Heat is transmitted by thermal conduction, convection, and radiation. The latter is of minor importance unless you consider a building on the moon. An air gap between two apartments certainly helps, but you need to suppress the convection. This is merely partially achieved by insulating materials like styrofoam. A full suppression of convection requires materials with sub-micrometer pores, e.g., silicate aerogels or polymer nanofoams.

The following material may used for insulation of buildings / packings:

1. The effects you describe exist only in very pure substances with a perfect crystal structure. Such can be obtained, for example, by epitaxy, but epitaxial technologies are very expensive. They are not applicable in the construction industry.

2. Epitaxial layers are very thin, so to get an acceptable result, you will need a lot of layers.

For example, let's take a pair of layers of Bismuth/Hydrogen-terminated diamond with a thermal conductivity of 8.5 MW m−2 K−1. Take a wall two bricks thick in winter. The usualy heat flux density is 58 W/m2, and the temperature drop throw the wall is usualy 37 K. Since the heat flux density through all pairs of layers is the same and equal to 58 W/ m2, the temperature difference between the two layers in a pair is 58/8500000 = 0.0000068 K, and the required number of pairs of layers is 37/0.0000068 = 5422414 pcs. It's very expensive. Therefore, it is better to take the advice of colleagues Ulrich Deiters and Kishore Kumar Sriramoju.

Dear V. A. Kapitanov , Thanks for your response- you obviously have a much deeper understanding of heat conduction than I do. But I don't understand why a perfect crystal structure is required in order to have thermal impedance at an interface. Isn't the issue basically the probability that a random phonon would reflect rather than pass through an interface?

I think that one of the alternating layers could be something quite amorphous and soft, such as a plastic. The other layer should be significantly stiffer, perhaps a ceramic. (I suspect that a metal would always be a good heat conductor, because its mobile electrons would do the job).

What am I not understanding? (I am a retired structural engineer, by the way, and I came up with the material mismatch concept by analogy with the way that a building's dynamic response to an earthquake can be limited by getting its natural modes of vibration to have significantly different frequencies compared to the geological foundation layers).

Dear mr. Ronald Ian Miller . Of course you have more experience in building industry, than me. I worked only with metallurgical ovens and a little in semiconductors productions. But your experience in seismic durability relatives to macroscopic vibration processes, here is about of very microscopic vibration processes.

You cited an article from wikipedia, that cited a few articles about very fine experiments with very pure materials with perfect structure.

Maybe i made a mistake in materials, maybe such effect will be in usual dirty materials also.

But i did not make a mistake in numbers. Data in the article, that you cited, give temperature difference between two layers in usual winter conditions 0.0000068 K only.

If you will use any usually materials (steel, wood, plastic) for the layers - you will get very more temperature difference between layers.

It will be 1...10 K because of air gap between layers.

Therefore you do not will need so huge quantity of layers - 5422414.

Because i agree with colleagues - you do not need such thermal isolations for buildings.

Your general idea of better thermal isolation does have merit, and as mentioned above is something that is harnessed in the semiconductor industry at very small scales. E.g., see https://www.nature.com/articles/srep14116, where they design atomically thin layers tuned to block phonon vibrations from propagating. This is a key design parameter in thermoelectric materials that need low thermal conductivity while meeting other electrical material requirements. They even suggest that the atomic ordering can beat the so called amorphous lower limit for thermal resistance. The presence of numerous interfaces can substantially decrease thermal conductance, and taking all these factors into account (numerous low conductance interfaces, low bulk thermal conductivity, suppressed convection and radiation) can build an extreme thermal insulator.

There is a reason such materials are used for very thin semiconductors, though. They are only generally practical for very thin layers (typically sub micron) and have difficulty scaling to very large areas (a few 10's of cm diameter typically) due to the conditions of growth required. That also makes them very expensive relative to something that would apply to the construction industry.

Applied at large scale, with macroscopic materials, I think you would find that the interfaces aren't as poor, nor the solids as low conductivity to make better candidates than many current conventional materials. Some of the reason is that, if you look at something like fiberglass insulation, it is already taking advantage of the features you suggested: the fibers are themselves a very low thermal conductivity material (glass/plastic), there are many very short fibers (large number of poor thermal interfaces), it is randomly arranged (amorphous analog), the arrangement traps lots of small static air gaps (static air has a very low thermal conductivity, and the isolated pockets can't convect), its extremely low cost per volume, and it can be easily shaped to size. R value 11 to 15 typical. So that's the competition.

there are certainly ways to get better, thinner insulation. Look at aerogels or space shuttle tiles for example. These use similar principles. The challenge is really keeping the insulating quality at the size and scale needed for the application.

Space shuttles are much easier to insulate thermally than buildings, since they are in the vacuum, where radiation is the only process available to transfer heat. therefore, a low emisivity (or high reflectivity) material at wavelenght corresponding to the surface temperature is very efficient. If not enough, because the outdoor temperature can be about 3 K , a layer of insulating material can be added. Since that material is under vacuum, it is about ten times more efficient than at atmospheric pressure.

So called vacuum insulation materials are available on the market, but, in my opinion, they cannot be used in the building industry, since much care is necessary when handling these materials. They cannot be cut, pierced, nailed.

A good point for space based applications like satellites, but with the space shuttle tiles themselves the majority of the insulating requirement was to deal with re-entry conditions where far more than radiation comes into play.

You are perfectly right! And there, evaporation of a part of the tiles comes into account, since such phenomenon needs a lot of heat!