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J. Phys. Chem. B 2005, 109, 6430-6435
Driving Forces of Phase Transitions in Surfactant and Lipid Systems Vitaly Kocherbitov* Biomedical Laboratory Science, Health and Society, Malmo¨ UniVersity, SE-205 06 Malmo¨, Sweden, and Physical Chemistry 1, Center for Chemistry and Chemical Engineering, P. O. Box 124, Lund UniVersity, SE-22100 Lund, Sweden ReceiVed: September 30, 2004; In Final Form: December 23, 2004
In aqueous surfactant and lipid systems, different liquid crystalline phases are formed at different temperatures and water contents. The “natural” phase sequence implies that phases with higher curvature are formed at higher water contents. On the other hand, there are exceptions to this rule, such as the monoolein/water system. In this system an anomalous transition from lamellar to reverse cubic phase upon addition of water is observed. The calorimetric data presented here show that the hydration-induced transitions to phases with higher curvature are driven by enthalpy, while the transitions to phases with lower curvature are driven by entropy. It is shown that the driving forces of phase transitions can be determined from the appearance of the phase diagram using the approach based on van der Waals differential equation. From this approach it follows that the slope of the phase boundary should be positive with respect to water content if the phase diagram obeys the “natural” phase sequence. The increase of entropy, which drives the anomalous phase transitions, arises from the increase of disorder of the hydrocarbon chains.
Introduction Self-association in aqueous surfactant and lipid systems leads to the formation of a wide range of crystalline, liquid crystalline, gel, and micellar phases.1-3 The formation of a particular phase depends on the geometry of surfactant or lipid molecule, water content, and the temperature of the system. Usually surfactant and lipid molecules having a big hydrophilic moiety (headgroup) and a small hydrophobic tail associate into normal structures (with positive curvatures), while molecules with small headgroup and big hydrophobic moiety tend to form reverse structures (with negative curvature; see Figure 1). For the complete characterization of a surface one should consider not only the principal curvature c but also the mean curvature and the Gaussian curvature. Many surfactants or lipids can form several different structures at different water contents. Usually, upon hydration, the added water molecules accumulate in the hydrophilic layer and expand it. As a result, the phases formed at higher water contents have higher curvature than phases formed at lower water contents. Therefore, a “natural” (i.e., expected from the curvature arguments) phase sequence upon addition of water is reverse micellarfreverse hexagonalflamellarfhexagonalfmicellar. Intermediate phases, especially cubic and reverse cubic, are also present in this sequence.1,4 Although not all the phases are observed in every real surfactant or lipid system, the general trend of increase of the curvature with hydration exists. On the other hand, “incorrect” phase sequences are found in some systems.1 The most well-studied example of such system is monoolein/water.5-7 In this system the reverse micellar phase turns into the lamellar phase (which is in agreement with the “natural” sequence), but then, upon further addition of water, a reverse cubic Ia3d phase is formed, i.e., curvature decreases * To whom correspondence should be addressed. Health and Society, Malmo¨ University, SE-205 06 Malmo¨, Sweden. Ph: +4640 6657946 Fax: +4640 6658100. E-mail:
[email protected] (Figure 2). One has to note that this is not a unique property of the monoolein/water system, but was observed in some other systems.8-10 The anomalous phase sequence in the monoolein/ water system cannot be explained by some specific interactions, e.g., by a chemical reaction present in the system (hydrocarbon chain can migrate between three positions in the glycerol headgroup). For example, it was found that in the phytantriol/ water system, a similar phase sequence is observed9 despite the absence of the reaction. This disagreement of the phase behavior in the monoolein/ water system with the natural phase sequence did not receive a proper explanation in the literature despite that this phenomenon has been known for decades. A number of studies of this system were performed, but the mechanism that drives the transition from the lamellar to the reverse cubic phase is still not fully understood. Here a thermodynamic study of the driving forces of phase transitions in surfactant and lipid systems is presented. The proposed approach gives a new insight into the nature of the anomalous phase transitions. Driving Forces of Phase Transitions To understand the reason for the abnormal sequence on phases in the monoolein/water system, one has to consider driving forces of phase transitions upon hydration or dehydration. In general case, the direction of any physicochemical process at constant temperature and pressure is determined by the ∆G the difference between Gibbs energies of the final and the initial states of the process. The particular form of ∆G depends on the type of a considered process (e.g., chemical reaction, mixing, phase transition, etc). For example, in a chemical reaction, the ∆G is equal the difference between Gibbs energies of products and reagents. For the case of hydration without a phase transition (swelling of a single phase) the initial state is the two-phase system of the considered phase and the infinitely small amount of pure water, the final state is the result of mixing and
10.1021/jp045555l CCC: $30.25 © 2005 American Chemical Society Published on Web 03/11/2005
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J. Phys. Chem. B, Vol. 109, No. 13, 2005 6431
Figure 1. Liquid crystalline phases with different curvatures. Curvature c is positive for normal (direct) phases and negative for reverse phases. In the “natural” phase sequence the curvature increases with the increase of the water content.
Figure 3. Gibbs energy of two phases at a phase transition. S and W denote surfactant and water respectively; superscripts 1 and 2 denote (1) phases. ∆x1f2 ) x(2) w - xw .
occurs when the curves of Gibbs energies of the two phases have the same tangent line. This condition can be rephrased as follows: the difference of Gibbs energies of the two phases G(2) - G(1) should be equal to the derivative of the Gibbs energy with respect to water content (∂G/∂x)(1) T,P multiplied by the change of the water content ∆x1f2 ) x(2) - x(1):
G(2) - G(1) ) ∆x1f2
Figure 2. Phase diagram of the monoolein/water system (reprinted with permission from ref 6).
equilibration of the initial state. If, after the equilibration, the water phase disappears, then hydration occurs and G(2) 0, then the phase transition does not occur, if G1f2 < 0, then a nonequilibrium transition can take place. The parameter G1f2 can be presented as the difference of the enthalpy and the entropy terms:
G1f2 ) H1f2 - TS1f2
(∂H∂x ) (∂S∂x)
H1f2 ) H(2) - H(1) - ∆x1f2 S1f2 ) S(2) - S(1) - ∆x1f2
(7) (1)
T,P
(1)
T,P
(8) (9)
van der Waals11 introduced the same parameter S1f2 using another approach (see the section van der Waals Differential Equation). Storonkin,12 extending van der Waals approach,
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proposed an interpretation of this parameter as the change of the entropy of the two-phase system in isothermo-isobaric formation of one mole of the second phase from the infinite amount of the first phase. Since in the equilibrium phase transition G1f2 ) 0, then according to eq 7
H1f2 ) TS1f2
(10)
In the eq 10 enthalpy and entropy terms have the same signs, which means that if a phase transition is endothermic (H1f2 > 0) then entropy change is positive (this entropy change is favorable for the transition), or if the transition is exothermic (H1f2 < 0) then the entropy change is negative (this entropy effect is unfavorable for the transition). In other words, an equilibrium phase transition is driVen either by enthalpy or by entropy, but not by both potentials simultaneously. Since the driving force of a phase transition depends on the value of its enthalpy change, the natural way to determine it is to use calorimetric measurements. Calorimetric Results To obtain thermodynamic information about driving forces of phase transitions in surfactant and lipid systems, one should use a method that would be applicable for the studies of hydration of condensed phases. The method of sorption calorimetry13,14 has previously been applied for studies of driving forces of hydration in surfactant and lipid systems.15,16 In this method a two-chamber calorimetric cell inserted into a doubletwin calorimeter is used. The method of sorption calorimetry allows simultaneous monitoring of the partial molar enthalpy of mixing of water Hm w and the activity of water. Recently it was shown17 that sorption calorimetry can be used to obtain the data about enthalpy term H1f2:
˜ xs(2) H1f2 ) H
(11)
where H ˜ is the area under the peak corresponding to the phase transition, on the curve partial molar enthalpy of mixing of water vs molar ratio and x(2) s is the mole fraction of the surfactant in the second (emerging) phase. Hence, the direction of the peak on the curve of partial molar enthalpy of mixing of water can be used as a criterion of the driving force of the phase transition. To show a typical pattern of phase transition behavior in a surfactant system, here we present the calorimetric data on hydration of DDAO (dimethyl dodecylamine oxide). The phase diagram of the DDAO/water system is well-known18-21 and it features the following phase sequence upon isothermal hydration: dry crystals, monohydrate, lamellar liquid crystals, normal bicontinuous cubic phase, normal hexagonal phase, and normal micellar phase. In other words, the phase sequence in this system is expected from the curvature arguments. The result of the measurement of the partial molar enthalpy of mixing of water in the system DDAO/water versus water content at 25 °C is presented in Figure 4 (a comprehensive calorimetric study of this system will be presented separately). The first, highly endothermic regime of the hydration is the melting of crystals of DDAO into lamellar liquid crystalline phase (the monohydrate was not formed in this experiment because of the kinetic reasons). Since the heat effect of melting is endothermic, the process is driven by entropy. The transitions between liquid crystalline phases upon hydration (lamellarfcubic and cubicf hexagonal) are both exothermic, i.e., H1f2 ) TS1f2 < 0, i.e., driven by enthalpy. Sorption calorimetric studies of other
Figure 4. Partial molar enthalpy of mixing of water as function of water content in the DDAO/water system at 25 °C. Lam, Cub, and Hex stand for lamellar, cubic, and hexagonal phases, respectively. The exothermic peaks correspond to the transitions between these phases.
surfactant/water systems15,22 with “natural” phase sequences also showed that phase transitions observed upon hydration are exothermic. As it was mentioned above, the monoolein/water system exhibits an abnormal phase sequence, therefore a calorimetric study of driving forces of transitions in this system is of a particular interest. We performed a sorption calorimetric study of this system at 25, 40, and 50 °C. Some of the results of this study have been presented elsewhere.23 Here we present the calorimetric data on partial molar enthalpy of mixing of water Hm w as function of water content at 40 °C and 25 °C (Figure 5a and 5b respectively). On the enthalpy curve presented in Figure 5a there is a peak at 6 wt % of water corresponding to the phase transition from the reverse micellar to the lamellar phase, which is in good agreement with the phase diagram (Figure 2). The peak is exothermic, which means that the transition is driven by enthalpy. This transition is expected from the natural phase sequence, and again, as in the DDAO/water system, the value of H1f2 is negative. The transition between the lamellar and the reverse cubic Ia3d phase at 25 °C was studied using method of desorption calorimetry,14 since it was not accessible using direct sorption methods because of very high water activity. This implies that in the experiment the transition occurred upon dehydration from the cubic to the lamellar phase, but the raw data were recalculated into the values of the enthalpy of hydration Hm w in order to discuss the transition to cubic phase upon hydration (for the comparison of the two methods see ref 14). Unlike all the transitions between liquid crystalline phases observed before, the transition from the lamellar phase to the reverse cubic phase (Figure 5b) is endothermic, H1f2 > 0. This means that, according to calorimetric data, unlike the other transitions, the phase transition from the lamellar to reVerse cubic phase is driVen by entropy. Before discussion of the molecular mechanism of this phenomenon, we will consider another way to determine the enthalpy effect H1f2. The van der Waals Differential Equation Sorption calorimetry is an effective experimental tool to determine the driving forces of phase transitions, but since this technique is not widely available, an alternative way of determination of driving forces of phase transitions (and H1f2) would be very useful. In this article we consider binary (two-
Phase Transitions in Surfactant and Lipid Systems
J. Phys. Chem. B, Vol. 109, No. 13, 2005 6433 (1) V1f2 dP ) S1f2 dT + (∂2G/∂x2)T,P ∆x1f2 dx
(12)
Taking into account eq 10 and the fact that usually surfactant and lipid systems are studied at a constant pressure, we obtain the following equation: (1) T(∂2G/∂x2)T,P ∆x1f2 dT (1) )dx H1f2
( )
(13)
where the derivative of temperature with respect to composition is the slope of the phase boundary. This and other forms of van der Waals differential equation were used to calculate H1f2 and S1f2 from the slope of dT/dx or vice versa.15,22 For the calculation of the enthalpy term H1f2
H1f2 ) -
Figure 5. (a) Partial molar enthalpy of mixing of water near the phase transition from the reverse micellar to the lamellar phase in the monoolein/water system at 40 °C. (b) Partial molar enthalpy of mixing of water near the phase transition between the lamellar and the reverse cubic Ia3d phase in the monoolein/water system at 25 °C.
TABLE 1: Driving Forces of Phase Transitions in the Monoolein/Water Systema transition
dT/dx
sign of H1f2
driving force
sign of ∆c
Lc - FI FI - LR LR - Ia3d Ia3d - Pn3m FI - Ia3d FI - HII
+ + +
+ (+) - (-) + (+) + -
S H S S H H
+ + +
a The phases are denoted in the same way as in Figure 2. The sign of H1f2 is determined from the appearance of the phase diagram using eq 14; values in parentheses denote calorimetric results. ∆c is the change of curvature in the phase transition.
component) systems, but the following analogy from onecomponent systems will help to understand the problem. There are two different ways to determine the enthalpy of vaporization of a pure substance ∆vapH: direct calorimetric measurements and calculation of the enthalpy from the temperature dependence of vapor pressure of the substance using Clapeyron equation. The latter method does not require any calorimetric measurements and is used when the temperature/pressure data are available. A two-component generalization of the Clapeyron equation is van der Waals differential equation, which provides a relation between three differentials: dT, dP, and dx in a binary system:
1f2 T(∂2G/∂x2)(1) T,P∆x
(dT/dx)(1)
(14)
one has to know the second derivative of the Gibbs energy with respect to composition. For the surfactant and lipid systems it can be calculated from the data on activity of water in binary mixtures. For the qualitative determination of the driving forces of phase transitions (i.e., the sign of H1f2), the particular value of the derivative does not need to be determined, because it is always positive according to the thermodynamic stability theory. If we define the first phase as having lower water content than the second phase, then ∆x1f2 is also positive. Hence it is easy to see that the enthalpy effect H1f2 and the slope of the phase boundary dT/dx have opposite signs. This fact gives an opportunity to determine the driving forces of the phase transitions from the appearance of the phase diagram. Let us consider the phase diagram of the monoolein/water system (Figure 2). The phase transition from the reverse micellar FI to the lamellar phase LR occurs upon hydration at temperatures up to 60 °C. The phase boundary has a positive slope dT/dxw, i.e., the temperature increases upon increase of water content in the micellar phase provided that the phases stay at the equilibrium. According to eq 14 this means that H1f2 < 0, the phase transition is exothermic and driven by enthalpy. The phase boundary of the next transition, from the lamellar LR to the reverse cubic Ia3d phase, has a negative slope and therefore positive heat effect H1f2. This is an independent proof that the transition to the Ia3d phase is driven by entropy. This also means that there are no specific interactions, which would balance the curvature-related increase of enthalpy, making the transition to cubic phase possible. The transition is enthalpically unfavorable. The same type of analysis for other transitions in the monoolein/water system is presented in Table 1. The main result of this analysis is the following: the transitions within the “natural” phase sequence, i.e., transitions to phases with higher curvature, are driven by enthalpy, while the transitions to the phases with lower curvature are driven by entropy. Molecular Level Interpretation We have shown by two independent methods that the transitions (upon hydration) to the phases that have lower curvatures are driven by entropy. To understand the molecular mechanism of this phenomenon, one should consider the structure of the molecule of monoolein (similar conclusions can be made for most of the surfactant or lipid molecules). The molecule of monoolein consists of a relatively small hydrophilic headgroup and a rather long hydrocarbon chain. All rearrangements of the positions of the molecules of monoolein can be
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Figure 6. Volume available for a hydrocarbon chain in the normal (left) structure is lower than in the reverse (right) structure.
accompanied by changes of enthalpy and entropy of the system. One can expect that the changes of enthalpy will be produced by the changes of the positions of headgroups, but not tails, since the former are more polar and their rearrangement can cause disruption or formation of hydrogen bonds. On the other hand, change of geometry of long hydrocarbon chains should not produce a high heat effect, but high entropy change. In particular, the entropy associated with the chains is higher the larger the volume available for the motion of every chain. The reason for that is the higher number of different conformations that chains can adopt in a larger available volume. Applying this idea to the structures of liquid crystalline phases, one can see that the volume available for every chain in a reverse structure is higher than in a normal structure (Figure 6). One should note that the total volume available for all hydrocarbon chains is almost the same in both structures (the hydrophobic moiety is often considered as an uncompressible liquid), but the volume available for every individual chain is different. Therefore, the more positive the curvature, the lower the entropy associated with the hydrocarbon tails, and vice versa, the more negative the curvature of a structure the higher the entropy of the hydrocarbon chains. In particular, for the transition from the lamellar LR to reverse cubic Ia3d phase, one can see that this transition is not favorable from the point of view of enthalpy change (the enthalpy increases which means that the system becomes more constrained energetically), but the increase of entropy of the tails balances this effect and makes the transition possible. The increase of entropy can balance the increase of enthalpy only if the size of the hydrocarbon tail is much larger than the size of the headgroup (which is the case for monoolein). Otherwise the gain of enthalpy prevents the formation of a phase from “nonnatural” phase sequence. For example, such transitions are not observed in surfactant systems, because the hydrocarbon tails in surfactants are usually shorter than in monoolien and the headgroups are more hydrophilic and/or bulky. Yet another interesting observation follows from the discussion presented above. In the “natural” phase sequence the curvature increases upon addition of water. This means that the entropy of the tails decreases, which gives the negative value of H1f2 (eq 10). Then, according to eq 13, the slope of phase boundaries dT/dxw should be positive. The theoretical natural phase sequence is usually presented in the literature without any slope of the phase boundaries. The discussion presented here shows that this sequence should be accompanied with the positive slope of the phase boundaries. One obvious exception from this rule is a transition to a normal micellar phase. In such transition the curvature increases, which tends to decrease the entropy of the tails, but at the same time formation of micelles introduces disorder on the aggregate level (isotropic micellar solution is more disordered than liquid crystalline phases). This leads to a situation when the slope of a phase boundary of the
transition from a liquid crystalline phase to a micellar solution changes its sign with temperature. The approach presented here can be used to consider not only aqueous but also systems based on solvents other than water. Finally, one has to note that the thermodynamic analysis described here is strictly valid only for truly binary (in the thermodynamic sense) systems. The “binary” lipid-lipid systems in the excess of water should be considered on the basis of thermodynamics of three-component systems. Conclusions The thermodynamic analysis of the driving forces of phase transitions in surfactant and lipid systems allow to draw the following conclusions. (i) Equilibrium phase transitions are driven either by entropy or by enthalpy, but not by both potentials simultaneously. (ii) The driving force of a transition can be determined either calorimetrically or by using van der Waals differential equation. The sign of the enthalpy term of the equation is the criterion of the driving force. (iii) The phase transitions of the “natural” phase sequence in surfactant and lipid systems observed upon hydration are normally driven by enthalpy. (iv) The anomalous phase transition from the lamellar to reverse cubic phase in the monoolein/water system is driven by the entropy change originating from the hydrocarbon tails. (v) The driving forces of a phase transitions can be determined from the analysis of the slopes of the phase boundaries in the phase diagram. Acknowledgment. The author thanks Olle So¨derman, Alexander Toikka, Emma Sparr, and Sven Engstro¨m for fruitful discussions. References and Notes (1) Seddon, J. M.; Templer, R. H. Polymorphism of Lipid-Water Systems. In Handbook of Biological Physics, Vol 1.: Structure and Dynamics of Membranes; Lipowsky, R., Sackmann, E., Eds.; Elsevier: Amstedam, 1995; pp 97. (2) Seddon, J. M. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 380. (3) Cevc, G. Chem. Phys. Lipids 1991, 57, 293. (4) Charvolin, J. J. Phys. (Paris) 1985, 46, 173. (5) Briggs, J.; Chung, H.; Caffrey, M. J. Phys. (Paris) 1996, 6, 723. (6) Qiu, H.; Caffrey, M. Biomaterials 2000, 21, 223. (7) Hyde, S. T.; Andersson, S.; Ericsson, B.; Larsson, K. Z. Kristallogr. 1984, 168, 213. (8) de Campo, L.; Yaghmur, A.; Sagalowicz, L.; Leser, M. E.; Watzke, H.; Glatter, O. Langmuir 2004, 20, 5254. (9) Barauskas, J.; Landh, T. Langmuir 2003, 19, 9562. (10) Misquitta, Y.; Caffrey, M. Biophys. J. 2001, 81, 1047. (11) van der Waals, J. D.; Kohnstamm, P. Lehrbuch der Thermostatik: das heisst des thermischen Gleichgewichtes materieller Systeme; Johann Ambrosius Barth: Leipzig, 1927. (12) Storonkin, A. V. Termodinamika geterogennykh sistem; Izd-vo Leningradskogo. un-ta: Leningrad, 1967. (13) Wadso¨, L.; Markova, N. ReV. Sci. Instrum. 2002, 73, 2743. (14) Kocherbitov, V.; Wadso¨, L. Thermochim. Acta 2004, 411, 31.
Phase Transitions in Surfactant and Lipid Systems (15) Kocherbitov, V.; So¨derman, O.; Wadso¨, L. J. Phys. Chem. B 2002, 106, 2910. (16) Markova, N.; Sparr, E.; Wadso¨, L.; Wennerstro¨m, H. J. Phys. Chem. B 2000, 104, 8053. (17) Kocherbiov, V. Thermochim. Acta 2004, 421, 105. (18) Lutton, E. S. J. Am. Oil Chem. Soc. 1966, 43, 28. (19) Mol, L.; Bergenstahl, B.; Claesson, P. M. Langmuir 1993, 9, 2926.
J. Phys. Chem. B, Vol. 109, No. 13, 2005 6435 (20) Fukada, K.; Kawasaki, M.; Kato, T.; Maeda, H. Langmuir 2000, 16, 2495. (21) Laughlin, R. G. The Aqueous phase behaVior of surfactants; Academic Press: London, 1996. (22) Kocherbitov, V.; So¨derman, O. Phys. Chem. Chem. Phys. 2003, 5, 5262. (23) Sparr, E.; Wadsten, P.; Kocherbiov, V.; Engstro¨m, S. Biochim. Biophys. Acta 2004, 1665, 156.
