”Have fun on sea and land
Unhappy it is to become famous
Riches, honors, false gliters of this world
All is but soap bubbles”

...although this ending quote only names his immortal.

Soft matter, a more beautiful name that can well encourage the young students¹, now has also been the titles of several significant journals. It seems that that generation of young students have now become the leading scientists of the academia. We have been familiar with such big fields as amphiphilic molecular self-assembly , block copolymers, superhydrophobic surfaces (the so-call lotus leaf effect), and biomacromolecular dynamics. Experimental works, however, have been accumulated to a point that some theoretical support is highly needed for further development, that is, the physics of soft matter – mathematical analysis of gels, droplets, bubbles, foams, etc. Here, in memory of the great pioneer, P. G. de Gennes, I am going to mention some of the theoretical aspects of soft matter phenomena, not a complete overview, nor a deep insight, though, because I am poor at physics and maths. We will start from the work by the Nobel Laureate himself, then come the heated topics of self-assembly and biomimics.

Fractal in Solution

2D Random walk. Source: Wikipedia.org

Addition of a small amount of polymer is sufficient to maintain a high viscosity of the solution, because polymer coils in solution belongs to the class of fractal objects, that is, they are tenuous. Imagine a spherical region with a radius R around a coil of polymer chain, R being much larger than the length of the repeating units, but much smaller than the actual size of the whole coil. Due to the random walking nature of polymer chains, only limited steps of walk lie inside the region R, the rest space of which is full of solvent, that is, the polymer coil is not closely packed. In addition the larger the radius of the imaginary region R, the smaller the density of polymer inside the region, and this decrease is exponential with a power D, called also the fractal dimension. This is why the term tenuous is used. A random walking polymer chain is a fractal object with D=2. Simply put, a very small concentration of such tenuous coils would seem to take a large volume fraction in the solution, and significantly affect the solution behavior in a great measure, such as reduced losses in turbulent flows, or the Toms effect.

Depletion Force

Two heavy balls lying on a rubber sheet with a distance not too large from each other, may come close together by themselves, due to the entropy-driven tendency to lower the free energy of the system. Similarly, a disturbance inside a flexibly structured fluid by occupation of two objects may also lead to their attraction, provided their distance is small enough. The most typical example of this ‘disturbance-attraction’ theory is the so-called depletion force, occurring between two close plates inside a colloidal solution when the distance of the two plates is smaller than the average diameter of the colloids². This theory is finding increasing applications in explaining self-assembly phenomena.

Ordered Structures

Typical phase diagram of diblock copolymer melt. Source: madtl.org

Now we come to the aspects related to the tendencies of most types of soft matter towards ordered structures such as micelles – intermolecular self-assembly driven by molecular amphiphilicity, self-assembly of colloids driven by entropy, and intramolecular self-organization of macromolecules such as block copolymers, DNA and proteins. There are also theories of self-organizations under non-equilibrium states, such as some ordered morphology formed under the flux of structured fluid. Most of the self-assembly occur concurrently with phase separation, and in practice, phase separation is indeed the most frequently employed strategy to induce self-assembly of many kinds. Macroscopic phase separation can be described by Flory-Huggins theory, or the mean-field theory, and well predicted by the well known χN factor. The parallel example for phase separation at microscale, or microphase separation, is the phase diagram of block copolymer with asymetric/immiscible blocks, where χN remains the governing factor. When it comes to kinetics, we have currently two types of treatment, the nucleation growth model and the spinodal decomposition model (animation).

Why Does the Red Blood Cell Adopt a Biconcave, Disk-Shaped Morphology?

Red blood cell. Source: flickr.com

Somatic red blood cell (RBC) consists of a bilayer of cell membrane and the plasma inside it, without any organelles. So the morphology of the RBC should be the result of hydrodynamic equilibrium. But why the biconcave disk? The answer took almost 30 years of discussion. At first someone³ explained that the morphology was the best for oxygen exchange, but at the very site of intensive exchange, the capillaries, RBC adopts a slipper-like shape. Then it was proposed that the uneven distribution of the thickness⁴ or the cholesterols⁵ molecules might lead to this morphology, but these were not consistent with experimental observations. Some then resorted to mathematical simulation and found the biconcave disk morphology to be energetically the lowest⁶. This sound encouraging but another morphology, dumbbell, is at the same lowest point as the biconcave disk⁷, whereas we never see a normal RBC that is dumbbell-like. The currently, most accepted answer relies on liquid crystal theory by W. Helfrich, the curvature elasticity⁸. Thanks to Helfrich, one of the once-regarded super-nature phenomenon, flickering in RBC, was proved⁹ to be within the recognition of human rationality.

Helix Morphologies

A Conch. Source: flickr.com

Bacteria, conchs, alga, DNA… Helix structures can be seen in every side of Nature. Within the academic community, it was found in 1984 that vesicle comprised of a bilayer of chiral molecules will decompose and re-assemble into a twisted ribbon at high temperature, and eventually form a coiled helix with an angle of 45 degree¹⁰. This phenomenon seems even familiar today because one of the approaches to yield carbon nanotubes is the coiling gap-fusing of a graphite sheet. Theoretically, these problems can be stated as how and why a ribbon-like structure coils into a chiral helix. In 1986, Helfrich put forward the first explanation – spontaneous torsion of the edges¹¹. de Gennes also joined in early¹², and proposed that the membranes that can coil up might bear some ferroelectricity, and it was the resultant polar charges along the edge that led to this ‘spontaneous torsion’. Based on this notion, Helfrich combined the ferroelectric model with liquid crystalline, and finally explained the 45 degree angle characteristics¹³. Although the works by Helfrich and de Gennes are phenomenological and not perfect, they paved the way to better explanations, and now the most acceptable one is the ‘tilted chiral lipid bilayers model’ proposed by the Chinese physicists in 1991¹⁴, which is proved by later experimental results¹⁵.

I have to stop here. Although I have only mentioned a very limited part of the world of soft matter, these examples show how theoretical research can make some miracles of the Nature a bit believable, and even controllable. And there is still another wisdom of scientific research I can learn from these stories – make sure the scale of object you are interested in, and choose the suitable model for that scale. Take the RBC membrane model for example. One may be more familiar with the traditional biological model, in which various proteins, holes and ion channels are inlaid in a vast area of bilayer. But when it comes to the morphology of the whole cell membrane, these objects are negligible because they are of a much smaller scale (nano) than what’s of interest (micro). This principle is also implemented in the example of polymer solution.

We lost a great scientist, but one of the encouragement of science is you never feel too depressed at a scientist’s death, because you can always feel his existence in the process of future research, his contribution fused into this cause towards the unknown.

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1. In the beginning of P.G. de Gennes’s Nobel Lecture, he mentioned: What do we mean by soft matter? Americans prefer to call it ‘complex fluids’. This is a rather ugly name, which tends to discourage the young students.
2. a) Macromolecules 1981, 14, 1637. b) ibid. 1982, 15, 492.
3. Ponder, E. Hemolysis and Related Phenomena. 1948 New Youk: Grune & Stratton.
4. Biophys. J. 1968, 8, 175.
5. J. Cell Biol. 1973, 56, 519.
6. J. Theor. Biol. 1970, 26, 61.
7. J. Physique 1975, 36-C1, 327.
8. a) Naturforsch C 1973, 28, 693. b) Naturforsch A 1978, 33, 305.
9. Phys. Rev. A 1990, 41, 3381.
10. Chem. Lett. 1984, 1713.
11. J. Chem. Phys. 1986, 85, 1085.
12. C. R. Acda. Sci. Ser. II 1987, 304, 259.
13. Phys. Rev. A 1988, 38, 3065.
14. a) Phys. Rev. Lett. 1990, 65, 1679. b) Phys. Rev. A 1991, 43, 6826.
15. The survey of the findings in RBC and helix morphologies is adopted from: Kunquan, Lu; Jixing, Liu Introduction to Soft Matter Physics. 2006 Beijing: Peking University Press.