Yeah, bakelite is just a resin, and not a great one as pure material, strong yes but I mean in terms of engineering properties... probably it's too brittle, too much shrinkage on casting, stuff like that? AFAIK it's never used that way so you'd have a hard time looking up the raw properties (but maybe it's out there and I'm just being a silly not looking for it right here and now), but with fillers, much as with many other resins, it improves in strength, flexibility, appearance, etc.
Being an aromatic/carbohydrate condensation polymer, it bonds well (even if not directly crosslinked) with natural materials like lignin and cellulose, hence basically sawdust, chopped fiber, linen, paper, etc. being common ingredients. I suppose in a sense, it acts like a super-lignin (lignin is also an aromatic polymer). It also holds mineral components well, so powdered and flaked fillers (silica, mica, whatever), fiberglass (chopped or sheet) are also handy.
As for conductivity -- as with metals' correlation between electrical and thermal conductivity, so too thermal conductivity and strength correlate. At least, to a gross level; and for similar reasons. Namely, strong chemical (or ionic) bonds -- high binding energy -- necessitate strongly coupled phonon waves (i.e., thermal motion). At the peak, you have extremely densely connected materials, like diamond; in the middle, you have the majority of crystalline elements and simple compounds: metals, oxide ceramics, etc.; and at the low end, loosely connected materials, like linear chain polymers (with weak e.g. Van der Waals forces between chains), thru-plane graphite or mica, and composites.
(And yes, mica is a poor (thru-plane) conductor; it's a better electrical insulator than thermal, hence its use for isolation (at least historically, but I mean it's certainly still available, and a must-have for high temperature insulation). Same goes for polyimide: it's a terrible conductor, but its high dielectric strength makes a thin layer usable. Indeed, comparing an organic polymer to an inorganic crystal should seem peculiar, but they are actually pretty comparable in these properties.)
You can always reduce the conductivity of a given material, by using less cross-section, or more length; but reducing cross-section reduces strength proportionally, and increasing length obviously has mechanical restrictions (you can't fit an arbitrary length into any application). This is true whether it's a of a solid plate vs. bar geometry, or a fibrous or composite bar, rope, foam, etc. Asbestos is basically fiberglass in crystalline form, not an especially poor conductor in bulk, but once fried apart into fibers, the trapped air and weak contact between fibers makes it a particularly effective insulator.
So, you might consider something like wood, which is really quite a capable material in terms of strength as an engineering material, and pretty low conductivity. But keep in mind, ballpark 5ksi isn't terribly strong as things go -- even your basic mild steel starts around 30ksi and they go up from there; even compared to solder, there are stronger tin alloys (at least give or take creep strength, which wood does better at), despite having a melting point lower than cellulose's, and there are heavier (but also more thermally conductive) materials, of comparable strength, like concrete (though that only in compression).
But most importantly, wood is an organic foam. Basically, if you compacted the cellulose-lignin composite to remove its porosity, obtaining a fully densified product (or give or take removing the lignin, or perhaps even crosslinking it further?), you'd end up with something -- oh, about as strong as low-alloy aluminum, I suppose, and much more conductive than plain wood (perhaps even more conductive than concrete? Or maybe just on par, I'm not sure offhand -- is there a figure for pure solid cellulose conductivity..? Which is kind of an imaginary material, but, there are ways to process wood to delignify and consolidate it, and such products might be the place to check for these properties?). In any case, clearly it will be more conductive, a testament to the strong ether chain bonds and hydrogen inter-chain bonds holding cellulose together. Maybe one or the other extreme (fully densified, or natural foam) is a suitable compromise for a given application, but never forget, it's weaker in both (strength and conductivity) because of structure, not an intrinsic material property.
An atomic/molecular bonding theory, like this, still leaves some room for certain materials to have more strength at less conductivity, or vice versa; but only within some bounds, I think.
Another figure to keep in mind: the stiffness, elastic modulus. Even on a nanoscopic scale, we might have simple crystals -- FCC, BCC, hexagonal, etc. -- which are highly connected and thus high strength, high modulus, and high (thermal) conductivity; or we might have complex crystals with poorly-connected chains, or spirals winding through them, or completely amorphous; more generally, materials having lower symmetry, and thus a lower upper-limit on connectivity. As a result, they will be softer -- lower modulus. A complex crystal, with lots of "free space" (relatively large and numerous vacancies, I suppose), could have more Van der Waals than covalent or ionic character bonding it together, and thus the strength or modulus is lower than would otherwise be suggested by the raw bonding energy of the material.
You can also have an apparent solid, but it's very stretchy indeed. Consider rubber, a network of side chains cross-linked together into a macromolecule. The side chains slide easily over one another, mostly filling space between the strongly-connected backbone, which has a chaotic path through the material. When stretched out, the backbone also straightens out -- perhaps in the fully-stretched state, the thermal conductivity goes up? But since it's also much longer (elongation >100% is common among rubber materials), it's not like the end-to-end conductivity will be higher (it'll be lower anyway due to the reduction in cross-section, and dominance of the side-chains acting like a liquid filler to a nanoscopic mesh).
And, note that I said "strongly coupled phonon waves" very carefully; we're not after the "number" of waves, or their energy per se; the energy band structure does matter, but the energy and density of states jointly dictate heat capacity (i.e., how many states are available to soak up that heat energy). Conductivity is about how easily those waves propagate across the material, which does depend on density of states, but also on boundary conditions, anisotropy and so on. Refraction and reflection at the boundary matters; these are (very small) sound waves, after all. A heterogeneous, granular material has lower conductivity because there's more boundaries, scattering waves around rather than letting them propagate freely. A granular substance like thermal grease, I mean, it's better than the liquid (oil) base itself, sure; again, Van der Waals forces are in play there, so it's not hard to improve -- but it's a far fraction of the conductivity of the filler it's based on. Put another way: as we go from 0% oil and 100% filler, to 100% oil and 0% filler, the curve rises gradually from the 100% oil side (as the path length through the poor conductor decreases; or if we're allowing convection in the fluid, it'll even drop as the material gels, blocking convection); but as we go from say 100% to 99% filler, the fact that at 100% the filler is a pure solid and at 99% it's completely fractured up, makes a much steeper difference. At practical mixtures (say 20/80%?), the performance is pretty middling, even for high-K fillers (ZnO is a common choice, ballpark 50 W/(m K) in bulk, but a typical thermal paste is just a few W/(m K)). But it's still wildly better than an air-filled space (air and solid material have a wide mismatch in acoustic properties, besides the air itself having low density and thus particularly poor propagation), let alone an effective vacuum (~10nm gaps are shorter than the MFP in air, but still not close enough for phonons to tunnel across the gap).
(Also, nonpolar liquids are really the extreme case, aren't they? Zero static tensile or compressive strength (unless confined hydraulically), but still some finite conductivity, even when convection is constrained, e.g. a liquid soaked into a foam or fiber product. The lower limit on strength is therefore zero. Though there is still a compressive modulus, which with the density, gives a speed of sound, so we might consider modulus the more fundamental or interesting property to compare.)
It's no accident that diamond has such high strength, modulus, thermal conductivity, and anomalously low heat capacity: the high-energy bonds restricts thermal motion into modes of comparably high energy, thus the number of states accessible at room temperature is small, and the heat capacity is small. (Compare bonds of some eV strength, to average 10s meV energy at room temperature.)
Tim
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