Thursday, November 24, 2016

Polymers in procession

Almost three years ago I became involved in an interdisciplinary project between physicists and chemists. The chemists were specialists in organic chemistry, that is to say, make complicated molecules mostly based on carbon. The physicists were specialists of the mechanics of soft materials, that is to say, how matter in between fluid and solid deform, break or flow.

Making these two groups of people work together was very difficult. Interdisciplinary science is hard. Scientists spend years or decades to understand enough a narrow field of knowledge to be able to make it progress. So when you put together scientists of different fields, they do not have the same vocabulary, the same methods, the same questions or the same expectations. When among physicists we were saying "We impose a constant shear stress" as a matter of fact, chemists were seeing us as
Physicist as seen by chemists
but we only meant "we apply a sideways constant force on the sample". And of course when chemists were telling us "This counter-ion is more chaotropic" we thought they were doing something like this:
Chemist as seen by physicists

To understand what the chemists meant I had to remember my chemistry classes like 15 years ago. Fortunately I quite liked chemistry in undergrads. I even defined myself as a chemical physicist, a much needed missing transmission belt. I was able to play the role of translator between the two groups. What the chemists meant was that the ion was disturbing a lot the water around itself.

At the end, we were able to work together. We made mechanical experiments on samples that were about a millimetre thick and we understood the results at the level of atoms. Conversely, we used this chemical understanding to design the mechanical properties of our samples. Let me explain to you what we did, in terms that both my physicist and chemist colleagues are able to understand.

All started with a new synthesis method used by the chemists. Polymers are long molecules where the same unit is repeated many times, a bit like a caterpillar. To make polymers the chemists started from a head and added about 70 body segments one by one. Then they added the chemical groups they wanted to each unit, like if they added legs to every body segment.

Here they managed to have a head with two negative charges and each body segments with one positive charge. In water the polymer schematically looks like that:

A polymer were most of the counterions are far away.
The minus charges floating around are counter ions. They are here to ensure that matter has a neutral charge in average. Some counter ions are floating far from the polymer, other are very close to the body segment they neutralise. We say that they are "condensed" on the polymer. The more condensed counter ions, the less the polymer looks charged from far away.

If you put that short linear polymer in pure water, it forms a very soft gel. Interestingly, you can inject it with a syringe. The gel is solid at rest, flows through the needle, and is solid again on the other side. Quite nice if you want to use a gel as a scaffold for cell growth in vivo. Nowadays, the gel is a soft solid that breaks irreversibly. You need a surgical procedure to put it in the body. With our type of gel a needle is enough.

Unfortunately for the applications, we found that our gel was very easily disturbed. If instead of pure water we used salty water the gel collapsed. If we started from a neutral head instead of the head bearing two minuses, no gel could form. Our mechanical measurements found no difference between the polymer solution and water alone. So we thought that the gel was formed due to charge interactions: minus head sticking to plus body. If no minus on the head, no gel. If salts, themselves charged, get in the way of the electrostatic attraction, no gel.

Also, something was quite strange: the gel was too soft. Like a thousand times too soft for such short polymers. A polymer gel is a 3D network whose edges are polymer chains and whose nodes are where chains meet, also called cross-links. The more meeting points you have, the harder the gel is. In other words, if you have short chains between cross-links, few body segments, the gel is hard. We measured the elasticity of the gel, and it was so soft that we predicted something like 60 000 body segments between meeting points! That is enough to make 880 of our short polymers!

Pine processionary caterpillars (source)
As the caterpillars on the picture above, our short polymers go on a single file.

So, we physicists were like "wow! that's strange" while the chemists were not caring much. Actually, the chemists were playing with their synthesis method to change the legs of the caterpillar.

Two ways to change the legs of the caterpillars: shape of leg correspond to the nature of the cation, either Immidazolium (aromatic cycle) or Pyrrolidinum (all single bonds). The colour corresponds to the counterion: F-, Cl-, Br- or I-.
For some compositions, the polymer was basically insoluble. No way to make a gel with it. To understand that, we have to remember that polymers are usually not very happy in water. What allows them to dissolve is their charges. If a polymer carries a lot of same charges (here pluses) these charges will repel each other, the polymer will stretch and will accept a lot of contact with water. If a polymer carries little charges, it will just collapse on itself to minimize the contact with water. You may remember from above that the more counter ions are condensed, the less charges the polymer carry, the less soluble it is.

A polymer with complete counterion condensation. Probably insoluble.

And indeed, we observed insolubility for the three compositions where the interaction between the repeated cation and its counterion was the strongest.

On the opposite, when the repeated cation and its counterion interacted weakly, we observed very strong gels, indicating shorter processions. Actually for two compositions we observed gels exactly 880 times stronger than the original one, meaning that the processions were just a single chain long.

So far so good, but all of this was learned by probing gently the softness of the gels, at deformations so low that they were not flowing but behaving as solids. To understand what is going on at larger strains, we have to have a look at the internal structure of a procession.

The procession at different scales.
As we said before, the monomers hates being in contact with water, so their preferred shape for the procession is a sphere. However plus charges prefer to be as far away as possible, so their preferred shape for the procession is a rod. It append that water-hating monomers are stronger on the small scales and that estranged charges are stronger on the large scales. So there is a scale D were the two influences balance. If the procession is just long enough to coil into a sphere of diameter D, then charges do not complain too much. But if the procession is longer, the charges refuse to make a larger sphere, and instead the procession grows into a cylinder of diameter D.

This cylinder does no grow in a straight line indefinitely. On scales large enough, counterions screen the charges from each other and the procession winds its way away.

Two charges in the mood for fight screened from each other by counterions.
So when we pushed harder on the gel to make them flow we found two threshold deformations. The first threshold corresponds to when the large scale winding path of the processions becomes extended. On small scales the procession is still collapsed to avoid contact with water. To stretch it further more monomers has to come in contact with water, it cost much more energy and this is visible on the mechanical measurements. The second threshold corresponds to the breaking of head to body bonds and it's when the gel flows.

Each circle is a blob of momomers collapsed to avoid contact with water.

For all compositions, the first threshold deformation is very small, telling us that the processions are almost linear at rest. It implies that the amount of charge condensation is directly related to the softness of the gel. So we are able to estimate charge condensation that varies from 10 free counterions per polymers (lots of charges) to one free counterion every 9 polymers in the procession (very few charges).

By contrast the second threshold vary widely between compositions between 10% and 800%.  Some gels flow immediately, others need to be stretched height time their initial size before flowing. This indicates that the head to body bonds are incredibly strong. Usually in water ionic bonds are about 100 times weaker that chemical (covalent) bonds. For our lowest charge polymer we measure head to body bonds that are within 20% of the carbon-carbon bond!

Our explanation is that with few charges the procession collapse around the head-to-body bond to avoid water. So the environment just around the bond is not water, it's hydrophobic polymer. Such environment is like an oil, where charges are few but interact very strongly. Indeed in oils other people have measured ionic bonds that strong. Actually this strategy is used by life itself: proteins can have just one charge in the middle of a large hydrophobic patch. When two such proteins with opposite charges meet the two hydrophobic patched stick together, expelling water from the direct environment of the charged and the ionic bond become very strong. This forms a lock and key mechanism that helps for example our immune system to recognise and block pathogens.

Time to wrap up, thanks for reading down to here. At the end, we have done very standard mechanical measurements at the millimetre scale to extract informations at the chemical level. Our model tells us what to change to tune the mechanical properties of our gel by a factor thousand. Thanks to a referee, we also did a back of the envelope calculation to see what these gels would give in a physiological environment, and we have a good candidate to inject in a living body. If anybody is interested on the biology side...


Srour H, et al. Ion pairing controls rheological properties of “processionary” polyelectrolyte hydrogels. Soft Matter. 2016. ArXiv 1611.07721.

Tuesday, February 9, 2016

Layered cake and floating crystals

Mille crepe. By Laitr Keiows - Own work, CC BY-SA 3.0,

The soil we stand on is like a mille crepe, a layered cake made by the slow deposition of solid matter on an ocean bottom, each era adding a layer of a different nature. The process that makes particles even slightly denser than water settle down is called sedimentation.

A particle is pulled down by gravity, slowed down by the viscosity of the solvent. It also gets kicked randomly by the atoms around. For a large and heavy particle like a canon ball this random motion is negligible and the particle sediment to the bottom. For a small and almost buoyant particle like a protein, this random motion dominates and the particle diffuses in any direction. In between we have the so called sedimentation-diffusion equilibrium. Particles settle down, but also diffuse up, and we observe that the concentration of particles changes depending on height. At the bottom we count more particles than at the top. This is what we call a density profile.

Equilibrium density profiles are a great tool for physicist. By measuring them, you can learn how your particles behave as a system. For example, if you observe a density that decreases exponentially with altitude, you known that the suspension behaves like an "ideal gas", which means that the particles almost do not interact. That's more or less the density profile of the gases in the atmosphere.

If you observe a sudden jump in a density profile, it means that you have an interface between two phases. For example between a gas of particles and a liquid of particles.

A colloidal gas-liquid interface. Picture by Paddy Royall.
If your particles are all the same size, you can even observe two consecutive jumps, from gas to liquid and then from liquid to crystal, where the particles are neatly aligned. Particles with different sizes would jumble the alignment. In general, it is quite difficult to make particles of different size crystallize.

There are several ways to get to this triple coexistence situation.  One possibility is that you first have the gas and the liquid that separate, and then the crystal forms from the liquid. A second possibility is crystals condensing from the liquid, settling down in sufficient quantities and only then does the liquid evaporates to form a gas layer on top. A third possibility is the crystals forming at the same time as gas bubbles, racing to the bottom or the top respectively. Only when gas and crystal layers sit on top of each other does some of the crystal melts to form a liquid layer in between.

My contribution was to add some more complexity to the first scenario. What if I add a few large particles (green) in the suspension of small particles (red) ?

At first, nothing changes: on top a gas that has almost no particle and on the bottom a mixture of many small and a few large particles.  If there was only small particles crystals would form at the bottom. But the large particles get in the way and no crystallisation occurs at the bottom.

Meanwhile the large particles settle faster than the small ones. So at the top of the liquid we soon have a layer devoid of large particles. Only small particles? Easy to make crystals then (big red blobs on the video below). Crystals are large, compact, and fall even faster than large particles. They outpace them and dive in the dense mixture of large and small particles. Splash!

And here we have something unexpected: the crystals float! I mean, yes, ice floats over water, we are accustomed to this. But water is an exception. Solid metal sink down into molten metal.

Actually we demonstrates that the mixture of small and large particles can get so dense without crystallizing that crystals made only of small particles can float in it.

The crystals are reasonably happy in there, not melting but not growing either. Since crystals are dropped continuously from the top, they end up filling pretty much the whole pool (where the large particles are) and even piling up over the level of the large particles.

Now the crystals that are over the level of the pool have no large particles to prevent their growth, so they grow and make a dense "ice pack" on top of the pool.

Final state of the limit between floating crystals (below) and the ice pack (above). This is the same place as the video above.

At the end, you get a pretty layered cake: gas on top, then a layer of liquid, then the ice pack, then the crystals made of small particles floating in the pool of large and small particles.

Details of the full layered sediment. Top: gas-liquid interface. Middle: ice pack. Bottom: crystals made of small particles in a small+large amorphous matrix.

Leocmach, M., Royall, C. P., & Tanaka, H. (2010). Novel zone formation due to interplay between sedimentation and phase ordering. EPL (Europhysics Letters), 89(3), 38006. doi:10.1209/0295-5075/89/38006