introduction to thermal conductivity and noise management
=materials =physics =explanation =audio
basics
Most people
understand, to some extent, the principle of Fourier's law - that heat
transfer is proportional to temperature difference. Most people reading this
probably also understand triple-glazed windows, fiberglass insulation, and
vacuum flasks, but:
When a window with 2 panes of glass has an extra
layer added in the middle, the gas inside the window is divided into 2
regions. Each region of gas has about the same friction, but each has half
the thermal gradient driving gas circulation, so gas circulation speed
decreases, reducing thermal conductivity.
When insulation is made of
fine fibers instead of large fibers, the effect is the same as adding layers
to windows: gas regions become smaller, and circulation becomes slower
because thermal gradients are smaller relative to friction of gas flow.
By removing all the gas, heat transfer from circulation can be
eliminated, but radiative heat transfer still happens, so the inside of
vacuum flasks should be reflective. Adding more layers of reflectors further
reduces heat transfer, and
that approach
is used in high-performance insulation for some spacecraft and cryogenic
devices.
complications
Different
materials have widely varying thermal conductivity. One popular conception
of thermal conductivity is that:
"liquids and plastics have low thermal conductivity because they mostly have weak hydrogen bonds, while solids with covalent or metallic bonding have stronger interactions and thus higher thermal conductivity"
However, if we look at a list of material thermal conductivities, that explanation doesn't hold up very well:
- Across
crystals having the same categories of bonds (metallic, covalent, etc),
thermal conductivity can vary widely. For example, copper has ~50x the
thermal conductivity of bismuth, and aluminum nitride has ~11x that of
aluminum oxide.
- With the exact same bonds in a different structure,
thermal conductivity can vary widely. For example, ice has ~3.5x the thermal
conductivity of water, and HDPE plastic has ~2x the thermal conductivity of
LDPE.
- With the exact same material at a different temperature, thermal
conductivity can very greatly. Notably, ultra-pure aluminum reaches a peak
of ~10^5 W/mK at ~3 K, ~400x its normal value.
To understand those facts, we must consider phonons.
phonon scattering
High-purity aluminum at low
temperatures also has low electrical resistance, because electrons in it can
travel ballistically across macroscopic distances. At higher temperatures,
vibrating aluminum atoms collide with those traveling electrons, greatly
increasing resistance.
In cold aluminum, heat is mostly conducted by
electrons, but it can also be conducted by atomic vibrations. Some patterns
of vibrations, called phonons, can travel continuously through a crystal.
Like electrons moving through aluminum, the travel of those phonons can be
disrupted by random vibrations and by irregularities in a crystal structure,
decreasing the distance they travel and thus thermal conductivity.
Electrical resistance and thermal conductivity can both be considered
analogous to optical transparency. Even a small amount of additives can make
glass go from mostly-transparent to mostly-opaque. As for thermal
conductivity, in diamond, even 3 ppm nitrogen impurity
noticeably affects it.
Because of phonon scattering, thermal
conductivity can decrease with temperature, but it can also increase with
temperature, because at higher temperature, more vibrational modes are
possible. So, crystals have some temperature at which their thermal
conductivity peaks.
With this understanding, we'd expect amorphous
materials to have low thermal conductivity, even if they have a 3d network
of strong covalent bonds. And indeed, typical window glass has a relatively
low thermal conductivity, ~1/30th that of aluminum oxide, and only ~2x that
of HDPE plastic.
noise management
Thermal phonon transmission
is also analogous to sound transmission, and choosing things to block or
absord sound is probably more relevant to most people than designing
materials for thermal conductivity. To block sound, we want something
amorphous or with lots of defects on the scale of sound wavelengths.
Considering human hearing sensitivity, 3cm to 2m wavelengths are relevant,
and especially 9cm. So, we'd expect that adding lots of objects 1-10 inches
wide to a room would reduce sound transmission significantly.
As far
as practical implications, well, that implies that planting trees around
freeways would be an effective way to block noise despite their low density.
I'm sure that using trees to block sound is something nobody has ever
thought of.
How about reducing noise levels in busy restaurants?
That's different from reducing average transmission distance.
What you want to absorb sound is materials with low density on their surface
on a sound wavelength scale, so they don't reflect sound.
What would
be something with appropriate scale and density, that's cheap and not too
bad aesthetically? Nets of thin cord seem reasonable given those criteria,
but another criteria is sufficient coupling to air
movement; enough of the surface area needs to be covered. So, typical good
materials for sound absorption are fine fibers and foam. Acoustic panels
often have spikes on the scale of wavelengths to provide a
density/reflectivity gradient, instead of a single continuous surface that
reflects sound;
anechoic chambers for radar testing use the same principle.
In
that case, "nets" of ~0.02mm thick film with ~9cm spacing would be
reasonable, but it's easier to take thin plastic sheet and cut holes in it.
And indeed, perforated plastic sheets are sometimes sold for sound-proofing,
but they're used as facing for objects (perforated polymer film acoustic
facing) because they're not self-supporting.
But what's something
that could be done cheaply with commonly-available materials? Here's my
proposal:
- Hang up a
net with perhaps 6" spacing.
- Get some plastic shopping bags with thin
plastic.
- Attach the plastic bags to the net intersection points,
perhaps by tying 1 handle with string or by poking a paperclip through the
bottom of the bag. Attach bags to about half the net intersections. It's
better for the bags to be somewhat crumpled, and upside-down ones would
probably work a bit better.
- For better aesthetics, you can get multiple
bag colors and arrange them in a pattern.
It's hard to do something much cheaper than that. As for the aesthetics, well, no comment.
polymer design
This post is
brought to you by me designing novel high-thermal-conductivity polymers for
axial-flux electric motors.
If you're trying to engineer a plastic
for higher thermal conductivity, an obvious approach is adding some filler
with high aspect ratio, such as carbon nanotubes or graphene nanoplatelets,
or perhaps something cheaper like talc, or a compromise like hexagonal boron
nitride. On a larger scale, carbon fiber also has quite high thermal
conductivity. But of course, the matrix properties are still important.
If you look up papers on epoxy resins with higher thermal conductivity,
you can find people trying to add side-chain liquid crystal polymers to
epoxy monomers, but of course, resin monomers have to flow well and
cross-linking tends to disrupt liquid crystal structures. Well, it's just
polymer physical chemistry; you just visualize the dipole moments and
hydrogen bonding and crystallization and crystal properties.