Headgroup concentration estimate

This calculation is for spherical micelles, but a similar calculation could be used to obtain estimates of salt concentrations for ionic wormlike micelles. Such salt concentrations for wormlike micelles are expected to be increased in comparison to spherical micelles. In fact, the addition of counterions or a sufficient increase in surfactant concentration often leads to a transition from spherical micelles to wormlike micelles. As the free counterion concentration in solution increases, so does the counterion binding. As a result, electrostatic repulsion between the charged head-groups is increasingly shielded and the mean cross-sectional (effective) headgroup... 

In an attempt to study the molecular nature behind the hydration force we performed a series of simulations on dipalmitoylphosphatidylcholine (DPPC) [10] and dilauroylphosphatidylethanolamine (DLPE) [11] membranes in their gel and liquid crystalline (l.c.) states. We will concentrate here on four simulations. All four of them were done on membranes in their l.c. states. Two of the simulations were performed on DLPE membranes and they differed by the amount of water per headgroup. In the first simulation we considered the case of 10.3 waters per head-group, which is about the experimentally estimated limit for full hydration [12-14]. In the second simulation we considered 20.5 waters per headgroup. This is well above the limit of full hydration, but allows us to perform a comparison with the simulation where the same number of waters per headgroup is used to study the full hydration of DPPC. We call the first and the second simulations... 

Whether the metal-binding agent is a polyelectrolyte or an ionic surfactant headgroup in a micelle, it is of interest to know the extent of binding of a metal ion to such a species/agent. Based on the work of Oosawa, Scamehorn et al. (1989) have suggested equations that relate the fraction of a metal ion that is bound to the micelle to the free (unbound) metal ions. The estimation of these fractions requires additional relations, such as the electroneutrality condition, concentrations of surfactants present as micelles... 

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