Tuesday, July 22, 2014

A key concept in glasses: the entropy crisis

The figure below introduces the idea of an "entropy crisis" and the Kauzmann temperature in glasses. It also leads to profound and controversial questions about the intimate connection between thermodynamics and kinetics in glasses.

Each solid curve shows the temperature dependence of the entropy of a supercooled liquid, relative to that of the crystal, above T_g, the glass transition temperature. T_m is the melting temperature of the crystal. The dashed curves are entropy in the glassy state.
The figure is taken from a very helpful review and adapted from Walter Kauzmann's classic 1948 paper.

What is going on?
The entropy of a liquid is greater than a solid [think latent heat of melting] so Delta S is positive. But, the specific heat capacity of a liquid is also greater than that of a solid [the vibrational, translational, and rotational degrees of freedom are all "softer" and less constrained]. Hence, the slope of Delta S vs. T must be positive.
Now, suppose that the liquid is supercooled so incredibly slowly that the glass does not form and you keep lowering the temperature, then at some temperature Delta S becomes negative. This extrapolated temperature [see the light blue straight line] is known as the Kauzmann temperature.

Why does this matter?
By the third law of thermodynamics, the entropy of the crystal goes to zero as the temperature goes to zero. Thus the supercooled liquid, could have negative entropy, which is physically nonsense.
Formation of the glass prevents this possibility. But, formation of the glass involves kinetics. So is there some deep connection between thermodynamics and kinetics? The review  discusses some possible connections. The extent of that connection is one of the controversial questions in glasses.

Monday, July 21, 2014

Don't try and do any work on your vacation

I sometimes here the following:

"I will be on vacation [holidays/leave] next week but I am planning to do some work on the paper".

"It turns out things were busier than I thought and I did not get to do much [or anything] on the paper."

Vacations are meant to be vacations. Work is for work time. You need the break. Furthermore, trying to simultaneously work and spend time with family or friends is usually stressful and frustrating for everyone involved.

Switch off. Take a break and enjoy it. Your productivity when you return will be greater.

Saturday, July 19, 2014

Undergrads should be taught that hydrogen bonds are quantum

There is a very nice paper in Chemistry Education Research and Practice 
What is a hydrogen bond? Resonance covalency in the supramolecular domain 
Frank Weinhold and Roger A. Klein

It relates to issues I have posted about before. In an earlier article Weinhold and Klein reviewed how most introductory chemistry textbooks claim that hydrogen bonding is essentially a classical electrostatic phenomena [some sort of dipole-dipole interaction], in spite of the fact that it is largely due to coherent quantum effects.
Similar electrostatics-type assumptions are deeply embedded in the empirical point-charge potentials of widely used molecular dynamics (MD) and Monte Carlo (MC) simulation methods (Leach, 2001). These methods make no pretense to describe chemical bonding and reactivity phenomena, but are widely presumed to adequately describe H-bonding phenomena. The ubiquity of such simulation potentials in many areas of materials and biochemical research tends to reinforce and perpetuate the corresponding electrostatics-type rationalizations of H-bonding in elementary textbooks. Neither the manner in which H-bonding is now taught to beginning students nor how it is “simulated” in MD/MC potentials has changed appreciably in the past half-century.
Building on the recent IUPAC revised definition of the H-bond , they propose several definitions that might be appropriate for inclusion in introductory texts. Here is the most technical version:
A fractional chemical bond due to partial intermolecular A–H[cdots, three dots, centered]:B ↔ A:[cdots, three dots, centered]H–Bresonance delocalization (partial 3-center/4-electron proton-sharing between Lewis bases), arising most commonly from quantum mechanical nB→ σ*AH donor–acceptor interaction.

I have emphasised before there is a "smoking gun" for this quantum view of the hydrogen bond: the existence of an excited electronic state that is a superposition of the same two "resonating" basis states [diabatic states] that make up the ground state. It should be observable in quantum chemistry calculations and in UV absorption experiments.

Weinhold and Klein also made the recommendation:
Expose students ASAP to modern theoretical discovery tools 
The ready web-based availability of WebMO and other resources for calculating and visualizing accurate wavefunctions places a powerful tool in the hands of chemical educators and their laptop-toting students in the modern WiFi-activated classroom. With suitable guidebooks or Youtube tutorials [e.g., Marcel Patek, Christopher C. Cummins, or other web-based tutorial materials listed here and here], students can soon be using the same powerful computational tools that are driving chemical discovery in research laboratories around the globe. With such access, the student's laptop or mobile device can serve not only as an in-class discovery tool but also as a patient tutor and pedagogical “oracle” to provide accurate answers (and vivid graphical imagery) concerning details of valency, hybridization, and bonding in chosen chemical species, long before mathematical mastery of the underling quantum theory is attained.
I thank Ross van Vuuren for bringing the article to my attention.

The paper is part of a special issue on Physical Chemistry Education.

Aside: it warmed my heart that the authors referenced my post Chemistry is Quantum Science, that highlighted one of Weinhold's earlier articles.

Thursday, July 17, 2014

A quantum lower bound for the charge diffusion constant in strongly correlated metals?

Previously I posted about some interesting theory and cold atom experiments that suggest that the spin diffusion constant D has a lower bound of about hbar/m, where m is the particle mass.

Coincidentally, on the same day Sean Hartnoll posted a preprint, Theory of universal incoherent metallic transport. Based on results involving holographic duality [AdS/CFT] he conjectures that the diffusion constant satisfies the bound,


where v_F is the Fermi velocity.
I have pointed out to Sean that the ratio of this lower bound for D to the cold atom one (hbar/m) is
2 T_F/T where T_F is the Fermi temperature and T the temperature. Thus, the experiments [when normalised for trap effects] and the theory give a value of D about an order of magnitude smaller than Sean's lower bound. [My earlier post also references 2D cold atom experiments that give values for D several orders of magnitude smaller].
Sean raises the issue about how much m and T_F are renormalised by interactions. However, given that the spin susceptibility undergoes a small renormalisation it is not clear to me this will be significant.
Also, in a strongly interacting system charge and spin diffusion constants might be different.

In my post I pointed out the paucity of derivations of the central equation, the "Einstein relation", D=conductivity/susceptibility. However, Sean's preprint has a nice simple derivation of this based on conservation laws, but also showing how particle-hole asymmetry complicates things.

Wednesday, July 16, 2014

A simple model for double proton transfer

I just finished a paper

Here is the abstract.

Four diabatic states are used to construct a simple model for double proton transfer in hydrogen bonded complexes. Key parameters in the model are the proton donor-acceptor separation R and the ratio, D1/D2, between the proton affinity of a donor with one and two protons. Depending on the values of these two parameters the model describes four qualitatively different ground state
potential energy surfaces, having zero, one, two, or four saddle points. In the limit D2=D1 the model reduces to two decoupled hydrogen bonds. As R decreases a transition can occur from a concerted to a sequential mechanism for double proton transfer.

I welcome comments and suggestions.

Tuesday, July 15, 2014

The conceptual chasm between neuroscience and psychology

The New York Times has a nice op-ed piece The Trouble with Brain Science by Gary Marcus, a psychologist. It is worth reading for several reasons. First, it is a nice accessible discussion of the status and challenges of neuroscience. Second, it illustrates the scientific challenges of understanding emergent phenomena. Third, it highlights some funding/political/stategic issues that are relevant to other fields.

The piece is stimulated by controversy concerning the Human Brain Project, "an approximately $1.6 billion effort that aims to build a complete computer simulation of the human brain", funded by the European Commission. The US has also funded a massive project, The Brain Initiative, focussed on developing new measurement techniques.
The controversy serves as a reminder that we scientists are not only far from a comprehensive explanation of how the brain works; we’re also not even in agreement about the best way to study it, or what questions we should be asking.
.... a critical question that is too often ignored in the field: What would a good theory of the brain actually look like?
..... biological complexity is only part of the challenge in figuring out what kind of theory of the brain we’re seeking. What we are really looking for is a bridge, some way of connecting two separate scientific languages — those of neuroscience and psychology....
We know that there must be some lawful relation between assemblies of neurons and the elements of thought, but we are currently at a loss to describe those laws.......
The problem with both of the big brain projects is that too few of the hundreds of millions of dollars being spent are devoted to spanning this conceptual chasm.
Some of the scientific and political issues here are also relevant to other areas of science. In most fields involving complex systems advances require a combination of advances in instrumentation, materials preparation, computational models, analytical model development, and concepts. All are necessary and interdependent. At any one time a challenge for setting priorities and allocating resources is to have an appropriate balance between all of these approaches and areas.

Unfortunately, currently it seems funding agencies think it easier to convince politicians to fund big projects involving large scale instrumentation and/or computation. Smaller single-investigator grants, and particularly those focusing on conceptual issues and simple models, are getting squeezed out.

Monday, July 14, 2014

Papers make the impact not the journals

There is an interesting PLOS ONE editorial about impact factors that ends:
With the usual flurry of Impact Factor announcements due to start any day now, it’s a good time to remember that it is the papers, not the journals they´re published in, that make the impact.
 It also shows the graph below of the citation distribution for the journal. Note how incredibly broad and asymmetrical the distribution is. I found this interesting because several years ago I wondered what the error bar was on Impact factors, which are often reported to several decimal places.
The editorial points out that the distribution is probably broader for PLOS ONE because it publishes articles from a diversity of fields. Hence, I would still like to see distributions from other journals.