Category Archives: materials

Blue diamonds, natural and CVD.

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The hope diamond resides in the Smithsonian. It really is a deep blue. It has about 5 ppm boron.

If you’ve ever seen the Hope Dimond, or a picture of it, you’ll notice a most remarkable thing: it is deep blue. While most diamonds are clear, or perhaps grey, a very few are colored. Color in diamonds is generally caused by impurities, in the case of blue diamonds, boron. The Hope diamond has about 5 ppm boron, making it a p-semiconductor. Most blue diamonds, even those just as blue, have less boron. As it turns out one of the major uses of my hydrogen purifiers hydrogen these days is in the manufacture of gem -quality, and semiconductor diamonds, some blue and some other colors. So I thought I’d write about diamonds, colored and not, natural and CVD. It’s interesting and a sort of plug for my company, REB Research.

To start off, natural diamond are formed, over centuries by the effect of high temperature and pressure on a mix of carbon and a natural catalyst mineral, Kimberlite. Diamonds formed this way are generally cubic, relatively clear, and inert, hard, highly heat conductive, and completely non-conducting of electricity. Some man made diamonds are made this way too, using high pressure presses, but gem-quality and semiconductor diamonds are generally made by chemical vapor deposition, CVD. Colored diamonds are made this way too. They have all the properties of clear diamonds, but they have controlled additions and imperfections. Add enough boron, 1000 ppm for example, and the diamond and the resulting blue diamond can conduct electricity fairly readily.

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Seeds of natural diamond are placed in a diamond growth chamber and heated to about 1000°C in the presence of ionized, pure methane and hydrogen.

While natural diamond are sometimes used for technical applications, e.g. grind wheels, most technical-use diamonds are man-made by CVD, but the results tend to come out yellow. This was especially true in the early days of manufacture. CVD tends to make large, flat diamonds. This is very useful for heat sinks, and for diamond knives and manufacturers of these were among my first customers. To get a clear color, or to get high-quality colored diamonds, you need a mix of high purity methane and high purity hydrogen, and you need to avoid impurities of silica and the like from the diamond chamber. CVD is also used to make blue-conductive diamonds that can be used as semiconductors or electrodes. The process is show in the gif above from “brilliantearth”.

Multicolored diamonds made by CVD with many different dopants and treatments.

To make a CVD diamond, you place 15 to 30 seed- diamonds into a vacuum growth chamber with a flow of methane and hydrogen in ratio of 1:100 about. You heat the gas to about 1000°C (900-1200°C) , while ionizing the gas using microwaves or a hot wire. The diamonds grow epitaxially over the course of several days or weeks. Ionized hydrogen keeps the surface active, while preventing it from becoming carbonized — turning to graphite. If there isn’t enough hydrogen, you get grey, weak diamonds. If the gas isn’t pure, you get inclusions that make them appear yellow or brown. Nitrogen-impure diamonds are n-semiconductors, with a band gap greater than with boron-blue diamonds, 0.5-1 volts more. Because of this difference, nitrogen-impure diamonds absorb blue or green light, making them appear yellow, while blue diamonds absorb red light, making them blue. (This is different from the reason the sky is blue, explained here.) The difference in energy, also makes yellow diamonds poor electrical conductors. Natural, nitrogen-impure diamonds fluoresce blue or green, as one might expect, but yellow diamonds made by CVD fluoresce at longer wavelengths, reddish (I don’t know why).

The blue moon diamond, it is about as blue as the hope diamond though it has only 0.36 ppm of boron.

To make a higher-quality, yellow, n-type CVD diamonds, use very pure hydrogen. Bright yellow and green color is added by use of ppm-quantities of sulfur or phosphorus. Radiation damage also can be used to add color. Some CVD diamond makers use heat treatment to modify the color and reduce the amount of red fluorescence. CVD pink and purple diamonds are made by hydrogen doping, perhaps followed by heat treatment. The details are proprietary secrets.


Orange-red phosphorescence in the blue moon diamond.

Two major differences help experts distinguish between natural and man-made diamonds. One of these is the fluorescence, Most natural diamonds don’t fluoresce at all, and the ones that do (about 25%) fluoresce blue or green. Almost all CVD diamonds fluoresce orange-red because of nitrogen impurities that absorb blue lights. If you use very pure, nitrogen-free hydrogen, you get clear diamonds avoid much of the fluorescence and yellow. That’s why diamond folks come to us for hydrogen purifiers (and generators). There is a problem with blue diamonds, in that both natural and CVD-absorb and emit red light (that’s why they appear blue). Fortunately for diamond dealers, there is a slight difference in the red emission spectrum between natural and CVD blue diamonds. The natural ones show a mix of red and blue-green. Synthetic diamonds glow only red, typically at 660 nm.

Blue diamonds would be expected to fluoresce red, but instead they show a delayed red fluorescence called phosphorescence. That is to say, when exposed to light, they glow red and continue to glow for 10-30 seconds after the light is turned off. The decay time varies quite a lot, presumably due to differences in the n and p sites.

Natural diamond photographed between polarizers show patterns that radiate from impurities.

Natural and CVD also look different when placed between crossed polarizers. Natural diamonds show multiple direction stress bands, as at left, often radiating from inclusions. CVD diamonds show fine-grained patterns or none at all (they are not made under stress), and man-made, compression diamonds show an X-pattern that matches the press-design, or no pattern at all. If you are interested in hydrogen purifiers, or pure hydrogen generators, for this or any other purposes, please consider REB Research. If you are interested in buying a CVD diamond, there are many for sale, even from deBeers.

Robert Buxbaum, October 19, 2020. The Hope diamond was worn by three French kings, by at least one British king, and by Miss Piggy. A CVD version can be worn by you.

Eight ways to not fix the tower of Pisa, and one that worked.

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You may know that engineers recently succeed in decreasing the tilt of the “leaning” tower of Pizza by about 1.5°, changing it from about 5.5° to about to precisely 3.98° today –high precision given that the angle varies with the season. But you may not know how that there were at least eight other engineering attempts, and most of these did nothing or made things worse. Neither is it 100% clear that current solution didn’t make things worse. What follows is my effort to learn from the failures and successes, and to speculate on the future. The original-tilted tower is something of an engineering marvel, a highly tilted, stone on stone building that has outlasted earthquakes and weathering that toppled many younger buildings that were built straight vertical, most recently the 1989 collapse of the tower of Pavia. Part of any analysis, must also speak to why this tower survived so long when others failed.

First some basics. The tower of Pisa is an 8 story bell tower for the cathedral next door. It was likely designed by engineer Bonanno Pisano who started construction in 1173. We think it’s Pisano, because he put his name on an inscription on the base, “I, who without doubt have erected this marvelous work that is above all others, am the citizen of Pisa by the name of Bonanno.” Not so humble then, more humble when the tower started to lean, I suspect. The outer diameter at the base is 15.5 m and the weight of the finished tower is 14.7 million kg, 144 million Nt. The pressure exerted on the soil is 0.76 MPa (110 psi). By basic civil engineering, it should stand straight like the walls of the cathedral.

Bonanno’s marvelous work started to sink into the soil of Pisa almost immediately, though. Then it began to tilt. The name Pisa, in Greek, means swamp, and construction, it seems, was not quite on soil, but mud. When construction began the base was likely some 2.5 m (8 feet) above sea level. While a foundation of clay, sand and sea-shells could likely have withstood the weight of the tower, the mud below could not. Pisano added length to the south columns to keep the floors somewhat level, but after three floors were complete, and the tilt continued, he stopped construction. What to do now? What would you do?

If it were me, I’d consider widening the base to distribute the force better, and perhaps add weight to the north side. Instead, Pisano gave up. He completed the third level and went to do other things. The tower stood this way for 99 years, a three-floor, non-functional stub. 

About 1272, another engineer, Giovanni di Simone, was charged with fixing the situation. His was the first fix, and it sort-of worked. He strengthened the stonework of the three original floors, widened the base so it wold distribute pressure better, and buried the base too. He then added three more floors. The tower still leaned, but not as fast. De Simone made the south-side columns slightly taller than the north to hide the tilt and allow the floors to be sort-of level. A final two stories were added about 1372, and then the first of the bells. The tower looked as it does today when Gallileo did his famous experiments, dropping balls of different size from the south of the 7th floor between 1589 and 1592.

Fortunately for the construction, the world was getting colder and the water table was dropping. While dry soil is stronger than wet, wet soil is more plastic. I suspect it was the wet soil that helped the tower survive earthquakes that toppled other, straight towers. It seems that the tilt not only slowed during this period but briefly reversed, perhaps because of the shift in center of mass, or because of changes in the sea level. Shown below is 1800 years of gauge-based sea-level measurements. Other measures give different sea-level histories, but it seems clear that man-made climate change is not the primary cause. Sea levels would continue to fall till about 1750. By 1820 the tilt had resumed and had reached 4.5°.

Sea level height history as measured by land gauges. Because of climate change (non man-made) the sea levels rise and fall. This seems to have affected the tilt of the tower. Other measures of water table height give slightly different histories, but still the sense that man change is not the main effect.

The 2nd attempt was begun in 1838. Architect, Alessandro Della Gherardesca got permission to dig around the base at the north to show off the carvings and help right the tower. Unfortunately, the tower base had sunk below the water table. Further, it seems the dirt at the base was helping keep the tower from falling. As Della Gherardesca‘s crew dug, water came spurting out of the ground and the tower tilted another few inches south. The dig was stopped and filled in, but he dig uncovered the Pisano inscription, mentioned above. What would you do now? I might go away, and that’s what was done.

The next attempt to fix the tower (fix 3) was by that self-proclaimed engineering genius, Benito Mussolini. In 1934. Mussolini had his engineers pump some 200 tons of concrete into the south of the tower base hoping to push the tower vertical and stabilize it. The result was that the tower lurched another few inches south. The project was stopped. An engineering lesson: liquids don’t make for good foundations, even when it’s liquid concrete. An unfortunate part of the lesson is that years later engineers would try to fix the tower by pumping water beneath the north end. But that’s getting ahead of myself. Perhaps Mussolini should have made tests on a model before working on the historic tower. Ditto for the more recent version.

On March 18, 1989 the Civic Tower of Pavia started shedding bricks for no obvious reason. This was a vertical tower of the same age and approximate height as the Pisa tower. It collapsed killing four people and injuring 15. No official cause has been reported. I’m going to speculate that the cause was mechanical fatigue and crumbling of the sort that I’ve noticed on the chimney of my own house. Small vibrations of the chimney cause bits of brick to be ejected. If I don’t fix it soon, my chimney will collapse. The wet soils of Pisa may have reduced the vibration damage, or perhaps the stones of Pisa were more elastic. I’ve noticed brick and stone flaking on many prominent buildings, particularly at joins in the chimney.

John Burland’s team cam up with many of the fixes here. They are all science-based, but most of the fixes made things worse.

In 1990, a committee of science and engineering experts was formed to decide upon a fix for the tower of Pisa. It was headed by Professor John Burland, CBE, DSc(Eng), FREng, FRS, NAE, FIC, FCGI. He was, at the time, chair of soil mechanics at the Imperial College, London, and had worked with Ove, Arup, and Partners. He had written many, well regarded articles, and had headed the geological aspects of the design of the Queen Elizabeth II conference center. He was, in a word, an expert, but this tower was different, in part because it was an, already standing, stone-on stone tower that the city wished should remain tilted. The tower was closed to visitors along with all businesses to the south. The bells were removed as well. This was a safety measure, and I don’t count it as a fix. It bought time to decide on a solution. This took two years of deliberation and meetings

In 1992, the committee agreed to fix no 4. The tower was braced with plastic-covered, steel cables that were attached around the second and third floors, with the cables running about 5° from the horizontal to anchor points several hundred meters to the north. The fix was horribly ugly, and messed with traffic. Perhaps the tilt was slowed, it was not stopped.

In 1993, fix number 5. This was the most exciting engineering solution to date: 600 tons of lead ingots were stacked around the base, and water was pumped beneath the north side. This was the reverse of the Mussolini’s failed solution, and the hope was that the tower would tilt north into the now-soggy soil. Unfortunately, the tower tilted further south. One of the columns cracked too, and this attempt was stopped. They were science experts, and it’s not clear why the solution didn’t work. My guess is that they pumped in the water too fast. This is likely the solution I would have proposed, though I hope I would have tested it with a scale model and would have pumped slower. Whatever. Another solution was proposed, this one even more exotic than the last.

For fix number 6, 1995, the team of experts, still overseen by Burland, decided to move the cables and add additional tension. The cables would run straight down from anchors in the base of the north side of the tower to ten underground steel anchors that were to be installed 40 meters below ground level. This would have been an invisible solution, but the anchor depth was well into the water table. So, to anchor the ground anchors, Burland’s team had liquid nitrogen injected into the ground beneath the tower, on the north side where the ground anchors were to go. What Burland did not seem to have realized is that water expands when it freezes, and if you freeze 40 meters of water the length change is significant. On the night of September 7, 1995, the tower lurched southwards by more than it had done in the entire previous year.  The team was summoned for an emergency meeting and the liquid nitrogen anchor plan was abandoned.

Tower with the two sets of lead ingots, 900 tons total, about the north side of the base. The weight of the tower is 14,700 tons.

Fix number 7: Another 300 tons of lead ingots were added to the north side as a temporary, simple fix. The fix seems to have worked stabilizing things while another approach was developed.

Fix number 8: In order to allow the removal of the ugly lead bricks another set of engineers were brought on, Roberto Cela and Michele Jamiolkowski. Using helical drills, they had holes drilled at an angle beneath the north side of the tower. Using hoses, they removed a gallon or two of dirt per day for eleven years. The effect of the lead and the dirt removal was to reduce the angle of the tower to 4.5°, the angle that had been measured in 1820. At this point the lead could be removed and tourists were allowed to re-enter. Even after the lead was removed, the angle continued to subside north. It’s now claimed to be 3.98°, and stable. This is remarkable precision for a curved tower whose tilt changes with the seasons. (An engineering joke: How may engineers does it take to change a lightbulb? 1.02).

The bells were replaced and all seemed good, but there was still the worry that the tower would start tilting again. Since water was clearly part of the problem, the British soils expert, Burland came up with fix number 9. He had a series of drainage tunnels built to keep the water from coming back. My worry is that this water removal will leave the tower vulnerable to earthquake and shedding damage, like with the Pavia tower and my chimney. We’ll have to wait for the next earthquake or windstorm to tell for sure. So far, this fix has done no harm.

Robert Buxbaum, October 9, 2020. It’s nice to learn from other folks mistakes, and embarrassments, as well as from their successes. It’s also nice to see how science really works, not with great experts providing the brilliant solution, but slowly, like stumbling in the dark. I see this with COVID-19.

If nothing sticks to teflon, how do you stick teflon to a pan? PFAS.

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When I was eight or nine year old, I went to the 1963-64 World’s Fair in New York. Among the attractions, in “the kitchen of the future”, I saw the first version of an amazing fry-pan that was coated with plastic. You could cook an egg on that plastic without any oil, and the egg didn’t stick. The plastic was called teflon, a DuPont innovation, whose molecule is shown below.

The molecular structure of Teflon. There is an interior carbon backbone that is completely enclosed with tightly bound fluorine atoms. The net result is a compound that does not bind readily to anything else.

Years later, I came to understand that Teflon’s high-temperature stability and non-stick properties derive from the carbon-fluorine bonds. These bonds are much stronger than the carbon-hydrogen bonds found in food, and most solid, organic things. Because of the strength of the carbon-fluorine bond, Teflon is resistant to oxidation, and to chemical interaction with other molecules, e.g. in food. It does not even interact with water, making it hydrophobic and non-wetting on metals. The carbon-carbon bonds in the middle remained high temperature stable, in part because they were completely shielded by the fluorine atoms.

This is a PFAS. The left side is just like teflon, and very hydrophobic. The right side is hydrophilic and highly bonding to pans, and many other things like water or cotton.

But as remarkable as teflon’s non-stick properties are, perhaps the most amazing thing was that it somehow sticks to the pan. For the first generation pans I saw, it didn’t stick very well. Still, the DuPont engineers had found a way to stick non-stick Teflon to a metal for long enough to cook many meals. If they had not found this trick, teflon would not have the majority of its value, but how did they do it? It turns out they used a thin coating of a di-functional compound called PFAS, a a polyfluoro sulphonyl (or polyfluoroalkyl) substance. The molecular structure of a common PFAS, is shown above.

Each molecule of PFAS has one end that’s teflon-like and another end that’s different. The non-Teflon end, in this case a sulfonyl group, is chosen to be both high temperature stable and sticky to metal oxides. The sulphonyl group above is highly polar, and acidic. Acidic will bind to bases, like metal oxides. The surface of the metal pan is prepared by applying a thin layer of oxide or amidine, making it a polar base. The PFAS is then applied, then Teflon. The Teflon-end of the PFAS is bound to teflon by the hydrophobicity of everything else rejecting it.

There are many other uses for PFAS. For example, PFAS is applied to clothing to make it wrinkle free and stain resistant. It can also be used as a super soap, making uncommonly stable foams and bubbles. It is also used in fire-fighting and plane de-icing. Finally, PFAS is the main component of Nafion, the most common membrane for PEM fuel cells. (I can think of yet other applications..) There is just one small problem with PFAS, though. Like teflon, this molecule is uncommonly stable. It doesn’t readily decompose in nature. That would be a small problem if we were sure that PFAS was safe. As it happens it seems safe, but we’re not totally sure.

The safety of PFAS was studied extensively before PFAS-teflon pans was put on the market, but the methodology has been questioned. Large doses of PFAS were fed to test animals, and their health observed. Since the test animals showed no real signs of ill-health though some showed a slight liver enlargement, PFAS was accepted as safe for humans at a lower exposure dose. PFAS was approved for use on pans and allowed to be dumped under conditions where humans would be exposed to 1/1000 of that used on the animals. The assumption was that there would be little or no health hazard at these low exposure levels.

But low risk is not no risk, and today one can sue for even the hint of an effect though use of a class action suit. That is, lawyers sue on behalf of all the people who might have been damaged. My city was sued successfully this way for complicity in sewage over-flows. Of course, since the citizens being paid by the suit are the same ones who have to pay for the damage, only the lawyers benefit. Still, the law is the law, and at least for some judges, putting anyone at risk is enough evidence of willful disregard to hand down a stinging judgement against the evil doer. Judges have begun awarding large claims for PFAS too. While no individual can get the claim more than a tiny amount of money, the lawyers can do very well.

There is no new evidence that PFAS is dangerous, but none is needed if you can get yourself the right judge. In this regard, an industry of judicial tourism has sprung up, where class-action lawyers travel to districts where the judges are favorable. For Teflon suits, the bust hunting grounds are in New York, New Hampshire, and California, and the worst are blood-red states like Wyoming and Utah. Just as different judges promote different precedents, different states allow vastly different PFAS concentrations in the water. A common standard, one used by Michigan, is 70 ppt, 1 billion times stricter than the amounts tested on animals. This is roughly 500 times stricter than the acceptable concentratios for lead, a known poison. The standard in New York is 7 times stricter than Michigan, 10 ppt. The standard in North Carolina is 140,000 ppt, in in several states there is no legal limit to PFAS dumping. There is no scientific logic to all of this, and skeptical view is that the states that rule more strictly for PFAS than lead do so make money for lawyers. Lead is everyone in the natural environment, so you can’t sue as easily for lead. PFAS is a man-made intruder, though, and a strict standard helps lawyers sue. You can find a summary of state by state regulations here.

Any guideline stricter than about 1000 ppt, presents a challenge to the water commissioner who must measure it and enforce the law. There are tricks, though. You can use the surfactant quality of PFAS to concentrate it by a factor of 100 or more. To do this, you take a sample of river water and create bubbles. Any bubbles that form will be highly concentrated in PFAS. Once PFAS can be identified this way, and the concentrators estimated, the polluters can be held liable. Whether we benefit from the strict rulings is another story. If I were making the law for Michigan, I’d probably choose a limit about 1 ppb, but I’m not making the law. The law, as written, may be an idiot, as Bumble said, but the Law is the Law.

In terms of Michigan fishing, while some rivers have PFAS concentrators above the MI-legal limit, they are generally not far over the line. I would trust the fish in the Huron River, even west of Wixom road but I’d suggest you avoid any foam you find floating there. The PFAS content of foam will be much higher than that of the water in general.

Robert E. Buxbaum, June 30, 2020, edited July 8, 2020. There are seven compounds known as PFAS’s: perfluorooctanesulfonic acid (PFOS), perfluorooctanoic acid (PFOA), perfluorononanoic acid (PFNA), perfluorohexanesulfonic acid (PFHxS), perfluoroheptanoic acid (PFHpA), and perfluorobutanesulfonic acid (PFBS).

Maximum height of an NYC skyscraper, including wind.

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Some months ago, I demonstrated that the maximum height of a concrete skyscraper was 45.8 miles, but there were many unrealistic assumptions. The size of the base was 100 mi2, about that of Sacramento, California; the shape was similar to that of the Eiffel tower, and there was no wind. This height is semi-reasonable; it’s about that of the mountains on Mars where there is a yellow sky and no wind, but it is 100 times taller than the tallest skyscraper on earth. the Burj Khalifa in Dubai, 2,426 ft., shown below. Now I’d like to include wind, and limit the skyscraper to a straight tower of a more normal size, a city-block square of manhattan, New York real-estate. That’s 198 feet on a side; this is three times the length of Gunther’s surveying chain, the standard for surveying in 1800.

Burj Khalifa, the world’s tallest building, Concrete + glass structure. Dubai tourism image.

As in our previous calculation, we can find the maximum height in the absence of windby balancing the skyscrapers likely strength agains its likely density. We’ll assume the structure is made from T1 steel, a low carbon, vanadium steel used in bridges, further assume that the structure occupies 1/10 of the floor area. Because the structure is only 1/10 of the area, the average yield strengthener the floor area is 1/10 that of T1 steel. This is 1/10 x 100,000 psi (pounds per square inch) = 10,000 psi. The density of T1 steel is 0.2833 pounds per cubic inch, but we’ll assume that the density of the skyscraper is about 1/4 this; (a skyscraper is mostly empty space). We find the average is 0.07 pounds per cubic inch. The height, is the strength divided by the density, thus

H’max-tower = 10,000psi / 0.07 p/in3 = 142, 857 inches = 11, 905 feet = 3629 m,

This is 4 1/4 times higher than the Burj Khalifa. The weight of this structure found from the volume of the structure times its average density, or 0.07 pounds per cubic inch x 123 x 1982x 11,905 = 56.45 billion pounds, or, in SI units, a weight of 251 GNt.

Lets compare this to the force of a steady wind. A steady wind can either either tip over the building by removing stress on the upwind side, or add so much extra stress to the down-wind side that the wall fails. The force of the wind is proportionals to the wind’s energy dissipation rate. I’ll assume a maximum wind speed of 120 mph, or 53.5 m/s. The force of the wind equals the area of the building, times a form factor, ƒ, times the rate of kinetic energy dissipation, 1/2ρv2. Thus,

F= (Area)*ƒ* 1/2ρv2, where ρ is the density of air, 1.29kg/m3.

The form factor, ƒ, is found to be 1.15 for a flat plane. I’ll presume that’s also the form factor for a skyscraper. I’ll take the wind area as

Area = W x H,

where W is the width of the tower, 60.35 m in SI, and the height, H, is what we wish to determine. It will be somewhat less than H’max-tower, =3629 m, the non-wind height. As an estimate for how much less, assume H = H’max-tower, =3629 m.
For this height tower, the force of the wind is found to be:

F = 3629 * 60.35* 2123 = 465 MNt.

This is 1/500 the weight of the building, but we still have to include the lever effect. The building is about 60.1 times taller than it is wide, and as a result the 465 MNt sideways force produces an additional 28.0 GNt force on the down-wind side, plus and a reduction of the same amount upwind. This is significant, but still only 1/9 the weight of the building. The effect of the wind therefore is to reduce the maximum height of this New York building by about 9 %, to a maximum height of 2.05 miles or 3300 m.

The tallest building of Europe is the Shard; it’s a cone. The Eiffel tower, built in the 1800s, is taller.

A cone is a better shape for a very tall tower, and it is the shape chosen for “the shard”, the second tallest building in Europe, but it’s not the ideal shape. The ideal, as before, is something like the Eiffel tower. You can show, though I will not, that even with wind, the maximum height of a conical building is three times as high as that of a straight building of the same base-area and construction. That is to say that the maximal height of a conical building is about 6 miles.

In the old days, one could say that a 2 or 6 mile building was inconceivable because of wind vibration, but we’ve found ways to deal with vibration, e.g. by using active damping. A somewhat bigger problem is elevators. A very tall building needs to have elevators in stages, perhaps 1/2 mile stages with exchanges (and shopping) in-between. Yet another problem is fire. To some extent you eliminate these problems by use of pre-mixed concrete, as was used in the Trump tower in New York, and later in the Burj Khalifa in Dubai.

The compressive strength of high-silica, low aggregate, UHPC-3 concrete is 135 MPa (about 19,500 psi), and the density is 2400 kg/m3 or about 0.0866 lb/in3. I will assume that 60% of the volume is empty and that 20% of the weight is support structure (For the steel building, above, I’d assumed 3/4 and 10%). In the absence of wind,

H’max-cylinder-concrete = .2 x 19,500 psi/(0.4 x.0866  lb/in3) = 112,587″ = 9,382 ft = 1.77 miles. This building is 79% the height of the previous, steel building, but less than half the weight, about 22,000,000,000 pounds. The effect of the wind will be to reduce the above height by about 14%, to 1.52 miles. I’m not sure that’s a fire-safe height, but it is an ego-boost height.

Robert Buxbaum. December 29, 2019.

Recycle nuclear waste

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In a world obsessed with stopping global warming by reducing US carbon emissions, you’d think there would be a strong cry for nuclear power, one of the few reliable sources of large-scale power that does not discharge CO2. But nuclear power produces dangerous waste, and I have a suggestion: let’s recycle the waste so it’s less dangerous and so there is less of it. Used nuclear fuel rods, in particular. We burn perhaps 5% of the uranium, and produce a waste that is full of energy. Currently these, semi-used rods are stored in very expensive garbage dumps waiting for us to do something. Let’s recycle.

I’ve called nuclear power the elephant in the room for clean energy. Nuclear fuel produces about 25% of America’s electricity, providing reliable baseline generation along with polluting alternatives: coal and natural gas, and less-reliable renewables like solar and wind. Nuclear power does not emit CO2, and it’s available whether or not the sun shines or the wind blows. Nuclear power uses far less land area than solar or wind too, and it provides critical power for our navy aircraft carriers and submarines. Short of eliminating our navy, we will have to keep using nuclear.

Although there are very little nuclear waste per energy delivered, the waste that there is, is hard to manage. Used nuclear fuel rods in particular. For one thing, the used rods are hot, physically. They give off heat, and need to be cooled. At first they give off so much heat that the rods must be stored under water. But rod-heat decays fractally. After ten years or so, rods can be stored in naturally cooled concrete; it’s still a headache, but a smaller one The other problem with the waste rods is that they contain about 1.2% plutonium, a material that can be used for atomic bombs. A major reason that you can’d just dump the waste into the ocean or into a salt mine is the fear that someone will dig it up and extract the plutonium for an a- bomb. The extraction is easy compared to enriching uranium to bomb-grade, and the bombs work at least as well. Plutonium made this way was used for the bomb that destroyed Nagasaki.

The original plan for US nuclear power had been that we would extract the plutonium, and burn it up by recycling it to the nuclear reactor. We’d planned to burry the rest, as the rest is far less dangerous and far less, long-term radioactive. We actually did some plutonium recycling of this sort but in the 1970s a disgruntled worker named Silkwood stole plutonium and recycling was shut down in the US. After that, political paralysis set in and we’ve come to just let the waste sit in more-or-less guarded locations. There was a thought to burry everything in a guarded location (Yucca Mountain, Nevada) but the locals were opposed. So the waste sits waiting to leak out or be stolen. I’d like to return to recycling, but not necessarily of pure plutonium as we did before Silkwood: there is no guarantee that there won’t be other plutonium thieves.

Instead of removing the plutonium for recycling, I’d like to suggest that we remove about 40% of the uranium in the rod, and all of the “ash”, this is all of the lighter atom elements created from the split uranium atoms. This ash is about 5% of the total. The resultant rods would have about 2% plutonium, 97.5% enriched uranium (about 1% enriched at this stage) plus about 0.5% higher transuranics. This composition would be a far less dangerous than purified plutonium. It would be less hot and it would not be possible to use it directly for atom bombs. It would still be fissionable, though, at the same energy content as fresh rods.

There is an uncommonly large amount of power available in nuclear fuel

Several countries recycle by removing the ash. Because no uranium is removed, the material they get has about half the usable life of a fresh rod. After one recycle, there is not much more they could do. If we remove uranium material is a lot more easily used, and more easily recycled again. If we keep removing ash and uranium, we could get many, many recycles. The result is a lot less uranium mining, and more power per rod, and fewer rods to store under guard.

The plutonium of multiply recycled rods is also less-usable for fission bombs. With each recycle, the rods build up a non-fisionabl isotope of plutonium: Pu 240. This isotope is not readily separated from the fissionable isotope, Pu 239, making multiply used rods relatively useless for fission bombs.

Among the countries that do some nuclear waste recycling are Canada, France, Russia, China, and Germany. Not a bad assortment. I would be happy to see us join them.

Robert Buxbaum September 9, 2019

Thermal stress failure

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Take a glass, preferably a cheap glass, and set it in a bowl of ice-cold water so that the water goes only half-way up the glass. Now pour boiling hot water into the glass. In a few seconds the glass will crack from thermal stress, the force caused by heat going from the inside of the glass outside to the bowl of cold water. This sort of failure is not mentioned in any of the engineering material books that I had in college, or had available for teaching engineering materials. To the extent that it is mentioned mentioned on the internet, e.g. here at wikipedia, the metric presented is not derived and (I think) wrong. Given this, I’d like to present a Buxbaum- derived metric for thermal stress-resistance and thermal stress failure. A key aspect: using a thinner glass does not help.

Before gong on to the general case of thermal stress failure, lets consider the glass, and try to compute the magnitude of the thermal stress. The glass is being torn apart and that suggests that quite a lot of stress is being generated by a ∆T of 100°C temeprarture gradient.

To calcule the thermal stress, consider the thermal expansivity of the material, α. Glass — normal cheap glass — has a thermal expansivity α = 8.5 x10-6 meters/meter °C (or 8.5 x10-6 foot/foot °C). For every degree Centigrade a meter of glass is heated, it will expand 8.5×10-6 meters, and for every degree it is cooled, it will shrink 8.5 x10-6 meters. If you consider the circumference of the glass to be L (measured in meters), then
∆L/L = α ∆T.

where ∆L is the change in length due to heating, and ∆L/L is sometimes called the “strain.”. Now, lets call the amount of stress caused by this expansion σ, sigma, measured in psi or GPa. It is proportional to the strain, ∆L/L, and to the elasticity constant, E (also called Young’s elastic constant).

σ = E ∆L/L.

For glass, Young’s elasticity constant, E = 75 GPa. Since strain was equal to α ∆T, we find that

σ =Eα ∆T 

Thus, for glass and a ∆T of 100 °C, σ =100°C x 75 GPa x 8.5 x10-6 /°C  = 0.064  GPa = 64MPa. This is about 640 atm, or 9500 psi.

As it happens, the ultimate tensile strength of ordinary glass is only about 40 MPa =  σu. This, the maximum force per area you can put on glass before it breaks, is less than the thermal stress. You can expect a break here, and wherever σu < Eα∆T. I thus create a characteristic temperature difference for thermal stress failure:

The Buxbaum failure temperature, ß = σu/Eα

If ∆T of more than ß is applied to any material, you can expect a thermal stress failure.

The Wikipedia article referenced above provides a ratio for thermal resistance. The usits are perhaps heat load per unit area and time. How you would use this ratio I don’t quite know, it includes k, the thermal conductivity and ν, the Poisson ratio. Including the thermal conductivity here only makes sense, to me, if you think you’ll have a defined thermal load, a defined amount of heat transfer per unit area and time. I don’t think this is a normal way to look at things.  As for including the Poisson ratio, this too seems misunderstanding. The assumption is that a high Poisson ratio decreases the effect of thermal stress. The thought behind this, as I understand it, is that heating one side of a curved (the inside for example) will decrease the thickness of that side, reducing the effective stress. This is a mistake, I think; heating never decreases the thickness of any part being heated, but only increases the thickness. The heated part will expand in all directions. Thus, I think my ratio is the correct one. Please find following a list of failure temperatures for various common materials. 

Stress strain properties of engineering materials including thermal expansion, ultimate stress, MPa, and Youngs elastic modulus, GPa.

You will notice that most materials are a lot more resistant to thermal stress than glass is and some are quite a lot less resistant. Based on the above, we can expect that ice will fracture at a temperature difference as small as 1°C. Similarly, cast iron will crack with relatively little effort, while steel is a lot more durable (I hope that so-called cast iron skillets are really steel skillets). Pyrex is a form of glass that is more resistant to thermal breakage; that’s mainly because for pyrex, α is a lot smaller than for ordinary, cheap glass. I find it interesting that diamond is the material most resistant to thermal failure, followed by invar, a low -expansion steel, and ordinary rubber.

Robert E. Buxbaum, July 3, 2019. I should note that, for several of these materials, those with very high thermal conductivities, you’d want to use a very thick sample of materials to produce a temperature difference of 100*C.

How tall could you make a skyscraper?

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Built in 1931, the highest usable floor space of the Empire State building is 1250 feet (381m) above the ground. In 1973, that record was beaten by the World Trade Center building 1, 1,368 feet (417 m, building 2 was eight feet shorter). The Willis Tower followed 1974, and by 2004, the tallest building was the Taipei Tower, 1471 feet. Building heights had grown by 221 feet since 1931, and then the Burj Khalifa in Dubai, 2,426 ft ( 739.44m):. This is over 1000 feet taller than the new freedom tower, and nearly as much taller than the previous record holder. With the Saudi’s beginning work on a building even taller, it’s worthwhile asking how tall you could go, if your only  limitations were ego and materials’ strength.

Burj Khalifa, the world’s tallest building, Concrete + glass structure. Dubai tourism image.

Having written about how long you could make a (steel) suspension bridge, the maximum height of a skyscraper seems like a logical next step. At first glance this would seem like a ridiculously easy calculation based on the math used to calculate the maximum length of a suspension bridge. As with the bridge, we’d make the structure from the strongest normal material: T1, low carbon, vanadium steel, and we’d determine the height by balancing this material’s  yield strength, 100,000 psi (pounds per square inch), against its density, .2833 pounds per cubic inch.

If you balance these numbers, you calculate a height: 353,000 inches, 5.57 miles, but this is the maximum only for a certain structure, a wide flag-pole of T1 steel in the absent of wind. A more realistic height assumes a building where half the volume is empty space, used for living and otherwise, where 40% of the interior space contains vertical columns of T1 steel, and where there’s a significant amount of dead-weight from floors, windows, people, furniture, etc. Assume the dead weight is the equivalent of filling 10% of the volume with T1 steel that provides no structural support. The resulting building has an average density = (1/2 x 0.2833 pound/in3), and the average strength= (0.4 x 100,000 pound/in2). Dividing these numbers we get a maximum height, but only for a cylindrical building with no safety margin, and no allowance for wind.

H’max-cylinder = 0.4 x 100,000 pound/in2/ (.5 x 0.2833 pound/in3) = 282,400 inches = 23,532 ft = 4.46 miles.

This is more than ten times the Burj Khalifa, but it likely underestimates the maximum for a steel building, or even a concrete building because a cylinder is not the optimum shape for maximum height. If the towers were constructed conical or pyramidal, the height could be much greater: three times greater because the volume of a cone and thus its weight is 1/3 that of a cylinder for the same base and height. Using the same materials and assumptions,

The tallest building of Europe is the Shard; it’s a cone. The Eiffel tower, built in the 1800s, is taller.

H’max-cone = 3 H’max-cylinder =  13.37 miles.

A cone is a better shape for a very tall tower, and it is the shape chosen for “the shard”, the second tallest building in Europe, but it’s not the ideal shape. The ideal, as we’ll see, is something like the Eiffel tower.

Before speaking about this shape, I’d like to speak about building materials. At the heights we’re discussing, it becomes fairly ridiculous to talk about a steel and glass building. Tall steel buildings have serious vibration problems. Even at heights far before they are destroyed by wind and vibration , the people at the top will begin to feel quite sea-sick. Because of this, the tallest buildings have been constructed out of concrete and glass. Concrete is not practical for bridges since concrete is poor in tension, but concrete can be quite strong in compression, as I discussed here.  And concrete is fire resistant, sound-deadening, and vibration dampening. It is also far cheaper than steel when you consider the ease of construction. The Trump Tower in New York and Chicago was the first major building here to be made this way. It, and it’s brother building in Chicago were considered aesthetic marvels until Trump became president. Since then, everything he’s done is ridiculed. Like the Trump tower, the Burj Khalifa is concrete and glass, and I’ll assume this construction from here on.

let’s choose to build out of high-silica, low aggregate, UHPC-3, the strongest concrete in normal construction use. It has a compressive strength of 135 MPa (about 19,500 psi). and a density of 2400 kg/m3 or about 0.0866 lb/in3. Its cost is around $600/m3 today (2019); this is about 4 times the cost of normal highway concrete, but it provides about 8 times the compressive strength. As with the steel building above, I will assume that, at every floor, half of the volume is living space; that 40% is support structure, UHPC-3, and that the other 10% is other dead weight, plumbing, glass, stairs, furniture, and people. Calculating in SI units,

H’max-cylinder-concrete = .4 x 135,000,000 Pa/(.5 x 2400 kg/m3 x 9.8 m/s2) = 4591 m = 2.85 miles.

The factor 9.8 m/s2 is necessary when using SI units to account for the acceleration of gravity; it converts convert kg-weights to Newtons. Pascals, by the way, are Newtons divided by square meters, as in this joke. We get the same answer with less difficulty using inches.

H’max-cylinder-concrete = .4 x 19,500 psi/(.5 x.0866  lb/in3) = 180,138″ = 15,012 ft = 2.84 miles

These maximum heights are not as great as for a steel construction, but there are a few advantages; the price per square foot is generally less. Also, you have fewer problems with noise, sway, and fire: all very important for a large building. The maximum height for a conical concrete building is three times that of a cylindrical building of the same design:

H’max–cone-concrete = 3 x H’max-cylinder-concrete = 3 x 2.84 miles = 8.53 miles.

Mount Everest, picture from the Encyclopedia Britannica, a stone cone, 5.5 miles high.

That this is a reasonable number can be seen from the height of Mount Everest. Everest is rough cone , 5.498 miles high. This is not much less than what we calculate above. To reach this height with a building that withstands winds, you have to make the base quite wide, as with Everest. In the absence of wind the base of the cone could be much narrower, but the maximum height would be the same, 8.53 miles, but a cone is not the optimal shape for a very tall building.

I will now calculate the optimal shape for a tall building in the absence of wind. I will start at the top, but I will aim for high rent space. I thus choose to make the top section 31 feet on a side, 1,000 ft2, or 100 m2. As before, I’ll make 50% of this area living space. Thus, each apartment provides 500 ft2 of living space. My reason for choosing this size is the sense that this is the smallest apartment you could sell for a high premium price. Assuming no wind, I can make this part of the building a rectangular cylinder, 2.84 miles tall, but this is just the upper tower. Below this, the building must widen at every floor to withstand the weight of the tower and the floors above. The necessary area increases for every increase in height as follows:

dA/dΗ = 1/σ dW/dH.

Here, A is the cross-sectional area of the building (square inches), H is height (inches), σ is the strength of the building material per area of building (0.4 x 19,500 as above), and dW/dH is the weight of building per inch of height. dW/dH equals  A x (.5 x.0866  lb/in3), and

dA/dΗ = 1/ ( .4 x 19,500 psi) x A x (.5 x.0866  lb/in3).

dA/A = 5.55 x 10-6 dH,

∫dA/A = ∫5.55 x 10-6 dH,

ln (Abase/Atop) = 5.55 x 10-6 ∆H,

Here, (Abase/Atop) = Abase sq feet /1000, and ∆H is the height of the curvy part of the tower, the part between the ground and the 2.84 mile-tall, rectangular tower at the top.

Since there is no real limit to how big the base can be, there is hardly a limit to how tall the tower can be. Still, aesthetics place a limit, even in the absence of wind. It can be shown from the last equation above that stability requires that the area of the curved part of the tower has to double for every 1.98 miles of height: 1.98 miles = ln(2) /5.55 x 10-6 inches, but the rate of area expansion also keeps getting bigger as the tower gets heavier.  I’m going to speculate that, because of artistic ego, no builder will want a tower that slants more than 45° at the ground level (the Eiffel tower slants at 51°). For the building above, it can be shown that this occurs when:

dA/dH = 4√Abase.  But since

dA/dH = A 5.55 x 10-6 , we find that, at the base,

5.55 x 10-6 √Abase = 4.

At the base, the length of a building side is Lbase = √Abase=  4 /5.55 x 10-6 inches = 60060 ft = 11.4  miles. Artistic ego thus limits the area of the building to slightly over 11 miles wide of 129.4 square miles. This is about the area of Detroit. From the above, we calculate the additional height of the tower as

∆H = ln (Abase/Atop)/ 5.55 x 10-6 inches =  15.1/ 5.55 x 10-6 inches = 2,720,400 inches = 226,700 feet = 42.94 miles.

Hmax-concrete =  2.84 miles + ∆H = 45.78 miles. This is eight times the height of Everest, and while air pressure is pretty low at this altitude, it’s not so low that wind could be ignored. One of these days, I plan to show how you redo this calculation without the need for calculus, but with the inclusion of wind. I did the former here, for a bridge, and treated wind here. Anyone wishing to do this calculation for a basic maximum wind speed (100 mph?) will get a mention here.

From the above, it’s clear that our present buildings are nowhere near the maximum achievable, even for construction with normal materials. We should be able to make buildings several times the height of Everest. Such Buildings are worthy of Nimrod (Gen 10:10, etc.) for several reasons. Not only because of the lack of a safety factor, but because the height far exceeds that of the highest mountain. Also, as with Nimrod’s construction, there is a likely social problem. Let’s assume that floors are 16.5 feet apart (1 rod). The first 1.98 miles of tower will have 634 floors with each being about the size of Detroit. Lets then assume the population per floor will be about 1 million; the population of Detroit was about 2 million in 1950 (it’s 0.65 million today, a result of bad government). At this density, the first 1.98 miles will have a population of 634 million, about double that of the United States, and the rest of the tower will have the same population because the tower area contracts by half every 1.98 miles, and 1/2 + 1/4 + 1/8 + 1/16 … = 1.

Nimrod examining the tower, Peter Breugel

We thus expect the tower to hold 1.28 Billion people. With a population this size, the tower will develop different cultures, and will begin to speak different languages. They may well go to war too — a real problem in a confined space. I assume there is a moral in there somewhere, like that too much unity is not good. For what it’s worth, I even doubt the sanity of having a single government for 1.28 billion, even when spread out (e.g. China).

Robert Buxbaum, June 3, 2019.

How long could you make a suspension bridge?

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The above is one of the engineering questions that puzzled me as a student engineer at Brooklyn Technical High School and at Cooper Union in New York. The Brooklyn Bridge stood as a wonder of late 1800s engineering, and it had recently been eclipsed by the Verrazano bridge, a pure suspension bridge. At the time it was the longest and heaviest in the world. How long could a bridge be made, and why did Brooklyn bridge have those catenary cables, when the Verrazano didn’t? (Sometimes I’d imagine a Chinese engineer being asked the top question, and answering “Certainly, but How Long is my cousin.”)

I found the above problem unsolvable with the basic calculus at my disposal. because it was clear that both the angle of the main cable and its tension varied significantly along the length of the cable. Eventually I solved this problem using a big dose of geometry and vectors, as I’ll show.

Vector diagram of forces on the cable at the center-left of the bridge.

Vector diagram of forces on the cable at the center-left of the bridge.

Consider the above vector diagram (above) of forces on a section of the main cable near the center of the bridge. At the right, the center of the bridge, the cable is horizontal, and has a significant tension. Let’s call that T°. Away from the center of the bridge, there is a vertical cable supporting a fraction of  roadway. Lets call the force on this point w. It equals the weight of this section of cable and this section of roadway. Because of this weight, the main cable bends upward to the left and carries more tension than T°. The tangent (slope) of the upward curve will equal w/T°, and the new tension will be the vector sum along the new slope. From geometry, T= √(w2 +T°2).

Vector diagram of forces on the cable further from the center of the bridge.

Vector diagram of forces on the cable further from the center of the bridge.

As we continue from the center, there are more and more verticals, each supporting approximately the same weight, w. From geometry, if w weight is added at each vertical, the change in slope is always w/T° as shown. When you reach the towers, the weight of the bridge must equal 2T Sin Θ, where Θ is the angle of the bridge cable at the tower and T is the tension in the cable at the tower.

The limit to the weight of a bridge, and thus its length, is the maximum tension in the main cable, T, and the maximum angle, that at the towers. Θ. I assumed that the maximum bridge would be made of T1 bridge steel, the strongest material I could think of, with a tensile strength of 100,000 psi, and I imagined a maximum angle at the towers of 30°. Since there are two towers and sin 30° = 1/2, it becomes clear that, with this 30° angle cable, the tension at the tower must equal the total weight of the bridge. Interesting.

Now, to find the length of the bridge, note that the weight of the bridge is proportional to its length times the density and cross section of the metal. I imagined a bridge where the half of the weight was in the main cable, and the rest was in the roadway, cars and verticals. If the main cable is made of T1 “bridge steel”, the density of the cable is 0.2833 lb/in3, and the density of the bridge is twice this. If the bridge cable is at its yield strength, 100,000 psi, at the towers, it must be that each square inch of cable supports 50,000 pounds of cable and 50,000 lbs of cars, roadway and verticals. The maximum length (with no allowance for wind or a safety factor) is thus

L(max) = 100,000 psi / 2 x 0.2833 pounds/in3 = 176,500 inches = 14,700 feet = 2.79 miles.

This was more than three times the length of the Verrazano bridge, whose main span is ‎4,260 ft. I attributed the difference to safety factors, wind, price, etc. I then set out to calculate the height of the towers, and the only rational approach I could think of involved calculus. Fortunately, I could integrate for the curve now that I knew the slope changed linearly with distance from the center. That is for every length between verticals, the slope changes by the same amount, w/T°. This was to say that d2y/dx2 = w/T° and the curve this described was a parabola.

Rather than solving with heavy calculus, I noticed that the slope, dy/dx increases in proportion to x, and since the slope at the end, at L/2, was that of a 30° triangle, 1/√3, it was clear to me that

dy/dx = (x/(L/2))/√3

where x is the distance from the center of the bridge, and L is the length of the bridge, 14,700 ft. dy/dx = 2x/L√3.

We find that:
H = ∫dy = ∫ 2x/L√3 dx = L/4√3 = 2122 ft,

where H is the height of the towers. Calculated this way, the towers were quite tall, higher than that of any building then standing, but not impossibly high (the Dubai tower is higher). It was fairly clear that you didn’t want a tower much higher than this, though, suggesting that you didn’t want to go any higher than a 30° angle for the main cable.

I decided that suspension bridges had some advantages over other designs in that they avoid the problem of beam “buckling.’ Further, they readjust their shape somewhat to accommodate heavy point loads. Arch and truss bridges don’t do this, quite. Since the towers were quite a lot taller than any building then in existence, I came to I decide that this length, 2.79 miles, was about as long as you could make the main span of a bridge.

I later came to discover materials with a higher strength per weight (titanium, fiber glass, aramid, carbon fiber…) and came to think you could go longer, but the calculation is the same, and any practical bridge would be shorter, if only because of the need for a safety factor. I also came to recalculate the height of the towers without calculus, and got an answer that was shorter, for some versions, a hundred feet shorter, as shown here. In terms of wind, I note that you could make the bridge so heavy that you don’t have to worry about wind except for resonance effects. Those are the effects are significant, but were not my concern at the moment.

The Brooklyn Bridge showing its main cable suspension structure and its catenaries.

Now to discuss catenaries, the diagonal wires that support many modern bridges and that, on the Brooklyn bridge, provide  support at the ends of the spans only. Since the catenaries support some weight of the Brooklyn bridge, they decrease the need for very thick cables and very high towers. The benefit goes down as the catenary angle goes to the horizontal, though as the lower the angle the longer the catenary, and the lower the fraction of the force goes into lift. I suspect this is why Roebling used catenaries only near the Brooklyn bridge towers, for angles no more than about 45°. I was very proud of all this when I thought it through and explained it to a friend. It still gives me joy to explain it here.

Robert Buxbaum, May 16, 2019.  I’ve wondered about adding vibration dampers to very long bridges to decrease resonance problems. It seems like a good idea. Though I have never gone so far as to do calculations along these lines, I note that several of the world’s tallest buildings were made of concrete, not steel, because concrete provides natural vibration damping.

A hydrogen permeation tester

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Over the years I’ve done a fair amount of research on hydrogen permeation in metals — this is the process of the gas dissolving in the metal and diffusing to the other side. I’ve described some of that, but never the devices that measure the permeation rate. Besides, my company, REB Research, sells permeation testing devices, though they are not listed on our site. We recently shipped one designed to test hydrogen permeation through plastics for use in light weight hydrogen tanks, for operation at temperatures from -40°C to 85°C. Shortly thereafter we got another order for a permeation tester. With all the orders, I thought I’d describe the device a bit — this is the device for low permeation materials. We have a similar, but less complex design for high permeation rate material.

Shown below is the central part of the device. It is a small volume that can be connected to a high vacuum, or disconnected by a valve. There is an accurate pressure sensor, accurate to 0.01 Torr, and so configured that you do not get H2 + O2 reactions (something that would severely throw off results). There is also a chamber for holding a membrane so one side is help in vacuum, in connection to the gauge, and the other is exposed to hydrogen, or other gas at pressures up to 100 psig (∆P =115 psia). I’d tested to 200 psig, but currently feel like sticking to 100 psig or less. This device gives amazingly fast readings for plastics with permeabilities as low as 0.01 Barrer.

REB Research hydrogen permeation tester cell with valve and pressure sensor.

REB Research hydrogen permeation tester cell with valve and pressure sensor.

To control the temperature in this range of interest, the core device shown in the picture is put inside an environmental chamber, set up as shown below, with he control box outside the chamber. I include a nitrogen flush device as a safety measure so that any hydrogen that leaks from the high pressure chamber will not build up to reach explosive limits within the environmental chamber. If this device is used to measure permeation of a non-flammable gas, you won’t need to flush the environmental chamber.

I suggest one set up the vacuum pump right next to the entrance of the chamber; in the case of the chamber provided, that’s on the left as shown with the hydrogen tank and a nitrogen tank to the left of the pump. I’ve decided to provide a pressure sensor for the N2 (nitrogen) and a solenoidal shutoff valve for the H2 (hydrogen) line. These work together as a safety feature for long experiments. Their purpose is to automatically turn off the hydrogen if the nitrogen runs out. The nitrogen flush part of this process is a small gauge copper line that goes from the sensor into the environmental chamber with a small, N2 flow bleed valve at the end. I suggest setting the N2 pressure to 25-35 psig. This should give a good inert flow into the environmental chamber. You’ll want a nitrogen flush, even for short experiments, and most experiments will be short. You may not need an automatic N2 sensor, but you’ll be able to do this visually.

Basic setup for REB permeation tester and environmental chamber

Basic setup for REB permeation tester and environmental chamber

I shipped the permeation cell comes with some test, rubbery plastic. I’d recommend the customer leave it in for now, so he/she can use it for some basic testing. For actual experiments, you replace mutest plastic with the sample you want to check. Connect the permeation cell as shown above, using VCR gaskets (included), and connect the far end to the multi-temperature vacuum hose, provided. Do this outside of the chamber first, as a preliminary test to see if everything is working.

For a first test live the connections to the high pressure top section unconnected. The pressure then will be 1 atm, and the chamber will be full of air. eave the top, Connect the power to the vacuum pressure gauge reader and connect the gauge reader to the gauge head. Open the valve and turn on the pump. If there are no leaks the pressure should fall precipitously, and you should see little to no vapor coming out the out port on the vacuum pump. If there is vapor, you’ve got a leak, and you should find it; perhaps you didn’t tighten a VCR connection, or you didn’t do a good job with the vacuum hose. When things are going well, you should see the pressure drop to the single-digit, milliTorr range. If you close the valve, you’ll see the pressure rise in the gauge. This is mostly water and air degassing from the plastic sample. After 30 minutes, the rate of degassing should slow and you should be able to measure the rate of gas permeation in the polymer. With my test plastic, it took a minute or so for the pressure to rise by 10 milliTorr after I closed the valve.

If you like, you can now repeat this preliminary experiment with hydrogen connect the hydrogen line to one of the two ports on the top of the permeation cell and connect the other port to the rest of the copper tubing. Attach the H2 bleed restrictor (provided) at the end of this tubing. Now turn on the H2 pressure to some reasonable value — 45 psig, say. With 45 psi (3 barg upstream) you will have a ∆P of 60 psia or 4 atm across the membrane; vacuum equals -15 psig. Repeat the experiment above; pump everything down, close the valve and note that the pressure rises faster. The restrictor allows you to maintain a H2 pressure with a small, cleansing flow of gas through the cell.

If you like to do these experiments with a computer record, this might be a good time to connect your computer to the vacuum reader/ controller, and to the thermocouple, and to the N2 pressure sensor. 

Here’s how I calculate the permeability of the test polymer from the time it takes for a pressure rise assuming air as the permeating gas. The volume of the vacuumed out area after the valve is 32 cc; there is an open area in the cell of 13.0 cm2 and, as it happens, the  thickness of the test plastic is 2 mm. To calculate the permeation rate, measure the time to rise 10 millitorr. Next calculate the millitorr per hour: that’s 360 divided by the time to rise ten milliTorr. To calculate ncc/day, multiply the millitorr/hour by 24 and by the volume of the chamber, 32 cc, and divide by 760,000, the number of milliTorr in an atmosphere. I found that, for air permeation at ∆P = one atm, I was getting 1 minute per milliTorr, which translates to about 0.5 ncc/day of permeation through my test polymer sheet. To find the specific permeability in cc.mm/m2.day.atm, I multiply this last number by the thickness of the plastic (2 mm in this case), divide by the area, 0.0013 m2, and divide by ∆P, 1 atm, for this first test. Calculated this way, I got an air permeance of 771 cc.mm/m2.day.atm.

The complete setup for permeation testing.

The complete setup for permeation testing.

Now repeat the experiment with hydrogen and your own plastic. Disconnect the cell from both the vacuum line and from the hydrogen in line. Open the cell; take out my test plastic and replace it with your own sample, 1.87” diameter, or so. Replace the gasket, or reuse it. Center the top on the bottom and retighten the bolts. I used 25 Nt-m of torque, but part of that was using a very soft rubbery plastic. You might want to use a little more — perhaps 40-50 Nt-m. Seal everything up. Check that it is leak tight, and you are good to go.

The experimental method is the same as before and the only signficant change when working with hydrogen, besides the need for a nitrogen flush, is that you should multiply the time to reach 10 milliTorr by the square-root of seven, 2.646. Alternatively, you can multiply the calculated permeability by 0.378. The pressure sensor provided measures heat transfer and hydrogen is a better heat transfer material than nitrogen by a factor of √7. The vacuum gauge is thus more sensitive to H2 than to N2. When the gauge says that a pressure change of 10 milliTorr has occurred, in actuality, it’s only 3.78 milliTorr.  The pressure gauge reads 3.78 milliTorr oh hydrogen as 10 milliTorr.

You can speed experiments by a factor of ten, by testing the time to rise 1 millitorr instead of ten. At these low pressures, the gauge I provided reads in hundredths of a milliTorr. Alternately, for higher permeation plastics (or metals) you want to test the time to rise 100 milliTorr or more, otherwise the experiment is over too fast. Even at a ten millTorr change, this device gives good accuracy in under 1 hour with even the most permeation-resistant polymers.

Dr. Robert E. Buxbaum, March 27, 2019; If you’d like one of these, just ask. Here’s a link to our web site, REB Research,

Why concrete cracks and why sealing is worthwhile

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The oil tanker Palo Alto is one of several major ships made with concrete hulls.

The oil tanker Palo Alto is one of several major ships made with concrete hulls.

Modern concrete is a wonderful construction material. Major buildings are constructed of it, and major dams, and even some ships. But under the wrong circumstances, concrete has a surprising tendency to crack and fail. I thought I’d explain why that happens and what you can do about it. Concrete does not have to crack easily; ancient concrete didn’t and military or ship concrete doesn’t today. A lot of the fault lies in the use of cheap concrete — concrete with lots of filler — and with the cheap way that concrete is laid. First off, the major components of modern concrete are pretty uniform: sand and rock, Portland cement powder (made from cooked limestone, mostly), water, air, and sometimes ash. The cement component is what holds it all together — cements it together as it were — but it is not the majority of even the strongest concretes. The formula of cement has changed too, but the cement is not generally the problem. It doesn’t necessarily stick well to the rock or sand component of concrete (It sticks far better to itself) but it sticks well enough that spoliation, isn’t usually a problem by itself.

What causes problem is that the strength of concrete is strongly affected (decreased) by having lots of sand, aggregate and water. The concrete used in sidewalks is as cheap as possible, with lots of sand and aggregate. Highway and wall concrete has less sand and aggregate, and is stronger. Military and ship concrete has little sand, and is quite a lot stronger. The lowest grade, used in sidewalks, is M5, a term that refers to its compressive strength: 5 Mega Pascals. Pascals are European (Standard International) units of pressure and of strength. One Pascal is one Newton per square meter (Here’ a joke about Pascal units). In US (English) units, 5 MPa is 50 atm or 750 psi.

Ratios for concrete mixes of different strength.

Ratios for concrete mixes of different strength; the numbers I use are double these because these numbers don’t include water; that’s my “1”.

The ratio of dry ingredients in various concretes is shown at right. For M5, and including water, the ratio is 1 2 10 20. That is to say there is one part water, two parts cement, 10 parts sand, and 20 parts stone-aggregate (all these by weight). Added to this is 2-3% air, by volume, or nearly as much air as water. At least these are the target ratios; it sometimes happens that extra air and water are added to a concrete mix by greedy or rushed contractors. It’s sometimes done to save money, but more often because the job ran late. The more the mixer turns the more air gets added. If it turns too long there is extra air. It the job runs late, workers will have to add extra water too because the concrete starts hardening. I you see workers hosing down wet concrete as it comes from the truck, this is why. As you might expect, extra air and water decrease the strength of the product. M-10 and M-20 concrete have less sand, stone, and water as a proportion to cement. The result is 10 MPa or 20 MPa strength respectively.

A good on-site inspector is needed to keep the crew from adding too much water. Some water is needed for the polymerization (setting) of the concrete. The rest is excess, and when it evaporates, it leaves voids that are similar to the voids created by having air mix in. It is not uncommon to find 6% voids, in commercial concrete. This is to say that, after the water evaporates, the concrete contains about as much void as cement by volume. To get a sense of how much void space is in the normal concrete outside your house, go outside to a piece of old concrete (10 years old at least) on a hot, dry day, and pour out a cup of water. You will hear a hiss as the water absorbs, and you will see bubbles come out as the water goes in. It used to be common for cities to send inspectors to measuring the void content of the wet (and dry) concrete by a technique called “pycnometry” (that’s Greek for density measurement). I’ve not seen a local city do this in years, but don’t know why. An industrial pycnometer is shown below.

Pyncnometer used for concrete. I don't see these in use much any more.

Pycnometer used for concrete. I don’t see these in use much any more.

One of the main reason that concrete fails has to do with differential expansion, thermal stress, a concept I dealt with some years ago when figuring out how cold it had to be to freeze the balls off of a brass monkey. As an example of the temperature change to destroy M5, consider that the thermal expansion of cement is roughly 1 x 10-5/ °F or 1.8 x10-5/°C. This is to say that a 1 meter slab of cement that is heated or cooled by 100°F will expand or shrink by 10-3 m respectively; 100 x 1×10-5 = 10-3. This is a fairly large thermal expansion coefficient, as these things go. It would not cause stress-failure except that sand and rock have a smaller thermal expansion coefficients, about 0.6×10-5 — barely more than half the value for cement. Consider now what happens to concrete that s poured in the summer when it is 80°F out, and where the concrete heats up 100°F on setting (cement setting releases heat). Now lets come back in winter when it’s 0°F. This is a total of 100°F of temperature change. The differential expansion is 0.4 x 10-5/°F x 100°F =  4 x10-4 meter/meter = 4 x10-4 inch/inch.

The force created by this differential expansion is the elastic modulus of the cement times the relative change in expansion. The elastic modulus for typical cement is 20 GPa or, in English units, 3 million psi. This is to say that, if you had a column of cement (not concrete), one psi of force would compress it by 1/3,000,000. The differential expansion we calculated, cement vs sand and stone is 4×10-4 ; this much expansion times the elastic modulus, 3,000,000 = 1200 psi. Now look at the strength of the M-5 cement; it’s only 750 psi. When M-5 concrete is exposed to these conditions it will not survive. M-10 will fail on its own, from the temperature change, without any help needed from heavy traffic. You’d really like to see cities check the concrete, but I’ve seen little evidence that they do.

Water makes things worse, and not only because it creates voids when it evaporates. Water also messes up the polymerization reaction of the cement. Basic, fast setting cement is mostly Ca3SiO5

2Ca3SiO5 + 6 H2O –> 3Ca0SiO2•H2O +3Ca(OH)2•H2O.

The former of these, 3Ca0SiO2•H2O, forms something of a polymer. Monomer units of SiO4 are linked directly or by partially hydrated CaO linkages. Add too much water and the polymeric linkages are weakened or do not form at all. Over time the Ca(OH)2 can drain away or react with  CO2 in the air to form chalk.

concrete strength versus-curing time. Slow curing of damp concrete helps; fast dry hurts. Carbonate formation adds little or no strength. Jehan Elsamni 2011.

Portland limestone cement strength versus curing time. Slow curing and damp helps; fast dry hurts. Carbonate formation adds little or no strength. Jehan Elsamni 2011.

Ca(OH)2 + CO2 → CaCO3 + H2O

Sorry to say, the chalk adds little or no strength, as the graph at right shows. Concrete made with too much water isn’t very strong at all, and it gets no stronger when dried in air. Hardening goes on for some weeks after pouring, and this is the reason you don’t drive on 1 too 2 day old concrete. Driving on weak concrete can cause cracks that would not form if you waited.

You might think to make better concrete by pouring concrete in the cold, but pouring in the cold makes things worse. Cold poured cement will expand the summer and the cement will detach from the sand and stone. Ideally, pouring should be in spring or fall, when the temperature is moderate, 40-60°F. Any crack that develops grows by a mechanism called Rayleigh crack growth, described here. Basically, once a crack starts, it concentrates the fracture forces, and any wiggling of the concrete makes the crack grow faster.

Based on the above, I’ve come to suspect that putting on a surface coat can (could) help strengthen old concrete, even long after it’s hardened. Mostly this would happen by filling in voids and cracks, but also by extending the polymer chains. I imagine it would be especially helpful to apply the surface coat somewhat watery on a dry day in the summer. In that case, I imagine that Ca3SiO5 and Ca(OH)2 from the surface coat will penetrate and fill the pores of the concrete below — the sales pores that hiss when you pour water on them. I imagine this would fill cracks and voids, and extend existing CaOSiO2•H2O chains. The coat should add strength, and should be attractive as well. At least that was my thought.

I should note that, while Portland cement is mostly Ca3SiO5, there is also a fair amount (25%) of Ca2SiO4. This component reacts with water to form the same calcium-silicate polymer as above, but does so at a slower rate using less water per gram. My hope was that this component would be the main one to diffuse into deep pores of the concrete, reacting there to strengthen the concrete long after surface drying had occurred.

Trump tower: 664', concrete and glass. What grade of concrete would you use?

Trump tower: 664′, concrete and glass. What grade of concrete would you use?

As it happened, I had a chance to test my ideas this summer and also about 3 years ago. The city inspector came by to say the concrete flags outside my house were rough, and thus needed replacing, and that I was to pay or do it myself. Not that I understand the need for smooth concrete, quite, but that’s our fair city. I applied for a building permit to apply a surface coat, and applied it watery. I used “Quickrete” brand concrete patch, and so far it’s sticking OK. Pock-holes in the old concrete have been filled in, and so far surface is smooth. We’ll have to see if my patch lasts 10-20 years like fresh cement. Otherwise, no matter how strong the concrete becomes underneath, the city will be upset, and I’ll have to fix it. I’ve noticed that there is already some crumbling at the sides of flags, something I attribute to the extra water. It’s not a problem yet, but hope this is not the beginning of something worse. If I’m wrong here, and the whole seal-coat flakes off, I’ll be stuck replacing the flags, or continuing to re-coat just to preserve my reputation. But that’s the cost of experimentation. I tried something new, and am blogging about it in the hope that you and I benefit. “Education is what you get when you don’t get what you want.” (It’s one of my wise sayings). At the worst, I’ll have spent 90 lb of patching cement to get an education. And, I’m happy to say that some of the relatively new concrete flags that the city put in are already cracked. I attribute this to: too much sand, air, water or air (they don’t look like they have much rock): Poor oversight.

Dr. Robert E. Buxbaum. March 5, 2019. As an aside, the 664 foot Trump Tower, NY is virtually the only skyscraper in the city to be built of concrete and glass. The others are mostly steel and glass. Concrete and glass is supposed to be stiffer and quieter. The engineer overseeing the project was Barbara Res, the first woman to oversee a major, NY building project. Thought question: if you built the Trump Tower, which quality of concrete would you use, and why.