Self-consistent field theory volume fraction profiles

Fig. 4.41 Density profiles calculated using mean-field self-consistent field theory for a PS587PI647 diblock in toluene at room temperature with a polymer volume fraction

This scaling law was compared with the results of self-consistent field theory by van der Linden and Leermakers (1992) they found that the profiles did follow a power law over the central region. In the limit of vanishing bulk volume fraction and infinitely long chains the power law exponent did indeed tend towards 2 as predicted by equation (5.2.38), but the corrections for finite relative molecular mass and bulk volume fractions are considerable. For calculations on a cubic lattice they found that the power law exponent a could be represented by... 

Cyclic polymers are unable to form tails and hence the conformational energy change on adsorption is less for the cyclic polymer at low relative molecular masses when the surface concentration is small. As the relative molecular mass increases, cyclics form larger loops that reduce the entropy change on adsorption whereas in the linear polymer the contribution of the tails to the entropy change becomes diluted at higher relative molecular masses. Figure 5.17 shows the volume fraction profiles calculated from self-consistent field theory, with the separate contributions from loops and tails. 

Figure 5.17. The volume fraction profile of a linear adsorbed polymer calculated from self-consistent field theory, with the separate contributions from loops and tails. Adapted from Fleer et al. (1993).

Figure 6.9. Volume fraction profiles of an end-grafted polystyrene brush, of relative molecular mass 105 000, imder various solvent conditions (O, toluene at 21 C and cyclohexane at A, 53.4 °C , 31.5 °C o, 21.4 °C and A, 14.6 "C), deduced from neutron reflectivity measurements (all the solvents are deuterated). Toluene at 21 °C is a good solvent and the solid line is the classical parabolic profile. The theta temperature for d-cyclohexane is 34 °C and the dashed line is the elliptical profile predicted by analytical self-consistent field theory for theta conditions. After Karim et al. (1994).

Figure 8.12. Volume fraction profiles for the PS brush layer of a PDMS-PS block copolymer at the air/ethyl benzoate interface. The dashed line is the best fit to neutron reflectometry data. The solid line is the volume fraction profile predicted by the self-consistent field theory of Baranowski and Whitmore (1995). After Kent et al. (1995).

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