A molecule that's bonded to other molecules is not as free to move as one that isn't.
Alcohol molecules do bond to water molecules in liquid form, which is why they don't easily separate when boiling or freezing.
However, when freezing, these polar molecules become 'stuck' in a grid, which limits their degrees of freedom (their ability to rotate).
Consequently, the microwave radiation has significantly less effect.
The way you stating this makes me think like "Oh the microwave photons transfer less energy to the polar molecules" but I don't think its that ( I am not sure anyway if you mean this), it is that the polar molecules need more energy (more photons or more energy per photon) to get them moving. And because microwave ovens at the current era are not sophisticated enough to focus more energy in the frozen areas(they would have to have some sort of image analysing to spot the frozen areas and laser beams to focus the energy in the frozen areas), the energy goes randomly inside the oven, so if you try to offer high energy you might defrost the frozen areas but you ll burn the rest of the food, if you don't offer high energy, the frozen doesn't melt good but the rest of the food gets warmed..
Perhaps a simple way of looking at it is that ice (solid water) is somewhat translucent in the microwave frequencies, while liquid water is very opaque. So why are some things opaque (at some particular frequency) while other things are transparent/translucent? That's a big can of worms. Here is my attempt at a simple explanation.
Microwave waves will create torques on the ice molecules causing them to temporarily absorb energy (imagine a molecule to rotate a little bit on a tight spring), but because they are trapped in a restricted structure, they then release that energy coherently with the microwave wave on the rebound. All the other molecules do this too, in unison (mostly). Energy goes in coherently and comes out (mostly) coherently because most of the ice molecules are acting together. (And, for the most part, the motion of the ice molecules in the presence of the microwave energy don't seem to matter if you view it forward or backward in time. More on this later.)
Imagine an array of buoys floating on the water. As a water wave travel's under it, the buoys rise up absorbing some energy (gravitational potential energy), but then they give that energy back coherently (mostly) as they fall on the other side of the wave. In a sense, the buoy array was transparent to the water wave. If you were to film the wave passing under the buoys, and then play it backwards, it would look pretty much identical to a wave traveling in the other direction. If you didn't know any better, you wouldn't be able to tell which way was forward in time and which way was backwards.
On the other hand, if the wave imparts energy in a non-coherent fashion, like a wave crashing on the rocks, it destroys the coherence, and thus the wave. Play that one backwards and its obvious which is forward and which is not. This water crashing onto the rocks is a thermodynamically irreversible process.
Liquid water molecules are free to rotate. That alone wouldn't cause decoherence; but higher-energy, rotating molecules bumping into other molecules certainly would. The chaos involved in spinning molecules bumping into each other, and imparting all sorts of chaotic behavior as a result, is most certainly thermodynamically irreversible. And that kills the coherency of the microwave wave. Thus energy that was once in the form of microwaves is converted into more random thermal energy in the water.
Ignoring reflections, this ratio of coherence to decoherence of a given material to a particular wave is one way to conceptualize transparency.
I should mention that liquids do not need to be polar to absorb microwaves. There are other modes of energy transfer. For example, oil molecules are not polar. But those molecules are long and complicated and they can vibrate in several modes, many of which are at microwave frequencies. Given the complicated nature of these molecules in relationship to nearby oil molecules, and even other atoms in a given molecule, their vibrational modes are rarely coherent with each other. Since the long and twisted oil molecules don't all vibrate in unison, they are bound to absorb the microwave energy in a thermodynamically irreversible process too.
I imagine that it's like this.
Consider a block on the ground.
When we push against it, it starts moving.
That is, we applied work on it, and now it has more energy.
Now consider a block that is stuck somehow.
We push against it, but it cannot move. Therefore we did not apply work and it did not gain energy.
Hmm... I guess we'll have to push real hard so that something breaks before we can actually apply work to it. And then it should get the full energy. ;)
Still, continuing the analogy, if we simultaneously push both loose blocks and stuck blocks, the loose blocks will get all the energy won't they?
Aha! So mixing the water with a couple of drops of oil might have the same effect as mixing it with alcohol?
That sounds as if that won't hit the brick wall of food and tax regulations.
If hope it freezes without fully separating.
(Running to the fridge and putting 3 new glasses in it.)
EDIT: Yep. That seems to be a problem. I can't seem to mix oil and water without it separating again within seconds.
There are Emulsifiers which can help there. Look on the contents labels of many prepared foods (sauces in particular) and the word "Emulsifiers" will be there. It won't be straightforward because they need to be appropriate. They can taste and may separate out during the deep freezing. Looks like you may have suddenly found another vast area of research you need to do.
I find the "ice doesn't heat easily because the molecules can't move as much" theory unconvincing. After all, this isn't too unlike a spring system; even if the spring is more rigid it can still absorb just as much energy. Just because something moves less doesn't mean it contains less energy.
One creeping suspicion I have is that people think ice has just one temperature, whereas an ice cube can be -1C or -100C. They look the same, but the time to melt it will be vastly different.
Oil and water don't mix but a layer of oil (as in under the food container) might create a buffer to disperse the energy better. I think that is the main problem is that the energy is distributed unevenly.
Glass apparently has similar behavior to water in the microwave (transparent at microwave frequencies when solid, opaque when liquid).
Steve Mould has a pretty good video on this -- except for the part where he insists that molecules must be polar to be heated, which isn't always a necessary requirement.
The loss factor (higher for water) and penetration depth (deeper as temperature rises) seem to be the significant variables. Note how they differ between water an ice and how they vary with temperature.
EDIT: One of those references mentioned that the heating mechanism can be explained entirely by Proton exchange between atoms, for both Ice and Water.
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