# Wall material effect on Van der Waals gas?

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• Swamp Thing
In summary: It would be accelerated towards another (stationary) molecule and then...The summary is that in a vdW gas, a molecule that bounces off a wall is accelerated towards another molecule, and then that accelerated molecule is accelerated towards another molecule.
Swamp Thing
Ref: Van der Waals Equation @ Wikipedia

the bulk of the particles do not experience a net force pulling them to the right or to the left. This is different for the particles in surface layers directly adjacent to the walls. They feel a net force from the bulk particles pulling them into the container, because this force is not compensated by particles on the side where the wall is (another assumption here is that there is no interaction between walls and particles, which is not true, as can be seen from the phenomenon of droplet formation; most types of liquid show adhesion). This net force decreases the force exerted onto the wall by the particles in the surface layer.

The above paragraph is explains how intermolecular attraction reduces the gas pressure, assuming that there is no attraction between walls and particles.

In practice, would there be a change in pressure from one kind of wall to another, if we ensure that there is no actual condensation? Are there materials that attract nitrogen molecules so strongly that the pressure is different when they are used to line the wall? Or maybe a similar effect in water vapor, steam, alcohol or acetone?

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Swamp Thing said:
Ref: Van der Waals Equation @ Wikipedia

The above paragraph is explains how intermolecular attraction reduces the gas pressure, assuming that there is no attraction between walls and particles.
I find the idea that intermolecular attraction should reduce pressure very hard to grasp.
Pressure is just due to collisions of molecules with the walls and I don't see that either the frequency of collisions or the momentum of each molecule when it collides with the wall changes due to intermolecular attraction.
I would think that each molecule just gets accelerated towards another molecule and slows down again as it moves away. On average the result should be the same as it is without attraction.

Is there some calculation or simulation that actually shows the pressure reduction?

Swamp Thing
There is no calculation about the effect of the wall, just a qualitative caveat that the described model ignores any possible effect the wall might have on gas pressure by virtue of molecular attraction.

I also thought that the caveat might be superfluous, but I was not sure.

---- Edit: --
Sorry, I think I misunderstood you. You are asking about the effect of forces between gas molecules, not between molecule and wall. That effect is indeed supposed to affect the gas pressure according to their derivation.

The idea is that a gas molecule that is emerging from the interior and heading towards the wall will tend to be drawn back towards the interior because of all the other molecules that are in there. This will slow it down a little, which in turn will reflect as reduced pressure when averaged over lots of molecules.

Philip Koeck said:
I find the idea that intermolecular attraction should reduce pressure very hard to grasp.
Pressure is just due to collisions of molecules with the walls and I don't see that either the frequency of collisions or the momentum of each molecule when it collides with the wall changes due to intermolecular attraction.
Intermolecular attraction is obviously a component of the total pressure. Just consider the case of liquid under tension. The molecules in a liquid under tension still collide with walls and carry momentum. It is just that the momentum so carried is less than the attraction of liquid molecules to the wall.
So how do you compare critical point transition from a gas to a wetting liquid (which is attracted to wall) to the transition from a gas to a nonwetting liquid (which is repelled by walls)?

Swamp Thing said:
Sorry, I think I misunderstood you. You are asking about the effect of forces between gas molecules, not between molecule and wall. That effect is indeed supposed to affect the gas pressure according to their derivation.

The idea is that a gas molecule that is emerging from the interior and heading towards the wall will tend to be drawn back towards the interior because of all the other molecules that are in there. This will slow it down a little, which in turn will reflect as reduced pressure when averaged over lots of molecules.
I would describe a vdW-gas more like a gas than a liquid so I would think of molecules flying around among other molecules.

I agree that molecules are slowed down when they fly away from other molecules, but they were accelerated towards the other molecules first, so the effect should be zero.
I'm probably oversimplifying a lot though.

If I think of a single molecule that has just bounced off a wall and all the other molecules are treated as stationary.

In an ideal gas this molecule could just continue in a straight line until it hits another wall with unchanged momentum.

In a vdW gas it might be accelerated towards another (stationary) molecule and then orbit around it half a circle and fly back to the wall it came from while being slowed down. When it hits the wall again it has the same momentum as when it left the wall, just like it would in an the ideal gas.

Is this picture too simple?

Philip Koeck said:
I would describe a vdW-gas more like a gas than a liquid so I would think of molecules flying around among other molecules.
The point is that van der Waals gas is a gas which shows some liquid properties.
Philip Koeck said:
I agree that molecules are slowed down when they fly away from other molecules, but they were accelerated towards the other molecules first, so the effect should be zero.
But it should not be zero. Indeed, in liquid, the attraction between molecules is strong enough that it allows the liquid to have negative pressure. A van der Waals gas is more gas than liquid, so the pressure cannot go negative, but it can have a nonzero effect, in the same direction.
For example, pV=nRT. This refers to the number of particles regardless of their mass. Which means that if some forces cause some though not all molecules in a gas to be attracted to each other, like
2NO2⇔N2O4
the pressure is diminished as n is halved even though the momentum carried by the molecules is unaltered.
It makes sense that weak attraction that does not actually suffice to bind molecules to permanent dimers also has effects on the same direction...

Swamp Thing and Philip Koeck
snorkack said:
The point is that van der Waals gas is a gas which shows some liquid properties.

But it should not be zero. Indeed, in liquid, the attraction between molecules is strong enough that it allows the liquid to have negative pressure. A van der Waals gas is more gas than liquid, so the pressure cannot go negative, but it can have a nonzero effect, in the same direction.
For example, pV=nRT. This refers to the number of particles regardless of their mass. Which means that if some forces cause some though not all molecules in a gas to be attracted to each other, like
2NO2⇔N2O4
the pressure is diminished as n is halved even though the momentum carried by the molecules is unaltered.
It makes sense that weak attraction that does not actually suffice to bind molecules to permanent dimers also has effects on the same direction...
That brings us right back to the OP's question.
If, for example, the walls are coated with molecules of the same kind as those in the gas, why wouldn't there be just as much attraction between the gas molecules and the walls?

snorkack said:
The point is that van der Waals gas is a gas which shows some liquid properties.

But it should not be zero. Indeed, in liquid, the attraction between molecules is strong enough that it allows the liquid to have negative pressure. A van der Waals gas is more gas than liquid, so the pressure cannot go negative, but it can have a nonzero effect, in the same direction.
For example, pV=nRT. This refers to the number of particles regardless of their mass. Which means that if some forces cause some though not all molecules in a gas to be attracted to each other, like
2NO2⇔N2O4
the pressure is diminished as n is halved even though the momentum carried by the molecules is unaltered.
It makes sense that weak attraction that does not actually suffice to bind molecules to permanent dimers also has effects on the same direction...
If I understand correctly, then the explanation you give makes more sense to me than the one on Wikipedia.

If molecules bind to each other temporarily then the number of particles in the gas actually decreases, which would explain the reduction in pressure.

Is that what you said?

Swamp Thing said:
Ref: Van der Waals Equation @ Wikipedia
The above paragraph is explains how intermolecular attraction reduces the gas pressure, assuming that there is no attraction between walls and particles.

In practice, would there be a change in pressure from one kind of wall to another, if we ensure that there is no actual condensation? Are there materials that attract nitrogen molecules so strongly that the pressure is different when they are used to line the wall? Or maybe a similar effect in water vapor, steam, alcohol or acetone?
I'm much happier with what I believe to be snorkack's explanation:
In a vdW-gas there's a certain probability that molecules bind for a short time.
This probability should be proportional to the molar density squared and would therefore lead to a reduction of "independent objects" in the gas and thus to a reduction of pressure proportional to the square of the molar density.
The effect of molecules binding to the walls would be very minor, simply because there are very few molecules close to the wall compared to the bulk of the gas.

The explanation given in Wikipedia doesn't make sense to me as it is.
I see that molecules moving from the wall to the interior tend to be accelerated, while those moving in the opposite direction tend to be decelerated, but I don't see why that would change the average momentum that molecules transfer to the wall as the long as the molecules are never bound to each other.

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Swamp Thing
Swamp Thing said:
Ref: Van der Waals Equation @ Wikipedia
The above paragraph is explains how intermolecular attraction reduces the gas pressure, assuming that there is no attraction between walls and particles.

In practice, would there be a change in pressure from one kind of wall to another, if we ensure that there is no actual condensation? Are there materials that attract nitrogen molecules so strongly that the pressure is different when they are used to line the wall? Or maybe a similar effect in water vapor, steam, alcohol or acetone?
I might have an answer now and I'd like to know what you think about it.

I would say that no matter what the properties of the wall are the molecules in a vdW-gas will feel no force from the wall on average.
Importantly this is only true as long as we remain within the idealization of the vdW-gas. In other words we don't discuss condensation on the walls. A vdW-gas doesn't condensate since it can't undergo phase transitions.

Anyway, here comes my rationalization of the pressure decrease in a vdW-gas compared to an ideal gas:

The molecules in the bulk have a tendency to align their dipole moments (which can also be induced in the case of symmetric molecules) so they form short lived and short range patches of order.
This means that the molecules are, on average, in a shallow potential well.

For a molecule at the wall of the container the situation is different. Even if the wall is lined with dipoles of some kind they are relatively fixed in orientation and cannot adapt to the dipole that the gas molecule happens to have.
This should mean that, on average, the gas molecules feel no force from the walls. They are attracted as often as they are repelled.

Therefore, on average, each molecule has to climb out of shallow potential well to reach the wall and will hit the wall with less kinetic energy than it had when it was in the bulk of the gas.

Philip Koeck said:
Even if the wall is lined with dipoles of some kind they are relatively fixed in orientation and cannot adapt to the dipole that the gas molecule happens to have.
This should mean that, on average, the gas molecules feel no force from the walls.

This is pretty convincing, but there is also an "on the other hand" consideration.

The Casimir force is often described as a more macroscopic version of the van der Waals force. See, for example, https://www.physicsforums.com/media/casimir-effect-what-causes-this-force.6926/. In that picture, walls that are very near to each other can attract each other via polarization in pretty much the same way that molecues do. This seems to imply that walls can attract molecules too.

Demystifier and Philip Koeck
Swamp Thing said:
This is pretty convincing, but there is also an "on the other hand" consideration.

The Casimir force is often described as a more macroscopic version of the van der Waals force. See, for example, https://www.physicsforums.com/media/casimir-effect-what-causes-this-force.6926/. In that picture, walls that are very near to each other can attract each other via polarization in pretty much the same way that molecues do. This seems to imply that walls can attract molecules too.
That's a really nice down-to-earth explanation of the Casimir force.

I'm not sure, however, about the way they describe surfaces in this video.
For reasons explained below I would think that even a perfectly clean surface of a nonpolar solid (metal or carbon for example) in vacuum is polarized since the electrons extend a bit further out into the surrounding vacuum and leave a slight excess of positive charge in the bulk.

I believe this must be true since there is a positive electrostatic potential in every solid, compared to that in the surrounding vacuum.

Now according to Poisson's equation you can only have a constant (on average) potential inside the solid and a different constant potential in the surrounding vacuum if there's a negative and a positive charge density (giving the potential a curvature) between the two areas.

Here I'm not looking at atomic detail, so you have to think of large scale only. Just consider the average potential in a volume around 1 μm3 for example so that you average over a large number of atoms.

This is rather important, for example, for a Zernike phase plate in electron microscopy, which consists of a thin carbon film with a hole (1-2 μm diameter) in it.
When this phase plate is placed in a back focal plane of the EM the unscattered wave-portion goes through the hole whereas scattered waves go through the carbon. The electron wave experiences a phases shift that's proportional to the projected electrostatic potential and it's the relative phase shift between scattered and unscattered electrons that creates phase contrast.
If a solid doesn't have a permanent dipole layer then I don't see how a phase plate would work.

Of course this would mean that 2 clean surfaces in vacuum would repel each other.

Is there something I have missed?

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Philip Koeck said:
Of course this would mean that 2 clean surfaces in vacuum would repel each other.

Is there something I have missed?

Let's try paging : @Demystifier , whose paper is quoted in the video -- I'm sure he can address your queries.

Demystifier
Philip Koeck said:
Is there something I have missed?
I think you missed quantum mechanics, i.e. the possibility of being in a quantum superposition. See my presentation http://thphys.irb.hr/wiki/main/images/2/2c/Casimir.pdf
page 25.

This thread is in classical physics forum, but Casimir effect and van der Waals force are quantum effects.

vanhees71
Philip Koeck said:
If molecules bind to each other temporarily then the number of particles in the gas actually decreases, which would explain the reduction in pressure.

In most situations, the fraction of the volume of gas in very near contact with the walls would be very small compared with the total volume of a container. This could be different in a sponge-like material in which there is a massive area of contact between solid and gas but, in simple situations, the energy between molecules and wall would be negligible.

Philip Koeck
Demystifier said:
I think you missed quantum mechanics, i.e. the possibility of being in a quantum superposition. See my presentation http://thphys.irb.hr/wiki/main/images/2/2c/Casimir.pdf
page 25.

This thread is in classical physics forum, but Casimir effect and van der Waals force are quantum effects.
I can understand the quantum superposition for molecules in a gas, but my question in post 12 was really about, for example, a very macroscopic carbon film, such as a phase plate in a TEM.
Would this carbon film have a layer of negative charge on its surface (balanced by some positive charge further inside the film)?

sophiecentaur said:
In most situations, the fraction of the volume of gas in very near contact with the walls would be very small compared with the total volume of a container. This could be different in a sponge-like material in which there is a massive area of contact between solid and gas but, in simple situations, the energy between molecules and wall would be negligible.
So one could test experimentally whether the container material influences the pressure in a gas.

Philip Koeck said:
Would this carbon film have a layer of negative charge on its surface (balanced by some positive charge further inside the film)?
As far as I know, it wouldn't. Or if it would, it's not explained by the Casimir effect.

Philip Koeck said:
So one could test experimentally whether the container material influences the pressure in a gas.
What sort of experiment would you envisage when you are trying to detect a tiny difference in temperature change for different wall materials. Maybe a dense open cell foam would have a detectable effect but how to measure it, What materials could you use for an A/B comparison?

Lord Jestocost
sophiecentaur said:
What sort of experiment would you envisage when you are trying to detect a tiny difference in temperature change for different wall materials. Maybe a dense open cell foam would have a detectable effect but how to measure it, What materials could you use for an A/B comparison?
Certainly not an easy experiment. Something like 2 containers made of the same material, one with a small surface and the other with a very large surface. If you have a known molar density of some gas in each of them you could look at the relationship between T and p and see how much they deviate from the vdW equation.

I think to get an appreciable effect you need to look at "mesoscopic systems", i.e., a gas in a small volume to see "finite-size effects" on the behavior of the gas. In the thermodynamic limit the boundary effects are completely gone.

Philip Koeck
Demystifier said:
As far as I know, it wouldn't. Or if it would, it's not explained by the Casimir effect.
This is a bit of a spin-off from the original question, but if we're discussing possible surface effects on gas pressure we have to know what the surface is like, I guess. Otherwise we could move this to a separate thread.

Here's my argument for surface charges (purely electrostatics, no QM):
In the bulk of a perfect crystal the charge density averaged over a volume containing an integer number of unit cells is zero. For an amorphous solid an average over a large enough volume will also give zero on average with small variations.

In the surrounding vacuum the charge density is also zero.

On the other hand we know that there is a positive electrostatic potential in every solid, compared to that in the surrounding vacuum. This can be tested by sending an electron wave through a solid and observing the phase shift compared to a wave that didn't go through the solid.

In this argument I'm not looking at atomic detail, so you have to think of large scale only. Just consider the average potential in a volume around 1 μm3 for example so that you average over a large number of atoms.

Now according to Poisson's equation you can only have a constant (on average) potential inside the solid and a different constant potential in the surrounding vacuum if there's a negative and a positive charge density (giving the potential a positive and a negative curvature) between the two areas.

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Philip Koeck said:
Of course this would mean that 2 clean surfaces in vacuum would repel each other.
I'll take that statement back. They wouldn't.

Swamp Thing said:
Ref: Van der Waals Equation @ Wikipedia
The above paragraph is explains how intermolecular attraction reduces the gas pressure, assuming that there is no attraction between walls and particles.

In practice, would there be a change in pressure from one kind of wall to another, if we ensure that there is no actual condensation? Are there materials that attract nitrogen molecules so strongly that the pressure is different when they are used to line the wall? Or maybe a similar effect in water vapor, steam, alcohol or acetone?
Back to the OP and also in response to @sophiecentaur and @vanhees71.

From the model described in Wikipedia I would conclude that the reduction of pressure due to intermolecular attraction would disappear if there's a similar attraction between the molecules and the wall.
This should be measurable even if the container is large and the wall area is minimal.

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