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Analytical Chemistry

Enhanced Diffusion: Real or Illusion?

Let’s think for a minute about what’s going on with tiny particles in solution, because we chemists spend an awful lot of time dealing with those. These particles vary in size from individual atoms all the way through small molecules, larger biomolecules and polymers, nanoscale engineered particles, micronized powders, etc., but the good news is that fluid and particle behavior is fairly well understood, up to a point.

You’ll want to know the Reynolds number (Re) for your fluid flow situation, which is the (dimensionless) ratio of inertial and viscous forces. Low Re means that viscous forces predominate, and you tend to have laminar flow (think of honey pouring out of a jar), but high-Re situations mean more turbulence, eddies, vortices, chaotic behavior, and so on. If the speed or viscosity of the fluid is changing across the system, then the Reynolds number can be used to predict where the onset of turbulence will be (although this will vary greatly depending on the geometry, such as flow through a tube, over a flat surface, around a spherical obstacle, etc.) That just-starting-into-turbulence regime, I should note, can be a real mathematical no-man’s-land. Getting further into flow will take you into the Navier-Stokes equations, which are simultaneously very useful and rather mysterious: it’s still unproven whether they necessarily have solutions in three dimensions and whether those solutions are mathematically smooth, and there’s a million dollars waiting for you if you can provide a solid answer.

Small particles in the kinds of solutions chemists care about tend to be low-Reynolds-number situations, which is good news. Edit: see this classic treatment of the situation. It’s an open question, though, if small molecules and biomolecules can or do propel themselves through these solutions under reaction conditions, and if so, how you could best prove that. You’d be most likely to see such effects as an increase in the diffusion coefficient, but such “enhanced diffusion” is controversial. It’s been reported, but I get the impression that on the theoretical side there are many competing models, and on the experimental side microscopy results can disagree with the spectroscopic ones, which can also disagree with each other.

There have been reports that Grubbs catalyst molecules display such enhanced diffusion in model systems, which wasn’t quite thought possible at such a small scale and at such low Reynolds numbers. A new paper, though, has a different opinion. The authors (from Univ. New South Wales-Sydney, Western Sydney Univ., and Univ. of Maine) believe that the whole thing is just convection currents in solution. Using a new time-resolved diffusion NMR method, they find a big discrepancy in the early stages of the reaction. The enhanced-diffusion proposal would have the largest effects on the diffusion coefficients at the very onset of the reaction, decreasing as the reaction proceeds. But this work finds that this effect starts off low and takes about 25 minutes to hit its peak, decreasing after that. And the apparent increase of the diffusion coefficient for the Grubbs catalyst species is probably an artifact from it being by far the largest molecular species in the system.

They show the same behavior for another reaction, this one Pd-catalyzed: the time scale is consistent with the development of convection currents. For the Grubbs-catalyzed reaction, this could be driven by the formation of the gaseous by-product, and for the Pd-catalyzed case, though an observed change in temperature. Indeed, the Pd-catalyzed reaction’s changes in diffusion coefficient disappeared entirely when the reaction was run in narrow 3mm NMR tubes rather than the standard-sized ones, which just shouldn’t happen if this were some intrinsic effect of molecular motion.

It looks, then, like the whole concept of “enhanced diffusion” in molecular systems is going to have to prove itself under more stringent conditions. It’s been reported in enzyme behavior as well, and the question is whether that’s real or also is explained by solution currents, instead. A recent paper has calculated that the observed amount of such enhanced diffusion doesn’t seem to make thermodynamic sense, and called for alternative explanations. Perhaps unaccounted-for convection currents are it?

17 comments on “Enhanced Diffusion: Real or Illusion?”

  1. Generics Novice says:

    Excellent read, but I have to give you extra kudos on that title. I can’t read that without the voice of a 1920’s showman popping into my head.

    1. Derek Lowe says:

      Yeah, that one just sort of came out when I started filling in the title line!

      1. John Wayne says:

        If you wave your hands around when saying, ‘real or illusion’ you change the mixing regime.

  2. MattF says:

    The classic lecture/reference on the behavior of fluids at small scales is Ed Purcell’s ‘Life at low Reynolds Number’.

    https://www2.gwu.edu/~phy21bio/Reading/Purcell_life_at_low_reynolds_number.pdf

    1. Derek Lowe says:

      Oh, you’re absolutely right – a classic, and I should have linked to it. Adding it now!

    2. 10 Fingers says:

      That was a total blast!

      Thanks for sharing.

  3. Mike Gilson says:

    Thanks for the shout-out!

    Possibly of interest.. Mudong and I have taken a broad look at the phenomenology of enhanced enzyme diffusion (EED) and proposed mechanisms for it here: https://arxiv.org/abs/1907.08909 (Ann Rev Biophys, in press). This review also looks at the cousin phenomenon of enzyme chemotaxis.

  4. Dave says:

    It *is* possible sometimes to “unmix” a fluid. See: https://www.youtube.com/watch?v=UpJ-kGII074

    1. Anonymous says:

      I remember the first time I saw that classroom demo. (1) My eyes were popping out of my head and (2) a huge smiling was spreading across my face. It was how I learned to stop thinking only like a fish and to think more like a microbe. I think that Howard Berg still does that demo in his seminars. (Does he travel with all that equipment or does he FedEx it ahead of time?)

    2. Anonymous Researcher snaw says:

      When I have posted that or similar videos on discussion threads, people have commented that it MUST be faked even when I assure them it’s been a standard classroom demo for decades (I first saw it at Purdue circa 1980).

      Practical note, if you build the apparatus yourself from the directions you can find online: the two most common choices of viscous fluid used are glycerin or corn syrup. Enough glycerin for the typical setup costs a fair bit so many people use corn syrup. Which works and is cheap, but you’d better include some preservative or your apparatus will soon turn into a microbiology demo because lots of bugs love sugar!

  5. haarp says:

    kudos as well for truncating the article at „goo“ on the main page.

  6. Simon Auclair says:

    John, is that hand wavium?

  7. metacelsus says:

    It’s been reported that sodium crocetinate can increase the rate of oxygen diffusion in water. See for example here: https://pubs.acs.org/doi/10.1021/ja981656j

    So, certain small molecules can alter diffusion coefficients.

  8. Nanochem says:

    Grubbs catalysts (or Pd ones) in NMR tubes spinning. Or those catalysts in flasks with magnetic bars stirring the solution (and those bars with different sizes and shapes, and different stirring speeds, …). I wonder if, in addition to other concerns, there is any mass transfer issue in the NMR experiments, especially with the 3 mm tubes.

  9. Ayusman Sen says:

    Several groups (https://doi.org/10.1021/acs.accounts.8b00288 and https://doi.org/10.1021/acs.accounts.8b00286) have shown that enzyme-attached particles also show enhanced diffusion in the presence of the substrate for the enzyme. These experiments were performed using optical microscopy and are free of the problems associated without other techniques.

  10. Enhanced diffusion of enzymes makes perfect sense from a theoretical viewpoint, as there are many mechanisms that can lead to such apparent behaviour in experimental observations. While some of these effects can be relatively simple (or trivial), others can be more subtle and non-trivial (see, e.g., https://pubs.acs.org/doi/10.1021/acs.accounts.8b00280, arXiv:1508.03219, arXiv:1611.02580, arXiv:1910.04526, arXiv:1911.02350). In the end, the question comes down to numbers, as each of these effects will have different parametric and scaling dependencies, so one needs to look into every single case where an observation is reported and try to estimate the contribution coming from every mechanism, to see which one might be the dominant player in each case. This has already been done for most reports of enhanced diffusion, with some exceptions still defying explanation. All in all, I think it is misleading to make a categorical statement about this phenomenon, no matter what that categorical statement is, as the observations can be due to many different reasons. I hope you find this comment helpful. I’ll be happy to clarify any point that might not be clear.

    1. Barry says:

      I, for one, find nothing in this comment helpful. Have you said anything?

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