Trusted, Bureaucrats
4,228
edits
Changes
Jump to navigation
Jump to search
<keywords content="diffusion rates{{Caution|If hard core NMR or physics theory is not to your taste, dimensionless units, hidden units, radian, relaxation rates, rotational correlation times, SI supplementary units, spherical harmonics" />please do not read any further!}}
'''Warning:''' If hard core The concept of the hidden radian unit is quite important for understanding relaxation in NMR or , in fact, any rotational process in physics theory . For example it is important for understanding the model-free equations, for reduced spectral density mapping, for SRLS, and for relaxation dispersion. In these cases, the reason is because relaxation rates are measured in rad/s. As described in [[#SI supplementary units]], the radian unit can be dropped because it is plainly obvious that NMR and relaxation is not an angular process and hence radian units are implied (if you didn't get that, that was sarcasm). Hence R2 can be said to your tastebe in units of 1/s, but never, ever Hz. Also note that because of the SI conventions described below, please do describing the correlation time in s units does not read any further!imply that there are no radian units. But reporting rates as Hz implies no radian units whereas reporting as 1/s instead indicates that radian units are present.
This is also a follow on The text below uses quotes from many different sources to demonstrate that the [https://mail.gna.org/public/relax-devel/2007-06/msg00012.html comprehensive hidden radian unit analysis of Abragam's relaxation equations]is actually very much present in everything we do in NMR.
Title: Nuclear Spin Relaxation in Liquids: Theory, Experiments, and
Applications
Authors: Józef Kowalewski, Lena Mäler
Subject: NMR relaxation
Year: 2006
Link:
http://books.google.com/books?id=MiUfcE1C9CQC&pg=PA14&dq=relaxation+rate+radian&lr=#PPA19,M1
Quote (page 15): "Because the natural unit for the angular frequency
is radians per second, the relaxation rate, or the inverse of
relaxation time, R2 = 1/T2, should indeed also be expressed in these
units. Usually, relaxation times are given in seconds (the rates are
given in 1/s), which tacitly implies that the radians can be omitted;
we note in parenthesis that the radian is considered a dimensionless
unit in physics."
Quote 2 (page 15): "The Fourier transform of an exponential decay is
Lorentzian centered at zero frequency, with the full width at
half-height (in Hertz) equal to Delta_nu = 1/(pi.T2)..."
Title: Modern Protein Chemistry: Practical AspectsAuthors: Gary C. Howard, William E. BrownSubject: NMR relaxationYear: 2001Link: http://books.google.com/books?id=MIxdC7GPz0sC&pgSee also =PA45&dq=rotational+correlation+time+radian&lr=Quote (page 45): "The actual relationship between the spin-spinrelation rate and the lines width (Delta_nu) is given by R2, the rateof spin-spin relaxation; T2 is the time constant for spin-spinrelaxation, Delta_nu = 1/pi . R2 = 1/(pi.T2)."
Title[[Category: Structural Biology: Practical NMR ApplicationsAuthor: Quincy TengSubject: NMR relaxationYear: 2005Link: http://books.google.com/books?id=dRmmGFkummIC&pg=PA36&dq=rotational+correlation+time+radian&lr=#PPA36,M1Quote (page 37): "...T1 relaxation is inversely proportional tocorrelation time tau_c..."Theory]]
Changed the {{warning}} to a {{caution}}.
A major point of confusion in the NMR field is that of the dimensionless and hidden radian unit. This often results in people mistakenly writing Hertz units when inverse seconds (or rad/s) should have been used. This issue can be traced back to the [http://en.wikipedia.org/wiki/International_System_of_Units SI] organisation itself. Specifically the SI supplementary units definitions whereby the assumption is made that if a process is rotational, a physicist should know that radian units are implicit.
== Introduction ==
This concept is quite important for understanding relaxation in NMR or, in fact, any rotational process in physics. It is important for understanding also a follow on from the model-free equations, for reduced spectral density mapping, for SRLS, and for relaxation dispersion. The reason is because relaxation rates are measured in rad[https://smail. As described in [[#SI supplementary units]], the radian unit can be dropped because it is plainly obvious that NMR and relaxation is an angular process and hence radian units are implied (that was sarcastic)gna. Hence R2 can be said to be in units of 1org/public/relax-devel/2007-06/s, but never, ever Hzmsg00012. Also note that because html comprehensive unit analysis of the SI conventions described below, describing the correlation time in Abragam's units does not imply that there are no radian units. But reporting rates as Hz implies no radian units whereas reporting as 1/s instead indicates that radian units are presentrelaxation equations].
== Source ==
</math>
where <math alt="theta''θ(t)">\theta(t)</math> '' and <math alt="phi''ϕ(t)">\phi(t)</math> '' are the time dependent spherical angles in the dimensionless radian units. The time ''t '' is normal time and hence has no hidden radian units. Spherical harmonics are the angular portion of the solution to Laplace's equation and, because it is angular, it is using the radian angular SI unit.
== Rotational correlation times ==
=== Book quotations ===
;Title:Nuclear Spin Relaxation in Liquids: Theory, Experiments, and Applications;Authors:Józef Kowalewski, Lena Mäler;Subject: NMR relaxation;Year:2006;Link: http://books.google.com/books?id=MiUfcE1C9CQC&pg=PA14&dq=relaxation+rate+radian&lr=#PPA19,M1;Quote (page 15)<blockquote>Because the natural unit for the angular frequency is radians per second, the relaxation rate, or the inverse of relaxation time, R2 = 1/T2, should indeed also be expressed in these units. Usually, relaxation times are given in seconds (the rates are given in 1/s), which tacitly implies that the radians can be omitted; we note in parenthesis that the radian is considered a dimensionless unit in physics.</blockquote>;Quote 2 (page 15)<blockquote>The Fourier transform of an exponential decay is Lorentzian centered at zero frequency, with the full width at half-height (in Hertz) equal to Delta_nu = 1/(pi.T2)...</blockquote> ;Title:Practical NMR Relaxation for Chemists;Author: Vladimir I. Bakhmutov;Subject: NMR relaxation;Year: 2004;Link: http://books.google.com/books?id=_gIh9KHIOx4C&pg=PA13&dq=rotational+correlation+time+radian&lr=;Quote (page 9): "<blockquote>...linewidths, Delta_nu, measured in Hz, aredirectly controlled by T1 and T2 relaxation times according to: Delta_nu = 1/(pi T1,2)</blockquote> ;Title:Modern Protein Chemistry: Practical Aspects;Authors:Gary C. Howard, William E. Brown;Subject:NMR relaxation;Year:2001;Link:http://books.google.com/books?id=MIxdC7GPz0sC&pg=PA45&dq=rotational+correlation+time+radian&lr=;Quote (page 45)<blockquote>The actual relationship between the spin-spin relation rate and the lines width (Delta_nu) is given by R2, the rate of spin-spin relaxation; T2 is the time constant for spin-spin relaxation, Delta_nu = 1/pi . R2 = 1/(pi T1.T2).</blockquote> ;Title:Structural Biology: Practical NMR Applications;Author:Quincy Teng;Subject:NMR relaxation;Year:2005;Link:http://books.google.com/books?id=dRmmGFkummIC&pg=PA36&dq=rotational+correlation+time+radian&lr=#PPA36,2M1;Quote (page 37)"<blockquote>...T1 relaxation is inversely proportional to correlation time tau_c...</blockquote>
