Micellization and adsorption behaviour of bile salt systems

Abstract

The interfacial and bulk phase properties of sodium cholate (NaC), sodium deoxycholate (NaDC), sodium taurocholate (NaTC), sodium taurodeoxycholate (NaTDC) and their equimolar binary and ternary combinations in aqueous solution have been investigated using surface tensiometry, conductometry, microcalorimetry, and fluorescence probing. The obtained experimental results are utilized to evaluate critical micellar concentration (cmc), counterion binding (f), surface excess, minimum area per molecule (A_min), thermodynamics of adsorption and micellization, and microenvironment of the bile-salt micelles. The magnitude of counterion binding and its temperature dependence was found to be low. Binary and ternary bile salt mixtures show higher and lower A_min values, respectively, compared with the ^idealA_min at the experimental temperatures. The low I₁/I₃ values of single and mixed bile salts suggest the microenvironment of the micellar entities to be nonpolar as hydrocarbons. The enthalpy of micellization values obtained following the methods of van’t Hoff and microcalorimetry have been compared. The composition of the mixed micelles have been estimated on the basis of regular solution, Clint, Rubingh and Rubingh–Holland theories along with the activity coefficients and interaction parameters at different temperatures.

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Introduction

Mixed surfactant systems are extremely important because of fundamental, technological, pharmaceutical and biological considerations. In recent years much attention has been devoted to the study of mixed solutions of natural and synthetic surfactants.^1,2 Combinations of amphiphilic compounds are particularly relevant in biochemistry and biology. Bile salts are biologically important molecules and considered as a special class of surfactants due to their characteristic structural features, composed of hydrophobic and hydrophilic moieties and surfactant-like properties.³ Bile salts play crucial roles in a number of physiological processes^4,5 such as lipid digestion, drug absorption, cholesterol solubilization, and so forth. The physiological function of bile salt systems depends on the formation of mixed species involving bile salts and biological lipids. Bile salts form mixed micelles with lipids⁶ by solubilizing them. This phenomenon is of crucial importance in intestinal absorption of the products of fat digestion such as fatty acids, monoglycerides, sterols, and vitamins.⁷ In combination with synthetic surfactants, bile salts are used in medicines. For example, mixed bile salt micelles prepared with phospholipids or salts of fatty acids such as sodium oleate, have been shown to be suitable as drug carriers for parenteral administration.⁸ In addition, studies of the chemical stability of incorporated drugs have been reported.⁹ The behavior of bile salt micelles is quite different from micelles formed by detergents. Bile salt micelles are smaller aggregates with high charge density and of different structure than conventional surfactant micelles. Bile salts form mixed micelles with a variety of other soluble and insoluble lipidic substances. It is important to mention that bile salts are advantageous over conventional surfactants in that mixed micelles of bile salts are locally and systematically well tolerated and have proven to be neither embryotoxic nor mutagenic.¹⁰ In the field of enzymology, bile salts have found wide applications as excipients in novel formulations to secure enzyme solubilization.¹¹

Considerable efforts have been focused on the study of mixed solutions of bile salts and synthetic detergents as well as lipids from the view point of interfacial and bulk phase properties.^12–14 However investigations dealing with the binary mixtures of bile salts are conspicuously rare¹⁵ while no reports on micelle formation and interfacial adsorption characteristics of ternary bile salt combinations are available to date, studies dealing with ternary mixtures of a number of synthetic detergents are recorded.^16–18

This communication presents for the first time a comprehensive study on micellization and adsorption of the conjugated and non-conjugated bile salts, for example, sodium cholate (NaC), sodium deoxycholate (NaDC), sodium taurocholate (NaTC), and sodium taurodeoxycholate (NaTDC) and their binary and ternary combinations using conductometry, tensiometry, fluorescence spectroscopy, and microcalorimetry. The composition of the bile salt aggregates and intermicellar interaction parameters have been estimated following the models of Clint,¹⁹ Rubingh,²⁰ and Rubingh–Holland.¹⁸ We believe that the obtained information will help to understand the behavior of bile salt systems in vivo.²¹

Experimental section

Materials

The sodium salts of deoxycholic acid, cholic acid, taurocholic acid and taurodeoxycholic acid obtained from Sigma Chemical Co., (purity ≥ 99%) were used as received. Pyrene, used as micellar probe in the fluorescence measurements, was a Sigma product with purity > 98%. It was purified by sublimation in vacuum. Stock solution of pyrene was prepared in absolute ethanol. The quencher, cetylpyridinium chloride (CpCl, Aldrich), was recrystallized twice from the mixed solvent system of acetone and isopropyl alcohol. All the solutions were prepared in doubly distilled water. The stock solutions of the bile salt micelles were prepared by dissolving the required amount of the bile salt in doubly distilled water which were further used to prepare solutions of the desired concentration.

Methods

Surface tension. The surface tension of the solutions was measured with a Krüss 8 (Germany) tensiometer by the platinum ring detachment method. The measured surface tension values were corrected according to the procedure of Harkins and Jordan.²² The concentrated surfactant solution was added in instalments using a Hamilton microsyringe and measurements were made after thorough mixing and temperature equilibration. Temperature was maintained within ±0.1 °C by circulating water from a HAAKE GH thermostat. The measurements were made at 10, 20, 30 and 40 °C. The accuracy of the measurements was within ±0.1 dyne cm⁻¹.

Fluorescence. Steady-state fluorescence experiments were carried out with a Kontron SFM 25 spectrofluorometer, connected to a PC. A 1 cm stoppered silica cell was used for the spectral measurements at four different temperatures as described above. Selecting 335 nm as the excitation wavelength of the pyrene (1 × 10⁻⁶ M), the emission spectra were collected from 360 to 420 nm. The micropolarity values were collected as the ratio of intensities of first (I₁) and third (I₃) vibronic peaks of pyrene which appear at 373 and 383 nm, respectively. The aggregation number N̄ was determined using the fluorescence quenching technique. Cetylpyridinium chloride (CpCl) was used as the quencher. The aggregation number was obtained from the slope of the plots of quencher concentration [Q] vs. according to the equation:²³

The excitation wavelength was taken at 320 nm for the quenching experiments and the solutions were prepared according to Stam et al.²⁴

Conductivity. Conductance measurements were taken by employing a Denver (USA) conductometer (Denver, model-50) using the cell with a cell constant of 1.01 cm⁻¹. The measured conductance values were accurate within ±0.5%. Conductivity measurements were taken as described earlier.¹⁶

Microcalorimetry. The microcalorimetric measurements were taken in an OMEGA Isothermal Titration Calorimeter of Microcal Inc., USA at 298 K by measuring heat change resulting from the injection of equimolar mixtures of bile salts into water. Aliquots of a concentrated solution of bile salts of appropriate volume were added in several instalments in a suitable volume of water taken in a cell and the resulting heat flow versus time profiles were measured. The addition of bile salt solution and the measurements of heat were as programmed. All the experiments were performed in triplicate to check the reproducibility.

Results and discussion

Critical micelle concentration (cmc)

The cmc’s of individual and mixed bile salt systems have been determined by surface tensiometry, conductometry and microcalorimetry. The concentration corresponding to the final break point in the plot of surface tension (γ) or conductivity versus logarithm of the total molar surfactant concentration (C_t) is taken as the cmc of the single and mixed surfactant combinations. In the case of mixed bile salt systems, we could hardly locate a break point in the conductivity versus concentration plots probably due to very low counterion binding characteristics. A representative tensiometric profile of all the systems at 20 °C is shown in Fig. 1. A dip in the tensiometric plot of NaC single surfactant system could be due to the small amount of impurity. The cmc values of single bile salts and their equimolar binary and ternary mixtures at different temperatures are contained, respectively, in Tables 1S–3S of ESI.† However, the data for some representative bile salt systems are given in Table 1. The agreement among the cmc values obtained by different methodologies is found to be reasonably satisfactory. It is known that the cmc values of the bile salts reported in the literature are not always consistent.^13,25 It is found that the cmc values of dihydroxy bile salts, NaDC and NaTDC are lower than those of trihydroxy salts, NaC and NaTC at all the temperatures studied. The obtained results are in keeping with the higher hydrophobic character of dihydroxy bile salts compared with that of trihydroxy bile salts. It is interesting to note that the bile salts possessing the same number of OH groups with taurine head groups have lower cmc values in comparison with those having COO⁻ head groups. This may be attributed to the bulky taurine head group for taurocholates compared with the simple COO⁻ head group of the non-conjugated bile salts. Similar observations have been reported in the literature.^18,25 The cmc values of binary surfactant combinations usually fall in between the cmc values of individual components.²⁰ It is found that the cmc values of the binary mixed systems investigated herein, where at least one of the members is a dihydroxy bile salt, are either less than that of the component with lower cmc or fall in between as is found usually. The cmc value of NaC–NaTC mixture is found to be higher than that of either of the components of the mixture. The cmc values of the equimolar ternary combinations are usually found to lie in between those of the component surfactants. However, it is noted that the cmc value of the NaC–NaTC–NaTDC mixture is lower than that of the component NaTDC.

Fig. 1 Plots of the surface tension, γ, of single, binary and ternary bile salt systems vs. the total surfactant concentration, C_t (M) at 20 °C.

Table 1 Critical micelle concentration, cmc, degree of counterion binding, f, maximum surface excess, Γ_max, minimum area per molecule, A_min, I₁/I₃ values, ^idealC_mix and ^idealA_min for different bile salt systems at different temperatures

System	T (°C)	f	cmc (mM) (S.T)	cmc (mM) (Cond)	Γmax/10^−6 (mol m^−2)	Amin (nm^2)	I1/I3
NaC	10	0.06	10.8	12.5	2.45	0.68	0.86
	20	0.08	7.78	8.25	2.58	0.64	0.88
	30	0.09	5.89	7.35	2.27	0.73	0.92
	40	0.08	6.10	7.50	2.45	0.68	0.96

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System	T (°C)	Cmix (mM)	^idealCmix (mM)	Γmax/10^−6 (mol m^−2)	Amin (nm^2)	^idealAmin (nm^2)	I1/I3
NaDC–NaTC	10	5.95	5.52	1.26	1.32	1.20	0.72
	20	3.92	4.84	1.37	1.21	1.20	0.75
	30	4.75	4.05	1.56	1.06	1.23	0.76
	40	4.83	4.22	1.16	1.43	1.11	0.79
NaTC–NaDC–NaTDC	10	3.85	3.31	1.58	1.05	0.97	0.72
	20	3.32	3.56	1.83	0.91	0.97	0.75
	30	3.20	3.36	1.85	0.90	0.99	0.76
	40	2.65	3.53	1.83	0.91	0.93	0.77

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The variation of cmc values of individual bile salts along with their equimolar binary and ternary mixed systems against temperature is shown in Fig. 2. The cmc values are found to decrease on increasing temperature from 10–30 °C beyond which the cmcs of single surfactants increase except for NaTDC in which case a minimum cmc value is observed around 20 °C. A similar variation of cmc values of NaC,²⁵ NaDC,²⁵ NaTC,¹⁸ and NaTDC¹⁸ obtained employing different methodologies has been reported. Equimolar binary combinations of bile salts exhibit a similar trend except for the NaTDC–NaDC and NaC–NaTC systems where a continuous decreasing trend is observed. Recently Hildebrand et al.²⁵ studied the cmc variation of NaC and NaDC and their equimolar mixtures with sodium oleate in the temperature range of 10–70 °C. On the basis of calorimetric results the authors attributed the appearance of minimum to entropy–enthalpy compensation phenomenon during micellization. The initial cmc decrease is ascribed to predominant entropic contribution to micelle formation while the driving force of aggregation becomes more and more enthalpy driven at higher temperature. Similar behavior was observed in the case of various bile salt systems^26,27 Small et al.¹⁸ put forward an explanation of the phenomenon by suggesting a balance between the monomer solubility and hydrophobic behavior of NaTC, NaTDC and their equimolar combinations. The equimolar ternary systems, however, depict a continuous cmc decrease against temperature. This suggests stabilization of micelles at increased temperature (up to 40 °C).

Fig. 2 Plots of the critical micelle concentration, cmc, versus temperature for (A) single, (B) binary and (C) ternary bile salt systems.

There is reliable evidence that bile salts self-assemble to form micelles whose size continuously increases with increasing amphiphile concentration.^28–30 Several models have been proposed to describe the unusual self-assembly of bile salts. The most accepted model is a two-step model³¹ involving the formation of primary and secondary micelles. In the first step, around cmc, small aggregates known as primary micelles begin to form, where a maximum of ten molecules can be associated.³¹ In the second step at higher concentration, large micelles called secondary micelles are formed by mutual association of primary micelles. The primary–secondary micelle scenario has been confirmed by simulations.^32,33 The two step model is also consistent with two cmc values³⁴ corresponding to two types of micelles. Thus it is concluded that at cmc₁ primary micelles are formed, and at cmc₂ self-assembly of primary micelles occur to form secondary micelles whose size increases with the increase in bile salt concentration. It has been reported in the literature³⁵ that NaDC exhibits two cmc values at 10 mM and 60 mM corresponding to the formation of primary and secondary micelles. Also a ¹H-NMR study confirmed the existence of primary micelles up to 100 mM concentration, beyond which self-assembly occurs.^36,37 Based on ESR measurements, at least two kinds of micelle were suggested to co-exist in dehydroxy bile salts at 100 mM concentration.³⁸ Li et al.³⁹ have shown an increase in micellar polydispersity and an average micellar size due to an increase in NaTC concentration only after 50 mM. For cholate and deoxycholate micelles, secondary micelles have been reported⁴⁰ to form beyond 100 mM concentration. Thus from the literature it may be concluded that self-assembly of bile salt micelles and polydispersity occurs only at higher concentration (>50 mM or 100 mM), which is a much larger concentration than the investigated concentration range of our experimental system. We have used the concentration of bile salts up to the maximum of 12 mM, indicating absence of secondary micelles and polydispersity in our investigated system.

Degree of counterion binding (f)

The fraction of the counterions bound to the micelles (f) of ionic surfactant systems can be determined conductometrically following the procedure of Evans⁴¹ by utilizing the plot of specific conductance against surfactant concentration. The results of single bile salt systems in the temperature range 10–40 °C are presented in Table 1S of ESI† and that of a representative system are contained in Table 1.

The obtained values of f are found to be low in accordance with the reported values.^42,43 In addition their temperature dependence was found to be very small. Small et al.¹⁸ showed that in the case of NaTC, the plot of log(cmc) versus log[NaCl] yielded a straight line with approximately zero slope indicating negligible counterion binding on its micelles while for NaTDC a slightly negative slope suggested less than one quarter of the ionic groups of its micelles bound to counterions. The authors also found even lower counterion binding for their mixed systems which were almost two thirds of the value for pure NaTDC micelles. In the case of ionic/nonionic¹⁶ as well as ionic/bile salt combinations¹³ very low counterion binding values have been reported. We could hardly locate a break point in specific conductance versus surfactant concentration plots in binary and ternary mixtures of bile salt systems indicating very low or negligible counterion binding characteristics. For this reason we have used cmc values obtained by the surface tension method for further analysis and interpretation of the results.

Surface excess and minimum area per molecule of the single and mixed bile salt systems

In order to calculate the amount of surfactant adsorbed per unit area at the air/aqueous solution interface for different systems, we followed Gibb’s adsorption equation¹³ (see ESI†). The maximum adsorption density (Γ_max) and the minimum area per surface active component (A_min) for the single, binary and ternary mixtures are given in the Tables 1S–3S of ESI† respectively. The results of some representative bile salt systems are contained in Table 1. Since dilute surfactant solutions were used, the dlog γ_± term was not considered in the calculation. A_min (in our case) refers to the average of that contribution of the components assuming equimolar composition of the amphiphiles at the interface. It is not possible to evaluate surface excess values of individual components in a multicomponent system by surface tensiometry measurement, however, an idea of the comparative relationship of total surface excess and corresponding minimum area per molecule of the surfactant combinations can be obtained.

The evaluated Γ_max values of individual bile salts (given in Table 1 of manuscript and Table 1S of ESI†) are found to be higher and thus corresponding lower A_min values than those reported by Jana et al.¹³ The reported trend in A_min followed the order NaDC > NaTDC > NaC at 30 °C. However, our results at approximately all temperatures maintained the sequence NaDC > NaTC > NaC > NaTDC. This indicates a more compact monolayer formed by the bile salt NaTDC. In the case of binary and ternary bile salt combinations, the A_min and Γ_max values are found to be intermediate in comparison with those of the components (Tables 2S and 3S of ESI†). A_min values for NaC–NaTDC are comparatively lower than those of the other binary mixtures while ternary mixtures NaTC–NaTDC–NaC show lower values. It is evident from Table 1 that the temperature dependence of the values doesn’t show any regular trend. The minimum area per molecule under an ideal mixing situation (^idealA_min) of the mixed entities can be expressed by the relation:

^idealA_min = ∑α_iA_i,min (2)

where α_i is the bulk mole fraction and A_i,min the minimum area per molecule for ith pure component at a given temperature. The ^idealA_min values obtained by eqn (2) are also included in Tables 2S and 3S (ESI†) and in Table 1 for representative ones. The binary mixtures of bile salts exhibit higher A_min values compared to ^idealA_min at all the experimental temperatures studied except for NaTC–NaTDC and NaTDC–NaDC combinations. However, the ternary bile salt mixtures show lower A_min values compared to ^idealA_min except for the NaTDC–NaDC–NaC system. The composition of the adsorbed mixed surfactant layer may not be equal to the bulk composition.⁴⁴ Thus these values may be to some extent erroneous. However increased charge repulsion among the amphiphiles of similar head groups may be responsible for higher A_min values. The unexpected surface tension behavior⁴⁵ may be attributed to factors other than interfacial composition. The obtained results indicate non-ideal mixing of the bile salt systems. A critical assessment of the results is needed to properly understand the phenomenon.

Thermodynamics of interfacial adsorption and micelle formation

The standard free energy of adsorption^13,46 at the air-saturated monolayer interface, ΔG^o_ad for single, binary and ternary bile salt systems was obtained from the relationship.

ΔG^o_ad = ΔG^o_m − (π_cmc/Γ_max) (3)

where π_cmc is the surface pressure at cmc (π_cmc = γ_o − γ_cmc) γ_o and γ_cmc being surface tension of water and that of a given surfactant system at its cmc, respectively) and Γ_max is the surface excess at the minimum adsorption level.

The free energy of micellization per mole of monomer unit, ΔG^o_m values¹³ can be evaluated by applying the equation:

ΔG^o_m = (1 + f)RT ln cmc (4)

where f is the fraction of counterions bound to the micelles.

Since the obtained values of f were very low for single bile salt systems and negligible in the case of binary and ternary combinations, they were not considered in the evaluation of ΔG^o_ad and ΔG^o_m values. The ΔG^o_ad, ΔG^o_m and π_cmc values of the representative individual, binary and ternary bile salt systems are presented in Table 2 and those of other bile salt systems are given in Table 4S of ESI.†

Table 2 ΔG^o_m, ΔH^o_m, ΔS^o_m, ΔG^o_ad and π_cmc values for NaC and equimolar NaDC–NaTC and NaTC–NaDC–NaTDC bile salt systems at different temperatures

System	T (°C)	ΔG^om(kJ mol^−1)	ΔH^om (kJ mol^−1)	ΔS^om (J K^−1 mol^−1)	πcmc (mN m^−1)	ΔG^oad (kJ mol^−1)
NaC	10	−10.7	21.6	114.1	29.4	−22.7
	20	−11.8	21.6	113.9	30.6	−23.7
	30	−12.9	8.3	73.4	31.8	−27.0
	40	−13.3	−2.9	33.2	33.9	−27.1
NaDC–NaTC	10	−12.1	27.8	140.9	28.8	−34.9
	20	−13.5	8.0	73.5	28.4	−34.2
	30	−13.5	−8.0	18.1	27.7	−31.2
	40	−13.9	−1.4	10.0	27.4	−37.5
NaTC–NaDC–NaTDC	10	−13.1	10.0	81.5	29.6	−31.9
	20	−13.9	6.7	70.2	28.5	−29.5
	30	−14.5	8.5	75.9	27.7	−29.4
	40	−15.4	15.2	97.9	26.9	−30.1

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The ΔG^o_m values for the single bile salts are found to be comparable with those reported in literature.¹³ The evaluated values do not show much difference in the case of individual and mixed systems at the experimental temperatures. However, the values for NaTDC and NaTC–NaTDC–NaC mixtures show more favourable spontaneity of micellization. Again ΔG^o_ad values of the single and mixed systems are found to be more negative compared with the ΔG^o_m values indicating a stronger interaction between amphiphiles at the air/aqueous solution interface than in the bulk phase. It may be mentioned that ΔG^o_ad values for the mixed bile salt systems are lower in magnitude (higher) compared to that of bile salt–CTAB mixed combinations reported by Jana et al.¹³ The result in our case may be due to repulsion between the similarly charged head groups.

For a complete thermodynamic analysis ΔH^o_m is required along with that of G^o_m. The temperature dependence of cmc can be used to estimate ΔH^o_m and hence ΔS^o_m assuming the aggregation number as well as counterion binding to be independent of temperature. The detailed procedure is given in ESI.† The data may provide an idea of the general trend found in the thermodynamics of micellization of the single as well as mixed bile salt systems. However, the evaluated thermodynamic properties (Table 4S of ESI† and Table 2 of the manuscript) are not accurate enough compared with those obtained from calorimetric determinations. The trend observed in the case of NaTC and NaTDC are more or less comparable with the data reported by Small et al.¹⁸ It is found that in the case of (a) NaC, NaTC, NaDC, NaC–NaTDC, (b) NaDC–NaTC, NaTC–NaTDC, NaC–NaDC (c) NaTDC, negative ΔH^o_m values are obtained beyond 30 °C, 20 °C and 10 °C for the systems (a), (b) and (c) respectively. The ΔS^o_m values for all the investigated systems are fairly positive except for a few cases at higher temperatures. The positive ΔS^o_m values are attributed to the randomness resulting from the melting of “icebergs” around the non-polar moiety⁴⁷ of the surfactant monomers during micellization and location of non-polar end in similar or like environments in the micelle interior. The process of micellization is found to be entropy driven for the studied systems at the experimental temperatures since TΔS^o_m > ΔH^o_m. Interestingly Small et al.¹⁸ reported enthalpy directed micellization of bile salts at temperatures higher than 50 °C.

The behavior of hydrophobic groups of amphiphilic molecules in water is considered as a case of entropy–enthalpy compensation phenomenon.⁴⁸ The compensation between ΔH^o_m and ΔS^o_m is depicted in Fig. 3 where the lines have the same slope but different intercepts at ΔS^o_m = 0. The different intercepts reflect varied hydrophobicities of the systems. The constant slope (= 0.29) of the compensation line represents T_c, compensation temperature, which characterizes the solvation phenomena of the process.⁴⁸ It may be said that during the process of micellization, both the hydrophobic hydration of the amphiphilic monomers and the hydrophilic hydration of ionic head groups (due to their mutual association) decrease, leading to the transfer of bile salts from their hydrophobically hydrated state in aqueous medium to the oily core of the micelles.

Fig. 3 Compensation plots of ΔH^o_m and ΔS^o_m for different bile–salt systems.

Microcalorimetric studies

Microcalorimetry is the most reliable method to explore the thermodynamics of self-aggregation of amphiphilic molecules. The cmc and enthalpy of micellization, ΔH^o_m can be obtained in a single run using the methodology. The cmc values of the bile salts and their mixtures at equimolar combination were determined using Isothermal Titration Calorimetry (ITC) at 298 K. The resulting heat flow versus time profiles of one of the investigated systems is exhibited in Fig. 4a.

Fig. 4 (a) Calorimetric traces (heat flow versus time) (b) reaction enthalpy versus total bile-salt concentration in mM (c) determination of ΔH^o_m and cmc at 25 °C.

The bile salt concentration in the injector was maintained appreciably high above the cmc, so that the injector contained a mixture of micelles and monomers. Initially, a series of relatively large endothermic peaks were observed when the bile salt solutions were injected into the reaction cell. The enthalpy changes occur due to micelle dissociation since the concentration in the reaction cell was below cmc.⁴⁹ The endothermic nature of these peaks (ΔH > 0) indicate that demicellization must lead to an overall entropy increase of the systems, since micelle dissociation is thermodynamically favorable below cmc (ΔG < 0); thus TΔS > ΔH. This entropy increase may be attributed partly to the release of the counterions associated with bile salt surfactants when micelles break down to monomers⁴⁹ and partly to the loss of orientation or packing arrangement of amphiphiles within micelles. It is pertinent to mention that the positive entropy change during micellization is not contradictory to the positive entropy change during demicellization. This is explained as: during micellization, change in entropy is a competition between two competitive factors, the orientation effect (packing of amphiphile monomers into micelles) and dehydration effect (melting/release of water molecules around the hydrophobic tail of the monomer).⁵⁰ It is reported that the dehydration effect is accompanied by a positive entropy change^51,52 and the orientation effect is accompanied by a negative entropy change.^52,53 Further positive contribution to entropy due to dehydration effect dominates the negative contribution to entropy due to orientation effect during micellization⁵⁰ making over all entropy of micellization positive. A quantitative estimation of the individual contributions of these two effects is difficult. In contrast during demicellization, the collective effect of breaking of the micelle into monomers and the release of counterions may lead to a positive entropy change. The two statements are not contradictory, as the negative entropy change due to packing of monomers during micellization is analogous to the positive entropy change due to breaking of micelles into monomers during demicellization. Positive values of entropy during micellization and demicellization are frequently reported in the literature.^54–57

An appreciable decrease in peak height was observed after a few injections because the bile salt concentration in the reaction cell exceeded the cmc and hence the micelle in the reaction cell was no longer dissociated. The enthalpy change is thus solely the result of micelle dilution effects⁵⁸ above the cmc. Fig. 4b depicts the dependence of enthalpy change (ΔH) per mole of bile salt injected into the reaction cell, calculated by integration of heat flow versus time profiles. The cmc of the bile salt solutions obtained from the inflexion point in ΔH versus bile salt concentration are presented in Table 3. The cmc values of the bile salt solutions obtained by surface tensiometry show fairly reasonable agreement with those determined calorimetrically except in a few cases. The reported cmc values of some of the bile salts are not always consistent.^13,18,25 The cmc value of NaTDC, for example, is found to be in the range of 2–70 mM, depending on the methodology used.¹³ The enthalpy change due to micellization is obtained from the difference in enthalpy between the final and initial plateau regions at the points of discontinuity in the sigmoidal enthalpograms (Fig. 4b) for dilution of concentrated bile salt solution in water (a prototype is shown in Fig. 4c). The ΔH^o_m values obtained following the procedure of Kreshek and Hargraves method⁵⁹ are presented in Table 3.

Table 3 Calorimetric determination of ΔH^o_m (kJ mol⁻¹) and cmc (mM) for various equimolar mixtures of bile salts at 25 °C, van’t-Hoff enthalpy ΔH^o_m (kJ mol⁻¹) at 20 °C

System	ΔH^om (kJ mol^−1)	cmc (mM)	van’t-Hoff enthalpy ΔH^om (kJ mol^−1)
NaTC–NaC	−0.85	9.69	5.1
NaTC–NaDC	−1.63	4.20	8.0
NaTC–NaTDC	−2.70	3.42	19.9
NaC–NaTDC	−2.94	2.63	14.6
NaDC–NaTDC	−3.16	3.61	4.3
NaC–NaDC	−1.16	7.05	3.7
NaC–NaDC–NaTDC	−1.85	2.72	8.0
NaTC–NaDC–NaC	−1.42	6.13	0.6
NaTC–NaDC–NaTDC	−2.34	3.32	6.7
NaTC–NaC–NaTDC	−2.02	5.17	6.6

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The observed large negative ΔH^o_m values for the more hydrophobic binary (NaDC–NaTDC, both are dihydroxy bile-salts) and ternary (NaTC–NaDC–NaTDC containing two dihydroxy bile-salts) systems probably resulted due to the unfavorable interaction involving water and hydrophobic mixtures of the bile salts. When hydrophobic molecules enter into water the mutual phobicity of the hydrophobic moieties and water leads to the exclusion of water molecules by a hydrophobic molecule resulting in aggregation (or so called ice berg formation)⁴⁷ of such water molecules. Hence during micellization, heat is released due to the release of such structures. The higher negative ΔH^o_m values of the more hydrophobic NaDC–NaTDC system are found compared with the lower negative values for the less hydrophobic NaC–NaTC combination. Therefore the microenvironment of the micelles containing dihydroxy bile salts seems to be more hydrophobic than those containing trihydroxy ones. This is also reflected from fluorescence measurements, discussed later. The calorimetric study of the bile salts may help towards a comprehensive understanding of the micelle formation process. However the associated factors like hydration, orientation, microenvironment and packing of the bile salt molecules influence the thermodynamic parameters and a quantitative interpretation of the phenomenon seems to be a very difficult proposition at this stage.

Correlation between calorimetric and van’t Hoff enthalpies

In order to evaluate thermodynamic parameters of the micellization of bile salts, the enthalpy of micelle formation is obtained directly using microcalorimetry, as well as by estimating the property utilizing the tensiometric cmc values at different temperatures following the van’t Hoff equation. In terms of the mass action principle, the standard free energy of micellization, ΔG^o_m is given by the following equation:where m and n are the numbers of counterions bound per micelle and the aggregation number of a micelle, respectively. The term m/n is thus equal to the fraction of the counterions (f) bound to the micelle. X_cmc is the cmc in mole fractional units. The enthalpy of micellization, ΔH^o_m can be calculated by using eqn (7) and (8) given in ESI.†

It is observed that although the cmc of bile salts determined by the calorimetry and other methods show fair agreement, the ΔH^o_m values obtained by the direct calorimetric method appreciably differ from those calculated by the van’t Hoff equation (Table 3). Literature⁶⁰ reports support the observation. It should be mentioned that such differences are often found and have been pointed out by Chatterjee et al.⁶¹ The changing aggregation number, shape, and the counterion binding of micelles not accommodated in the van’t Hoff rationale, are considered to affect the ΔH^o_m value of the process. The contributions of the above mentioned factors, on the other hand, are inherent in the direct determination of ΔH^o_m by calorimetry. Thus, the observed discrepancy of the results by the two approaches is not unusual. Corkill^62,63 proposed a relationship for the evaluation of ΔH^o_m of nonionic surfactants accounting for the contribution of aggregation number and the effect of changing aggregation number on the micellar surface charge. Holtzer and Holtzer⁶⁴ provided an explanation of the electrostatic free energy of the micelle formation process of ionic surfactants (on the basis of similar considerations) and pointed out the inefficiency of the van’t Hoff approach. The calorimetrically obtained ΔH^o_m values are found to be lower in magnitude compared with those estimated by the van’t Hoff method.⁶⁵ This is reflected in the results of the present study. The lower values of ΔH^o_m obtained by calorimetry may be due to hydrophobic interaction and breaking of icebergs with associated exothermic heat change during micellization. This makes the resultant ΔH^o_m more exothermic compared with the van’t Hoff result where the second exothermic process does not influence the enthalpy of n(monomer) ↔ micelle formation equilibrium obtained from the temperature dependence of cmc. It may be mentioned that the two methods have a basic difference; while the calorimetry provides the integral heat of micellization, the van’t Hoff method deals with differential heat treatment.⁶⁶ Thus, the direct method of calorimetry registers all sorts of heat changes; the sum of which is compounded as the heat of micellization. This may include the contribution from: (a) dissociation of micelles (b) changes in the bile salt–bile salt interactions (c) changes in the hydration or counterion binding (d) molecular rearrangement, mixing etc. Although calorimetry is the most accurate method, a major limitation is that the method measures only the overall enthalpy change of a system and it is not possible to directly isolate the contribution of different mechanisms. Ideally the methodology should be used in combination with other methods providing complementary information regarding the system. A quantitative accounting incorporating pragmatic concepts and additional information are thus needed to resolve the issue.

Micropolarity of the bile salt micelles

The ratio of intensity of first to the third fluorescence vibronic peaks (I₁/I₃) in a monomeric pyrene fluorescence emission spectrum yields information about the solubilization site sensed by pyrene in surfactant micelles. The ratio is known to be a sensitive index of the polarity in the microenvironment.³⁷ A low value of I₁/I₃ indicates a nonpolar environment while its high value suggests a polar environment. Characteristic values of I₁/I₃ are 0.6, 1.04, 1.23, 1.33, and 1.84 in cyclohexane, toluene, ethanol, methanol, and water, respectively.⁶⁷ These micropolarity values of the representative single, binary and ternary bile salt systems are presented in Table 1 (for rest, see Tables 1S–3S of ESI†). The low I₁/I₃ values of individual as well as their combinations indicate the microenvironment of the micelles to be nearly non-polar like hydrocarbon solvents.⁶⁷ Thus it may be considered that pyrene is solubilized in the core of bile salt micelles.⁶⁸ In contrast in the case of ordinary surfactants, pyrene is considered to reside in the palisade layer of micelles. The micropolarity of the systems (at all temperatures) follows the order: NaTC > NaC > NaTDC > NaDC. Pyrene is exposed to the more hydrophilic environment of trihydroxy bile salts than the dihydroxy ones. Spin label studies⁶⁹ revealed that trihydroxy bile salts form smaller micelles compared with those of dihydroxy systems. This suggests that pyrene monitors more polar environment in trihydroxy bile salt solutions due to their more exposed hydroxy groups in relatively smaller micelles. For a given number of hydroxy groups on the hydrophobic surface of bile salts, the micropolarity in the core of the micelles with the bulky taurine terminal group is more hydrophilic than in the bile salts having a COO⁻ terminal group.

Binary combinations of the trihydroxy bile salts NaTC–NaC show a more hydrophilic microenvironment compared with those of the dihydroxy NaDC–NaTDC systems. Other mixed solutions of di- and trihydroxy bile salts exhibit intermediate or nearly similar micropolarities. The micropolarity values are found to be closely comparable with those of the component dihydroxy bile salts suggesting their predominance in mixed micelles. The data in Table 4 (Table 5S of ESI†) support this observation indicating a higher mole fraction of dihydroxy bile salts in mixed micelles. In the case of ternary mixtures, the micropolarities are more or less comparable with one another having values in between those of NaTC and NaDC.

Table 4 Critical micelle concentration: C_mix (experimental), ^idealC_mix and ^RHC_mix, micellar mole fraction, X_i, activity coefficients, g_i, for equimolar binary and ternary bile salt systems according to Rubingh’s formulation and Rubingh–Holland treatment respectively at different temperatures

System	T (°C)	Cmix (mM) (S.T)	^idealCmix (mM)	^RHCmix (mM)	X1	X2	X3	g1	g2	g3
NaDC–NaTC	10	—	—	—	0.610	—	—	1.049	1.124	—
	20	—	—	—	0.596	—	—	0.864	0.726	—
	30	—	—	—	0.749	—	—	1.050	1.544	—
	40	—	—	—	0.729	—	—	1.048	1.405	—
NaTC(1) : NaDC(2) : NaTDC(3)	10	3.85	3.31	3.46	0.225	0.183	0.591	0.986	1.355	0.970
	20	3.32	3.56	2.24	0.342	0.146	0.511	0.325	1.343	0.627
	30	3.20	3.36	2.16	0.362	0.102	0.536	0.325	2.334	0.539
	40	2.65	3.53	2.59	0.248	0.269	0.483	0.651	1.017	0.621

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Temperature dependence shows an increase in I₁/I₃ values with temperature for all pure and mixed systems. This may point to a slightly increased water penetration into the micelles due to a loosening of their structure and exposure of pyrene to a more hydrophilic microenvironment.

Interactions in bile salt mixed micelles

In a multicomponent mixed micellar system, the cmc values of mixtures are related to individual cmc values of the components by the Clint equation.¹⁹ The evaluated ideal cmc values (^idealC_mix) for some equimolar binary and ternary systems at different temperatures along with the experimentally determined cmc values are contained in Table 1 (see Tables 2S and 3S of ESI†). The observed differences between the ideal and experimental values indicate the degrees of non-ideality of the systems investigated. In the case of NaTC–NaTDC, NaC–NaTDC and NaC–NaDC binary mixtures negative deviations of C_mix from ^idealC_mix at the experimental temperatures except for the NaC–NaDC system at 40 °C are observed. The deviation is found to be positive for NaTDC–NaDC at low temperatures and negative at higher temperatures. Hildebrand et al.²⁵ observed a similar trend for the bile salt–sodium oleate mixed system. All the ternary systems except NaTC–NaDC–NaC show a negative deviation of experimental cmc values from those of the ideal ones at different temperatures. A conspicuously high negative deviation of C_mix from ^idealC_mix is observed in the case of the ternary mixture of NaTC–NaTDC–NaC. Interestingly the bile salt combinations comprising NaTDC show a negative deviation.

Rubingh²⁰ provided a theoretical treatment to estimate the micellar mole fraction X_i, activity coefficients g_i, of the components of the binary surfactant systems and intermolecular interaction parameter β, on the basis of experimental cmc values. Table 4 depicts the micellar composition X₁ (the mole fraction of the first component), activity coefficients, g₁ and g₂ of one bile salt and the β values of one binary bile salt mixture (for all bile salt systems, see ESI†). The evaluated β values show a similar trend as found in the deviation of C_mix from ^idealC_mix described above. The average value of β for the systems NaTC–NaTDC, NaC–NaDC and NaC–NaTDC at studied temperatures exhibit negative values indicating a synergistic behavior. On the contrary positive β values of NaDC–NaTC and NaC–NaTC combinations suggest antagonistic interaction. Probably the positive β value of NaDC–NaTC is a manifestation of stearic repulsion between the bulky head groups. The antagonistic behavior of the NaC–NaTC mixture may be attributed to the less favorable interaction involving trihydroxy bile salts and reflected in their large cmc values and higher aqueous solubilities. The deviation of activity coefficients from unity indicates non-ideality of the systems.

Jana et al.¹³ reported antagonistic interactions between cetyltrimethylammonium bromide (CTAB) and a few bile salt mixtures and on the contrary synergism between sodium dodecylsulphate (SDS) and the bile salts at higher proportions. Similar trends were observed for sodium oleate–nonionic surfactant mixtures.⁷⁰ Synergistic behavior of NaC and NaDC with alkyl sulphates has been reported in the literature,⁷¹ which, however seems illogical in view of the similar charges on the head groups.

The mixed micellar composition X, activity coefficients g_i, and the interaction parameter β of ternary combinations have been evaluated using a pseudobinary Rubingh’s treatment^16,18,72 where two surfactants are paired and treated as one component and a third as the other. The cmc of the paired component has been taken as that in their equimolar binary mixtures. In the case of ternary bile salt mixtures, twelve sets of results stand for three possible pairings and the results are given in Table 6S of ESI.† The results show that, X₁ and β clearly depend on the method of selection for the pairing of the three components. The β values are found to be positive or negative at different temperatures. Interestingly the NaTDC–NaTC–NaC combination depicts negative β at all temperatures irrespective of the pairing selection of the components thereby suggesting synergism. A_min values also show unusual behavior. The calculated activity coefficients are found to be more or less of normal magnitude except in a few cases. The deviation of the activity coefficient values from unity and that of the X₁ value from 0.5 suggest non-ideality.

Holland and Rubingh¹⁷ proposed a generalized multicomponent nonideal mixed micellar model based on the pseudo-phase separation approach. The model has been successfully applied to a number of micellar compositions^16,17 and activity coefficients. It involves an effective utilization of net interaction parameters obtained experimentally from the cmc values of binary systems. In accordance with this treatment the activity coefficients g_i, g_j, … of micelle forming surfactant species i, j, … in an n-component mixture are presented on a general basis by the equation:

where β_ij represents the net (pairwise) interaction between component i and j, and X_j is the mole fraction of jth component in the micelles. At cmc, the relation:holds where terms C_i and C_j are the cmc values of the ith and jth components in their pure state, respectively. The interaction parameter, β_ij can be obtained independently from binary mixtures using Rubingh’s method. The activity coefficients of a three component system i.e., g₁, g₂ and g₃ at the mixed cmc can be evaluated by the above equations utilizing the method of successive substitution and maintaining the constraint that the sum of X_i’s equals unity. We have used the Levenberg–Marquardt⁷³ method, an efficient numerical technique for function minimization and evaluation of multiple unknowns from multiple equations. The values of g_i thus obtained can be used to evaluate ^RHC_mix, the mixed micellar cmc of ternary systems following the equation:where α_i, g_i and C_i are the bulk mole fraction, activity coefficients and cmc of the pure ith component respectively.

The mole fraction values of each component in one of the ternary mixed micelles viz., X₁, X₂ and X₃, their activity coefficients g₁, g₂ and g₃ along with the predicted cmc following the Rubingh–Holland method, ^RHC_mix, are presented in Table 4 (see Table 7S of ESI† for all ternary systems).

The activity coefficient values are found to be within the normal range although deviations from unity suggest non-ideal behavior. It is found that the micellar mole fraction of NaTDC is higher in all the ternary mixtures studied while in the case of NaTC–NaDC–NaC combinations predominance of NaDC is observed. In general at least one of the dihydroxy components is seen to predominate in the mixed micelles. This behavior in ternary mixtures is also shown in the pseudobinary Rubingh treatment for ternary systems as discussed earlier.

Conclusions

Bile salts, a special group of biosurfactants, have been of interest to colloid and interface scientists.⁵ Because, bile salt systems are physiologically important, extensive studies have been carried out on the physicochemical properties of single bile salt systems.^4–7 Considerable attention has been given in recent years towards the study of mixed micelle formation of bile salts and lipids to explore the nature of interaction both in bulk and at the air–water interface.^12–14 Although physicochemical studies of binary bile salt systems are rare,¹⁵ the ternary bile salt systems remain unexplored. The present detailed investigation of the interaction of bile salts in solution with reference to mixed micelle formation, the thermodynamics of micellization, the behavior at the air–water interface and in the bulk, and the micropolarity of the micelles would be worthwhile.

The cmcs of NaC, NaDC, NaTC, NaTDC and their equimolar binary and ternary mixtures obtained by tensiometry, conductometry, and microcalorimetry show a reasonably fair agreement. The degree of counterion binding of the bile salt micelles is found to be rather low consistent with the previous findings,^42,43 while it is almost absent in the mixed micellar system. In comparison with the ^idealA_min values, the A_min of the binary and ternary bile salt mixtures are found to be higher and lower, respectively. The ΔG^o_ad values of the bile salt mixtures are observed to be more negative than the ΔG^o_m values. The enthalpy of micellization (ΔH^o_m) process reflects the entropy–enthalpy compensation phenomenon.⁴⁸ The microcalorimetrically determined enthalpy values are observed to be more exothermic than those by van’t Hoff enthalpies in tune with the earlier reports for other micellar systems.⁶⁵ Fluorescence probing studies indicate that the microenvironment of the bile salt micelles is nearly non-polar like that of a hydrocarbon solvent. The cmc, activity coefficient, composition of the bile salt micelles and intermicellar interaction parameters evaluated following the treatments of Clint,¹⁹ Rubingh²⁰ and Rubingh–Holland¹⁷ predict nonideal behavior of the bile salt mixtures. The article will be helpful to study the ability of these mixed bile salt systems to act as suitable drug carriers.⁸ In addition, the study may act as a preliminary investigation for solubilization of drugs by mixed bile salt systems.⁹ Further the application of these mixed bile salt systems can be tested in future in the field of enzymology as excipients in novel formulations to stabilize enzymes.¹¹

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Footnote

† Electronic supplementary information (ESI) available. The information provides brief thermodynamic overview to calculate surface excess and minimum area per molecule of single and mixed bile salt systems. Further, theory behind thermodynamics of micelle formation and adsorption at the air/aqueous solution interface has also been discussed. Critical micelle concentration, C_mix (experimental) and ^idealC_mix (for mixed system), maximum surface excess, degree of counterion binding, f (for pure bile salts), Γ_max, minimum area per molecule, A_min (experimental), ^idealA_min (for mixed system) and I₁/I₃ values for single bile salt systems and their equimolar binary and ternary combination are contained in Table 1S–3S† respectively at different temperatures. Table 4S contains various thermodynamic parameters of different bile salt systems at different temperatures. Table 5S and 6S contains micellar mole fraction, X₁, interaction parameter, β, activity coefficients, g₁ and g₂ of two components for equimolar binary (Rubingh’s formulation) and ternary bile salt systems (according to Rubingh’s pseudobinary treatment) at different temperatures respectively. Rubingh–Holland treatment parameters for equimolar ternary bile salt systems at different temperatures are contained in Table 7S. See DOI: 10.1039/c5ra20909a

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