  Lipid monolayers with phase coexistence are a frequently used model for lipid
membranes. In these systems, domains of the liquid-condensed phase always
present size polydispersity. However, very few theoretical works consider size
distribution effects on the monolayer properties. Because of the difference in
surface densities, domains have excess dipolar density with respect to the
surrounding liquid expanded phase, originating a dipolar inter-domain
interaction. This interaction depends on the domain area, and hence the
presence of a domain size distribution is associated with interaction
polydispersity. Inter-domain interactions are fundamental to understanding the
structure and dynamics of the monolayer. For this reason, it is expected that
polydispersity significantly alters monolayer properties. By means of Brownian
dynamics simulations, we study the radial distribution function (RDF), the
average mean square displacement and the average time-dependent self-diffusion
coefficient, D(t), of lipid monolayers with normal distributed size domains. It
was found that polydispersity strongly affects the value of the interaction
strength obtained, which is greatly underestimated if polydispersity is not
considered. However, within a certain range of parameters, the RDF obtained
from a polydisperse model can be well approximated by that of a monodisperse
model, suitably fitting the interaction strength, even for 40%
polydispersities. For small interaction strengths or small polydispersities,
the polydisperse systems obtained from fitting the experimental RDF have an
average mean square displacement and D(t) in good agreement with that of the
monodisperse system.
