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14 .                             / R² = 0.979       .

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^Np_s

Figure 6.4: Scaling relation for the average brush height for attractive chains tethered to a
hard wall at different reduced temperatures, (a) < z > vs N_g p_g at T* = 3 (theta solvent),
and (b) < z > vs N_gp_g at T* = 2 (bad solvent), for N_g = 50, 100 and 200 at different
grafting densities. Symbols are the prediction from modified iSAFT and the dashed curves
are linear fit to this data.

Next, the attraction are added between the segments of the polymer brush to
study the effects of decreasing the quality of the (implicit) solvent. The quality of the
solvent is varied by changing the reduced temperature (T* = kT∕e). Reduced theta
temperature, T_g = 3.0, as shown by Grest and Murat [230]. They calculated this
value of the theta temperature by simulating dilute free chains and calculating their
mean square radius of gyration, < Rg >. For a single chain, < Rg >~ N_g where
V = 1/2 for a theta solvent, 0.59 for a good solvent and 1/3 for a poor solvent. Thus
the calculations for T* > Tg corresponds to a good solvent condition, and T*(< Tg)
corresponds to a poor solvent condition.

Figure 6.3a shows the density profile of polymer brushes in different solvent con-

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