Jie Song

Xin Shen

Fangyu Liu

Xinshuang Zhao

Yuandou Wang

Shuxin Wang

Pinyi Wang

Jinjun Wang

Feng Su
email: sufeng@qust.edu.cn

Suming Li
email: suming.li@umontpellier.fr

Ca 2+ based metal-organic framework as enzyme preparation to promote the catalytic activity of amylase

Keywords: Metal-organic frameworks, enzyme preparation, amylase, catalysis

Enzyme preparation can protect the enzyme conformation in storage, transportation, and operation process, but excessive additives can affect enzyme performance. In this work, a Ca 2+ based metal-organic framework (UTSA-280) was prepared to encapsulate amylases (αamylase, pullulanase, and glucoamylase) in situ. After release from UTSA-280, the relative activity of α-amylase and pullulanase increased to 177.8 and 201.0 %, respectively, as compared to pure enzymes. Mechanism explorations indicate that amylase released from UTSA-280 has more Ca 2+ on its surface with stronger combination, which probably leads to the activation effect to metal ion activating enzyme. Besides, UTSA-280 could protect enzymes from heat, organic solvent, and trypsin, which is beneficial for the storage, transportation, and operation of enzyme. Therefore, it is concluded that MOFs could be a promising metal ion activating enzyme preparation material with activity promoting and protective effects.

Introduction

Traditional enzyme preparations usually suffer from a number of disadvantages such as excessive additives, redundant purification operations, and reduced activity, which could restrain their application [START_REF] Silva | Practical insights on enzyme stabilization[END_REF][START_REF] Singer | Multiple effects of trehalose on protein folding in vitro and in vivo[END_REF]. Enzyme preparations often possess a small portion of active enzyme molecules, while a large amount of additives such as inactive proteins, preservatives, salts, and polymers are added to maintain the enzyme conformation on storage conditions [START_REF] Costa | Studies of stabilization of native catalase using additives[END_REF][START_REF] Parthasarathy | Synthesis of polymeric microcapsule arrays and their use for enzyme immobilization[END_REF][START_REF] Duskey | Tween® preserves enzyme activity and stability in PLGA nanoparticles[END_REF][START_REF] Fan | Biodegradable membrane of poly (l-lactide acid-dioxanoneglycolide) and stereocomplex poly (lactide) with enhanced crystallization and biocompatibility[END_REF]. However, excessive additives could affect the enzyme performance [START_REF] Limoges | Catalysis by immobilized redox enzymes. Diagnosis of inactivation and reactivation effects through odd cyclic voltammetric responses[END_REF]. On the other hand, addition of enzyme activators such as metal ions is often ineffective and costly because high concentrations of activators are needed due to their low accessibility to and weak interactions with enzyme molecules in the catalytic process [START_REF] Shisler | Monovalent Cation Activation of the Radical SAM Enzyme Pyruvate Formate-Lyase Activating Enzyme[END_REF]. For example, a large amount of ammonium sulfate usually used in the salting-out process, as well as high operating temperature of spray drying, can significantly affect the enzyme performance [START_REF] Gummadi | Purification and biochemical properties of microbial pectinases-a review[END_REF]. Therefore, it is of crucial importance to develop advanced materials for uses in enzyme preparation.

In enzyme applications, metal ions (Mn 2+ , Zn 2+ , Ca 2+ , Fe 2+/3+ ) are often required to monitor the activity of enzymes [START_REF] He | Metal-nucleobase hybrid nanoparticles for enhancing the activity and stability of metal-activated enzymes[END_REF]. For example, Ca 2+ ions are considered to have crucial roles for maintaining α-amylase structures in their correct conformations and improving the thermal resistance [START_REF] Goyal | A novel raw starch digesting thermostable α-amylase from Bacillus sp. I-3 and its use in the direct hydrolysis of raw potato starch[END_REF][START_REF] Liao | Influence of calcium ions on the thermal characteristics of α-amylase from thermophilic Anoxybacillus sp. GXS-BL[END_REF][START_REF] Bush | The calcium requirement for stability and enzymatic activity of two isoforms of barley aleurone α-amylase[END_REF]. Mao and Kinsella found that banana α-amylase activity increased significantly when calcium was incorporated into the assay medium [START_REF] Mao | Amylase activity in banana fruit: properties and changes in activity with ripening[END_REF]. Mg 2+ and K + are typical activators of methionine adenosyltransferase (MAT) from all sources which can enhance its activity and reaction rate [START_REF] Liu | Structure of a thermostable methionine adenosyltransferase from Thermus thermophilus HB27 reveals a novel fold of the flexible loop[END_REF]. Therefore, metal ions are excellent stabilizer and activator of enzymes, and incorporating metal ions as a component is a promising approach for metal ion activating enzyme preparations.

Metal-organic frameworks (MOFs) are an emerging class of crystalline materials assembled by organic links and metal ions or clusters. Owing to their unique properties such as high surface areas, ultra high porosity, high thermal stability, and good surface chemistry, MOFs have become an ideal material for the preparation of enzyme/MOF biocomposites [START_REF] Doonan | Metal-Organic Frameworks at the Biointerface: Synthetic Strategies and Applications[END_REF].

In fact, MOFs present several advantages for enzyme encapsulation, i.e. mild preparation environments (room temperature, aqueous solution), high loading efficiency and good protection for enzymes [START_REF] Liang | Metal-Organic Framework-Based Enzyme Biocomposites[END_REF][START_REF] Liang | Metal-Organic Framework-Based Enzyme Biocomposites[END_REF]. In the past decade, great efforts have been made to develop enzyme@MOF composites for enzyme immobilization. However, these heterogeneous biocatalytic systems suffer from the decrease of enzyme activity caused by the immobilization and diffusion processes. Interestingly, unstable MOFs could degrade under mild conditions, releasing metal ions which could become enzyme activator. Therefore, enzyme-MOF composites could be promising as high-performance enzyme preparations.

Amylases are a class of industrial enzymes representing approximately 30% of the world enzyme production [START_REF] Mobini-Dehkordi | Application of alpha-amylase in biotechnology[END_REF]. Amylases are used in many industrial processes such as food, fermentation, paper, sugar and pharmaceutical industries. Calcium ions play an important role in monitoring the structure, activity, and thermal stability of some amylases [START_REF] Goyal | A novel raw starch digesting thermostable α-amylase from Bacillus sp. I-3 and its use in the direct hydrolysis of raw potato starch[END_REF][START_REF] Liao | Influence of calcium ions on the thermal characteristics of α-amylase from thermophilic Anoxybacillus sp. GXS-BL[END_REF], thus affecting their performance [START_REF] Declerck | Hyperthermostabilization of Bacillus licheniformis α-amylase and modulation of its stability over a 50 C temperature range[END_REF][START_REF] Torrance | Evolution of binding sites for zinc and calcium ions playing structural roles[END_REF]. However, there is no report on the use of Ca 2+ based MOF for amylase preparation in spite of its potential in activating amylases.

In this study, a Ca 2+ based MOF, namely UTSA-280, was synthesized as Ca 2+ activating enzyme preparation for α-amylase and pullulanase as shown in Scheme 1. UTSA-280 could efficiently encapsulate enzymes in-situ under mild synthesis conditions. The release performance of enzyme@UTSA-280 and the activity of released enzymes were evaluated.

Mechanism experiments were performed to understand the strong increase in enzyme activity.

The enzyme protection performance and size control of enzyme@UTSA-280 were also explored to further evaluate the potential of UTSA-280 as enzyme preparation material. Scheme 1. Schematic description of enzyme@UTSA-280 preparation by in-situ method.

Materials and methods

Materials and reagents

Squaric acid (98%), calcium nitrate tetrahydrate (Ca(NO3)2•4H2O, 99%), starch (analytical grade) and pullulan (analytical grade) were purchased from Mucklin (Shanghai, China). α-Amylase (from Bacillus subtilis, 4000 U g -1 ) was obtained from Coolaber (Beijing, China). Glucoamylase (from Aspergillus niger variant strain, >100,000 U g -1 ) was purchased from Meilunbio (Dalian, China). Pullulanase (from Klebsiella, >1000 U g -1 ) was obtained from Mucklin (Shanghai, China). Citric acid (≥99.5%), sodium citrate dihydrate (99%), fluorescein isothiocyanate (FITC, ≥90%), HEPES buffer solution (pH 7.0), MES monohydrate (99%), polyvinylpyrrolidone (PVP, MW: 10 kDa) were supplied by Mucklin (Shanghai, China). All enzymes were further purified before use (Supplementary data). All solvents were of analytical grade and used as received.

Synthesis of materials 2.2.1 Synthesis of UTSA-280

UTSA-280 was synthesized as follows. Aqueous solutions of Ca(NO3)2•4H2O (2 mL, 26 mg mL -1 ) and sodium squarate (2 mL, 15 mg mL -1 ) were mixed under stirring. The reaction then proceeded for 1 h at room temperature. The resulted white crystals were washed 3 times with water, and collected by centrifugation.

Synthesis of enzyme@UTSA-280

Enzyme@UTSA-280 was prepared by using in situ method. A solution of Ca(NO3)2• 4H2O (2 mL, 26 mg mL -1 ) was mixed with a solution of sodium squarate (2 mL, 15 mg mL -1 ) containing enzymes at various concentrations, and reaction proceeded for 1 h at room temperature. The resulted enzyme@UTSA-280 crystals were washed 3 times with water, and collected by centrifugation.

Calculation of encapsulation efficiency and loading content

The encapsulation efficiency and loading content of enzymes was determined via standard Bradford assay. Typically, the enzyme encapsulation efficiency of the preparations was calculated via determining the enzyme concentration of the supernatant solution before and after encapsulation by Bradford assay. The encapsulation efficiency and loading content were calculated from the following formulae:

Encapsulation efficiency % = 𝐶 0 -𝐶𝑠 𝐶 0 × 100% ̇ ( 1
)
Where C0 is the initial enzyme concentration before encapsulation, and Cs is the enzyme concentration of supernatant after encapsulation.

Loading content (𝑚𝑔 𝑚𝑔 -1 ) = 𝑊 0 -𝑊 𝑠 𝑊 𝑀 -(𝑊 0 -𝑊 𝑠 )

Where W0 is the weight of enzyme before encapsulation, Ws is the enzyme weight in supernatant after encapsulation, and WM is the weight of enzyme@UTSA-280.

Characterization

X-ray diffraction (XRD) patterns were recorded in the 2θ range from 5 to 50° on a Rigaku dmax 2500 diffractometer using Cu Kα (λ = 1.5418 Å) radiation, with a scan speed of 1 sec/step, and a step size of 0.02°. Fourier transform infrared (FT-IR) spectra were registered using a Thermo Fisher spectrometer in ATR mode. 128 scans were made for each measurement in the wavenumber range from 500 to 4000 cm -1 at a resolution of 2 cm -1 . Circular dichroism (CD) measurements were performed using a spectropolarimeter BioLogic MOS-450. The spectra were collected at a rate of 60 nm per minute and a response time of 16 s. Scanning electron microscopy (SEM) was realized using JSM-7610F filed-emission microscope. Freeze-dried crystals were gold-coated for 90 s and observed using an electron beam at accelerating voltage of 10.0 kV.

Activity test of α-amylase

The activity of α-amylase was determined according to the 3, 5-dinitrosalicylic acid (DNS) method [START_REF] Liao | Influence of calcium ions on the thermal characteristics of α-amylase from thermophilic Anoxybacillus sp. GXS-BL[END_REF]. 2 mg of α-amylase@UTSA-280 was placed in 1 mL of citrate buffer (50 mM, pH 6.0), and released α-amylase was determined by using Bradford method. The concentration of original and released α-amylase was adjusted to 0.1 mg mL -1 . 50 μL of original α-amylase or released α-amylase (50 μg mL -1 ) were added in 5 mL of HEPES buffer (50 mM, pH 7.0) containing 1.0 wt% soluble starch. The relative activity (%) was the ratio between the activities of released and original α-amylases. All measurements were repeated three times.

The activity of pullulanase and glucoamylase was determined using the same method, and the detailed steps are described in Supplementary data.

Enzymatic kinetic parameters determination

Enzymatic kinetic parameters were determined according to the literature [START_REF] Adnan | Kinetics and thermodynamic studies of alpha amylase from Bacillus licheniformis mutant[END_REF]. The kinetic constants (Vmax, Km, Kcat) were derived from Lineweaver Burke plot by using eq. 3 and eq. 4.

1/𝑉 = (𝐾 𝑚 /𝑉 𝑚𝑎𝑥 ) * 1/[𝑆] + 1/𝑉 𝑚𝑎𝑥 (3)
𝐾 𝑐𝑎𝑡 = 𝑉 𝑚𝑎𝑥 /[𝑒] (4)
Where [S] is the substrate concentration, and [e] is the molar concentration of α-amylase.

To determine the kinetic parameters of released and pure α-amylase, experiments were performed at 37 ℃ with different concentrations of soluble starch of 0.1 to 2.0 wt% in HEPES buffer solution (pH 7.0), at an initial enzyme concentration of 10 μg mL -1 and a reaction time of 1 min. The amount of produced glucose was determined by DNS method.

Enzyme protection assay

Pure α-amylase powder (10 mg) and α-amylase@UTSA-280 composite (10 mg) were treated by exposure to heat (80 ℃), trypsin solution (1 mg mL -1 ), and acetone for 1 h. After treatment, α-amylase was released from UTSA-280 in citrate buffer (pH 6.0), and the enzyme concentration was determined by using Bradford method. Then, the activity of pure and released α-amylases was measured by using DNS method and compared to untreated enzymes.

Results and discussion

Characterization of UTSA-280

UTSA-280 was synthesized by reaction between calcium nitrate hexahydrate and sodium squarate under mild conditions in water [START_REF] Lin | Molecular sieving of ethylene from ethane using a rigid metal-organic framework[END_REF]. Sodium squarate was previously obtained by neutralization of squaric acid using NaOH, as shown in Supplementary data [START_REF] Cohen | Preparation and Reactions of Derivatives of Squaric Acid. Alkoxy-, Hydroxy-, and Aminocyclobutenediones1[END_REF]. In assynthesized UTSA-280, the Ca atom (pentagonal bipyramidal) is coordinated by seven O atoms from five squarate linkers and one water molecule, resulting in one-dimensional channels (Fig. 1a). The hydrogen bonding between coordinated H2O molecules and O atoms of squarate linkers could further stabilize the framework by restrain the rotation of the organic linkers (Fig. 1b). The XRD pattern of UTSA-280 exhibits high crystallinity in comparison with the calculated pattern, as shown in 3.2 Characterization of α-amylase@UTSA-280 α-amylase@UTSA-280 was synthesized in-situ under mild conditions. In this reaction, αamylase is added together with metal ions and ligand, and α-amylase is loaded during the crystallization process of MOFs. Bradford method was employed to determine the enzyme concentration in α-amylase@UTSA-280. A calibration curve was first established using αamylase as the standard. A good linearity was obtained from the regression line in the 0.1-1.5 mg mL -1 range (Fig. 2a). The encapsulation efficiency and loading content of αamylase@UTSA-280 were then calculated (Fig. 2b-c). With increasing the initial enzyme concentration from 1.0 to 5.0 mg mL -1 , the encapsulation efficiency decreases from 61% to 38%, and the loading content increases from 0.036 to 0.109 mg mg -1 . α-Amylase@UTSA-280 at enzyme concentration of 2 mg mL -1 was selected for subsequent experiments as it has suitable encapsulation efficiency (59.2 ± 1.0 %) and loading content (0.070 ± 0.004 mg mg -1 ).

Fig. 2d shows the XRD patterns of α-amylase@UTSA-280 and UTSA-280. Both present the same diffraction peaks, indicating that enzyme encapsulation didn't affect the crystalline structure and crystallinity of UTSA-280, even at an enzyme concentration of 5 mg mL -1 in the synthesis process (Fig. S1). In the FT-IR spectra (Fig. 2e), a band assigned to the bending vibration of the N-H group is detected at 1646 cm -1 for α-amylase and α-amylase@UTSA-280, but not for UTSA-280, thus demonstrating the successful synthesis of α-amylase@UTSA-280.

The thermal stability of α-amylase@UTSA-280 was evaluated by TGA under nitrogen atmosphere in comparison with α-amylase (Fig. 2f). In the TGA thermogram of αamylase@UTSA-280, a weight loss of 6.9 % is observed from 50 to 96 ℃, corresponding to the loss of H2O molecules. Weight loss of 9.9% between 168 to 287 ℃ belongs to α-amylase decomposition and the loss of H2O coordinated with Ca ions in UTSA-280. Weight loss beyond 430 ℃ mainly results from the MOF framework. In contrast, an almost continuous weight loss is observed for α-amylase beyond 200°C due to its decomposition. In SEM image of αamylase@UTSA-280 (Fig. 2g), rod-like aggregates of crystals are observed. α-Amylase was labeled by FITC (Supplementary data). Confocal laser scanning microscopy (CLSM) shows a uniform distribution of FITC-labeled α-amylase in UTSA-280 (Fig. 2h). All these data prove that α-amylase is successfully encapsulated in UTSA-280.

Enzyme release behavior of α-amylase@UTSA-280

The absorbance of α-amylase was determined at 540 nm in MES buffers at various pH in order to determine the suitable releasing pH value. As shown in Fig. 3a, α-amylase exhibits high activity between pH 5.0-7.0. Therefore, the enzyme release behavior from αamylase@UTSA-280 was evaluated in this pH range (Fig. 3b). Biphasic release profiles are observed in all cases with initial faster release followed by slower release. The release rate increases with pH decrease, which could be attributed to the accelerated degradation of MOFs under acidic conditions. The degradability and enzyme loading properties of UTSA-280 make it a potential enzyme preparation material.

Maintaining enzyme conformation during the storage and operation process is crucial for the application of enzymes. Thus, the secondary structure of α-amylase was determined using circular dichroism (CD) to confirm the protective effect of MOFs. Released α-amylase was collected via ultrafiltration with 8 kDa MWCO device to remove impurities (digested ligands and metal salts). Notably, both pristine α-amylase and released α-amylase exhibit a typical αhelix structure without any difference [START_REF] Konno | Conformational diversity of acid-denatured cytochrome c studied by a matrix analysis of far-UV CD spectra[END_REF], suggesting that the in-situ encapsulation process did not affect the conformation of enzyme (Fig. 3c).

Catalytic activity test

The catalytic activity of released α-amylase was determined using soluble starch as the substrate in HEPES buffer (50 mM, pH 7.0). The concentration of produced glucose was measured using a previously established calibration curve (Fig. S2) [START_REF] Miller | Use of dinitrosalicylic acid reagent for determination of reducing sugar[END_REF]. Fig. 4a shows the glucose concentration changes as a function of reaction time in the presence of pristine αamylase, released α-amylase, α-amylase + Na2C4O4, α-amylase + Ca 2+ , and UTSA-280. The added concentrations of Ca 2+ and Na2C4O4 were 11.75 mM, i.e. equal to that of released αamylase. Higher glucose concentration is obtained for released α-amylase during the whole reaction period up to 20 min. The relative activity of released α-amylase is 177.8% compared to pristine α-amylase. In contrast, direct addition of Ca 2+ or squaric acid has no effect on the enzyme activity, and pure UTSA-280 material has no catalytic effect. Further investigation suggests that a relatively high concentration (100 mM) of free Ca 2+ is required to achieve a relative activity of 127.0 % at an incubation enzyme concentration of 2 mg mL -1 (Fig. 4c), and the Ca 2+ concentration during synthesis (79.2 mM) does not have such a promoting effect. Fig. 4d shows that sodium squarate has little influence on the activity of α-amylase. Therefore, the enhanced activity is likely related to the release process. These results suggest that metal ion activators from the enzyme/MOF matrix could strongly ameliorate the enzymatic activity, which might be attributed to the enhanced interactions between calcium ions and enzyme molecules during the release process.

Exploration of mechanism for the increase of enzymatic activity

Energy dispersive X-ray spectroscopy (EDX) was used to characterize the released αamylase in comparison with purchased one so as to figure out the mechanism for the increase of enzymatic activity. Released α-amylase and α-amylase incubated with Ca 2+ were collected via ultrafiltration, 3 times washing with deionized water to remove free Ca 2+ , and freezedrying. As shown in Fig. 5a-c and Table 1, released α-amylase has higher Ca 2+ content (10.7

±2.3 % of weight, 4.3±1.1 % of atom) than purchased α-amylase (2.8±0.4 % of weight, 0.7 ±0.1 % of atom) and α-amylase incubated with Ca 2+ (4.7±0.6 % of weight, 1.6±0.2 % of atom). Inductively coupled plasma-optical emission spectrometry (ICP-OES) was also used to quantify the Ca 2+ content of these three groups, as shown in Fig. S3. The Ca 2+ content of released α-amylase, pristine α-amylase, and α-amylase incubated with Ca 2+ are 99.7±3.3, 4.7±1.1, and 29.2±4.7 μg mg -1 , respectively. ICP-OES data are consistent with those of EDX, which revealed that MOF encapsulation enhances enzyme activity more effectively than direct addition of metal ions. These results suggest that the improved enzymatic activity could result from more interaction between Ca 2+ ions and α-amylase. The enzymatic kinetic parameters of α-amylase released from UTSA-280 were determined by using Lineweaver Burke plot (Fig. S4) and Michaelis-Menten model [START_REF] Adnan | Kinetics and thermodynamic studies of alpha amylase from Bacillus licheniformis mutant[END_REF][START_REF] Michaelis | Die kinetik der invertinwirkung[END_REF]. The results revealed that released α-amylase has a Vmax of 0.25 mM s -1 , Km of 0.27 mM, and Kcat of 1.25*10 3 s -1 , while untreated α-amylase has Vmax, Km and kcat of 0.14 mM s -1 , 0.46 mM and 0.69*10 3 s -1 , respectively (Table 2). The lower Km value of released α-amylase implies higher affinity towards substrates while the higher Kcat of released α-amylase could be attributed to the activation effect of Ca 2+ from UTSA-280, which is consistent with literature data [START_REF] Torabizadeh | Immobilization of thermostable α-amylase from Bacillus licheniformis by cross-linked enzyme aggregates method using calcium and sodium ions as additives[END_REF]. activating enzyme) were also encapsulated in UTSA-280 to better understand the activation effect of UTSA-280. The enzyme concentration was determined by Bradford method using enzyme standard calibration curves (Fig. S5-6). And the encapsulation efficiency and loading content of pullulanase (64.1 ± 2.4%, 0.150 ± 0.011 mg mg -1 ) and glucoamylase (44.2 ± 3.2%, 0.110 ± 0.004 mg mg -1 ) were then obtained (Fig. S7). FT-IR spectra and CLSM data prove the successful encapsulation of the two enzymes in UTSA-280 (Fig. S8-10). In addition, XRD and SEM data demonstrate the high crystallinity of UTSA-280 after enzyme encapsulation (Fig.

S11-12

). Then, pullulanase and glucoamylase were released from UTSA-280 and their catalytic activity was evaluated in the pH range from pH 4.0 to 8.0 (Fig. S13-14). As shown in Fig. S15, the activity of released pullulanase shows a dramatic increase (201 ± 28 %), which may be attributed to the fact that pullulanase is a Ca 2+ activated enzyme. Meanwhile, glucoamylase, which is not a Ca 2+ activated enzyme, shows no activity increase. These findings prove that this strategy can be applied to other Ca 2+ activated amylases, suggesting that MOFs could serve as metal ion activated enzyme preparation. Thus MOFs materials with different metal ions can be selected according to metal ions-activated enzymes. The size control of MOFs is important as it affects the release performance of enzymes.

Polyvinylpyrrolidone (PVP) is a water soluble polymer with low toxicity and high thermal stability [START_REF] Arul | Size controlled synthesis of Ni-MOF using polyvinylpyrrolidone: New electrode material for the trace level determination of nitrobenzene[END_REF]. PVP is widely used as a capping agent to prevent colloidal aggregation, thus allowing to control the size of nanoparticles, especially MOFs [START_REF] Wei | Rapid mechanochemical encapsulation of biocatalysts into robust metal-organic frameworks[END_REF]. The size of UTSA-280 was adjusted by using PVP to further modulate the release performance of α-amylase from UTSA-280. As shown in Fig. 7a-f and Fig. S16, the crystal size of UTSA-280 decreases from above 1000 μm to below 100 μm with increase of PVP concentration from 0.1 to 1.0 mg mL -1 . It is also noteworthy that larger crystal size of UTSA-280 leads to higher loading content (Fig. 6g), and thus leading to higher final concentration of released enzyme (Fig. 6h). XRD patterns show that α-amylase@UTSA-280 synthesized using PVP as capping agent presents the same crystalline structure as that synthesized without PVP (Fig. S17). Fig. 6 (a-f) SEM images (30 ×) of, (g) loading content of, and (h) enzyme release profiles from α-amylase@UTSA-280 synthesized using PVP capping agent at concentrations of 0.1, 0.2, 0.4, 0.6, 0.8, 1.0 mg mL -1 . Test conditions: 10 mg material in 1 mL citrate buffer (50 mM, pH 6.0) at room temperature.

Protection assay of α-amylase@UTSA-280

It is of major importance to preserve enzyme activity during the storage and operation process. The confined space created by MOFs should provide excellent protection to enzymes [START_REF] Wei | Rapid mechanochemical encapsulation of biocatalysts into robust metal-organic frameworks[END_REF]. The protection performance of UTSA-280 to α-amylase was evaluated by exposure to 20 heat (80 ℃), trypsin (1 mg mL -1 ), and organic solvent (acetone) for 1 h. As shown in Fig. 7, the relative activity of α-amylase decreases to 67.2, 37.4, and 76.5% after treatment by heat, trypsin, and acetone, respectively. In contrast, the relative activity of enzyme in αamylase@UTSA-280 is 80.1, 65.6, and 86.4% after the same treatments. These findings indicate that UTSA-280 could efficiently protect α-amylase against harsh conditions.

Moreover, sodium squarate presents good biocompatibility according to MTT and live-dead staining experiments. The cell viability is above 81% for all groups (Fig. S18), and no apparent apoptosis is observed (Fig. S19). Therefore, UTSA-280 could facilitate the storage, transport, and operation of enzyme preparations.

Conclusions

MOFs are able to function as metal ion activator and protector, and is thus a material of choice for enzyme preparations, especially metal-activated enzyme preparations. However, there is no research reported on MOFs as a metal ion activated enzyme preparation, so far. In this work, α-amylase and pullulanase were successfully encapsulated in situ in a Ca 2+ based MOF (UTSA-280) under mild conditions. The enzyme@UTSA-280 composite crystals could degrade rapidly in acidic environment and release enzyme. Importantly, the structural integrity of released enzyme was preserved as evidenced by CD spectra. The relative activity of released α-amylase and pullulanase increased to 177.8 % and 201.0 % as compared to original enzyme.

Mechanistic investigation proves that the increase of enzyme activity could be attributed to the activation by Ca 2+ . Ca 2+ could activate α-amylase and pullulanase, but has no effect on glucoamylase which is not Ca 2+ activated enzyme. Enzyme activity tests after exposure to heat, trypsin, and acetone showed that α-amylase@UTSA-280 provides good protection to enzyme molecules. In addition, the size and enzyme release rate of α-amylase@UTSA-280 can be tailored by using PVP capping agent at different concentrations. Compared with current enzyme preparations, this MOFs based platform present several advantages. Firstly, MOFs could combine the advantages of metal ion activation and enzyme protection, especially for metal ion activating enzymes. Secondly, the preparation conditions are milder than those used in traditional methods such as salting out or spray drying. Thirdly, this platform could avoid the use of excessive additives to maintain the enzyme conformation on storage conditions. Last but not least, this platform can efficiently activate enzymes by providing small amount of activator. Compared to direct addition of activator, this platform is more friendly to applications which require post-processing and purification. Therefore, enzyme@MOFs preparations are most promising for applications in the field of enzyme production, biocatalytic production, and food processing.

prepared the specimens and made FT-IR and CD measurements, X. Zhao, Y. Wang, and S.

Wang performed kinetic studies of enzymes, P. Wang made FITC-labeling of enzyme; J. Wang, F. Su and S. Li co-initiated the work, and revised the manuscript. All authors discussed and contributed the discussion and analysis of the results regarding the manuscript. All authors have given approval for the final version of the manuscript.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  Fig. 1c. The FT-IR spectrum of UTSA-280 shows various characteristic signals (Fig. 1d), especially those at 1088, 1450, and 3231 cm -1 , corresponding to C-O, C=C, and O-H bonds, respectively. TGA data reveal the good thermal stability of UTSA-280 (Fig. 1e). A weight loss of 7.2 % is observed from 50 to 96 ℃, corresponding to the loss of H2O molecules in the channels. Weight loss of 10.2 % between 156 to 303 ℃ corresponds to the loss of H2O coordinated with Ca 2+ ions. Weight loss beyond 392 ℃ results from the framework decomposition. UTSA-280 exhibits a cylindrical crystal structure as shown in Fig. 1f, in agreement with high crystallinity. All these data demonstrate the successful synthesis of uniform UTSA-280 crystals.

Fig. 1

 1 Fig. 1 Structure and characterization of UTSA-280: (a) Crystal structure of UTSA-280,

Fig. 2 .

 2 Fig. 2. Characterization of α-amylase@UTSA-280: (a) linear fitting of α-amylase by Bradford

Fig. 3

 3 Fig. 3 (a) Absorbance of α-amylase at different pH values; (b) enzyme release profiles in citrate

Fig. 4

 4 Fig. 4 (a) Glucose concentration changes as a function of reaction time in the presence of pristine α-amylase, released α-amylase, α-amylase + Na2C4O4, α-amylase + Ca 2+ , and UTSA-

Fig. 5 .

 5 Fig. 5. Energy dispersive X-ray spectroscopy (EDX) of (a) released α-amylase, (b) pristine αamylase, and (c) α-amylase incubated with Ca 2+ (11.75 mM) for 1 h. (n=3)

Fig. 7

 7 Fig.[START_REF] Limoges | Catalysis by immobilized redox enzymes. Diagnosis of inactivation and reactivation effects through odd cyclic voltammetric responses[END_REF] Relative activity of nude α-amylase and α-amylase@UTSA-280 after 1 h exposure to heat (80 ℃), trypsin (1 mg mL -1 ), organic solvent (acetone). The enzyme activity was measured

Table 1 .

 1 Element contents of released α-amylase, pristine α-amylase, and α-amylase incubated

	with Ca 2+ (11.75 mM) for 1 h determined by EDX (n=3)
	Element	Weight %	Atom %
	C	15.8±1.8	20.9±1.9
	Released α-amylase
	O	65.9±0.8	65.9±0.4

Table 2

 2 Kinetic parameters for released α-amylase and pristine α-amylase.

		Vmax [mM s -1 ]	Km [mM]	Kcat [10 3 s -1 ]
	Released α-amylase	0.25	0.27	1.25
	Pristine α-amylase	0.14	0.46	0.69
	3.6 Size control of UTSA-280

Acknowledgments

The work was financially supported by the Shandong Provincial Natural Science Foundation (ZR2020QH271, ZR2021ME208, ZR2022ME083).

Author Contributions


Marcos Lopes
email: lopes@enib.fr

Leal Júnior

Laurent Pino

Mahmoud Barati

Luc Saint-Sulpice

Laurent Daniel

Shabnam Arbab Chirani

Marcos Lopes Leal Júnior

Electric resistivity evolution in NiTi alloys under thermomechanical loading: phase proportioning, elasticity and plasticity effects

Keywords: SMA, NiTi, martensite transformation, electric resistivity, plasticity, phase proportioning, phase transformation kinetics

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Introduction

Shape memory alloy wires exhibit impressive behaviors, such as superelasticity, pseudoplasticity and shape memory effect under thermomechanical loading. These features are triggered by shear lattice distortion, a diffusionless process known as martensitic transformation that occurs between a parent austenite and a product martensite crystal structures. Such peculiar characteristics are very useful in various industry applications. Among the different options of SMA composition, the NiTi alloys are the most employed due to their steadier behavior upon cyclic use and their wide range of operating conditions when compared to others SMAs [START_REF] Rao | Design of Shape Memory Alloy (SMA) Actuators SpringerBriefs in Computational Mechanics[END_REF][START_REF]Introduction Shape Memory Alloy Engineering ed Lecce L and Concilio A[END_REF].

However, one of the main drawbacks for the usage of SMAs in engineering applications is the evolution of thermomechanical response upon cycling (also denoted as functional fatigue). This shortcoming makes it difficult to accurately design and control SMA-based devices in industry [START_REF] Leary | [END_REF]4].

Among the major actors of the evolution of the properties of SMAs, the interactions between phase transformation and plasticity are the most significant. These interactions take place at the microstructural level and impact directly the macroscopic behavior. In some cases, where the microstructure is more complex compared to others SMAs, as for NiTi alloys, this relation can be even more pronounced.

Being the most influential mechanism, the coupling between phase transformation and plasticity can occur in two different ways: upon repeated loading and under conditions that exceed the elastic domain. In the first case, the propagation of austenite/martensite interfaces results in lattice defects (mainly composed of slip dislocations (plasticity)) and residual stressinduced martensite (RSIM) (initiated due to internal stress accumulation) [5,6,7]. Then, the effects of the interactions are gradually accumulated, leading to a degradation of the functional properties. In the second case, plastic effects are more intense and complex. In some works [8,9,10,11], the authors investigated this phenomenon and analyzed the evolution of different parameters during high stress experiments. It was highlighted that for temperatures much higher than A f , dislocation slip can occur during transformation, resulting in a considerable amount of unrecoverable deformation and changing considerably the kinetics of MT (martensitic transformation) or DT (detwinning).

Therefore, the understanding of phase transformation (MT and DT) kinetics and its interactions with other mechanisms become a key-factor to the design of SMA-based devices. But despite the large amount of studies on these mechanisms, very few studied its impact on a macroscopic scale, which is the scale of usage.

The understanding of the aforementioned mechanisms is also fundamental for modeling aspects. Presently, several modeling strategies can be employed to simulate the behavior of SMAs. The models can be defined at micro, micro-macro and macroscopic scales. Typically, in micro and micro-macro approaches (extensively detailed models), the phenomena are treated at the grain/crystal or lattice particles levels. Its modeling is mostly based on the Ginzburg-Landau theory or on molecular dynamics and the description of effects such as nucleation or interface motion are often implemented [START_REF] Savi | Mathematical Problems in Engineering[END_REF][START_REF] Cisse | [END_REF]14,15]. On the other hand, for macroscopic approaches, phenomenological considerations and experimental fitting are employed to determine the interactions between the most influential mechanisms and its kinetics.

Different investigation methods are employed to analyze the kinetics and interactions at different scale levels. The most implemented techniques are the observations of the microstructure by transmission electron microscopy (TEM) [5,6,9,16], high-energy X-ray diffraction [8,5] or in-situ electric resistivity [START_REF] Barati | Smart Materials and Structures[END_REF][START_REF] Gédouin | [END_REF]19,20,21]. The amount of data provided by each of these methods varies a lot, as well as the cost of their usage. While X-ray diffraction and TEM analysis contribute with precise and fine resolution images of the microstructure and its rearrangement, electric resistivity measurements provide the user with real-time microstructural state response in a more approachable way.

The purpose of the present work is to analyze the kinetics of the phase transformation for a NiTi wire and some of its main interaction mechanisms at a macroscopic level (usage scale). The experiments are performed by employing electric resistivity measurement under different thermomechanical loading paths. The impact of elastic and plastic strain interactions during phase transformation is determined by using two phase proportioning techniques implemented in a macroscopic approach. Is worth mentioning that, in most of the similar studies, the effect of elastic and plastic strain components are not consid-ered [19,22,23,24,25].

Furthermore, the validity of the most employed relation to the description of the kinetics of MT/DT (a linear correspondence between the volume fraction of the stress-induced martensite and the transformation strain component [26,[START_REF] Gédouin P A | Étude et commande d'actionneurs à base d'alliages à mémoire de forme[END_REF]) is also evaluated through the comparison of two different microstructural states.

Materials and experimental procedures

Studied materials

In this study, two NiTi wires have been considered. The first is a 0.51 mm diameter NiTi equiatomic wire produced by Dynalloy and the second is a 0.39 mm diameter wire produced by Fort Wayne M etals (graded as #6).

The Dynalloy wire (DN) is designed to actuation end and shows TWSME (Two-way shape memory effect). The most common procedure used to provide this property to SMAs is the training [START_REF] Barati | Smart Materials and Structures[END_REF][START_REF] Otsuka | [END_REF][START_REF] Kumar | Introduction to Shape Memory Alloys Shape Memory Alloys: Modeling and Engineering Applications[END_REF][START_REF] Urbina | [END_REF]31,32]. The Fort Wayne M etals wire (FW) does not show TWSME, it is also indicated to actuation usage.

First, phase transformation temperatures M s , M f , A s , A f , R s and R f of both wires were determined by differential scanning calorimetry (DSC) in order to set the temperature conditions for testing. These parameters indicate at which temperature the forward phase transformation and reverse phase transformation starts (temperatures with subscripts "s") and finishes (subscripts "f ") in a stress-free condition.

In some cases, an intermediate phase, the R-phase (rhombohedral) is also present in the material and it is denoted by R s/f . All transformation temperatures are presented in figure 1. In order to identify the mechanical and the electrical response of the NiTi wires, thermomechanical tests were performed with displacement, force and electric voltage measurements. In these tests, the two different commercial wires were used.

Experimental conditions

The thermomechanical experiments were performed using a Zwick electromechanical testing machine (Zwick Z050) equipped with an extensometer to measure the axial strain ε, with a thermal chamber (Zwick BW91250) to control the temperature T surrounding the specimen and with a 500 N load cell to determine the axial stress σ.

Two different loading paths were used to analyze the behavior of the wires: isothermal tests were performed to investigate the superelastic (SE) and pseudoplastic (PP) behaviors, while anisothermal tests investigate the shape memory effect. For isothermal loading, a low strain rate of 10 -4 /s was set, whereas for anisothermal ones, a temperature rate of ± 4 °C/min was imposed. In both types of loading, the temperature was measured by a Ktype thermocouple placed on the specimen and a four-wire lead measurement method was used to feed the specimen with DC current and to record the voltage variation between extensometers as shown in figure 2a. This method consists in applying a low constant electric current between the ends of the wire and in measuring the resulting electric voltage between the pair of extensometer arms. For this, the specimen needs to be electrically isolated from the testing machine and from the extensometer to avoid external noise (see figure 2b). The resulting voltage is used to calculate the resistivity of the specimen during testing (see next section).

Resistivity analysis

By adopting the same procedure as in [33], it is possible to calculate the voltage variation during thermomechanical loading. The voltage variation is linked to phase transformations and to the geometrical changing of the specimen during testing. Equation 1shows that the specimen's electric resistance is a function of the electric resistivity of the material, geometrical characteristics and axial strain when the volume of the specimen is considered constant.

R = L 2 V 0 ρ = (L 0 (1 + ε)) 2 V 0 ρ, (1)
∆R = 2L V 0 ρ∆L + L 2 V 0 ∆ρ, (2)
where R is the electric resistance, L the length, V the volume, ρ the total resistivity and ε the strain of the wire. The subscript "0" indicates the initial value of each parameter. By differentiating this equation and using the relation equation [START_REF] Leary | [END_REF], the connection between the voltage variation and the two major contributing factors are demonstrated in equation ( 5) and equation (6).

∆U = i∆R, (3)
∆U = U 0 ∆R R 0 = U 0 ∆R ε R 0 + ∆R ρ R 0 , (4)
∆U ρ = U 0 ∆R ρ R 0 = U 0 (1 + ε) 2 ∆ρ ρ 0 , (5)
∆U ε = U 0 ∆R ε R 0 = 2U 0 (1 + ε)ε, (6)
In this study, only the resistivity related to the phase transformation electric voltage (∆U ρ ) is analyzed and the final expression for the resistivity measurement is then presented in equation (7).

ρ = ρ 0 1 + ∆U ρ U 0 (1 + ε) 2 . ( 7
)
The electric resistivity itself can be written as a function of the electric resistivity of each pure state present in the material, volume fraction of the states and the temperature as

ρ = ρ (ρ A , ρ M T , ρ M σ , ρ R , z A , z M T , z M σ , z R , T ) , (8)
where the subscripts A, M T , M σ and R are used to indicate the resistivity (ρ i ) and volume fraction (z i ) of the austenite, thermally-induced martensite, stressinduced martensite and R-phase, respectively. In this work, all the R-phase components will not be considered in the analysis (ρ R and z R = 0), since their appearance does not occur on the different loading paths considered here [START_REF] Urbina | [END_REF]34,[START_REF] Zhou | International[END_REF]. Therefore, each of the others remaining pure states (A, M T and M σ ) may be considered a function of temperature, elastic and plastic strain [START_REF] Barati | Smart Materials and Structures[END_REF]33], as

ρ i = ρ i (T, ε el , ε p ), (9)
by differentiating this equation, the following can be obtained,

∆ρ i = ∂ρ i ∂T ∆T + ∂ρ i ∂ε el ∆ε el + ∂ρ i ∂ε p ∆ε p . (10)
In this equation, one can observe the possible contribution of three different mechanisms on the variation of the resistivity of a pure state.

Finally, by using the serial mixture-law in conjunction with condition that the sum of all volume fractions is equal to one, the resistivity relationship is given by:

ρ = (1 -z M T -z M σ )ρ A + z M T ρ M T + z M σ ρ M σ . (11)
In the next sections, two different techniques of phase proportioning based on resistivity measurements are presented. These approaches will be essential to clarify the influence of the strain and temperature components on the resistivity response.

Two-state phase proportioning post processing

In order to study the MT kinetics and the volume fraction of the different states during thermomechanical loading, a two-state phase proportioning method based on the electric resistivity variation is implemented [START_REF] Gédouin | [END_REF]. For this approach, only the thermomechanical loading paths that one single state/phase transformation follows can be analyzed (A ←→ M σ or M T -→ M σ ). In this case, the total resistivity of the material is calculated by the following relation:

ρ(T ) = (1 -z M σ )ρ l (T ) + z M σ ρ M σ (T ), (12)
where l represents M T or A state. The resistivity of each pure phase/state (ρ i , with i = M σ , M T or A) is considered to be temperature-dependent only (the change in resistivity due to elastic and plastic deformations is not accounted for):

ρ i (T ) = µ i T + ρ 0 i , (13)
where µ i is the slope of electric resistivity response, corresponding to ∂ρ i /∂T and the strain components are zero (∂ρ i /∂ε el and ∂ρ i /∂ε p = 0) and ρ 0 i is the reference electric resistivity value at 0 °C.

By rearranging the elements in equation ( 12), the volume fraction of each state (A + M σ or M T + M σ ) is then given by:

z M σ = ρ(T ) -ρ l (T ) ρ M σ (T ) -ρ l (T ) , (14)
z l = 1 -z M σ . (15)
Thus, by measuring the temperature and the resistivity during loading and by using the resistivity of pure phases/states, it is possible to determine the volume fraction of each state/phase during certain loading paths.

Three-state phase proportioning post processing

For more complex loading paths, in which three different states can be present, another approach is proposed. The adopted method is the same as the one developed by [START_REF] Barati | Smart Materials and Structures[END_REF], for a CuAlBe SMA. In this post processing, the effective elastic modulus (E) and the resistivity (ρ) are dependent on the volume fraction of each state. The effect of the plastic strain is not considered, then the total strain can be decomposed into three components (elastic, transformation and thermal), as shown in equation (16).

ε = ε el + ε tr + ε th , (16)
The strain components are calculated as,

ε el = σ E(z M σ , z M T , z A ) , (17)
ε th = α(T -T 0 ), (18)
where σ, is the nominal stress, α is the thermal expansion coefficient and T 0 is the reference temperature.

To evaluate the transformation strain, a supplementary equation is necessary. The relation between the volume fraction of stress-induced martensite and the transformation strain (equation ( 19)), proposed by [26,36,37] is adopted. This relation assumes that the evolution of stress-induced martensite volume fraction is proportional to the transformation strain, as shown in the experiment of [START_REF] Gédouin | [END_REF], performed on a CuAlBe alloy.

z M σ = ε tr γ , (19)
The parameter γ corresponds to the maximum transformation strain.

In this approach, the resistivity evolution of each pure state is also considered as temperature-dependent only (equation ( 13)), as in the previous post processing technique.

Finally, the transformation strain and the volume fraction of each of the three states are estimated by using equations (20) to (25):

σ = (a + bε tr )(ε -ε el -ε th ), (20)
where σ corresponds to mechanical stress and a and b terms to:

a = 1 - ρ -ρ A ρ M T -ρ A E A + ρ -ρ A ρ M T -ρ A E M , (21) b = 1 - ρ M σ -ρ A ρ M T -ρ A E M -E A γ , (22)
where E M and E A are the elastic moduli of the martensite (considered the same for thermallyinduced and stress-induced martensite) and austenite, respectively. The transformation strain is given by:

ε tr = (a -b(ε -ε th ) 2 -4b(σ -a(ε -ε th )) 2b - (a -(b(ε -ε th )) 2b , (23)
and the volume fraction of each state is calculated as:

z M T = ρ -ρ A ρ M T -ρ A - ε tr γ ρ M σ -ρ A ρ M T -ρ A , (24)
z A = 1 -z M T -z M σ , (25)

Results and discussion

Identification of material parameters

Given the experimental procedure, the aim of this section is to identify the material parameter values needed for the phase proportioning. First, in order to collect the standard characteristics of pure phases, different tests were realized and the identified parameters values are presented in tables 1 and 2.

The elastic moduli and the γ parameter were extracted from superelastic tests at different temperatures and in different phases (figures 3a and 4a). Additional material parameters and the phase diagrams are presented in figures 5 and 6. Then, the electric properties µ and ρ 0 were extracted from shape memory effects tests at different stress levels (figures 7 and8) and by considering that the evolution of the resistivity of a pure phase is a linear function of the temperature as in equation [START_REF] Cisse | [END_REF].

The resistivity diagram of each wire are shown in figures 7 and8.

The curves represent the evolution of electric resistivity at different levels of loading. Each linear stage, corresponds to an almost pure thermally-induced martensite, stressinduced martensite or austenite.

The non-linear stages (transient state) reveal the phase transformation process.

As mentioned in the previous section, the R-phase can also be present in the wires' microstructure. The apparition of the R-phase is very prominent in the resistivity diagram due to its higher electric resistivity value and thus easy to identify in certain conditions, as indicated by the arrows in figures 7 and 8. For the studied wires, the A ←→ R and the R -→ M σ /M T phase transformations can take place. The conditions in which they occur are estimated by using the resistivity measurements and the temperaturestress slope (C R ) as 20MPa/°C, based on the literature ( [22,34,[START_REF] Helbert | Smart Materials and Structures[END_REF][START_REF] Wang | [END_REF]), and they are indicated by a darker zone on the phase diagrams (figures 5 and 6).

It is worth noting that the curves signaled as "Th. tr" denote Thermally Treated. In fact, due to the accumulation of internal stress in training process, the trained wires (in this case, the DN) do not show a thermally-induced pure state in any thermomechanical condition. So, in order to achieve this pure state for the phase proportioning calculation, a mild and short tempering process with maximum temperature of 250 °C (value far from the melting point or aging treatment temperatures [START_REF] Otsuka | [END_REF]) was performed. In figure 7, one can note that the resistivity evolution for the pure austenite phase is the same for the Th. tr. and as received DN wire. In addition, the stress vs. strain response (figure 9) shows the typical slight difference between trained and as built SMAs [START_REF] Urbina | [END_REF]. Thus, in this case, the employed procedure can be seen as a thermal flash, used to eliminate the residual martensite from the material, that does not change considerably the microstructural state [START_REF] Moreau | Etude par diffraction des rayons X des effets du cyclage pseudo-élastique de l'alliage à mémoire de forme Cu-Al-Be These de doctorat Metz[END_REF][START_REF] Saint-Sulpice | [END_REF].

Once the thermomechanical and electrical properties are acquired, the analysis of the MT/DT kinetics and the influence of the plasticity on resistivity measures can be performed.

In the next sections, phase proportioning methods will be used in order to observe each of those phenomena in the material.

Results of two-state phase proportioning

After post-processing of acquired test data, the obtained results are plotted in two different figures for each loading.

First, a pseudoplastic loading was performed (figures 10 to 13). By observing only the stress vs. strain response, the behavior seems to agree with the standard SMA-response based on literature experimental curves [START_REF] Rao | Design of Shape Memory Alloy (SMA) Actuators SpringerBriefs in Computational Mechanics[END_REF][START_REF]Introduction Shape Memory Alloy Engineering ed Lecce L and Concilio A[END_REF][START_REF] Kumar | Introduction to Shape Memory Alloys Shape Memory Alloys: Modeling and Engineering Applications[END_REF] Typically, the end of SP (strain plateau) is associated with the end of phase transformation or reorientation. Meanwhile, when the resistivity is observed, it shows an increase before and after the SP section. The same pattern is observed by analyzing the z M σ evolution in figures 11b and 13b.

This behavior indicates that after the phase transformation/reorientation takes place (SP section), other microstructural motions occur. Similar analyses performed in NiTi by [42,43] are in agreement with these observations and show that this microstructural rearrangement corresponds to a twinning mode in martensite of (001) type (also called compound twin) during pseudoplastic loading. Besides, in figure 13b, the relation between z M σ and ε tr is almost linear until the end of the SP and then, a slope lower than 1/γ is achieved. This highlights the fact that after the SP, a different kinetics evolution takes place due to the multistage character of the martensite reorientation. This change of kinetics can be associated with an intrinsic NiTi characteristic and plastic effects, originated from high-stress levels or training processes. Independently from its origin, a non negligible difference between the supposed linear evolution between z M σ and ε tr and the kinetic of MT/DT of this material is observed. This discrepancy can have an unfavorable effect on modeling and design aspects since, by default, this linear relationship is employed in NiTi SMAs.

In the next sections, the impact of this assumption will be evaluated and then the influence of the elastic and plastic strain on the resistivity measurements will also be clarified.

Results of three-state phase proportioning

As it was already described before, a relation between z M σ and ε tr is required for the three-state phase proportioning processing. By considering the linear relation this approach in NiTi wires, figures 14 and 15 shows the composition of different states during an isothermal loading at 100 °C. When analyzing the evolution of each volume fraction during the loading in figure 15a, the result shows an unreal composition.

First, at 100 °C no thermally-induced martensite should be present in the wire, as it can be checked in the phase diagram (figure 5) and yet, an amount of ±15 % is reached at 6 % of load.

Moreover, negative values for z M T are indicated. In addition, negative values for z M T are obtained, where they are inconsistent with a real condition.

Tests using the same method were carried out in FW wires and at other thermomechanical conditions and similar results were obtained. It can therefore be deduced that equation (19) shows some limitations for this type of alloy and that its adoption may lead to erroneous results when designing NiTi based structures

Elasticity influence on electric resistivity

Once the limits of the MT/DT and the phase proportioning methods are evaluated, the next step is to determine the influence of the elastic and plastic strain on the resistivity measurements. First, an isothermal loading-unloading path (0 MPa → 400 MPa → 0 MPa → start of MT) is proposed to analyze elasticity effect on electric resistivity. The results of loading in both wires are presented in figures 16 to 19.

For stress values below 400 MPa, the wires behave elastically and in this zone the resistivity does not evolve considerably. Then, for higher stress values the resistivity starts to rise, indicating the beginning of MT or apparition of M σ , before the SP zone, as already mentioned. Thus, one can consider ∂ρ A /∂ε el = 0.

Then, to evaluate the relations ∂ρ M T /∂ε el and ∂ρ M σ /∂ε el , some tests were performed, but no conclusive results on the irrelevancy of elastic deformation on the variation of resistivity in the M T or M σ state were obtained. In fact, since the MT/DT starts and ends in the surroundings of the SP, a pure elastic state will only appear in a very narrow window at low temperatures. So, in these conditions, it is not possible to differentiate whether or not there is an influence of the elasticity. Based on the results for austenite phase and on other observations from the literature ( [33]), the resistivity of all phases will be considered independent from the elastic strain.

Plasticity influence on electric resistivity

To investigate the impact of plastic strains, observations during pseudoplastic and superelastic loading for both wires were performed. First, when comparing figure 10 and figure 12, a considerable difference on resistivity evolution can be observed, especially in the zone with higher strain values.

At this state, the wire is subjected to higher stress condition, triggering the apparition of dislocation slips [5,8,44].

Furthermore, for the FW wire, the resistivity increases very little after the end of the SP while for the DN one, the resistivity decreases. This difference between the two responses can be associated with the interaction between plasticity and detwinning. In this case, as the DN wire was subjected to training, it has more accumulated dislocations than the FW one and when the loading evolves to a higher stress zone, the impact of plasticity is more pronounced.

By examining the impact of plasticity in figure 10a, one can observe that z M σ rises until 7 % of deformation, and then it starts decreasing. This reduction would take place only in case of reverse phase transformation, but this condition is possible considering the loading history. Then, it can be inferred that plasticity mechanisms are responsible for this apparent reduction of the stress-induced martensite volume fraction, so the resistivity of the stress-induced martensite depends on the interaction between plasticity and martensite transformation.

In order to highlight the effect of plasticity in resistivity measurements, two last tests were performed in a severe stress condition for the DN wire. Figures 20 and21 show the result for an imposed 14 % strain on a DN wire. It can be noted that the maximum stress achieved was about 1400MPa, a value probably beyond the elastic limit of the material. Then, for the stress vs. strain curve, the evolution of z M σ corresponds to the occurrence of plasticity mechanisms in two different moments. First, during the effective phase transformation, dislocation slips are probably triggered by transformation-induced plasticity (TRIP) mechanisms [8,31,[START_REF] Xiao | Smart Materials and Structures[END_REF][START_REF] Zhang | [END_REF], which is linked to the change in the slope of the z M σ evolution. Second, when the phase transformation is finished, the twinninginduced plasticity (TWIP) becomes the major actor, which is responsible for the abrupt change of z M σ /ε tr relation and for the z M σ value beyond 1 [10,11,47]. Furthermore, the resistivity curve shows again an incompatible evolution with the presented loading in figure 21, increasing over the maximum possible value of (resistivity for the full stress-induced martensite). In this case, the main cause for the exceedance of the z M σ and ρ M σ values is the plasticity, the only additional effect introduced in the loading, when compared to the same loading performed in figure 14. The same pattern can also be seen in the thermomechanical loading in figures 22 and 23. For this loading the plasticity mechanisms are more pronounced during the reverse transformation.

Two other relations remain to be defined (∂ρ M T /∂ε p and ∂ρ A /∂ε p ). However, they are harder to be highlighted by conventional testing conditions. The occurrence of thermally-induced martensite associated with plastic strain is possible but unlikely, because the twinned martensite will detwin and transform into stress-induced martensite before reaching higher stress values (when the plasticity would appear). Still, a comparison between two different microstructural states (with and without dislocations) could be performed in order to indirectly evaluate the impact of the ε p , but this mentioned experiment was not performed in this work, thus, the first mentioned relation still remains to be evaluated.

For the second relation, the possible impact of the plasticity on the austenite phase will be only possible under severe temperature condition, approaching to unusable operating conditions for superelastic and SME SMAs. So, it is as well considered non-influent in this analysis.

Finally, one can say that one of the responsible factors for the difference between the supposed linear evolution of z M σ /ε tr and the found results for the NiTi alloy is the plasticity.

Conclusion

In order to study the kinetics of the phase transformation as well as the impact of plasticity on the thermomechanical behavior of NiTi wires, phase proportioning methods based on electric resistivity measurements were employed.

At first, the performed experiments demonstrated that for this material, a multi-stage reorientation of the martensite can take place during pseudoelastic loading. This suggests that, contrary to the employed linear relation that supposed a single microstructure motion, a different kinetics evolution can occur.

Then, it is evidenced that the plasticity affects the relation between martensite volume fraction and 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 transformation strain. Meanwhile, results show that plastic strain and its accumulation via training effects change considerably the supposed linear relation. Thus, tasks involving this assumption can provide erroneous results as the ones presented with the threephase proportioning post processing.

In addition, the influence of elasticity and plasticity on resistivity measurements was evaluated. It was revealed that there is no influence on the resistivity of pure phases caused by elastic deformation. However, it was shown that the plastic deformation has a significant impact on the resistivity variations. These results highlight the effect of plasticity on the MT/DT kinetics.

In summary, it can be concluded that the plasticity plays an import role in the kinetics of the MT and DT on NiTi wires, and it can be observed by macroscopic resistivity measurements. Then, a new relation describing this phenomenon must be establish. However, the quantification of this influence was not performed. Further studies on the quantification of the impact of plastic strain on the resistivity is required.

Figure 1 :

 1 Figure 1: DSC test for DN (a) and FW (b) wires.

  Four-wire lead measurement method. (b) Experimental setup.

Figure 2 :

 2 Figure 2: Experimental setup for voltage variation measurement.

Figure 3 :Figure 4 :

 34 Figure 3: SE/PP (a) and SME (b) tests for DN wires.

Figure 5 :

 5 Figure 5: DN phase diagram.

Figure 6 :

 6 Figure 6: FW phase diagram.

Figure 7 :

 7 Figure 7: DN resistivity diagram.

Figure 8 :

 8 Figure 8: FW resistivity diagram.

Figure 9 :

 9 Figure 9: Comparison between as received and "Th. tr." DN wire at 120 °C.

Figure 10 :Figure 11 :Figure 12 :Figure 13 :

 10111213 Figure 10: Stress\ resistivity vs. strain (a) and resistivity vs. temperature (b) for an isothermal loading at -40 °C -DN wire.

Figure 14 :Figure 15 :Figure 16 :Figure 17 :

 14151617 Figure 14: Stress\ resistivity vs. strain (a) and resistivity vs. temperature (b) for an isothermal loading at 100 °C -DN wire.

Figure 18 :Figure 19 :

 1819 Figure 18: Stress\ resistivity vs. strain (a) and resistivity vs. temperature (b) for an isothermal loading at 100 °C -FW wire.

Figure 20 :Figure 21 :

 2021 Figure 20: Stress\ resistivity vs. strain (a) and resistivity vs. temperature (b) for an isothermal loading at 100 °C -DN wire.

Figure 22 :Figure 23 :

 2223 Figure 22: Strain\ resistivity vs. temperature (a) and resistivity vs. temperature (b) for an anisothermal loading at 600 MPa -DN wire.

Table 1 :

 1 DN wire properties.

	Phase	E	γ	µ x10 -9	ρ 0 x10 -7
	state	(GPa) (%) (Ω.m/K)	(Ω.m)
	M σ M T	44.6	6.5	1.34 1.34	7.07 7.69
	A	80.9		0.34	6.88

Table 2 :

 2 FW wire properties.

	Phase	E	γ	µ x10 -9	ρ 0 x10 -7
	state	(GPa) (%) (Ω.m/K)	(Ω.m)
	M σ M T	45.2	6.7	1.39 1.08	8.66 7.35
	A	82.9		0.29	7.34