Corrosion resistance of galvanic pairs of titanium with silver amalgams in artificial saliva using electrochemical methods

ABSTRACT

Silver amalgams are used to fill damaged teeth, while titanium (cp Ti and Ti-6Al-4V) is used in dental implants due to its biocompatibility and osseointegration capacity. The interaction of these materials in the oral cavity, through saliva, can generate galvanic corrosion and release metallic ions harmful to the health of users. This study evaluates the corrosion resistance of galvanic couples formed by high-copper silver amalgam (Duralloy) and titanium (CP Ti and Ti-6Al-4V) using electrochemical methods (potentials, current densities, Evans diagrams, and Mansfeld correction formulas in aerated artificial saliva). The results indicate that the combination of Duralloy with CP Ti and Ti-6Al-4V presents the highest corrosion resistance, which is corroborated by long-term current density curves.

Keywords:
Corrosion; Dental alloys; Artificial saliva; Polarization curves; Long-duration curves

1. INTRODUCTION

In dentistry, metal alloys play a crucial role in the restoration of damaged or missing teeth, seeking to preserve both masticatory function and dental aesthetics. These alloys are used in a wide range of applications, including direct fillings (amalgams), bridges, crowns, partial or full dentures, inlays, implants, and orthodontic wires [¹,²,³]. Among the most common alloys are Co-Cr, Ni-Cr, titanium, titanium alloys, stainless steels, and copper-based alloys (Cu-Ni, Cu-Al, Cu-Zn), which are used in both molten and cast states. However, these alloys are subject to corrosion in the oral environment due to the action of saliva and other electrolytes, which facilitate chemical and electrochemical reactions. This corrosion can manifest itself in various forms, including general corrosion, galvanic corrosion, pitting corrosion, fissure corrosion, cavitation corrosion, and microbiological corrosion. Corrosion is a critical factor affecting the durability and performance of dental restorations, so its study is essential to optimize the selection and application of these materials [⁴,⁵,⁶,⁷].

Silver amalgam fillings have been used as a dental restorative material for over 150 years. Research on the toxicity of mercury in these amalgams has been conducted by analyzing corrosion products released in the mouth and in systems simulating the oral cavity, using artificial saliva as the electrolyte [⁸]. In 2004, the World Health Organization established a mercury tolerance of 1.6 µgHg/kg of body weight. Subsequently, on September 24, 2020, in Chicago, the American Dental Association (ADA) endorsed the U.S. Food and Drug Administration (FDA) statement that existing evidence does not show that dental amalgam is harmful to the general population [⁹,¹⁰,¹¹,¹²,¹³,¹⁴]. This statement reaffirmed the ADA’s position since August 2009 that dental amalgam is a safe, affordable, and durable material used to restore the teeth of more than 100 million Americans [⁹–¹⁴].

Titanium has been used in dental implants since 1965, when Dr. Per-Ingvar Brånemark placed the first implant in Gösta Larsson in Gothenburg, Sweden. According to Arakelyan [¹⁵], the last two decades have seen an increasing trend in the use of dental implants. In the United States, for example, the proportion of people with dental implants increased from 0.7% to 5.7% between 2000 and 2016, and experts predict that by 2026 this figure could reach 23% [¹⁶]. Currently, Mg-Ti alloys are being used to improve biocompatibility, create composites with polymers, and enhance the tribological properties of titanium and Ti-6Al-4V by providing adequate mechanical support through coating with thin and strong nanocomposites [¹⁷,¹⁸,¹⁹].

The presence of dissimilar metal alloys in the mouth can generate galvanic couplings, where saliva acts as an electrolyte and forms batteries that produce electric currents [¹, ²⁰, ²¹]. These currents are due to the release of metal ions from amalgams and dissimilar alloys, which can manifest as stains or pass into the digestive tract. Some of these ions are eliminated, while others are stored in organs such as the liver, kidneys, lungs, and brain [²², ²³]. Due to the absence of national regulations specifying suitable alloys to minimize galvanic effects, this study determined the corrosion resistance of galvanic pairs of pure titanium (Ti cp) and Ti-6Al-4V with high- and low-copper silver amalgams in aerated artificial saliva. To do so, electrochemical methods and long-term current density curves versus time were used.

2. MATERIALS AND METHODS

2.1. Materials

To carry out this work the following materials were used: cp Ti (commercially pure titanium), Ti-6Al-4V alloy and two high and low copper silver amalgams whose chemical composition (supplied by the manufacturers) is shown in Table 1.

Table 1
Chemical composition of cp Ti, Ti-6Al-4V and silver amalgams in % mass.

MATERIAL	TRADENAME	CODE	CHEMICAL COMPOSITION (% m/m)
Low Copper amalgam	Standalloy F	1	Ag 71-Sn 25,7-Cu 3,3
High Copper amalgam	Duralloy S	2	Ag 45-Sn 31-Cu 24
Cp Ti	Commercially pure Ti	3	Ti 99,76-(others) 0,24
Ti-6 Al-4 V	Ti-6 Al-4V	4	Ti 90,33-Al 5,3-V 4,12-Fe 0,25

Silver amalgam fillings are a dental restorative material commonly used to fill cavities caused by caries. These alloys, composed of mercury, silver, tin, and copper, offer durability and resistance to masticatory forces. However, they are susceptible to corrosion in the oral environment due to interaction with saliva and fluids containing ions and corrosion potentials [²⁴].

Commercially pure titanium (CP Ti) and Ti-6Al-4V alloy are widely used materials in dental restorations, each with distinct applications and properties. Ti CP, known for its high biocompatibility, is commonly used in dental implants, while Ti-6Al-4V, recognized for its mechanical strength, is used in supporting structures such as bridges and crowns. Both materials exhibit excellent corrosion resistance in the oral environment due to a protective oxide layer on their surfaces, which protects them from degradation in oral fluids [²⁵].

2.2. Preparation of test pieces

• The Ti-6A1-4V specimens were prepared in a fully automatic Casmatic machine (for the smelting and casting of Ti). This process was carried out in a closed enclosure with two chambers, which were alternately flooded and evacuated with argon. The material was melted in the upper chamber using an electric arc in a copper crucible with protective gas (argon). After melting, the crucible was inverted, and the molten mass flowed through a cylinder subjected to constant circulation of the same gas [²⁶]. The specimens were 1 cm high by 0.8 cm in diameter. The cp Ti was prepared in the same way as the Ti-6Al-4V alloy and then rolled to simulate the deformation due to mechanical processing to which it was subjected by the dental technician. The specimens tested were 1 cm × 1 cm × 0.2 cm sheets.

• The high and low copper silver amalgams were crushed and condensed according to the instructions suggested by the manufacturers [²⁷]. In both cases the test tubes were cylinders measuring 0.5 cm high by 0.8 cm in diameter.

2.3. Electrolyte

The electrolyte used to measure open circuit corrosion potentials, plot potentiodynamic polarization curves and galvanostatic immersion curves, was a previously developed experimental saliva [²⁸], which reproduces the electrochemical behavior of natural saliva, and whose formula is shown in Table 2. The electrolyte was prepared with deionized water of 18.20 MΩ-cm electrical resistivity and with analytical grade. The natural pH of the solution was 6.5.

Table 2
Chemical composition of the solution used [²⁸].

COMPONENT	NaCl	KCl	CaCl2.2H2O	KH2PO4	Na2HPO2.12H2O	KSCN	KHCO3	H8C6O7
CONCENTRATION (g/L)	0,600	0,720	0,220	0,680	0,856	0,060	1500	0,030

2.4. Electrochemical methods

The electrochemical corrosion methods used in this work were tests to evaluate the corrosion of a material using controlled oxidation and reduction reactions. In this case, to determine the corrosion current density of galvanic pairs in artificial saliva of the alloys under study, the following were performed:

• Corrosion potential measurements. – The electrode potential of each alloy was measured against a saturated calomel electrode in a three-electrode cell with a Princeton Applied Research model 173 potentiostat in artificial saliva aerated at 27 ºC. Measurements were made in triplicate with different test tubes of each alloy, previously allowing the potential to stabilize for one hour in the solution, continuously aerating it with a fish tank aerator at approximately 80 bubbles per minute.

• Polarization curves. – The polarization curves in artificial saliva were drawn in triplicate using the same cell and the same potentiostat as the one used to measure the electrode potential. The reference electrode was also saturated calomel and the counter electrode was platinum. The scanning speed was 12 mV/min controlled with a PAR 175 Universal Programmer and the curves were recorded with a XT PAR grapher model REO 151. Before starting the curves, the corrosion potential was measured in the same way as in the previous section. The anodic and cathodic curves of each alloy were drawn separately with different test tubes starting from the electrode potential.

• Corrosion potentials of galvanic couples. – Dental alloys corrode in the oral environment by the action of saliva and dentin fluids, so that when they are electrically coupled, both are polarized and corrode at a new speed. When metals A and B are coupled, the mixed potential of the galvanic couple, Vcorr.PG, is found at the intersection of the polarization curves where the total oxidation rate is equal to the total reduction rate and the polarization current density is Icorr.GC [²⁹]; this process that allows determining the potential and current density of the galvanic couples is called the Evans method.

• Measurement of galvanic currents. –The electric currents between dissimilar metals placed in an electrolytic medium are called galvanic currents and circulate from the less noble metal (anode) to the more noble metal (cathode). These currents are measured by short-circuiting the electrodes and inserting between them a zero resistance ammeter such as a potentiostat-galvanostat. Figure 1 shows a diagram of the experimental arrangement in which one of the materials is connected to the working electrode terminal (WE), while the other material is connected to the reference electrode (RE) which in turn is short-circuited to the counter electrode (CE). The potentiostat acts as a zero resistance ammeter when the working electrode is polarized to zero volts with respect to the reference electrode [³⁰, ³¹].

Figure 1
Diagram of the experimental device for the Princeton Applied Research Model 273 A potentiostat to operate as a zero resistance ammeter.

The recording of the current intensity versus time curves was carried out in triplicate with a computer connected to the potentiostat with Drop View software. Before the start of the test, the test pieces (of equal areas) were properly installed in the electrochemical cell facing each other at a distance of 10 mm. The electrolytic medium was the artificial saliva described above. Each test lasted 100 hours and the current density was measured every 10 minutes. During the time that the pair was immersed, air was circulated in the solution at a frequency of 50 bubbles per minute. At the end of the test, the data were saved to graph the intensity versus time curves of the couples under study.

In all the galvanic couples of amalgams with dental alloys, the amalgams were connected to the reference electrode terminal (ER) short-circuited with the counter electrode (CE) and the dental alloys to the working electrode terminal (WE). With this configuration, currents with positive sign are due to the dissolution of the amalgams and negative ones to the dissolution of the coupled alloy.

3. RESULTS AND DISCUSSION

3.1. Corrosion potentials of silver amalgams and titanium-based dental alloys

Table 3 shows the average corrosion potentials and their standard deviations of the alloys under study, ordered from the most noble to the most active, forming a galvanic series in aerated artificial saliva. The high corrosion potential of high-copper silver amalgam (Duralloy) is related to its high copper content (24%) and the low content of this metal in Standalloy (3%) makes it vulnerable to corrosive attack in agreement with the results of HAYDAR et al. [³²]. The corrosion current density and the Tafel cathodic slopes of these alloys are also shown.

Table 3
Corrosion potentials, corrosion current densities and Tafel cathodic slopes of the dental alloys under study in aerated artificial saliva.

MATERIAL	TRADENAME	CODE	Vcorr (Vsce)	Icorr (µA/cm2)	bc (Vsce)
High copper amalgam	Duralloy	2	-0,230 ± 0,012	0,033	0,167
Alloy of Ti	Ti-6Al-4V	4	-0,304 ± 0,011	0,138	0,110
Pure Ti	cp Ti	3	-0,319 ± 0,015	0,134	0,156
Low copper amalgam	Standalloy	1	-0,381 ± 0,018	0,083	0,194

cp Ti and Ti-6Al-4V alloy have lower corrosion potentials than Duralloy, so they will always act as anodes, but they have the advantage of forming a titanium oxide film on their surface that makes them very resistant to corrosion, comparable to noble metals.

When cp Ti and Ti-6Al-4V alloy form galvanic pairs with Standalloy, they will always act as cathodes because their corrosion potentials are higher than this amalgam.

3.2. Potentiodynamic polarization curves

Polarization curves were determined under static conditions at room temperature of 37°. Figure 2 shows the polarization curves of silver amalgams. Low copper amalgam (Standalloy) has an active zone extending from – 0.370 V_sce to – 0.100 V_sce and its breakdown potential is -90 mV_sce; from this value the current density increases rapidly. The most corrosive phase of low copper amalgam is the γ₂ or Sn-Hg phase, due to the formation of tin oxychloride from the tin of the γ₂ phase and also to the release of mercury [³², ³³]. High copper amalgams (Duralloy) have no γ₂ phase and the most corrosion-resistant phase of these alloys is the Ag-Hg phase [³⁴]. The passive zone extends from 0.260 V_sce to 1.100 V_sce with an average current density of 3.80 µA/cm2; from 1.100 V_sce the current density increases rapidly due to the release of oxygen by the decomposition of the solution [³⁵].

Figure 2
Polarization curves of low and high copper silver amalgams in aerated artificial saliva.

Figure 3 shows the overall polarization curves of commercially pure titanium (cp Ti) and the Ti-6Al-4V alloy in aerated artificial saliva. It is observed that the titanium alloy has better corrosion resistance properties than commercially pure titanium, in agreement with the results obtained by CÓRDOBA ROMÁN [³⁶] in Ringer solution with a saturated calomel reference electrode. The passive zone of cp Ti extends from -0.16 V_sce to 1.250 V_sce with an average current density of 0.70 µA/cm2 and that of Ti-6Al-4V from -0.180 V_sce to approximately 1.250 V_sce with an average current density of 0.30 µA/cm2 in that region; From 1.300 V_sce onwards the current density increases due to the dissolution of the passivating oxide film and the onset of a pitting process on the sample surface. During this process oxygen was also released according to SPECK and FRAKER [³⁷].

Figure 3
Polarization curves of Ti-based alloys in aerated artificial saliva.

3.3. Corrosion potentials and current densities of galvanic couples

3.3.1. Evans method

The instantaneous corrosion potentials and current densities of galvanic couplings between different materials are obtained using the Evans method described above. In this case, Figure 4 shows the superposition of the polarization curves of commercially pure titanium (cp Ti) and the Ti-6Al-4V alloy with the anodic curves of Standalloy and the cathodic curves of Duralloy. The corrosion potentials and current densities associated with the resulting galvanic couples are presented in Table 4.

Figure 4
Superposition of polarization curves of Standalloy and Duralloy amalgams with those of the Ti-based alloys in aerated artificial saliva.

Table 4
Potentials and corrosion current densities of galvanic pairs of silver and titanium amalgams.

MATERIAL	Notation of GC	Vcorr.couple (VSce)	Icorr.couple (µA/cm2) (EVANS)	Icorr.couple (µA/cm2) (MANSFELD)
Standalloy/cp Ti	(GC1,3)	-0,327	0,096	0,140
Stanadalloy/Ti-6Al-4V	(GC1,4)	-0,313	0,120	0,194
Duralloy/cp Ti	(GC2,3)	-0,270	0,107	0,148
Duralloy/Ti-6Al-4V	(GC2,4)	-0,284	0,150	0,158

3.3.2. Mansfeld correction formulas

Table 4 also shows that the corrosion current densities of galvanic couples of amalgams with titanium alloys are lower than the current densities of the decoupled anode alloys, violating the condition of galvanic couple theory that states that the current density of a galvanic couple is higher than the current density of the decoupled anode. This would lead to the erroneous assumption that galvanic coupling of these alloys increases the corrosion resistance of the galvanic couplings under study. To correct this error we will use the Mansfeld formulas for small polarization ranges [¹⁰]. That is, when coupling metal A to metal B (more noble than A) a small shift of the corrosion potential of metal A occurs. Therefore, the potential of the galvanic couple of the two dissimilar coupled metals is located very close to the corrosion potential of the uncoupled anode and Tafel-type behavior does not occur. Therefore, the anodic and cathodic reactions occur at an appreciable rate on the anode.

In this case the galvanic current (I_corr.GC) is not equal to the metal dissolution current A. This last current is the sum of the cathodic currents on the anode (I_A,c) and on the cathode (I_B,c):

(1) $${\text{I}}_{\text{A},\text{a}}={\text{I}}_{\text{A},\text{c}}+{\text{I}}_{\text{B},\text{c}}$$

while the galvanic current is equal to the cathodic current on metal B:

(2) $${\text{I}}_{\text{corr}.\text{GC}}={\text{I}}_{\text{B},\text{c}}={\text{I}}_{\text{A},\text{a}}–{\text{I}}_{\text{A},\text{c}}$$

From which

(3) $${\text{I}}_{\text{A},\text{a}}={\text{I}}_{\text{corr}.\text{GC}}+{\text{I}}_{\text{A},\text{c}}$$

The magnitude of the galvanic couple current density (I_corr.GC) is determined using Evans diagrams and the cathodic current density of anode A is calculated using the formula:

(4) $${\text{I}}_{\text{A,c}}={\text{I}}_{\text{corr}\text{.A}}\text{exp}\left(-\frac{\left({\text{V}}_{\text{corr}\text{.GC}}-{\text{V}}_{\text{corr}\text{.A}}\right)}{{\text{0,434 b}}_{\text{c}}}\right)$$

where V_corr.GC is the galvanic couple corrosion potential, V_corr.A and I_corr.A are the corrosion potential and corrosion current density of the decoupled anode; b_c is the cathodic Tafel slope of the anode material (A).

The polarization range (V_corr.GC – V_corr,A.) of the galvanic couples of silver amalgams with titanium is very small, less than 0.16 V_sce, so formulas (3) and (4) will be used to determine the true anode dissolution current density (I_A,a) for the galvanic couple corrosion potential. We will illustrate the calculation of I_A,a considering the galvanic couple GC1,3 (Standalloy/cp Ti). The galvanic current density is: I_corr.PG(1,3) = 0.096 µA/cm2 and the current density I_A,c corresponding to the anode of this pair is determined using formula (4) and the data in Tables 3 and 4:

$${\text{I}}_{A,c}=\left(0.0\text{83 µ}A\text{/}c{m}^{\text{2}}\right)\left[\frac{(-0.327+0.381}{0.434\times 0.194}\right]\text{= 0}\text{.044 µ}A\text{/}c{m}^{\text{2}}$$

Replacing in formula (3) we have:

$${\text{I}}_{A,a}\text{= 0}\text{.140 µ}A\text{/}c{m}^{\text{2}}$$

Which is the corrosion density of the galvanic couple GC1.3 considered in this work; the other values are shown in Table 4.

3.4. Galvanic current curves

Figure 5 shows the immersion curves of low copper silver amalgam galvanic couples with titanium-based dental alloys: CP Ti and Ti-6Al-4V:

Figure 5
Corrosion current density of low-copper silver amalgam galvanic couples with Ti-based dental alloys.

For cp titanium the current density drops from 0.53 µA/cm2 to 0.04 µA/cm2 in 3 hours and then to 0.012 µA/cm2 in 6 hours, maintaining approximately constant nanometric values for the rest of the test time, in agreement with the results of GROSGOGEAT et al. [³⁸].

For the Ti-6Al-4V alloy the current density dropped from 0.10 µA/cm2 to 0.014 µA/cm2 in 11 hours and then to 0.006 µA/cm2 in the following 89 hours of the experiment. This means that for these couples the galvanic current densities start from relatively high values, rapidly decrease with time and finally reach very low stable values [³⁹, ⁴⁰].

Also included in Figure 5 are the galvanic couples that suffered accelerated corrosion: (a) For Standalloy/cp Ti (crevice in amalgam) the current density drops from 0.52 µA/cm2 to 0.03 µA/cm2 in 13 hours, then slowly increases to 0.05 µA/cm2 in 19 hours. The amalgam then undergoes crevice corrosion with the current density rising to 0.40 µA/cm2 in 3 hours. This value remained approximately constant for the rest of the test time (green dashed curve plateau). (b) For Standalloy/Ti-6Al-4V (crevice in amalgam), the amalgam underwent crevice corrosion after 43 hours of exposure in the electrolytic solution (artificial saliva), with the current density increasing from 0.020 µA/cm2 to 0.15 µA/cm2 in the following 10 hours and maintaining that value until the end of the test (solid violet curve plateau).

Figure 6 shows the immersion curves of high copper silver amalgam galvanic couples with Ti-based dental alloys: cp Ti and Ti-6Al-4V.

Figure 6
Corrosion current density of high copper silver amalgam galvanic couples with Ti-based dental alloys.

For titanium cp the current density rises “exponentially” from -0.07 µA/cm2 to 0.0 µA/cm2 in 29 hours and then slowly increased to 0.002 µA/cm2 in the remaining 71 hours of the experiment.

For the Ti-6Al-4V alloy the current density also rises rapidly from -0.07 µA/cm2 to 0.0 µA/cm2 in 13 hours and then gradually increased to 0.009 µA/cm2 in 87 hours. In both cases, the titanium is first activated and then passivated by the formation of an oxide layer on the surface of the sample, the amalgam begins to dissolve until the test ends in accordance with the results of RAHIMI et al. [⁴¹].

The current density for the Duralloy/Ti-6Al-4V couple (dotted curve) in which the amalgam undergoes crevice corrosion increases rapidly from 0.045 µA/cm2 to 0.0 µA/cm2 in 6 hours. It then slowly increases due to amalgam dissolution to 0.03 µA/cm2 in 57 hours. In the last section of the curve, the amalgam undergoes crevice corrosion and the current density increases to 0.08 µA/cm2 in 37 hours, i.e., three times more than in the last 57 hours.

In the galvanic curves shown in Figure 5, the low-copper silver amalgam (Standalloy) dissolved faster than cp titanium and its alloy Ti-6Al-4V, because its open-circuit corrosion potential is more negative than the electrode potentials of the Ti-base alloys. However, in the galvanic curves shown in Figure 6, titanium and its alloy begin the dissolution process and then change polarity when the titanium is passivated and the amalgam is activated, a result consistent with those obtained by other researchers [⁴²,⁴³,⁴⁴]. Initially, titanium and its alloy act as anodes for approximately 10 to 12 hours and then as cathodes. In the first stage, the galvanic current is generated by forming titanium oxide (TiO₂), which is a passivating oxide that prevents the flow of electrons by acting as an n-type semiconductor [⁴⁴, ⁴⁵].

The average corrosion current densities of the galvanic couples of silver amalgams with cp Ti and Ti-6Al-4V are very low, ranging between 2.5 nA/cm2 and 14 nA/cm2, in the stable zone, free of corrosion accelerated by the crevice effect. However, they are sufficient to form corrosion products on amalgams, titanium surfaces and in the electrolytic solution. When accelerated corrosion occurs due to poor amalgam conformation, the current density increases as shown in Figures 5 and 6, probably to the point of plugging the porosities and fissures with insoluble corrosion products. Micrographs of the surface of the Ti and Ti-6Al-4V specimens after removal of the corrosion products showed a light blue oxide film, probably titanium oxide, which protected the metal from corrosion by the medium.

4. CONCLUSIONS

From the results obtained in this work it can be deduced:

1. The galvanic series of the alloys studied in aerated artificial saliva shows that the low-copper silver amalgam (Standalloy F) has the lowest open-circuit corrosion potential, so it will always act as the anode in all the galvanic couples it forms with Ti CP and Ti-6Al-4V.

2. The high-copper silver amalgam (Duralloy S) has the highest corrosion potential and the lowest current density of the alloys considered in this study, so it will always act as the cathode and will be the most resistant to corrosion in the oral environment in which it operates.

3. The galvanic couples of Ti CP and Ti-6Al-4V with Duralloy amalgam in aerated artificial saliva are highly resistant to corrosion, with both the pure metal and its alloy acting as anodes. Results are corroborated by the long-term galvanostatic curves.

4. Galvanic couples of low-copper amalgams (Standalloy) with Ti CP and Ti-6Al-4V are not recommended in the oral cavity because the amalgam acts as an anode, leading to deterioration of this material.

5. Evans diagrams may be insufficient to determine the corrosion current densities of galvanic couples under certain conditions, such as in the case of the combination of Duralloy and Ti CP. Therefore, Mansfeld correction formulas must be used to ensure that the galvanic couple current density is greater than the corrosion current density of the alloy acting as the anode.

In future work, we will investigate the galvanic couples formed between Co-Cr, Ni-Cr alloys and stainless steels used in crowns, and CP titanium and its alloy (Ti-6Al-4V) used in abutments and implants, since the current densities of these couples in the oral cavity may increase over time due to the presence of cracks or corrosion in the surrounding tissues.

DATA AVAILABILITY

The full dataset supporting the findings of this study is available upon request to the corresponding author.

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Publication Dates

• Publication in this collection
  22 Sept 2025
• Date of issue
  2025

History

• Received
  27 Jan 2025
• Accepted
  15 July 2025