# What determines heat conductivity of a solid electric insulator?

Andrew Hamilton
Science 13 Apr '09 12:41
1. 13 Apr '09 12:41
I have been trying to understand what determines the heat conductivity of solid pure substances (i.e. NOT composites) that have no air gaps and is an electric insulator. For example, why is the heat conductivity for nylon so much less than that for diamond? -there is bound to be some difference but I don’t understand why it is such a BIG difference ( AT LEAST a 3600 fold difference!!! -why such a massive difference!!!? ). I tried looking this up on the net but I didn’t get at far as I would have liked:

http://en.wikipedia.org/wiki/Thermal_conductivity

-it says for an electric conductor:
“…freely moving valence electrons transfer not only electric current but also heat energy….”

Ok, I have no problem with that. But I am straining to understand what determines the heat conductivity of an electric insulator (consisting of a pure substance and with no air gaps) such a nylon etc
-it goes on to say:

“…However, the general correlation between electrical and thermal conductance does not hold for other materials, due to the increased importance of phonon carriers for heat in non-metals. …”

So I looked up phonon carriers ( http://en.wikipedia.org/wiki/Phonon ) and found this to be VERY complex and difficult to understand!
-so this is what I want to ask -is there any ‘rules of thumb’ that we can use to estimate the heat conductivity of a electrically-insolating solid pure substance with no air gaps such as nylon etc that doesn’t involve horribly complex mathematic? -I mean, can you get an estimate of the heat conductivity of such a substance just by knowing, for example, what proportion of the chemical bonds are C-C bonds and proportion of the chemical bonds are C-N bonds etc?

I also got this from: http://en.wikipedia.org/wiki/Thermal_conductivity

“….Dense gases such as xenon and dichlorodifluoromethane have low thermal conductivity. An exception, sulfur hexafluoride, a dense gas, has a relatively high thermal conductivity due to its high heat capacity….”

What does its high heat capacity got to do with it? -I mean, why should a high heat capacity make the thermal conductivity higher? -and is this true just for gasses or is this true regardless of whether it is a gas/liquid/solid?

I would greatly appreciate any insight into this as this has long puzzled me.
2. 13 Apr '09 13:13
Yeah, I think phonons are responsible for most heat transfer in insulators, but I don't think there are any such rules of thumb.
3. sven1000
Astrophysicist
14 Apr '09 21:51
High heat capacity molecules can transfer the energy more efficiently through their motions. Relatively small momentum transfers will result in relatively high heat transfer.
4. 15 Apr '09 10:15
Originally posted by sven1000
High heat capacity molecules can transfer the energy more efficiently through their motions. Relatively small momentum transfers will result in relatively high heat transfer.
I am not sure what you mean but do you mean that a molecule with high heat capacity can ‘store’ more heat (through its internal vibrations between the atoms of that molecule) and thus when it collides with a neighbouring molecule (in a gas or liquid phase) it tends to transfers more heat to that other molecule simply because has more heat ‘stored’ within it that CAN be transferred?

And what about a solid crystalline-like structure such as diamond? -I mean, would a higher heat capacity also tend to increase heat conductivity? -if so, then I am having difficulty visualising how that works so I hope someone could give me some insight into that.
5. 15 Apr '09 10:22
Originally posted by KazetNagorra
Yeah, I think phonons are responsible for most heat transfer in insulators, but I don't think there are any such rules of thumb.
damn
6. sven1000
Astrophysicist
16 Apr '09 17:43
Originally posted by Andrew Hamilton
I am not sure what you mean but do you mean that a molecule with high heat capacity can ‘store’ more heat (through its internal vibrations between the atoms of that molecule) and thus when it collides with a neighbouring molecule (in a gas or liquid phase) it tends to transfers more heat to that other molecule simply because has more heat ‘stored’ wi ...[text shortened]... ng difficulty visualising how that works so I hope someone could give me some insight into that.
Yes, that is what I meant.

In a solid structure, the atoms or molecules still vibrate, but they have more of a fixed relationship to their neighboring atoms than they would in a gas. Imagining the carbon atoms in a diamond as balls all connected by springs. If you vibrate one of the atoms, it sets off vibrations in all the neighboring atoms, transmitting its energy through the structure. If you imagine using the same springs, but using more massive balls (analogous to atoms with higher heat capacity, thus able to store more energy) then vibrating one of these massive balls will transmit much more energy through the structure than before, when we used smaller masses.
7. 16 Apr '09 18:063 edits
Originally posted by sven1000
Yes, that is what I meant.

In a solid structure, the atoms or molecules still vibrate, but they have more of a fixed relationship to their neighboring atoms than they would in a gas. Imagining the carbon atoms in a diamond as balls all connected by springs. If you vibrate one of the atoms, it sets off vibrations in all the neighboring atoms, transmit ...[text shortened]... s will transmit much more energy through the structure than before, when we used smaller masses.
Thanks for that ðŸ™‚
-but wouldn’t that mean that you should expect the thermal conductivity of crystal silicon to be greater than that of diamond?

thermal conductivity of silicon crystal = 147-157 W/mK
thermal conductivity of diamond = 900-2320 W/mK (the estimate varies considerably but is definitely higher than silicon crystal)

-I suppose this simplistic model is complicated by those difficult to calculate phonons? ðŸ˜•
8. 16 Apr '09 19:03
Originally posted by Andrew Hamilton
Thanks for that ðŸ™‚
-but wouldn’t that mean that you should expect the thermal conductivity of crystal silicon to be greater than that of diamond?

thermal conductivity of silicon crystal = 147-157 W/mK
thermal conductivity of diamond = 900-2320 W/mK (the estimate varies considerably but is definitely higher than silicon crystal)

-I suppose this simplistic model is complicated by those difficult to calculate phonons? ðŸ˜•
The springs differ, too. ðŸ˜‰
9. 16 Apr '09 19:301 edit
Originally posted by KazetNagorra
The springs differ, too. ðŸ˜‰
-oh, of course, I forgot about that!
The C-C bond is a lot stronger than the Si-Si bond thus I assume the C-C bonds are more efficient at transmitting heat than those of Si-Si.
The “springs” in diamond are stiffer.
10. sasquatch672
Don't Like It Leave
22 Apr '09 02:28
Originally posted by Andrew Hamilton
I have been trying to understand what determines the heat conductivity of solid pure substances (i.e. NOT composites) that have no air gaps and is an electric insulator. For example, why is the heat conductivity for nylon so much less than that for diamond? -there is bound to be some difference but I don’t understand why it is such a BIG difference ( ...[text shortened]... s/liquid/solid?

I would greatly appreciate any insight into this as this has long puzzled me.
There are a few rules of thumb. Molecules with a more highly ordered lattice structure are better conductors. Atoms with more free electrons in their valence shell are better conductors. The opposite is also true. This is your first ten minutes of heat transfer.
11. 22 Apr '09 03:43
Originally posted by sasquatch672
There are a few rules of thumb. Molecules with a more highly ordered lattice structure are better conductors. Atoms with more free electrons in their valence shell are better conductors. The opposite is also true. This is your first ten minutes of heat transfer.
I would suggest a Heat Transfer class or at least a book.

There is no simple formula.