WLF Polymer Shift Factor Calculator

Time-Temperature Superposition (TTS): Calculate decimal shift factor ($\log a_T$), shifted relaxation time, and free-volume dynamics above $T_g$.

Reference Temp $T_{ref}$ or $T_g$ (°C):

Target Temp $T$ (°C):

Constant $C_1$:

Constant $C_2$ (°C):

Reference Relaxation Time $\lambda_{ref}$ (s):

Shift Factor ($\log_{10} a_T$)

Linear a_T: --

Shifted Relaxation ($\lambda$)

-- s

Rate Acceleration: -- x

Temperature Difference ($T - T_{ref}$)

-- °C

WLF valid range: Tg to Tg+100°C

Fractional Free Volume ($f$)

-- %

Universal fg ~ 2.5% at Tg

WLF Equation:

• $\log_{10}(a_T) = \frac{-C_1 (T - T_{ref})}{C_2 + (T - T_{ref})}$. Universal constants: $C_1^g = 17.44, C_2^g = 51.6^\circ\text{C}$.

• Higher temperatures expand polymer free volume, shifting molecular relaxation processes to exponentially faster timescales.

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