Hi Jeff and all who contributed to answering his question,
There is one aspect of the “variable delay” CPMG technique that worries me somewhat and I think it is actually the result of an approximation that many people just take for granted (or are unaware of).
If you take the basic CPMG sequence as being 90-tau-180-2*tau-180-2*-tau- etc, with the phase of the first (90 degree) pulse orthogonal to all the subsequent (180 degree) pulses, then in the limit that tau-> zero you are left with an on-resonance T1rho sequence (90-spinlock). This means that even if you have no effects due to dynamics, as you change the tau spacing from long to short to zero the value you measure must change (presumably smoothly) from T2 to T1rho. While these two may be the same in the extreme narrowing limit, they are not necessarily so otherwise. Which suggests that what you measure as “T2” may depend on the tau spacing even in the absence of exchange phenomena.
The approximation that I referred to in the first paragraph is that the duty cycle is generally so low that you can effectively ignore the effects of relaxation during the pulses, which I believe is not always the case.
Please enlighten me.
Kind regards,
Alan
> On 1 Feb 2017, at 18:14, Ellena, Jeffrey F. (jfe) <jfe_at_eservices.virginia.edu> wrote:
>
> Thanks to Jaison, Dmitry, David H., Robert, Dejan, Sameer, Ranjith, and Gennady for responding to my relaxation dispersion questions and to Genevieve and David R. for eliciting answers. Most of the answers were helpful; two were exceptionally helpful and are reproduced below. The second answer below greatly enhanced my understanding of the CPMG relaxation dispersion experiments and helped us (me and a local collegue) to think about analysis of relaxation dispersion data in a more rigorous way.
> Best,
> Jeff
>
> Answer1
> 1/ I consider nu CPMG or "CPMG B1 field" like the B1 field calculated from PW90.
>
> 1/(4*PW90) - 'time for a 360 degree rotation' - gives you the
> B1 field in Hz.
>
> In a CPMG pulse train, t'-180-t'-t'-180-t' (t'=t-pw180/2) - 4*t is the time for a 360, hence, the CPMG frequency or "CPMG B1
> field"=1/(4*t) in Hz.
>
> 2/
> In some expts, (eg: J Phys Chem B 112 5898 (2008) paper) minimum two (t-18o-t) periods can be used - experiments where imperfections in N180 pulses are compensated for
> (- in this case phase cycling of the N180 between the two t-180-t periods - Figure 1, CW CPMG sequence).
>
> Answer2
> Your inquiry regarding inter-pi-pulse spacing in CPMG relaxation studies was passed on to me and I think I may be able to shed some light on the issue. Before getting into the nitty-gritty, I'd just like to say that this issue has, historically, been an inconvenience and a source of error for these sorts of studies and it is a shame that a standard convention does not exist. At the end of the day, it all actually boils down to aesthetic; allow me to elaborate....
>
> One CPMG "unit" can be represented (<--delta-->PI-PULSE<--delta-->). The first question regarding aesthetic is "do we define delta as tau_cp/2 such that the total time for a single CPMG unit is 2*delta=2*(tau_cp/2)=tau_cp, or do we define delta as tau_cp such that the total time for a single CPMG unit is 2*delta=2*tau_cp. Historically, Loria and Palmer used the former, not the latter, convention (i.e. they define delta as tau_cp/2). Let's stick with this convention for the purposes of this discussion, so that one CPMG unit becomes (<--tau_cp/2-->PI-PULSE<--tau_cp/2-->).
>
> The dispersion in relaxation rates, as you know, is achieved by varying tau_cp/2 during a constant relaxaiton period (say, T), such that an integral number of pi-pulses fit into the period T. The consequence is that varying tau_cp/2 changes the rate at which the pi-pulses are applied. In other words, 1 pi pulse is applied for every 2 time periods tau_cp/2, which really means 1 pi pulse is applied for each tau_cp such that the rate of pi-pulsing is 1/tau_cp. The relevant equations for analysis of relaxation dispersion data via CPMG (i.e. the carver-richards equation, Luz-Meiboom equation, Bloch-McConnell equations, and the menagerie of all of the other analytical approximations), as used historically by Loria and Palmer, rely on the definitions established so far. However, Kay (and many others, including Kern, Peng, etc) started using a different definition for what constitutes a single CPMG unit.
>
> Unlike the classic definition of a CPMG unit that I've established thus far, Kay's convention is to call 2 of these classic units as a single CPMG unit - i.e. a single CPMG unit for him is (<--delta-->PI-PULSE<--delta-->|<--delta-->PI-PULSE<--delta-->), or in terms of our convention delta = tau_cp/2 we can represent this as (<--tau_cp/2-->PI-PULSE<--tau_cp/2-->|<--tau_cp/2-->PI-PULSE<--tau_cp/2-->). Thus using Kay's definition of a single CPMG unit, we see that it lasts a time 4*delta=4*(tau_cp/2)=2*tau_cp. This is exactly where that factor of two that is in question comes from! Now we must ask WHY he chose to do this!?
>
> The rationale behind Kay's definition of the length of a CPMG unit being twice as long as that the classic definition is because by using the classic definition of the CPMG unit, we need to have an even number of these units crammed into a relaxation period T. This has to do with the self-compensating behavior of the refocusing pulses in regards to imperfect pulse-lengths (I refer you to the wonderful review paper by Loria and Kempf titled "Measuring Intermediate Exchange Phenomena", where they address this in one or two of the paragraphs). Thus, using the classic definition of the CPMG unit, the minimum number of these that we'd have to cram into a relaxation period T is 2 such units, which lasts a total time 2*tau_cp. Well, this is where Kay's definition comes in. Since he calls the time 2*tau_cp as the time it takes to complete one minimum "full CPMG cycle" (i.e. 2 classic CPMG units), the strength of an effective field that would rotate your magnetization vector 360 degrees in a time 2*tau_cp (let's call this field the "CPMG field") is such that, when converted from Tesla to frequency units becomes nu_cpmg = 1 cycle for each period 2*tau_cp = 1/(2*tau_cp). Since the units are now "cycles per second", we can treat this as Hertz. Contrast this with the classic definition of a CPMG unit, which only represents half of a minimum CPMG cycle, and so the units are "per second" and not Hertz (which is cycles per second, with "cycles" being a fictitious unit). As you can see, this becomes extremely pedantic and unnecessarily complicated for no reason. Thus, if you use Kay's definition, you will have to modify all of the relevant analytical equations using the relationship 1/tau_cp = 2*nu_cpmg.
>
> As if this didn't already give you a headache, let me throw one more caveat your way to watch out for. In some papers, instead of defining the inter-pi-pulse delay (i.e. delta) as tau_cp/2, they define it as tau_cp. Thus, in the classic case 1/tau_cp turns into 1/(2*tau_cp), BUT nu_cpmg becomes 1/(2*(2*tau_cp))=1/(4*tau_cp)!
>
> I hope that wasn't terribly confusing and that at least some of it makes sense. My suggestion is stick to the Palmer/Loria classic definitions with tau_cp/2 and plotting your relaxation rates vs. 1/tau_cp and using the equations as found in their papers. Please let me know if I can clarify anything or if you have any other questions!
>
> From: Ellena, Jeffrey F. (jfe)
> Sent: Wednesday, January 25, 2017 4:03 PM
> To: ammrl_at_ammrl.org
> Subject: CPMG relaxation dispersion
>
> Can anyone tell me why nu CPMG in many of the Kay lab CPMG experiments is 1/2Tcp where Tcp is the time between 180 CPMG pulses instead of 1/Tcp? Also why is 4 the minimum number of required Tcp-Pn180-Tcp periods instead of 2? Please see papers below. Thanks for considering this.
> Refs.
> JACS 123 967 (2001)
> J Phys Chem B 112 5898 (2008)
> Best,
> Jeff Ellena
Received on Fri Feb 03 2017 - 01:17:57 MST