Czichos H., Saito T., Smith L.E. (Eds.) Handbook of Metrology and Testing

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258 Part B Chemical and Microstructural Analysis

0.1 mm

a) b)

Fig. 5.79a,b Dislocation contrasts observed in an indented CdTe

surface. (a) SEM-CL image showing dislocations in dark contrast

and (b) OM image showing dislocation etch pits developed after

(a) was recorded

waves resulting in diffraction peak broadening and

peak shifts along the direction normal to the defect

planes. Analogously to the effect of ﬁnite crystal size

on diffraction, the peak broadening width is inversely

proportional to the mean distance between adjacent

fault planes. Unlike the size effect, however, the ef-

fects are different depending on the nature of the

defects. The peak broadening is symmetric in stack-

ing faults but asymmetric in twin boundaries. The peak

shift is absent for some types of stacking faults but

is induced in directions that depend on the types of

stacking faults in other cases. The analytical detail

may be found in a comprehensive textbook by Snyder

et al. [5.72].

Mechanical Spectroscopy

Internal friction (Sects. 5.1.2 and 5.3.1) provides a sen-

sitive tool to study the motion of dislocations at very

low stresses. A typical application is to elementary

processes of dislocation motion in metals and ionic

crystals. Dislocation pinning is applied to detect the

migration of defects and impurities.

Recoverable atomic motion in grain boundaries

can be studied by means of mechanical spectroscopy

(Sect. 5.1.2), e.g., the anelastic relaxation of grain

boundaries is observed above room temperature in

coarse-grained fcc metals but below room temperature

in nanocrystalline fcc metals.

5.4 Molecular Architecture Analysis

The materials in the scope of this section include

simple molecules, polymers, macromolecules (super-

molecules) as well as biomolecules such as proteins.

The rapidly advancing techniques relating to DNA anal-

ysis are out of the scope of this section. Molecules

on large scales can have higher-order structures that

perform important functions, especially in biopoly-

mers. The primary structure of proteins, for example, is

a sequence of amino acids (peptide) that constitutes sec-

ondary structures in forms such as helices and sheets.

The secondary structures linked in a protein are usually

folded to tertiary structures that may further become as-

sociated to a quaternal structure that brings about such

bioactivity as allosteric effects. This section addresses

mainly nuclear magnetic resonance (NMR) in consid-

erable detail for its unique power in the analysis of the

architecture of macromolecules. Although single crys-

tal x-ray diffraction is another important technique for

structural determination of macromolecules, we only

brieﬂy mention some points speciﬁc to macromolecu-

lar samples. The large molecules may be pretreated by

chromatographic techniques to separate or decompose

them into constituents or smaller fragments that can

be analyzed by simpler methods. After the preprocess-

ing, the molecules or the fragments may be subjected

to standard analysis such as FT-IR, Raman scatter-

ing, and ﬂuorescence spectroscopy for identiﬁcation of

the constituent bases, as described in other sections

(Sects. 5.1.2 and 5.2.3). In this section, we mention

only optical techniques based on the circular dichroism

exhibited by helix molecules and the ﬂuorescence reso-

nant energy transfer (FRET) that provides information

on the proximity of two stained molecules.

5.4.1 Structural Determination

by X-Ray Diffraction

The principle of structural analysis by x-ray diffraction

in macromolecules is essentially the same as that of sin-

gle crystal diffraction and powder diffraction already

described in Sect. 5.1.1. For the growth of molecu-

lar crystals, the synthesis of the material molecules is

necessary. Thanks to progress in genetic engineering

such as the advent of the polymerase chain reaction

(PCR) technique, even large biomolecules such as pro-

teins can be synthesized in sufﬁcient amounts. However,

macromolecules and polymers tends to be condensed to

amorphous or very disordered aggregates (Sect. 5.2.2);

Part B 5.4

Nanoscopic Architecture and Microstructure 5.4 Molecular Architecture Analysis 259

the growth of single crystals at high quality is gener-

ally difﬁcult for such materials. The direct method is

applicable only to molecules of 100 or fewer atoms

because, as molecular size increases, the ambiguity in

phase determination rapidly increases. The heavy atoms

substitution method works for molecules larger than

600 atoms. So a gap is present for molecules in the inter-

mediate size range. In principle, as long as a good single

crystal sample is obtained, there is no limitation on the

molecular size. The maximum size so far achieved by

making full use of up-to-date methods is as large as

that of ribosome (4 × 10

in molecular weight), though

normally, the maximum size subject to routine analysis

is ≈10

in molecular weight. The powder diffraction

technique is also applicable to large molecules, but the

accuracy is limited due to the difﬁculty in separation of

diffraction peaks, which are more crowded than from

small molecules. The maximum molecular size is sev-

eral thousands of atoms. For more details on x-ray

structural analysis of macromolecules, see [5.73].

5.4.2 Nuclear Magnetic Resonance (NMR)

Analysis

Standard structural analysis by NMR proceeds follow-

ing (1) sample preparation, (2) NMR spectra measure-

ments, (3) spectral analysis to assign NMR signals to

the responsible nuclei and ﬁnd the connectivity of the

nuclei through bonds and space, (conventionally the

term signals is used rather than peaks because NMR

resonances are not always observed as peaks.) and ﬁ-

nally (4) the deduction of structural models using the

knowledge obtained in (3) as well as information from

other chemical analyses as a constraint in the proce-

dure of ﬁtting model to experiment. The ﬁnal step (4)

is like forming a chain of metal rings of various shapes

(e.g., amino acid residues in proteins) on a frame hav-

ing knots in some places linked to others on the chain.

For this reason, particularly for macromolecules such as

proteins, it is difﬁcult to determine the complete mo-

lecular structure uniquely from NMR analysis alone.

Since we can only deduce possible candidates for the

structure, it is better to refer to models rather than struc-

tures. This is in marked contrast to structural analysis by

x-ray diffraction in which the crystal structure is more

or less determined from the diffraction data alone. Nev-

ertheless, NMR has advantages over x-ray diffraction

methods in many respects such as

1. Single crystal samples are not needed. The samples

may be amorphous or in solution.

2. Effects of intermolecular interactions, that may

change the molecular structure, can be avoided by

dispersing samples in suspending solution.

3. Dynamic motion of molecules can be detected.

4. A local structure can be selectively investigated

without knowing the whole structure.

5. Fatal damage due to intense x-ray irradiation, that

is likely to happen in organic molecules, can be

avoided.

Points 2–4 are of particular importance for proteins

that function in solution, changing their local conforma-

tional structure dynamically.

In this chapter, we will describe only steps (2) and

(3) in some detail, leaving (1) and (4) to good text-

books [5.74–76] except for a few words on step (1).

Before proceeding to the experimental details, we

brieﬂy summarize the information that NMR spectra

contain.

Information Given by NMR Spectra

Nuclei other than those containing both an even num-

ber of protons and neutrons (such as

Cand

have a nonzero nuclear spin I. The magnetogyric ra-

tio γ

giving the nuclear magnetic moment (Sect.5.1.2)

is a natural constant speciﬁc to the nuclear species.

Table 5.4 lists isotopic nuclei commonly contained in

organic molecules having hydrocarbons in the back-

bones. Among them, proton

H, carbon

Cand

nitrogen

N are characterized by the smallest nuclear

spin 1/2. As explained later, this fact, together with the

fact that

H in very high natural abundance has a large

value, provides the reason why mainly these isotopes

are used for high-resolution NMR measurements. As far

as stated in the following, we consider only the case of

I = 1/2 for simplicity. The values of the Larmor (not

angular) frequency at a typical magnetic ﬁeld of 2.35 T

are listed in the ﬁfth column in Table 5.4 for various iso-

lated nuclei. It should be noted that, with increasing γ

the energy difference of the two spin states, and hence

the population difference and the magnetization to be

detected in experiments, increase, so the sensitivity of

NMR is high particularly for protons that have a large

value.

The magnetic ﬁeld B

felt by the nuclear spins may

differ from the external ﬁeld due to many causes.

Chemical Shift. The external magnetic ﬁeld is shielded

by the diamagnetic current of s electrons or enhanced

by the paramagnetic current of p and d electrons sur-

rounding the nucleus. In contrast to the shielding ﬁeld

Part B 5.4

260 Part B Chemical and Microstructural Analysis

Table 5.4 Properties of nuclear species commonly used for NMR analysis of macromolecules. After [5.77]

Nuclear species Nuclear spin I Magnetogyric ratio Natural abundance Larmor frequency

() γ

(10

rad s

−1

) (%) (MHz)

H 1/2 18.861 99.985 100.000

H 1 2.895 0.015 15.351

H 1/2 20.118 Radioactive 106.663

C 0 − 98.0 −

C 1/2 4.743 1.1 25.144

N 1 1.363 99.634 7.224

N 1/2 −1.912 0.366 10.133

O 0 − 99.762 −

O 5/2 −2.558 0.038 13.557

O 0 − 0.200 −

NMR resonance frequency of isolated nuclei at a typical magnetic ﬁeld of 2.35 T

from s electrons (Fig. 5.80a), which is isotropic in the

sense that it is directed along the magnetic ﬁeld due to

the isotropic nature of s electrons, the shielding ﬁeld

is anisotropic when the electrons are, e.g., π electrons

in double bonds (Fig. 5.80b). In all these cases, the

applied magnetic ﬁeld induces a screening current of

electrons surrounding the nucleus which exerts an ad-

ditional local ﬁeld on that nucleus. Since the degree

of screening depends on the chemical environment of

the nucleus, the difference in the nuclear environment

σB

–1

σB

–1

a) b)

Fig. 5.80a,b The magnetic shielding by electrons induc-

ing the chemical shifts in NMR. (a) Isotropic shielding by

s electrons, (b) anisotropic shielding by π electrons

H2 H1

H1-H2

(Hz) J

H1-H2

(Hz)

H (ppm)

Fig. 5.81 Chemical shifts and J-coupling in molecules

containing two protons in different environments (sche-

matic)

results in a small shift, called the chemical shift δ,of

the resonance frequency. As illustrated by a schematic

NMR spectrum in Fig. 5.81 of protons in a molecule

which contains two protons at different positions, the

chemical shift can differ depending on the chemical

environment. Thus, the chemical shift is used to dis-

criminate the position in a molecule at which the probed

nuclei are situated. Since the chemical shift increases

proportionally with the external ﬁeld, the shift is usually

expressed by a fraction (in unit of ppm) of the Larmor

frequency of the nucleus, which also increases linearly

with the ﬁeld.

Spin–Spin Coupling (Connection Through Bonds). In

Fig. 5.81, the two sets of spectral signals corresponding

to different chemical shifts further splits to two sig-

nals with small separations. This is due to the spin–spin

coupling mediated by electrons contributing chemical

bonds linking the two spins: as shown in the top left

illustration in Fig. 5.82, a nuclear spin interacts with

electrons surrounding the nucleus, then the spins of the

electrons interact with other electrons through an ex-

change interaction when chemical bonds are formed,

and the latter electrons interact with another nuclear

spin. Unlike the direct dipole–dipole interaction be-

tween magnetic moments that operates only in a small

distance, such indirect spin–spin coupling extends to

a larger distance of up to 3–4 bonds. In contrast to the

chemical shift, the magnitude of the spin–spin coupling

is independent of the external magnetic ﬁeld and there-

fore the splits of the resonance frequency due to the

spin–spin coupling are expressed by a coupling con-

stant J scaled in units of microwave frequency. Due

to the origin of the spin–spin coupling (hereafter called

Part B 5.4

Nanoscopic Architecture and Microstructure 5.4 Molecular Architecture Analysis 261

–1

J = 120–150Hz 150–170 Hz 240–260 Hz

J =6–12 Hz 2–5 Hz 12–19Hz 5–11 Hz –3–2 Hz

trans gauche trans cis gem

Fig. 5.82 J-coupling in various bases

J-coupling), the value of J can vary and even change

its sign depending on the character and the number

of chemical bonds intervening between the two spins.

Some typical values of J are indicated in Fig. 5.82 be-

tween two

H nuclei or

Hand

C connected with

different types of chemical bonds. Thus, the value of

the spin coupling constant J reﬂecting the interaction

through bonds provides information of the steric local

conﬁguration of the molecule.

Nuclear Overhauser Effect (Connection Through

Space). In contrast to the spin–spin interaction me-

diated by electrons, the magnetic moments associated

with two nuclei can directly interact through the clas-

sical dipole–dipole interaction. Since the strength of

the dipole–dipole interaction depends quadratically

on the product of the magnetogyric ratios and de-

cays rapidly with the internuclear distance d as d

−3

the dipole–dipole interaction acts virtually only be-

tween two proton nuclei within a distance of ≈ 5Å

in diamagnetic molecules. Since electrons inducing

paramagnetism have a large magnetogyric ratio, they in-

a) b) c)

Fig. 5.83a–c Level diagrams illustrating the nuclear Overhauser effect (NOE), which operates between nuclei close in

space. For details, see the text

teract so strongly with nuclear spins that NMR becomes

very broad or unobservable.

The dipole–dipole interaction gives rise to the fol-

lowing nuclear Overhauser effect (NOE) that provides

powerful methods for structural determination. Gener-

ally, systems of nuclear spins, once disturbed, attempt

to recover their equilibrium state. The recovery or re-

laxation takes place via two different processes: the

spin–lattice relaxation in which the excited energy is re-

leased to the heat bath (usually lattice) by ﬂipping of

spins, and the spin–spin relaxation in which only the

coherence of spins is lost without energy dissipation.

The relaxation processes are characterized by ﬁrst-order

time constants, called the vertical time constant T

for

the former and the transverse time constant T

for the

latter.

As an illustrative relevant example, we consider two

protons, I and S, that are supposed not to be J-coupled,

for simplicity. The energy level diagram of the two-spin

system in thermal equilibrium is shown in Fig. 5.83a,

in which the state α

, for example, indicates that the

spin of I is up (α) while the spin of S is down (β). In

Part B 5.4

262 Part B Chemical and Microstructural Analysis

the absence of J-coupling, the levels α

and β

are

nearly degenerate with a small difference due to pos-

sible chemical shifts in I and S. The number of dots

on each level indicates the level population. Now, we

assume that, as shown in Fig. 5.83b, the S spins are se-

lectively irradiated with microwaves at the resonance

frequency so that the populations are equalized between

the levels linked by W

, called single-quantum pro-

cesses, achieved by the ﬂipping of a single spin. Once

the populations are disturbed this way, spin–lattice re-

laxation occurs via single-quantum transitions between

and β

, α

and β

for I, and between α

and α

, β

and β

for S, both observable as

singlet NMR spectra. The spin–lattice relaxation may

also occur by transitions between α

and β

, called

double-quantum processes W

, that correspond to si-

multaneous ﬂipping of both spins. The populations may

also be recovered by the transition between β

and

, called a zero-quantum process W

, which causes

spin–spin relaxation. The relaxation through W

and

are normally forbidden but becomes allowed when

there are magnetic ﬁeld ﬂuctuations that act as an alter-

nating ﬁeld at various frequencies, which induces spin

ﬂipping. The ﬁeld ﬂuctuations are generated by the dif-

fusional or rotational motion of nuclei and molecules

(Fig. 5.83c) that cause ﬂuctuations in the local ﬁeld af-

fected by the dipole–dipole interaction. Generally, the

ﬂuctuation-induced relaxation rate becomes maximum

when the resonance condition ω

≈ 1 is satisﬁed,

where τ

is the correlation time of the ﬂuctuation and

ω

is the relevant transition energy. Since ω

=ω

for

and ω

= 2ω

for W

, normally ω

1inlarge

molecules or molecules in viscous solution for which τ

is large, and hence relaxation through W

and W

is in-

efﬁcient in such systems. For the process W

,however,

the two levels are close in energy (ω

≈0) so that re-

laxation through W

can be efﬁcient when ω

≈1is

satisﬁed, thereby dominating the spin–spin relaxation.

In any cases, the excited spin systems recover their

thermal populations with a rate affected by the cross re-

laxation processes W

and W

due to the dipole–dipole

interaction, if present. This NOE effect, originating

from an interaction through space, is exploited for de-

termination of the conformation of macromolecules.

Experimental Methods

Vector Model in Rotating Frame. In modern NMR ex-

periments, we do not anymore measure the absorption

of a continuous microwave, but instead measure a re-

sponse of the spin system to a sequence of microwave

pulses and Fourier transform the oscillatory current sig-

nal response to the pulses to obtain an NMR spectrum.

Experimentally, in addition to the static magnetic ﬁeld

along the z-axis, we apply another magnetic ﬁeld to the

spins with a small intensity 2B

alternating at an angu-

lar frequency ω with a coil (transmitter) that is wound

around the sample with its axis (taken as x-axis) nor-

mal to the z-axis. One of the circularly rotating ﬁelds of

intensity B

gives rise to two effects: it forces the pre-

cession of the spins to synchronize and to tip away from

the z-axis. A simple calculation shows that, if one views

the precessing spin from the coordinate system O-x



rotating around the z-axis at the alternating frequency ω,

the spin feels an effective magnetic ﬁeld composed of

a static ﬁeld B

directing along the x



-axis and a con-

stant ﬁeld B

−ω/γ

along the z-axis. Therefore, if we

prepare spins under a static ﬁeld B

and at time t =0we

apply a rotating ﬁeld B

that satisﬁes the resonance con-

dition ω =ω

(=γ

), only the ﬁeld B

remains and

causes the spins to turn coherently around the x



-axis at

a small angular frequency of γ

. Therefore, if we fo-

cus on the magnetization, the average of the magnetic

moments associated with spins rather than the spins

themselves, we can draw pictures like Fig. 5.36a–c, in

which the magnetization is represented by a thick vec-

tor. Hereafter we will repeatedly use such classical vec-

tor models in rotating frames for intuitive interpretation.

High-Resolution NMR. As mentioned already, the ab-

solute magnitude of chemical shifts becomes larger as

the external magnetic ﬁeld B

is increased while the

ﬁne structure due to J-coupling is ﬁxed in magnitude.

Therefore, the use of a higher magnetic ﬁeld allows one

to resolve overlapping signals closely split with very

small differences in chemical shifts (Fig. 5.84). Espe-

Higher B

ΔδαB

Fig. 5.84 Chemical shifts Δδ increasing with magnetic

ﬁeld and invariable spin–spin couplings J

and J

. The use

of high ﬁeld enhances the resolution of NMR

Part B 5.4

Nanoscopic Architecture and Microstructure 5.4 Molecular Architecture Analysis 263

cially in macromolecules such as proteins, substantial

overlapping of NMR spectra are common and the re-

moval of the overlaps is requisite. One experimental

solution is to use an extremely high-ﬁeld (superconduct-

ing) magnet the strength of which being, in terms of

the equivalent

H resonance frequency, as high as, e.g.,

800 MHz.

One-Dimensional (1-D) NMR. Free Induction De-

cay (FID). An extensive range of modern techniques

developed for NMR experiments are solely devoted

to separate complicated signals, such as shown in

Fig. 5.85, without artifacts. Some of the tasks can be

solved, as well as through the use of high-ﬁeld magnets,

by one-dimensional NMR (1-D-NMR) schemes that are

illustrated by pulse sequence diagrams. The simplest

case, though rarely encountered in practice, is illustrated

by a vector model shown in Fig. 5.86a–c. In the ini-

tial state (Fig. 5.86a) the magnetization vector is aligned

along the z-axis, and in the second step (Fig. 5.86b) we

apply a rotating ﬁeld at a reference frequency ω for

a duration Δt that just satisﬁes γ

Δt = π/2sothat

the magnetization is tipped onto the y



axis. We may

not be able a priori to set the reference frequency ω

identical to the resonance Larmor frequency ω

to be

measured. In such off-resonance cases, the magnetiza-

tion vector in the rotating frame would rotate with a rate

−ω. In the third step (Fig. 5.86c), since the rotating

ﬁeld is switched off (free), the coherent magnetization

remains in the y



axis. This means that the magneti-

zation starts to rotate in the laboratory frame with the

Larmor frequency ω

and can be detected as an oscilla-

tory induction current ﬂowing the transmitter coil, now

acting as a receiver coil, as illustrated in Fig. 5.86d, with

a decay due to relaxation processes. When the nuclei are

isolated such that they have a single Larmor frequency,

H (ppm)

7.77.87.98.08.18.28.38.48.58.68.78.88.9 7.6

NH-H

Fig. 5.85 NMR spectrum showing chemical shifts and

J-coupling in cyclic-GRGDSPA peptides (Courtesy of

Prof. I. Shimada)

the Fourier transform of the free induction decay (FID)

curve has a signal at the Larmor frequency, as shown in

Fig. 5.87a, which represents the NMR spectrum of the

nuclei.

When multiple resonance signals coexist, the du-

ration of the π/2 pulse Δt should be short enough

(≈10 μs, with B

being correspondingly large) for the

alternating frequency to spread over a range covering

the chemical shifts of the nuclei concerned, so that all

the nuclei can be tipped nonselectively with a single

pulse. Such pulses are called hard pulses. In contrary,

the longer and weak pulses, called soft pulses, tip a spe-

ciﬁc nucleus selectively. The FID and NMR spectrum

in Fig. 5.87b are those obtained by using a hard π/2

pulse. Conventionally NMR spectra are displayed with

the frequency axis increasing to the left.

a) b)

c) d)

π/2 pulse

Time

FID

a) b) c)

Fig. 5.86 (a–c) The magnetization response in vector

model in the rotation frame and (d) free induction decay

(FID)

Frequency

Time

Frequency

Fig. 5.87a,b Fourier transform NMR spectra (right) ob-

tained from FID curves (left)

Part B 5.4

264 Part B Chemical and Microstructural Analysis

More general procedures of 1-D-NMR consist of

ﬁrst to perturb the spin system from equilibrium some-

how (preparation), to allow it to evolve after the

perturbation for various periods (evolution), and then to

detect what has happened in the evolution period by col-

lecting the subsequent FID (detection). If the evolution

is spin relaxation, we can measure the spin relaxation

time. In practice, however, the FID decays more rapidly

than expected from the true spin relaxation time. The

main cause is the spatial inhomogeneity of the external

magnetic ﬁeld. In this case, the spin echo technique al-

lows us to avoid the artifact. The idea of spin echoes

is embedded in various schemes of pulse NMR experi-

ments. Since there are too many variations of 1-D-NMR

having their own acronyms, only two schemes are pre-

sented here to touch on some of the ideas.

Spin Decoupling. If we can determine whether or not

a pair of neighboring signals are really coupled to each

other, this method allows the assignment of the signals.

Also if the doublet splitting can be suppressed, it al-

lows the simpliﬁcation of complex spectra. Consider

two spins A and X that are J-coupled with a coupling

constant J. If the spin X is irradiated selectively but

strongly with a microwave pulse at the resonance fre-

quency, the resonance A loses its doublet splitting (spin

decoupled) because the spin X ﬂips so rapidly that the

A spin feels only the average of the spin states of X.

If we examine the presence or the absence of such spin

decoupling effects for pairs of doublets in a complex

NMR spectrum, we can identify J-coupled pairs within

a distance of 3–4 bonds in the molecular network.

Selective Polarization Inversion (SPI). Another exam-

ple is given by again considering a J-coupled pair of

spins, A and X, but in this case, the pair is supposed

to be heteronuclear, e.g., A is

CandXis

H, as il-

lustrated by an energy level diagram in Fig. 5.88a. The

level notation βα, for example, indicates that the A

(

C) spin is down (β) while the X (

H) spin is up (α).

Due to the large difference in γ values between A and

X, the level population in thermal equilibrium differs

considerably. The bottom diagram in Fig. 5.88ashows

the schematic NMR spectrum with the vertical bars rep-

resenting the intensity. Now, consider that the resonance

between αα and αβ is selectively excited by a soft pulse

so as to invert the populations, as shown in Fig. 5.88b.

Then the NMR signals are drastically changed, as il-

lustrated by the bottom spectrum, because the signal

intensity is determined by the population difference.

The negative signal means that the FID component is

out of phase by π with the positive signal. Such changes

would not be observed if A and X are completely

independent, which signiﬁes that the two spins are cou-

pled somehow. Unlike the NOE effect, the change is

immediate in the case of J-coupling, so we can dis-

tinguish whether they are dipole-coupled or J-coupled.

A subsidiary merit of polarization transfer techniques

is that weak NMR signals, such as that of

C, can be

enhanced.

Two-Dimensional (2-D) NMR. In small molecules, sig-

nal assignment may be possible through 1-D-NMR

experiments, but in large molecules such as proteins

that yield bewilderingly complex spectra, we need

more sophisticated NMR measurement schemes. Two-

dimensional NMR (2-D-NMR) is a successful solution

to this problem. The idea is to sort out crowded NMR

signals in a two-dimensional map according to which

pairs of signals are coupled to each other. The methods

may be regarded as double resonance techniques that

can be extended to multidimensional NMR by using ap-

a) b)

CΠ

ββ

αβ

βα

ββ

βα

αα

αβ

αα

Fig. 5.88a,b Heteronuclear selective polarization inver-

sion (SPI). (a) In thermal equilibrium, (b) when

His

selectively excited

π/2 pulse

Fig. 5.89a,b Pulse sequences for 2-D-NMR; (a) heteronu-

clear 2-D-NMR,

(b) homonuclear 2-D-NMR (COSY)

Part B 5.4

Nanoscopic Architecture and Microstructure 5.4 Molecular Architecture Analysis 265

propriate relays of pulse sequences. Two representative

schemes that are most commonly used are explained

brieﬂy.

An example of pulse sequence diagram for 2-D-

NMR experiments is shown in Fig. 5.89a, in which two

heteronuclear spins of

Cand

H are assumed to be

J-coupled. Before FID is detected for

C spins, two

π/2 pulses separated by a time t

are applied to the

spins. Figure 5.90 depicts what happens in the vector

model. After the magnetization of

H is turned to the



-axis by the ﬁrst π/2 pulse, the

H spins start to ro-

tate in the rotating frame at a rate Ω

= δ

± J

/2,

where δ

is the chemical shift of the

H spins and J

is the constant of J-coupling with

C, provided that

the reference frequency is set at the Larmor frequency

of the isolated

H. The diagrams in the second column

indicate this rotation at time t

increasing downward.

By the second π/2 pulse, the

H spins have turned fur-

ther around the x



-axis, as shown in the third column.

At this moment, the FID of

C spins, not of

H, is ac-

quired by applying a π/2 pulse on

C. When t

= 0,

the magnetization of

H is inverted, so the

C signal

changes drastically reﬂecting the inverted population

H, as in the case of SPI experiments in Fig.5.88 (the



-component, not turned by the second π/2 pulse, does

not affect the J-coupling). At the arbitrary time t

,the

magnetization of

H after the second π/2 pulse on

has a z-component of magnitude M cos Ω

,asshown

in the second line of the third column in Fig. 5.90,

so the

C signal intensity (schematically shown in

the right column) is modulated accordingly. Since the

C signal modulation has a period of 2πΩ

−1

,ifwe

repeat such measurements systematically changing the

time t

, the Fourier transform of the

C signal inten-

sity with respect to t

gives the NMR spectrum of the

H spins with a chemical shift δ

and the doublet split-

ting magnitude J

. This may be regarded as a double

resonance or

C-NMR-detected NMR of

H spins. In

other words, the

C resonance signal acts as though

it is labeled with the resonances of the

H spins that

are J-coupled to the

C. If the π/2 pulses on

H are

hard and hence nonselective, we will obtain an NMR

spectrum in two dimensions for frequency ν

(corre-

sponding to t

) and for frequency ν

(corresponding to

), as illustrated in Fig. 5.91. The signals on the diag-

onal line (diagonal peaks) are always present, but the

off-diagonal signals (cross peaks) indicate the presence

of J-coupling between the corresponding

C nuclei

and

H nuclei. It is obvious that, even if the 1-D spectra

are complicated, the connectivity through J-coupling is

more easily resolved in such 2-D spectrum.

Mcos Ω

= δ

±J

Fig. 5.90 Vector model for heteronuclear 2-D-NMR. For details,

see the text

The homonuclear version of the above scheme is

called correlated spectroscopy (COSY) and is widely

used to ﬁnd J-couplings between

H nuclei. The pulse

sequence, shown in Fig. 5.89b, is similar to that in

Fig. 5.89a, except that the FID measured is now for

itself. Although the precise interpretation needs a quan-

tum mechanical description, the cause of the cross

peaks may be inferred by analogy to the heteronuclear

case above. Figure 5.92 shows an example of COSY

Cross peaks

Diagonal peaks

Fig. 5.91 Schematic 2-D-NMR spectrum of

Cand

J-coupled with each other

Part B 5.4

266 Part B Chemical and Microstructural Analysis

H (ppm)

1.5

2.0

2.5

3.0

3.5

4.0

4.5

2.02.53.03.54.0

Fig. 5.92 DQF (double quantum-ﬁltered)-COSY spectrum

of cyclic-GRGDSPA peptides (Courtesy of Prof. I. Shi-

mada)

(a more sophisticated double-quantum-ﬁltered COSY)

spectrum obtained for the same peptide molecules

whose 1-D spectrum was shown in Fig. 5.85.

In the 2-D-NMR experiments discussed so far, the

pulse sequence generally consists of preparation, evo-

lution and detection stages. In Fig. 5.89a, the ﬁrst π/2

pulse corresponds to preparation, the duration t

until

the second π/2 pulse to evolution, and the acquisi-

tion of FID to detection. In more sophisticated schemes

cos Ω

Fig. 5.94a–h Vector model of NOESY

Preparation

Evolution

Mixing

Detection

π/2 pulse π/2 pulseπ/2 pulse

Fig. 5.93 The pulse sequence for NOESY experiments

of 2-D-NMR, we add another stage, mixing, follow-

ing evolution. Figure 5.93 shows the pulse sequence

in NOESY (NOE spectroscopy) extensively used for

analysis of macromolecules. The corresponding vec-

tor model is shown in Fig. 5.94. The sequence of the

ﬁrst π/2 pulse (Fig. 5.94a,b), an evolution time t

(Fig. 5.94b,c), and the second π/2 pulse (Fig. 5.94c,d)

is the same as in Fig. 5.90 except that we consider two

spins, I and S, having different resonance frequencies

but coupled through a dipole–dipole interaction. During

the mixing stage, which lasts for t

(Fig. 5.94e,f), the

z-components of the magnetization (the x



-components

have no effect and are not shown), which arise from

the population difference of the spin states, exchange

their populations due to the NOE effect. Thus, the inten-

sity of the NMR signals measured in the detection stage

(Fig. 5.94f,g) tells us how rapidly the relaxation has oc-

curred. Similarly to the COSY spectrum, the NOESY

spectrum is displayed with one axis representing the fre-

quencies of the I spin and another axis the frequencies

of the S spin. The cross peaks indicate that the two nu-

clei giving the signals are closer than ≈ 5 Å in space so

that they are dipole–dipole coupled.

Part B 5.4

Nanoscopic Architecture and Microstructure 5.4 Molecular Architecture Analysis 267

Sample Requirements. Finally, some comments are

added on the requirements for samples. Since NMR

signals are proportional to the number of spins, for

a sufﬁciently high signal-to-noise ratio to be achieved,

the sample amount must usually be greater than sev-

eral milligrams or 1 mM, which may be difﬁcult. As

mentioned before, nuclei with spin I > 1/2 are not

very suitable for NMR experiments because the spec-

trum broadens due to the strong quadrupole interaction

(Sect. 5.1.2). Even if we conﬁne ourselves to I = 1/2

nuclei, however, there are other causes of spectral

broadening that prohibit us from conducting high-

resolution NMR measurements. In actual experiments,

an inhomogeneity in the external magnetic ﬁeld induces

an apparently rapid decay in the FID or a broadening

of the NMR spectra. Although the effect of magnetic

ﬁeld inhomogeneity could be removed by the spin echo

technique, there still remains a cause of spectral broad-

ening due to the variation of molecular orientations,

which gives rise to different degrees of anisotropic

shielding and as a result continuously varying chem-

ical shifts. When the molecules are so small that they

rotate rapidly in the medium, the variation of chemical

shifts is averaged and consequently the NMR spectral

signals become sharpened. While small molecules in

solution beneﬁt from this motional narrowing effect,

large molecules cannot do so if their rotation rate is too

small. Thus, NMR analysis generally becomes difﬁcult

for large molecules that lack mobility. Although many

techniques, such as sorting signals according to inten-

tionally controlled spin relaxation lifetime, have been

developed to escape the difﬁculty, an upper limit exists

around 3 × 10

in molecular weight for which struc-

tural analysis by NMR is practically possible. This is

in great contrast to x-ray diffraction methods in which

much larger molecules, such as ribosome (4 × 10

molecular weight), can in principle be analyzed if single

crystals can be grown.

5.4.3 Chemophysical Analysis

Chromatography

Chromatography is a generic term for techniques

that separate complex mixtures into their components,

which are distributed with a variable probability be-

tween a stationary and a mobile phase; the methods are

based on the percolation of the mobile phase through

the solid phase in what is known as a column. The mo-

bile phase is gaseous in gas chromatography (GC)and

is liquid in liquid chromatography (LC). There are var-

ious schemes for chromatography further depending on

the type of stationary phase (solid or liquid) and hence

on the principle of molecular separation (ion exchange,

afﬁnity difference, gel-ﬁltration, hydrophobic interac-

tion etc.).

As illustrated in Fig. 5.95, chromatographic meas-

urements are conducted by constantly injecting into

a column a sample mixture carried by a mobile phase

and recording a chromatogram, a chart that plots the

amount of an analyte reaching a detector placed at the

outlet of the column versus the time t starting from the

sample injection. The retention time, t

, is the time be-

tween sample injection and a peak in the chromatogram,

while t

is the time taken for the mobile phase just to

pass through the column. The molecular species can

be identiﬁed from their retention time and their to-

tal amount is measured from the integrated area of

the corresponding peak. Among the various types of

detectors, the most common are thermal conductive de-

tectors, which are sensitive to any species. Using a mass

spectrometer as the detector, one can obtain more struc-

tural information of the separated molecular species.

GC is suitable for routine analysis and has high reso-

lution, short measurement time, low cost, and requires

a small amount of sample (1–10 μl in a liquid sam-

ple and 0.2–10 ml in a gaseous sample) as long as the

boiling temperature of the sample is below 300

◦

C; LC

is applicable to multicomponent, less volatile or py-

rolitic (thermally decomposable) samples that are not

covered by GC. The limitation of ordinary chromatogra-

phy is that peaks in chromatograms have no signiﬁcant

structure, unlike those observed in photospectroscopy

methods that provide detailed information on the possi-

ble variety of each components. Nevertheless, there is

room for further improvements in detection techniques

Time

Analyte A Detector

Mobile phase

Stationary phase

mobile

stationary

Detected

signal

Fig. 5.95 General experimental conﬁguration of chro-

matography

Part B 5.4