A Comprehensive Analysis of Selected Anionic Surfactants Behaviour in Aqueous Systems Containing Metal Ions and Inorganic Acid

: The inﬂuence of co-ions on the adsorption properties of two surfactants: ABS (dodecyl-benzene sulfonic acid) and its sodium salt ABSNa50 in the aqueous systems, has been studied and discussed. On the basis of experimental measurements of equilibrium and dynamic surface tension, a series of parameters were determined, such as critical micelle concentration (CMC), adsorption parameters, diffusion coefﬁcients, and the micellar dissociation constant. It was proved that values of CMC vary according the contents of accompanying metal ions (zinc(II), copper(II), cobalt(II), nickel(II)) and hydrochloric acid in the system under discussion. Moreover, it was found that as the concentration of surfactant in the system increases, the estimated values of the diffusion coefﬁcients decrease. The obtained results indicate the need to analyse the basic surface properties of surfactants in case of their application in the systems containing additional substances.


Introduction
Surfactants, due to their unique properties, reduce surface tension, adsorb at the interface, and self-aggregate. Due to these properties, these compounds are utilized in daily life and industry, as well as in natural processes. On the one hand, they are essential for breathing (pulmonary surfactants), and on the other hand, they are used as detergents [1,2]. The widespread use of these types of compounds means that they are often present in aquatic systems and should be examined in a wide range. The surface activity of this group of compounds depends on several factors. First, the structure of the surfactants and, in particular, the interactions between the hydrophobic and hydrophilic groups should be considered. Therefore, it is important to test a wide range of surfactants. Moreover, the other conditions such as electrolyte additive, pH, temperature, etc. affect surfactant properties in solution. For example, surface activity of the surfactants will depend on the metal ionic content in the system. These ions can bind to surfactant molecules. Studies indicate that these interactions depend on charges, size, ion specific effect, and coordination ability. Therefore, on the basis of the studies carried out for one metal, it is not possible to generalise the results for a whole range of salts [3]. These effects have been studied and described in the literature for several surfactants and associated salts, such as the anionic surface activity compounds: sodium dodecyl sulfate (SDS) [4][5][6][7] and N-lauroylsarcosine sodium salt [7], the cationic surfactants: alkyltrimethylammonium bromids [8] and hexadecyltrimethylammonium bromide [5], the amphoteric surfactant: cocamidopropyl betaine [9] and the nonionic surfactants: OP-10 [10] and polyoxyethylene nonylphenyl ether [11,12]. dynamic surface tension) of the two commercial anionic surfactants ABS and ABSNa50. Although ABS and ABSNa50 are widely used, interactions with other compounds in aqueous media are poorly explored.

Materials and Methods
There were two commercial anionic surfactants applied: ABS acid (dodecylbenzene sulfonic acid; CAS number: 85536-14-7; IUPAC name: 4-(tridecan-3-yl)benzene-1-sulfonic acid), and for comparison sodium salt ABSNa50 (sodium dodecylbenzene sulfonate (C10-13 alkyl derivatives); CAS number: 68411-30-3; IUPAC name: sodium 4-undecylbenzenesulfonate), purchased from PCC Exol SA, Brzeg Dolny, Poland (Table 1). They were used as received, without any purification. This approach was intended to study the compounds and their interactions as they are commonly used. Since earlier studies in the group had shown a significant correlation betwe surface properties and metal ions and acid present in aqueous medium in the case o modal surfactant-SDS [4], it seems important to investigate commercially availab surfactants in this area. Therefore, taking into account the information presented abov the objective of this paper was to investigate the influence of type of metal ions an presence of HCl in various concentrations on the surface properties (CMC, adsorpti parameters, and dynamic surface tension) of the two commercial anionic surfactants A and ABSNa50. Although ABS and ABSNa50 are widely used, interactions with oth compounds in aqueous media are poorly explored.

Materials and Methods
There were two commercial anionic surfactants applied: ABS acid (dodecylbenze sulfonic acid; CAS number: 85536-14-7; IUPAC name: 4-(tridecan-3-yl)benzene-1-sulfon acid), and for comparison sodium salt ABSNa50 (sodium dodecylbenzene sulfona (C10-13 alkyl derivatives); CAS number: 68411-30-3; IUPAC name: sodiu 4-undecylbenzenesulfonate), purchased from PCC Exol SA, Brzeg Dolny, Poland (Tab 1). They were used as received, without any purification. This approach was intended study the compounds and their interactions as they are commonly used. Since earlier studies in the group had shown a significant correlation between surface properties and metal ions and acid present in aqueous medium in the case of a modal surfactant-SDS [4], it seems important to investigate commercially available surfactants in this area. Therefore, taking into account the information presented above, the objective of this paper was to investigate the influence of type of metal ions and presence of HCl in various concentrations on the surface properties (CMC, adsorption parameters, and dynamic surface tension) of the two commercial anionic surfactants ABS and ABSNa50. Although ABS and ABSNa50 are widely used, interactions with other compounds in aqueous media are poorly explored.
The surface tension measurements were performed using a Krüss (K-12) tensiometer (Krüss GmbH, Hamburg, Germany) with a platinum ring, at room temperature (298 K). The three-time measurements accuracy was ±0.05 mN/m. The CMC was estimated in the typical way, as a point of intersection by fitting the pre-micellar and post-micellar data of the surface tension isotherm. The relationship between surface tension and surfactant concentration in the case of the formation of micelles in the solution can be presented as: where g(c) = 1 if c ≤ CMC and 0 if c > CMC, A is the slope of γ = f(ln(c)), and γ CMC is the surface tension at the concentration above CMC. The adsorption parameters of surfactants were calculated using the Szyszkowski equation. The DST measurements were performed with the bubble method (SITA Messtechnik t60 tensiometer (SITA Messtechnik GmbH, Dresden, Germany)) according to the procedure described in [4]. The measurements made it possible to estimate the value of the diffusion coefficients and the micellar dissociation constants and consequently, to determine whether the diffusion affects the ABS and ABSNa50 adsorption.

Determination of CMC and Adsorption Parameters
The CMC value is a crucial parameter describing each micelle-forming compound. Therefore, its determination is very important. CMC depends mainly on compound structure, type of solvent used, the presence of other substances, mainly strong electrolytes, and the temperature. The basic parameters describing surface activity of the anionic surfactant (AS) were estimated from surface tension measurements [33]. The CMC values were obtained using the relationship between surface tension (γ) versus the logarithm of ABS concentration in the aqueous solutions e.g., the water-AS, water-AS-M(II)) and hydrochloric acid (HCl-AS, HCl-AS-M(II), where AS-anionic surfactant) systems. The representative plots of γ versus log c applied for the determination of CMC are shown in Figure 1a-f (ABS).
The relations shown in Figure 1a-f have a typical shape that indicates the formation of micelles in the solution according to the Equation (1). Furthermore, Figure 1g,h shows a comparison of the CMC values obtained, taking into account the effect of both the concentration of hydrochloric acid and the type of heavy metal ion used. As can be seen, the nature of the figures obtained in the radiation diagram indicates a much greater effect of the HCl concentration than of the type of metal ion on micelle formation in the system containing the ABS surfactant. The figures are not only similar, but also the result of the integration of the areas showed a much smaller variance in the case of Figure 1h (0.122 and 3.67 × 10 −3 , for (g) and (h), respectively).
The determination of the CMC value for the system containing ABS surfactant was presented and compared with the ABSNa50 one for which the CMC results were presented in our previous paper [19] (Figure 2). structure, type of solvent used, the presence of other substances, mainly strong electrolytes, and the temperature. The basic parameters describing surface activity of the anionic surfactant (AS) were estimated from surface tension measurements [33]. The CMC values were obtained using the relationship between surface tension (γ) versus the logarithm of ABS concentration in the aqueous solutions e.g., the water-AS, water-AS-M(II)) and hydrochloric acid (HCl-AS, HCl-AS-M(II), where AS-anionic surfactant) systems. The representative plots of γ versus log c applied for the determination of CMC are shown in Figure 1a-   integration of the areas showed a much smaller variance in the case of Figure 1h (0.122 and 3.67 × 10 −3 , for (g) and (h), respectively).
The determination of the CMC value for the system containing ABS surfactant was presented and compared with the ABSNa50 one for which the CMC results were presented in our previous paper [19] (Figure 2). The results presented in Figure 2a show that the anionic surfactants show the maximum values of CMC for systems with water (2.33 mmol/L and 1.52 mmol/L, for ABS and ABSNa50, respectively). The obtained results of CMC for ABS in water are greater compared to those presented in the literature (0.385 [42], 0.551 [43], and 1.29 [44] mmol/L) while the values of γ are similar (33.0 in this paper about 33.2 [42] and 32.9 mN/m in [43]). The discrepancies in the presented CMC results are probably due to the various suppliers of surfactants (Sigma-Aldrich, Fluka, and TCI in the citied papers, respectively, The results presented in Figure 2a show that the anionic surfactants show the maximum values of CMC for systems with water (2.33 mmol/L and 1.52 mmol/L, for ABS and ABSNa50, respectively). The obtained results of CMC for ABS in water are greater compared to those presented in the literature (0.385 [42], 0.551 [43], and 1.29 [44] mmol/L) while the values of γ CMC are similar (33.0 in this paper about 33.2 [42] and 32.9 mN/m in [43]). The discrepancies in the presented CMC results are probably due to the various suppliers of surfactants (Sigma-Aldrich, Fluka, and TCI in the citied papers, respectively, and PCC Exol here) and, in consequence, the possibility of applying different procedures for obtaining the compound and impurities after synthesis. Moreover, as mentioned before, the tests presented in this paper were carried out using the commercial preparation without purification to make the results as close as possible to the real conditions. In the case of the sodium salt of ABS, a comparison of the results directly is not available since this is a mixture of different alkyl length acid derivatives (C10-C13). However, the obtained results are similar to those for the pure compound-sodium dodecylbenzene sulfonate (1.52 in this paper and 1.1 in [45], 2.85 in [46] or 2.73 mmol/L in [47]).
The aggregation of anionic surfactants was investigated taking into account the equilibrium surface tension (G). In the initial stage, as the concentration of surface-active compound increases, the G decreases dramatically and then decreases more slowly [41,42], as was presentd for surfactants under consideration in Figure 1. The dramatic decrease of G is a typical effect, originating from the adsorption of ABS and ABSNa50 molecules at the interface. Moreover, as presented in Figure 1a, the G-log c plot can be divided into three concentration regions, suggesting a gradual aggregation occurring during the adsorption process. The ABS surfactant in the aqueous solution can form species such as negatively charged soap (C 18 H 29 SO 3 − ), neutral acid (C 18 H 29 SO 3 H), and due to the hydrogen bonds present, also acid-soap dimers [42]. The presence of these compounds in the system, or rather the chemical equilibria present in the dilute solution, which change with increasing ABS concentration, is responsible for the blurring of the first breakpoint and the presence of the second one. With an increase in ABS concentration, the micelles begin to form, and then they are partially transformed into vesicles as a consequence of the acid-soap dimers formation by hydrogen bonding. The shift in equilibrium for high concentrations of ABS is responsible for the formation of micelles and subsequently vesicles due to dimer formation. The acid-soap dimers formation results in the pseudo binary mixed amphiphilic system, which contains a composite of single and double-chained amphiphiles [42,43]. The aggregation behaviour of the ABS surfactant in water could be explained by the dimer mechanism involving hydrogen bonds ( Figure 3). not available since this is a mixture of different alkyl length acid derivatives (C10-However, the obtained results are similar to those for the pure compound-so dodecylbenzene sulfonate (1.52 in this paper and 1.1 in [45], 2.85 in [46] or 2.73 mmo [47]).
The aggregation of anionic surfactants was investigated taking into accoun equilibrium surface tension (ɣ). In the initial stage, as the concentration of surface-a compound increases, the ɣ decreases dramatically and then decreases more sl [41,42], as was presentd for surfactants under consideration in Figure 1. The dra decrease of ɣ is a typical effect, originating from the adsorption of ABS and ABS molecules at the interface. Moreover, as presented in Figure 1a, the ɣ-log c plot c divided into three concentration regions, suggesting a gradual aggregation occu during the adsorption process. The ABS surfactant in the aqueous solution can species such as negatively charged soap (C18H29SO3 − ), neutral acid (C18H29SO3H), and to the hydrogen bonds present, also acid-soap dimers [42]. The presence of compounds in the system, or rather the chemical equilibria present in the dilute solu which change with increasing ABS concentration, is responsible for the blurring o first breakpoint and the presence of the second one. With an increase in concentration, the micelles begin to form, and then they are partially transformed vesicles as a consequence of the acid-soap dimers formation by hydrogen bonding shift in equilibrium for high concentrations of ABS is responsible for the formati micelles and subsequently vesicles due to dimer formation. The acid-soap di formation results in the pseudo binary mixed amphiphilic system, which conta composite of single and double-chained amphiphiles [42,43]. The aggregation beha of the ABS surfactant in water could be explained by the dimer mechanism invo hydrogen bonds (Figure 3).  The surfactant aggregation is also greatly influenced by the properties of solvent and coexisting ions. Knowledge about the CMC and the behaviour of surfactants in the hydrochloric acid medium and the presence of heavy metal ions is essential. Finally, anionic surfactants are used to support the removal of metals from wastewater and soil [7,43]. From the results shown in Figure 2 it was found that the presence of both metal ions and HCl changed the CMC values. Regardless of the metal ions, the CMC values in ABS systems shift toward lower concentrations as the HCl concentration increases. Similar correlations were observed for ABSNa50 [19] and SDS [4]. The resulting relationship is quite different from that of the systems containing ABS and poly(ethylene glycol) as an additive. In this case, the addition of PEG shifts the CMC value towards higher concentrations, which confirms that the surfactant aggregation with PEG causes the formation of small self-assembled micelles. Moreover, the authors showed that with the higher molecular mass of PEG used, the shift of CMC is greater [42]. The shift in CMC to lower concentrations, as well as the decrease in the γ min values obtained in this study (presence of salts and inorganic acid) could be explained by the presence of strong electrolytes in the systems under consideration. The presence of electrolytes promotes the aggregation of ionic surfactants by minimizing the electrostatic repulsions between the hydrophilic main groups of surfactants. This phenomenon results in a tighter packing of molecules, which consequently contributes to the possibility of micelle formation at a much smaller surfactant concentration. In addition, it should be noted that the presence of electrolytes can cause a salt effect accompanied by the displacement of polar surfactant head groups from water into the interface to form micelles. A similar effect of reduction of both the CMC and the minimum surface tension values was observed for sodium dodecylbenzene sulfonate with the addition of NaCl [46] and KCl, NH 4 Cl, and MgCl 2 [47] or other ionic surfactants, e.g., the cationic surfactant CTAB [48] or SDS [49] with NaCl. This relationship for the systems studied is presented in Figure 4 in the form of the multivariate Kernel density estimation. The surfactant aggregation is also greatly influenced by the properties of solvent and coexisting ions. Knowledge about the CMC and the behaviour of surfactants in the hydrochloric acid medium and the presence of heavy metal ions is essential. Finally, anionic surfactants are used to support the removal of metals from wastewater and soil [7,43]. From the results shown in Figure 2 it was found that the presence of both metal ions and HCl changed the CMC values. Regardless of the metal ions, the CMC values in ABS systems shift toward lower concentrations as the HCl concentration increases. Similar correlations were observed for ABSNa50 [19] and SDS [4]. The resulting relationship is quite different from that of the systems containing ABS and poly(ethylene glycol) as an additive. In this case, the addition of PEG shifts the CMC value towards higher concentrations, which confirms that the surfactant aggregation with PEG causes the formation of small self-assembled micelles. Moreover, the authors showed that with the higher molecular mass of PEG used, the shift of CMC is greater [42]. The shift in CMC to lower concentrations, as well as the decrease in the γmin values obtained in this study (presence of salts and inorganic acid) could be explained by the presence of strong electrolytes in the systems under consideration. The presence of electrolytes promotes the aggregation of ionic surfactants by minimizing the electrostatic repulsions between the hydrophilic main groups of surfactants. This phenomenon results in a tighter packing of molecules, which consequently contributes to the possibility of micelle formation at a much smaller surfactant concentration. In addition, it should be noted that the presence of electrolytes can cause a salt effect accompanied by the displacement of polar surfactant head groups from water into the interface to form micelles. A similar effect of reduction of both the CMC and the minimum surface tension values was observed for sodium dodecylbenzene sulfonate with the addition of NaCl [46] and KCl, NH4Cl, and MgCl2 [47] or other ionic surfactants, e.g., the cationic surfactant CTAB [48] or SDS [49] with NaCl. This relationship for the systems studied is presented in Figure 4 in the form of the multivariate Kernel density estimation.  The results indicate that the CMC reduction is related to the additional ions in the system that come from the dissociation of acid and their interactions with the surfactants, but the explanation of this phenomenon is not so obvious. It should be noted that as the concentration of HCl increases, a lower scatter of the obtained CMC results for different metal salts is observed. This indicates that the presence of acid determines to a much larger extent the surface The results indicate that the CMC reduction is related to the additional ions in the system that come from the dissociation of acid and their interactions with the surfactants, but the explanation of this phenomenon is not so obvious. It should be noted that as the concentration of HCl increases, a lower scatter of the obtained CMC results for different metal salts is observed. This indicates that the presence of acid determines to a much larger extent the surface behaviour of the analyzed ionic surfactants in comparison to the presence of metal. However, in the case of the aqueous solutions containing only metal salts, a significant difference in the CMC obtained for the Co(II) ions containing systems is observed. In the other cases, the values are similar. This behaviour of the system may be due to the differences in the van der Waals radius (R) (Zn 139 pm, Cu 140 pm, Ni 163 pm, and Co 200 pm) and the same valence (Z). Cations with high Z/R values are more hydrated and can be treated as water structure makers [47]. The aspect of hydration energy is also relevant to the study in question. Furthermore, it can be seen from the density graph (Figure 4) that the CMC shift towards the lower concentration occurs up to a certain concentration (about 1 mol/L HCl), after which it remains almost constant, regardless of the metal ion under investigation. This phenomenon can be explained by the achievement of the maximum charge shielding by the counter ions, so the addition of more salt will not cause significant changes. Thus, with the addition of HCl, there will be much fewer monomers in equilibrium with micelles.
The Szyszkowski equation (Equation (2) was applied for the ABS and ABSNa50 adsorption description in the presented system and determination of the other adsorption parameters according to Equations (3)-(6) ( Figure 5) [51].
The adsorption parameters were determined by the non−linear regression with the support of the MathCad Prime 4.0 program and are presented in Figure 6 and Table 2. The surface excess at the interface (Γ Sz ) determines the number of surfactant molecules per unit area of the saturated adsorption layer. The ABS and ABSNa50 molecules accumulated on the surface have a smaller affinity for the intermolecular interactions in the surface layer. From the results presented in Figure 6, for selected systems, it can be observed that Γ ∞ increases sharply with the increasing surfactant concentration and after that the curves reach the plateau, indicating the complete saturation of the phase boundary. Similar relationships were obtained for all the systems analysed. The obtained value of the surface excess for ABS in water is approximately twice higher than that presented in the paper (2.41 vs. 1.34 × 10 −6 mol/m 2 ) [43]. These differences may result from different origins of the surfactants. In the other cases, comparison of the obtained results is not possible because such results are not available in the literature. In the HCl-AS-Cu(II) systems Γ ∞ (mol/m 2 ) reaches higher values for higher hydrochloric acid concentration, with the highest values in the systems with 6 mol/L HCl for both surfactants. This increase of Γ ∞ values with more concentrated HCl was not observed for the other heavy metals containing systems (HCl-AS-M(II)) examined in this paper. However, in this case Γ ∞ values are also the highest in the 3 or 6 mol/L HCl systems for cobalt, zinc and nickel.
Water 2022, 14, x FOR PEER REVIEW 10 of 21 the surface layer. From the results presented in Figure 6, for selected systems, it can be observed that Γ ∞ increases sharply with the increasing surfactant concentration and after that the curves reach the plateau, indicating the complete saturation of the phase boundary. Similar relationships were obtained for all the systems analysed. The obtained value of the surface excess for ABS in water is approximately twice higher than that presented in the paper (2.41 vs. 1.34 × 10 −6 mol/m 2 ) [43]. These differences may result from different origins of the surfactants. In the other cases, comparison of the obtained results is not possible because such results are not available in the literature. In the HCl-AS-Cu(II) systems Γ ∞ (mol/m 2 ) reaches higher values for higher hydrochloric acid concentration, with the highest values in the systems with 6 mol/L HCl for both surfactants. This increase of Γ ∞ values with more concentrated HCl was not observed for the other heavy metals containing systems (HCl-AS-M(II)) examined in this paper. However, in this case Γ ∞ values are also the highest in the 3 or 6 mol/L HCl systems for cobalt, zinc and nickel.    Moreover, the curves of Γ ∞ (mol/m 2 ) vs. c (mol/L) for Cu(II) show a steeper shape at the beginning and the plateau of the plot is reached faster with the system containing ABSNa50 than ABS. On the other hand, the Γ ∞ values in the HCl-AS-Cu(II) systems are significantly higher for ABS than ABSNa50 surfactants (3 or 6 mol/L HCl), slightly higher (water-AS-Cu(II)) or at a similar level (0.1 or 1 mol/L HCl). The higher Γ ∞ were generally obtained in the systems containing ABSNa50 than ABS in the presence of cobalt, zinc, and nickel salts.
The values of the ∆G ads are negative in all cases, indicating that the molecules of ABS and ABSNa50 have an excellent ability to adsorb at the interface. These values are usually smaller for the systems with ABS surfactant and the presence of cobalt(II), zinc(II), and nickel(II) ions than for the systems containing ABSNa50. The more negative values of the Gibbs free energy of adsorption suggest more spontaneous ABS adsorption. The values of ∆G ads are slightly higher or the same for ABSNa50 with Cu(II) systems.
A min is the surface area covered by the adsorbed surfactant molecules at the maximum packing of the molecules. The obtained values of A min in the considered systems are in the range from 0.114 to 0.689 nm 2 . The highest vales of A min are found in the systems without HCl and heavy metal ions and may be a consequence of strong repulsion between the same charged heads of the surfactant. For the ionic surfactants A min could decrease with the alkyl chain elongation, nevertheless, this correlation is not a rule, and the additive of other chemicals, such as HCl or heavy metal ions, affects the adsorption parameters [52]. In the presented system with or without heavy metals, the A min is usually higher for ABS than for ABSNa50. The addition of HCl of the increasing concentration as well as heavy metal ions changed the minimum molecular area but the changes were not in one direction. Moreover, the addition of such inorganic compounds could change the equilibrium among electrostatic and hydration interactions, van der Waals forces, and counteract the mutual repulsion between the heads [46].

Determination of the Dynamic Surface Tension of the Anionic Surfactants in the Aqueous Solution and Role of Diffusion
The measurement and control of the dynamic surface tension (DST) for the surfactant containing solutions have a substantial role in many industrial and biological processes, e.g., agriculture (for easy spread of pesticides onto leaves), paint and coating industries, aerosol formation, as well as in biological processes, e.g., for effective functioning of the alveoli in the lung or in the analysis of human biological fluids, where a change in DST may be a diagnostic tool [53].
DST measurements were obtained using the bubble method. The changes in DST with time (life time of bubble) for different concentrations of ABS and ABSNa50 and such systems as water-AS; HCl-AS with and without heavy metal ions are presented in Figure 7. This Figure presents only the selected examples due to many data.
As presented in Figure 7 at higher surfactant concentrations, it is quicker to achieve equilibrium surface tension than at lower ones for all examined systems. The same relationship was observed for various surfactants [48,[54][55][56]. In the water-AS systems, the DST is higher compared to that in the HCl-AS or HCl-AS-M(II) systems. As it was mentioned previously, the addition of HCl salts causes the changes in the system composition, and therefore the dynamic surface tension decreases. Due to the small difference in the structure of surfactants, the evolutions of DST changes with time look very similar for the same concentration of HCl and heavy metals (Figure 7e,f). When the HCl concentration increases (Figure 7i,j) despite the same surfactant and heavy metals, the plots mentioned above look different at the same surfactant concentration. With the HCl addition, the systems needed more time to reach equilibrium. Such behaviour is observed at higher surfactant concentrations. When the surfactant concentration is small, the changes are not so visible. At a large concentration of ABS or ABSNa50, more molecules of surfactants adsorb at the interface than at the small surfactant concentration, and the dynamic surface tension values are much lower. This behaviour was also observed previously in the earlier studies for the similar systems containing SDS [19] as well as by other researchers e.g., Qazi et al. [48] who studied the effect of high concentrations of NaCl on the surface tensions in equilibrium and dynamic stage of solutions containing the cationic (CTAB) or nonionic (Tween 80) surfactants or Le et al. (Aerosol-OT in 10 mM NaCl solution) [57]. The observed relationships indicate that there are differences only when the aqueous systems are compared with the other systems containing metal ions and acid. It should be assumed that, even if the surfactant forms ionic pairs in the presence of other ions, this does not affect the dynamics of the adsorption process significantly. The presence of such ion pairs and the resulting change in the surfactant nature should not significantly slow down adsorption largely. The decrease in CMC, as electrolytes are added to the aqueous surfactant solution, seems to play an important role. A decrease in CMC means that the monomer concentration in the system is significantly reduced, which consequently slows down the adsorption process. In the systems under consideration the moving of micelles to the interface and then demicellation in the subsurface layer can be expected, which indicates that the kinetics of the adsorption will be affected by both micellar diffusion and monomer adsorption [58]. Moreover, with the addition of acid and metal ions in the systems under consideration, a large amount of micelles is present and it is expected that their diffusion to the interface will influence the adsorption kinetics to a large extent. As presented in Figure 7 at higher surfactant concentrations, it is quicker to achieve equilibrium surface tension than at lower ones for all examined systems. The same relationship was observed for various surfactants [48,[54][55][56]. In the water-AS systems, the DST is higher compared to that in the HCl-AS or HCl-AS-M(II) systems. As it was mentioned previously, the addition of HCl salts causes the changes in the system composition, and therefore the dynamic surface tension decreases. Due to the small difference in the structure of surfactants, the evolutions of DST changes with time look very similar for the same concentration of HCl and heavy metals (Figure 7e,f). When the HCl concentration increases (Figure 7i,j) despite the same surfactant and heavy metals, the plots mentioned above look different at the same surfactant concentration. With the HCl addition, the systems needed more time to reach equilibrium. Such behaviour is observed at higher surfactant concentrations. When the surfactant concentration is small, the changes are not so visible. At a large concentration of ABS or ABSNa50, more The equations shown in Figure 8 are used to quantify the kinetic of adsorption. There are required three assumptions in order to obtain the linear short-time approximation relationship between γ(t) and t 1/2 and to fit the experimental DST data: (1) no back diffusion, (2) Henry's equation of state must be fulfilled, (3) the forward adsorption as a result of the spherical geometry is much smaller in comparison to the planar surface [53,60,61]. Equation (8) found applicability when k 2 πt >> 1, whereas the relative value of monomer concentration α is equal to 1 for the nonionic surfactants and less than 1 for the ionic surfactant (c > CMC) and α = 1 at c < 10 CMC. For c >> CMC α is stated as: where β is the degree of counterions binding at the micelles. Values of D t→0 , D t→∞ and k 2 for all considered systems (were obtained and are collected in Table 3, whereas the illustrations of the short-and long-time approximation for the HCl-AS-M(II) systems are presented in Figure 9. As follows from Figure 9 which presents the selected examples of surface tension (N/m) versus time (t 1/2 or t −1/2 ), the obtained R 2 coefficients are high, therefore the diffusion coefficients were calculated. Due to the fact that D values are significantly dependent on the curve fitting, when the determination coefficients were low or very low the diffusion coefficients are not showed.  As it was observed based on the diffusion coefficients, the values collected in Table 3 increase with the increasing surfactant concentration. The same relationship was observed for the other surfactants, for example, dodecyltrimethylammonium bromide [61]. When the concentration of surfactant is small, the greater mobility of molecules is observed. At the same time, at higher surfactant concentrations, the diffusion coefficients are smaller, indicating smaller surfactant particles mobility. Such observations indicate that diffusion plays a role in the surfactant adsorption. The results indicate that adsorption is significantly influenced by the surfactant monomer concentration, while As it was observed based on the diffusion coefficients, the values collected in Table 3 increase with the increasing surfactant concentration. The same relationship was observed for the other surfactants, for example, dodecyltrimethylammonium bromide [61]. When the concentration of surfactant is small, the greater mobility of molecules is observed. At the same time, at higher surfactant concentrations, the diffusion coefficients are smaller, indicating smaller surfactant particles mobility. Such observations indicate that diffusion plays a role in the surfactant adsorption. The results indicate that adsorption is significantly influenced by the surfactant monomer concentration, while the formation of micelles has no effect on the kinetics of adsorption. Such observation is in agreement with the Ward and Tordai's theory, according to which the characteristic adsorption time correlates only with the monomer concentration. On the other hand, it is assumed that at the concentrations above CMC, the adsorption mechanism changes from the diffusion-controlled to the adsorption barrier-controlled one or mechanism based on the mixed diffusion-adsorption barrier [58,62].
The values of derivatives dγ/dt −1 and dγ/dt −1/2 were applied also for calculations of the k 2 constant. As it was pointed out the significant changes in the surfactant concentration by an order of magnitude, e.g., from 10 −3 to 10 −4 (concentration decrease) cause an increase of k 2 , whereas at the value 10 −3 Fainerman and Makievski [63] also measured the DST of the sodium tetradecylsulphate, sodium bexadecylsulphate solutions and Triton X-100 in water to obtain the constant micelle dissociation rate and observed that this parameter has higher value when the higher surfactant concentration is considered, particularly for ionic surface activity compounds (for c > 10-30 CMC). This phenomenon can be described by a transition of the micelle shape and a strengthening of the intermolecular repulsion in the system. Moreover, the k 2 parameter increases with increasing temperature for the ionic surfactant as a consequence of the nature of molecular interactions in the case of ionic and nonionic surfactants.

Conclusions
The surface properties and the adsorption parameters of the anionic surfactant dodecylbenzene sulfonic acid (ABS) with the heavy metal ions and hydrochloric acid containing systems were presented and compared with the results for sodium dodecylbenzene sulfonate (ABSNa50). The critical micelle concentrations (CMC) obtained based on the adsorption isotherms were the highest in the water containing system being 2.33 mmol/L and 1.52 mmol/L, for ABS and ABSNa50, respectively. The adsorption of ABS and ABSNa50 at the interface and the dramatic decrease of Gwith the decrease in the surfactant concentration were observed. The aggregation behaviour of the ABS in water could be explained by the dimer mechanism involving hydrogen bonds. The addition of both HCl and heavy metal ions changed the CMC by a shift toward lower concentrations with the increasing HCl concentration for both surfactants. It was observed that varying the concentration of hydrochloric acid had a more significant effect on the CMC values obtained in relation to different metal ions at constant concentration. The obtained values indicate that the adsorption of ABS and ABSNa50 surfactants at the air/water interface is spontaneous and controlled by diffusion.
In conclusion, the presented analyses of the behaviour of the anionic surfactants in the system containing heavy metal ions and HCl acid are very significant from a practical point of view. Based on them, it is possible to design systems in which micelles will be characterized by specific stability controlling the surfactant structure, its concentration or physicochemical conditions (e.g., presence of electrolyte, temperature, and pressure) enabling for technological processes as well as design control. Further research in this area, in particular on the behaviour of surfactants at different metal ion concentrations, should be continued.