Surface Selectivities in Wet Chemically Modified PVC Films. Influence

Wet chemical modification reactions of PVC films in solvent/nonsolvent mixtures were performed. Three thiol compounds of different size and reactivity...
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Langmuir 2005, 21, 4425-4430

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Surface Selectivities in Wet Chemically Modified PVC Films. Influence of Reaction Conditions Miguel Herrero, Rodrigo Navarro, Nuria Garcı´a, Carmen Mijangos, and Helmut Reinecke* Instituto de Ciencia y Tecnologı´a de Polı´meros, CSIC, Juan de la Cierva 3, E-28006 Madrid, Spain Received November 17, 2004. In Final Form: February 15, 2005 Wet chemical modification reactions of PVC films in solvent/nonsolvent mixtures were performed. Three thiol compounds of different size and reactivity were used varying the solvent quality, temperature, and reaction times. The evolution of the concentration gradients within the films was studied using confocal Raman spectroscopy and attenuated total reflectance Fourier transform infrared spectroscopy. Surface selectivities were calculated and discussed in terms of the different relative reaction rate constants.

Introduction The surface properties of polymeric materials are important to many of their applications. Sometimes, a desired polymer surface cannot be obtained from the material itself and modification reactions have to be employed. Dependent on the application for which a modification reaction is performed, it can be necessary to create modifier groups which are situated just at the surface or also in the interior of the film. For example, adhesion properties of a surface and also the phenomenon of hydrophobic recovery are determined by functional groups situated in a layer of several micrometer thickness below the surface1 while wettability is influenced mainly by the outermost atomic layer.2 Modification of a polymer surface can be achieved by means of various chemical or physical processes.3-5 Of special interest are wet chemical treatments of films6 because they present a successful method to produce welldefined and reproducible surfaces. A further advantage of wet chemical treatments is the possibility to obtain modifications in a layer from the nanometer range to the micrometer range when the appropriate reaction medium is chosen. PVC is known to have excellent film-forming properties. Certain disadvantages of this material, as for example its sensitivity toward UV irradiation, make it desirable to protect the polymer film selectively at the surface while maintaining the good mechanical properties of the bulk. In previous work it has been shown that PVC films can be modified and functionalized at the surface via nucleophilic substitution of chlorine atoms using mixtures of solvents and nonsolvents for the polymer.7 The solvent tends to expand the chains, facilitating in this way the * Corresponding author: e-mail, [email protected]; tel, 34915622900 ext. 271; fax, 34-915644853. (1) Lee, L. H. Fundamentals of Adhesion; Plenum Press: New York, 1991. (2) Morra, M.; Occhiello, E.; Grabassi, F. J. Colloid Interface Sci. 1989, 504, 132. (3) Clark, D. T.; Feast, W. J. Polymer Surfaces; John Wiley & Sons: Chichester, 1978. (4) Garbassi, F.; Morra, M.; Occhiello, E. Polymer Surfaces; John Wiley & Sons: Chichester, 1994. (5) Chan, C. M. Polymer Surface Modification and Characterization; Hanser Publishers: Munich, 1993. (6) Mittal, K. L.; Lee, K. W. Polymer Surfaces and Interfaces: Characterization Modification and Application,VSP: Utrecht, 1997. (7) Sacrista´n, J.; Mijangos, C.; Reinecke, H. Polymer 2000, 41, 5577.

penetration of the reactant into the polymer chains and the reaction itself. The proportion of solvent to nonsolvent greatly influences the kind and extent of modification which is taking place. Further parameters which control the distribution of the modified groups are the type of the modifier, the reaction time, and temperature. We have also shown that confocal Raman microscopy is an excellent means to analyze chemical structures and gradient compositions in transparent films modified on a microscale8 and that a surface selectivity can be defined in order to describe the distribution of modified groups within the polymer film.8 This parameter determines if a modification reaction modifies homogeneously all the interior of a film or if it is limited to a thin layer at the surface. Knowing how the surface selectivity of a reaction depends on the experimental conditions of the film modification makes it possible to tailor a film according to the application for which it is destined. The aim of the present work is to use depth profiles of films modified under different experimental conditions and study systematically the influence of these parameters on the distribution of the modifier in the film. Of special interest is to understand under which conditions a modification reaction evolves with time toward a homogeneously modified film or toward a film with increasing surface selectivity. Therefore, attenuated total reflectance Fourier transform infrared (FTIR-ATR) spectroscopy and confocal Raman microscopy were used which can be considered complementary techniques. When FTIR-ATR spectroscopy is performed using a diamond as the internal reflection element, a sample depth of 1-2 µm can be analyzed.9 On the other hand, with Raman microscopy in the confocal mode, transparent films of up to 50 µm thickness can be scanned through obtaining profiles with a depth resolution of 1-2 µm. Experimental Part Film Modification. Films have been prepared by casting from THF solutions. They were dried in a vacuum at 40 °C for 1 week prior to use. To allow the film to react on both sides and avoid folding or contact with the reactor wall, PVC films with dimensions 60 mm × 20 mm and a thickness of about 50 µm were clamped in Teflon frames. The frames were immersed in a 0.5 M solution of the (8) Sacrista´n, J.; Mijangos, C.; Spells, S.; Yarwood, J.; Reinecke, H. Macromolecules 2000, 33, 6134. (9) Mirabella, F. M. Appl Spectrosc. Rev. 1985, 21, 45.

10.1021/la047172k CCC: $30.25 © 2005 American Chemical Society Published on Web 04/07/2005

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respective modifier. In order to follow the kinetics of the reaction and obtain films of different degree of modification, samples were taken out from the solution at different time intervals, washed with water, extracted for 24 h in ether, and dried. Materials. Commercial bulk polymerized PVC with a weight average molecular weight of Mw ) 58000 g/mol was obtained from ATOCHEM, Spain. The tacticity measured by 13C NMR was syndio ) 30.6%, hetero ) 49.8%, and iso ) 19.6%. As the nucleophiles for the modification reactions, 4-mercaptophenol, 4-methoxybenzenethiol, and 2-naphthalenethiol were used which had been purchased from Aldrich with purities of 97%, 97%, and 99%, respectively. Confocal Raman Microspectroscopy. Raman spectra were recorded on a Renishaw Ramascope 2000 spectrometer using the 632.8-nm line of a He-Ne laser. This instrument was equipped with a Peltier-cooled charge-coupled device (CCD) detector, a holographic grating (1800 grooves/mm), and a Raman holographic edge filter, which prevented the backscattered laser radiation from entering the spectrograph. The stigmatic single spectrograph was attached to a Leica microscope. The Ramascope was set up in the confocal mode with a 100× short-workinglength objective (numerical aperture (NA) value of 0.95), a slit width of about 15 µm, and a CCD of 576 × 384 pixels (pixel size 22 µm). The long axis (576 pixels) defines the spectral dimension, and the short axis describes the height of the image. The arrangement of the CCD and the slit acted as a synthetic confocal aperture. The depth resolution of the confocal arrangement in air has previously been checked, using a silica sample as a reference material and has been determined as 2.7 µm by the full width at half-maximum criterion.10 A depth profile of a sample was obtained by focusing the microscope stepwise (2 µm steps) through the polymer film and recording a spectrum at each step. For apparent penetration depths of up to 20 µm, accumulation times (t) per spectrum (window from 1200 to 1750 cm-1) were usually t ) 3 min. Greater depths required t ) 5-10 min to obtain an adequate signal-tonoise ratio. When different accumulation times were used for recording the different spectra of a set, scattering intensities were normalized, using the appropriate accumulation time. To correct the obtained depth profiles for the influence of the refractive index of the sample the length scale of the obtained profiles is multiplied by the refractive index of the polymer. ATR Measurements. Spectra were recorded at ambient temperature on a Perkin-Elmer Spectrum One FTIR spectrometer equipped with an internal reflection element of diamond using an accumulation of four runs and the same pressure of the crystal on the surface in each sample. In both, ATR and Raman measurements, absolute degrees of modification of the film surfaces were obtained from the spectra using calibration curves recorded on homogeneously modified samples whose modifier content had previously been determined by NMR spectroscopy.

Results and Discussion In a previous paper7 we have shown that the distribution of modifier groups in wet chemically modified films can be understood supposing that the complete reaction comprises three steps, each of them with its own reaction rate constant: The first step is the swelling of the polymer film by the reaction medium, that is, the diffusion of the solvent into the film (k1), the second step is the transport of the modification agent to the functional groups of the polymer (k2), and the third step is the reaction itself (k3). Generally, swelling of the polymer is the fastest process. In the case of the PVC/DMF-H2O system studied it has been shown that at room temperature complete swelling to equilibrium is achieved between 30 min (DMF/H2O 7:1) and 3 h (DMF/H2O 3:1), which is about an order of magnitude quicker than the reaction times necessary to observe a significant modification between PVC and the modifiers. (10) Tabaksblat, R., Meier, J.; Kip, B. J. Appl. Spectrosc. 1992, 46, 60.

Herrero et al. Chart 1

Whether a modification reaction of a polymer film occurs homogeneously inside the film or whether it can be controlled to take place selectively at the surface depends on the rate constants for steps 2 and 3. If k2 > k3, the modification agent is distributed in the interior of the polymer until the reaction begins and a homogeneously modified film is obtained. On the other hand, if k2 < k3, membrane modification can be stopped until the agent has completely penetrated the film and a gradient of the degree of modification inside the film will be observed. The larger the ratio of k3/k2, the higher the selectivity of the reaction with respect to the surface. In the present study we attempt to confirm this model using different modifier agents of different reactivities (k3) and sizes (-k2). In this work we have studied PVC films which were modified using three aromatic thiol compounds of different substitutents and van der Waals radii. Aromatic thiols are known to react under certain conditions in a very clean way and without the formation of secondary byproducts with this polymer.11-13 The structures of the modifiers used are depicted in Chart 1. Determination of k3 and k2. The rate constant k3 for the reaction between PVC and the studied modifier has been determined for each solvent mixture and temperature recording the kinetic course of the modification at the film surface. Therefore the degree of modification of the surface has been measured as a function of time by FTIRATR (Figure 1a). The degree of modification which is defined as the relative molar amount of PVC units modified is determined using the ratio of the peak intensities at 1590 cm-1 (corresponding to the C-C streching vibration of the aromatic rings of the modifier molecules) and at 1435 cm-1 (corresponding to the C-H deformation of the PVC structure). The evaluation of the data is performed considering a first-order reaction. This supposition is justified, on one hand, because of the large excess of modifier used with respect to the chlorine concentration and, on the other, is demonstrated by the linear relationship obtained in a logarithmic presentation of the chlorine concentration against time for low conversions (Figure 1b). From the slope of the curves the rate constants k3 were calculated for reactions in different experimental conditions. The dependence of k3 on the reaction medium and the modifier used is depicted in Figure 2. It is shown that the rate constant depends strongly on the medium in which the reaction is carried out being the highest k3 values (11) Herrero, M.; Tiemblo, P.; Reyes, J.; Mijangos, C.; Reinecke, H. Polymer 2002, 43, 2631. (12) Reinecke, H.; Mijangos, C. Polym. Bull. 1996, 36, 13. (13) Lo´pez, D.; Mijangos, C.; Reinecke, H. J. Appl. Polym. Sci. 1999, 74, 1178.

Surface Selectivities in PVC Films

Figure 1. (a) Degree of modification at the surface as a function of time as determined by ATR-FTIR spectroscopy for the reaction of PVC with 4-methoxythiophenol at 50 °C in DMF/H2O at 2:1 (9), 3:1 (O), 4:1 (2), 5:1 (3), and 6:1 ([). Lines are guides for the eyes. (b) Corresponding semilogarithmic plot with fits of the linear regions.

Figure 2. Comparison of k3 as a function of the reaction medium for the reaction of PVC films and different modifiers at 50 °C: 4-mercaptophenol (9), 4-methoxythiophenol (2), and 2-thionaphthol (O).

observed in highly swelling solvent mixtures. Considerable differences in the reactivities can also be stated when

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comparing the different thiol compounds used as the modifiers. These differences can easily be explained by the electronic and steric nature of the compounds. The methoxy group for example has a relatively high positive mesomeric effect, which increases the electron density in the aromatic system and the nucleophilicity of the tiolate and therefore exhibits the highest reaction rate. To compare also the different rate constants k2 which describe the diffusion of the modifier to the Cl groups of the polymer, the theory of diffusion-controlled reactions is considered. According to this theory the rate constant k2 is essentially determined by the hydrodynamic radius rh of the modifier existing in a linear relationship between k2 and 1/rh. The hydrodynamic radii of the three compounds are calculated by group contribution.14 Their values are used as relative k2 constants and are summarized in Table 1. To compare the surface selectivities which can be expected for the different modifiers, the ratio of k3 and k2 is calculated for each of them by multiplication of k3 and rh. As can be seen, significant differences can be observed. The highest value corresponds to 4-methoxythiophenol, indicating that by using this compound the highest surface selectivities should be obtained. The ratio is more than 1.5 times lower for 2-naphthalenethiol and even 6 times lower for 4-mercaptophenol, which can be expected to be the least surface-selective agent. To check the above model and prepare films with different distributions of modifier groups, modification reactions with the three thiol compounds in different proportions of dimethylformamide/water (from 2:1 to 6:1) and at different temperatures between 30 and 60 °C were performed. The reaction conditions were chosen according to the knowledge gained from previous work7,15 where the appropriate ranges for the composition of the reaction mixture and temperature had been determined in which transparent modified films are obtained. For the characterization of the modified films, confocal Raman microscopy was used. This technique has recently been shown8,16-22 to be an excellent means for analyzing the distribution of modifier groups in the interior of transparent polymer films. To obtain the depth profile of the films, a Raman microscope is focused stepwise (2 µm) through the polymer laminate while recording at each step the spectral region which contains a modifier band (1600 cm-1 due to the stretching vibration of the aromatic rings) and a constant reference signal (1420 cm-1 due to the C-H deformation of the PVC structure) giving rise to a series of spectra such as those shown in Figure 3. After normalization of the spectra with respect to the reference band and correction of the apparent length scale necessary due to the effect of the refractive index difference between sample and ambient,18-20 a depth profile like that in Figure 4 can be constructed. Films modified at different reaction times were analyzed in order to visualize the evolution of the profiles with time. (14) van Krevelen, D. W. Properties of Polymers, 3rd ed.; Elsevier: New York; 1990; p 535. (15) Reyes, J.; Herrero, M.; Tiemblo, P.; Mijangos, C.; Reinecke, H. Polymer 2003, 44, 2263. (16) Hajatdoost, S.; Olsthoorn, M.; Yarwood. J. Appl. Spectrosc 1997, 51, 1784. (17) Vyo¨rykka¨, J.; Paaso, J.; Tenhunen, M.; Tenhunen, J.; Iitti, H.; Vuorinen, T.; Stenius, P. Spectroscopy 2003, 57 (9), 1123. (18) Sacrista´n, J.; Mijangos, C.; Spells, S.; Yarwood, J.; Reinecke, H. Macromol. Chem. Phys. 2002, 203, 678. (19) Everall, N. Appl. Spectrosc. 2000, 54, 773. (20) Everall, N. Appl. Spectrosc. 2000, 54, 1515. (21) Reinecke, H.; Spells, S.; Sacristan, J.; Mijangos, C.; Yarwood, J. Appl. Spectrosc. 2001, 55, 1660. (22) Xiao, C.; Flach, C. R.; Marcott, C.; Mendelsohn, R. Appl. Spectrosc. 2004, 58, 382.

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Table 1. Reaction Rates of Different Modifier Compounds at 30 °C in 4:1 DMF/H2O

4-metoxythiophenol (PVC-OMe) 4-mercaptophenol (PVC-OH) 2-thionaphthol (PVC-Naf)

k3 (s-1)

rh ∼ 1/k2 (cm-3/mol)

k3rh

1.83 × 10-6 0.37 × 10-6 1.03 × 10-6

77 66 86

1.41 × 10-4 0.24 × 10-4 0.89 × 10-4

Figure 3. Series of Raman spectra as a function of depth of a PVC film modified with 4-methoxythiophenol in 4:1 DMF/ H2O for 7.5 h at 60 °C. Figure 5. Evolution of the surface selectivities with reaction time of a PVC film modified with 4-mercaptophenol at 40 °C in different DMF/H2O mixtures: 3:1 (9), 4:1 (O), 5:1 (2), and 6:1 (3).

Figure 4. Depth profile as obtained from the series of Raman spectra shown in Figure 3.

The surface selectivity is calculated using expression 18 where d is the thickness of the film, f(M) a function which describes the evolution of the degree of modification with depth x, and Msurf is the degree of modification at the surface of the film. Both values can be obtained from the Raman peak intensities. According to the definition of the surface selectivity, values between 0 and 1 are possible, with 0 corresponding to a completely homogeneously modified film and 1 to a film with an infinitely thin modified outer surface layer.

SS ) 1 -

∫0d/2 f(M) dx (1/2)dMsurf

(1)

From the Raman peak intensities shown in the depth profiles such as those in Figure 4, Msurf and the values of the integral of eq 1 can be obtained and the surface selectivity calculated for each profile. Dependence of the Surface Selectivity on the Reaction Medium. The reaction medium in which a

modification of a polymer film is carried out can be expected to have a very strong influence on the distribution of the modifier groups. The use of a nonswelling medium leads to a polymer film where only the outermost atomic layers are modified. The other extreme is a good solvent for the polymer having as a consequence the complete dissolution of the film. In this study solvent mixtures of a good solvent (DMF) and a nonsolvent (H2O) for PVC have been used which were known to allow the reaction without dissolving the films. In Figure 5 the evolution of the surface selectivities with reaction time of a PVC film modified with 4-mercaptophenol in different DMF/H2O mixtures is shown. From these curves two conclusions can be drawn: on one hand, it becomes evident that a good reaction medium leads to a film with low surface selectivity. In fact, it is shown that the better the reaction medium the lower the values of SS. Surface selectivities higher than 0.9 can be observed when the reaction is performed in a bad reaction medium like DMF/H2O 3:1 while a good solvent mixture like DMF/H2O 6:1 leads to a nearly homogeneously modified film with SS values near zero. This result is easily explained by the different swelling behavior of the film in the different media. In a bad medium where nearly no swelling of the polymer takes place the reaction is basically limited to regions near the surface where a sufficiently high modifier concentration is present. A highly swelling medium, on the other hand, opens the structure, the diffusion of the modifier into the inner of the film is accelerated, and the reaction can start simultaneously in all the film leading to a more or less homogeneous modification. A second result deduced from Figure 5 is the fact that all curves have a negative slope indicating a homogenization of the film when they are exposed to the reaction medium for a long time. Arguing in terms of the different reaction rates v2 and v3 for step 2 and step 3, this means that v3/v2 decreases with time. This decrease can be explained by a decrease of v3 and/or by an increase of v2: The reaction rate v3 depends on k3 and the concentrations

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Figure 6. Evolution of the surface selectivities with reaction time of a PVC film modified with 2-thionaphthol at 50 °C in different DMF/H2O mixtures: 2:1 (9), 3:1 (O), 4:1 (2), 5:1 (3), and 6:1 ([).

Figure 7. Evolution of the surface selectivities with reaction time of a PVC film modified with 4-mercaptophenol in 4:1 DMF/ H2O at 30 °C (9), 40 °C (O), 50 °C (2), and 60 °C (3).

of the reactants, that is, chlorine atoms and modifier molecules. For the nucleophilic substitution of chlorine in PVC, it has been shown that the rate constant k3 is independent of time and conversion leading to a copolymer with a statistical distribution of modifier groups.23 Consequently, the decrease of the reaction rate v3 has its origin in the decreasing concentration of chlorine sites available for the reaction. A second reason for the decrease of the surface selectivity with time is the increase of v2, that is, the acceleration of the diffusion process of the modifier upon modification. As has been shown recently,24 the modification of PVC with up to 10 mol % nucleophiles leads to an increase of the specific and free volumes of the polymer chains which are likely to be the origin of the increase of D and v2 with time. Interestingly, PVC films modified with 2-naphthalenethiol show a different behavior, which is depicted in Figure 6. While in poorly swelling reaction media (DMF/H2O 2:1 and 3:1) the surface selectivities decrease with time, better solvents and high temperatures lead to an inversion of this tendency and the modification becomes more surface (23) Mijangos, C.; Lo´pez, D. Macromolecules 1995, 28, 1364. (24) Tiemblo, P.; Guzma´n, J.; Riande, E.; Mijangos, C.; Herrero, M.; Espeso, J.; Reinecke, H. J. Polym. Sci. Polym. Phys. 2002, 40, 964.

Figure 8. Comparison of surface selectivities obtained with modifiers 4-mercaptophenol (O), 4-methoxythiophenol (2), and 2-thionaphthol (9) (a) in 4:1 DMF/H2O at 50 °C; (b) in 5:1 DMF/ H2O at 30 °C; and (c) in 5:1 DMF/H2O at 60 °C.

selective. It is likely that in this case the relatively bulky modifier and the favorable conditions for a high degree of modification at the surface decrease the diffusion coefficient with conversion due to steric hindrance. This hypothesis is supported by the fact that in all films which show this tendency an overall degree of modification of at least 10 mol % is present. Furthermore, it has to be considered that steric hindrance is enhanced as we deal not only with bulky naphthalene groups which are connected to the polymer chains and hinder the modifier transport but also with the modifier molecules themselves which are bulky and make it even more difficult to diffuse to the reactive sites in the inner of the film. Temperature Dependence of the Surface Selectivity. In Figure 7 the evolution of the surface selectivities measured in a PVC film modified with 4-mercaptophenol at different reaction temperatures is presented. A similar

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behavior to that in Figure 5 is observed showing a decrease of SS with reaction time, which has been discussed above. Furthermore, it can be stated that the highest surface selectivities are obtained when low reaction temperatures are used while higher temperatures lead to a homogenization of the distribution of modifier groups in the film. One reason for this result is an enhanced swelling of the polymer films due to stronger polymer-solvent interactions. A temperature increase is therefore equivalent to the use of a better reaction medium. For further reasons to explain why higher temperatures lower the surface selectivity, the temperature dependence of k3 and D has to be considered. For both of them an Arrhenius-like dependence of the temperature can be supposed. Consequently, the temperature dependence of SS is given by

SS (T) ∼ k30/D0 exp[(∆Eak3 - ∆EaD)/RT] The fact that an increase of temperature produces a decrease of SS indicates that the diffusion process has a higher activation energy than that of k3 and is strongly favored by the increase of the temperature. Influence of the Type of Modifier on the Surface Selectivity. During the discussion of the influence of the reaction medium on the surface selectivity, it has been shown that different modifiers may show different behaviors. In Figure 8 the surface selectivities and their evolution with time are compared for the three modifiers used in this work. It can be seen that the distribution of modifier in the film depends strongly on the reaction conditions used during the modification reaction. In the mixture DMF/H2O 4:1 at 50 °C (Figure 8a), the highest surface selectivities are observed for the 4-methoxythiophenol modifier while the lowest SS values are measured with 2-naphthalenethiol. This order can be explained by the large difference in the reaction rate constants of 4-methoxythiophenol and the other thiol compounds. Interestingly, in Figure 8b, using a slightly better reaction mixture (DMF/H2O 5:1) but a lower temperature (30 °C), the highest surface selectivity is observed for the 4-mercaptophenol modifier. This behavior is interpreted to be due to the formation of hydrogen bonds between OH groups introduced in the PVC film upon

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modification. These bonds built a physical network which hinders chain mobility and causes a strong reduction of the diffusion coefficient for the modifier. However, at higher temperatures (60 °C, Figure 8c), which not only activate the reactivities of the modifiers but do also produce a stronger swelling of the films, these OH groups are better solubilized, hydrogen bonds are no longer efficient, and, consequently, a nearly homogeneously modified film is obtained. Under these highly reactive conditions the bulky naphthol modifier shows the highest surface selectivity, which has been explained above. Conclusions In the present paper it has been shown that films with different concentration gradients across the films can be obtained by wet chemical surface treatments varying the reaction conditions and the type of the modifier. It is shown that, as a function of the reaction conditions, time may push the reaction toward a homogeneous modification or toward a film with increasing surface selectivity. In general, low temperatures and reaction media which do not swell the polymer lead to films with a high surface selectivity. Furthermore, the use of modifiers with a high reaction rate constant or modifiers carrying functional groups which can form a physical network by the formation of hydrogen bonds favor high degrees of modification at the film surface. Relative surface selectivities of different modifiers can well be estimated using the rate constants determined at the surface. However, special effects such as hydrogen bonding or steric hindrance may influence the surface selectivity of the reactions. Also the evolution of the concentration gradient of the modifier with time depends on the reaction conditions and may lead toward a film with higher surface selectivity or toward a homogeneously modified one. The combination of FTIR-ATR and confocal Raman microscopy is an excellent means to elucidate the structure and distribution of modified groups within transparent polymer films. Acknowledgment. The authors are grateful to the Ministerio de Ciencia y Tecnologı´a (MCYT) and MAT20022978 for financial support. LA047172K