ANALYTICAL SELF-CONSISTENT-FIELD MODEL OF WEAK POLYACID BRUSHES

An analytical self-consistent-field theory has been developed for a we ak polyacid brush in which the degree of dissociation is controlled by the external pH of the solution. This theory gives analytical equatio ns for the total brush thickness and for the root-mean-square (rms) th ickness, the polymer profile, the end-point distribution function, and the local degree of dissociation of the brush molecules as a function of pH and the salt concentration. These results are in excellent agre ement with the numerical model of Israels, Leermakers, and Fleer (Macr omolecules 1994, 27, 3249). Simple asymptotic expressions for the rms thickness and the degree of dissociation are also obtained. These appr oximate relations are found to be in good agreement with both the nume rical model and a recent scaling analysis (Zhulina, Birshtein, and Bor isov. Macromolecules 1995, 28, 1491). A pronounced difference between the dependences of the total thickness and rms thickness on the salt c oncentration is found: the total thickness decreases monotonically as a function of the salt concentration, whereas the rms thickness passes through a maximum. This difference is shown to be due to the quite di fferent shape of the profiles in various regimes of the brush behavior . Simplified approximate expressions are obtained for the position and the height of this maximum in the rms thickness.