Effect of Oligomerization of Counterions on Water ... - ACS Publications

Article pubs.acs.org/JPCB

Effect of Oligomerization of Counterions on Water Activity in Aqueous Cationic Surfactant Systems Vitaly Kocherbitov*,†,‡ and Olle Söderman§ †

Biomedical Science, Faculty of Health and Society and ‡Biofilms Research Center for Biointerfaces, Malmö University, SE-20506 Malmö, Sweden § Physical Chemistry, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, SE-22100 Lund, Sweden S Supporting Information *

ABSTRACT: A sorption calorimetry study of cationic cetyltrimethyl ammonium surfactants with four different counterions was performed. The counterions were acetate, succinate, citrate, and butyl tetracarboxylate with formal charges ranging from 1 to 4, respectively. The counterions with 2−4 charges can be considered as oligomers. In all the cases, hydration experiments started with dry solid phases that upon water uptake went through solid-state phase transitions and hexagonal to micellar cubic phase transitions. It was found that in liquid-crystalline phases the activity of water increased with the degree of oligomerization or, equivalently, the formal charge of the counterions. The results are discussed in terms of the forces acting between the colloidal aggregates. It is argued that under the conditions investigated, the so-called strong-coupling theory can be used to describe the electrostatic forces between the charged colloidal objects. Therefore, we suggest that the observed dependence of water activity on the degree of polymerization is due to the entropy of mixing of the counterions in the water volume, which we describe using Flory−Huggins theory.

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INTRODUCTION Surfactant phase behavior conveys a wealth of information ranging from properties of fundamental interest such as molecular interactions to technical characteristics important in the formulation of various household products. 1,2 In applications, surfactants are often used together with polymers, and, consequently, a number of studies have been devoted to surfactant/polymer phase behavior.3,4 To simplify the studies of aqueous polyelectrolyte/surfactant systems, Piculell and co-workers introduced the concept of complex salts in which the counterions to ionic surfactants were polyions.5 In a thermodynamic language, this reduces the number of components to two compared to the situation when both the surfactant and the polymer have their own counterions. As a result, the determination of the chemical potential of one of the components, say water, also gives the chemical potential of the surfactant and the counterion by means of the Gibbs−Duhem relation. It is also possible to investigate the influence of the connectivity of counterions by successively going from monovalent counterions to divalent counterions, trivalent counterions, and so on.6,7 While investigating cetyltrimethyl ammonium surfactants with carboxylate counterions bearing two, three, and four charges, Norrman and Piculell observed that micelles with mono- and divalent counterions could be infinitely diluted without any phase separation, whereas micelles with trivalent and tetravalent counterions show a different behavior. In the trivalent case, they phase separate into two liquid micellar © 2016 American Chemical Society

solutions, whereas for the tetravalent case, the cubic phase is in equilibrium with a dilute micellar solution. These differences in the phase behavior are the results of changes in the balance of repulsive and attractive forces between the charged micelles as the counterion valency increased. This is in agreement with the results of Monte Carlo simulations treating the interactions between charged colloidal particles and how they are influenced by the valency of the counterions.2,5 Rough phase diagrams were also presented.7 In this work, we focus on the concentrated phases of the surfactants with water studied in ref 7. The study of water-poor surfactant phase diagrams is considerably more complex than that of the corresponding diagrams in the water-rich regime, not the least due to slow kinetics and uncertainties as to whether one has reached equilibrium or not. Here, we use a sorption calorimetry method developed by Wadsö and coworkers.8−10 The approach is capable of detecting with great precision phase transitions when water is adsorbed onto an initially dry sample of surfactant. The method is based on a continuous scanning of the water content11 as opposed to the traditional methods in which the phase behavior is investigated at discrete surfactant concentrations. In addition, the method allows for a complete thermodynamic characterization of the uptake of water because changes in both partial molar entropy Received: March 25, 2016 Revised: June 23, 2016 Published: June 24, 2016 6961

DOI: 10.1021/acs.jpcb.6b03104 J. Phys. Chem. B 2016, 120, 6961−6968

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The Journal of Physical Chemistry B

sorption chamber (Hsorp w ). Whereas the first parameter is constant at a constant temperature, the second one is systemand concentration-dependent and can be calculated by multiplying the enthalpy of evaporation of pure water, Hvap w , by the ratio of the thermal powers recorded in the sorption and vaporization processes.10 Thus, the partial molar enthalpy of mixing of water was calculated according to the following equation

and enthalpy are detected,12,13 including detection of changes associated with passing through narrow two-phase areas (areas with widths less than 1% in wt fraction units can be detected). When water uptake occurs within one liquid-crystalline phase, one observes the swelling pressure and, in favorable cases, whether the swelling is driven by entropy and/or enthalpy.14 The swelling of surfactant systems, in particular lipid-based systems, is an important topic, and there is still disagreement concerning the molecular origin of the obtained pressures.14−23 At short distances between the colloidal interfaces, one typically detects a strongly varying force; if the decay length of this short-range force is assumed to vary exponentially, it is typically of a few angstroms.14,15,19−21 At longer distances, the forces between charged interfaces are dominated by electrostatic effects. For monovalent ions, the forces are well described on the level of Poisson−Boltzmann approximation. For higher valencies, more accurate electrostatic treatments, including, for instance, correlation and image effects, must be used.24 Here, we present binary isothermal phase diagrams, at 25 °C, of cetyltrimethyl ammonium in water with four different counterions, namely, acetate, succinate, citrate, and butyl tetracarboxylate, with formal charges ranging from 1 to 4, respectively. All four surfactants form hexagonal phases and at a higher dilution, a normal micellar cubic phase. The phase behavior at higher surfactant concentrations is complex, with the formation of different hydrates. Partial molar enthalpies, entropies, and swelling pressures are presented and discussed in the framework of electrostatic and other possible contributing mechanisms underlying the pressure and its variation with counterion valency. We use strong-coupling (SC) theory25 to describe the electrostatic forces between the charged colloidal rods in the hexagonal phase and discuss the variation in water activity with the degree of polymerization in terms of the entropy of mixing of the counterions in the hydrophilic region of the hexagonal phase.

H wmix = H wvap + H wvap

P sorp Pvap

(1)

where Psorp is the experimentally observed thermal power of sorption of water in the sorption chamber.

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RESULTS AND DISCUSSION Solid-State Behavior. The experimentally obtained sorption isotherms of the four surfactant salts are shown in Figure 1 (the same data plotted as functions of water activity are presented in Figure S1 of Supporting Information). In the coordinates used in Figure 1, the horizontal parts of the curves correspond to two-phase mixtures (that require constant water activities). The vertical parts of the curves and the parts with

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MATERIALS AND METHODS Surfactant Salts. The surfactants used were gifted by Lennart Piculell, and the ion-exchange procedures used to obtain them are described in ref 5. Before sorption calorimetric experiments, the surfactants were dried in a vacuum in 3 Å molecular sieves for 24 h. To prevent sorption of water by the surfactants, the transfer of the samples from the vacuum-drying pistol to the calorimetric cell was performed in a dry atmosphere. Sorption Calorimetry. Sorption calorimetric experiments were conducted in a 20 mm two-chamber sorption calorimetric cell inserted in a double-twin microcalorimeter.9,10 The samples studied were placed in the upper chamber, whereas in the lower chamber, pure water was injected. During sorption experiments, thermal powers P (the derivatives of the released or absorbed heat with respect to time) were measured in the two chambers continuously and independently from each other. To calculate the amount of water evaporated in the vaporization chamber, the thermal power recorded in the vaporization chamber, Pvap, was integrated with respect to time and then divided by the heat of evaporation of pure water, Hvap w . The activity of water, aw, in the sorption experiments was calculated based on diffusion laws as described in ref 26. The partial molar enthalpy of mixing of water, Hmix w , can be considered as the sum of the enthalpies of two processes: evaporation of pure water in the vaporization chamber (Hvap w ) and sorption of water in the

Figure 1. (a) Water activities in the four surfactant systems as functions of the mass fraction of water. (b) The region of the transition from the hexagonal (“Hex”) to the micellar cubic (“Cub”) phase is shown. 6962


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The Journal of Physical Chemistry B significant slopes correspond to one-phase systems. All four systems presented in Figure 1 share the following common features. First, at least one phase transition involving a solid phase is observed in all surfactant systems at a low water content ( 90% when vapor diffusion becomes slow and thus the values of Pvap and Psorp become low; see eq 1). However, the peak corresponding to the phase transition is clearly seen. The enthalpy effect of a phase transition can be characterized by the enthalpy parameter of the van der Waals differential equation,12,27,28 H1→2, which by definition is ⎛ ∂H ⎞(1) ⎟ H1 → 2 = H (2) − H (1) − Δx1 → 2⎜ ⎝ ∂x ⎠T , P (1)

(2)

(2)

where H and H are the enthalpies of the 1st and 2nd phases, and x is the water content (for the illustration of the H1→2 parameter, see the Supporting Information). This parameter can be calculated from the area of the peak on the enthalpy curve relative to the value of the hydration enthalpy in 11,29 the first phase, Hm(1) w , which is taken as a baseline H1 → 2 = (1 − x w(2))

∫r

r (2) (1)

(H wm − H wm(1)) dr

(3)

where r is the water-to-surfactant mole ratio. The practical use of parameter H1→2 lies in the possibility of calculating the slopes of phase boundaries in the temperature−composition diagrams from isothermal data using the van der Waals differential equation12,27,28 ⎛ dT ⎞ ⎜ ⎟ ⎝ dx ⎠

(

RT 2

(1)

=−

d ln aw (1 − x)dx

(1)

)

T ,P 1→2

H

Δx1 → 2 (4)

In the case of the four surfactants considered in this work, the slopes of the phase boundaries between the hexagonal and micellar cubic phases are almost vertical (see Table 1) in the 6963


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Table 1. Thermodynamic Parameters of Phase Transitions from the Hexagonal to the Micellar Cubic Phase for the Four Surfactantsa Δxw

x(hex) w counterion

charge

aw

acetate succinate citrate BTCA

−1 −2 −3 −4

0.933 0.907 0.927 0.938

(hex)

( ) da w dx w

2.72 6.37 9.86 11.9

wt

mol

wt

mol

ΔH1→2, J/mol

0.448 0.367 0.368 0.360

0.939 0.956 0.971 0.977

0.025 0.021 0.027 0.031

0.0055 0.0036 0.0031 0.0028

−50 −110 −120 −120

(hex)

( ddTx ) 3.9 3.9 7.0 9.5

× × × ×

103 103 103 103

a

In parameters calculated per mole of surfactant, one mole of surfactant contained 1, 2, 3, and 4 moles of hydrocarbon tails for acetate, succinate, citrate, and BTCA, respectively. Concentration x in the expression for the slope of the phase boundary is the mole fraction of water.

phases is small despite a considerable difference in their structures. Water Activity in Liquid-Crystalline Phases. Figure 1b displays water activity data for the hexagonal and cubic phases in the four surfactants investigated. The activities vary smoothly in each phase, and at a constant mass fraction of water, the activity of water increases with an increase in the charge (degree of oligomerization) of counterions. We note that this agrees with the surfactant phase behavior observed in previous studies. Indeed, in the case of BTC, the cubic phase is in equilibrium with a roughly 5 wt % surfactant solution. Thus, for BTC, the activity of water at the point when the two-phase region, cubic/water, begins (at the end of the cubic phase) should be close to 17 and thus larger than for the other investigated counterions, as for these, the cubic phases are in equilibrium with concentrated micellar solutions (with lower water activities). The activity of water is related to the osmotic pressure Posm through

Figure 3. Hexagonal-to-cubic phase transition in CTA succinate. Water activity, black curve; partial molar enthalpy of mixing of water (kJ/mol), red curve.

Posm = −

T−x representation. For comparison, the slope of the phase boundary in the transition between the lamellar and bicontinuous cubic phases in the β-octyl glucoside−water system was about an order of magnitude lower.27 In general, the phase boundaries in the phase diagrams of ionic surfactants tend to be steeper than those of nonionic surfactants. One classical example is the phase diagram of dodecyltrimethylammonium chloride.30 This difference between ionic and nonionic surfactants can be explained by the weaker temperature dependence of strong ionic interactions compared to stronger temperature dependence of weak nonionic hydrophilic interactions. Indeed, water−ion interactions persist at high temperatures, whereas, for example, water−polyethylene oxide interactions weaken at higher temperatures. The phase transitions from the hexagonal to the micellar cubic phase in all four systems exhibit exothermic heat effects, which means that they are driven by enthalpy.12 This also implies a negative entropy effect of the transitions (H1→2 = TS1→2), which probably arises from stronger confinement of the hydrocarbon tails in more positively curved aggregates12 (cubic micellar structure). The main contribution to the negative enthalpy change of the phase transition most likely comes from larger separations between the cationic surfactant headgroups in the more positively curved structures. The heat effects discussed here are however very low. In terms of energies per surfactant molecule, the enthalpy values listed in Table 1 are in the range of 0.02−0.05kT, which shows that the energy difference between the hexagonal and cubic micellar

RT ln(a w ) Vw

(5)

where Vw is the molar volume of water at a temperature T and R is the gas constant. The osmotic pressure is in turn proportional to the force between two nearest aggregates of a periodic structure (cylinders, spheres, or sheets). The coefficient of proportionality is also dependent on the topology of the system. For example, for hexagonally ordered, infinitely long cylindrical aggregates, the osmotic pressure can be written according to19,31 Posm =

3 f (di) Ldi

(6)

where f(di) is the force between two cylindrical aggregates with axial separation di and L is the unit length. As a consequence, the measurement of water activities in a colloidal system is in fact the measurement of the forces acting between the colloidal aggregates. This has been a longstanding topic within colloidal science. In general, the force between charged macroions is divided as follows f (di) = fvdW (di) + fES (di) + fHF (di)

(7)

where subscripts vdW, ES, and HF refer to van der Waals forces, electrostatic forces, and the so-called hydration force, respectively.31 In the present system, two additional forces may also play a role, namely, a deformation force on account of rather short distances between the aggregates that may lead to a deformation of the cylindrical aggregates5 (in fact, molecular dynamics simulations suggest that the aggregates have a nearly 6964


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The Journal of Physical Chemistry B hexagonal shape in cross section32) and a bridging force due to the possibility of the counterions to bridge between two neighboring cylinders.33 Of these forces, the contribution from the attractive van der Waals force can be estimated from the relations in ref 34. For the case of two long parallel cylinders with radii of 20 Å, the closest distance between the cylinders of 10 Å, and a Hamaker constant of 0.5 × 10−20 J,34 the contribution of the van der Waals force to the osmotic pressure is around 2%, in agreement with that found in ref 5. Of the other forces, the hydration and deformation forces are always repulsive, and their magnitudes are not expected to be substantially dependent on the connectivity between the counterions. Indeed, there are two different interpretations of the origin of hydration forces. The first interpretation deals with energies of interactions and the structure of water in the aqueous layer.20,23 These parameters should not be dependent on the connectivity between the ions in concentrated systems in which the average distances between the ions are low and comparable to the size of ions (see the discussion below). The second interpretation deals with the so-called protrusion forces35 that arise from small-amplitude thermal movements of surfactant molecules (in the present case, only their cationic parts) in the direction normal to the aggregate surface. In an electrolytically dissociated system, these protrusions should not be significantly dependent on the connectivity between the counterions. The electrostatic force can be repulsive or attractive depending on the conditions, and the bridging force is always attractive. In addition, the electrostatic and bridging forces may or may not depend on the charge of the counterions. The hexagonal phases presently under study are in fact very concentrated, and the distances between the cylindrical (or hexagonal prism-like) aggregates are relatively small. In Table 2, we summarize some pertinent data for the geometry of the hexagonal phases.

φciaq =

−

Ac Succ2− Citr3− BTC4−

b Φmin CTA

c Φmax CTA

dmin (Å)d i

dmax (Å)d i

0.507 0.591 0.586 0.598

0.623 0.771 0.759 0.692

8 4 4 6

12 9 9 9

(8)

where Φci is the volume fraction of counterions in the total system and ΦCTA is the volume fraction of surfactant ions in the total system. The detailed calculations of the volume fractions and the parameters used are given in the Supporting Information. In the hexagonal phase, the center-to-center distance of the counterions can be estimated from dciaq

⎛ φ ⎞1/3 0 ⎟⎟ = σ ⎜⎜ aq φ ⎝ ci ⎠

(9)

where σ is the effective diameter of the counterions and φ0 is the volume fraction for close packing of equal spheres (0.74). In Table 3, we listed the parameters relevant for this calculation. Table 3. Volume Fractions of Counterions in the Aqueous Parts of the Hexagonal Phases and the Average Distances Between the Counterions Therein counterion

φaq,max ci

φaq,min ci

σ (Å)a

daq,min (Å) ci

daq,max (Å) ci

Ac− Succ2− Citr3− BTC4−

0.26 0.38 0.35 0.24

0.16 0.16 0.16 0.17

5.5 6.2 7.2 7.8

8 8 9 11

9 10 12 13

σ is the effective molecular diameter as calculated from the molecular volume, Vm , obtained from group volumes.36

a

As can be seen from Tables 2 and 3, the average distances between the counterions are larger than or equal to the distances between the surfaces: dci ≥ di. According to SC theory, the electrostatic force between the interacting surfaces depends only on the charge density of the surfaces and not on the charge of the counterions. Moreover, the counterion distribution tends toward a uniform distribution in the water region between the charged objects.37 In addition, we mention the bridging effect. In ref 33, it is argued that it is this effect that dominates the attractive component in a system similar to ours but with larger (larger degree of polymerization) counterions. In ref 38, Monte Carlo simulations show that the effects of bridging become less important as the polymer gets stiffer and for a rod it appears to be insignificant. In conclusion, of the forces making up the total interaggregate force in the present case, none depends significantly on the degree of oligomerization of the counterion. However, there is one effect that we have not included so far in the analysis, that is, the entropy of mixing of counterions in the water volume. As argued in refs 25, 39, this can be obtained from Flory−Huggins theory and we represent water activity as

Table 2. Geometrical Parameters of the Hexagonal Phasesa counterion

Φci 1 − ΦCTA

a

Volume fractions have been obtained from group volumes36 as outlined in the Supporting Information. bVolume fractions of rods at the start of the transition to the cubic phase. cVolume fractions of rods at the point where the hexagonal phase is first formed. dThe closest distance between two neighboring surfaces, assuming that the radius of the rod is 17 Å5. The cross-sectional area of the rod is assumed to be a regular hexagon.

As it is evident from Table 2, distance di at the point where the hexagonal phase turns into a cubic phase is around 10 Å, which corresponds to three water layers. The system is dense, with a high charge density. For such systems, Strong-Coupling (SC) theory can be used to describe the electrostatic forces between the charged colloidal objects.37 A criterion for the SC theory to be applied is that the average distance between the counterions is larger than the distance between the charged surfaces. In the present case, the volume fraction of counterions in the aqueous part of the hexagonal phase, φaq ci , is large. It can be estimated from

⎛ 1⎞ ln a w = ln(1 − φp) + ⎜1 − ⎟φp + χφp2 ⎝ r⎠

(10)

or, after expansion of the logarithm function, as φp ⎛ 1⎞ ln a w ≈ − + φp2⎜χ − ⎟ ⎝ r 2⎠

(11)

where χ is the parameter describing the energy of water− monomer interactions (compare to water−water and mono6965


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The Journal of Physical Chemistry B mer−monomer interactions) in the framework of regular solution theory and r is the degree of polymerization. According to eqs 10 and 11, the higher the degree of polymerization at the same concentration, the higher the the water activity. Indeed, as follows from Figure 1b (even though plotted versus mass fraction and not volume fraction as required by eqs 10 and 11), both in the hexagonal and cubic phases, the following ascending sequence of water activities is observed: acetate (−1), succinate (−2), citrate (−3), and BTCA (−4). For a constant water content, the logarithm of water activity plotted as a function of reciprocal degree of polymerization has an approximately linear dependence (Figure 4) as can be appreciated from eqs 10 and 11 ln a w = −

φp r

+ const

(12)

Figure 4. Logarithm of water activities for the four surfactants vs the reciprocal degree of polymerization at a constant mass fraction of water (35 wt %, the hexagonal phase). Figure 5. The activity of water as a function of the volume fraction of counterions in the aqueous (hydrophilic) part of the system (a) and the osmotic pressure (in Pa) as a function of the reciprocal volume fraction of surfactants in the total system (b). The parts of the curves for lowest water contents (involving solid-state equilibria) are omitted for clarity.

The observed negative slope of this line (0.125) should be equal to the fraction of the polymer, as follows from eq 12. However, a quantitative comparison of these two values is not straightforward because of the structural complexity of the system. Indeed, Flory−Huggins theory assumes a simple isotropic solution of polymer in a solvent and regular solution-type interactions. However, in the liquid-crystalline system considered, practically all interactions between oligomeric counterions and water occur in the aqueous part of the structure, whereas the hydrophobic part is excluded from these interactions and thus should be excluded from the calculation of the volume fraction. Therefore, the volume fraction of the polymers should be calculated as the volume fraction of the counterions in water, that is, according to eq 8 (an open question remains whether the headgroups should be included in the calculations, but in this work, they are excluded). The activities of water in the liquid-crystalline phases plotted versus the volume fractions of counterions in the aqueous regions are shown in Figure 5a. Interestingly, the phase transitions from the hexagonal to cubic phases are observed at the same volume fractions for all four surfactants, which was not the case when the mass fraction of water in the total system was used as the concentration variable. The reason for this fact is not completely clear, but it emphasizes the importance of interactions in the hydrophilic part of the system for phase transitions.

Another phenomenon that is clearly observed through this manner of data representation is the change in the order of water activities compared to those in the sorption isotherm shown in Figure 1. A clear deviation from the ascending order of water activities as a function of degree of polymerization is seen: in the hexagonal phase, the activity of water for acetate is highest, not lowest as expected. The ascending order of water activities for the remaining three substances is still intact: succinate (−2), citrate (−3), and BTCA (−4). This apparent anomaly for the case of CTA acetate is in all likelihood not caused by differences in physicochemical interactions leading to a different water activity. Rather, the reason for this effect is found to be the selected concentration variable: the volume fraction of counterions in the aqueous region. Although the selected set of four counterions represents a good model for studying the effect of connectivity, it has a shortcoming, that is, the difference between the counterions is not only in the connectivity. Unlike the other three counterions, the acetate contains a methyl group (CH3), which is bulkier than the methylene groups (CH2) found in the other three counterions. As a result, the density of the acetate ion (about 1.1 g/cm3) is much lower than those of the other three counterions (which 6966


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The Journal of Physical Chemistry B are in the range of 1.5−1.6 g/cm3). Consequently, the volume fraction of counterions becomes higher in the case of acetate, that is, the acetate curve moves to the right. One should also note that as an alternative to water activities the interactions of solute with solvent can be considered using the concept of osmotic pressure (see eq 5). In Figure 5b, the dependences of osmotic pressures on the reciprocal volume fraction of the solute (surfactant molecules including counterions) are presented. According to these results, the osmotic pressure decreases upon increasing the degree of polymerization. This result is in line with the Flory−Huggins approach. Indeed, from a comparison of eqs 5 and 11, it follows that the osmotic pressure should be inversely proportional to the degree of polymerization (plus a polymerization-degree-independent constant). The molecular-level interpretation of the osmotic pressure results can be based on the fact that for noninteracting solute molecules the osmotic pressure is given by Posm = ρRT, where ρ is the number density of the molecules. For the counterions, the number density is inversely proportional to the degree of polymerization, which defines the osmotic pressure sequence. In the present system, the molecules cannot be considered noninteracting, but the qualitative dependence of the osmotic pressure on the degree of polymerization is the same. In light of the discussion presented above, a question of the most adequate concentration variable for the interpretation of thermodynamic activity curves arises. Flory−Huggins theory was derived in terms of volume fractions, but this approach should not be considered as the ultimate thermodynamic truth. In fact, the chemical potential change (the logarithm of thermodynamic activity) is defined through molar, not volume, concentrations. The volume fractions can, on the other hand, be useful in modeling of certain types of solutions (such as the regular ones used in Flory−Huggins theory). Indeed, for spherical molecules, in an isotropic unstructured solution, the energy of interactions depends on the size of molecules as the size affects the number of intermolecular contacts. On the contrary, for systems with strong interactions (ionic or hydrogen-bonded), the interaction energy is less dependent on the molecular size but is dominated by the number of contacts between the strongly interacting groups. The volume of groups not taking part in these contacts (e.g., methyl groups) has a minor effect on the interaction energies as long as the groups are small enough (less than 1 nm40) not to break hydrogen bonds in the system. From this point of view, an alternative representation of concentration for modeling interactions in this system is the molar concentration of oxygen atoms. Indeed, the strongest attractive interactions in the hydrophilic layer are the hydrogen-mediated interactions between the oxygen atoms of water and the oxygen atoms of counterions. In this case, the degree of polymerization will not be 1, 2, 3, and 4 but 2, 4, 6, and 8, respectively. Figure 6 shows the dependence of the logarithm of the water activity on the reciprocal degree of polymerization according to this approach. The dependences appear approximately linear for both concentrations (the higher water content corresponds to the cubic phase). The negative deviation for citrate probably arises from the fact that it has an additional OH group that forms additional hydrogen bonds. The slopes of the straight lines in Figure 6 are 0.248 and 0.121, which values can be compared to the oxygen mole fractions in the system: 0.161 and 0.100 respectively. The agreement for the more dilute cubic phase is reasonable, whereas the agreement for the more concentrated

Figure 6. Logarithm of water activities for the four surfactants vs the reciprocal number of oxygens in the counterions at constant mole ratios of water oxygens to carboxyl oxygens. The numbers in the legend show water to counterions oxygen ratios.

system is only semiquantitative, which is probably due to the fact that interactions between the counterions and the positively charged surfactant headgroups are not included in the model. The discussion above shows that the experimentally observed dependence of water activity on the degree of polymerization of the ionic groups in the surfactant−water mixture in concentrated regimes is consistent with the entropic effect in the spirit of Flory−Hugging theory.

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CONCLUSIONS We have performed a sorption calorimetric study of the interactions of four cationic surfactants with water. The conclusions are as follows: 1. Oligomerization of counterions increases the activity of water in the liquid-crystalline phases of the surfactants, which is suggested to be due to a decrease in the entropy of mixing upon oligomerization. 2. The sorption calorimetry data reveals a complex solidstate behavior of the cationic surfactants with the formation of solid hydrates. 3. The transition from the hexagonal to the micellar cubic phase is driven by enthalpy for all four surfactants. 4. The energy difference between the hexagonal and the cubic micellar phase is very low; it is in the range of 0.02−0.05kT per surfactant molecule.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b03104. Sorption isotherms as functions of water activity, details of calculation of volume fractions, data on the solid-state behavior of the four surfactants (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +46 40 6657946. Notes

The authors declare no competing financial interest. 6967


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ACKNOWLEDGMENTS The authors thank Sergei Gavryushov and Per Hansson for fruitful discussions. V.K. acknowledges Gustav Th Ohlsson foundation for financial support. O.S. is grateful for financial support from the Swedish Research Council (VR) through the Linnaeus Center of Excellence “Organizing Molecular Matter”.

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