Dynamic properties of dioctanoyl peroxide guest molecules constrained within the urea tunnel structure: A combined incoherent quasielastic neutron scattering and solid state 2H nuclear magnetic resonance investigation

Dynamic properties of dioctanoyl peroxide guest molecules constrained within the urea

tunnel structure: A combined incoherent quasielastic neutron scattering and solid state

2 H nuclear magnetic resonance investigation

Pascale Girard, Abil E. Aliev, François Guillaume, Kenneth D. M. Harris, Mark D. Hollingsworth, Albert-José

Dianoux, and Paul Jonsen

Citation: The Journal of Chemical Physics 109, 4078 (1998); doi: 10.1063/1.477008

View online: http://dx.doi.org/10.1063/1.477008

View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/109/10?ver=pdfcov

Published by the AIP Publishing

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JOURNAL OF CHEMICAL PHYSICS

VOLUME 109, NUMBER 10

8 SEPTEMBER 1998

Dynamic properties of dioctanoyl peroxide guest molecules constrained

within the urea tunnel structure: A combined incoherent quasielastic

2

neutron scattering and solid state H nuclear magnetic

resonance investigation

Pascale Girard

Institut Laue-Langevin, BP 156X, 38042 Grenoble Cedex, France and Laboratoire de Physico-Chimie

´

Moleculaire, UMR 5803 CNRS-Universite de Bordeaux I, 351 cours de la Liberation,

33405 Talence Cedex, France

Abil E. Aliev

Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ,

United Kingdom

Franc¸ois Guillaume^a)

´

Laboratoire de Physico-Chimie Moleculaire, UMR 5803 CNRS-Universite de Bordeaux I,

´

351 cours de la Liberation, 33405 Talence Cedex, France

Kenneth D. M. Harris^b)

School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom

Mark D. Hollingsworth

Chemistry Department, Indiana University, Bloomington, Indiana 47405

´

Albert-Jose Dianoux

Institut Laue-Langevin, BP 156X, 38042 Grenoble Cedex, France

Paul Jonsen

Chemagnetics NMR Instruments, 7 Claro Court Business Centre, Claro Road, Harrogate HG1 4BA,

United Kingdom

͑Received 19 February 1998; accepted 20 May 1998͒

The dynamic properties of dioctanoyl peroxide guest molecules within the urea host tunnel structure

in the dioctanoyl peroxide/urea inclusion compound have been investigated by incoherent

2

quasielastic neutron scattering ͑IQNS͒ and solid state H nuclear magnetic resonance ͑NMR͒

techniques. The IQNS investigations were carried out on samples of urea inclusion compounds

containing perdeuterated urea to ensure that the incoherent scattering is dominated by the dioctanoyl

peroxide guest molecules. Using semioriented polycrystalline samples, translational motions of the

guest molecules along the tunnel were investigated separately from reorientational motions of the

guest molecules about the tunnel axis. The ²H NMR experiments used dioctanoyl peroxide

deuterated selectively in both the ␣ CD₂groups and urea with natural isotopic abundance. The

dynamic models that have been found to describe the translational and reorientational motions of the

2

guest molecules from the IQNS and H NMR data are discussed in detail. The reorientational

dynamics of the guest molecules about the tunnel axis can be described by a model of uniaxial

rotational diffusion in a twofold potential, and the translations of the guest molecules along the

tunnels can be interpreted by a model of translational jumps between sites with unequal probabilities

of occupation. These models differ markedly from those found previously to describe the dynamic

of Physics. ͓S0021-9606͑98͒70332-0͔

‘‘host’’ structure,³within which there are parallel one-

I. INTRODUCTION

dimensional tunnels. In the ‘‘conventional’’ urea inclusion

compounds, the host structure is hexagonal ͑P6₁22; aϭb

Ϸ8.2; cϷ11.0 Å͒ at ambient temperature, with the effective

tunnel ‘‘diameter’’ ranging between about 5.5 and 5.8 Å.

This host structure is stable only when the tunnels are packed

densely with ‘‘guest’’ molecules. Because of the spatial con-

straints of the urea tunnel, only guest molecules based on

sufﬁciently long alkane chains and with a limited degree of

substitution are suitable for inclusion within the urea tunnel

It is widely recognized that urea inclusion compounds

are attractive systems for studying many of the fundamental

physicochemical phenomena that underpin the properties of

molecular solids, and as such they have been widely inves-

tigated for several years.^1,2In these crystalline solids, the

urea molecules form an extensively hydrogen-bonded

a͒

Electronic mail: francois@loriot.lsmc.u-bordeaux.fr

b͒

Electronic mail: K. D. M. Harris@bham.ac.uk

0021-9606/98/109(10)/4078/12/$15.00

4078

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J. Chem. Phys., Vol. 109, No. 10, 8 September 1998

Girard et al.

4079

structure, and such guest molecules are constrained to adopt

linear, extended conformations. In the present paper, we fo-

cus on the dynamic properties of dioctanoyl peroxide ͑OP͒

guest molecules within the urea tunnel structure. First, a brief

overview of relevant background information is given.

For all ‘‘conventional’’ urea inclusion compounds, there

is an incommensurate structural relationship⁴between the

periodic repeat distance (c_h) of the host structure along the

tunnel axis and the periodic repeat distance (c_g) of the guest

molecules along the tunnel axis. While we focus here on

these ‘‘conventional’’ urea inclusion compounds, we note

that for certain guest molecules there is a commensurate re-

lationship between the host and guest substructures^5–9—in

general, this is also associated with signiﬁcant changes in the

urea tunnel structure.

substructures along the tunnel. For all diacyl peroxide/urea

inclusion compounds so far investigated ͑nϭ6, 9, and 10͒,

the offset ͑denoted ⌬_g͒ along the tunnel axis between the

positions of guest molecules in adjacent tunnels is ⌬_g

Ϸ4.6 Å, at ambient temperature. These well-deﬁned corre-

lations between the positions of guest molecules in adjacent

tunnels are presumably mediated by strong interactions be-

tween the host and guest substructures, and the intermodula-

tion function for incommensurate inclusion compounds

clearly plays a crucial role in this regard.

Many urea inclusion compounds undergo a phase transi-

tion ͑the temperature of which depends on the length and

substitution pattern of the guest molecule͒ from a high tem-

perature phase, in which the host structure is hexagonal, to a

low temperature phase, in which the host structure is ortho-

rhombic. For alkane/urea inclusion compounds, this behavior

has been demonstrated directly by x-ray diffraction.^20–22In

contrast, for the lauroyl peroxide/urea inclusion compound,

there is no evidence ͑from powder x-ray diffraction

experiments²³in the range 40–298 K and differential scan-

ning calorimetry²⁴͒ for the occurrence of a similar phase

transition.

It has been shown¹⁰that the diffraction pattern of incom-

mensurate urea inclusion compounds can be indexed in a

four-dimensional superspace, and measurement of all aspects

of the diffraction pattern ͑including satellite reﬂections͒ has

been achieved recently.^11,12Thus, the composite structure of

the incommensurate urea inclusion compounds cannot be de-

scribed using conventional three-dimensional space group

formalism and a superspace group approach¹³is required.

Clearly the physicochemical properties of urea inclusion

compounds should depend markedly on the nature of the

interactions between the host and guest substructures, and for

the incommensurate materials many properties should there-

fore depend on the nature of the intermodulation function. A

ﬁrst attempt was made recently¹⁴to reﬁne the structure of the

heptadecane/urea inclusion compound in a four-dimensional

superspace group, and to derive the intermodulation func-

tion. The intermodulation function is important not only with

regard to the structural properties of the composite crystal,

but also with regard to the dynamic¹⁵and conformational¹⁶

properties of the guest molecules. For example, speciﬁc col-

lective excitations—the so-called sliding modes of the host

and guest substructures¹⁷—are expected for these quasiperi-

odic materials.

The prototypical family of ‘‘conventional’’ urea inclu-

sion compounds is that with alkane guest molecules, and

several detailed studies of fundamental structural and dy-

namic properties of these inclusion compounds have been

reported. However, progress toward understanding funda-

mental properties of urea inclusion compounds also relies on

understanding the behavior of systematic families of guest

molecules containing well-deﬁned functional groups. In

alkane/urea inclusion compounds, diffraction studies¹⁸indi-

cate that there is a one-dimensional periodic arrangement of

the guest molecules along the tunnels, with only weak lateral

correlation between guest molecules in adjacent tunnels.

Urea inclusion compounds containing other families of guest

molecules, however, exhibit markedly different behavior.

For example, urea inclusion compounds containing diacyl

It has been shown^25,26by incoherent quasielastic neutron

scattering ͑IQNS͒ spectroscopy that, in the high temperature

phase of the alkane/urea inclusion compounds, large ampli-

tude translational and reorientational motions of the guest

molecules occur on the picosecond time scale. ²H NMR

spectroscopy has also been used^16,27–29to demonstrate that

there is substantial motion of the guest molecules in the

alkane/urea inclusion compounds. However, much less is

known at present about the dynamic properties of function-

alized alkane guest molecules within the urea tunnel struc-

ture.

We now extend this previous research to consider dy-

namic properties of diacyl peroxide guest molecules within

the urea tunnel structure, selecting the dioctanoyl peroxide/

urea ͑OP/urea͒ inclusion compound for these studies. In view

of the substantial contrasts between the structural properties

of the diacyl peroxide/urea and the prototypical alkane/urea

inclusion compounds, signiﬁcant differences in the dynamic

properties may be anticipated. As different aspects of the

dynamic properties of the guest molecules may occur on

different time scales, we exploit the speciﬁc advantages of a

2

combined approach using IQNS spectroscopy and H NMR

spectroscopy.^30–32

II. EXPERIMENT

A. Materials

Full details of the synthesis of the materials studied in

this work are given in the Appendix. For the experiments

described in this paper, inclusion compounds containing dif-

ferent levels of deuteration of OP and urea were used, with

h₃₀-OP/d₄-urea used for IQNS studies and d₄-OP/h₄-urea

peroxide CH ͑CH ͒ CO OO CO͑CH ͒ CH guest mol-

͓

͔

3

2 6

3

2

ecules exhibit a substantially ordered, three-dimensional pe-

riodic arrangement of the guest molecules.¹⁹These inclusion

compounds have the ‘‘conventional’’ urea tunnel structure

and it has been suggested¹⁹that there is an incommensurate

relationship between the periodicities of the host and guest

used for H NMR studies. The following abbreviations are

used: d₄-urea denotes fully deuterated urea ͑in practice

around 96% deuteration͒; d₄-OP denotes OP deuterated in

all hydrogen positions within the ␣-CH₂groups

CH ͑CH ͒ CD CO OO CO CD ͑CH ͒ CH h₄-urea re-

͓

͔

3

2 5

2

2 5

3

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4080

J. Chem. Phys., Vol. 109, No. 10, 8 September 1998

Girard et al.

fers to urea with natural isotopic abundances; h₃₀-OP refers

to OP with natural isotopic abundances. In all cases, powder

x-ray diffraction conﬁrmed that the crystals had the hexago-

nal tunnel structure of the conventional urea inclusion com-

pounds at ambient temperature. Differential scanning calori-

grams were recorded on a Perkin-Elmer Pyris I instrument.

No phase transitions were observed for OP/urea between 108

and 353 K.

͑ii͒

Neutron momentum transfer vector Q parallel to the

tunnel axis—denoted Q_ʈgeometry. In this geometry,

the tunnel axes of all the crystals lie in the scattering

plane and motions of the guest molecules along the

tunnel axis can be studied. With the tunnel axes

aligned at an angle of 135° with respect to the inci-

dent neutron beam, Q is strictly parallel to the tunnel

axis only for the scattering angle 2␪_Bϭ90°. For other

scattering angles, the reorientational motions about

the tunnel axis make a weak contribution to the scat-

tering proﬁle. This contribution is taken into account

in the calculations discussed below.

B. IQNS experiments

The use of the h₃₀-OP/d₄-urea inclusion compound for

the IQNS experiments ensures that incoherent neutron scat-

tering from the h₃₀-OP guest molecules represents more than

ϳ98% of the total incoherent neutron scattering from the

inclusion compound.

Typically, Ϸ100 single crystals of h₃₀-OP/d₄-urea were

placed in grooved aluminium containers ͑slab type͒ such that

the urea tunnel axes ͑long axis of the crystal morphology͒ of

all crystals were parallel to each other. The orientations of

the crystals with respect to rotation about this axis were ran-

dom. The following experimental geometries were consid-

ered ͑Fig. 1͒, allowing translational motions of the guest

molecules along the tunnel axis and reorientational motions

of the guest molecules about the tunnel axis to be studied

independently:

IQNS spectra were measured in both Q_Ќand Q_ʈgeom-

etries for semioriented polycrystalline samples of

h₃₀-OP/d₄-urea using the time-of-ﬂight spectrometers IN6

and IN5 at the Institut Laue-Langevin ͑Grenoble, France͒, at

temperatures in the range 150–300 K. The instrumental reso-

lutions were 130 ␮eV ͑full width at half maximum height͒

for wavelength ␭₀ϭ4.6 Å on IN6 and 80 ␮eV for ␭₀ϭ5 Å

on IN5. The corresponding experimental energy windows

used in our analysis were Ϫ2 meVϽប␻Ͻ2 meV.

Elastic scans in the Q_Ќgeometry were performed using

the backscattering spectrometer IRIS ͑instrumental resolu-

tion 15 ␮eV͒ at the ISIS neutron spallation facility ͑Ruther-

ford Appleton Laboratory, Didcot, UK͒, at temperatures in

the range 50–270 K.

͑i͒

Neutron momentum transfer vector Q perpendicular

to the tunnel axis—denoted Q_Ќgeometry. This geom-

etry allows reorientational motions of the guest mol-

ecules about the tunnel axis to be studied. With the

tunnel axes of all crystals perpendicular to the scatter-

ing plane, Q is perpendicular to the tunnel axis for all

scattering angles 2␪_B. For the experiments performed

on the IRIS and IN6 spectrometers ͑see below͒, the

angle between the plane of the sample container and

the incident neutron beam was 135°, allowing only

To determine the line shape of the instrumental resolu-

tion function R(␻) as a function of 2␪ for each spectrom-

B

eter used, the IQNS spectrum of a vanadium standard ͑with

the same dimensions as the sample of h₃₀-OP/d₄-urea͒ was

recorded for both the Q_Ќand Q_ʈgeometries. The detectors

were normalized using the spectra for vanadium, and other

corrections were performed using conventional procedures.³³

For all data collections, the transmission was more than 90%,

ensuring that the effects of multiple scattering can be ne-

glected in the data analysis.

scattering angles 2␪ smaller than ϳ110° to be inves-

B

2

C. H NMR experiments

tigated. In order to investigate Q_Ќspectra at larger

2␪_B, additional experiments were performed on the

IN5 spectrometer ͑see below͒ with the angle between

the plane of the sample container and the incident

neutron beam equal to 45°—in this case, scattering

²H NMR spectra for a polycrystalline sample of

d₄-OP/h₄-urea were recorded at 46.1 MHz on a Bruker

MSL300 spectrometer. A standard Bruker 5 mm high-power

probe and a Bruker B-VT1000 temperature controller ͑sta-

bility and accuracy ϳϮ1 K͒ were used. The convention-

angles 2␪ between ϳ20 and 70° could not be ana-

B

lyzed.

al quadrupole echo (90°) Ϫ␶Ϫ(90°)

Ϫ␶ Ϫacquire

Ј

␾Ϯ␲/2

͓

␾

Ϫrecycle pulse sequence³⁴was used, with 90° pulse dura-

͔

tion 1.75 ␮s and echo delay ␶ϭ15 ␮s (␶ ϭ10 ␮s). Quad-

Ј

rupole echo signals were left shifted prior to Fourier trans-

formation and phase cycling was employed to eliminate

quadrature phase errors. Other relevant experimental param-

eters are dwell time 1 ␮s, number of acquisitions 1024, and

acquisition time Ϸ5 ms.

III. THEORETICAL BACKGROUND AND LINE SHAPE

ANALYSIS

A. IQNS spectroscopy

FIG. 1. Experimental geometries used for the IQNS experiments: ͑a͒ Q_Ќon

IN6, ͑b͒ Q_Ќon IN5, ͑c͒ Q_ʈgeometry. In ͑a͒ and ͑b͒, the ﬁlled circles

symbolize the tunnel axes perpendicular to the scattering plane, and in ͑c͒

the broken line symbolizes the tunnel axes parallel to the scattering plane.

In the quasielastic energy transfer window (ប␻

Ͻ3 meV), the incoherent neutron scattering law S(Q,␻) can

be written³⁵as

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J. Chem. Phys., Vol. 109, No. 10, 8 September 1998

Girard et al.

4081

S Q,␻͒ϭe^Ϫ2W͑Q͒e^{Ϫប␻/k T}S_dQ,␻͒ꢀ R ␻͒ϩB Q͒,

B

tional motions of the guest molecules about the tunnel axis

contribute to the IQNS spectrum in Q_Ќgeometry.

͑

͑1͒

Finally, it has been shown previously³⁸that within the

time scale probed by IQNS spectroscopy, the urea molecules

may be considered as ‘‘static.’’ The theoretical spectra, as

given by Eq. ͑1͒, were corrected by taking into account the

additional elastic scattering due to the residual amount

T

where e^Ϫ2W(Q)is the Debye–Waller factor, e^Ϫប␻/kis in-

troduced to fulﬁll the detailed balance condition, S_d(Q,␻) is

the incoherent neutron scattering law due to diffusive mo-

B

1

tions of the H nuclei, R(␻) is the instrumental resolution

function, B(Q) is an energy-independent background, and ^ꢀ

is the convolution operator. For restricted motions ͑i.e., re-

orientations and restricted translations͒, the scattering law

S_d(Q,␻) takes the following form:

1

͑ϳ4%͒ of H nuclei in the d₄-urea.

Theoretical models were ﬁtted to the experimental IQNS

data through Eq. ͑1͒ ͓with Eqs. ͑2͒–͑5͔͒ using standard

methods.³⁹

NϪ1

S_dQ,␻͒ϭA Q͒.R ␻͒ϩ

A Q͒.R ␻͒ꢀ L ⌬ ,␻͒,

͑ ͑ ͑

i i i

͑

͚

0

iϭ1

2

B. H NMR spectroscopy

͑2͒

A nucleus with spin greater than 1/2 has an electric

quadrupole moment which interacts with the electric ﬁeld

gradient at the nucleus. For H nuclei in solids, this quadru-

where A₀(Q) is the elastic incoherent structure factor ͑EISF͒

and represents the fraction of elastic intensity in the quasi-

elastic proﬁle, and L_i(⌬_i,␻) represent Lorentzian functions

with half width at half maximum height ͑HWHM͒ given by

⌬_i. The formal expression of the above scattering function

depends upon the experimental scattering geometry. For the

semioriented samples of h₃₀-OP/d₄-urea used here, the scat-

tering law S_d(Q,␻) takes the following form ͑after circular

averaging over all orientations of the guest molecules in a

plane perpendicular to the tunnel axis͒:

2

polar interaction is usually so large that other nuclear spin

interactions are negligible in comparison with it. For a single

crystal containing one type of ²H nucleus, the ²H NMR spec-

trum comprises a pair of peaks, the frequency separation of

which depends on the orientation of the crystal with respect

to the applied magnetic ﬁeld. For a polycrystalline sample

containing a random distribution of crystal orientations, su-

perposition of such pairs of peaks for all crystal orientations

gives a characteristic ²H NMR ‘‘powder pattern.’’ When the

S_dQ,␻͒ϭS^rQr sin ␣,␻͒ꢀ S^tQ cos ␣,␻͒.

͑3͒

͑

d

g

d

2

rate of molecular motion is intermediate on the H NMR

S^r_d(Qr_gsin ␣,␻) is the quasielastic proﬁle due to the uniaxial

reorientational motions of the guest molecules about the tun-

nel axis ͑with gyration radius r_gfor the ¹H nuclei͒,

S^t_d(Q cos ␣,␻) is the quasielastic proﬁle due to translational

motions of the guest molecules along the tunnel axis, and ␣

is the angle between the neutron momentum transfer vector

Q and the tunnel axis at energy transfer ប␻. Equation ͑3͒

assumes that there is no correlation between reorientational

and translational motions of the guest molecules. This as-

sumption has been shown^36,37to be justiﬁed in the case of an

incommensurate relationship between the host and guest sub-

structures.

time scale ͑i.e., time scale between 10^Ϫ3and 10^Ϫ8s͒, the

appearance of the ²H NMR spectrum depends critically upon

the exact rate and mechanism of the molecular motion. The

2

effect of molecular motion on the H NMR spectrum can be

understood in terms of reorientation, with respect to the ap-

plied magnetic ﬁeld, of the electric ﬁeld gradient ͑EFG͒ ten-

2

sor at the H nucleus. In its principal axis system, the EFG

tensor ͑denoted V^PAS͒ has principal components V_xx, V_yy

,

and V_zz, with the axes assigned such that

V_yy

͉

V_zz

͉

у

͉

V_xx

͉

у

͉

. The V^PAStensor is traceless, and it is convenient to

characterize it in terms of the following two independent

parameters: ͑a͒ the static quadrupole coupling constant ␹,

deﬁned as eQV_zz/h; ͑b͒ the static asymmetry parameter ␩,

For Q_ʈgeometry, both reorientational and translational

motions in Eqs. ͑1͒–͑3͒ are considered and the angle ␣ is

given by

deﬁned as ␩ϭ(͉V_xx͉Ϫ͉V_yy͉)/͉V_zz͉ ͑note that 0р␩р1͒. For

the ²H nuclei in d₄-OP, it is valid to assume that the z axis of

V^PASlies along the direction of the C–D bond.

␭₀Q

␲

ប␻

␲

␣ϭcos^Ϫ1

Ϫ

,

͑4͒

2

ͩ

ͩ ͪͪ

In general, H NMR line shapes in the rapid motion

4␲ ␭₀Q E₀

4

regime ͑i.e., frequency of motion greater than ϳ10⁸s^Ϫ1͒ can

be simulated as though they are ‘‘static’’ spectra but using a

motionally averaged ͑‘‘effective’’͒ quadrupole coupling con-

where E₀is the incident neutron energy and Q is

2

1/2

8␲

ប␻

Qϭ

1ϩ

Ϫ 1ϩ

cos 2␪ ͒ .

͑5͒

͑

ͱ

*

stant ͑denoted ␹ ͒ and a motionally averaged ͑‘‘effective’’͒

ͫ

ͩ

ͪ

ͬ

B

2

0

2E₀

E₀

␭

*

asymmetry parameter ͑denoted ␩ ͒, which generally differ

In this geometry, the momentum transfer vector Q is strictly

parallel to the tunnel axis (␣ϭ0°) for the scattering angle

2␪_Bϭ90° and for ប␻ϭ0. In the ﬁtting procedure for Q_ʈ

spectra, the Debye–Waller factor and the background B(Q)

were ﬁtted independently for each scattering angle, because

for experiments on oriented single crystals the contribution

of the internal and external vibrations to the intensity de-

pends on the orientation of Q with respect to the tunnel axis.

For Q_Ќgeometry, ␣ϭ90° for all values of scattering

from the static quadrupole coupling constant ͑␹͒ and static

asymmetry parameter ͑␩͒. Furthermore, in considering such

spectra to be represented by an ‘‘effective’’ static deuteron

*

with quadrupole interaction parameters ␹ and ␩ , the ori-

entation of the principal axis system of the EFG tensor for

this effective deuteron is generally different from the orien-

tation of the principal axis system of the EFG tensor in the

sites occupied by the true deuteron during the motion.

2

Simulations of quadrupole echo H NMR spectra were

angle 2␪ and energy transfer ប␻, and only the reorienta-

obtained using the TURBOPOWDER program.⁴⁰The line shape

B

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J. Chem. Phys., Vol. 109, No. 10, 8 September 1998

Girard et al.

FIG. 3. IQNS spectrum recorded in Q_ʈgeometry (2␪_Bϭ90°) for

h

₃₀-OP/d₄-urea at 150 K. Note the scale expansion by the factor of 100.

FIG. 2. Elastic intensity as a function of temperature for h₃₀-OP/d₄-urea

͑diamonds͒ and C₁₉H₄₀/d₄-urea ͑circles͒: the elastic intensity was normal-

ized with respect to the spectra recorded at 50 K for h₃₀-OP/d₄-urea and 8

K for C₁₉H₄₀/d₄-urea.

and vibrational motions. As discussed below, fast reorienta-

tional motions of the guest molecules are detected in Q_Ќ

geometry in the temperature range 230–323 K on the time-

of-ﬂight spectrometers IN5 and IN6.

In Q_ʈgeometry, the quasielastic proﬁles indicate the ex-

istence of very weak inelastic modes at about 2.2 meV,

shown in Fig. 3, which do not overlap with the quasielastic

proﬁle arising from diffusive translations of the guest mol-

ecules along the tunnel axis. These inelastic excitations have

been assigned previously in alkane/urea inclusion com-

pounds to the density of states of the sliding of the host and

guest substructures relative to each other.⁴³It is important to

note that the maxima of the density of states for alkane/urea

inclusion compounds have been observed previously⁴⁴in the

range 0.8–1.2 meV.

From the plot of the width ͑HWHM͒ of the quasielastic

proﬁles in Q_Ќand Q_ʈgeometries shown in Fig. 4 ͓deter-

mined by ﬁtting each scattering angle using Eq. ͑2͒ with

Nϭ2͔, it is clear that the translational and reorientational

relaxation mechanisms are signiﬁcantly different. For reori-

entational motions ͑Q_Ќgeometry͒, the width of the quasi-

elastic broadening increases continuously as the elastic mo-

mentum transfer Q increases, suggesting that the dynamic

process is diffusive. For translational motions ͑Q_ʈgeometry͒,

the width of the quasielastic broadening increases only

smoothly as Q increases, suggesting that the dynamic model

involves only two or perhaps three Lorentzian functions. In

addition, the time scales of both motions are signiﬁcantly

different, with the broadening of the Q_Ќspectra more than

two times larger than the broadening of the Q_ʈspectra.

simulations take into account distortions in the intensities of

shoulders in the H NMR spectrum arising from the ﬁnite

2

pulse power. In these spectral simulations, the line broaden-

ing factor was 3 kHz, and typically 60 to 100 crystal orien-

tations were considered in calculating the powder pattern. As

discussed below, in order to obtain satisfactory agreement

2

between experimental and simulated H NMR spectra, it is

necessary to optimize several parameters that deﬁne the dy-

2

namic process. H NMR line shape analysis in the case of

dynamic models with a large number of variables is poten-

tially problematic, as the uniqueness of the ﬁtting procedure

is not necessarily straightforward to establish. In order to

overcome this difﬁculty, the work reported here has com-

bined the SIMPLEX optimization technique⁴¹with the pro-

2

grams for H NMR line shape simulations ͑see Ref. 42 for

further details͒. We emphasize that this approach provides an

objective assessment of the level of agreement between ex-

perimental and simulated ²H NMR spectra, and removes

much of the subjectivity that is inherent in the traditional

approach based on visual comparison of experimental and

2

simulated H NMR spectra.

IV. RESULTS

A. Qualitative assessment

First, we discuss qualitative aspects of the IQNS spectra

recorded on the high-resolution IRIS spectrometer. The tem-

perature dependence of the elastic peak intensity in Q_Ќge-

ometry for h₃₀-OP/d₄-urea ͑at elastic momentum transfer

Qϭ1.3 Å^Ϫ1͒ is shown in Fig. 2. No discontinuity is ob-

served in the temperature range investigated, suggesting that

no structural phase transition occurs in this range. The tem-

perature dependence of the elastic peak intensity for the

h₄₀-nonadecane/d₄-urea

͑C₁₉H₄₀/d₄-urea͒

inclusion

compound,²⁵recorded under similar conditions ͓on the IN10

spectrometer at ILL ͑Grenoble͔͒ is also shown in Fig. 2,

illustrating the fundamentally different dynamic behavior of

the guest molecules in the h₄₀-nonadecane/d₄-urea and

h₃₀-OP/d₄-urea inclusion compounds. The variation of the

elastic intensity with increasing temperature for

h₃₀-OP/d₄-urea shown in Fig. 2 is due to fast reorientational

FIG. 4. Variation of the widths ͑HWHM͒, as a function of Q, of the quasi-

elastic broadenings in the IQNS spectra recorded for h₃₀-OP/d₄-urea in Q_ʈ

and Q_Ќgeometries at 300 K.

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Girard et al.

4083

FIG. 6. Theoretical effective potential function V(␸) ͑calculated using

␸₀ϭ56.5° and ␥ϭ9͒ for the model of uniaxial rotational diffusion. The

potential barriers ⌬V₁and ⌬V₂are deﬁned in the ﬁgure.

orientations of the C–D bond in the two sites. However, as

discussed previously,⁴⁶this two-site jump model can be

ruled out, as it cannot ﬁt the IQNS data in Q_Ќgeometry.

FIG. 5. Experimental ͑left side͒ and simulated ͑right side͒ ²H NMR spectra

for d₄-OP/h₄-urea. The simulated spectra were calculated assuming a model

of uniaxial rotational diffusion of the CD₂groups in a twofold potential, as

discussed in the text.

B. Reorientational dynamics

2

From qualitative analysis of the IQNS and H NMR

spectra, we expect that a model of reorientational diffusion

in a two-fold potential could ﬁt both the IQNS spectra in Q_Ќ

geometry and the ²H NMR spectra. Reorientational diffusion

of the OP molecules in a twofold potential corresponding to

the following orientational distribution function⁴⁷has been

considered,

Clearly, the IQNS line shapes may be rationalized using

models in which the reorientational and translational motions

of the guest molecules are uncorrelated.

²H NMR spectra of d₄-OP/h₄-urea, recorded from 89 to

250 K, are shown in Fig. 5. The frequency separation

P ␸͒ϭF e^{Ϫ␥ cos͑␸ϩ␸}ϩe^{Ϫ␥ cos͑␸Ϫ␸}

,

͑6͒

͒

0

͑

͓

͔

(⌬ _sϷ122 kHz) between the perpendicular peaks

v

͑‘‘horns’’͒ in the spectrum recorded at 89 K is characteristic

of a static H NMR powder pattern, and the best-ﬁt simula-

where F is a normalization factor and ␥ is deﬁned below ͓Eq.

͑10͔͒. The corresponding effective ͑mean force͒ potential for

reorientations is,

2

tion of this spectrum ͑Fig. 5͒ is obtained assuming no motion

of the deuterons, with static quadrupole coupling constant

␹ϭ163 kHz and static asymmetry parameter ␩ϭ0. These

values are typical for deuterons of CD₂groups in alkyl

V ␸͒

͑

ϭϪln Fϩ␥ cos ␸͒cos ␸ ͒

͑

0

k_BT

chains.⁴⁵The changes in the H NMR spectrum in the tem-

2

Ϫln 2 cosh ␥ sin ␸͒sin ␸ ͒͒͒.

͑7͒

͑

0

perature range 110–250 K are characteristic of the deuterons

passing through an intermediate motion regime. Within the

constrained environment of the urea host structure, reorien-

tation of the C–D bonds ͑of the CD₂groups͒ within the

d₄-OP molecule is likely to take the form of reorientation

about the tunnel axis. The angle between each C–D bond

and the tunnel axis is ϳ90°, and we therefore focus on mod-

els involving reorientation of the deuteron about an axis per-

pendicular to the C–D bond. From qualitative assessment of

The potential barrier ⌬V₁between the two minima, deﬁned

in Fig. 6, is given ͑for ␥Ͼ1͒ by,

⌬V₁

ϭϪln 2ϩ␥ 1Ϫcos ␸ ͒͒,

͑8͒

͑

0

k_BT

and the potential barrier ⌬V₂, also deﬁned in Fig. 6, is,

⌬V₂

ϭϪln 2ϩ␥ 1ϩcos ␸ ͒͒.

͑9͒

͑

0

k_BT

2

the H NMR spectra in the range 110–250 K, it is immedi-

ately clear that the d₄-OP molecules do not undergo motions

such as continuous rotation, three-site 120° jumps, or six-site

60° jumps about the tunnel axis, as the ²H NMR spectrum in

the upper intermediate motion regime and rapid motion re-

gime for such motions would regain the axially symmetric

The relationship between ␥ and the activation energies ⌬V₁

and ⌬V₂is,

1

⌬V₁

␥ϭ

ln 2͒ϩ

͑

ͫ

ͬ

1Ϫcos ␸ ͒

k_BT

͑

0

*

(␩ ϭ0) Pake powder pattern line shape, but with width

1

⌬V₂

scaled by a factor of 1/2 compared with the spectrum in the

slow motion regime. Instead, the observed changes in the ²H

NMR line shape for d₄-OP/urea resemble those for models

involving two-site jumps of the deuteron. The observed

ϭ

ln 2͒ϩ

͑

.

͑10͒

ͫ

ͬ

1ϩcos ␸ ͒

k_BT

͑

0

The rotational diffusion process that we have considered is

deﬁned by the orientational distribution function given in Eq.

͑6͒, and our approach has employed the ﬁnite difference ap-

proximation to the Smoluchowski equation for simulating

2

changes in the H NMR line shape are reproduced reason-

ably well by simulations based on a two-site jump model

40

both IQNS spectra⁴⁸and H NMR spectra. The dimension

2

with 2␸₀ϭ113°, where 2␸ denotes the angle between the

0

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4084

J. Chem. Phys., Vol. 109, No. 10, 8 September 1998

Girard et al.

TABLE I. Final parameters obtained by ﬁtting the model of uniaxial rota-

tional diffusion in a twofold potential to the Q_ЌIQNS line shapes of

h₃₀-OP/d₄-urea. The angle ␸ was ﬁxed at 56.5°.

0

D_r/ps^Ϫ1

␥

T/K

230

250

260

278

300

4.90ϫ10^Ϫ2

7.10ϫ10^Ϫ2

1.15ϫ10^Ϫ1

1.37ϫ10^Ϫ1

1.67ϫ10^Ϫ1

10.6

9.0

7.6

7.2

6.2

of the rate matrix was taken as Nϭ24 ͑corresponding to a

grid spacing ␦ϭ15° on a circle͒. To obtain the ﬁnal theoret-

2

ical IQNS and H NMR line shapes for this model of rota-

tional diffusion, the master equation for the orientational dis-

tribution function has been considered with the following

parameters varied in the ﬁtting procedure: ␥, ␸₀, and D_r͑the

rotational diffusion coefﬁcient͒.

In ﬁtting the IQNS data in Q_Ќgeometry, the standard

gyration radius for alkanes (r_gϭ1.39 Å) was taken. Thus,

Eq. ͑1͒ was ﬁtted to the experimental IQNS spectra in Q_Ќ

geometry using Eqs. ͑2͒–͑5͒ with ␣ϭ90°. In the preliminary

FIG. 8. Comparison between the experimental and ﬁtted IQNS spectra ͑IN5

spectrometer͒ for h₃₀-OP/d₄-urea in Q_Ќgeometry. Left side: as a function

of temperature for Qϭ2.1 Å^Ϫ1; right side: as a function of Q at T

ϭ300 K.

stage of ﬁtting, we found that the parameters ␥ and ␸ gave

0

good results at 300 K with 5Ͻ␥Ͻ6 and 40°Ͻ␸₀Ͻ70°.

Because of the large uncertainty in the value of ␸₀, this

parameter was ﬁxed at 56.5° ͑based on the value found from

tained by extrapolating from the ﬁtted values of ␥ from the

IQNS data analysis at higher temperatures. In the tempera-

ture range 230–300 K probed by the IQNS experiments, ␥ is

found to have an approximately linear dependence on tem-

perature described by ␥ϭ24.2Ϫ0.061 (T/K). The starting

2

preliminary ﬁts of the H NMR data using a two-site jump

model⁴⁶͒ and the other parameters ␥ and D_rwere reﬁned

simultaneously. The best agreement between the experimen-

tal and theoretical scattering functions was obtained with the

parameters listed in Table I. To illustrate the quality of the

ﬁts, the experimental and theoretical EISFs are compared in

Fig. 7 and the experimental and theoretical scattering proﬁles

are compared in Fig. 8.

2

value of ␥ at the temperature of each of the measured H

NMR spectra was then estimated by extrapolation from this

linear relationship. Although this is an approximation, our

earlier ﬁnding that the ²H NMR spectra are rather insensitive

to the value of ␥ lends justiﬁcation to this approach. In ﬁtting

2

With regard to ﬁtting this model to the experimental H

NMR spectra, it is anticipated that there may be a signiﬁcant

degree of correlation between different parameters deﬁning

the model ͑as for ﬁtting to the IQNS data͒, and caution must

therefore be observed. Preliminary simulations for this

2

the H NMR line shape at each temperature, the value of ␥

was initially ﬁxed and the following parameters were opti-

*

mized using the SIMPLEX algorithm: D_r, ␸₀, and ␹ ͑the

motionally averaged quadrupole coupling constant͒. Allow-

2

model suggested that the H NMR line shape is particularly

*

ing ␹ to vary with temperature effectively subsumes within

sensitive to the value of ␸₀, and substantially less sensitive

to the value of ␥ ͑in contrast to the case of ﬁtting the IQNS

data͒. For this reason, and in order to keep the number of

ﬁtted parameters as low as possible, approximate values of ␥

the model the occurrence of small amplitude motions that are

2

rapid on the H NMR time scale but not straightforward to

model explicitly. In the present case, these motions may

comprise rapid small-amplitude ‘‘wobbling’’ of the d₄-OP

2

at the temperatures of the H NMR experiments were ob-

*

molecule. The fact that ␹ decreases as temperature in-

creases is consistent with the amplitude of such motions in-

creasing as temperature increases. As shown in Fig. 5, the

rotational diffusion model gives a satisfactory ﬁt to the ex-

perimental ²H NMR spectra throughout the temperature

range investigated ͑110–250 K͒. The optimum values of the

parameters at each temperature are shown in Table II.

Comparison of Tables I and II shows that there is good

agreement in ﬁtting the same model of rotational diffusion in

a twofold potential to both the IQNS and ²H NMR data. The

angle between the most probable orientations of the OP guest

molecules ͑with respect to reorientation about the tunnel

axis͒ is 116°, and the rotational diffusion coefﬁcients D_r

obtained from both techniques are of the same order of mag-

FIG. 7. Comparison between the experimental and theoretical EISFs in Q_Ќ

geometry for h₃₀-OP/d₄-urea at 300 K. The theoretical curve ͑solid line͒ is

for the model of uniaxial rotational diffusion discussed in the text.

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Girard et al.

4085

Lorentzian functions for QϾ1.5 Å^Ϫ1͒. As a ﬁrst approxima-

tion, we have considered a model of translational jumps over

three equally spaced sites with unequal populations, as

shown schematically in Fig. 10. For this model ͑with Nϭ3͒,

the structure factors determining the scattering law in Eq. ͑2͒

are,

TABLE II. Final parameters obtained by ﬁtting the model of uniaxial rota-

tional diffusion in a twofold potential to the ²H NMR line shape for

d₄-OP/h₄-urea.

*

␥

␸₀/°

␹ /kHz

T/K

D_r/ps^Ϫ1

110

140

150

200

250

6.90ϫ10^Ϫ6

1.97ϫ10^Ϫ4

2.06ϫ10^Ϫ4

1.50ϫ10^Ϫ2

4.60ϫ10^Ϫ2

17.5

15.7

15.1

12.0

9.0

58

59

58

57

160

158

155

151

2

1Ϫp ͒

͑

1

A₀Q͒ϭ p ͒²ϩ

ϩ2p₁1Ϫp ͒cos Qd͒

͑ ͑

1

͑

1

2

1Ϫp ͒

͑

1

ϩ

cos 2Qd͒,

͑

2

nitude in the 200–250 K temperature range, representing

continuity in dynamic behavior between the temperature re-

gions over which the two techniques are sensitive to the dy-

namic process. Furthermore, the ﬁt of the experimental val-

ues of ␥ using Eq. ͑10͒ shown for example in Fig. 9͑a͒, gives

⌬V₁ϭ7.1Ϯ0.5 and ⌬V₂ϭ26.2Ϯ0.5 kJ mol^Ϫ1over the full

experimental temperature range. As an illustration of the

compatibility between the parameters obtained from ﬁtting

3p₁1Ϫp ͒

͑

1

A₁Q͒ϭ

Ϫ2p₁1Ϫp ͒cos Qd͒

͑ ͑

1

͑

2

͑11͒

p₁1Ϫp ͒

͑

1

ϩ

cos 2Qd͒,

͑

2

1Ϫp ͒

1

͑

1

A₂Q͒ϭ

Ϫ

cos 2Qd͒,

͑

2

the IQNS and H NMR results, the dependence of ln(D_r) on

T^Ϫ1is shown in Fig. 9͑b͒. On the usual assumption of

where p₁is the probability of occupation of site 1 and d is

the distance between adjacent sites. The widths of the

Lorentzian functions in Eq. ͑2͒ are,

Arrhenius behavior D ϭD exp(ϪE /k T) , the activation

͓

͔

r

0

a

B

energy is estimated to be E_aϭ15 kJ mol^Ϫ1with

D₀ϭ102 ps^Ϫ1. We note that the activation energy obtained

from the Arrhenius plot compares well with (⌬V₁

ϩ⌬V₂)/2.

Ϫ1

2␶

2p₁␶

⌬₁ϭ

,

⌬₂ϭ

,

͑12͒

1Ϫp ͒

1

͑

1

Ϫ1

where ␶ is the characteristic time of the motion and ␶

is

C. Translational dynamics

the jump rate from site 1 to site 2 or site 3. The best agree-

ment between the experimental and theoretical scattering

functions was obtained with the parameters listed in Table

III. Comparison of the experimental and theoretical EISFs

͑Fig. 11͒ and the experimental and theoretical scattering

proﬁles ͑Fig. 12͒ demonstrates the good quality of the ﬁts.

We note that the jump distance found using this jump model

For Q_ʈgeometry, we have ﬁtted the experimental spectra

using Eq. ͑3͒ with the parameters describing the reorienta-

tional contribution, listed in Table I, kept ﬁxed during the

reﬁnement. Initially, we considered a model of translational

diffusion in a onefold potential as developed for alkane/urea

inclusion compounds,²⁶but the Q_ʈspectra could be ﬁtted

using this model only for QϽ1.5 Å^Ϫ1. In agreement with

the qualitative analysis of the IQNS spectra reported in Sec.

IV A, this model is unable to predict the fact that the width

͑HWHM͒ is nearly constant for QϾ1.5 Å^Ϫ1͑see Fig. 4͒.

Clearly a model of translational diffusion in a more complex

potential is required. With the information obtained from

qualitative analysis of the data in Q_ʈgeometry ͓i.e., that it is

sufﬁcient to consider two or perhaps three Lorentzian func-

tions ͑in addition to the weak contribution due to reorienta-

tional motions͒ to ﬁt the quasielastic broadening͔, we must

consider a model of translational diffusion in a potential with

very large barriers ͑small barriers would involve too many

is dϷ1.8 Å at all temperatures investigated by IQNS, i.e.,

Ϫ1

␶

^Ϫ1ϭ␶

͓

0

dϷc_h/6. Assuming Arrhenius behavior

ϫexp(ϪE /k T) , the activation energy is found to be E

͔

a

B

a

ϭ13 kJ mol^Ϫ1with ␶^Ϫ1ϭ0.2 ps^Ϫ1

.

0

V. DISCUSSION

The results reported here for the reorientational and

translational dynamics of OP guest molecules in the urea

tunnel structure have important consequences that relate to

our broader understanding of the structural and dynamic

properties of urea inclusion compounds.

FIG. 9. ͑a͒: Temperature dependence of the parameter ␥.

The continuous line is the best ﬁt of Eq. ͑10͒ to the data.

͑b͒: Plot of ln(D_r) vs T^Ϫ1for the model of uniaxial rota-

tional diffusion in a twofold potential. The symbols rep-

resent experimental values and the solid line represents

the best ﬁt of the Arrhenius equation to the data.

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4086

J. Chem. Phys., Vol. 109, No. 10, 8 September 1998

Girard et al.

TABLE III. Final parameters obtained by ﬁtting the three-site jump model

for translations to the Q_ʈIQNS line shapes of h₃₀-OP/d₄-urea.

^Ϫ1/ps^Ϫ1

d/Å

p₁

T/K

␶

250

260

285

300

0.7ϫ10^Ϫ2

1.3ϫ10^Ϫ2

1.9ϫ10^Ϫ2

2.3ϫ10^Ϫ2

1.75

1.78

1.80

1.82

0.90

0.86

0.80

0.78

First, we believe that our strategy of combining ²H NMR

and IQNS techniques ͑and, in the case of IQNS, using two

spectrometers with different instrumental resolutions͒ repre-

sents a comprehensive approach for establishing the reorien-

tational dynamics of the guest molecules. In view of the

hexagonal structure of the urea host tunnel, it is perhaps

surprising that we have found a model of rotational diffusion

of the guest molecules in a twofold potential with rather

large barriers, and we may conclude that the hexagonal de-

scription of the urea tunnel structure is true only on an aver-

age basis. Indeed, as the basic guest structure in the OP/urea

inclusion compound is known¹⁹to comprise six orientation-

ally distinguishable monoclinic domains, it is not surprising

that the local structure of the host should also be lower than

hexagonal. From the temperature dependence of the rota-

tional diffusion coefﬁcient, there is no indication of any

structural phase transition within the temperature range in-

vestigated. The reorientational behavior of the OP molecules

is probably inﬂuenced largely by the CvO groups and their

interaction with the urea tunnels ͑the CvO groups are ori-

ented approximately perpendicular to the tunnel axis, di-

rectly toward urea molecules͒. These interactions are un-

doubtedly inﬂuential in dictating the nature of the

intermodulation function.

FIG. 11. Comparison between the experimental and theoretical EISFs in Q_ʈ

geometry for h₃₀-OP/d₄-urea at 300 K. The theoretical curve ͑solid line͒ is

for the dynamic model discussed in the text.

We now assess plausible structural interpretations of the

reorientational dynamics of the OP guest molecules deduced

2

from the IQNS and H NMR data. The plausible conforma-

tion of the OP guest molecules within the urea tunnel is the

conformation with point group C₂, in which the twofold axis

passes through the center of the O–O bond and the dihedral

angle C–O–O–C denoted ␹. This conformation with ␹

Ϸ120° is adopted in the pure crystalline phase of OP⁴⁹and

in the structures of other long chain diacyl peroxides.⁵⁰The

conformation with point group C_2h, in which all carbon at-

oms lie in the same plane and the dihedral angle C–O–O–C

is ␹ϭ180°, is considered unlikely. The OP molecule may ﬁt

within the urea tunnel only if the conformation of the alkyl

chains is close to the ‘‘all-trans’’ conformation. Further, we

assume that all OP guest molecules exist in the same confor-

mational state within the urea inclusion compound. The dy-

Previous x-ray diffraction experiments¹⁹on OP/urea

have shown that there is three-dimensional positional order-

ing of the guest molecules, with the basic guest structure

having monoclinic space group symmetry C2/m or C2. The

twofold axis ͑unique axis of the monoclinic system͒ is per-

pendicular to the tunnel axis of the host structure, and there

are six equivalent, but orientationally distinguishable ways in

which this basic guest structure can be oriented with respect

to the host structure. In practice, a single crystal of the OP/

urea inclusion compound contains all six orientationally dis-

tinguishable domains of the basic guest structure, and ͑as

discussed above͒ the average host structure ͑hexagonal͒ is an

average over the local host structures ͑lower than hexagonal͒

in these six domains.

FIG. 12. Comparison between the experimental and ﬁtted IQNS spectra

͑IN5 spectrometer͒ for h₃₀-OP/d₄-urea in Q_ʈgeometry. Left side: as a func-

tion of temperature with Qϭ2.2 Å^Ϫ1; right side: as a function of Q at T

ϭ300 K.

FIG. 10. Schematic representation of the model of translation jumps be-

tween three sites with unequal probability of occupation.

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Girard et al.

4087

ing interconversion between two conformations of the OP

molecules is in better agreement with our experimental ﬁnd-

ings and our knowledge and intuitive understanding of the

structural characteristics of the OP/urea inclusion compound.

Currently, there is no experimental knowledge of the confor-

mation adopted by the OP guest molecules inside the urea

tunnel; such information may provide an independent assess-

ment of the validity of the proposed relaxation mechanism.

Further diffraction studies will signiﬁcantly improve our un-

derstanding of this and many other aspects of the OP/urea

inclusion compound. Such studies are planned in the near

future.

For translational motions of the OP guest molecules

along the tunnel axis, we have shown ﬁrst that the amplitude

of antitranslational vibrations of the two substructures is very

small, and second that the maximum of their density of states

is at about 2.2 meV. In addition, the translational diffusion

mechanism of the guest molecules involves ‘‘jumps’’ ͑i.e.,

translational diffusion in a potential with large barriers͒ be-

tween speciﬁc positions along the tunnel axis separated by

approximately c_h/6. These results suggest very strongly that

there is ‘‘pinning’’ of the guest molecules at speciﬁc posi-

tions along the urea tunnels, although not necessarily com-

mensurate with the host substructure. In agreement with this

conclusion, no ‘‘sliding mode’’ with acoustic type behavior

could be observed for OP/urea by Rayleigh–Brillouin

scattering⁵¹because of the resulting ‘‘gap’’ in the dispersion

branch. Despite the fact that the model used here to describe

the translational dynamics of the OP guest molecules in a

three-fold potential is to a large extent arbitrary, the jump

distances deduced from IQNS ͑of the order of 1.8 Å͒ are

clearly of signiﬁcant magnitude. Recalling that the basic

guest structure exhibits three-dimensional ordering, with a

well-deﬁned structural relationship between the positions of

guest molecules in adjacent tunnels ͑with ⌬_gϭ4.6 Å͒, it is

probable that the translations are strongly cooperative both

for guest molecules within each tunnel and for guest mol-

ecules in adjacent tunnels.

FIG. 13. Schematic representation of the orientations of the OP molecules in

urea viewed along the tunnel axis: ͑a͒ and ͑b͒ assuming C₂conformation for

OP reorienting as a whole; ͑c͒ and ͑d͒ assuming dynamic interconversion

between Ϫ␹ and ϩ␹ conformations (C₂) of the OP molecules. The open

circles represent the CvO group of the OP molecule closer to the viewer

and the arrow represents the C₂symmetry axis.

namic model indicates that the CH₂(CD₂) groups of each

OP molecule interconvert between two orientations ͑with

2␸_oϭ116°͒, and we now consider how this may be recon-

ciled with knowledge of the molecular and crystal symmetry.

For OP molecules with the C₂conformation, a dynamic

model involving reorientation of these molecules about the

tunnel axis between two preferred orientations is consistent

with the space group C2 for the average basic guest structure

provided the two orientations are as shown in Figs. 13͑a͒ or

13͑b͒. In these cases, the CvO bonds point approximately

toward the corners of the hexagonal urea tunnels ͑in projec-

tion͒. A second possible interpretation of the dynamics is

that the OP molecules in the C₂conformation undergo dy-

namic interconversion between two mirror-image conforma-

tional states with ␹ϭ2␸_oϷ116°. These enantiomeric con-

formations ͑denoted ϩ␹ and Ϫ␹͒ are energetically

equivalent for the isolated molecule, but within the chiral

urea tunnel structure they give rise to different diastereoiso-

meric host/guest relationships, and are therefore not energeti-

cally equivalent. This second dynamic model is consistent

with the average symmetry of the basic guest structure being

described by space group C2 , provided the two-fold axes of

the molecule and the crystal are coincident ͓see Figs. 13͑c͒

and 13͑d͔͒. In support of this interpretation of the dynamics,

molecular modeling suggests that a conformation of the OP

molecule with ␹ in the range 100 to 120° and with ‘‘all-

trans’’ alkyl chains can be readily accommodated within the

urea tunnel, and that interconversion between the ϩ␹ and

Ϫ␹ conformations is associated with little change in the

overall shape and volume of the molecule. Furthermore, for

this dynamic model involving interconversion between ϩ␹

and Ϫ␹ conformations of the guest molecule, the two-fold

symmetry axis is retained when the interconversion ceases at

sufﬁciently low temperature; this may be consistent with the

absence of evidence for a phase transition in OP/urea at low

temperature.

VI. CONCLUDING REMARKS

We have shown in this paper that a single model of

uniaxial reorientational diffusion in a twofold potential pro-

2

vides a basis for interpretation of both H NMR and IQNS

spectra ͑Q_Ќgeometry͒ for the OP/urea inclusion compound.

The combination of these two techniques is a very powerful

strategy for probing motions on very different characteristic

time scales, and should be applied in future studies of the

reorientational dynamics of other molecular solids over a

wide range of temperatures.

We have shown that a model of uniaxial reorientational

diffusion in a twofold potential is consistent with the hydro-

gens ͑deuterons͒ of the OP guest molecules occupying two

preferred positions with respect to reorientation about the

tunnel axis, with the angle between these positions differing

by ϳ116°, and a relaxation mechanism implying conforma-

tional interconversion of the OP molecules is proposed.

Clearly, the orientational distribution function for the guest

molecules in OP/urea is substantially more restricted than

that for the guest molecules in alkane/urea inclusion com-

In summary, the proposed relaxation mechanism involv-

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4088

J. Chem. Phys., Vol. 109, No. 10, 8 September 1998

Girard et al.

pounds. Models used previously ͑in ﬁtting IQNS data͒ to

describe the reorientational motion of the guest molecules in

alkane/urea inclusion compounds comprised reorientational

diffusion in a onefold potential,²⁶and further insights into

the orientational characteristics of the guest molecules in

nonadecane/urea have been established from computer simu-

lation studies.³⁷

in D₂O ͑1 h͒ and 8.0 g of 13.8% DCl in D₂O ͑3 h in an

ultrasonic bath͒. The mixture was extracted three times with

a total of 37 mL of dry ether and dried over anhydrous

Na₂SO₄to give 4.675 g of a clear oil. The exchanged

C₈H₁₅CO₂D was heated with 90% D₂SO₄in D₂O ͑38.7 g͒ for

60 h at 96 °C to form a black solution that was poured into

cold H₂O ͑100 mL͒ after cooling to room temperature. After

extraction with three 50 mL portions of pentane, NaCl ͑3 g͒

was added to break up emulsions, and the aqueous layer was

further extracted with a total of 200 mL of pentane. The

combined pentane extracts were dried over anhydrous

Na₂SO₄and condensed to give 4.67 g of a yellow oil. The

partially deuterated decanoic acid was exchanged twice with

DCl/D₂O, extracted with pentane, and condensed to give

4.31 g of a yellow oil, which was heated to 90 °C under N₂

for 25 h with 90% D₂SO₄in D₂O ͑38.25 g͒. The black reac-

tion mixture was poured into H₂O ͑80 mL͒, NaCl ͑7.5 g͒ was

added, and the labeled acid was extracted four times with a

total of 375 mL of pentane. The organic layer was extracted

three times with a total of 100 mL of 1 M aqueous KOH,

then the aqueous layer was acidiﬁed ͑50 mL of 4.4 M HCl͒

and extracted with ﬁve 40 mL portions of CH₂Cl₂and one 40

mL portion of pentane. After drying over anhydrous

Na₂SO₄, the yellow oil was distilled with a Kugelrohr

͑75 °C, 0.25 mm Hg͒ to give 2.74 g ͑50% overall͒ of the

product as a clear oil. ¹H NMR ͑200 MHz, CDCl₃͒: d 0.88 ͑t,

3H, Jϭ7 Hz͒, 1.29 ͑m, 8H͒, 1.62 ͑t, 2H, Jϭ7 Hz͒, 2.32 ͑t,

0.15H, Jϭ7 Hz͒ ͑93% atom% D by this method͒.

For the translational component of the motion along the

tunnel axis, the inelastic features ͑‘‘side-peaks’’͒ observed in

the IQNS spectra in Q_ʈgeometry occur at higher energy for

OP/urea than for the alkane/urea inclusion compounds. This

signiﬁes a higher energy for the antitranslational vibrations

of the host and guest subsystems in OP/urea, presumably on

account of the additional interaction between the CvO

groups of the OP guest molecules and the urea molecules

that form the wall of the tunnel. In addition, unlike the situ-

ation for alkane/urea inclusion compounds, the translational

diffusion of OP molecules along the urea tunnels is not

‘‘continuous,’’ but can be interpreted in terms of jumps be-

tween speciﬁc sites. The combined knowledge of the trans-

lational dynamics is consistent with the possibility that local

distortions of the tunnel wall may involve the establishment

of CvO¯H–N hydrogen bonds, similar to those observed

recently^6–8in commensurate urea inclusion compounds con-

taining alkanedione guest molecules.

ACKNOWLEDGMENTS

We are grateful to ILL and EPSRC for generous alloca-

tions of neutron beam time which allowed the IQNS experi-

ments described in this paper to be performed, and to Uni-

versity of London Intercollegiate Research Services and BP

Research International for access to facilities for solid state

NMR spectroscopy. The Nufﬁeld Foundation, NATO, the

2. Octanoyl chloride-2,2-d₂

Octanoic acid-2,2-d₂͑1.23 g, 8.4 mmol͒ was stirred with

SOCl₂͑1.80 g, 15.1 mmol͒ for 12 h at room temperature.

The excess SOCl₂was removed under vacuum and the prod-

uct was distilled under vacuum ͑26 °C, 0.15 mm Hg͒ to yield

1.27 g ͑91.8%͒ of a clear oil. Mass spectral analysis ͑EI͒ of

the methyl ester ͑formed by adding 5 mL of the acid chloride

to 1 mL of MeOH͒ gave the following integrated intensities:

m/e ͑relative intensity͒ 158 ͑M^ϩfor d₀, 0.64͒, 159 ͑M^ϩfor

d₁, 16.84͒, 160 ͑M^ϩfor d₂, 100͒. Comparison with unla-

beled methyl octanoate ͑Eastman Kodak͒ ͑158 ͑M^ϩ, 100͒,

159 ͑M^ϩ1, 18.95͒, 160 ͑M^ϩ2, 1.9͒ showed that the labeled

ester contained 86.9% of ␣-d₂and 12.6% of ␣-d₁material

´ ´

British Council, the ‘‘Direction Generale de la Recherche et

de la Technologie,’’ and NSF ͑Grant No. CHE-9423726͒ are

thanked for ﬁnancial support. Professor R. G. Grifﬁn is

thanked for providing the TURBOPOWDER program.

APPENDIX: PREPARATION OF MATERIALS

Octanoic acid ͑99%͒, octanoyl chloride ͑99%͒, D₂SO₄

͑98%, 99.5ϩ atom % D͒, 20% DCl ͑99ϩ atom % D͒ and

pentane ͑HPLC grade͒ were obtained from Aldrich Chemical

Co. and used without further puriﬁcation. Deuterium oxide

͑99.8%͒ and deuterium chloride ͑35% w/w in D₂O, 99 atom

% D͒ were obtained from General Intermediates of Canada.

Urea-d₄͑98ϩ atom % D͒ and MeOD ͑99.5 atom % D͒ were

obtained from Sigma Chemical Co. and were used without

further puriﬁcation. Diethyl ether and THF were distilled

from sodium benzophenone ketyl, and pyridine ͑Terochem͒

was distilled from CaH₂before use. Thionyl chloride ͑BDH

Chemicals͒ and H₂O₂͑Fisher, 30%͒ were used as purchased.

All glassware used for exchanges was dried before use.

2

͑93.1% total H incorporation͒.

3. Dioctanoyl peroxide-2,2-2 ,2 -d

Ј Ј

4

To a stirred solution of octanoyl chloride-2,2-d₂͑0.91 g,

5.53 mmol͒ in ether ͑20 mL͒, hydrogen peroxide ͑30%, 0.48

g, 4.13 mmol͒ was added over 1 min at 1 °C. Pyridine ͑0.54

g, 6.8 mmol͒ in Et₂O ͑10 mL͒ was added dropwise over 24

min while keeping the temperature below 3 °C. After warm-

ing over 10 min to 20 °C, the solution was stirred at 20 °C

for 15 min before cold Et₂O ͑10 mL͒, cold H₂O ͑10 mL͒ and

cold pentane ͑15 mL͒ were added, and the layers were sepa-

rated. The organic layer was washed three times with a total

of 25 mL of cold, 0.5 M HCl, twice with 10 mL portions of

cold, 5% aqueous NaHCO₃, once with 10 mL of cold, satu-

rated, aqueous NaCl, dried over Na₂SO₄and then ﬁltered

through a glass frit to give a clear oil ͑0.75 g, 93.2%͒ after

1. Octanoic acid-2,2-d₂

A mixture of octanoic acid ͑5.46 g, 37.9 mmol͒, DCl in

D₂O ͑7.83 g, 8.0% DCl͒ and dry THF ͑22 mL͒ was stirred

vigorously under N₂for 2.3 h before the layers were sepa-

rated. This procedure was repeated with 7.86 g of 12.4% DCl

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J. Chem. Phys., Vol. 109, No. 10, 8 September 1998

Girard et al.

4089

evaporation of solvent. This clear oil was dissolved in

MeOH ͑4.5 mL͒ and cooled to 5 °C to give a white powder

͑0.46 g͒, which was collected at 5 °C and used immediately

for formation of urea inclusion compounds.

¹¹R. Lefort, J. Etrillard, B. Toudic, F. Guillaume, T. Breczewski, and P.

Bourges, Phys. Rev. Lett. 77, 4027 ͑1996͒.

¹²T. Weber, H. Boysen, M. Honal, F. Frey, and R. B. Nader, Z. Kristallogr.

211, 238 ͑1996͒.

¹³S. van Smaalen and K. D. M. Harris, Proc. R. Soc. London, Ser. A 452,

677 ͑1996͒.

¹⁴T. Weber, H. Boysen, F. Frey, and R. B. Nader, Acta Crystallogr., Sect. B:

Struct. Sci. 53, 544 ͑1997͒.

4. Dioctanoyl peroxide-2,2,2 ,2 -d /urea

Ј Ј

4

¹⁵J. Ollivier, Ph.D. thesis, University of Rennes I, 1997.

¹⁶A. El Baghdadi, E. J. Dufourc, and F. Guillaume, J. Phys. Chem. 100,

1746 ͑1996͒.

In a 50 mL Erlenmeyer ﬂask, octanoyl peroxide-

2,2,2 ,2 -d ͑0.46 g͒ was dissolved in 10 mL of MeOH and

Ј Ј

4

then mixed with 25 mL of 1.8 M urea in MeOH. This solu-

tion was suspended in a 1 L Dewar ﬂask containing H₂O at

room temperature and cooled over 12 h to 5 °C to form 1.0 g

of hexagonal urea inclusion compound crystals.

¹⁷H. Cailleau and C. Ecolivet, Mater. Sci. Forum 100&101, 367 ͑1992͒.

¹⁸K. Fukao, J. Chem. Phys. 101, 7882 ͑1994͒; ibid. 101, 7893 ͑1994͒.

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431, 245 ͑1990͒.

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5. Dioctanoyl peroxide

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L. Yeo, B. M. Kariuki, H. Serrano-Gonzalez, and K. D. M. Harris, J. Phys.

To a stirred solution of octanoyl chloride ͑99%, 10.33 g,

63.5 mmol͒ in Et₂O ͑60 mL͒ was added a cold solution of

30% aqueous H₂O₂͑5.28 g, 46.5 mmol͒ at 4 °C over 1 min.

Pyridine ͑5.91 g, 74.5 mmol͒ in Et₂O ͑15 mL͒ was added

dropwise over 1.5 h, keeping the temperature at 4–5 °C. Af-

ter addition of 13 mL of cold Et₂O and 33 mL of cold H₂O,

the layers were separated. The organic layer was washed

three times with a total of 100 mL of cold 0.5 M aqueous

HCl, 33 mL of cold 5% aqueous NaHCO₃, and then with 25

mL of cold, saturated aqueous NaCl before drying over an-

hydrous Na₂SO₄and condensing to give 8.39 g ͑95.3%͒ of a

clear oil. Crystallization from MeOH ͑50 mL͒ at Ϫ20 °C

gave a ﬁrst crop of a white powdery solid, which was col-

lected at 5 °C.

22

´

Chem. B 101, 9926 ͑1997͒.

²³K. D. M. Harris and I. Gameson ͑unpublished results͒.

²⁴E. H. Bocanegra, K. D. M. Harris, F. Guillaume, and E. J. MacLean

͑unpublished results͒.

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͑1990͒.

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Chim. Biol. 88, 1721 ͑1991͒.

²⁷H. L. Casal, D. G. Cameron, and E. C. Kelusky, J. Chem. Phys. 80, 1407

͑1984͒.

²⁸K. D. M. Harris and P. Jonsen, Chem. Phys. Lett. 154, 593 ͑1989͒.

²⁹M. S. Greenﬁeld, R. L. Vold, and R. R. Vold, Mol. Phys. 66, 269 ͑1989͒.

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³¹F. Fujara, W. Petry, W. Schnauss, and H. Silescu, J. Chem. Phys. 89, 1801

͑1988͒.

³²F. Fujara, W. Petry, R. M. Diehl, W. Schnauss, and H. Silescu, Europhys.

Lett. 14, 563 ͑1991͒.

³³F. Rieutord, Institut Laue Langevin, Technical Report 90RI17 ͑1990͒.

6. Dioctanoyl peroxide/urea-d₄

³⁴J. H. Davis, K. R. Jeffrey, M. Bloom, M. I. Valic, and T. P. Higgs, Chem.

Urea-d₄͑98ϩ atom % D, 1.95 g, 30.5 mmol͒, dioctanoyl

peroxide ͑1.11 g, 3.88 mmol͒ and MeOD ͑99.5 atom % D,

23.7 mL͒ were added to a 50 mL Erlenmeyer ﬂask, which

was sealed and then suspended in an ultrasonic bath for 45

min ͑highest Tϭ32 °C͒ to dissolve all solids. The ﬂask was

transferred to a Dewar ﬂask containing H₂O at 34 °C, which

was placed in a cold room at 5 °C. After 30 h, 1.18 g of

hexagonal needles were collected at 5 °C in a glove bag

purged with N₂.

Phys. Lett. 42, 390 ͑1976͒.

35

´

M. Bee, Quasielastic Neutron Scattering ͑Adam Hilger, Bristol, 1988͒.

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͑1996͒.

³⁷M. Souaille, F. Guillaume, and J. C. Smith, J. Chem. Phys. 105, 1529

͑1996͒.

³⁸K. D. M. Harris, F. Guillaume, S. P. Smart, C. Sourisseau, and A.-J.

Dianoux, J. Chem. Res. 276 ͑1992͒.

39

´

M. Bee, Institut Laue Langevin, Technical Report 84BEO5T͑1984͒.

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5411 ͑1987͒.

⁴¹J. A. Nelder and R. Mead, Comput. J. ͑UK͒ 7, 308 ͑1965͒.

⁴²A. E. Aliev and K. D. M. Harris, Magn. Reson. Chem. ͑in press͒.

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¹K. Takemoto and N. Sonoda, Inclusion Compounds, edited by J. L. At-

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1993͒, p. 131.

²M. D. Hollingsworth and K. D. M. Harris, Comprehensive Supramolecu-

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¨

and F. Vogte ͑Pergamon, New York, 1996͒, Vol. 6, pp. 177–237.

³A. E. Smith, Acta Crystallogr. 5, 224 ͑1952͒.

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Ser. A 430, 615 ͑1990͒.

⁴⁶P. Girard, A. E. Aliev, F. Guillaume, K. D. M. Harris, M. D. Holling-

sworth, A.-J. Dianoux, and P. Jonsen, Physica B 234–236, 112 ͑1997͒.

⁴⁷F. Guillaume, J. Doucet, C. Sourisseau, and A.-J. Dianoux, J. Chem. Phys.

91, 2555 ͑1989͒.

⁵M. D. Hollingsworth, B. D. Santarsiero, and K. D. M. Harris, Angew.

Chem. Int. Ed. Engl. 33, 649 ͑1994͒.

⁶M. E. Brown and M. D. Hollingsworth, Nature ͑London͒ 376, 323 ͑1995͒.

⁷M. E. Brown, J. D. Chaney, B. D. Santarsiero, and M. D. Hollingsworth,

Chem. Mater. 8, 1588 ͑1996͒.

⁴⁸F. Guillaume, V. Rodriguez, J. P. Ryckaert, P. Girard, and A. J. Dianoux

͑in preparation͒.

⁴⁹M. D. Hollingsworth and K. D. M. Harris, unpublished results ͑see K. D.

M. Harris, Ph.D. thesis, University of Cambridge, 1988͒.

⁵⁰J. M. McBride, S. B. Bertman, D. Z. Ciofﬁ, B. E. Segmuller, and B. A.

Weber, Mol. Cryst. Liq. Cryst. Inc. Nonlin. Opt. 161, 1 ͑1988͒.

⁵¹D. Schmicker, S. van Smaalen, C. Haas, and K. D. M. Harris, Phys. Rev.

B 49, 11572 ͑1994͒.

⁸M. D. Hollingsworth, M. E. Brown, A. C. Hillier, B. D. Santarsiero, and J.

D. Chaney, Science 273, 1355 ͑1996͒.

⁹M. D. Hollingsworth, K. D. M. Harris, J. D. Chaney, U. Werner-

Zwanziger, M. E. Brown, J. C. Huffman, and S. P. Smart ͑in preparation͒.

¹⁰K. D. M. Harris and J. M. Thomas, J. Chem. Soc., Faraday Trans. 86,

2985 ͑1990͒.

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Dynamic properties of dioctanoyl peroxide guest molecules constrained within the urea tunnel structure: A combined incoherent quasielastic neutron scattering and solid state 2H nuclear magnetic resonance investigation

DOI: 10.1063/1.477008

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