Energy transfer speed of polymer network and its scaling-law of elastic modulus-New insights

The elastic modulus E of a solvent-absorbable polymer network and its polymer-fraction φ (or, conversely, water content) obey a scale-law E ∼ φ ν. In particular, for a polymer network paired with a good solvent, ν = 2.3. We now provide a fresh look at this problem from the perspective of energy transfer speed defined for a complex fractal network. Two core algorithms are designed, showing that the elastic modulus actually stands for the ability to transfer energy within a certain matter. Our algorithms can directly give the scaling exponent of ν = 2.3. It is much easier to understand the scaling law E ∼ φ ν from the perspective of energy transfer speed.