We measured the 1H 90 degree pulse widths for 20, 40, ..., 120 mM salt concentrations. The pulse was increased with increasing salt concentration. Is there any relation governing this?
The increase in the 1H 90* pulse width as a function of increased salt concentration is an inevitable phenomena in NMR measurements.This effect is even larger when it comes to Cryoprobe (higher Q). The main reason for the increase in the 1H 90° pulse width is simple, though the increase in salt concentration is advantageous to prevent your sample aggregation and improve sample solubility but this has negative effect on the NMR technical part . As you increase the salt concentration you are increasing the conductivity of the solution. Therefore it affect the matching/tuning of NMR circuit. Improper tuning and matching leads to RF power loss. i.e you are not delivering correct rf power in to the sample. That's why the width is longer then usual as a function of salt concentration. So you have to be careful about tuning and matching. Be careful about higher salt concentration that would leads to heating up of the sample and might cause severe damage to probe.This can be prevented by choosing proper salt concentration or low conducting salts instead of NaCl / KCl. This effect is negligible for hetero nuclei such as 13C, 15N.
Chemical shifts are mainly depends on the surrounding environment. Suppose if your sample is aggregated with low salt concentration you can see the changes in the chemical shift when you compare the same sample which is not aggreagated. Therefore its purely depends on the system behavior with respect to salt concentration.
As per I know there is know exact mathematical equation or a constant to quantify the effect of salt on the 90°pulse.
This is mainly explained by the inherent "shielding" effect of salt ions on the environment of your molecules and increase sample conductivity. It introduce noise and reduce the efficiency of your rf pulses (tuning and matching are modified). Higher pulse power needed induce sample heating (which gives line broadening) and radiation damping. The two ways I know to reduce the effect, without dilution, are :
(i) to use shaped tubes which reduced the noise introduced on the lateral side of tubes (please see : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3065960/). You can find it on Bruker store but it is quite expensive.
(ii) The simplest way, I recommend, is to reduce the diameter of tubes (from 5mm to 3mm).
If you are in the sub-molar concentration of salts, you should be able to work classically by adapting pulse power (take care to not damage the probe). What is your proton 90° pulse duration? Keep 1H pulse width < 12us on 3mm sample tubes.
The effect on chemical shifts is not simple. Shielding effect is of course present but it is very difficult to predict salts' effect as you also have Curie effect contact, paramagnetic effect of some ions, osmotic pressure modifications with neutralization of polar charges, hydrophobic effects of some ions, etc, which modify the structure and properties of molecules.
I disagree with Vasantha about an explanation relying on the conductivity of the solution. The NMR circuit is an RLC circuit so changes in the resistance will affect the overall frequency of your tuning. However, your sample is not a part of this circuit and its resistance value has no effect on the matching tuning. And if the argument he made were correct, you would expect the effects to be the same for all nuclei being measured (which he states it is not).
The explanation hinges on how large the H1 field is. Think about it this way: your sample is sitting inside of a coil of wire (a solenoid). Physics (E&M) tells us that when you apply an electric current to a solenoid, a magnetic field is made which points along the axis of the solenoid. This is what we call H1...which is perpendicular to the field of your larger magnet.
NMR works because everything is made up of nuclear spins which precess (like a dreidel...or a toy top) around the axis of your external field. In other words, all the spins want to point up. When you apply the H1 field, this rotates your spins to an angle which depends on how long you apply the pulse.
Changing the conductivity of your sample does not affect H1. I'm not really an expert on liquid NMR but I can try a reasonable guess for why the t90 might change. One of the hard parts of describing liquid NMR (as opposed to solids) is that the nuclei are moving around all the time. This is why you expect to have very narrow lines (on the order of ppm). Adding salt to a liquid sample is typically done because you want to adjust some of the relaxation times. My guess is that the salt acts like a brake on your system making it harder for your proton spins to rotate...and easier for you to make a measurement. From the simplest perspective, you'd expect this to have more of an effect on proton than 13C or 15N...proton is typically more reactive than these other two nuclei so it should feel the brakes more.
Anyways, there are a bunch of quantum mechanical formulas which govern this but there's not really a simple formula for calculation what the t90 will be. An experimental measurement is always the best way to find it.
The salt is just like a shield, you should be careful with the concentration because too high salt concentration with affect tune and shimming which are critical for getting a decent spectrum. The chemical shift would change if the salt ion could bind to your compound by any force.