SimScience - Membranes - Advanced, page 17

Two types of membrane: fluid and tethered

In amphiphilic films the constituent surfactant molecules are bound together only by rather weak forces - they can easily flow around each other. These films are thus often called fluid membranes. Other interesting 2 dimensional (*) systems are films made of molecules bound by strong covalent (*) bonds. Indeed, red blood cell membranes are composed of a bilayer formed from phospholipid molecules attached to an underlying network of strongly bound protein molecules - the spectrin network - as we have seen already. The properties of such tethered (sometimes called polymerized or crystalline) surfaces are quite different from their `fluid' cousins. For example, we expect tethered surfaces to undergo a crumpling transition (*) at some temperature. Such a transition separates a regime where the typical surfaces are very small and folded in upon themselves from a `flat' phase in which surfaces are smooth. This transition is NOT expected for fluid surfaces - which are thought to always be crumpled at long distance. It is also possible to have behaviors intermediate between the fluid and tethered phases - specifically there is the possibility of a hexatic (*) phase.

In a crystalline surface the constituent molecules are typically arranged in a regular, triangular lattice. Such a lattice is shown below

[diagram]

Diagram of a triangular lattice

We can put a defect into this lattice by picking one bond (edge of a triangle) deleting it and replacing it by a new bond between adjacent vertices as shown in the next figure

[diagram]

Diagram of a triangular lattice with one defect Diagram showing the coordination numbers of each vertex

Such a bond or link flip creates two vertices with five neighbors and two with seven neighbors. A dislocation (*) comprises a pair of neighbor vertices which are five and seven-fold coordinated. Thus such a link flip move generates a bound pair of dislocations. If the bonds are represented by elastic springs it is clear that such a link flip move will cost energy (*). This is also true of a single dislocation. Thus one would imagine that `perfect' lattices would be preferred over lattices with say one dislocation. However, notice that there are very many different lattices with one such defect corresponding to the number of possible vertices at which to place the center of the dislocation. But there is only one `perfect' lattice. Physicists say that the lattice plus defect has a higher entropy (*) than the perfect lattice. As the temperature is increased (and hence the size of random fluctuations) it eventually becomes more likely to see defects even though they are not the lowest energy surfaces.

Thus tethered surfaces which allow for the occasional breaking of covalent (*) bonds may enter such a phase. In this phase their energy (*) can depend now on the number and position of these defects. This can increase the effective bending energy of the surface at large distances and cause a new phase transition (*) associated with what has come to be called crinkled (*) surfaces. There are many experiments underway to search for such surfaces in real physical and biological systems.