Ghosh Souradeep, Kundagrami Arindam
Deparment of Physical Sciences and Centre for Advanced Functional Materials, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, India.
J Chem Phys. 2024 Feb 28;160(8). doi: 10.1063/5.0178233.
We present a theoretical model to study the effect of counterion size on the effective charge, size, and thermodynamic behavior of a single, isolated, and flexible polyelectrolyte (PE) chain. We analyze how altering counterion size modifies the energy and entropy contributions to the system, including the ion-pair free energy, excluded volume interactions, entropy of free and condensed ions, and dipolar attraction among monomer-counterion pairs, which result in competing effects challenging intuitive predictions. The PE self-energy is calculated using the Edwards-Muthukumar Hamiltonian, considering a Gaussian monomer distribution for the PE. The condensed ions are assumed to be confined within a cylindrical volume around the PE backbone. The dipolar and excluded volume interactions are described by the second and third virial coefficients. The assumption of freely rotating dipoles results in a first-order coil-globule transition of the PE chain. A more realistic, weaker dipolar attraction, parameterized in our theory, shifts it to a second-order continuous transition. We calculate the size scaling-exponent of the PE and find exponents according to the relative dominance of the electrostatic, excluded volume, or dipolar effects. We further identify the entropy- and energy-driven regimes of the effective charge and conformation of the PE, highlighting the interplay of free ion entropy and ion-pair energy with varying electrostatic strengths. The crossover strength, dependent on the counterion size, indicates that diminishing sizes favor counterion condensation at the expense of free ion entropy. The predictions of the model are consistent with trends in simulations and generalize the findings of the point-like counterion theories.
我们提出了一个理论模型，用于研究抗衡离子大小对单个、孤立且柔性的聚电解质（PE）链的有效电荷、大小和热力学行为的影响。我们分析了改变抗衡离子大小如何改变系统的能量和熵贡献，包括离子对自由能、排除体积相互作用、自由离子和凝聚离子的熵，以及单体 - 抗衡离子对之间的偶极吸引力，这些导致了相互竞争的效应，对直观预测提出了挑战。使用Edwards - Muthukumar哈密顿量计算PE的自能，其中考虑了PE的高斯单体分布。假设凝聚离子被限制在PE主链周围的圆柱形体积内。偶极和排除体积相互作用由第二和第三维里系数描述。自由旋转偶极的假设导致PE链发生一级的线圈 - 球状体转变。在我们的理论中参数化的更现实、较弱的偶极吸引力将其转变为二级连续转变。我们计算了PE的尺寸标度指数，并根据静电、排除体积或偶极效应的相对主导地位得出指数。我们进一步确定了PE有效电荷和构象的熵驱动和能量驱动机制，突出了自由离子熵和离子对能量在不同静电强度下的相互作用。取决于抗衡离子大小的交叉强度表明，尺寸减小有利于抗衡离子凝聚，但以自由离子熵为代价。该模型的预测与模拟趋势一致，并推广了点状抗衡离子理论的结果。
