Scientists and “Being Smart”, part 1: Relating to “Normal”

The always wonderful Chad Orzel has just written a new book and New York magazine published a fascinating excerpt that’s been resonating a lot with my friends, science-minded and non-science-minded alike. Orzel relates how people often tell him that he’s so smart when they learn that he’s a physicist. While it is incredibly flattering to have other people say you must be smart, Orzel points out it comes with an unacknowledged downside:

There’s a distracting effect to being called “really smart” in this sense — it sets scientists off as people who think in a way that’s qualitatively different from “normal” people. We’re set off even from other highly educated academics — my faculty colleagues in arts, literature, and social science don’t hear that same “You must be really smart” despite the fact that they’ve generally spent at least as much time acquiring academic credentials as I have. The sort of scholarship they do is seen as just an extension of normal activities, whereas science is seen as alien and incomprehensible.

A bigger problem with this awkward compliment, though, is that it’s just not true. Scientists are not that smart — we don’t think in a wholly different manner than ordinary people do. What makes a professional scientist is not a supercharged brain with more processing power, but a collection of subtle differences in skills and inclinations. We’re slightly better at doing the sort of things that professional scientists do on a daily basis — I’m better with math than the average person — but more importantly, we enjoy those activities and so spend time honing those skills, making the differences appear even greater.

A friend in law school argued that this can be a benefit: people seem to have fewer uninformed opinions that they’re compelled to share regarding fluid dynamics than philosophy. I think that’s true to a point, though people also have lots of uninformed opinions on issues that are more controversial, like GMOs, ecology, and climate science. What I think is useful to consider is the nature of how all these fields relate to their people’s lives. People use the end results (whether that’s a tangible product or knowledge) of scientific and engineering research, but they don’t need an understanding of those systems to be able to use their products. People are in sociological, cultural, and political systems everyday and so they have at least a folk or commonsense understanding of how those things work, and so they react when people in these fields tell them their knowledge is incomplete, if not often wrong.

But you also see this a bit in misunderstanding of science: part of the reason people have strong opinions on things like food, ecosystems, and the climate is that they also interact with those systems everyday, and so they have a folk understanding of those too. The discrepancy between someone’s folk understanding and that of a scientific observer is why we have the”this winter is cold so global warfming is a myth” meme. There’s a reason this meme is so resonant to some, though. It’s common in science communication to just treat non-scientists as empty buckets waiting to be filled with scientific information that they’ll appreciate (or maybe even “f***ing love” it), and to assume the major limit in public understanding of science and scientific issues is that they just don’t know enough. This is called the deficit model, and what’s key to know about it is that it is typically wrong. It’s true that a random non-scientist won’t know as much about a given scientific field as someone actually working it. (There is a good chance they know something about it and you should engage that, though). What’s really important, though, is that people don’t engage with science in a vacuum. Everyone brings their own baggage, in the forms of folk knowledge, cultural assumptions, moral values, and more. Scientists, and science communicators more broadly, need to engage with those issues beyond just pure scientific knowledge to truly engage with the public, otherwise people think you’re treating them like idiots.

It’s also generally more interesting to approach science communication this way. Sure, I like informing people of the latest trends and results from research (and studies show people are interested in science news) or other neat concepts that come up in my work and as someone in the field, I’m more aware of this information. But I’m not going to have an equal back and forth about the topic of my old research with most people at UVA, except for the dozen or so people working on similar projects, because it took several years to get to that point. And that can be fine! I know I listen to law students, history majors, sociology majors, philosophy majors, policy students, biologists, and more have incredibly deep conversations on their areas of expertise all the time and learn a lot just from listening.

Even without finding someone who studies the sociology of science and technology, though, I can probably have an interesting conversation with almost anyone about social or ethical implications/questions related to my work. When I did work on the CO2 converstion project, lots of people right away grasped at the implications for climate change work. And that’s the kind of conversation that’s probably most helpful in grounding science and engineering into normalcy.

This is also why I tend to hate saying I “dumb down” things if I’m talking to people outside of my fields. There’s 11 schools at UVA and over 100 academic programs and I know people in all those are “really smart” and they are also all smarter than me in several things. (And of course, as Orzel points, this extends way beyond other people in academia or even college graduates; it’s just that my life is still mostly school.) The reason I change how I talk isn’t because these other people outside my lab and department are dumb; it’s to acknowledge that they all have expertise in different areas than I do and I want to share some of my expertise with them (without forcing them to also have all my training) in a way they can appreciate. Meeting people where they are is generally just good practice and science communication is no exception.

A Nobel for Nanotubes?

A popular pastime on the science blogosphere is doing Nobel predictions; educated guesses on who you think may win a Nobel prize in the various science categories (physics, chemistry, and physiology or medicine). I don’t feel like I know enough to really do detailed predictions, but I did make one. Okay, more of a dream than a prediction. But I feel justified because Slate also seemed to vouch for it. What was it? I think a Nobel Prize in Physics should be awarded for the discovery and study of carbon nanotubes.

One potential issue with awarding a prize for carbon nanotube work could be priority. Nobel prizes can only be split between three people. While Iijima is generally recognized as the first to discover carbon nanotubes, it actually seems that they have really been discovered multiple times (in fact, Iijima appears to have imaged a carbon nanotube in his thesis nearly 15 years before what is typically considered his “discovery”). It’s just that Iijima’s announcement happened to be at a time and place where the concept of a nanometer-sized cylinder of carbon atoms could both be well understood and greatly appreciated as a major focus of study. The paper linked to points out that many of the earlier studies that probably found nanotubes were mainly motivated by PREVENTING  their growth because they were linked to defects and failures in other processes. The committee could limit this by awarding the prize for the discovery of single-walled nanotubes, which brings the field of potential awardees down to Iijima and one of his colleagues and a competing group at IBM in California. This would also work because a great deal of the hype of carbon nanotubes is focused on single-walled tubes because they generally have superior properties than their multi-walled siblings and theory focuses on them.

No matter what, I would say Mildred Dresselhaus should be included in any potential nanotube prize because she has been one of the most important contributors to the theoretical understanding of carbon nanotubes since the beginning. She’s also done a lot of theoretical work on graphene, but the prize for graphene was more experimental because while theorists have been describing graphene since at least the 80s (Dresselhaus even has a special section in that same issue), no one had anything pure to work with until Geim and Novoselov started their experiments.

In 1996, another form of carbon was also recognized with the Nobel Prize in Chemistry. Rick Smalley, Robert Curl, and Harold Kroto won the prize for their discovery of buckminsterfullerene (or “buckyballs”) in 1985 and further work they did with other fullerenes and being able to the prove these did have ball-like structures. So while the prize for graphene recognized unique experimental work that could finally test theory, this prize was for an experimental result no one was expecting.   Pure carbon has been known to exist as a pure element in two forms, diamond and graphite, for a long time and no one was expecting to find another stable form. Fullerenes opened people’s minds to nanostructures and served as a practical base for the start of much nanotechnology research, which was very much in vogue after Drexler’s discussions in the 80s.

Six diagrams are shown, in two rows of three. Top left shows atoms arranged in hexagonal sheets, which are then layered on top of each other. This is graphite.

Six phases of carbon. Graphite and diamond are the two common phases we encounter in normal conditions.

So why do I think nanotubes should get the prize? One could argue it just seems transitional between buckyballs and graphene, so it would be redundant. While a lot of work using nano-enhanced materials does now focus on graphene, a great deal of this is based on previous experiments using carbon nanotubes, so the transition was scientifically important. And nanotubes still have some unique properties. The shape of a nanotube immediately brings lot of interesting applications to mind that wouldn’t come up for flat graphene or the spherical buckyballs: nano-wires, nano “test tubes”, nano pipes, nanomotors, nano-scaffolds, and more.  (Also, when describing nanotubes, it’s incredibly easy to be able to say it’s like nanometer-sized carbon fiber, but I realize that ease of generating one sentence descriptions is typically not a criterion for Nobel consideration.) The combination of these factors make nanotubes incredibly important in the history of nanotechnology and helped it transition into the critical field it is today.

News Publications without Science Sections

Inspired by Dr. Danielle Lee’s recent Twitter musings that STEM coverage directed towards minority communities is rare, which is compounded by the lower recognition that black scientists, engineers, and technologists get in their professional communities and the lack of STEM-focused coverage in African American media, I was curious to see how other major “thought leader” publications fared.

No Science or Science-Related Sections

JET – Though the website seems more lifestyle-focused than I expected, so maybe this is unfair

The National Review – Okay, their website is confusing, because I see a “Space” tag that doesn’t actually lead anywhere and they evidently have a “Planet Gore” section that is devoted to what they view as climate change hypocrisy. “Human Exceptionalism” is probably notable as the only column that routinely talks about bioethics in mainstream political publications.

No Science Sections, but Tech(nology), Health, or Other Science-Related Sections

The New Republic – Has a Technology section, which mainly seems to exist chronicle technical developments as they relate to politics or the economy

The Atlantic – Has Health and Tech sections, with science stories kind of split between them

EBONY – Has health (subsection of Wellness) and tech (subsection of Life); tech seems more consumer focused

The Daily Beast – has a combined “Tech + Health” section

ABC News – Has Tech and Health sections, and strangely, in that order

CNN - Has Tech and Health sections

MSNBC - Has Health and a “Green” section

NewsOne – Has a Health section

Some surprises

In contrast to ABC, CBS News has a joint Science and Technology section and a separate Health section and NBC News has separate Health, Tech, and Science sections.

Similarly, Fox News has separate TechScience, and Health sections, and I would have expected them to parallel CNN in structure. Also, I’m really surprised that they list Health as the last of those sections since if the stereotype of Fox News watchers/readers as being older holds true, I would expect them to be more interested in health and wellness articles.

Multiversal Fiction is Getting Dandy, Baby

I’m a bit slow to try to write this under the time crunch of beating the Space Dandy finale that premieres at 12:30 AM, so forgive any typos. But I just want to say I’ve been incredibly impressed by the way ideas of multiple universes have been getting used in fiction lately. True, the idea has been mainstream at least since the Star Trek introduced a “Mirror Universe” in the original series episode “Mirror, Mirror”. But typically they’re never a major part of the plot. Star Trek didn’t touch the Mirror Universe again until the second season of Deep Space Nine. (Although, as books go, I thought the His Dark Materials series was a really interesting take on parallel universes and I read that over a decade ago.)

But Space Dandy and two other recent pieces of on-screen fiction seem like a turning point in treating a multiverse as more fully realized setting, not just a plot device. If you’re fuzzy on the details of most episodes, you might wonder why I think the multiverse is an integral element of Space Dandy since it isn’t explicitly talked about much. But if you think a about how strongly the show seem to try to disrupt its own continuity, it makes a lot more sense if you think of many episodes taking place in their own (mostly parallel) universes. Consider the ways these episodes end:

  • In the very first episode, Dandy, all of the Aloha Oe, and the entire planet they were visiting is destroyed when they try to use a faulty secret weapon. The second episode explicitly mentions that the end of the first episode did happen and admits it gives a weak “handwave” about Dandy, Meow, and QT are still here.
  • In the fourth episode, the entire universe ends up zombified (even the narrator!) and it’s stated to be a kind of paradise. In the fifth episode, we go back to seeing a non-zombie Aloha Oe crew.
  • In the seventh episode, some combination of a bomb reacting with an incredibly questionable fuel supply ends up sending Dandy into the far future.  The episode ends with a confused Dandy landing near a giant statue of himself in the style of a Buddha.
  • In the eighth episode, nothing renders crew of the Aloha Oe permanently incapacitated, but the semi-antagonist Dr. Gel ends up sucked into a black hole. He reappears only a few episodes later, no worse for the wear.
  • In the eleventh episode, the being responsible for wiping the crew’s memories earlier reappears and evidently triggers an intergalactic war between various factions of storage media that seemed to heavily imply major disruption we never see.
  • Episode 14, the second season premiere, has Dandy, Meow, and QT meet dozens of their counterparts from parallel universes, and end up dragging them all to their home universe. This seems to result in weird distortions to their universe, and to fix it, they pull one of the cosmic strings to try to send everyone back to their respective universes. This mostly works, although the narrator’s closing mentions that the Aloha Oe crew with the depressed Dandy and the terrifying Meow and QT have now ended up in the universe of the Dandy, Meow, and QT we have been following.
  • In episode 21, it’s explicitly stated that Dandy has died. But the embodiment of strange purgatory like planet he is on sends his consciousness to a universe where hasn’t died yet.
  • Episode 24 introduces us to Dandy’s ex, Catherine, a being from a 4D universe who left Dandy to date Paul, the ruler of a 2D universe. Part of why Catherine left Dandy is that because he actually isn’t the Dandy she knew. It turns out that the nature of warp travel in Space Dandy is more like switching which universe you’re aware you’re in. While 3D warpers don’t realize it, higher dimensional beings like Catherine can see the different universes and know the difference.
  • Episode 25 has an expert witness explain a bit about the nature of Pyonium, which has come up several times in the series. He mentions that Pyonium can “cross dimensions”. It’s also noted that Dandy shows a Pyonium signal and forensics couldn’t detect his DNA.

It’s the reveal of the 25th episode that  seems especially important. We have been following Dandy and co. across multiple dimensions, and this seems to be a key part of who Dandy is, even if he didn’t know it. And it also explains why he may be so important to the antagonists of the show, who also keep reappearing despite their own canonical deaths or disappearances. But these all seem to be important. I bet the finale (which is just starting) is about to take us across the universes and I hope we’re going to deal with the ramifications of all the dimension-jumping we’ve been doing.

EDIT: Sounds like I may be wrong already. A character has already mentioned that using the Pyonium will help people access multiple universes, but it’s talked about as a way to basically control probabilities by choosing which universe you’re in. I hope they go over this more.

This Power-Generating Shoe Isn’t Ready for Prime Time Yet, but This Kid’s Project is Still Pretty Cool

This is a video by a Angelo Casimiro, a 15-year-old Filipino participating in this year’s Google science fair. And he has seriously tweaked his shoes to do something cool: they spark. And I don’t mean spark like  those kids’ shoes that have stripes that dimly light as you walk that you really wanted to try but evidently you couldn’t wear because none of them could support your ankles (okay, that last part may not have applied to everyone else…). Angelo’s new shoes actually generate a little bit of electricity each time he takes a step. This is incredibly cool.

But just because I can, I’m going to bury the lede for a bit, because I want to contextualize this. Angelo did this as a test to see if it could work AT ALL, and he says he’s nowhere near a final product that you might buy. So before dreams of daily jogging to power your iPhone and laptop dance in your head, we need to look at the electricity we can create and how much we actually use.

Duracell’s basic alkaline non-renewable AA battery has a charge of about 2500-3000 miliampere-hours (mAh), which I estimated based on multiplying the number of hours it was used by the constant currents applied in the graphs on the first page here. The two basic rechargeable NiMH AA batteries have charges of 1700 and 2450 mAh. The battery in my Android smartphone has a charge of 1750 mAh, based on dividing the energy (6.48 watt-hours) by its operating voltage (3.7 V). Based on Angelo’s best reported current of 11 mA on his Google science fair page, it would take 159 hours to fully charge my phone. That’s nearly a week of non-stop running! (Literally! There’s only 168 hours in a week. You could only spend 9 hours doing anything besides running that week if you wanted to charge the phone, or replace one of the two AA batteries it takes to power my digital camera) However, I might be overestimating based on his averages. At around the 3:50 mark in the video, an annotation says that Angelo was able to charge a 400 mAh battery after 8 hours of jogging. That would translate to about 33 hours of jogging to charge my cell phone. No one I know would want to do that, but that is significantly less than jogging non-stop for almost 7 days.

But as Angelo points out, while you not be able to power your phone with his shoe, lots of sensors and gadgets that could go into smart clothes could be powered by this. In the video, he says he was able to power an Arduino board. An Arduino is a common mini-CPU board with extras people often use to make nifty devices, from how Peter Parker locks his room door in The Amazing Spider-Man movie to laser harps you can play by touching beams of light (note that the Arduino isn’t necessarily powering all the other components it is controlling in these cases), so you could potentially control smart clothes that respond to your moving.  A study by MIT’s Media Lab also looked at putting piezoelectric material in shoes and found they could power an RFID transmitter, which can be used to broadcast information to either devices. So perhaps your gym shoes could also act as your gym ID. The 400 mAh battery Angelo mentions is pretty close to the charge of batteries in small blood sugar monitors and over double the charge of some smaller hearing aid batteries.

But in relation to another recent science fair controversy, let’s put Angelo in context. No, he did not “invent” a new way to “charge your phone with your shoes“. Angelo himself points out that his work is more like a proof of concept than anything close to a product, and his numbers show you really won’t want to charge energy heavy devices with it. And MIT and DARPA, that branch of the US Department of Defense that funds crazy research schemes, have both looked at similar systems. (DARPA has looked at piezo-boots that could help power soldiers’ electronics.) Angelo and DARPA also both realize the limits of this: with our current materials, there’s only so much you can stuff into footwear before you run out of room or make it harder to walk. So instead, people have shifted to different goals for piezoelectricity: instead of having the material move with a single person who has to provide all the energy, we can place it where we know lots of people will walk and split the work. In Europe, high foot traffic areas have been covered with piezoelectric sidewalks to power lights, and in Japan, commuters walking through turnstiles in Tokyo and Shibuya stations help power ticket readers and the signboards that guide them to their trains.

Two distinct images. The left image shows a turnstile for ticketing. There is a black strip of material running through it. The right image shows a figure with an explanation in Japanese describing the power-generating nature of the strip.

Piezoelectric strip in ticket turnstile in Japanese subway station, from 2008

But none of this means that Angelo hasn’t done good technical work. It’s just that his effort falls more on the engineering side than the science side. Which is perfectly fine, because Google has categories for electronics and inventions and that other big science fair everyone talks about is technically a science AND engineering fair. Angelo’s shoe modification is posted on instructables and is something you could do in your home with consumer materials. The MIT Media Lab study still worked with custom-made piezoelectrics from colleagues in another lab. So the fact that Angelo could still manage to charge a battery in a reasonable (if you don’t need power right away) amount of time is incredibly impressive. And he also seems quite skilled at designing the circuits he used. As a 15 year old, he easily seems to know more about the various aspects of his circuit he needs to consider than I did through most of my time in college (granted, you didn’t need to know any particularly complicated circuity to be a physic majors). He’s definitely on to a great start if he wants to study engineering or science in college.

What Happens When You Literally Hang Something Out to Dry?

I got a question today!  A good friend from high school asked:

Hey! So I have a sciencey question for you. But don’t laugh at me! It might seem kinda silly at first, but bear with me. Ok, how does water evaporate without heat? Like a towel is wet, so we put it in the sun to dry (tada heat!) but if its a kitchen or a bathroom towel that doesn’t see any particular increase in temp? How does the towel dry? What happens to the water? Does it evaporate but in a more mild version of the cycle of thinking?
It’s actually a really good question, and the answer depends on some statistical physics and thermodynamics. You know water is turning into water vapor all the time around you, but you can also see that these things clearly aren’t boiling away.

I’ve said before that temperature and heat are kind of weird, even though we talk about them all the time:

It’s not the same thing as energy, but it is related to that.  And in scientific contexts, temperature is not the same as heat.  Heat is defined as the transfer of energy between bodies by some thermal process, like radiation (basically how old light bulbs work), conduction (touching), or convection (heat transfer by a fluid moving, like the way you might see soup churn on a stove).  So as a kind of approximate definition, we can think of temperature as a measure of how much energy something could give away as heat.
The other key point is that temperature is only an average measure of energy, as the molecules are all moving at different speeds (we touched on this at the end of this post on “negative temperature”). This turns out to be crucial, because this helps explain the distinction between boiling and evaporating a liquid. Boiling is when you heat a liquid to its boiling point, at which point it overcomes the attractive forces holding the molecules together in a liquid. In evaporation, it’s only the random molecules that happen to be moving fast enough to overcome those forces that leave.
We can better represent this with a graph showing the probabilities of each molecule having a particular velocity or energy. (Here we’re using the Maxwell-Boltzmann distribution, which is technically meant for ideal gases, but works as a rough approximation for liquids.) That bar on the right marks out an energy of interest, so here we’ll say it’s the energy needed for a molecule to escape the liquid (vaporization energy). At every temperature, there will always be some molecules that happen to have enough energy to leave the liquid. Because the more energetic molecules  leave first, this is also why evaporating liquids cool things off.
A graph with x-axis labelled

Maxwell-Boltzmann distributions of the energy of molecules in a gas at various temperatures. From http://ibchem.com/IB/ibnotes/full/sta_htm/Maxwell_Boltzmann.htm

You might wonder that if say, your glass of water or a drenched towel is technically cooling off from evaporation, why will it completely evaporate over time? Because the water will keep warming up to room temperature and atomic collisions will keep bringing up the remaining molecules back to a similar Boltzmann distribution.
My friend also picks up on a good observation comparing putting the towel out in the sun versus hanging it in a bathroom. Infrared light from the sun will heat up the towel compared to one hanging around in your house, and you can see that at the hotter temperatures, more molecules exceed the vaporization energy, so evaporation will be faster. (In cooking, this is also why you raise the heat but don’t need to boil a liquid to make a reduction.)

There’s another factor that’s really important in evaporation compared to boiling. You can only have so much water in a region of air before it starts condensing back into a liquid (when you see dew or fog, there’s basically so much water vapor it starts re-accumulating into drops faster than they can evaporate). So if it’s really humid, this process goes slower. This is also why people can get so hot in a sauna. Because the air is almost completely steam, their sweat can’t evaporate to cool them off.

There Are Probably No Nanoparticles in Your Food… At Least, Not Intentionally

Recently, Mother Jones posted an article about “Big Dairy” putting microscopic pieces of metal in food. Their main source is the Project on Emerging Nanotechnologies and its Consumer Products Inventory, a collaboration between the Wilson Center and Virginia Tech. Unfortunately, the Mother Jones piece seems to misunderstand how the CPI is meant to be used. But another problem is that the CPI itself seems poorly designed as a tool for journalists.

So what’s the issue? The Mother Jones piece mainly focuses on the alleged use of nanoparticles of titanium dioxide (TiO2) in certain foods to enhance colors, making whites whiter or brightening other colors. First, the piece makes an error in its description of TiO2 as a “microscopic piece of metal”. Titanium is a metal, but metal oxides are not, unless you consider rust a metal (which would also be wrong). But another issue is “microscopic”. Just because something is microscopic, which generally means smaller than your eye can see, doesn’t mean it’s a nanomaterial. The smallest thing you can see at a normal reading distance is about a tenth of a millimeter, which is 1000 times bigger than the 100 nanometer cut-off we typically use to talk about nanoparticles.

A clear glass dish holds a bright white powder.

Titanium dioxide is a vivid white pigment, even as macroscopic particles.

And that’s what confuses me most here. As you can see above, titanium dioxide is white as a powder, but in that form it’s several hundred nanometers wide at minimum, if not on the scale of microns (1000 nanometers). In fact, nanoparticles of TiO2 are too small to scatter visible light and so they can’t appear white. A friend reminded me how sunscreens have switched from large TiO2 particles to actual nanoparticles precisely because it helps the sunscreen go on clearer. I’m not naive enough to think food companies wouldn’t try to cut a buck to help improve and standardize appearances, but I also don’t think food scientists are dumb enough to pay for a version of a material they can’t fulfill the purpose they’re adding it for. So TiO2 is probably used in some foods, but not on a nanoscale that radically changes it’s health properties.

But I don’t entirely blame Mother Jones. The thing is, the main reason I had a hunch the article seemed wrong is because one of my labmates at UVA has been working with TiO2 nanotubes for the last three years, and I’ve seen his samples. If I didn’t know that, and I just saw PEN include TiO2 on its list of nano additives, I would be inclined to believe it. PEN saw the Mother Jones piece and another similar article and responded by pointing out that the inventory categorized their inclusion of TiO2 in the products as having low confidence it was actually used. But their source is an environmental science paper including actual chemical analyses of food grade TiO2, so why do they give that low confidence? Also, PEN claims the CPI is something the public can use to monitor nanotechnology in products, so maybe they should rethink how confident they are in their analysis if they want to keep selling it that way.

The paper CPI references in the TiO2 claim is interesting too. That paper actually shows that most of the TiO2 is around 100 nm (figure below). But like I said, that’s kind of pushing the limit on how small the particles can be and still look white. It might be that the authors stumbled across a weird batch, as they note that in liquid products containing TiO2, less than 5% of the TiO2 could go through filters with pores that were 450 nanometers wide. Does the current process used to make food grade TiO2 end up making a lot of particles that are actually smaller than needed? Or maybe larger particles are breaking down into the smaller particles that Weir sees while in storage. This probably does need more research if other groups can replicate these results.

A histogram showing the distribution of particle sizes of TiO2. Categories go from 40 nanometers to 220 nanometers in intervals of 10. The greatest number of particles have diameters of 90-100 or 100-110 nanometers.

Distribution of TiO2 particle sizes in food grade TiO2. From Weir et al, http://pubs.acs.org/doi/abs/10.1021/es204168d?journalCode=esthag