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Frigid Legos®

February 10, 2020

Gravitation is likely the first principle of physics discovered by children. While diapers provide some cushioning, every fall provides some reinforcement that you can't fool Mother Nature. After gravitation, thermal conductivity might be a child's next most important physical principle. Children learn at a young age that cold metal objects extract heat from their hands much faster with mittens off than on; and that a pot-holder should be used when grabbing the handles of hot pots and pans on a stove top.

Portion of a poster of a woman holding hot coffee (Henri Meunier, 1897).

Portion of a poster of a woman holding hot coffee.

My paternal grandfather, who emigrated from Italy, drank his breakfast coffee from a soup bowl into which he crushed biscuits.

I surmise that this was the way breakfast coffee was taken in his home region of Calabria.

(An 1897 lithograph by Henri Meunier, United States Library of Congress Prints and Photographs division digital ID cph.3b49736, via Wikimedia Commons


Materials having low thermal conductivity and thermal barrier coatings (TBCs) are important parts of many of today's advanced technologies. Our homes are kept warmer in the winter and cooler in the summer because of their glass fiber insulation. One extreme application for thermal barrier coatings is as a protection of turbine engine blades from the heat of burning fuel in gas turbine engines. Since turbine engine efficiency increases with operating temperature, turbine blades are employed at extremely high temperatures, and they are protected from damage by a combination of air cooling channels and a thermal barrier. Yttria-stabilized zirconia (YSZ), which is zirconium oxide containing about 7% yttrium oxide, is a common TBC material for this application (see figure).

Figure caption

Cross-section of a turbine engine blade thermal barrier coating showing its columnar structure.

While electrons participate somewhat in heat transfer in metals, heat transfer is mostly done by Phonons, the quantized acoustic vibrations in crystals.

The columnar structure reduces the number of phonon modes that are allowed to propagate, and this reduces the thermal conductivity.

(Photograph from a 1990 NASA report.[1] Click for larger image.)


I did research on turbine blade alloys and coatings about a decade ago, but even small turbine blades are expensive items, so I don't have any keepsakes at my house. What are underfoot at my house and the houses of my grandchildren are many pieces of the popular Lego® construction sets. Physicists at Lancaster University (Lancaster, Lancashire, England) have recently performed thermal conductivity measurements at the opposite end of the temperature scale, at temperatures just a few thousandths of a degree above absolute zero. Most interestingly, these measurements were on Lego® pieces formed from acrylonitrile butadiene styrene (ABS) plastic. Their research appears in an open access paper in the December 23, 2019, issue of Scientific Reports.[2-4]

Although marketed as a toy, the Lego® pieces have physical and mechanical properties that might be useful in the construction of laboratory experiments. In 2012, BBC News wondered how many Lego® bricks could be stacked before the bottom brick would be crushed.[5] Engineers at the Open University (UK) found that 2 x 2 bricks (the ones with four coupling cylinders) have a mass of 1.152 grams and can withstand an average compression force of 4,240 newtons. A calculation shows that you can stack 375,000 such bricks before the bottom brick collapses, and this tower would reach a height of 3,591 meters (11,781 feet, 2.17 miles).[5] Adding some carbon nanotubes to the Lego® ABS plastic might be a good start to building a space elevator.

The expertise of the Lancaster physics team is in measurements at ultra-low temperature. Their equipment is capable of cooling small objects to temperatures as low as 1.6 millidegrees using a method called dilution refrigeration that's based on the mixing of two liquid helium isotopes, helium-3 (3He) and helium-4 (4He). When a mixture of these fluids is cooled below 1 kelvin, the less dense (3He) floats atop the (4He), although some (3He) atoms remain in the bottom (4He) layer. Since the vapor pressure of (3He) is higher than that of (4He), pumping the vapor will cause these atoms to migrate to the top layer. Energy is required for this transfer, and the overall effect is to cool the liquid helium mixture.

Lego pieces in a helium dilution refrigerator

Lego® pieces in the Lancaster University helium dilution refrigerator.

Just visible is a stack of Lego® bricks at the left, hidden by a supporting rod. A Lego® figure of a "Cryonaut" can be seen at the center.

(Still image from a Lancaster University YouTube Video.)


Why is it important to measure the low temperature thermal conductivity of Lego® pieces? Dilution refrigerators, such as the one used by Lancaster physics team in this experiment, require a high degree of thermal isolation from the environment, and this is accomplished by low thermal conductivity radiation shield spacers and support rods.[3] Some plastic materials with low thermal conductivity are available, but they are expensive. LEGO® blocks are quite inexpensive, have good mechanical properties; and, as the experiment has shown, exhibit a thermal conductivity that's lower than commonly used materials.[2]

The measured thermal conductance of the stack of LEGO® blocks was (8.7 ± 0.3) x 10−5 T1.75±0.02 WK−1 m−1 in the temperature range from 70 mK to 1.8 K. One reason for the low thermal conductivity is the minimal surface contact made between assembled bricks that leads to a high thermal resistance (see figure).[2]

Figure caption

Left image, a graph of the experimental thermal conductivity data in which the vertical temperature gradient across the stack of Lego® bricks is plotted against the heat load. Right image, a cross-section of the Lego® brick connections showing the minimal contacting surfaces that lead to high thermal resistance. Both images are from Ref. 2, and they are licensed under the Creative Commons Attribution 4.0 International License.[2]


As Dmitry Zmeev, a lecturer and EPSRC Research Fellow at Lancaster University who led the research team, explains,
"Our results are significant because we found that the clamping arrangement between the LEGO® blocks causes the LEGO® structures to behave as an extremely good thermal insulator at cryogenic temperatures... This is very desirable for construction materials used for the design of future scientific equipment like dilution refrigerators." [3]
The Lancaster team's next step is to design, 3D print, and test an improved thermal insulator for dilution refrigerators.[3]

References:

  1. William J. Brindley and Robert A. Miller, "Thermal Barrier Coating Evaluation Needs," NASA Technical Memorandum 103708, Lewis Research Center (Cleveland, Ohio, 1990), Prepared for the Conference on Nondestructive Evaluation of Modern Ceramics, Columbus, Ohio, July 9-12, 1990 (PDF File).
  2. J. M. A. Chawner, A. T. Jones, M. T. Noble, G. R. Pickett, V. Tsepelin, and D. E. Zmeev, "LEGO® Block Structures as a Sub-Kelvin Thermal Insulator," Scientific Reports, vol. 9, article no. 19642, December 23, 2019, doi:10.1038/s41598-019-55616-7. This is an open access article with a PDF file here.
  3. The coolest LEGO® in the Universe, Lancaster University Press Release, December 23, 2019.
  4. The World's Coolest LEGO Set, Lancaster University YouTube Video, December 23, 2019.
  5. Ruth Alexander, "How tall can a Lego tower get?" BBC News, December 4, 2012.

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