Thermodynamic Properties of Cetyltrimethylammonium Bromide in Ethanol-Water Media With/without the Presence of the Divalent Salt

order NaCl ＞ NaBr ＞ KCl ＞ KBr conductivity methods different the standard Abstract: The physicochemical properties of cetyltrimethylammonium bromide (CTAB) in pure water and ethanol-water mixtures in the presence and absence of MnSO 4 .6H 2 O were studied by measuring the conductivity at room temperature. The concentration range of CTAB was ~1.00 × 10 –5 M to ~1.00 × 10 –2 M and the concentration of MnSO 4 .6H 2 O was 0.001 M, 0.005 M, 0.01 M. With increasing ethanol content in the solvent composition, the critical micelle concentration (CMC) and the degree of micellar dissociation (α) of CTAB increased. With the help of CMC and α, the standard free energy of micellization (Δ G m ο ) was evaluated. With an increase in ethanol content, the negative values of Δ G m ο decreased. CTAB micellization was tested in the context of specific solvent parameters. The solvent conductivity ratio at CMC to limiting conductivity was employed as a solvophobic influence. The addition of salt (MnSO 4 .6H 2 O) decreases the CMC of CTAB due to the screening of the electrostatic repulsion of the head groups. Here, we report that micellization is strongly influenced by salt concentration. micellization, micellization,

unique component of the micelle aggregates. A cosolvent is a mixture of water and alcohol, whose various physical properties lie between those of water and alcohol; therefore, this solvent has significant importance in many applications.
The effect of salts on surfactants is still a hot issue in many areas. Recently, Ullah et al. studied the effect of salts on potassium N-cocoyl glycinate KCGl to see the interfacial behaviors using the oscillating drop shape analysis method. The experimental data of KCGl with salts may provide a hypothetical basis for its useful application in detergents, pharmaceuticals, cosmetics, petroleum and daily chemical industries 10 . Forland et al. studied the behavior of the micellar shape and size of sodium dodecyl sulfate in sodium chloride solutions using alcohol as the solvent media using small-angle neutron scattering SANS , dynamic light scattering DLS , and viscosity measurements. They found that sodium chloride and alcohols strongly influence the process of micellization 11 . Niraula et al. evaluated the CMC of SDS in water and methanol-water mixtures in the presence of studied salts is found in the order NaCl NaBr KCl KBr by conductivity methods at different temperatures. They also calculated the standard free energy of micellization, standard enthalpy of micellization, the standard entropy of micellization, the standard free energy of transfer and heat capacity of micellization 12 . Shah et al. investigated the effect of methanol and potassium chloride on the conductivity of an aqueous solution of CTAB at various temperatures. They reported that conductivity increases with increasing concentration of potassium chloride, whereas conductivity decreases with an increase in the volume fraction of methanol. The CMC values of CTAB in the presence and absence of potassium chloride increase with temperature 13 .
There have been many studies on CTAB in the presence of monovalent salts 13 17 . However, studies of CTAB in the presence of divalent salts are limited 17 19 . The CMC and various physical parameters of CTAB in the presence and absence of MnSO 4 .6H 2 O by varying the concentration of the cosolvent at room temperature have not been studied yet.
Here, we determine several parameters like pre-micellar, post-micellar slopes, critical micelle concentration CMC , degree of micellar dissociation α , standard free energy of micellization ΔG o m , the free energy of surfactant tail transfer ∆ G o trans of CTAB in the presence and absence of MnSO 4 .6H 2 O in the ethanol-water system at room temperature using conductivity methods and their correlation with the percentage of ethanol . We also correlate the values of the ratio of initial conductance to conductance at CMC K 0 /K CMC with the percentage of ethanol  24 . This type of calibration with the help of aqueous potassium chloride was also found in the literature 23 .

Study of conductance
The specific conductance of an electrolyte solution is a measure of its ability to conduct. The conductometric method is the most widely used because it is simple and accurate. The specific conductance of CTAB increased with an increase in the concentration of salt which is due to the increase in the number of ions per unit volume of the solution. The specific conductance of CTAB in distilled water was found to be the highest in comparison with the different volume fractions of ethanol. The reason for the decrease in specific conductance of CTAB with the addition of ethanol in the absence and presence of the salt is due to the decrease in the dielectric constant of the solution 25 .
Such types a decrease in the specific conductance of CTAB with the addition of ethanol was also found in the literature 26 . The specific conductance of CTAB in distilled water in the presence of 0.005 M salt was found to be higher than that of the different percentage of ethanol in the presence of 0.005 M salt Fig. 1 . Figure 1 is an in- teresting plot of conductance with concentration and gives linear fitting curves below and above the breakpoint. The description of the breakpoint of two straight-line fitting curves will be discussed later.

Study of critical micelle concentration CMC
The plots of specific conductance versus the concentration of cetyltrimethylammonium bromide in pure water and 10 , 20 and 30 of ethanol in the absence and the presence of 0.001 M and 0.01 M salt are depicted in Figs. 2a-c, respectively. The point of intersection of the two straight lines of the plot is the CMC. The CMC of CTAB increases with an increase in the volume fraction of ethanol. An increase in the volume fraction of ethanol results in increases in CMC at a fixed temperature. Such types of agreement were also found in the literature 27 . It is observed that the conductance of surfactant solutions decreases with an increase in the percentage of ethanol in both the premicellar and post-micellar regions.
In the conductance versus concentration graph, the slope of the line below the CMC is called the premicellar slope S 1 and the slope of the line above the CMC is called the Post-micellar slope S 2 . The values of the Pre-micellar slope S 1 and Post-micellar slope S 2 of CTAB in water and the presence of salts for the percentage of ethanol at room temperature are given in the form of log S 1 and log S 2 in Table 1.
The degree of dissociation α is the ratio of the post-micellar slope to the premicellar slope. Here, we use an approximation that both the straight lines do not change gradually about CMC. Straight lines are drawn through the upper and the lower part of the plot; the point of intersection showed the concentration at which micelles are formed. Such plots are shown in Fig. 1 as well as in Figs. 2a-c for the CTAB with and without salt in water and water-ethanol mixtures where there is more pronounced curvature near the point of intersection 28 . The intersection point between two slopes indicates the CMC and was determined by fitting the data points above and below the break to two equations of the form y mx c where m is the slope and c is the intercept and solving simultaneously for the point of intersection. These results of CMC and α S 2 /S 1 are summarized in Table 2. Besides, the CMC value changes largely with temperature and the surfactant may decompose at high temperature so to avoid this effect on CMC we fixed all the measurements at room temperature. If the room temperature becomes less than 298.15 K, the solution is heated to the desired temperature 298.15 K just before the conductance measurement. This minimizes   The Harkins-Corrin plot is a common plot of log CMC versus log CMC salt , as shown in Fig. 3. The log CMC values were found to decrease with the increase in salt concentration. The reason maybe because of the structural transitions in micelles as the increase of concentration of salt 15 .
3.3 Correlation of log S 1 and log S 2 with the percentage of ethanol The plot of log S 1 with the percentage of ethanol in the presence and absence of salt is depicted in Fig. 4a. The value of log S 1 decreases with increasing the percentage of ethanol . The value of log S 1 is very high in the pres-  Fig. 4b. Similarly, the value of log S 2 decreases with increasing the percentage of ethanol . Like log S 1 , the value of log S 2 is very high in the presence of salt in comparison to the absence of salt.
Hence the values of log S 1 and log S 2 decrease with increasing the percentage of ethanol both in the presence and absence of salt.

Calculation of Gibbs free energy of micellization
The thermodynamic property, Standard Gibb s free energy of micellization ΔG o m , was calculated from the following relation 30,31 . Here, R is the universal gas constant, T is the absolute temperature and X cmc is the mole fraction of surfactant at CMC. The critical micelle concentration CMC , degree of micelle ionization α and standard free energy of micellization ΔG o m of CTAB in the absence and presence of salt in water and 10 , 20 and 30 of ethanol are given in Table 2. Table 2 displays the value of CMC critical micelle concentration , α degree of ionization , ΔG o m standard free energy of micellization in water and presence of salt in water, 10 , 20 and 30 of ethanol measured at different concentrations. The data shows that the CMC, as well as degree of ionization α , increases with an increase in the percentage of ethanol, firstly due to the alcohol molecule intercalated between surfactant ions which increase the average distance between ionic head groups for steric reasons and the dielectric constant of the palisade layer is the second effect. Such types of results have been reported for the surfactants in alcohol and alcohol-like polar solvent and water mixture 26,32 . It is observed that the values of α of CTAB are higher in the presence of ethanol than in the absence of it. With an increase in the concentration of ethanol α value keeps on increasing due to an increase in the surface area of the ionic head group.
The values of CMC of CTAB increase with the increase in ethanol content which can be explained based on hydrophobic interaction between tails and electrostatic repulsion between ionic heads. These are two important factors for micellization. Hydrophobic interaction depends on the dielectric constant of the medium 26 . The value of the dielectric constant of alcohol is lower in comparison to water. When alcohol is added to water, the dielectric constant of the medium decreases due to which hydrophobic interaction becomes less, which increases the CMC. Due to the lower dielectric constant of the medium, the electrostatic repulsion between the head group increases and the formation of CMC is less favorable, hence CMC increases 27 .
CMC decreases in the presence of salt. With the increase in concentrations of salt, α as well as CMC also further decreases. Such types of results were reported in the previous literature 33 . By adding salt, the Debye length is decreased 34 , the repulsive force between two ions decreases because of the screening effect. The screening affects the head groups of CTAB. The screening induces closing to CTAB each other and forming micelle at a lower concentration. But the decrease in the dielectric constant cause increases Debye-length, which eventually decreases the CMC.
In other words, as the salt is added, the electrostatic repulsive force between ionic head groups of the CTAB molecules is reduced by shielding of micelle charge, so that spherical micelles are more closely packed by the surfactant ions 35,36 , hence a decrease in the CMC values after adding salt. It is noticed that salt decreases the CMC of ionic surfactant CTAB 37 due to the screening of the electrostatic repulsion among the polar head groups and movement of the hydrophobic alkyl chain away from the  aqueous environment, so that less electrical work is required to form micelles. At the point when metal ions are included in a surfactant arrangement, hydration happens pretty much for various metal ions. Since hydration cycles may likewise be a purpose behind separating the icebergs structure of liquid water around the monomer, the degree of hydration ought to be a direct deciding element for the degree of separation of icebergs , thus, the degree of entropy increment. On this premise, it may be presumed that the entropy driving impact is stronger for trivalent metal ions than for divalent metal ions because the hydration impacts of the trivalent metal ions are much stronger than those of the divalent metal ions, subsequently causing a stronger impact of bringing down the CMC of CTAB. Additionally, this idea can be applied for monovalent metal ions 38 . Hence the CMC of CTAB in the presence of 0.01 M of MnSO 4 .6H 2 O seems 0.15 mM in Table 2 whereas the CMC of CTAB in the absence and presence of 0.01 M NaCl was found 0.924 mM and 0.56 mM respectively from the literature 39 .
Accordingly, the addition of inorganic electrolytes brings down the CMC of surfactants 40 and upgrades the surface activity, which certainly favors their practical use since numerous industrial uses of surfactants lie in their ability to frame micelles 41 . As indicated by 42 , divalent counterions are required to be more viable than monovalent ions in screening electrostatic interactions and decreasing surfactant headgroup territory because a a more prominent charge screens all the more successfully, b each divalent ion is all the more unequivocally pulled in to a total, and c divalent ions can now and again cause charge inversion. Furthermore, divalent salts, affect the micelle size 43 , reactivity, yield fusion of surfactant aggregates 44 and modify the phase diagram of the surfactant 45 . Hence the stronger affinity of divalent ions to surfactant aggregates strongly complicates the understanding of the physical phenomena related to the ion specificity 46 .
It is also observed that the value of the standard free energy of micellization is negative in water as well as in all percentage of ethanol Table 2 . It indicates the process of micellization is spontaneous. The values of ΔG o m , generally, increase with the addition of ethanol in the water at different concentrations of salt. This indicates that when ethanol is added to the mixture, the formation of micellization is less stable in the monomer state.

Correlation of ΔG o trans with the percentage of ethanol
The micellization process is affected due to the addition of alcohol, and the effect can be studied using the free energy of surfactant tail transfer ΔG o trans 31 .

Correlation of α with the percentage of ethanol
The plots of the degree of micellar dissociation α with the percentage of ethanol in the presence and absence of salt are depicted in Fig. 5b. For the solution without salt, the value of α first increases slightly then increases sharply with an increasing percentage of ethanol . For the solution of salt, the value of α increases uniformly with an increase in the percentage of ethanol .

Correlation of CMC with the percentage of ethanol
The concentration of the surfactant above which the micelle form and all additional surfactant added to the system go to the micelle. The plots of CMC with the percentage of ethanol in the presence and absence of salt are depicted in Fig. 5c. For both cases, the value of CMC increases with increasing the percentage of ethanol . The CMC of a solution without salt is always higher than with salt. The Debye length is directly proportional to the ratio of the square root of dielectric constant to the charge on the ions. By adding ethanol, the Debye length is decreased; the electrostatic repulsion force between the head group of surfactants increased 47 due to which the hydrophobic interaction become weak 48 ; as a result, the CMC of the solution increased 32, 49, 50 .

Correlation of K 0 /K CMC with the percentage of ethanol
Mukhim and Ismail in the year 2011 used the ratio of the solvent surface tension to the limiting surface tension 51 at the CMC, γ 0 /γ CMC to describe the solvophobic effect 52 . Similarly, our research group has already used the importance of K 0 /K CMC , the ratio of initial conductance to the conduc-tance at CMC 22,53 .
The plot of the ratio of initial conductance to conductance at CMC K 0 /K CMC with the percentage of ethanol in the presence and absence of salt are depicted in Fig. 5d. For both cases, the value of K 0 /K CMC decreases with increasing the percentage of ethanol . The value of K 0 /K CMC of a solution without salt is always higher than with salt for a given percentage of ethanol . The salt present in surfactant is converted to their corresponding metal salts which are precipitated as scum. The insoluble scum sticks on the clothes and so the cleaning capacity of surfactant is reduced. Hence, the higher the ratio values of K 0 /K CMC , the better the cleansing action.  Table 3 . The relation of these parameters with the free energy change ΔG o m gives not only the stability of the solution but also relate micellization of molecular association, the fluidity, polarity, and solvent structure. The Gibbs free energy for the solution increases with the in-    Fig. 6a. 3.10 Correlation of ΔG o m with the solvophobic parameter S p The solvophobic parameter, S p , is calculated by Gibbs energies of transfer of hydrocarbons from the gas into a given solvent 54 . The S p values are only available for the solvent mixtures of water-methanol, water-ethanol, wateracetone, and water-ethylene glycol 54 , although their compositions are different from those investigated in the present work. Wang et al. 55 developed a correlation method with which the S p values of the mixed solvents can be predicted at any composition from those of the corresponding pure liquids. S p is the measure of the property of solute which avoids the solvent to make the solution. The solvophobic parameter of water is high whereas it decreas-    es with the addition of ethanol Table 3 . The plots of standard Gibb s free energy of micellization ΔG o m with the solvophobic parameter of the solution in the presence and absence of salt are depicted in Fig. 6e. For the solutions with and without salt, the free energy curve decreases with the increasing value of the solvophobic parameter. Gibb s free energy of the solvent with water is higher than that of salt.
The plots of the degree of micellar dissociation α with the solvophobic parameter S p in the presence and absence of salt are depicted in Fig. 6f. For the solution without salt, the value of α first decreases sharply and then decreases slowly with the increasing value of the solvophobic parameter. Whereas, for the solution with salt, the free energy curve decreases uniformly with the increasing value of the solvophobic parameter.

Conclusions
The following conclusions have been drawn from the results and discussion. The conductivity of cetyltrimethyl ammonium bromide was measured in pure water including in 10 , 20 and 30 ethanol as well as in the presence of

Conflicts of Interest
There are no conflicts to declare.

Acknowledgments
AB and TPN acknowledge The World Academy of Sciences TWAS , Italy for research grants.

Author Contributions
A.B. and T.P.N. were involved in project conceptualization and design. P.B. conducted the research and analyzed the data; prepared the manuscript and had primary responsibility for the content; and contributed to the laboratory. A.B. and T.P.N are also involved in manuscript editing. All authors read and approved the manuscript.