Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea.
Department of Physics, Pusan National University, Busan 46241, Korea.
Sci Rep. 2017 Sep 5;7(1):10551. doi: 10.1038/s41598-017-09974-9.
Counterion condensation onto a charged cylinder, known as the Manning transition, has received a great deal of attention since it is essential to understand the properties of polyelectrolytes in ionic solutions. However, the current understanding is still far from complete and poses a puzzling question: While the strong-coupling theory valid at large ionic correlations suggests a discontinuous nature of the counterion condensation, the mean-field theory always predicts a continuous transition at the same critical point. This naturally leads to a question how one can reconcile the mean-field theory with the strong-coupling prediction. Here, we study the counterion condensation transition on a charged cylinder via Monte Carlo simulations. Varying the cylinder radius systematically in relation to the system size, we find that in addition to the Manning transition, there exists a novel transition where all counterions are bound to the cylinder and the heat capacity shows a drop at a finite Manning parameter. A finite-size scaling analysis is carried out to confirm the criticality of the complete condensation transition, yielding the same critical exponents with the Manning transition. We show that the existence of the complete condensation is essential to explain how the condensation nature alters from continuous to discontinuous transition.
抗衡离子在带电圆柱上的凝聚，即 Manning 转变，自其对理解离子溶液中聚电解质的性质至关重要以来，已经引起了广泛关注。然而，目前的理解仍然远远不够完整，并提出了一个令人困惑的问题：虽然在大离子相关性下有效的强耦合理论表明抗衡离子凝聚具有不连续性，但平均场理论总是在相同的临界点预测连续转变。这自然导致了一个问题，即如何将平均场理论与强耦合预测协调起来。在这里，我们通过蒙特卡罗模拟研究了带电圆柱上的抗衡离子凝聚转变。通过系统地改变圆柱半径与系统大小的关系，我们发现除了 Manning 转变之外，还存在一种新的转变，其中所有抗衡离子都被束缚在圆柱上，并且热容在有限的 Manning 参数下下降。我们进行了有限尺寸标度分析以确认完全凝聚转变的临界点，得到与 Manning 转变相同的临界指数。我们表明，完全凝聚的存在对于解释凝聚性质如何从连续转变为不连续转变至关重要。
