Stirring is a very general word, like “dispersion”... By simple laboratory mixer You can improve macroscopic dispersion of nanoparticles in the laboratory vessel, but You will not get below Kolmogorov size scale, fare above nanoparticle size. This is usually a limes inferior of normal “mixing”. But in Your case DNA is a long molecule, above Kolmogorov size. I think that nanoparticles attach to DNA by diffusion (despite mixing), and dispersion of DNA in the solution can be improved by mixing.

Once we had a problem how to improve interaction between immobilized antibody and small protein. We have applied electrophoresis with an AC electric field, so small charged object move back and forth, while immobilized or large (DNA) will not move. This increase probability of collision and interaction.

"stirring" not only is necessary, it is essential. Colloid science actually still lacks a complete fundamental understanding of how colloidal dispersions are formed. For polymer matrix based colloids, I have delivered a (relatively complete) non-equilibrium thermodynamical theory of how these are formed and what structures are built then (based on a whole lot of experimental data, you can find in my RG pages).

In these systems, we need to go beyon a critical shear rate (which I have determined) otherwise no dispersion happens.

My understanding of low viscosity colloidal systems is similar, but I have not attempted to draft a complete theory for this: you need turbulence in your colloidal systems, otherwise nothing happens.

You can not wait for diffusion to do the job, diffusion is a process leading to equilibrium, but any colloidal system is only available in non-equilibrium state. Hence, if you want to change anything (like improve dispersion, or adsorb something else on some nanoparticle surface like you said: DNA on Au particles), you have to exchange one interfacial combination against another one, A-B against A-C, that requires work to be put into the systems (you have to overcome interfacial adhesion forces first), and this is usual done by turbulent flow.

The problem as I see it, is, that most people do not characterize their stirring, and just "somehow" stirr. Too much not really exact science ongoing in this field ...

Interesting responses, so far. By stirring I mean agitation by a magnetic stirrer bar, not any form of high energy fluid processing. By dispersion, I mean here that the nanoparticles do not precipitate, even after a very long time, and that the liquid is completely clear, with a particle size between 5 and 40 nm. Once I have made a homogeneous mixture, for example, of antibodies and gold nanoparticles, I cannot see how further stirring can have an effect on mass transport on the size scale of the reactants. The portions of liquid that are moved about relative to each other are much larger that the particles, so that the individual particles will not "feel" the stirring. Am I not right? I would like to encourage a discussion. I do not think that this is as trivial as it seems.

yes, I understood well that you meant stirring with a magnetic bar. Nevertheless: this is turbulent flow, not laminar. Turbulent flow is clearly, without any doubt, a non-equilibrium process, laminar flow is equilibrium.

Turbulence has an extremely wide range (small or high or infinite Reynold's number), while stirring with a magnetic bar, you easily generate a vortex - a typical turbulence phenomenon, and that helps you creating or improving the dispersion.

Please do not ask me when or under which stirring energy input your system could already be ok, I have no idea about the specific system you are looking at.

you are right, this is by far not trivial at all, turbulence science is extremely complicated (I am not an expert in it), dispersion / colloidal science and non-equilibrium is extremely complicated, I know a little bit about that.

You wrote: "The portions of liquid that are moved about relative to each other are much larger that the particles, so that the individual particles will not "feel" the stirring. Am I not right?"

- sorry, you are wrong. "turbulence" means that you create a macroscopically visible vortex, but that one dissipates into smaller and smaller vortices, finally down to the micro and nanoscale, depending on the energy (shear rate / turbulence) you had put in.

- I can not tell you how small the vortices are which you create and which are already ok, or not yet sufficient, but that is the principle behind dispersion.

In other words: if no vortices, no dispersion

Mathias, Bernhard, Mixing phenomena has been described by Kolmogorov many years ago (1941), Please read (with references):

http://en.wikipedia.org/wiki/Turbulence

Tomek

this is known, but "mixing" anbd "dispersion" (= preparation of colloidal systems) are not the same, and at least as far as I know, there is no theoretical description of dispersion involving turbulence (except for what i had published for polymer systems). It would be highly interesting for me to get to know anything in that direction which I might have overlooked so far.

Hello, I'm not sure if I get it right, but I believe that different matters are being discussed at the same time... When you want to graft a molecule on a preexisting nanoparticle, the process taking place (and thus the necessary optimal conditions) are not the same as when you want to grow nanoparticles from a metal salt solution. However, since I always do my syntheses by coprecipitation and I'm not familiar with the seeded growth of gold nanostars, I looked it up (for example in doi:10.1021/jp312149d) and I believe I understand that at some stage there is actually some stirring. I think it really depends on what you need, i.e. for grafting I'd rather be stirring so that the solution is homogeneous (= no concentration gradients), the particles are well suspended and the ligands have access to their entire surface. For seeded growth, I'm not sure, but maybe in some cases it could proceed more smoothly if the solution is still and the ions are allowed to gather around the seed to form the particles? Anyway, as Mr. Wessling put it, there is much we don't know about colloidal dispersion, but I'd like to add that we do know that the stability of lyophobic colloids is of kinetic origin, and stirring is one of the most common ways to input energy in a system... so I guess we should not be surprised by the fact that most dispersion protocols do involve stirring! When you prepare micelles or liquid crystals, which are thermodynamically stable systems, you can let them work their way to the final nanostructure on their own, even if it may take quite a long time if the system's viscosity is high... but dispersions are totally another matter altogether... Anyway thank you for this chance to discuss this matter, it is interesting and not trivial indeed!

thanks, this is why for creating dispersions (or dispersed nanoparticles) with hard-to-disperse materials, one needs higher shear rate / stronger turbulence.

Dr. Baumert an myself have recently submitted our new (parameter-free) theory of turbulence in shear-thickening dispersions / emulsions for publication in Physica Scripta, a (shorter) paper was recently published in preparation of a conference in Prag:

https://www.researchgate.net/publication/290789681_Turbulent_mixing_in_non-Newtonian_dispersions

This one applies to already finished dispersions / emulsions.

A (semi-empirical) theory for the dispersion *process* itself can be found here:

https://www.researchgate.net/publication/290789681_Turbulent_mixing_in_non-Newtonian_dispersions

Conference Paper Turbulent Mixing in Non-Newtonian Dispersions

@Sanjeev: Turbulence really begins with a macroscipic instability or vortex, as Bernhard mentioned earlier; but the primary vortex (family) does not "dissipate into smaller and smaller eddies". The funny thing observed already early (and underpinned by a mechanistic model by Hans Herrmann) is that this cascade is actually almost free of friction and the dissipation of the mech energy happens only at the very last stage of the cascade, at the very smallest (Kolmogorov) scale. I.e. in between, the cascade is like a magic clockwork with a minimum of friction. If you wish, that part of the cascade may be related with Prigogine's principle of minimum entropy production (1946?) valid for linear (generalized) force-flux relations.

Thanks for the interesting discussion!

Just re-reading this old discussion I started some time ago. It is true, there is a little misunderstanding. I am not asking if I have to stir to cause the dispersion of particles. They are already in a dispersion and have no tendency to flocculate, aggregate or precipitate. This is typical for many dispersions of gold nanoparticles. Some people even refer to them as solutions, which is probably not correct. I want to react the surface of these particles with a molecule in solution. Lets not insist on DNA but it is usually a larger molecule, say an antibody, BSA or a dendrimer. I still believe that the stirring by a normal stirrer bar does not improve mass transport on the length scale of the reactants. The mixture is completely homogeneous to begin with. By diffusion and surface reaction it is not likely to become heterogeneous on a scale addressed by a stirrer bar. I am still happy to learn that I am wrong.