Effect of head-tail ratio and the range of the head-head interaction in amphiphilic self-assembly

We investigate cluster autocorrelations, critical micelle concentration (CMC), and size distribution for amphiphiles of the type H(x)T(y) as a function of the amphiphilic factor alpha = x/y for a fixed length l = x + y using a combination of reptation and kink-jump Monte Carlo (MC) moves in a two-dimensional (2D) square lattice. We find that the CMC decreases monotonically as a function of the alpha-parameter. For a fixed chain length l of the molecule, the symmetric molecules of the type H(l/2)T(l/2) with alpha = 1 tend to form circular micelles with relatively narrow distribution in cluster sizes. As we decrease the alpha-parameter to introduce head-tail asymmetry, the size distribution becomes polydisperse with occurrences of more elongated micelles. A calculation of the cluster autocorrelation function reveals that for the same chain length, symmetric amphiphiles take significantly less time to equilibrate and therefore simulation of much longer molecules is possible. Next we study the effect of the head-head repulsion term beyond next nearest neighbors. In general, the presence of a longer-range repulsive interaction reduces the average size of the micelles. We also notice that for l = 5, while H(2)T(3) molecules produces spherical micelles, the H(1)T(4) molecules( alpha = 0.25) often form vesicles. Our systematic studies bring out relevant information for controlling shapes and sizes of micelles to be used as templates in the design of self-assembled nanostructures.