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Nuclear Magnetic Resonance (NMR)
Probe the Composition, Structure, Dynamics and
Function of the Complete Range of Chemical
Entities: from small organic molecules to large
molecular weight polymers and proteins.
One of the
Techniques
MOST
Routinely
used
Analytical
Common NMR Utility
• Structural (chemical) elucidation
• Natural product chemistry.
• Synthetic organic chemistry. Analytical tool of choice of
synthetic chemists.
• Study of dynamic processes
• Reaction kinetics.
• Study of equilibrium (chemical or structural).
• Structural (three-dimensional) studies
• Proteins.
• DNA. Protein/DNA complexes
• Polysaccharides
• Drug design
• Structure Activity Relationships by NMR
• Medicine - MRI
NMR: “fingerprint” of the compound’s chemical structure
2-phenyl-1,3-dioxep-5-ene
1H
NMR spectra
13C
NMR spectra
Protein Structures from NMR
2D NOESY Spectra at 900 MHz
Lysozyme Ribbon Diagram
NMR History
1937
1946
1953
1966
1975
1985
Rabi predicts and observes nuclear magnetic resonance
Bloch, Purcell first nuclear magnetic resonance of bulk sample
Overhauser NOE (nuclear Overhauser effect)
Ernst, Anderson Fourier transform NMR
Jeener, Ernst 2D NMR
Wüthrich first solution structure of a small protein (BPTI)
from NOE derived distance restraints
1987
3D NMR + 13C, 15N isotope labeling of recombinant proteins
(resolution)
1990
pulsed field gradients (artifact suppression)
1996/7 new long range structural parameters:
- residual dipolar couplings from partial alignment in liquid
crystalline media
- projection angle restraints from cross-correlated relaxation
TROSY (molecular weight > 100 kDa)
Nobel prizes
1944 Physics Rabi (Columbia)
1952 Physics Bloch (Stanford), Purcell (Harvard)
1991 Chemistry Ernst (ETH)
2002 Chemistry Wüthrich (ETH)
2003 Medicine Lauterbur (University of Illinois in Urbana ),
Mansfield (University of Nottingham)
Some Suggested NMR References
“Basic One- and Two-Dimensional NMR Spectroscopy” Horst Friebolin
“Modern NMR Techniques for Chemistry Research” Andrew E. Derome
“NMR and Chemistry- an introduction to the
fourier transform-multinuclear era” J. W. Akitt
“Nuclear Magnetic Resonance Spectroscopy” R. K Harris
“Protein NMR Spectroscopy: Principals and Practice”
John Cavanagh, Arthur Palmer, Nicholas J. Skelton, Wayne Fairbrother
“NMR of Proteins and Nucleic Acids” Kurt Wuthrich
“Tables of Spectral Data for Structure Determination of Organic Compounds”
Pretsch, Clerc, Seibl and Simon
“Spectrometric Identification of Organic Compounds”
Silverstein, Bassler and Morrill
Some NMR Web Sites
The Basics of NMR
Hypertext based NMR course
http://www.cis.rit.edu/htbooks/nmr/nmr-main.htm
Educational NMR Software All kinds of NMR software
http://www.york.ac.uk/depts/chem/services/nmr/edusoft.html
NMR Knowledge Base
A lot of useful NMR links
http://www.spectroscopynow.com/
NMR Information Server
News, Links, Conferences, Jobs
http://www.spincore.com/nmrinfo/
Technical Tidbits
Useful source for the art of shimming
http://www.acornnmr.com/nmr_topics.htm
BMRB (BioMagResBank)
http://www.bmrb.wisc.edu/
Database of NMR resonance assignments
Basic NMR Spectrometer
Information in a NMR Spectra
g-rays x-rays UV VIS
1) Energy E = hu
h is Planck constant
u is NMR resonance frequency 10-10
Observable
Name
10-8
IR
m-wave radio
10-6 10-4
10-2
wavelength (cm)
Quantitative
100
102
Information
d(ppm) = uobs –uref/uref (Hz)
chemical (electronic)
environment of nucleus
peak separation
(intensity ratios)
neighboring nuclei
(torsion angles)
Peak position
Chemical shifts (d)
Peak Splitting
Coupling Constant (J) Hz
Peak Intensity
Integral
unitless (ratio)
relative height of integral curve
nuclear count (ratio)
T1 dependent
Peak Shape
Line width
Du = 1/pT2
peak half-height
molecular motion
chemical exchange
uncertainty principal
uncertainty in energy
Source of the NMR Signal
From Quantum Theroy: Nuclear Spin (Think Electron Spin)
NMR “active” Nuclear Spin (I) = ½:
1H, 13C, 15N, 19F, 31P
 biological and chemical relevance
 Odd atomic mass
NMR “inactive” Nuclear Spin (I) = 0:
12C, 16O
 Even atomic mass & number
Quadrupole Nuclei Nuclear Spin (I) > ½:
14N, 2H, 10B
 Even atomic mass & odd number
Zeeman Effect and Nuclear Spin Quantum Number
Zeeman effect: splitting of energy levels in magnetic field
E= gBo
g magnetogyric ratio (radians/Tesla) - unique value per nucleus
1H: 26.7519 x 107 rad T-1 s-1
Bo applied magnetic field
- units:Tesla (Kg s-2 A-1)
NMR frequency: n = g Bo / 2p
I: hyperfine interaction associate with magnetization due to nuclear spin
quantum transitions
2I +1 possible energy levels
For I =1/2: m= -1/2 & 1/2
m: magnetic quantum number
NMR Spectra Terminology
TMS
CHCl3
7.27
increasing d
low field
down field
high frequency (u)
de-shielding
Paramagnetic
600 MHz
1H
0
decreasing d
high field
up field
low frequency
high shielding
diamagnetic
150 MHz
13C
ppm
92 MHz
2H
Increasing field (Bo)
Increasing frequency (u)
Increasing g
Increasing energy (E, consistent with UV/IR)
Another Viewpoint: Magnetic Moment (Nuclear Spin)
It is a vector quantity that gives the direction and magnitude
(or strength) of the ‘nuclear magnet’
magnetic moment (m) = g I h / 2p
quantized by Planck’s constant (h)
By convention:
spin +1/2 => a - low energy state
spin -1/2 => b
Analogous to
current moving in a
loop which induces
a magnetic field
(right-hand rule)
Magnetic alignment
= g h / 4p
Bo
In the absence of external field,
each nuclei is energetically degenerate
Add a strong external field (Bo).
and the nuclear magnetic moment:
aligns with (low energy)
against (high-energy)
NMR Sensitivity
The applied magnetic field causes an energy
difference between aligned(a) and unaligned(b) nuclei
b
Low energy gap
DE = h n
Bo > 0
a
Bo = 0
The population (N) difference can be determined from
Boltzmman distribution: Na / Nb = e DE / kT
The DE for 1H at 400 MHz (Bo = 9.5 T) is 3.8 x 10-5 Kcal / mol
Na / Nb = 1.000064
Very Small !
~64 excess spins per
million in lower state
NMR Sensitivity
NMR signal depends on: signal (s) % g4Bo2NB1g(u)/T
1)
2)
3)
4)
5)
Number of Nuclei (N) (limited to field homogeneity and filling factor)
Gyromagnetic ratio (in practice g3)
Inversely to temperature (T)
External magnetic field (Bo2/3, in practice, homogeneity)
B12 exciting field strength
Na / Nb = e
DE = g h Bo / 2p
DE / kT
Increase energy gap -> Increase population difference -> Increase NMR signal
DE
≡
Bo ≡
g
g - Intrinsic property of nucleus can not be changed.
(gH/gC)3
1H
for
13C
is 64x (gH/gN)3 for
is ~ 64x as sensitive as
13C
15N
is 1000x
and 1000x as sensitive as
15N
!
Consider that the natural abundance of 13C is 1.1% and 15N is 0.37%
relative sensitivity increases to ~6,400x and ~2.7x105x !!
NMR Sensitivity
Increase in Magnet Strength is a Major Means to Increase Sensitivity
But at a significant cost!
~$800,000
~$2,00,000
~$4,500,000
NMR Frequency Range (expensive radios)
g-rays x-rays UV VIS
10-10
10-8
IR
m-wave radio
10-6 10-4
10-2
wavelength (cm)
DE = h n
DE = g h Bo / 2p
100
102
n = g Bo / 2p
For 1H in normal magnets (2.35 - 18.6 T), this frequency is
in the 100-800 MHz range.
Classical View of NMR (compared to Quantum view)
Precession or Larmor frequency: w = 2pn  wo = g Bo (radians)
angular momentum (l)
l
wo
m
Bo
Simply, the nuclei spins about its
axis creating a magnetic moment m
Maxwell: Magnetic field ≡ Moving charge
Apply a large external field (Bo)
and m will precess about Bo at its
Larmor (w) frequency.
Important: This is the same frequency obtained from the energy
transition between quantum states
Bulk magnetization (Mo)
Now consider a real sample containing numerous nuclear spins:
Mo % (Na - Nb)
m = mxi + myj +mzk
z
z
Mo
x
y
x
y
Bo
Since m is precessing in the xy-plane, Mo =
Bo
∑ mzk – m-zk
m is quantized (a or b), Mo has a continuous number of states, bulk property.
An NMR Experiment
We have a net magnetization precessing about Bo at a frequency of wo
with a net population difference between aligned and unaligned spins.
z
z
Mo
x
y
x
y
Bo
Bo
Now What?
Perturbed the spin population or perform spin gymnastics
Basic principal of NMR experiments
An NMR Experiment
To perturbed the spin population need the system to absorb energy.
z
Mo
x
B1
Bo
y
i
Transmitter coil (y)
Two ways to look at the situation:
(1) quantum – absorb energy equal to difference in spin states
(2) classical - perturb Mo from an excited field B1
An NMR Experiment
resonant condition: frequency (w1) of B1 matches Larmor frequency (wo)
energy is absorbed and population of a and b states are perturbed.
z
Mo
B1
w1
z
x
B1 off…
x
(or off-resonance)
y
y
Mxy w
1
And/Or: Mo now precesses about B1 (similar to
Bo) for as long as the B1 field is applied.
Again, keep in mind that individual spins flipped up or down
(a single quanta), but Mo can have a continuous variation.
Right-hand rule
An NMR Experiment
What Happens Next?
The B1 field is turned off and Mxy continues to precess about Bo at frequency wo.
z
x
y
Mxy
Receiver coil (x)
wo
 NMR signal
FID – Free Induction Decay
The oscillation of Mxy generates a fluctuating magnetic field
which can be used to generate a current in a receiver coil to
detect the NMR signal.
NMR Signal Detection - FID
Mxy is precessing about z-axis in the x-y plane
Time (s)
y
The FID reflects the change in the magnitude of Mxy as
the signal is changing relative to the receiver along the y-axis
Again, it is precessing at its Larmor Frequency (wo).
y
y
NMR Signal Detection - Fourier Transform
So, the NMR signal is collected in the Time - domain
But, we prefer the frequency domain.
Fourier Transform is a mathematical procedure that
transforms time domain data into frequency domain
Laboratory Frame vs. Rotating Frame
To simplify analysis we convert to the rotating frame.
z
z
x
Bo y
Mxy
x
wo
Laboratory Frame
y
Mxy
Rotating Frame
Simply, our axis now rotates at the Larmor Freguency (wo).
In the absent of any other factors, Mxy will stay on the x-axis
All further analysis will use the rotating frame.
Chemical Shift
Up to this point, we have been treating nuclei in general terms.
Simply comparing 1H, 13C, 15N etc.
If all 1H resonate at 500MHz at a field strength of 11.7T,
NMR would not be very interesting
The chemical environment for each nuclei results in a unique local
magnetic field (Bloc) for each nuclei:
Beff = Bo - Bloc --- Beff = Bo( 1 - s )
s is the magnetic shielding of the nucleus
Chemical Shift
Again, consider Maxwell’s theorem that an electric current in a loop
generates a magnetic field. Effectively, the electron distribution in the
chemical will cause distinct local magnetic fields that will either add to or
subtract from Bo
HO-CH2-CH3
Beff = Bo( 1 - s )
de-shielding
high shielding
Shielding – local field opposes Bo
Aromaticity, electronegativity and similar factors will contribute
to chemical shift differences
The NMR scale (d, ppm)
Bo >> Bloc -- MHz compared to
Hz
Comparing small changes in the context of a large number is cumbersome
d=
w - wref
wref
ppm (parts per million)
Instead use a relative scale, and refer all signals (w) in the spectrum to the
signal of a particular compound (wref ).
IMPORTANT: absolute frequency is field dependent (n = g Bo / 2p)
CH 3
Tetramethyl silane (TMS) is a common reference chemical
H3C
Si
CH 3
CH 3
The NMR scale (d, ppm)
Chemical shift (d) is a relative scale so it is independent of Bo. Same
chemical shift at 100 MHz vs. 900 MHz magnet
IMPORTANT: absolute frequency is field dependent (n = g Bo / 2p)
At higher magnetic fields an NMR
spectra will exhibit the same chemical
shifts but with higher resolution because
of the higher frequency range.
Chemical Shift Trends
• For protons, ~ 15 ppm:
Acids
Aldehydes
Aromatics
Amides
Alcohols, protons a
to ketones
Olefins
Aliphatic
ppm
15
10
7
5
2
0
TMS
Chemical Shift Trends
• For carbon, ~ 220 ppm:
C=O in
ketones
Aromatics,
conjugated alkenes
Olefins
Aliphatic CH3,
CH2, CH
ppm
210
150
C=O of Acids,
aldehydes, esters
100
80
50
0
TMS
Carbons adjacent to
alcohols, ketones
Predicting Chemical Shift Assignments
Numerous Experimental NMR Data has been compiled and general trends identified
• Examples in Handout
• See also:
 “Tables of Spectral Data for Structure Determination of
Organic Compounds” Pretsch, Clerc, Seibl and Simon
 “Spectrometric Identification of Organic Compounds”
Silverstein, Bassler and Morrill
• Spectral Databases:
 Aldrich/ACD Library of FT NMR Spectra
 Sadtler/Spectroscopy (UV/Vis, IR, MS, GC and NMR)
Predicting Chemical Shift Assignments
NH2
Predict the chemical shifts of:
D
A
C
NO2
B
da
dd
dc
db
Benzene Shift
NO2 effect
NH2 effect
Change sign since table lists as downfield shift
7.27
0.95
-0.75
7.27
0.33
-0.75
7.27
0.17
-0.24
7.27
0.95
-0.63
From table 3-6-1 in handout:
Substituent
Shift relative to benzene (ppm)
ortho
meta
para
NO2
-0.95
-0.17
-0.33
NH2
0.75
0.24
0.63
Total
7.47 ppm
6.85 ppm
7.20 ppm
7.59 ppm
Predicting Chemical Shift Assignments
Predict the chemical shifts of:
Cb
|
C–C–C–C–C–C
a
2 a b g d
Chemical shift is determined by sum of carbon types.
From Table 3.2 in handout:
d=Bs + ∑ DmAsm +gSN3 +DsN4 - empirical formula
S – number of directly bonded carbons
Dm – number of directly bonded carbons having M attached carbons
Np – number of carbons P bonds away
d2 = B2 + [1xA23+ 1xA21 ] + [1xg2] + [1xD2]
d2 = 15.34 + [1X16.70 +1x0] + [1x-2.69] +[1x0.25] = 29.60 ppm
Coupling Constants
Energy level of a nuclei are affected by covalently-bonded neighbors spin-states
1
H
13
1
1
H
H
three-bond
C
one-bond
Spin-States of covalently-bonded nuclei want to be aligned.
+J/4
I
-J/4
bb
S
ab
J (Hz)
ba
S
+J/4
I
aa
I
S
The magnitude of the separation is called coupling constant (J) and has units
of Hz.
Coupling Constants
IMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei.
Multiplets consist of 2nI + 1 lines
I is the nuclear spin quantum number (usually 1/2) and
n is the number of neighboring spins.
The ratios between the signal intensities within multiplets are governed by
the numbers of Pascals triangle.
Configuration
Peak Ratios
A
1
AX
1:1
AX
1:2:1
AX
1:3:3:1
AX
1:4:6:4:1
2
3
4
Coupling Constants
NMR Relaxation
After the B1 field (pulse) is removed the system needs to “relax” back to equilibrium
Mz = M0(1-exp(-t/T1))
T1 is the spin-lattice (or longitudinal) relaxation time constant.
Think of T1 as bulk energy/magnetization exchange with the “solvent”.
Please Note: General practice is to wait 5xT1 for the system to have fully relaxed.
NMR Relaxation
Mx = My = M0 exp(-t/T2)
Related to line-shape
(derived from Hisenberg uncertainty principal)
T2 is the spin-spin (or transverse) relaxation time constant.
In general: T1 T2
Think of T2 as the “randomization” of spins in the x,y-plane
Please Note: Line shape is also affected by the magnetic fields homogeneity
NMR Time Scale
Time Scale
Slow
Intermediate
Fast
Range (Sec-1)
Chem. Shift (d)
k << dA- dB
k = dA - dB
k >> dA - dB
0 – 1000
Coupling Const. (J)
k << JA- JB
k = JA- JB
k >> JA- JB
0 –12
T2 relaxation
k << 1/ T2,A- 1/ T2,B
k = 1/ T2,A- 1/ T2,B
k >> 1/ T2,A- 1/ T2,B
1 - 20
NMR time-scale refers to the chemical shift timescale.
Exchange Rates from NMR Data
dobs = f1d1 + f2d2
f1 +f2 =1
k = p Dno2 /2(he - ho)
k = p Dno / 21/2
k = p (Dno2 - Dne2)1/2/21/2
h – peak-width at half-height
n – peak frequency
e – with exchange
o – no exchange
f – mole fraction
d – chemical shift
k = p (he-ho)
Continuous Wave (CW) vs. Pulse/Fourier Transform
NMR Sensitivity Issue
A frequency sweep (CW) to identify resonance is very slow (1-10 min.)
Step through each individual frequency.
Pulsed/FT collect all frequencies at once in time domain, fast (N x 1-10 sec)
Increase signal-to-noise (S/N) by collecting multiple copies of FID
and averaging signal.
S/N
% r number of scans
NMR Pulse
A radiofrequency pulse is a combination of a wave (cosine) of
frequency wo and a step function
*
=
tp
Pulse length (time, tp)
The fourier transform indicates the pulse covers a range of frequencies
FT
Hisenberg Uncertainty principal again: Du.Dt ~ 1/2p
Shorter pulse length – larger frequency envelope
Longer pulse length – selective/smaller frequency envelope
Sweep Width
f ~ 1/t
NMR Pulse
NMR pulse length or Tip angle (tp)
z
Mo
z
x
qt
tp
x
B1
y
y
Mxy
qt = g * tp * B1
The length of time the B1 field is on => torque on bulk magnetization (B1)
A measured quantity – instrument dependent.
NMR Pulse
Some useful common pulses
z
z
90o pulse
Mo
Maximizes signal in x,y-plane
where NMR signal detected
x
p/2
90o
y
x
y
z
180o pulse
Inverts the spin-population.
No NMR signal detected
Mo
Mxy
z
x
y
Can generate just about any pulse width desired.
p
180o
x
y
-Mo
NMR Data Acquisition
Collect Digital Data
ADC – analog to digital converter
The Nyquist Theorem says that we have
to sample at least twice as fast as the
fastest (higher frequency) signal.
Sample Rate
- Correct rate,
correct frequency
SR = 1 / (2 * SW)
-½ correct rate, ½
correct frequency
Folded peaks!
Wrong phase!
SR – sampling rate
Quadrature detection
carrier
Frequency of B1 (carrier) is set to center of the spectra.
• small pulse length to excite entire spectrum
• minimizes folded noise
carrier
If carrier is at edge of spectra, then peaks are
all positive or negative relative to carrier. But
excite twice as much including noise
How to differentiate between peaks upfield and downfield from carrier?
Quadrature detection
PH = 0
B
B
PH = 90
Use two detectors
90o out of phase.
F
w (B1)
F
PH = 0
F
S
F
S
Phase of Peaks
are different.
PH = 90
Receiver Gain
The NMR-signal received from the resonant circuit in the probehead
needs to be amplified to a certain level before it can be handled by the
computer.
The detected NMR-signals vary over a great range due to differences in
the inherent sensitivity of the nucleus and the concentration of the
sample.
Data Processing – Window Functions
The NMR signal Mxy is decaying by T2 as the FID is collected.
Good stuff
Mostly noise
Sensitivity
Resolution
Emphasize the signal and decrease the noise by
applying a mathematical function to the FID
F(t) = 1 * e - ( LB * t ) – line broadening
Effectively adds LB in Hz to peak
Line-widths
Can either increase S/N
or
Resolution
Not
Both!
LB = 5.0 Hz
Increase Sensitivity
FT
LB = -1.0 Hz
Increase Resolution
FT
NMR Data size
A Number of Interdependent Values (calculated automatically)
digital resolution (DR) as the number of Hz per point in the FID
for a given spectral width.
DR = SW / SI
SW - spectral width (Hz)
SI - data size (points)
Remember: SR = 1 / (2 * SW)
TD
Also: SW = 1/2DW
Total Data Acquisition Time:
AQ = TD * DW= TD/2SWH
Should be long enough to
allow complete delay of FID
Higher Digital Resolution requires longer acquisition times
Dwell time DW
Zero Filling
Improve digital resolution by adding zero data points at end of FID
8K data
8K FID
No zero-filling
8K zero-fill
16K FID
8K zero-filling
MultiDimensional NMR
Up to now, we have been talking about the basic or 1D NMR experiments
1D NMR
More complex NMR experiments will use multiple “time-dimensions” to obtain
data and simplify the analysis.
In a 1D NMR experiment the FID acquisition time is the time domain (t1)
Multidimensional NMR experiments may also
observe multiple nuclei (13C,15N) in addition to 1H.
But usually detect 1H.
MultiDimensional NMR
2D COSY (Correlated SpectroscopY):
Correlate J-coupled NMR resonances
A series of FIDs are collected where the delay between 90o
pulses (t1) is incremented. t2 is the normal acquisition time.
MultiDimensional NMR
During the t1 time period, peak intensities are modulated at a frequency
corresponding to the chemical shift of its coupled partner.
Solid line connects diagonal peaks
(normal 1D spectra). The off-diagonal
or cross-peaks indicate a correlation
between the two diagonal peaks – J-coupled.
Karplus Equation – Coupling Constants
J = const. + 10Cosf
Relates coupling constant to
Torsional angle.
Used to solve Structures!
Karplus Equation – Coupling Constants
For Protein Backbones
Nuclear Overhauser Effect (NOE)
Interaction between nuclear spins mediated through empty space (#5Ă) (like
ordinary bar magnets). Important: Effect is Time-Averaged!
Give rise to dipolar relaxation (T1 and T2) and specially to cross-relaxation
and the NOE effect.
Perturb 1H spin population
affects 13C spin population
NOE effect
the 13C signals are enhanced by a factor
1 + h = 1 + 1/2 . g(1H)/g(13C) ~ max. of 2
DEPT Experiment: Distortionless Enhancement by Polarization Transfer
13C
spectra is perturbed based
On the number of attached 1H
Takes advantage of different
patterns of polarization transfer
1H-13C NOE
2D NOESY (Nuclear Overhauser Effect)
Diagonal peaks are correlated by through-space
Dipole-dipole interaction.
NOE is a relaxation factor that builds-up during
The “mixing-time (tm)
The relative magnitude of the cross-peak is
Related to the distance (1/r6) between the
Protons (≥ 5Ă).
Basis for solving a Structure!
Protein NMR
Number of atoms in a protein makes NMR spectra complex
Resonance overlap
Isotope label protein with 13C and 15N
and spread spectra out in 3D and 4D
Protein NMR
How do you assign a
protein NMR spectra?
A collection of “COSY”-like
experiments that sequentially
walk down the proteins’
backbone
3D-NMR experiments that
Require 13C and 15N labeled
Protein sample
Detect couplings to NH
Protein NMR
Assignment strategy
We know the primary sequence of the protein.
Connect the overlapping correlation between NMR experiments
Protein NMR
Molecular-weight Problem
Higher molecular-weight –> more atoms –> more NMR resonance overlap
More dramatic:
NMR spectra deteriorate with increasing
molecular-weight.
MW increases -> correlation time increases
-> T2 decreases -> line-width increases
NMR lines broaden to the point of not being detected!
With broad lines, correlations (J, NOE) become less-efficient
Protein NMR
How to Solve the Molecular-weight Problem?
1) Deuterium label the protein.
• replace 1H with 2H and remove efficient relaxation paths
• NMR resonances sharpen
• problem: no hydrogens -> no NOEs -> no structure
• actually get exchangeable (NH –NH) noes can
augment with specific 1H labeling
2) TROSY
• line-width is field dependent