Supersingular mass distributions in gelling systems

Area of Science:

• Physics
• Physical Chemistry
• Materials Science

Background:

• Disperse systems undergoing rapid binary coagulation can form gels in finite time.
• A diverging integral at low particle masses complicates traditional analysis of particle mass spectra before gelation.
• Existing models struggle to define total particle mass concentration due to this divergence.

Purpose of the Study:

• To investigate the time evolution of disperse systems leading to gelation.
• To address the challenge of defining total particle mass concentration in pregelation stages.
• To formulate new equations for universality mass spectra and analyze postcritical behavior.

Main Methods:

• Introducing the second moment of the particle mass spectrum as a scaling parameter.
• Formulating equations for universality mass spectra.
• Analyzing the asymptotic behavior of particle mass spectra for systems with a product kernel.
• Investigating postcritical dynamics.

Main Results:

• A novel approach using the second moment successfully defines pregelation mass spectra.
• The derived equations accurately reproduce the asymptotic form of particle mass spectra for product kernel systems.
• Time dependencies for gel mass, second moment, and particle number concentrations in the postcritical period were determined.

Conclusions:

• The second moment scaling provides a robust method to analyze gelation dynamics.
• The study offers a new framework for understanding universality in particle mass spectra.
• The findings contribute to the understanding of phase transitions in colloidal and polymeric systems.