 So, now let us see if we can understand how to follow solvent dynamics using ultrafast spectroscopy and as we are going to discuss by the end of this module this sometimes solvation can be ultra slow as well and first of slow study of solvation dynamics can give us some useful and interesting information. So, the way one studies solvation dynamics is you start from what we have discussed earlier you start with the molecule which has near 0 dipole moment and you excite it and the molecule should be such that there is a charge transfer in the excited state ultrafast charge transfer. So this is the situation in the ground state your molecule with no dipole moment and solvent molecules are oriented in whatever way they are oriented in around the solute molecule upon excitation charge transfer has to take place. Now this excitation takes place in ultrafast time scale at a second that is not enough time for the solvent molecules to reorient that is what I think Prajit was saying in the earlier module. Then given enough time the solvent dipoles would reorient around the 2 poles of the newly created solute dipole and you would get a happy situation like this and as we have discussed due to favorable dipole-dipole interaction you are going to get a stabilization of the excited state. Now see in case this molecule is fluorescent then what is the situation if you can record emission spectra at different times after excitation and we have discussed earlier in this course how one can do that one can do it either by gated emission or one can record steady state and time resolved data and construct the time resolved emission spectrum from there we are going to come back to that in a moment. Now the point is at time t equal to 0 you get emission at some particular maximal frequency as time passes there is going to be a red shift because the energy gap between the ground state and the excited state and the ground state would keep decreasing because of stabilization of the ground state and the fact that the corresponding excited state is of higher energy than the state that we actually excited the unsolvated state this is something we discussed in the previous module. So what you get is a time resolved stroke shift time dependent stroke shift TDSS as it called of the emission spectrum. So in this case one works with the maximum emission maximum of this time resolved emission spectra and from there we construct this solvent response function c of t which is given as nu at time t nu means as I said the maximum of emission spectrum at time t minus the emission maximum at time infinity time infinity means you do not really have to measure up to time infinity it means the time after which there is no further stroke shift and that is a contentious issue I will come back to that in a moment denominator is nu 0 minus nu infinity when nu 0 is the emission maximum at the instant of excitation nu infinity is what we have discussed already. Now see what are the problems associated with this how do you know nu 0 how do you know nu infinity that is what the problem is because if the lifetime is say in tens of nanoseconds lifetime of the excited state and solvation time is some 1 picosecond into picosecond then there is no problem because you would go from the higher energy unsolvated state to the completely stabilized state which will persist for a few nanoseconds. So you get nu infinity without hassle the problem arises if solvation time is comparable to the lifetime which we are going to show is the case in many cases then you do not know whether solvation is complete or not if solvation is not complete within the time scale of the measurement then nu infinity is not determined accurately that is one problem the second problem is how do you determine nu 0 the easiest way of doing it is well to feed the decays to multi exponential fitting functions and then construct the time resolved emission intensities by putting t equal to 0 now there is a problem with that the problem there is what is the time resolution of your experiment what is the instrument response function if you are going to do if you can excite with an atos second pulse atos again detection and do this experiment perhaps you will get the accurate value of nu 0 every time otherwise nu 0 is subject to errors associated with the full width of maximum of instrument response function. Now different people have proposed different ways of determining nu 0 all of them have some approach and some cons one way of determining nu 0 sometimes is people have considered the emission spectrum in non-polar solvents that may or may not be correct because even the ground state energy may not be exactly the same the energy gap between the ground state and the locally excited state may or may not be the same between polar and non-polar solvents as first approximation they are but not always another way that has been done is that the solvent has been frozen and you perform measurements at liquid nitrogen temperature this seems to yield a good result because when the solvent is frozen then there will be no reorientation so you look at the same excited state that you are going to excite anyway the only hesitation about that is that the polarity of the medium as we have seen for the mabn can be temperature dependent so no method is 100% full proof you have to work within whatever limitation it might have. Now let us come back to this fraction itself what does it denote nu at t-nu at infinity divided by nu at 0-nu at infinity what is the significance of this fraction okay nu 0-nu infinity what is that that is a total stoke shift what is nu t-nu infinity stoke shift that is yet to happen so this fraction c of t is the fraction of solvation that is yet to happen okay as has been discussed very nicely in this golden paper it has been cited I do not know how many thousand times the very famous paper by Bakshi, Oxtoby and Fleming 1987 what they have discussed is that due to linear response theory in the simplest case scenario you expect this c of t to decay exponential however most of the time you do not get a simple exponential decay you get something like this okay because there are different modes of solvation that are there it is not a very simple phenomenon as we are going to present very briefly about water there are different things that happen that is why you usually do not get there are cases in which you get single exponential as we are going to show but many times you do not get a simple single exponential decay of your solvent response function so generally c of t is fitted as a multi exponential function and each of the time constants is called a solvation time and the challenge is is it possible to assign each of the solvation time to some kind of a mode of motion of the solvent molecule okay. So let me show you some example of time dependence stoke shift data from our own lab here what do you expect if solvation takes place then you expect we have talked about what the signature of an excited state process is in this case solvation is taking place of the excited state so it is also an excited state process so you expect a fast decay in the blue end which corresponds to the in this case unsolvated locally excited state and you expect a rise time in the red end because that corresponds to the solvated excited state that is being formed so this is a typical kind of curve that you would expect okay. So what you do is you fit this kind of a time result fluorescence data to multi exponential function and you generate the intensity at some particular wave number by I nu bar SS multiplied by sum over I AI e to the power minus t by tau I divided by sum over I AI tau I it comes from the fact that what is this I nu bar SS that is the emission intensity at a particular wave number. Now emission intensity at a particular wave number is essentially integral of time resolved intensity from 0 to infinity it comes from there it is a standard integral which turns out to be sum over I AI tau I which is the total intensity and you get this kind of an expression. Now when you do this you are going to get time resolved emission intensity for different frequencies and when you plot them against frequency for different times you get this kind of a picture. This is an example of time resolved emission spectra and here we see from our lab an example of how C of t changes with time you can see it decays but it does not decays single exponentially one thing you can see we have not told you what the molecule here molecule is here does not really matter but one thing you can see is that the solvation is faster at least a long component of solvation is faster for methanol than for one propanol the reason is understandable one propanol is more viscous than methanol. So similarly there can be many other reasons many other factors that can influence solvation dynamics okay so to start with let us talk about solvation dynamics in non-equal solvents of course non-equal solvents can be classified in 2 parts apoptic solvent and alcohol in 1987 from ground flaming ground flaming group has made significant contribution to the field of solvation dynamics and not only flaming the students who later on went on to become independent researchers they have also done significant work so you can think flaming school comprising Kastner, Marancheli all these people have contributed big time the other players are Mark Berg well of course was a Bimann Berg, Chippos, Kankan, Bhattacharya these people have done a lot of work Ahmed Zuel towards after getting Nobel Prize got interested in the field of solvation dynamics will not really talk about his work here but you can read it and there are many groups in India which who have studied this Nancy Levinger has done significant work on solvation dynamics in things like reverse masses. So that is something that I leave for you to read yourselves it is a very interesting body of literature that has been created starting from say 1985 1987 until now new infinity has not been reached even now plenty of work is going on using solvation dynamics. So this particular work on the Kastner, Marancheli and flaming used this kind of a probe and let me show you the decays fluorescence decays in DMSO. So as you see in the blue end 570 nanometer you have a fast decay that almost gets over within 30 picosecond the red end of the spectrum 730 nanometer you see a distinct rise and here you see a long lived excited state that is the solvated state that is being formed okay. So this is the signature of solvation that we were talking about from there they constructed the time resolved emission spectrum and here in this early work they did not really bother working out C of t they simply plotted nu at time t against t as you understand you can rearrange that equation right and you can still get solvation time and these are the solvation parameters that they obtained. So as you see for acetonite trial linear response theory holds very nicely there is a single exponential decay associated with a 0.4 400 femtosecond decay sorry that is for acetonite trial for DMSO is the same thing but the decay is slower 3.1 picosecond. So you see acetonite trial and DMSO are they a protein what kind of solvents are they both are a protein solvents still there is an almost order of magnitude difference in solvation time that depends on the polarity of the solvent by enlarge so here you see a signature of polarity. Then when you go to nitrobenzene things get a little more complicated because you get double exponential nature of decay first one is 3.4 2.3 is I think calculated theoretically and second one is 6.3 picosecond. So if you look at nu bar infinity and you better look at nu 0 – nu infinity here also you see a lot of difference I think this is in 1000s of centimeter inverse or something this one is 1200 this is 770 this is 1080 so even the extent of stabilization not just dynamics depends on the solvent and even that has a story to tell from there the moment you go to protic solvents methanol has a 3.3 nanosecond single exponential solvation time butanol has a 66 this is nanosecond 3.3 picosecond 66 picosecond and 100 picosecond. So of course for butanol which is a more viscous solvent you get slower solvation times and due to viscosity different kinds of modes get decoupled and that is why you see not one but two different solvation times. This is only one example of solvation in a protic solvents mananchally especially has done a very thorough job I remember this JCP paper of 1994 or 1995 where I think there are several probes and like 30 40 solvents so of that paper I think 4 pages of that paper were just tables like this the small table. So exhaustive work has been done in non-equal solvents to understand the factors that contribute to solvation dynamics polarity, viscosity, hydrogen bonding everything matters. Having done this the next question that was asked is what about solvation dynamics in water. Now this is a very important and fundamental question that has been dealt with significantly after the report that I am going to show you because after all the entire life is based on water right. So understanding what happens in water is an interesting question that has persisted and water is not a simple liquid right. Sometimes figuratively we say something is as simple as water that is a completely wrong sentence scientifically whereas we should say as simple as hot water because in hot water some hydrogen bonds are broken. Water itself is an abnormal liquid as you all know it should not have been a liquid in the first place because H2S is a gas oxygen and sulfur oxygen is lighter the reason why water is liquid is hydrogen bond. So all the life processes are dependent on this extraordinary liquid that is water it is important to study solvation dynamics in water in many different forms. So the first report of this came in 1994 once again from Graham Fleming's group and the importance of this work is highlighted in the fact that it was published in Nature. Here similar TDSS studies were performed using Kumarin 343 so this has become one of the most used fluorescence probes after this study okay. So there are Kumarin 120 is 1, 343 is 1. So using this Fleming and coworkers got this kind of time resolved this is all femtosecond optical gating experiment okay. You can see first decay in the blue end rise in the red end and you can note the full scale of the experiment 2 picosecond. Of course this is a zoomed in picture they did do the experiment for much longer time and having done this they obtained the C of t and so how it evolves in time there is a lot of data in this we are only giving you an overview the expectation is that you are going to read this paper is extremely important should be read in detail I am not presenting that even the numbers here. So here this is the experimental time evolution of C of t and the other things that you see are theoretical fit and all that and this is how the oscillation takes place that is shown using molecular dynamics. So crux of the matter is that it is multi exponential in fact there is an initial Gaussian component it is not exponential all the way and what Fleming and coworkers did in this paper is that using experiment as well as molecular dynamics they could attribute the different solvation times to different kinds of motion of water the orientation liberation what is the meaning of liberation? Liberation means restricted rotation. So remember when we take water in isolation that is what we are used to thinking it is just HOH but water is not present in isolation in its liquid state as we know it is an associated liquid there are hydrogen bonds. So when a water molecule tries to rotate very often what happens is this hydrogen bond with the next water molecule hinders the rotation it cannot rotate all the way it comes back so that becomes a kind of an oscillator emotion which is identified as a low frequency vibration and motion it is not really rotating this kind of emotion back and forth. So that of course has energy that is much more than rotational motion but significantly less compared to vibrational motion in the next module we will actually show you the spectrum of water IR spectrum where you will see what kind of wave numbers are associated with this liberation. So this different modes of water how they contribute to solvation that is what was worked out in this paper please read it. So this was 1994 the next year the same group Fleming's group published a paper in Faraday Journal of Chemical Society Faraday Transaction. So what they showed the experiment they did there is that they took two probes C343 and C420 and they performed the experiment not in just water but in cyclo-dextrin in equest cyclo-dextrin solution. Cyclo-dextrin as we might have said earlier I do not remember if you have is a macro molecule that looks like an ice cream cup without a bottom and the reason why cyclo-dextrin is interesting is that the outer surface of cyclo-dextrin is polar the inner surface is non-polar so it can be used to solubilize non-polar solutes in water non-polar molecules in water it is used very frequently in drug formulation and all that. So in cyclo-dextrin Fleming's group found that solvation gets slowed down significantly this is a comparison of the time evolution of C of t between water and cyclo-dextrin and these are the associated solvation times. So you see that in addition to the picosecond component that was there first of all they did not observe a less than picosecond component this was a TCS physics experiment. And more importantly hundreds of picosecond component and in one case what they observed as a nanosecond component came in so you have slowing down of solvation by an order of magnitude and this paper sparked a series of work that has resulted in publication of I do not know how many thousand of paper half of my PhD thesis was inspired by this one paper. So the explanation initially was actually not correct what everybody thought was that you have bound water and free water so free water rotates quickly free water moves quickly and contributes to the first component of solvation bound water moves slowly and contributes to the slow component of solvation that is not quite right. As has been elucidated later mainly by the group of Professor Bhivan Bakshi there is a dynamic equilibrium remember I talked about dynamic exchange of solvents in the previous module or maybe in this module so what they showed is that the bound water is actually you can think frozen it does not participate in solvation as such however there is a dynamic exchange between bound and free water it is always the free water that is reorienting around the newly created diaper moment. But there is an exchange and if you remember your lessons from chemical kinetics if there is some equilibrium associated with that you have to take that into account the forward and backward rate constant and this exchange is what is associated with the slow component of water that is something that is that came out very nicely in this Nandi Bakshi theory and this is the cartoon representation of let us say a protein to which water is hydrogen bonded and here you have the regular network of free water there is a dynamic equilibrium between bound and free water when they considered that that is when they could arrive at this long solvation time. So if you look at the energies this is the situation for free water this is the situation for bound water there is a barrier crossing back and forth this K1 and K2 have to be considered when you build the kinetics scheme for solvation that is what causes slow solvation okay. So now let me take a detour with this from the main agenda of the course the title of our course is ultrafast processes now we have arrived at something that is not ultrafast which is not ultra slow maybe but definitely not ultra fast slow and the question to be asked is so what I mean why would we even be interested in slow solvation well slow solvation has in the last 20-22 years emerged as a marker of bound water as we have said and what has been shown later on is that you can actually use it by combining with confocal microscope capable of performing lifetime measurements FLIM this can give you an insight into really small volumes like never before. So in the next 3 minutes or 4 minutes let me present to you a brief summary of work done in one group that of frozen concovertage area in ISES in which they used a confocal FLIM setup fluorescence lifetime imaging microscopy setup when I say confocal what it essentially means is this that this is where your sample is right so the excitation light is focused on to a particular point in the sample focal point as you know cannot be less than lambda by 2 in diameter that is the diffraction limit and then there is a dichroic mirror that sends the this is the laser light this is the fluorescence light the dichroic mirror sends the fluorescence into this objective of the microscope after which the direction takes place. Now if you have work with sufficiently small concentrations you can look at single molecules by this technique so suppose you use an excitation wavelength of 400 nanometer what is the resolution you have 200 nanometer now suppose you use this microscope to study something like a cell what is the size of a cell microns you can see cells very easily under a not very sophisticated optical microscope yeah so the thing is since the cells are like 20,000 30,000 times larger than the resolution that we have in confocal microscopy you have the capability to look at not only the cell as a whole but also at different parts of the cell if you have a fluorescent probe that goes and binds to a mitochondria you can look at mitochondria selectively if there is something that goes and binds to some microtubules then you can look at microtubules selectively if there is something that will go and bind to say lysosome you will be able to see lysosome selectively and this technique has been used very effectively by groups like for example Yamuna Christians group who migrated from NCBS to UChicago few years ago gave a talk in our institute last year so one can look at different components of cell by using selectively by using confocal microscopy now if your confocal microscope is capable of measuring lifetimes you can measure lifetimes at different locations of the cell does not always have to be a cell of anything of that dimension and if your system is fitted with a grating and detector typically EMCCD then you can measure fluorescence spectrum as well in our setup we currently cannot do it so if you have an EMCCD and a grating combination as well as a lifetime measurement accessory FLIM then you can study solvation dynamics in different parts of the cell as well and that is what has been done by Vartacharia group this is one example what they did is they worked with CHO cell what is CHO Chinese hamster ovary the different there are several different cell lines that people work with this is Chinese hamster ovary. So there you see they use 2 dyes one is DCM this is DCM and the other is DAPI this is DAPI so DCM is known to localize in cytoplasm will not get into the detail of why that one can study DAPI is known to bind to nucleus. So what you see here is that if you look at the decays fluorescence decays they are definitely wavelength dependent and then if you record the emission spectrum as well you can get an idea of solvation times in different parts of the cell using DCM you can get the solvation time in cytoplasm using DAPI you can get the solvation time in nucleus using something else you can get a lifetime of something else and the good thing is here even if there is a distribution of DCM between the 2 different parts of the cell you can using confocal microscopy look at say cytoplasm once and record all your data there then look at say Golgi body another time record all your data in Golgi body. So coupling this time resolved emission spectroscopy with microscope gives us this very powerful technique of looking at dynamics in different parts of a very small volume like that of a cell and this is what a typical confocal image looks like and here looking at this image one can identify things like lipid droplets this is a nucleus this is a cytoplasm and recording fluorescence decays at different parts of the cell like this what Bhattacharya group was able to do is that they were able to work out the C of T is at different parts you see this is the decay of C of T in the nucleus this is the one in cytoplasm and this is what is there in lipid droplets. So if you look at the times in bulk what is it is about 1 picosecond in nucleus it is about 750 picosecond cytoplasm a little slower 1100 picosecond lipid droplets 3 times slower 3600 picosecond okay. And what has been proposed is that using these you can in fact later on this technique has been expanded to differentiate between say cancer cells and non-cancerous cells. So this is a way in which one can extend this time resolved ultrafast technique to think of applications in biological systems or even in micro heterogeneous materials okay. I think we will stop here today and next day we will talk about since we are talking about water now next day what we will do is we will talk a little more about water we are going to revise something that I think we did a little hurriedly any burnings work remember science 2003 science 2005 we are going to talk about that in little more detail and we will continue with the work from the same group in which they have shown how vibration energy gets redistributed into different modes of water. So today we talked about liberation and all we come back to that but from a different perspective in the next module and then after that have I talked about ESIPT at all in this course you are talking about x-ray intermolecular proton transfer then for the sake of historical accuracy we will do that since we are talking about photo acids anyway. Then what we will do is we will move over there is one debate that I would like to present if we get time and that is okay maybe we can do that as an extension of ESIPT ESPT then we will move over from molecules to nano clusters and then nano material.