Reorientations in pivalic acid (2,2-dimethyl propanoic acid) - III. High-resolution incoherent neutron scattering in the plastic phase

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Reorientations in pivalic acid (2,2-dimethyl propanoic acid) - III. High-resolution incoherent neutron

scattering in the plastic phase

W. Longueville, M. Bée

To cite this version:

W. Longueville, M. Bée. Reorientations in pivalic acid (2,2-dimethyl propanoic acid) - III. High-

resolution incoherent neutron scattering in the plastic phase. Journal de Physique, 1987, 48 (8),

pp.1317-1323. �10.1051/jphys:019870048080131700�. �jpa-00210558�

Reorientations in pivalic ^acid (2,2-dimethyl propanoic acid)

III. High-resolution incoherent neutron scattering ^{in the} plastic phase

W. Longueville ^{and M. Bée}

Laboratoire de Dynamique des Cristaux Moléculaires (U.A. 801), Université des Sciences et Techniques ^de Lille, 59655 Villeneuve d’Ascq Cedex, ^France

(Requ ^{le 19} septembre ^1986, révisé le 27 janvier ^1987, accepté ^{le 31}

1987)

Résumé.

Cette étude fait suite à celles [1, 2] concernant déjà

produit. ^{Elle les} complète par : a) ^la

diffusion des protons ^acides (D

0,56

10-10 m2s-1 ; 03C4

^10-9 s) ; b) la réorientation des méthyles ^{dans la} phase plastique (03C4M3

^0,26

^10-9 s). ^Elle permet par ailleurs de ^montrer que, de part ^et d’autre de la transition, ^les méthyles ^toument plus lentement que les t-butyles.

Abstract.

This study follows those [1, 2] already concerning ^this compound. ^It completes ^them by : a) ^the

acid protons ^diffusion (D

^0.56

10-10 m2 s-1; 03C4 ~10-9s) ; b) ^the methyl groups reorientation in the

plastic phase (03C4M3

^0.26

^10-9 s). ^This study allows also to show that,

both sides of the transition point, methyl groups

slower than the t-butyl

Classification

Physics ^Abstracts

61.12

61.50E

61.50K

1. Introduction.

Among ^the tertiary butyl compounds, pivalic ^acid (2,2 dimethylpropanoic acid) appears ^to be an

interesting subject ^{for the} study of molecular motions. Especially it is worth-while to investigate

the behaviour of the methyl groups and of the t-butyl

itself at the phase transition ( Tt

²⁸⁰ K), ^between

the low temperature ^triclinic phase [3] ^{and the} high temperature, orientationally disordered phase [4].

Another stimulating problem is the mechanism of the acid proton dynamics. Both in the low-tempera-

ture and in the plastic phase, pivalic ^{acid molecules}

are linked in dimer units by ^two hydrogen ^bonds.

NMR, ^{IR or} IQNS studies of similar hydrogen-

bonded carboxylic ^{acids are a debated} point ^concern- ing ^{a double} proton exchange ^{mechanism or reorien-}

tations of the central carboxylic ring [5, 6].

The last question ^{is the exact mechanism of dimer}

reorientation between the ( 110 ) lattice directions in the plastic phase, ^the probability ^for breaking ^and

formation which allows an exchange ^{of the acid} proton ^{between two molecules.}

The former motions, ^i.e. methyl ^and t-butyl reorientations, ^were analysed by ^{NMR tech-} niques [7]. The values of the characteristic times obtained in the low-temperature phase ^{incited us to}

carry ^{out a} similar study by high-resolution ^IQNS.

From the analysis ^{of the} spectra ^{measured with the} backscattering spectrometer IN10 of the Institut

Laue-Langevin ^{in Grenoble,} it turned out that both

methyl ^and t-butyl jumps ^{occur on the 10-1° s time}

scale [1].

The agreement with the conclusions of the NMR

analysis and also the lack of information provided by

other dynamical analysis-techniques, yielded ^{to start}

the refinement with the results of this NMR study.

The correlation times taken as initial values for the refinement procedures, ^assumed reorientations fas-

ter for the methyl groups than for the t-butyl ^ones.

The correlation times related to these motions tend to confirm the values obtained by Albert et al.

whilst in both cases the activation energies ^deduced

from an Arrhenius plot ^are definitely smaller than those suggested from Raman spectroscopy [8, 9].

Actually, ^{it is} possible that the rather poor statis- tics originating from the low neutron flux, ^{and also}

the small accessible energy-range with respect ^{to the} instrumental resolution, ^{made the} refinement con-

verge ^to another minimum. Moreover, ^later exper- iments gradually provided ^a series of arguments against ^{the idea of} fast-rotating methyl groups. ^We shall retain the following :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019870048080131700

1318

i) Time-of-flight ^neutron spectrometry exper- iments in the plastic phase [2] ^{could be} interpreted correctly only under the assumption ^of methyl

groups « immobile » ^{on the} 10-11-10-12 time scale.

We can make an extrapolation through ^the phase

transition of the Arrhenius law obtained in the low

temperature phase ^{for the} reorientations of these groups. ^The prediction ^{is a small} broadening ^{of the} spectra ^{in the} plastic (c.a. ¹² iiev f.w.h.m.). ^{Such a} broadening ^should have been evidenced on IN6, ^at

least with the best instrument resolution (70 f.Le V f.w.h.m.). ^{The inelastic} part ^{of the} spectra ^reveals torsional vibration lines at 256 and 263 cm-1 in the

case of the CH3 groups and 185 cm-1 ¹ for the

CD3 groups, in accordance with Raman results.

Within the harmonic oscillator approximation, ^a potential ^{barrier of about 16 kJlmol can be} evaluated, ^{a value} appreciably larger than found from IN10 in the low temperature phase (9 . 8 kJlmol) .

ii) ^{Several IQNS} studies with similar t-butyl ^com- pounds, concluded slow methyl ^motions, especially

in the case of (CH3)3-CC-Cl ^and (CH3)3-CC-CN [10-12]. ^The phase transition is found to be as-

sociated with a drastic change ^{in the} dynamics ^{of the} t-butyl group, whilst the motion of methyl groups appears unaffected. Other trimethyl compounds [13, 14] ^also give evidence of the intramolecular nature of the potential acting ^{on the} CH3 ^groups.

iii) ^{A recent 2H NMR} analysis ^of t-butyl ^halides [15] ^{led to the} correction of the conclusions of

previous measurements [7], ^{in the sense of slow} methyl reorientations.

Thus we estimated that it was necessary ^{to reana-}

lyse ^our data in the low-temperature phase, taking

into account all the information provided by ^{the IN6} experiment ^{and also} by performing ^new IN10 exper- iments in the plastic phase ^{in order to} observe the reorientations of the methyl groups ^{at room} tempera-

ture. This study ^{must be carried out with the} D1 compound, (CH3)3CCOOD, ^{in order to avoid}

contributions from the acid proton. An eventual motion of this latter atom, ^{on the} 10-1° s time scale,

can be evidenced by comparison ^with spectra ^ob- tained with the Do compound (CH3)3CCOOH.

From IN6 experiments, motions of the acid proton

were shown to be related to 180°-jumps ^{of the}

central carboxylic rings ^{of the} dimer units about the dimer long ^axes. This result has recently ^been

confirmed by ^a single crystal study ^{of the} D9 species (CD3)3CCOOH using ^{the thermal} backscattering

instrument IN13 [16]. Anyway, methyl ^{motions in}

the plastic phase ^{will be} superimposed with simul- taneous occurrence of t-butyl ^{and whole molecule}

reorientations. From the IN6 results, ^{these latter can} be described by ^a combination of a rotational uniaxial diffusion of the t-butyl groups about their

three fold axis and of fluctuations of the long ^dimer

axis about their equilibrium orientation along ^the (110) ^lattice directions. The average amplitude ^of

the librational distribution is about 10°.

2. Experimental description.

The experiments performed ^{in the} low-temperature phase using ^the backscattering spectrometer IN10, and those in the disordered phase using ^time-of- flight spectroscopy ^have already been described elsewhere [1, 2]. ^New experiments ^{were carried out}

in the plastic phase by high-resolution spectroscopy

(IN10). ^{The weak neutron flux available from the}

instrument imposed ^a restriction of our analysis ^{to a} single temperature ^T

^{300 K and to the} isotopic

varieties Dl (acid proton deuterated alone) ^and Do (fully hydrogenated). ^The measurement of the instrumental resolution function was made by ^cool- ing ^the sample ^{down to 4 K. This was} done between two sequences ^of recording ^{at 300} K, that is without any change ⁱⁿ geometry. ^Two vanadium-standard measurements, ^{one at the} beginning and the other at the end of the experiment ^{allow a} calibration of the detector and analyser efficiencies. The incident neutron wavelength ^was

The regions ^{of the} analyser crystals corresponding ^to Bragg ^{circles were} carefully covered with cadmium.

Values of scattering angles ^{2 0, elastic momentum}

transfers Q ^and resolution (f.w.h.m.) ^{are listed in}

table I. Polycrystalline, ^compact pivalic ^{acid was}

filled in a flat cylindrical container, ^{of 50 mm}

diameter with thickness 0.3 mm. With the container

Table I.

List of ^the scattering angles (2 8), corresponding ^{elastic momentum} transfer (Q) ^and f. ^{w.h. m} (AE)

of ^the instrument resolution function ^{in the INIO} experiment.

perpendicular ^{to the neutron beam the} transmission factor was about 0.85. All the experiments ^have

been made with an angle ^{of 115°} between the slab and the incident neutron beam.

3. Comparison ^{of the} spectra ^from Do ^and Di. ^Acid proton ^diffusion.

After the usual corrections of the experimental ^raw

data we can report (Fig. 1) ^the spectra (1 ^and 2) ^at

small momentum transfer.

Fig. 1.

Comparison, ^{for the two smallest} Q values, between the spectra ^{at T}

³⁰⁰ K, ^{for the} Do ^and Dl species. Spectra ^{have been} artificially ^{shifted to} clearly

evidence the broadening difference.

Because of departures from strict backscattering

the spectra ^{are not centered at hw}

^0.

The dotted curves have been artificially ^{shifted to}

lower energy ^{in order to} show the different broaden-

ing ^{of the two} spectra ^more clearly.

From a simple inspection it is clear that :

i) ^{at T}

^{300 K, the} spectra obtained with the

Do species ^are definitely wider than the correspond- ing spectra ^{obtained with} Dl ;

ii) these latter are strictly ^{identical to similar} spectra provided by ^{the vanadium} reference, ^that is, purely ^{elastic ;}

iii) ^{there is no} broadening ^{of the} Do spectra ^at

T=4K.

For larger Q values the quasi ^elastic scattering provided by ^the methyl group rotation becomes

important ^{and the} small difference between the

Do ^and Dl spectra is obscured.

The obvious broadening ^{of the} Do spectra, ^at T

300 K, ^is unambiguous ^{because the} experiment

at T

4 K was performed ^{between two series of}

measurements at T

300 K, ^{which lead to the same}

result. Considering ^the difference between the

Do ^and Dl molecules, it is clear that this broadening

originates ^{from the} dynamical behaviour of the acid proton. ^The previous experiment using ^{the time-of-} flight spectrometer ^IN6 [2], gave evidence of a quasi

elastic broadening, ^{of c.a. 200 f.LeV for the 180°} jump

reorientations of the central carboxylic rings ^{of the}

dimers. This value, ^{far too} large for the energy- range of the present backscattering experiment (i.e.

± 12 ue V), ^was recently ^confirmed by measurements with the thermal backscattering ^IN13 [16]. Anyway,

it is a well-known feature, ⁱⁿ IQNS, that any bounded motion produces ^a noticeable broadening

of the spectra ^at large Q, typically ^when Qd == w,

where d is the jump-distance (2.21 ^{A in that} case).

This consideration also permits ^{to rule out the} hypothesis ^{about the} proton-exchange mechanism, which would occur on an even smaller distance

(d

^0.56 A), and the whole-dimer tumbling ^about

its centre of mass with a radius of gyration ^{for the}

proton ^{of 0.37} A.

When considering the contribution to the scatter-

ing ^{of the} t-butyl group, which ^scatters significantly

because of its nine hydrogen atoms, ^the spectra obtained with the D, compound ^{are not} significantly

broadened in the Q-range. Again from the exper- iment with IN6, ^the t-butyl reorientations are known to occur on a much shorter time-scale. The previous

remark on jump distances also holds in case of

methyl ^rotations about their threefold axis.

The only description capable ^of taking ^{into ac-}

count the broadening ^{of the} low-Q _spectra ^{is based}

on the formation and breaking ^{of the} dimers, ^which

allows the exchange ^{of acid} proton ^{between two} molecules and, ^a longer time-scale, ^{a diffusion of}

this atom through the lattice. This hypothesis ^was already ^{used to} interpret NMR results [17, 18], ^as

discussed in a previous paper [2]. ^{It is} supported by

the conclusions of the IQNS study with the time-of-

flight technique which shows large amplitude ^oscilla-

tions of the t-butyl parts ^{of a} dimer unit with respect

to each other, associated with a deformation of the central carboxylic ring. ^{Such a motion is} likely ^to

favour a breaking of the dimers into monomers.

Actually ^{this mechanism assumes the} breaking ^{of a} neighbouring ^dimer during ^{the life-time of the two}

individual monomers. It is reasonable to consider that the breaking probability ^{for a dimeric unit is}

enhanced in the immediate vicinity ^{of an} already

broken _one, because of the local modification of the molecule arrangement. Anyway, ^{even if the two} original ^{monomers have a} large ^{chance to recom-} bine, ^there is, ^{as far as the acid} proton is concerned

an exploration of the local surroundings resulting

from the tumbling ^{of the monomer to which it} belongs.

Under these conditions, ^{in order to} get insight ^into

the characteristic time associated with this motion,

the contribution to the scattered intensity originating

from the acid proton ^{was described} by ^{the usual}

1320

«

DQ2 scattering ^{law » for} translational (unbounded)

diffusion

Simultaneously the contribution from the rest of the molecule was taken into account by ^a scattering ^law

of the form

The parameters, ^{i.e. the EISF} (elastic ^incoherent scattering function) ao(Q) ^{and the} characteristic time _{T 1} were determined from the results of the IN6

study. ^{From the} refinement, ^this scattering ^function

was found to correctly describe the data obtained with the D1 compound. Actually, taking ^{into account}

the large ^{amount of} purely ^elastic scattering (ao (Q ) = 0.88 ^at Q = 0,3 A-1) and the wide

broadening observed in the t.o.f. study, SD¡ (Q, ^{Cl) )}

appears ^on the IN10 energy-range of analysis, ^{as a} purely elastic line on an almost flat background, ^with negligible amplitude, ^{so that no} difference is seen when comparing with the vanadium spectrum

(Fig. 1). ^The appropriate scattering ^law

was compared ^{with the} experimental Do spectra.

This formula describes the spectra ^as strong ^elastic

term 9 superimposed ^{on a small} quasi ^elastic

10 1

one (10).

The whole expression ^must be convoluted with the Lorentzian instrumental resolution functions of IN- 10.

So, ^the general spectral shape ^{will be a} slightly

broadened Lorentzian curve rather than the usual well separated contributions from the elastic and

quasi ^{elastic terms.}

Actually taking ^{into account the} broadening

oberved on IN6 as a large Lorentzian curve of time T 1 this formula turns out to be well approximated by

The refinement yielded ^{a diffusion constant}

The jump-diffusion ^{model of} Chudley-Elliott [19]

enables us to evaluate the characteristic time be-

tween two jumps.

which was found to range between

=10- 9 s and

T =

5 x 10-11 s, depending ^{on whether we consider}

the elementary mechanism :

i) ^{of a} complete tumbling ^{of the monomer about}

its centre of mass (f

^5.55 A), ^or,

ii) ^{of a} reorientation of an individual monomer

from one crystallographic ^direction ( 110 ) ^{to another} next-neighbour ^one (f

^1.336 A).

(i) ^{is a} special ^case (ii) ^{and it is} impossible ^{to know}

the experimental ^mean characteristic time

at least with the instruments used.

4. Methyl reorientation at room temperature.

The use of the deuterated compound D1 ^{allows to} neglect ^the scattering ^{from the acid} proton. ^In figure ^{2 the} integrated intensity ^{of the} spectra ^has

Fig. ^2.

^{For the} D¡ species ^{at T}

³⁰⁰ K, comparison

between the integrated intensity

Q (o ) and the EISF for uniaxial rotation of the t-butyl group and large amplitude oscillation of the three fold

(- 10°).

been reported, ^{as obtained} after the usual correc-

tions for the detector and analyser efficiency ^deter-

mined from the vanadium standard measurement.

Clearly, ^a strong decrease of the intensity ^{occurs at} large Q values, ^{which is found to} correspond exactly

to the decrease of the purely ^elastic part ^{of the} spectra recorded with IN6. Referring ^to these t.o.f.

results (2), ^the quasi ^elastic broadening of the IN10

spectra ^can result from :

i) ^the tumbling ^{of the monomers} after the break-

ing ^{of the} hydrogen bonds ;

ii) ^the occurrence of 120°-reorientations ^{of the} methyl groups around their threefold axis, ^as suggested ^from a) ^{their behaviour in other similar t-} butyl compounds (e.g. (CH3 )3CCN), b) ^the analysis

of the inelastic part of the IN6 spectra, ^and c) ^their dynamics ^{in the} low-temperature ^triclinic phase.

A distinction between these different motions is

theoretically possible ^{from the} analysis ^{of the EISF.}

In practice ^{this turns out to} be difficult when the characteristic times related to the various motions

are distributed over a large range. Indeed, the very

narrow energy-window ^{of the} spectrometer ^IN10 prevents ^{us from the} observation of the whole quasi-

elastic spectrum, and thus the normalization of the total scattered intensity ^becomes impossible. ^A possible way ^to by-pass ^this difficulty ^{is to} cool ^the sample ^{down to} very low temperature ^{in order} to’

freeze all the reorientations and to force all the

scattering ^{into the elastic} peak. ^{But this method} requires ^the knowledge ^{of the} Debye-Waller ^factor

at the temperature ^{of the} experiment, ^a value which must be obtained from a different instrument

(instead ^of IN10, e.g. ^a t.o.f. instrument). ^{In the} present case, the mean-squared amplitude of transla- tion measured with IN6 is (U2) ~ ^{0.42 A2 at}

T

300 K.

Experimental values of the EISF were obtained in the following way. The absolute ^amount of purely

elastic scattering ^{at T = 300} K, Iel(Q), ^{was deter-}

mined from a refinement of the Dl spectra multiplied by ^{a scale} factor, ^A. Therefore :

The EISF values, Ao (Q ), ^{are obtained} by ^a

renormalization law where 14 K (Q ) is the absolute

intensity ^{of the same} spectra ^{at T}

^{4 K and} exp (- (U2) Q2) ^the Debye-Waller factor, ^{i.e. :}

A better agreement ^is found with the theoretical variation evaluated on the basis of methyl ^rotations

than with that predicted by ^the monomer-tumbling

model (Fig. 3).

The quasi-elastic broadening ^{was found to be} nearly independent ^of Q. Because all the other motions are largely ^{outside the IN10 scale, methyl}

reorientations were taken as the main reason for this

broadening. ^The 120° reorientation jump-model ^in-

volves a unique Lorentzian function, ^{whose hwhm}

was found equal ^to DEM 3

^{2.5 ± 0.5} ueV, ^corre- sponding ^{to a residence} time between methyl jumps.

1

Fig. ^3.

Comparison between the experimental ^EISF

values for the Dl species ^at 300 K and models for : 1°) ^t- butyl groups rotation, oscillation of the three fold _axes,

methyl groups jumps (120°) ; 2°) ^Monomer tumbling.

This time is much longer than the characteristic times associated with the uniaxial rotation of the t-

butyl group in the range 278 K T 303 K. How- ever, it is of the order of a tenth of the IN6- resolution at the incident wavelength ^A

^5.9 A (c.a. ^{25 tiev} hwhm). ^{This tends to} confirm the

suggestion that the smaller values of the EISF deduced from the IN6 experiments ^{at neutron} wavelength A

^{5.9 A were} effectively ^{due to the} methyl ^rotations.

5. Methyl reorientations in the low-temperature phase.

The coherence of all the results concerning ^the dynamics ^of pivalic acid, requires to return to our

previous interpretation of the IN10 data in the low- temperature phase. Figure ⁴ gives ^a comparison ^of

the experimental ^EISF determined at T

254 K,

215 K and 178 K with the theoretical variations

predicted by various models based on methyl reorientations, t-butyl reorientations, ^or both. These values were found from the method described in the

original paper [1] ^{but now under the} assumption ^{of t-} butyl reorientations only. They agree with the values

reported in this former analysis. However it turns out that the interpretation ^{at T = 178 K was} wrong.

There, ^{it was concluded that the} experimental ^EISF

at this temperature ^tends towards the methyl ^{+ t-} butyl jump model but that the correlation time related to the motion of the t-butyl reaches the limits of the instrument. This statement was based on the

implicit assumption ^of methyl groups faster ^{than the}

1322

Fig. ^4.

Comparison ^of experimental ^{EISF at T}

254 K, ^T

^{215 K} and T = 178 K with models based upon

methyl reorientations, t-butyl reorientation

both.

Curves

referred to

(1), (2) ^and (3), respectively.

whole t-butyl group. Actually, ^the experimental

EISF values at T

178 K are close to the theoretical

curve corresponding ^to t-butyl reorientations only,

as illustrated in figure ^4.

Spectra ^{recorded at the same} temperature ^were refined simultaneously. The relevant correlation times are reported ⁱⁿ figure ^{5. At T}

¹⁷⁸ K, ^the jump-rate associated with methyl groups is ^too small

Fig. ^5.

Correlation times t-butyl ^and methyl ^reorienta-

tion in the low temperature phase ^and methyl ^reorienta-

tions at T

300 K.

to be refined. Even at T

215 K, ^the broadening ^is

very small (c.a. ^0.1 ReV) ^and just ^{at the limit of the}

instrument energy-range. Clearly, ^{it is not} possible

to derive an Arrhenius law from just ^two values, including ^{a rather}

poor

value for T

215 K.

However, these values seem to be fitted to the activation energy of 16.3 kJ.mol-1 deduced from Raman spectroscopy ^{and inelastic neutron scatter-} ing. ^In figure 5, ^a straight line with this activation energy has been drawn, passing through ^the point corresponding ^to the value in the plastic phase,

which seems to indicate that a slight change might

occur at the transition.

If only ^{the two} points ^{at T}

300 K and T

254 K were taken into account, ^the resulting ^activa-

tion enthalpy ^{would be} definitely ^too large.

Experimental ^values of the correlation time for the reorientations of the t-butyl group yield ^an

activation energy HB ^{= 13} kJ.mol- l. The quasi-elas-

tic broadening just ^below the transition is roughly equal ^{to 10} ReV. ^{It is worth to} point ^{out that a small} broadening had been observed with IN6 also is this temperature range. The IN6 data agree with the

same activation energy of 13 kJ. mol - 1. The slight

deviation between the two series of measurements is

acceptable ^when accounting ^{for IN6 mean resolution} (c.a. ^{90 J.Le V} f.w.h.m.).

6. Conclusion.

The critical analysis of all the information obtained with previous experiments and from the present backscattering study, ^{enables us to} give ^a precise description of the motions of pivalic acid in its solid

phases, ^and to correct our former conclusions con-

cerning ^the dynamics ^{of the} methyl groups.

In the plastic phase, ^{in addition to} t-butyl ^uniaxial rotations, ^120° jumps ^{of the} methyl groups ^are evidenced but on a much slower time-scale. Simul-

taneously, ^the breaking of the dimer into monomers

is confirmed. This process is certainly ^favoured by

the oscillations of the two parts ^{of the} molecule with respect ^to each other and the deformation of the central carboxylic ring. ^{As a result of this} breaking

of the dimers and of the recombination of monomers

with neighbouring ones, ^{one can} find acid protons which migrate in the lattice.

In the low temperature phase, methyl ^{motions are} definitely slower than t-butyl reorientations. They experience ^a strong intramolecular potential ^{so that}

no drastic change ^{in their motion occurs at the} phase

transition. This means that the phase transition is

closely ^{related to the} dynamics ^{of the} t-butyl groups.

The possible proton exchange mechanism between

two carboxylic groups of ^a dimer was not confirmed

in the IN10 study.

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