Practical Rheology: G-Values G', G'' and tan

Introduction

• Understanding G' and G'' is crucial in formulation science.
• Often considered difficult but simplified with modern apps.
• Elastic response: sample closely follows oscillating force.
• Plastic response: sample lags behind oscillating force.

G-Values Explained

• G' (Storage Modulus): Measures the elastic component of a material.
• G'' (Loss Modulus): Measures the plastic or viscous component.
• tan (Tangent): Ratio of G''/G'. Indicates the nature of the material:
  • tan < 1: Material is more elastic.
  • tan > 1: Material is more plastic.

Theoretical Background

• A sample is placed between two discs; stress is applied in a sinusoidal motion.
• Pure Elastic Solid: Returns to original position upon stress release.
• Pure Liquid: Does not return to original state upon stress release.
• Real-world materials: Mixture of elastic and plastic properties.

Measurement and Analysis

• Modulus (G):* Calculated as Maximum_Stress/Maximum_Strain.
• Phase angle difference between stress and strain provides insights into elastic vs. plastic nature.
• G* can be split into G' and G'', with tan as a useful comparative metric.

Practical Measurements

• Virtual experiments derive values of G*, G', G'', and tan.
• Choice of measurement equipment: Rheometer or DMA (Dynamic Mechanical Analyzer).*

Importance of Frequency and Temperature

• Measurements depend heavily on frequency and temperature.
• Deborah Number (De): Ratio of system's relaxation time to measurement timescale.
  • De < 1: G'' dominates, material is plastic.
  • De > 1: G' dominates, material is elastic.
• Critical to ask for frequency and temperature conditions when analyzing G' and G'' data.
• Time-temperature superposition principle applies.

Conclusion

• Understanding G', G'', and tan is essential for interpreting material properties.
• Always consider frequency and temperature in rheological measurements.
• Use available apps to simplify and visualize these complex concepts.