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Wednesday, April 17, 2024

The Physics of the N95 Face Mask

It’s 2022, and by now we’ve all been wearing masks for nearly two years. And unless you are a surgeon or a construction worker who was already wearing them daily, in those two years you’ve probably learned a lot about them—which ones you like best, where to get them, and whether you have any extras stashed in a coat pocket or somewhere in your car.

But do you know what makes the prized N95 mask so special? Let’s find out.

Electric Charges

The fibers in regular cloth or paper face masks filter out particles by physically blocking them—but the fibers in an N95 mask also use a great physics trick. These fibers are electrically charged.

Electric charge is one of the fundamental properties of all particles. Just about everything around you is made of three particles: the proton, the electron and the neutron. (For now, let's ignore muons and neutrinos—both fundamental particles that actually exist—as well as other particles that are theoretically possible.)

Just as every particle has a mass, it also has a charge. The proton has a positive electric charge with a value of 1.6 x 10-19 coulombs, the unit for measuring electric charge. The electron has the exact opposite charge. That leaves the neutron with zero charge (thus the "neut" part of “neutron”).

The electric charge is a key part of the electrostatic interaction, the force between electric charges. The magnitude of this force depends on the magnitudes of the two charges and the distance between them. We can calculate this force with Coulomb's law. It looks like this:

In this expression, k is a constant with a value of 9 x 109 N×m2/C2. The charges are q1 and q2 and the distance between them is r. This will give a force in newtons. If the two charges are both the same sign (either both positive or both negative) then this will be a repulsive force. If the two charges are different signs, then the force is attractive.

If everything is made of electrons and protons, shouldn't there be electric forces between everything? Well, sort of. Electrons and protons are super tiny. That means that even a small drop of water will have something like 1022 protons in it. That drop will probably have the same number of electrons. (And no one cares about the neutrons—at least for now.) That makes the overall charge of this drop of water equal to zero coulombs. Even if you have extra electrons in your water, the total charge is going to be small, since the electron charge is puny. Essentially, most of the stuff you can see is electrically neutral with no electric forces.

How Do You Charge Something?

Remember that one time you took a sock out of the clothes dryer and it stuck to your shirt? If that's a static electricity interaction, how did the sock get charged?

To make a sock negatively charged, there's only one way to do it—make sure the sock has more electrons than protons. You are going to need a lot of electrons, maybe something on the order of 1013 extra electrons. (To give you an idea of how large this number is, it would be the total number of bills you'd need to give everyone on earth $1,000 in singles.) All those extra electrons would give the sock an overall negative charge of around 1 microcoulomb (1 x 10-6 C).

If you want to make that same sock positively charged, instead of adding electrons you would remove them. This would leave the sock with more protons than electrons for an overall positive charge. But you can’t just remove protons from most objects willy-nilly. Well, you can, but it might be super bad. Think back to the periodic table of elements. Let's say you start with an object that’s made of carbon, which has six protons in the nucleus. If you removed one of these protons, it would no longer be carbon. It would be boron, which has five protons—and you would have just created a nuclear reaction.

On the other hand, if you take away an electron from carbon, it's just a carbon ion. It doesn’t transform into a different element.

OK, but how do you add or remove electrons? You really only have two options. The most common method is to transfer electrons from one surface to another by rubbing them. I know that seems silly, but it's true. If you get a plastic pen and rub it on your wool sweater, both the pen and sweater will become charged. But which one will get the electrons? The answer depends on the two types of materials—and you can figure it out with the help of a thing called a triboelectric series. Using that, we would find that the wool is positively charged and the pen is negative.

If you need another example, this is what happens if you rub a cotton shirt on a plastic playground slide:

In this case, the child in the photo (it's an older picture of one of my boys) went down the slide with the shirt rubbing against the plastic. Those excess electrons spread over his body and got into his hair. Since all the hair was negatively charged, each strand repelled the others. The only way they could get as far as possible from the other strands was to stand up.

This is a cool picture, but you need two things for this to happen. First, you need very thin and light hair. (Curly hair will just stay curly and not stand up.) Second, the air needs to be dry. It turns out that an electrically charged child will attract water—I will show you why down below—and when the water hits them, it removes the charge.

There is another way to get excess electrons onto an object—shoot them at it. Yes, there is such a thing as an "electron gun." But maybe you have already seen something that’s similar: Old-style cathode ray televisions shot a stream of electrons to hit the screen to make those pretty pictures. So it is possible to charge something without touching it.

Interaction Between Charged and Uncharged Objects

If you’re wearing an N95 mask, the objects you want to stop are the tiny wet blobs that come out of a person's nose and mouth and could possibly carry a virus. These are essentially uncharged.

You might think that an electrically-charged N95 face mask would only be good for stopping electrically charged objects, but you can have an interaction between uncharged and charged objects.

Let's start with a simple demonstration you can do at home. Start with a plastic pen (or some other small plastic thing) and one of those plastic grocery bags. Now rub the pen with the bag. It should become electrically charged. If you can’t get it to work, you might need to change up materials—you could try rubbing the plastic pen against some wool or your hair. Now tear up some paper into tiny pieces and put them on the table. When you bring the charged pen near the paper, you get some magic-looking physics.

Here's how mine worked. I'm using a small plastic pipe—it just works better than a pen:

Those are just normal pieces of paper with no net charge. So why are they attracted to the plastic?

The answer is polarization. Let's consider the simplest model of a molecule of paper. This pretend paper molecule is a sphere with just two charged particles, a proton and an electron. (If you are thinking back to the periodic table, yes, this would make it hydrogen paper. No, it totally doesn’t exist.)

Here's my model of this:

In atoms, the negative electron acts like it is spread over the blue region. We call it an “electron cloud.” I know that seems weird, but weird stuff happens with tiny objects like molecules. The important thing is that the center of the negative blue cloud is at the same location as the positive charge. In this state, it's unpolarized.

Now let's say the positively charged pen is brought near the paper molecule. The electron cloud will get pulled toward the pen (because they are oppositely charged), and the positive proton will get pushed away.

Here's what the paper molecule will look like now:

(Note: This is not even close to being the correct scale.)

The paper molecule is now polarized. The positive pen interacts with both the negative electron and the positive proton. However, the effective location of the negative electron cloud is closer to the pen than the proton. The magnitude of the electric force between charges decreases as the separation distance increases. This means the attractive force between the pen and the electron is greater than the repulsive force between the pen and the proton. So there is an overall attractive force pulling the paper toward the pen, even though the paper is neutral.

Yes, that's just one molecule—but if the same thing happens with every molecule in the piece of paper you can get an attractive force. That's cool, right?

Did you notice in my demo that some of the paper is attracted and then repelled by the plastic pipe? That can happen. When the paper hits the positive pipe, some of the negative electrons transfer from the paper to the pen. Now the paper is also positive and the pen repels it to make it fly away.

Something similar happens with water—but it's technically different. Actually, this is another great demonstration to try: Get your charged plastic pen and bring it near a very thin stream of water from a faucet. Here's what happens:

Notice that some of the water drops are attracted to the degree that they partially circle the charged pipe. Why does water do this? A water molecule is made of two hydrogen atoms and one oxygen (yeah, H2O). But because of the way these atoms are arranged, there is a permanent charge separation. Here is a rough model:

It just so happens that the two hydrogen atoms acting like this are more positive, and the oxygen acts like it's negative. Because of the bent angle of the bonds, this makes a charge separation such that this water molecule is polarized. A water droplet near a charged object will rotate in such a way that the oppositely charged end of the molecule will face the object and then be attracted to it. That's why you can bend a stream of water with a charged piece of plastic.

How the N95 Mask Works

Now imagine something similar to the electrically charged pen and the water—but at a much smaller scale. Instead of a pen, you have a bunch of plastic fibers. Instead of the water you have the drops that fly out of someone’s mouth. This is essentially what happens in an N95 mask. The fiber in the mask attracts those drops, keeping the wearer from inhaling them. At a very small scale (like that of respiratory aerosols and fibers), things tend to stick together, due to what's called the van der Waals interaction. This is basically an attractive interaction between two uncharged objects because of very slight charge separations.

With an N95 fiber, you don't have to rub it with some other material to get it charged. The fibers in the mask are created from an “electret” material; this word comes from combining electric and magnet. No, it's not an electromagnet—it is a permanently electrically charged object, just in the way that a bar magnet on your fridge is.

There are a couple of ways to make electret materials. One is to bombard the stuff with electrons so that they get stuck in the fiber to make it stay charged. The other method is to heat up a material in an electric field. The increase in temperature allows the molecules in the material to rotate into a polarized state, due to their interaction with the electric field. Once the material cools off, the molecules stay polarized. This makes a slightly different electret material, in that it creates an electric effect even though it’s still neutrally charged.

So, the electret fibers in an N95 mask not only block small particles by getting in the way, they can also attract them with the electric interaction, so they get stuck to the fibers. This means that those water droplets carrying a virus don’t get inhaled, and the mask wearer won’t be infected. Of course, an N95 also blocks other small particles, like dust, paint, and other toxic stuff that might not be great for a person to inhale into their body.

So there you have it—the N95 mask doesn't just help us all get past this terrible pandemic, it can also teach us some awesome physics.

Update 1-28-2022 4:48 pm ET: This story was updated to correct information about the charge separation in the atoms of a water molecule.

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