Bulk free energy gain

However, this choice of t / implies that surfaces of stems need to be formed first before any gain in the bulk free energy of the stems. 

The fourth term is a polarisation term. Here E(z) = di/z/dz is the electric field at position z. In previously published SCF results for charged bilayers, this last term is typically absent. It can be shown that the polarisation term is necessary to obtain accurate thermodynamic data. We note that all qualitative results of previous calculations remain valid and that, for example, properties such as the equilibrium membrane thickness are not affected significantly. The polarisation term represents relatively straightforward physics. If a (united) atom with a finite polarisability of erA is introduced from the bulk where the potential is zero to the coordinate z where a finite electric field exists, it will be polarised. The dipole that forms is proportional to the electric field and the relative dielectric permittivity of the (united) atom. The energy gain due to this is also proportional to the electric field, hence this term is proportional to the square of the electric field. The polarisation of the molecule also has an entropic consequence. It can be shown that the free energy effect for the polarisation, which should be included in the segment potential, is just half this value... 

The first term in Eq. (5.11) reflects the gain in the bulk energy while the second term accounts for the variation in the total free energy associated with the replacement of the substrate/amorphous and vapour/amorphous interfaces (dAi) by the substrate/crystal and vapour/crystal interfaces. The last term represents the increase in the total free energy due to the increase in the crystal/amorphous interface (dA2). Taking into account Eq. (5.11) and the expressions for dV, dAi and dA2 given above, dG/dN can be expressed as ... 

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