If it’s a powder it’s a laser diffraction experiment not DLS. No nanosized particles in a powder.

Dear Prof. Alan,

Mighty thanks for your interest.

Material is carbon nanotubes which have some alumina particles after ball milling process. Do you think diffraction method would be more practical?

Yes.

X-ray diffraction can help but remember it does not provide the particle size. It can give you the size distribution of the coherently scattering domains with an upper limit of the order of 100 nm. You can follow the milling using diffraction (either in batch mode or in situ) and see if it is effective. Your alumina is a contaminant though, so better to use something else for the milling, that you can leach more easily (alumina is one of the most stable compounds that we have)

Dear Leoni,

Mighty thanks for your time and detailed answe.🙏🏻

Hi Amin,

In answer to the more general part of your question, DLS can be used to resolve multiple components in mixture, however it is a relatively low resolution technique compared to some other measurements. Difference in scattering intensity between different size components can also mean that results are skewed or one component may be masked.

Here is an application note on resolving mixtures using DLS wit the Zetasizer Nano

https://www.malvernpanalytical.com/en/learn/knowledge-center/application-notes/AN101104ResolvingParticleSize.html

As Alan has said, if you material is a powder then it is probably best characterised by laser diffraction than by DLS, however if you want a qualitative measure of the how your material has changed during your process, then DLS may still be able to help.

Here is an app note discussing monitoring of a milling process using DLS.

https://www.malvernpanalytical.com/en/learn/knowledge-center/application-notes/AN101104MonitoringPigmentMilling.html

Dear Alexander,

Really appreciate your interest towards this issue and replying the proposed question.

🙏🏻

Amin Khajeh

Issue with any top down technique is that no matter what the constitution of the milling balls is, they'll contaminate the product. Same with sonication - easy to show by sonicating 18 MOhmcm-1 water where the conductivity will increase to 10 - 11 MOhmcm-1 in a matter of minutes as the tip probe is slowly dissolved with cavitation.

In order to watch the progress of your ball mill then laser diffraction is the only viable route. Have a look at the recent 're-do':

https://www.malvernpanalytical.com/en/learn/events-and-training/webinars/W190528DispNanoMat.html

Look at things like comminution limit and limit of (dry) ball milling.

In answer to your removal question, warm (50 C - take extreme care; plastic not glass as the latter is dissolved in this manner) caustic soda (say 50%) at high pH's (> 12) will dissolve alumina as the latter is amphoteric. I don't think carbon is dissolved in this manner. You'd need a lot of washing with DI water to remove traces of alkali after the processing.

Bear in mind two things that will make it difficult to interpret your data (!):

1. Scattering intensity varies as the fourth powder [CORRECTION: sixth power] of the particle diameter for a given material. It also scales with the refractive index difference between the particles and the liquid. I suspect the alumina will scatter much more strongly than the CNTs so unless you have very high percentages of the CNTs, you may not see them.

2. WIth laser diffraction, you have to provide good estimates of a variety of optical properties of the sample. As far as I know there aren't any commercial instruments that can deal correctly with heterogenous systems.

You may be able to see differences in DLS and LD when the ratio of the alumina and CNTs changes (or their size) but interpretation will be prone to a lot of assumptions. However, the information could still be useful if you are trying to control a process and you have already identified the ratios (or whatever measure you choose) as critical quality attributes.

You need to ask yourself what are you going to do with the results? What decision(s) will the results help you to make.

Dear Prof. Miller,

I really appreciate for devoting your time and energy on this case. With you reply, you educated me while answered my question perfectly.

🙏🏻

Dear Prof. Alan,

I wanted to let you know how much I appreciated your prompt help with this case project.

John Francis Miller

Hi John

Not sure where you're coming from on this, but my understanding always was that in the Mie (interpreted - it covers all sizes, polarizations, RRI's etc) region equal volumes scatter with equal intensities i.e. proportional to the third power or volume. This is logical as light traverses a volume of space and particle). In the Rayleigh region (lambda/10 > x) then it's a volume squared or r6 dependence. In the geometric optics region (Fraunhofer) it's effectively the projected area or a d2 dependence.

The scattering also depends on the optical contrast which is the ratio of the particle's RI to that of the continuous phase surrounding it (not a difference).

If you know the proportions of components (and one can ignore anything < 10 volume %) then Gladstone-Dale will allow a calculation of the effective RI (weighted volumes of components). I suspect in the poster's case it's virtually all CNT's with some alumina contamination. The big issue here is what dimension is measured with CNT's as there is a dependence of the orientation of the 'tube' to the incident radiation. Ideally one would want them to flow align in a wet stream but we still have an interpretation of 'equivalent scattering' to make. The z-axis of the CNT will be the effective RI if the tubes truly flow align - I suspect that they won't - it'll be like trying to flow spaghetti down a tube.

DLS is a much lower resolution technique than laser diffraction because of the limited information that's collected (effectively the correlogram interpreted as an exponential decay). If we have angular dependence of scattering we have much more information to process with laser diffraction.

Alan F Rawle Yes, not sure why I said fourth and not sixth. I agree that Mie theory can fully describe any distribution. I'm not sure if either Watson or Deep Thought could find the "right" solution from experimental data (my money would be on Deep Thought). It's that pesky infinite number of solutions issue.

John Francis Miller Thanks for the clarification. T-matrix (mainly after Michael Mishchenko; a really nice guy) and DDA (Discrete Dipole Approximation) are 2 of the more modern routes for predicting the scattering from irregular objects. They're both grounded in Mie theory. One big use in the last 15 years or so is the ability to predict (and interpret) both the size and shape of ice crystals in the upper atmosphere (done by the people at Bracknell in the UK; an MOD establishment). I presented at the 2008 ELS XI conference in the UK and already there 400000 elements had been used in DDA - and now I'm 11 years out of date! One paper I like from there is attached. The Bracknell work was also highlighted at that conference in an excellent paper and they have an enormously powerful computer there.

As you state, the ill-conditioned nature of the inverse problem is the real issue. Take a look at this for entertainment:

The life of Gustav Mie and the development of the Lorenz-Mie solution to Maxwell’s equations http://tinyurl.com/mt97tp3

Alan F Rawle Very interesting! I wonder, is the moon used as the incident light source. There must be a tremendous amount of information to be had from the halo we see especially on cold nights.

John Francis Miller Yes, simple Fraunhofer allows us to estimate the ice crystals in the halo around the moon at around 32 microns diameter. See Slide 33 in:

Ashes to ashes, dust to dust: what it means to Mie

https://www.brainshark.com/malvern/vu?pi=714445203&text=M021507&r3f1=

BTW, my comment in slide 28 first bullet point is incorrect.

And slides 46 onward in:

How to measure particle size distribution

https://www.brainshark.com/malvern/vu?pi=zG2zBLMdoz5chz0&nodesktopflash=1

John Francis Miller You were probably thinking 4th power as in the Rayleigh region the scattering intensity is proportional to 1/lambda4 and onto all the blue sky/red sky stuff.

Perhaps your system will be micelles, or micelles with nanoparticles. Take a look and get acquainted with the problems that accompany research through DLS.

Article Structure of Micelles of Sodium Dodecyl Sulphate in Water: a...

Yuri Mirgorod The poster states that there are 2 powders. Thus, not a DLS application.