First Published 2018 November 28

Prereading Note: I’ll apologize in advance for what will likely be most of my posts until the end of the semester. Of all the classes I’m in, only one has a final, my class on polymers. So as a way to review, I’ll be describing different concepts here, if only so that I know that I know them.

I was wrong on calculating M_{w}.^{1} To calculate M_{w}, you do as I said, and take the chains, 10 of 10 and 10 of 100. Multiply the number of chains by their mass, and sum them (total: 1100). Divide the mass sums of each chain length by the total mass (1/11,10/11). Multiply these numbers by the sum mass of each length (1/11*100+10/11*1000) We end up with a M_{w} of approximately 920, which now that I look at it, seems much more reasonable.

M_{n} just is the arithmatic mean of the masses. To find it, you sum the mass of all of the chains and divide by the number of chains that are measured.

To find M_{w}, you can also sum each chain multiplied by the square of the mass and then divide by the sum of chains multiplied by masses.

M_{w}

M_{e} is the molecular mass required for entanglements to form, as well as the molecular mass between the entanglements apparently, which is really weird and I should reconfirm this with the textbook.

Today, I’ll be discussing the different ways of measuring the mass of a polymer. As far as I remember, there are only four that are relevant to me for the final: M_{n}, M_{w}, M_{z}, and M_{e}. I’ll discuss each one in turn, first with how you calculate it, and then what it is used for.

So, first is M_{n}. M_{n} is the number average molecular mass of a polymer. As such, like M_{w} and M_{z}, it’s only useful for thermoplastics. To calculate M_{n}, you divide the mass of each polymer chain by its numerical representation, then sum all of those. So, if you have 10 chains with a mass of 10, and 10 with a mass of 100, it’s 10/2+100/2 = 55 for M_{n}. Since M_{n}^{2} is the molecular weight most concerned with the number of short chains, it’s good for telling you about how a polymer will yield, especially once it begins to crack.

Next is M_{w}. M_{w} is the weight average molecular mass, and is the most common/useful of them. To calculate M_{w}, you divide the mass of each polymer chain by its mass representation, then sum all of those. So, in the initial example, 10 chains of 10 and 10 chains of 100, you would get 100+1000=1100, and then 100/1100+1000/1100 = around 92. So, we immediately see that M_{w} is more easily measured, because it’s easier to measure the mass of a polymer than the number of chains. M_{w} is most relevant for the processability of the polymer, especially its flow in the molten state.

M_{z} is weird. Like M_{w}, it weights the mass, but it takes it the next step, and does the square of the mass. M_{w} is relevant mostly in governing die swell, also known as melt-elasticity.

Finally, we have M_{e}. M_{e} is the measure of the mass between entanglements. Off the top of my head^{3} I don’t know how this is measured. But, it’s mostly useful for knowing how strong the polymer will be in the rubber phase.^{4}

So, yeah. There’s four major ways to say the mass of a polymer. Oh! Also, the difference between M_{n} and M_{w} is known as the Molecular Weight Distribution, MWD. That tells you how much strain softening will occur. A larger (broader) MWD will lead to more strain softening.

In conclusion, polymers are weird. Hopefully by the end of these posts you’ll understand why if you don’t already.