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_xT_y as a function of the amphiphilic factor α = 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 α-parameter. For a fixed chain length l of the molecule, the symmetric molecules of the type H_l/2T_l/2 with α = 1 tend to form circular micelles with relatively narrow distribution in cluster sizes. As we decrease the α-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 H₂T₃ molecules produces spherical micelles, the H₁T₄ molecules( α = 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.     

Qr空间及其闭图像定理

在qw＊拓扑的基础上定义了Q空间和Qr空间,重点给出了在拟桶偶对条件下的Qr空间的有界算子的闭图像定理以及描述Qr空间几何特征的重要结论.