Thursday, May 15, 2014

Strange patterns

For more than a year, I am trying to understand that



Or more dynamically, this




This is no leopard or fish skin pattern, nor salad dressing-like demixing. It appears when I make a yogurt in a very thin container, actually in a gap of a tenth of a millimetre thick, between two glass plates. Important detail: the glass is made extremely slippery, nothing appears with usually sticky glass.



The pattern is random but there is a well defined size. I can change the thickness of the cell (from 50 microns to one millimetre) and the pattern will scale up accordingly.



By the way, there is nothing living in my yogurt, no bacteria. The gelation is induced by slow and homogeneous acidification by chemicals. You can see the process of gel formation at high magnification in the video below. At first, things move around, this is Brownian motion. Then the gel forms and everything stops. Then the pattern appears.




It took me a couple of month to understand what these patterns are. I let you guess until next time.


Sunday, April 27, 2014

Testing rupture models

How do materials break ? This question is the starting point of my present post-doc in France. People have good ideas on how metals and crystals break, because their structures are known for a century or two. But when you turn your attention to more messy materials, like composites, concrete, paper, gels, etc. the answers are far less convincing.


concrete 8

Popular (because simple) models of fractures are called fibre bundle models. Imagine a cotton yarn, or a rope made of many interlocked fibres. If you pull on it hard enough and for long enough, a fibre will break. The pulling strength will be shared by all the other fibres, until an other one breaks. The more broken fibres, the less remaining fibres, the more often a new fibre breaks. Sounds like a random action movie scene, isn't it?


Breaking wire rope

A first simple model is to consider that the fibres are independent from each other and each of them has a slightly different breaking threshold. The only way fibres interact with each other is by sharing evenly the load. This model is good at describing how paper breaks. It predicts that over a given load threshold, the material will always break. The stronger you pull, the faster it breaks, conversely if you pull just a minute amount above the threshold it will take a very long time to break. For most of the process, you may even not notice that you are damaging your rope. That's why in the movies it's always when the last guy crossing the rope bridge who falls.


A mode refined version of the model says that when a fibre breaks, the load it bear is split among its neighbouring fibres. It makes sense when you consider an actual rope, made of smaller twines, made of even smaller threads, etc. until you get to the individual fibres. What this new model predicts is the absence of threshold load. If you pull on your material long enough, it will break, whatever your strength. Of course, the weaker you are, the longer you'll have to wait. An other interesting prediction is the appearance of fractures, or regions where all the fibres are broken. Can this explain the fractures and cracks observed in many materials? That's on this question that I started my own research.


I selected a system that indeed looks like a network of fibres:

Casein gel seen by Transmission Electron Microscopy from Kaláb 1983
This is a gel obtained by slow acidification of a solution of milk protein (sodium caseinate), or in plain English: a yoghurt. The picture above was made by electron microscopy, and the white fibres you see are one hundred time thinner that a human hair. The black voids are occupied my water that flows throughout the network.


Unstirred yoghurt do behave very much like a hard solid, except that it is much weaker. You don't need a powerful machine to fracture it, a spoon is enough.

Yaourt à la vanille

And once it is broken, the cracks won't heal. It is very different from a liquid or from pastes that you can stir to erase the memory of the system. If you stir a yoghurt you just destroy it further.


Sketch of a Couette cell an visualisation of the fractures

Now, I don't trust myself to apply a constant force with a spoon, especially if the experiment is set to run for a week. So I make my yoghurt between two concentric cylinders of a machine called a rheometer, which is able to rotate the inner cylinder with a constant force until the next power cut. Step by step: I pour the protein solution in the rheometer at rest, the gel forms during 17 hours as the solution acidifies, and only then I apply the force.


As you see on the picture above, after some time fractures appear in the yoghurt and grow vertically. By the way, the picture was taken by a standard webcam. This is not rocket science. The picture above shows only the bottom half of the yoghurt, there are fracture also growing from the top. When bottom and top fracture meet, the gel breaks completely.


I repeated this experiment many times, varying the applied load and thus the time needed to break the yoghurt completely. At high load, I am limited by the recording frequency of the rheometer, so my minimal breaking time is slightly less that a second. On low load, patience is the limiting factor, as well as evaporation and mold growth. Still I have an experiment that lasted 11 days. That is a factor 10 million between the longest and shortest experiments, enough to prove that there is no meaningful load threshold. That is a first win for the model.


Edit March 29th, 2014

A video of the rupture. Nothing seems to append and then ...

Sunday, February 10, 2013

Up-goer five Glass

Here is my attempt to explain my thesis using only the ten hundred most used words in English. I used the marvellous Up-Goer Five text editor by Theo Sanderson inspired by XKCD.

When you cool a water-like stuff, you get a hard stuff. In many hard stuffs, the bits are lining straight. But in other hard stuffs there is no straight line.

The hard stuff that make the walls of a can do have straight lines. Because of those lines you can make the can smaller by pushing down on it without breaking it into pieces. Window glass has no line, so if you push it too strong it will break into pieces, but if you push it just a little bit it is harder that a can, you can't make it smaller by pushing it. Having no lines makes hard stuffs even harder. Also, that is because there is no straight line in window glass that the light can get through, straight lines stop light or make it funny.

Sometimes you want very very hard stuffs, or see-through hard stuffs, so you don't want lines in it. Sometimes you want hard stuffs that you can push hard without breaking, or hard stuff that stop light or make it funny, so you need lines. It is very important to know how to make lines or not to make lines.

The problem is: no one knows how to control the lines. Also, no one knows why stuffs without lines can be hard at all!

Water-like stuffs have no lines and they are not hard. So it is not lines that decide if a stuff is hard or not. What decides then? People had this idea: if bits of stuff group together they become hard. If you stick those groups together, you can make hard stuff. You can group bits of stuff by five, that makes them very hard. You can also makes groups of six which are quite hard.

By the way, if you make groups of six, it is easy to make lines out of it, so you have made a hard stuff with lines. But if you make groups of five, you can't make lines, so you have made a hard stuff without lines.

Is this idea right? To know this, I looked at stuffs that are still water-like but cold enough to become hard. If I cool down a little more, they become hard stuff without line. These stuffs are in between water-like stuff and no-line-hard stuff. Actually they are a little bit hard. People found that some parts of it are slow and some parts are fast. The colder you get, the larger those fast and slow parts become.

What people think, it that hard parts must be slow. So I looked if there was groups of five or groups of six, there was, and if they are slow or fast. I found that both kind of groups are slow, but groups of six are much slower than groups of five. This is a surprise! Also, I found that the more I cool down, the more groups of six I see. I don't see more groups of five. So it is the groups of six that are important to make the stuff hard, not the groups of five.

So, what makes stuffs without lines hard is not groups that can't make lines. It is groups that could make lines but there is something in the way. Maybe that is the groups of five that get in the way.

Saturday, March 17, 2012

Count on your neighbour

Counting how many stuff you have is important
Scrooge counting his money
... but boring
counting sheeps
During last week, I saw a few times one of my fellow lab member printing a picture like this
Phase contrast microscopy picture of nucleation
and putting a cross on each white object. He was counting them. The first time I saw this, I thought he had to do it for one or two pictures. But at the end of the week, I asked him what he was doing and if I could help.


The above picture is taken when a phase A nucleates into a phase B. This appends for example if you cool a liquid below it's crystallization temperature. A crystal nucleus will appear from time to time and grow. The probability to form a nucleus (nucleation rate) is a very important physical parameter: if nucleation is extremely rare, you will have a single nucleus in you bottle that will grow to form a single crystal before the birth of the next nucleus. This is exactly what you want for example when you make a silicon wafer for microelectronics. If nucleation rate is high, then you will have many nuclei growing at the same time and at the end a material that is made of many different crystals. You may want this in ice creams, because small crystals have a more pleasant texture than big ones.




The only method to measure the nucleation rate in a given system is to count the number of nuclei function of time. So my colleague was counting ... for the whole week. He had done two dozens of experiments at different temperatures and compositions, and took a series of picture for each (like every couple of second for a few minutes). This makes hundreds if not thousands of pictures to analyze. And his plan was to do it by hand.

Try to count how many nuclei are in the above picture. This is a task that need careful attention: large nuclei have a good contrast, but there are many smaller ones very difficult to tell from the background. That's why my colleague was printing and crossing the counted nuclei.

As I told you in a previous post, this kind of procedure can be fully automatized. The programming takes time, so if you have only a few pictures to analyze, this may not be a good idea. In addition, this counting is tricky because the objects can have very different sizes and contrasts. However I, sitting 3 steps away, had already developed and tested such a program. The physical signification is different (I am tracking polydisperse colloidal particles) but the technology is the same. So yes, I could help.

An hour later my colleague had in his computer a script counting the nuclei for him, a picture per second or less, automated to treat a whole time series automatically without human intervention. Setting-up Python and dependencies on his computer took half of the time. We should have communicated earlier, before he had spent a week doing what the script could do in an hour.

Result of the localization. Original image (red) superimposed with localized positions (cyan squares)
As you can see on the picture above, the result is not 100% perfect, but quite close. For example there are problems when nuclei are fusing and there are also (very few) centers counted multiple times. I think I know how to adapt better my program to this situation, but my colleague told me it was enough precision for him.

This gives an other motivation to explain (in a future post) how this counting/localizing method is working.

Tuesday, January 3, 2012

Mikan stacking fault

Never leave a crystallographer with a pile of fruits.

HCP(left)-FCC(right) stacking fault
Even if I do not consider myself a crystallographer, I spent most of my PhD identifying local symmetries in materials. And the pioneers of the land of symmetries in materials are the crystallographers, so I owe them most of my analysis tools ... and the tetris-o-philia.

The FCC side, note how the 3rd layer's fruits sit on top of voids in the first layer
During new year's vacation in my family in law, my daughter (in the background of the upper picture) started emptying the reserve of mandarin to bring them on the living room's table. This got me started at piling the fruits.
The HCP side. 1st layer and 3rd layers sit on top of each other
The pile begins by a layer where the fruits form hexagons. This is the most compact way of packing disks of the same size in 2D, and thus spheres of the same size on the same plane. Real fruits have different sizes, but anyway.

For the second plane, you have two possibilities that are mirror image of each other, a translation, a rotation of 30 degree, etc. In short, this is not a real choice because you have no reference point.

The same alternative has richer consequences in the third plane. Depending on your choice, you end whether with
  • 3rd layer's fruits sitting on top of 1st layer's fruits
  • 3rd layer's fruits sitting on top of 1st layer's voids
Because you have the first layer as a reference, the choice is no more silent. You end with two different crystals: Hexagonal compact (HCP) and Face-centered cubic (FCC).

FCC is left, HCP right, and the grain boundary in the middle (hole in the 3rd layer)
Now let's be messy. I made two different choices of 3rd layer in two different places. The line where the two stacking meet is a stacking fault. It is not possible to pack same-size spheres efficiently on this line. Evidence is the hole you can see on the pictures.
FCC is right, HCP left, and the grain boundary in the middle (hole in the 3rd layer)
Finally, I added a fourth layer, with fruits sitting on top of the ones of the 2nd layer. No fault in this fourth layer, I can continue my stack if I want. However the fruits immediately over the fault line have a little more space to rattle. The same holds for the fruits immediately below (2nd layer).

If you think about the stacking of a crystal of hard spheres, the price paid to have such a stacking fault is the spheres you could not fit in because of the line. In my very small crystal, I could have fit 2 more spheres without the fault. This is a global penalty.

On the other hand, the space gained to rattle by the spheres neighbouring the fault line increases their (vibrational) entropy and thus decreases their free energy. This is a local gain.

When you balance the global penalty with the local gain, you end up with quite a lot of stacking lines.

Saturday, December 17, 2011

Unifiying conference

I am frustrated when I cannot go to an international conference once a year. But at the end of it I am worn out. Usually it lasts a week. This time it was two weeks in a row. I wonder how I am still able to think.

International scientific conference are at the heart of the research world, at least as important as scientific publications. Without conferences, you would not know who is working in your field. That is where you discover that paper authors are not only names but human beings. Dr. X who is contradicting your results is actually a very friendly guy an the best person to chat to or to go to restaurant with. Pr. Y whose intuitions are always stunningly genial can be a frightening freak, a reckless egocentric or ... a very seducing man/woman.

There are the personalities you discover and the ones you are eager to meet again. From conferences to conferences the bonds tighten (often despite the scientific disagreements) and from these irregular contacts emerges a community, a human community closely related to the abstract "scientific community".

But scientific conferences are not only a bunch of old chaps meeting once a year. This is a powerful way to exchange ideas and to be able to dig into what other researchers have discovered. If you have read someone's paper, you are able to ask him/her questions to clarify and discuss his/her work. If not, hearing his/her presentation may make you read the referring article.

In practice, a conference consists in a series of oral presentations of various lengths. Typically a researcher invited by the organisers will have an hour to expose his/her research in front of everybody, a researcher selected by the organisers will have 30 minutes, and the others will have only a poster presentation. I am at the poster level, so I stuff my results on a A0 that I hang in the dedicated place off the conference hall and during the so called "poster session" time I stand by, ready to explain my work to anybody interested. This also implies some advertising skill beforehand.
My poster for Unifying Concepts in Glass Physics 2011
Except your short time under the spotlight (your talk or your poster session), the conference consists mainly in listening to other's stories. In the past week I have listen to 8-10 talks every day, each representing at least months and more probably years of work condensed in 30 minutes or an hour. The previous week was more like 6 talks a day. Anyway, this is an enormous amount of information, a all you can eat buffet that I will slowly digest from now on.

I will probably post here in the future some reflexions or discussions that result from this conference.

Sunday, November 27, 2011

Seminar and meetings in France

I'm giving a seminar in the Ecole Normale Supérieure (ENS) in Lyon, France the 6th of December. Just after that I'll be in Paris for 2 consecutive meetings:
Both seminar and poster are about the same stuff I talked about in Kanto-softmatter workshop and in a previous post. Here is the more formal abstract.
A link between local structural ordering and slow dynamics has recently attracted much attention from the context of the origin of glassy slow dynamics [1, 2]. There have been a few candidates for such structural order [3, 4], icosahedral order, exotic amorphous order, and crystal-like order. Each type of order is linked to a different scenario of glass transition. Thus, revealing the order responsible for slow dynamics is crucial for our understanding of the glass transition. Here we experimentally access local structural order in polydisperse hard spheres by its particle-level observation with confocal microscopy. We identify the key structures as icosahedral and face-centred-cubic(fcc)-like order, excluding any other simple local symmetry. We find that both types of order are statistically associated with slow particles. However, when approaching the glass transition, the icosahedral order does not grow in size whereas crystal-like structures grow. It is the latter that governs the dynamics and is linked to dynamic heterogeneity. This questions the direct roles of the icosahedral ordering in glassy slow dynamics and stresses the importance of the structural order compatible with the avoided first order transition, crystallization. Our finding also suggests that the growing lengthscale of structural order is essential for the slowing down of dynamics and the nonlocal cooperativity in particle motion.

References

  1. Cavagna, A. Supercooled liquids for pedestrians. Physics Reports 476, 51124, 2009.
  2. Berthier, L. & Biroli, G. Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 83, 587, 2011.
  3. Steinhardt, P., Nelson, D. & Ronchetti, M. Bond-orientational order in liquids and glasses. Phys. Rev. B 28, 784805, 1983.
  4. Tarjus, G., Kivelson, S. A., Nussinov, Z. & Viot, P. The frustration-based approach of super-cooled liquids and the glass transition: a review and critical assessment. J. Phys.: Condens. Matter 17, R114R1182, 2005.
  5. Lubchenko, V. & Wolynes, P. Theory of structural glasses and supercooled liquids. Annu. Rev. Phys. Chem. 58, 235266, 2007.
  6. Tanaka, H., Kawasaki, T., Shintani, H. & Watanabe, K. Critical-like behaviour of glass-forming liquids. Nature materials 9, 324Ð31, 2010.
Reconstruction from confocal microscopy coordinates. Only structured particles are shown for clarity.