Effective Curvature Elastic Constants for Membrane-Polymer Systems

Abstract

Membranes can be described using a model of mathematical surfaces where the membrane's properties are characterised by the three membrane curvature elastic constants 'spontaneous curvature', 'bending rigidity' and 'saddle-splay modulus'. Experiments show that the addition of polymers can change the properties of a membrane system considerably. One example is the polymer-boosting effect which has been discovered recently for oil-water-amphiphile mixtures. The scattering data has been described successfully by the membrane model. The effect of the polymers has been taken into account by effective membrane curvature elastic constants. The concept of effective curvature elastic constants will be introduced, and the effects of different kinds of polymer additions to membrane systems discussed in the literature will be reviewed. Using the model of freely-jointed chains for the polymers, the effects of polymers anchored to membranes will be studied for several systems by means of Monte Carlo simulations. A simulation technique is described which allows to calculate the polymer effect with high accuracy in the limit of small membrane curvatures. The effects of self-avoidance and of different polymer architectures are investigated. The self-avoidance effect for linear polymer chains is found to be small. However, the simulations show that star polymers increase the efficiency of the polymer. The effects on the bending rigidity and the spontaneous curvature per arm increase with the functionality (i.e. the number of arms) of the star, whereas the effect on the saddle-splay modulus does not depend on the functionality. Scaling arguments confirm the behaviour observed in the simulations. The properties of anchored ring polymers are studied and the effects of knots are discussed. An algorithm is presented which can be employed to calculate the effect of adsorbed polymers on the curvature elastic constants in the limit of small curvatures. For linear chains in the lamellar phase, the effect of the confined geometry is investigated, again in the limit of small membrane curvatures. The simulations show that for polymers anchored to membranes, at a small lamellar spacing the effect on the membrane curvature elastic constants changes qualitatively. While for large interlayer spacings the polymer increases the bending rigidity and decreases the saddle-splay modulus, effects of opposite sign are observed for lamellar spacings smaller than the radius of gyration of the free chain. With a model for polymers anchored to a fluctuating membrane, the polymer effect is simulated for the whole fluctuation spectrum of the membrane. We obtain a universal scaling function with a maximum at large fluctuation lengths