First Published 2018 November 30
Prereading note: I actually looked in my notes for this one!
Today we’re talking about the factors that affect Tg and Tm. Factors that affect Tg will affect all polymers, while the factors that affect Tm will only affect semi-crystalline thermoplastics.
There are four main kinds of factors that affect Tg: intramolecular forces, intermolecular forces, chain length, and timescale.
The intramolecular forces that affect Tg are: chain stiffness, side groups, and cross link density. As chain stiffness goes up,1 Tg goes up. This is because as the amount of energy it takes to rotate along a bond2 increases, so too does Tg. As side groups become bulkier, they increase Tg, for the same reason. As cross-link density goes up, so does Tg, This is because it’s hard to rotate around a link, because the side group is suddenly large. Also, if cross-link density isn’t 0, there is no Tm.
The intermolecular forces that affect Tg are: side group dipole moments,3 side group chain length, and plasticizers. As the side groups become more polar, Tg goes up, because it draws the different polymer chains closer together. For that same reason, as side groups become longer, Tg goes down, because it keeps them further away. For that same reason, plasticizers also tend to lower Tg.
Third, assuming the molecular mass is less than Me,4 the increase of molecular mass will increase Tg. Above Me, there is effectively no difference in Tg for chain length.
Finally, everything in polymers is time dependent. This makes sense when you think about how free energy diagrams work. At any temperature above 0K, there’s some energy. Given enough time, any bond can rotate, because it’ll at some point be able to overcome its energy barrier. Heating it just makes that happen faster. So, Tg decreases as the time-scale you view it from increases. This also works in reverse, so a polymer that’s being stressed at high rates will remain solid at higher temperatures than one that is not.
In order of importance, the intramolecular forces are more important than the intermolecular forces are more important than the other two in governing Tg.5
So, assuming cross-link density is 0, eventually the polymer will become viscous.6 This is affected mainly by the same factors that influence Tg, which is why they have the relationship I talked about in Polymer Review 2. As interactions between the chains goes up, Tm goes up. As chain stiffness goes up, Tm goes up. As branching7 goes up, Tm goes down. As delta S8 goes up, Tm goes down. To explain this, Tm can also be expressed as delta H9 divided by delta S10. Turning a crystal, which is highly ordered, into a liquid, which is not, increases the entropy of the state a lot. So, somehow that also works in reverse? This part is where the physics goes beyond me.
To lower delta S, you can orient the polymer more. This leads well into crystals which is almost certainly the topic of tomorrow’s post.
First Published 2018 November 29
Prereading note: as with the rest of these posts, it’s written mainly from memory, and will1 be consulted and fixed for accuracy before examinations.
Corrections (since I looked at some notes):
Below Tg, the molecule is only able to vibrate. Above Tg, the molecule is able to rotate at each of its bonds. Above Tm2 or Tv3, the molecule is able to move, and flows through a process known as reptation.
Tm is double Tg for symmetric polymers,4 and 1.5 for the rest.
Polymers with crosslinks are thermosets, which are like epoxies and what most rubbers are, and elastomers, which are less tightly cross-linked thermosets.
Tm is where crystallization can begin in a polymer. I’ll probably think about how that works tomorrow.
Polymers are super cool, for a variety of reasons. The one that I’m thinking of today is that they take all of the things that you get told in chemistry class exist but don’t matter, and then suddenly make them matter. The two examples of that I’m thinking of are the fact that the main force holding polymers together is their Van Der Waals interactions, which is the force I’ve5 always been able to ignore as non-significant for a material. The other is that polymers treat all energy as energy. That is, the temperature that a polymer needs to be at to behave as a liquid is lower if mechanical energy is supplied.
Speaking of, there are a few phases that polymers exist in. I’ll briefly discuss them from lowest to highest temperature.
At the coldest, a polymer is in what’s known as the “glassy” state. Here, it is solid, brittle, and the chains are held rigid.
When you heat up, you’ll eventually reach the glass transition temperature, Tg. This is the temperature range where the polymer would be described as “leathery.” It also corresponds to a quick drop in modulus.6 This is due to the fact that below Tg, the energy needed to break the Van Der Waals bonds is higher, because the polymer is moving less. Once you reach Tg, however, the polymers move enough on their own that the Van Der Waals forces effectively disappear. The only thing that gives the polymer strength then is the entanglements, which we talked about yesterday as Me. Above Tg, you’re in the rubber phase. This is where a polymer behaves a lot like what we think rubber does. And, right near Tg, the material exhibits a lot of damping.
After Tg, you reach what’s known as Tm, which is the temperature where the polymer stops acting like a solid, and begins acting like a fluid. Apparently it’s only melting when crystals do that, so that isn’t what happens to many polymers. One interesting tidbit is that polymers that are crystalline7 will have a Tm equal to 1.5x the Tg in Kelvin.
The information about Tm only applies to thermoplastics, polymers that don’t have chemical crosslinks. If a polymer has crosslinks, it never reaches the viscous phase. Instead, it stays at the “rubber plateau” for modulus until the material ultimately burns.8
The other thing to note that is different about amorphous and semi-crystalline polymers is that the drop at Tg is much larger in amorphous polymers than in semi-crystalline, because Tg is where amorphous regions fail, while Tm is where the crystalline sections fail. So, since a semi-crystalline polymer has a much smaller composition of amorphous polymer, it loses less strength.
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 Mw.1 To calculate Mw, 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 Mw of approximately 920, which now that I look at it, seems much more reasonable.
Mn 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 Mw, you can also sum each chain multiplied by the square of the mass and then divide by the sum of chains multiplied by masses.
Mw
Me 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: Mn, Mw, Mz, and Me. I’ll discuss each one in turn, first with how you calculate it, and then what it is used for.
So, first is Mn. Mn is the number average molecular mass of a polymer. As such, like Mw and Mz, it’s only useful for thermoplastics. To calculate Mn, 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 Mn. Since Mn2 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 Mw. Mw is the weight average molecular mass, and is the most common/useful of them. To calculate Mw, 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 Mw is more easily measured, because it’s easier to measure the mass of a polymer than the number of chains. Mw is most relevant for the processability of the polymer, especially its flow in the molten state.
Mz is weird. Like Mw, it weights the mass, but it takes it the next step, and does the square of the mass. Mw is relevant mostly in governing die swell, also known as melt-elasticity.
Finally, we have Me. Me is the measure of the mass between entanglements. Off the top of my head3 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 Mn and Mw 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.
First Published: 2018 November 27
Tonight, I had the wonderful opportunity to see Bat Out Of Hell at the Dominion Theatre. It was an odd show for a lot of reasons.
Plot wise, it definitely felt like Peter Pan. There were some fun fourth wall breaks, including the orchestra coming out with broken instruments. It was really fun, especially as a sing-along.
First Published: 2018 November 26
Today, I had the wonderful fortune of watching “Pinter at the Pinter,” a series of Pinter shows at the Harold Pinter Theatre. It was confusing. Apparently I don’t really understand absurdism. But, such is life.
The stage was fantastic, and spun. The lighting was minimal, but well executed. The ukulele playing was mediocre, which was sad. All of the other sounds were beautifully done, whether as subtle or blatant effect
First Published: 2018 November 25
Revelations 1:8 “‘I am the Alpha and the Omega,’ says the Lord God, ‘the one who is and who was and who is to come, the almighty.’”
Today is the last Sunday in the1 year, the Feast of Christ the King.2 It’s a great way to end the year, especially because we get a line from my3 favorite book, Revelations.
We also get to use today as a way to reflect on the year we’ve had, and whether we’ve lived this Year of Grace4 as if Christ was “King of the Universe.”5
Since I’m preparing for the end of my semester and time abroad, the ending of the year is the first of a lot of endings I’m going to have to be ready for. But, that’s neither here nor there.
Today is the last Sunday in the6 year. It’s the feast of Christ the King.7 So, today is the day we celebrate the idea of Christ as the “one who is and who was and who is to come” as a part of the Trinity.
And, we get a reading out of the book of Revelations, which is always nice in a reading. But, today, as the last day of the year, so it’s time that I think about endings. My liturgical year has almost ended, and so the Year of Grace has too. I wonder what Pope Francis will decide next year will be.
First Published: 2018 November 24
I’ve realized lately that one of the biggest problems I’m beginning to have in my life is that everything means more than one thing. So, for instance, the title of this post, “rolls”, could refer to one of two things, both of which are applicable to today, which is odd.
The first and most obvious of these is the food kind. Small little loaves of bread. Today, I decided to try making rolls out of normal bread dough. But, since I measured exactly nothing, I can’t give the recipe.
The oven was set to its hottest temperature, probably 2501 and I kneaded the dough around 5 times over 3ish hours. It baked until crunchy, and was then drizzled with butter.
The other kind of roll is the musical roll. Although wikipedia defines music roll differently, in the Celtic Folk tradition, a roll is a way to break up notes. As you probably know about bagpipes, they can’t play staccato or tongued notes.2 So, to differentiate between a half note and two quarter notes, supplementary notes are played between them. A roll is where you play the note, the note above it, and the note below it, in a quick fashion. There’s more to it than that, especially in terms of spacing, timing, and etc. but that’s a basic3 summary. I worked on making my rolls on the penny whistle4 today.
First Published: 2018 November 23
As I’ve mentioned time and time again, I enjoy making food, and I enjoy competing. Somehow1 my coaches throughout life have found out these two facts. This is the first time that a coach has connected the two, however.
So, in a little over 6 weeks,2 I’ll be competing against nominally the entire diving squad, though, like many diving meets, it looks like most people aren’t there to win. Therefore, I need a winning recipe.
Baking competitions are a lot like diving. A perfectly baked cookie will bring in less points than a good cake, because the cake is harder. So, I need a recipe that balances ease, apparent difficulty,3 reproducibility, taste, and appearance. If I didn’t care about the apparent difficulty, I’d likely just make my toffee chip chocolate cookies. But, they seem too easy.
So, I think I’ll try to make “Chocolate Budino” or, at least a variation on that recipe. Now, like many people, I found out that youtube4 cooking videos exist, and fell in love with them. They have some interesting tips for how to improve chocolate baked goods, which I’ll likely try to incorporate. But, this is definitely something I shouldn’t put as much internal pressure on myself as I have.
I was informed last night that in a little over a month, I’ll be participating in a baking competition. Now, as I’ve mentioned more than once, I like to make food. I’ve also mentioned that I like competition, so this should be a great thing for me.
But, here comes the hard part: what do I make? My initial idea was to make my chocolate toffee cookies,5 but with a few modifications.
I’ve begun watching youtube food videos, and I understand wholly why people watch them. It’s super entertaining and informative. A few highlights from what I’ve learned is that you can brown butter to add more flavour6 to food, and that you can add espresso powder to chocolate foods to make them taste more deep.
So, I’d planned on browning the butter in the cookies,7 and adding some coffee in as well. However, I also realized that I had chicory coffee at home, and wondered if that might not be a better profile, since it would be a little nuttier.
But, as a wise friend helped me realize “Good cookies are good. Great cookies are good. Awesome cookies are great.” What he meant was that people tend not to discriminate too finely between different levels of cookie. I agreed, and so thought about what else I could make.
Bread was eliminated for much the same reason, because there’s not a huge difference in how a normal person perceives a good to great loaf, and I don’t know that I can make an excellent loaf 100% of the time.8 So, since the challenge began with someone’s banana bread recipe, it was suggested I do that.
But, banana bread for me has always just been a good comfort food. So, like with cookies, it’s not something that can really show how amazing I am at baking.
Then, I remembered that I used to make a recipe called “Chocolate Budino.” It’s effectively a chocolate pudding cake, and, when served warm, acts somewhat like a chocolate lava cake. So, as above, I may add in browned butter and espresso to make it more rich, but that seemed like a good way to distinguish myself.
Then the options arose again. I could either make it small, as in a cupcake mold, or large, the size of a 8" cake or so.9 There are advantages and disadvantages to both, so I was not sure which I’ll do.
Then the question became one of serving the cake. I could present it on its own, but that lacks a lot of the cool factor that we love when we bake. So, I decided I’d add some sort of side to the dessert.10
I like fruit, especially strawberries, so I decided I’d do strawberries on the side. But, then the question becomes how, and I was unsure.
Next, people suggested ice cream. But, I’m trying to showcase my talents, so buying ice cream is out. Making ice cream is a pain, and no-churn ice cream is fake.
So, I realized what I really wanted was something creamy. Hmmm, whipped cream.
I thought about what I tended to associate with chocolate and strawberries, and it’s mint. So, I thought I’d do a fresh mint whipped cream, and serve that with mint and strawberry.
Then the question returned to the size. As another friend pointed out, a cake sized budino would be more easily decorated, as well as looking more professional.11 So, I realized that I could do a full size cake, cut a nice slice out of it, and have a strawberry on the top, along with a sprig of mint and the cream. I’m still not sure where the cream will go, but I envision it along the side of the cake slice, with the cake topped with some sort of decorative strawberry flower. Maybe the cream could have a slice leaning on it with the mint sprig.
So, in conclusion, I try way too hard.
probably because I’m horrible with secrets↩︎
I think. I refuse to check↩︎
I dream of a 5211A equivalent↩︎
this is a noun that isn’t a proper noun↩︎
yes I’m British now, deal with it↩︎
not in the toffee, since that’s already browned↩︎
especially since I’ll be in a scary kitchen↩︎
yes an 8" cake is 8", but it made sense that the time↩︎
no I’m not taking it too seriously, I just refuse to lose↩︎
man I have no clue how to write the words there. Do you say “as well as” and then a gerund? or a regular verb? or what↩︎
First Published: 2018 November 22
For those of you in America, today is Thanksgiving! As my high school math teacher used to say, “Thanksgiving is the best holiday;” while I don’t agree necessarily, it is a nice sentiment. But, I learned that Thanksgiving isn’t a thing in the UK. It’s not that it doesn’t make sense, just that it hurts.
At around 1:30 this afternoon, I realized that, time zones included, if I were home I would have just finished the first knead of my bagels. Instead, I had just finished one class, and was preparing to attend another.
Of course, bagels aren’t the most common Thanksgiving tradition.1 When I mentioned last night that I make bagels for the holiday, one of my diving teammates asked, “Oh, so your family’s Jewish?” I don’t think that’s why, but it’s certainly why I have the cookbook.
I’m just kind of bummed. At the Thanksgiving dinner that the lovely Grinnell in London staff set up, we had turkey, mashed potatoes, sweet potatoes, something resembling stuffing, and cranberries. Due to a mistake, we didn’t have pumpkin pie. But, as I ate it, I just realized how little the food on Thanksgiving means to me. It’s always been more about the feeding others, at least for me, and the companionship and fellowship. The food is great and all, but I prefer the fact that I’m sharing the food with my friends and family. So, from across the pond, a happy Thanksgiving to everyone who’s celebrating.
Thanksgiving is an American holiday. Or, at least, Thanksgiving being celebrated today is an American custom. Here, on the other side of the pond, nothing really seems notable about it. I’ll still have all of my classes, and none of my traditions from home.
Now, before I start talking specifics about the traditions, I’d like to talk a bit about my traditions in general. At some point or points in my early life,2 I was assigned the homework of bringing a list of family traditions to school. Of course, I didn’t really think we had any.
As I look back, I realize we have many, and I’ll probably write about them later. But, I realized we also didn’t have as many as I’d like. We used to make pasta and bread, and don’t any more. We used to have large groups of people, and don’t anymore.3
So, as Thanksgiving approached my freshman year, I had an idea. Since people had been bugging me about making bagels,4 and I had a lot of friends who couldn’t make it home for Thanksgiving, I suggested to my family that we host a large party for it.
They agreed, and so the schedule began. I awoke at around 6am to begin the different bagel recipes.
We made three kinds of bagel dough: a normal bagelly dough, a Guinness dough,5 and a tequila dough.6 Within the initial dough, we made regular, poppy seed, everything, cinnamon, and blackberry.78
Of course, when you have around 200 bagels to make and shape, it’s great to have friends come. So, my 7 or so helpers and I made the outrageous number of bagels. As the crowd arrived, the bagels were ready, so people ate them. And, as friends had to depart for whatever reasons, they were able to take the bagels with them.
That’s another nice tradition that I’m glad for. My bagels fed not only the Rebelsky Family Thanksgiving Extravaganza,9 but also the Women’s Basketball House, and some others.
After bagels, we ate and played board games through the end of the day.
Last year functioned similarly, though I actually have a schedule!10
6:30 AM: Bagel Bonanza (100 cups of flour!) Begins!!!11
7:00 AM: Breakfast begins (pancakes)12
3:00 PM: Dinner!13
5:00 PM: Dessert14
6:30 PM: Games!15
The bagels we made were: regular, cinnamon, cinnamon raisin,16 salt,17 poppy seed, everything, blueberry, blackberry, strawberry,18 apple and cinnamon,19 asiago,20 Rosemary, and Rosemary and olive oil.21
In total, we went through more than 100 cups of flour, and more than 400 bagels. It was great! I still have no clue where they all ended up, though I know that some left with everyone I could make take some.
But anyways, this year that will not be happening, which is sad. Hopefully next year it will again.
for some reason↩︎
middle and high school↩︎
help which of the two no mores is correct↩︎
side note, never tell people you know how to make anything that’s that much effort↩︎
guess what the secret ingredient was↩︎
can you guess this one?↩︎
because we couldn’t find blueberries↩︎
I think that’s all↩︎
which I believe is what it was called in 2017↩︎
also list of bagels!↩︎
I started around 6 so that if anyone showed up then they could enjoy it↩︎
for the helpers↩︎
breakfast ended before then, but no scheduled events took place↩︎
I don’t know if Dinner ended then or not↩︎
this didn’t end. Some say you can still hear the players arguing about a loophole in the rules↩︎
i.e. take cinnamon and add raisin↩︎
which were disappointing imo↩︎
no you have too many berries↩︎
i.e. take cinnamon and add apple chunks↩︎
for some reason↩︎
an oilier rosemary↩︎
First Published: 2018 November 21
Today was a new beginning for me! I began my second paper journal since arriving in London. Thankfully, it was a duplicate of the first, so I’m able to see what’s changed.
For instance, where I spilled almond oil on it at the beginning of the semester,1 it’s still oily. The pages have gotten darker, the cover has faded, and it’s showing signs of use.
The new one, on the other hand, still looks nice. I can’t wait to see if this one fills, and what it fills with.
Additionally, I got ahead on blogging for the first time!2
Today, is the 21 of November. I like the 21sts of the months, because that’s when solstices and equinoxes.3 In many cultures, the equinox or solstice is a day of new beginning.
Today was a new beginning for me! I began my second paper journal since arriving in London. Thankfully, it was a duplicate of the first, so I’m able to see what’s changed.
For instance, where I spilled almond oil on it at the beginning of the semester,4 it’s still oily. The pages have gotten darker, the cover has faded, and it’s showing signs of use.
The new one, on the other hand, still looks nice. I can’t wait to see if this one fills, and what it fills with.