1. MRSFall 2006 Meeting Nov.27-Dec.1, 2006 Boston USA
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MRSFall 2006 Meeting Nov.27-Dec.1, 2006 Boston USA
By ARAVAMUDHAN, Sankarampadi Department of Chemistry North Eastern Hill University SHILLONG INDIA Session MM17.2: December 1, :00AM
Title of the Talk: Line Shapes in Magnetic Resonance and the Average Static Magnetic Field in the Medium: The Role of Discreteness and Continuum within the Material
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MRSFall 2006: Dec.1,2006: MM17.2: 11:00AM

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The task would be to calculate the induced field inside the cavity σcavity
Organic Molecular single crystal : a specimen of arbitrary shape
I.V.E Sphere
Induced field calculation by discrete summation σinter
Continuum
σIVE = σinter + σM
Discrete
I.V.E. Cavity
Added σinter
Shifts the
line position
σcavity = σBulk +σM O
Inner Volume Element I.V.E H O
σintra / σM O O
4 point star indicates the molecule at a central location. Structure of a typical molecule on the right
σIVE(S) σM O H
In-homogeneity can cause line shape alterations: O
not simply shifts only
Proton Site with σintra
single sharp line
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3. Intra molecular Shielding σ=‘σM’
Line (position) shifts & Line shape changes
NMR Line for only
Intra molecular Shielding σ=‘σM’
Added intermolecular : σInter Contributions causes a shift downfield or up field σ = ‘σM’+‘σInter’ ’+‘σB (homogeneous)’
Homogeneous no line shape alterations
Slightly inhomogeneous
Nearly spherical
& shifted
& shifted
Highly inhomogeneous
Cylindrical
Inhomogeneous Magnetization can cause line shape alterationsσ = ‘σM’+‘σInter’ ’+‘σB (in-homogeneous)’
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(1-3.cos2θ) term causes +ve & -ve contributing zones
See drawing below
Lattice
summation
Shell by Shell
Induced field varies as R-3
Number of molecules in successive shells increase as R2
Magnetic Field
Product of above two vary as R-1
Each moment contributes to induced field
The above distance dependences can be depicted graphically
Dashed lines: convergence limit
2 A˚ equal spacing
Benzene
Molecule &
Its magnetic
moment
When the R becomes large, the R-1 term contribution becomes smaller and smaller to become insignificant
-ve zone
{χM . (1-3.COS2θ)}/(RM)3
+ve
Magnetic field direction
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First and Foremost it is to be pointed out that trying to sum the induced field contributions in the discrete region by taking the molecule by molecule contributions from the neighborhood, results in a convergence of the summed value to a total sum, which can be termed as Intermolecular contributions. This convergence is depicted below in the actual single crystalline case of an Organic molecular single crystalline system.
The summed up contributions from within Lorentz sphere as a function of the radius of the sphere. The sum reaches a Limiting Value at around 50Aº. These are values reported in a M.Sc., Project (1990) submitted to N.E.H.University. T.C. stands for (shielding) Tensor Component .Convergence occurred in this particular case at 50 Aº radius.
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Description of a Procedure for Evaluating the Induced Field Contributions from the Bulk of the Medium
The Case of a Cylindrically shaped specimen would be illustrated
Radial Vector with polar coordinates: r, θ, φ. (Details to find in 4th Alpine Conference on SSNMR presentation Sheets 6-8)
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Study of PORUS Materials could be complimentary since the voids produce FIELD Gradients.
This Field Gradients are attributed (1) to Δχ values among the other specimen characteristic parameters.
The field variations due to such Susceptibility Anisotropy are typically the induced field distributions due to in-homogeneity of the specimen medium.
The inhomogeneous medium and the summation procedure conveniently applicable are discussed at
Thus the methods of calculating the induced fields by the alternative summation procedure could further substantiate the trends and applicability of the experimental procedures for the measurement of induced field distribution.
Internal Magnetic Field Gradients: Experimental Study, Page 153 Abstract EMR-17, EUROMAR2008
Reference therein: Song,Y.-Q. Using Internal magnetic Fields…..Pore Size Distributions….Porus Media, Concepts In Magnetic Resonance, 2003, V.18A, No2,P,97-110
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Correlating ‘r’ and ‘r -3’
Calculation of the Induced Field Distribution in the region outside the magnetized spherical specimen
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A cylinder shaped specimen (Blue line in the plot below)
The points on the Blue line would be specified and at these Calculated field values an NMR line would be placed after adding the sum total of intra and intermolecular contributions to induced fields.
Calculations at 9 points along the axis
Zero ind. Field Points
Not to be discussed in this presentation
Distance along the axis
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11. Only inter molecular value 5
Only inter molecular value 5.80E-07 was added and the line shape was plotted with those values : NEXT GRAPHICAL PLOT
A Graph
of the data in table
Cylinder
By Calculation
Trend line interpolation 7
-2.87E-07
-2.9E-07 6
-1.9E-07 5
-1.87E-07
-1E-07 4
3.25E-08
-2.8E-08 3
2.8E-08 2
6.45E-08
6.8E-08 1
9.2E-08
9.35E-08
1E-07 -1 -2 -3 -4 -5 -6 -7
Overlapping last three lines
Lines at interpolated values
Only inter molecular value 5.80E-07 can be set = 0
No intra molecular Value; inter-
molecular value (in I.V.E) set=0 in subsequent plots; only cavity field is used to generate
line shapes
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Same graph as displayed in previous slide
Gradual increase of component lines broadens the lines and can cause the change in the appearance of overall shape. Illustration with 4 different width values
10 times that of red Width 2.5 times that of green
Width twice that of blue
Width twice that of red
Same width as above
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Line at σIVE
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14. QUESTIONS, REMARKS & COMMENTS Picture: A VIEW at NEHU Campus
END OF PRESENTATION
QUESTIONS, REMARKS & COMMENTS
Picture: A VIEW at NEHU Campus
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