LAMELLAR ORDERING IN SYMMETRICAL DIBLOCK COPOLYMERS

We calculate the lamellar period L and interphase thickness a of an in compressible melt of symmetric diblock copolymers from the onset of ph ase segregation (weak segregation limit) to the limit where segregatio n is almost complete (strong segregation limit) by numerically solving a mean field lattice model, where the lattice spacing is taken small enough to approximate a continuum. Our results for L and a agree with previously derived theoretical formulas in both limits. Based on the f irst few terms of a Fourier series expansion of the density profile, w e show analytically that L = 0.844R(chi(N))0.571 at the weak segregati on limit, where R is the unperturbed molecular radius of gyration, chi the Flory interaction parameter, and N the number of statistical segm ents per molecule; the compressibility of the melt-even in the incompr essible limit-must be taken into consideration to get the correct depe ndence of L on chi(N), and the Fourier series approximation turns out to be accurate over a very small range of chi(N).