Influences of NaCl and Na2SO4 on the Micellization Behavior of the Mixture of Cetylpyridinium Chloride + Polyvinyl Pyrrolidone at Several Temperatures

Herein, the conductivity measurement technique is used to determine the interactions that may occur between polyvinyl pyrrolidone (PVP) polymer and cetylpyridinium chloride (CPC) surfactant in the presence of NaCl and Na2SO4 of fixed concentration at variable temperatures (298.15–323.15 K) with an interval of 5 K. In the absence or presence of salts, we observed three critical micelle concentrations (CMC) for the CPC + PVP mixture. In all situations, CMC1 values of CPC + PVP system were found to be higher in water than in attendance of salts (NaCl and Na2SO4). Temperature and additives have the tendency to affect counterion binding values. Various physico-chemical parameters were analyzed and demonstrated smoothly, including free energy (ΔG0m), enthalpy (ΔH0m) and entropy change (ΔS0m). The micellization process is achieved to be spontaneous based on the obtained negative ΔG0m values. The linearity of the ΔHmo and ΔSmo values is excellent. The intrinsic enthalpy gain (ΔH0*m) and compensation temperature (Tc) were calculated and discussed with logical points. Interactions of polymer hydrophobic chains or the polymer + surfactant associated with amphiphilic surface-active drugs can employ a strong impact on the behavior of the gels.


Introduction
Surfactants are substances that can reduce the surface tension of a solvent. Aggregation behavior of amphiphilic substances, which is basically a non-covalent interaction, is a normal and spontaneous phenomenon [1]. The structural configuration of surfactant molecules, and the presence of polar and non-polar portions, helps them to be self-assembled in an aqueous medium at a certain concentration which is termed as critical micelle concentration (CMC) [2]. Micelles can easily incorporate feebly soluble drugs, organic chemicals, or polymers inside their hydrophobic core and facilitate the solubility of various substances and bioavailability as well [3,4]. However, surfactants act as a good recipient regarding drug delivery systems. Studies have suggested that insertion of external substances may impact on the physical properties of aggregates such as adding or departure of counter ion binding, reaction rate, and catalytic activity [5,6]. Gelation is the gel preparation process from a system through polymers.

Materials
The materials used in this study were of analytical grade and used without further purification. The chemical names, purity, CAS numbers, mass fraction, and other information are mentioned in Table 1.

Solution Preparation and Conductivity Measurement
CPC + PVP solutions, both in water and salts media, were prepared using distilleddeionized water considering molal concentrations. The specific conductivity of used distilled-deionized water was 1.7-2.0 μS cm −1 maintaining temperature range 298. 15-323.15 K. Electric balance machine (Mettler Toledo, Greifensee, Switzerland) and 4510 conductivity meter (Jenway, Staffordshire, UK) were used for taking the weight of samples and measuring specific conductivity (κ) for preparing different solutions. The conductivity meter had a glass cell electrode specifying cell constant 0.97 cm −1 and to calibrate the meter, appropriate concentration of freshly collected KCl solution was employed. Throughout the whole work of conductivity measurement, alternate current (AC) having a frequency of 60 Hz was maintained. In terms of explaining the procedure, initially, 25 mmol kg −1 aqueous solution of CPC in PVP was prepared and subsequently, this solution was inserted into the 20 mL solution of PVP at specific temperature both in attendance/nonattendance of salts. Then, salts solutions were also prepared and added to observe the impacts of salts during conductivity study. After every addition of solution, time was maintained to achieve temperature equilibration and conductivity value was recorded; then, this process was employed for every system. Our process of conductivity technique has good matching with others [6,[23][24][25]. The RM6 Lauda circulating water bath was used and the error of temperature within ±0.2 K was considered. The values of CMC were calculated from the intersection points of κ versus concentration of CPC plots for the CPC + PVP assembly by using Origin software.

Materials
The materials used in this study were of analytical grade and used without further purification. The chemical names, purity, CAS numbers, mass fraction, and other information are mentioned in Table 1.

Solution Preparation and Conductivity Measurement
CPC + PVP solutions, both in water and salts media, were prepared using distilleddeionized water considering molal concentrations. The specific conductivity of used distilled-deionized water was 1.7-2.0 µS cm −1 maintaining temperature range 298.15-323.15 K. Electric balance machine (Mettler Toledo, Greifensee, Switzerland) and 4510 conductivity meter (Jenway, Staffordshire, UK) were used for taking the weight of samples and measuring specific conductivity (κ) for preparing different solutions. The conductivity meter had a glass cell electrode specifying cell constant 0.97 cm −1 and to calibrate the meter, appropriate concentration of freshly collected KCl solution was employed. Throughout the whole work of conductivity measurement, alternate current (AC) having a frequency of 60 Hz was maintained. In terms of explaining the procedure, initially, 25 mmol kg −1 aqueous solution of CPC in PVP was prepared and subsequently, this solution was inserted into the 20 mL solution of PVP at specific temperature both in attendance/non-attendance of salts. Then, salts solutions were also prepared and added to observe the impacts of salts during conductivity study. After every addition of solution, time was maintained to achieve temperature equilibration and conductivity value was recorded; then, this process was employed for every system. Our process of conductivity technique has good matching with others [6,[23][24][25]. The RM6 Lauda circulating water bath was used and the error of temperature within ±0.2 K was considered. The values of CMC were calculated from the intersection points of κ versus concentration of CPC plots for the CPC + PVP assembly by using Origin software.

The CMC and β for the Aggregation of CPC + PVP Mixture in Aqueous and Salts Media
The aggregation of surfactants has been investigated by different distinguished research teams applying a number of experimental techniques such as surface tension, conductivity, density, viscosity and ultrasound velocity measurements, fluorescence spectroscopy, NMR Spectroscopy, etc. [26,27]. Among these techniques, conductivity technique is a simple, trustworthy, and broadly used method to evaluate CMC for ionic amphiphiles. Ionic surfactants ionize into ions in H 2 O; consequently, specific conductivity has the tendency to increase with enhancing of surfactant contents. Nevertheless, the incremental increase in conductivity undergoes deviation from the initial trend when a certain concentration of surfactant is developed. Such behavior was detected by many researchers in their studies which is mainly owing to the micelle creation [6,20,[28][29][30]. The dependence of the specific conductivity, κ, on surfactant concentration is shown in Figure 1.

The CMC and β for the Aggregation of CPC + PVP Mixture in Aqueous and Salts Media
The aggregation of surfactants has been investigated by different distinguished research teams applying a number of experimental techniques such as surface tension, conductivity, density, viscosity and ultrasound velocity measurements, fluorescence spectroscopy, NMR Spectroscopy, etc. [26,27]. Among these techniques, conductivity technique is a simple, trustworthy, and broadly used method to evaluate CMC for ionic amphiphiles. Ionic surfactants ionize into ions in H2O; consequently, specific conductivity has the tendency to increase with enhancing of surfactant contents. Nevertheless, the incremental increase in conductivity undergoes deviation from the initial trend when a certain concentration of surfactant is developed. Such behavior was detected by many researchers in their studies which is mainly owing to the micelle creation [6,20,[28][29][30]. The dependence of the specific conductivity, κ, on surfactant concentration is shown in Figure  1. For all the cases of CPC + PVP mixed system, three break points were obtained. The concentration of surfactant achieved at the break point has been taken as the CMC, and the successive CMC values were expressed as CMC1, CMC2, and CMC3, respectively. The CMC1 can be associated with the formation of the PVP (polymer): CPC complex (critical aggregation concentration); the CMC2 corresponds to free CPC micellization (critical micelle concentration in the presence of PVP), and the third break point (CMC3) refers to the structural modifications in micelles as a sphere to rod transition [31]. The third critical For all the cases of CPC + PVP mixed system, three break points were obtained. The concentration of surfactant achieved at the break point has been taken as the CMC, and the successive CMC values were expressed as CMC 1 , CMC 2 , and CMC 3 , respectively. The CMC 1 can be associated with the formation of the PVP (polymer): CPC complex (critical aggregation concentration); the CMC 2 corresponds to free CPC micellization (critical micelle concentration in the presence of PVP), and the third break point (CMC 3 ) refers to the structural modifications in micelles as a sphere to rod transition [31]. The third critical micelle concentration indicates that the spherical micelle turns into a rod shape. Chakraborty et al. [32] described three CMCs (critical aggregation concentration (CAC), polymer saturation concentration (c s ), and free micellization concentration (c m * )) for the assembly of the mixture of SCMC and CTAB. Bhattarai has achieved three CMC values for the aggregation of the CTAB + sodium polystyrene sulfonate mixture [33]. In spite of the existence of multiple CMC for an association of polymer + surfactant mixture, a single CMC is also stated in the literature [34][35][36][37]. Chai et al. [38] investigated the interaction amid PVP and a gemini surfactant by NMR in a D 2 O medium at 298 K. They confirmed the CMC, CAC, and additive saturated concentration (C 2 ) by measuring chemical shift and self-diffusion coefficients, respectively. Mukhim and Ismail [39] reported CMC values of 0.841 and 0.75 mmol kg −1 for the micellization of CPC in water and 0.32 mmol kg −1 NaCl solution, respectively, at 298 K by means of surface tension measurement technique. The decrease in CMC values in NaCl solution compared to water medium has good agreement with the current study. Varade et al. [40] investigated the impact of electrolyte (NaCl and NaBr) on the CMC value of CPC using different techniques (surface tension/conductance/viscosity/dynamic light scattering (DLS)/small angle neutron scattering). From surface tension and conductivity techniques, Varade et al. [40] stated that CMC value of CPC was found to be 0.98 and 0.95 mM, respectively at 303 K and obtained a decrease in CMC value in the occurrence of salt. The DLS study showed that, in presence of electrolytes, the repulsive interactions will cause a rise in the diffusion coefficient and therefore a reduction in the apparent diameter of the micelles, i.e., a decrease in CMC of CPC was observed [40].
The extent of micelles dissociation, α, has been computed from the ratio of the slopes corresponding to the linear regions below and above CMC. If S 1 and S 2 are the slopes below and above CMC 1 , respectively, then S 2 and S 3 are the slopes below and above CMC 2 , and S 3 and S 4 are the slopes below and above CMC 3 , respectively. Then, α 1 , α 2 , and α 3 can be determined from the ratios S 2 /S 1 , S 3 /S 1 , and S 4 /S 1 , respectively. The fraction of bound counter ions, β, at CMC can be obtained by subtracting the α value from unity, i.e., β = (1 − α).
The effect of PVP on the CPC aggregation has been investigated considering the five different concentrations of PVP in the range 0.01-0.10% (w/v). The CMC values for the CPC + PVP system in H 2 O having several concentrations of PVP at 303.15 K are depicted in Table 2. The CMC values initially tend to upsurge with the increase in PVP content, attain optimum value, and then undergo decline with the increase in PVP content. Sardar et al. [41] investigated the interactions between PVP and cationic surfactant (both conventional/gemini) while they achieved the enhancement of CAC and CMC values with the rise of PVP contents [40]. The change of CMC values for the CPC + PVP aggregation as a function of PVP content indicates the survival of interaction between CPC and PVP. Additionally, the micelle development phenomenon is a delayed process in the manifestation of PVP. All the CMC values for the CPC + PVP aggregation in aq. NaCl and Na 2 SO 4 solution have been obtained to be lower in magnitudes in comparison to aqueous medium ( Table 3). The reduction in CMCs is due to the decreased electrostatic repulsions between the charged head group of the amphiphiles [39]. The effect is much more pronounced in aq. Na 2 SO 4 solution than in case of aq. NaCl solution. Sulfate ion is multicharged and exists left in the Hoffmeister series compared to the single charged anion Cl − . Therefore, the salting out tendency might be more pronounced in case of sulfate which reduces CMC to a greater extent at the identical ionic strength [42]. Barbosa et al. [43] achieved three CMC values for the SDS +PEO mixture in aq. salts solution including NaCl and Na 2 SO 4 . They also obtained a decreasing trend of CMC in the manifestation of these salts. They described that, although NaCl could not interact with PEO, the counter ions of surfactant interact with micelles and macromolecules, which allows the increase in the surfactant's chemical the potential, and thus the effect of NaCl results in the reduction in both CAC and CMC values. Akhlaghi and Riahi [44] reported the effect of different salts on the CMC of TX-100, and they obtained greater effect of NaCl in reducing CMC in comparison to Na 2 SO 4 .

Effects of Temperature on the Association of CPC and PVP Mixture
As the surfactants are used broadly in the applied purposes, its aggregation process experiences an alteration of temperature depending on the seasonal time and applied regions. To understand the impacts of temperature on the aggregation of CPC + PVP mixture, we have selected a range of temperature 298.15-323.15 K in the current investigation, which also covers both room temperature and body temperature. The conductivity and CMC values of the CPC + PVP mixture experience a dependency on the temperature variation.
The CMC values of the CPC + 1% (w/v) PVP mixture in H 2 O, H 2 O + NaCl, and H 2 O + Na 2 SO 4 media at several temperatures are shown in Table 3.
In aqueous medium, the CMC 1 values for the aggregation of CPC + PVP mixture undergo an enhancement with the rise of temperature while the CMC 2 and CMC 3 values primarily experience an upsurge with the escalation of temperature, reach an optimum value, and then undergo reduction with the gradual growth of temperature. For the aggregation of CPC + PVP mixture in H 2 O + NaCl medium, the CMC 2 values suffer a fall with the rise of temperature while the CMC 1 and CMC 3 values primarily experience a reduction with the increase in temperature, reach the least value, and then experience an increase with the gradual intensification of temperature. In H 2 O + Na 2 SO 4 medium, the CMC 2 values undergo a fall with the rise of temperature, while the CMC 1 and CMC 3 values primarily experience a reduction with an increase in temperature, touch the lowest value, and then experience a rise with the gradual intensification of temperature.

Energetics of the Aggregation of CPC + PVP Mixture in Aqueous and Salts Media
The feasibility of the aggregation process can be understood from the knowledge of standard free energy change (∆G 0 m ). It also signifies the spontaneity of the corresponding phenomena. The values of ∆G 0 m for CPC + PVP mixture in water and aq. salts solution have been assessed using the following equation [45][46][47][48][49][50][51].
The symbols R, T, and X cmc in the above equation imply the universal gas constant, study temperature (in Kelvin), and mole fractional value of CMC, respectively. The values of X cmc were computed from the ratios of the number of moles of amphiphiles at CMC and the overall number of moles existing in the CPC + PVP mixture in H 2 O/aq. salts solutions.
The changes in free energy (∆G 0 m ) values were determined only considering the CMC 1 . The values of ∆G 0 1,m are depicted in Table 4. The  This is a common occurrence for the aggregation of surface active materials [25,51]. A similar pattern was reported by Masalci [54], where the ∆G 0 values follow the trend we noticed. It is also reported by Masalci [54] that ∆G 0 is shown to fall to higher negative values as the temperature rises when the polymer is increased in quantity. In the absence of electrolytes in the solution, ∆G 0 1,m values become more negative as the temperature rises, eventually remaining nearly constant. The drops of ∆G 0 1,m values as the temperature rises indicate that the surfactant's hydrophilic group has desolvated [55]. Sharma et al. [56] reported ∆G 0 m value of −16.98 kJ mol −1 for the assembly of 0.1% (w/v) PEG-4000 and CPC mixture, and the ∆G 0 m experienced an upsurge with the escalation of temperature. The ∆G 0 m value of −29.03 kJ mol −1 for the aggregation of PVP + cationic gemini (16-5-16) surfactant at 303 K was stated by Azum et al. [57] and the negative values of their investigation were increased with enhancing temperature. A decrease in spontaneity for the aggregation of the mixture of bovine serum albumin and CPC in aq. glycerol and dimethyl sulfoxide solutions has been achieved by Sharma et al. [58]. In the current study, the free energy of micellization for CMC 2 and CMC 3 were also negative, which revealed the spontaneous occurrence of the processes (not given in tabular form).
The ∆G 0 t values are negative in the present investigation for the shift of CPC + PVP system from H 2 O to H 2 O + NaCl medium. The −∆G 0 t values were also obtained for the mixture of TTAB and promethazine hydrochloride in H 2 O + NaCl medium [59]. Similar characteristics of PVP + CPC system on the basis of the values of ∆G 0 t have been published for the SCAP + PVP and SDS + PVP system [19,60]. For the aggregation of CPC in aq. 0.05 to 0.5% PVP solutions, Sood obtained ∆G 0 t values of −0.49 to -0.64 kJ mol −1 while the −∆G 0 t values enhanced slightly with the growing concentration of PVP [19]. The average value of ∆G 0 t for CPC + PVP (mol. wt. 40,000) for variation of C PVP from 0.05 to 0.5% and CPC+ PVP (mol. wt. 3, 60,000) for variation of C PVP range 0.01 to 0.07% is comparable with our observed data [31]. Azum et al. [53] obtained negative transfer free energy for the micellization of PVP + cationic gemini surfactant, and they obtained no specific trend with temperature. The −∆G 0 t values disclose the feasibility of the interactions between the components present in the system.
Anand and Yadav [61] achieved the negative values of −∆G 0 t , and the negative values increased and underwent a fall with the enhancing of PVP contents and temperature of the study, respectively. In the case of sodium sulfate solutions, the ∆G 0 t values are positive, which indicates that the surfactant system prefers to stay in the aqueous medium than the salt solution.
A second-order polynomial fitting of lnX CMC vs. T plot was achieved nonlinear (Figure 2). The values of fitting parameters (A, B, and C (regression constants)) have been exposed in Table 5. The enthalpy (∆H o m ) has thus been computed applying the following Equation (6):      Figure 3) has been calculated from a linear connection amid ∆H 0 m and ∆S 0 m with R 2 value in the range of 0.9989-0.9992 using the following equation [66][67][68][69][70][71][72][73][74][75]: The compensation temperature, T c , and the intrinsic enthalpy gain, ∆H 0, * m are represented by the slope and intercept, respectively. Table 6 shows the values of ∆H 0, * m and T c for the CPC + 0.1% (w/v) PVP systems in H 2 O and aq. salts solution.

Media
Isalts ∆ , * Tc R 2 mmol kg −1 kJ mol   According to Equation (7) above, the R 2 value in the range of 0.9989-0.9992 was given in Table 6. The T c and ∆H 0, * m describe the solute-solute and solute-solvent interactions, respectively, for the self-assembly process of amphiphiles [75]. The greater negative ∆H 0, * m value indicates that micellization is preferred even when ∆S 0 m = 0 [70,71]. If entropy change value becomes zero, ∆H o m becomes equal to ∆H 0, * m which refer the solute-solute interactions and the contribution of solvent effect might be ignored [73].  [74]. With a few exceptions, the T c values for CPC + PVP were found to be nearly comparable to biological fluid [72]. Sugihara and Hisatomi [70] discovered a similar compensatory effect for the aggregation of charged amphiphiles in H 2 O medium. The T c values have been described as the proof of hydrophobic interaction between the studied components [71]. García-Mateos et al. suggested the presence of hydrophobic interactions between CPC and PVP [31]. On the basis of higher negative ∆H 0, * m and greater T c values, Shi et al. reported that zwitterionic surfactants form more tighter and stable micelles compared to the anionic/cationic and nonionic amphiphiles [73].

Conclusions
The conductivities of PVP + CPC mixed systems were measured in H 2 O/H 2 O + NaCl/H 2 O + Na 2 SO 4 solutions at various temperatures to insight into the interaction between PVP and CPC. The degree of interaction was determined by the values of CMC, β, and certain thermodynamic factors. Both the micellization of PVP + CPC mixed systems and β values were temperature dependent in aqueous and electrolytes media. At all temperatures, the values of ∆H o m and ∆S o m indicate the presence of hydrophobic interaction between PVP and CPC in aqueous and electrolytes media. The ∆G 0 1,m values show that, the spontaneity of self-aggregation is almost similar in case of water and aq. NaCl medium whereas the negative values are lower in aq. Na 2 SO 4 solutions. The values of ∆H o, * m vary from −35.66 to −38.05 kJ.mol −1 , indicating that the micelle produced is stable. The T c values are very similar to those of a biological system. Here, investigation of the interaction of surfactant and polymer in presence of low molecular weight electrolyte was carried out because low to moderate amphiphiles concentrations are used to form hydrogels, as self-assembly makes several approaches to attain gelation available.