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SCMF – Single Chain Mean Field Theory


The Single Chain Mean Field (SCMF) theory was originally proposed by Ben-Shaul, Szleifer and Gelbart  to describe micellization of block copolymers. This method has further been developed to describe the structure of phospholipid membranes at the molecular level. SCMF is one of the theoretical tools exploited in the Molecular Simulation group in Tarragona.

 The SCMF theory describes a single molecule surrounded by the mean fields. It takes explicitly into account the structure of an individual molecule at a coarse-grained level similar to coarse-grained MC or MD simulations. However, as distinct from simulations, the interactions of the molecule with the environment are described through the mean molecular fields. The mean fields determine the most probable conformations of the molecule through the probabilities of individual molecule. In turn, the mean fields are calculated as the average properties of individual conformations. This self-consistence closure defines the set of nonlinear equations that can be solved numerically. The solution of such equations gives the equilibrium structures and the concentration profiles of all components in the system as well as the most probable conformations of individual molecules.

mean field

The SCMF methodology is adapted for parallel computation via OpenMP shared memory platform.

The SCMF theory is particularly suitable for the description of nano-objects like polymeric drug carriers: it gives a detailed microscopic information on the configurations of the chains, the optimal shape and structure of drug delivery systems, the distribution of chains in the aggregate, the critical micellar concentrations as well as the critical aggregation concentration, the optimal aggregation number and the size distributions. The method is quite universal: it can be applied to solutions of linear or branched polymers, solutions of low-molecular weight surfactants and various additives, mixtures of various components and structural and shape transitions.

Szleifer, I., Ben Shaul, A. & Gelbart, W. M. Chain statistics in micelles and bilayers: Effects of surface roughness and internal energy. The Journal of Chemical Physics 85, 5345–5358 (1986).
Szleifer, I., Ben Shaul, A. & Gelbart, W. M. Chain organization and thermodynamics in micelles and bilayers. II. Model calculations. The Journal of Chemical Physics 83, 3612–3620 (1985).
Pogodin, S. & Baulin, V. Equilibrium Insertion of Nanoscale Objects into Phospholipid Bilayers. Current Nanoscience 7, 721–726 (2012).
Pogodin, S. & Baulin, V. A. Coarse-Grained Models of Phospholipid Membranes within the Single Chain Mean Field Theory. Soft Matter 6, 2216–2226 (2010).

Main equations

Single Chain Mean Field theory

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