What do I have to do with polyacrylate ?

It happens that a researcher deviates a little from his mainstream research. This is one of the cases. Dott. Pier Giuseppe Marcon came to us suggesting that polyacrylate could have peculiar thermodynamics characteristics and decreasing its and surrounding temperature when wet and around to 20-30 Centigrades. He arrived to me because of this blog. I suggested that I was certainly able to figure out a way to simulate the dynamics of the substance but, at the state of art of our knowledge, I was not the right person to talk about because the polyacrylate needed some charcgerisation before I could envision its thermodynamics modelling. Therefore I involved a  colleague, Rosa di Maggio, for getting the work done.  The result is this paper, in which I learned a few things. First of all that phases of matter are not that well defined as I believed initially. Secondly that water can form compounds when it is not free. That cannot be considered exceptional findings but made me to reflect that neglecting water chemical bounding can bring to mistakes.

The paper can be found by clicking on the Figure above (from Britannica) you get the paper. Its abstract reads: "Super-adsorbent polymers have the capacity to immobilize huge quantities of water in the form of hydrogel, thanks to their confguration. A commercial sodium polyacrylate (PA) was analysed as such and at diferent water uptakes, indicated through the weight ratios PA:H2O. The hydrogels were prepared using diferent type of water (tap, distilled and deuterated) and characterized by Infrared and Raman spectroscopic analyses, nuclear magnetic resonance experiments, CHN elemental analysis, measurements of thermal conductivity and difusivity. All the measurements were done in order to assess applications of PA:H2O gels as Thermal Energy Storage systems for improving thermal performances of building envelope through passive solar walls. It has been observed that the behaviour of the hydrogels depends both on temperature and water content. In certain conditions such as low weight ratios, a spontaneous and quick cooling of the hydrogel could be observed. The curves of heat fow and average specifc heat (cp) were determined as a function of temperature in order to investigate the states of water in PA hydrogels. When a few water molecules are present, they are mainly and strongly bonded with carboxylate groups. Increasing the amount of water, greater shells of solvation around ionic groups form and water molecules can even interact with neighbouring non-polar hydrocarbon groups. At very high amount of water molecules, they are much more involved into H-bonds among themselves, rather than with PA, so that water pools form into the links of polymeric network. Bulk-like water can freeze and melt. Whatever the amount of water in the hydrogel, its thermal capacity is higher than dry polymer, because the heat can be absorbed by the continuous desorption of water from polymer to bulk-like water (watergel→waterliquid), which can evaporate as temperature approaches 100 °C (watergel→waterliquid→watervapour)."

Next will be to envision a theory for the behavior shown. A glimpse of it can be found on this note.

Non-equilibrium Thermodynamics

I am starting to rewrite S.R. de Groot and P. Mazur, (dGM) Non-equilibrium thermodynamics book. Better, at the moment, I am trying the rewrite its PART A. What do I mean for rewriting ? Mostly two things: the first that I want to learn what it says, driving a slower dance with it, and the second is that I do not fully endorse what I understand so far from it. My differentiation is especially about the role of entropy, which, I think, is treated in a way that strongly derives from the idiosyncrasies of the equilibrium thermodynamics. I already wrote jointly with Matteo Dall’Amico something about thermodynamics, and possibly the two flows could merge in one final product. My goal is not thermodynamics, per se, but the thermodynamics of the hydrological cycle, of which I am a scientist. I believe that thermodynamics has to evolve towards a science of dynamical structures that allows for describing fluxes of information, besides energy and mass, with the final goal to understand ”life organisation”. The latter, however, is for future people. I will attack only water movements, and, maybe, some related cycles, as the carbon cycle. However water flows through plants, an plants are life. So let’s see where I will could arrive in the next fifteen years.

In what follows, what between ” ” is a verbatim transcription of dGM book. I believe their material is copyrighted, however, mine is distributed under CC license 3.0

You can follow the growth of the book while I am writing it, and comment it, if you like. To this scope I am using the Authorea tools. So:

Non-equilibrium Thermodynamics

1 - Introduction and motivation
2 - Conservation of mass
3 - Conservation of momentum
4 - Conservation of Energy

Other chapters will follow.

What is life ? (by Erwin Schroedinger) and Hydrology

The excuse for this blog post was the reading of an old (1944) little book entitled “What is life ?” by Erwin Schroedinger. It presents the point of view of a physicist on life, before the discover of DNA, and actually influenced the subsequent research by Watson and Crick. 

My reading, besides being influenced by a general curiosity, had a scope. Hydrology, especially in its very modern declination called ecohydrology (see also here) has a lot to do with the complexity of physical, chemical and biological interactions.  However even the more physical aspects of hydrology deployed in space, present patterns, heterogeneities, feedbacks that are by themselves of an overwhelming degree of complexity. Therefore getting the method there, for life understanding,  could help for a method here, in hydrology.  The whole book is all enjoyable, however, my commentary here covers mostly three chapters, the first and the sixth, and very little the seventh.  Excerpts from the book are in italics, my own notes in normal characters. 

CHAPTER 1 - The Classical Physicist’s Approach to the Subject

INTRODUCTION

“.. though warned at the outset that the subject-matter was a difficult one a …, even though the physicist’s most dreaded weapon, mathematical deduction, would hardly be utilized. The reason for this was not that the subject was simple enough to be explained without mathematics, but rather that it was much too involved to be fully accessible to mathematics.”

Here  I see a parallel with many hydrological processes, say for instance, the hillslope processes. Many outstanding colleagues support the idea that the physics of the argument is too much complex to be treated mathematically. 

“The large and important and very much discussed question is: How can the

events in space and time which take place within the spatial boundary of a living organism

be accounted for by physics and chemistry? The preliminary answer which this little book will

endeavor to expound and establish can be summarized as follows: The obvious inability of present-day physics and chemistry to account for such events is no reason at all for doubting that

they can be accounted for by those sciences. “

Now, just substitute to “living organism”  “river basin” and you have an answer to the first question for hydydrology. It is indubitably that actually, in these seventy years, passed by the publication of the book, also biology itself, and molecular biology in particular did a lot of steps in the direction traced by E.S., as is, at the same level, clear that hydrology processes knowledge, and the establishment of Hydrology as a physical Science, since the work by P. Eagleson, made extraordinary jumps forward.

STATISTICAL PHYSICS. THE FUNDAMENTAL DIFFERENCE IS  STRUCTURE

“Yet the difference which I have just termed fundamental is of such a kind that it might easily appear slight to anyone except a physicist who is thoroughly imbued with the knowledge that the laws of

physics and chemistry are statistical throughout.”

This statement applies verbatim to Hydrology.

THE NAIVE PHYSICIST APPROACH TO THE SUBJECT

“I propose to develop first what you might call 'a naive physicist's ideas about organisms', that is,

the ideas which might arise in the mind of a physicist who, after having learnt his physics and, more especially, the statistical foundation of his science, begins to think about organisms and

about the way they behave and function and who comes to ask himself conscientiously whether

he, from what he has learnt, from the point of view of his comparatively simple and clear and

humble science, can make any relevant”

Substitute “organisms” with hydrology, hydrological processes, watersheds, at your convenience.

WHY ATOMS ARE SO SMALL ?

“Why are atoms so small? … Suppose that you could mark the molecules in a

glass of water; then pour the contents of the glass into the ocean and stir the latter thoroughly so as to distribute the marked molecules uniformly throughout the seven seas; if then you took a

glass of water anywhere out of the ocean, you would find in it about a hundred of your marked

molecules. ”

Besides being a truly hydrological example, attributed to Lord Kelvin, it also envision the scales of hydrology from molecule (in the quantum domain) to oceans (the so call, global hydrology). 

CHAPTER 6 - Order, Disorder and Entropy

A REMARKABLE GENERAL CONCLUSION FROM THE MODEL

“From Delbruck's general picture of the … substance it emerges that living matter, while not eluding the 'laws of physics' as established up to date, is likely to involve 'other laws of physics' hitherto unknown, which, however, once they have been revealed, will form just as integral a part of this science as the former.”

Substitute Delbrucks’s with “modern Hydrology’; “living matter” with “hydrological processes”. Where these other laws are, is the new frontier of hydrology. A frontier, already envisioned by some time indeed, because, I cannot deny that I can see in it the “Gold medal search” of Ignacio Rodriguez-Iturbe own work.

….

LIVING MATTER EVADES THE DECAY TO EQUILIBRIUM 

“ When a system that is not alive is isolated or placed in a uniform environment, all motion usually comes to a standstill very soon as a result of various kinds of friction; differences of electric or

chemical potential are equalized, substances which tend to form a chemical compound do so,

temperature becomes uniform by heat conduction. After that the whole system fades

away into a dead, inert lump of matter. A permanent state is reached, in which no

observable events occur. The physicist calls this the state of thermodynamical equilibrium, or of

‘maximum entropy' “

There is poetry in this sentence: but it could be subtly imperfect: natural systems usually work under disequilibrium conditions. In fact E.S. remarks it later in the chapter. However, not only living organisms but also eco-hydro-systems work the same way, even if at a more aggregate and “higher” level of organisation. Organisation of spatial physical systems, like river networks, and hydrological interactions work the same way, and often they show the same type of complex organisation. For their organisation, obviously, we would less inclined to talk about evading equilibrium conditions, and there we would be probably correct, but at the same time a little wrong …

IT FEEDS ON ‘NEGATIVE ENTROPY’

“By eating, drinking , breathing and (in case of plants) assimilating. The technical term is metabolism. The Greek word means change or exchange. Exchange of what? Originally the underlying idea is, no doubt, exchange of material …That the exchange of material should be the essential thing is absurd …  For a while in the past our curiosity was silenced by being told that we feed upon energy …Needless to say, taken literally, this is just as absurd. … Every process, event, happening -call it what you will; in a word, everything that is going on in Nature means an increase of the entropy of the part of the world where it is going on.”

I do not completely agree with the phrases excerpts. E.S. himself, in commenting further, does move out of this strict vision. Entropy represents uncertainty of kinetic energy microscopic configurational space. However, it is driven by energy which is, as well as mass (because space-time is locally hyperbolic and we work in non relativistic conditions), conserved. Is just the feeding up with heat that move water from a less entropic state (ice) to a more entropic state (vapor). Once in an energetic state, water molecules configuration is the most probable (more or less), but as experience teaches, the way the passage between energetic states is obtained, can strongly affects the final “metastable” configuration (and, for instance, snow flakes, are an example). So for living systems, as well as for the hydrological fluxes and states, metastable, out of equilibrium states are the key. Once the systems are not anymore fed up with mass and energy, the system decay to a stable state, which is, at the same time a state of feasible minimal potential energy and  feasible maximum   entropy. Metastability is intrinsic to everything. The universe itself, as we conceive it, is a metastable state  that moves out of the Big Bang. It would be an oddity if the same would not be true for hydrological fluxes.

CHAPTER 7 - Is Life based on the Laws of Physics ?

The tile itself is compelling. E.S. certainly opens many question as: NEW LAWS HAS TO BE EXPECTED IN THE ORGANISM. He concludes that new laws are to be expected emerging (but the word meaning was not there seventy years ago) from disorder, or organising the new order appearing at macroscopic scales:

“The orderliness encountered in the unfolding of life springs from a different source. It appears

that there are two different 'mechanisms' by which orderly events can be produced: the

'statistical mechanism' which produces order from disorder and the new one, producing order from order” 

The same type of problematics can arise even in watershed hydrology (read the title: Is Hydrology based on the Laws of Physics ?). The current practice declares that the collective work of many water molecules, and their interactions can be describe under certain circumstances, by macroscopic laws, in which the collective behaviour, the spatial structure of the problem, or other situations, are more important than the simple molecular dynamics (think to the residence time interpretation of the Instantaneous Unit Hydrograph, for the Italians, here, or, remaining on the same topic, the fact that the hydrologic response is mainly determined by the geomorphic organisation, than Navier-Stokes equation)

In the “THE NEW PRINCIPLES ARE NOT ALIEN TO PHYSICS”, E.S. in fact claims that the new physics is still physics, even if, in some sense, super-physical.  He seems to me  in a search, that is not certainly concluded, of  a unifying principle for understanding the stratification of reality, even the physical one,  in layers, each one governed by its own rules. This was enunciated more recently (translation into English is mine) as follows: 

“ We cannot deny that our universe is not a chaos; we recognise being, objects thet we recall with names. These object or things are forms, structures provided of a certain   stability; fill a certain portion of space and perdure for a certain time …” 

(R. Thom, Structural stability and morphogenesys,1975)

The search for scaling, scale invariance and scale breaking in hydrology, that made history in the last two decades,  was the analogous search of understanding these higher levels of organisation of the hydrological processes that still are quite elusive indeed.

_______________________________________________________________________________

On the same topics of What is life ? I found also the Ph.D thesis by Nathaniel Virgo , entitled “Thermodynamics and the structure of living systems”. He is also author of interesting papers referred on his website.

The thesis, besides, E.S. works cites also the previous work by Morowitz and an interesting paper by Schneider

References

- N.Virgo, Thermodynamics and the structure of living systems, University of Sussex, 2011

- Morowitz, H. (1968). Energy flow in biology. New York and London: Academic Press.

- Morowitz, H. (1978). Foundations of bioenergetics. Academic Press.

- Schneider, E. D., & Kay, J. J. (1994). Life as a manifestation of the second law of thermodynamics. Mathematical and Computer Modelling, 19(6–8), 25–48.

Thermodynamics

It is strange that I did not dedicate any post to thermodynamics, since it was one of "the topics" of my work during the last years. As usual I approached Thermodynamics by analysing  a physical process. It was the dynamics of freezing soil (e.g. see Dall’Amico et al., 2011) where phase transitions in soil under capillary effects was the problem under scrutiny.  To get rid of the tens of empirical equations, and desperate after the reading of some nonsensical books and papers, I literally understood what the words of C. Truesdall wanted mean with:

“Thermodynamics today is a blend of statements from most of the founders: Gibbs, Planck, Boltzmann, even from information theory. Confusion is nearly universal. Constitutive properties are not delimited, just pulled out from under the table as needed.”

I decided to calm down, and face it from the scratch. 

Reading the firsts chapters of Dall’Amico thesis would give you a quick synthesis of what I learned with Matteo: it is a good introduction to the topic. Dall'Amico introduces a new and fresh notation that can help the understanding. 

For a more in-deep information, I selected the following list of books and papers (which you should read, with Dall'Amico notation in mind).

I would start from:

• Callen, H. (1985), Thermodynamics and an Introduction to Thermodynamics, John Wiley and & Sons.

And continue with:

• Aharon Katzir Katchalsky, P.F. Curran (1965), Nonequilibrium Thermodynamics in Biophysics, Harvard University Press,  - 248 pp

the latter was a revelation (I really loved their chapter on diffusion). Callen, on his side, with his axiomatic approach, frees your mind from several encrustations that you can have learnt before.

Those three references above should do the main work. However, I would add some other books and papers:

• Zia, R. K. P., Redish, E., & McKay, A. (2009). Making sense of the Legendre Transform. American Journal of Physics, 77(7), 614–622. 

the above, for really understanding the role of Legendre transform

• Bohren, C., and B. Albrecht (1998), Atmospheric Thermodynamics, 402 pp. (I understand, not a cheap book but it also contains a lot of good stuff)

This book above made me gain consciousness about the nonsensical algebra notation of Thermodynamics: I  agree with their criticism, which I completely endorse (actually also  Callen and  Katchalsky-Curran books mildly use the traditional notation. I say mildly because, once you are advised, you can read through it, in their books).  Other clarifying chapters can be found in:

• Müller, I and Weiss, W (2005),  Entropy and Energy: A Universal Competition, Springer & Verlag (Müller is also author of a history of thermodynamics).

Particularly I liked Muller and Weiss chapters on ideal gas and ideal rubber, and many other parts, indeed.

The classic on non-equilibrium thermodynamics is the old Dovers’book by De Grot and Mazur. However, in reading it one gets the idea of a great generality, and I keep in my bookshelf, but, at the same time, inherits a sense of frustration for the too concise treatment of the subject.

I would also mention one (defeated ?) but stimulating view on thermodynamics, the Jaynes one's   explained in

• W.T. Grandy’s book: Entropy and Time Evolution of Macroscopic Systems, Oxford University Press, 2008 

Going more specialised, I would also read

• Zdunkowsky, W. , and Bott, A., Thermodynamics of the atmosphere, A course in theoretical meteorology, Cambridge University Press, 2004.
• Ganguly, J. Thermodynamics in Earth and Planetary Sciences, Springer 2010

and finally I would also include in the lectures

• Reguera, D., Rubi, J. M. and Vilar J.M.G.,  The mesoscopic dynamics of thermodynamic systems, Phys. Chem. B, 2005, 109 (46), pp 21502–21515, DOI: 10.1021/jp052904, 2005

This last contribution open the way to the generalisation of thermodynamics to include small systems, in which the presences of few atoms would otherwise prevent to apply thermodynamics.

There are other books are in my bookshelf, but which I mentioned above can be enough for starting. I am pretty sure that also some good web coursewares is out there, and I would thanks if someone can address them to me.