Investigation of the impacts of simple electrolytes and hydrotrope on the interaction of ceftriaxone sodium with cetylpyridinium chloride at numerous study temperatures

Abstract

Herein, interactions between cetylpyridinium chloride (CPC) and ceftriaxone sodium (CTS) were investigated applying conductivity technique. Impacts of the nature of additives (e.g. electrolytes or hydrotrope (HDT)), change of temperatures (from 298.15 to 323.15 K), and concentration variation of CTS/additives were assessed on the micellization of CPC + CTS mixture. The conductometric analysis of critical micelle concentration (CMC) with respect to the concentration reveals that the CMC values were increased with the increase in CTS concentration. In terms of using different mediums, CMC did not differ much with the increase in electrolyte salt (NaCl, Na₂SO₄) concentration, but increased significantly with the rise of HDT (NaBenz) amount. In the presence of electrolyte, CMC showed a gentle increment with temperature, while the HDT showed the opposite trend. Obtained result was further correlated with conventional thermodynamic relationship, where standard Gibb’s free energy change $(\mathrm{\Delta }{G}_m^o)$, change of enthalpy $(\mathrm{\Delta }{H}_m^o)$, and change of entropy $(\mathrm{\Delta }{S}_m^o$) were utilized to investigate. The $\mathrm{\Delta }{G}_m^o$ values were negative for all the mixed systems studied indicating that the micellization process was spontaneous. Finally, the stability of micellization was studied by estimating the intrinsic enthalpy gain ($\mathrm{\Delta }{H}_m^{o,\ast }$) and compensation temperature (T_c). Here, CPC + CTS mixed system showed more stability in Na₂SO₄ medium than the NaCl, while in NaBenz exhibited the lowest stability.

Introduction

In the presence or absence of aqueous environment, different amphiphilic substances such as surfactants (Seymour 1979; Molina-Bolivar et al. 2001, 2002; Ghasemi and Bagheri 2020; Bhattarai et al. 2022; Alghamdi et al. 2023; Ahmed et al. 2022), drugs (Dutta et al. 2022; Kumar et al. 2022; Hasan et al. 2022; Akter et al. 2022), polymers (Khalil et al. 2012; Lashkarbolooki et al. 2020), etc. have ability to form self-aggregates, which are called micelles (aggregates). In these circumstances, the aggregation phenomenon happens spontaneously via various forces (van der Waals forces, H-bonding, hydrophobic/electrostatic/donor–acceptor interactions) (Whitesides and Grzybowski 2002) and the minimum amphiphiles concentration which is required for the development of micelles (aggregates) is termed as critical micelle concentration (CMC). Surfactants (usually contain both hydrophobic and hydrophilic parts) are usable in many places, e.g. pharmaceutical research, industry of cosmetics and perfumes even as antiseptics and disinfectants, etc. (Seymour 1979; Gonzalez-Perez et al. 2003; Barbosa et al. 2005; Mirgorodskaya et al. 2016; Dey et al. 2017; Zhuang et al. 2021; Niraula et al. 2022; Rub et al. 2022; Hoque et al. 2023b). When any two surfactants (anionic, cationic, or nonionic) are interacted, mixed micelles are also formed (Siddiqui et al. 2014). The existence of drug, polymer, dye, or other additives can influence the formation of micelles (Molla et al. 2017). The micellization also depends on the experimental environments (temperature, concentration, salts of both inorganic and organic (may hydrotrope (HDT)), solvent effect, and so on) (Dutta et al. 2022; Kumar et al. 2022; Hasan et al. 2022; Akter et al. 2022; Molla et al. 2017).

HDTs are amphiphilic compounds that means they contain both polar (hydrophilic) and non-polar (hydrophobic) parts in their structures. But the hydrophobic part is short and thus cannot aggregate spontaneously like surfactant. As for example, sodium benzoate (NaBenz) is a small amphiphilic molecule which possesses carboxylate part (as charged/hydrophilic nature) and phenyl group (as hydrophobic part) (Martin et al. 2016). Due to having both hydrophilic and hydrophobic part, they are capable of solubilizing the substances that are not able to be soluble in water easily or insoluble (mainly organic compounds) (Burns 1999). The tail parts of HDT molecules are lesser (having carbon number less than 7) than the primitive surfactant molecules (Hatzopoulos et al. 2011). They can undergo self-aggregates in solution that are more effective than other amphiphiles which can form self-aggregates (Balasubramanian et al. 1989; Roy and Moulik 2003). Nature of self-aggregations of HDT molecules can be observed by different processes such as viscometric, tensiometric, dye-solubilization, conductometric, UV–Visible spectrophotometric, isothermal titration calorimetry, etc., and corresponding concentration is called critical minimum HDT concentration (MHC) (Srinivas et al. 1997; da Silva et al. 1999). HDTs expose impact on the aggregation nature of surfactant (micellization) and other properties of surfactants. The solution behaviour of surfactants in the presence of HDTs is published in the literature (Mukhim et al. 2010; Khan et al. 2011). Detergents systems having HDTs (as additives) are highly effective in both aqueous and oil mediums.

A quaternary ammonium salt CPC (cationic surfactant, Scheme 1A) has various usable advantages for example as reducing dental plaque, gingivitis with the help of 0.05% CPC (Silva et al. 2009), antiviral effects in patients with influenza to shorten the period and cruelty of the virus (Popkin et al. 2017; Mukherjee et al. 2017), can scupper viral capsids (Baker et al. 2020), and can also effect on enveloped viruses like coronaviruses (Vergara-Buenaventura and Castro-Ruiz 2020). It was discovered that the CMC values of the CPC + PVP system were greater in H₂O than in the presence of NaCl and Na₂SO₄ (Ahmed et al. 2022). For the quick and easy wound dressings process with a control antibacterial agents release, cetylpyridinium chloride was electrostatically immobilized to poly(vinyl alcohol) hydrogels (Yunoki et al. 2014). In aqueous solutions, the aggregation sodium caprylate (SCAP) and CPC in the existence of the polymer polyvinyl pyrrolidone and different non-ionic surfactants has been also studied (Sood 2019). The polymer–surfactant interactions are crucial in terms of industrial application like pharmaceuticals, detergents, paints and coating, food as well as cosmetics. Surfactants affect emulsification capacity, colloidal stability, and interfacial tension in these mixed systems, whereas polymers offer regulation of colloidal stability and rheological characteristics (Nikas and Blankschtein 1994). CPC is also used as mouthwashes, toothpastes, lozenges, as well as breathe and nasal sprays.

Scheme 1.

Molecular structure of A CPC and B CTS

Ceftriaxone sodium trihydrate (CTS; Scheme 1B), a cephalosporin antibiotic, is used widely in the treatment of bacterial infections as it inhibits the growth of bacteria. Depending on the bacterial condition, CTS is used to treat infections of the lungs, bladder, bones, joints, gonorrhea, meningitis, etc. The CTS drug can interact with different surfactants (cationic, anionic, or non-ionic) such as tetradecyltrimethylammonium bromide (TTAB), Triton X-100, and Tween-80 at varied environmental conditions which have already reported (Rahman et al. 2019a; Nazrul Islam et al. 2023)). The fact that the CMC value of TTAB changes when CTS is included in the TTAB solution indicates that TTAB interacts with CTS. This interaction, as well as the magnitudes of CMC of TTAB + drug combinations, depends on the used alcohol concentration and system temperature (Rahman et al. 2019a).

In earlier, the interaction of CPC with polymer/ biopolymer in H₂O, aq. NaCl/Na₂SO_4, and NaBenz solutions was described (Vlachy et al. 2006; Hoque et al. 2023a; Varade et al. 2005). On the basis of the above discussion and literature survey, it can be concluded that the interaction of CTS drug with CPC in numerous experimental situations is still important. In addition, sodium salts are important as body nutrients, normalize blood pressure, and maintain ion balance. Benzoic acid salt sodium benzoate (NaBenz) uses as food and fruit juices preservation (Amann and Peskar 2002) and hydrotropic in nature. In this instance, we attempted to study the influences of electrolytes and NaBenz (as HDT) on the aggregation nature of CPC + CTS drug mixture through conductivity method. The CMC, counterion binding (β), thermodynamic parameters ($\mathrm{\Delta }{G}_m^0,\mathrm{\Delta }{H}_m^0,\text{and},\mathrm{\Delta }{S}_m^0$), and enthalpy–entropy compensation variables for the association of CPC + CTS mixture micellization in aq. electrolytes and NaBenz solutions have been determined and discussed in detail.

Materials and method

Materials

Chemicals utilized in this analysis are of the analytical grade. CTS (purity: 99%, CAS: 104376-79-6), CPC (purity: 99%, CAS: 6004–24-6, source: Sigma-Aldrich), NaCl (purity 0.99, CAS:7647–14-5, Merck, Mumbai, India), Na₂SO₄ (purity: 99%, CAS:7757–82-6, Merck, Mumbai, India), and NaBenz (purity: 99%, CAS: 7647–14-5, BDH, England) were employed in the present study. Distilled–deionized H₂O is applied for solution preparation having specific conductivity (κ) close to 1.8 μS cm⁻¹.

Method

In the beginning, CPC (25 mmol kg⁻¹) stock solutions were made in a variety of solvent (CTS + H₂O/CTS + H₂O + NaCl /Na₂SO₄/NaBenz media with the necessary concentration of CTS and salts). A Metler Toledo conductivity meter (model FiveGo F3) with a polycarbonate body (the cell constant of 0.524 cm⁻¹ is introduced by manufacturer) was applied to test the conductivity values of the CPC + CTS solutions in the H₂O/salt + H₂O media. Following the methodology outlined in the literature (Vlachy et al. 2006; Rahman et al. 2019a; Hoque et al. 2023a), the experiments in the present study were carried out. The measurement error for the κ values was around 0.5%. Using medium with the required concentrations of CTS and salt, 20 mL of solvent (CTS + H₂O/CTS + salt + H₂O) was added to a test tube, and then, the conductivity of the employed solvent displayed by the equipment was recorded first. The stock CPC solution was then slowly added into solvent under study. The values of κ were determined for every experimental run once the proper mixing and permitting enough time for temperature equilibration. The CMC value of the system has been detected by a noticeable breakpoint in the κ- [surfactant] plots (Rub et al. 2023).

To observe the effect of pH, different buffer solutions, e.g. phosphate buffer, tris buffer, and borax buffer, were prepared for desired pH (Robinson and Stokes 1972) and used in the current investigation. Phosphate buffer was prepared by using 0.1 M KH₂PO₄ and 0.1 M NaOH, Tris buffer was prepared by 0.1 M tris (C₄H₁₁NO) and 0.2 M HCl, and borax buffer was prepared by using 0.025 M borax (Na₂B₄O₇.10H₂O) and 0.2 M HCl. The pH was measured by using HI 2211 pH/ORP Meter HANNA instruments meter. The observed pH for phosphate buffer was 6.4 and was adjusted to 6.83 by adding 0.1 M NaOH. The similar procedure was followed for tris buffer 7.4 and borax buffer 9.4.

Results and discussion

Determination of CMC, α, and β for the micellization of CPC + CTS mixture

The micellization of ionic and non-ionic surfactant is related with the changes of several physico-chemical properties of the system (Rahman et al. 2019b; Rub et al. 2021). The development of surfactant micelle can be predicted from the abrupt changes of properties like conductivity, surface tension, absorbance, density, etc. (Whitesides and Grzybowski 2002). In the present study, the alteration of the conductivity of cationic surfactant + CTS drug mixture has been investigated. Information regarding the micelle formation can be obtained by examining the CMC, degree of ionization (α), and counterion binding (β). The impact of changing experimental conditions (e.g. type of additive, temperature, concentration, etc.) can participate in the modification of micelle developing properties of a surfactant, which in turn can provide information on the intermolecular interaction. Figure 1 shows the plot of specific conductivity as a function of the surfactant (CPC) concentration in the aqueous (aq.) Na₂SO₄ solution at 298.15 K temperature. A sharp breakpoint was found in the present assessment for the whole circumstances. At low CPC concentrations, the presence of free ions (CP⁺ and Cl⁻) should be responsible for the initial upsurge of the conductivity. However, near the CMC of this mixed system, these ions start to trap on the micellar surface, which reduces the rate of increment of the conductivity. In addition, this bulky micellar moiety is not capable of moving as fast as a free ion; therefore, the conductivity of the system exhibited as less responsive with the increase in surfactant concentration. Here, Table 1 represents the effect of changing experimental conditions on the CMC value of CPC + CTS mixed system.

Fig. 1.

Plot of κ versus [CPC] for the aggregation of CPC + CTS in aq. Na₂SO₄ (1.67 mmolkg⁻¹) at 298.15 K

Table 1.

Micellar parameters for the association of CPC + CTS mixture in study media at several temperatures

Medium	T	CMC	XCMC (× 105)	α	β
	K	mmol kg−1
H2O	298.15	1.06	1.910	0.37	0.63
	303.15	1.23	2.216	0.42	0.58
	308.15	1.37	2.469	0.42	0.58
	313.15	1.42	2.559	0.45	0.55
	318.15	1.36	2.451	0.45	0.55
	323.15	1.20	2.162	0.57	0.43
NaCl + H2O	298.15	0.33	0.595	0.38	0.62
	303.15	0.42	0.757	0.44	0.56
	308.15	0.48	0.865	0.46	0.54
	313.15	0.54	0.973	0.53	0.47
	318.15	0.52	0.937	0.53	0.47
	323.15	0.45	0.811	0.53	0.47
Na2SO4 + H2O	298.15	0.24	0.432	0.15	0.85
	303.15	0.19	0.342	0.23	0.77
	308.15	0.20	0.360	0.16	0.84
	313.15	0.22	0.396	0.22	0.78
	318.15	0.26	0.469	0.17	0.83
	323.15	0.31	0.559	0.34	0.66
NaBenz + H2O	298.15	6.39	11.51	0.62	0.38
	303.15	5.55	9.999	0.60	0.40
	308.15	5.09	9.171	0.60	0.40
	313.15	4.32	7.783	0.59	0.41
	318.15	4.12	7.423	0.62	0.38
	323.15	3.98	7.171	0.65	0.35

The micellization is related to the value of α where a greater value represents the disfavoured micelle formation (Sepulveda and Cortes 1985). The degree of ionization (α) was estimated by using the slopes in pre- and post-micellar regions of the CMC point. Here, the α was determined by using the ratio of S₂/S₁, where S₂ and S₁ represent the slopes of the straight line that appeared above and below the CMC point, respectively. The counterion binding (β) was obtained from the relation: β = (1 – α). All the results for these micellar parameters along with the relevant experimental conditions are shown in Table 1. The α value at 298.15 K temperature was the lowest for Na₂SO₄ (0.15), while it was the maximum for NaBenz (0.65)-added system. The α values were increased with increase in temperature from 298.15 to 323.15 K. A fluctuation was observed for the Na₂SO₄ salt, where initially the value varied without any specific trend but eventually goes in the increasing direction. Surprisingly this value remains almost the same for the NaBenz-added mixed system.

The change of CMC of the CPC + CTS system with respect to the concentration of CTS in water medium is shown in Fig. 2. This result demonstrates that micellization was interrupted by the increase in CTS concentration in the system. Here, CTS may disrupt the hydrophobic interaction between surfactant molecules in water. This interruption may reduce the ability of CPC to form a micelle, which appeared by increasing CMC value with the increase of concentration of CTS (C_CTS). An opposite effect has been previously observed for the cefixime trihydrate (CMT) + DTAB mixed system, where micellization of DTAB was favoured at higher concentrations of CMT (Joy et al. 2022).

Fig. 2.

Variation in CMC as a function of [CTS] for the aggregation of CPC + CTS in H₂O media

Effect of simple electrolytes and hydrotropic salt on the micellization of CPC + CTS mixture

The electrolyte in the surfactant system functions as a counterion and is capable of modifying the properties of the solvent. At 298.15 K temperature, the micellization was favourable for the simple electrolytes (NaCl and Na₂SO₄), as early CMC was observed. However, formation of micelle disfavoured for the HDT (NaBenz) (Table 1). The effect of concentration of electrolytes and hydrophobic salt on the CPC + CTS mixed system is represented in Fig. 3. Here, with the increase in NaCl salt concetration, the CMC value firstly declined by a small amount and then starts to increase. On the other hand, Na₂SO₄ always showed a slightly decreasing trend. However, CMC was boosted up as the concentration of NaBenz increased in the system. This result indicates that CMC is dependent on the concentration and properties of additives used.

Fig. 3.

Variation in CMC as a function of [salt] or [HDT] for the aggregation of CPC + CTS mixture at 303.15 K

The addition of electrolyte salt (NaCl and Na₂SO₄) into the system usually stimulates the salting-out process, and this may increase the interaction among the hydrophobic part, which is the potential to modify the formation of the micelle (Poša et al. 2010). In this process, the electrolyte salt can pull out the opposite pole of the water molecule from the micellar surface. In addition, the electrolyte plays the role of a counterion in the mixed system and reduces the mobility of the ions that is capable of delaying the creation of micelle of a surfactant system. On the other hand, the HDT (NaBenz) usually acts as a solubilizing agent, which at a lower concentration increases the ionic interactions, but at a higher concentration stimulates the molecular aggregation (Jain 2008). However, both of these impacts can disfavour the formation of micelle (i.e. the CMC values are enhanced).

The anionic part of the additive (Cl⁻, SO₄²⁻, and benzoate) should play a significant role in the micellization phenomenon. The anions of employed electrolytes can reduce the surface charge of the micelle. A schematic diagram for the mechanism of reducing surface charge of micelle is viewed in Fig. 4. This surface charge screening can clarify the relative impact on the CMC of CPC + CTS mixed system. In this comparison, obtained results demonstrate that SO₄²⁻ion favours the micellization more than Cl⁻ ion. This is expected due to the large size and charge of SO₄²⁻ ion compared to Cl⁻ ion. A similar impact has been seen in earlier for DTAB surfactant, where micellization was favoured for the Na₂SO₄ and Na₃PO₄ over NaBr salt (Hossain et al. 2022). In another study, (Varade et al. 2005) showed the effect of Cl⁻ and Br⁻ ion on the micellization of CPC surfactant in an aqueous system. They found that Cl⁻ is more hydrated and less effective than Br⁻ ion to neutralize the ionic character of micellar surfaces.

Fig. 4.

Effect of electrolytes A and B on the micelle charge neutralization

Effect of temperature on the micellization of CPC + CTS mixture

In this study, a definite ionic strength of electrolyte / HDT was used for the same range (298.15 to 323.15 K) of temperature with a 5 K interval, which provides the opportunity to see the influence of temperature on the aggregation property of employed system. The relation of conductivity with respect to the concentration of surfactant (CPC) at various temperature is shown in Fig. 5. Here, the specific conductivity of CPC + CTS mixture in the presence of electrolyes /NaBenz increases with the escalation of temperature. This result identifies that temperature is a dominant parameter that can modify the micellization process. The results obtained for the temperature effect on different micellar parameters of CPC + CTS mixed system are shown in Table 1. In aqueous and aq. NaCl media, the CMC values firstly increase, reach a maximum value, and then decrease with an increase in temperature (Fig. 6). In aq. Na₂SO₄ solution, the CMC values showed the opposite trend in comparison to aqueous and aq. NaCl media. Most interestingly, the CMC values in NaBenz medium are higher in magnitudes compared to aqueous and aq. NaCl/ Na₂SO₄ solutions while the CMC values decrease gradually with the rise of temperature.

Fig. 5.

Plot of κ versus [CPC] for the aggregation of CPC + CTS in aq. Na₂SO₄ (1.67 mmol kg⁻¹) at numerous study temperatures

Fig. 6.

Changes of CMC of CPC + CTS as a function of temperature in study media

The justification for the modification of micellization due to the rise of temperature is jointly responsible for two opposing factors. Firstly, the destruction of the hydration shell nearby the hydrophilic part of CPC surfactant at a higher temperature favours the formation of a micelle (Siddiqui et al. 2014). Secondly, the disruption of the water structure around the hydrophobic part at a higher temperature has the ability to disfavour the micellization process (Varade et al. 2005; Banipal et al. 2014). In this study, the result indicates that the first factor becomes dominating over the second one for the micellization of study system in aqueous and aq. NaCl solution (at higher temperatures), aq. Na₂SO₄ solution (at lower temperatures), and over the whole range of working temperatures in aq. NaBenz solution. On the other hand, second factor becomes dominating over the first one for the micellization of CPC + CTS mixed system in aqueous and aq. NaCl at lower temperatures while the similar behaviour is obtained in case of aq. Na₂SO₄ solution at higher temperatures.

Effect of pH on the micellization

The pH of the human body varies depending on the organ of the body. The control release of drug at the target point is therefore dependent on the pH. Again, the pH of the medium can alter the CMC of the surfactant which is as excipient in the formulation of drug. As the maximum solubilization and activity of drug are obtained at the CMC of the surfactant (Bhardwaj et al. 2014), the estimation of CMC at different pH is important. Moreover, the degradation of drug is dependent on the pH of the medium (Usman et al. 2020). From the importance point of view, we have studied the effect of pH on the aggregation of CPC + CTS mixture. The micellar parameters for CPC + CTS mixture in different buffur media at 303.15 K temperature are provided in Table 2. The lower values of CMC of sodium dodecyl sulfate (SDS) as compared to aqueous medium were reported in phosphate buffer by Fuguet et al. (Fuguet et al. 2005). Again, Z.H. Ren studied the dependency of CMC of the surfactant on pH (Ren 2014). In our study, we observed the reduction of CMC of CPC + CTS mixture from aqueous to phosphate buffer (Table 2), which is in well agreement with the result of Fuguet et al. (Fuguet et al. 2005). Again, the CMC values of CPC + CTS mixture were compared in different buffer media and we observed that CMC values in borax buffer are higher than tris buffer which in turn is higher than that in phosphate buffer (Table 2).

Table 2.

Micellar parameters for CPC + CTS mixture in different buffur media at 303.15 K temperature

Medium	pH	CMC	α	β
		mmol kg−1
H2O	6.95	1.23	0.37	0.63
Phosphate buffer	6.83	0.53	0.36	0.64
Tris buffer	7.40	0.77	0.37	0.63
Borax buffer	9.40	0.92	0.54	0.46

Energetics of the micellization of CPC + CTS mixture

To understand the interaction properties of the CPS + CTS mixture in the presence of additive salt, the energetics of the micellization process was characterized. Here, different thermodynamic parameters (standard Gibb’s free energy change $(\mathrm{\Delta }{G}_m^o)$, change of enthalpy $(\mathrm{\Delta }{H}_m^o)$, and change of entropy $(\mathrm{\Delta }{S}_m^o$)) for the micellization were determined using the standard thermodynamic Eqs. (1), (4), and (5). The spontaneity or feasibility of a micellization process is usually determined by the value of $-\mathrm{\Delta }{G}_m^o$; here more negative $\mathrm{\Delta }{G}_m^o$ value indicates the more spontaneous process for the micellization. The $\mathrm{\Delta }{G}_m^o$ of the CPS + CTS mixed system was estimated using the following equation (Rafati et al. 2008; Kumar and Rub 2017; Mahbub et al. 2019, 2020, 2021; Rub 2020; Sharma et al. 2020; Kumar et al. 2021; Rub et al. 2022; Ruhul Amin et al. 2022).

$$\mathrm{\Delta }{G}_m^o=\left(1+\beta \right){\text{RTlnX}}_{\text{CMC}}$$ 1

$$\mathrm{\Delta }{H}_m^o=-\left(1+\beta \right){\text{RT}}^2\left(\frac{\partial \text{ln}{X}_{\text{CMC}}}{\partial T}\right)$$ 2

where X_CMC, R, and T represent the mole fraction of CPC at CMC, molar gas constant, and temperature, respectively, for the CPS + CTS mixed system. The plot of $ln{X}_{\text{CMC}}$ versus temperature provides the quantity $\frac{\partial \text{ln}{X}_{\text{CMC}}}{\partial T}$ for Eq. (2). A sample plot of $\text{ln}{X}_{\text{CMC}}$ versus temperature for CPS + CTS mixed system for aqueous and NaBenz additive is shown in Fig. 7. A nonlinear relationship was clearly achieved from this study, which can be mathematically represented by Eq. (3).

$$ln{X}_{\text{CMC}}=A+BT+C{T}^2$$ 3

Fig. 7.

Plot of $ln{X}_{\text{CMC}}$ versus T for CPC + CTS in A aqueous and B aq. NaBenz media

Here A, B, and C are constants that can be obtained by regression analysis (second-order polynomial fitting). The achieved values for these regression constants are shown in Table 3. Finally, the value of values$\mathrm{\Delta }{H}_m^o$ was obtained from Eq. (4).

$$\mathrm{\Delta }{H}_m^o=-\left(1+\beta \right)R{T}^2\left[B+2CT\right]$$ 4

Table 3.

Fitting variables (A, B, and C) acquired from lnX_CMC versus T plot

Medium	csalt	A	B	C	R2
	mmol kg−1
H2O	0.00	− 148.31	0.8812	− 0.0014	0.9947
NaCl + H2O	5.01	− 195.85	1.1732	− 0.0019	0.9892
Na2SO4 + H2O	1.67	156.43	− 1.1009	0.0018	0.9324
NaBenz + H2O	5.01	44.135	− 0.325	0.0005	0.9866

The computational analysis of Eqs. (1) and (4) was used to calculate the value of $\mathrm{\Delta }{G}_m^o$ and $\mathrm{\Delta }{H}_m^o$, respectively, and eventually the value for $\mathrm{\Delta }{S}_m^o$ was estimated by following the thermodynamic relation given in Eq. (5).

$$\mathrm{\Delta }{S}_m^o=\left(\mathrm{\Delta }{H}_m^o-\mathrm{\Delta }{G}_m^o\right)/T$$ 5

The negative values of $\mathrm{\Delta }{G}_m^o$ for CPC + CTS mixture were obtained in all the electrolytes and HDT media studied as shown in Table 4, which indicates that the micellization in all studied media was spontaneous. The $\mathrm{\Delta }{G}_m^o$ for aqueous and NaCl medium was found as − 43.90 and − 48.32 kJ mol⁻¹, respectively at 298.15 K temperature (Table 1). The more negative value of $\mathrm{\Delta }{G}_m^o$ in aq.Na₂SO₄ medium represents a more feasible micellization process than aq. NaCl medium, which in turn is more feasible compared to aq. medium. However, the lowest negative value of $\mathrm{\Delta }{G}_m^o$ was obtained for NaBenz HDT which reveals the less spontaneity of micellization, and this result is consistent with the delayed micellization (greater CMC value). The $-\mathrm{\Delta }{G}_m^o$ values for the micellization of CPC + CTS mixture followed the trend: $-\mathrm{\Delta }{G}_m^o$(aq.Na₂SO₄) > $-\mathrm{\Delta }{G}_m^o$(aq. NaCl) > $-\mathrm{\Delta }{G}_m^o$(aq. medium) > $-\mathrm{\Delta }{G}_m^o$(aq. NaBenz).

Table 4.

Thermodynamics variables for the micellization of CPC + CTS mixture

Medium	csalt	T	$\mathrm{\Delta }{G}_m^0$	$\mathrm{\Delta }{H}_m^0$	$\mathrm{\Delta }{S}_m^0$
	mmol kg−1	K	kJ mol−1	kJ mol−1	J mol−1 K−1
H2O	0.00	298.15	− 43.90	− 55.87	− 40.15
		303.15	− 42.68	− 39.09	11.84
		308.15	− 42.95	− 22.93	64.96
		313.15	− 42.67	− 5.535	118.6
		318.15	− 43.53	12.55	176.3
		323.15	− 41.27	29.32	218.5
NaCl + H2O	5.01	298.15	− 48.32	− 48.17	0.5147
		303.15	− 46.36	− 25.30	69.46
		308.15	− 46.00	− 2.711	140.5
		313.15	− 44.17	20.10	205.2
		318.15	− 45.02	44.25	280.6
		323.15	− 46.30	69.90	359.6
Na2SO4 + H2O	1.67	298.15	− 56.64	37.68	316.4
		303.15	− 56.14	12.93	227.8
		308.15	− 59.08	− 12.26	151.9
		313.15	− 57.64	− 38.37	61.54
		318.15	− 59.40	− 68.44	− 28.41
		323.15	− 53.94	− 89.99	− 111.5
NaBenz + H2O	5.01	298.15	− 31.02	27.38	195.9
		303.15	− 32.50	23.37	184.3
		308.15	− 33.35	18.62	168.6
		313.15	− 34.73	13.62	154.4
		318.15	− 34.71	7.955	134.1
		323.15	− 34.61	2.168	113.8

The values of $\mathrm{\Delta }{H}_m^o$ and $\mathrm{\Delta }{S}_m^o$ were negative and positive at lower and higher working temperature respectively for both aqueous and NaCl medium (Table 4). The opposite trend was detected in aq. Na₂SO₄. The significance of $\mathrm{\Delta }{H}_m^o$ and $\mathrm{\Delta }{S}_m^o$ is that the enthalpy contributes only to the micellization at lower temperature while the micellization process becomes entropy controlled at higher investigated temperatures, the results observed in case of aqueous and NaCl medium. However, the opposite trend has seen for Na₂SO₄. Noticeably, for NaBenz medium the values of $\mathrm{\Delta }{H}_m^o$ and $\mathrm{\Delta }{S}_m^o$ are positive while the values decreased with the rise of temperature. Consequently, the dominating factor in this case is guessed to be only entropy. The negative and positive values of $\mathrm{\Delta }{H}_m^o$ represent the formation and destruction of supramolecular interactions (ion–ion, ion–dipole, dipole–dipole, etc.), while only positive result indicates the occurrence of hydrophobic interaction in amongst the participated molecules (Hasan et al. 2020). However, when both negative $\mathrm{\Delta }{H}_m^o$ and positive $\mathrm{\Delta }{S}_m^o$ are appeared in the result, it can also be considered for hydrophobic interactions (Bhardwaj et al. 2016). The existence of both hydrophobic and electrostatic interactions was found previously for the aggregation of TTAB/ CTAB with diclofenac sodium (Banipal et al. 2017), where $\mathrm{\Delta }{H}_m^o$ and $\mathrm{\Delta }{S}_m^o$ showed negative sign in the presence of ethanol.

Thermodynamics of transfer for the micellization of CPC + CTS mixture

The thermodynamics of transfer properties in the current investigation were estimated using Eqs. (6)–(8) (Das et al. 2014; Sood and Sharma 2016; Dey et al. 2017; Aktar et al. 2019).

$$\mathrm{\Delta }{G}_{m,\text{tr}}^o=\mathrm{\Delta }{G}_m^o\left(\text{aq}\text{. additive}\right)-\mathrm{\Delta }{G}_m^o\left(\text{aq}.\right)$$ 6

$$\mathrm{\Delta }{H}_{m,\text{tr}}^o=\mathrm{\Delta }{H}_m^o\left(\text{aq}\text{. additive}\right)-\mathrm{\Delta }{H}_m^o\left(\text{aq}.\right)$$ 7

$$\mathrm{\Delta }{S}_{m,\text{tr}}^o=\mathrm{\Delta }{S}_m^o\left(\text{aq}\text{. additive}\right)-\mathrm{\Delta }{S}_m^o(\text{aq}.)$$ 8

The $\mathrm{\Delta }{G}_{m,t}^o$ was negative in aqueous NaCl and Na₂SO₄ media as shown in Table 5. This indicates that all micellization processes in the presence of these two simple electrolytes were more spontaneous than that in water. The lowest spontaneity was found for NaCl-containing medium at 318.15 K, while for Na₂SO₄ this trend was the opposite where the intermediate temperature showed more spontaneous behaviour. On the other hand, the $\mathrm{\Delta }{G}_{m,t}^o$ was positive in NaBenz medium throughout the temperature studied which implies that the aggregation experiences low spontaneity in NaBenz medium. The values of $\mathrm{\Delta }{H}_{m,t}^o$ and $\mathrm{\Delta }{S}_{m,t}^o$ were positive for NaCl medium that indicating an endothermic process, and the absorbed energy from the surrounding may use for the water structure destruction that ultimately disrupts the hydrophobic interaction. By increasing the temperature, the value exhibited a rise-up trend that indicates more water structure breaks down by the upsurge of temperature. However, in aq. Na₂SO₄ and aq. NaBenz media, the values of $\mathrm{\Delta }{H}_{m,t}^o$ and $\mathrm{\Delta }{S}_{m,t}^o$ were positive at lower temperatures and negative at higher temperatures. Thus, the results demonstrate the transition of an endothermic process to exothermic with the rise of temperature.

Table 5.

Values of the thermodynamics of transfer for the micellization of CPC + CTS mixture

Medium	csalt	T	$\mathrm{\Delta }{G}_{m,t}^0$	$\mathrm{\Delta }{H}_{m,t}^0$	$\mathrm{\Delta }{S}_{m,t}^0$
	mmol kg−1	K	kJ mol−1	kJ mol−1	J mol−1 K−1
NaCl + H2O	5.01	298.15	− 4.417	7.706	40.66
		303.15	− 3.685	13.78	57.63
		308.15	− 3.051	20.22	75.50
		313.15	− 1.498	25.63	86.64
		318.15	− 1.492	31.70	104.3
		323.15	− 5.028	40.58	141.1
Na2SO4 + H2O	1.67	298.15	− 12.74	93.55	356.5
		303.15	− 13.46	52.02	216.0
		308.15	− 16.14	10.67	86.98
		313.15	− 14.97	− 32.84	− 57.04
		318.15	− 15.87	− 80.99	− 204.7
		323.15	− 12.67	− 119.3	− 330.0
NaBenz + H2O	5.01	298.15	12.88	83.26	236.1
		303.15	10.18	62.46	172.5
		308.15	9.599	41.55	103.7
		313.15	7.938	19.16	35.83
		318.15	8.819	− 4.593	− 42.16
		323.15	6.657	− 27.16	− 104.6

Entyhalpy–entropy compensation for CPC + CTS mixture micellization

The aim of studying enthalpy–entropy compensation for CPC + CTS mixture in existence of several additives is to find the solute–solute and solute–solvent interaction present in the mixed system (Das et al. 2014; Sood and Sharma 2016). The enthalpy–entropy compensation of surfactant assembly was also detected and described by Sugihara and Hisatomi (Sugihara and Hisatomi 1999). Equation (9) is utilized to assess the enthalpy–entropy compensation behaviour.

$$\mathrm{\Delta }{H}_m^o=\mathrm{\Delta }{H}_m^{o,\ast }+T_c\mathrm{\Delta }{S}_m^o$$ 9

Here, $\mathrm{\Delta }{H}_m^{o,\ast }$ connotes the intrinsic enthalpy while T_c stands for compensation temperature. The estimated values of $\mathrm{\Delta }{H}_m^{o,\ast }$ can reveal the solute–solute interaction, while T_c serves the purpose of identifying solute–solvent interaction. The graphical presentation for the plot of $\mathrm{\Delta }{H}_m^o$ versus $\mathrm{\Delta }{S}_m^o$ demonstrates a linear relationship (Fig. 8), where the slope provides the value of T_c. The correlation efficient obtained from different mediums was ranged from 0.9985 to 0.9999 (Table 6). The negative values $\mathrm{\Delta }{H}_m^{o,\ast }$ for all the mediums studied indicate a more stable state after the formation of micelle. Here, the more negative values appeared for Na₂SO₄ (− 57.60 kJ mol⁻¹), while minimum values were exhibited by NaBenz (− 33.16 kJ mol⁻¹). This result suggested that in terms of stability, CPC + CTS mixture should be more stable in the presence of Na₂SO₄ while for aq. NaBenz medium this stability was the lowest. Similar maximum stability for Na₂SO₄ medium was previously reported for the micellization of surfactant system (Joy et al. 2022). The estimated T_c values for CPC + CTS mixture were maximum (329.51 K) for NaCl containing medium, while for aqueous, aq. Na₂SO₄, and aq. NaBenz media, the T_c values were 324.84, 302.97, and 307.09 K, respectively. Usually, the T_c values within the range of 311.2–312.8 K represent the existence of zwitter ion (Zheng et al. 2020). As the values of T_c lie in between 270 and 330 K temperature, this surfactant system can be used for the estimation of H₂O content in the biological system (Lumry and Rajender 1970). The reported T_c values are 332, 283, and 343 K in H₂O, aq. sodium salicylate, and aq. NaCl solutions, respectively, for the micellization of cationic gemini surfactant (Kumar and Parikh 2012).

Fig. 8.

$\mathrm{\Delta }{H}_m^0$ vs. $\mathrm{\Delta }{S}_m^0$ plot for the assembly of CPC + CTS mixture in A water and B aq. NaBenz media

Table 6.

Variables for the $\mathrm{\Delta }{H}_m^0$ vs. $\mathrm{\Delta }{S}_m^0$ compensation associated with the micellization of CPC + CTS mixture

Medium	csalt	$\mathrm{\Delta }{H}_m^{0,\ast }$	Tc	R2
	mmol kg−1	kJ mol−1	K
H2O	0.00	− 43.37	324.84	0.9998
NaCl + H2O	5.01	− 48.307	329.51	0.9999
Na2SO4 + H2O	1.67	− 57.60	302.97	0.9991
NaBenz + H2O	5.01	− 33.16	307.09	0.9985

Moghaddam and co-workers (Moghaddam et al. 2016) obtained enthalpy–entropy compensation for the micellization of different non-ionic surfactants, and the reported T_c values for the respective surfactants in aq. medium were in the range of 309.5–314.4 K. The T_c values have been taken as the characteristic of hydrophobic interaction between solute and solvent for a specific system (Jolicoeur and Philip 1974; Thompson and Love 2013).

Conclusions

The influence of several set of experimental conditions was investigated on the micellization of a surfactant (CPC) and a drug (CTS) mixture using conductivity method. The aim of this study was to gather information regarding their intermolecular forces for the CPC + CTS mixed system. Several micellar parameters (e.g. CMC, α, and β) proved that this micellization is dependent on the type of additive used, the content of the ingredient, and temperature of the system. The electrolyte showed its ability to pull the water molecule from the micellar surface, and this function was highly reliable on the ionic strength of the electrolyte. However, the HDT (NaBenz) always showed a different trend than the electrolyte (NaCl, Na₂SO₄). The employed electrolytes favour the micelle development of CPC + CTS system while the HDT imposes the delayed micellization; the effects have been found to be augmented with the upsurge of additives concentrations. The overall result demonstrates a less favourable tendency for the HDT than the electrolyte in terms of the stability of CPC + CTS mixed system. The overall result identifies several intermolecular forces such as ion–ion, ion–dipole, H–bonding, electrostatic, and hydrophobic interactions. However, it can be anticipated that these forces may play a significant role in the association of CTS drug with the CPC surfactant molecule. This outcome may assist other researchers to design an appropriate condition for the implementation of this drug molecule that can reduce the ongoing limitation of this medicine for a specific disease.

Funding

Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R53), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

Declarations

Conflict of interest

The authors declare that they have no conflict of interest.