Gelation Time of Network-Forming Polymer Solutions with Reversible Cross-Link Junctions of Variable Multiplicity

Area of Science:

• Polymer Chemistry
• Physical Chemistry
• Materials Science

Background:

• Understanding gelation dynamics is crucial for controlling material properties.
• Existing models often simplify the complex kinetics of cross-linking reactions.

Purpose of the Study:

• To theoretically calculate the gelation time (tg) for solutions of functional (associating) molecules.
• To establish a relationship between macroscopic gelation behavior and microscopic reaction parameters.

Main Methods:

• Kinetic equation for stepwise cross-linking reactions.
• Decomposition of gelation time into relaxation time (tR) and a thermodynamic factor (Q).
• Analysis of scaled concentration (x) and its relation to the association constant (λ(T)).

Main Results:

• Gelation time (tg) is a product of relaxation time (tR) and thermodynamic factor (Q), both dependent on scaled concentration (x).
• The superposition principle holds with λ(T) as a concentration shift factor.
• Gelation time follows a power law in the high concentration region, with the exponent related to cross-link multiplicity (k).
• Retardation effects due to cross-linking reversibility were calculated, aiding in gel processing optimization.

Conclusions:

• Microscopic parameters of cross-linking reactions can be estimated from macroscopic gelation time measurements.
• The thermodynamic factor (Q) exhibits a singularity at the equilibrium gel point, while relaxation time (tR) remains continuous.
• The study provides a framework for understanding and controlling gelation in systems with reversible cross-linking, applicable to materials like hydrophobically-modified water-soluble polymers.