Cylindrical colloids on a fluid membrane

[摘要] We theoretically study the adhesion and membrane-mediated interaction of cylindricalcolloids to a flat fluid membrane. There are two ways to approach thisproblem. The first way, based on energy, requires finding the equilibrium shape ofthe membrane given the placement of the particle(s). In order to do so, we need toknow how the energy of the surface depends on its shape (i.e. the surface Hamiltonian),as well as how the adhered colloid deforms the membrane. The secondway to approach this class of problems is ;;geometrical”, where forces between themembrane-adhered particles are related directly to the geometry of the deformedmembrane via the surface stress tensor. The surface Hamiltonian allows finding thestress at any point on the membrane in terms of local geometry. The force actingon the colloid can then be found by integrating this surface stress tensor along anycontour enclosing the colloid.In this thesis, using the approach based on free energy calculations, we look intothe problem of cylindrical colloids adhering to a membrane with fixed constant adhesionenergy between the membrane and the colloids. Angle-arclength parameterizationis used in order to treat the problem beyond small gradient approximation.We present three different cases here: single cylinder adhering on a membrane, twocylinders adhering on the same side of the membrane, and two cylinders adheringon different sides of the membrane. For the single cylinder case we present a structuralphase diagram to separate no wrapping, partial wrapping and closure statesand we compare it to the phase diagram obtained for a related system of sphericalcolloids. For two cylinders adhered on the same side of the membrane we obtainrepulsive interaction and transition from shallow to deep wrapping as the cylindersmove apart from each other. We also look into a phase where two cylinders arevertically stacked and discuss its energetics. For two cylinders adhering to the oppositesides of the membrane, attractive interaction is obtained in accordance withprevious results and we further show that in that case two cylinders are generallyin contact and a first-order transition from shallow to full wrapping is possible. Inthe last section, we put a framework for the class of problems where the particleis between the membrane and the supporting interface, where adhesion is assumedbetween the interface and the membrane.

[发布机构] University of Waterloo

[效力级别] adhesion

[关键词] colloid;adhesion;membrane;interaction;Physics