Pulsed deuteron NMR investigations of structure and dynamics of solid polymers

119

Journal of AioIecu!arStructrrre,lll(lS83) 11-133 E%evierScience Publishers B-V., Amsterdam -Printed in The Netherlands

PULSEDOEUTERON NMRINVESTIGATIONS OF STRUCTURE ANDDYNAMICSOF SOLID POLYMERS H.W.SPIESS Institut fiir Physikatische Chemie, UniversitBt D-6500 Mainz (West Germany)

Mainz, Jakob-Welder-Weg

15,

ABSTRACT Pulsed deuteron NMRis described, which recently has been developed to become a powerful tool for studying structure and molecclar dynamics in solid polymers. The techniques that have been developed in this area are described, analyzing the response of the I = 1 spin system to the sotid echo two-pulse and the Jeener-Broekaert three-pulse sequence, respectively. By applying these techniques to selectively deuterated polymers, slow rotational motions involving different segments of the monomer unit can be monitored over a range of approximately 8 orders of magnitude of characteristic frequencies. In addition, moticnal heterogeneities can be detected. In drawn fibres the complete orientational distribution of the polymer chains can be determined from the analysis of deuteron NMR‘line shapes. The techniques are illustrated by experimental examples including order and chain mobility in the amorphous regions of linear polyethylene, chain dynamics of polystyrene in the vicinity of the glassmition and the phenyl motion in polycarbonate. INTRODUCTION Deuterons represent almost ideal spin labels for studying and dynamics of solidsand solid polymers. The solid state dominated by the quadrupole given

coupling

of the I = 1 spin,

molecular structure spectra are completely the NMRfrequency

being

by + 6 (3 cos2 6 - 1 - n sin2 0 cos 2 0)

il) = ?I =W

(I)

I,

Q where 6 = 3 e2 q Q/8 %, e2 q Qfh is the quadrupole Cl

asyrmnetry parameter and the orientation

coupling

of the magnetic

constant,

field

n is the

in the principal

axes system of the field gradient tensor (FGT) is specjfied by plar angles e and Q (ref. 1). Thfs teads to powder patterns of a total width of 250 kHz for rigid

solids,

whereas the tine width of

are highly resolved, fact that the field rials is essentially ally

suited

offering polymers,

to monitor

002%2860/83/Qo3.0o

lines

is l-2

kHz, the spectra

therefore. The analysis of the data is simplified due to the gradient in C-H bonds we corranonly deal with in organic mateaxially symmetric about that bond.Deuterons are thus idethe C-H bond direction

the posibitity liquid

individual

to elucidate

crystals,

molecular

membranes etc.

in space,

both static

motions and molecular

Since the properties

Q 1983 EXsevierScience Puiilishe~~B.V.

and dynamic, order

in

of such materials

120 are

closely

related

providing

to molecular

information

perties

of

that

such systems

paper

It will

be shown how pulsed

tion

about

both, order

determination the

type

wide range

molecular

of

and timescale

have been successfully

giving

details

cf.

ref.

and numerous

2 for

of

molecular

slow

techniques

will

motions

motions

be described

distribution

already

experimental

provide

of

the

and ref.

over

pro-

NMR line

3 for

which shapes.

science order,

As far allow

as

the

e.g.,

for

These

tech-

and reviews

have been published

molecular

area.

infotma-

an extraor-

Hz).

function,

in polymer

examples

in this unique

(10 MHz to 0.01

from deuteron

applied

to

molecular

orientational

in a drawn fibre

niques

capable of

we have developed

frequencies

the

NMR is

understanding

level:

NMR can be used

characteristic

the complete

chains

a much better

on the methods

deuteron

is concerned of

polymer

concentrate

deuteron

and order,

allow

on a molecular

In this

dinary

I will

motion

should

recently,

respectively.

MOLECUL.AR MOTIONS The use of time

pulsed

scales

Broekaert

deuteron

NMR for

involved

are most

easily

three-pulse

sequence

(ref.

studying

molecular

discussed 4),

motions

in connection

depicted

for

and the different with

convenience

the Jeenerin Fig.

1.

1 The generalized Jeener-Broekaert three-pulse sequence (ref..4) and the Note that-Fourier transform of the NM. s>gnals following the-various pulses. solid echo and the aligrment echo starts at times delayed by the pulse separation-r; after the second and third pulse, respectively.

Fi8---

Fourier single

transform pulse

yields,

(FT)

of the

free

in principle,

induction the

true

decay

(FID)

absorption

G(t),following

spectrum.

a

The large

121 width

of

the

solid

since

terons, ceiver.

This

which

probla

offers

the whole

range

ized

shape

is

this

where w is

a diagonal

of

an exchange

these

a system equal

In solid

values.

caused

a finite

by the molecular

motion

notation

with

and pi is

the

E is

a vector

giving

the

as descibed

components

‘$

(ref.

the

rate

T2*,

= z exp

Theoretical

details line

are

plotted

i.e.

solid

corresponding in Fig.

2 for

rl

spectra

for

in the

rapid

coupling

n = 0.

with

Clearly

the

time

about

lid

can be observed is

4 vs.

of

set

of

local-

frequencies.

has on the NMR line in ref.

limited

NMR lines

(i.e.

scale

the

of

order

the different matrix

affected s.

for

1,

fre-

transitions

probabilities with

all

by motions line

of

compowith

For powder samples wide

cor-

this

techniques

have tc

i.e.

range

the

of

over is

of

in hydrocarbon

transition

to a time

: = 1, although

in absence

the

line

shape

This

due to the

times

is

than the FIO.

to the

line

the FID decays

the width

of

width

for

is

fact the

the entire

of mo-

solid that

Detection of

re-

averagd

sensitive

the

appreciably

2)

TI = 200 ::s,

leads

which

tetra-

(ref.

and for

in the

9. As an

by the

chains

spectra times

of

= z/Z):

in ref.

related

higher

kHz) whereas

($,

(3)

given

considerably

much longer

the order

_?

are

the motion

of

response

two sites

correlation

limit

of magnitude.

inverse

shapes

the absorption

by TzX corresponding 1-2

echo - TV)

between

parameter

the motion for

line

times

time T2 ‘* is

solid

kink-motion

exchange

correlation

0 + z)(t

jumps

asymmetry

1 order

deuteron

(-i

a variety

the dynamic

scale

spectra,

echo

= 0,

with the

powder for

to the

echo

quadrupole

. exp

calculated

Note that

of

can ade-

time-independent

relaxation

by FT of

and calculated

chapes

angle,

motions

whet-.? the transverse

(i ,W +;i)~~

solid

or

motions

and 7 is a vector

will

and somewhat faster

K(tI,T1)

echo

molecular

8) _

can be studied

tion

6)

changes

in detail

uk specifying

transition

k orientations

signal

a few vs at most,

against

5,

(2)

set

This

instead

Somewhat slower

gion.

re-

covering

polymers

.Y

in one of

to unity.

be employed

hedral

deu-

the

(refs. solids

rotational

be strongly -5 relation times ~~ in the range 10 -6 ss -= 10 =c c signal is essentially unobservable and conventional

example,

rigid

between

matrix

the finite

between

1O-7 sZ

technique of

confonmational

Such restricted

a matrix

(i ,w +,)t

finding nents

exchange

echo

of

we obtain

= rj . exp

quencies

solid

in FT NMR of

the dead-time

‘H spectra

restricted

state.

Using

by the

problems

during

shape may change.

highly

as generating

spin

lost

7).

line

in the glassy

well-known.

p_ 448 ff.

the

involve

generates

is

undistorted

250 kHz (ref.

be treated

The effect

G(t)

of

often

motions

quately

information

can be overcome

of motion,

will

however,

spectra,

a means to record

In presence dynamics

state

considerable

echo the

of

so-

the

individual on a time

powder spectrum

(i.e.

250 kH.z), shorter

.than T2? by about two orders of magnitude.

.

R:

lZ,:

lo.Ls

s-10%

lOdS

Cl16

Fig. .2. Calculated 2H NNRpowder spectra for jumps between two tetrahedral sites. spectra. Right column: ?I = 200 US, Left coluinn: T = 0, i.e. true absorption 531 id ech A spectra. Aie&iuction factor giving the total normalized intensity of the spectra for z 1 = 200 3s. It should be no&d that in the transition ly vanishes tegrated

as manifested

intensities

sotid. echo intensity motion.

region

the solid

echo s+gnal virtual:

in the reduction-factor R giving the ratio of the inThe echo- and absorption spectrum, respectively.

of solid

thus provides

additional

information

about the molecular

123 In polymers one will

often

processes.

The solid

echo technique

transverse

relaxation limitation

longitudinal

relaxation

minutes.

laxation

be interested

just

described

time T21t being of the order

The ultimate veral

particularly

in rather

is still

slow dynamic

limited

by the

of a few hundred vs at most.

in every NM!?experiment, however, is not T2* but the 2 which for H in solids can be as long as se-

time TI,

The spin aliglgnent

and is limited

technique

(ref.

10) circumvents transverse thus ultraslow motions with correlation

by TI only,

re-

times T2* 5 =C 2 TI become accessible to experiment. Spin alignTent is a long lived state of quadrupolar order of the I = 1 spin system corresponding to 2 terms in the spin density matrix proportional to I=. The deuteron spins are thus aligned created

parallel

and antiparallel

by application

0, = n/4.

Application

This WR signal tion F(t2,TIST2) depending

to the external

of the Jeener-Broekaert of a reading

is directly

pulse

proportional

= < sin [LQ(O)TI]

.

field.

sequence,

($ = z/4)

generates

to a single

sin [Wq(T2)t2]

cf.

particle

This state Fig.

is

1, with

an alignment

echo.

correlation

func-

>

of wQ and thus on the molecular orientation in the evolution period t = 0 and the detection period at t = ~2, respectively, for details cf. ref. 10. Here the general terminology of two- and higher dimensional

NMR(refs.

on the values

11-14)

can be considered

has been adopted,

because the alignment three dimensional NMRexperiment.

as a

experiment,

in fact,

The correlation function, Eq. (4) can be analyzed for different dynamic processes. This has been done for molecular jumps in single crystals (ref. 10) and in pohders (ref. 15). In order to test the ‘technique we used a model compound, hexamethylenetetramine jumps. As illustrative spectra,

obtained

(HMT), which in the solid

state

undergoes

slow tetrahedral

examples,

experimental and calculated spin alignment by FT of the aligment echo starting at the echo maximumare

presented in Fig. 3 for two different mixing times TV. one being short, the other being long compared with the correlation time of the motion, for a number of evolution

times T1. Characteristic

where the variation

of ‘1

motion and *c is obtained

line

is used to differentiate directly

*C*

shape changes are observed, between different

from the decay of the alignment

types of echo with

increasing ~2, for details cf. ref. 15. By using the different techniques described here the correlation time of the motion in WT could be followed over 8 orders of magnitude (refs. 8 and 16) up to =C = 66 s as shown in Fig. 4. This clearly

demonstrates

the potential

of these

new techniques.

: 124

.. :

t2=lms-t,

Fig. the Note

3.

@Sservec-and

influence the

strong

of

X,=200

calculated

spin

the tetrahedral influence

of

the

jump

alignment motion

evolution

ms >>tt

spectra for

time

long ‘1

of

solid

mixing

on the

line

EMT showing times T2=- Tc. shape.

125

lO(Ie

70

1

16’

11i2 1O-3 ldL 10-5

1O-b

L

Fig. 4. Correlati.on times for the tetrahedral jump motion in solid I-MTobtained 16). from deuteron line shape analysis (ref. 1) and deuteron spin alignment (ref. These methods can be used to study chain.mobility ultraslow

motions associated

with the glass

in polymers.

transition

In particular

the

of amorphous polymers

(ref.17) can be elucidated emp’loying deuteron spin alignment. Partial information about the rotationai motions involved can be obtained simply by following the decay of the alignment echo itself. This is illustrated in Fig. 5 which compares the decay of the alignment echo for large angle jumps characteristic of conformational

changes and diffusive

reorientation

of the chains

by small angles,

re-

spectively (ref. 18). For jumps through fixed angles the aligrment echo decays with a time constant corresponding directly to the correlation time of the jump process

to a constant

level

being inversely

proportional

to the number of

126

TETRAHEDRAL

JUMPS

1.0

.s

.2

.l

Fig. 5. Decay of the alignment echo height as a function of the mixing time = for t-m differentmotional mechanisms. Note the strong dependence of the deca$ curves on the evolution time ‘1 in case of small angle diffusion. sStes

being

interchanged.

Contrary

to the line

shapes,

cf.

Fig. 3, the time con-

%.&ant of this decay is almost independent of the evolution time T1'(ref. 15).

On the ether

hand, for

a diffusive

motion involving

rotations

by small but not

weTl-ciefin,ed angles the echo decay depends strongly on T~, becoming more rapid with increasing TV_ It should be noted that the alignment echo for rotational diffusi-on

decays appreciable

0n.a time scale

much shorter

TV. This means that

127

by proper

choice

technique

is capable

tions

by less

of TI. subject

to the condition

of detecting

than 10’.

ultraslow

Such highly

TI c T2*, the spin alignment

motions

restricted

even if

diffusive

they involve

motions

been observed for the -polystyrene chains in the amorphous glassy the vicinity of the glass transition (ref. 18). The techniques described here were also amorphous regions of linear polyethylene the molecular temperature

motions

gion.

The deuteron

tions gical

accessible constraints

spectra

bility

thus allows

available

for

aspect

details

the substantial

see ref.

in semicrystalline

distritution

and rigid

different

the

solid

times

echo.

1) this

fractions,

of correlation

Since

between spin

separation

ly and only partially carbonate

f.

at various

respectively,

is highly

relaxed

is

temperatures.

heterogeneity.

sequence

motions

do exist, 21).

directly,

partially

relaxed

and the

sequence

inefficient

This material

for

which

Pulsed deu-

because mole-

for

As an example Fig.6

spectra

and mo-

and amorphous regions,

shape. It also shortens to reparate the signals

relatively

effective.

deuteron

in chain mo-

where rigid

times (ref.

by taking

a saturation

diffusion

NMR

of semicrystalline

votional

NMRcan be employed to map out such a distribution

for

(-ref.

pulsed deuteron

materials

cular motion does not only change the NMRline lattice relaxation time. This can be exploited mobile

topoloof such a

2, 19, 20.

can often be identified with crystalline In amorphous polymers, however, localized

may show a considerable

re-

number of confona-

differences

of polymer dynamics involves

This phenomenon is well-known bile fractions respectively.

over a

to the melting

the increasing

through the various

us to elucidate

respectively,

Another important

teron

reflect

in amorphous polymers and in the amorphous regions

polymers,

and in

were detected through the spin alignment technique. In have a finite lifetime of a few hundred 2s only (ref.

The uni,que information

techniques

be followed

to the chain as the temperature is raised. Long-lived limiting the chain mobility in the amorphous regions

semicrystalline material the melt such constraints 20).

changes could

the way from the -f-relaxation

directly

state

used to study the chain mobility in the in considerable detail (ref. 19). Here

due to conformational

range of 250 K all

rota-

have indeed

the spin from the spectra generating

deuterons presents

the phenylgrotips

ful-

of poly-

shows a pronounced low tempera-

ture mechanical’

relaxation in the glassy state and has favorable mechanical properties, in particular a high impact strength. 3y deuteron NMR we were able to show (refs. 2, 22) that only restricted localized motions of the phenylgroups exist flips

in this material. Above room tenperature all phenylgroups augment& by substantial fluctuations about the same axis

undergo 180’ as obtained from

a line shape analysis of the spectra at 334 K, cf. Fig. 5 and ref. 2. At lower temperatures this flipping motion is frozen for part of the sample,the molecular motion of the mobile fraction remains essentially unchanged, however. The

mobile fraction:

total spectra

Fig.

6.

Deuteron

NHR spectra

partially relaxed

for

structure is depicted on top). Left column: Total spectra. Right column: Partially relaxed number of mobile

phenylgroups

the

spectra

phenylgroups

spectra decreases

in

corresnonding considerably

polycarbcnate

to the mobile with decreasing

(molecular groups only. temperature,

corresponding to about 10% only of the total sample at 150 K. Our study shows that the mechan’ical propktles of solid amorphous-polymers apparently are closely relatedto the heterogeneity &such local motions (ref. 22).

:

129 MOLECULAR ORDER In addition

to prov7’ding dynamic informatton

ly ordered

solids

gree of molecular solved

NMRline

stribution

can also order,

be-used

e.g.

to obtain

in ordered

As a specific

example

an unfaxially

drawn fibre.

let

us

NMRline

detailed

information

in drawn fibres

shapes can be analysed

of molecules

deuteron

shapes in partialabout the de-

(ref.

23). In fact these highly rethe complete orientational di-

to yield

systems.

consider

the

The analysis

orientation

of

of NMRspectra

hydrocarbon

in this

chains

case yields

in pri-

mari’ly the distribution of C-H bond directions relative to the external magnetic field. For hydrocarbons it is use,u f ! to calculate the spectra for parallel chains chains, as in the crystalline regions of polyethyle first, Fig. 7. For all-trans ne, the C-H bonds are in parallel 3, 24).

For a chain wh7’ch also

planes

contains

and form a planar distribution gauche conformers.

(refs.

as in the amorphous

regions of polyethylene, we have in addition C-H bonds on a cone at an angle of 35’ with the chain direction, forming a conical distribution, cf. Fig. 7. The

CRYSTALLINE all-trans

AMORPHOUS trans. gauche I

=.hL/ I.-I

I/

A*/

\

_

pianar

-

+. conical

\p:

Fig. 7. Schematic representation of selected hydrocarbon chains in the crystalline and in the amorphous regions of polyethylene, respectively. For ensembles of chains unifonly distributed around the dashed lines the deuterons form planar and confcal dfstributions as indicated-

DRAW

DIRECTION

Fig. 8. Calculated deuteron NMRline chapes for planar and conical distributions, respectively for different angles between the direction of order and the magnetic field, for details see text. corresponding angles

subspectra

can easily

for

ensembles of parallel

be calculated

dered solid the total such subspectra,.nhere

analytically

line shape is obtained the wei‘ghting factors

(refs.’

chains 3, 24).

inclined

at different

In a partially

by a weighted superposition depend on the orientational

orof distri-

bution functl’on of the poiymer chains. As an example, Fig. 8 gives line shapes respectively, for a Gaussian orientatiofor planar and conl’cal dis.trjbutTons, for different nal distributions with .a widths of f 9’ and f lZ”, respectively, angles- between the direction of order and the magnetic field. Note that the spectra at a given angle are-n3tmalized to the same integrated intensity. A wei.ghtedsupar~~ition spectra

for

of ,these spectra -in turn was.fitted

the amorphous regions

to the experimental

of a drawn sample of ‘linear

polyethylene,

as

131 shown in Fig;, 9. The detailed distribution phous regions

in this

case

analysis

(ref.

is not uniform,

did not show order

at all.

25) shows that the orientational

in particular about 25% of the amor-

The gauche-content

was determined

to

distribution, normally used to be 26%. The second moment of the orientational specify the average molecular order (ref. 23) in the amorphous regions as calculated

from the numbers given

stalline

ones (ref.

above is 0.66 only,

compared with 0.99 in the cry-

24).

DRAW DIRECTION

,;f-

Fig. 9. Observed and calculated 2H NMRspectra of the amorphous regions of a The data were taken at 143 K in ordrawn sample (x=9) of linear polyethylene. der to freeze in molecular motion. For small angles a, the line shapes of the crystalline regions (ref. 24) is apparent because the separation of the NMR signals from amorphous and crystalline regions, respectively is incomplete. Another type of partially ordered systems is provided by liquid crystals which In recent years polymeric can be ordered through electric and magnetic fields. of polymers with 1 iquid crystals have been synttestied, combining properties

_132

those of liquid NMRstudies

crystals.

of molecular

viewed in ref.

Molecular

powerful processes

after

transform

tool

line

and deuteron been re-

.

Only four years

bining

phase behaviour,

26.

coNcLusIdN

by Fourier

structure,

order and motion in such systems has recently

for

2H powder sbectra methods,

studying

shape analysis

with correlation

type of molecular

solids

have first

pu1~ed~i-l NMRhas rapidly

developed

mo’lecular

of rigid

motions and the degree

with making use of deuteron

been recorded

to become a

of order.

spin alignment,

By comdynamic

ti;nes between 0.1 PS and 100 s can be studied.

motion involved

can often

directly-be

inferred,

e.g.,

The rotatio-

nal jump motionshave been detected not only in solids but in other materials well, including polymers, liquid crystals, membranes, and even proteins_

as

ACKNOMLEDGCIEMTS It is a pleasure to thank my co-workers who have been involved in the various experiments and Prof. H. Sillescu for numerous discussions, concerning in particular

the polymer aspects

of this

the Deutsche Forschungsgemeinschaft

work. The continous is gratefully

financial

acknowledged.

support

by

133 REFERENCES 1 2 3

6

:: 14

:; 17

18 19 20

z: 23

22: 26

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