A Phase Fluctuation Theory of Polymer Viscoelasticity
Abstract
Amorphous polymers are modeled as a heterogeneous network of nanoscale cells. A cell is a homogeneous region within the network. Amorphous polymers have time-dependent properties because the phase of the cells is time-dependent. The cells fluctuate between the glass and elastomer phase with a period tau. The values of tau vary from cell to cell over several orders of magnitude, and are a strong function of temperature. Whether a given cell responds as glassy or elastomeric depends on the ratio between its period of phase fluctuation (tau j) and the period of observation (1/f), where f is the test frequency. We express this ratio as (tau j x f), and present equations for modulus and energy loss as functions of ( j x f). If ( j x f) >> 1, the cell will have a glassy modulus. If (tau j x f) << 1, the cell will have an elastomeric modulus. The condition (tau j x f) = 1 has special significance. It occurs at the glass transition temperature of the cell, and is the condition of maximum energy loss. Energy stored during glass phase deformation is lost as heat if the cell fluctuates to the elastomer phase. More specifically, the energy is dissipated as the heat of fusion when the cell fluctuates back to the glass phase. The energy loss is a function of strain rate, because strain rate controls the level of stress in glassy cells between phase fluctuations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 31, 2023
- Accession Number
- AD1216962
Entities
People
- Thomas D. Juska
Organizations
- Pennsylvania State University