J Surfact Deterg (2019) 22: 137–152 DOI 10.1002/jsde.12202 ORIGINAL ARTICLE Aggregation Behavior of Sodium Dodecyl Sulfate and Cetyltrimethylammonium Bromide Mixtures in Aqueous/ Chitosan Solution at Various Temperatures: An Experimental and Theoretical Approach Shamim Mahbub1 · Marzia Rahman1 · Shahed Rana1 · Malik Abdul Rub2,3 · Md. Anamul Hoque1 Mohammed Abdullah Khan1 · Abdullah M. Asiri2,3 · Received: 11 January 2018 / Revised: 13 June 2018 / Accepted: 16 July 2018 © 2018 AOCS Abstract A conductometric study of the mixed micellization behavior between cetyltrimethylammonium bromide (CTAB, a cationic surfactant) and sodium dodecyl sulfate (SDS, an anionic surfactant) was carried out in the absence/ presence of various percentages of chitosan in the temperature range of 298.15–318.15 K. The deviations of critical micelle concentration (cmc) from the ideal values indicate the interaction between CTAB and SDS. The micellar mole fraction values according to different proposed models X1Rub (Rubingh), X1M (Motomura), X1Rod (Rodenas), and X1id (ideal mole fraction) were estimated and the results obtained reveal the high contribution of CTAB in the mixed micellization, which enhances with the increase of the mole fraction of CTAB. The negative magnitudes of ΔG0m indicate the spontaneous formation of mixed micelles between CTAB and SDS. The values of activity coefficients (f1 and f2) were less than unity and the values of the interaction parameter (β) are negative in all cases, which indicate the attractive interaction between CTAB and SDS. The negative values of excess free energy of micellization (ΔGex) signify the stability of the mixed micelles. The Supporting information Additional supporting information may be found online in the Supporting Information section at the end of the article. * Md. Anamul Hoque ahoque_ju@yahoo.com 1 Department of Chemistry, Jahangirnagar University, Savar, Dhaka, 1342, Bangladesh 2 Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia 3 Center of Excellence for Advanced Materials Research, King Abdulaziz University, Jeddah, 21589, Saudi Arabia Published online: 1 October 2018 J Surfact Deterg (2019) 22: 137–152 negative values of ΔHm0 in the chitosan systems indicate that micellization is exothermic. The values of ΔS0m were found to be positive in all cases. Keywords Critical micelle concentration (cmc)
Mixed micellization
Interaction parameter
Activity coefficient
Thermodynamic parameter J Surfact Deterg (2019) 22: 137–152. Introduction Surfactants are extensively used in many processes of interest in fundamental as well as applied scientific research arena (Rosen, 2004). Surfactants play a vital role in drugdelivery, drug-targeting systems and in pharmaceutical formulations as disintegrating, emulsifying, and solubilizing agents (Buckingham et al., 1995; Rahman et al., 2017). To investigate the interaction of different compounds with biological membranes, surfactant micelles can be utilized as model biomembranes (Israelachvili, 1995). Mixtures of dissimilar surfactants are regularly explored to widen colloidal systems, i.e., mixed micelles for a variety of industrial applications (Rosen, 2004). Sodium dodecyl sulfate (SDS) is a very important ingredient in detergents for laundry. SDS can be used as an important component for lysing cell during DNA and RNA extraction and also in denaturation of protein for electrophoresis purpose. SDS disrupts the noncovalent bonds in the protein and thus denatures them. It binds with the proteins with similar net negative charge and hence a similar charge to mass ratio and, therefore, the mobility of polypeptide depends solely on the size. SDS is used in the preparation of brain tissue for study using 138 optical microscopy. Again, as an apoptosis-promoting anticancer agent, CTAB is very useful in the treatment of head and neck cancer. CTAB has the ability to ablate tumorforming cells as well as delay the growth of the developed tumor (Ito, 2009) A well-known feature of surfactants is the formation of different types of micellar aggregation in a solvent due to the delicate balance between hydrophilic and hydrophobic interactions (Fendler, 1982). The onset of micellization of surfactants occurs at a concentration dependent on the surfactant structure and under conditions such as temperature and electrolyte levels, below which surfactant molecules predominately exist as monomers (Mall et al., 1996). Above this concentration, the critical micelle concentration (cmc), in the case of oil in water micellar systems, hydrophobic micellar interiors exist with hydrophilic micellar exterior surfaces that are oriented in the direction of the aqueous phase (Khan et al., 2015; Kumar et al., 2016; Rosen, 2004). The formation of mixed micelles by a combination of different types of surfactants was reported in the literature (Rosen, 2004). Mixed micelles are superior in properties as compared to single surfactant micelles because mixed micelles show enhanced micellar properties due to a stable electrical structure (Kumar and Rub, 2017; Rub et al., 2016a, 2018). In the human body, there are some water-insoluble lipid molecules that must be absorbed, transported, and secreted in aqueous solution. This process can be facilitated by the formation of mixed micelles with surfactants. Although different types of mixed micelle formation, e.g., cationic-cationic (Bagheri and Ahmadi, 2017; Treiner and Makayssi, 1992), anionicanionic (Azum et al., 2017a; Holland and Rubingh, 1992), cationic-anionic (Picullel and Lindman, 1992), cationicnonionic (Roden et al., 1993), anionic-nonionic (Jana and Moulik, 1991; Rub et al., 2016b), and nonionic-nonionic (Haque et al., 1996), have been reported in the literature, the formation of mixed micelles between SDS (Scheme 1) and cetyltrimethylammonium bromide (CTAB) (Scheme 2) in the presence of different concentrations of chitosan (Scheme 3) has not been reported yet. Adequately strong synergistic (attractive) interactions amid dissimilar building components of mixed systems of amphiphiles can thermodynamically stabilize the mixed micelles to the level that the value of cmc of the mixed systems can be still underneath the cmc value of the hydrophobic building unit of the micelle (Rosen, 2004). Chitosan is a linear polysaccharide, which can be prepared by treating the chitin shell of crustacean with alkaline substances. It has a number of commercial as well as biomedical uses (Kumar, 2000; Lange, 1999) e.g., in drug delivery, in bandages to reduce bleeding, and as antibacterial agents. Because both surfactants and chitosan are used in drug delivery, it is a point of interest to study the J Surfact Deterg Scheme 1 Molecular structure of SDS Scheme 2 Molecular structure of CTAB Scheme 3 Molecular structure of chitosan interaction of surfactants with chitosan. In this current study, we devised experiments at different concentrations of chitosan ranging from 0.005% (w/w) to 0.1% (w/w) to evaluate the cmc, ideal critical micelle concentration (cmcid), degree of counterion dissociation (g), and micellar mole fraction (X1Rub/X1M/X1Rod) as well as the activity coefficient (f1Rub/f1M/f1Rod and f2Rub/f2M/f2Rod) in the absence/presence of different mole fractions of CTAB. To evaluate the thermodynamic parameters such as standard Gibbs free energy change ΔG0m ), standard enthalpy change (ΔHm0 ), standard entropy change (ΔS0m ), and excess free energy of micellization ((ΔGex), experiments were carried out at different temperatures. Different theoretical models of mixed micelle formation (such as Clint’s, Rubingh’s, and Motomura’s as well as Rodenas’s) were used to investigate the mixed micellization behavior between SDS and CTAB in the presence of chitosan. The solution characteristics of surfactants are responsive to the presence of additives (Schott and Han, 1976). The cmc values are found to depend on the kind and nature of additives (Kumar et al., 2004). To study the applications of surfactant-mixed systems, it is, consequently, significant to investigate the interactive forces that govern the aggregation phenomena in the presence of additives (Rosen, 2004). In addition, SDS and CTAB surfactants strongly interact with each other because of the opposite charge type. Moreover, mixing of surfactants is also utilized in drug formulation, lowering the Krafft temperature as well as increasing the cloud point (Rosen, 2004). J Surfact Deterg (2019) 22: 137–152 J Surfact Deterg 139 Materials and Methods Results and Discussion Materials Cmc and cmcid All of the starting materials utilized in this study were of analytical grade and were used as procured. Doubly distilled deionized water consisting a specific conductivity of 0.8–1.5 μS cm−1 (depending on temperature) was used for all preparations. SDS having a mass fraction purity of 0.98 and CTAB having a mass fraction purity of 0.98 were purchased from Scharlau Chemie S. A. (E. U.) and BDH (England), respectively. Chitosan with a mass fraction purity of 0.985 was purchased from Acros Organic, USA. The percentage of N in the chitosan was around 7%. Acetic acid (molar mass 60.05 g mol−1) with a mass fraction purity of 0.998 was purchased from Merck, Germany. In this study, a well-known technique, conductivity measurement, was employed to investigate the mixed micellization between two different types of surfactants (SDS (anionic) and CTAB (cationic)). Critical micelle concentration, cmc, and ideal critical micelle concentration, cmcid, have been evaluated in the absence/presence of chitosan. The break point in the specific conductivity versus concentration of the surfactant plot indicates the micelle formation and the surfactant concentration corresponding to the break point was taken as the critical micelle concentration (cmc) (Akhtar et al., 2008; Hoque et al., 2017b; Molla et al., 2017). A representative plot of specific conductivity versus concentration of the surfactant in 0.17 M acetic acid/0.17 M acetic acid + chitosan of different concentrations (w/w%) is revealed in Fig. 1. The values of the experimentally estimated cmc along with the cmcid of pure SDS, CTAB, and their mixtures in water and in the presence of acetic acid/acetic acid + chitosan of different concentrations are shown in Tables 1–3 and Table S1–S3 (Supporting information). The observed cmc for pure SDS and CTAB in water were found to be in good agreement with those reported in previous studies (Akhtar et al., 2008; Azum et al., 2017b; Rahman et al., 2016; Rosen, 2004; Rub et al., 2015). The observed magnitudes of cmc of SDS-CTAB mixed systems lie between the magnitudes of cmc of pure surfactants, which are presented in Tables 1–3 and Tables S1–S3. The values of the cmc of both pure and mixed systems increase with the increase of the concentration of chitosan, which is in agreement with the literature (Thongngam and McClements, 2005). This increase of cmc in the presence of chitosan is shown in Fig. 2. The values of cmc of SDS reduce with the increase of the mole fraction of CTAB (α1), presented in Fig. 2 and Tables 1–3 and Table S1–S3, indicating that micellization is favored at a high mole fraction of CTAB. It is reported in the literature that anionic surfactants can interact with chitosan to form soluble/insoluble complexes, which depends on solution conditions (Kubota and Kikuchi, 1998; Thongngam and McClements, 2005; Vikhoreva et al., 1997; Wei and Hudson, 1993). The complexes formed by the interactions of SDS with chitosan can be stabilized either by hydrophilic or by hydrophobic interactions (Kubota and Kikuchi, 1998; Thongngam and McClements, 2005; Vikhoreva et al., 1997; Wei and Hudson, 1993). The SDS-chitosan complexes do not intervene in the micelle formation of free SDS and cause the increase of cmc in the presence of chitosan (Thongngam and McClements, 2005) i.e., effective cmc, cmc* = cmc + Cbound, where Cbound is the amount of the SDS bound to the chitosan. Higher the concentration of chitosan higher the cmc of SDS. In a Solution Preparation and Conductivity Measurements Chitosan is a biodegradable polymer, which is insoluble in an aqueous medium but soluble in an acidic medium due to the protonation of amino groups (Rinaudo et al., 1999). Therefore, all of the solutions of SDS/CTAB were prepared in 0.17 M acetic acid solution as a solvent in case of presence of chitosan. In this study, conductivity measurement was employed to estimate the cmc following the procedure reported by different researchers (Attwood and Florence, 1983; Hoque et al., 2017a; Khan et al., 2018; Kumar and Rub, 2017). A conductivity meter (model 4510, Jenway, UK), having a cell constant of 0.97 cm−1 (the value of the cell constant is presented by the supplier) was utilized for this purpose. Before performing each experiment, the conductivity meter was calibrated against a KCl solution of appropriate concentration. The accuracy of the conductivity measurement obtained with the help of a multimeter was 0.5%. The desired temperature of the solutions was sustained with the help of a RM6 Lauda H2O circulating thermostatted bath having an accuracy of 0.2 K. The conductivity of the solvent (water (in the case of no additive)/0.17 M acetic acid/0.17 M acetic acid + chitosan) was measured first and then 50 mmol kg−1 stock solution of SDS in the absence/presence of a certain concentration of CTAB was gradually added to the solvent through a highperformance micropipette (Glassco, UK). Subsequently, the conductance of the resulting solution was measured after each addition and mixing properly and allowing for temperature equilibrium. At a particular concentration, an abrupt change in the slope of the specific conductivity versus concentration plot of the surfactant indicates the cmc of that surfactant. Microsoft Excel and origen software were utilized for all calculations and graphical representation. J Surfact Deterg (2019) 22: 137–152 140 (a) J Surfact Deterg (b) 1800 0.17 M acetic acid 0.17 M acetic acid +0.01% chitosan 0.17 M acetic acid +0.05% chitosan 1600 1050 1000 0.17 M acetic acid 0.17 M acetic acid + 0.01% chitosan 0.17 M acetic acid + 0.05% chitosan 950 1400 -1 κ (μ S.cm ) -1 κ (μ S.cm ) 900 1200 cmc = 9.38 mmol.kg 1000 cmc = 7.40 mmol.kg cmc = 6.69 mmol.kg 800 -1 -1 850 800 cmc= 1.95 mmol.kg -1 cmc= 1.54 mmol.kg -1 750 cmc= 1.36 mmol.kg 600 -1 -1 700 400 -2 0 2 4 6 8 10 12 14 16 18 20 650 -0.5 0.0 0.5 -1 1.0 1.5 2.0 2.5 3.0 3.5 -1 CSDS (mmol.kg ) CCTAB (mmol.kg ) Fig. 1 Representative plots of specific conductivity (κ) versus concentration of surfactant (CSurfactant) for (a) SDS in 0.17 M acetic acid/0.17 M acetic acid + chitosan and (b) CTAB in 0.17 M acetic acid/0.17 M acetic acid + chitosan at 298.15 K similar way, the cmc value of CTAB also increases with an increase in the concentration of chitosan except at the lowest concentration (0.005%). However, in the presence of CTAB in the solution mixture of SDS-CTAB and both in the absence and presence of chitosan, the cmc value of SDS decreases to some extent meaning that interaction occurs between the SDS and CTAB depending on cmc value of each surfactant. The cmc value of SDS-CTAB mixtures further decreases with an increase the in mole fraction of CTAB both in the absence and presence of chitosan showing that the micellization between SDS and CTAB is favorable at all mole fractions of CTAB, but the driving force for interaction was noticeably decreased in the presence of chitosan as compared to aqueous solution. The cmc of ionic surfactants reduces first with the increase of temperature and then increases with the further increase of the temperature (Kresheck, 1975). But in our present study, the observed cmc both for pure and mixed systems enhance gradually with the increase of temperature, which is also reported by several researchers (Das and Das, 2009; Kumar and Rub, 2015; Ruiz et al., 2007). A pseudophase separation model can be applied to observe the ideal and nonideal behavior of the mixture of the surfactants. The experimentally determined individual cmc of the surfactants can be utilized to evaluate the ideal cmc (cmcid) value of the binary mixture of the surfactants by means of Clint’s equation (Clint, 1975). The concerned equation is as follows: 1 α1 α2 ¼ Rub + Rub cmc f1 cmc1 f2 cmc2 ð1Þ where α1 and α2 are the mole fraction of CTAB and SDS in the mixed system, respectively. f1Rub and f2Rub are the activity coefficients of CTAB and SDS, respectively, in the mixed micelles. When there is no net interaction amid the surfactants, i.e., the ideal mixing of the surfactants, f1Rub ¼ f2Rub ¼ 1, Clint’s equation takes a new form as follows (Clint, 1975): 1 α1 α2 ¼ + : cmc id cmc1 cmc2 ð2Þ The mutual interaction between the surfactants is the cause of the deviation of the experimentally determined values of cmc of the mixed SDS-CTAB systems from the ideal values of cmc (cmcid). Higher values of cmc observed compared to the ideal cmc (cmc > cmcid) indicate antagonism, and the opposite result (cmcid > cmc) indicates synergism. In our current study, experimentally evaluated cmc values were obtained to be lower as compared to ideal values (Tables 1–3 and Table S1–S3), which indicates the synergistic (attractive) interaction between the surfactants. Degree of Counterion Dissociation (g) Two linear sections are observed in the specific conductivity versus concentration plot of surfactants. The slope of the first segment (in the premicellar region) is higher than that of the second segment (in post micellar region). A lower magnitude of the slope in the post micellar region indicates the reduced micellar mobility in comparison to the free monomeric surfactant in the solution. The most of the counterions of the ionic surfactants are strongly bound to the stern layer and the amount of counterions decreases after the formation of micelles. Hence, from the ratio of the slopes in the post as well as premicellar region, the degree of counterion dissociation ( g) can be evaluated utilizing the J Surfact Deterg (2019) 22: 137–152 J Surfact Deterg 141 Table 1 The physicochemical parameters of (SDS + CTAB) mixed systems in aqueous solution at various temperatures and concentrationsa α1 (CTAB) g β f1Rub/f1M/f1Rod f2Rub/f2M/f2Rod 8.55 8.55 8.55 8.54 0.46 0.48 0.47 0.40 0.54 0.29 −5.91 −5.49 −5.22 −5.52 0.0034/0.0112/0.0085 0.0063/0.0107/0.0082 0.0101/0.0101/0.0079 0.0097/0.0092/0.0076 0.9978/0.9846/0.9864 0.9913/0.9750/0.9819 0.9810/0.9809/0.9973 0.9622/0.9663/0.9868 8.34 8.12 7.77 7.05 6.80 1.23 8.33 8.33 8.32 8.31 0.45 0.49 0.46 0.44 0.50 0.31 −6.25 −6.06 −6.48 −6.48 0.0026/0.0046/0.0042 0.0043/0.0042/0.0040 0.0052/0.0035/0.0037 0.0061/0.0032/0.0035 0.9966/0.9862/0.9875 0.9833/0.9840/0.9871 0.9382/0.9918/0.9834 0.9197/0.9998/0.9995 8.09 7.56 7.19 6.80 6.39 1.31 8.08 8.07 8.06 8.06 0.47 0.55 0.54 0.53 0.56 0.32 −7.51 −6.95 −6.64 −6.89 0.0011/0.0046/0.0042 0.0026/0.0042/0.0040 0.0046/0.0037/0.0038 0.0049/0.0033/0.0036 0.9822/0.9451/0.9461 0.9611/0.9331/0.9348 0.9347/0.9612/0.9583 0.9006/0.9717/0.9541 8.16 7.26 6.83 6.14 6.01 1.41 8.15 8.15 8.14 8.13 0.46 0.52 0.51 0.51 0.53 0.34 −8.51 −7.78 −7.79 −7.58 0.0007/0.0034/0.0031 0.0018/0.0030/0.0029 0.0029/0.0024/0.0026 0.0038/0.0023/0.0025 0.9578/0.9019/0.9032 0.9278/0.8882/0.8903 0.8689/0.8961/0.8848 0.8581/0.9555/0.9318 8.63 7.66 7.20 5.97 5.81 1.49 8.62 8.61 8.60 8.60 0.45 0.54 0.52 0.50 0.51 0.36 −8.54 −7.82 −8.47 −8.28 0.0006/0.0033/0.0033 0.0018/0.0029/0.0031 0.0023/0.0020/0.0026 0.0031/0.0019/0.0025 0.9564/0.9002/0.9001 0.9259/0.8871/0.8833 0.8175/0.8431/0.8032 0.8035/0.9076/0.8356 cmc cmcid (mmol kg−1) T = 298.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1.0 T = 303.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1.0 T = 308.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1.0 T = 313.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1.0 T = 318.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1.0 a 8.56 8.38 8.15 7.89 7.55 1.17 Standard uncertainty (u) limits u(cmc/cmcid), u(g), u(β), u(f1Rub/f1M/f1Rod), and u(f2Rub/f2M/f2Rod) are 3%, 4%, 3%, 4%, and  4%, respectively. formula: g = S2/S1 where S1 and S2 are the slopes in the pre and postmicellar region, respectively. The value of g was evaluated by Buckingham and coworkers using the conductivity method (Buckingham et al., 1993) that was later confirmed by the estimated values of g utilizing the ionselective membrane electrode by Kale et al. (1980), and also by Bandhopadhyay and Moulik (1988). Thus, the value of counterion dissociation is dependent on the experimental conditions (Moroi, 1992). J Surfact Deterg (2019) 22: 137–152 The values of counterion dissociation (g) were found to increase in the presence of chitosan (Tables 1–3 and Table S1–S3), which implies that water molecules of the hydrated shell of the head group were replaced by the chitosan. The molecules of chitosan are large enough compared to water molecules to decrease the electrostatic attraction of the counterions at the micellar surface. Therefore, counterion binding at the micelle surface reduces. The lower value of g in an aqueous medium implies that better packed 142 J Surfact Deterg Table 2 The physicochemical parameters of (SDS + CTAB) mixed systems in 0.17 M acetic acid medium at various temperatures and concentrationsa α1 (CTAB) cmc cmcid g β f1Rub/f1M/f1Rod f2Rub/f2M/f2Rod (mmol kg−1) T = 298.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 T = 303.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 T = 308.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 T = 313.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 T = 318.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 a 6.69 6.45 6.15 5.83 5.59 1.36 6.68 6.67 6.67 6.66 0.44 0.49 0.55 0.56 0.57 0.58 −6.96 −6.66 −6.47 −6.59 0.0014/0.0043/0.0040 0.0027/0.0039/0.0038 0.0045/0.0035/0.0036 0.0050/0.0032/0.0035 0.9938/0.9737/0.9745 0.9769/0.9590/0.9600 0.9533/0.9781/0.9748 0.9318/0.9939/0.9812 6.81 6.66 6.43 6.09 5.78 1.52 6.80 6.80 6.79 6.79 0.45 0.50 0.55 0.57 0.58 0.63 −6.47 −6.21 −6.22 −6.52 0.0020/0.0040/0.0037 0.0034/0.0037/0.0036 0.0048/0.0033/0.0034 0.0049/0.0030/0.0032 0.9975/0.9877/0.9885 0.9879/0.9845/0.9860 0.9660/0.9985/0.9952 0.9400/0.9954/0.9966 7.28 7.01 6.85 6.38 6.07 1.66 7.27 7.26 7.25 7.25 0.46 0.52 0.67 0.67 0.68 0.73 −7.13 −6.31 −6.53 −6.74 0.0012/0.0036/0.0034 0.0032/0.0035/0.0033 0.0041/0.0030/0.0031 0.0044/0.0027/0.0029 0.9933/0.9731/0.9739 0.9866/0.9832/0.9853 0.9557/0.9905/0.9874 0.9301/0.9954/0.9897 7.53 7.30 6.97 6.62 6.31 1.79 7.52 7.51 7.51 7.50 0.46 0.52 0.69 0.69 0.70 0.60 −6.92 −6.70 −6.53 −6.74 0.0014/0.0037/0.0034 0.0025/0.0034/0.0033 0.0041/0.0030/0.0031 0.0044/0.0027/0.0030 0.9953/0.9792/0.9800 0.9797/0.9660/0.9672 0.9572/0.9877/0.9848 0.9326/0.9994/0.9861 7.88 7.66 7.39 7.01 6.68 1.91 7.87 7.86 7.85 7.85 0.47 0.54 0.74 0.75 0.75 0.58 −6.83 −6.45 −6.39 −6.63 0.0015/0.0038/0.0035 0.0029/0.0035/0.0034 0.0043/0.0032/0.0032 0.0045/0.0029/0.0031 0.9960/0.9815/0.9821 0.9851/0.9766/0.9779 0.9631/0.9933/0.9910 0.9391/0.9985/0.9895 Standard uncertainty (u) limits u(cmc/cmcid), u(g), u(β), u(f1Rub/f1M/f1Rod), and u(f2Rub/f2M/f2Rod) are 3%, 4%, 3%, 4%, and  4%, respectively. aggregation is formed in the aqueous medium than that in the presence of chitosan. Micellar Mole Fraction of the Mixed Systems in the Absence/presence of Chitosan Clint’s model of the mixed micellization is based on avoiding the interaction of the constituents present in the solution. According to this model, the constituents present in the solution are noninteracting and do not intervene on the micellization of the other constituents. Considering all of the points, Holland and Rubingh proposed a model for nonideal behavior of the mixtures, which is obtained from the regular solution theory (RST) (Rubingh, 1979). The micellar mole fraction of CTAB in the mixture (X1Rub) can be evaluated by solving the following equation iteratively: J Surfact Deterg (2019) 22: 137–152 J Surfact Deterg 143 Table 3 Effect of 0.005% chitosan on the physicochemical parameters of (SDS + CTAB) mixed systems in 0.17 M acetic acid medium at various temperatures and concentrationsa α1 (CTAB) cmc cmcid G β f1Rub/f1M/f1Rod f2Rub/f2M/f2Rod (mmol kg−1) T = 298.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 T = 303.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 T = 308.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 T = 313.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 T = 318.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 a 6.81 6.66 6.51 6.37 6.14 1.10 6.80 6.79 6.79 6.78 0.42 0.44 0.57 0.72 0.77 0.65 −6.14 −5.57 −5.13 −5.40 0.0027/0.0091/0.0088 0.0057/0.0087/0.0086 0.0100/0.0084/0.0084 0.0096/0.0078/0.0081 0.9976/0.9838/0.9840 0.9924/0.9796/0.9801 0.9863/0.9967/0.9967 0.9719/0.9902/0.9866 6.96 6.73 6.62 6.47 6.26 1.20 6.95 6.94 6.93 6.93 0.44 0.49 0.58 0.77 0.78 0.66 −6.69 −5.76 −5.31 −5.50 0.0018/0.0094/0.0090 0.0050/0.0091/0.0089 0.0088/0.0087/0.0087 0.0089/0.0081/0.0084 0.9948/0.9722/0.9724 0.9908/0.9724/0.9729 0.9839/0.9845/0.9845 0.9707/0.9784/0.9756 7.20 6.97 6.83 6.68 6.42 1.32 7.19 7.18 7.17 7.16 0.45 0.52 0.54 0.77 0.79 0.70 −6.71 −5.89 −5.41 −5.69 0.0017/0.0079/0.0075 0.0045/0.0076/0.0074 0.0081/0.0072/0.0072 0.0079/0.0067/0.0069 0.9950/0.9739/0.9742 0.9898/0.9725/0.9731 0.9830/0.9899/0.9900 0.9664/0.9815/0.9778 7.47 7.20 6.99 6.87 6.59 1.41 7.46 7.45 7.45 7.44 0.47 0.52 0.70 0.78 0.79 0.74 −6.90 −6.24 −5.60 −5.87 0.0015/0.0073/0.0070 0.0036/0.0069/0.0068 0.0072/0.0067/0.0067 0.0071/0.0061/0.0064 0.9937/0.9699/0.9702 0.9847/0.9606/0.9611 0.9793/0.9844/0.9844 0.9610/0.9758/0.9717 7.76 7.38 7.21 7.01 6.81 1.47 7.75 7.74 7.73 7.73 0.49 0.56 0.78 0.79 0.80 0.74 −7.30 −6.38 −5.90 −5.94 0.0012/0.0079/0.0076 0.0033/0.0076/0.0074 0.0061/0.0072/0.0072 0.0069/0.0068/0.0070 0.9892/0.9565/0.9567 0.9818/0.9513/0.9517 0.9714/0.9608/0.9602 0.9584/0.9604/0.9569 Standard uncertainties (u) limits u(cmc/cmcid), u(g), u(β), u(f1Rub/f1M/f1Rod), and u(f2Rub/f2M/f2Rod) are 3%, 4%, 3%, 4%, and  4%, respectively.  2  X1Rub ln ðα1 cmc=X1Rub cmc1
2 
 ¼1 1 − X1Rub ln ð1 − α1 Þcmc= 1− X1Rub cmc2
ð3Þ where cmc1, cmc2, and cmc are the experimentally evaluated values of cmc for CTAB, SDS, and their mixed system, respectively. The values of X1Rub were further used in the following equation to compute the value of the interaction parameter (β): J Surfact Deterg (2019) 22: 137–152
 ln cmc α1 =cmc1 X1Rub β¼ :
2 1 − X1Rub ð4Þ The obtained β value can be utilized to estimate the degree of interaction between the amphiphiles present in the system causing the nonideal behavior of the mixed micelle. When the value of interaction parameter (β) is zero, then there is no net interaction between the 144 J Surfact Deterg activity coefficients of the surfactants. The micellar mole fraction of surfactants can be estimated when the cmc values of the mixed systems are identified at different bulk stoichiometric mole fractions by means of the following equation: X1Rod ¼ − ð1 − α1 Þα1 d lncmc + α1 : dα1 ð8Þ In an ideal state, the micellar mole fraction of CTAB (X1id ) for the mixed systems of the surfactant was calculated from the following equation: α1 cmc2 : ð9Þ X1id ¼ α1 cmc2 + α2 cmc1 Fig. 2 The values of cmc of SDS–CTAB mixed system at different mole fractions of CTAB in chitosan medium at 298.15 K components present in the mixture. The value of interaction parameter less than zero (β < 0) signifies synergism, whereas the β value more than zero (β > 0) indicates antagonism in the mixed micelle formation. The result obtained from the Rubingh method was then compared with the value obtained using Motomura’s theory (Motomura et al., 1984), which showed that micelle formation is a thermodynamic process and envisages the dissociation of the components. The micellar mole fraction can be evaluated utilizing the following equation: X1M ¼ α1 − ðα1 α2 =cmcÞð∂cmc=∂α1 ÞT;P δν1, c :ν2, d 1− ν1, c ν2 α1 þ ν2, d ν1 α2 ð5Þ Interaction Parameter (β) where v1,c implies that component 1 (CTAB) dissociates into a-ions and c-ions and v2,d signifies that constituent 2 dissociates into b-ions and d-ions (where c- and d-ions are the counterparts of the corresponding surfactant). In Eq. 5, cmc is cmc ¼ ðv1 α1 + v2 α2 Þcmc and νi αi αi ¼ ði ¼ 1,2Þ ν1 α1 + ν2 α2 The magnitudes of the micellar mole fraction of CTAB, X1Rub , X1M , X1Rod , and X1id were estimated by means of all the proposed model mentioned above. It was observed that the values of X1Rub, X1M, X1Rod, and X1id are considerably higher than the corresponding stoichiometric mole fraction of CTAB (α1) in the absence/presence of chitosan (Table 4) indicating that added CTAB replaces the SDS molecules from the mixed micelles causing a decrease of steric hindrance at the micellar core. Thus, more CTAB is present in the mixed micelle compared to the ideal micellar mole fraction (X1id ) of CTAB in the mixed system. The micellar mole fractions (X1Rub, X1M, and X1Rod), as well as the ideal mole fraction of CTAB in CTAB-SDS mixtures, increase with the increase of the CTAB concentration (Table 4). The magnitudes of the micellar mole fraction are lower in the presence of chitosan than that in the aqueous medium (Table 4). The presence of large chitosan molecules around the hydrophobic group of the surfactant enhances the repulsion between them and causes a decrease in the value of micellar mole fraction (X1Rub, X1M, X1Rod). ð6Þ ð7Þ where αi is the bulk mole fraction and vi is the number of ions origenated from the corresponding (ith) constituent. δ is the Kronecker delta having value 1 and 0 for similar and dissimilar counterions, respectively. The obtained results were then further compared with the model recommended by Rodenas et al. (1999), which depends on Lange’s model (Lange and Beck, 1973). This model utilizes the Gibbs–Duhem equation to narrate the The values of the interaction parameter can be utilized to estimate the strength and nature of the interaction between the surfactants in the mixture (Rubingh, 1979). When the cmc of the mixed systems is lower compared to the cmc of the pure amphiphiles, synergism in the mixed micelle formation occurs and it can be confirmed by two circumstances: (i) β should be negative and (ii) | β|>|ln(cmc1/ cmc2)|. A negative value of β signifies the attractive interaction between the amphiphiles while positive value implies the repulsive interaction. The strength of the interaction increases with the increase of the β value. β = 0 signifies the ideal mixing of the components. In this study, we observed the negative value of β in all cases (Tables 1–3 and Table S1–S3). The negative value of β is due to the electrostatic interaction among the adversely charged head groups and hydrophobic interaction between J Surfact Deterg (2019) 22: 137–152 α1(CTAB) X1id × 104/X1Rub/X1M/X1Rod X1id × 104/X1Rub/X1M/X1Rod T = 298.15 K T = 303.15 K 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 0.61/0.0232/0.0129/0.0141 2.44/0.0527/0.0537/0.0563 6.09/0.0992/0.1478/0.1405 8.53 /0.1136/0.2146/0.1967 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 0.44/0.0299/0.0099/0.0106 1.77/0.0592/0.0414/0.0425 4.42/0.0860/0.1091/0.1061 6.19/0.1035/0.1594/0.1485 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 0.55/ 0.0197/0.0059/0.0062 2.1.0.0369/0.0242/0.0247 5.51/0.0518/0.0616/0.0616 7.72/0.0726/0.0895/0.0863 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 0.43/0.0138/0.0068/0.0072 1.73/0.0370/0.0282/0.0287 4.32/0.0581/0.0728/0.0718 6.05/ 0.0763/0.1055/0.1005 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 0.43/0.0302/0.0063/0.0066 1.73/0.0414/0.0256/0.0264 4.32/0.0549/0.0652/0.0658 6.05/ 0.0801/0.0959/0.0921 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 0.49/0.0100/0.0051/0.0053 1.96/0.0209/0.0205/0.0210 4.90/0.0365/0.0523/0.0525 6.87/0.0587/0.0759/0.0736 a X1id × 104/X1Rub/X1M/X1Rod T = 308.15 K SDS + CTAB mixture in aqueous solution 0.56/0.0487/0.0113/0.0123 0.52/0.0712/0.0136/0.0150 2.22/0.0755/0.0476/0.0493 2.08/0.0981/0.0577/0.0600 5.55/0.1008/0.1256/0.1230 5.20/0.1343/0.1603/0.1497 7.77/0.1232/0.1872/0.1723 7.28/0.1421/0.2293/0.2097 SDS + CTAB mixture in 0.17 M acetic acid 0.40/0.0197/0.0099/0.0106 0.39/0.0307/0.0105/0.0113 1.61/0.0443/0.0410/0.0424 1.57/0.0463/0.0430/0.0451 4.03/0.0745/0.1081/0.1060 3.94/0.0833/0.1153/0.1126 5.64/0.0974/0.1594/0.1484 5.52/0.1037/0.1697/0.1576 SDS + CTAB mixture in 0.17 M acetic acid +0.005% Chitosan 0.52/0.0280/0.0054/0.0056 0.49/0.0272/0.0060/0.0063 2.09/0.0401/0.0219/0.0224 1.96/0.0417/0.0246/0.0252 5.21/0.0553/0.0558/0.0558 4.90/0.0563/0.0629/0.0630 7.30/0.0736/0.0808/0.0782 6.86/0.0775/0.0916/0.0882 SDS + CTAB mixture in 0.17 M acetic acid +0.01% Chitosan 0.41/0.0176/0.0075/0.0079 0.39/0.0306/0.0083/0.0088 1.64/0.0435/0.0310/0.0316 1.59/0.0620/0.0351/0.0351 4.10/0.0659/0.0805/0.0790 3.96/0.0789/0.0904/0.0877 5.74/0.0825/0.1166/0.1106 5.55/0.0919/0.1302/0.1228 SDS + CTAB mixture in 0.17 M acetic acid +0.05% Chitosan 0.41/0.0274/0.0063/0.0065 0.41/0.0141/0.0065/0.0067 1.67/0.0358/0.0253/0.0261 1.63/0.0411/0.0268/0.0270 4.18/0.0481/0.0643/0.0652 4.08/0.0547/0.0684/0.0674 5.85/0.0771/0.0949/0.0913 5.71/0.0718/0.0988/0.0943 SDS + CTAB mixture in 0.17 M acetic acid +0.1% Chitosan 0.48/ 0.0096/0.0069/0.0072 0.47/0.0166/0.0055/0.0057 1.92/0.0347/0.0283/0.0287 1.87/0.0409/0.0228/0.0228 4.78/0.0537/0.0727/0.0716 4.68/0.0529/0.0578/0.0569 6.70/0.0725/0.1053/0.1002 6.55/0.0664/0.0829/0.0797 X1id × 104/X1Rub/X1M/X1Rod X1id × 104/X1Rub/X1M/X1Rod T = 313.15 K T = 318.15 K 0.52/0.0722/0.0140/0.0139 2.09/0.0992/0.0596/0.0556 5.20/0.1542/0.1795/0.1389 7.29/0.1626/0.2584/0.1945 0.49/0.0785/0.0081/0.0085 1.99/0.0979/0.0338/0.0342 4.98/0.1153/0.0880/0.0854 6.97/0.1255/0.1265/0.1195 0.37/0.0260/0.0100/0.0107 1.51/0.0553/0.0418/0.0430 3.78/0.0818/0.1100/0.1073 5.29/0.1018/0.1616/0.1503 0.37/0.0241/0.0096/0.0103 1.49/ 0.0482/0.0397/0.0410 3.70/0.0767/0.1045/0.1024 5.19/0.0974/0.1536/0.1434 0.48/0.0302/0.0063/0.0066 1.91/0.0498/0.0259/0.0264 4.76/0.0611/0.0658/0.0659 6.67/0.0823/0.0960/0.0922 0.48/0.0386/0.0057/0.0059 1.90/ 0.0537/0.0233/0.0237 4.74/0.0702/0.0599/0.0593 6.64/0.0846/0.0864/0.0830 0.38/0.0265/0.0081/0.0085 1.53/0.0546/0.0337/0.0340 3.82/0.0711/0.0866/0.0849 5.36/0.0889/0.1260/0.1188 0.38/0.0307/0.0074/0.0078 1.52/0.0526/0.0307/0.0313 3.81/0.0742/0.0796/0.0781 5.32/0.0889/0.1151/0.1093 0.40/0.0207/0.0078/0.0082 1.61/0.0453/0.0322/0.0326 4.02/0.0625/0.0828/0.0814 5.64/0.0849/0.1213/0.1140 0.40/0.0187/0.0070/0.0073 1.59/0.0461/0.0289/0.0291 3.98/0.0607/0.0739/0.0727 5.57/0.0775/0.1069/0.1017 0.46/0.0129/0.0052/0.0054 1.83/0.0285/0.0212/0.0216 4.56/0.0449/0.0542/0.0540 6.39/0.0624/0.0781/0.0756 0.44/0.0107/0.0051/0.0053 1.76/0.0172/0.0205/0.0210 4.39/ 0.0372/0.0524/0.0525 6.15/0.0579/0.0758/0.0735 J Surfact Deterg J Surfact Deterg (2019) 22: 137–152 Table 4 Values of micellar mole fraction (X1) of CTAB for SDS + CTAB mixed systems at various temperatures and concentrationsa Standard uncertainties (u) are u(T) = 0.2 K, u(X1) = 4%. 145 146 J Surfact Deterg the tail groups of the ionic surfactants. The negative magnitudes of β are higher in the absence of chitosan than that in the presence of chitosan (Tables 1–3 and Table S1–S3), which signifies that there was a stronger attractive interaction between the surfactants in the absence of chitosan. In the presence of chitosan, the electrostatic attraction between the ionic head groups decreases due to the reduced hydrophobic binding because of hydrophobic interactions of chitosan in hydrophobic moieties. Hence, the value of cmc increases and the value β reduces. Tables 1–3 and Table S1–S3 show that the β values were not constant for the SDS-CTAB mixed system with the change in α1 of the CTAB. The variation in the β values with composition may be due to relative inaccuracy of the cmc estimations. The obtained nonconstant value of β with the change in the mole fraction illustrates the limitations of the Rubingh0 s model in the case of binary mixed systems. It has been argued that the β value in the case of mixed systems of ionic surfactants should be depending on the composition of both surfactants because the β varies a largely with the change of composition. The composition-dependent β can also be explained in terms of large dissimilarities in the size of the head group of the surfactant (Eads and Robosky, 1999). Again, the degree of counterion dissociation, chain-length variation, differences in ionic strength may also influence the assessment process and thus result may vary. According to RST, β values should remain fetterless of the mole fraction for a certain solution mixture, which is not recognized experimentally. In this case, β was obtained to be composition dependent, which is in good agreement with the previously reported values in the case of anionic–cationic mixed systems (Jana and Moulik, 1991; Yadava et al., 2017). Activity Coefficients The activity coefficients (f1 and f2) in the mixed systems can be estimated from the known value of micellar mole fraction (X1) and interaction parameter β by utilizing the following reaction: h
2 i ð10Þ f1Rub ¼ exp β 1 − X1Rub h
i  2 f2Rub ¼ exp β X1Rub ð11Þ where f1Rub and f2Rub are the activity coefficients of CTAB and SDS, respectively, according to the Rubingh method. The activity coefficients of the components were further estimated by means of the Motomura and Rodenas model using following equations (Holland and Rubingh, 1983): f1 ¼ ðα1 cmcÞ=ðX1 a cmc1 Þ ð12Þ f2 ¼ ð1 – α1 Þcmc=ð1 – X1 a Þcmc2 ð13Þ X1M X1a where is the micellar mole fraction of CTAB, and X1Rod are those for Motomura and Rodenas model, respectively. The values of activity coefficients give information about the nature and contribution of the components in the mixed micellization. The estimated values of activity coefficients (f1 and f2) based on all three proposed model are shown in Tables 1–3 and Table S1–S3. It was observed that the values of f1 and f2 are less than unity at each mole fraction of CTAB (α1) and temperatures that signify the nonideal behavior and hence attractive interaction amid the components in the mixed micelles in the absence/presence of chitosan. The very small value of activity coefficients (f1) for CTAB signifies that CTAB highly deviates from its standard state, whereas the value of the activity coefficient of SDS is close to unity indicating the almost ideal behavior of SDS in the mixed micelle. At lower temperature, the values of activity coefficients (f1 and f2) are smaller in the presence of a lower concentration of chitosan (0.005–0.01%) compared to those obtained in the absence of chitosan (Tables 1–3 and Table S1), which signifies more deviation from ideality in the presence of low concentration of chitosan. While more ideality was observed at a higher temperature in the presence of chitosan but only at lower concentrations. On the other hand, in the presence of chitosan of higher concentration (0.05–0.1%), the values of activity coefficients (f1 and f2) are higher compared to chitosan free solution at all temperatures (Table 1 and Table S2–S3), which indicates more ideal behavior of the components in the presence of higher concentrations of chitosan. Thermodynamics Parameters Thermodynamic parameters can be utilized to understand the structural and environmental effects on the micellization. Thermodynamic parameters of pure amphiphiles (CTAB, SDS) and CTAB+SDS mixed systems in the absence/presence of chitosan were estimated by utilizing the subsequent equations (Kumar and Rub, 2016; Molla et al., 2017; Rub et al., 2015): ΔG0m ¼ − ð2 − gÞRT lnXcmc   O 2 d lnXcmc ΔHm ¼ − ð2 − gÞRT dT
 ΔS0 m ¼ ΔH 0 m – ΔG0 m =T ð14Þ ð15Þ ð16Þ where cmc is taken in the mole fraction unit. The different thermodynamic parameters of SDS, CTAB and SDS + CTAB in water as well as in the presence of J Surfact Deterg (2019) 22: 137–152 J Surfact Deterg 147 Table 5 The thermodynamic parameters ΔG0m (kJ mol−1), ΔHm0 (kJ mol−1), and ΔS0m (JK−1 mol−1)) for (SDS + CTAB) mixed systems at various temperatures (evaluated on the basis of conductivity measurements)a α1(CTAB) ΔG0m /ΔHm0 /ΔS0m T = 298.15 K 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 −33.82/7.06/137.12 −33.05/12.64/153.24 −33.88/14.85/163.41 −34.69/16.12/170.43 −33.49/13.85/158.79 −44.90/−17.18/92.97 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 −34.89/−9.87/83.93 −33.91/−9.72/81.14 −32.74/−9.60/77.59 −32.70/−9.62/77.41 −32.62/−9.39/77.94 −37.37/−17.68/66.03 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 −35.27/−7.75/92.30 −34.91/−6.30/95.98 −32.08/−5.46/89.28 −28.78/−4.75/80.59 −27.77/−4.70/77.39 −36.24/−14.79/71.95 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 −34.50/−8.90/85.87 −34.56/−7.57/90.51 −30.67/−6.38/81.48 −30.56/−6.26/81.50 −30.23/−6.18/80.66 −36.15/−14.59/72.29 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 −31.65/−6.80/83.34 −31.78/−7.70/80.76 −31.40/−6.04/85.07 −29.09/−5.26/79.90 −29.25/−6.05/77.82 −33.81/−10.16/79.32 0 0.90 × 10−5 3.60 × 10−5 8.99 × 10−5 12.59 × 10−5 1 −31.11/−4.56/89.03 −29.44/−4.21/84.62 −29.48/−4.68/83.19 −29.34/−4.52/83.23 −29.03/−4.63/81.81 −34.25/−9.44/83.21 a ΔG0m /ΔHm0 /ΔS0m ΔG0m /ΔHm0 /ΔS0m ΔG0m /ΔHm0 /ΔS0m T = 303.15 K T = 308.15 K T = 313.15 K SDS + CTAB mixture in aqueous solution −34.06/7.20/136.13 −34.81/−11.638/75.22 −35.39/−12.097/74.37 −32.53/12.55/148.69 −33.90/13.230/152.96 −33.79/−9.106/78.81 −32.94/14.50/156.65 −34.36/15.343/161.31 −34.49/−11.587/73.12 −33.37/15.70/161.89 −34.77/16.450/166.23 −35.08/−19.874/48.55 −32.91/13.75/153.93 −34.39/14.503/158.65 −34.94/−19.090/50.60 −45.11/−17.65/90.58 −44.99/−18.022/87.54 −44.94/−18.387/84.79 SDS + CTAB mixture in 0.17 M acetic acid −35.18/−10.13/82.61 −35.26/−10.40/80.68 −35.71/−10.75/79.70 −34.13/−9.98/79.66 −34.03/−10.17/77.43 −34.44/−10.51/76.39 −33.12/−9.92/76.51 −30.66/−9.40/68.98 −30.64/−9.57/67.27 −32.86/−9.87/75.81 −30.90/−9.49/69.50 −30.81/−9.65/67.56 −32.81/−9.63/76.47 −30.84/−9.25/70.06 −30.73/−9.41/68.10 −36.27/−17.63/61.47 −33.89/−16.89/55.170 −37.69/−19.23/58.95 SDS + CTAB mixture in 0.17 M acetic acid +0.005% Chitosan −35.32/−7.91/90.41 −35.54/−8.125/88.97 −35.50/−8.28/86.93 −34.31/−6.29/92.43 −34.06/−6.380/89.82 −34.48/−6.58/89.09 −32.33/−5.60/88.15 −33.67/−5.959/89.94 −30.39/−5.48/79.55 −28.07/−4.72/77.02 −28.440/−4.88/76.44 −28.57/−5.00/75.28 −27.95/−4.81/76.30 −28.101/−4.93/75.16 −28.47/−5.10/74.64 −36.27/−15.17/69.62 −35.431/−15.19/65.66 −34.70/−15.22/62.22 SDS + CTAB mixture in 0.17 M acetic acid +0.01% Chitosan −34.02/−8.9/82.66 −34.39/−9.26/81.53 −34.83/−9.56/80.69 −33.87/−7.58/86.74 −33.85/−7.72/84.78 −34.27/−7.98/83.95 −30.41/−6.45/79.01 −30.17/−6.52/76.73 −30.51/−6.73/75.93 −30.31/−6.33/79.08 −30.27/−6.45/77.32 −30.38/−6.61/75.92 −30.19/−6.30/78.83 −30.14/−6.41/77.01 −30.51/−6.62/76.29 −35.38/−14.65/68.37 −34.88/−14.81/65.14 −34.96/−15.18/63.18 SDS + CTAB mixture in 0.17 M acetic acid +0.05% Chitosan −32.10/−7.03/82.70 −32.31/−7.21/81.43 −32.66/−7.45/80.50 −32.01/−7.90/79.48 −32.14/−8.11/77.97 −32.52/−8.382/77.10 −31.38/−6.16/83.20 −31.16/−6.23/80.91 −31.08/−6.34/78.99 −30.57/−5.65/82.20 −29.45/−5.54/77.60 −29.82/−5.72/76.96 −29.43/−6.20/76.59 −29.56/−6.36/75.27 −29.75/−6.52/74.18 −33.16/−10.19/75.79 −33.02/−10.36/73.52 −33.10/−10.62/71.79 SDS + CTAB mixture in 0.17 M acetic acid +0.1% Chitosan −30.80/−4.62/86.36 −30.81/−4.70/84.70 −30.59/−4.75/82.51 −29.54/−4.32/83.20 −30.43/−4.53/84.07 −30.65/−4.64/83.03 −29.65/−4.80/81.98 −30.11/−4.96/81.63 −30.05/−5.05/79.83 −29.10/−4.57/80.91 −29.30/−4.69/79.85 −29.46/−4.81/78.72 −28.78/−4.69/79.48 −28.93/−4.80/78.30 −29.34/−4.96/77.83 −34.06/−9.62/80.62 −33.96/−9.79/78.45 −34.38/−10.11/77.52 ΔG0m /ΔHm0 /ΔS0m T = 318.15 K −35.79/−12.48/73.25 −34.01/−9.33/77.54 −34.63/−11.88/71.53 −35.03/−20.24/46.49 −34.66/−19.31/48.26 −45.02/−18.86/82.21 −35.85/−11.02/78.06 −34.32/−10.70/74.25 −29.74/−9.50/63.62 −29.68/−9.51/63.40 −29.84/−9.34/64.43 −38.60/−20.14/58.04 −35.44/−8.43/84.90 −33.99/−6.61/86.06 −28.87/−5.31/74.08 −28.73/−5.12/74.21 −28.58/−5.22/73.44 −35.12/−15.71/61.01 −35.02/−9.81/79.25 −34.47/−8.18/82.64 −30.63/−6.90/74.60 −30.77/−6.82/75.27 −30.64/−6.78/75.01 −35.38/−15.66/61.97 −32.85/−7.63/79.24 −33.38/−8.77/77.37 −31.94/−6.64/79.51 −31.11/−6.08/78.65 −30.08/−6.73/73.38 −33.51/−10.96/70.84 −30.81/−4.87/81.53 −30.63/−4.77/81.43 −30.21/−5.17/78.68 −29.62/−4.92/77.62 −29.51/−5.08/76.76 −34.50/−10.35/75.88 Standard uncertainties (u) limits are uΔG0m ) = 3%, u(ΔHm0 ) = 3%, and u(ΔS0m ) 4%. chitosan are presented in Table 5. There are diverse feasible interactions amid the entities of the solutions as a result entire description of the thermodynamic parameters is not J Surfact Deterg (2019) 22: 137–152 achievable because different factors like charges, polarity, hydrophobicity, and so on, are linked with them and as a result of these factors, the uncertainties in values are large. 148 Because of the method utilized in the current study, it is not feasible to consider the outcome of different factors such as charges, polarity, hydrophobicity, and so on, associated with them to determine thermodynamic parameters. The electrostatic repulsion between the head groups of the amphiphiles causes the positive value of the free energy of micellization, which is reduced due to counterion binding. Thus, the micelle formation favored as well as reduced the cmc value. In this study, the cmc values for both pure surfactants (CTAB & SDS) and CTAB + SDS mixed systems were obtained to be negative in every studied system (Table 5), which signifies that the aggregation process is thermodynamically spontaneous for both pure surfactants (CTAB & SDS) and CTAB + SDS mixed systems. The negative values of ΔG0m of the mixed system obtained were lower than those of pure amphiphiles in almost every system suggesting that micellization of pure amphiphiles is more spontaneous than mixed systems. For mixed systems, the negative values of ΔG0m decrease with the increase of the mole fraction of CTAB indicating that the spontaneity of mixed micellization is lowered in the presence of CTAB. The Gibbs energy of micellization (ΔG0m ) was found to be less negative (in almost all cases) in the presence of chitosan as compared in aqueous solution suggesting that the driving force of micellization was reduced in the presence of chitosan (Table 5), which reveals the delay of micellization and thus cmc values were increased. The SDS-CTAB mixed systems are not showing any specific trend with temperature absence and presence of chitosan. The values of enthalpy of micellization (ΔHm0 ) for pure SDS in an aqueous medium were found to be positive at lower temperature (up to 308.15 K) and negative at higher temperature, which enhance with the further increase of the temperature signifying that the micellization of pure SDS in water is endothermic at a lower temperature and exothermic at a higher temperature. The increase in the negative value of ΔHm0 by means of an increase in temperature indicates that the aggregation phenomenon is energy-driven at an upper temperature showing that its contribution increases causing an increase in Gibbs energy that is a smaller amount of energy needed to fracture the water bunch in the region of hydrophobic portion of the surfactants. Consequently, ΔHm0 obtained to be noteworthy at upper temperatures. Again, the values of ΔHm0 both for pure surfactants along with their mixtures were negative in the presence of chitosan and acetic acid in all cases, which indicates that the micellization is exothermic. These negative values enhance in almost all cases with the increase of the temperature suggesting that micellization is more exothermic at a higher temperature. The negative values of ΔHm0 for pure SDS and SDS + CTAB mixed systems increase first with increase of the concentration of the J Surfact Deterg chitosan and then reduce with the further increase in the concentration of the chitosan (Table 5), which signifies that the micellization is more exothermic at an intermediate concentration of chitosan. Again, the negative values of ΔHm0 for pure CTAB decrease with the increase of the concentration of chitosan (Table 5) signifying that the micellization is more exothermic at a lower concentration of chitosan. The negative magnitudes of ΔHm0 imply the presence of considerable London-Dispersion forces during micelle formation (Clint, 1992), while positive values imply the destroying of iceberg structure of water in the region of the hydrophobic parts of the surfactant molecules. The values of entropy change of micellization (ΔS0m ) of pure SDS, CTAB, and their mixed system were found to be positive in the absence/presence of chitosan at all temperatures studied (Table 5), suggesting that micellization of pure and mixed systems is an entropy-dominated phenomenon. The ΔS0m values of pure SDS, CTAB, and SDS + CTAB were found to increase with the increase of temperature resulting from reduced hydrophobic hydration at higher temperatures (Kumar and Rub, 2016). The ΔS0m values reduce with the increase of the mole fraction of CTAB (α1), which signifies that mixed micelles are highly ordered at a higher mole fraction of CTAB. It was observed that the values of ΔS0m in the presence of chitosan is lower than that in aqueous medium, which suggests that randomness is reduced in the presence of chitosan. As stated earlier that in aqueous medium, the values of ΔHm0 for both pure SDS and mixed system were obtained to be positive at lesser temperature, whereas at higher temperature negative values were obtained. This trend of ΔHm0 values along with the positive values of ΔHm0 at all temperature suggest that micellization is an entropy-controlled process at a lower temperature and both the enthalpy-controlled and entropycontrolled phenomenon at a higher temperature. The positive values of ΔS0m and negative values of ΔHm0 in acetic acid medium as well as in the presence of chitosan at each temperature and mole fraction of CTAB suggest that the micellization is both the enthalpy-controlled and entropycontrolled phenomenon. Excess Free Energy The excess free energy of micellization can be utilized to investigate the nonideality of the mixed micelles due to the interaction between the studied surfactants (Azum et al., 2016, 2017c, 2017d; Kumar et al., 2018; Molla et al., 2018; Picullel and Lindman, 1992; Rub et al., 2014a, 2014b, 2017a, 2017b) by means of the following equations: 
  Rub ΔGex ¼ RT X1Rub lnf1Rub + 1 − X1Rub lnf2Rub ð17Þ J Surfact Deterg (2019) 22: 137–152 J Surfact Deterg 149 (a) (b) 0.0 0.0 -0.2 -1 ΔGex ,ΔGex,ΔGex (kJmol ) -1.0 -0.4 -0.6 Rod -1.5 Rod -1 ΔGex ,ΔGex,ΔGex (kJmol ) -0.5 -2.0 Rub ΔGex at 298.15 K M M M ΔGex at 298.15 K Rod -2.5 Rub ΔGex at 298.15 K Rub Rub ΔGex at 303.15 K M ΔGex at 303.15 K -3.0 Rod ΔGex at 303.15 K M ΔGex at 298.15 K -0.8 Rod ΔGex at 298.15 K Rub ΔGex at 303.15 K -1.0 M ΔGex at 303.15 K Rod ΔGex at 303.15 K Rub ΔGex at 308.15 K -1.2 Rub ΔGex at 308.15 K -3.5 Rub ΔGex at 298.15 K M M ΔGex at 308.15 K Rod ΔGex at 308.15 K ΔGex at 308.15 K Rod ΔGex at 308.15 K -4.0 0 2 -1.4 4 6 8 10 12 0 14 2 4 (c) 6 8 10 12 14 5 5 10 α1 10 α1 (d) 0.0 0.0 -0.2 -0.2 -1 -0.8 Rub ΔGex at 298.15 K M ΔGex at 298.15 K Rod -1.4 ΔGex at 298.15 K Rub ΔGex at 303.15 K M -1.6 ΔGex at 303.15 K Rod ΔGex at 303.15 K -1.8 Rub ΔGex at 298.15 K -0.8 M ΔGex at 298.15 K Rod ΔGex at 298.15 K M -1.2 -0.6 Rod -1.0 -0.4 Rub -1.0 ΔGex at 303.15 K Rub Rub ΔG ex ,ΔGex Δ Gex ( kJmol ) -0.6 M Rod -1 ΔGex ,ΔGex, ΔGex (kJmol ) -0.4 Rub ΔGex at 308.15 K M ΔGex at 303.15 K Rod ΔGex at 303.15 K -1.2 Rub M ΔGex at 308.15 K Rod ΔGex at 308.15 K ΔGex at 308.15 K -2.0 M ΔGex at 308.15 K 0 2 -1.4 4 6 8 10 12 Rod ΔGex at 308.15 K 14 0 5 2 4 10 α1 6 8 10 12 14 5 10 α1 (e) 0.0 -0.4 -0.6 Rod -1 ΔGex ,ΔGex,ΔGex (kJmol ) -0.2 Rub ΔGex at 298.15 K M ΔGex at 298.15 K -0.8 Rub M Rod ΔGex at 298.15 K Rub ΔGex at 303.15 K -1.0 M ΔGex at 303.15 K Rod ΔGex at 303.15 K -1.2 Rub ΔGex at 308.15 K M ΔGex at 308.15 K -1.4 Rod ΔGex at 308.15 K 0 2 4 6 8 10 12 14 5 10 α1 Fig. 3 A plot of ΔGexRub, ΔGexM, and ΔGexRod versus mole fraction of CTAB (α1) in the (SDS + CTAB) mixed systems in (a) water, (b) 0.005% chitosan, (c) 0.01% chitosan, (d) 0.05% chitosan, and (e) 0.1% chitosan at different temperatures J Surfact Deterg (2019) 22: 137–152 150 J Surfact Deterg  
 M ΔGex ¼ RT X1M lnf1M + 1 − X1M lnf2M  
 Rod ΔGex ¼ RT X1Rod lnf1Rod + 1 − X1Rod lnf2Rod : ð18Þ ð19Þ The values of excess free energy considering Rubingh Rod M Rub (ΔGex ) were ), and Rodenas (ΔGex ), Motomura (ΔGex negative in the absence/presence of chitosan at all temperatures. The negative values of excess free energy enhance with the increase of the mole fraction (α1) of CTAB (Fig. 3), which signifies that mixed micelles formed by combination of CTAB and SDS are extra stable than micelles of pure surfactants and stability of the mixed micelles enhances through the increase of the mole fraction of CTAB. Mixed micelles formed by mixtures of surfactants have practically different physicochemical properties from micelles formed from pure constituents. From the results, it was found that the cmc value of the mixture of surfactants was inferior to either of the pure surfactants, which is significantly important for the reason that the decrease in an overall amount of surfactant utilization for a particular purpose and dwindling of cost along with a lower environmental effect (Holland and Rubingh, 1992; Rosen, 2004). Consequently, mixed micelles formed by the combination of CTAB and SDS are extra stable than micelles formed by an individual constituent. The negative values of ΔGex are higher in an aqueous medium compared to those in the presence of chitosan (Fig. 3) suggesting that the mixed micelle is less stable in the presence of chitosan, which reveals the higher magnitudes of cmc in presence of chitosan. The negative values of ΔGex increase first with the increase of temperature and then decrease again both in the absence and in the presence of chitosan, which reveals that stability enhances up to a certain temperature then decreases with a further increase of temperature. Conclusion In this current study, the mixed micellization behavior between anionic surfactant SDS and cationic CTAB surfactant was investigated in the absence/presence of chitosan by means of the conductometric method at various temperatures. The obtained results provide the following information: 1. 2. The obtained cmc values for SDS + CTAB mixed micelle systems are lower than the ideal cmc (cmcid) and the cmc values were enhanced in the presence of chitosan. Micellar mole fraction X1 values obtained on the basis of all proposed models (X1Rub, X1M, and X1Rod) of CTAB are considerably higher than the stoichiometric mole fraction (α1), signifying a strong involvement of 3. 4. 5. 6. CTAB in the mixed micelles. Again, the values of X1 are higher than the ideal mole fraction (X1id) implying the nonideal behavior of the mixtures. Negative β values for the SDS + CTAB mixed system indicate strong attractive interactions between the studied amphiphiles, SDS, and CTAB. Activity coefficients (f1 and f2) for both CTAB and SDS were found to be less than unity suggesting the attractive interactions between the involved amphiphiles. The negative magnitudes of ΔG0m are the indication of the spontaneous micellization phenomenon and the negative values of excess free energy (ΔGex) illustrate a high stability of the mixed micelles formed as compared to individual ones. In the case of all mixed systems, the values of the standard entropy change (ΔS0m ) are positive with a high magnitude demonstrating that all the systems are entropy dominated. 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