How I Practice

First Published: 2018 December 8

Draft 2: 8 December

Earlier this week I was asked to reflect on how I practice. I can boil my practice routine down into three pieces: making non-practice time useful, impromptu practice, and scheduled practice.

Non-practice time being useful is probably the bit of how I practice music that is weirdest to others. It’s somewhat like The Music Man, where I visualize what I would want the piece to sound like, but there’s more to it. For example, when I know I’ll be unable to practice cornetto for a while, I’ll make a special point of listening to different professional cornettists so I can evaluate what of their playing I like and dislike. The variety is also important, so that you can figure out what separates you from any given professional as well as what separates you from all professionals in performance. I also sometimes listen to recordings I’ve made of myself, though I am loath to do so.

When I talk about how I don’t always practice music, something that people will comment is that I play instruments a lot. And, sure, that’s true. But, playing the hurdy gurdy or hammer dulcimer shouldn’t really help me play cornetto, especially since the instruments are so different. However, much like how lifting improves performance in most athletic endeavors, I’ve found that playing any instrument, or even just listening to music, helps you with every instrument you play. I have no clue why this is, but it’s been incredibly helpful for me to understand. So, when I’m at Grinnell and bored, I’ll start playing one of the many instruments I have access to and know how to play. Here in London, I’ll pull out my ukulele or penny whistle, or even just headphones while I’m on the endless subway rides. The idea of using wasted time sort of flows into my other kind of using wasted time method.

For instance, when I practice bagpipes ¹ I often just use the practice chanter silently. The important piece of bagpipes is having quick and sure fingers, so just fingering the practice chanter is often all that I need to improve. When I don’t even feel like doing that, I’ll often visualize the music that I’m supposed to be learning. Sometimes that’s me playing the melody in my head,² sometimes it’s me thinking of fingerings, and still other times it’s just me thinking of the sound of the instrument. One important thing about playing is knowing how you want the instrument to sound. Sometimes I do feel like playing though, such as last night while waiting for trains to arrive. There, I practiced playing my penny whistle. It was time I wasn’t able to be otherwise productive in, so I used it for music.

That idea of music at whenever time is more or less how my impromptu practicing works. The only difference between it and how I practice instruments above is that the impromptu practices are me trying to learn something, rather than just playing by ear or memory. That is, when I’m playing like I talked about in the wasted time section, I’m usually playing melodies I already know by heart or just fiddling around on the instrument. When I’m impromptu practicing, I’m trying to learn something new. It’s an odd distinction, but it works for me.

Finally, there’s “dedicated” practice time. When I have a large block of time,³ I’ll tend to work on multiple instruments. Multiple here means however many I’m planning on performing on within the next 3 months while at school, exist within easy reach at home when there, or with me while abroad. So, I’ll pick an instrument⁴ and start playing it. This semester, that’s tended to alternate between cornetto and bagpipe, and those are really the two I’ll focus on in dedicated time. It happens when I’ve set aside a piece of time to go and practice at a space. I almost never use the fully allotted time, except for when I have an activity on the other side of it, because then I inevitably want to keep practicing.⁵

So, that’s how I practice.

Draft 1: 6 December

Today, I was asked to reflect a little on how I practice. The prompt came because I was asked how I know what I should focus on when I practice, especially since⁶ people teaching lessons never tell you to stop working on something. I said something along the lines of “Don’t forget the old exercises, but stop focusing on them/trying to improve them,” and that’s pretty true for me. I never really stop playing pieces that I’ve learned before.

Sometimes, this is as simple as me playing the first line of a piece that I last worked on two years before because my mind gets caught there, since some of the warmup I do stays the same. Other times, it’s listening to old recordings of myself, so that I can hear how my playing has changed.⁷ Even other times, I’ll play old things when I feel too discouraged, as a sort of diagnostic “is it the piece or me that isn’t working today?” questionnaire. It’s about 50/50 which one it will be. Finally, sometimes it’s just that I’ll see the piece as I page through my folder. So, I never really stop thinking about a piece.

But, that’s not the whole of how I practice. So, I don’t immediately shred the idea of the pieces I’ve played before. What do I do instead?

There’s a couple pieces to the way I practice, which vary based on my opportunities. The worst part of my time in London has been my difficulty with finding space to practice in. So, I can’t always⁸ practice the instruments I learn with sound. Thankfully, depending on the instrument, that’s not a huge issue.

For instance, when I practice bagpipes ⁹ I often will just use the practice chanter silently. The important piece of bagpipes is having quick and sure fingers, so just fingering the practice chanter is often all that I need to improve. Other times that I can’t practice, as I mentioned above, I’ll listen to old recordings of myself. But, I don’t do that a ton, for obvious reasons.¹⁰ Instead, I’ve found¹¹ that listening to experts and professionals play is another way to improve. So, when I know I’ll be away from the cornetto for a bit, I’ll make a special point of listening to different cornettists, so that I can evaluate what of their playing I like and don’t dislike. The variety is also important, so that you can figure out what separates you from any given professional as well as what separates you from all professionals in playing. But, that’s not always a great time, because sometimes I like to listen to other music that the instruments I play.

That’s where the weirdest part of my practicing comes in. I’ve found that when I work on any instrument, my performance on every instrument improves. I think it’s a lot like weight-lifting for sports. Yes, you’re probably better off spending any given hour practicing a sport, rather than lifting. But, if you’re not sure which sport you’ll be competing in, or can’t practice that sport for whatever reason, lifting will still improve your athletic performance. Likewise, because every instrument I play has some sort of expressive device that differs from the others I play, I can focus on playing musically and expressively, even when reading music. Somehow working on penny whistle flourishes helps me work on cornetto articulation.

Finally, when I really don’t feel like practicing at all, I’ll visualize music.¹² That is, I think about the piece I’ll be performing, while I’m walking around, or sitting, or just bored, and think about what it would sound like in a perfect world. As much as The Music Man claims that it works, I’m surprised more people don’t try it.

But, all this is more accurately titled “how I don’t practice,” so I should probably explain how I do. When I have a large block of time,¹³ I’ll tend to work on multiple instruments. Even when I don’t I sometimes try two or three.

Anyways, I’ll pick whichever instrument I think needs the most care,¹⁴ and start playing it. This semester, that’s tended to alternate between cornetto and bagpipe, and those are really the two I’ll focus on in dedicated time.

Oh, that’s also another difference: the idea of dedicated practice and free practice. I’ll come back to that later. So, I’ll start on one of the instruments. When I become unable to play it, because of either mental or physical exhaustion, I’ll switch to the other. This will continue until I run out of time or mental energy to do any more playing.¹⁵ Then, I’ll be done.

Of course, that’s in the dedicated time. That is, the block of time I’ll set up and say “I’ll be going here for this time frame to do this.”¹⁶ At other times, I’ll just be finding myself in need of a way to occupy myself, and I’ll just start playing because I can. There’s a place for both, and I think it’s important, especially for me, to have both forms of practicing. Anyways, that’s how I practice.

Northumbrian Pipe Museum Review

First Published: 2018 December 7

Draft 1

Today, I had the wonderful opportunity to go to the Morpeth Chantry and Northumbrian Bagpipe Museum. While I wouldn’t recommend a trip to Morpeth just for the museum, the city was lovely, and I would highly recommend seeing it.

The museum itself was about the size of a typical exhibit in a full-sized museum, which was a little disappointing. More disappointing was the lack of examples of how the instrument sounds or chances to make it sound myself. They did have a cool thing where they’d rigged a set of the pipes to a piano keyboard so you could play a tune and make it sound, but it was broken.¹

However, they’re a completely different beast from either Scottish war pipes or uilleann pipes. They’ve got a closed chanter, and are bellows driven, and look really cute. All this is to say: if anyone has² a set of Northumbrian Pipes in need of a home, I promise to love and care for them.

The Dilemma of Digital Diaries

First Published: 2018 December 6

Draft 12(?): 4 December 2018

The internet forces change on almost every aspect of human life. These changes can be controversial, especially in literature. Particularly for diaries, the idea shifting from analog to digital formats seemed risk-filled in the early days of the internet.¹ But, while the shift in diaries from ink to bits is not inherently problematic, it can alter the form of both diary forms: those meant for the author’s consumption and those meant for public consumption. Many see that public diaries turn into social media posts and blogs, while private diaries turn into password-protected blogs or word documents.

The transition of private diary from analog to digital is a straightforward process. Instead of penning out the words on a paper, the author types the words on a document or webpage. Because of the nature of digital transcription, future archivists will be unable to note handwriting, margin notes, struck words or images drawn. However, a variety of benefits are gained in the switch. For example, if the journal is stored online, the author can access it from anywhere, not only in a single book. It is also far easier to encrypt via software than to cypher by hand. Furthermore, storing the diary digitally allows for easier search, as modern word processors has automated search capabilities. Finally, digital media often save metadata such as location, when words are typed, and what edits are made. These data are not the same as handwriting and margin notes, but can still inform the future reader about the author. While the private digital diary may lose some of the forms that readers can use to learn about the author through how they write, alternate forms of gathering knowledge that are unique to digital media arise to replace them.

The digital public diary, on the other hand, is far more contentious. When discussing the intersection of social media and diaries, it’s important to define both terms. A diary is a work that “focuses on expressing the reality of a contemporaneous account of the author’s passage through time.”² Meanwhile, Wikipedia defines social media as “interactive computer-mediated technologies that facilitate the creation and sharing of information, ideas, career interests and other forms of expression via virtual communities and networks.”³ Within these two definitions, we see that the two appear to have some, but not total, overlap. Each definition contains a component crucial to understanding its distinction. For diaries, that component is “contemporaneous account of the author’s passage through time;” for social media, it’s the word “interactive.” Obviously, not all social media are contemporaneous, nor even accounts of authors’ passages through time. One social media with no account of time is Wikipedia, as its social media entry mentions. Because of this distinction, we see that claims of social media being modern diaries are not inherently true. That is, while social media can be diaries, it does not need to be.

However, some social media, such as Instagram, do function as a type of diary where people post photos with attached captions for public viewing. These status updates are reminiscent of the letter-diaries of James Boswell and Frances Burney, which were read aloud and shared between friends and family. However, Instagram-as-public-diary lacks the crucial component of social media: interaction. People cannot enter into dialogue with the author as in a fully interactive Wikipedia page. Rather, they can comment in ways that clearly come from other entities. So, while diaries themselves are not social media, they can inhabit a social medium. That is, a diary on Instagram is not a social medium, while Instagram itself is.

But this doesn’t address the question of how digitizing public diaries can affect their content. Specifically, many users of Instagram have two profiles: a public profile with information to show that they live a fulfilling life filled with culturally normative behavior, and a private profile (known as a “finsta”) designed to show a small group of peers that they live an exciting life that defies cultural norms. In such a way, the writer of a public diary is now able to appear both societally acceptable and rebellious to different parties, simply by choosing which profile to post on. Likewise, a reader is able to see two disparate views of the author.

The platform itself can also affect the nature of the content. Due to Instagram’s image-centric nature, the focus of a Instagram-hosted diary will be photographic memories of life. In contrast, a Wordpress-diary will focus more on textual accounts of life, due to its text-centric nature. This diversity of platform gives an unprecedented level of choice to authors in how they record their thoughts, especially since they are able to use multiple platforms.

The change of diaries to digital format does not occur without changes to the medium itself. But some of these changes in form can aid future readers in understanding the person they read about, just as other changes can be hindrances. Imagine if we not only had the personal thoughts of Burney written in letters, but photos that she found important coupled with captions explaining why. And, by making diary production digital, authors are now able to choose exactly how to best express their thoughts, which reveals more about themselves.

Whoops

First Published: 2018 December 5

Draft 1

Today, I was planning on posting my final diary essay. Unfortunately, I never saved the document, and apparently closed it. So, I lost the 12 drafts that I wrote, and only have the final draft. Goes to show what your professors always tell you: save early and often. But, I still have the final draft, which I’ll probably post tomorrow when I’m feeling less annoyed at myself.

Christmas Concert

First Published: 2018 December 4

Draft 1

Tonight, I had the wonderful opportunity to attend the Chandos Chamber Choir Christmas Concert at Christ¹ the Holy Redeemer Church. In addition to hearing some lovely early music carols, as well as some modern takes on those early songs, there were also some audience sing-alongs. It was great fun, especially because I didn’t know all of the carols. Sadly, they didn’t have the audience sing my two favorite carols,² but that’s life.

Overall, the concert was a great experience. The choir was good, and the brass quintet was spectacular. They served mince pies, so I had my first ever, which apparently means I get to make a wish. Since finals week is coming up, I’m sure you can guess what I wished for.

Creative Cartography Final Project

First Published 2018 December 3

Draft 2

One of the classes I’m enrolled in while abroad is Creative Cartography.¹ The goal of the class is to explore the different ways that maps can express information and authorship. For a final project, we were assigned the task of creating our own unique map of London. So, being a musical child like I am, I decided to make my end product something auditory.

While discussing with my professor, we had many potential ideas. But, what ended up seeming most fruitful was a one hour walk, where I would follow a series of strangers, logging myself with a stopwatch. Every time that I made a turn, I would start a new lap on the watch. By the end of the hour, I’d accumulated 426 times, so 425 turns. Along with that, I had GPS data tracking my movements and a heart rate monitor that was linked to that GPS.

To create the music, I then needed to find a way to convert the raw data into something musical. I decided to create a melody that could be played solely on the white notes of the piano, rather than other scale options, for a variety of reasons. Had I chosen a pentatonic scale, the data would be harder to express. Had I chosen a chromatic scale, the final piece would have sounded incredibly atonal.

So, I assigned the time in seconds that I had lasted before turning as the basis for the melody. If I walked for less than a second, I would make the melody note an A, for 1-1.99, B, and so on through the scale. Of course, I knew that some of my turns would last seven or more seconds, so I would then repeat. That is, If it took 7-7.99 seconds, I would still have an A. But, in doing so, I would obscure a lot of data.

To combat this, I decided that I would use multiple voices in the final piece. I chose ninth chords, because they have an interesting lack of resolution to them that I thought might allow my music to feel more natural, especially as they tend to have forward movement that is needed when imagining a walk. If the turn would last for less than seven seconds, it would be the root of the chord, seven to 13.99, the third, and so on through the ninth. I assumed that I would then be able to uniquely identify each number of seconds. But, I ended up having ten turns that lasted more than 35 seconds. I decided that I would simply deal with that problem by ignoring it, looping at 35 seconds.

I then had to choose the way that each ninth chord would be constructed. I decided that I didn’t want diminished fifths from the bass, because I didn’t feel like it. My watch was accurate to the .01 seconds, so I kept that in mind.

To decide whether the third would be major or minor, I looked at the fractional time. If it was less than .5, I would make it minor. Otherwise, the third would be major.

The fifth was perfect.

The seventh was major if within .25 seconds 0. That is, from 0-.24 fractional seconds, it would be major. .25-.74 was minor, and .75 and up was again major.

The ninth was determined by the final digit. If the fractional second was even (.00,.02,.04...), it would be major. Otherwise, it would be minor.

By doing this, I constructed a lot of chords that don’t exist in the diatonic world. Of course, then I needed to find a way to automate the calculation of the data, because manually computing 426 data points sounded like a horrible idea, especially since I wouldn’t have the time. So, I automated the production of each note of the chord. I then plotted the melody and bass line, deciding that each chord would be root position. What was left was four voices. Using the principle of parsimonious voice leading,² I crafted each of the lines by hand. I then uploaded the midi data to a synthesizer, where I mixed the levels a bit until I was satisfied. I did nothing with dynamics or fading because that seemed to detract from the music itself. For tempo, I chose 120 as that is the typical person’s cadence. For voicing, I made sure that the bass was always the lowest and that the soprano was always the highest. The other voices, because of how I wrote them, progressed steadily higher throughout the piece. It creates an interesting effect of growing movement. Happily, it resolves on a CMaj7,9 chord, which fits the C diatonic scale.

If you want to listen, it’s currently hosted on Soundcloud.

Draft 1

One of the classes I’m enrolled in while abroad is Creative Cartography.³ The goal of the class is to explore the different ways that maps can express information and authorship. For a final project, we were assigned the task of creating our own unique map of London. So, being a musical child like I am, I decided to make my end product something auditory.

While discussing with my professor, we had many potential ideas. But, what ended up seeming most fruitful was a one hour walk, where I would follow a series of strangers, logging myself with a stopwatch. Every time that I made a turn, I would start a new lap on the watch. By the end of the hour, I’d accumulated 426 times, so 425 turns. Along with that, I had GPS data tracking my movements and a heart rate monitor that was linked to that GPS.

To create the music, I then needed to find a way to convert the raw data into something musical. Although I’d initially thought of using either a chromatic or pentatonic scale, as those each have their own benefits, I ended up deciding to use the C Ionian⁴ mode as my basis for melody. There has to be a better way to say that. Maybe: I decided to use the diatonic scale with no accidentals. I decided to create a melody that could be played solely on the white notes of the piano. That’s better.

So, I assigned the time in seconds that I had lasted before turning as the basis for the melody. If I walked for less than a second, I would make the melody note an A, for 1-1.99, B, and so on through the scale. Of course, I knew that some of my turns would last seven or more seconds, so I would then repeat. That is, If it took 7-7.99 seconds, I would still have an A. But, in doing so, I would have obscured a lot of the data.

So, I decided that I would have multiple voices. I chose ninth chords, because they have an interesting lack of resolution to them that I thought might allow my music to feel more natural. So, if the turn would last for less than seven seconds, it would be the root of the chord, seven to 13.99, the third, and so on through the ninth. I assumed that I would then be able to uniquely identify each number of seconds. But, I ended up having ten turns that lasted more than 35 seconds. I decided that I would simply deal with that by ignoring it, looping at 35.

Then, I had to choose the way that each ninth chord would be constructed. I decided that I didn’t want diminished fifths from the bass, because I didn’t feel like it. My watch was accurate to the .01 seconds, so I kept that in mind.

To decide whether the third would be major or minor, I looked at the fractional time. If it was less than .5, I would make it minor. Otherwise, the third would be major.

The fifth was perfect.

The seventh was major if within .25 seconds 0. That is, from 0-.24 fractional seconds, it would be major. .25-.74 was minor, and .75 and up was again major.

The ninth was determined by the final digit. If the fractional second was even (.00,.02,.04...), it would be major. Otherwise, it would be minor.

By doing this, I constructed a lot of chords that don’t exist in the diatonic world. Of course, then I needed to find a way to automate the calculation of the data, because manually computing 426 data points sounded like a horrible idea, especially since I wouldn’t have the time. So, I automated the production of each note of the chord. I then plotted the melody and bass line, deciding that each chord would be root position. What was left was four voices. Using the principle of parsimonious voice leading,⁵ I crafted each of the lines by hand. I then uploaded the midi data to a synthesizer, where I mixed the levels a bit until I was satisfied. I did nothing with dynamics or fading because that seemed to detract from the music itself.

If you want to listen, it’s currently hosted on Soundcloud.

Reflections on Today’s Gospel

First Published: 2018 December 2

Luke 21:27 “And then they will see the Son of Man coming in a cloud with power and great glory.”

Draft 1

Happy first Sunday in Advent, New Liturgical Year, and First Night of Hanukkah! Advent has always been my favorite season in the Church. It helps that I have really 5 options: Advent, Christmas, Lent, Easter, and Ordinary Time. But, Advent has always been nice because it’s the period where we wait for a wholly positive event to occur. Unlike Easter, which saves our souls at the cost of the Lord’s life, Christmas is nothing more or less than a celebration of the birth of our Savior.

And yet, the Gospel today is not about Christ the meek child being born to a virgin, surrounded by shepherds. Instead, it’s a reference and prophesy about the Lord’s next coming. It tells us that we must stay awake and vigilant, and not be snared by the problems of our life. And really, that’s what Advent is about. It’s a preparatory season where we assess ourselves and begin to hope that we could be worthy to welcome the baby Jesus into the world.

It’s interesting reading today’s readings, because they fall really nicely in a chronology. The First Reading talks about the first coming of Jesus, the season we celebrate in just a few weeks. The Psalm and Second Reading tell us the message Jesus often spoke, that we are to be holy and loving through all that we do. Then, the Gospel talks about the second coming. It’s a great reminder of the way we are to view Advent, which is a celebration of the Lord’s birth, life, and second coming.

Polymer Review Part 4

First Published 2018 December 1

Draft 1

As I mentioned yesterday, today we’re talking about crystals. Polymers are known as semi-crystalline, because they have both crystalline and amorphous sections. Some might wonder why polymers can’t be wholly crystalline.¹ As I² have mentioned before, polymers are weird because more or less all of their strength comes from the inter-molecular forces that hold them together, as opposed to normal matter, which I have no clue how it works apparently. Anyways, if a polymer is fully crystalline, it doesn’t have any entanglements with other polymer chains, and so will become a powder, because each polymer is wholly self contained. So, in short, they can it just isn’t useful.

Semi-crystalline³ polymers are especially useful when used in applications where the Heat Distortion Temperature (HDT) is useful, because for most crystalline polymers, the HDT is far larger than the T_g. Another way to increase the HDT of a polymer is through addition of glass particles. Those increase stiffness, and effectively just shift the modulus of the material directly upwards. Since amorphous polymers lose strength so quickly around T_g, the addition of glass does nearly nothing. However, crystalline polymers lose strength more slowly, so the addition of particles is helpful.

Crystals in polymers form as lamellae, the ordered regions within a polymer. Lamellae clump together into spherulites, which are what looks like the crystal in a polymer. In order for crystals to form, the polymer must not be atactic.

Polymers can only crystallize when below T_m, because that’s what T_m means. When below T_m, polymer crystallization rate is affected by two factors: nucleation and growth.

Nucleation is the formation of the spherulites. It occurs more quickly the further below T_m you get, until T_g is reached, because then the polymer can’t move. Other ways to increase the rate of nucleation include strain/shear stress. In a wholly homogenous polymer, the polymer will spontaneously crystallize, but that is slow. Most polymers have a nucleating agent added to them, commonly sorbitol. But, almost anything in a polymer, including dyes, other polymers, and glass particles can also act as a nucleation point. In general, the more nucleation points there are, the smaller the final size of a spherulite.⁴ Small spherulite size can be beneficial, especially if it can be made smaller than the wavelength of light, so a bottle can be see through.⁵ The rate of nucleation increases as T drops until T_g.

The other factor, growth, is exactly what it sounds like. Once nucleated, the spherulites grow. Their growth rate is fastest somewhere between T_m and T_g, though closer to T_m. This is because as T increases, the flexibility of the polymer chain increases. That makes it easier to align, but also easier to unalign. So, by plotting the two rates together, you can find the optimal temperature to cool to in order to let a polymer crystalize.

If, after cooling below T_g, you realize the polymer needs to be more crystalline, then you can anneal it. That is, you can raise it above T_g so that the polymer can form into crystals.

Fun fact: although incredibly regular, the chain stiffness of polycarbonate is such that it is not crystalline in consumer uses because of the time required.

Polymer Review Part 3

First Published 2018 November 30

Prereading note: I actually looked in my notes for this one!

Draft 1

Today we’re talking about the factors that affect T_g and T_m. Factors that affect T_g will affect all polymers, while the factors that affect T_m will only affect semi-crystalline thermoplastics.

There are four main kinds of factors that affect T_g: intramolecular forces, intermolecular forces, chain length, and timescale.

The intramolecular forces that affect T_g are: chain stiffness, side groups, and cross link density. As chain stiffness goes up,¹ T_g goes up. This is because as the amount of energy it takes to rotate along a bond² increases, so too does T_g. As side groups become bulkier, they increase T_g, for the same reason. As cross-link density goes up, so does T_g, 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 T_m.

The intermolecular forces that affect T_g are: side group dipole moments,³ side group chain length, and plasticizers. As the side groups become more polar, T_g goes up, because it draws the different polymer chains closer together. For that same reason, as side groups become longer, T_g goes down, because it keeps them further away. For that same reason, plasticizers also tend to lower T_g.

Third, assuming the molecular mass is less than M_e,⁴ the increase of molecular mass will increase T_g. Above M_e, there is effectively no difference in T_g 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, T_g 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 T_g.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 T_g, which is why they have the relationship I talked about in Polymer Review 2. As interactions between the chains goes up, T_m goes up. As chain stiffness goes up, T_m goes up. As branching⁷ goes up, T_m goes down. As delta S⁸ goes up, T_m goes down. To explain this, T_m 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.

Polymer Review Part 2

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.

Draft 2: 30 November

Corrections (since I looked at some notes):

1. Below T_g, the molecule is only able to vibrate. Above T_g, the molecule is able to rotate at each of its bonds. Above T_m² or T_v³, the molecule is able to move, and flows through a process known as reptation.

2. T_m is double T_g for symmetric polymers,⁴ and 1.5 for the rest.

3. Polymers with crosslinks are thermosets, which are like epoxies and what most rubbers are, and elastomers, which are less tightly cross-linked thermosets.

4. T_m is where crystallization can begin in a polymer. I’ll probably think about how that works tomorrow.

Draft 1

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, T_g. 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 T_g, the energy needed to break the Van Der Waals bonds is higher, because the polymer is moving less. Once you reach T_g, 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 M_e. Above T_g, you’re in the rubber phase. This is where a polymer behaves a lot like what we think rubber does. And, right near T_g, the material exhibits a lot of damping.

After T_g, you reach what’s known as T_m, 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 T_m equal to 1.5x the T_g in Kelvin.

The information about T_m 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 T_g is much larger in amorphous polymers than in semi-crystalline, because T_g is where amorphous regions fail, while T_m is where the crystalline sections fail. So, since a semi-crystalline polymer has a much smaller composition of amorphous polymer, it loses less strength.