Statistical Evaluation and Optimization of Sol-Gel Dip Coating Deposition Parameters of Multilayered Conversion Coatings for Anticorrosive Alumina Film

Abstract

Multilayered conversion coatings (MCCs) can be produced on carbon steel via sol-gel dip coating to improve the corrosion resistance of alumina film/conversion coating/carbon steel systems in a saline medium. Nonetheless, the deposition parameters used to produce the MCCs can affect this performance, and the optimum conditions are generally found using univariate studies. In this work, Silica/boehmite (SB) and boehmite/silica (BS) MCCs were produced on carbon steel via sol-gel dip coating, using a central composite experimental design to evaluate the effects of deposition time (t), substrate removal speed (v), and heat treatment time (HT) on corrosion resistance of the complete system in a saline medium. This unprecedented statistical study allowed us to determine optimal MCC deposition conditions for producing coating systems with superior anti-corrosive properties. v and HT had the most significant impact on anticorrosive performance. The SB-MCC system, optimized at t = 116 s, v = 368 mm/min, and HT = 70 min, showed the best corrosion resistance (R_g = 81.6 kΩ cm²). Improved surface roughness and better coverage of sharp structures enhanced alumina adhesion, increasing stability in saline environments compared to BS-MCC/alumina.

Keywords:
Design of experiments; Desirability function; Boehmite; Silica; Alumina

1. Introduction

The application of multilayered coatings allows the formation of more than one interface, increasing the substrate adhesion and reducing the mechanical stress and internal defects usually observed during a coating process¹. Additionally, the combined effects of each layer’s properties are also available, which is an advantage compared to single coatings². Coating systems of different natures can be produced, giving rise to hybrid materials that can present improved anticorrosive, electrical, optical, electromagnetic, and mechanical properties³-⁷.

Multilayered conversion coatings (MCCs) have also shown improved barrier properties⁸-¹². Braga et al.¹³ described intermediate multilayers composed of silica and boehmite deposited in different sequences using a dip coating technique that increased the corrosion resistance of alumina film on carbon steel substrate exposed to a saline medium. These conversion coatings act directly to improve adhesion, giving rise to essential interfacial properties, which include generating effective and continuous anchoring points during the material's service life, insolubility, impermeability, and flexibility¹⁴.

Compared to more conventional methods, the main advantages of producing conversion coatings by dip coating in sol-gel are the homogeneity of the layer formed and greater control of the film thickness and porosity¹⁵. Furthermore, the technique allows the opportunity to coat substrates of different shapes, sizes, and natures¹⁶, such as glass, plastics, metals, and ceramics¹⁷. However, the conditions for producing MCCs by dip coating have not been thoroughly studied since the only dip coating deposition parameter studied was the heat treatment temperature¹³,¹⁸-²⁰. Nonetheless, the thickness of the xerogel films obtained before heat treatment is significant for the characteristics of the coating produced after the heating stage²¹, which can be manipulated by the dip coating deposition conditions²²-²⁴. Additionally, the barrier properties of the MCCs depend on the coating parameters²⁰,²⁵-²⁷. Therefore, it is necessary to analyze the influence of the deposition parameters, such as the deposition time, the speed at which the substrate is removed from the sol, and the heat treatment time, on the material properties.

The multivariate study of these parameters using statistical tools such as the design of experiments (DOE) and desirability function has been recently used to determine the optimal conditions to deposit a single boehmite conversion coating by dip coating in sol-gel on carbon steel, for subsequent covering with alumina film, resulting in an improved anti-corrosive system to be used in a saline environment²⁸. Considering the MCCs, a multivariate study may permit an enhanced understanding of how the deposition conditions of MCCs are related to the anti-corrosive properties of the coating system after being covered with an alumina film, contributing to the advancement of studies on coatings produced by dip coating techniques. Furthermore, determining the optimal conditions for MCC deposition makes producing a coating system with customized properties possible. However, to the best of our knowledge, no multivariate studies statistically relate the deposition conditions to produce MCCs by sol-gel dip coating with the anti-corrosive characteristics of the obtained materials systems. Additionally, determining optimal dip coating deposition conditions has not yet been reported for multilayer films.

Although promising results were obtained for silica/boehmite and boehmite/silica conversion coatings¹³, some pores and defects were still observed on these MCCs. Considering this point and the lack of multivariate analysis and optimization of the deposition conditions to produce MCCs using dip coating in sol-gel, this work aims to evaluate the effects of the deposition time, removal speed, and heat treatment time used to prepare the MCCs on the anti-corrosive performance of alumina film/MCC/carbon steel substrate in a saline medium. This work also intends to contribute to a better understanding of the formation of MCCs and the production of customized conversion coatings with the advantages and improvements of a multilayer system.

2. Experimental Procedures

2.1. Preparation of the carbon steel substrate

AISI 1020 carbon steel discs (surface area of 4.96 cm²) were abraded in silicon carbide paper ranging from 120 to 600 grit and then polished on 3 μm particle size metallographic alumina. Before the deposition, the samples were cleaned with acetone in an ultrasound for five minutes and then activated in 4 mol L⁻¹ KOH solution for 5 min at 75 °C²⁹. The production of hydroxyl radicals on the steel surface improves the interaction and, consequently, the adhesion between the surface and the sol by hydrogen bonding.

2.2. Multilayer conversion coatings produced according to DOE matrix

The silica layer was produced from a tetraethyl orthosilicate (TEOS) sol with a molar ratio TEOS:water (H₂O):ethanol (EtOH) equal to 4:90.5:5.5. Glacial acetic acid was added slowly under stirring until the sol pH reached 2.5²⁹. The sol was stirred until a homogenous suspension was achieved, standing for 24 h. The boehmite layer was obtained from a 0.4 mol L^-1 boehmite aqueous solution (Boehmite Disperal P2, kindly provided by Sasol®). This solution was stirred for six hours and stood for 24 h before the deposition process on the substrate²⁹. Only sols prepared using a maximum age of one week were used to produce the MCCs studied in this work²⁸.

In a previous work¹³ it was shown that when a TEOS/boehmite xerogel was deposited on the steel substrate and heat-treated at 600 °C, the conversion coating was composed of a mixture of silica, boehmite, alumina, and iron oxides, leading to the best electrochemical behavior among all the alumina film/(silica/boehmite) conversion coating/carbon steel substrate systems studied. On the other hand, the best temperature to heat-treat a boehmite/TEOS xerogel film to obtain the system showing the best anti-corrosive performance was obtained at 500 °C. Thus, these temperatures were used to produce silica/boehmite (600 °C) and boehmite/silica (500 °C) conversion coatings, following a 2³ central composite experimental design with axial points²⁸. The other parameters, deposition time (t), removal speed (v), and heating time (HT), were varied using the DOE matrix (Tables 1 and 2, for silica/boehmite and boehmite/silica conversion coatings, respectively), in which both the real and coded values of the studied parameters are presented. Therefore, from now on, the silica/boehmite and boehmite/silica samples were denominated SB_xS and BS_xS, respectively, where “x” is the Run number in Tables 1 and 2.

Table 1
DOE matrix, response variables, and additional electrochemical data for ASB_xS systems.

Run no.	Deposition conditions
	(Independent variables) to produce the SBxS conversion coatings			Response variables			Additional electrochemical data
	t (s)	v (mm min-1)	HT (min)	Rg (kΩ cm2)	Rp (kΩ cm2)	SBxSthickness (μm)	Cg (F cm-2)	Porosity	Circuit	χ2	Ecorr V
								(%)
1	100 (-1)	100 (-1)	60 (-1)	3.71	3.58	2.070	3.96 x 10-05	1.17 x 10-02	Fig. 4B	0.0122	-0.442
2	300 (1)	100 (-1)	60 (-1)	36.32	32.80	2.166	2.79 x 10-06	8.48 x 10-06	Fig. 4A	0.0208	-0.220
3	100 (-1)	300 (1)	60 (-1)	73.20	69.90	2.594	1.98 x 10-06	6.11 x 10-06	Fig. 4A	0.0199	-0.239
4	300 (1)	300 (1)	60 (-1)	41.93	38.50	2.863	3.21 x 10-06	1.39 x 10-05	Fig. 4A	0.0187	-0.249
5	100 (-1)	100 (-1)	180 (1)	2.17	1.94	2.145	7.58 x 10-05	0.125	Fig. 4B	0.0136	-0.520
6	300 (1)	100 (-1)	180 (1)	23.82	20.20	2.637	6.21 x 10-07	3.10 x 10-05	Fig. 4A	0.0217	-0.256
7	100 (-1)	300 (1)	180 (1)	34.50	21.30	2.481	1.56 x 10-05	6.20 x 10-05	Fig. 4A	0.0184	-0.289
8	300 (1)	300 (1)	180 (1)	14.87	33.70	2.885	5.42 x 10-06	2.08 x 10-05	Fig. 4A	0.0142	-0.261
9	32 (-1.682)	200 (0)	120 (0)	12.36	10.40	2.031	1.16 x 10-06	2.18 x 10-05	Fig. 4A	0.0133	-0.211
10	368 (1.682)	200 (0)	120 (0)	11.64	10.18	2.528	2.14 x 10-05	2.79 x 10-03	Fig. 4B	0.0158	-0.425
11	200 (0)	32 (-1.682)	120 (0)	4.91	4.27	1.907	8.64 x 10-07	3.09 x 10-02	Fig. 4B	0.0162	-0.493
12	200 (0)	368 (1.682)	120 (0)	47.50	39.60	2.904	3.21 x 10-08	3.82 x 10-06	Fig. 4A	0.0169	-0.193
13	200 (0)	200 (0)	19 (-1.682)	42.90	41.74	2.152	4.32 x 10-06	1.07 x 10-05	Fig. 4A	0.0214	-0.241
14	200 (0)	200 (0)	221 (1.682)	22.05	21.98	2.114	8.52 x 10-04	2.22 x 10-02	Fig. 4B	0.0149	-0.551
15	200 (0)	200 (0)	120 (0)	21.15	20.60	2.141	1.28 x 10-05	1.41 x 10-04	Fig. 4A	0.0206	-0.324
16	200 (0)	200 (0)	120 (0)	18.43	17.90	2.132	1.45 x 10-05	1.59 x 10-04	Fig. 4A	0.0198	-0.323
17	200 (0)	200 (0)	120 (0)	19.11	18.50	2.138	2.04 x 10-05	1.40 x 10-04	Fig. 4A	0.0211	-0.319

Table 2
DOE matrix, response variables, and additional electrochemical data for ABS_xS systems.

Run no.	Deposition conditions
	(Independent variables) to produce the BSxS conversion coatings			Response variables			Additional electrochemical data
	t (s)	v (mm min-1)	HT (min)	Rg (kΩ cm2)	Rp (kΩ cm2)	BSxSthickness (μm)	Cg (F cm-2)	Porosity (%)	Circuit	χ2	Ecorr V
1	100 (-1)	100 (-1)	60 (-1)	14.9	12.4	2.587	2.32 x 10-06	2.52 x 10-02	Figure 4B	0.0154	-0.589
2	300 (1)	100 (-1)	60 (-1)	13.6	14.0	2.614	3.96 x 10-06	1.48 x 10-04	Figure 4A	0.0169	-0.585
3	100 (-1)	300 (1)	60 (-1)	15.0	12.9	2.771	2.17 x 10-07	1.31 x 10-02	Figure 4B	0.0177	-0.752
4	300 (1)	300 (1)	60 (-1)	16.1	14.3	2.809	2.69 x 10-06	2.93 x 10-04	Figure 4A	0.0185	-0.560
5	100 (-1)	100 (-1)	180 (1)	10.6	10.4	1.996	2.00 x 10-05	9.28 x 10-03	Figure 4B	0.0132	-0.403
6	300 (1)	100 (-1)	180 (1)	11.5	10.4	2.043	2.33 x 10-05	7.05 x 10-03	Figure 4B	0.0124	-0.607
7	100 (-1)	300 (1)	180 (1)	8.54	8.06	2.107	1.43 x 10-05	6.95 x 10-03	Figure 4B	0.0145	-0.619
8	300 (1)	300 (1)	180 (1)	11.8	11.8	2.213	1.00 x 10-05	6.11 x 10-03	Figure 4B	0.0122	-0.478
9	32 (-1.682)	200 (0)	120 (0)	12.8	10.9	1.964	8.75 x 10-06	6.54 x 10-04	Fig. 4A	0.0173	-0.624
10	368 (1.682)	200 (0)	120 (0)	13.1	12.1	2.053	1.71 x 10-05	6.52 x 10-02	Figure 4B	0.0098	-0.632
11	200 (0)	32 (-1.682)	120 (0)	5.29	5.56	1.845	2.17 x 10-04	1.89 x 10-02	Figure 4B	0.0146	-0.500
12	200 (0)	368 (1.682)	120 (0)	8.01	10.1	2.796	1.44 x 10-03	2.76 x 10-03	Figure 4B	0.0195	-0.534
13	200 (0)	200 (0)	19 (-1.682)	17.3	17.5	2.281	1.86 x 10-07	1.70 x 10-03	Figure 4B	0.0166	-0.587
14	200 (0)	200 (0)	221 (1.682)	14.9	15.9	2.094	2.39 x 10-06	2.51 x 10-05	Figure 4A	0.0117	-0.642
15	200 (0)	200 (0)	120 (0)	14.8	12.9	1.982	2.36 x 10-06	4.36 x 10-04	Figure 4A	0.0149	-0.598
16	200 (0)	200 (0)	120 (0)	14.8	12.6	1.999	1.94 x 10-06	3.97 x 10-04	Figure 4A	0.0155	-0.601
17	200 (0)	200 (0)	120 (0)	14.9	12.9	2.008	2.32 x 10-06	4.56 x 10-04	Figure 4A	0.0157	-0.586

For the silica/boehmite conversion coatings (SB_xS) production, the carbon steel coupons were immersed in the TEOS sol during t time, using the dip coater MARCONI. At the end of the coating time, the substrate was removed using v removal speed and dried at room temperature (around 25 ^oC) for 2 minutes for the solvent evaporation and drying of this xerogel film. Next, the same coupons coated with the TEOS xerogel film were immersed in the boehmite solution for the same t time and removed from the boehmite solution at v removal speed. The deposited multilayer xerogel film was heat-treated at 600 °C in a muffle furnace (TECNAL) during HT heating. The boehmite/silica conversion coatings (BS_xS) were produced analogously, using t, v, and HT according to the DOE matrix, but reversing the immersion/removal sequence: the coupons were first immersed in the boehmite solution and then in the TEOS sol. In this case, after the multilayer deposition, the heat treatment temperature used was 500 °C. Figure 1 schematically shows the production procedure of SB_xS and BS_xS conversion coatings.

Figure 1
Steps for producing silica/boehmite (SB_xS) and boehmite/silica (BS_xS) conversion coatings according to the DOE matrix.

2.3. Production of final alumina film onto the steel covered with the multilayered conversion coatings

Alumina sol was prepared using aluminum isopropoxide as the precursor, acetic acid as the catalyst, and ethanol as the solvent. The molar ratios used were: water:precursor = 20; solvent:precursor = 5; and solvent:catalyst = 2.5. The sol was kept at 70 °C, under stirring, during the first 4 hours¹³ and was then kept at room temperature during the following 14 hours of intermittent mixing¹³,²⁹. Only alumina sols prepared using a maximum age of one week were used to produce the alumina films studied in this work²⁸.

The coupons pretreated with silica/boehmite and boehmite/silica conversion coatings prepared following the conditions described in Tables 1 and 2 were immersed in alumina sol for 60 seconds, removal at a controlled speed of 100 mm min^-1, and dried at room temperature for 2 min, using the same dip coating equipment mentioned before. This procedure was repeated once more to form a two-layer coating. The final coated samples were then heated in a muffle furnace at 500 °C for 30 min¹³. After being covered with alumina, the samples were denominated ASB_xS and ABS_xS when alumina was deposited on SB_xS and BS_xS samples, respectively. As mentioned, "x" is related to the Run number in the DOE matrix (Tables 1 and 2).

2.4. Determination of the response variables

2.4.1. Electrochemical evaluation of the alumina film/MCCs/steel substrate systems (ASB_xS and ABS_xS systems)

The electrochemical evaluation of the alumina film/MCCs/steel substrate systems was performed in a 3.5% w/v NaCl solution at 25 °C, using a potentiostat/galvanostat AUTOLAB PGSTAT 302N. These samples were used as the working electrodes in a three-electrode electrochemical cell, in which the reference electrode was a saturated calomel electrode (SCE), and the counter electrode was a platinum spiral.

Electrochemical impedance spectroscopy (EIS), linear polarization resistance (LPR), and potentiodynamic polarization (PP) experiments of the ASB_xS and ABS_xS systems were performed to evaluate their anti-corrosive characteristics using the conditions earlier applied in²⁸. Briefly, the EIS analysis was performed at the open circuit potential (OCP) after stabilization for 180 min, using an amplitude of 10 mV and a frequency range from 10⁵ Hz to 10^-3 Hz. The LPR tests were conducted immediately after the EIS experiments by varying the potential between ± 10 mV around the OCP at a 0.1 mVs^-1 scan rate. Finally, the PP curves of the systems were obtained using a potential range between ± 500 mV around the OCP and a scan rate of 1.0 mVs^-1. The same electrochemical analyses were also performed for the uncoated substrate for comparison.

The electrochemical responses of global corrosion resistance (R_g) and polarization resistance (R_p), obtained in these experiments, were used as the DOE response variables. R_g was obtained by the sum of the charge transfer resistance of the substrate (R₁) and the resistance of the protective coating (R₂), the latter composed of the conversion coating and the alumina film (Equation 1)²¹,²⁸. The determination of R₁ and R₂ will be explained later.

$R_g=R_1+R_2$ (1)

The porosity of each system was also obtained using Equation 2³⁰, in which R_p,cs is the polarization resistance of the bare carbon steel, βa_cs is the slope of the anodic branch (obtained from the PP experiments of the uncoated substrate), and ΔE_corr represents the difference between the corrosion potentials of the coated samples (E_corr) and the uncoated carbon steel (E_corr,cs)²⁸.

$Porosity=\frac{R_{p,cs}}{R_p}\times {10}^{\frac{-\left|\Delta E_{corr}\right|}{\beta a_{cs}}}$ (2)

2.4.2. Coating thickness

The third response variable of the DOE matrix, the conversion coatings thickness (SB_xS_thickness and BS_xS_thickness), was measured using a magnetic induction probe (DUALSCOPE), according to DIN EN ISO 2178³¹, in five different regions of the respective coated surfaces. The thickness of the total systems covered with alumina film (ASB_xS and ABS_xS) was also measured using the same methodology. The standard deviation never surpassed 5% of the average thickness value in all cases.

2.5. Statistical evaluation of the DOE matrix

The response variables of the DOE matrix, obtained as described in section 2.4, were used for the statistical analysis performed using the software STATISTICA for Windows, version 7.0. A quadratic mathematical model was determined for each response variable (R_g, R_p, and the thickness of the conversion coatings – SB_xS_thickness and BS_xS_thickness), and only statistically significant effects (p < 0.05) were considered. The desirability function was used to determine the optimal conditions to produce the silica/boehmite and the boehmite/silica conversion coatings that, after covering with alumina film, should present the highest values for R_g and R_p³².

2.6. Characterization of samples produced under selected conditions

The silica/boehmite and boehmite/silica conversion coatings produced using the conditions obtained from their respective desirability analyses (SB_DS and BS_DS samples) were characterized by SEM using a scanning electron microscope JEOL JSMG510LV with an accelerating voltage of 20 kV and a secondary electron detector (SEI). The phase identification of the conversion coatings’ components produced under the selected conditions was determined by XRD using the diffractometer model BROOKER D8 and k_α-Cu radiation. The roughness of these conversion coatings was determined using a Mitutoyo SJ-210 roughness meter, following ISO 4287-1997³³, in three different regions of the sample. Finally, the thickness of the xerogel films (h) was measured using the same procedure described in section 2.4.2. Those SB_xS and BS_xS samples showing the worst anticorrosive performance were also characterized for comparison.

After covering all these samples with an alumina film, their cross-sections were evaluated by SEM-EDS analyses using a Hitachi TM3000 microscope with a 15 kV beam and backscattered electron detector. Then, EIS experiments were performed after 0 h, 24 h, 120 h, and 240 h of exposure to the corrosive medium studied, following the procedure described in section 2.4.1. Furthermore, the OCP measurements of these selected systems were monitored during this period in contact with the saline medium, using a saturated calomel reference electrode. After this exposure time, the surfaces were also analyzed by SEM to observe the formation of corrosion products.

3. Results and Discussion

3.1. Electrochemical results

The Nyquist plots of the alumina/MCCs/carbon steel substrate systems using the silica/boehmite and boehmite/silica conversion coatings produced under the conditions described in Tables 1 and 2 are shown in Figures 2A and 2D, respectively. The choice of the equivalent electrical circuits used to simulate the EIS data and obtain the electrochemical properties for each sample (Figure 3) was based on the sample porosity (Equation 2) and the Nyquist results. Tables 1 and 2 show the response variables (R_g, R_p, and the conversion coatings’ thicknesses), the additional electrochemical results obtained by simulating the EIS data, and the porosity values of the samples containing silica/boehmite and boehmite/silica conversion coating covered with alumina film (ASB_xS and ABS_xS systems), respectively. Complete data obtained from simulations of these EIS experiments are available in Tables S1 and S2 in the Supplementary Material.

Figure 2
Nyquist diagrams obtained in EIS tests of (A) ASB_xS and (D) ABS_xS samples in NaCl 3.5% m/v from the Design of Experiments; Schematic representation of (B, C) compact and porous ASB_xS samples, respectively; and (E, F) compact and porous ABS_xS samples, respectively.

Figure 3
Equivalent electrical circuits used to simulate the EIS data.

All the ASB_xS and ABS_xS systems showing porosity values lower than 10^-3% (Tables 1 and 2, respectively) and presenting an EIS profile typical of compact coatings (represented by the schematics in Figures 2B and 2E, respectively) were simulated using the circuit in Figure 3A. On the other hand, samples with porosity values higher than 10^-3% suggests that the alumina film was probably deposited on a heterogeneous and defective MCC, as shown in Figures 2C and 2F.

Most of the ASB_xS systems were considered composed of compact coatings (Figure 2C). This layering scheme suggests that the deposition of the boehmite xerogel film over the TEOS xerogel film during the immersion sequence covered the defects and uncovered areas commonly observed in silica coatings produced by the TEOS sol²⁹,³⁴. On a more homogeneous surface composed of a boehmite and silica mixture, obtained after heat treatment of the double-layer conversion coating, the deposited alumina film is also compact. It reduces the system's porosity and eliminates the need for a resistor-constant phase element pair associated with possible pores and defects. Therefore, the circuit presented in Figure 3A was chosen to simulate these results. However, those ASB_xS samples with porosity higher than 10^-3% were considered as porous coatings (Figure 2D). In these cases, an additional time constant is present in the circuit used to simulate these samples (Figure 3B), related to the presence of defects and pores in the alumina film deposited on a heterogeneous and defective silica/boehmite conversion coating.

Regarding the systems containing boehmite/silica conversion coating (ABS_xS), the TEOS xerogel film was deposited on a boehmite xerogel film, leading to a conversion coating surface predominantly composed of a silica layer after heat treatment. The results previously reported by our research group for alumina films deposited on silica-containing conversion coatings showed porosity values greater than 10^-3% and several cracks¹³,²⁹. Thus, it was expected that the alumina film deposited on the boehmite/silica conversion coatings produced in this work would present similar characteristics. This assumption was confirmed since ten conditions of the boehmite/silica DOE matrix presented EIS data consistent with the layer scheme shown in Figure 2F. On the other hand, only five conditions used to produce the samples containing silica/boehmite conversion coating resulted in porous systems.

The two series time constants shown in Figure 3A are related to a compact system composed of alumina film + MCC acting as a protective coating (R₂//CPE₂) and the carbon steel substrate (R₁//CPE₁). In Figure 3B, the other time constant (R_def//CPE_def) parallel to the series circuit represents a defective layer containing cracks, pores, and defects observed in some samples²⁸,³⁵,³⁶. In this case, the MCCs produced were not considered protective. In the circuits of Figure 3, R_o represents the ohmic resistance, R₁ is the charge-transfer resistance, R₂ is the resistance of the protective coating, and R_def is the resistance of the defective layer. CPE₁, CPE₂, and CPE_def are the pseudocapacitances (also known as constant-phase elements) of the substrate, the ceramic coating, and the defective layer, respectively. The capacitances C₁ and C₂ were calculated based on CPE₁ and CPE₂ using Equation 3³⁷,³⁸. They are related to the capacitance of the electric double layer and the capacitance of the ceramic coating, respectively. N_i defines the equivalence degree of the constant-phase elements for the capacitive component in this equation. The global capacitance (C_g), considering the capacitances of the ceramic coating and the substrate, was also obtained (Equation 4) to allow a better evaluation of the capacitive effect. The capacitance of the defective layer (C_def) was calculated using Equation 5. The simulation fit was considered adequate for an error value ≤ 5%³⁹.

$C_i=CP{E}_i{}^{\frac{1}{N_i}}\times {\left(\frac{R_o{R}_i}{R_o+R_i}\right)}^{\left(\frac{1}{N_i}-1\right)}$ (3)

$\frac{1}{C_g}={{\displaystyle \sum }}_{i=1}^n\frac{1}{C_i}$ (4)

$C_{def}=CP{E}_{def}{}^{\frac{1}{N_{def}}}\times {\left(\frac{R_o{R}_{def}}{R_o+R_{def}}\right)}^{\left(\frac{1}{N_{def}}-1\right)}$ (5)

Considering the results obtained in Tables 1 and 2, it is possible to observe that both ASB_xS and ABS_xS systems prepared under the DOE matrices conditions led to more protective systems. Higher R_g and R_p values and lower C_g values were obtained in all these tests compared to the values observed for the uncoated carbon steel substrate (R_ct = 0.20 kΩ cm²; R_p= 0.39 kΩ cm²; and C_dl = 6.98 x 10^-3 F cm^-2). It can also be noted that most of these values were also superior to the R_ct and C_dl values of the ASB600 (R_ct = 12.09 kΩ cm² and C_dl = 1.17 x 10^-4 F cm^-2) and ABS500 (R_ct = 3.05 kΩ cm² and C_dl = 5.32 x 10^-4 F cm^-2) samples¹³. These coating systems were produced using 600 ^oC and 500 ^oC of heat treatment temperature, respectively, and the same univariate conditions (t = 60 s, v = 100 mm min^-1, HT = 120 min)¹³. The highest improvement was verified for the ABS500 system, as all the anti-corrosive parameters found in that previous work were enhanced in the present study. However, the complete evaluation of the effects of the deposition parameters on the R_g and R_p values will be presented in the next section.

3.2. Statistical evaluation

The results shown in Tables 1 and 2 were used to evaluate statistically the effects of the deposition parameters studied (t, v, and HT) on the response variables R_g and R_p, obtained from the electrochemical analyses of the ASB_xS and ABS_xS systems, and the thickness of the silica/boehmite (SB_xS_thickness) and boehmite/silica (BS_xS_thickness) conversion coatings. The Pareto diagrams (Figures 4 and 5) and Equations 6 to 11 describe the quadratic models obtained for the relationships between response variables and factors showing statistical significance. The models were fitted for each system, and the R² values were 0.897, 0.877, and 0.903 for R_g, R_p, and SB_xS_thickness for the ASB_xS system, which means that the models explain about 90%, 88%, and 90% of the results, respectively. Similarly, for the ABS_xS system, R² values of 0.924, 0.893, and 0.730 for R_g, R_p, and BS_xS_thickness were obtained, meaning that the models explain approximately 92%, 89%, and 73% of the results, respectively.

Figure 4
Pareto diagrams of the effects of the studied silica/boehmite deposition parameters on the response variables (A) R_g; (B) R_p, and (C) SB_xS_thickness.

Figure 5
Pareto diagrams of the effects of the studied boehmite/silica deposition parameters on the response variables (A) R_g; (B) R_p, and (C) BS_xS_thickness.

$\begin{array}{l}{R}_g\left(k\Omega c{m}^2\right)=19.15+2.35t+13.19v-7.68HT+\\ 3.74v^2+5.95H{T}^2-9.40tv+3.83tHT-5.21vHT\end{array}$ (6)

$\begin{array}{l}{R}_p\left(k\Omega c{m}^2\right)=18.59+2.06t+12.03v-7.39HT+\\ 2.42v^2+5.93H{T}^2-8.31tv+4.11tHT-4.90vHT\end{array}$ (7)

$S{B}_x{S}_{thickness}\left(\mu m\right)=2.124+0.153t+0.255v+0.139v^2$ (8)

$\begin{array}{l}{R}_g\left(k\Omega c{m}^2\right)=14.08+0.33t+0.40v-1.55HT-\\ 0.44t^2-2.66v^2+0.68H{T}^2+0.60tv+0.55tHT-0.55vHT\end{array}$ (9)

$\begin{array}{l}{R}_p\left(k\Omega c{m}^2\right)=12.81+0.64t+0.55v-1.15HT-\\ 0.50t^2-1.80v^2+1.34H{T}^2+0.44tv\end{array}$ (10)

$\begin{array}{l}B{S}_x{S}_{thickness}\left(\mu m\right)=1.983+0.027t+0.17v-\\ 0.20HT+0.051t^2+0.16v^2+0.11H{T}^2\end{array}$ (11)

For the ASB_xS system (Figure 4), the most significant influence on all the response variables studied was the positive v linear effect (p < 0.0008, p < 0.001, and p < 0.0005, for R_g, R_p, and SB_xS_thickness, respectively). Concerning the electrochemical properties, the second most statistically significant effect was the linear and negative HT effect (p < 0.003 for both R_g and R_p), as shown in Figures 4A and 4B, while for the SB_xS_thickness (Figure 4C), the linear and positive t effect was the second most significant factor (p < 0.008). The deposition time (t) also exhibited a linear and positive effect on the R_g and R_p, although it was the factor with the smallest statistical significance (p < 0.025 for R_g and p < 0.033 for R_p), as shown in Figures 4A and 4B. Except for v (p < 0.019), Figure 4C shows that none of the deposition parameters studied showed a quadratic effect with statistical significance on SB_xS_thickness, as well as their interactions (p > 0.05). Positive and quadratic v effects were also observed on Rg and Rp with statistical significance (p < 0.013 for R_g and p < 0.029 for R_p).

Although the linear effect of v was not the most significant among those affecting R_g, R_p, and BS_xS_thickness for the ABS_xS system, it also presented positive statistical significance on the anti-corrosive properties (p < 0.002 for R_g and p < 0.007 for R_p) and the BS_xS_thickness (p < 0.0005). Nonetheless, the linear and quadratic effects of all the deposition parameters studied, including their interactions, presented statistical significance on R_g (Figure 5A). The quadratic effect of v (p <0.00004 for R_g and p < 0.0008 for R_p) and the linear effect of HT (p < 0.0001 for R_g and p < 0.002 for R_p), were all negative. The positive quadratic effect of HT (p < 0.0007 for R_g and p < 0.002 for R_p) was the most significant for the anti-corrosive properties. t also showed a positive linear effect (p < 0.002 for R_g and p < 0.005 for R_p) with statistical significance on R_g and R_p, although it was not the most significant effect (Figures 5A and 5B). On R_g, statistical significance was observed for v x HT with a negative effect, while t x v and t x HT presented positive effects (p < 0.001 for the three interactions). Only the interaction t x v presented a significant positive effect (p < 0.019) on R_p.

Considering the negative linear HT effect and the positive linear v effect on R_g and R_p for both ASB_xS and ABS_xS systems, this result indicates that the most protective systems would be obtained by increasing the removal speed and decreasing the heat treatment time. This response completely diverges from what has been observed in the systems containing boehmite single conversion coatings²⁸, where the linear effect of v was negative, and that of HT was positive on R_g and R_p. The present result may be related precisely to the complexity of the MCCs produced in these systems. It must be remembered that the MCCs already have a thicker xerogel film (one layer of boehmite over another of TEOS, or vice versa) than those containing single boehmite conversion coatings. The thickness values of the SB_xS and BS_xS conversion coatings presented in Tables 1 and 2, respectively (average values: 2.346 ± 0.328 μm for SB_xS and 2.245 ± 0.332 μm for BS_xS), are greater than those obtained for the single boehmite conversion coatings (average value: 1.534 ± 0.0830μm)²⁸. Thus, increasing the heat treatment time could lead to the collapse of pores and the formation of defects¹³, causing a decrease in the anti-corrosive performance of the systems. Therefore, the negative linear effect observed for HT on R_g and R_p can be justified.

The linear and positive v effect on the anti-corrosive properties (R_g and R_p) for samples containing silica/boehmite conversion coating may be mainly related to the deposition of a boehmite xerogel film over a TEOS xerogel film. The Landau-Levich-Derjaguin equation (Equation 12)⁴⁰ relates the thickness of the xerogel films produced by dip coating (h) with the substrate removal speed (v), viscosity (σ), surface tension (γ_LV), density(ρ) of the sol, and the gravity acceleration (g), for low viscosity sols (0.1 Pa s) and removal speeds up to 300 mm min^-1. Knowing that the boehmite solution has low viscosity (8.97 x 10^-4 Pa s)²¹ compared to the maximum value predicted by this theory, it has almost no influence on the thickness of the silica/boehmite xerogel film. Thus, a very high removal speed is required to form a boehmite xerogel film with sufficient thickness to cover the typical flaws in the TEOS xerogel film¹³,²⁹,³⁴. Additionally, this result suggests that the boehmite xerogel film formation stage affected the barrier properties of the MCCs more intensively than that of the TEOS xerogel film formation.

$h=\mathrm{0,94}\frac{{\left(\sigma \cdot v\right)}^{\frac{2}{3}}}{{\gamma }_{LV}{}^{\frac{1}{6}}{\left(\rho \cdot g\right)}^{\frac{1}{2}}}$ (12)

The same linear and positive v effect was observed on the electrochemical properties of samples containing boehmite/silica conversion coating. However, this effect may be related to the low-volatile solvent (water) used to prepare the boehmite xerogel film in this work and the difficulty of drying this xerogel completely at room temperature in the 2 min between the substrate immersion in the boehmite solution and the TEOS sol (Figure 1). During the subsequent TEOS xerogel film deposition on the still wet surface covered with the boehmite film, it is likely that part of this film be removed. This phenomenon was already reported by Karimi Sahnesarayi et al.²⁴ when producing titania coating with more than one deposition cycle. If v is low, the boehmite xerogel film will be thin, and it may be partially removed while still wet during the deposition of the TEOS xerogel film. At higher v values, however, the boehmite xerogel film deposited on the carbon steel surface will have a considerable thickness, and the partial removal of the xerogel could not affect this thickness significantly. Additionally, the deposition of the TEOS film using high v values will enable the deposition of thick TEOS films, which may compensate for removing part of the boehmite film volume, making the thickness of the boehmite/TEOS film suitable. Thus, after the heat treatment, the boehmite/silica conversion coating will be adequate to improve the corrosion barrier effect of these systems.

Some points must be considered regarding the positive and linear t effect on the electrochemical responses obtained for ASBxS and ABSxS systems. It is known that using long deposition times (t), the reactions between the components of the boehmite solution and the TEOS sol with the predominant elements of the substrate and between the boehmite and TEOS xerogel films may occur for a more extended period¹⁶,⁴¹-⁴³. In this way, the subsequently deposited alumina film can be more stable and adherent¹³,²⁹,⁴⁴,⁴⁵, leading to more protective coating systems. This result corroborates what is generally reported in the literature for sol-gel coatings²³,⁴⁶-⁴⁸ and agrees with what has been observed for the boehmite conversion coating²⁸. The present results also suggest the greater importance of the boehmite xerogel film formation stage compared to that of the TEOS xerogel film. It has already been reported that the deposition time does not influence the thickness of silane xerogel films due to the saturation of the interactions between the silanol groups and the metal surface, achieved at low deposition times³⁴,⁴⁹.

As already mentioned, the parameter with the most significant influence with statistical significance on SB_xS_thickness was v, with a linear and positive effect (Figure 4C), corroborating the results for the thickness of single conversion boehmite coatings²⁸. Nonetheless, the quadratic and positive effect of v on SB_xS_thickness indicates that extremely high v values may lead to thicker films, which could favor the presence of defects after the heat treatment²¹,²⁸,⁵⁰. It could lead to a decrease in R_g and R_p values. Therefore, although the linear and positive effect of v was the most statistically significant and positive effect for the anti-corrosive properties, it is important that the applied speed was not extremely high to avoid the formation of defective conversion coatings.

Regarding the thickness of the boehmite/silica conversion coating (BS_xS_thickness), shown in Figure 5C, all parameters presented linear and quadratic effects with statistical significance. However, the interactions among the deposition parameters (v x HT, t x v, and t x HT) did not present statistical significance on this variable (p > 0,05). The linear and positive effect observed for both t and v on BS_xS_thickness (p < 0.017 for t and p < 0.0005 for v) corroborated univariate studies that reported that increasing t and v improved the production of thick coatings by dip coating⁴⁷,⁴⁸. Furthermore, HT showed a negative linear effect with statistical significance (p < 0.0003), probably due to the contraction caused by the heat treatment in the coating, promoting its compaction²²,⁴⁸,⁵¹.

The positive linear effect of t on BS_xS_thickness can also be related to the impact of this parameter on the thickness of boehmite conversion coatings²⁸, which was the first deposited layer in this case, since t does not influence the thickness of conversion coatings produced from TEOS sols³⁴,⁴⁹. Different from the works of Franquet et al.⁴⁹ and Van Ooij et al.³⁴, in the boehmite/silica samples, the TEOS xerogel film was deposited on the boehmite xerogel film. It means that the hydroxyls of the silanol groups of the TEOS sol and those of the boehmite xerogel film may have interacted more intensively and for a longer time than would occur with the carbon steel surface, contributing to the response that increasing t led to the increase in BS_xS_thickness.

All interactions between the deposition parameters significantly influenced the anti-corrosive properties of the ASB_xS systems. Equations 6 and 7 show that both t x v and v x HT interactions had negative effects on R_g (p < 0.003 for t x v and p < 0.009 for v x HT) and R_p (p < 0.004 for t x v and p < 0.010 for v x HT), indicating that the variation of these parameters in opposite directions would lead to an increase in the response variables⁵². Since the increase in v increases the SB_xS_thickness due to an increase in the thickness of the xerogel film (Equation 12), it is necessary to decrease HT to avoid defects and failure formation during the heat treatment stage that would lead to a decrease in the anti-corrosive performance of ASB_xS systems.

Analogously, the negative t x v interaction can be explained, considering that higher values of R_g and R_p are obtained when high v and low t values are used simultaneously. Therefore, the simultaneous increase in v and decrease in t could improve the TEOS/boehmite xerogel film thickness to ensure an adequate xerogel film thickness that, after heat treatment, would not lead to an MCC presenting flaws and defects. On the contrary, this simultaneous effect (Figure 4C) would favor the subsequent deposition of alumina film and, consequently, the anti-corrosive performance of the system.

On the other hand, the t x HT interaction influence on R_g and R_p of the ASB_xS systems showed a positive effect, as shown in Figures 4A and 4B (p < 0.017 for R_g and p < 0.015 for R_p). These figures also show that the HT effect is almost 8 times and 11 times higher than those of t for R_g and R_p, respectively. Therefore, high R_g and R_p values could be obtained at low HT values, almost independent of t, likely ranging from intermediate to lower t values. Thus, at low deposition and heat treatment times (t and HT), the xerogel film formed by the superposition of TEOS and boehmite xerogel films may present fewer defects after the heat treatment step²⁸,⁵³, since it is a naturally thick multilayer conversion coating due to the double deposition cycle.

The t x HT interaction showed a significant positive effect only on the R_g (p < 0.001) of the ABS_xS systems (Figure 5A). However, the linear and negative effect of HT is much greater than that observed for the t x HT interaction. Therefore, high R_g values were also observed at low HT values and mainly low t values, as already shown for the ASB_xS systems. Although the v x HT interaction exhibited a negative effect (p < 0.001), as shown in Figure 5A, the negative influence of the quadratic v effect, which presented the highest statistical significance among all the parameters studied for this variable, may lead to the highest R_g values, observed at intermediate v values and low HT values. This result suggests that there must be an optimum v value that produces boehmite/TEOS xerogel films with an adequate thickness. After overcoming heat treatment for a short period, this MCC would favor the production of protective boehmite/silica conversion coatings, leading to systems with high R_g values.

The t x v interaction showed a positive effect with statistical significance for both R_g and R_p (p < 0.001 for R_g and p < 0.019 for R_p), as shown in Figures 5A and 5B. This result indicates that an increase in the response variables can be obtained with the simultaneous increase in the parameters⁵⁴. However, the quadratic and negative effect of v for both response variables will likely distort the mathematical responses for R_g and R_p, forming a parabolic profile. Then, an intermediate v value should be used to favor systems with high values of R_g and R_p. Although the quadratic effects of t (p < 0.002 for R_g and p < 0.011 for R_p) may also contribute to the parabolic profile, the linear and positive effect of t for R_p suggests that if higher values of t are used, coatings with improved anti-corrosive characteristics will be obtained. The cause for this result would probably be the higher interaction between the TEOS and boehmite xerogel films. In this scenario, it is possible to observe that the most protective systems may be obtained at average values of v and t.

3.3. Desirability and predicted values

The desirability function gathered the electrochemical responses (R_g and R_p) in a weighted manner and provided a unique solution for optimizing the deposition conditions of the silica/boehmite and boehmite/silica conversion coatings³², which in this case means maximizing the R_g and R_p values. Each response variable ŷ_i(x) was converted to an individual desirability function d_i(ŷ_i(x)), which is a dimensionless measure between 0 and 1, given by Equation 13. For desirable responses, d_i(ŷ_i) = 1; for undesirable responses, d_i(ŷ_i) = 0.

${\text{d}}_{\text{i}}\left({\widehat{y}}_{\text{i}}\left(\text{x}\right)\right)=\left[\begin{array}{cc}0& {\widehat{y}}_{\text{i}}\left(\text{x}\right)<{\text{L}}_{\text{i}}\\ {\left(\frac{{\widehat{y}}_{\text{i}}\left(\text{x}\right)-{\text{L}}_{\text{i}}}{{\text{U}}_{\text{i}}-{\text{L}}_{\text{i}}}\right)}^s& {\text{if L}}_{\text{i}}\le {\widehat{y}}_{\text{i}}\left(\text{x}\right)\le {\text{U}}_{\text{i}}\\ 1& {\widehat{y}}_{\text{i}}\left(\text{x}\right)>{\text{U}}_{\text{i}}\end{array}\right]$ (13)

In this equation, L_i and U_i are, respectively, the lower and upper values within the limit of the mathematical model obtained, while s is a parameter that expresses how important it is for ŷ_i(x) to be close to the maximum (s = 1, to maximize R_g and R_p)⁵⁴. The L_i and U_i values for R_g and R_p of the ASB_xS and ABS_xS systems are shown in Table 3, as well as the predicted values for R_g and R_p of these systems when the SB_xS and BS_xS conversion coatings are produced under the optimized conditions. Based on the individual desirability results, it was possible to determine the global desirability D = 1 using Equation 14, where r_i is the importance of each variable relative to the others, which can range from 1 (the least important) to 5 (the most important)⁵⁵. In this study, both variables were considered equally important since it was desired to maximize both properties. Thus, the r_i used for R_g and R_p was 5.

Table 3
Desirability function settings for each response variable for ASB_xS and ABS_xS systems.

Desirability function settings	ASBxS		ABSxS
	Rg (kΩ cm2)	Rp (kΩ cm2)	Rg (kΩ cm2)	Rp (kΩ cm2)
Li	2.17	1.94	5.29	5.56
Ui	73.2	69.9	17.3	17.5
Predicted values	83.1	74.7	18.1	18.4
Optimal deposition parameters	Codified	Real	Codified	Real
t	-0.841	116 s	+0.841	284 s
v	1.682	368 mm min-1	+0.841	284 mmmin-1
HT	-0.841	70 min	-1.682	19 min

$\text{D}={\left(d_1^{r_1}x{d}_2^{r_2}x\dots x{d}_n^{r_n}\right)}^{\frac{1}{\sum r_i}}={\left({\displaystyle \prod }_{i=1}^n{d}_i^{r_i}\right)}^{\frac{1}{\sum r_i}}$ (14)

Figures 6A and 7A show the curves of the individual desirability of each response and the global desirability for the ASB_xS and ABS_xS systems, respectively. The codified and real values for each parameter studied to obtain the global desirability and the optimal R_g and R_p values for both systems are shown in Table 3.

Figure 6
(A) Individual desirability curves and global desirability determination; global desirability response surfaces for interaction (B) t x v; (C) t x HT; and (D) v x HT for the ASB_xS systems.

Figure 7
(A) Individual desirability curves and global desirability determination; global desirability response surfaces for interaction (B) t x v; (C) t x HT; and (D) v x HT for the ABS_xS systems.

From this moment on, ASB_DS and ABS_DS systems will refer to the samples produced by applying the deposition parameters determined by the desirability function (in these cases, x = D). The electrochemical properties (R_g and R_p values) predicted for the ASB_DS system were more than three times higher than those predicted for the ABS_DS sample. According to the optimization, the SB_DS conversion coating used in the ASB_DS system should be produced using deposition and heating times below the average and with the highest substrate removal rate. On the other hand, in the ABS_DS system, the conversion coating should be produced using deposition time and substrate removal rate above the average value and minimum heat treatment time (in the studied domain).

The desirability surfaces, shown in Figures 6B, 6C, and 6D (ASB_xS) and Figures 7B, 7C, and 7D (ABS_xS) show how the sequence of the formation of boehmite and TEOS xerogel films influenced the optimum conditions for depositing the conversion coatings. To obtain the best anti-corrosive performances after covering with alumina film, the studied multilayer systems must be produced by applying completely different t, v, and HT.

3.4. Characterization of samples produced under selected conditions

Based on the results found in the experimental design and the desirability studies, the ASB_DS and ABS_DS samples (whose conversion coatings were produced under optimal conditions and coated with an alumina film to obtain the best anticorrosive properties in a 3.5% w/v NaCl solution) were selected to be characterized to confirm the hypotheses proposed in the discussion. For comparison, the ASB₅S and ABS₁₁S samples (which presented the lowest R_g and R_p values among those produced according to the design matrices presented in Tables 1 and 2, respectively) were also evaluated using the same techniques.

The micrographs in Figures 8A and 8B show the surfaces of SB_DS and SB₅S conversion coatings (without alumina film). In both images, it is possible to observe the formation of sharp structures typical of boehmite conversion coating²⁹,⁴⁵ on a smoother surface.

Figure 8
SEM images of (A) SB_DS; (B) SB₅S; (D) BS_DS, and (E) BS₁₁S conversion coatings; XRD patterns of (C) silica/boehmite and (F) boehmite/silica conversion coatings on carbon steel produced under the selected conditions.

The most apparent difference between these surfaces was the area covered by the sharp structures. As previously mentioned, the linear and positive effect of v on R_g, R_p, and SB_xS_thickness (Figure 4) was related to the deposition step of the boehmite xerogel film covering the TEOS xerogel film. These micrographs confirmed this hypothesis since the surface area covered by sharp structures in the SB_DS conversion coating (produced using v = 368 mm min^-1) is higher than in the SB₅S conversion coating (deposited with v = 100 mm min^-1). The higher removal speed used during the deposition of the SB_DS conversion coating allowed the formation of a more uniform surface (Figure 8A) with fewer poorly covered regions compared to the SB₅S surface (Figure 8B). Thus, the deposition of the alumina film on the SB_DS surface should be more successful than on the SB₅S surface, making the expected anti-corrosive performance for ASB_DS superior to that obtained for ASB₅S.

As t showed a small positive linear effect on R_g and R_p (Figures 4A and 4B), the values used for SB_DS and SB₅S were close (116 s for SB_DS and 100 s for SB₅S). Therefore, it is likely that this deposition parameter did not influence the morphologies shown in Figures 8A and 8B. On the other hand, the linear and negative effect of HT on R_g and R_p of the ASB_xS samples (Figures 4A and 4B) may also have contributed to the lower defect density observed in SB_DS compared to SB₅S since SB_DS was heat-treated for 70 min while SB₅S had a heat treatment time of 180 min, both at 600 °C. Nonetheless, there was no significant variation related to the thickness of the xerogel films: h (SB₅S) = 2.597 ± 0.184 μm and h (SB_DS) = 2.412 ± 0.251 μm.

Sharp structures were still present on the surface of the best SB coating produced using univariate conditions (SB600)¹³. This sample was prepared using the same v value used in the SB₅S sample (100 mm min^-1), although using smaller t and HT values (60 s and 120 min, respectively). It showed a homogeneous and smooth morphology in which silica and aluminum oxides seem to be mixed, although several pores can be observed on its surface. It is known that a conversion coating with more defined structures increases its roughness and promotes the adhesion of the films further deposited onto its surface²⁸,²⁹. Therefore, a smooth surface like that observed for the SB600 sample can hinder the alumina film attachment and decrease the anti-corrosive performance of the coating system. Comparing the present surface results obtained for the SB_DS with those obtained for SB600¹³, the surface improvement in the sample produced using the optimized conditions can be clearly noted.

Figures 8D and 8E show the micrographs of the BS_DS and BS₁₁S samples, respectively, and it is possible to observe that an upper smooth layer covers the sharp structures below. This feature has already been reported in the literature for this type of coating¹³. While the BS_DS surface does not present any apparent cracks, a crack of approximately 1 μm wide can be observed in the BS₁₁S sample. Similar cracks were observed throughout this sample and resulted from the longer heat treatment time applied in the BS₁₁S production (HT = 120 min) compared to that used to prepare the BS_DS sample (HT = 19 min). Therefore, the linear and negative effect of HT observed for R_g, R_p, and BS_xS_thickness (Figure 5) directly influenced the differences observed in the morphologies of these samples, which may have likely contributed to the production of a more efficient alumina/MCC system, leading to improved anti-corrosive performance for the ABS_DS sample compared to the ABS₁₁S sample. Also, the thickness of the BS_DS xerogel film (h = 3.124 ± 0.113 μm) was significantly higher than that of BS₁₁S xerogel film (h = 1.986 ± 0.205 μm), confirming the most significant statistical significance effect of this parameter on this response variable.

The higher difference between the thicknesses of the BS_DS and BS₁₁S xerogel films (1.228 μm) compared to that obtained between the SB_DS and SB₅S samples (0.185 μm) can be discussed based on the linear and positive effect of v on the thickness of the boehmite/silica conversion coating, as mentioned in section 3.2. The small thickness of BS₁₁S was expected due to the influence of the low-volatility solvent used in the boehmite xerogel film and the possible partial removal of the still-wet film formed in the first deposition cycle (boehmite xerogel) during the second deposition cycle with TEOS sol. Thus, by using a higher v in the deposition of BS_DS than in the BS₁₁S deposition (284 mm min^-1 for BS_DS and 32 mm min^-1 for BS₁₁S), a higher thickness was initially obtained, and a thicker TEOS film was also deposited under this condition. Therefore, the possible removal of the boehmite film portion was likely compensated²⁴.

Although the linear effect of t positively affected the three response variables (Rg, Rp, and BSxS_thickness), the deposition times used to produce the two conversion coatings were close (284 s for BS_DS and 200 s for BS₁₁S). Therefore, as previously discussed for the ASB_DS and ASB₅S samples, this parameter was not highly significant on the morphology of the BS_DS and the BS₁₁S surfaces.

The best BS sample produced using univariate conditions (BS500)¹³ presented a cracked surface where the boehmite microstructure could be observed inside. This surface characteristic is similar to that verified for the BS₁₁S sample (Figure 8E), which was produced using the same HT value (120 min). Although a higher v value was used to prepare the BS500 sample (100 mm min^-1), a high density of failures may be detrimental to the subsequent coating with alumina film. Therefore, the surface improvement obtained when the desirability conditions were used to produce the BS conversion coating may favor the barrier property of the alumina/MCC/substrate system exposed to the saline corrosive medium.

Figures 8C and 8F show the XRD patterns of the multilayer conversion coatings produced under optimal conditions and under those presenting the worst anticorrosive performances according to their respective design matrix results. It can be observed that, regardless of the deposition conditions used, peaks related to the presence of Fe from the carbon steel substrate were observed at 2θ = 44.673°, 65.021°, and 82.333° (PDF #06-0696). Peaks related to iron oxides are also present at 2θ = 35.640° (PDF #30-1088) and 36.820 (PDF #26-1136) for Fe₂O₃; and at 2θ = 30.095°, 56.942°, and 62.335° (PDF #19-0629), for Fe₃O₄. Diffraction lines related to aluminum oxyhydroxide and oxide (2θ = 33.152° (PDF #47-1308), 35.150° (PDF #43-1484), 36.899° (PDF #05-0355), and 56.705° (PDF #47-1292)) and to silica (2θ = 23.930° (PDF #33-0664), 29.855° (PDF#48-0476), 33.127° (PDF #47-1300), 42.401° (PDF #38-0360), 49.211° (PDF #34-0717), 53.327°, 53.874° (PDF #45-0131), and 62.073° (PDF #46-1242)) were all observed for both samples. Thus, despite the different deposition conditions, no differences in the deposited phases could be noted.

The conversion coatings produced under the conditions determined by the desirability function (SB_DS and BS_DS) presented rougher surfaces when compared to the SB₅S and BS₁₁S surfaces, respectively. The highest roughness was obtained in the SB_DS sample (R_a = 0.269 ± 0.023 μm), followed by the BS_DS sample (R_a = 0.225 ± 0.008 μm). Meanwhile, the average roughnesses of the SB₅S and BS₁₁S samples were, respectively, 0.155 ± 0.030 μm and 0.107 ± 0.012 μm. The greater roughness exhibited by the SB_DS and BS_DS samples can contribute to obtaining alumina/MCC/carbon steel systems with improved anticorrosive performance, as predicted by the desirability function.

Surface roughness is essential for the adhesion of protective coatings to metal substrates and can be achieved by applying conversion coatings⁵⁶. According to the Wenzel model, increased surface roughness improves adhesion forces and wettability⁵⁷. It occurs due to the presence of larger grooves, which lead to better anchoring conditions for the coating⁵⁸. Similar results were found by Tiringer et al.⁵⁹ when depositing a silane conversion coating by sol-gel dip coating on an aluminum substrate for further covering with a polymeric film. The authors associated the best anti-corrosive properties with the converted surfaces showing enhanced roughness. Thus, it can be inferred that the deposition conditions (t, v, and HT) used to produce the conversion coatings influenced the roughness of the surfaces to be covered with alumina film and, consequently, may affect the corrosion protection of the alumina film/MCC/carbon steel substrate systems in a saline environment.

Figure 9 shows the SEM-EDS of the cross-section of the selected MCC samples after covering them with alumina film. The results of the samples containing silica/boehmite and boehmite/silica conversion coating produced under the optimal deposition conditions are presented in Figures 9A and 9C, respectively. In both cases, it is possible to observe a delineated and less defective coating system. On the other hand, the MCC samples produced under the conditions in which, after coating with alumina film, the worst electrochemical performances were obtained –and ASB₅S ABS₁₁S (Figures 9B and 9D, respectively) – exhibited failed and porous surfaces, similar to those verified for the MCCs in the previous univariate study¹³. In fact, the ASB₅S sample presented more defects than the ASB600 sample, indicating that the deposition conditions chosen may also decrease the quality of the coating system. These results confirm the use of the equivalent electrical circuit of Figure 3A for the ASB_DS and ABS_DS samples and Figure 3B for the ASB₅S and ABS₁₁S samples. It also confirmed that the MCC thickness was unaffected for the ASB_DS and ASB₅S samples (Figures 9A and 9B), even with the increase in v. On the other hand, thicker coatings were obtained for ABS_DS compared to ABS₁₁S (Figures 9C and 9D), probably due to the increase in v and t and decrease in HT. Additionally, the EDS analyses confirmed that multilayer conversion coatings were produced and that mixed iron, aluminum, and silicon oxides were produced under the conditions used.

Figure 9
SEM-EDS cross-section images of the selected conversion coatings covered with alumina film: (A) ASB_DS, (B) ASB₅S, (C) ABS_DS, and (D) ABS₁₁S samples.

The conversion coatings produced under the selected conditions and coated with alumina film were analyzed by EIS tests over 240 h of exposure to 3.5% w/v NaCl solution. The analyses were performed after 0 h, 24 h, 120 h, and 240 h of contact with the corrosive medium. The Nyquist diagrams of all these tests are found in the Supplementary Material (Figure S1). The EIS data were simulated using the circuits in Figure 3, and the complete data are available in Table S3. Figure 10 shows the variation of R_g, C_g, R_p, and OCP of these samples over the studied time.

Figure 10
(A, E) R_g, (B, F) C_g, (C, G) R_p, and (D, H) OCP variation of the selected samples containing silica/boehmite and boehmite/silica conversion coatings, over 240 h of exposure to the 3.5% w/v NaCl solution; SEM images of the surface after 240 h of exposure to the corrosive medium of the (I) ASB_DS, (J) ASB₅S, (K) ABS_DS, and (L) ABS₁₁S samples.

Figure 10A shows the variation of R_g over 240 h of exposure to the corrosive medium for samples ASB_DS and ASB₅S. The ASB_DS sample presented the best anticorrosive performance (initial R_g = 81.6 kΩ cm²) and stability over the time studied in the corrosive environment (R_g reduction of 28%). Comparing the R_g value found experimentally for ASB_DS with that mathematically predicted by the desirability function (83.1 kΩ cm²), it is noted that the anti-corrosive performance obtained experimentally showed a slight difference from the value predicted statistically (difference of 4.81%). The morphology of the SB_DS sample (Figure 8A) shows a layer with sharp structures with a few uncovered regions, which may have contributed to the better R_g value and higher stability. In addition, the high roughness of the SB_DS surface was also a factor that may have promoted enhanced adhesion between the alumina film and the converted surface, impacting the stability of the coating in the corrosive environment compared to the other samples studied. This kind of surface morphology is similar to that found for the single boehmite conversion coating produced under optimal conditions²⁸, which, after coating with alumina film, presented an R_g reduction of only 4.27% after 240 h in contact with the saline medium.

The differences in the initial R_g values and the stability of the ASB_DS and ASB₅S samples may be related to the characteristics of their respective conversion coatings. More uncovered regions with a sharp-structured layer can be noted in the SB₅S surface (Figure 8B), although its morphology was like that of the SB_DS sample (Figure 8A). The less uniform distribution of these structures, typically associated with the boehmite coating⁴⁵, on the SB₅S surface may also justify the lower roughness found for this conversion coating (R_a = 0.155 ± 0.030 μm). These pointed structures are generally responsible for the enhanced anchoring points¹³,²⁹. Consequently, this result may explain the worse anti-corrosive performance presented by the ASB₅S system compared to the ASB_DS sample. The apparent lack of adherence and the porosity observed in the coating shown in Figure 9C may confirm this result. The ASB₅S sample presented an initial R_g value equal to 2.17 kΩ cm², which is approximately 79 kΩ cm² lower than the value obtained for ASB_DS at the same time. After 240 h exposed to the corrosive environment, the sample presented a reduction of 38% in its R_g value.

Compared to the R_g values of the ASB_DS system (Figure 10A), the ABS_DS sample (Figure 10E) exhibited an inferior performance, which may be explained by the presence of defects in the cross-section image of Figure 9C. An initial R_g of 22.2 kΩ cm² was obtained experimentally, which is 4.1 kΩ cm² higher than the value predicted by the desirability function (approximately 19% difference). Also, its stability over 240 h in contact with the corrosive medium was lower than that of the ABS₁₁S sample, with a reduction in R_g of 65%. Although the ABS₁₁S sample presented a small initial R_g value (5.29 kΩ cm²), after exposure to the corrosive medium for 240 h, this value decreased by only 44%. The uniform morphology and the presence of a blister-like lumps surface exhibited by the BS_DS sample (Figure 8D) may have led to its higher roughness (R_a = 0.225 ± 0.008 μm), contributing to a more efficient coating with alumina film and a higher R_g value compared to the system produced with the BS₁₁S conversion coating. However, the absence of sharp structures in the outer layer may have impacted the final system formed due to the smaller number of anchoring points and lower chemical interaction with the alumina film, leading to a higher decrease in the stability of the ABS_DS system over time. It is important to mention that the R_g value of the ABS_DS sample was still higher than that of the ABS₁₁S system after 240 h of exposure to the saline environment (7.77 kΩ cm² and 2.96 kΩ cm², respectively).

Regarding the C_g variation (Figure 10B) for both ASB_DS and ASB₅S systems, the value of this variable after 240 h in contact with the corrosive medium was approximately 10 times greater than the initial value. However, throughout the study, the C_g value of the ASB_DS sample was one order of magnitude lower than that of the ASB₅S sample, indicating a lower tendency to corrosion⁶⁰. When the ABS_DS and ABS₁₁S samples are compared (Figure 10F), it is noted that the ABS₁₁S presented the highest C_g variation among all the samples, with an increase of 20 times after the studied period. However, the ABS_DS sample presented an interesting behavior: its C_g value decreased by approximately 45% after 240 h of testing. This behavior suggests that the electrolyte absorption decreased during the experiment time, probably due to the formation of inert oxides in the regions of the coating presenting defects⁴⁵.

The same R_g variation trend was observed for the R_p of the MCCs-containing samples (Figures 10C and 10G). The initial R_p value for ASB_DS was 75.8 kΩ cm², which was 1.1 kΩ cm² higher than the value predicted by optimization. The difference between the initial R_p of ASB_DS and ASB₅S was approximately 73.9 kΩ cm², confirming that the optimal conditions contributed to the production of a superior anti-corrosive coating system when compared to the conditions of Run no. 5 of the DOE (Table 1). Throughout the 240 h of exposure to the corrosive environment, the stability of ASB_DS was confirmed (Figure 10C) since the R_p reduction was 24% (and 28% for R_g). Similar behavior was presented by the ASB₅S sample, which had an Rp reduction of 36% and an R_g reduction of 38% (Figure 10A).

The difference between the R_p value obtained experimentally for ABS_DS and the value predicted mathematically in the optimization was positive, 6.5 kΩ cm², which means that the anti-corrosive performance promoted by the application of the optimal deposition conditions of the boehmite/silica conversion coating was even better than that predicted by the desirability function. Nonetheless, the R_p trends for the ABS_DS and ABS₁₁S samples (Figure 10G) are also similar to that verified for R_g (Figure 10E). The ABS₁₁S sample showed a smaller R_p initial value (5.56 kΩ cm²) than the ABS_DS sample (24.9 kΩ cm²), although presenting higher stability after 240 h in the corrosive medium (51% and 71% reduction, for ABS₁₁S and ABS_DS samples, respectively).

Another way to verify the stability of these systems is performing daily monitoring of their OCP values over 240 h of exposure to the corrosive medium. In general, the more positive the OCP of an electrode in operation, the lower the tendency for participation in electrochemical corrosion reactions⁶¹. The initial OCP value of the ASB₅S sample was 0.113 V, which was more negative than that of the ASB_DS one. The results shown in Figure 10D indicate that the main change in OCP occurred in the first 24 h for both samples, with a decrease of approximately 18% for the ASB_DS sample and 17% for the ASB₅S sample. From 24 h until the end of the study, the OCP variation for the ASB_DS sample was only 6% to more negative values direction, indicating that the system's stability in the corrosive medium was achieved. The ASB₅S sample showed a constant OCP value between 24 and 72 h and a slight variation to more negative potentials until the end of the study (6% reduction in OCP between 72 h and 240 h).

On the other hand, the ABS_DS sample showed a higher OCP variation to more negative potential values than ASB_DS, resulting in a 79% reduction in its initial OCP value (Figure 10H). Also, although presenting an initial OCP value more positive than that measured for the ABS₁₁S sample, the final OCP of the ABS_DS and ABS₁₁S samples were close (difference of 10 mV), confirming that the ABS_DS system presented less stability when compared to the ABS₁₁S one. A variation of approximately 14% of the initial OCP after 24 h of exposure to the corrosive medium was observed for the ABS₁₁S sample, followed by a less intense reduction until 216 h (approximately 8.5%) and an intense OCP variation to more negative values (reduction of 13%) in the last 24 h.

SEM analysis was performed on the surfaces of these systems after 240 h of exposure to the corrosive medium. Figures 10I and 10J show that, although more typical corrosion product structures are present on these surfaces than those verified for the systems containing single boehmite conversion coating²⁸, the ASB_DS and ASB₅S samples did not present many cracks due to corrosion after 240 h in contact with the corrosive medium. Nonetheless, some pores can be noted on the ASB₅S surface, which is not observed on the ASB_DS sample surface. On the other hand, both ABS_DS and ABS₁₁S samples (Figures 10K and 10L) presented pores, defects, and corrosion products on their surfaces. Although the ABS₁₁S sample presented higher stability during the long-term study, its initial anti-corrosive performance was lower than that of ABS_DS, which may explain the higher amount of corrosion products and defects on its surface compared to ABS_DS. Therefore, these images corroborate the electrochemical performance and stability demonstrated by these samples (Figures 10A to 10H).

The cross-section micrographs shown in Figure 9 also help to explain the anti-corrosive behavior presented by these samples. The optimal deposition conditions used to produce the SB_DS and BS_DS conversion coatings were decisive in producing more compact and without-defect coatings and, therefore, presenting improved corrosion resistance and stability over 240 h of exposure to the corrosive environment after coating with an alumina film.

4. Conclusion

The use of statistical tools such as experimental design and desirability function allowed to evaluate how the deposition time (t), speed of substrate removal from the sol/solution (v), and heat treatment time (HT) used in the production of the silica/boehmite and boehmite/silica conversion coatings influenced the corrosion resistance of coating systems containing MCCs and alumina film, and to predict the optimum conditions to produce these systems with improved anti-corrosive performances in a saline medium. The response variables R_g, R_p, and conversion coating thickness were statistically influenced by the deposition parameters (t, v, and HT) used to produce the conversion coatings.

Using the optimized conditions predicted by the desirability function to produce the silica/boehmite (t = 116 s, v = 368 mm min^-1 and HT = 70 min) and boehmite/silica (t = 284 s, v = 284 mm min^-1 and HT = 19 min) multilayer conversion coatings, the systems obtained after covering with alumina film (ASB_DS and ABS_DS) showed improved R_g and R_p values (ASB_DS: R_g = 81.6 kΩ cm² and R_p = 75.8 kΩ cm²; ABS_DS: R_g = 65.0 kΩ cm² and R_p = 71.3 kΩ cm²). Under optimal conditions, the silica/boehmite conversion coating showed a surface morphology with pointed structures, unlike the boehmite/silica conversion coating. As a result, more adherent and no defective coating systems were observed for the ASB_DS sample, leading to more effective corrosion protection than the ABS_DS one. Furthermore, the ASB_DS system exhibited higher stability for long periods in contact with the corrosive medium when compared to the ABS_DS system (ASB_DS: R_g reduction = 28.2% and R_p reduction = 24.4%; ABS_DS: Rg reduction = 65.0% and Rp reduction = 71.3%).

The experimental design proved useful in the multivariate study of the effects of deposition parameters used to prepare conversion coatings on the anticorrosive performance of ASB_xS and ABS_xS multilayer systems produced by sol-gel dip coating. Furthermore, using the desirability function allowed the determination of the optimal conditions to produce coating systems with the highest global and polarization resistance values. Such conditions promoted the formation of a conversion coating surface composed of mixtures of iron oxide, silicon oxides, and aluminum oxide/oxyhydroxide, presenting the necessary roughness to ensure the adhesion of the final alumina film prepared by sol-gel dip coating.

Supplementary material

The following online material is available for this article:

Table S1

Complete results obtained from the simulation of EIS data in NaCl 3.5% w/v solution of samples containing silica/boehmite conversion coatings produced according to experimental design.

Table S2

Complete results obtained from the simulation of EIS data in NaCl 3.5% w/v solution of samples containing boehmite/silica conversion coatings produced according to experimental design.

Table S3

Complete results obtained from the simulation of EIS data of samples containing conversion coatings produced under selected conditions over 240 h of exposure to NaCl 3.5% w/v solution.

Figure S1

Nyquist diagrams of (A) ASB_DS; (B) ASB₅S; (C) ABS_DS and (D) ABS₁₁S over 240 h in 3.5% w/v NaCl solution.

5. Acknowledgments

The authors would like to thank the Rio de Janeiro Research Foundation (FAPERJ), the Brazilian National Research Council (CNPq), the Postgraduation Support Program (PROAP), and the Rio de Janeiro State University (UERJ) for the financial support. This study was financed in part by the "Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES)" – Finance Code 001.

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Publication Dates

• Publication in this collection
  19 May 2025
• Date of issue
  2025

History

• Received
  09 Jan 2025
• Reviewed
  13 Apr 2025
• Accepted
  21 Apr 2025