Equilibrium size distribution and phase separation of multivalent, molecular assemblies in dilute solution

Area of Science:

• Physical Chemistry
• Materials Science
• Chemical Physics

Background:

• Multivalent molecules possess specific interaction sites enabling binding with multiple neighbors.
• Understanding self-assembly and phase separation is crucial for designing advanced materials and predicting solution behavior.

Purpose of the Study:

• To theoretically investigate the self-assembly and phase separation of multivalent molecules in dilute solutions.
• To differentiate the equilibrium size distributions of linear versus branched molecular assemblies.
• To analyze the conditions leading to sol-gel transitions and their impact on phase separation critical points.

Main Methods:

• Theoretical investigation of molecular self-assembly.
• Analysis of equilibrium size distributions for linear and branched assemblies.
• Application of effective Flory-Huggins theory to describe phase separation.

Main Results:

• Linear assemblies exhibit exponential decay in size distribution, while branched assemblies follow a power law with an exponential cutoff.
• Finite, branched assemblies can be unstable, leading to a sol-gel transition at a critical concentration.
• Non-specific interactions drive phase separation, with critical points dependent on assembly size distributions.

Conclusions:

• The structural differences between linear and branched multivalent assemblies significantly influence their self-assembly dynamics and size distributions.
• Sol-gel transitions are a key feature of unstable branched assemblies, affecting macroscopic properties.
• The phase separation behavior in dilute solutions is effectively modeled by Flory-Huggins theory, highlighting the importance of molecular architecture.