Category Archives: REB Research products

Adding H2 to an engine improves mpg, lowers pollution.

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I month ago, I wrote to endorse hythane, a mix of natural gas (methane) and 20-40% hydrogen. This mix is ideal for mobile use in solid oxide fuel cell vehicles, and not bad with normal IC engines. I’d now like to write about the advantages of an on-broad hydrogen generator to allow adjustable composition fuel mixes.

A problem you may have noticed with normal car engines is that a high hp engine will get lower miles per gallon, especially when you’re driving slow. That seems very strange; why should a bigger engine use more gas than a dinky engine, and why should you get lower mpg when you drive slow. The drag force on a vehicle is proportional to speed squared. You’d expect better milage at low speeds– something that textbooks claim you will see, counter to experience.

Behind these two problems are issues of fuel combustion range and pollution. You can solve both issues with hydrogen. With normal gasoline or Diesel engines, you get more or less the same amount of air per engine rotation at all rpm speeds, but the amount of air is much higher for big engines. There is a relatively small range of fuel-air mixes that will burn, and an even smaller range that will burn at low pollution. You have to add at least the minimal fuel per rotation to allow the engine to fire. For most driving that’s the amount the carburetor delivers. Because of gearing, your rpm is about the same at all speeds, you use almost the same rate of fuel at all speeds, with more fuel used in big engines. A gas engine can run lean, but normally speaking it doesn’t run at all any leaner than about 1.6 times the stoichiometric air-to-fuel mix. This is called a lambda of 1.6. Adding hydrogen extends the possible lambda range, as shown below for a natural gas – fired engine.

Engine efficiency when fueled with natural gas plus hydrogen as a function of hydrogen amount and lambda, the ratio of air to stoichiometric air.

The more hydrogen in the mix the wider the range, and the less pollution generally. Pure hydrogen burns at ten times stoichiometric air, a lambda of ten. There is no measurable pollution there, because there is no carbon to form CO, and temperature is so low that you don’t form NOx. But the energy output per rotation is low (there is not much energy in a volume of hydrogen) and hydrogen is more expensive than gasoline or natural gas on an energy basis. Using just a little hydrogen to run an engine at low load may make sense, but the ideal mix of hydrogen and ng fuel will change depending on engine load. At high load, you probably want to use no hydrogen in the mix.

As it happens virtually all of most people’s driving is at low load. The only time when you use the full horse-power is when you accelerate on a highway. An ideal operation for a methane-fueled car would add hydrogen to the carburetor intake at about 1/10 stoichiometric when the car idles, turning down the hydrogen mix as the load increases. REB Research makes hydrogen generators based on methanol reforming, but we’ve yet to fit one to a car. Other people have shown that adding hydrogen does improve mpg.

Carburetor Image from a course “Farm Power”. See link here. Adding hydrogen means you could use less gas.

Adding hydrogen plus excess air means there is less pollution. There is virtually no CO at idle because there is virtually no carbon, and even at load because combustion is more efficient. The extra air means that combustion is cooler, and thus you get no NOx or unburned HCs, even without a catalytic converter. Hydrogen is found to improve combustion speed and extent. A month ago, I’d applied for a grant to develop a hydrogen generator particularly suited to methane engines. Sorry to say, the DoT rejected my proposal.

Robert Buxbaum June 24, 2021

Upgrading landfill and digester gas for sale, methanol

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We live in a throw-away society, and the majority of it, eventually makes its way to a landfill. Books, food, grass clippings, tree-products, consumer electronics; unless it gets burnt or buried at sea, it goes to a landfill and is left to rot underground. The product of this rot is a gas, landfill gas, and it has a fairly high energy content if it could be tapped. The composition of landfill gas changes, but after the first year or so, the composition settles down to a nearly 50-50 mix of CO2 and methane. There is a fair amount of water vapor too, plus some nitrogen and hydrogen, but the basic process is shown below for wood decomposition, and the products are CO2  and methane.

System for sewage gas upgrading, uses REB membranes.

C6 H12 O6  –> 3 CO2  + 3 CH4 

This mix can not be put in the normal pipeline: there is too much CO2  and there are too many other smelly or condensible compounds (water, methanol, H2S…). This gas is sometimes used for heat on site, but there is a limited need for heat near a landfill. For the most part it is just vented or flared off. The waste of a potential energy source is an embarrassment. Besides, we are beginning to notice that methane causes global-warming with about 50 times the effect of CO2, so there is a strong incentive to capture and burn this gas, even if you have no use for the heat. I’d like to suggest a way to use the gas.

We sell small membrane modules too.

The landfill gas can be upgraded by removing the CO2. This can be done via a membrane, and REB Research sells a membranes that can do this. Other companies have other membranes that can do this too, but ours are smaller, and more suitable to small operations in my opinion. Our membrane are silicone-based. They retain CH4 and CO and hydrogen, while extracting water, CO2 and H2S, see schematic. The remainder is suited for local use in power generation, or in methanol production. It can also be used to run trucks. Also the gas can be upgraded further and added to a pipeline for shipping elsewhere. The useless parts can be separated for burial. Find these membranes on the REB web-site under silicone membranes.

Garbage trucks in New York powered by natural gas. They could use landfill gas.

There is another gas source whose composition is nearly identical to that of landfill gas; it’s digester gas, the output of sewage digesters. I’ve written about sewage treatment mostly in terms of aerobic bio treatment, for example here, but sewage can be treated anaerobically too, and the product is virtually identical to landfill gas. I think it would be great to power garbage trucks and buses with this. Gas. In New York, currently, some garbage trucks are powered by natural gas.

As a bonus, here’s how to make methanol from partially upgraded landfill or digester gas. As a first step 2/3 of the the CO2 removed. The remained will convert to methanol. by the following overall chemistry:

3 CH4 + CO2 + 2 H2O –> 4 CH3OH. 

When you removed the CO2., likely most of the water will leave with it. You add back the water as steam and heat to 800°C over Ni catalyst to make CO and H2. That’s done at about 800°C and 200 psi. Next, at lower temperature, with an appropriate catalyst you recombine the CO and H2 into methanol; with other catalysts you can make gasoline. These are not trivial processes, but they are doable on a smallish scale, and make economic sense where the methane is essentially free and there is no CNG customer. Methanol sells for $1.65/gal when sold by the tanker full, but $5 to $10/gal at the hardware store. That’s far higher than the price of methane, and methanol is far easier to ship and sell in truckload quantities.

Robert Buxbaum, June 8, 2021

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.

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,

Of God and gauge blocks

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Most scientists are religious on some level. There’s clear evidence for a big bang, and thus for a God-of-Creation. But the creation event is so distant and huge that no personal God is implied. I’d like to suggest that the God of creation is close by and as a beginning to this, I’d like to discus Johansson gauge blocks, the standard tool used to measure machine parts accurately.

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A pair of Johansson blocks supporting 100 kg in a 1917 demonstration. This is 33 times atmospheric pressure, about 470 psi.

Lets say you’re making a complicated piece of commercial machinery, a car engine for example. Generally you’ll need to make many parts in several different shops using several different machines. If you want to be sure the parts will fit together, a representative number of each part must be checked for dimensional accuracy in several places. An accuracy requirement of 0.01 mm is not uncommon. How would you do this? The way it’s been done, at least since the days of Henry Ford, is to mount the parts to a flat surface and use a feeler gauge to compare the heights of the parts to the height of stacks of precisely manufactured gauge blocks. Called Johansson gauge blocks after the inventor and original manufacturer, Henrik Johansson, the blocks are typically made of steel, 1.35″ wide by .35″ thick (0.47 in2 surface), and of various heights. Different height blocks can be stacked to produce any desired height in multiples of 0.01 mm. To give accuracy to the measurements, the blocks must be manufactured flat to within 1/10000 of a millimeter. This is 0.1µ, or about 1/5 the wavelength of visible light. At this degree of flatness an amazing thing is seen to happen: Jo blocks stick together when stacked with a force of 100 kg (220 pounds) or more, an effect called, “wringing.” See picture at right from a 1917 advertising demonstration.

This 220 lbs of force measured in the picture suggests an invisible pressure of 470 psi at least that holds the blocks together (220 lbs/0.47 in2 = 470 psi). This is 32 times the pressure of the atmosphere. It is independent of air, or temperature, or the metal used to make the blocks. Since pressure times volume equals energy, and this pressure can be thought of as a vacuum energy density arising “out of the nothingness.” We find that each cubic foot of space between the blocks contains, 470 foot-lbs of energy. This is the equivalent of 0.9 kWh per cubic meter, energy you can not see, but you can feel. That is a lot of energy in the nothingness, but the energy (and the pressure) get larger the flatter you make the surfaces, or the closer together you bring them together. This is an odd observation since, generally get more dense the smaller you divide them. Clean metal surfaces that are flat enough will weld together without the need for heat, a trick we have used in the manufacture of purifiers.

A standard way to think of quantum scattering is that the particle is scattered by invisible bits of light (virtual photons), the wavy lines. In this view, the force that pushes two flat surfaces together is from a slight deficiency in the amount of invisible light in the small space between them.

A standard way to think of quantum scattering of an atom (solid line) is that it is scattered by invisible bits of light, virtual photons (the wavy lines). In this view, the force that pushes two blocks together comes from a slight deficiency in the number of virtual photons in the small space between the blocks.

The empty space between two flat surfaces also has the power to scatter light or atoms that pass between them. This scattering is seen even in vacuum at zero degrees Kelvin, absolute zero. Somehow the light or atoms picks up energy, “out of the nothingness,” and shoots up or down. It’s a “quantum effect,” and after a while physics students forget how odd it is for energy to come out of nothing. Not only do students stop wondering about where the energy comes from, they stop wondering why it is that the scattering energy gets bigger the closer you bring the surfaces. With Johansson block sticking and with quantum scattering, the energy density gets higher the closer the surface, and this is accepted as normal, just Heisenberg’s uncertainly in two contexts. You can calculate the force from the zero-point energy of vacuum, but you must add a relativistic wrinkle: the distance between two surfaces shrinks the faster you move according to relativity, but measurable force should not. A calculation of the force that includes both quantum mechanics and relativity was derived by Hendrik Casimir:

Energy per volume = P = F/A = πhc/ 480 L4,

where P is pressure, F is force, A is area, h is plank’s quantum constant, 6.63×10−34 Js, c is the speed of light, 3×108 m/s, and L is the distance between the plates, m. Experiments have been found to match the above prediction to within 2%, experimental error, but the energy density this implies is huge, especially when L is small, the equation must apply down to plank lengths, 1.6×10-35 m. Even at the size of an atom, 1×10-10m, the amount of the energy you can see is 3.6 GWhr/m3, 3.6 Giga Watts. 3.6 GigaWatt hrs is one hour’s energy output of three to four large nuclear plants. We see only a tiny portion of the Plank-length vacuum energy when we stick Johansson gauge blocks together, but the rest is there, near invisible, in every bit of empty space. The implication of this enormous energy remains baffling in any analysis. I see it as an indication that God is everywhere, exceedingly powerful, filling the universe, and holding everything together. Take a look, and come to your own conclusions.

As a homiletic, it seems to me that God likes friendship, but does not desire shaman, folks to stand between man and Him. Why do I say that? The huge force-energy between plates brings them together, but scatters anything that goes between. And now you know something about nothing.

Robert Buxbaum, November 7, 2018. Physics references: H. B. G. Casimir and D. Polder. The Influence of Retardation on the London-van der Waals Forces. Phys. Rev. 73, 360 (1948).
S. Lamoreaux, Phys. Rev. Lett. 78, 5 (1996).

Isotopic effects in hydrogen diffusion in metals

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For most people, there is a fundamental difference between solids and fluids. Solids have long-term permanence with no apparent diffusion; liquids diffuse and lack permanence. Put a penny on top of a dime, and 20 years later the two coins are as distinct as ever. Put a layer of colored water on top of plain water, and within a few minutes you’ll see that the coloring diffuse into the plain water, or (if you think the other way) you’ll see the plain water diffuse into the colored.

Now consider the transport of hydrogen in metals, the technology behind REB Research’s metallic  membranes and getters. The metals are clearly solid, keeping their shapes and properties for centuries. Still, hydrogen flows into and through the metals at a rate of a light breeze, about 40 cm/minute. Another way of saying this is we transfer 30 to 50 cc/min of hydrogen through each cm2 of membrane at 200 psi and 400°C; divide the volume by the area, and you’ll see that the hydrogen really moves through the metal at a nice clip. It’s like a normal filter, but it’s 100% selective to hydrogen. No other gas goes through.

To explain why hydrogen passes through the solid metal membrane this way, we have to start talking about quantum behavior. It was the quantum behavior of hydrogen that first interested me in hydrogen, some 42 years ago. I used it to explain why water was wet. Below, you will find something a bit more mathematical, a quantum explanation of hydrogen motion in metals. At REB we recently put these ideas towards building a membrane system for concentration of heavy hydrogen isotopes. If you like what follows, you might want to look up my thesis. This is from my 3rd appendix.

Although no-one quite understands why nature should work this way, it seems that nature works by quantum mechanics (and entropy). The basic idea of quantum mechanics you will know that confined atoms can only occupy specific, quantized energy levels as shown below. The energy difference between the lowest energy state and the next level is typically high. Thus, most of the hydrogen atoms in an atom will occupy only the lower state, the so-called zero-point-energy state.

A hydrogen atom, shown occupying an interstitial position between metal atoms (above), is also occupying quantum states (below). The lowest state, ZPE is above the bottom of the well. Higher energy states are degenerate: they appear in pairs. The rate of diffusive motion is related to ∆E* and this degeneracy.

A hydrogen atom, shown occupying an interstitial position between metal atoms (above), is also occupying quantum states (below). The lowest state, ZPE is above the bottom of the well. Higher energy states are degenerate: they appear in pairs. The rate of diffusive motion is related to ∆E* and this degeneracy.

The fraction occupying a higher energy state is calculated as c*/c = exp (-∆E*/RT). where ∆E* is the molar energy difference between the higher energy state and the ground state, R is the gas constant and T is temperature. When thinking about diffusion it is worthwhile to note that this energy is likely temperature dependent. Thus ∆E* = ∆G* = ∆H* – T∆S* where asterisk indicates the key energy level where diffusion takes place — the activated state. If ∆E* is mostly elastic strain energy, we can assume that ∆S* is related to the temperature dependence of the elastic strain.

Thus,

∆S* = -∆E*/Y dY/dT

where Y is the Young’s modulus of elasticity of the metal. For hydrogen diffusion in metals, I find that ∆S* is typically small, while it is often typically significant for the diffusion of other atoms: carbon, nitrogen, oxygen, sulfur…

The rate of diffusion is now calculated assuming a three-dimensional drunkards walk where the step lengths are constant = a. Rayleigh showed that, for a simple cubic lattice, this becomes:

D = a2/6τ

a is the distance between interstitial sites and t is the average time for crossing. For hydrogen in a BCC metal like niobium or iron, D=

a2/9τ; for a FCC metal, like palladium or copper, it’s

a2/3τ. A nice way to think about τ, is to note that it is only at high-energy can a hydrogen atom cross from one interstitial site to another, and as we noted most hydrogen atoms will be at lower energies. Thus,

τ = ω c*/c = ω exp (-∆E*/RT)

where ω is the approach frequency, or the amount of time it takes to go from the left interstitial position to the right one. When I was doing my PhD (and still likely today) the standard approach of physics writers was to use a classical formulation for this time-scale based on the average speed of the interstitial. Thus, ω = 1/2a√(kT/m), and

τ = 1/2a√(kT/m) exp (-∆E*/RT).

In the above, m is the mass of the hydrogen atom, 1.66 x 10-24 g for protium, and twice that for deuterium, etc., a is the distance between interstitial sites, measured in cm, T is temperature, Kelvin, and k is the Boltzmann constant, 1.38 x 10-16 erg/°K. This formulation correctly predicts that heavier isotopes will diffuse slower than light isotopes, but it predicts incorrectly that, at all temperatures, the diffusivity of deuterium is 1/√2 that for protium, and that the diffusivity of tritium is 1/√3 that of protium. It also suggests that the activation energy of diffusion will not depend on isotope mass. I noticed that neither of these predictions is borne out by experiment, and came to wonder if it would not be more correct to assume ω represent the motion of the lattice, breathing, and not the motion of a highly activated hydrogen atom breaking through an immobile lattice. This thought is borne out by experimental diffusion data where you describe hydrogen diffusion as D = D° exp (-∆E*/RT).

Screen Shot 2018-06-21 at 12.08.20 AM

You’ll notice from the above that D° hardly changes with isotope mass, in complete contradiction to the above classical model. Also note that ∆E* is very isotope dependent. This too is in contradiction to the classical formulation above. Further, to the extent that D° does change with isotope mass, D° gets larger for heavier mass hydrogen isotopes. I assume that small difference is the entropy effect of ∆E* mentioned above. There is no simple square-root of mass behavior in contrast to most of the books we had in grad school.

As for why ∆E* varies with isotope mass, I found that I could get a decent explanation of my observations if I assumed that the isotope dependence arose from the zero point energy. Heavier isotopes of hydrogen will have lower zero-point energies, and thus ∆E* will be higher for heavier isotopes of hydrogen. This seems like a far better approach than the semi-classical one, where ∆E* is isotope independent.

I will now go a bit further than I did in my PhD thesis. I’ll make the general assumption that the energy well is sinusoidal, or rather that it consists of two parabolas one opposite the other. The ZPE is easily calculated for parabolic energy surfaces (harmonic oscillators). I find that ZPE = h/aπ √(∆E/m) where m is the mass of the particular hydrogen atom, h is Plank’s constant, 6.63 x 10-27 erg-sec,  and ∆E is ∆E* + ZPE, the zero point energy. For my PhD thesis, I didn’t think to calculate ZPE and thus the isotope effect on the activation energy. I now see how I could have done it relatively easily e.g. by trial and error, and a quick estimate shows it would have worked nicely. Instead, for my PhD, Appendix 3, I only looked at D°, and found that the values of D° were consistent with the idea that ω is about 0.55 times the Debye frequency, ω ≈ .55 ωD. The slight tendency for D° to be larger for heavier isotopes was explained by the temperature dependence of the metal’s elasticity.

Two more comments based on the diagram I presented above. First, notice that there is middle split level of energies. This was an explanation I’d put forward for quantum tunneling atomic migration that some people had seen at energies below the activation energy. I don’t know if this observation was a reality or an optical illusion, but present I the energy picture so that you’ll have the beginnings of a description. The other thing I’d like to address is the question you may have had — why is there no zero-energy effect at the activated energy state. Such a zero energy difference would cancel the one at the ground state and leave you with no isotope effect on activation energy. The simple answer is that all the data showing the isotope effect on activation energy, table A3-2, was for BCC metals. BCC metals have an activation energy barrier, but it is not caused by physical squeezing between atoms, as for a FCC metal, but by a lack of electrons. In a BCC metal there is no physical squeezing, at the activated state so you’d expect to have no ZPE there. This is not be the case for FCC metals, like palladium, copper, or most stainless steels. For these metals there is a much smaller, on non-existent isotope effect on ∆E*.

Robert Buxbaum, June 21, 2018. I should probably try to answer the original question about solids and fluids, too: why solids appear solid, and fluids not. My answer has to do with quantum mechanics: Energies are quantized, and always have a ∆E* for motion. Solid materials are those where ω exp (-∆E*/RT) has unit of centuries. Thus, our ability to understand the world is based on the least understandable bit of physics.

Survey on hydrogen use

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My company makes hydrogen generators: devices that make ultra-pure hydrogen on demand from methanol and water using a membrane reactor. If you use hydrogen, please fill out the following survey. I need to know my customers needs better, e.g. so that I will know if I should add a compressor. Thanks.

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Robert Buxbaum, June 13, 2018

Hydrogen permeation rates in Inconel, Hastelloy and stainless steels.

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Some 20 years ago, I published a graph of the permeation rate for hydrogen in several metals at low pressure, See the graph here, but I didn’t include stainless steel in the graph.

Hydrogen permeation in clean SS-304; four research groups’ data.

One reason I did not include stainless steel was there were many stainless steels and the hydrogen permeation rates were different, especially so between austenitic (FCC) steels and ferritic steels (BCC). Another issue was oxidation. All stainless steels are oxidized, and it affect H2 permeation a lot. You can decrease the hydrogen permeation rate significantly by oxidation, or by surface nitriding, etc (my company will even provide this service). Yet another issue is cold work. When  an austenitic stainless steel is worked — rolled or drawn — some Austinite (FCC) material transforms to Martisite (a sort of stretched BCC). Even a small amount of martisite causes an order of magnitude difference in the permeation rate, as shown below. For better or worse, after 20 years, I’m now ready to address H2 in stainless steel, or as ready as I’m likely to be.

Hydrogen permeation data for SS 340 and SS 321.

Hydrogen permeation in SS 340 and SS 321. Cold work affects H2 permeation more than the difference between 304 and 321; Sun Xiukui, Xu Jian, and Li Yiyi, 1989

The first graph I’d like to present, above, is a combination of four research groups’ data for hydrogen transport in clean SS 304, the most common stainless steel in use today. SS 304 is a ductile, austenitic (FCC), work hardening, steel of classic 18-8 composition (18% Cr, 8% Ni). It shares the same basic composition with SS 316, SS 321 and 304L only differing in minor components. The data from four research groups shows a lot of scatter: a factor of 5 variation at high temperature, 1000 K (727 °C), and almost two orders of magnitude variation (factor of 50) at room temperature, 13°C. Pressure is not a factor in creating the scatter, as all of these studies were done with 1 atm, 100 kPa hydrogen transporting to vacuum.

The two likely reasons for the variation are differences in the oxide coat, and differences in the amount of cold work. It is possible these are the same explanation, as a martensitic phase might increase H2 permeation by introducing flaws into the oxide coat. As the graph at left shows, working these alloys causes more differences in H2 permeation than any difference between alloys, or at least between SS 304 and SS 321. A good equation for the permeation behavior of SS 304 is:

P (mol/m.s.Pa1/2) = 1.1 x10-6 exp (-8200/T).      (H2 in SS-304)

Because of the song influence of cold work and oxidation, I’m of the opinion that I get a slightly different, and better equation if I add in permeation data from three other 18-8 stainless steels:

P (mol/m.s.Pa1/2) = 4.75 x10-7 exp (-7880/T).     (H2 in annealed SS-304, SS-316, SS-321)

Screen Shot 2017-12-16 at 10.37.37 PM

Hydrogen permeation through several common stainless steels, as well as Inocnel and Hastelloy

Though this result is about half of the previous at high temperature, I would trust it better, at least for annealed SS-304, and also for any annealed austenitic stainless steel. Just as an experiment, I decided to add a few nickel and cobalt alloys to the mix, and chose to add data for inconel 600, 625, and 718; for kovar; for Hastelloy, and for Fe-5%Si-5%Ge, and SS4130. At left, I pilot all of these on one graph along with data for the common stainless steels. To my eyes the scatter in the H2 permeation rates is indistinguishable from that SS 304 above or in the mixed 18-8 steels (data not shown). Including these materials to the plot decreases the standard deviation a bit to a factor of 2 at 1000°K and a factor of 4 at 13°C. Making a least-square analysis of the data, I find the following equation for permeation in all common FCC stainless steels, plus Inconels, Hastelloys and Kovar:

P (mol/m.s.Pa1/2) = 4.3 x10-7 exp (-7850/T).

This equation is near-identical to the equation above for mixed, 18-8 stainless steel. I would trust it for annealed or low carbon metal (SS-304L) to a factor of 2 accuracy at high temperatures, or a factor of 4 at low temperatures. Low carbon reduces the tendency to form Martinsite. You can not use any of these equations for hydrogen in ferritic (BCC) alloys as the rates are different, but this is as good as you’re likely to get for basic austenitc stainless and related materials. If you are interested in the effect of cold work, here is a good reference. If you are bothered by the square-root of pressure driving force, it’s a result of entropy: hydrogen travels in stainless steel as dislocated H atoms and the dissociation H2 –> 2 H leads to the square root.

Robert Buxbaum, December 17, 2017. My business, REB Research, makes hydrogen generators and purifiers; we sell getters; we consult on hydrogen-related issues, and will (if you like) provide oxide (and similar) permeation barriers.

The hydrogen jerrycan

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Here’s a simple invention, one I’ve worked on off-and-on for years, but never quite built. I plan to work on it more this summer, and may finally build a prototype: it’s a hydrogen Jerry can. The need to me is terrifically obvious, but the product does not exist yet.

To get a view of the need, imagine that it’s 5-10 years in the future and you own a hydrogen, fuel cell car. You’ve run out of gas on a road somewhere, per haps a mile or two from the nearest filling station, perhaps more. You make a call to the AAA road-side service and they show up with enough hydrogen to get you to the next filling station. Tell me, how much hydrogen did they bring? 1 kg, 2 kg, 5 kg? What did the container look like? Is there one like it in your garage?

The original, German "Jerry" can. It was designed at the beginning of WWII to help the Germans to overrun Europe.

The original, German “Jerry” can. It was designed at the beginning of WWII to help the Germans to overrun Europe. I imagine the hydrogen version will be red and roughly these dimensions, though not quite this shape.

I figure that, in 5-10 years these hydrogen containers will be so common that everyone with a fuel cell car will have one, somewhere. I’m pretty confident too that hydrogen cars are coming soon. Hydrogen is not a total replacement for gasoline, but hydrogen energy provides big advantages in combination with batteries. It really adds to automotive range at minimal cost. Perhaps, of course this is wishful thinking as my company makes hydrogen generators. Still it seems worthwhile to design this important component of the hydrogen economy.

I have a mental picture of what the hydrogen delivery container might look like based on the “Jerry can” that the Germans (Jerrys) developed to hold gasoline –part of their planning for WWII. The story of our reverse engineering of it is worth reading. While the original can was green for camouflage, modern versions are red to indicate flammable, and I imagine the hydrogen Jerry will be red too. It must be reasonably cheap, but not too cheap, as safety will be a key issue. A can that costs $100 or so does not seem excessive. I imagine the hydrogen Jerry can will be roughly rectangular like the original so it doesn’t roll about in the trunk of a car, and so you can stack a few in your garage, or carry them conveniently. Some folks will want to carry an extra supply if they go on a long camping trip. As high-pressure tanks are cylindrical, I imagine the hydrogen-jerry to be composed of two cylinders, 6 1/2″ in diameter about. To make the rectangular shape, I imagine the cylinders attached like the double pack of a scuba diver. To match the dimensions of the original, the cylinders will be 14″ to 20″ tall.

I imagine that the hydrogen Jerry can will have at least two spouts. One spout so it can be filled from a standard hydrogen dispenser, and one so it can be used to fill your car. I suspect there may be an over-pressure relief port as well, for safety. The can can’t be too heavy, no more than 33 lbs, 15 kg when full so one person can handle it. To keep the cost and weight down, I imagine the product will be made of marangeing steel wrapped in kevlar or carbon fiber. A 20 kg container made of these materials will hold 1.5 to 2 kg of hydrogen, the equivalent of 2 gallons of gasoline.

I imagine that the can will have at least one handle, likely two. The original can had three handles, but this seems excessive to me. The connection tube between two short cylinders could be designed to serve as one of the handles. For safety, the Jerrycan should have a secure over-seal on both of the fill-ports, ideally with a safety pin latch minimize trouble in a crash. All the parts, including the over- seal and pin, should be attached to the can so that they are not easily lost. Do you agree? What else, if anything, do you imagine?

Robert Buxbaum, February 26, 2017. My company, REB Research, makes hydrogen generators and purifiers.

New REB hydrogen generator for car fueling, etc.

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One of my favorite invention ideas, one that I’ve tried to get the DoE to fund, is a membrane hydrogen generator where the waste gas is burnt to heat the reactor. The result should be exceptional efficiency, low-cost, low pollution, and less infrastructure needs. Having failed to interest the government, I’ve gone and built one on my own dime. That’s me on the left, with Shua Spirka, holding the new core module (reactor, boiler, purifier and purifier) sized for personal car fueling.

Me and Shua and our new hydrogen generator core

Me and Shua and our new hydrogen generator core

The core just arrived from the shop last week, now we have to pumps and heat exchangers. As with our current products, the hydrogen is generated from methanol water, and extracted 99.99999% pure by diffusion through a metal membrane. This core fit in a heat transfer pot (see lower right) and the pot sits on a burner for the waste gas. Control is tricky, but I think I’ve got it. If it all works like it’s supposed to, the combination should be 80-90% energy-efficient, delivering about 75 slpm, 9 kg per day. That’s the same output as our largest current electrically heated generators, with a much lower infrastructure cost. The output should be enough to fuel one hydrogen-powered automobile per day, or keep a small fleet of plug-in, hydrogen-hybrids running continuously.

Hydrogen automobiles have a lot of advantages over Tesla-type electric automobiles. I’ll tell you how the thing works as soon as we set it up and test it. Right now, we’ve got other customers and other products to make.

Robert Buxbaum, February 18, 2016. If someone could supply a good hydrogen compressor, and a good fuel cell, that would be most welcome. Someone who can supply that will be able to ride in a really excellent cart of the future at this year’s July 4th parade.