We investigate theoretically charge regulation of weakly dissociating polyacids by potentiometric titration of their aqueous solutions. By treating deprotonation and cation binding to the polyacids as reversible reactions in our model, the ionization constant of acid groups along the polyacid chain is adjusted from its intrinsic value by electrostatic correlations. If electrostatic correlations are modeled with a Debye-Hückel electrostatic free energy that ignores the connectivity of acid groups, the theory follows Henderson-Hasselbalch behavior for monoacids at low polyacid concentrations, and does not capture the shift of the ionization constant from its intrinsic value with increasing pH. Using a random phase approximation (RPA) that captures the chain connectivity, the shift of the ionization constant is predicted, which is found to directly originate from the electrostatic repulsions along the polyacid chain. We make predictions for titration of rodlike and Gaussian coil polyacids, and find that the former is followed by hydrophilic poly(acrylic acid), while the latter is followed more closely by hydrophobic poly(acrylamido-2-methyl-1-propanesulfonic acid). The results suggest that development of more advanced free energy models that allow chain configurations to self-adjust with changing pH and chain hydrophobicity could provide accurate a priori modeling of charge regulation of polyacids.

我们研究了通过电位滴定水溶液对弱解离多元酸的电荷调节理论。通过在我们的模型中将去质子化和与多元酸结合的阳离子视为可逆反应，沿着多元酸链的酸基团的电离常数通过静电相关从其内在价值进行调整。如果使用Debye-Hückel静电自由能建模静电相关性，而忽略了酸基团的连通性，则该理论遵循低多元酸浓度下单酸的Henderson-Hasselbalch行为，并且无法捕获电离常数与其内在值的偏移增加pH值。使用捕获链连接性的随机相位近似（RPA），可以预测电离常数的变化，它被发现直接来自沿多元酸链的静电排斥。我们对棒状和高斯线圈多元酸的滴定进行了预测，发现前者紧随其后的是亲水性聚丙烯酸，而后者紧随其后的是疏水性聚丙烯酸丙烯酰胺基-2-甲基-1-丙烷磺酸。结果表明，开发更高级的自由能模型，该模型允许链结构随pH值和链疏水性的变化而进行自我调整，可以为多元酸的电荷调节提供准确的先验模型。后者紧随其后的是疏水性聚（丙烯酰胺基-2-甲基-1-丙烷磺酸）。结果表明，开发更高级的自由能模型，该模型允许链结构随pH值和链疏水性的变化而进行自我调节，可以为多元酸的电荷调节提供准确的先验模型。后者紧随其后的是疏水性聚（丙烯酰胺基-2-甲基-1-丙烷磺酸）。结果表明，开发更高级的自由能模型，该模型允许链结构随pH值和链疏水性的变化而进行自我调整，可以为多元酸的电荷调节提供准确的先验模型。