In 1976 Israelachvili introduce the concept of molecular packing parameter to predict molecular self-assembly in surfactant solution. This is a very complicated method and it's too theoretical. In the literature there are many discussion on it and looks to this concept from thermodynamic view and it seems to be more theoretical than practical.
http://pubs.acs.org/doi/abs/10.1021/la010831y
The concept of molecular packing parameter is widely invoked in the literature to explain, rationalize and even predict molecular self-assembly in surfactant solutions. The molecular packing parameter is defined as vo/aelo, where vo is the surfactant tail volume, lo is the tail length, and ae is the equilibrium area per molecule at the aggregate surface. A particular value of the molecular packing parameter can be translated via simple geometrical relations into specific shape and size of the equilibrium aggregate. This is the predictive application of the concept of molecular packing parameter, as discussed in the literature. In calculating the packing parameter, the dominant notion in the literature is that the surfactant headgroup determines the surface area per molecule of equilibrium aggregates ae. It follows that, given a headgroup, the molecular packing parameter vo/aelo is fixed, because the volume-to-length ratio (vo/lo) of the tail is a constant independent of the tail length for common surfactants. Therefore, in this view, the surfactant tail has no role in determining the size and shape of equilibrium aggregates. We show that this is contrary to fact, by focusing on the neglected role of the surfactant tail. Illustrative calculations are presented in this paper to demonstrate that the surfactant tail does also control equilibrium aggregate structures. It is shown that the role of the tail can be either explicit via modification of the area ae and thus of the packing parameter, or implicit via other means, without modifying ae or the packing parameter.
http://pubs.acs.org/doi/abs/10.1021/la010831y
J. Chem. SOC.F, araday Trans. 2, 1981,77, 601-629
The above-mentioned paper by Mitchell & Ninham gives a better description of molecular packing parameter. It also gives simple formulae to calculate this parameter from structural parameters such as aggregation number, hydrodynamic radius and water pool radius (in case of reverse micelles) of the organized assembly. In our recent papers, we have used this parameter to correlate variations observed in solute rotation and isomerization rate constants in case of reverse micelles. I am attaching these papers for your reference.
Maybe you can use the LB-Film Technique as well for calculation, we use it for Lipids at the air water interface and observe it with brewster angle microscopy
Best regards
CHristian
I have done MD simulations for various high molecular weight copolymer micelles with different morphologies in water. Could anyone help me on how I can calculate the packing parameter from the MD simulations? Is it possible to extract it from structural properties of the micelle?
Actually the concept is very simple and we use it in undergraduate teaching. The CPP is really just a geometric argument that gives the average curvature of the interface and this indicates the likely aggregate structure. The original paper also points out that this is an oversimplification as it does not include effects such as elasticity. Note that the head group area is determined experimentally from surface tension data. Hence it should be noted that the head group area is sensitive to surfactant chain length. Regarding the criticism of Yu-Hung Chen above, "Therefore, in this view, the surfactant tail has no role in determining the size and shape of equilibrium aggregates". This is not correct, whilst V/l is (nearly) a constant the molecular packing parameter is influenced by the chain length through the measured head group area (that is strongly chain length dependent). Additionally, di and tri chain surfactants require that the chain volume is multiplied by 2 and 3 respectively.
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