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Unique Dynamic Correlation Length in Supercooled Liquids

We present a direct comparison of the number of dynamically correlated molecules in the shear-mechanical and dielectric relaxations of the following seven supercooled organic liquids: triphenylethylene, tetramethyl-tetraphenyl-trisiloxane, polyphenyl ether, perhydrosqualene, polybutadiene, decahydroisoquinoline, and tripropylene glycol. For each liquid we observe that the numbers of dynamically correlated molecules in the shear and in the dielectric relaxation are proportional. We show that this proportionality can be explained by the constancy of the decoupling index of the shear and dielectric relaxation times in conjunction with time-temperature superposition. Moreover the value of this proportionality constant is related to the difference in stretching of the shear and dielectric response functions. The most significant deviations from unity of this constant are found in a liquid with strong hydrogen bonds and in a polymer.