Polymer Knot in Solution near the θ Point

We study knot effects on polymer dynamics in aqueous solution by dissipative particle dynamics. A methodology to identify the θ point is developed by combining simulation data and analytical methods. Polymer internal motions are investigated systematically by gradually changing solvent quality from a good to poor case. In a good solvent, the knot length grows with fluctuations (breathing stage) and then moves to chain ends (moving stage) to release. Nearby the θ point from the good solvent side, the breathing effect becomes stronger with a weak moving effect. As a result, it is easy for the knot to release because of strong fluctuations in chain conformation. In a poor solvent, both breathing and moving effects are weak. A knot is confined in the chain and suppresses polymer condensation because of the excluded volume effect. Our results are useful for the interpretation of relevant experiments and industrial applications of polymer knots.