Purification of an impure substance (e.g. DMSO) can be done by a phase transition, but the process of distillation is not the only phase transition purification process. Nor is it necessarily the most safe, considering the hazard Garnet mentioned.
The process of freezing and thawing an impure substance will tend to segregate it from its impurities. DMSO has a freezing point (or melting point) near room temperature. This makes it convenient as well as nontoxic to purify DMSO by a freeze-thaw process, rather than a vaporize-condense process (i.e. distillation) Zonal melting is a type of freeze-thaw process in which a relatively small section of the batch is melted and this narrow molten zone is moved slowly through the batch, which is usually contained in a long and narrow tube. Extremely high levels of purification can be attained this way because the process can be repeated with increasingly successful outcomes. Purification by zonal melting was invented around 1951 by Pfann to purify germanium crystals to make the earliest commercially successful transistors. It soon became a highly successful method of ultra-purifying many other substances, both inorganic and organic. But it doesn't work equally well for all substances or for all impurities in the same substance. So I don't want to raise false hopes that it can remove the stench from DMSO until I find out if others have already done so (such as Gaylord (?)) Matthew
