Nuclear spin relaxation in a vinylidene fluoride and trifluoroethylene copolymer (70/30). - II. The one-dimensional fluctuations in the paraelectric phase.

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Nuclear spin relaxation in a vinylidene fluoride and trifluoroethylene copolymer (70/30). - II. The

one-dimensional fluctuations in the paraelectric phase.

Jérôme Hirschinger, Bernard Meurer, Gilbert Weill

To cite this version:

Jérôme Hirschinger, Bernard Meurer, Gilbert Weill. Nuclear spin relaxation in a vinylidene fluoride and trifluoroethylene copolymer (70/30). - II. The one-dimensional fluctuations in the paraelectric phase.. Journal de Physique, 1989, 50 (5), pp.583-597. �10.1051/jphys:01989005005058300�. �jpa- 00210939�

Nuclear spin relaxation in

a

vinylidene ^fluoride

and trifluoroethylene copolymer (70/30).

II. The one-dimensional fluctuations in the paraelectric phase.

Jérôme Hirschinger, Bernard Meurer and Gilbert Weill

Institut Charles-Sadron (CRM-EAHP), ^CNRS-ULP Strasbourg, 6, ^rue Boussingault, 67083 Strasbourg ^{Cedex, France}

(Reçu le 20 avril 1988, accepté ^sous forme définitive le 7 octobre 1988)

Résumé. ²⁰¹⁴ La phase paraélectrique ^d’un copolymère 70/30 de fluorure de vinylidène (PVDF) ^et

de trifluoroéthylène (TrFE) ^{a été} étudiée par relaxation nucléaire spin réseau du 1H et du

19F, complétée par l’analyse de la forme de la précession libre dans des échantillons orientés et non orientés. Les mesures de T1 ^ont été effectuées entre 6 et 300 MHz, ^{celles de}

T103C1

^{entre 3 et}

100 kHz et à différentes températures. Deux modes de relaxation ont été identifiés : un mouvement rapide anisotrope (03C4c ^~ 10-10-10-11 s) responsable ^{de la} dispersion ^« unidimension- nelle ^» caractéristique ^{en 03C9-1/2 de}

(T1)-1

^{et de}

(T103C1)-1;

^{un mouvement} lent considéré comme

isotrope (03C4c ^{~ 10-5-10-6} s). Ces deux modes coexistent dans la phase amorphe alors que le mode

rapide décrit seul la dynamique ^{de la} phase cristalline. L’ensemble des résultats est bien décrit par la diffusion des orientations grace ^{à un mouvement à} 3 liaisons (vilbrequin) ^{ou un mouvement de} paires de liaisons en sens opposé. La coupure nécessaire de la densité spectrale ^en 03C9-1/2 aux basses fréquences peut être attribuée aux mouvements lents qui créent de nouvelles orientations dans les chaînes.

Abstract. ²⁰¹⁴ Measurements of the hydrogen and fluorine nuclear spin-lattice relaxation times

T1 ^{from 6 to} 300 MHz and T103C1 ^{from 3 to} 100 kHz have been performed ^{at different} temperatures in the paraelectric phase ^{of a 70/30} VF2/TrFe copolymer ^and analysis of the FID signals ^{on both}

oriented and non-oriented samples ^has been carried out. Two relaxation modes have been determined : a fast anisotropic ^motion (with the fastest correlation time 03C4c of order

10-10 ~ 10-11 s)

showing the characteristic ^« one-dimensional » 03C9-1/2 dispersion ^of

(T1)-1

^and

(T103C1)-1; a

slow motion considered as isotropic (03C4c

~10-5-10-6s).

^{The two modes} operate ^{in the} amorphous phase while the fast motion alone describes the dynamics ^{in the} crystalline phase. ^No

one-dimensional kink motion can explain the observed data. Good agreement with all the

experimental results is provided by three-bond crankshaft motions or cranklike counterrotational

pair transitions. The necessary low frequency cut-off in the spectral density ^is attributed to the slow motion creating ^new orientations in the chains.

Classification

Physics ^Abstracts

61.40 - 76.60 ^- 77.80B

1. Introduction.

In part I, ^reference

[1],

the nuclear spin relaxation in the ferroelectric

phase

^{of a 70/30}

VF2/TrFE copolymer

has been studied. This second part ^{is devoted to the NMR} study ^{of the}

JOURNAL DE PHYSIQUE. - T. 50, N’ 5, MARS 1989 32

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01989005005058300

paraelectric phase. By ^various techniques

[2-5],

^the paraelectric phase ^of VF2-TrFE copolymers appears ^to be dynamically disordered. Nuclear magnetic ^{resonance is then} expected ^{to be a}

powerful

method for

investigating

the molecular motion associated with the Curie transition, ⁱⁿ particular by the determination of the spectral

density

^{of the}

microscopic

fluctuations

J(w) [6].

^In polymers,

J(w) generally

results from the superposition ^{of several}

molecular modes

[7].

Moreover, ^the spectral density of each mode is greatly ^affected by ^the dimensionality

[8]

^{or the} anisotropy

[9]

^{of the} dynamic process.

J(co)

should then be probed

over a very large

frequency

range,

especially

^{when the} temperature range is limited by phase

transitions. For nuclei with large

gyromagnetic

^ratios

y(1H, 19F),

measurements of the spin-

lattice relaxation in the laboratory ^frame Tl ^can easily ^be performed ^{in a} range of

w between 107 and 2 x 109 rd/s. In the absence of

expensive

^field cycling equipment

[10],

^the low-frequency ^behavior

of J(w )

^{can be observed} by measuring ^the spin-lattice relaxation time in the rotating ^frame

Tl P

for different

magnitudes

^{of the}

spin-lock

^field

Hl . (JJI

= yHl ^then

goes

typically

^{from 3 x 104 to 106 rd/s. A better} understanding ^{of the} dynamics ^{is also}

provided

by measurement of the transverse relaxation or the so-called free induction decay

(FID)

signal allowing ^the determination of which part of the local dipolar ^field

HL

^is actually

modulated by the molecular motion, especially ^{for an oriented} sample. ^A correlation with the

spin-lattice relaxation is then possible. ^{Such an} analysis has been carried out in the following study.

2. Experimental.

Apart ^{from the} measurements of Tl ^at the Larmor

frequencies

PL ⁼ 188, ^{200 and 300 MHz}

carried out on Bruker CXP spectrometers, all the NMR

experiments

^{have been}

performed

^on

the modified Bruker SXP spectrometer ^as

reported

ⁱⁿ part I, ^{where the} samples ^{are also}

described

[1].

3. Theory.

3.1 SPIN-LATTICE RELAXATION. ^- In the absence of the transient Overhauser effect, ^the

relaxation times Tl ^{of the} ’H and 19F resonance are given, in the weak collision limit, by ^the expressions

[6] (see

^Part

1) :

with

where w is the ’H Larmor angular

frequency

^and

âMF, âMF

^and

AMHF

^are,

respectively,

the

’H,

^19F homonuclear and ’H heteronuclear second moments that are modulated by ^the

molecular motion. Furthermore, ^{at a} spin-lock angle 0 ⁼ 90°, ^{we have}

[11] ( W 1 w)

3.2 TRANSVERSE RELAXATION. - Assuming ^{that the} fluctuation

frequencies

of the local field have a

temperature-independent

^Gaussian distribution, ^{the FID} signal

M (t )

^is given ^as

[12]

where M2 RL ^{is the} « rigid lattice » second moment and

03A6 (T )

^the autocorrelation function

(correlation function)

^{of the} motion, ^{the Fourier} transform of which is

J(w).

4. Results.

4.1 Tl RELAXATION DATA. - The relaxation is, ^within expérimental accuracy, exponential

for both the IH and 19F resonances

(Fig. 1)

^{above 70 °C.} Tl ^increases steadily ^with increasing temperature. ^{Plots of}

(T1)-

^{l as a} function of

( vL)-

^{1/2 are} linear and go through ^the origin except for Larmor frequencies higher ^{than 60 MHz below 90 °C where a} slight ^deviation

towards longer relaxation times is observed

(Fig. 2).

^{No transient} Overhauser effect has been detected over the entire temperature range.

Fig. ^{1. -} Ti relaxation decay ⁱⁿ ’H resonance at 100 °C (cooling run). The distribution of the residuals for the exponential ^fit ( Tl ^{= 156 ± 5} ms ) ^is shown in the insert.

Fig. ^{2. -}

(Tl )-1

^{data as a} function of

(VL)-l/2

^{in ’H} (a) ^{and 19F} (b) ^{resonance at 80} (0), ⁹⁰ (a), ¹⁰⁰ (X),

110 (e) ^{and 120} (+) ^°C (cooling run).

4.2

Tl p

RELAXATION DATA. ^- The relaxation which seems exponential ^at high frequencies

( v 1 = (ô 1/2 ir >. 30 kHz)

appears ^to be biexponential ^{at low}

frequencies (vi

¹⁵

kHz) (Fig. 3).

^{However, since the two time constants are} close each other

(differing

only by ^factor

3),

the ratio of the intensities was fixed according ^{to an} analysis presented ^{below to obtain}

consistent values

(four

parameter

fits).

^{The slow} component

(Tl pL)-l is

consistent with a

( v 1 )- uz

^variation going through ^the origin

(Fig. 4).

Fig. ^{3. -} Distribution of the residuals for a one exponential (a)

(Tl,

^{= 2.3 ± 0.05 ms) and}

biexponential (b)

(TIPs

^{= 1.1 ± 0.05 ms ;} Tl PL ⁼ 3.9 ± 0.07 ms) ^{fit to the} experimental ^{data at 120 °C}

with v 1 = 3 ^{kHz. A better} agreement ^{with the} experimental decay ^is provided by ^the biexponential ^fit.

Fig. ^4.

( T1 P L )-1

^{as a} function of

(v1)- 1/2

^{in ’H resonance at 60 MHz} (cooling run). The insert shows the variation of the global

(Tl P )-1

^{at high frequency i.e. when a} separation ^{in two} components ^fails. Thé temperatures ^{are defined} by ^{the same} symbols ^{as in} figure ^2.

4.3 FID ANALYSIS. ^- The ’H FID signal ^{has been fitted} by ^{the POLFIT} procedure

[13]

^to give the total second moment M2 of the material. In unoriented samples, ^{the second moment}

in the paraelectric phase

(2 ±

^0.2

Gz)

drops considerably, ^as compared ^to the ferroelectric

phase

(13.5

^{± 0.5}

G2) ;

^this is evidence for strong motional disorder

[2].

Moreover, ^{in the case}

of an oriented sample,

figure

11 shows that the variation of M2 ^{as a} function of the angle

y between the draw direction and the

applied

^field

Ho

^{does not show at} 120 °C, ^{the «} rigid

lattice » minimum observed at y = 45°

(see Part I),

but rather a

continuously decreasing

value with increasing ^y.

5. Interpretation of the results.

The amount of spin ^{diffusion between the} crystalline ^and amorphous regions ^{is known to be} dependent ^on the average size of domains, ^the spin ^diffusion coefficient and the relative

magnitude ^{of the} spin-lattice relaxation time in the two phase

[7, 14, 15].

By

comparison

^with

the results in the ferroelectric phase :

(i)

^{from the} large dynamic disorder evidenced by ^the drop in the second moment at the transition

[2]

^one expects ^a reduction of the spin ^diffusion coefficient

[14].

(ii)

the relaxation rates are

higher

than in the crystalline ferroelectric phase

[1].

(iii)

small-Angle-X-ray-Scattering

(SAXS)

studies demonstrate that the long period ^{in the} paraelectric phase ^is higher than in the ferroelectric phase

[5].

Hence, ^the spin diffusion between the crystalline ^and amorphous

phases

^{which has been}

shown to be already weak below the Curie

point Tc [1]

^{is not} likely ^{to have a} significant ^effect

on the relaxation in the paraelectric phase. Exponential decays ^could only ^come from similar relaxation times for the crystalline ^and amorphous regions,

implying

^{that the same} type ^of motion is occurring ^{in both}

phases.

However, ^the

7Bp

biexponential decays indicate that a

distinction between amorphous ^and crystalline ^{motions is} possible ^{at low}

frequencies.

^We shall, therefore, ^assume the coexistence of two independent processes in the amorphous phase : ^{A fast}

(high frequency)

anisotropic motion indexed fm which also occurs in the

crystalline phase ^{and a slow}

(low frequency) isotropic

motion indexed sm. In other words, ^the remaining correlation of the dipolar interaction will be further reduced by ^{the slow motion.}

We have then

with

As when

and

One remarks that the AM2’s ^of

equations (1)

^to

(4)

^are simply ^{the «} rigid lattice » second moments appearing in the denominators or

(7)

^and

(8).

^{One must, of course,} separate ^{out the}

homonuclear and heteronuclear contributions to the expressions ^{of the} spin-lattice ^relaxation

rates. With these assumptions it is obvious that relaxation in the amorphous phase ^is

equal

^or

faster than that in the crystalline phase. This is the reason why ^we have fixed the the less mobile fraction

(

^{= 75}

%)

^deduced from the FID analysis

[2].

The fact that this value is higher ^{than the} crystalline ^{fraction in the} ferroelectric phase

(

^{= 55}

%) [1]

^{can be} explained by ^{either an increase of} crystallinity during ^the transition or the existence of a constrained

amorphous phase ^{which does not have the low}

frequency

^mode

(see below).

5.1 AMORPHOUS HIGH FREQUENCY AND CRYSTALLINE MOTION. ^- The

Tl (IH, 19p)

^and

Tl P (’H)

long

component c -1 dispersion (Figs.

^{2 and}

4)

^{has to} be related to the ^« long ^time T - 1/2 tail » of the correlation

function 4> fm( T)

^{since, if}

f’n( T ) - ( Td/2 r T )1

^when

T is much longer ^{than the} correlation _{time Td} we have

Moreover, ^{it can be seen from} figure 5 that the absence of transient Overhauser effect is consistent with the CI) - 1/2

dispersion.

^{The «} long ^time T - 1/2 tail ^» of the correlation function is

highly characteristic of the one-dimensional

(lD)

^nature of the fluctuations

[8].

^This general property arises from the slowness of the regression of the fluctuations in a 1D system. ^A

good

illustration is given by the random walk of a particle

[16].

^{Indeed, in one} dimension, ^the probability ^{P to find a} particle ^{with a} diffusion coefficient D in the interval x, x + Ax after a time T will be

equal

^to

Ax/2(7rDr)1/2, providing

^that

T > x2/D.

^More

generally, ^{in a} system ^of dimension d, ^{P will be} proportional ^to T-d/2 for long ^times

[16].

^In

other words, ^the particle ^under consideration has a higher ^{chance of} coming ^{back to} its initial

position

in the 1D system, ^{as it must. The}

high-frequency

^deviation

(Fig. 2)

^{indicates that,}

Fig. ^{5. -} Calculated Overhauser effect amplitude I, (defined ^{in Part 1 section} III) ^{as a} function of wrd for different correlation function or distribution of correlation times (the OM2’s ^{are those for « rod-}

like » rotation and translation of the chains, ^see appendix) : BPP, Hunt-Powles, Kimmich-Voigt ^and

Williams-Watts (/3 = 1/2) correlation functions are respectively represented by ^{-, - -- - .}

and ^{- -} curves. Distribution of correlation times [41] : Fuoss-Kirkwood /3 ^{= 0.2} (-.-.-.-),

/3 ^{= 0.5} (----) ; Cole-Davidson 6 ⁼ 0.2 (---), 8 ^{= 0.5} (-). ^{All the} spectral densities which give ^a negligible 1+ ^at W Td 1 present ^the W -1/2 dependence.

near 80 °C, w ^{is close to} the correlation frequency rd 1. _{However, W Td} remains less than unity since, ^at v L ⁼ 300 MHz, ^the variation of Tl ^{as a function of} temperature still does not present

a minimum above Tc. ^{In order to} calculate the correlation time _Td, one must determine the homonuclear and heteronuclear second moments modulated by ^{the fast} motion. Lattice sums

have been computed ^{for different} simple modes of molecular motion and a reasonable agreement ^with experimental data is obtained for a complete ^rod-like rotation and translation about the main axis

(Appendix).

^{In the 19F resonance} it is noted that measurement of the

dipolar contribution to M2 ^are hampered by the considerable chemical shift of fluorine

(Fig. 6).

^When introducing ^the calculated

AM2

^{values and} expression

(9)

^of

Jfm(w )

ⁱⁿ

equations

(1)

^and

(2)

^and

fitting

^{to the}

spin-lattice

relaxation data the same correlation times within 10 % are found from the ’H and 19F resonances : Td increases from about 15 to 70 ps between 120 and 80 °C i.e. the condition (Ô _Td 1 is effectively valid. These findings ^constitute

clear verification of the consistency of both the

J’( w ) expression

^{and the}

âMrn

^{values. One}

notes that

the úJl independent

^{term of} equation

(4),

which is of the order of

( Tl )-1 [17]

^at

60 MHz

(

^{= 10}

s-1),

^{can be} neglected

(Fig. 4).

The values of Ti pL lead to correlation times about three times higher than those extracted from the Ti ^data

(1).

^{Such a} difference can

easily

^{be accounted for} by ^a very ^narrow distribution of correlation times since Tl ^{is sensitive}

to

frequencies

¹⁰³

higher

^than

Tl P .

^{Indeed, the} temperature

dependence

of Td obtained from all the spin-lattice relaxation experiments give ^{the same} activation energy 10 ± 1 kcal/mol.

According ^to

(5)

^{and since}

Td(AMfm)1/2

1, ^the crystalline ^FID

signal

^is

[18]

Since

OM2m

^{Td «}

OM2m t

for observable times t equation

(10)

^{is well}

approximated

by ^a

Gaussian signal ^{of second moment}

AMsm

^{i.e. the} crystalline ^{FID is} entirely ^dominated by ^the part of the local field which is not motionally

averaged

leaving ^no information on

4> fm( T ).

Fig. ^{6. -} Line-shape ^{at 120 °C in} 19p resonance ( vL ⁼ 56.4 MHz ). ^{The two} non-equivalent ^fluorine

nuclei are apparent.

(1) ^{It is noted that,} although Hi = HL, the weak-collision limit is valid since Td

The first model of molecular motion leading ^{to a} spectral density proportional ^to llJ -112 has been introduced as a « defect diffusion » model by ^Glarum

[21].

^In polymeric

materials a « defect » is readily associated with a rotational isomer or « kink » diffusing up and down the chain

[8, 22].

^{Such a} motion has been used by ^{Ishii et al.}

[20]

^{for the} analysis ^{of the}

frequency

^and angular dependence ^of

Tl

^{in oriented}

VF2-TrFE

samples. ^{On the other hand,} improvements ^{to Glarum’s} model have been noted by several authors. Notably Bordewijk

[23]

^{included all the defects of the system. Kimmich and} Voigt

[22]

introduced defect having ^a

« restoring

capability

^{». Skinner and} Wolynes

[24]

considered defects having varying degrees

of frictional

damping

^of the defect motion. It should be noticed that the long ^time T - 1/2 variation of the correlation function is then not always ^fulfilled.

In what follows we try ^to combine the information derived from

Tl

and that derived from the anisotropy ^of M2 in the oriented sample ^to get ^more information about the type ^{of motion} involved. We start with kink motion which are favoured by ^the hexagonal symmetry ^{of the} lattice

[5].

5.1.1 0° or 180°-kinks. In NMR, the relevant expression ^{of the} correlation function is

where 0

( T )

^{is the} angle through ^{which an} intemuclear vector rotates between ^{T =} 0 and time

T. Hence, if the reference internuclear vector is rotated by ^an angle ^{of 0° or} 180° after the passage of the kink the final ^state is equal ^to the initial state and the dynamics ^are adequately

described by the Kimmich Voigt correlation function

[22]

^which

effectively

^{shows the} long

time 7» -1/2 tail

(Fig. 7a).

^The occurrence of both 0" and 180°-kinks has often been suggested ⁱⁿ

polyethylene [25].

Assuming that the correlation frequency of the kink motion is much higher

than the linewidth and neglecting ^the length of the kinks

[25],

^{there is no motional} averaging

of

M2

^{for the 0°-kink}

(«

rigid ^{lattice »}

conditions)

^{and the} resulting ^{motion is a «} flip-flop ^{» for}

the 180°-kink

[26].

In any case, the decrease in the second moment is much less than the one

due to the complete rotation of the chain. The study ^on the oriented sample

(Appendix)

clearly confirms that both 0° and 180°-kink diffusion is in disagreement ^{with our} M2 ^results.

5.1.2 Other kinks. - Diffusing ^{120° or 600-kinks} will results in flipping motion between 3 or 6

symmetrical positions already suggested by Legrand ^{et al.}

[27]

^and gives ^{the same} M2 averaging ^as complete ^{rotation of} the chains. Such a motion is favored by ^the hexagonal symmetry of the unit cell. However,

although

^{there are still} only ^two

possible

interaction states, ^{the final state is no} longer

equivalent

^to the initial state after the passage of ^a 120° or

60’-kink since

P2 (0 )= P2 (120° )

⁼

P’(60’).

^{Skinner and} Wolynes

[24]

^have considered that the arrival of a

subsequent

^kink

(second

^{defect on} Fig.

7b)

^{will restore the initial state. In the}

case of 120° or 60°-kinks, ^the

subsequent

^kink may ^or may not restore the initial state.

However, ^this consideration is in fact uncritical since, ^{in the limit where the defects} diffuse,

the Skinner-Wolynes correlation function is found to be

equal

^{to the} empirical Williams and Watts relaxation function

exp (- T / T d)/3

^{with (3 = 1/2 which was also obtained}

by Bordewijk [23]

assuming ^{defects without}

restoring capability (Fig. 7c).

Therefore, this Williams-Watts correlation function which tends to zero much more

rapidly

^than T - 1/2 generally ^{describes the}

diffusion of kinks rotating the chains by ^an angle ^{which is not 0° or 180°. In} conclusion, ^kink

diffusion is not able to explain ^our spin-lattice ^and transverse relaxation data simultaneously.

It is then necessary ^to find another explication ^{for the} observed « one-dimensional » fluctuations.

Fig. ^{7. - The different} types of fluctuation associated with the correlation functions discussed in the text. a) Kimmich-Voigt correlation function ; b) Skinner-Wolynes correlation function and

c) Williams-Watts correlation function with 8 ^{= 1/2.}

5.1.3 Diffusion of ^the orientations

along

the chains. ^- Since the dynamically ^disordered

conformation of the chain in the paraelectric crystalline phase ^{is known to be a} statistical mixture of TG, TG ^{and TT} sequences

[4,

28,

29]

^the reorientations of the C-C bonds could be viewed as generated ^{on a diamond} lattice. Of _course, in the crystalline part ^{of the} sample, ^the

chain linearity ^{has to be} maintained during ^{the motions. This condition is} easily introduced by

the restriction to consideration of three-bond motions which do not create new orientations.

Their unique ^but important ^{effect is to cause} diffusion of the existing C-C orientations along

the chain

[30].

^The complete autocorrelation

function 03A6 (03C4)

^{for an} intemal bond of such an

« infinite ^» chain has been calculated by ^{Valeur et al.}

[31]

^{and indeed} presents ^the long ^time Ir - 1/2 decay. ^{In a chain} consisting ^{of a} statistical mixture of TG, TG and TT sequences, it

immediately appears that all the odd C-C bonds will have the ^same orientation, ^for example ^a

(Fig. 8).

^{The movement of the} intemuclear vectors

(along

which the dipole interaction between 1H and 19F nuclei bound to the same carbon is

acting)

^are exchanged by ^{the three-}

bond motions, but the odd C-C bonds remain oriented along ^a

(Fig. 9).

Even if this is not

always ^true

(since

1H-19F pairs ^{cannot be} exactly parallel ^to lH-lH or 19F-19F’

pairs)

^{the three-}

bond motions cause

diffusion of

^each internuclear vector among three possible orientations

generated by rotations of 120° about _a, so that the one-dimensional nature of the fluctuations is entirely preserved. ^In fact, since NMR does not

distinguish

^{between two} of the three orientations

(

^±

120°)

^this type of fluctuation is similar to the one described by ^{the Kimmich-} Voigt correlation function

[22]

^{where two} of the three positions corresponds ^{to the defect}

state. The similarities between the defect diffusion and the three-bond motions on a diamond lattice have also been observed by McBrierty ^and Douglass

[7].

However, although ^the

structural reorientation involved in a three-bond motion is

effectively

^{the same as for} diffusing TGTG _sequences or « Pechhold kinks »

[32]

^{which are « 0°-kink », the} fundamental

Fig. ^{8. - An} example of the chain backbone composed ^of TG, ^TG and TT sequences in the diamond lattice

(TGTGTTTGTGTGT G ).

The sequences 2-3-4-5 is changed in 2-3’-4’-5 by the three-bond motion depicted ⁱⁿ figure ^9.

Fig. ^{9. -} Effect of the three-bond motion on the ’I-1

-’I-I,

^{’9F-’9F and ’H-19F} intemuclear vectors. The

« positions » 2(3) ^and 4(5) ^are exchanged by the three-bond motion.

difference is that the kink diffusion is a point-defect ^mechanism

implying

^{a small}

equilibrium population

of defects

[25]

^and,

consequently

^{it has} only ^a slight ^{effect on the second moment}

[26].

On the other hand, three-bond motions are not localized

phenomena

^so that, ^{on the time} scale of the inverse of the line width

(a

^few

03BCs),

^{all the} internuclear vectors will have spent ^an

equal

^{time at} the three symmetrical

positions

ⁱⁿ

good

agreement ^{with our}

M2

^results

(Appendix).

^{It is worth}

noticing

that, ^{unlike the}

point-defect

mechanism, ^{such a diffuse}

disorder is in agreement ^{with the} large entropy change,

occurring

^{at the} transition

[33].

Another source for one-dimensional fluctuations may be the

correlated jumps [34].

^However,

since these

pair

wise transitions involve translations of the chain tails attached to the

transforming

pairs ^{such a motion}

(which

^could happen ^{in the} amorphous

phase)

^is unlikely ^to

occur within a crystalline ^{lattice. As mentioned} by Lovinger

[35],

^a « flexible crankshaft » mechanism remains more

probable

^and similarly

explains

^the thermally ^{induced transform-}

ation from the a to the _y crystalline form in the homopolymer

PVF2.

In any ^case, the

important feature is that the motion requires ^{diffusion of} orientations along the chain in order to show the 1D fluctuations. This property ^{is indeed verified} by both the counterrotational

pair-transition

jump [34]

^{and the} three-bond motion.

5.2 AMORPHOUS LOW FREQUENCY MOTION. ^- According ^to

equation (8)

^the amorphous spin-lattice relaxation rate due to the slow motion is

where subscripts S and ^{L refer to} the short and long

Tl,,

components.

The

(Ti P )-1

dispersion ^{at 80 and 120 °C} is shown in figure 10. Above 15 kHz, ^{since the}

Tl P

^{component values become similar to each other, brute} separation ^{is no} longer possible : ^a

separation

^at

high frequencies

^has nevertheless be performed assuming that the observed relaxation rate is the weighted ^{sum of two} components, ^the amplitudes ^ratio being ^{fixed and}

Tl PL

by extrapolating the w - 1/2

Tl,,L

from lower radio

frequency

^fields. The correlation

frequency ^{of the slow motion at about 100 °C} is then found to be in the range 15-30 kHz

(Fig. 10)

^{i.e. the} correlation time of the slow motion Te is between 3 and 6 03BCs.

One can easily ^check that the slow motion has no influence on Tl relaxation at the Larmor

frequencies

used in this study ^{so that the} crystalline ^and amorphous

Tl’s

^are

equal.

In the absence of complementary data and due to the likely isotropic ^nature of the slow

motion, ^{we are} assuming ^an exponential correlation function

for 03A6sm(,r) [6].

With the values of

AM2s’ --

^{2.3 G2 and}

àM2f’ =--

^{11 G2} deduced from the FID analysis

[2]

and Tc from

Tl p

^{results, since}

Td(âMtn)l/2

^{1 the lH FID} signal is written according ^to equation

(5)

Fig. ^{10. -}

( TiP )-1

^{as a function} of v at ⁸⁰ (à) ^{and 120} (+) ^°C.