What do I do? 6: Rocket nozzles

When people find out that I am doing a PhD in Chemistry, they often ask, somewhat foolishly (by those who aren't really that interested), what it is I do.  I then find myself in a position of trying perform a juggling act to find the balance between a number of things.  How in detail do they want me to go?  Where's the right place between talking over their head, and sounding like a condescending jerk.  Are they actually interested, or are they just being polite.  Based on their background, what parts will they find most interesting?  On top of that, I need to plot a coherent course through my thought process so that if they are interested, they don't get lost in the maze inside my head.

So, I've decided to write it down, and see if I can make a logical series of articles about what I do, starting with the background information that's needed, eventually ending up on what I do day to day. Today I'm going to talk about designing a laval nozzle.

3D printed cross section of the first nozzle I designed that worked

So I'm changing up from what I've been talking about in this series so far, and I'm looking at getting more into the background needed to understand what my main PhD project has been.  I want to talk about something that I spent a little more than a year of my life learning enough math and going through trial and error until I came up with something that works.  My first major project in my lab was to write a computer program that would perform the math to calculate the contour of a de Laval nozzle, which is the same type of nozzle that is used on the bottom of rocket ships.

Why is it used on the bottom of rocket ships, and why do we want it in our lab?  The answer is the same.  De Laval nozzles are designed to have a wall that shapes the cloud of gas expanding out through them into a uniform flow, all molecules in the flow going the same direction, with the same speed, pressure, and temperature.  In thermodynamics, this type of flow is called isentropic.  Having the uniform flow is useful for rocket ships, because then all of the expansion is used as thrust in the direction the ship wants to go, yielding the highest efficiency for the engine.  For our experiment, we're not so interested in the supersonic speed of the expanding gas so much as we are the cooling properties, and the uniformity of the flow after exiting the nozzle.  I'll talk more about why we care in a later post.

Designing the nozzle, despite the fact that it's a solved problem that they've been doing since the 60's, was not trivial for me.  It involved a lot of math that I hadn't really ever learned, fluid dynamics, most of which I hadn't even heard of before, and combing through old textbooks and papers trying to put together an algorithm that was only ever partially reported in any one place. I found a lot of interesting information in an old NACA paper talking about the design, that included their FORTRAN script.  (NACA is the organization that later became NASA). After months of teaching myself the math I needed to be able to solve the problem, I finished a script that calculated the core of the nozzle, or the shape that it would be if life were ideal and the gas didn't interact with the walls of the nozzle.  It looks like this.

The black line is the shape of the core of the nozzle.  The hundreds of green and red lines that are there are the "characteristics" that I calculated in order to find where that black line was.  The characteristic lines are calculated so that the mass flux (amount of mass passing through them over time) of each line is exactly the same.  By calculating those lines, then matching them so the flux is equal across all of them, I was able to find my ideal core.  All told, to find this single nozzle, I calculated something like 1.2 million points.  But since I programmed the computer to do it, it only takes about 20 seconds.

Once I had the core, I had to go back, and adjust where the wall needed to be to account for the fact that we do not in fact live in an ideal world (sorry to disappoint you).  To do that, I needed to learn even more fluid dynamics, and more thermodynamics.  But once I did that, and solved the problem, it adds another 20 seconds to my program, and gives me an adjustment to the contour that follows more or less the same shape, but slightly bigger.

When I got this final shape working, I was pretty excited.  It had been a long time coming.  And finally, it was time to have my theoretical work turned into something physical.  I 3D printed a cross section of the first nozzle (to keep on my desk to show off how awesome I am), and sent the design to the machine shop to be made out of metal.  Here's what it looks like.

Kind of hard to see.  That's why I made the cross section print.  It was amazing to finally have something I could hold in my hands that was a result of all the work I'd been doing.  The final test, to make sure that I had done everything correctly, was to actually install the nozzle in the experiment, and measure the flow at many points throughout the chamber, to test that we were seeing a uniform flow coming out that we could use in our experiment.  We have an apparatus built specifically for that, which I may talk about later.  But the payoff is that the flow does work. If you were to look at the stream going past you with the nozzle on the right, the pressure inside it looks like the gif below over the course of about 40 microseconds (we pulse it, instead of flow continually).  There are a few frames where we get really good uniform flow, which is exactly what the design goal was.

This was an extremely challenging project (mostly because I didn't know enough math when I started to be able to do it), but when I saw the final result, it was totally worth it.  And since this is a rocket nozzle, the fact that I designed and made it makes me a rocket scientist, which is a fun fact I can use in 2 truths and a lie some day.

What do I do? 5: Microwave Spectroscopy in France

When people find out that I am doing a PhD in Chemistry, they often ask, somewhat foolishly (by those who aren't really that interested), what it is I do.  I then find myself in a position of trying perform a juggling act to find the balance between a number of things.  How in detail do they want me to go?  Where's the right place between talking over their head, and sounding like a condescending jerk.  Are they actually interested, or are they just being polite.  Based on their background, what parts will they find most interesting?  On top of that, I need to plot a coherent course through my thought process so that if they are interested, they don't get lost in the maze inside my head.

So, I've decided to write it down, and see if I can make a logical series of articles about what I do, starting with the background information that's needed, eventually ending up on what I do day to day. Today I'm going to talk about microwave spectroscopy.

You may remember my general post about spectroscopy, where I talked about how the energy of different regions of the electromagnetic spectrum correspond to the spacing between energy levels for different types of motion in the molecule.  Last time I talked about infrared spectroscopy, where we were looking at vibrational energy ladders.  This week, I want to talk about my main project in France, using a microwave spectrometer.  Microwaves you'll remember correspond to the rotation of a molecule.

Why am I interested in the rotational energy states of a molecule? A major benefit of rotational spectroscopy is that it is 100% dependent on the structure of the molecule.  If you can properly analyze what you are seeing in the spectrum, you can recreate the shape of the molecule.  Vice versa, with the structure of the molecule, you can perfectly predict what the spectrum will look like (that's a  slight lie.  In theory you should be able to...).  And because no two molecules are identical (if they are, we call them the same molecule), this spectrum acts like a fingerprint for the molecule, and can be used to identify the molecule with certainty.  This comes in handy when you want to monitor a reaction in real time, and need to be able to tell multiple molecules apart.  It also comes in handy when trying to identify what molecules we're seeing with our telescopes.  Rotational spectra can also give information like temperature, pressure, and concentration.  In the main experiment I do in California, we can use it to watch how the amount present of a particular molecule changes over time.  There are two challenges with using rotational spectroscopy this way.

The first problem is that going from a spectrum of the molecule to the structure of the molecule is extremely difficult if you know nothing about the molecule.  For anything that is not a straight line of atoms, the spectrum produced is complicated.  Here's an example of a small portion of the spectrum of vinyl cyanide, a relatively small molecule (smallecule) with only 7 atoms.

All of those are part of the fingerprint of vinyl cyanide.  To be fair, this spectrum is transitions that involve vibrational and rotational quantum states, but I have the spectrum for just pure rotation, and it is not any more clear than that.  There is so much data in these measurements, that my monitor doesn't have a fraction of the pixels it would need to display all of it at once.  If you zoom in further, there are even more lines hiding inside of other ones.  Imagine what it would look like if you had more than one molecule in the mixture, instead of just vinyl cyanide.

Ok Zach.  So you can't use rotational spectroscopy on unknown molecules.  But if you know what molecule you have, you can predict what the spectrum will look like.  So using it to monitor your reactions should be easy.

hahahahaha.  *tears of laughter and sadness...

If we could solve the quantum mechanical equations (schrodinger in particular) for the molecules, you would be right.  But there is really only 1 molecule we can do that for.  H₂⁺.  Yep.  Not even H₂ with both it's electrons.  H₂ as long as it only has 1 electron.  The predictions we can make for other molecules range from pretty good to not even close.  In order to figure out the exact shape of a molecule, to the point needed for predicting it's spectrum, you need to fit it to experimental data.

The stage is now set for what I'm doing here in the lab in France.  Our goal here is to select molecules that look interesting, or are relevant, or haven't been studied, and actually measure the rotational spectra, then fit the computational guesses of the structure of those molecules to our data, so predictions in other regions get better.  I jokingly call it stamp collecting, because we're collecting molecular data.

We have two experiments set up to allow us to do this study.  We have one cell for studying stable molecules, and one for producing a plasma discharge, and studying the crazy things that makes.  While I've been here, I've helped build both set ups, and I've used them for studying multiple molecules, and have been working on the analysis of the data.  Work done here then can be compared to telescope data to identify features in them, or used in labs like my California lab for studies of kinetics.

Experimental setup at ISMO.  The cell lit up at the front (with a plasma) is for studying molecules produced in a plasma, while the cell in the back is used for studying stable molecules.

Next week I'm going to change gears, and write about fluid dynamics, particularly the math that I did in designing a rocket nozzle.

What do I do? 4: Infrared Spectroscopy in France

When people find out that I am doing a PhD in Chemistry, they often ask, somewhat foolishly (by those who aren't really that interested), what it is I do.  I then find myself in a position of trying perform a juggling act to find the balance between a number of things.  How in detail do they want me to go?  Where's the right place between talking over their head, and sounding like a condescending jerk.  Are they actually interested, or are they just being polite.  Based on their background, what parts will they find most interesting?  On top of that, I need to plot a coherent course through my thought process so that if they are interested, they don't get lost in the maze inside my head.

So, I've decided to write it down, and see if I can make a logical series of articles about what I do, starting with the background information that's needed, eventually ending up on what I do day to day. Today I'm going to talk about infrared spectroscopy and synchrotron radiation.

I started to write this, and realized that I really should break my 2 main projects in France into 2 (or 3) different posts, so that they don't get too long. This one will be about the project that I've been working on periodically while I've been here.  The principal investigators (PIs, a term that you should read to be a fusion of my boss/head scientist/adviser/person who gets the money so I can do science, but don't always understand the details of what I do) that I work with here had "beam time" on the SOLIEL Synchrotron, so we spent most of January, and then a few days here and there since working over there and making use of that facility.

If you're not familiar with what a syncrotron is, it is a type of particle accelerator designed to be used as a light source for various experiments (it's a really big lightbulb in the spectroscopy post's diagram).  Electrons are accelerated to a significant portion of the speed of light in bunches, which are then stored in a ring with electronics and magnets that keep them flowing in a circular path around the synchrotron (the storage ring at SOLEIL is 113 meters in diameter, which is about 371 feet for my american friends.  That's just a little longer than a football field).  While the particles velocity is constant, at every bend in the ring, they "accelerate" as they change direction, which causes them to release energy as light.  This light is directed to the beamlines, which then use it for various scientific purposes, such as spectroscopy.  Light from the beamline is very intense, and covers a large range of wavelengths, so it can be filtered to make it useful source for many applications.  The link to SOLEIL has some pretty good diagrams to help visualize this process, so check that out (I realize the website is in French).

Image of a fraction of the storage ring and facilities of the beamlines from the catwalk above it inside the synchrotron facility.  

The beamline that I got to work on specializes in infrared spectroscopy.  You may remember from previous posts that infrared light typically corresponds to difference in energy levels between vibrational states of molecules.  We're interested primarily in molecules that have been, or may be detected in space, and so all of our projects revolve around that.  While some of the stable molecules that exist on Earth can also be found in space, there are also many unstable and highly reactive molecules in the interstellar medium, and so we need a way to produce those in the lab.  For the set of experiments I've been doing here, our method for synthesizing radicals is to produce a plasma inside a cell, which in turn promotes some crazy chemistry, and produces fragments of the original species, as well as reactions that create molecules through recombinations of the original atoms.

 I've included a couple of pictures of what that plasma looks like, mostly because I think they look awesome.  Inside plasma (which is a state of matter), you get all sorts of crazy chemistry, and energy is being released, and so it gets very colorful.  The color the plasma turns is dependent on the molecule the plasma is formed from, and recently the plasma we've been producing in the lab has been orange.  The one pictured here was our injection of ammonia, hoping that we could strip off a hydrogen and make NH2, then measure it (spoiler warning: we could). 

Raw data before treatment

The lab here is very interested in this characterization of molecules, in the pursuit of assisting in their detection in space, so that's what the purpose of our experiments here has been.  I'm extremely interested in building instruments to make that possible.  While I was at SOLEIL, I was excited to learn about the synchrotron source, get to help set up and optimize the experiment for performing both stable measurements and discharge measurements, then get to work on the data

Data after treatment

analysis of this data.  One of the things I spent a lot of my time while we were at SOLEIL doing (because once we're set up and optimized, the computer does all the actual data acquisition) was working on writing scripts in python to clean up the data, and perform some of the analysis.  A problem with raw data is that there is a lot of information inside that we don't really want that originates with electronics, optics, and other parts of the measuring equipment, rather than the thing we want to study.  On the right is an example of some of the data, and what I did to help clean out those pieces of information that we didn't really want.  The data here is a combination of both vibrational spectroscopy and rotational spectroscopy.  We call it rovibronic data.

What do I do? 3: Emission Spectroscopy

When people find out that I am doing a PhD in Chemistry, they often ask, somewhat foolishly (by those who aren't really that interested), what it is I do.  I then find myself in a position of trying perform a juggling act to find the balance between a number of things.  How in detail do they want me to go?  Where's the right place between talking over their head, and sounding like a condescending jerk.  Are they actually interested, or are they just being polite.  Based on their background, what parts will they find most interesting?  On top of that, I need to plot a coherent course through my thought process so that if they are interested, they don't get lost in the maze inside my head.

So, I've decided to write it down, and see if I can make a logical series of articles about what I do, starting with the background information that's needed, eventually ending up on what I do day to day. Today I'm going to talk about the basics of emission.

Last week you might remember that I wrote about spectroscopy, which uses light to investigate the energy levels of molecules.  After talking about it generally, I talked a little more about absorption spectroscopy, which involves the study of the light that absorbed by the molecule.  That's actually the type of spectroscopy that I have been using during my time in France, and I'll go into more details about that in a later post.  But today I want to talk about another major type of spectroscopy, emission spectroscopy, which can use either fluorescence or phosphorescence.

The main difference between fluorescence and phosphorescence stems from what is "allowed."  While I didn't talk about it last week, there are rules to what transitions you can have between energy states (rungs).  So certain transitions can be "allowed" or they might be "forbidden."  A lot of times, you'll hear the phrase "classically forbidden," because those transitions can still happen, as the rules are only there in the simplifications that physicists made in trying to solve molecular systems.  However, forbidden transitions are usually orders of magnitude slower than the allowed transitions (and oftentimes much weaker).  That's going to come back and be important later.

You might remember a diagram like the one to the right from the previous posts.  I added an extra
electronic energy rung on this one, because we're going to need it for phosphorescence.  For now, focus on the rungs on the left.  You'll see our normal absorption arrow, just like last week, as well as an emission down arrow for the type of emission known as fluorescence.  It's called fluorescence for historical reasons, as one of the early molecules studied with this phenomenon was fluorite, but a molecule does not require fluorine in it to fluoresce.  For something to fluoresce, it must first absorb a photon of light and transition from v=0 in the lowest ladder to v=3 in the upper left ladder. (for now, think of a photon as 1 unit of light).  Then through processes that don't emit energy as light, the molecule relaxes to a lower energy state, before dropping down and emitting a photon of light at a wavelength corresponding to the difference in the higher and lower energy levels.  This is an allowed transition, so the process is very fast (much less than a second).  So if you turn off your pump source (the light that is exciting the molecules), the molecule stops fluorescing very quickly.  If you've ever  been to a roller skating rink, or a laser tag arena, you've seen this phenomenon.  It's what causes the white dye in your clothes to glow under a black (UV) light.  It's actually pretty clever of clothing manufacturers.  The dye's they use for white contain a molecule that absorbs light very efficiently in the UV region of the spectrum, which then emit fluorescence in a broad region of the visible spectrum.  The result is white light emitted, which make whites look whiter in the sunlight.  They also make you a highly visible target in a lasertag deathmatch.

Now look at the right side rung.  This represents an electronic energy state with which a transition with the ground state is "forbidden."  But when you read "forbidden" you should really just read it as "slow".  For phosphorescence to occur, the molecule must first be excited to the upper state through absorption.  Then, following this "allowed" transition, if the molecule is in an energy state on the left ladder that is very close in energy to a forbidden state in the right ladder, it can cross over into that electronic energy state.  From this excited electronic state, light can return to the ground state through an emission event called phosphorescence, releasing photons of light again at a different wavelength than was absorbed.  For a sample of many molecules, this process is slow, and will continue to take place for seconds after the pump light source is taken away.  If you've ever had the pleasure of falling asleep beneath a field of "glow-in-the-dark" stars, you've experienced phosphorescence.  Mark Rober has an awesome video, where he builds a glow-in-the-dark shadow wall and talks even more about this process, that I recommend checking out.

I've never done any phosphorescence spectroscopy (although, apparently it has been done), but fluorescence is one of the detection techniques that we're using in my lab in California.  Fluorescence spectroscopy setups are similar to absorption, but the light you're interested in looking at is not the light that you're pumping the molecule with.  Several methods are used to ignore the light from the source, and only look at photons originating from the sample.  The first is to detect perpendicular (90 degrees off) to the light source.  This minimizes the number of photons that are coming from the light source to the detector (90 degrees gives you the least amount of scattered light).  We also use extra filters typically, only looking at light that is longer in wavelength than the excitation source.  So you'll often see wavelength filters both before the sample, and after the sample.  The equations that ultimately get used to quantify the sample are also different from absorption spectrometers, but that is more complicated than I want to get into here.

You now have enough background, that I could write about the basics of what I have been doing with my time in France.  Next week I'll start writing about what it is I've been doing here, and why it matters, before moving on towards what my main project has been during my PhD work at UC Davis.

What do I do? 2: Spectroscopy

When people find out that I am doing a PhD in Chemistry, they often ask, somewhat foolishly (by those who aren't really that interested), what it is I do.  I then find myself in a position of trying perform a juggling act to find the balance between a number of things.  How in detail do they want me to go?  Where's the right place between talking over their head, and sounding like a condescending jerk.  Are they actually interested, or are they just being polite.  Based on their background, what parts will they find most interesting?  On top of that, I need to plot a coherent course through my thought process so that if they are interested, they don't get lost in the maze inside my head.

So, I've decided to write it down, and see if I can make a logical series of articles about what I do, starting with the background information that's needed, eventually ending up on what I do day to day. Today I'm going to talk about the basics of spectroscopy.

Spectroscopy an important tool used in interrogating molecules (my favorite way of describing it.  Conjures an image of a Hollywood crime drama, with a molecule cuffed to a table,a detective throwing a chair at the window trying to get answers).  It's used in the food industry as a quality assurance tool, by pharma companies to analyze composition of drugs, in the medical field for many tests looking for symptoms of disease, in forensic science for investigating crimes, and by scientists in many fields to study whatever it is they are interested in.

So what is spectroscopy?  Last week I wrote about the different ways that molecules store energy, and the ladder of states that result from that.  I've updated that post with a visual of what those states might look like.  The goal of spectroscopy is to use light to measure the distances between the rungs on the molecular energy ladder.

So how is light related to energy?  Trick question.  It's not related, it is a form of energy.  Light is more than just the familiar brightness that allows you to see..  Visible light makes up a small portion of the electromagnetic spectrum, only the wavelengths between 400 and 800 nanometers. (if you imagine an infinite field of equally spaced waves, the wavelength is the distance between two consecutive peaks.  1 nanometer = 0.000000001 meters, or 1/1 billion meters).  Different wavelengths correspond to different colors that we see.  I found this cool tool that lets you move a slider around on to find your favorite color's approximate wavelength (I like 469).  Visible light is not the only portion of the spectrum that you have had interactions with.  If you've ever had a sunburn, it's from the interaction of ultraviolet light with the DNA in your skin.  The warmth that you feel from the sun is mostly infrared light.  Doctors use x-ray light to examine bones.  Your car radio receives information through radiowaves.  Your cell phone does the same, but in the microwave region.  Your microwave oven?  Yep.  That's light too.  These are all words used to describe light at different wavelengths.

There is an equation called Planck's equation that allows us to convert the wavelength of light into the energy corresponding to that wavelength.  As the wavelength decreases, energy goes up, so shorter wavelengths, like those of UV and x-ray, have more energy that longer, such as radio or infrared.  And here's why we care, in the context of spectroscopy.  Different wavelengths of light roughly map onto the spacing of the different types of rungs on the molecular energy ladders.  I've included a table showing those relationships.


Ok.  So know we've talked about light, how it's energy, and how the energy of different regions of the spectrum can map on to the spacings between the molecular energy ladders.  Now we just need to put these concepts together to understand spectroscopy.  Lets say we have a molecule that is in the X¹∑⁺ v=0  state in the diagram on the right (that corresponds to the lowest electronic rung (or state), and the lowest vibrational state inside that electronic state. X¹∑⁺ is what's called a term symbol.  They contain a lot of information about a molecules electronic state, but I'm not going to go into that now). If we shine a light on this molecule, with an energy that is equal to the difference in energy between X¹∑⁺ v=0 and V¹∑⁺ v=3 state, the energy from that light can be absorbed by the molecule (for a visual see the red arrow).  This condition of the energy of the light matching the energy difference of the states is called the resonance condition, and is the basis for spectroscopy.  It can also go the other way.  If a molecule is in an excited state, it can drop down to a lower energy state, and emit a flash of light, as shown in the diagram as the green arrow.


So there are two ways we can use this simplified picture of spectroscopy to measure properties about the molecule.  We can hit the molecule with many different wavelengths of light, and see which ones it absorbs, or we can give the molecule an excess of energy, and look at the light that it emits.   Both methods give us the basic information on relative spacing of states in the molecule.  Because the molecular energy ladder spacings are unique to each molecule, we can identify which molecule we're looking at, based on the spectroscopy we perform.  That's how it works in theory.

In practice, we have to build an instrument that allows us to select which light the molecule absorbs/emits.  The basic schematic for an absorption spectrometer can be seen below.  I'll outline some of the critical components. The light source, which is represented by a lightbulb, is the light that is used for measurement.  This light source could be as simple as an actual light bulb, or it could be something like a laser, microwave generator, or particle accelerator.  The type of source used is dependent on what is being studied, and the specifics of the instrument.  It is also necessary to have a way of distinguishing the wavelength of the light, as represented by the vertical black screen with a slit below.  This doesn't have to be before the sample, it could be after, or it could be in the processing of the data later.  How well we can distinguish between wavelengths gives the resolution of the technique.  The box below represents the sample that is being measured.  Light passes through it, and some is absorbed.  What is left passes into the detector, represented by the eye.  By comparing this to the light that would be detected with nothing in the sample cell, the wavelengths the molecule absorbs can be identified, and used to characterize the sample.

Next week, I'm going to talk a little more about the emission types of spectroscopy (not because they reaaally apply to what I do, but because I think they're awesome, and you've seen their effects in real life).  So stay tuned.

What do I do? 1: Using the word Quantum correctly.

When people find out that I am doing a PhD in Chemistry, they often ask, somewhat foolishly (by those who aren't really that interested), what it is I do.  I then find myself in a position of trying perform a juggling act to find the balance between a number of things.  How in detail do they want me to go?  Where's the right place between talking over their head, and sounding like a condescending jerk.  Are they actually interested, or are they just being polite.  Based on their background, what parts will they find most interesting?  On top of that, I need to plot a coherent course through my thought process so that if they are interested, they don't get lost in the maze inside my head.

So, I've decided to write it down, and see if I can make a logical series of articles about what I do, starting with the background information that's needed, eventually ending up on what I do day to day.  Today I'm going to talk quantum mechanics.

In Ant-Man and the Wasp, there is a moment where Scott is sitting confused in a room with a bunch of "physicists" who are talking about the quantum realm.  Eventually, he asks them , "Do you guys just put the word quantum in front of everything?"  I wanted to cheer.  Thanks to Hollywood, some people might not realize that quantum is a word that actually means something; it's not just a way of adding the sound of legitimacy to the science that you're talking about.

When I talk about something being "quantum," what I mean is that it can be described by discrete values (whole numbers, none of that fraction or decimal crap).  To illustrate the difference, start with the speed of a car measured by classical physics.  When we talk about the speed, it's a continuum of speeds.  You can be going 90 mph, or 90.1 mph, or 90.000000000000009 mph, etc.  The jumps in speed (or energy) of large objects are infinitesimally small.  The playground analogy to this difference is a slide.  Smooth transitions between each measurement, or smooth enough that it doesn't make a difference at the level we can measure it. In quantum mechanics (physics) the transitions between energy levels are not so smooth.  This happens as the object you're looking at gets smaller and smaller. (This can be explained with the particle-in-a-box model, which I may write a post about at some point in the future).  When you enter this realm the steps between different energies become less smooth, and you end up with discrete energy levels that have gaps between them.  The playground analogy to this type of energy spacing is a ladder, with the rungs on the ladder representing discrete energy levels.  A cool point here is to remember that these two theories aren't actually separate.  As something gets bigger, the spacing between the energy levels gets smaller and smaller, and eventually becomes close enough to a continuum that it doesn't make a difference.

So now that we've talked about what the energy levels look like, we need to talk about how molecules store their energy.  There are 4 main ways that molecules store energy (ignoring a bunch of the other ways they can store energy).  The first 3 are related to the classical physics description of kinetic energy.  Imagine a baseball screaming it's way into the stands after a homerun.  Its energy is manifest through the speed it is moving.  This is the first way a molecule can store energy, through translational movement.  Next, imagine a tennis serve with a lot of topspin.  Some of the power from the serve goes into the translational movement of the ball, but some of it goes into the rotational spin of the ball.  The second way molecules store energy is through rotation (there are several types of "spin" a molecule can have, but for my work, only the overall molecular spin matters for this explanation).  Next, imagine some curly hair, that you stretch downwards, then let go of, and it springs back and forth (maybe a spring is a better analogy, but I like the curly hair one, so I'm sticking with it).  You've put energy into it when you pull it down, then the springing motion is how the hair stores that energy. If you've got two atoms in a molecule, bonded together, the bond acts like a spring, it can store energy in these vibrations.  The last way a molecule stores energy is related to potential energy in classical physics. Potential energy can be thought of a child sitting at the top of the slide.  Before they go down the slide, they have a lot of potential energy.  When they're going down the slide, some of that potential energy is transformed into kinetic energy.  At the bottom of the slide, they have less potential energy than before (although, if they're a typical toddler, not that much less energy (too be clear, that's a joke, unrelated to the analogy...)).  The last way that molecules can store energy is as potential energy, with the energy stored in the orbitals of the electrons.  These are called electronic energy levels.

The spacing between these energy levels varies, but in general, it can be thought that electronic

This is a visual diagram showing relative energies between states. 

Here, we're zoomed in on 2 of the electronic energy rungs, and we show

a few of the vibrational energy rungs  It is not to scale, but the values show

what the spacing is for these states.  EE stansd for Electronic Energy which

is the amount of energy each state has, relative to the lowest energy state. 

ve gives the distance between the vibrational "rungs" of the energy ladder.

energy spacing is bigger than vibrational energy spacing which is bigger than rotational energy spacing, which is bigger than translational energy spacing. 
So imagine the electronic energies as the rungs on that playground ladder.  If you zoom into a close up of 1 rung, you'll be able to see that rung is actually made up of a ladder with many vibrational energy rungs.  Then if you zoom in on one of those rungs, you'll be able to see each of those are made of an even smaller ladder of rotational energy rungs.  And if you do it again, you will be able to see the translational energy rungs. 

Now, this is all a simplification.  The truth is always more complicated.  But this is a basic idea of what "quantum" actually means, and it gives us a framework to understand what my next post will be, which is spectroscopy.

One Year

One year ago today, I posted the following status on Facebook:

"Either time travel never gets invented or what's happening now leads to some good things, and I'm not willing to believe that time travel never happens. #UCBuchanan"

The status, while somewhat lighthearted, was in response to what I worried would be the 2+ years of my PhD coming crashing down around me.  My QE, which was scheduled for 2 days later had just been canceled, because of a poor decision I'd made.  After what was arguably the worst 3 months of my life, followed by the worst week, March 12 last year was probably the worst day I've had.  I remember walking out of the office in shock, walking through the arboretum on campus, glad my sunglasses hid my tears.

At some point, I found myself on a bench thinking about what I was going to do.  Three days before, I'd had a conversation with my friend Sommer, where I was whining and wondering if I should just quit.  She was probably sick of me complaining to her, but her response was: 

"Zach. If you make that decision now, really decide that you are done, then that's it. You should talk to Kyle about getting a Master's. But the other option is at least to try as hard as you can to finish and get to your QE on Tuesday. I can almost promise that you will be more mad at past Zach if just give up now."

Sitting on that bench, thinking about that conversation, I decided I wanted to be optimistic, and I wanted to keep trying as hard as I could, and I posted that Facebook status.  Then I followed Sommer's other advice, went home, strung up my hammock and read a book for the first time in weeks.  The next day, I was back at it, trying to get to the point where I could pass my exam, which I eventually did, a couple months later.

It was still a hard few months.  I had to work to not be jealous as we celebrated the other 2 people in my group passing their exams on their first try.  I had to deal with my boss not being very happy that I hadn't finished mine when I should have.  I still had to go through about 15 iterations of revisions for the report that was required for my exam.  But I did pass, and I did it on the first try.  

My QE experience sucked.  Here are few things that happened in the 6 month stretch leading up to it. I'd experienced feelings of real anxiety for the first time. I'd woken up many times in the middle of the night, realizing that I'd been muttering chemistry explanations under my breath. I'd wake up tired regardless of how much I slept.  I'd put aside my hobbies, ignored my friendships, and had 2 potential relationships fall apart.

I'm extremely grateful to the people who supported me and put up with my crap during that time.  I learned a lot from my QE experience, both in terms of science, and about myself.  Here are some examples:

• It currently takes me about 200 hours to write a good paper.  So start writing early
• Decide what you want, and work hard to get it.
• Having good friends can make a huge impact on your mental health
• I learned what coherence is (I've since mostly forgotten...)
• Making time for hobbies has a huge impact on my mental health
• Getting enough sleep has a huge impact on my mental health
• I'm an optimist

So here's the moral of my post.  I still think time travel can be a thing.  While I came away with some scars, good things have come from that terrible experience for me.  I'm stronger, more grown up, and a better scientist.  I feel a little less like an impostor.  And I think more good things are coming.