[GeLe5000]

Hello.

Since I've learned that a Fullerene molecule (60 C) behaves as a wave (wavelenght = 2.5 picometers)  when crossing a crystal at a speed +/- 210 m/s, I wonder if a molecule of that size in aqueous  solution could acquire such a speed from the Brownian agitation that its wave would have a lenght in the micrometer, nanometer or picometer range.

Does someone know how fast a molecule (1 nanometer) can move in a liquid, at room temperature?

[mjc123]

To give you a ball-park figure, how fast would it move in a gas at room temperature?

[GeLe5000]

All right. There's the Maxwell–Boltzmann distribution. It's a first problem.
Then going from a gas to a an aqueous solution. It's another problem.
And thirdly, how can we calculate the speed given to a macromolecule by collisions with water molecules ?

Too many problems for me. That's why I hoped that a direct measure had been made somewhere.

Thank you anyway.

[Enthalpy]

Hi GeLe5000,

what do you call "fullerene crossing a crystal"? A true regular legitimate solid isn't easy to cross for a medium-sized molecule. And if this is a thermal diffusion process, then 210m/s is too much for the thermal energy of fullerene at reasonable temperature.

Beware with "behaves as a wave". A typical C-C distance is 140pm. And why any matter is a wave too, do not infer its behaviour by analogy with light.

From Brownian motion, all molecules have the same mean kinetic energy in a gas, which you can compute from Boltzmann. This is a first approximation in a liquid - and usually the last approximation too because doing better would be difficult. Just try it.

[GeLe5000]

I reply with a few excerpts from the Web page http://www.univie.ac.at/qfp/research/matterwave/c60/

210m/s is too much for the thermal energy of fullerene at reasonable temperature.

"The velocity distribution is very broad and faster than purely thermal"

Beware with "behaves as a wave". A typical C-C distance is 140pm. And why any matter is a wave too, do not infer its behaviour by analogy with light.

"We have observed de Broglie wave interference of the buckminsterfullerene C60 with a wavelength of about 3 pm through diffraction at a SiNx absorption grating with 100 nm period."

[Enthalpy]

"We have observed de Broglie wave interference of the buckminsterfullerene C60 with a wavelength of about 3 pm through diffraction at a SiNx absorption grating with 100 nm period."

Nice one. The wave behaviour is made patent by the grating that produces interferences much wider than a molecule thanks to geometry. It also needs vacuum so the coherence is kept up to the interference pattern.

What I wanted to point out is that, during a diffusion in a solid for instance (I can't access your link presently), you'll observe collisions, but very little wave behaviour.

And as an order of magnitude, the thermal speed of gas molecules resembles the speed of sound there, like 340m/s for air at 300K. It varies as a kinetic energy, hence sqrt(T/m), so if the molecules weigh 60*C instead of 2*N, the thermal speed is slower than 200m/s.

[Enthalpy]

Maybe you meant this address
http://www.univie.ac.at/qfp/research/matterwave/c60/ (not ftp as in your link)

I still don't see why the fullerene should "cross a crystal". The diffraction grating consists of matter that stops the fullerene molecules, and of slits consisting of void characterised by an absence of matter full of vacuum where there is no solid, which permits the fullerene to fly through.

The emission speed results from an oven around 900K. 210m/s make 2.1*RT at that temperature, so something achieves to convert into speed some internal heat (mainly vibrations for fullerenes). With a gas it's called a nozzle, and this should apply to C₆₀ too because it sublimates near 600°C.

At the exit of a nozzle (or after an oriented expansion, which doesn't really need a convergent-divergent), the molecules have mostly parallel and uniform speeds. Depending on the pressure ratio and the gamma factor, more or less heat remains in the expanded gas, which adds some random (Brownian) speed to the expansion speed. Expansion to low vacuum would leave very little heat in a good gas, but a fullerene is a bad candidate for efficient expansion.

Useful to meditate: the source of particles, here the oven containing fullerene, is not coherent at all. The many molecules have no relationship in the phase of their wavefunctions. So, different molecules don't make any interference pattern. You observe interferences only because lone molecules interfere with themselves. This implies that each molecules passes through all slits.

[Enthalpy]

Here some suggestions for the experiment.

At least on the sketch, the oven resembles a barrel with a hole. A true and good nozzle would expand and cool the fullerene better, to obtain a narrower velocity distribution. Authentic De Laval, at least down to a pressure where the mean free path is smaller than the divergent. The narrow throat may need special fabrication. Seek a high pressure ratio, by a big oven pressure if needed. Try optionally to mimic the gas temperature at the nozzle's walls.

Heat the fullerene after it sublimates, before the expansion. This shall limit its condensation during the expansion.

Add a gas to the fullerene in the oven to make the expansion more efficient? Argon, methane... Problem: I don't know how to remove the gas from the beam. Maybe the detector can discriminate the fullerene from the gas?

Add mechanical choppers on the path, especially near the collimation slits, to keep only the fullerene molecules with nearly the mean velocity. You lose some beam intensity but improve the diffraction pattern.

Use a mechanical speed to impart the 200m/s or more. Up to 500m/s are easily accessible to a rotating disk of metal, more with carbon fibres. Heat the fullerene very little, just enough for slow sublimation at the rotating part. The emission is more in the plane, so less heat achieves the same beam intensity, and the speed is more uniform.

Use microphones as detectors. The kinetic energy is 6*RT at 300K, so cold microphones are better. With a piezoelectric or piezoresistive material, with micromachined silicon or with electrets, you can cover an area with microphones, so the experiment is faster than by scanning the diffraction pattern area. I feel microphones easier than the power laser too.

[GeLe5000]

Thank you for all these technical details.

Up to 500m/s are easily accessible

I have a naive question : Is it really necessary to accelerate so much the molecules ? There must be a pressure to force them into the grid ? Or waves only exist at high speeds ?

[Enthalpy]

My attempt is to obtain a uniform speed. At similar random speed, a bigger mean speed reduces the relative variation. But it has drawbacks: it makes smaller interference fringes.

Through the grating? There, the molecules fly feely through vacuum.

Everything is wave, at any speed. But observing the consequences may need some heavy apparatus, for instance the described experiment. Or no apparatus at all: matter has a volume because electrons are waves, even when immobile.

As a rule of thumb, wave behaviour is more easily observed for light objects like electrons. It's more difficult for heavier objects like atoms. Getting interferences with molecules like fullerenes is recent and still a subject of enthusiasm. And no-one hopes to see interferences for planets.

[GeLe5000]

electrons are waves, even when immobile.

Strange to me, since following Lambda = (h / m . v), Wavelength = infinite when v = 0. What kind of wave is it when the wavelength is infinite ? I had thought about that recently and had come to the conclusion that if the wavelength is infinite the wave doesn't exist. Because the particle is precisely located and there's no more a probability wave ?

If you find that my knoweldge in quantum physics is too bad, just tell me. I don't want to bother you but will keep reading (re-re-...reading) books in this field.

[Enthalpy]

The following sketch is adapted from the description at
http://www.univie.ac.at/qfp/research/matterwave/c60/

I resembles what one expects from a diffraction setup, but the wavelength differs from optics, hence so do the distances, grating's period, fringes separation. The light beam is strong and concentrated to ionize the molecules on its path, and a detector senses the charges, around 1 to 100 per second.

The dimensions and magnitudes were a tour de force in 1999. Meanwhile, interferences were obtained with heavier objects like proteins, but the experiment with fullerenes remains admirable.

[Enthalpy]

electrons are waves, even when immobile.

Strange to me, since following Lambda = (h / m . v), Wavelength = infinite when v = 0. What kind of wave is it when the wavelength is infinite ? I had thought about that recently and had come to the conclusion that if the wavelength is infinite the wave doesn't exist. Because the particle is precisely located and there's no more a probability wave ?

It's more a matter of wording, and I don't care so much about - sometimes I even choose the words to provoke thoughts. Orbitals are stationary: their module doesn't evolve over time. I like to call the electron "immobile" then. Though, for the p, d, f...orbitals, the phase of the wavefunction depends on the time and the angle(s) around the nucleus, so locations of constant phase rotate around the nucleus, which defines an angular momentum and a magnetic momentum. And even for the s orbitals, the (standing) wave drops with the distance to the nucleus, so it has a characteristic length; if you write it as a sum of sines, I mean a sum of plane waves, which is nothing more than a Fourier transform, you get a distribution of wavelengths for the electron, hence a distribution of possible speeds, momenta and so on. In that sense, the electron as an orbital is not immobile; the uncertainty over its momentum relates (Heisenberg) with the uncertainty over its location, that is, the size of the orbital.

If you find that my knowledge in quantum physics is too bad, just tell me. I don't want to bother you but will keep reading (re-re-...reading) books in this field.

You don't bother! If some time I'm tired I can just neglect to answer. But apologies to let your thread drift!

If you have gotten your first course about QM, it's normal and inevitable that you have to digest it. It needs time and efforts.

[Enthalpy]

Here's how a mechanical chopper could look like to pick only the molecules within a narrow speed distribution.

In optics, similar choopers are often pairs of teethed disks, 50% solid, with the proper distance and relative phase. Here I suggest instead a helix (and didn't check if I'm the first, of course). It can be long for increased speed selectivity without letting other speed domains pass through. The helix can be thin to let most molecules with adequate speed pass through. Just 5mm groove width and 200mm helix length would leave +-2.5% speed tolerance, and the corresponding fraction of the beam intensity, sure.

Alloys achieve peripheral speeds like 400 to >600m/s, and turbine superalloy can be baked for vacuum operation. The design must prevent dynamic flexural instability. Some ceramic bearings can run in vacuum, and magnetic bearings of course. The peripheral speed, angle and number of threads let accommodate varied molecule speeds. A high peripheral speed lets evacuate to the sides the molecules with bad speed.

After short thinking, building the chopper between the slits seems feasible. If not, it can fit before the slits.

Marc Schaefer, aka Enthalpy

[Enthalpy]

The helix idea belongs to the category
 "exists already"
rather than to the category
 "doesn't work".
Here: eprints.soton.ac.uk