We present Atacama Large Millimetre Array (ALMA) 2mm continuum observations of a complete and unbiased sample of 99 870micron-selected sub-millimeter galaxies (SMGs) in the Extended Chandra Deep Field South (ALESS). Our observations of each SMG reach average sensitivities of 53 microJy/beam. We measure the flux densities for 70 sources, for which we obtain a typical 870micron-to-2mm flux ratio of 14 +/- 5. We do not find a redshift dependence of this flux ratio, which would be expected if the dust emission properties of our SMGs were the same at all redshifts. By combining our ALMA measurements with existing Herschel/SPIRE observations, we construct a (biased) subset of 27 galaxies for which the cool dust emission is sufficiently well sampled to obtain precise constraints on their dust properties using simple isothermal models. Thanks to our new 2mm observations, the dust emissivity index is well-constrained and robust against different dust opacity assumptions. The median dust emissivity index of our SMGs is $betasimeq1.9pm0.4$, consistent with the emissivity index of dust in the Milky Way and other local and high-redshift galaxies, as well as classical dust grain model predictions. We also find a negative correlation between the dust temperature and $beta$, similar to low-redshift observational and theoretical studies. Our results indicate that $betasimeq2$ in high-redshift dusty star-forming galaxies, implying little evolution in dust grain properties between our SMGs and local dusty galaxy samples, and suggesting these high-mass and high-metallicity galaxies have dust reservoirs driven by grain growth in their ISM.
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