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tokens: L183 (L134N), Taurus, and IC 5146). In the discussion that follows, we must recognize that the observed (i.e. line of sight) extinction to a source is not necessarily the same as the ‘local’ extinction, that is, to say the extinction of the source relative to the interstellar radiation field, so there will always be some uncertainty/natural scatter in the values of A th . However, the near-universality of these dependencies implies that the relevant processes must be largely independent of the dust properties; such as the size distribution and the dust grain morphology and porosity, etc. In the following section, we describe the nature of interstellar ices and the criterion for ice mantle growth. In Section 3 , we describe the various microscopic mechanisms that determine A th , and in Section 4 we compare the relative importances of these processes. Section 5 describes our chemical model, and the results are presented in Section 6 . Possible alternative causes of the A th phenomenon are discussed in Section 7 . Our conclusions and discussion are presented in Section 8 . 2 THE REQUIREMENT FOR ICE MANTLE GROWTH Interstellar ices are predominantly composed of H 2 O, CO, and CO 2 , with CO and CO 2 having abundances of ∼27–32 per cent and ∼19 per cent, respectively, relative to H 2 O in Taurus and low-mass young stellar objects (YSOs) (Chiar et al. 2011 , table 4). CO, being more volatile, is typically less abundant in high mass YSOs. Other species (such as CH 3 OH, NH 3 , OCN − , and other organics/COMs) typically account for ≲10 per cent of the ice. The relative abundances of the major ice components are fairly similar in different environments, although real differences exist and there are often significant variations in the abundances of the complex organics. Whilst there is evidence for significant source to source variations in the relative abundances of H 2 O, CO, and CO 2 , the total contribution of O-bearing ice molecules to the oxygen budget follows similar trends in different souces (e.g. Whittet et al. 2009 ). The chemistry of the main components is straightforward; CO ice is believed to be formed (primarily) due to the freeze-out of CO from the gas phase. By contrast, H 2 O and CO 2 are probably formed by surface reactions. At least four distinct H 2 O formation mechanisms are possible (van Dishoeck et al. 2013 ), but in the relatively low density/high hydrogen atom abundance environments that we are considering in this study, the main channel is simple hydrogenation: The latter reaction being in competition with As gas-phase chemistry is not believed to be important, this means that the formation rate of H 2 O ice is mainly determined by the rate at which oxygen atoms stick to grains and are subsequently hydrogenated to H 2 O molecules. If these are the only relevant reactions, then it also follows that the abundances of H 2 O and CO 2 ice should be approximately correlated, which is indeed seen to be the case (e.g. Noble et al.