Titration curves exhibit characteristics similar to sigmoid curves, but they are not symmetrical, which limits the accuracy of modeling them with a sigmoid function. The discussion emphasizes that while the sigmoid shape may resemble certain titration curves, particularly for strong monoprotic acids and bases, the actual functional form is more complex and typically involves polynomial equations. The Henderson-Hasselbalch equation can describe parts of the curve, but it does not capture the entire titration process accurately. Additionally, titration curves are not periodic or cyclic, and the mathematical modeling should reflect the specific chemical interactions involved. Overall, the consensus is that using a sigmoid function for titration curves is inadequate, and a more precise polynomial approach is recommended.