 Good morning. So, welcome to today's lecture. We were discussing sensitivity enhancement and in previous lectures we have seen that like NOE is a method to enhance the sensitivity. NOE if you remember we were if two spins are coupled, we were perturbing one spin and because of this perturbation the signal for other spin was getting enhanced. So, we will continue with that and today we will continue with selective polarization inversion that also we discussed in the last class. So, here what we discussed that if two spins are coupled say spin is proton and carbon-13. So, energy level for these two spins are something like this big delta is for say proton and the small delta is maybe for carbon-13. So, two signal A1 and A2 for proton, X1 and X2 for carbon. So, what we have seen that this is insensitive nuclei which is coupled with a sensitive nuclei and what we want to increase the signal of insensitive nuclei which is 13C. So, we had seen that if we somehow perturb or saturate or transfer the polarization of say one of the transition from the more sensitive nuclei which is H by applying a selective pulse. So, selective pulse can be say 180 degree pulse then population of these gets inverted and because of this population inversion the essentially signal for X gets enhanced. So, if you population invert of A1 the X that was signal which was earlier very small say something like this now it becomes quite large, but one thing happens that the sign actually it changes. So, enhancement also we have seen that it is given by a factor which is gamma A divided by gamma X. Gamma A is a gyromagnetic ratio of proton and gamma X is gyromagnetic ratio of the X nuclei. So, suppose we are doing it for carbon proton. Now, gamma for proton is four times more than the carbon 13 therefore signal enhancement that we get in X is four times and this is huge or substantial enhancement in the intensity of X transition. So, that is what we had seen. So, let us take a real example and we will see how much enhancement we are getting for. So, here we are taking chloroform chloroform is CH 13 C and here we have CL CL and CL. So, we have two spin system proton is sensitive nuclei and carbon 13 is insensitive nuclei. We are say recording a spectrum for carbon 13 on any reasonable spectrometer say 400 megahertz. Now, because both of these are coupled so carbon 13 spectrum for X which is 13 C will be coming to here X1 and X2 these are the two transition for carbon 13. Since they are coupled so you are getting splitting and this splitting you remember will be J of CH which is generally 140 or 125 hertz. Now, if you decouple it so you get signal enhancement because of now both spins will merge and give you enhanced signal. But here selective polarization transfer if you saturate the signal coming from like proton. So, if you remember proton will be also splitted into two which we were calling in the previous slide A1 and A2. So, say we perturb A1 with a selective pulse selective 180 degree pulse. Now, signal for 13 C will be enhanced and you look at the enhancement factor here for like X2 it is quite a bit of enhanced and for X1 also it is enhanced, but for X2 it is quite a bit and this enhancement is generally given by gamma A divided by gamma X. So, generally 4 times enhancement that is what we get for say X2 spin or maybe 5 times actually. So, 1 plus 4 that is 5 times enhancement we are getting and for this one we will get 1 minus gamma A divided by gamma X. So, that is 3. So, 3 and 5 we are getting enhancement average is 4. So, 4 times enhancement we are getting for 13 C signal and if we perturb A2 spin so this will be giving us 5 times enhancement and 3 times. So, this is plus 5 minus 3. So, essentially 4 times enhancement we get for chloroform. This is fantastic. So, that is what we saw in the case 4 time enhancement for carbon 13 and if we like take it something like say nitrogen 15. So, nitrogen 15 we get 10 time enhancement and that we can see because the gamma for nitrogen is actually 10 times less than proton. So, that is what happens. So, for if we take it say gamma for proton and gamma for nitrogen and 15 that is 10 times. So, for nitrogen we get 10 times enhancement and this is very very substantial. So, that is what we do in SPI selective population inversion or this is also called selective polarization transfer. In both case we are getting quite a bit of enhancement, but the problem is that we have to select a transition and apply a transition selective pulse for inverting the population of either A1 and A2. So, for this case now we need to get it a selective population inversion which is many times in multiplate it becomes difficult. We get all those selective enhancement, but selecting a 180 degree pulse which is very very specific to particular transition is difficult and when there is a crowded spectrum then selecting a transition which can be inverted is very difficult and therefore we discussed and another experiment which is called inept. So, insensitive nuclei enhancement by polarization transfer concept is same we are transferring the polarization from A spin to X spin, but now we are we do not have to be selective in inversion. So, we explain this experiment we start with a 90 degree pulse on A spin which is sensitive nuclei like proton and that selectively brings the magnetization to XY plane then simultaneously pulse is applied on A spin and X spin and in vector diagram we saw that during the stow period they start moving apart and then you apply then they turn it back in this direction and again if you apply 180 degree pulse on Y there are actually direction changes and during this stow period they come in minus Y direction. So, you apply and bring A spin to Z direction of so this will be say IZ and then you apply a 90 degree X pulse on carbon 30 spin. So, that becomes say SY. So, that can be detected. So, now to circumvent the issue related selective inversion this inept can works and they that if you look at all here we are using is hard pulse. So, we are not now transition selective pulse and we achieve essentially transferring the polarization from high gamma nuclei which is proton to low gamma nuclei which is carbon. So, now magnetization is starting from here comes here and we can detect it S nuclei or X nuclei which is 13 C and it works in similar manner it selectively transfer the polarization from proton to carbon. So, we get an enhancement of four factor that we are saying one important parameter here was tau and tau is a time delay where we can select 1 by 4 J. So, this depends upon the coupling between these two spins carbon 13 and proton. Say typically for carbon 13 proton J value is 125 or 140 hertz, 120 to 140 hertz we can write and J H N. So, this is 1 H 13 C and this is 1 N 15 it is actually 90 hertz. So, that means this tau period if you are transferring the polarization from proton to nitrogen you have to keep here tau around 2.7 millisecond for N H transfer and for carbon transfer it is less than that. So, total tau period here should be for nitrogen transfer 5.4 millisecond and for carbon it will be 1 by 2 into J which is say 140 hertz that will comes around total is 1.5 millisecond. So, inept has some disadvantage, disadvantage that we had that actually it gives us relative like incorrect relative intensity because of different spins and multiplates that we have seen and here one important parameter that we discuss is heteronuclear J coupling. So, if you are you have to select that tau times which is suited to 1 by 4 J. Now, then if the J coupling is quite a strong we have enough time if J coupling is weak then we have different time. So, we have to tune our tau and that is one of the demerit of this inept. The second problem is in case of multiplicity. So, if multiplicity comes then how the spectrum is going to be that is difficult. So, three problem the relative intensity and it depends upon heteronuclear J coupling and multiplicity of spins can cause the intensity anomaly of the spectrum that we achieved in inept. Now, here one can see an example if you have a spins which is say AX, A2X and A3X here inversion is going to be like this. So, X3, X2 and X1 intensity anomaly and some will be positive and negative signal if we record an inept signal. So, we need to know which is coming from which one and this is going to be difficult because negative and positive signal both we are getting in same spectrum. To circumvent that actually one can do a trick in inept and what we can do we can add another say spin a consequence. Inept sequence with this regard of multi plate distortion one can design an experiment which is called refocus inept. Refocus inept means we are adding an extra spin a consequence to the classical inept sequence. So, this additional spin a consequence is identical to the first one and it is added after the last 90 degree pulse and this helps us in refocusing the positive negative signal component. So, what actually it is if you look at here like inept we are starting from a 90 degree then we are waiting for a time tau which is 1 by 4 J. Now, we are simultaneously applying 180 degree pulse on A spin and X spin. We are waiting for again tau and then we are applying a 90 degree Y pulse on say proton followed by a 90 degree X pulse on carbon. So, A spin and X spin. Here we saw that we are getting a positive and negative signal. So, then we are saying let us do an spin echo added. So, that means spin echo is tau we are same tau here we are putting then applying again simultaneously 180 degree pulse on both spin and then we are waiting for tau. So, that actually changes the phase of all three's transition and then it becomes positive. So, here we can see we are getting negative positive negative, but if we do refocusing inept we are getting actually positive positive and positive that is what is the beauty of refocusing inept all signal becomes positive and extra thing we are doing here is applying an spin echo. So, if you remember spin echo is like a 90 tau 180 on both spin tau that refocus all the signal and gives us the positive signal. So, in vector diagram let us try to understand what is happening here. So, we are starting from say Z direction for A spin. We applied a 90 degree X pulse. So, if you remember last time we had drawn this schematic Z, X and Y. So, we started with Z direction of A spin we applied an X pulse. So, that means it went to minus Y direction. Now, here we are waiting for tau period. So, spin starts defaging like this we applied 180 degree pulse on X. So, it inverse the direction then we applied another 180 degree pulse on X. So, that changes the direction now we are waiting for tau. So, they come together and then we apply a 90 degree pulse on Y. So, now it goes to Z direction and here the magnetization on C13 we applied. So, this comes to Y direction and now we we detected that Y that was like this. So, now we are waiting for tau period. So, these spins again starts to move like this. They defage like this we applied simultaneously 180 degree pulse they invert and then we applied actually another tau period. So, they again come closer. So, they are now perfectly aligned in the detector plane and we are detecting it and because of this direction all 3 become now positive. That is what we achieved by adding the extra spin echo sequence after in a all signal become positive. Good. So, let us look at the summary of all those. So, what we are saying now this is our molecule where we are detecting the nitrogen signal for this molecule. So, nitrogen is one of the insensitive nuclei as you know it is gamma is 10 times less than proton. So, if we directly detect nitrogen we are getting very less signal and this is say J is 90 hertz. So, it will be separated by 90 hertz. Then we can enhance the signal by NOE and we can enhance by this NOE signal we can get it. If we do selective polarization transfer the same signal of these 2 will be enhanced for one for this and one for this. If we put up the signal for proton we are getting enhancement into transition of nitrogen one will be positive another will be negative. If we do inept we get this signal and if we do refocus inept both signal will be now positive and that is what we have here. So, by doing selective polarization transfer and inept we are getting certainly enhanced signal and that enhancement is substantial. So, that is what we are getting. So, here is just normal signal here selective polarization transfer because of inept and because of refocus inept all positive signal and if you compare from here to here we are getting substantially enhanced signal. So, that is what is all about polarization transfer in inept signal. Now, I will come to another important concept of polarization transfer is something called Hartmann-Hahn matching condition. So, qualitatively I will explain it you today and then in the next class we will look at more details of what actually Hartmann-Hahn matching condition is. Now, all the time we want to enhance the signal of X nuclei which is low from the more signal which is proton. So, proton has say higher signal and carbon has lower signal that is what we have say gamma of proton is more gamma of 13C is less and that is actually this is 4 times less. So, we want to enhance the signal for 13C how to do that. Now, even on the same as spectrometer that we recorded, so if B0 is same the signal for proton is going to be 4 times higher than the carbon. So, we learned the trick of inept and refocused inept to start with polarization transfer then inept and refocused inept we enhance the signal of 13C. But still we were not getting rid of say B0, B0 effect is there. Now, suppose we do some experiment something like this if the say energy level of proton is like this. So, this is say for proton and energy level for carbon is like this 13C. Now, if we want to transfer this polarization from here to here we can we do some experiment. So, energy for proton is like this and carbon is like this can we do some trick where we can match the energy level of both of these somehow. If you match it the polarization transfer from more abundant nuclei will happen to the less abundant nuclei and probably we can enhance the signal. So, that means we have to match the energy gap between carbon 13 and proton to transfer this signal. How to do that? That is next set of experiment which we can say that we bring in the same environment by doing some trick by doing some locking or you can like say some condition we apply where we start matching the energy gap between these two and that is called either you put them in rotating frame of reference or we can do something called we can match them by Hartman-Heyen matching condition. If you do that the polarization from H nuclei can be increased and that is actually called spin locking or Hartman-Heyen matching condition. So, let us see what actually we have to do and that mostly use this Hartman-Heyen matching condition is the crocs in the solid state NMR. So, here say proton signal and this is for carbon. Now, we want to see this is for 13c and this is for proton we want to match this condition. So, if we say here is omega H and here is omega 13c and if we want to match this condition we do something so that we bring them in a same plane or XY plane and lock them there by applying some pulse and during that probably the with a something called zero quantum flip flop the polarization will transfer from more abundant nuclei to the less abundant nuclei which is 13c. If you do that magnetization will transfer. So, this is called Hartman-Heyen matching condition in solid state how it is done if you say omega H and in solid if you if you know little bit we spin the sample with some frequency omega R with omega 13c if we match this condition then polarization from H spin transfer to X spin H spin to X spin which is 13c and signal can be enhanced. Same concept is used in liquid state where you bring them in XY plane and you lock them applying a weak RF pulse that briefly I mentioned to you in ROG. If you lock them in XY plane the magnetization from H spin will transfer to the X spin and that is called actually spin lock spin lock. So, locking spins in a particular direction for some time and then magnetization will transfer it says like a simple analogy you can take. So, there are two class of people one class is proton and one class is 13c they are not talking to each other but these guys has more energy than the 13c. If you lock them in a room for some time after talking to each other some energy level will be transferred from the more energy guys to less energy guys and that is how you can enhance the energy of the low energy people. So, that is called polarization transfer. So, essentially what we have to do by applying this weak RF pulse what essentially we are doing is matching this condition where we are putting gamma A into B1A is equal to gamma X into B1X. So, now this is not happening in the Ziemann term like if you remember Ziemann is B0 field. So, B0 is main magnetic field. So, earlier if you have seen gamma A B0 is not equal to gamma X B0 and that is how transfer is not happening. So, we are changing from here to here where by applying a weak RF pulse we are trying to match the condition where gamma A which is for proton and gamma X will match. So, now we are applying a weak RF pulse on proton and carbon and we try to match this condition this is called Hartmann-Hahn matching condition. Gamma of say 1H B1 gamma of 13C and B1 on 13C. So, gamma on B1 on proton. So, that means we are applying 2 B1 field 1 on proton 1 on carbon and by matching this condition we can transfer the polarization from proton to carbon. So, that means we have to apply a RF pulse on proton and an RF pulse on carbon which actually equalizes this or which matches this condition then polarization from H-spin will transfer to X-spin and this matching condition is called Hartmann-Hahn condition. So, this is Hartmann-Hahn condition. So, this condition is at the heart of many of the like Rozy experiment or Toxy experiment where bring the magnetization in XY plane and we lock them for some time by applying an RF pulse on H-spin and X-spin and this is also in the heart of all the polarization transfer dipolar based polarization transfer that happens in solid state where we enhance the signal of X-spin by transferring the polarization from H-spin in solids and we detect on X-spin because in solid we generally detect on X-spin because of the lines are sharp for X-spin. So, this trick we will discuss little more quantitatively in the next class where we learn how to do this transfer basically I mentioned to you we are going to match this condition in selective polarization transfer or by spin locking and matching the Hartmann-Hahn condition. So, we will continue from there and we discuss something called 1D Rozy experiment and 1D Toxic experiment for long transfer from proton spin to coupled X-spin. So, I will stop it here if you have any question please write to us and don't hesitate to ask we will try to respond everything. Thank you very much.