Mesoscopic models of lipid bilayers and bilayers with embedded ...

26 Surface tension in lipid bilayers
tion 1/No from a given pair (i, j), where No is the total number of slabs that intersect
the line of centers between particle i and j. Periodic boundary conditions are always
taken into account in this calculation. The integral in equation 3.5 now becomes
Ns
Ns
γ = [PN(k) − PL(k)]∆zs = γ(k) (3.12)
k=1
where ∆zs = Lz/Ns is the (uniform) width of the slabs and γ(k) is the local surface
tension in slab k.
To illustrate the application of this method with a very simple example, we plot in
figure 3.1 the distribution of the local surface tension γ(z) across an oil/water interface
(the interface is perpendicular to the z-axis), calculated from a DPD simulation
of oil- and water-like phase separated particles. In the same figure we also plot the
oil, water and total densities profiles to better characterize the shape of the pressure
profile. Note that, because of periodic boundary conditions, the interfaces in
the simulation box are actually two. The maximum of the surface tension is at the
0.6
0.4
0.2
0.0
−0.2
γ(z)
oil water
k=1
0 2 4 6 8 10
Z
Figure 3.1: Surface tension profile γ(z) (solid black), and oil (dashed black), water (dot-dashed
black), and total (solid gray) density profiles across the interfaces (perpendicular to the z-axis)
between phase separated oil and water. Because of periodic boundary conditions, there are
two interfaces. Note that the densities have been rescaled and shifted for better comparison
with the surface tension (hence the scale in the graph ordinate refers to the surface tension
only).
oil/water interfaces where there are large repulsive forces between oil and water, and
the density is lower than in the bulk phases. Moving away from the interface (in
both directions since the system is fully symmetric), as a consequence of the repulsive
forces at the interface, there is a thin region of compressed fluid where the surface
tension becomes (slightly) negative. The surface tension becomes again positive
oil