iMechanica - thermodynamics of nanoscale small systems - Comments

time-temperature equivalence for a viscouselastic material

Henry Tan — Sat, 08 Sep 2007 15:59:24 -0400

How does the time-temperature equivalence for a viscouselastic material be viewed at molecular scale?

How temperature affects the viscoelastic behaviour?

Henry Tan — Sat, 08 Sep 2007 15:56:04 -0400

How temperature affects the viscoelastic behaviour? especially viewed from the behaviour of molecular movements?

Mr Tan, But it

Aneet — Tue, 15 May 2007 10:38:47 -0400

Mr Tan,

But it should make sense, as the molecules/atoms vibrate or move around, they do so because they have velocity. And when we talk about molecular dynamics wont we say KE = (1/2)mv2 where KE = (3/2)NkT (for a 3D system, K - Boltzmann's constant?)

Then we do have energy and thus 'temperature'.

Aneet

Ortwin Hess

Henry Tan — Sun, 15 Apr 2007 23:18:11 -0400

Professor Ortwin Hess
Department of Physics
University of Surrey

His recent interests include nano-thermodynamics.
http://www.ph.surrey.ac.uk/profiles?s_name=Ortwin_Hess

Thermodynamics and nanotechnology

Henry Tan — Fri, 13 Apr 2007 15:56:23 -0400

Thermodynamics, largely driven into being by the steam engine, should be pushed into a further mature stage, driven by the nanotechnology that controls matter on the atomic scale.

temperature at the tip of the nano-indenter

Henry Tan — Fri, 13 Apr 2007 01:36:15 -0400

Nanoindentation is a fundamental, evolving, and complementary discipline (Michelle, http://imechanica.org/node/1237).

It iis an interesting topic among imechanicians from many different backgrounds:
Experimental Nanomechanics (Xiaodong, http://imechanica.org/node/606);
Viscoelastic Contacts (Michelle, http://imechanica.org/node/842);
On the uniqueness of measuring elastoplasticproperties from indentation (Xiaodong, http://imechanica.org/node/1222).

The nanoindentation measurements can be even more interesting, when accounting for the temperature at the tip of the nano-indenter.

Nanotubes may have no 'temperature'

Henry Tan — Fri, 13 Apr 2007 00:56:28 -0400

An interesting news headline in nanotechwire.com
http://www.nanotechwire.com/news.asp?nid=1064&ntid=133&pg=9

Physicists have made a bizarre discovery: the concept of temperature is meaningless in some tiny objects. Although the concept of temperature is known to break down on the scale of individual atoms, research now suggests that it may also fail to apply in rather larger entities, such as carbon nanotubes.

The blossoming field of nanotechnology relies on being able to manipulate materials that are made from just a few thousand atoms. Carbon nanotubes, for example, are tiny cylinders that could be used to make miniature electronic devices.

Ortwin Hess from the University of Surrey, Guildford, UK and colleagues say that if you took the temperature at one end of a 10-micrometre nanotube, it would not necessarily have the same temperature as the other end, no matter how long it was left to reach a thermal equilibrium. Such a nanotube is about as long as a sheet of paper is thick.

quotation by Thomas Jefferson

Henry Tan — Fri, 23 Mar 2007 12:53:00 -0400

Dear Cetin:

The quotation by Thomas Jefferson was not on “American approach on getting things done”, but on his views of mathematics (he was enthusiastic about mathematics).

A complete quotation should be:

"…… Having to conduct my grandson through his course of mathematics, I have resumed that study with great avidity. It was ever my favorite one. We have no theories there, no uncertainties remain on the mind; all is demonstration and satisfaction."

nanoscale thermodynamics

Henry Tan — Thu, 22 Mar 2007 23:33:22 -0400

Many thanks to Sukumar for bringing Tsallis's non-extensive statistics into our attention.

As the size of systems becomes smaller to nanoscale, effects of ﬂuctuations and contributions from surface play more important roles.

I searched the literature, there are currently three approaches for nanoscale thermodyamics:

(1) generalizing the Boltzmann-Gibbs statistics as to take account of the non-extensive feature of such systems, e.g., Tsallis statistics (http://en.wikipedia.org/wiki/Tsallis_entropy);

(2) a modiﬁcation of the Boltzmann-Gibbs statistics by adding subdivision energy;

(3) non-equilibrium thermodynamics including work ﬂuctuations.

Boltzmann distribution

Henry Tan — Thu, 22 Mar 2007 21:36:47 -0400

In the derivation of the Boltzmann distribution for a small system, the system and the reservoir are in thermal contact, exchanging energy. All other modes of interactions between the system and the reservoir are blocked: no exchange of molecules, of volume, or anything else.

This block requirement works fine for macroscopic system.

However, for a nanoscale system the energy changes are associated with volume change which cannot be ignored as in macroscopic systems.

Therefore, the Boltzmann distribution needs to be modified to characterize nanoscale systems.

one has to learn at least three times

Henry Tan — Thu, 22 Mar 2007 17:00:49 -0400

Sommerfeld's words remind me of Zhigang's comment (http://imechanica.org/node/207):

"...... As many people say, thermodynamics is a subject that one has to learn at least three times."

propagation and scattering of high-frequency phonons

Henry Tan — Thu, 22 Mar 2007 16:27:30 -0400

Dear Cetin,

Thank you for the information.

I am learning the UIUC Physics Professor James P. Wolfe’s phonon-imaging technique, and will be benefited a lot from his book.

Laser excitation of a crystal produces a local source of thermal energy, composed of quantized lattice vibrations (phonons). Phonon imaging can be used to examine the propagation and scattering of high-frequency phonons in crystals.

Thermodynamics is a funny subject

Henry Tan — Thu, 22 Mar 2007 14:34:14 -0400

Arnold Sommerfeld, the theoretical physicist and teacher, once said, maybe even more than once, that:

"Thermodynamics is a funny subject.

The first time you go through the subject you don't understand it at all.

The second time you go through it, you think you do understand it, except for one or two small points.

The third time you go through it, you know you don't understand it, but by that time you are so used to the subject that it doesn't bother you any more."

I think I am in the stage of second time.

Statistical mechanics is a bridge

Henry Tan — Thu, 22 Mar 2007 12:01:19 -0400

Dear Zhigang,

Here I used continuum to mean macroscopic matter.

Although temperature and entropy can be defined for a small system (even for a single electron or a single atom), but in practice (applications) statistical mechanics is used as a bridge between the behavior of macroscopic matters and the laws of nature governing microscopic dynamics of their constituents.

Extensive vs. non-extensive entropy

N. Sukumar — Thu, 22 Mar 2007 00:17:23 -0400

I'll keep it short (lest I am off-the-mark). The additivity of entropy S = S1 + S2 assumes extensivity, whereas for systems that interact/exhibit long-range interactions (gravitational field is an example), the notion of entropy has been generalized to describe such non-extensive systems. Such entropic measures (Renyi, Tsallis and others are well-known) lead to non-extensivity, and the presence of an additional term (S = S1 + S2 + S1*S2*(1-q)). Tsallis statistics as it has come to be known is purported to be a generalization of Gibbs-Boltzmann statistics. Tsallis's entropic measure is non-extensive when q is not equal to 1 (q = 1 reduces to Shannon's measure). Tsallis entropy has received (for and against) much attention in the physics literature and also in areas outside it (networks, turbulence, finance, etc.) and it is used to describe many a complex systems (edge of chaos) that exhibit power-law distributions. An article that appeared in Science summarizes the gist of it all; Tsallis's original article appeared in 1988. So, instead of the Shannon entropy measure, use of Tsallis's non-extensive entropic measure in Jaynes's maximum-entropy formalism has been pursued.

thermodynamics of nanoscale small systems

Henry Tan — Thu, 15 Mar 2007 18:29:40 -0400

How to measure the temperature of a nanotube?