Hi Sneha Verma ,

I am not sure I understand the symbolic lines (of code?) you wrote above, and I never dealt with COMSOL before. I am also not sure what kind of computational/analytical method(s) you are using in these calculations.

But what I do know is that, depending on the characteristic wavelength or range of wavelengths in your system, dependent scattering effects (i.e., near-field and far-field effects) for two (very) close nanoparticles, as per your description, should be considered. That is, radiation extinction by one nanoparticle will be influenced by the presence of the other nanoparticle, and in that case, we can not simply "sum" the extinction cross-sections of the nanoparticles.

Also, I advise you to revise the conditions under which this "4 nm" interparticle separation distance was defined. If you do some simple calculations, you will see that in order to have a well-dispersed system of 10-nm nanoparticles with a separation of 4 nm, the particle concentration will be unrealistic.

Hello Omar Z. Sharaf ,

First of all thank-you very much for your immediate response,

But, Sir this is to inform you that I am using the Rf module in frequency domain to solve this problem and, also want to mention you that had already benchmark the results of single sphere including Au.

Additionally, according to your suggestion, I tried to change the separation distance between two spheres, but still the situation is same. I am still confused how to calculate the surface integral and volume integral of both spheres? and is there any possibility to calculate the surface integral and volume integral of both spheres separately and convolute it in order to avoid the radiation extinction by the nano spheres?

I am also attaching the screenshot to get a good picture of an idea.

Looking Forward for your response.

Thank you in advance.

Sneha Verma

Several points many of which may be useless:

• From van de Hulst, the avoidance of multiple scattering has to be when particles are separated by more than 3d (so 60 nm in your case). With 4 nm it will be difficult in the real world to get light in and out of the system
• In the 20 nm region, we're into Rayleigh scattering, so approximations will work as good as the more computer-intensive Mie theory. For a sphere, scattering is basically isotropic if we ignore the polarization dependence.
• The scattering from a peanut (representing 2 agglomerating particles has been discussed). See attached. Obviously in this case we have an orientation dependence of the particle to the impinging radiation
• I'd be modeling single particles on Philip Laven's MiePlot. Nice freeware. Not sure how this can help you, though, with 2 (or more) particles

Alan F Rawle

Really Appreciate your answer Sir.

Yeah. I have got little bit idea that this is not the realistic case as it would be very difficult to handle gold nano spheres with less separation distance while experiments..

1. But I still have doubt, Is there any thumb rule by which we can decide the separation distance of nanoparticle that will not influence the scattering of other particle.

2. Additionally, I did some simulation by putting the higher separation distance between the nano spheres but sadly to say, I am not able to calculate the commutative scattering Parameters.

3. There is one paper published recently and in that article they calculated the same with 10nm separation distance.

Kindly have a look of this article.

Thank you in advance.

Sneha Verma

Re: Point 1. Van de Hulst's 3 diameters is a 'rule of thumb' for multiple scattering.

Thank you for attaching the interesting paper.