Tag Archive: popular science

Oct 25

Newsflash: Materials of the Future

This summer, I had the pleasure of being interviewed by Kim Verhaeghe, a journalist of the EOS magazine, on the topic of “materials of the future“. Materials which are currently being investigated in the lab and which in the near or distant future may have an enormous impact on our lives. While brushing up on my materials (since materials with length scales of importance beyond 1 nm are generally outside my world of accessibility), I discovered that to cover this field you would need at least an entire book just to list the “materials of the future”. Many materials deserve to be called materials of the future, because of their potential. Also depending on your background other materials may get your primary attention.

In the resulting article, Kim Verhaeghe succeeded in presenting a nice selection, and I am very happy I could contribute to the story. Introducing “the computational materials scientist” making use of supercomputers such as BrENIAC, but also new materials such as Metal-Organic Frameworks (MOF) and shedding some light on “old” materials such as diamond, graphene and carbon nanotubes.

Aug 12

Dangerous travel physics

Tossing coins into a fountain brings luck, tossing them of a building causes death and destruction?

 

We have probably all done it at one point when traveling: thrown a coin into a wishing well or a fountain. There are numerous wishing wells with legends describing how the deity living in the well will bring good fortune in return for this gift. The myths and legends often originate from Celtic, German or Nordic traditions.

In case of the Trevi fountain, there is the belief that if you throw a coin over your left shoulder using your right hand, you will return to Rome…someday. As this fountain and legend are iconic parts of our western movie history, many, many coins get tossed into it (more than 1 Million € worth each year, which is collected an donated to charity).

In addition to these holiday legends, there also exist more recent “coin-myths”: Death by falling penny. These myths are always linked to tall buildings, and claim that a penny dropped from the top of such a building could kill someone if they hit him.

Traveling with Newton

In both kinds of coin legends, the trajectory of the coin can be predicted quite well using Newton’s Laws. Their speed is low compared to the speed of light, and the coins are sufficiently large to keep the world of quantum mechanics hidden from sight.

The second Law of Newton states that the speed of an object changes if there is a force acting on it. Here on earth, gravity is a major player (especially for Physics exercises). In case of a coin tossed into a fountain, gravity will cause the coin to follow a roughly parabolic path before disappearing into the water. The speed at which the coin will hit the water will be comparable to the speed with which it was thrown…at least if there isn’t to much of a difference in height between the surface of the water and the hand of the one throwing the coin.

But, what if this difference is large? Such as in case of the penny being dropped from a tall building. In such a case, the initial velocity is zero, and the penny is accelerated toward the ground by gravity. Using the equations of motion for a uniform accelerated system, we can calculate easily the speed at which the coin hits the ground:

x = x0 + v0*t + ½ * g * t²

v=v0+g*t

If we drop a penny from the 3rd floor of the Eiffel Tower (x0=276.13m, x=0m, v0=0 m/s, g=-9.81m/s²) then the first equation teaches us that after 7.5 seconds, the penny will hit the ground with a final speed (second equation) of -73.6 m/s (or -265 km/h)*. With such a velocity, the penny definitely will leave an impression. More interestingly, we will get the exact same result for a pea (cooked or frozen), a bowling ball, a piano or an anvil…but also a feather. At this point, your intuition must be screaming at you that you are missing something important.

All models are wrong…but they can be very useful

The power of models in physics, originates from keeping only the most important and relevant aspects. Such approximations provide a simplified picture and allow us to understand the driving forces behind nature itself. However, in this context, models in physics are approximations of reality, and thus by definition wrong, in the sense that they do not provide an “exact” representation of reality. This is also true for Newton’s Laws, and our application above. With these simple rules, it is possible to describe the motion of the planets as well as a coin tossed into the Trevi fountain.

So what’s the difference between the coin tossed into a fountain and planetary motion on the one hand, and our assorted objects being dropped from the Eiffel Tower on the other hand?

Friction as it presents itself in aerodynamic drag!

Aerodynamic drag gives rise to a force in the direction opposite to the movement, and it is defined as:

FD= ½ *Rho*v²*CD*A

This force depends on the density Rho of the medium (hence water gives a larger drag than air), the velocity and surface area A in the direction of movement of the object, and CD the drag coefficient, which depends on the shape of the object.

If we take a look at the planets and the coin tosses, we notice that, due to the absence of air between the planets, no aerodynamic drag needs to be considered for planetary motion. In case of a coin being tossed into the Trevi fountain, there is aerodynamic drag, however, the speeds are very low as well as the distance traversed. As such the effect of aerodynamic drag will be rather small, if not negligible. In case of objects being dropped from a tall building, the aerodynamic drag will not be negligible, and it will be the factors CD and A which will make sure the anvil arrives at the ground level before the feather.

Because this force also depends on the velocity, you can no longer make direct use of the first two equations to calculate the time of impact and velocity at each point of the path. You will need a numerical approach for this (which is also the reason this is not (regularly) taught in introductory physics classes at high school). However, using excel, you can get a long way in creating a numerical solution for this problem.[Excel example]

As we know the density of air is about 1.2kg/m³, CD for a thin cylinder (think coin) is 1.17, the radius of a penny is 9.5 mm and its mass is 2.5g, then we can find the terminal velocity of the penny to be 11.1 m/s (40 km/h). The penny will land on the ground after about 25.6 seconds. This is quite a bit slower than what we found before, and also quite a bit more safe. The penny will reach its terminal velocity after having fallen about 60 m, which means that dropping a penny from taller buildings (the Atomium [102 m], the Eiffel Tower [276.13 m, 3rd floor, 324 m top], the Empire State Building [381 m] or even the Burj Khalifa [829.8 m]) will have no impact on the velocity it will have when hitting the ground: 40km/h.

This is a collision you will most probably survive, but which will definitely leave a small bruise on impact.

 

*The minus sign indicates the coin is falling downward.

Jun 30

I have a Question: about thermal expansion

“I have a question”(ik heb een vraag). This is the name of a Belgian (Flemisch) website aimed at bringing Flemisch scientists and the general public together through scientific or science related questions. The basic idea is rather simple. Someone has a scientific question and poses it on this website, and a scientist will provide an answer. It is an excellent opportunity for the latter to hone his/her own science communication skills (and do some outreach) and for the former to get an good answer to his/her question.

All questions and answers are collected in a searchable database, which currently contains about fifteen thousand questions answered by a (growing) group of nearly one thousand scientists. This is rather impressive for a region of about 6.5 Million people. I recently joined the group of scientists providing answers.

An interesting materials-related question was posed by Denis (my translation of his question and context):

What is the relation between the density of a material and its thermal expansion?

I was wondering if there exists a relation between the density of a material and the thermal expansion (at the same temperature)? In general, gasses expand more than solids, so can I extend this to the following: Materials with a small density will expand more because the particles are separated more and thus experience a small cohesive force. If this statement is true, then this would imply that a volume of alcohol should expand more than the same volume of air, which I think is puzzling. Can you explain this to me?

Answer (a bit more expanded than the Dutch one):

Unfortunately there exists no simple relation between the density of a material and its thermal expansion coefficient.

Let us first correct something in the example given: the density of alcohol (or ethanol) is 46.07 g/mol (methanol would be 32.04 g/mol) which is significantly more than the density of air which is 28.96 g/mol. So following the suggested assumption, air should expand more. If we look at liquids, it is better to compare ethanol (0.789 g/cm3) to compare water (1 g/cm3) as liquid air (0.87 g/cm3) needs to be cooled below  -196 °C (77K). The thermal expansion coefficients of wtare and ethanol are 207×10-6/°C and 750×10-6/°C, respectively. So in this case, we see that alcohol will expand more than water (at 20°C). Supporting Denis’ statement.

Unfortunately, these are just two simple materials at a very specific temperature for which this statement is true. In reality, there are many interesting aspects complicating life. A few things to keep in mind are:

  • A gas (in contrast to a liquid or solid) has no own boundary. So if you do not put it in any type of a container, then it will just keep expanding. The change in volume observed when a gas is heated is due to an increase in pressure (the higher kinetic energy of the gas molecules makes them bounce harder of the walls of your container, which can make a piston move or a balloon grow). In a liquid or a solid on the other hand, the expansion is rather a stretching of the material itself.
  • Furthermore, the density does not play a role at all, in case of the expansion of an ideal gas, since p*V=n*R*T. From this it follows that 1 mole of H2 gas, at 20°C and a pressure of 1 atmosphere, has the exact same volume as 1 mole of O2 gas, at 20°C and a pressure of 1 atmosphere, even though the latter has a density which is 16 times higher.
  • There are quite a lot of materials which show a negative thermal expansion in a certain temperature region (i.e. they shrink when you increase the temperature). One well-known example is water. The density of liquid water at 0 °C is lower than that of water at 4 °C. This is the reason why there remains some liquid water at the bottom of a pond when it is frozen over.
  • There are also materials which show “breathing” behavior (this are reversible volume changes in solids which made the originators of the term think of human breathing: inhaling expands our lungs and chest, while exhaling contracts it again.) One specific class of these materials are breathing Metal-Organic Frameworks (MOFs). Some of these look like wine-racks (see figure here) which can open and close due to temperature variations. These volume variations can be 50% or more! 😯

The way a material expands due to temperature variations is a rather complex combination of different aspects. It depends on how thermal vibrations (or phonons) propagate through the material, but also on the possible presence of phase-transitions. In some materials there are even phase-transitions between solid phases with a different crystal structure. These, just like solid/liquid phase transitions can lead to very sudden jumps in volume during heating or cooling. These different crystal phases can also have very different physical properties. During the middle-ages, tin pest was a large source of worries for organ-builders. At a temperature below 13°C β-tin is more stable α-tin, which is what was used in organ pipes. However, the high activation energy prevents the phase-transformation from α-tin to β-tin to happen too readily. At temperatures of -30 °C and lower this barrier is more easily overcome.This phase-transition gives rise to a volume reduction of 27%. In addition, β-tin is also a brittle material, which easily disintegrates. During the middle ages this lead to the rapid deterioration and collapse of organ-pipes in church organs during strong winters. It is also said to have caused the buttons of the clothing of Napoleon’s troops to disintegrate during his Russian campaign. As a result, the troops’ clothing fell apart during the cold Russian winter, letting many of them freeze to death.