 Welcome back to this course on nanostructured materials. We are in the module 4 and we are discussing optical properties of nanomaterials. This is the lecture number 10 of module 4 and we have 12 lectures in total in this module. This is going to be the second lecture on optical properties of nanostructured materials. So, in the previous lecture on optical properties, we discussed some of the basics of what happens when a particle size decreases, what happens to its optical properties, what happens to its color and why those changes in color take place. Specifically, we discussed about the nature of bonds and the nature of bands and the different discrete levels, which can be incorporated within the energy gap by impurities, which can cause different low energy absorptions, which can cause two photon absorption and emission. Then, the change in the shape of the density of states versus energy plots, how you can continuously change the density of states and energy in a bulk solid, which you cannot in say a nano well or a nano wire or a nano dot that is a quantum dot. So, what happens when you change a bulk particle to a nano sized particle and how it changes with the dimensionality, whether you lower the dimension to nano size along only one dimension or two dimension or all three dimensions will give rise to different changes in the density of states versus energy. That will bring rise to changes in the absorption of energy and the excitation of an electron from a valence band to a conduction band and what are the different types of properties, which you can expect in a semiconductor like cadmium selenide, which we saw how it gave different types of colors in colloidal solutions of cadmium selenide having the same material, but having different sized particles. That was one example, then we looked at different other types of optical transitions, the fluorescence and phosphorescence in these systems and what happens when the size decreases to the nano dimension. So, let us continue on that and on the second lecture. So, in semiconductors you have a conduction band and you have a valence band as discussed earlier and you have an energy gap and when you make a small sized semiconductor particles, then you have more discretized energy levels instead of a band, where you have a continuum of available energy states. Now, you have discrete energy states of course, the band gap is there and the band gap is enhanced this is much larger than the band gap in a bulk semiconductor. So, the band gap also increases along with discretization of the energy states. So, this effect is also called quantum confinement because we are confining the electrons and because the energy gap is becoming higher and electron cannot be excited easily unless you give higher energy. So, increase in the band gap and confinement appears for particles with around 10,000 atoms and that may be the size of like 0.5 nanometer particle when compared to a bulk particle which is around 1 micron. Now, when you have an electron which moves from the ground state which is the valence band to the excited state which is the conduction band. So, you have a hole left behind and that hole is positively charged because it is the absence of the electron which went into the conduction band. Now, this pair of electron and hole together because in this semiconductor now you have an electron in the conduction band and a hole in the valence band together these two particles will be called an electron hole pair and it is also called as an exciton. So, what is an exciton? An exciton is a electron and hole pair and that has been created because the particle has absorbed energy which has been given and that energy is larger than the band gap and so an electron is excited and it leaves behind a hole in the valence band and together the electron and hole pair is called an exciton. So, this is the basics of absorption of radiation creating excitons. Now, what we discussed earlier also what happens as the size decreases? As the size decreases the band gap changes. So, we can tune the band gap it is called the tunable band gap in semiconductors and this has been plotted for several semiconductors and for bulk silicon for example, you have a value of 1.14 electron volts and for bulk gallium arsenide you have a value of 1.5 electron volt. Now, these values can change depending on the size of the nanoparticle. So, here you have some quantum dot which has a band gap of around 5 electron volts when it is very small around say 10 angstroms or 0.1 nanometer and when it is like 30 angstroms. So, 30 angstroms 1 angstrom is like 0.1 nanometer. So, 30 angstrom is like 3 nanometers. So, if you do this study then you can see the band gap varying from 5 e v to around 2 e v when you are changing the size of the quantum dot. The diameter of the quantum dot is changing from say 1 nanometer because 10 angstroms is 1 nanometer and this is in angstroms. So, 1 nanometer particle has a band gap of 5 electron volts and 3 nanometer particle has a band gap of around 2. So, you can vary a considerable amount say around 3 electron volts in this particular semiconductor where by just varying the size or the diameter of the particle. Now, this change in the diameter and the band gap reflects it in its colors. So, if you plot the optical density with energy for particles of the same kind. So, you have cadmium selenide particles these are quantum dots and these are having different diameter. So, you have 21 angstrom. So, it has an absorption at around 2.6 electron volts. When you go to higher particle size say 40 angstroms which is 4 nanometers your band gap is now close to 2.01 or 2.02 electron volts. So, from 2.02 electron volts at 4 nanometers which is a larger particle if you decrease the size of the particle to around 21 nanometer the band gap has increased to around 2.56 electron volts and this shift in the band gap can show the variation in colors. So, a large particle will have a smaller band gap and will have a color which is towards the red if it absorbs and this shift to higher energy in as the size of the particle become smaller you are shifting to a higher energy this is typical of size effects quantum size effects. And also it shows you the discrete structure of the spectra in addition you also see that the intensity of the absorption. So, it becomes more intense more sharp and more intense as the size of the particle is decreasing. So, if when it is 21 angstrom is much sharper and when it is 40 angstroms it is little broader. So, not only the wavelength or the energy shifting but the intensity also changes as you change the size of the quantum dots or the size of the semiconductor and this can be cadmium selenide it can be studied in other quantum dots as well. Now, this so far we were looking at semiconductors which have a valence band and which have a conduction band and there is a band gap and you are changing the band gap of the semiconductor by changing the size of the particle. So, that is about semiconductors in metals what happens because in metals you do not have a band gap. So, the color of a metal nanoparticle normal bulk metals are normally black in color or very shiny and but when you make nano sized metal particles colloidal solutions you will see colored solutions even for metal particles. So, but the absorption phenomena is not the same as in semiconducting nanoparticles because metals do not have a band gap whereas, semiconductors have a band gap. So, what is this color in metals due to? So, if you look at metal nanoparticles there is this property of surface plus bond resonance which occurs especially if your nanoparticles are metals. So, in this what happens when if you apply an electromagnetic field the electromagnetic field is like a light is also electromagnetic field. So, whenever you shine light there is electromagnetic field and if that nanometer size particle the size is smaller than the wavelength of the light which you are passing. In that case there can be a oscillation of the conduction electrons because in metals you have conduction electrons the electrons are present in the conduction band. So, these electrons can have coherent oscillation if the size of the particle is much smaller than the wavelength of the light which you are passing. So, if the wavelength of the electromagnetic radiation which we is light here is much smaller than the size of the metal particle then the conduction electrons of the metal particle can oscillate coherently that means in phase with the conduction band electrons and this is basically due to the interaction with the electromagnetic field and this is called surface plasmon resonance plasmon is basically quantized oscillations of conducting electrons of the conduction band. So, all the metals will have conduction electrons and they if they oscillate as light falls on it then you will have surface plasmon resonance. So, this is the schematics where you have this metal particle and this is the electric field and this shows the oscillations and this electron cloud. So, this electron cloud can oscillate along with the electromagnetic radiation which is light if the particle size is much smaller than the wavelength of the incoming light beam. So, a wavelength of the incoming light beam is of this length because you have one crest and one trough makes the wavelength and you see the particle is much smaller than the wavelength of the light coming. Suppose the particle had been this big and this is the wavelength then you will not see this surface plasmon resonance. So, this you can see when the size of the particle is much smaller than the wavelength of the light and then you will see these oscillations of the conduction band electrons and that is called the plasmon. Now, when you have that when you have this kind of particle which you consider as a dipole. So, you can have in a dipole positive and negative arrangement creating a net dipole moment if there is a shift in the electron density then you can write the equation for the dipole moment as a function of the dielectric constants and the applied electric field. So, if the metal cluster is placed in an electric field because electromagnetic radiation or light is associated with the oscillating electric field it also has oscillating magnetic field, but light has a oscillating electric field. So, that means whenever you have light you have an electric field and the metal particles are now in the electric field. So, the negative charges will be displaced from the positive ones in the presence of a electromagnetic field and then you can write this equation where this is a electric polarizability if this whole quantity where epsilon is the dielectric constant of the particle and epsilon m is the dielectric constant of the medium. So, and E naught is the applied electric field from the electromagnetic radiation. So, if this entire term is the electric polarizability alpha then you can write alpha is equal to this and then you see in the denominator if you want to make alpha very large then you need this to be very small. Now, this can be very small or you can make this whole thing go to infinity when this goes to 0. Now, here this will go to 0 when epsilon plus 2 epsilon m becomes equal to 0 and that can happen only when epsilon is equal to negative of 2 twice of the epsilon of the medium. So, that is what is written in a different way that if the magnitude of this term which is in the denominator becomes a minimum then this will become very high. So, you want to know when alpha will be high that is when will the electric polarizability be very high if this is high then this will be high. So, now so there are two things one is the electric the dielectric constant of the particle and the dielectric constant of the medium and these two have to be taken into consideration and depending on their numbers you can find out when this will become a huge value and that is when we call surface plus 1 resonance to occur or S P R to occur when this value will become a very high and that will happen. So, you will have surface plus 1 resonance when epsilon prime becomes equal to negative of 2 epsilon m that is because of this equation that this is in the denominator and you want to make this whole term very large. So, that will happen only when epsilon plus 2 twice epsilon m becomes equal to 0 and this epsilon of the nano material is can be written as the epsilon 1 and epsilon 2 with the epsilon 1 is the real part and epsilon 2 is the imaginary part of the complex dielectric constant of the metal. So, similarly you can write the dielectric constant of the medium in which you have this metal particles embedded. So, what you basically want is this equation that is the real part of the dielectric constant of the metal should be equal to negative of twice of the dielectric constant of the medium and then you will have a resonance of the oscillating electrons. So, these is the oscillating electron cloud. So, it is up there and down there and that will oscillate such that there will be a resonance between the incident light wave or the optical beam and that can happen exactly when this value matches. So, this is the criteria for surface plus 1 resonance to occur and that depends on the dielectric constant of the metal and the dielectric constant of the medium in which the metal has been impregnated or supported and or the medium through which the light is being passed. Now, according to the Drude model we can rewrite the real part of the dielectric constant and the imaginary part of the dielectric constant using these equations where we incorporate the dielectric constant at infinite or very high frequency and we incorporate the plasma frequency omega p and there is a dielectric relaxation frequency omega d and. So, using these equations you know the relation between the real part of the dielectric constant to the plasma frequency. Similarly, the complex part of the plasma of the dielectric constant can be written in terms of the plasma frequency and the relaxation of the damping frequency. Now, you can ultimately find out that the plasma frequency of the metal is related to the density, the number density of the electrons, the velocity of the electrons at the Fermi energy and the mean free path of the conduction electrons. So, the plasma frequency you can kind of understand if you know the mean free path of the conduction electrons and the velocity of the electrons at the Fermi energy which is called V f. If you know that then you can determine the omega p which is the plasma frequency and that is related to these numbers here. So, here this is the various constants are there the electronic charge, the mass and the dielectric constant dielectric permittivity of free space. So, if you know the plasma frequency of course, you know the plasma energy from that one can find out what kind of particles will show what kind of plasma frequency or plasma energy and from that you can find out if the plasma frequency or energy is lying in the visible region or not. If it lies in the visible region then due to this surface plasma resonance you will see a color if it does not lie in the visible region you will not see the color. So, if you look at that the if you calculate the plasma frequency of different metals and with different sizes then you can calculate you can see which one will be red in color which one will be blue in color etcetera. So, in this chart you can see that if the plasma on energy goes from say 3.5 electron volts there to around 0.5 electron volts you scan the region from ultraviolet to the infrared and here different particles with different morphology have been have do show different colors which has been represented here for example, if you have silver nanospheres. So, if you make silver particles of a particular size then you will be having a color which is in around blue in color, but it may also have green color depending on the size of the nanoparticles. So, there is a broad range of plasma on energies for silver nanospheres from starting from around 410, 420 nanometers to around approximately 580 nanometers. So, it is a big energy region that means with silver nanospheres you can get different energies from the green to the violet by changing just the size of the nanospheres of silver. However, if you have gold shows much more variety and much more range. So, if you have gold nanospheres you can vary the plasma on energy and the color associated with that plasma on energy from say 600 nanometers to something around 780, 760 nanometers just by changing the diameter of the gold nanospheres you can get all these colors from the yellow orange to the red using gold nanospheres, but you cannot get blue color with gold nanospheres as shown using surface plasma on. If you have a structure which is not a sphere, but made of gold and it is in the form of nano shells. So, it is like a strip of gold particles in a circular fashion with a certain thickness without any thing filled inside. So, that is like a nano shell or a nano egg if you can make it can vary from 600 nanometers to 9000 nanometers is a very large range. So, changing the shell thickness and changing the diameter of the nano shell you can have all kinds of colors from green, yellow, red, brown and even colorless those particles which have a plasma on energy in the mid infrared say 3000 nanometers. You are already in the infrared very large wavelength very small energy you can get colorless particles of gold. So, you can not only get brown color red color you can get colorless particles of gold as shown in the figure. Then you can get using nano rods you can get from nearly bluish in color to up till brown color with nano triangles gold can be also made in triangular form not only as a disk not only as a sphere not only as a nano rod gold can also be made as a triangle. So, these triangles are very useful because see where they absorb these triangles can absorb in the infrared mid infrared whenever you can have anything absorb in the infrared that means you can heat that material. So, if you have gold nano triangles in your body say you inject gold nano triangle somewhere people have shown how then it will heat up the cells around it. So, this is using near IR or mid IR energy which gets absorbed by this nano triangles of gold it can heat the surroundings by picking up energy. So, range of energies are possible for the same material if you change the dimensions or you change the shape you can get a large range of energies using the SPR band. So, this is a very particular for metal nanoparticles this is not for semiconductor nanoparticles this is for metal nanoparticles for semiconductor nanoparticles of course you can change color, but then you have to worry not about surface plasmon, but you have to worry about the band gap and how what is the band width how discrete are the levels etcetera. So, that is for semiconductor nanoparticles and this is for metal nanoparticles where the color can come from the surface plasmon resonance. Now, this plasma oscillation is basically a fluctuation of the free electrons the density fluctuation of the free electrons or free electrons means those electrons which are in the conduction band. In the conduction band the electrons are not held to the core tightly and so the electrons are supposed to be free to move. So, they may be called as free electrons in metals many times we use the term free electrons basically they are electrons in the conduction band and they can supposedly move around. That means, delocalized over all the different atoms in the cluster or in the nanoparticle. So, if you have a fluctuation density fluctuation of free electrons which are present in a metallic solid then you can have what is called the plasma oscillation. So, the plasmon's oscillate at the plasma frequency which is related to the free electron density and the effective mass. Now, if you confine these plasmon's this was in the bulk that they are oscillating with a plasma frequency when you confine the plasmon's to surfaces which can interact with light. So, if you have a wave which is going through the material and the material can interact with the slide then it can form what is called a propagating surface plasmon polariton. So, that is called an SPP band surface plasmon polariton and that happens when plasmon's are confined to surfaces they are not present in the bulk they are only confined to surfaces and then this kind of surface polaritons can form and that results if you have confinement that means, if you decrease the size of the particle then this surface plasmon polariton modes they get affected. So, earlier if you look in the bulk the plasma frequency is related to the free electron density and the effective mass in this fashion where in the nanoparticles where you observe the surface plasmon polaritons where confinement is there because now you cannot have the plasmon's in anywhere in the bulk they are only in the surface. So, confinement effects are there in this polaritons and this equation of the plasma frequency changes and now you see a factor 1 by 3 has come in the in finding out the frequency of the nanoparticles when it is showing resonant SPP modes or resonant surface plasmon polariton modes. So, different whether the plasmon's are confined or they are in the bulk you will have different plasmon frequencies that is what is being told and hence you will have different colors because the frequency will be related to energy being absorbed and that will be related to the colors which are given out or which you see for the different nanoparticles. Now, Michael Faraday as discussed earlier was the first to report the synthesis of colloidal metal particles and in this case the colloidal metal was gold. So, it was a gold particles which are kept here in this solution and you can see they are stable even today the particles do not settle down it is a clear looking solution is basically made up of gold nanoparticles in this colloidal solution and long back in 1908 me tried to explain the phenomena of the color of these metallic colloids and that he did by solving Maxwell's equation and he predicted that for homogeneous metal particles you will have optical extinction only when the size of the particle here it is written 2 r that means twice the radius as the diameter of the particle is much smaller than the wavelength of the light which you are using to see the particles. So, me predicted that this kind of optical extinction involves scattering as well as absorption. So, there is an incoming beam there will be an intensity of the incoming beam and when it gets scattered or it gets absorbed then that intensity gets lost and that is also you can say is called extinction. So, me tried to explain this extinction based on scattering and absorption and he predicted that this kind of extinction will be valid when the size of the particle is much much smaller than the wavelength of the light and that is what we discussed earlier also that you will have this oscillations of the conduction electrons of the metal particles when the size of the particle is much smaller than the wavelength of the light. So, the wavelength of light is this big and the size of the particle is only this big because the size is much small then you see this SPR band and then you can see colors of metals in colloids as seen by Michael Faraday long back around 1856 and 1857 and that is remarkable Faraday's contribution not only in other fields of electromagnetism and laws of electrolysis, but also in nanoscience where the first metal nanoparticle was synthesized in the laboratory by Michael Faraday as gold nanoparticles. So, this is the solution of gold nanoparticles and the color explained by Mies theory based on extinction due to scattering and absorption for particles which are much smaller than the wavelength of light. Now, when you have two particles two metal particles how will these plasmon interact? So, will there be a shift in the surface plasmon band? So, if we try to understand the interaction between particles and the fields around these particles an isolated sphere or a particle the polarization direction does not matter it does not matter whether vector is pointing this way or that way, but when there are two particles it will matter in which way these dipoles are being shown and how they are present? If they are present in the same in the same direction then the interaction it will be in one way and in this case it will be in a different way. So, this is a longitudinal coupling of the two metal particles to the oscillations of the conduction band electrons in the two particles and this coupling results in a shift of the SPR band to lower frequency. So, the restoring force in the longitudinal coupling is actually reduced when this one couples to this one. So, that is because they produce a resultant which is opposing the original plasmon vector. So, the restoring force is reduced by coupling to the neighbor and the SPR the band shifts to lower frequency where the force is reduced you shift to lower frequency and if it has a transverse component. So, there are these two particles metal particles and these are the vectors and if they have a transverse interaction transverse coupling then the restoring force is increased by coupling. So, the resonance will shift to higher frequencies. So, there are two possibilities of coupling of two metal nanoparticles the coupling with can be longitudinal and then longitudinal means the two dipoles are kind of arranged in the same direction and they have a restoring force which reduces tries to reduce the coupling. So, basically the resonance the SPR band will shift to lower frequency or lower energy whereas, in the transverse case the SPR band will shift to higher frequency. This is with the interaction of particles because in many systems nanoparticles will not be alone they will have neighbors and so particle particle interaction will be there between these metal nanoparticles and one has to understand what happens to the plasmon's dipolaritons when the coupling takes place. So, the size dependence that is say gold particles we say bulk gold is yellow in color and when we decrease the size of the particles all kinds of colors can be seen. Now, all these colors at different size of the gold particles are not coming due to one reason there are two reasons why you see color in gold particles one is that the geometric factor the blue the purple the large size particles the color is explained by me theory where the particle acts as a scatterer. So, light scattering by the metal sphere can be explained is used to explain by me theory which gives rise to the gold blue and purple colors these colors for large particles this is when the metal nanoparticle is larger than approximately 30 nanometers. Then the these particles the reason because of this large particles having colors is that some of the electrons which are oscillating with the field are not in phase. So, some electrons get behind phase and this is called phase retardation or retardation effect and for that the color can change. So, this change in color for the larger nanoparticles of metals is explained by me theory where the light scattering by the metal spheres involves electrons. But all the electrons are not oscillating with the light in phase some electrons are lagging in phase and this phase retardation can cause these colors the subsequent at the small size level when you are below a certain size say 5 nanometers 3 nanometers 4 nanometers at that size the changes in color which is more towards reddish brown to orange and then finally, it becomes color less at very small size those are due to quantum size effects which we had discussed earlier. In quantum size effects we had discussed as you reduce the size of the particles the band gap is increasing the energy states become more discrete and this is called the quantum size effect and the color changes associated with that or the changes in optical properties associated with these small particles say less than 5 nanometer particles is due to quantum confinement and can also be said is due to the quantum size effect. However, the color changes at large sized particles at 30 nanometers 25 nanometers etcetera is explained by me as due to scattering from scattering of light leading to its resonance with the conduction band electrons which is called the SPR. But all the electrons are not resonating in phase some electrons because of the large size of the particle are lagging and hence it causes a shift in the color in the large size particles. Whereas, in the quantum regime when you are talking of very small particles the variations in the color are due to quantum effects are due to changes in the density of states with energy are changes due to the bandwidth or the discretization of the energy levels. So, there are two different area two different phases by which you can explain the color. So, the color the range of size of particles depends on the color depends on the range of size of particles in one range the higher range the color can be explained by the me theory and at lower dimensions the color changes can be explained using the quantum confinement or quantum size effects. So, at very small size the colors are basically reddish brown to orange or color less and those are due to quantum size effects. But at large size this blue violet and red at this size you can explain using light scattering by a sphere by as explained by the me theory. Now, what is the effect of the surrounding medium if you have a metal particle and you have some solvent molecules say water or ethanol or cyclohexane how does the surface plasmon band or the S P R peak which is shown here like a how does this change as a function of the environment. So, here you can see that you have spherical silver particles and these spherical silver particles have an absorption around 440 nanometers. So, this is the absorption of the spherical silver nanoparticles. Now, if you move them from suppose they were in air now if you move the air remove the air and add some other liquid which has a refractive index of say 1.44 then you get the plot B. So, from A which has a maxima at 440 nanometers you now get B which has a maxima around 500 nanometers. So, this is a shift of 60 nanometers by changing the environment from air to some liquid which has a refractive index of around 1.44 and then further change can be observed if you change the refractive index of the medium from 1.44 to 1.48 you will get the next plot and like that there is a continuous shift in the maxima of the absorption of this energy due to the surface plasmon resonance by the change in the environment. So, it is highly sensitive the S P R band is sensitive to the environment and this sensitivity of the S P R band for metal nanoparticles especially of gold silver etcetera can detect adsorbate induced changes in the dielectric constant of the surrounding nano environment. So, the sensitivity of the S P R band can be utilized for a device which can sense what is happening in its environment. If you make any changes in its environment it can immediately detect because it will change its absorption of the surface plasmon bond. So, suppose a pure S P R band for gold nanoparticles is at 440 nanometers if you add some liquid around the gold nanoparticles and it shifts to 460 nanometers then we are sure that the environment is doing something to change this S P R band. So, it is a sensitive tool and if properly applied you can make it a chemo sensor that is sensing molecules of different types or biosensing which is again sensing molecules of different type, but of biological relevance that means of relevance to life and medicine. So, you can use the S P R band very effectively in biological applications in medical applications for chemo sensing and biosensing. So, this particular example as I mentioned was for silver nanoparticles and the particle size the particle size was fixed what you change is the environment around the particles. And as you change the environment of the particles that is you change the liquid in which the particles are present and change the refractive index of the liquid then the absorption the surface plasmon band changes and you can follow these changes very effectively. Now, one thing is about environment the other is about surface modification what about if you put some molecules or some functional groups on the surface of these gold particles. So, there will be what is called surface modification and the optical properties of metal particles like gold particles or silver particles etcetera are influenced by their environment. And if you change using a controlled manner the surface you can alter their properties in a very controlled manner. So, you can do controlled properties of nanoparticle assemblies by the separation between the particles that is how much distance the two interacting particles should be. If you can control by using some methodology then there will be very interesting approach towards biosensing by controlling the inter particle interactions within these assemblies of metal nanoparticles. Also you can code these metal particles with a uniform shell of inert material like silica or titanium etcetera you can cover them these metal particles with silica titanium etcetera and control the distance between the particles. So, the two metal particles will be separated even if they try to touch each other since there is a outer shell they will be away from each other by at least twice the thickness of the one shell or some of the shell thickness of the shells formed around the two particles. So, you can control interactions by controlling the distance by keeping the particles at different distances chemically or physically or by introducing shells around the particles with particular shell thicknesses which will allow one to keep the particles at specific distances and hence control the surface plasma. Now, further so to that this is an example of silica coated gold nanoparticles. So, you have got gold nanoparticles here and these gold nanoparticles have been covered with silica. So, that is what I was telling that if you consider this particle inside and this particle inside they may have important interactions, but those can be controlled by varying the shell thickness of silica on gold particles. So, different types of thicknesses can be formed and what is given is you can make particles with 10 nanometers with 23 nanometers with 58 nanometers and with 83 nanometers different size of particles and they are gold coated with different shell thicknesses. So, the particle size is not varying the shell thickness is varying and in this case the particle is small of say 15 nanometer and the shell thickness is also of similar order of around 10 nanometers. So, this is most uniform here of course, the particle size the core has increased although the thickness has been kept constant in all of them of 15 nanometers. So, this type of silica coated gold nanoparticles are of importance for many applications and their thickness of the shell can be monitored and controlled and that will control when you try to bring the particles together the metal particles will come to some close distance and that distance can be controlled by controlling the shell thickness that is the amount of silica around the gold particles. Now, what happens to the spectra that is the absorption when you have this kind of shells around the gold particles. So, this is a plot of the absorbance of this gold colloids which have been coated with silica and you see the dark bold line is the surface plasmon band of the gold particles with no silica shell. So, there is this is the surface plasmon band which is coming around 520 nanometers approximately now that has zero shell thickness. So, there is no silica on top of these gold particles but when you add or make a 2 nanometer thick shell around this gold particle you see that the intensity has gone up and there may be a slight shift in the peak of this gold silica core shell nanostructures. When it is 4 nanometer you can clearly see the shift in the surface plasmon as well as the intensity will get affected and this is the pictures of these particles of gold with different silica with a 60 nanometer silica shell and what has been changed is the refractive index of the liquid in which these particles have been dropped. So, you have the gold particles which are covered with 60 nanometer silica shell and you put them in some liquid which has a refractive index of 1.45, 1.42. So, you are varying the refractive index of the liquid of the medium and you see the shift in a color using the same nanoparticle 15 nanometer gold particle and 16 nanometer thick silica shell on top of the gold particles and you are adding the same particles to four different solvents and what is different in these solvents is the refractive index of the solvents and you can see variation of these gold silica nanoparticles in the depending on the environment and this has lot of importance in future applications. So, with that we come to an end to today's lecture and this was the 10th lecture of the module 4 and the second lecture on optical properties and in our next lecture we will complete our study on optical properties of nanostructured materials and that will be our 11th lecture and then the last lecture will be the 12th and last lecture of the module and the last lecture of the course which will be on mechanical properties of nanostructured materials. So, thank you very much and we will meet for the next lecture.