 In the last couple of modules we have talked about how one can study how the bond breaks. So we talked about what is called snapshots of bond breaking today and also we have talked about an important excited state process twisted intermolecular charge transfer. Today we will discuss another process solvation dynamics and the reason why one is interested in solvation dynamics is this even in class 11 or so everybody is familiar with this diagram right. So what this diagram tells us is why is it that polar molecules are soluble in polar liquids sometimes you talk about why ions are soluble in polar liquids. So the reason why polar molecule is soluble in polar liquid is that the energy is minimized due to favorable solute dipole solvent dipole interaction this is something that everybody knows why is it that non-polar solutes are not soluble in polar liquids yes so generally we say they are hydrophobic right. So some people say that this term hydrophobic is not right because it is not as if there is any repulsion between these non-polar solutes and polar solvents it is just that if you put it in a terms of a little more general interactions the cohesive force of the solvent in that case is much more than the adhesive force between the solute and solvent it is just that the solute molecules like each other very much. So they do not care about the solute molecule that is why they do not dissolve because after all the same non-polar solvent solute does dissolve in non-polar solvents okay but we do not have to get into that for the moment here we are going to concern ourselves only with solution of polar solvents polar solutes in polar solvents. Now the question that one asks in solvation dynamics is how much time does it take for solvation to take place and the reason why this question is interesting fundamentally is that solvation of polar transition states transition states are polar more often than not we have seen an example of such a polar transition state in case of say DMABN in the last module. So solvation of these steps is often the rate determining step so if you know solvation dynamics in principle you should be able to tell how much time a reaction takes place so this would be a very important step this is a very important step in understanding reactions that take place in solutions. So there is a lot of literature this one for example published in 1991 where it says that activation of transition state this has been studied for reactant and solvent energy flow for a model SN2 reaction in water. This reaction is chloride reacting with CH2Cl forming Cl CH3 plus chloride it might look trivial actually it is not how do you know that this chloride is going in that chloride is going out you can do it easily by using different isotopes of chlorine and the good thing about this is that what kind of potential well would this reaction have if I think of reactant energy of product it would be a symmetric double well potential right. So it turns out that for this thing this kind of reaction the rate determining step is solvation. Another Jax paper published in 1985 by another stalwart Kosovar this was on mechanism of fast intermolecular electron transfer reaction there he made a comment solvent motion controls the rate of fast intermolecular electron transfer and then in solvation is slow if it is too slow then it may not be actually complete before that the reaction might take place if that is the case then you can have barrier crossing not only in the forward direction but also in the backward direction. So how fast solvation is often determines the dynamics of reactions involving polar intermediates polar transition states. So before we get into the question of how much time it takes for solvation and how we determine it experimentally. Let us remind ourselves of something that is very fundamental in this field not dynamics really but how do you get some quantitative measure of solvation experimentally. Of course experiment here starts with some theoretical model and the theoretical model one uses here is Onsega reaction field model. This is discussed in detail in Lakovic's principle of fluorescence textbook and it provides reference to the original papers for those who are interested to put it very qualitatively the model is like this in this model the solvent is modeled as a dielectric continuum a block with the same dielectric constant everywhere alright. Now to consider the solute in the solution first of all we know once again from maybe class 6 class 7 physical science we know that one of the properties of matter is that two different things cannot occupy the same space. So if you are going to put solute inside the same inside the solvent you have to create space for it. So what Onsega did was that first of all to consider the solution he considered a spherical cavity the diameter of which is exactly the molecular diameter of the solute. So you have this dielectric continuum some dielectric constant epsilon and you have a cavity in it what is the meaning of cavity epsilon you can consider it to be 0 there is nothing in it cavity means vacuum and the size of the cavity is that the molecule can just fit in that cavity. So that is how solvent is modeled. The solute is modeled once again without considering the chemical structure. So if you see this is a physical model right. If you look at other physical models if you think of things like say bond charging bond charging is another process that takes place that is considered for solvation. In all these physical models there is no molecular structure because if you consider molecular structure you have to use quantum mechanics. So these are models that are actually formulated using classical mechanics and it does almost all the work. So in this case the solute is modeled as a dipole moment which fits exactly inside this cavity that we have created okay. So see if I take water and if I take some apoptic solvent which has the same dipole moment they would be modeled in a similar fashion right dipole moment of that same diameter provided the diameter of the molecules are also same. So what you would miss out on in this model is specific intermolecular interaction like hydrogen bonding alright. So that is something that this model cannot accommodate. So this model would work only when the interaction is purely electrostatic okay. Now when I say purely electrostatic why am I saying that? I am saying that because all the interaction that arises henceforth is because of the presence of this dipole moment inside the cavity until now whatever we said epsilon is same everywhere. Now the moment you put this dipole moment inside the cavity what will happen? Let us say the dipole moment is placed in such a way you see this minus sign here can you see yeah minus sign inside the spherical cavity let us say that is the negative end of the dipole this plus sign let us say there is a positive end of the dipole that is how the dipole is aligned let us say. What will happen? This plus charge here is going to polarize the dielectric in its nearest vicinity so that the dielectric now develops a minus sign here. The minus sign of the solute dipole on this side is going to polarize the dielectric around it so that the dielectric in immediate vicinity has a plus sign. So what we generate even without considering molecular structure is micro heterogeneity in the solution micro heterogeneity around the solute molecule solute dipole let us say alright. So now what is the situation you have a solute dipole and the solute dipole is contained in a cavity one side of which is minus one side is plus so one side minus one side plus what does that remind you of one side minus one side plus what do you create that way? Capacitor yes you create an electric field right plus and minus of course a field will be created. Now this field is created as a result or as a reaction to the introduction of the solute molecule in the cavity is that right? So this is called on-segar reaction field. I am skipping the entire mathematics here I am trying to build the physical justification mathematics you read Lacovitch's book you will understand it is not very difficult but sometimes what happens is when we do just the math we do not even think of the physical insight that is more important. So what you have here is you have on-segar reaction field produced as a result of introduction of this solute dipole into the solvent which is a structure less continuum alright. Now the dipole is subjected to this reaction field right so what will happen and the good thing is that the dipole is nicely aligned with the reaction field also because the reaction field is produced as a result of the dipole. So minus side of the reaction field is near the plus side of the dipole moment and dipole and the plus side of the electric field is near the minus side of the solute dipole. So what kind of interaction will you have you will only have stabilization yeah if you had a fixed field let us say I have 2 plates and I apply an electric field there one side one plate is positively charged one plate is negatively charged inside that I forcibly turn the dipole around then you can have repulsive interaction as well not in this case. In this case the interaction is intrinsically an attractive stabilizing interaction because the field is produced as a result of the field is produced in reaction to the solute dipole and so the solute dipole is nicely aligned to it okay. So this field is going to stabilize the dipole right you are going to have stabilization as a result of interaction of this dipole with the reaction field okay. So this is what the story is now think of a situation where I have a molecule whose ground state is more or less non-polar excited state is polar can you think of any such molecule yeah ground state is non-polar excited state is polar dipolar. So in charge transfer takes place of course one side of the molecule will become positively charged one side will be negatively charged so DMABN could be an example on Nile rate could be an example ANH, TNS all these things could be examples. So when that happens according to one secret reaction field this would be the situation now we bring in the structure of the solvent dipoles here we are still not considering molecular structure but we are at least recognizing the fact that the solvent molecules are dipolar in nature. So in the ground state the solvent dipoles are oriented in whatever way they are because ground state dipole moment of the solute is well let us say less not 0 may be less here it is said it is I think mu G mu G is the dipole moment of the ground state. In the excited state you have a different dipole moment mu E in this case let us say mu E is greater than mu G now what will happen you will have stabilization due to consider reaction field if you go through the reaction you will see that the this picture is only to recognize the molecular nature the derivation is completely based on dipole and field no molecular structure at all. But since we know that solutes the dipole moments we can think that this dipole moments will reorient so that you have on the minus side of the solute dipole you have solvent molecules pointing the plus sides and on the other side you have the solvent molecules pointing the minus side and that causes the stabilization okay. So this is the molecular picture on cigarette reaction field is the gross physical derivation. So then what happens to the corresponding ground state should we have here in this diagram it shows that the ground state of this solvated species has a higher energy compared to the ground state of the unsolvated species why is that so ground state means the dipole moment is gone dipole moment is back to mu G. So why is it that this arrangement has a higher energy than this arrangement because yes you are right in this case the it was this structure because it is not only solute solvent interaction. So if you read say book this book on electrochemistry part 1 you will see that while considering solution of a polar solute in polar solvent you consider not only solute solvent interaction but also solute solvent interaction because let us not forget that solvent molecules are present in very large number what is the concentration of water in water 55 molar. So the millions of solvent molecules compared to egg 1 solute molecule. So solvent-solvent interaction also contributes very strongly to the energy of this solution. So here the thing is in the excited state you go from this unorganized solvent situation to organized solvent situation or what is called the solvent-bark situation because of strongly favorable solute solvent interaction however if the dipole moment is restored from the high value of mu e to the low value of mu g then that favorable solute solvent interaction is gone and when that is gone what is lacking in this structure is the favorable solvent-solvent interaction that is present here. So this is actually more unstable than this so you can draw an energy cycle like this. So what will happen if you look at absorption spectrum and emission spectrum you record absorption spectrum and you record emission spectrum. If you go to a more polar solvent then stabilization will be greater. So the stroke shift between absorption and emission is going to be larger right. So here stroke shift provides a way of telling how polar the solvent is and of course it will work only when mu e is greater than mu g. So this is some data using ANS and you can see how emission spectra are getting redshifted and if you go through this Onsega reaction field model derivation you will arrive at something that is equally well known that is called Lippard-Motterga equation and Lippard-Motterga equation is something like this where it says Hc delta nu delta nu means nu A minus nu F where usually these are written in terms of wave number. The stroke shift in wave number is equal to 2 delta F by A cube mu e minus mu g whole square plus some constant. What is mu e minus mu g the difference in the dipole moment created upon excitation. The dipole well difference between the dipole moment created upon excitation and dipole moment of the ground state. What is delta F? Delta F is this we are referred to delta F in one of the earlier modules epsilon minus 1 by 2 epsilon plus 1 minus n square minus 1 by 2 n square plus 1 this is a measure of what is called orientation polarizability of the solvent. So the idea is that if you make this plot of nu A minus nu F stroke shift against delta F then you are going to get a slope which is proportional to square of mu e minus mu g. So greater the charge separation in the excited state steeper will be the curve. And here we have an example of ANS versus TNS you see that in this case delta mu turns out to be 9 dy in this case delta nu turns out to be 46 dy. So of course this has a much more polar excited state compared to ground state so this will be a better marker of polarity compared to this one okay. So what we have presented so far is the effect of solvation on steady state spectrum we have not talked about dynamics yet. So the question is how do we study the dynamics of the excited state going from unsolvated one to a solvated one right that is what we want to discuss. Now in this case theory preceded experiment and lots of theoretical approaches homogeneous dielectric model, inhomogeneous dielectric model, dynamic exchange model and molecular theories you can see that in the order that they are written you are actually going from a coarser theory to a finer theory to start with a model where the dielectric is homogeneous as we have said already on second model. Then you have to consider that dielectric may not be homogeneous so after all once again if you go back and read some basic physical chemistry text book like book recent read this electric chemistry book what is said is that see in the immediate vicinity of an ionic solute what is the dielectric constant of bulk water 80 or something like that right. What is the dielectric constant of water around say sodium ion yeah much less it is about 5 it is about 5 because the natural order orientation of the water dipole molecules is disrupted in the immediate vicinity of sodium their solute solvent interaction takes place. So now just around the solute it is 5 in the bulk it is 80 so it is impossible that there is a step jump from 5 to 80 right so it goes in steps. So first solvation shell, second solvation shell, third solvation shell that way you have a gradual change from 5 to 80 well when I say gradual it is not really very gradual it is quite steep. But inhomogeneity of dielectric is an important factor that has to be accounted for and that has been done in theoretical approaches. Then when you consider the molecular well even before that the third thing that you have to consider and we are going to harp upon this a little later as well is dynamic exchange. See this is not a static picture you have a solvent bulk model fine you have some of the solvent dipoles oriented nicely around the solute dipole but it is not as if that the solvent dipole that is there present in the first solvation shell is going to be there forever. It is not as if the solvent dipoles that are not bound by the solute are going to be there forever there is an exchange between the two and as it turns out that this exchange between bound and free dipole solvent dipoles actually has an important role to play in the dynamics because when you talk about dynamics what do you have to do you have to write a lot of differential equations right what do we do in kinetics first order process second order process what happens when we talk about some complex process if there are several steps you have to write differential equation for each and every step right. Here since dynamic exchange is a reality one needs to account for it while building the model and finally you have to consider the solvent molecules as solvent molecules not just dipoles the problem with that is that how many solvent molecules do you have Avogadro number let us say yeah if you are going to consider all of them to have some particular structure and you are going to use quantum mechanics for all of them that is not going to work right. Then what is used mostly here is statistical mechanical models statistical mechanical models with explicit solvent structure okay. So this is how the theory has evolved and you can get a an overview of this different kinds of theories from this very informative review by Prof. Bhivan Bakshi and now Prof. Bhivanjana solution dynamics and dipolar liquids published in 2010 there are many other reviews as well. Now one thing that has been referred to constantly while talking about solvation dynamics or otherwise is dielectric relaxation dielectric relaxation measurements are actually important here because the longitudinal relaxation time in simple liquids the solvation time. So lot of dielectric relaxation experiments have also been done in this context but that again gives a bulk picture dielectric relaxation measurement does not have the capability of going near a solute and looking at it for that one has to use spectroscopy. So this module was an introduction to the process of solvation itself in the next module we are going to discuss how one can use ultrafast spectroscopy to study the dynamics of solvation.