Thermal instability in lamellar phases of lecithin : a planar undulation model

2014 Under heating, a hydrated egg lecithin multilamellar sample in a planar geometry (lamellae normal to the plates) shows a periodic striation instability, followed at higher heating by the socalled « ear-like » domains. We first demonstrate that a normal lamellae contraction under heating can result into a lamellar undulation instability in a planar sample, as well as in a homeotropic geometry. Assuming a strong anchoring of the lamellae on the plates, with the force free condition on the lamellae outer surface, the undulations are localized close to the plates. The spatial period and the threshold are estimated. Observations of hydrated DLL samples of various thicknesses allow us to identify the periodic striations with this localized undulation instability. J. Physique LETTRES 44 (1983) L-793 L..798 15 SEPTEMBRE 1983, Classification Physics Abstracts 61.30E 62.20 The so-called « ear of wheat-like » domains have been observed [1] in hydrated egg lecithin multilamellar samples subjected to an A.C. electric field. A further study of this phenomenon [2] has demonstrated that : a) the ear-like domains are generated by Joule heating and b) below the threshold for ear-like domains, periodic striations occur above a lower heating threshold of typical temperature jump AT ’" 1 °C. To explain this observation we propose in this letter a layer undulation thermal instability analogous to the one currently observed in smectic liquid crystals under dilation [3], or else in heated lamellar lecithin phases [4], but in a different geometry. Let us first resume the fmding of reference 2. a) At room temperature (T = 27 °C) a lamellar phase of hydrated egg lecithin (10 % wt. H20) placed in between two transparent Sn02 coated parallel electrodes (sample thickness d ~ 5-50 ~m) takes spontaneously an « homeotropic » alignement, with the layers parallel to Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019830044018079300 L-794 JOURNAL DE PHYSIQUE LETTRES the electrodes. The first effect of a low frequency (1 kHz) A.C. electric field seems to reorient the lamellae perpendicular to the glass plates, i.e. to induce a homeotropic to planar transition. After that, for voltage of about 60 V, most of the effects observed in planar monodomains are just due to Joule heating, from the relatively large A.C. current (10-100 mAjcm2 in the aqueous phases) flowing through the sample. This was demonstrated by the observation of a non aqueous lamellar phase prepared with synthetic dilauroyl lecithin (DLL, Fluka) and ethylene glycol : in absence of water, the current through the sample was much lower, and no instability could be induced up to applied voltages 175 V. On the other hand, by purely heating the sample, instabilities in the form of rows of focal conics, merging into « ear-like » domains under further heating, were observed. b) Below the threshold heating for structure disruption by focal conics, at a much lower AT 0.5 to 1 ~C, quasi periodic striations occur. An example of these striation is shown on figure 1, which represents the picture of a thin (d = 20 ~) planar monodomain of hydrated DLL (10 % wt. H20) at T = 27 ~C, seen between crossed polarizers under a microscope. Picture 1 a is more or less uniformly dark, because polarizer and analyser, parallel to the edges, are oriented along the optical eigen-axes of the planar uniaxial texture. More precisely, the lamellae are normal to the plates and parallel to the small side of the picture. This is deduced from the observation of the direction of easy motion of bubbles in the sample. Heating is usually achieved by removing the thermal filter of the microscope. For a temperature increase of AT = 1 ~C (measured by thermocouples inside the sample), one observes (Fig. lb) the periodic striations as a system of dark lines parallel to the optical axis, separated by brighter lines. The average period (distance between three adjacent lines) varies from 4-7 ~m, several times lower than the width of the ear-like domains. This instability is reversible, i.e., it disappears slowly by lowering the temperature. At higher thermal excitation, the periodic striations have an organizing action on the ear-like domains. The focal conics are arranged in rows, with the ellipses in the plane of the sample and the hyperbolae along some of the periodic striations. Resuming these observations on DLL, we look now at the periodic striations. By rotating slightly the polarizer, we note a lateral shift of the dark lines. As these lines are oriented perpendicular to the lamellae, it is reasonable to think that the periodic striations could be explained by a thermal undulation instability of the lamellae seen from the side. Undulation instability under heating was indeed observed [4] in lamellar lecithin samples with very low water content (2 % wt.) in the homeotropic geometry. The thermal thickness expansion coefEcient j8 of lipid bilayers in egg lecithin is known [5] to be negative :/!==2013 2 x 10’~/~C. This contraction is one order of magnitude larger than, say, the thermal volume expansion of water (0.207 x 103/~C) and is probably related to the increased disorder of lipid chains in the bilayers. When heated between two fixed parallel plates, the lamellae are submitted to a dilative strain. Above the instability threshold, the lamellae undulate to fill better the space. Elastic free energy is now stored also as lamellae curvature energy rather than uniform lamellae dilation. The new point in the present planar geometry is that the lamellae are not parallel but perpendicular to the fixed boundary plates. Let us show that, provided the lamellae anchoring is strong enough on the electrodes, one can also observe an analogous undulation instability in planar orientation, but localized close to the plates. Our geometry is described in figure 2. z is the normal to the lamellae. The plates are parallel to y (in the plane of the lamellae) and z. x is the direction of observation. The striations are observed parallel to z, i.e. can be described as an undulation u ~ exp(iqy) [q/~y, u//z], where u is the normal distortion of the lamellae. We call B ~ 108 cgs [6] the constant pressure elastic modulus of the 1-dimensionnal « crystal » of lamellae. Let us call K (~ 10-6 cgs) the Franck curvature constant of the layers. The quantity £ = (KjB)1/2 is the penetration length, of the order of the distance between lamellae. The measured [4] ~, is in the range of 100 A for almost dry samples, and could be a little larger in our case, to account for the higher water content of our samples. L-795 THERMAL UNDULATIONS IN LAMELLAR LECITHIN Fig. 1. Planar texture of hydrated DLL : d = 20 gm, T = 27 "C. The lamellae are vertical parallel to the left side elongated bubble. a) Before heating ; b) after heating (AT 1 ~C), showing periodic striations. The small side of the picture corresponds to 250 um. L-796 JOURNAL DE PHYSIQUE LETTRES The problem of layer contraction under heating, with fixed boundary plates, is exactly the same as the one of layers with fixed spacing, attached to linearly expanding plates along z, which simplifies the notations. We write the elastic free energy of the lamellar system as [7] : The first term represents the layer compression, in presence of a layer tilt. Expanded in u, it contains a third order term which will lead to the instability. The last term is the layer curvature contribution. In the linear regime, u obeys the Euler equation : We look for a solution u ~ exp(iqy) W(x) V(z). This implies the relationship :