Calculating Chemical Cross-Link Density Effects on Trapped Shear Modulus
Trapped shear modulus rises linearly with chemical cross-link density while interstitial woven constraint scales effective shear stiffness by factor 1.4 to 2.2.
Flory Rehner Equation
Equilibrium Formula
Thermodynamic relationships describe the interaction between a cross-linked polymer and a solvent during the swelling process. The flory rehner equation relates the volume fraction of the polymer in a swollen state to the density of the network. This calculation allows a lab to determine the effectiveness of a finish on linen cloth by measuring how much fluid the resin absorbs.
Mathematical Application
Testing procedures involve immersing a sample of the cured resin in a specific solvent until the weight becomes constant. Once the equilibrium is reached, the flory rehner equation converts the observed volume change into a value representing the cross-link density. This method provides a more accurate assessment than simple mechanical stretching for highly delicate coatings.
Mill quality control teams use the resulting data to adjust the catalyst levels in the finishing bath. Results help in identifying whether a batch of treated flax has been under-cured or over-cured. Consistency in these readings ensures that every yard of fabric responds identically to moisture.
Input Requirement
Accuracy depends on the precise determination of the interaction parameter between the polymer and the liquid. Slight errors in the initial dry weight of the sample will propagate through the entire calculation.