Hockey sticks have gotten bendier in recent years, with an extreme example shown below: Alex Ovechkin getting about 3″ of bend using a 100# stiffness stick. Bending the stick allows a player to get more power out of wrist shots by increasing the throw distance of the puck. There is also some speed advantage to the spring energy stored in the stick — quite a lot in Mr Ovechkin’s case.
Alexander Ovechkin takes a wrist shot using a bendy stick.
A 100# stiffness stick takes 100 pounds of force in the middle to get 1″ of bend. That Ovechkin gets 3″ of bend with his 100# stick suggests that he shoots with some 300 lbs of force, an insane amount IMHO. Most players use a lot less force, but even so a bendy stick should help them score goals.
There is something that bothers me about the design of Alex Ovechkin’s stick though, something that I think I could improve. You’ll notice that the upper half of his stick bends as much as the lower half. This upper-bend does not help the shot, and it takes work-energy. The energy in that half of the bend is wasted energy, and its release might even hurt the shooter by putting sudden spring-stress on his wrist. To correct for this, I designed my own stick, shown below, with an aim to have no (or minimal) upper bend. The modification involved starting with a very bendy stick, then covering most of the upper half with fiberglass cloth.
I got ahold of a junior stick, 56″ long with 60# flex, and added a 6″ extension to the top. Doing this made the stick longer, 62″ long (adult length) and even more bendy. One 1″ of flex requires less force on a longer stick. I estimate that, by lengthening the stick, I reduced it to about 44#. Flex is inversely proportional to length cubed. I then sanded the upper part of the stick, and wrapped 6 oz” fiberglass cloth (6 oz) 2-3 wraps around the upper part as shown, holding it tight with tape at top and bottom when I was done. I then applied epoxy squeezing it through the cloth so that the composite was nearly transparent, and so the epoxy filled the holes. This added about 15g, about 1/2 oz to the weight. Transparency suggested that the epoxy had penetrated the cloth and bonded to the stick below, though the lack of total transparency suggests that the bond could have been better with a less viscous epoxy. Once the epoxy had mostly set, I took the tape off, and stripped the excess fiberglass so that the result looked more professional. I left 23″ of fiberglass wrap as shown. The fiberglass looks like hockey tape.
Assuming I did the gluing right, this hockey stick should have almost all of the spring below the shooter’s lower hand. I have not measured the flex, but my target was about 80 lbs, with improved durability and the new lower center of bend. In theory, more energy should get into the puck. It’s a gift for my son, and we’ll see how it works in a month or so.
Original hardware brass screws from my door and locks, plus one of the stainless screw that I used as a replacement.
I just replaced the door knob assembly on my home and found that it was held in place by a faceplate that was attached by two, 5/8″, brass screws. These screws, shown at right with their replacement, would not have been able to withstand a criminal, I think. Our door is metal, foam filled, and reasonably strong. I figure it would have withstood a beating, but the brass screws would not, especially since only 1/4″ of the screw is designed to catch foam. Look closely at the screws, and you will see there are two sizes of pitch, each 1/4 long. Only the last 1/4″ looks like it was ever engaged. The top 1/4″ may have been designed to catch metal, but the holes in the door were not tapped to match. The bottom 1/4″ held everything. Even without a criminal attack, the screw at right was bent and beginning to go.
Instead of reusing these awful screws or buying similar ones, I replaced them with stainless screws, 1 3/4″ long, like the one shown in the picture above. But then I had a thought — what were the other locks on my door attached with? I checked and found my deadbolt lock was held in by two of the same type of sorry, 5/8″ brass screws. So I replaced these too, using two more, 1.75″ stainless steel. Then, in my disgust, I thought to write this post. Perhaps the screws holding your door hardware is as lousy as was holding mine. Take a look.
In 1905 and 1908, Einstein developed two formulations for the diffusion of a small particle in a liquid. As a side-benefit of the first derivation, he demonstrated the visible existence of molecules, a remarkable piece of work. In the second formulation, he derived the same result using non-equilibrium thermodynamics, something he seems to have developed on the spot. I’ll give a brief version of the second derivation, and will then I’ll show off my own extension. It’s one of my proudest intellectual achievements.
But first a little background to the problem. In 1827, a plant biologist, Robert Brown examined pollen under a microscope and noticed that it moved in a jerky manner. He gave this “Brownian motion” the obvious explanation: that the pollen was alive and swimming. Later, it was observed that the pollen moved faster in acetone. The obvious explanation: pollen doesn’t like acetone, and thus swims faster. But the pollen never stopped, and it was noticed that cigar smoke also swam. Was cigar smoke alive too?
Einstein’s first version of an answer, 1905, was to consider that the liquid was composed of atoms whose energy was a Boltzmann distribution with an average of E= kT in every direction where k is the Boltzmann constant, and k = R/N. That is Boltsman’s constant equals the gas constant, R, divided by Avogadro’s number, N. He was able to show that the many interactions with the molecules should cause the pollen to take a random, jerky walk as seen, and that the velocity should be faster the less viscous the solvent, or the smaller the length-scale of observation. Einstein applied the Stokes drag equation to the solute, the drag force per particle was f = -6πrvη where r is the radius of the solute particle, v is the velocity, and η is the solution viscosity. Using some math, he was able to show that the diffusivity of the solute should be D = kT/6πrη. This is called the Stokes-Einstein equation.
In 1908 a French physicist, Jean Baptiste Perrin confirmed Einstein’s predictions, winning the Nobel prize for his work. I will now show the 1908 Einstein derivation and will hope to get to my extension by the end of this post.
Consider the molar Gibbs free energy of a solvent, water say. The molar concentration of water is x and that of a very dilute solute is y. y<<1. For this nearly pure water, you can show that µ = µ° +RT ln x= µ° +RT ln (1-y) = µ° -RTy.
Now, take a derivative with respect to some linear direction, z. Normally this is considered illegal, since thermodynamic is normally understood to apply to equilibrium systems only. Still Einstein took the derivative, and claimed it was legitimate at nearly equilibrium, pseudo-equilibrium. You can calculate the force on the solvent, the force on the water generated by a concentration gradient, Fw = dµ/dz = -RT dy/dz.
Now the force on each atom of water equals -RT/N dy/dz = -kT dy/dz.
Now, let’s call f the force on each atom of solute. For dilute solutions, this force is far higher than the above, f = -kT/y dy/dz. That is, for a given concentration gradient, dy/dz, the force on each solute atom is higher than on each solvent atom in inverse proportion to the molar concentration.
For small spheres, and low velocities, the flow is laminar and the drag force, f = 6πrvη.
Now calculate the speed of each solute atom. It is proportional to the force on the atom by the same relationship as appeared above: f = 6πrvη or v = f/6πrη. Inserting our equation for f= -kT/y dy/dz, we find that the velocity of the average solute molecule,
v = -kT/6πrηy dy/dz.
Let’s say that the molar concentration of solvent is C, so that, for water, C will equal about 1/18 mols/cc. The atomic concentration of dilute solvent will then equal Cy. We find that the molar flux of material, the diffusive flux equals Cyv, or that
where Cy is the molar concentration of solvent per volume.
Classical engineering comes to a similar equation with a property called diffusivity. Sp that
Molar flux of y (mols y/cm2/s) = -D dCy/dz, and D is an experimentally determined constant. We thus now have a prediction for D:
D = kT/6πrη.
This again is the Stokes Einstein Equation, the same as above but derived with far less math. I was fascinated, but felt sure there was something wrong here. Macroscopic viscosity was not the same as microscopic. I just could not think of a great case where there was much difference until I realized that, in polymer solutions there was a big difference.
Polymer solutions, I reasoned had large viscosities, but a diffusing solute probably didn’t feel the liquid as anywhere near as viscous. The viscometer measured at a larger distance, more similar to that of the polymer coil entanglement length, while a small solute might dart between the polymer chains like a rabbit among trees. I applied an equation for heat transfer in a dispersion that JK Maxwell had derived,
where κeff is the modified effective thermal conductivity (or diffusivity in my case), κl and κp are the thermal conductivity of the liquid and the particles respectively, and φ is the volume fraction of particles.
To convert this to diffusion, I replaced κl by Dl, and κp by Dp where
Dl = kT/6πrηl
and Dp = kT/6πrη.
In the above ηl is the viscosity of the pure, liquid solvent.
The chair of the department, Don Anderson didn’t believe my equation, but agreed to help test it. A student named Kit Yam ran experiments on a variety of polymer solutions, and it turned out that the equation worked really well down to high polymer concentrations, and high viscosity.
As a simple, first approximation to the above, you can take Dp = 0, since it’s much smaller than Dl and you can take Dl to equal Dl = kT/6πrηl as above. The new, first order approximation is:
D = kT/6πrηl (1 – 3φ/2).
We published in Science. That is I published along with the two colleagues who tested the idea and proved the theory right, or at least useful. The reference is Yam, K., Anderson, D., Buxbaum, R. E., Science 240 (1988) p. 330 ff. “Diffusion of Small Solutes in Polymer-Containing Solutions”. This result is one of my proudest achievements.
The glory of American screws and bolts is their low cost ubiquity, especially in our coarse thread (UNC = United National Coarse) sizes. Between 1/4 inch and 5/8″, they are sized in 1/16″ steps, and after that in 1/8″ steps. Below 3/16″, they are sized by wire gauges, and generally they have unique pitch sizes. All US screws and bolts are measured by their diameter and threads per inch. Thus, the 3/8-16 (UNC) has an outer diameter (major diameter) of 3/8″ with 16 threads per inch (tpi). 16 tpi is an ideal thread number for overall hold strength. No other bolt has 16 threads per inch so it is impossible to use the wrong bolt in a hole tapped for 3/8-16. The same is true for basically every course thread with a very few exceptions, mainly found between 3/16″ and 1/4″ where the wire gauges transition to fractional sizes. Because of this, if you stick to UTC you are unlikely to screw up, as it were. You are also less-likely to cross-thread.
I own one of these. It’s a tread pitch gauge.
US fine threads come in a variety of standards, most notably UNF = United National Fine. No version of fine thread is as strong as coarse because while there are more threads per inch, each root is considerably weaker. The advantage of fine treads is for use with very thin material, or where vibration is a serious concern. The problem is that screwups are far more likely and this diminishes the strength even further. Consider the 7/16″ – 24 (UNF). This bolt will fit into a nut or flange tapped for 1/2″- 24. The fit will be a little loose, but you might not notice. You will be able to wrench it down so everything looks solid, but only the ends of the threads are holding. This is a accident waiting to happen. To prevent such mistakes you can try to never allow a 7/6″-24 bolt into your shop, but this is uncomfortably difficult. If you ever let a 7/6″-24 bolt in, some day someone will grab it and use it, in all likelihood with a 1/2″ -24 nut or flange, since these are super-common. Under stress, the connection will fail in the worst possible moment.
Other UNF bolts and nuts present the same screwup risk. For example, between the 3/8″-24 and 5/16″-24 (UNF), or the #10-32 (UNF) and also with the 3/16″- 32, and the latter with the #8-32 (UNC). There is also a French metric with 0.9mm — this turns out to be identical to -32 pitch. The problem appears with any bolt pair where with identical pitch and the major diameter of the smaller bolt has a larger outer diameter (major diameter) than the inner diameter (minor diameter) of the larger bolt. If these are matched, the bolts will seem to hold when tightened, but they will fail in use. You well sometimes have to use these sizes because they match with some purchased flange. If you have to use them, be careful to use the largest bolt diameter that will fit into the threaded hole.
Where I have the option, my preference is to stick to UNC as much as possible, even where vibration is an issue. In vibration situations, I prefer to add a lock nut or sometimes, an anti-vibration glue, locktite, available in different release temperatures. Locktite is also helpful to prevent gas leaks. In our hydrogen purifiers, I use lock washers on the ground connection from the power cord, for example.
I try to avoid metric, by the way. They less readily available in the US, and more expensive. The other problem with metric is that there are two varieties (Standard and French — God love the French engineering) and there are so many sizes and pitches that screwups are common. Metric bolts come in every mm diameter, and often fractional mm too. There is a 2mm, a 2.3mm, a 2.5mm, and a 2.6mm, often with overlapping pitches. The pitch of metric screws and bolts is measured by their spacing, by the way, so a 1mm metric pitch means there is 1mm between threads, the the equivalent of a 24.5 pitch in the US, and a 0.9mm pitch = US-32. Thread confusion possibilities are endless. A M6x1 (6mm OD x 1mm pitch) is easily confused with a M5x1 or a M7x1, and the latter with the M7.5×1. A M8x1.25 is easily confused with a M9x1.25, and a M14x2 with an M16x2. And then there is confusion with US bolts: a 2.5mm metric pitch is nearly identical to a US 10tpi pitch. I can not rid myself of US threads, so I avoid metric where I can. As above, problems arise if you use a smaller diameter bolt in a larger diameter nut.
For those who have to use metric, I suggest you always use the largest bolt that will fit (assuming you can find it). I try to avoid bringing odd-size bolts into their shop, that is, stick to M6, M8, M10. It’s not always possible, but it’s a suggestion. I get equipment with odd-size metric bolts too. My preference is to stick to UNC and to avoid odd numbers.
Robert Buxbaum, January 23, 2024. Note: I’ve only really discussed bolt sizes between about #4 and 1″, and I didn’t consider UNRC or UNJF or other, odd options. You can figure these issues out yourself from the above, I think.
Leading up to the Cybertruck launch 4 weeks ago, the expert opinion was that it was a failure. Morgan Stanley, here dubbed it as one, as did Rolling Stone here. Without having driven the vehicle, the experts at Motor trend, here, declared it was worse than you thought, “a novelty” car. I’d like to differ. The experts point out that the design is fundamentally different from what we’ve made for years. They claim it’s ugly, undesirable, and hard to build. Ford’s F-150 trucks are the standard, the top selling vehicle in the US, and Cybertruck looks nothing like an F-150. I suspect that, because of the differences, the Cybertruck can hardly fail to be a success in both profit and market share.
Cybertruck pulls a flat-bed trailer at Starbase.
Start with profit. Profit is the main measure of company success. High profit is achieved by selling significant numbers at a significant profit margin. Any decent profit is a success. This vehicle could trail the F-150 sales forever and Musk could be the stupidest human on the planet, so long as Tesla sells at a profit, and does so legally, the company will succeed. Tesla already has some 2 million pre-orders, and so far they show no immediate sign of leaving despite the current price of about $80,000. Unless you think they are all lying or that Musk has horribly mispriced the product, he should make a very decent profit. My guess is he’s priced to make over $10,000 per vehicle, or $20B on 2 million vehicles. Meanwhile, no other eV company seems to be making a profit.
The largest competing electric pickup company is Rivian. They sold 16,000 electric trucks in Q3 2023, but the profit margin is -100%. This is to say, they lose $1 for every $1 worth of sales –and that’s unsustainable. Despite claims to the contrary, a money-losing business is a failure. The other main competitors are losing too. Ford is reported to lose about $50,00 per eV. According to Automotive News, here, last week, Ford decided to cut production of its electric F-150, the Lightning, by 50%. This makes sense, but provides Cybertruck a market fairly clear of US e-competition.
2024 BYD, Chinese pickup truck
Perhaps the most serious competitor is BYD, a Chinese company backed by the communist government, and Warren Buffet. They are entering the US market this month with a new pickup. It might be profitable, but BYD is relatively immune to profitability. The Chinese want dominance of the eV market and are willing to lose money for years until they get it. Fortunately for Tesla, the BYD truck looks like Rivian’s. Tesla’s trucks should exceed them in range, towing, and safety. BYD, it seems, is aiming for a lower price point and a different market, Rivian’s.
A video, here, shows the skin of a Cybertruck is bulletproof to 9mm, shotgun, and 45 caliber machine gun fire. Experts scoff at the significance of bulletproof skin — good for folks working among Mexican drug lords, or politicians, or Israelis. Tesla is aiming currently for a more upscale customer, someone who might buy a Hummer or an F-250. This is more usable and cheaper.
Don’t try this with other trucks.
Another way Cybertruck could fail is through criminal activity. Musk could be caught paying off politicians or cheating on taxes or if the trucks fail their safety tests. So far, Cybertruck seems to meet Federal Motor Vehicle Safety Standards by a good margin. In a video comparison, here, it appears to take front end collisions as well as an F-150, and appears better in side collisions.
This leaves production difficulty. This could prevent the cybertruck from being a big success, and the experts have all harped on this. The vehicle body is a proprietary stainless steel, 0.07″ thick. Admittedly it’s is hard to form, but Tesla seems to manage it. VIN number records indicate that Tesla had delivered 448 cybertrucks as Friday last week, many of them to showrooms, but some to customers. Drone surveys of the Gigafactory lot show that about 19 are made per day. That’s a lot more than you’d see if assembly was by hand. Assuming a typical learning curve, it’s reasonable to expect some 600 will be delivered by December 31, and that production should reach 6000 per month in mid 2024. At that rate, they’ll be making and selling at the same rate as Rivian or Ford, and making real money doing it. The stainless body might even be a plus, deterring copycat competition. Other pluses are the add-ons, like the base-camp tent option, a battery extension, a ramp, and (it’s claimed) some degree of sea worthiness. Add-ons add profit and deter direct copying (for a time).
Basecamp, tent option.
So why do I think the experts are so wrong? My sense is that these people are experts because of long experience at other companies — the competitors. They know what was tried, and that innovation failed. They know that their companies chose not to make anything like a Cybertruck, and not to provide the add-ons. They know that the big boys avoid “novelty cars” and add-ons. There is an affinity among experts for consensus and sure success, the success that comes from Chinese companies, government support and international banking. If the Cybertruck success is an insult to them and their expertise. Nonetheless, if Cybertruck succeeds, they will push their companies towards a more angular design plus add-ons. And they will claim cybertruck is no way novel, but that government support is needed to copy it.
A lot of cities push rain barrels as a way to save water and reduce flooding. Our water comes from the Detroit and returns to it as sewage, so I’m not sure there is any water saving, but there is a small cash saving (very small) if you buy 30 to 55 gallon barrels from the city and connect them to the end of your drain spout. The rainwater you collect won’t be pure enough to drink, or safe for bathing, but you can use it to water your lawn and garden. This sounds OK, even patriotic, until you do the math, or the plumbing, or until you consider the wood-chip alternative.
The barrels are not cheap, even when subsidized they cost about $100 each. Add to this the cost and difficulty of setting up the collection system and the distribution hose. Water from your rain barrel will not flow through a normal nozzle as there is hardly any pressure. Expect watering to take a lot longer than you are used to.
40 gallon rain barrels. Two of these give about 70 usable gallons every heavy rain fall. That’s about 70¢ worth.
In Michigan you can not leave the water in your barrel over the winter, the water will freeze and the barrel will crack. You have to drain the tank completely every fall, an almost impossible task, and the tank is attached to a rainspout and the last bit of water is hard to get out. Still, you have to do it, or the barrel will crack. And the savings for all this is minimal. During a rainy month, you don’t need this water. During a dry month, there is no water to use. Even at the best, the The marginal cost of water in our town is less than 1¢ per gallon. For all the work and cost to set up, two complete 40 gallon tanks (like those shown) will give you at most about 70 usable gallons. That’s to say, almost 70¢ per full filling.
How much lawn can you water? Assume you like to water your lawn to the equivalent of 1″ of rain per week, your 70 gallons will water about 154 ft2 of lawn or garden, virtually nothing compared to the typical Michigan 2000 ft2 lawn. You’ll still have to get most of your water from the city’s main. All that work, for so little benefit.
Young trees with chip volcanos, 1 ft high x18″. Spread the chips to the diameter of the leaves.You don’t need more than 2″.
A far better option is wood chips. They don’t cover a lawn, but they’re great for shrubs, trees or a garden. Wood chips are easy to spread, and they stop weeds and hold water. The photo at left shows a wood chips around the shrubs, and a particularly poor use of wood chips around the trees. For shrubs, trees, or a garden, I suggest you put down 1 to 2 inches of wood chips. Surround a young tree at that depth to the diameter of the branches. Do not build a “chip volcano,” as this lazy landscaper has done.
Consider that, covering 500 ft2 of area to a depth of 1.5 inches will take about 60 cubic feet of wood chips. That will cost about $35 dollars at the local Home Depot. This is enough to hold about 1.25″ or rainwater, That’s about 100 ft3 or water or 800 gallons. The chips prevent excess evaporation while preventing weeds and slowly releasing the water to your garden. You do no work. The chips take almost no work to spread, and will keep on working for years, with no fear of frost-damage. A as the chips stop working, they biocompost slowly into fertilizer. That’s a win.
There is a worst option too, called a rain garden. This is often pushed by environmental-gooders. You dig a hole near your downspout, perhaps ten feet in diameter, by two feet deep, and plant native grasses (weeds). When it rains, the hole fills with water creating a mini wetland that will soon smell like the swamp that it is. If you are not lucky, the water will find a way to leak into your basement. If that’s your problem look here. If you are luckier, your mini-swamp will become the home of mosquitos, frogs, and snakes. The plants will grow, then die, and rot, and look awful. It is very hard to maintain native grasses. That’s why people drain swamps and grow trees or turf or vegetables. If you want to see a well-maintained rain garden, they have two on the campus of Lawrence Tech. A wetland isn’t bad, but you want drainage, Make a bioswale or muir.
Robert Buxbaum, May 31, 2023. I ran for water commissioner some years back.
Franklin’s walking stick, willed to General Washington. Now in the Smithsonian.
Many famous people carried walking sticks Washington, Churchill, Moses, Dali. Until quite recently, it was “a thing”. Benjamin Franklin willed one, now in the Smithsonian, to George Washington, to act as a sort of scepter: “My fine crab-tree walking stick, with a gold head curiously wrought in the form of the cap of liberty, I give to my friend, and the friend of mankind, General Washington. If it were a Scepter, he has merited it, and would become it. It was a present to me from that excellent woman, Madame de Forbach, the dowager Duchess of Deux-Ponts”. A peculiarity of this particular stick is that the stick is uncommonly tall, 46 1/2″. This is too tall for casual, walking use, and it’s too fancy to use as a hiking stick. Franklin himself, used a more-normal size walking stick, 36 3/8″ tall, currently in the collection of the NY Historical Society. Washington too seems to have favored a stick of more normal length.
Washington with walking stick
Walking sticks project a sort of elegance, as well as providing personal protection. Shown below is President Andrew Jackson defending himself against an assassin using his walking stick to beat off an assassin. He went on to give souvenir walking sticks to friends and political supporters. Sticks remained a common political gift for 100 years, at least through the election of Calvin Coolidge.
Andrew Jackson defends himself.
I started making walking sticks a few years back, originally for my own use, and then for others when I noticed that many folks who needed canes didn’t carry them. It was vanity, as best I could tell: the normal, “old age” cane is relatively short, about 32″. Walking with it makes you bend over; you look old and decrepit. Some of the folks who needed canes, carried hiking sticks, I noticed, about 48″. These are too tall to provide any significant support, as the only way to grasp one was from the side. Some of my canes are shown below. They are about 36″ tall, typically with a 2″ wooden ball as a head. They look good, you stand straight, and they provides support and balance when going down stairs.
Some of my walking sticks.
I typically make my sticks of American Beech, a wood of light weight, with good strength, and a high elastic modulus of elasticity, about 1.85 x106 psi. Oak, hickory, and ash are good options, but they are denser, and thus more suited to self-defense. Wood is better than metal for many applications, IMHO, as I’ve discussed elsewhere. The mathematician Euler showed the the effective strength of a walking stick does not depend on the compressive strength but rather on elastic constant via “the Euler buckling equation”, one of many tremendously useful equations developed by Leonhard Euler (1707-1783).
For a cylindrical stick, the maximum force supported by a stick is: F = π3Er4/4L2, where F is the force, r is the radius, L is the length, and E is the elastic modulus. I typically pick a diameter of 3/4″ or 7/8″, and fit the length to the customer. For a 36″ beech stick, the buckling strength is calculated to be 221 or 409 pounds respectively. I add a rubber bottom to make it non–scuff and less slip-prone. I sometimes add a rope thong, too. Here is a video of Fred Astaire dancing with this style of stick. It’s called “a pin stick”, in case you are interested because it looks like a giant pin.
Country Irishmen are sometimes depicted with a heavy walking stick called a Shillelagh. It’s used for heavier self-defense than available with a pin-stick, and is generally seen being used as a cudgel. There are Japanese versions of self defense using a lighter, 36″ stick, called a Han-bo, as shown here. There is also the wand, as seen for example in Harry Potter. It focuses magical power. Similar to this is Moses’s staff that he used in front of Pharaoh, a combination wand and hiking stick as it’s typically pictured. It might have been repurposed for the snake-on-a-stick that protects against dark forces. Dancing with a stick, Astaire style, can drive away emotional forces, while the more normal use is elegance, and avoiding slips.
The main products of my company, REB Research, involve metallic membranes, often palladium-based, that provide 100% selective hydrogen filtering or long term hydrogen storage. One way to understand why these metallic membrane provide 100% selectivity has to do with the fact that metallic atoms are much bigger than hydrogen ions, with absolutely regular, small spaces between them that fit hydrogen and nothing else.
Palladium atoms are essentially spheres. In the metallic form, the atoms pack in an FCC structure (face-centered cubic) with a radius of, 1.375 Å. There is a cloud of free electrons that provide conductivity and heat transfer, but as far as the structure of the metal, there is only a tiny space of 0.426 Å between the atoms, see below. This hole is too small of any molecule, or any inert gas. In the gas phase hydrogen molecules are about 1.06 Å in diameter, and other molecules are bigger. Hydrogen atoms shrink when inside a metal, though, to 0.3 to 0.4 Å, just small enough to fit through the holes.
The reason that hydrogen shrinks has to do with its electron leaving to join palladium’s condition cloud. Hydrogen is usually put on the upper left of the periodic table because, in most cases, it behaves as a metal. Like a metal, it reacts with oxygen, and chlorine, forming stoichiometric compounds like H2O and HCl. It also behaves like a metal in that it alloys, non-stoichiometrically, with other metals. Not with all metals, but with many, Pd and the transition metals in particular. Metal atoms are a lot bigger than hydrogen so there is little metallic expansion on alloying. The hydrogen fits in the tiny spaces between atoms. I’ve previously written about hydrogen transport through transition metals (we provide membranes for this too).
No other atom or molecule fits in the tiny space between palladium atoms. Other atoms and molecules are bigger, 1.5Å or more in size. This is far too big to fit in a hole 0.426Å in diameter. The result is that palladium is basically 100% selective to hydrogen. Other metals are too, but palladium is particularly good in that it does not readily oxidize. We sometime sell transition metal membranes and sorbers, but typically coat the underlying metal with palladium.
We don’t typically sell products of pure palladium, by the way. Instead most of our products use, Pd-25%Ag or Pd-Cu. These alloys are slightly cheaper than pure Pd and more stable. Pd-25% silver is also slightly more permeable to hydrogen than pure Pd is — a win-win-win for the alloy.
In terms of raw strength though, pounds/in2, wood is not particularly strong, only about 7000 psi (45MPa) both in tension and compression, about half the strength of aluminum. It is thus not well suited to supporting heavy structures, like skyscrapers. (I calculate the maximum height of a skyscraper here), but wood can be modified to make it stronger by removing most of the air, and replacing it with plastic. The result is a stronger, denser, flexible composite, that is typically transparent. The flower below is seen behind a sheet of transparent wood.
A picture of a flower taken through a piece of transparent super-wood.
To make a fairly strong, transparent wood, you take ordinary low-density wood (beech or balsa are good) and soak it in alkali (NaOH). This bleaches the wood, softens the cellulose, and dissolves most of the lignin. You next wash off the alkali and soak the wood in a low viscosity epoxy or acrylic. Now, put it in a vacuum chamber to remove the air — you’ll need a brick to hold the wood down in the liquid. You’ll see bubbles in the epoxy as the air leaves. Then, when the vacuum is released, the wood soaks up the epoxy or acrylic. On curing, you get a composite strong and transparent, but not super strong.
To make the wood really strong, super-strong, you need to compress the uncured, epoxy soaked wood. One method is to put it in a vice. This drives off more of the air and further aligns the cellulose fibers. You now cure it as before (you need a really slow cure epoxy or a UV-cure polymer). The resultant product have been found to have tensile strengths as high as 270 MPa in the direction of alignment, over 40,000 psi. This is three times stronger than regular aluminum, 90 MPa, (13,500 psi). It’s about the strength of the strongest normal aluminum alloy, 6061. It’s sort of expensive to make, but it’s flexible and transparent, making it suitable for space windows and solar cells. It’s the lightest flexible transparent material known. It’s biodegradable, and that’s very cool, IMHO. See here for a comparison with other, high strength, transparent composites.
Robert Buxbaum, November 10, 2022. I think further developments along this line would make an excellent high school science fair project, college thesis, or PhD research project. Compare different woods, or epoxies, different alkalis, and temperatures, or other processing ideas. How strong and transparent can you make this material, or look at other uses. Can you use it for roof solar cells, like Musk’s but lighter, or mold it for auto panels, it’s already lighter and stronger, or use it as bullet-proof glass or airplane windows.
There are two ASTM-approved methods for measuring the gas permeability of a material. The equipment is very similar, and REB Research makes equipment for either. In one of these methods (described in detail here) you measure the rate of pressure rise in a small volume.This method is ideal for high permeation rate materials. It’s fast, reliable, and as a bonus, allows you to infer diffusivity and solubility as well, based on the permeation and breakthrough time.
Exploded view of the permeation cell.
For slower permeation materials, I’ve found you are better off with the other method: using a flow of sampling gas (helium typically, though argon can be used as well) and a gas-sampling gas chromatograph. We sell the cells for this, though not the gas chromatograph. For my own work, I use helium as the carrier gas and sampling gas, along with a GC with a 1 cc sampling loop (a coil of stainless steel tube), and an automatic, gas-operated valve, called a sampling valve. I use a VECO ionization detector since it provides the greatest sensitivity differentiating hydrogen from helium.
When doing an experiment, the permeate gas is put into the upper chamber. That’s typically hydrogen for my experiments. The sampling gas (helium in my setup) is made to flow past the lower chamber at a fixed, flow rate, 20 sccm or less. The sampling gas then flows to the sampling loop of the GC, and from there up the hood. Every 20 minutes or so, the sampling valve switches, sending the sampling gas directly out the hood. When the valve switches, the carrier gas (helium) now passes through the sampling loop on its way to the column. This sends the 1 cc of sample directly to the GC column as a single “injection”. The GC column separates the various gases in the sample and determines the components and the concentration of each. From the helium flow rate, and the argon concentration in it, I determine the permeation rate and, from that, the permeability of the material.
As an example, let’s assume that the sample gas flow is 20 sccm, as in the diagram above, and that the GC determines the H2 concentration to be 1 ppm. The permeation rate is thus 20 x 10-6 std cc/minute, or 3.33 x 10-7 std cc/s. The permeability is now calculated from the permeation area (12.56 cm2 for the cells I make), from the material thickness, and from the upstream pressure. Typically, one measures the thickness in cm, and the pressure in cm of Hg so that 1 atm is 76cm Hg. The result is that permeability is determined in a unit called barrer. Continuing the example above, if the upstream hydrogen is 15 psig, that’s 2 atmospheres absolute or or 152 cm Hg. Lets say that the material is a polymer of thickness is 0.3 cm; we thus conclude that the permeability is 0.524 x 10-10 scc/cm/s/cm2/cmHg = 0.524 barrer.
This method is capable of measuring permeabilities lower than the previous method, easily lower than 1 barrer, because the results are not fogged by small air leaks or degassing from the membrane material. Leaks of oxygen, and nitrogen show up on the GC output as peaks that are distinct from the permeate peak, hydrogen or whatever you’re studying as a permeate gas. Another plus of this method is that you can measure the permeability of multiple gas species simultaneously, a useful feature when evaluating gas separation polymers. If this type of approach seems attractive, you can build a cell like this yourself, or buy one from us. Send us an email to reb@rebresearch.com, or give us a call at 248-545-0155.
