Aggregation of Polyampholytes : Sequence-Dependent Structure, Thermodynamics, and Kinetics

다국어 초록 (Multilingual Abstract)

Charge sequence plays a central role in the aggregation of polyampholytes （PAs） with nonzero net charge, especially when cohesive interactions and electrostatic repulsion are closely balanced. This thesis investigates sequence-dependent PA aggregation using coarse-grained molecular dynamics simulations and theoretical analyses. Dimerization is first examined as the elementary association process. At fixed net charge, local sequence features such as minority-charge blockiness and block position strongly affect dimer stability, contact organization, and association/dissociation kinetics. This trend is supported by random phase approximation （RPA） analysis, which links dimerization propensity to finite-wavelength microphase instability. Beyond dimerization, different charge sequences lead to distinct aggregatemorphologies, including compact droplets, core–corona micelles, connected micelles, and transient network-like structures. Polyelectrolyte-like terminal blocks promote corona formation and stabilize micelle-type aggregates, whereas shorter or more mixed terminal segments favor droplet-like structures. Charge sequence also controls self-assembly kinetics: micelle-forming sequences exhibit stronger kinetic barriers and history dependence, while droplet-forming sequences allow more active restructuring through unimer exchange, aggregate merging, and bridge-mediated core–core connections. Salt-dependent aggregation is further examined using simulations with explicit mobile ions, supported by RPA analysis. Changes in salt concentration alter the electrostatic screening length, thereby producing sequence-dependent aggregation responses. Blocky sequences show pronounced, weakly non-monotonic aggregation, whereas well-mixed sequences display weaker, nearly monotonic behavior. The RPA analysis connects these trends to salt-dependent shifts of spinodal lines and changes in the characteristic wave vector of microphase instability. These results show that PA aggregation is governed by net charge, sequence blockiness, tail architecture, counterion localization, corona formation, and kinetic barriers. This work provides a unified physical picture of sequence-dependent aggregation in synthetic charged polymers and intrinsically disordered protein-like systems.

목차 (Table of Contents)

• 1 Introduction 1
• 2 Dimerization 5
• 2.1 Model and Simulation Description 10
• 2.1.1 Polyampholyte Model 10
• 2.1.2 Molecular Dynamics Simulations 12
• 2.1.3 Charge Sequence Classification 17
• 2.2 Thermodynamics 19
• 2.2.1 Dimer Formation 19
• 2.2.2 Counterion Regulation and Box Model 23
• 2.2.3 RPA Stability Analysis 28
• 2.2.4 Dimerization Free Energy 36
• 2.2.5 Energy Considerations 43
• 2.3 Kinetics of Dimerization 47
• 2.3.1 Simulation Setup 48
• 2.3.2 Charge Sequence Ensemble 50
• 2.3.3 Dimer Structures and Contact Maps 53
• 2.3.4 Dwell Times and Survival Probabilities 58
• 2.3.5 Fokker–Planck Type Approach 65
• 2.3.6 Dynamic Contact Maps 74
• 2.3.7 Survival Times of Inter-Block Contacts 75
• 2.4 Discussion 87
• 3 Larger Aggregate Formation 91
• 3.1 Model and Simulation Setup 93
• 3.2 Morphologies of Larger Aggregates 95
• 3.2.1 PA Solutions at Various Concentrations 96
• 3.2.2 Charge Regulation and Core Structure 99
• 3.2.3 Tail Statistics of Micelle Coronas 104
• 3.2.4 Aggregate Size Distributions 108
• 3.2.5 Polyelectrolyte-Brush Model of the Corona 113
• 3.2.6 Transient Network of ProTα 121
• 3.3 Self-Assembly Kinetics 125
• 3.3.1 Size Distributions and Grand Potentials 128
• 3.3.2 Time Evolution of Aggregate Sizes 131
• 3.3.3 Switching Maps and Survival Probabilities 134
• 3.3.4 Core–Core Contacts and PA-End Bridging 138
• 3.3.5 Mass Exchange in the Unimer-Depleted Regime 143
• 3.3.6 Fokker–Planck Analysis 151
• 3.3.7 ProTα Network Dynamics 161
• 3.4 Discussion 164
• 4 Salt-Dependent Aggregation 169
• 4.1 Model and Simulation Setup 170
• 4.2 Results and Analysis 174
• 4.2.1 Aggregation near Theta-Solvent Conditions 174
• 4.2.2 Single-Chain and Local Charge Response 177
• 4.2.3 Partial Charge Structure Factors 180
• 4.2.4 Polymeric Charge Structure Factor 186
• 4.2.5 RPA Analysis of Phase Instability 190
• 4.3 Discussion 198
• 5 Conclusion 203
• References 208