand how managers seek to reconcile conflicting pressures associated with the pursuit of sustainability in relation to their own individual roles, social structures and psycho-social traits. For example, [START_REF] Carollo | Activists in a suit': Paradoxes and metaphors in sustainability managers' identity work[END_REF] find that managers accept and maintain sustainability-related tensions and paradoxes but the faithing processes underlying these phenomena have remained obscure. We add that current research in hybrids and institutional logics has not yet fully explained in what conditions multiple logics and paradoxes persist without resulting in an organization that has a continuous sense of competing goals or conflicting identities [START_REF] Schildt | Organizational settlements: Theorizing how organizations respond to institutional complexity[END_REF], particularly when seeking to address sustainability challenges [START_REF] Jay | Navigating paradox as a mechanism of change and innovation in hybrid organizations[END_REF]. It constitutes yet another stream of studies that have largely ignored the syncretic 'faithing' processes that are at play in business environments, despite their potential to substantiate explanations of the blending processes discussed by several authors in this field, including [START_REF] Rao | New forms as settlements[END_REF]; [START_REF] Thornton | The institutional logics perspective: A new approach to culture, structure, and process[END_REF][START_REF] York | Converging winds: Logic hybridization in the Colorado wind energy field[END_REF]. For example, [START_REF] York | Converging winds: Logic hybridization in the Colorado wind energy field[END_REF] focus on how actors respond to logic incompatibility (economising versus https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 ecologising) by discussing three mechanisms: elaboration, assimilation and hybridisation.

They note: 'contrary to prior work on compromise and logic assimilation, we find that attempts by less powerful actors to gain voice did not resolve incompatibility, but rather motivated eventual contestation'. We introduce the critical role of actors as missionaries and believers in shaping the way in which incompatible logics are dealt with. Our propositions suggest that actors can not only tolerate divergences between idea systems but also actively negotiate adoption of syncretic forms that preserve logic multiplicity. Therefore, our framework highlights the distinctive role of missionaries and believers, leading us to contribute insights on agentic processes of conciliation and mediation between multiple logics and complementing thereby the works of, e.g., [START_REF] York | Converging winds: Logic hybridization in the Colorado wind energy field[END_REF][START_REF] Carollo | Activists in a suit': Paradoxes and metaphors in sustainability managers' identity work[END_REF][START_REF] Carollo | Activists in a suit': Paradoxes and metaphors in sustainability managers' identity work[END_REF].

Conclusion

In this article, we used analogical reasoning to explore syncretism as the combination of elements from two or more idea systems in the corporate context through transposition, assimilation and / or hybridisation. We articulated the core elements of a theory of syncretism for CS including its underlying construct antecedents (syncretic roles: missionaries and believers) and assumptions (see Table 1).

Syncretic engagement from business missionaries and believers who are exposed to a diversity of idea systems will hopefully help research to raise some of the difficult issues of organisational transformation for sustainable development in business communities. Wright and Nyberg vehemently warn that our society will meet self-destruction if business continues its current practice of converting grand environmental challenges into 'the more familiar and less threatening discourses of profit maximization and shareholder value ' (2017, p. 1657). In this effect, the syncretic framework developed in this article will contribute as a useful https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440 conceptual resource for advancing the sustainability agenda by legitimising, and perhaps reinforcing, the determination of 'extraordinary individual innovators and entrepreneurs' (Elkington, Hartigan, & Litovsky, 2010, p. 83) to develop and adhere to ideas of sustainable entrepreneurship and intrapreneurship.

Critics of the syncretic approach advocated here may stress that management practice and scholarship is an essentially secular field, limiting the value of an understanding of faithing and religious processes. For them, perspectives based on paradoxes (as reviewed by [START_REF] Hahn | A paradox perspective on corporate sustainability: Descriptive, instrumental, and normative aspects[END_REF] or ideologies (as reviewed by [START_REF] Haase | Ideologies in markets, organizations, and business ethics: Drafting a map: Introduction to the special issue[END_REF] may seem sufficient to understand the cultural processes involved in firms developing their CSR towards CS [START_REF] Maon | Organizational stages and cultural phases: A critical review and a consolidative model of corporate social responsibility development[END_REF]. However, as Frederick (1998, p. 52) explores, the religious impulse that seeks for meaning in life is inherent in all humans. It manifests itself in corporate life, even if for some the sought meaning is to be found in 'the daily worship of corporate power and glory' amongst 'managers who disregard the planetary damage of their reckless ecological decisions, or who uncaringly cut off at midcareer the productive lives of down-sized employees.' He concludes that 'it is time to rip the mask of religious furtiveness off the corporate face. Personal religious philosophies of all kinds abound in the workplace.' One only has to examine the ongoing public debate about man-made climate change, and the persistence of climate change denial in the face of over-whelming scientific evidence and consensus, to realise the extent to which key sustainability debates play out in a world of faiths rather than facts.

https://www.sciencedirect.com/science/article/abs/pii/S0016328720301440

BELIEVER 'Representative of target idea system(s)'

Religion / culture Believer as client: Truth is found within a dominant idea system, leading to a critical evaluation of elements of target idea systems (i.e., enduring customs, beliefs and practices pertaining to a specific social and cultural context).

Religion / culture Believer as critical agent of faith: Exploration based on the adaptation of a 'dominant' idea system that may be infused with elements of target idea system(s), so that faith becomes integrated with the cultural identities of believers Religion / culture Need to relate to an external source of power for personal and spiritual advancement. No authentic niche beyond the reach of hegemonic power.

Religion / culture Capacity to resist hegemonic power and enact one's own cultural agency.

Management


Marco Revelli Beaumont

Christophe Faulmann

Dominique De Caro

Maximilien Cazayous

Yann Gallais

Alain Sacuto

Claude Pasquier

Pascale Auban Senzier

Miguel Monteverde

Kane Jacob

Marco Revelli Beaumont

Lydie Valade

Reproducible nanostructuration of the superconducting κ-(BEDT-TTF)2Cu(NCS)2 phase

Keywords: BEDT-TTF, nanoparticle, SQUID, superconducting transition

Introduction

The -(BEDT-TTF) 2 Cu(NCS) 2 phase, (BEDT-TTF: bis(ethylenedithio)tetrathiafulvalene) prepared as single crystals in 1988, has been intensively studied because it was the first molecule-based superconductor to exhibit a critical temperature higher than 10 K [START_REF] Urayama | Crystal Structures of Organic Superconductor, (BEDT-TTF) 2 Cu(NCS) 2 , at 298 K and 0.4 K[END_REF]. From the 1990s, thin films [START_REF] Awano | Thin Films of (BEDT-TTF) 2 Cu(NCS) 2 Prepared by an Electrodeposition Method[END_REF] and nanorod arrays [START_REF] Huang | Controlled Growth and Field-Emission Properties of the Organic Charge-Transfer Complex of [END_REF] of -(BEDT-TTF) 2 Cu(NCS) 2 have also been reported. Some of us have shown that roughly spherical nanoparticles of molecule-based conductors could be prepared either by a chemical or an electrochemical route by adding to the solution a growth controlling agent, such as an amphiphilic molecule, an ionic liquid or a long alkyl-chain quaternary ammonium salt [START_REF] Caro | First nanoparticles of Bechgaard salts[END_REF][START_REF] Caro | Colloidal Solutions of Organic Conductive Nanoparticles[END_REF][START_REF] Caro | Nanoparticles of molecule-based conductors[END_REF][START_REF] Caro | Four Molecular Superconductors Isolated as Nanoparticles[END_REF][START_REF] Chtioui-Gay | Synthesis, characterization, and thermoelectric properties of superconducting (BEDT-TTF) 2 I 3 nanoparticles[END_REF]. We have already described the synthesis of nanoparticles of -(BEDT-TTF) 2 Cu(NCS) 2 by a chemical or an electrochemical route. The chemical method was achieved by refluxing a tetrahydrofurane (THF) solution of BEDT-TTF and Cu(NCS) 2 in the presence of long alkyl-chain aconitate esters [START_REF] Cormary | Facile synthesis of nanoparticles of the moleculebased superconductor κ-(BEDT-TTF) 2 Cu(NCS) 2[END_REF]. The solid obtained (yield about 70 %) consists in spherical nano-objects which are actually made of aggregated individual small particles ranging from 3 to 10 nm. The electrochemical method was performed in a two-compartment electrochemical cell containing BEDT-TTF, Cu(NCS) and the ionic liquid [EMIM][SCN] (EMIM + : ethylmethylimidazolium), acting as supporting electrolyte, provider of an additional SCN -ligand, and finally as a growth controlling agent [START_REF] Caro | Adjusting the cation and anion nature in ionic liquids used for the growth control of nanoparticles of organic conductors[END_REF]. The solid grown on the anode (yield about 20 %) exhibits well dispersed nanoparticles (mean size: 10 nm). However, this electrochemical route does not show reproducibility. In order to ensure selective and reproducible formation of NPs of the -(BEDT-TTF) 2 Cu(NCS) 2 phase, we have explored two synthetic routes using a different stabilizing agent vs. the above cited ones, ndodecanoic acid (abbreviated as DA), and performing a one-pot or a new two-pot procedure. We identified a reproducible synthesis of -(BEDT-TTF) 2 Cu(NCS) 2 nanoparticles and report on their chemical characterisation and super-conductive properties.

Results and discussion

The amphiphilic n-dodecanoic acid, also called lauric acid has been widely used to control the growth of metal, metal oxide or metal sulphide nanoparticles. It might also have an organizing effect on the nanoparticles [START_REF] Liveri | Controlled Synthesis of Nanoparticles in Microheterogeneous Systems[END_REF]. Following the procedure reported in [START_REF] Cormary | Facile synthesis of nanoparticles of the moleculebased superconductor κ-(BEDT-TTF) 2 Cu(NCS) 2[END_REF] for the synthesis of nanoparticles of -(BEDT-TTF) 2 Cu(NCS) 2 with aconitate esters i.e. by heating a mixture of BEDT-TTF and Cu(NCS) 2 at reflux in THF in the presence of 0.3, 0.5, 1, 5, 10 or 20 molar equivalents of DA vs. BEDT-TTF, a black solid is obtained (yield in the 4060 % range). To check sample purity, we focused on infrared transmission spectroscopy analysis. It is a powerful tool to investigate organic conductors quality as it provides a qualitative product characterization to detect unreacted starting compounds and possible impurities [START_REF] Müller | A Novel, Nonelectrochemical Synthesis of the Organic Superconductor κ-(BEDT-TTF) 2 Cu(NCS) 2[END_REF][START_REF] Zamboni | FT-IR Absorption Spectra of Polycrystalline Pressed Samples of the Organic Metals and Superconductors -(BEDT-TTF) 2 I 3 and (BEDT-TTF) 2 Cu(NCS) 2[END_REF]. Whatever the molar ratio DA/(BEDT-TTF), the infrared spectrum exhibits four peaks at 2068, 2099, 2110 and 2125 cm -1 . The sharp doublet at 2068 and 2110 cm -1 is the -(BEDT-TTF) 2 Cu(NCS) 2 finger-print that corresponds to two CN stretching modes of the Cu(NCS) 2 anions [START_REF] Müller | A Novel, Nonelectrochemical Synthesis of the Organic Superconductor κ-(BEDT-TTF) 2 Cu(NCS) 2[END_REF][START_REF] Zamboni | FT-IR Absorption Spectra of Polycrystalline Pressed Samples of the Organic Metals and Superconductors -(BEDT-TTF) 2 I 3 and (BEDT-TTF) 2 Cu(NCS) 2[END_REF], whereas the two other peaks at 2099 and 2125 cm -1 are not present in the bulk material and have not been assigned yet.

Electron micrographs of the solids evidence both nanoparticles (sometimes severely aggregated) and micrometre-sized crystals. The lack of selectivity in both the desired phase and the morphology led us to reject this one-pot synthetic route.

We have then explored a two-pot synthetic procedure. A THF solution of Cu(NCS) 2 and DA at room temperature is dropwise added to a THF solution of BEDT-TTF and DA at 90°C. For a molar ratio DA/BEDT-TTF of 2, a black solid, further denoted as NPs, precipitates in a 40 % yield. It exhibits two CN vibration modes at 2066 and 2109 cm -1 which are the adequate peaks found in the infrared spectrum of microcrystalline -(BEDT-TTF) 2 Cu(NCS) 2 [START_REF] Müller | A Novel, Nonelectrochemical Synthesis of the Organic Superconductor κ-(BEDT-TTF) 2 Cu(NCS) 2[END_REF][START_REF] Zamboni | FT-IR Absorption Spectra of Polycrystalline Pressed Samples of the Organic Metals and Superconductors -(BEDT-TTF) 2 I 3 and (BEDT-TTF) 2 Cu(NCS) 2[END_REF].

The absence of C=O vibrational modes implies the absence of DA within the solid. Electron micrographs evidence roughly spherical nanoparticles with an average diameter of 28 nm and a standard deviation of 4 nm (Fig. 1). Upon dropwise addition, the copper salt Cu(NCS) 2 is introduced in a medium where BEDT-TTF is in excess and exhibiting a highly structured environment due to the long alkyl-chain carboxylic acid. Therefore, the germination process is more closely control-led and the growth process is quickly blocked, leading to well dispersed nanoparticles. Moreover, this synthetic route allowing the preparation of NPs is reproducible. To ensure that we synthetized the -phase, we performed an XRD measurement of NPs and compared it to a bulk reference synthetized in the usual electrochemical way [START_REF] Urayama | A new ambient pressure organic superconductor based on BEDT-TTF with Tc higher than 10 K (Tc = 10.4 K)[END_REF]. The two spectra are superimposable (Fig. 2), indicating NPs is indeed the expected -(BEDT-TTF) 2 Cu (NCS) 2 phase.

Fig 2. XRD spectra of NPs and bulk

From the XRD spectrum, it has been possible to estimate the size of the nanoparticles by using Scherrer equation on several diffraction peaks, from 10 to 50° in 2. Over this latter range of 2, the average size of crystallites is ca. 42 nm, whereas it is ca. 31 nm between 28° and 50°. These values agree with the size observed by TEM measurements.

To complete the spectroscopic analysis, we also recorded a Raman spectrum at 15 K to compare the bulk and the NPs (Fig. 3). Main phonons are reported with their corresponding modes. Differences in intensities between the bulk and the NPs are due to random orientation of the NPs. In particular, the peaks at 1411 and 1454 cm -1 are strongly enhanced for the NPs [START_REF] Sugai | Raman-active molecular vibrations in the organic superconductor κ-[bis(ethylenedithio)tetrathiafulvalene] 2 Cu(NCS) 2[END_REF]. Indeed, the phonon intensities between NPs and bulk are different. Bulk is oriented so Raman selection rules can be applied. NPs are oriented in all directions, as if it was a polycrystalline bulk, and Raman selection rules cannot be used to select specific phonon modes. Phonons NPs intensities are then an averaged response (of all possible bulk orientations). We also notice peak broadening for NPs. The two lines at 2076 and 2110 cm -1 are due to distinct CN environments in the unit cell [START_REF] Kornelsen | Infrared optical properties of the 10-K organic superconductor (BEDT-TTF) 2 [Cu(NCS) 2 ] [where (BEDT-TTF) is bis(ethylenedithio)tetrathiafulvalene[END_REF], in agreement with infrared measurements. The most intense band at 1476 cm -1 is assigned to the C=C stretching vibration of the central carbon atoms of the BEDT-TTF molecule [START_REF] Zamboni | Resonant Raman Scattering On Single Crystals Of (BEDT-TTF) 2 Cu[END_REF]. Despite intensities variations and broadening of phonons peaks, there are no main differences in peaks positions between the NPs and the bulk. Raman measurements show that the structural properties of the bulk are preserved at the nanoscale. with χ vol the volume susceptibility (dimensionless), χ mass the mass susceptibility, 𝑀 𝐶𝐺𝑆 the measured magnetization, ρ the density and V cell the volume of a unit cell.

In blue, we plot the effect of diamagnetic shielding, i.e. zero-field cooling (ZFC) and in red, the effect of magnetic flux expulsion, the Meissner effect, i.e. field cooling (FC). The two curves were recorded in the temperature range from 1.9 to 10.7 K. The dash line indicates the temperature where the magnetization starts to decrease, which is the signature of the superconducting transition for the NPs, T c = 9.1 K. This temperature is close to the one observed in the bulk (T c ≃ 9.5 K). The ratio between Meissner susceptibility (FC) and shielding susceptibility (ZFC) is a lower bound to the superconducting volume fraction. From χ 𝑣𝑜𝑙 𝑀𝐾𝑆 (𝐹𝐶) χ 𝑣𝑜𝑙 𝑀𝐾𝑆 (𝑍𝐹𝐶) , measured at H = 10 G and T = 1.9 K, we estimate a superconducting fraction of 40% , in agreement with bulk measurements [START_REF] Tokumoto | Anisotropy of magnetization and Meissner effect in organic superconductor κ-(BEDT-TTF) 2 Cu(NCS) 2[END_REF][START_REF] Veith | Normal and superconducting properties of bis(ethylenedithio)tetrathiafulvalenium bisthiocyanatocuprate[END_REF]. This is a rough estimate since the anisotropy and demagnetization factors may modify the basic formula of the superconducting volume fraction. Therefore, superconductivity in the NPs of typical diameter 30 nm is still present with a critical temperature of the same order of magnitude as in a bulk sample. Superconductivity in the NPs also indicates that the coherence length is shorter than 30 nm (in agreement with values of the bulk where the in-plane coherence length is ξ // ≈ 7.5 nm and the out-of-plane coherence length is ξ ⊥ ≈ 0.5 nm) [START_REF] Friemel | Fluctuation effects in the organic superconductor κ-(BEDT-TTF) 2 Cu(NCS) 2[END_REF]. Figure 5 shows a clear magnetization loop characteristic of a superconductor in both cases. For NPs, the hysteresis loop is of smaller area as compared to the bulk one suggesting a lower critical current.

In this work, 30 nm diameter nanoparticles of the superconducting phase -(BEDT-TTF) 2 Cu(NCS) 2 have been synthesized in a reproducible manner using lauric acid in a two-pot procedure. The one-pot synthesis, using the same reactants leads to inhomogeneous nanoparticles, whose IR spectrum does not correspond to the bulk. In addition to reproducibility of the synthesis, it is confirmed that superconductivity occurs in nanoparticles of κ-(BEDT-TTF) 2 Cu(NCS) 2 at size down to 30 nm, since the isolated nanoparticles exhibit a T c of 9.1 K, i.e. in the same range as the bulk. Nevertheless, since both Raman and SQUID measurements show some small discrepancies between NPs and bulk, works are in progress to investigate more carefully these nanoparticles.

Experimental section

Characterization techniques

For transmission electron microscopy observation, powder (about 0.5 mg) is dispersed in diethyl ether (2 mL) under slow stirring for 1 min. The TEM specimens are then prepared by evaporation of droplets of the suspension deposited on carbonsupported copper grids. The experiments are performed on a JEOL Model JEM 1011 operating at 100 kV.

Infrared spectra (in KBr matrix) are registered at room temperature on a Perkin Elmer Spectrum GX spectrophotometer. X-ray diffraction data are collected at room temperature with a Bruker D8 Advance diffractometer working in the Bragg-Brentano configuration () using Ni filtered CuK radiation (0.15418 nm) and fitted with a SuperSpeedVantec Detector.

Raman spectra are obtained using a triple subtractive T-64000 Jobin-Yvon spectrometer with a cooled CCD detector. An unpolarized 532 nm laser line (green) from an Oxxius-Slim solid state laser is used.

Magnetic susceptibility is measured using a Quantum design MPMS XL-7, operating at an external magnetic field H = 10 G on a 5 mg NPs sample. Measurements are done in primary vacuum with a helium gas exchange for thermalization.

Fig 1 .

 1 Fig 1. TEM image of NPs. Inset: Size distribution of the nanoparticles, the red line corresponds to a Gauss fit.

Fig 3 .

 3 Fig 3. Unpolarized Raman spectra of NPs and bulk at 15 K in the range of 200 -2200 cm -1 . Some phonons are reported with their corresponding mode.

Finally

  , in order to investigate the superconductivity of the NPs we performed d.c. magnetization measurements in a SQUID magnetometer. The temperature dependence of the d.c. volume susceptibility of the NPs is shown in Fig. 4.

Fig 4 .

 4 Fig 4. Temperature dependence (in blue) of the zerofield cooling (ZFC) and (in red) of the field cooling (FC) of the NPs. The dash line indicates T c = 9.1K.

Fig 5 .

 5 Fig 5. Isothermal magnetization at 1.9K for the NPs (in red) and the bulk (in blue).