What does radiofrequency really do in NMR & MRI?

In NMR, the protons’ frequencies are affected by the magnet which makes them precess around its magnetic field so now all protons will have different frequencies according to their environment including shielding and de-shielding effects. As I read, the radio frequency pulses only change the resonance of protons and make their $\omega$ angle change ($180^\circ$) to be induced inside the coil and make signals that can be measured.


But if this true why do we have to use different gradient coils and phase encoding gradient coils in MRI, if the protons really have different frequencies? 




The radiofrequency pulses and the gradients have completely different purposes in NMR. Radiofrequency pulses are the basic building block of NMR experiments, you use them to manipulate your spin populations and coherences. While each proton has a different frequency depending on its environment, you generally can't (or don't) target individual protons with your pulses. In most experiments you hit either all protons with your pulses, or a specific group of protons. 


Gradients have different purposes in NMR and MRI, what they allow you to do is to change the magnetic field depending on the position inside your sample. In NMR this allows you to remove unwanted signals and select specific coherences. 


In MRI, the gradients are what makes imaging possible. They allow you to encode the spatial position of your protons into their frequency. In NMR you look at all the molecules in your sample at once, you don't care *where* your molecules are floating around. In MRI the position is important, as you want to know what the protons *at a particular point in the body* are doing. Gradients also allow you to only look at a slice of the body and not all of it at once.


I'll skip phase encoding in gradients as it is MRI-specific and I don't know much about it. Each part of your question has whole books written about it, so this is a drastically simplified answer.


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The purpose of MRI is to get *spatial* information from the spins. It is true that chemical shifts give protons in different *chemical* environments different frequencies, however, the chemical shifts will not reflect any spatial information. For example, all of the water in the body has (roughly) the same chemical shift, whereas fat all has (roughly) a different chemical shift than water, but (roughly) the same chemical shift as all other fat in the body. If you left out the magnetic field gradients and the phase encode pulses, you would simply end up with a stand 1D proton NMR spectrum that had two broad peaks in it (one for water and the other for fat).


The gradient coils artificially spread out the precession frequencies much more than the chemical shifts do (in fact, the chemical shift differences are largely overwhelmed by the gradient coils). RF pulses with a bandwidth sufficient to excite the frequencies spread out by the gradient coils will have no problem with the relative small difference created by the chemical shifts, so all of the spins are still excited (Note: A 180º pulse would produce no signal. A 90º pulse would produce the maximum signal, but for signal-to-time reasons, MRI typically uses trains of small angle pulses, often as small as just a few degrees).


However, we can't ignore the chemical shifts entirely. After-all, we interpret differences in precession frequency as differences in position. This means that spins with different chemical shifts will produce images that show up at different positions in our final MRI image! Even worse than simple *ghosting* depending on the MRI protocol, you may get very bizarre artifacts due to the chemical shift differences... A great many clever protocols have been developed that exploit off-resonant effects to selectively excite only a narrow chemical shift bandwidth or to minimize the resulting artifacts, etc.


I would highly recommend getting a copy of Dwight Nishamura's book **Principles of Magnetic Resonance Imaging**. Very readable with lots of insight on what the spins are doing and what the pulse sequences are doing. One of the best introductions to MRI that I've read. He discusses this issue of chemical shift artifacts about half-way through the book if I remember correctly.


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