Author: bugman
Date: Mon Jun 17 14:15:36 2013
New Revision: 20174
URL: http://svn.gna.org/viewcvs/relax?rev=20174&view=rev
Log:
Expanded the modelling of dispersion data section of the relax user manual.
Modified:
branches/relax_disp/docs/latex/bibliography.bib
branches/relax_disp/docs/latex/relax.tex
branches/relax_disp/docs/latex/relax_disp.tex
Modified: branches/relax_disp/docs/latex/bibliography.bib
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/bibliography.bib?rev=20174&r1=20173&r2=20174&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/bibliography.bib (original)
+++ branches/relax_disp/docs/latex/bibliography.bib Mon Jun 17 14:15:36 2013
@@ -501,6 +501,28 @@
size = {2 p.},
sourceid = {ISI:000073645600043},
year = 1998
+}
+
+@Article{Bloch46,
+ Author = {Bloch, F.},
+ Title = {Nuclear induction},
+ Journal = physrev,
+ Volume = {70},
+ Number = {7-8},
+ Pages = {460-474},
+ address = {ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA},
+ doc-delivery-number = {UB265},
+ doi = {10.1103/PhysRev.70.460},
+ issn = {0031-899X},
+ language = {English},
+ number-of-cited-references = {14},
+ publisher = {AMERICAN PHYSICAL SOC},
+ research-areas = {Physics},
+ times-cited = {2053},
+ type = {Article},
+ unique-id = {ISI:A1946UB26500003},
+ web-of-science-categories = {Physics, Multidisciplinary},
+ year = 1946
}
@Article{Bloembergen48,
@@ -4162,6 +4184,30 @@
year = 1963
}
+@Article{McConnell58,
+ Author = {McConnell, H.M.},
+ Title = {Reaction rates by nuclear magnetic resonance},
+ Journal = jcp,
+ Volume = {28},
+ Number = {3},
+ Pages = {430-431},
+ address = {CIRCULATION FULFILLMENT DIV, 500 SUNNYSIDE BLVD,
+ WOODBURY, NY 11797-2999},
+ doc-delivery-number = {WA154},
+ doi = {10.1063/1.1744152},
+ issn = {0021-9606},
+ journal-iso = {J. Chem. Phys.},
+ language = {English},
+ number-of-cited-references = {7},
+ publisher = {AMER INST PHYSICS},
+ research-areas = {Physics},
+ times-cited = {1114},
+ type = {Article},
+ unique-id = {ISI:A1958WA15400013},
+ web-of-science-categories = {Physics, Atomic, Molecular \& Chemical},
+ year = 1958
+}
+
@Article{Meiboom61,
Author = {Meiboom, S.},
Title = {Nuclear magnetic resonance study of proton transfer
Modified: branches/relax_disp/docs/latex/relax.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/relax.tex?rev=20174&r1=20173&r2=20174&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/relax.tex (original)
+++ branches/relax_disp/docs/latex/relax.tex Mon Jun 17 14:15:36 2013
@@ -105,6 +105,8 @@
\newcommand{\Ronerhoprime}{\mathrm{R}_{1\rho}'}
\newcommand{\Rtwoeff}{\mathrm{R}_{2\textrm{eff}}}
\newcommand{\Rtwozero}{\mathrm{R}_2^0}
+\newcommand{\RtwozeroA}{\mathrm{R}_{2A}^0}
+\newcommand{\RtwozeroB}{\mathrm{R}_{2B}^0}
\newcommand{\tex}{\tau_\textrm{ex}}
\newcommand{\taucpmg}{\tau_\textrm{CPMG}}
Modified: branches/relax_disp/docs/latex/relax_disp.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/relax_disp.tex?rev=20174&r1=20173&r2=20174&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/relax_disp.tex (original)
+++ branches/relax_disp/docs/latex/relax_disp.tex Mon Jun 17 14:15:36 2013
@@ -22,14 +22,41 @@
\section{The modelling of dispersion data}
-The modelling of relaxation dispersion data can be catergorised into two
distinct methodologies:
-
-\begin{itemize}
-\item Optimisation of models based on analytical, closed-form expressions
derived from the Bloch-McConnell equations subject to certain conditions.
-\item Optimisation of models via numerical integration of the
Bloch-McConnell equations.
-\end{itemize}
-
-Only the optimisation of the analytic models is currently supported in
relax. These models are dependent upon whether the data originates from a
CPMG-type or $\Ronerho$-type experiment. For the CPMG-type experiments, the
models currently supported are:
+For a system under the influence of chemical exchange, the evolution of the
transverse magnetisation is given by the \citet{Bloch46} equations as
modified by \citet{McConnell58} for chemical exchange -- the Bloch-McConnell
equations.
+For a two state exchange jumping between states A and B, the equation is:
+
+\begin{equation} \label{eq: Bloch-McConnell}
+ \frac{d}{dt} \left[
+ \begin{array}{c}
+ M_A^+(t) \\
+ M_B^+(t)
+ \end{array}
+ \right] = \left[
+ \begin{array}{cc}
+ -i\Omega_A-\RtwozeroA-\pB\kex & \pA\kex \\
+ \pB\kex & -i\Omega_B-\RtwozeroB-\pA\kex \\
+ \end{array}
+ \right] \left[
+ \begin{array}{c}
+ M_A^+(t) \\
+ M_B^+(t)
+ \end{array}
+ \right] .
+\end{equation}
+
+The solution to this equation then Fourier transformed to produce the NMR
spectrum. However the analytic or closed-form frequency-domain solution
remains intractable.
+
+Solutions can nevertheless be found by either making assumptions or
restrictions about the exchange process and then analytically
solving~\ref{eq: Bloch-McConnell} or by numerical simulation.
+The modelling of relaxation dispersion data can hence be catergorised into
these two distinct methodologies:
+
+\begin{description}
+\item[Analytical models:]\index{relaxation dispersion!Analytical model}
Optimisation of models based on analytical, closed-form expressions derived
from the Bloch-McConnell equations subject to certain conditions.
+\item[Numerical models:]\index{relaxation dispersion!Numerical model}
Optimisation of models via numerical integration of the Bloch-McConnell
equations.
+\end{description}
+
+Currently only the optimisation of the analytic models is supported in relax.
+These models are dependant upon whether the data originates from a CPMG-type
or $\Ronerho$-type experiment.
+For the CPMG-type experiments, the models currently supported are:
\begin{description}
\item[`R2eff':]\index{relaxation dispersion!R2eff model} This is the model
used to determine the $\Rtwoeff$ values and errors required as the base data
for all other models,
@@ -49,7 +76,9 @@
\item[`M61 skew':]\index{relaxation dispersion!M61 skew model} The
\citet{Meiboom61} 2-site equation for all time scales with $\pA \gg \pB$ and
with parameters \{$\mathrm{R}_{1\rho}'$, $\dots$, $\pA$, $\dw$,
k$_\textrm{ex}$\},
\end{description}
-Except for `R2eff' and `No Rex', these CPMG and $\Ronerho$ models are fit to
clusterings of spins, or spin blocks. The models are described in more
detail below. The parameters are given in Table~\ref{table: dispersion
parameters}.
+Except for `R2eff' and `No Rex', these CPMG and $\Ronerho$ models can be fit
to clusterings of spins, or spin blocks.
+The models are described in more detail below.
+The parameters are given in Table~\ref{table: dispersion parameters}.
\begin{sidewaystable}
\begin{center}
r20174 - in /branches/relax_disp/docs/latex: bibliography.bib relax.tex relax_disp.tex