3.1. SA-OA Mixture
The π-A isotherms for the mixed films of SA and OA, together to those of the individual components, are shown in
Figure 1; in
Figure 2 the values of mean area are plotted vs. the molar fraction at several surface pressures.
Mixed monolayers show a first collapse that practically coincides with that of OA (π = 30 mN·m
−1), and when the proportion of SA increases, a second collapse is observed (isotherms 4 and 5 in
Figure 1) which does not reach the value observed for SA (π = 58 mN·m
−1). This is an indication that at high surfaces pressures, OA forms a separated phase from SA which collapses at surface pressure (30 mN·m
−1); meanwhile, the collapse of the SA phase is influenced by the presence of OA. Thus, the OA molecules strongly distort on the compactness of the SA molecules and hamper the formation of a more rigid film.
A study of the mean area per molecule (
Figure 2) shows positive deviations from the straight line; these deviations are more pronounced at low surface pressures and when the OA content is X
OA = 0.425. At high surface pressures and with all compositions except for the OA content of X
OA = 0.425, the mean area approaches a straight line. Positive deviations indicate mixing but with unfavourable interactions with respect to pure components. Null deviations indicate an ideal mixing or phase separation. As two collapses can be observed in the isotherms when the SA is in high proportion, this indicates that a phase separation has occurred. As experimental points are not on the straight line, this means that partial miscibility still exits, that is, a partial segregation of one component occurs but the rest of this component remains on the mixed film.
Figure 3 presents the variation of the elastic modulus, Equation (1), along the isotherm compression for the different mixed films of SA and OA. According to the reported criteria, that is C
s−1: <100 mN·m
−1 for LE state, 100–250 mN·m
−1 for LC state, >250 mN·m
−1 for S state [
47,
51], OA shows an LE state, meanwhile SA shows an LE state below 9 mN·m
−1, an LC state between 9–24 mN·m
−1 and an S state up to 24 mN·m
−1. On the other hand, mixed films show an LE state, and for those with higher OA content, the compressibility behaviour is similar to that of pure OA; however, when the SA content is high, an LC state appears at higher surface pressures.
It is also seen that when the SA content increases, the surface pressure at the inflection point in the isotherm, or at the first maximum point in the elastic modulus plot, decreases. In contrast, the second maximum point in the elastic modulus plot increases with more SA content. These results also point to a partial mixing at low surface pressures but a segregation at high surface pressures, especially at high SA content.
To gain a deeper understanding at the molecular level, the surface pressure-area isotherms of SA-OA mixtures were further analysed using the equation of state. For this study, the virial state equation, Equation (2), was applied.
Figure 4 shows the plots of (πA/kT) vs. π for the several studied compositions, which can be adjusted with a polynomial of 2n degree. The values of the virial coefficients are tabulated in
Table 1. The values of
b1)12 and
b1E, obtained from Equations (3)–(5), are tabulated in
Table 2.
Results for
b1 coefficients (see
Table 2) indicate a gradual decrease from the OA pure component to the SA one. A similar fact occurs for the
b0 coefficient. The higher value for
b1 of OA is due to the higher repulsive interactions between molecules in this fatty acid, relative to the SA. The higher value for
b0 of OA is due to a lesser degree of aggregation in this fatty acid with respect to the SA. The values of
b1)m are in between those of the SA and OA, but higher than those of the ideal behaviour, that is, the
b1E values are positive. This indicates more repulsive interactions in the mixed films between SA and OA molecules with respect to the separate components. The values of
b1)12 are positive and higher than the mean value (
b1)1 +
b1)2)/2 = 0.09105, which also indicates more repulsion in the mixed film between molecules. The higher values of
b1)12 occur when the content of OA is low, being higher than the value of
b1 of pure OA. This fact can be attributed to the fact that OA breaks the compactness of SA, which results in an increase of the
b1 coefficient (much more repulsion in respect to pure components).
As positive deviations are higher for low OA content, low XOA, this means that OA places partially in between SA, destabilizing the compactness of SA. When there is a low SA content, it can better mix with the fluid phase of OA, the interactions are less unfavourable and the positive deviations are lower. Thus, the domain formation or phase separation could be more notable for low XOA, that is, for high SA content.
Introducing the values of virial coefficients in Equations (6)–(9) and (10)–(13), values of
GE and Δ
Gmix were calculated and are reported in
Table 3. It is seen that
GE exhibits positive values which were considered as small deviations from zero excess free energy; the values of Δ
Gmix are slightly negative. These values are in agreement with the previous comments about the mixing of the components in the film, that is, the interaction between components is not favoured but the entropic factor (see Equation (9)) leads to energetically favourable mixing, even with slightly negative values of Δ
Gmix. Mixing is less favoured especially at higher SA contents and higher surface pressures.
3.2. DPPC-POPC Mixture
Figure 5 shows the π-A isotherms of mixed films of DPPC and POPC, together with those of the individual components. It was observed that the phase change of DPPC at π = 8 mN/m (the first inflection point) are influenced by the presence of POPC, as well as the collapse pressure, indicating that DPPC and POPC are partially miscible. The inflection point is clearly visible at the lowest content of POPC and the surface pressure at which this point occurs increases with the POPC content.
Figure 6 shows the mean area per molecule vs. the POPC molar fraction, at several π. Positive deviations respect to the ideal case (straight line) were generally observed, but at low and high π, the mixed film with X
POPC = 0.394 presents negative deviations which indicate less repulsive interactions or more attractive interactions (favourable interactions in respect to the individual components). In both cases, deviations from the straight line indicate a certain degree of miscibility. This fact will be commented upon later.
Figure 7 shows the elastic modulus of DPPC, POPC and DPPC-POPC mixed films, obtained from the isotherms of
Figure 5 using Equation (1). DPPC presents a phase change from LE to LC at π around 8 mN/m, and POPC only presents LE state. The fact that DPPC can present the LC state in the monolayer is related to the chain melting temperature of 41 °C for DPPC, against that of −2 °C for POPC [
52]. Thus, at the temperature of the present work, POPC is always in the LE state; however, DPPC can change from the LE to the LC state when compressing. The DPPC-POPC studied mixed films only presents the LE state, with an inflection at high DPPC contents, and the inflexion surface pressure increasing when the DPPC content decreases. This fact clearly confirms that POPC mixes with DPPC, and thus that POPC molecules hamper a more compaction of DPPC molecules and the phase change to a LC state.
An analysis of the isotherms using the virial state equation has been done.
The plot of πA/(kT) vs. π (
Figure 8) can be fitted with a polynomial of 2n degree (see Equation (2)), and the treatment reported in Equations (3)–(5) is applied to them. The values of the obtained virial coefficients are tabulated in
Table 4 and the values of
b1)12 and
b1E in
Table 5.
It is shown in
Table 4 that the
b1 values increase with the POPC content. This indicates more repulsive interactions for POPC, and that the presence of POPC in the DPPC matrix also increases the repulsive interactions between molecules with respect to DPPC molecules. The value of
b0 for POPC is lower than that of DPPC, indicating more aggregation in POPC than in DPPC (even POPC has an unsaturation in the hydrocarbon chain, the oleoyl chain is larger. Another explanation could be in the phase change of DPPC that makes the polynomial fit more problematic). The values of
b1)m are in between those of the DPPC and POPC, but higher than those of the ideal behaviour, that is, the
b1E values are positive. This indicates more repulsive interactions in the mixed film between DPPC and POPC molecules with respect to the separate components. The values of
b1)12 are positive and higher than the mean value (
b1)1 +
b1)2)/2 = 0.1667, which also indicates more repulsion in the mixed film between molecules.
The higher values of b1)12 occur when the content of POPC is low, being higher than the value of b1 of pure POPC, except for XPOPC = 0.394. This fact can be attributed to POPC breaking the compactness of DPPC, which results in an increase of the b1 coefficient (much more repulsion in respect to pure components). As has been seen previously, when XPOPC = 0.394, the excess area is negative, which is in agreement with the fact seen now that the b1)12 is the lowest value for the mixed films, and lower than that of pure POPC. Thus, the mixed film with XPOPC = 0.394 is the most favourable among them.
Introducing the values of virial coefficients in Equations (6)–(9) and (10)–(13), values of
GE and Δ
Gmix have been calculated and reported in
Table 6. It is seen that values of
GE are slightly positive, except for X
POPC = 0.394 at low surfaces pressures; the values of Δ
Gmix are slightly negative. These values are in agreement with the previous comments about the mixing of the components in the film, that is, the interaction between components is not favoured but the entropic factor (see Equation (9)) leads to energetically favourable mixing. The mixing is especially favoured for X
POPC = 0.394, including the case of 35 mN/m of surface pressure which is close to the lateral pressure of biological membranes. Nevertheless, the positive values of
GE at 35 mN/m could indicate a propensity for phase separation, as is discussed in reference [
45].
3.3. Discussion
Isotherms indicate that a certain miscibility between components can be present in both cases: SA-OA and DPPC-POPC mixed films. The area vs. molar fraction (A vs. X) analysis shows this effect of miscibility, but with less favourable interactions in respect to the individual components. Thus, the miscibility should be attributed to entropic factors. The less favourable interactions could be due, at least in part, to the presence of unsaturation in the hydrocarbon chains. The effect of unsaturations has also been discussed in reference [
53] for the case of mixed films of a fatty acid and a phospholipid. The less favourable interactions lead to the partial phase segregation that is observed for the SA-OA system at high pressures and/or at high SA content. For the DPPC-POPC system, there is a composition (X
POPC ≈ 0.4) where the mixed film is more energetically favourable. A notable difference between both systems is that while the OA-SA system at X
OA ≈ 0.4 presents less favourable interactions, those of the POPC-DPPC system at X
POPC ≈ 0.4 are more favourable.
The values of the elastic modulus are more similar to those of the more fluid component (OA or POPC). The behaviour of the elastic modulus plot at high surface pressures is different, comparing both systems. The DPPC-POPC system presents only one maximum, meanwhile the OA-SA system presents two maxima with a clear phase in SA for the second maximum.
The analysis of the virial coefficients is similar in both systems, with the b1 values between those of the individual components. When comparing the b1 values for the fatty acids OA, SA and their mixed films with the b1 values for the phospholipids POPC, DPPC and their mixed films, lower values are observed, which indicates that these fatty acids can compact more easily than phospholipids. However, when analysing the excess values of b1E the differences are less significant, and give rise to the results derived from the area and energy analysis.
Ocko and Kelley [
33] studied mixed monolayers of saturated stearic acid and of monounsaturated elaidic acid (the trans isomer of the oleic acid), and also observed poor miscibility with phase separation. Seoane et al. [
34] reported mixed films of cholesterol with saturated or unsaturated fatty acids, but these are not discussed here due to the peculiar characteristics of cholesterol. Several authors [
23,
25,
26,
27,
30,
32] have also observed phase separation in fatty acid mixed monolayers of fluorinated and hydrogenated amphiphiles.
Comparing the behaviour of the POPC-DPPC mixed films with that of the unsaturated phospholipids POPC-POPE [
35], it is shown that POPC-POPE mixed films demonstrate favourable mixing at all compositions, with negative values of the excess area,
AE, and with more negative values of the mixing energy, Δ
Gmix. Comparing the values of the virial coefficient
b1 for DPPC, POPC and POPE [
35], it was observed that DPPC presents the lowest value. As
b1 is related to exclusion volumes and interactions between molecules, this means that the presence of a double bond provides higher exclusion volumes and more repulsive interactions between molecules. In contrast, the excess values
b1E are always negative for the POPC-POPE mixed films [
35] but positives for the POPC-DPPC ones (present work). This is in agreement with the obtained values of
GE which are positive for the POPC-DPPC mixed films, but negative for the POPC-POPE ones. Thus, mixed films of a saturated and an unsaturated phospholipid seems to be energetically less favourable than those of two unsaturated phospholipids, at least from the cited systems that do not present enormous differences. On the other hand, Domenech et al. [
36] suggest that cardiolipin and POPE can form separated phases under certain conditions, and that cardiolipin might be laterally segregated from POPE, even though thermodynamic analysis indicates miscibility.
Wydro and Witkowska [
44] studied mixed films of phospholipids with different chains and unsaturations, through the mixtures of DPPG with DPPE, DSPE and DOPE. The results proved non ideal behaviour, as in the present case, and that the presence of the double bond in DOPE hamper the mixing and the layer compactness. The behaviour is also influenced by the type and length of the acyl chain. The values of
GE for DPPG-DOPE mixtures are positive (as in the present case) compared to the negative values of
GE for DPPG-DPPE and DPPG-DSPE mixed films, in which they exhibit saturated chains. The values of Δ
Gmix for DPPG-DOPE are negative (as in the present case) but less negative than those for DPPG-DPPE and DPPG-DSPE. Thus, as in the present case of the mixed films of POPC-DPPC, those of DPPG-DOPE present mixing due to the entropic factor. Dynarowicz et al. [
37] studied miscibility and phase separation in mixed PC monolayers and found miscibility at low surface pressures but phase separation at high surface pressures.
Thus, phase separation is usual in mixed lipid monolayers due to differences in length, chemical groups or unsaturations in the acyl chain, differences in the headgroup, or the composition and surface pressure conditions.