Dear Parva Chhantyal

Interaction between the light and particles can be precisely described by Maxwell equations. In this description light is treated as electromagnetic wave. Base on these equations Gustav Mie has presented a complete solution and described how to calculate light energy scattered by a sphere. When I was working on light scattering I have made a program calculating light energy around the sphere. You can download it and use it freely. It is based on Mie theory and I have employed reverse recurrence in the calculations. Results were compared with other solutions and revealed very good accuracy. You can download it from our webpage:

http://www.biomedlab.ichip.pw.edu.pl/content/view/33/8/lang,english/

Tomek

Hi parva, the explanation from the paper correct about the shifting absorbance vis particle size. the phenomena occurred by the quantum confinement effect. so you can read and search about the quantum confinement effect which make your concept clearly.

good luck

I am confused - when you say, "small particles have narrow peak and big particles have broad," are you talking about your own personal data? Because the paper seems to show the opposite. Figure 1 shows that the unannealed sample (smallest particle size) has the broadest peak, the sample annealed at 200 C (intermediate particle size) has a less-broad peak, and the sample annealed at 400 C (largest particle size) has the narrowest peak. This trend holds for both Au and Ag.

As for the peak shift, you say, "when the particle size increases, absorbance vs wavelength curve shifts to right (red shift) and vice-versa (blue shift)." This theory is only for quantum-confined excitons, i.e., excitons whose effective Bohr radius (the average distance between electron and hole) is greater than, or on the same order as, the particle size in which the exciton is confined. Because metals are highly conductive, the effective exciton Bohr radius is essentially zero, so they will not display quantum confinement effects. It is typically only in semiconductors that quantum confinement comes into play - because in semiconductors the exciton Bohr radius is on the order of ~5 nm. See the Wikipedia page on quantum dots for more information.

Plasmonics is not my research area, but my speculation would be that the surface curvature has an effect on the "rigidity" of the plasmon resonance, causing the observed energy shift. With a very low surface curvature (large particle size) the surface plasmon becomes "stiffer" because the orbitals are overlapping to a greater degree (they are closer together,) resulting in a higher-energy resonance (and therefore the observed blue-shift for larger particles.) With a high surface curvature (small particle size) the surface plasmon becomes "looser" because the orbitals have more "elbow room" (they are slightly farther apart,) resulting in a lower-energy resonance (and therefore the observed red-shift for smaller particles.) By the same intuition, if you take a straight spring and perturb it, the wave will propagate at a given speed (with the velocity corresponding to the energy.) If you bend that spring so it is curved rather than straight and perturb it, the wave will propagate at a slower speed (because bending the spring has caused it to become somewhat less stiff.) This is just my intuition.

Muneer, why would you expect quantum confinement to play a role when we're dealing with metallic nanoparticles (especially of such large size, d > 10 nm)? Quantum confinement is typically observed in semiconductors, not metals.

Dear Parva Chhantyal

Interaction between the light and particles can be precisely described by Maxwell equations. In this description light is treated as electromagnetic wave. Base on these equations Gustav Mie has presented a complete solution and described how to calculate light energy scattered by a sphere. When I was working on light scattering I have made a program calculating light energy around the sphere. You can download it and use it freely. It is based on Mie theory and I have employed reverse recurrence in the calculations. Results were compared with other solutions and revealed very good accuracy. You can download it from our webpage:

http://www.biomedlab.ichip.pw.edu.pl/content/view/33/8/lang,english/

Tomek

Many of your doubts will be clear read this article http://www.ucl.ac.uk/~ucaptt0/Thanh%20Anal%20Chem%20on%20size%20of%20Au.pdf

or

http://pubs.acs.org/doi/abs/10.1021/ac0702084

Determination of Size and Concentration of Gold Nanoparticles from

UV/vis Spectra

The doubt raised by you is interesting and quite natural, for Gold nanoparticles when the particle size are small (5-10 nm) the absorbance we get is around 520 nm wheras after some time or after coalescence it shown red shift, the article link above shows red shift corelation with particle diameter of gold.

I'd say, you confuse the dependence of attenuance (absorption + scattering) on particle size, which applies for any particles in general be it dielectrics, semiconductors, or metals with absorption due to surface plasmon resonance, which is specific for metallic nanostructures. In the former case, decreasing the particle size leads to the blue-shift. In the latter one - to the red-shift, but there is no inconsistency here, as we deal we different physical phenomena. The red-shift is explained by the increase of damping constant of electrons. You can read the discussion here:

http://iopscience.iop.org/0957-4484/19/7/075710/

For any particles not exhibiting surface plasmons, this process is simply irrelevant and cannot cause any change in the spectra. At the same time, the blue-shift of scatterance is rather universal for nanoparticles made of any material.

Wavelength of absorbance depends on particle size

it is true with increase in particle size it will red shift. But broadness and narrow peak depends upon monodispersity in size as well as shape.

If your sample is polydisperse let us say spheres of 50 nm +(-) 40 nm. you will get broad peak.

If You have dispersion like 50 nm+(-)10 nm. You will get narrow peak. Same apply for if you have multiple shape.

Unfortunately, term absorbance often is used interchangeably for extinction. Usually extinction is measured including loss due to scattering and absorbance. The dependence described as function of particle size (blue shift for smaller particles) is related to scattering not to absorption. For strongly absorbing particles of carbon black the contribution of absorption is also higher for very small particles.

Thank you everyone for the answers. I really appreciate it. I came across one article recently (attached here). I think this explains it quite well though I found some flaw in there (May be but correct me if I am wrong). For eg. In the first paragraph of the section 2.2, they said ''The maximum of the plasmon absorption clearly blue-shifts with decreasing gold mole fraction'' whereas in Figure 3, they have shown the red-shift with decreasing mole fraction. I am also bit confused with their Part (c) of Figure 3. I think the x-axis should be wavelength but not particle diameter?

@Mark Schwab- No, I am not talking about my data but the general theory of UV-absorption spectra with respect to particle diameter as shown and explained in Figure 1 of the attached article here.

http://pubs.acs.org/doi/abs/10.1021/jp9917648