Numerical Simulations of a Smectic Lamellar of Amphiphilic Molecules

This thesis deals with the liquid crystalline lamellar phase Lα built by amphiphilic molecules in aqueous solutions, and its interaction with macromolecules. We perform molecular dynamics simulations to study thermal fluctuations and defects appearing in a stack of parallel amphiphilic bilayers separated by layers of solvent. The idealized, coarse-grained model represents the solvent with soft spheres and the amphiphiles with bead-and-spring tetramers (two solvophilic beads and two solvophobic beads). The algorithm used for this thesis describes the lamellar phase in the isobaric isothermal ensemble without surface tension (N,P, T, γ = 0). First, we verify that the model exhibits a liquid-crystalline lamellar phase, which we characterize. In a second part, we study the elasticity of this smectic lamellar phase. The position fluctuation spectra of the bilayers are computed, and compared to the predictions of the “Discrete Harmonic”(DH) theory for the elasticity of smectic phases. The bilayer fluctuations observed in the simulation of a stack of fifteen bilayers are well described by the DH-theory, so that the two elastic constants - the bending rigidity Kc and the smectic compressibility modulus B - can be computed. Then, we investigate the point defects appearing in the smectic because of thermal fluctuations. It turns out that transient pores spontaneously nucleate in the bilayers of the lamellar phase. On the contrary, necks and passages between the bilayers are rarely detected. The size and shape distributions of the pores are investigated. The relationship between their area a and their contour length c is well described by the scaling law a ∝ c2/3 - the same scaling as two dimensional closed random walks. Additionally, the surface tension is zero. Therefore we consider that the energy of a pore depends explicitly only on the contour length of the pore. The effective free energy of individual pores and the line tension of the pore edge are then estimated from the contour-length distribution. Besides, a time-dependent analysis shows that the displacement of the pores within the bilayers during their life-time is very limited. In the last chapter of this thesis, we investigate a lamellar phase doped by a solventsoluble flexible linear polymer inserted between two bilayers. Two polymer types were simulated: adsorbing or non-adsorbing. In both cases, the interactions between the bilayers are softened in the presence of a polymer. However, the conformations of the chain strongly depend on the interactions between the polymer and the bilayers: An adsorbing polymer remains aligned with the bilayers and confined in the thin solvent layer, whereas a non-adsorbing polymer condenses into a globule. Contrarily to standard hypothesis, a non-adsorbing polymer locally modifies the interlamellar spacing, and triggers the formation of pores in its vicinity.

Diese Arbeit behandelt die flüssig-kristalline lamellare Phase (die sogenannte Lα Phase), die amphiphile Moleküle in wässriger Lösung ausbilden. Diese lamellare Phase besteht aus mehrere Lagen paralleler amphiphiler Doppelschichten, die durch Lösungsmittel voneinander getrennt sind. Wir studieren mittels Molekulardynamiksimulationen die thermischen Fluktuationen der Doppelschichten und die Defekte, die in der lamellaren Phase auftreten können, und die Auswirkungen eines Makromoleküls, das zwischen die Doppelschichten gestetzt wird. In dem zugrundeliegenden, idealisierten “coarse-grained” Modell werden das Lösungsmittel als weiche Kugeln und die Amphiphile als Tetramere (zwei hydrophile Kugeln und zwei hydrophobe Kugeln) repräsentiert. Der Algorithmus, der in dieser Arbeit verwendet wird, beschreibt die lamellare Phase im isobaren isothermen Ensemble ohne Oberflächenspannung (NPT, γ = 0). Zuerst verifizieren wir, daß das Modell tatsächlich eine stabile Lα Phase bildet, und charakterisieren ihre flüssig-kristallin