 We have discussed ultrafast processes in molecules at length, not really at length because it is really a vast field, we have talked about only some of the processes, we have not talked about even things like freight that we promise to discuss and we have not talked about photoisomerization. Ultrafast dynamics in molecules is really a very rich field which has been pursued for a long, long time and there are thousands of good papers that one needs to read. But then in this course we cannot really go through the entire body of literature that is there in this field, we can only introduce you and then it is up to you to read and learn more. So and we have to finish in a given time frame as well, so what we will do now is that we will keep molecules aside and we will move on to things that are of great interest over the last 20, 25 years, so we will talk about nanoparticles. Today we are going to talk about plasmonic nanoparticles to start with then we will talk about what happens when you break down nanoparticles further, is there something between molecules and nanoparticles that is called nanoclusters and today we are focusing on things like gold. When you talk about nanoparticles generally you would be interested either in gold, silver all these things metal nanoparticles or you would be interested in semiconductor nanoparticles. We have done a lot of work on silica as well but for now we will not get into that. So after this we are going to talk about semiconductor nanocrystals, solar cells and perovskites. So for now let us begin our discussion on plasmonic nanoparticles. What is the meaning of a plasma? What is a plasmon can somebody tell me? That is phonon, quantum of vibration is phonon. See electron is like unit charge right, quantum of charge, phonon is quantum of vibration, photon is quantum of light. Similarly plasmon is also quantum of something, what is that something? The name suggests that it is plasma, plasma we have studied from childhood that it is the fourth state of matter, plasma essentially means ionized gas. Now here we are not going to work with gases, we are going to work with what happens when you ionize the gases you set electrons free. So plasmon is essentially a quantum of free electron that is present mostly on the surface of metals. So this surface plasmon have been of lot of interest over the last 25 years or so. One called localized surface plasmon resonance is quite well known, more or less well understood and it has been used extensively to do things like augmentation of signals, enhancement of fluorescence. So you might, well I do not think I mentioned this earlier, we have talked about radiative rates and non-radiative rates. Now generally in whatever molecules we have discussed so far we have only talked about suppression of non-radiative processes so that the fluorescence quantum will goes up. But there is another way of doing it. The other way of doing it is to play around with the radiative rate. Of course you understand radiative rate constant is directly related to Einstein's B coefficient which is related to epsilon. So you are basically saying how one can increase epsilon and one way of doing it is by using plasmonics. Joseph Lackiewicz especially has done a lot of work on this, he started with silver islands and then he worked with silver nanoparticles as well. So using it what you do is you enhance KR. What happens when you enhance KR, radiative rate constant? Fluorescence quantum will goes up right but lifetime goes down because do not forget lifetime is 1 by KR plus KNR. So KR appears in the denominator of lifetime. So lifetime going down with fluorescence quantum will going up provided no mistake has been made is a sure shot signature of what Lackiewicz likes to call radiative rate engineering and that is done by using plasmonics. In fact nowadays SPR spectrometers are available commercially where one can enhance the signal from weakly emitting samples and all and it is used extensively in things like sensing. So that is why surface plasmon resonance is interesting and useful. So now where does it come from? We will paint a very, very qualitative picture actually there is a lot of theory that one needs to discuss if one needs to understand surface plasmon resonance quantitatively. We will not try to do that in the limited scope of this course, we will just point you to this picture that is available I think even in Wikipedia. So what happens is in metals why are metals conducting the simplest theory that is used to describe conduction of metals is that of free electron, free electron theory right. So where one says that since the work function is small all the electrons are more or less free they can move easily and so on and so forth. So what happens is these electrons form sort of a cloud the free electron and then you have a hard core that is the metal nanoparticle, noble metal nanoparticle we are going to talk about gold almost exclusively we will refer to silver and platinum and nickel ones but in this discussion as well as in the nanoprocessor discussion we will talk mostly about gold that does not mean gold is the only thing other metal nanoparticles also give very good surface plasmon resonance. So what happens is this is the gold nanoparticle let us say and this is the cloud of electrons you can think. So this cloud of electrons can oscillate and what happens when they oscillate if the cloud of electrons goes up then in this ensemble the top portion is slightly negative partially negative and the bottom portion is slightly positive so you create a dipole when it goes down then the bottom portion is slightly negative the top portion is slightly positive okay. So what you have essentially is you have an oscillating dipole due to the movement you can think of the surface plasmon that is almost always depicted in this manner you see the surface plasmon going down then this side is minus and here the metal ions you can say are exposed a little bit so this side is plus and here it is the opposite phase. So now what you have essentially then is that when the surface plasmon going up and down you create an oscillating dipole moment once again let me reiterate that we are painting a very very qualitative picture here. So what happens when you have an oscillating dipole if you remember what you studied in basic molecular spectroscopic courses why is it that polar molecules are microwave active because when the dipole moment rotates the z component of dipole moment fluctuates it goes up comes down to 0 goes to the opposite direction and keeps on oscillating here also this oscillating electric field is set up and you can think that that electric field can interact with light that is incident on it okay and that is why there is an absorption remember in the classical picture absorption of light is always associated with resonance between the electric field of light and some kind of fluctuating electric field in the molecule or material whatever it is. So when the frequencies match of the oscillations that is when resonance is achieved and light absorption takes place alright. Now this frequency of oscillation depends on several things first of all composition you might think what am I talking about and we have said gold nanoparticle so why where is composition coming from we will come to that in a few minutes geometrical shape if it is a sphere or if it is a rod or if it is a prism we have different kinds of oscillation in fact when it is a gold nanoprism you can have many kinds of oscillation so you have a really broad surface plasma resonance and nature of the chemical environment what do you have around it do you have a coat of silica do you have polymer do you have solvent even that is important and we will see why that is important before that let me show you at least one spectrum of you can see this is one of the earlier works 2019 years ago this is the kind of spectrum that you expect to see in well what we conventionally call absorption spectrum okay. So what you can see is at 2.5 nanometer you can see a band forming here 4.6 15 16 nanometer now here the band has become prominent and it is quite sharp right then when you make bigger nanoparticles when you go to 120 nanometer there is a further redshift and then it becomes really broad for different reasons we are not going to that is not really what we want to discuss today what we do want to discuss is what happens after you excite this so essentially when you excite the molecules this excess energy not molecules sorry nanoparticle this excess energy in the nanoparticle and it has to equilibrate it equilibrates by several mechanisms first thing that happens the fastest one is electron electron scattering right. So you have this electron here a lot of electrons around remember it is a plasma right lots of free electrons are there so electron scattering gives rise to reinstatement of the ground state if you want to call it that okay the other thing that can happen is that you can have electron phonon coupling phonon is basically this lattice vibration right when we talk about solid now you cannot talk about normal modes of molecules anymore you must talk about the vibrations of the lattice as a whole as we have seen earlier in this course many new kinds of vibrations can arise when you are association like what happened in water remember what happened in liquid water we did not have just the symmetric stretch and bend and symmetric stretch we also had liberational motion and that too were of different kinds so similarly here in lattice which is an even more associated system you have different kinds of vibration and these vibrations can be activated further if the excess energy is transferred to them that is called electron phonon coupling and then what happens is if you remember what happened in water you excite one mode of vibration and then the energy gets transferred to things like liberation right the same thing happens in the crystal lattice as well one kind of phonon transfers energy to another so that is called phonon phonon coupling that is how the heat gets dissipated heat means excess energy here gets dissipated okay I should mention here that for the initial slides I am grateful to my student Bala he is the one who made it and he is the one who sort of taught us in our group about surface plasma resonance and stuff alright so now this electron electron scattering is the fastest and we will show you some data later that takes place in hundreds of femtosecond really really fast then you have electron phonon coupling that takes place typically in 1 to 4 picosecond and phonon phonon coupling is the slowest step that takes place in 100 picosecond. So let me show you another diagram other than this where the relaxation is divided into two kinds radiative and non-radiative the non-radiative processes are essentially land out damping involving electron hole pairs and elastic scattering which causes defacing and radiative decay consists of well scattering of photons and there is some what you can call fluorescence as well we are not going to discuss the topic of photo luminescence of gold nanoparticles but I will give you a recent reference at the end this is an interesting thing that has come up over the last 5 years or so it makes sense to read it by our sense. What we will do is we will mostly present to you literature from this review that was published well 8 years ago it is by Heartland so let so what this review does is that it discusses in a good amount of detail the dynamics post excitation of noble metal nanoparticle nanostructures this is one review that I recommend that everybody should read we are not going to discuss everything in the module today there will be a lot of things that are left for ourselves to read alright so let me start with by showing you a transition piece of transient absorption data recorded by Elsage group link at that time was a student opposed dog with Elsage so what you see is this one on the top for your reference is the extinction spectrum that I showed you a little earlier this is your surface plasma resonance band and the main feature the dominating feature in the transient absorption spectrum is a ground state bleach that exactly corroborates with this band and what link and Elsage and other people did was that they looked at the ground state bleach recovery dynamics and they got 2 time constants you can see the trace here 2 time constants 3.1 picosecond and 90 picosecond 3.1 picosecond was assigned to electron photon couple phonon coupling and the longer 90 picosecond component was assigned to phonon phonon coupling so what did they not see what is it that they missed that means something right there are 3 processes so electron electron scattering is missed because it is too fast for the resolution of the set of the used we are going to show you some data there as well now this is a very important difference between molecules and materials when you talk about materials and you want to do pump probe spectroscopy with them some interesting feature arises well you have seen earlier in case of seven as a indole also that if you pump at higher energies lower frequencies what happened there there was an additional first component due to s2 to s1 relaxation right or due to relaxation of s2 just you can say so something similar but more prominent happens in nanoparticles because you see the absorption is really a continuum except for that it is not a continuum but there is a p and then it just goes up so you in principle you can excite in you can pump in many many different wavelengths but if you pump at higher energies not only for plasmonic nanoparticles but also for semiconductor nanoparticles interesting phenomena start showing up especially for semiconductor nanoparticles so that is what we will discuss in one of the future modules so here what is important is when you want to talk about some time constant you should not forget what the pump power is one thing is you can excite at higher energy the other thing is if you excite by a greater pump power then a lot of interactions can happen and this is an example of heartland group as early as 2000 what they showed was that you look at these decays at different pump power the tau the electron phonon coupling time constant actually goes up right that is due to further interactions that are there now what they showed is that first of all if you look at this time constant how do you know what the time constant is so what they did is in this graph in the inset they extrapolated it to 0 pump power so this is sort of like the infinite dilution we must have read right actually you cannot achieve infinite dilution but you always extrapolate and find out what it is so by extrapolation they found that at notionally 0 pump power the electron phonon coupling time constant is equal to 0.65 picosecond which interestingly is exactly the same as what is there for bulk hold with increase in pump power the time constant becomes longer the time constant becomes longer means what coupling is more efficient or less efficient yeah less efficient why because radiative not radiative the rate constant is actually reciprocal of tau right so when you talk about coupling you have to talk about the rate constant and then the interesting thing that they showed here is that this time constant they got when they plotted against diameter and again this is a semi lock plot where the x axis is logarithmic so that they can show data from say 3 nanometer all the way to 120 nanometer the time constant remains exactly the same irrespective of the size of the nanoparticle okay this is one thing. Now let us see an example where the electron-electron coupling is actually observed experimentally this time it is not gold it is silver this is the work of Brewer and coworkers once again way back in 2000 here you see what they have done is they have done an experiment at a very good resolution full scale here is one and you can more or less understand how many points there are it looks like a straight line isn't it a little uneven straight line so wherever there is change in slope that is a point so there are there are may be 500 points or more within this 0 to 1 picosecond time window and also note the quality this quality is excellent right it is a linear scale y axis is linear there you get this kind of data I mean if I will not tell you that x axis is in picosecond and I tell you it is TCSPC data you might believe this is excellent data so that is why they could get this small time constant data quality has to be outstanding if one wants to talk about very precise measurements so this electron-electron coupling time was found to be where is the electron-electron coupling time here excited and then see there is a rise right why is there a rise because equilibration has to take place among the electrons that are there first you have done a quantum of excitation that has to get redistributed among all the electrons before anything else can happen so that comes up actually as a rise and this rise time is found to increase from say 100 femtosecond to 300 femtosecond the second second plot depending on what the nanoparticle radius is right now do not worry about what this line is or what this curve is just look at the points remember this silver and it increases from actually their observation was with 2 nanometer so there about 150 femtosecond time constant was there and it went up to 300 femtosecond and from the data you can see that the trend is there it is not an oscillation a fluctuation once again it is impossible to get believable data I mean it is impossible to differentiate between 300 femtosecond and 150 femtosecond if you do not have data of this kind I am sure this was a very very painstaking experiment especially 19 years ago okay. So we have talked about spherical nanoparticles so far gold and silver and we have shown you what the electron scattering time is in the last slide and we have talked about electron phonon coupling as well phonon phonon coupling is just the longer longest time scale that you have here. So this is where we will end this module in the next module we will talk about gold nanodots and composite nanoparticles.