I read in an article, (Application of ionic liquids as plasticizers for poly(methyl methacrylate)), that the glass temperature of polymer decrese while incorporating ionic liquids (ILs).
Liquids that can be absorbed by glassy polymers will usually plasticize the material. Glassy polymer chains have cohesive energy density that will keep the immobile below a certain temperature without addditional force. Adding the liquids (solvents) and allowing them to be absorbed by the glassy polymer means you're getting the liquid molecule to break up the polymer-polymer interaction (at least where the liquid is present) - it's very analogous to lubrication. So your (glass) transition temperature of turning into an immobile glassy solid becomes lower. Another note: as the temperature gets lower, polymer density goes up, i.e. the chains get closer to each other, and at some point the polymer-polymer cohesive energy overwhelms any thermal kinetic energy - and that's why you get a glass transition. This also goes for small molecules that are in a supercooled state (i.e. prevented from crystallizing).
Adding liguid ionics (which are non symmetric in nature) to polymers will increase the disorder inside (by breaking inter-molecular forces ... etc as Kaoru said).
Polymers are classified as glasses with higher disorder and and as super-cooled liquids (in continuous motion) that will some time try to reach crystallinity. Adding the liquid ionics will increase disorder and lower transition temperature.
These are great responses so far. Frustration is the common theme. The most common room temperature ionic liquids are composed of a bulky cation with a concentrated charge center, e.g. alkylmethylimidazolium (various lengths of the alkyl chain), and an anion with concentrated charge, e.g. anything as simple as chloride ions and more complicated anions similar to Ntf2. The bulky parts of the cations like to "corrupt" the charge ordering at room temperature by interfering with the interactions between the covalently bonded positive charge center and the smaller anion charge center. But in a plastic this bulky substituent of the cation, which is typically organic in quality, will be the most likely to interact with organic polymers composed predominantly of alkyl chains which form extended lipid-like domains. Imagine a blob of apolar organic material composed of waxy domains. Now visualize what would happen if I inserted into this blob the same apolar chains, but before I insert them I covalently attach a concentrated positive charge and counterbalanced those positive charges with anions free to move around the system (at high enough temperature of course). You end up with apolar domains whose configuration space is now frustrated by repulsion between the independent anion and the cation charge center which is covalently attached to its cation's apolar segment. The result is a disruption of the blobbish conglomeration of those apolar carbon chains all interacting through charge dispersion by the much stronger Coulombic force associated with static charge interaction. Compare 1/r7 with 1/r2 when comparing dispersion to Coulombic forces (note 1/r6 and 1/r are the dominant parts of the energy of interaction in dispersion and Coulombic forces, respectively; to get the forces you must take the negative derivative with respect to r, which is what I've shown above).