Feel the pulse: fundamental facts

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  • Published: Nov 1, 2011
  • Author: David Bradley
  • Channels: NMR Knowledge Base
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Ergo ergodicity

Pulsed-field gradient nuclear magnetic resonance (PFG-NMR) spectroscopy and single molecule fluorescent spectroscopy have been used to probe a fundamental physical phenomenon - an ergodic experiment that reveals how a dynamic system gives the same mean result as would a single particle in repeated experiments.

The ergodic theorem posits that at a fundamental level, individual particles in a dynamic system follow the same rules of chaotic behaviour as does the multiparticle dynamic system as a whole. Put another way, one can extrapolate from the observed behaviour of a single particle in the system to the whole system. However, there is scant evidence for the ergodic theorem despite the wide-ranging implications if it were proven to hold true.

Now, a collaborative effort by chemist Christoph Bräuchle's team at LMU Munich and Jörg Kärger?s group at Leipzig University have used nuclear magnetic resonance spectroscopy to validate the ergodic theorem, bringing it one step closer to a full-blown theory of dynamic systems. They investigated the diffusive behaviour of an ensemble of particles and the trajectories taken by single molecules in the same system using fluorescent tracers and high-resolution imaging. Specifically, the LMU team tracked the individual molecules while the researchers in Leipzig studied the collective behaviour of the system as a whole. "It will be very interesting to take a closer look at systems that do not conform to the tenets of the ergodic theorem and to determine the reasons for their aberrant behaviour," says Bräuchle.

Diffusion usually refers to the random motion of particles due to their thermal energy and is, of course, a well-studied and well-known phenomenon that underpins countless physical observations in nature as well as playing a critical role through science, technology and industry. For chemists, diffusion is key to bringing reactants into close proximity so that they can react and the ergodic theorem is considered relevant in the dynamics of diffusive processes. In terms of diffusion, the theorem implies that repeated measurements of a given variable, such as distance covered by a particle in a given time, should be the same as average value obtained for a collection of particles, if the system is in equilibrium.

Superficiality

Superficially simple systems are never quite what they seem and as Kärger explains, although diffusion has been investigated for at least a century and a half, ergodicity and its relation to diffusion are not fully understood nor experimentally verified. The problem being, of course, that until very recently studying a single particle in isolation as opposed to multiparticle ensembles has not been possible. However, pulsed-field gradient nuclear magnetic resonance (PFG-NMR) spectroscopy, a technique for which Kärger's group is well known can obtain useful information about diffusive systems, while single-molecule spectroscopy and single-molecule microscopy can now follow the trajectories of single particles. Optical tracking allows the researchers to visualize molecules using fluorescence so that they can localise and monitor their positions with nanometre precision.

The final obstacle that lies in the path to understanding ergodicity, is that using these two approaches is almost mutually exclusive. NMR measurements need high concentrations of the molecules in question with large diffusion coefficients, while single-molecule spectroscopy works only with extremely dilute solutions of species with small diffusion coefficients. The team has found a way to circumvent this obstacle by using a specific organic dye with a high fluorescence yield in combination with porous silicate glasses containing networks of nanometric channels The dye molecules can diffuse through these channels so that the researchers were able to set up their experiments to be compatible with both methods and so they could perform single-molecule and ensemble measurements on the same system.

Ergodic observations

In the end, they discovered that the diffusion coefficients obtained using each technique agreed with each other. The first experimental confirmation of the ergodic theorem in this context. The team will next examine systems in which the theorem might not apply. "The diffusion of nanoparticles in cells looks like an interesting example," says Bräuchle, "and for us the important thing is to find out why the ergodic theorem doesn?t hold in this case."

 


The views represented in this article are solely those of the author and do not necessarily represent those of John Wiley and Sons, Ltd.

Pulsed-field gradient nuclear magnetic resonance (PFG-NMR) spectroscopy and single molecule fluorescent spectroscopy have been used to probe a fundamental physical phenomenon - an ergodic experiment that reveals how a dynamic system gives the same mean result as would a single particle in repeated experiments.
Ergodic diffusion paths

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