Dielectric constant doesn't mean much by itself, unfortunately.
Pure metals have a dielectric constant in the thousands. That doesn't mean you can use them as a capacitor -- the phase of that displacement current is almost perfectly imaginary, which is to say, resistive rather than capacitive current flow.
Polyalcohols tend to have labile protons. More simply, glycerin is chemically "wet": despite not itself being H2O, it can participate in many interactions the way H2O can.
Besides having huge affinity for water, it can also dissolve ionic salts. Offhand, it looks that NaCl is soluble to the tune of 10%wt, so it is an effective ionic solvent.
I don't even know how you dry it -- can you dry it? Concentrated sulfuric acid or P2O5 certainly isn't going to do (dehydration, condensation reactions), and anhydrous salts will simply dissolve in it (ruling out usual suspects like CaCl2).
Not only will you need to ensure it is very dry, but it will need to be free of ions, just as you'd use deionized water for an application like this. The apparatus needs to be extremely clean, for the same reason; even then, ions simply dissolve from everything, everywhere, somehow or another, and the water needs to be cycled fairly often through an ion exchange resin, or replaced with fresh.
The biggest problem though is that alcohols tend to have strong dielectric losses to begin with, and I think glycerin will be one such case. Typically, there is a relaxation time constant in the mere ~kHz, where the k goes from large to small, and while it's dropping off, it's very lossy (tan delta ~ 1).
Here's a study of PVA:
http://www.ufrgs.br/lapol/insulating_characteristics.pdfPVA is alternating CH2s and CHOHs, while glycerin is HOH2C-CHOH-CH2OH (three CHOHs plus two H end caps, no CH2s), and it's also liquid (which means the OH protons are moving around constantly). I would expect PVA to perform better, and clearly it doesn't perform all that well (depending on whatever they're doing there, different temperatures, and heat treatment I think?). I believe water has a similar response?
Likewise, you can infer based on chemistry, what might perform actually well -- if those protons are locked down in bonds instead, say in esters, amides or hydrocarbons -- the dielectric constant will be a lot lower, true, but it will be a lot flatter with respect to frequency, and that's the important part.
PET (a polyester) for example, has a modest k, and reasonable enough losses (and various other features: stability, cost of raw materials, ease of manufacture..) that it's commercially important as a capacitor type already.
Still pretty lossy, enough that you can't use it for, say, resonant power supplies (or radio transmitters, CW Tesla coils, induction heaters..), but it can be okay for pulsed applications when the internal heating isn't enough to burn a hole through the thing. (It may be hard to find caps that are constructed for pulsed application too, though -- heavy metallization, thicker leads, noninductive build.)
Downside of course being... interesting and all, but there aren't any esters in liquid form that are also cheap. Well, except for esters of glycerin, oddly enough -- fats are triglycerides (three fatty acids stuck onto a glycerin backbone). Not much k, they're mostly hydrocarbon -- but it satisfies everything else.
Tim
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