Lori Gonnet

Alain Chamayou

Christiane André-Barres

Jean-Claude Micheau

Brigitte Guidetti

Tohru Sato

Michel Baron

Michel Baltas

Rachel Calvet

Elucidation of the Diels-Alder Reaction Kinetics between Diphenylfulvene and Maleimide by Mechanochemistry and in Solution

Keywords: Diels-Alder, Mechanochemistry, Ball-milling, Kinetics, Mechanisms

The Diels-Alder reaction kinetics between diphenylfulvene and maleimide using mechanochemistry and in liquid state is described. This reaction was carried out in solid state using a modified vibratory ball-mill with temperature control and in solution with toluene as solvent. The effect of temperature, ball mass, material, additives, and aging reaction were studied. We reported for the first time the kinetics of a mechanochemical reaction depending on the ratio ball mass/mass of the reagent. A new kinetic model has been established that corresponds well to our experimental data and allows an estimation of the global activation energy. In solution, the retro Diels-Alder reaction was observed. The reaction was second order for the formation of endo and exo and first order for the retro Diels-Alder reaction. The grinding method shows many advantages compared to solution: shorter reaction time, total reaction, and better selectivity.

INTRODUCTION

One of the main goals of organic synthesis is the research and development of efficient and environmentally safe methods. Since the 2000s a lot of stringent regulations for the chemical and pharmaceutical industries have appeared especially in terms of efficiency, waste management, and energy input. All these issues are now addressed and termed as "Green Chemistry", a multifaceted field dealing with what we call the 12 principles of Anastas and Warner. [START_REF] Anastas | Green Chemistry: Theory and Practice[END_REF] Among the most important principles are atom economy, preventing the use of solvents, increase of selectivity, minimization of chemical waste and energy. [START_REF] Poliakoff | [END_REF] In relation to the two latter points, in fact organic reactions and processes are usually conducted in solution (mostly organic) and frequently by introducing thermal energy that we have to balance at the end of the reaction with cooling energy as well.

By focusing on the Green Chemistry aspects, the desire to unveil alternative energy sources for chemical transformations under mild conditions led to the discovery of alternative energy systems, [START_REF] Varma | Chemical Activation by Mechanochemical Mixing, Microwave and Ultrasonic Irradiation[END_REF] among them the mechanochemical synthesis.

Mechanochemical methods deal with chemical transformations induced by mechanical energy, such as compression, shear, or friction. [START_REF] Baig | Alternative Energy Input: Mechanochemical, Microwave and Ultrasound-Assisted Organic Synthesis[END_REF][START_REF] Stauch | Advances in Quantum Mechanochemistry: Electronic Structure Methods and Force Analysis[END_REF][START_REF] Mcnaught | Compendium of Chemical Technology[END_REF] The sophisticated technique of ballmilling or mechano-milling is the adaptation from the traditional grinding methods using a mortar and pestle. These mechano-milling methods are generally conducted in vibration mills or planetary mills.

In the past decade, minerals, inorganic compounds, and polymers were the main subjects of investigation. [START_REF] Takacs | The Historical Development of Mechanochemistry[END_REF] The organic mechanochemistry has remained undeveloped until the pioneering work reported by Toda in the 1980s [START_REF] Toda | Oxidative Coupling Reactions of Phenols with Iron(III) Chloride in the Solid State[END_REF] and Kaupp. [START_REF] Kaupp | Solvent-Less Organic Synthesis[END_REF] Due to several advantages, the mechanochemistry area has received significant attention over solution-based chemical methods and process developments. The mechanochemical formation of the carbon-carbon bond (aldol reaction, Michael addition, Morita-Baylis-Hillman, Wittig, Suzuki, cycloaddition reactions), heterocyclic synthesis, carbon-heteroatom formation, multicomponent reactions, and C-H functionalization are popularly known in literature. [START_REF] Achar | Mechanochemical Synthesis of Small Organic Molecules[END_REF] The mechanistic understanding of the mechanochemical reactions is still unclear. Several models have been proposed, among them: hot spot, magma-plasma, spherical, kinetic, and impulse models are the most well-known. They are supported by dislocation and phonon and short-live-active center theories. [START_REF] Cintas | Enabling Technologies Built on a Sonochemical Platform: Challenges and Opportunities[END_REF][START_REF] Baláz | Hallmarks of Mechanochemistry: From Nanoparticles to Technology[END_REF][START_REF] Zhang | Mechanochemistry of Topological Complex Polymer Systems[END_REF][START_REF] Cintas | Interplay Between Mechanochemistry and Sonochemistry[END_REF] In-situ analyses by X-ray powder diffraction and Raman spectroscopy have allowed a complete quantification of the kinetics to understand the chemo-mechanical reactivity. [START_REF] Lukin | Tandem In Situ Monitoring for Quantitative Assessment of Mechanochemical Reactions Involving Structurally Unknown Phases[END_REF] It has also been reported by us and others that some reactions follow zero-order kinetics. [START_REF] Declerck | Solvent-Free Synthesis of Peptides[END_REF][START_REF] Oliveira | Lowering the Activation Energy under Mechanochemical Conditions: The Case of 2,3-Diphenylquinoxaline[END_REF][START_REF] Gil-Gonzalez | Unveiling Mechanochemistry: Kinematic-Kinetic Approach for the Prediction of Mechanically Induced Reactions[END_REF] In recent years, different phenomenological models have been applied to ball mill reactions to describe the apparent kinetics of mechanochemical transformations. [START_REF] Colacino | Processing and Investigation Methods in Mechanochemical Kinetics[END_REF][START_REF] Carta | Kinetics of Mechanochemical Transformations[END_REF] In their principles these approaches take into account the very efficient stirring of the powder in the milling vessel leading to a global chemical homogeneity. However, depending on the critical loading conditions (CLCs), the activation of the transformation occurs in a small fraction of the powder which is trapped in the colliding zone of the milling media. Improving the description of this active trapped volume (geometry, rheological conditions, and so forth) is a way to obtain more precise modeling. A model taking into account the formation of a rubber-like coating around the milling media has been reported to understand the "snowball" kinetic effect observed during a mechanochemical Knoevenagel condensation carried out in ball mill. [START_REF] Carta | Phenomenological Inferences on the Kinetics of a Mechanically Activated Knoevenagel Condensation: Understanding the "Snowball" Kinetic Effect in Ball Milling[END_REF] The Diels-Alder reaction involves a conjugated diene and an alkene, also called dienophile. This reaction gives rise to a variety of cyclohexene compounds. Several groups have studied the Diels-Alder reaction by mechanochemistry and in particular the mechanochemical parameters such as the frequency of the grinding apparatus, [START_REF] Zhang | Mechanochemical Diels-Alder Cycloaddition Reactions for Straightforward Synthesis of Endo-Norbornene Derivatives[END_REF][START_REF] Andersen | Decoupling the Arrhenius Equation via Mechanochemistry[END_REF][START_REF] Andersen | Exploring Stable, Sub-Ambient Temperatures in Mechanochemistry via a Diverse Set of Enantioselective Reactions[END_REF] the nature of the bowls and balls material, [START_REF] Andersen | Decoupling the Arrhenius Equation via Mechanochemistry[END_REF][START_REF] Mckissic | Comparison of Shaking versus Baking: Further Understanding the Energetics of a Mechanochemical Reaction[END_REF] the number of balls, [START_REF] Mckissic | Comparison of Shaking versus Baking: Further Understanding the Energetics of a Mechanochemical Reaction[END_REF] the ball mass, and ball diameter. [START_REF] Mckissic | Comparison of Shaking versus Baking: Further Understanding the Energetics of a Mechanochemical Reaction[END_REF] Finally, we have to mention the studies on the reactivity of retro Diels-Alder reaction by mechanical activation depending on the geometry of the molecules. [START_REF] Stevenson | Controlling Reactivity by Geometry in Retro-Diels-Alder Reactions under Tension[END_REF][START_REF] Wang | Stereochemical Effects on the Mechanochemical Scission of Furan-Maleimide Diels-Alder Adducts[END_REF] Except in rare cases, [START_REF] Haruta | Force-Induced Dissolution of Imaginary Mode in Mechanochemical Reaction: Dibenzophenazine Synthesis[END_REF] all these studies on organic mechanochemistry suffer from poor knowledge of the action of mechanochemical forces on chemical reactants.

In order to elaborate and develop future selection rules for mechanochemical reactions, it is essential to point out the increasing need for a more interdisciplinary approach between experimental, physicochemical, and theoretical chemists. [START_REF] Smalø | Mechanochemistry: The Effect of Dynamics[END_REF] In that respect, we wish to report here a detailed model study of a Diels-Alder reaction between diphenylfulvene and maleimide by a mechanochemical method and in solution. The interest for this reaction was warranted by its kinetics. Diels-Alder reaction is a concerted reaction in which bond breaking in reactants and bond making in products occur in a single step involving a transition state A (Figure 1). The possibility of a retro Diels-Alder pathways is also present. The mechanism of a single step reaction appeared easier to study than that of multi-step reactions.

The choice of the diphenylfulvene 1 was oriented essentially because of its melting point (mp 81 °C) that permits us to examine the mechanochemical reaction in a suitable range of temperatures where the reactant can remain solid. In this work, we have examined the following mechanochemical parameters, namely: material and the mass of the ball, temperature, influence of grinding auxiliaries, and/or autocatalysis effect and aging. A mechanochemical kinetic model was proposed. The reaction was conducted in toluene and its kinetics was recorded for mechanistic purposes. A comparison between the reaction in solid state and in solution, at the experimental and mechanistic level, is presented.

RESULTS AND DISCUSSION

Mechanochemical Diels-Alder Reaction. The reactions were carried out in a modified vibratory ball-mill Pulverisette 0 (Fritsch, Germany) equipped with a single ball (Figure S1, Supporting Information, SI). A heating/cooling coil was added to the experimental apparatus around the vessel for the temperature setting. The total powder mass of 2.843 g, i.e., 2 g of diphenylfulvene (1 equiv, 8.68 mmol) and 843 mg of maleimide (1 equiv, 8.68 mmol) was maintained for all experiments. For kinetic sampling, the grinding is stopped after preset grinding periods. Each sample which represents less than 1% of the total amount of powder in the mill is discarded after analysis.

The reaction products were monitored by analytical HPLC and compounds were extensively examined by NMR spectroscopy (Figure 2). The endo 3a and exo 3b products were quantified from their two-proton integration multiplets around 3.7 and 3.5 ppm, respectively (see SI Figure S2, for more details).

Influence of Ball Material and Mass. Three types of balls material have been used: brass, copper, and stainless steel. The ball material can influence the kinetics. Higher density balls have been used to obtain higher impact energy. [START_REF] Andersen | Exploring Stable, Sub-Ambient Temperatures in Mechanochemistry via a Diverse Set of Enantioselective Reactions[END_REF][START_REF] Mckissic | Comparison of Shaking versus Baking: Further Understanding the Energetics of a Mechanochemical Reaction[END_REF] For metalcatalyzed organic reactions, a catalytic effect on the surface of the metals is also possible. [START_REF] Fulmer | Solvent -Free Sonogashira Coupling Reaction via High Speed Ball Milling[END_REF] The characteristics of the balls used for the Figure 3 experiments are displayed in Table 1.

Figure 3 shows that the ball material has no influence on this reaction. On the contrary, a significant effect is observed by changing the ball mass. The reaction proceeds faster when using a heavier ball. Results using a 507 g stainless steel ball in comparison to a 171 and 109 g, respectively, show clearly significant conversion and an increase of the reaction rate. This is in agreement with the fact that grinding can be faster and more effective with a heavier ball. [START_REF] Oliveira | Lowering the Activation Energy under Mechanochemical Conditions: The Case of 2,3-Diphenylquinoxaline[END_REF][START_REF] Michalchuk | Ball Size or Ball Mass -What Matters in Organic Mechanochemical Synthesis[END_REF] It is important to note that the endo 3a/exo 3b ratio (98/2) does not change whatever the operating conditions are.

Influence of Pregrinding of Starting Materials. Diphenylfulvene 1 and maleimide 2 were ground separately during 1 h at 24 °C. Then, they were mixed together, and the Diels-Alder reaction was conducted at the same temperature, using the same experimental protocol and analytical methods (Figure 4).

Comparison of the two graphs shows a significant acceleration when using the preground starting compounds. After 3.6 h of grinding, the conversion ratio has reached 80% vs only 30% if not preground. In both cases, the final part of the two graphs (6-8 h) is similar. The conversion is complete and the endo 3a/exo 3b ratio (98/2) remains the same.

Granulometric analyses were carried-out to estimate the effect of grinding on the particle size. As shown in Figure 5, there is no effect on diphenylfulvene 1, while the particle size distribution of maleimide 2 becomes bimodal. Smaller particle size is observed (<50 μm) but also larger (1000 μm), indicating a potential agglomeration of the smaller particles.

The smaller particles size of the maleimide 2 could lead to an increase of the developed surface. Indeed, the higher contact area could induce an acceleration of the reaction rate.

Influence of the Temperature. The reaction between maleimide and diphenylfulvene was also studied under different milling temperatures, varying from 14 °C to 62 °C (Figure 6). Results show a significant increase of the reaction rate with the temperature. Indeed, while a total reaction was observed after 6.5 h of milling at 24 °C, but only 18 min were needed at 62 °C to achieve completion. In all experiments, the ratio of endo 3a/exo 3b (98/2) of the Diels-Alder adduct 3 remained the same in all aliquots examined by analytical HPLC through the whole temperature and time range showing that the high selectivity of the Diels-Alder mechanochemical reaction between diphenylfulvene 1 and maleimide 2 was not so sensitive in the explored temperature range.

For all the experiments shown above, the evolution of the Diels-Alder mechanochemical reaction follows a sigmoidal curve. An induction period (up to 25% conversion) is followed in the second part by an acceleration before the rate decreases again as the reaction goes to completion. [START_REF] Hutchings | Feedback Kinetics in Mechanochemistry: The Importance of Cohesive States[END_REF] This sigmoidal kinetic curve is apparently analogous to those encountered in autocatalysis. 33 This is a strong indication of the presence of some feedback process whose detailed nature remains to be understood. In that respect, we wished to examine if an autocatalysis-like phenomenon issued by the final products might be responsible of the acceleration process. A reaction was thus performed at 24 °C in the presence of 20% of the Diels-Alder adduct 3 corresponding to the amount present after 2 h of grinding during previous experiments.

The results obtained show that the addition of 20% of final product 3 increases the reaction rate and that the sigmoidal shape of the kinetics is lost (no more an acceleration period). A similar result with an even better response has been found in a test experiment conducted by introducing 20% of pyrogenic silica instead of the Diels-Alder adduct 3, always keeping the same total mass (Figure 7). Pyrogenic silica was selected because it has a median diameter d 50 close to the final product (Table 2) and because it is well-known that silica acts as a catalyst for the Diels-Alder reaction. [START_REF] Veselovsky | Dramatic Acceleration of the Diels-Alder Reaction by Adsorption on Chromatography Adsorbents[END_REF] In this way, we could be able to know if the final product 3 acts as a catalyst, like silica.

From these experiments, it can be inferred that under mechanochemical conditions a positive feedback mechanism is operating. Such a situation is often encountered in the framework of autocatalyzed reactions. [START_REF] Horváth | Law of Mass Action Type Chemical Mechanisms for Modeling Autocatalysis and Hypercycles: Their Role in the Evolutionary Race[END_REF] However, in this specific case, such autocatalysis-like evolution is not due to a simple molecular mechanism, but more likely to a complex combination of rheological and physicochemical phenomena. From this point of view, the silica acceleration effect is instructive, because it was assumed to originate from a preassociation mechanism resulting from a rigid anchoring of the reaction partners within a critical bonding distance. Under ball-milling, such preassociation could occur in tiny cocrystal phases whose influence or size is slowly increasing as the reaction processes. Such an assumption is supported by the aging studies where it is shown that the rate increases after previous cogrinding, but above all, that the sigmoidal shape remains if the cogrinding is short, but disappears after longer cogrinding. Traces or seeds of such tiny cocrystal phases are likely to persist within the added Diels-Alder adduct 3, hence the acceleration effect.

Aging. During all the grinding experiments detailed above, it was observed that the Diels-Alder reaction continues even if the grinding stops (aging). Indeed, some chemical reactions can occur spontaneously between solid reagents, in some cases facilitated by humidity, organic vapors, the addition of catalysts, heating, or brief grinding. [START_REF] Huskic | Accelerated Ageing Reactions: Towards Simpler, Solvent-Free, Low Energy Chemistry[END_REF] In our case, this phenomenon does not take place when diphenylfulvene and maleimide are simply mixed without previous cogrinding. So, the aging reaction was studied after 15 min and 1 h of grinding at 24 °C (Figure 8). The conversion rates are 4% and 8%, respectively, after 15 min and 1 h of grinding. The reaction mixture was then left at room temperature (22 °C) and its evolution was followed by analytical HPLC. The conversion rate is significantly faster after a longer grinding time. This may be due to the larger creation of a cocrystal after 1 h, in which the molecules are positioned to react. This was also confirmed by calorimetric analyses, where a higher heat release was observed after longer grinding times (SI Figure S4). Kinetics. The reaction kinetics of Diels-Alder by mechanochemistry was then studied to have a better understanding of the mechanism of the transformation during grinding. Experiments concerning the influence of the ball mass and the ratio ball mass/reagent mass lead to the hypothesis that the specific energy brought to the reagents seems to be one of the major parameters of the apparent kinetics of the transformation. In that respect, a preliminary semiempirical model can be proposed and its adequacy will be verified with the set of experimental results. During a reaction by grinding, the ratio ball mass/mass of the reagent influences the rate of the transformation notably through the creation of contact surface around the active grains under the effect of the grinding. The variation of the mass (m) of a reagent can be considered to be dependent on the ratio of the ball mass (M b ) to m (eq 1). This equation has therefore been integrated (eq 2) and reformulated (eq 3) according to the conversion rate X (eq 4).

i

k j j j y { z z z dm dt k M m b - = (1)
The integration of eq 1 leads to eq 2:

m m kM t 1 2 ( ) 0 2 2 b - = (2)
The mass of reagent can be replaced by its expression with the conversion rate X and eq 2 becomes eqs 3 and 4

X X k M m t 2 2 2 b 0 2 - = (3) X X A A k M m 2 with 2 t 2 b 0 2 - = = (4) with X m m m 0 0 = - (5)
This simple kinetic model was then applied to our reaction records performed with our mechanochemical apparatus. For all experiments, a linearization of the experimental points was obtained as much as more than 80% of the reaction (Figure 9). This result suggests that this model can be used as a first approximation for the Diels-Alder reaction by mechanochemistry. However, as this model is limited to the early part of the reaction, the slowed-down final part of the curve is not expected to be reproduced. Let us say that such a slow-down of the final part is common to all kinds of kinetics and that its mechanistic information is relatively poor. The apparent rate constants A delivered by this kinetic model are gathered in Table 3.

The relationship between temperature and reaction rate constant is generally described by the Arrhenius equation (eq 6) and its linearized form (eq 7). The Arrhenius equation can be also valid to determine the activation energy of solid state reactions. [START_REF] Galwey Andrew | A Theoretical Justification for the Application of the Arrhenius Equation to Kinetics of Solid State Reactions (Mainly Ionic Crystals)[END_REF][START_REF] Galwey | Application of the Arrhenius Equation to Solid State Kinetics: Can This Be Justified? Thermochim[END_REF] k k e E RT 0

/ a = - (6) k k E R T ln ln 1 0 a = - (7)
where k the rate constant, k 0 the pre-exponential factor, E a the activation energy for the reaction, R the universal gas constant, and T the absolute temperature.

According to eq 6, the plot of log A vs 1/T is shown on Figure 10. All points from 14 to 56 °C are nicely aligned. However, the last point at 62 °C is a slight departure. This deviation from linearity is significant since all experiments were made in triplicate. One possible explanation could be related to the endothermic effect of the melting of the powder mixture. DSC measurements were performed to find out if a possible contact eutectic melting formation was occurring (Figure 11).

For diphenylfulvene 1 and maleimide 2, an endothermic peak, corresponding to the melting points, was found (81 °C for diphenylfulvene 1 and 94 °C for maleimide 2). Then the equimolar mixture of the reagents was analyzed. We can observe the beginning of the melting endotherm of diphenylfulvene 1 at 77 °C followed by an exotherm at 84 °C and melting endotherm of maleimide 2 at 90 °C. A slight shift for both melting endothermic peaks is observed because the masses of each of the reagents, diphenylfulvene 1 and maleimide 2, present in the mixture are smaller than those of the same reagents analyzed alone (for each analysis, a total sample mass of 5 mg is analyzed). In addition, the endotherm of diphenylfulvene 1 is not fully visible due to the exothermic peak present at 84 °C. This exothermic peak can be attributed to the start of the reaction and occurs during the fusion of diphenylfulvene 1, i.e., at the moment when the reagents come into contact. In the case of the grinding experiment at 62 °C, the melting temperature of diphenylfulvene (77-81 °C) may be reached locally at the impact point. The melting endotherm is probably confounding the temperature measurements by extracting heat from the system. At lower temperatures (from 14 to 56 °C), the reaction between the solids prevails, as indicated by the straightforward linear decrease of ln A with 1/ T.

An activation energy of 67 kJ/mol was estimated for the linear range, i.e., up to 56 °C. This value is of the same order of magnitude as that reported in the literature for other mechanochemical Diels-Alder reactions (between 30 and 115 kJ/mol). [START_REF] Klemm | Molecular Complexation and Kinetics for Diels-Alder Condensation of Naphthylalkenes with Tetracyanoethylene[END_REF][START_REF] Rosokha | Substituent-Induced Switch of the Role of Charge-Transfer Complexes in the Diels-Alder Reactions of o-Chloranil and Styrenes[END_REF][START_REF] Rowley | Kinetics of Diene Reactions at High Temperatures[END_REF] Previous work on the synthesis of 2,3diphenylquinoxaline using our mechanochemical apparatus showed an activation energy between 15 and 92 kJ/mol. [START_REF] Oliveira | Lowering the Activation Energy under Mechanochemical Conditions: The Case of 2,3-Diphenylquinoxaline[END_REF] Quantum calculations are in progress to determine the best transition state geometries. [START_REF] Linder | On the Method-Dependence of Transition State Asynchronicity in Diels-Alder Reactions[END_REF] They will be the subject of a further publication.

Liquid State Diels-Alder Reaction. For comparison purposes, the reaction between diphenylfulvene 1 and maleimide 2 was also carried out in toluene at different temperatures: 70, 80, and 105 °C and monitored by NMR (Figure 12a,b,d) and HPLC (Figure 12c). At 70 °C (Figure 12a) a sharp decrease of the diphenylfulvene 1 in less than a day and a stabilization at around 10% is witnessed. At 80 °C (Figure 12b), this consumption is faster, the stabilization at 10% is reached in about 10 h of reaction. Simultaneously, it is noteworthy to consider the evolution of the endo 3a/exo 3b ratio moving slightly from 93/7 to 91/9 after 6 days at 70 °C and more significantly from 92/8 to 88/12 after 3 days at 80 °C. All these variations suggest the presence of a retro-Diels reaction. A very interesting result is also observed when conducting the reaction at 105 °C (Figure 12 c,d). The NMR monitoring for a more than a 5-week period (Figure 12d) and the HPLC one for more than 20 h (Figure 12c) show a sharp decrease of the starting diphenylfulvene 1 during the first hours of the reaction and then a slight increase before a further decrease (5% present after 5 weeks). At the same time, while the endo adduct 3a is the major one in the beginning of the reaction, it decreases and becomes the minor one after 15 days. At 105 °C, the endo 3a/ exo 3b ratio evolves from 88/12 at 20 h to 29/71 after 8 weeks.

These results clearly show that (i) the endo product 3a is the kinetically controlled adduct, (ii) the reaction is not complete even at the higher temperature after several weeks, and (iii) the retro Diels-Alder reaction is also operating. The following mechanism is assumed for the diphenylfulvene 1/ maleimide 2 Diels-Alder reaction in solution (Figure 13).

We assume that the formation of the endo 3a and exo 3b products is second order (eq 8) and that the retro Diels-Alder is first order (eqs 9 and 10). The differential equations in agreement with this model are as follows:

d dt d dt k k k k diph mal ( )d i p h m a l e n d o e x o d x d x [ ] = [ ] = - + [ ][ ] + [ ] + [ ] - - (8)
d dt k k endo diph mal endo d d [ ] = [ ][ ] - [ ] - (9)
d dt k k exo diph mal exo x x [ ] = [ ][ ] - [ ] - (10)
These differential equations can be numerically integrated with any empirical values of the rate constants. To obtain the experimental rate constants, a homemade iterative optimization software was used. 43 This software allows us to simulate the evolution of the substrate and the products and to adjust the rate constants until the simulated curves exactly fit the experimental kinetic data. The results of the optimization of the kinetics for the reactions at 70 °C, 80 °C, and 105 °C are shown in Figure 14. The experimental points overlap perfectly for the reactions at 70 °C and 80 °C (Figure 14a,b) with the simulated curves. For the experiments at 105 °C, the curves (kinetic model) are very close to the markers but do not fully overlap. Indeed, for the reactions at 70 °C and 80 °C, the reaction monitoring was carried out directly in the NMR tube inside the NMR spectrometer at the desired temperature, whereas for the reactions at 105 °C, the conversion rates were determined for the 8 weeks period by HPLC (Figure 14c) and by NMR analyses but after sampling in a flask. Experiments at 105 °C may thus be subject to more experimental error. The rate constants obtained are listed in Table 4. These results show that the endo product 3a is the kinetic one consequently, the exo product 3b is the thermodynamic one. The equilibration is very slow since it occurs through the retro Diels-Alder reaction. The rate constant k -x is very small and can only be determined precisely from the long-term experiment at 105 °C. However, the reaction at 105 °C for 8 weeks is too long to allow the relatively fast k d and k -d to be accurately obtained.

Figure 15 shows the application of the Arrhenius equation to the rate constants determined in solution. Table 5 summarizes the activation energies obtained in liquid state and by mechanochemistry.

In mechanochemistry, the apparent rate constants measure the overall rate of this process from the maleimide 2 and diphenylfulvene 1 consumption including grinding, endo 3a/ exo 3b product formation, and potentially retro-Diels-Alder, thus also resulting in an activation energy E a value of the overall process. On the contrary, in liquid medium, the rate constants and the E a have been estimated from the main steps. Therefore, these values cannot be compared directly. In solution, the endo product 3a is the kinetic one with an activation energy determined at 38 kJ/mol, while the thermodynamically more stable exo product 3b has an activation energy of 50 kJ/mol (Table 5). The E a of endo product 3a for the retro Diels-Alder reaction is quite high (121 kJ/mol). Under mechanochemical conditions detailed before, the Diels-Alder reaction between diphenylfulvene and maleimide is much more efficient (total reaction), faster, and potentially too fast to show any retro Diels-Alder transformations, i.e., no endo/exo equilibration was observed. We think that this lack of mechanochemical equilibration is the consequence the high retro-Diels activation energy (121 kJ/ mol). Such a value cannot be attained when using our mechanochemical apparatus. The pre-exponential factor, k 0 , is higher by mechanochemistry. This result means that molecular state encounters are more efficient with this method, which is consistent with a faster transformation rate by mechanochemistry than in solution [total reaction after 18 min at 62 °C using mechanochemistry and reaction equilibrium after 2 days in toluene at 70 °C (C = 2.9 mol/L)].

CONCLUSIONS

We reported here a detailed model study of a Diels-Alder reaction between diphenylfulvene 1 and maleimide 2 by a mechanochemical method and in toluene. The effect of the experimental conditions for the mechanochemical reaction were studied (material and mass of the ball, temperature, influence of grinding auxiliaries, and aging). Our results demonstrated the influence of the ball mass, temperature, and an aging phenomenon. Grinding auxiliaries play the same role as the Diels-Alder adducts upon the reaction progress indicating only a positive mechanical role of the adducts/ auxiliaries by accelerating the reaction when present at 20%. In mechanochemistry, the transformation is complete, and the very selective ratio of the Diels-Alder adducts 3 remains unchanged (endo 3a/exo 3b 98/2) through the whole temperature and time range. This is an indication that the Diels-Alder mechanochemical reaction between diphenylfulvene 1 and maleimide 2 is very selective. [START_REF] Howard | Switching Chemoselectivity: Using Mechanochemistry to Alter Reaction Kinetics[END_REF] The deleterious retro Diels-Alder reaction is inhibited. A kinetic model linking the transformation kinetic to the mechanical energy given to the reactants through the ratio mass of the ball/mass of reactants has been proposed. It fits well with our experimental data up to 88% conversion and allows an estimation of the global activation energy.

In toluene, the reaction is much slower and not complete. The corresponding retro Diels-Alder is occurring. The kinetic endo product 3a is slowly transformed into the thermodynamic exo 3b. The ratio endo 3a/exo 3b evolves during 6 weeks at 105 °C from 88/12 to 29/71. It has been found that the retro-Diels reaction exhibits a high activation energy (121 kJ/mol). We believe that this high value explains why the retro-Diels reaction does not occur in our mechanochemistry apparatus allowing us to obtain the kinetically controlled adduct with very high selectivity.

ASSOCIATED CONTENT

* sı Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acssuschemeng.0c08314.

Experimental procedures, computation parameters, DSC, calorimetric measurements, and 1H and 13C spectral data of all compounds (PDF)

Figure 1 .

 1 Figure 1. Diels-Alder reaction between diphenylfulvene 1 and maleimide 2.

Figure 2 .

 2 Figure 2. NMR spectra of (A) diphenylfulvene 1, (B) maleimide 2, (C) crude mixture after 8 h of milling at 24 °C showing the formation of endo 3a product, and (D) crude mixture after 1 week in toluene at 105 °C showing the formation of exo 3b and endo 3a product.

Figure 3 .

 3 Figure 3. Effect of the ball (a) material and (b) mass (Table1) on the mechanochemical diphenylfulvene 1/maleimide 2 Diels-Alder reaction at 44 °C.

a

  All balls have the same diameter (50 mm) and are empty. They are filled with different solids (sand and lead beads) to change their mass.

Figure 4 .

 4 Figure 4. Effect of a pregrinding of starting materials on the mechanochemical diphenylfulvene 1/maleimide 2 Diels-Alder reaction at 24 °C.

Figure 5 .

 5 Figure 5. Particle size distribution of (a) diphenylfulvene 1 and (b) maleimide 2 before and after 1 h of grinding.

Figure 6 .

 6 Figure 6. Effect of the temperature on the mechanochemical diphenylfulvene 1/maleimide 2 Diels-Alder reaction.

Figure 7 .

 7 Figure 7. Effect of various additives (final product and grinding auxiliary) on the mechanochemical diphenylfulvene 1/maleimide 2 Diels-Alder reaction. All the experiments were carried out with the same total mass of powder (2.843 g).

Figure 8 .

 8 Figure 8. Effect of substrate aging (pregrinding) on the mechanochemical diphenylfulvene 1/maleimide 2 Diels-Alder reaction.

Figure 9 .

 9 Figure 9. (a) Evolution of the diphenylfulvene conversion rate at 44 °C and (b) linearization by the kinetic model (eq 3a,b). The points are aligned up to approximately X = 0.88 (i.e., when X 2 -2X = -0.99).

Figure 10 .

 10 Figure 10. Determination of the activation energy of the mechanochemical diphenylfulvene 1/maleimide 2 Diels-Alder reaction.

Figure 11 .

 11 Figure 11. DSC thermograms of diphenylfulvene 1, maleimide 2, and mixture of reagents

Figure 12 .

 12 Figure 12. Evolution of diphenylfulvene 1/maleimide 2 Diels-Alder reaction in toluene at different temperatures: (a) 70 °C, (b) 80 °C with NMR monitoring, (c) 105 °C with HPLC monitoring, and (d) 105 °C with NMR monitoring. Note the longer time scale in d.

Figure 13 .

 13 Figure 13. Proposed mechanism for the diphenylfulvene 1/maleimide 2 Diels-Alder reaction in liquid state.

Figure 14 .

 14 Figure 14. Kinetic modeling of the Diels-Alder reaction (a) evolution at 70 °C for 4 days; (b) at 80 °C for 4 h. Both experiments "a" and "b" were monitored by NMR. Note the perfect correspondence between the experimental points and the simulated model (c) at 105 °C for 2 h and (d) at 105 °C for 8 weeks. Experiment "c" was monitored by HPLC and "d" by NMR. Note the relatively good reproduction of the evolutions by the model.

Table 4 . 3 × 7 a

 437 Rate Constants from the Kinetic Analysis of the Diphenylfulvene 1/Maleimide 2 Diels-Alder Reaction in Solution a,b temperature (°C)k d (M -1 •s -1 ) k -d (s -1 ) k x (M -1 •s -1 ) k -x (M -1 •s -1 10 -3 3.0 × 10 -6 3.2 × 10 -4 ∼0 105 a 1.1 × 10 -2 2.5 × 10 -5 1.2 × 10 -3 ∼0 105 b 0.7 to 1.2 × 10 -1 5.6 to 10 × 10 -4 9.3 × 10 -4 2.9 × 10 -Short-term reaction monitored by HPLC. b Long-term reaction monitored by NMR.

Figure 15 .

 15 Figure 15. Determination of the activation energies of the liquid state diphenylfulvene 1/maleimide 2 Diels-Alder direct-and retroreactions.

Table 1 .

 1 Milling Balls Used for the Diels-Alder Reaction

	milling ball	ball material	ball mass (g) a
	BR	brass	171
	CU	copper	171
	SS1	stainless steel	171
	SS2	stainless steel	507
	SS3	stainless steel	109

Table 2 .

 2 Comparison of the Grain Sizes of the Various Additives According to Their d 50 Median Diameter

	material	d 50 (μm) a
	final product 3	32
	sand	246
	silica gel	125
	pyrogenic silica	37

a d 50 : median diameter

Table 3 .

 3 Apparent Rate Constants at Different Temperatures

	entry grinding temperature (°C) time (min)	A (min -1 )	R 2a
	1	14	5 to 250	1.03 × 10 -3	0.993
	2	24	5 to 220	2.24 × 10 -3	0.995
	4	44	5 to 80	1.16 × 10 -2	0.992
	5	56	1.5 to 13	3.61 × 10 -2	0.966
	6	62	1.5 to 8	1.11 × 10 -1	0.996

Table 5 .

 5 Activations Energies of the Diphenylfulvene 1/Maleimide 2 Diels-Alder Direct-and Retro-Reactions by Mechanochemistry and in the Liquid State

	E a (kJ/mol)	ln k 0

a Note the measurement time interval and the good correlation coefficients confirming the linearization by the kinetic model.

ACKNOWLEDGMENTS

The authors would like to gratefully acknowledge the Region Occitanie for the thesis grant (L.G.) and the CNRS, University Paul Sabatier, IMT Mines Albi and JSPS for financial support. The ICT facilities (ICT, Toulouse, France, http://ict.ups-tlse. fr/) and especially those of NMR and Mass spectrometry are gratefully acknowledged for carrying out the corresponding analyses. We also want to thank Sylvie Del Confetto, Severine Patry, and Philippe Accart for HPLC, calorimetry, and particles sizes analyses.

AUTHOR INFORMATION Corresponding Authors

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interest.


Maurilio Evandro Giuseppe Betini
email: evandrobetini@gmail.com

Cristiano Pereira Gomes

Stefano Mucsi

Marcos Tadeu D'azeredo Orlando

Temístocles De

Sousa Luz

Marie-Noëlle Avettand-Fènoël

Jesualdo Luiz Rossi

Marcos Tadeu D'

Azeredo Orlando

Temístocles De Sousa Luz

Marie-Noëlle Avettand-Fénoël

Effect of Nitrogen Addition to Shielding Gas on Cooling Rates and in the Microstructure of Thin Sheets of Duplex Stainless Steel Welded by Pulsed Gas Tungsten Arc Welding Process

Keywords: duplex stainless steel, cooling rates, nitrogen, GTAW, thermal cycle, microhardness

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

Introduction

Duplex stainless steels (DSS) have basically a microstructure consisting of austenite and ferrite. In general, DSS has around 50% of each phase in the base material but typically a variation of 35 to 60% in ferrite content results in acceptable properties [START_REF] Gunn | Duplex stainless steels, microstructure, properties and applications[END_REF][START_REF] Alvarez-Armas | Duplex stainless steels: brief history and some recent alloys[END_REF] .

The main commercial factor pushing the advance, the development and use of duplex stainless alloys was the increase of activity in the offshore oil industry which demanded a stainless steel material to handle aggressive environments and new steel production techniques [START_REF] Alvarez-Armas | Duplex stainless steels: brief history and some recent alloys[END_REF] . The new technique using addition of nitrogen and lowering of carbon content made it possible to produce much cleaner steels improving high temperature stability as shown by duplex structure [START_REF] Gunn | Duplex stainless steels, microstructure, properties and applications[END_REF][START_REF] Alvarez-Armas | Duplex stainless steels: brief history and some recent alloys[END_REF][START_REF] Messer | Duplex stainless steel welding: best practices[END_REF][START_REF] Pohl | Effect of intermetallic precipitations on the properties of duplex stainless steel[END_REF][START_REF] Bettahar | Microstructure and mechanical behavior in dissimilar 13Cr/2205 stainless steel welded pipes[END_REF] . Thus, the DSS alloys have become a suitable alternative to austenitic stainless steels due to their special combination of good mechanical properties and corrosion resistance and lower costs [START_REF] Gunn | Duplex stainless steels, microstructure, properties and applications[END_REF][START_REF] Alvarez-Armas | Duplex stainless steels: brief history and some recent alloys[END_REF][START_REF] Liou | Effects of alloying elements on the mechanical properties and corrosion behaviors of 2205 duplex stainless steels[END_REF] . The nuclear industry, especially requests alloys with high thermal stability in pipes for power generation systems and safe transportation equipment's for radioactive material [START_REF] Cárcel-Carrasco | Effects of x-rays radiation on AISI 304 stainless steel welding with AISI 316l filler material: a study of resistance and pitting corrosion behavior[END_REF][START_REF] Fujii | Effects of radiation on spinodal decomposition of ferrite in duplex stainless steel[END_REF][START_REF] Betini | Study on welding thermal cycle and residual stress of UNS s32304 duplex stainless steel selected as external shield for a transport packaging of Mo-99[END_REF] . DSS also presents satisfactory weldability, however it is possible to occur the formation of excessive ferrite, nitrides and intermetallic phases in the solidifying zone (SZ) and in the heat affected zone (HAZ) [START_REF] Gunn | Duplex stainless steels, microstructure, properties and applications[END_REF][START_REF] Alvarez-Armas | Duplex stainless steels: brief history and some recent alloys[END_REF][START_REF] Hosseini | Nitrogen loss and effects on microstructure in multipass TIG welding of a super duplex stainless steel[END_REF] . These formations of deleterious phases need to be avoided and a balanced ferrite / austenite microstructure must be maintained [START_REF] Bermejo | Effect of shielding gas on welding performance and properties of duplex and superduplex stainless steel welds[END_REF] .

The GTAW (gas tungsten arc welding) processes are generally preferred because they produce very high-quality welds [START_REF] Alvarez-Armas | Duplex stainless steels: brief history and some recent alloys[END_REF][START_REF] Messer | Duplex stainless steel welding: best practices[END_REF][START_REF] Tseng | The effect of pulsed GTA welding on the residual stress of a stainless steel weldment[END_REF] . In many cases distortion is the major problem in welding of thin sections. However, the distortion is controlled in pulsed and magnetic arc oscillation GTAW process [START_REF] Tseng | The effect of pulsed GTA welding on the residual stress of a stainless steel weldment[END_REF] . Weld root quality of stainless-steel pipe and tubes can be ensured by using an inert purging gas [START_REF] Messer | Duplex stainless steel welding: best practices[END_REF][START_REF] Bettahar | Microstructure and mechanical behavior in dissimilar 13Cr/2205 stainless steel welded pipes[END_REF][START_REF] Bermejo | Effect of shielding gas on welding performance and properties of duplex and superduplex stainless steel welds[END_REF] . The pure Ar is the most commonly used purging gas in GTA welding of several grades of steels [START_REF] Cárcel-Carrasco | Effects of x-rays radiation on AISI 304 stainless steel welding with AISI 316l filler material: a study of resistance and pitting corrosion behavior[END_REF][START_REF] Bermejo | Effect of shielding gas on welding performance and properties of duplex and superduplex stainless steel welds[END_REF] . However, 2% nitrogen is recommended in pure argon mixture for shielding gas and optimizing the phase balance, impact toughness and corrosion resistance of DSS [START_REF] Muthupandi | Effect of nitrogen addition on formation of secondary austenite in duplex stainless steel weld metals and resultant properties[END_REF] . Taking all aspects into account, Ar + 2%N 2 is the preferred shielding gas for welding duplex and super duplex with the GTAW process [START_REF] Liou | Effects of alloying elements on the mechanical properties and corrosion behaviors of 2205 duplex stainless steels[END_REF][START_REF] Betini | Study on welding thermal cycle and residual stress of UNS s32304 duplex stainless steel selected as external shield for a transport packaging of Mo-99[END_REF] .

Several authors have been mentioning the important role of N 2 in the microstructure evolution by being the strongest austenite forming alloying element [START_REF] Liou | Effects of alloying elements on the mechanical properties and corrosion behaviors of 2205 duplex stainless steels[END_REF][START_REF] Betini | Study on welding thermal cycle and residual stress of UNS s32304 duplex stainless steel selected as external shield for a transport packaging of Mo-99[END_REF][START_REF] Hosseini | Nitrogen loss and effects on microstructure in multipass TIG welding of a super duplex stainless steel[END_REF][START_REF] Muthupandi | Effect of nitrogen addition on formation of secondary austenite in duplex stainless steel weld metals and resultant properties[END_REF][START_REF] Sales | Effect of nitrogen in shielding gas of keyhole GTAW on properties of duplex and superduplex welds[END_REF][START_REF] Zhang | Effects of nitrogen in shielding gas on microstructure evolution and localized corrosion behavior of duplex stainless steel welding joint[END_REF][START_REF] Basyigit | The effects of nitrogen gas on microstructural and mechanical properties of TIG welded s32205 duplex stainless steel[END_REF][START_REF] Moreno | Determination of nitrogen in duplex stainless steels by EPMA[END_REF] . Moreover, N 2 is an economical and efficient substitute for nickel [START_REF] Hosseini | Nitrogen loss and effects on microstructure in multipass TIG welding of a super duplex stainless steel[END_REF][START_REF] Moreno | Determination of nitrogen in duplex stainless steels by EPMA[END_REF] . Generally, DSS has a low bulk nitrogen content standardized in the range 0.15% -0.35%. Moreno et al. [START_REF] Moreno | Determination of nitrogen in duplex stainless steels by EPMA[END_REF] determined using electron probe microanalysis (EPMA) technique an average content of N 2 in the range 0.045% -0.070%wt in ferrite and 0.520% -0.770%wt in austenite for five different DSS alloys. The addition of C and N 2 strengthens both ferrite and austenite by dissolving at interstitial sites in the solid solution [START_REF] Alvarez-Armas | Duplex stainless steels: brief history and some recent alloys[END_REF][START_REF] Basyigit | The effects of nitrogen gas on microstructural and mechanical properties of TIG welded s32205 duplex stainless steel[END_REF][START_REF] Moreno | Determination of nitrogen in duplex stainless steels by EPMA[END_REF][START_REF] Bobadilla | On the nitrogen diffusion in a duplex stainless steel[END_REF] . Materials Research During welding process, the austenite dissolves while being heated, it is followed by grain growth in the delta ferrite region, and finally restoring to the austenitic phase during cooling [START_REF] Sieurin | Austenite reformation in the heataffected zone of duplex stainless steel 2205[END_REF][START_REF] Mohammed | Effects of heat input on microstructure, corrosion and mechanical characteristics of welded austenitic and duplex stainless steels: a review[END_REF] . However, the loss of nitrogen and a decrease of austenite content during GTAW welding would lead to toughness reduction [START_REF] Hosseini | Nitrogen loss and effects on microstructure in multipass TIG welding of a super duplex stainless steel[END_REF][START_REF] Moreno | Determination of nitrogen in duplex stainless steels by EPMA[END_REF] . Hosseini et al. [START_REF] Hosseini | Nitrogen loss and effects on microstructure in multipass TIG welding of a super duplex stainless steel[END_REF] monitored economical content and microstructure for each weld pass in super duplex stainless steel, by using wavelength dispersive X-ray spectrometry; It was observed that after four passes a loss of nitrogen from 0.28% in the base metal -BM to 0.17% (in mass) for low heat input. Karlsson et al. [START_REF] Karlsson | Low energy input welding of duplex stainless steels[END_REF] using low heat input autogenously laser welding on 2507 SDSS observed highly ferritic microstructures with nitride precipitates due to nitrogen loss at high cooling rates. During the thermal cycle, the alloy is heated to a very high temperature above 1350 °C for a short time, held for a few seconds and subsequently cooled to room temperature [START_REF] Karlsson | Low energy input welding of duplex stainless steels[END_REF][START_REF] Tan | Influence of welding thermal cycles on microstructure and pitting corrosion resistance of 2304 duplex stainless steels[END_REF] . Later on, in the cooling stage, the austenite re-precipitates around ferrite grain boundaries [START_REF] Xavier | An experimental and numerical approach for the welding effects on the duplex stainless steel microstructure[END_REF] . In this way, adjustment of a low cooling rate and proportion of N 2 allows adequate austenite formation, but not too low cooling rate in order to avoid precipitation of intermetallic phases [START_REF] Bobadilla | On the nitrogen diffusion in a duplex stainless steel[END_REF][START_REF] Tan | Influence of welding thermal cycles on microstructure and pitting corrosion resistance of 2304 duplex stainless steels[END_REF][START_REF] Xavier | An experimental and numerical approach for the welding effects on the duplex stainless steel microstructure[END_REF][START_REF] Chen | Influence of cooling rate on microstructure evolution and pitting corrosion resistance in the simulated heat-affected zone of 2304 duplex stainless steels[END_REF] . Westin 24 reported that high ferrite contents resulted in Cr-rich nitrides formation in HAZ and SZ due to large ferrite grain supersaturated in nitrogen. If the gas protection is insufficient during welding or if the nitrogen is added to the shielding gas, the formation of chromium nitrides caused by an uptake of nitrogen from the atmosphere may occur [START_REF] Xavier | An experimental and numerical approach for the welding effects on the duplex stainless steel microstructure[END_REF] .

Nitrogen is added to argon shielding gas in duplex stainless-steel welds to preserve weld metal nitrogen levels [START_REF] Zhang | Effects of nitrogen in shielding gas on microstructure evolution and localized corrosion behavior of duplex stainless steel welding joint[END_REF][START_REF] Basyigit | The effects of nitrogen gas on microstructural and mechanical properties of TIG welded s32205 duplex stainless steel[END_REF] . According to Zhang et al. [START_REF] Zhang | Effects of nitrogen in shielding gas on microstructure evolution and localized corrosion behavior of duplex stainless steel welding joint[END_REF] , there are two ways to compensate for the nitrogen loss during welding: one is directly adding the nitrogen to the BM and filler wires in the originally producing supplies [START_REF] Muthupandi | Effect of nitrogen addition on formation of secondary austenite in duplex stainless steel weld metals and resultant properties[END_REF][START_REF] Moreno | Determination of nitrogen in duplex stainless steels by EPMA[END_REF][START_REF] Xavier | An experimental and numerical approach for the welding effects on the duplex stainless steel microstructure[END_REF] or a proper proportion of nitrogen gas is added into shielding gas and backing gas during welding [START_REF] Bermejo | Effect of shielding gas on welding performance and properties of duplex and superduplex stainless steel welds[END_REF][START_REF] Sales | Effect of nitrogen in shielding gas of keyhole GTAW on properties of duplex and superduplex welds[END_REF][START_REF] Basyigit | The effects of nitrogen gas on microstructural and mechanical properties of TIG welded s32205 duplex stainless steel[END_REF][START_REF] Chen | Influence of cooling rate on microstructure evolution and pitting corrosion resistance in the simulated heat-affected zone of 2304 duplex stainless steels[END_REF][START_REF] Westin | Microstructure and properties of welds in the lean duplex stainless steel LDX 2101[END_REF][START_REF] Tsuge | The effect of nitrogen on the localized corrosion resistance of duplex stainless steel simulated weldments[END_REF][START_REF] Bhatt | Influence of nitrogen in the shielding gas on corrosion resistance of duplex stainless steel welds[END_REF][START_REF] Westin | Effect of nitrogen-containing shielding and backing gas on the pitting corrosion resistance of welded lean duplex stainless steel LDX 2101(r) (EN 1.4162, UNS S32101)[END_REF] .

The main goal in the present work was to assess the effects of the nature of the nitrogen amount in the shielding gas (2% N 2 in Ar) on cooling rates, microstructural properties, microhardness and grain size of 1.8 mm thickness sheets of UNS S32304 duplex stainless-steel autogenously welded by pulsed GTAW process. The amounts of phases were evaluated by microstructural image phase analysis and electron probe microanalysis (EPMA) technique was used to measure the N 2 contents in transversal profile of welds.

Materials and Methods

The specimens were obtained with dimensions of 72 x 72 x 1.8 mm 3 . Table 1 shows the chemical composition of used UNS S32304 duplex stainless steel. The alloy's chemical composition was certified by the commercial supplier Aperam South America S/A.

The microstructure of the ferrite and austenite was observed by optical microscopy (OM). The specimens for microstructure investigation were ground successively from P300 to P2000 grit emery paper and polished using diamond pastes of 6 µm, 3 µm and 1µm. With the purpose of characterization of various types of austenites in the welding zones, the as-polished specimens were etched in Behara I solution for 15-20 s. The optical microstructures of the SZ and HAZ were observed by means of the Image J® software with bright light micrographs according to ASTM E562 29 standard to determine the phases ratios. The free application 3D Builder® was used to better illustrate dual phase proportion in base metal and solidified zone.

Thin samples were clamped in a welding table in order to reproduce the conventional set welding process. The DSS sheets were welded using GTAW process with pulsed current and direct polarities were used with automatic drive systems. The batch of samples was welded using two commercial kinds of pure argon and a mixture of argon and 2% of nitrogen shielding gas. The gas flow rate in both cases was 10 L.min -1 . The schematic diagram of the welding process is shown in Figure 1. The AWS Class EWTh-2 electrode was kept negative and was located at 2 mm with a 60° angle from the sheet, according to direct polarity process. The electrical current and voltage values were measured for each welding step. In the case of the pulsed current, the wave was maintained in balance with background time and pulse values equal to 0.9 s. Table 2, indicates the welding and thermal cycle parameters.

Regarding the parameters such as voltage (U), pulsed and background current (I p , I b ), pulsed and background time (t p , t b ), the welding speed (v) along with 60% arc efficiency for the pulsed GTAW welding, it was possible to calculate the welding heat input (H) per mm using equation 1 [START_REF] Tseng | The effect of pulsed GTA welding on the residual stress of a stainless steel weldment[END_REF] . The welding heat input shown in Table 2 was determined using the average voltage, current and welding speed.

. . . . . H t t v U I t I t 60 p b p p b b = + + Q Q V V (1)
The thermal cycles were measured during welding by inserting thermocouples type K and S in the UNS S 32304 DSS sheet, in small drilled holes and inserting the thermocouple tip in this hole. The temperature was measured and recorded using a data acquisition system. Four thermocouples were positioned and fixed to the sample sheet's surface at different distances, along transversal and longitudinal lines of the weld bead. The thermocouples were located at 0 mm, 3 mm and 4.5 mm from the joint line.

The signals from the thermocouples were acquired by 8-channel universal data acquisition system amplifier using MX board -PT1000 for room temperature automatic conditioning. The measured total error limit at 300 K ambient temperature was ± 1 K and the temperature drift (K type) was used K/10K ratio where the uncertainty was ≤ ± 0.5.

An electron probe micro-analyzer (EPMA) was used to quantitatively evaluate the nitrogen in the welded regions. This electronic microprobe is equipped with four WDS (wavelength dispersive spectrometer) spectrometers. For the point quantifications it was used voltage acceleration of 10 kV and beam current of 100 nA.

The crystal used to detect the Kα of N was PC2. The N 2 profile was composed of EPMA-WDS point analyses distributed over a 4300 µm line for sample welded using pure Ar and a 4500 µm line for welding using Ar+2%N 2 shielding gas, crossing the base metal, heat-affected zone till center of solidified zone.

Vickers microhardness was performed for both welds using 0.5 N of load for 15 s (HV 0.05 ). A microhardness tester was used to determine microhardness maps on the cross sections of the welded sheets. The thickness of the sheets is 1.8 mm. In the total, five lines with 140 hardness points for 60 µm steps were performed for each sample passing through the base metal, ZAC and SZ.

Results and Discussion

In order to study thermal cycles, the temperature distributions were plotted for both specimens as shown in Figure 2. First, the sheet welded using pure Ar as shielding gas is shown in Figure 2a. The thermocouples TK1 and TK2 (4.5 mm away from the welding line) were placed closer to the weld bead where the peaks of temperature and cooling rate were close to 543 °C with 10.6 °C.s -1 and 556 °C with 12.1 °C.s -1 , respectively. In this region of the sheet (HAZ), the holding time were maintained between 500 °C and 600 °C for 6 s, approximately, for both TK1 and TK2 thermocouples that leads to precipitations of secondary phases as α', σ, ε and π [START_REF] Zhang | Effects of nitrogen in shielding gas on microstructure evolution and localized corrosion behavior of duplex stainless steel welding joint[END_REF][START_REF] Tan | Influence of welding thermal cycles on microstructure and pitting corrosion resistance of 2304 duplex stainless steels[END_REF][START_REF] Westin | Microstructure and properties of welds in the lean duplex stainless steel LDX 2101[END_REF] . The TK3 thermocouple presented a peak of temperature around 760 °C at 3 mm away from the center of welding line. This value is higher than that obtained in other thermocouples for the HAZ which was measured a cooling rate of 53.2 °C.s -1 . The welding process with high cooling rate lead to ferritization with coarse grains of ferrites in the welding zone [START_REF] Garzón | Growth kinetics of secondary austenite in the welding microstructure of a UNS S32304 duplex stainless steel[END_REF] .

The Figure 2b shows the thermal cycles for welding with Ar+2%N 2 as shielding gas. The thermocouples TK1 and TK2 (4.5 mm distant from the melting pool) presented peaks of temperature and cooling rates near to 759 °C -25.2 °C.s -1 and 773 °C -26.5 °C.s -1 , respectively. The holding time were maintained above 700 °C for 4 s which would lead to possible intermetallic phases as M 23 C 6 , γ 2 , χ and σ [START_REF] Tan | Influence of welding thermal cycles on microstructure and pitting corrosion resistance of 2304 duplex stainless steels[END_REF][START_REF] Garzón | Growth kinetics of secondary austenite in the welding microstructure of a UNS S32304 duplex stainless steel[END_REF] . For TK1 and TK2 also were subjected to holding time above 500 °C for 15 s approximately that would lead to higher precipitation of secondary phases such as α', ε and π [START_REF] Zhang | Effects of nitrogen in shielding gas on microstructure evolution and localized corrosion behavior of duplex stainless steel welding joint[END_REF][START_REF] Tan | Influence of welding thermal cycles on microstructure and pitting corrosion resistance of 2304 duplex stainless steels[END_REF][START_REF] Garzón | Growth kinetics of secondary austenite in the welding microstructure of a UNS S32304 duplex stainless steel[END_REF] . Voltage (V) 11 11 Pulse current -I p (A) 150 140

Background current -I b (A) 80 70

Pulse time -t p (ms) 0.9 0.9

Background time -t b (ms) 0.9 0.9

Welding speed (cm.min -1 ) 35 35 Arc efficiency (%) 60 60

Heat input (kJ.mm -1 ) 0.20 0.17

Through the TK3 thermocouples it is shown a temperature peak and cooling rate around 947 °C and 27.5 °C.s -1 at 3 mm from the center of the solidified zone. Through the thermal cycle it is also possible to suggest that the beneficial effect of the addition of 2% N 2 on the stabilization of the temperature distribution during cooling process. This stabilization can be seen from 56 s at time on the graph shown in Figure 2b, and it can be observed that all curves are dropping at the same slope. This curve behavior could not be observed for the sample welded using pure Ar (Figure 2a). Lin et al. [START_REF] Lin | Effect of nitrogen content and retained ferrite on the residual stress in austenitic stainless steel weldments[END_REF] , also showed that the peak temperature of a thermal cycle increased with increasing N 2 content as more heat is carried into shielding gas. Thus, increasing the N 2 content more heat is carried into the work piece and increases the weld metal area [START_REF] Tseng | Effect of nitrogen addition to shielding gas on residual stress of stainless steel weldments[END_REF] . In addition, according to the study by Tseng and Chou 12 , using pulsed GTAW process higher ratio amplitude can reduce the temperature difference between the melting zone and the unaffected base metal in welding and therefore the welding residual stress can be reduced. The Figure 3 shows the temperatures on the bottom of the center of welding zone (0 mm) and HAZ (3 mm and 4.5 mm) during passage of the welding. In these points it was obtained values in the order of 1173 °C for welding with pure Ar and 1221 °C for welding with Ar + 2% N 2 , which suggests an influence of the shielding gas on the temperature distribution of welding. In addition, all welding points measured with the mixture of Ar + 2% N 2 presented higher temperature than welding with pure Ar.

Figure 4 shows an optical micrograph of the microstructure that consisted of austenite and ferrite for the as received material. The ferrite phase is shown as dark, while the light region is austenite phase (see Figure 4a). In the continuous ferrite matrix is embedded island-like austenite phase without apparent secondary phase precipitation. Both grains are elongated along the rolling direction. Figure 4b shows the quantitative evaluation of the content of both ferrite and austenite phases. Based on microstructural investigations and using image analyzer software the amounts of phases in different zones of the joints were estimated. Up to five OM images were collected for each zone (SZ, HAZ and BM) and then were processed. In order to detail the modifications in the biphasic microstructures and content variations of phases due to the welding conditions, optical micrographs were obtained, and the separation of the ferrite and austenite phases was attained with image editing effect.

Micrographs for both samples are shown in Figure 4 using the modified Behara I reagent to reveal the etched microstructure. The chemical etching resulted in a blue coloration for ferrite and a yellow coloration for austenite as reported in the literature [START_REF] Zhang | Effects of nitrogen in shielding gas on microstructure evolution and localized corrosion behavior of duplex stainless steel welding joint[END_REF][START_REF] Zucato | Microstructural characterization and the effect of phase transformations on toughness of the UNS S31803 duplex stainless steel aged treated at 850 ºC[END_REF][START_REF] Abas | Experimental study of the thermal diffusivity and heat capacity concerning some duplex stainless steel[END_REF] .

The Figure 4 b shows the micrograph of the solidified zone for welded sheet using pure Ar as shielding gas. The Behara I reagent also resulted in dual effect of dark colors (blue) for ferrite and clear (yellow) for the austenite microstructure.

In this way, through the chemical etching it was possible to observe the ferrite morphology separately from the austenite as well as the austenite fraction phase resulting from the welding process with pure Ar as shielding gas. Besides that, secondary austenite was observed quite dispersed inside the ferrite coarse grains.

The microstructure of the solidified zone of the sample welded with Ar + 2% N 2 as the shielding gas using purge gas is presented Figure 4c. For the identification of ferrite and austenite phases, the same modified Behara I etching was used.

For ferrite resulting from the nitrogen addition in shielding gas, it is shown as a dark (brown) color and the voids that are occupied by the austenite. For austenite shown in bright light (yellow) color, this phase is more evident in the regions at the grain boundary of ferrite and less dispersed than the sample welded with pure Ar (see Figure 4b). Thus, the separation of the phases as in Figure 4, shows the relationship with the changes of the austenite fractions as described in the diagram showed in Figure 5.

Figure 5 shows the evolution of the austenite volumetric fraction regarding the composition of the shielding gas in the SZ, HAZ and BM. The percentages of austenite are significantly affected by the addition of nitrogen in the shielding gas and this leads to changes in the total austenite content after the welding process. About N 2 supplementation in the shielding gas, the increase of the austenite content in the SZ was shown: 22% to 37% and HAZ: 23% to 25.3%, which agrees with the results of Tahaei et al. [START_REF] Tahaei | Effect of the addition of nickel powder and post weld heat treatment on the metallurgical and mechanical properties of the welded UNS S32304 duplex stainless steel[END_REF] and Zhang et al., [START_REF] Zhang | Effects of nitrogen in shielding gas on microstructure evolution and localized corrosion behavior of duplex stainless steel welding joint[END_REF] .

The addition of N 2 in the shielding gas significantly increases the amount of austenite for the DSS and GTAW welds. Zhang et al. [START_REF] Zhang | Effects of nitrogen in shielding gas on microstructure evolution and localized corrosion behavior of duplex stainless steel welding joint[END_REF] reported that N 2 in the shielding gas mainly promotes the formation of primary austenite, suppressing Cr 2 N precipitation at the root of the weld. According to Westin et al. [START_REF] Westin | Effect of nitrogen-containing shielding and backing gas on the pitting corrosion resistance of welded lean duplex stainless steel LDX 2101(r) (EN 1.4162, UNS S32101)[END_REF] , nitrogen can increase the temperature of ferrite transformation into austenite. Consequently, the higher content of nitrogen makes the alloy less sensitive to the fast cooling rates due to more efficient austenite reform and delays the ferritization [START_REF] Westin | Effect of nitrogen-containing shielding and backing gas on the pitting corrosion resistance of welded lean duplex stainless steel LDX 2101(r) (EN 1.4162, UNS S32101)[END_REF] . As seen in the present work, the microstructural changes in DSS that occur during welding can lead to the variation of the phase balance in SZ and HAZ.

In Figure 6, the microstructures of the UNS S32304 duplex alloy are shown in three different orthogonal directions. The first image, Figure 6a, shows the base metal in the three directions with indication of the rolling directions. No intermetallic phase was observed, both for samples as received and for the base metal.

The evolution of the microstructure of ZTA and SZ is strongly dependent on the base metal microstructure, peak temperature, residence time at high temperatures and cooling rates [START_REF] Muthupandi | Effect of nitrogen addition on formation of secondary austenite in duplex stainless steel weld metals and resultant properties[END_REF] . DSS typically have δ ferrite, primary austenite γ 1 , secondary austenite γ 2 , σ, χ, carbides and nitrites. For the solidified zone of DSS, the austenite phases are generally formed from ferrite in different modes: allotriomorphic austenite in the borders of ferrite grains (GBA), intragranular austenite (IGA) and austenite Widmanstätten (WA) within the grains [START_REF] Badji | Effect of post weld heat treatment on microstructure and mechanical properties of welded 2205 duplex stainless steel[END_REF] . For Figure 6b and Figure 6c, the effects of GTAW welding with 99.9% Ar as shielding gas and a mixture of Ar + 2% N 2 in three orthogonal directions are presented. The microstructure observed in both welded samples consists of large ferrite grains with intragranular austenite, grain border austenite and Widmanstätten austenite (γ w ). For the solidified zone, with Ar + 2% N 2 (Figure 6c), elongated and thicker austenite grains are evident.

Figure 7 shows the cross-section profile of nitrogen amounts in mass%, for sheet welded with pure Ar. As reported in the literature, the loss of nitrogen in ZTA and SZ are unavoidable in GTAW welding using pure Ar as shielding gas [START_REF] Muthupandi | Effect of nitrogen addition on formation of secondary austenite in duplex stainless steel weld metals and resultant properties[END_REF][START_REF] Zhang | Effects of nitrogen in shielding gas on microstructure evolution and localized corrosion behavior of duplex stainless steel welding joint[END_REF][START_REF] Hosseini | A novel arc heat treatment technique for producing graded microstructures through controlled temperature gradients[END_REF] . Hosseini et al. [START_REF] Hosseini | A novel arc heat treatment technique for producing graded microstructures through controlled temperature gradients[END_REF] obtained a cross-section profile of nitrogen in superduplex stainless steel subjected to a GTAW arc by WDS analysis. The author still considers the amount of nitrogen in the solidified zone as virtually zero. As seen in Figure 7, a large number of point measurements of nitrogen within the ZTA and SZ are zero. The loss of nitrogen is accompanied by the reduction of the amount of austenitic phase leading to a lower corrosion resistance and loss of mechanical properties [START_REF] Hosseini | Nitrogen loss and effects on microstructure in multipass TIG welding of a super duplex stainless steel[END_REF] .

The Figure 7b, presents a slightly more expressive nitrogen amount content profile for samples welded with the gas mixture Ar + 2% N 2 as protection gas. However, the reduction of the amount of nitrogen is relative to the base metal, which is evident. Zhang et al. [START_REF] Zhang | Effects of nitrogen in shielding gas on microstructure evolution and localized corrosion behavior of duplex stainless steel welding joint[END_REF] assessed the content of nitrogen for each phase in the welding zone through quantitative element mapping using EPMA.

As reported by Zhang, the 2% N 2 addition in the shielding gas also promoted the nitrogen solution in the austenite [START_REF] Zhang | Effects of nitrogen in shielding gas on microstructure evolution and localized corrosion behavior of duplex stainless steel welding joint[END_REF] . According to Lin et al. [START_REF] Lin | Effect of nitrogen content and retained ferrite on the residual stress in austenitic stainless steel weldments[END_REF] , experimental results show that the heat input increases with the increased welding voltage caused by the increased nitrogen content of the shielding gas. The authors also observed steeply decreases of the ferrite amount using nitrogen in shielding gas.

For the present work, it was also observed a higher concentration of nitrogen in allotriomorphic austenite (γ A ) grains than in austenite grains type Widmansttätten. This fact is reinforced by the low amount of nitrogen found for the measurements path as described in the nitrogen measurement profile. According to Eghlimi et al. [START_REF] Eghlimi | Effect of current type on microstructure and corrosion resistance of super duplex stainless steel claddings produced by the gas tungsten arc welding process[END_REF] , the lowest amount of Cr, Mo and N in the Widmansttätten austenite grains is due to their formation at low temperatures when most of the alloying elements have already been consumed by the allotriomorphic austenite grain boundaries.

The microhardness test was performed on the cross section of the welded samples. With the extracted data the microhardness maps were constructed and compared with the generated images from the microstructure of the welded region, as seen in Figure 8. The microhardness was measured in an area of 1.8 mm x 8 mm which surrounds the base metal with the position of the thermocouple, the ZAC and the SZ observed through the micrographs of the cross section from both samples. Observing the Figure 8, the base metal region highlighted in green on the microhardness map (approximately 220 HV 0.05 ) is in accordance with that informed by the steel supplier. The sample welded with pure Ar as protection gas, see Figure 8a, presented islands of hardness mainly at the center of the weld bead. The same phenomenon is observed for the sample welded with Ar + 2% N 2 (see Figure 8b), where the islands with high hardness are larger and more evident.

A large amount of allotriomorphic austenite (γ A ) of columnar ferrite grain contours is also observed in the micrographs, and especially in the equiaxial ones, with this region having higher hardness. The high amount of γ A was favored by the high concentration of nickel and under the influence of N 2 in the shielding gas [START_REF] Ruiz | Microstructural and ultrasonic characterization of 2101 lean duplex stainless steel welded joint[END_REF] . According to Ruiz et al. [START_REF] Ruiz | Microstructural and ultrasonic characterization of 2101 lean duplex stainless steel welded joint[END_REF] , the microhardness is higher in the austenite than in the ferrite and the nitrogen, as already discussed, contributes strongly to the austenite reforming. Materials Research

Conclusion

Through the welding thermal cycles, it was possible to determine the temperatures of the duplex stainless steel in the melt pool and in the heat-affected zones. The higher peak temperature (947 °C) for the sample welded with addition of N 2 in the shielding gas did not directly imply on the increase of the cooling rate. The highest cooling rate was found for welding with pure Ar.

Based on results of the cooling rates and quantitative phase analysis, it was possible to conclude that the fast cooling of the welding zone is straightly related to the amount of austenitic phase. The amount of austenite decreased considerably for the sample welded using pure Ar. The intragranular austenite and grain edge for welded sample using pure Ar for three directions observed are smaller than ferrite for welding using the mixture Ar + 2% N 2 as the shielding gas, can suggest a direct relationship with the increase of microhardness in the solidified zone for this sample.

The addition of N 2 in the shielding gas increased the hardness of the solidified zone. By the nitrogen amount profile measurements in the cross section, it is shown that it is possible to achieve a good level of nitrogen in the microstructure with adequate shielding gas aiming the increase of austenite phase.

Figure 1 .

 1 Figure 1. Schematic impression of the GTAW process on thin plates of duplex stainless steel UNS S32304.

Figure 2 .

 2 Figure 2. Distribution of temperatures for samples (a) pure Ar and (b) Ar + 2% N 2 with pure argon as purging gas. It shows the temperature variation measured with each thermocouple for the UNS 32304 duplex stainless steel, 1.8 mm long stripe, while being welded.

Figure 3 .

 3 Figure 3. Peaks of temperature for thermal cycles of welding.

Figure 4 .

 4 Figure 4. Microstructure of the transversal profiles of the both samples welded with a) pure Ar and b) Ar+2%N 2 as shielding gas.

Figure 5 .

 5 Figure 5. The effects of shielding gas composition on the austenite content of the HAZ and solidified zone in DSS.

Figure 6 .

 6 Figure 6. Three-dimensional microstructure of duplex stainless steel UNS S32304 welds in base metal and solidified zone of the GTAW welded joints using b) pure Ar and c) Ar+2%N 2 as shielding gas. The polishing samples were etched for 30 seconds in modified Behara I reagent, composed of 20 mL hydrochloric acid (HCl), 80 mL distilled water and 1 g potassium metabissulfide (K 2 S 2 O 5 ).

Figure 7 .

 7 Figure 7. Nitrogen concentration as a function of transversal position measured by EPMA for both GTAW process with a) pure Ar and b) Ar+2%N 2 as shielding gas.

Figure 8 .

 8 Figure 8. Microhardness maps on transversal direction of the GTAW welded joints using a) pure Ar and b) Ar+2%N 2 as shielding gas.

Table 1 .

 1 Chemical composition (% mass and ppm) of the duplex stainless steel UNS S32304 used in the present study.

	Cr	Ni	Mo	Mn	Si	C	P	S	Ti	Cu	Co	N ppm	Fe
	22.210	3.521	0.255	1.402	0.250	0.016	0.023	0.001	0.004	0.417	0.091	1030	Bal.

Table 2 .

 2 Welding parameters used for the pulsed GTAW process.

	Sample	#6	#7
	Shielding gas (10 L.min -1 )	Pure Ar	Ar+2%N 2

Betini et al.

Acknowlodgments

The authors want to thank Erasmus Mundus (EBW+), CAPES and CNPq for the financial support.