The Lamellar Phase

When comparable amounts of oil and water are mixed with surfactant a bicontinuous, isotropic phase is formed [6]. This bicontinuous phase, called a microemulsion, can coexist with oil- and water-rich phases [7,1]. The range of order in microemulsions is comparable to the typical length of the structure (domain size). When the strength of the surfactant (a length of the hydrocarbon chain, or a size of the polar head) and/or its concentration are large enough, the microemulsion undergoes a transition to ordered phases. One of them is the lamellar phase with a periodic stack of internal surfaces parallel to each other. In binary water-surfactant mixtures, or in... 

Typical runs consist of 100 000 up to 300 000 MC moves per lattice site. Far from the phase transition in the lamellar phase, the typical equilibration run takes 10 000 Monte Carlo steps per site (MCS). In the vicinity of the phase transitions the equilibration takes up to 200 000 MCS. For the rough estimate of the equihbration time one can monitor internal energy as well as the Euler characteristic. The equilibration time for the energy and Euler characteristic are roughly the same. For go = /o = 0 it takes 10 000 MCS to obtain the equilibrium configuration in which one finds the lamellar phase without passages and consequently the Euler characteristic is zero. For go = —3.15 and/o = 0 (close to the phase transition) it takes more than 50 000 MCS for the equihbration and here the Euler characteristic fluctuates around its mean value of —48. 

The second difference is related to the structure of the lamellar phase. The Euler characteristic has been assumed zero in the whole lamellar phase by Gompper and Kraus [47], whereas we show that it fluctuates strongly in the lamellar phase between the transition line and the topological disorder fine. The notion of the topological disorder line has not appeared in their paper. We think that the topological disorder line is much closer to the transition... 

FIG. 12 The behavior of the internal energy U (per site), heat capacity Cy (per site), the average Euler characteristic (x) and its variance (x") — (x) close to the transition line and at the transition to the lamellar phase for/o = 0. The changes are small at the transition and the transition is very weakly first-order. The weakness of the transition is related to the proliferation of the wormhole passages, which make the lamellar phase locally very similar to the microemulsion phase (Fig. 13). Note also that the values of the energy and heat capacity are not very much different from their values (i.e., 0.5 per site) in the Gaussian approximation of the model [47]. (After Ref. 49.)... 

Summarizing the detailed studies of the basic Landau-Ginzburg model presented in the preceding sections and in the present one suggest that this type of simplified model is not sufficient to describe all the effects related to the ordering in microemulsions. In particular, the only stable ordered phase in the model is the lamellar phase and all the cubic phases are only meta-... 

For diffuse and delocahzed interfaces one can still define a mathematical surface which in some way describes the film, for example by 0(r) = 0. A problem arises if one wants to compare the structure of microemulsion and of ordered phases within one formalism. The problem is caused by the topological fluctuations. As was shown, the Euler characteristic averaged over the surfaces, (x(0(r) = 0)), is different from the Euler characteristics of the average surface, x((0(r)) = 0), in the ordered phases. This difference is large in the lamellar phase, especially close to the transition to the microemulsion. x((0(r)) =0) is a natural quantity for the description of the structure of the ordered phases. For microemulsion, however, (0(r)) = 0 everywhere, and the only meaningful quantity is (x(0(r) = 0))-... 

Typically the formulation may contain up to 60% active with builder salts and a water level of about 30-40% [52]. The weight ratio of LAS/AE may range from 1.5 1 up to 4 1. The combination of LAS and AE is especially effective for two reasons. First, LAS and AE interact strongly to form the lamellar phase liquid crystals. Second, both ingredients can be introduced into the liquid formulation as a 95 + % active liquid to control the amount of water going into the formulation. LAS can be introduced into the formulation as sulfonic acid and neutralized in situ. 

Polar lipids form different kinds of aggregates in water, which in turn give rise to several phases, such as micellar and liquid crystalline phases. Among the latter, the lamellar phase (La) has received the far greatest attention from a pharmaceutical point of view. The lamellar phase is the origin of liposomes and helps in stabilizing oil-in-water (O/W) emulsions. The lamellar structure has also been utilized in creams. We have focused our interest on another type of liquid crystalline phase - the cubic phase... 

Monoolein will also form the cubic phase together with lecithin (e.g. dioleoyl phosphatidylcholine, see Figure 1), but above about 50% (w/w) lecithin the cubic phase is transformed into the lamellar phase (2). Moreover, water may be replaced by glycerol, completely or partly, in the cubic phase. Vegetable oils, e.g. sesame oil, can be incorporated to some extent (a few percent) in the cubic phase, and the same holds for bile salts. 

In vivo Release of Desmopressin and Somatostatin. The in vivo release of Desmopressin and Somatostatin after subcutaneous and intramuscular injections of the peptide in the cubic or the lamellar phase has been studied in the rabbit. Blood was sampled at regular intervals, and systemically absorbed Desmopressin and Somatostatin were determined as the specific immunoreactitvity in plasma of the actual peptide. For details of the analyses with dDAVP, consult ref. 9. For comparison, Desmopressin-like and Somatostatin-like immunoreactitvity (dDAVP-LI and SRIF-LI) in plasma after intravenous bolus injections of the two peptides were determined as well. 

The cubic phases with Somatostatin were allowed to swell to the water swelling limit, while the Desmopressin preparations were of the lamellar phase type, i.e. with low water content, and were therefore assumed to swell in vivo. Approximately 0.5 g of either cubic or lamellar phase was injected, corresponding to 2.5-3.0 mg peptide per kg body weight. 

The dDAVP preparations used in this study were prepared in low water contents so that the lamellar phase was formed, which in turn was injected into the rabbits. The reason for this was the fact that the lamellar phase with its mucous-like rheology is easier to inject than the stiff cubic phase. Since the lamellar phase swells into the cubic phase in excess water according to the phase diagram in Figure 1, a phase transition was expected also in the in vivo situation. The transition was found to be very fast as judged by inspection of the injection site immediately after administration. 

In all cases a connective tissue encapsulation of the injected phases was found, and, in most cases, some of the phase remained. In a few animals there were signs of irritation, either in the connective tissue capsule or in the surrounding tissue. Moreover, injections of the lamellar phase, which swell to the cubic phase in vivo, seemed to be slightly more irritating than injections of the fully swelled cubic phase, most probably due, in the former case, to dehydration of the surrounding tissue. However, no difference was found between sc and im administration. It should be noted that the monoolein used was not of pharmaceutical grade. 

Figure 7. Topological fluctuations of the lamellar phase at different points of the phase diagram, (a) Single fusion between the lamellae by a passage (this configuration is close to the topological disorder line), (b) Configuration close to the transition to the disordered microemulsion phase the Euler characteristic is large and negative.

Here scalar order parameter, has the interpretation of a normalized difference between the oil and water concentrations go is the strength of surfactant and /o is the parameter describing the stability of the microemulsion and is proportional to the chemical potential of the surfactant. The constant go is solely responsible for the creation of internal surfaces in the model. The microemulsion or the lamellar phase forms only when go is negative. The function/(<))) is the bulk free energy and describes the coexistence of the pure water phase (4> = —1), pure oil phase (4> = 1), and microemulsion (< ) = 0), provided that/o = 0 (in the mean-held approximation). One can easily calculate the correlation function (4>(r)(0)) — (4>(r) (4>(0)) in various bulk homogeneous phases. In the microemulsion this function oscillates, indicating local correlations between water-rich and oil-rich domains. In the pure water or oil phases it should decay monotonically to zero. This does occur, provided that g2 > 4 /TT/o — go- Because of the < ), —<(> (oil-water) symmetry of the model, the interface between the oil-rich and water-rich domains is given by... 

Figure 14. The phase diagram of the gradient copolymer melt with the distribution functions g(x) = l — tanh(ciit(x —fo)) shown in the insert of this figure for ci = 3,/o = 0.5 (solid line), and/o — 0.3 (dashed line), x gives the position of ith monomer from the end of the chain in the units of the linear chain length. % is the Flory-Huggins interaction parameter, N is a polymerization index, and/ is the composition (/ = J0 g(x) dx). The Euler characteristic of the isotropic phase (I) is zero, and that of the hexagonal phase (H) is zero. For the bcc phase (B), XEuier = 4 per unit cell for the double gyroid phase (G), XEuier = -16 per unit cell and for the lamellar phases (LAM), XEuier = 0.

---