www.elsevier.com/locate/chemphys

Chemical Physics 323 (2006) 545–552

Diffusional behavior of n-paraffins with various chain lengths in ureaadduct channels by pulsed field-gradient spin-echo NMR spectroscopy

Sunmi Kim, Shigeki Kuroki *, Isao Ando

Department of Chemistry and Materials Science, International Research Center of Macromolecular Science,

Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan

Received 24 February 2005; accepted 21 October 2005Available online 17 November 2005

Abstract

The diffusion coefficients (D) of n-paraffin molecules (n-CnH2n+2) with various chain-lengths (n = 8, 12, 21, 26, 28 and 32) in the longchannels of a deuterated urea-d4 adduct have been measured at 25 �C by means of pulsed field-gradient spin-echo 1H NMR method. Theaim is to clarify diffusional behavior of the n-paraffin molecules in the urea adduct channels. From the experimental results, it is foundthat n-paraffin molecules are diffusing in the long channels and have two kinds of diffusion components, namely a fast (D � 10�10 m2/s)and a slow diffusion component (D � 10�11 m2/s). The diffusing-time (D) dependence of the diffusion coefficients of the n-paraffins showssome likely evidence of restricted diffusion since the n-paraffin molecules are confined in the urea channel. The diffusion coefficients (D)decrease as the carbon number increases from 8 to 28, and very slowly decreases as the carbon number increases from 28 to 32.� 2005 Elsevier B.V. All rights reserved.

Keywords: Urea adduct; n-Paraffin; Channel cavity; Diffusion coefficient; Diffusion process; High field-gradient NMR

1. Introduction

Recently, the structure and dynamics of n-paraffins inone-dimensional channels of urea-d4 have been studied byvarious methods such as X-ray diffraction [1], 2H NMR[2–4], incoherent quasi-elastic neutron scattering [5,6],Raman scattering [7,8] and computer science [9,10]. It iswell known that urea forms adducts with long channelsin which linear chain molecules such as n-paraffins, fattyacids and alkanones are embedded. From many studiesof the structure of urea and its urea adducts, it has beenrevealed that urea inclusion compounds consist of ureamolecules forming long honeycomb-like (hexagonal) chan-nels with diameters of 5.5–5.8 A. The urea molecules areheld together by hydrogen bonds and have guest moleculesembedded in the channels at room temperature. The chan-nels may be long length and of sufficient diameter to

0301-0104/$ - see front matter � 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemphys.2005.10.024

* Corresponding author. Tel.: +81 3 5734 2880; fax: +81 3 5734 2889.E-mail address: skuroki@polymer.titech.ac.jp (S. Kuroki).

include linear n-paraffins and other molecules [1,11,12]. Ifthe temperature decreases below room temperature (e.g.,ca. �123 �C for urea/n-hexadecane adduct), the urea-adduct crystals occur at a solid–solid phase transition asso-ciated with a change of the host urea network structurefrom the hexagonal form to the orthorhombic form. Thephase transition temperature is chain-length dependentand for a given n-paraffin in the urea adduct it is substan-tially lower than for the rotator phase transition tempera-ture of the crystalline phase of the n-paraffin [13].

Further, it is shown that n-paraffin chains in long chan-nels of the urea adduct at low temperatures take the all-trans zigzag conformation and their molecular motion isfrozen. In the high-temperature range, the n-paraffin chainsundergo rotational motions around the chain axis [2,5,14–18]. Most recently, molecular motion of n-paraffin chainsin long channels of urea adducts has been studied bysolid-state NMR [2,3,19,20]. Conformation and rotationalmotions of the n-paraffin chains in the long channel of theurea-d4 adduct have been clarified. Nevertheless, someproblems related to the dynamics of the n-paraffin chains

546 S. Kim et al. / Chemical Physics 323 (2006) 545–552

in the urea adduct channel remain. For example, (1) are then-paraffin chains diffusing in the channel cavities of theurea adduct? (2) what, if they are diffusing, is the diffusioncoefficient? (3) what is the diffusion process? and (4) how isthe diffusional behavior of the n-paraffin chains affected byvarying the chain length?

In our preliminary work [21], the diffusion coefficients(D) of n-C21H44 in the urea-d4 adduct have been success-fully measured in the temperature range from 0 to 75 �Cby means of the pulsed field-gradient spin-echo (PFGSE)1H NMR method. From these experiments, it has beenreported that n-C21H44 molecules are diffusing in the longchannel cavities of the urea-d4 adducts and have two kindsof diffusion components, a fast diffusion component(D � 10�10 m2/s) and a slow diffusion component(D � 10�12 m2/s).

In the present work, we aim to measure systematicallythe diffusion coefficients, D, of n-C8H18, n-C12H26, n-C21H44, n-C26H54, n-C28H58 and n-C32H66 in long channelsof the deuterated urea-d4 adduct at 25 �C by means of thePFGSE 1H NMR method. Thus, we aim to elucidate thechain-length dependence of the diffusion of the n-paraffins.Furthermore, we aim to measure the diffusion coefficientsof n-C12H26 and n-C26H54 in the urea-d4 adduct channelsby varying the diffusing-time D by means of PFGSE 1HNMR and pulsed field-gradient stimulated-echo (PFGStE)NMR methods, and to elucidate the diffusion process ofthe guest molecules in the urea adduct channels.

2. Experimental

2.1. Materials

n-C8H18 (purity: >98%), n-C12H26 (purity: >98%),n-C21H44 (purity: >98%), n-C26H54 (purity: >98%),n-C28H58 (purity: >98%), n-C32H66 (purity: >98%) anddeuterated urea-d4 (purity: >98%) purchased from AldrichChemical Co. are used without further purification. Deu-terated urea-d4 is used for observing the 1H NMR signalof the n-paraffins in the NMR experiments. The ureaadduct sample used for the PFGSE NMR experiments isprepared by slow cooling after mixing a methanol solutionof urea-d4 with a methanol solution of the n-paraffin atroom temperature as described elsewhere [22,23].

In the NMR experiments, we used hexagonal crystalswith an average length of 10 mm and a cross-section withdiameter of ca. 0.43 mm.

2.2. Measurements

2.2.1. Field-gradient 1H NMR experiments

The diffusion coefficient measurements of the n-paraffinsin the urea-d4 adduct in the rotator phase have been car-ried out on a Bruker DSX-300 NMR spectrometer witha field-gradient generator system (the maximum field-gra-dient strength: 11.6 T/m) operating at 300.11 MHz at25 �C. In this field-gradient 1H NMR experiment, the

echo-signal intensity is measured by varying the field-gra-dient strength g from 0 to 11.6 T/m, the gradient pulseinterval D is 5 ms, the gradient pulse width d is 1 ms forall the samples. The diffusion coefficients of n-C12H26

and n-C26H54 in the urea-d4 adduct have been measuredat various diffusing times, in order to explain in detailthe diffusional behavior of the n-paraffin molecules withina channel cavity. The diffusing time corresponds to thetime interval D between the first and second gradientpulses. Diffusion coefficients of n-C12H26 and n-C26H54 inthe urea-d4 adduct have been measured by using a pulsedfield-gradient spin-echo [24–27] pulse sequence (p/2pulse–s–p pulse) and a pulsed field-gradient stimulated-echo (PFGStE) pulse sequence (p/2 pulse–s1–p/2 pulse–s2–p/2 pulse) [28–30]. It has been shown that the PFGSE1H NMR method is a powerful method for the elucidationof the diffusional behavior of polymer systems [21,28,30–46], such as probe molecules and probe polymers in poly-mer gels, polymer liquid crystals and n-paraffins in therotator phase. The 1H chemical shifts d are calibrated rel-ative to tetramethylsilane (d = 0 ppm).

In practice, the diffusion constant D is determinedthrough the spin-echo intensity attenuation in the presenceof the pulsed field gradients by the following equation. Thisis achieved by varying the field-gradient strength g, theduration d of the gradient pulse and the time interval Dbetween the two pulses.

½AðgÞ=Að0Þ� ¼ exp½�c2g2Dd2ðD� d=3Þ�; ð1Þwhere A(g) and A(0) are the echo-signal intensities with andwithout the gradient field, respectively, and c is the gyromag-netic ratio (for the proton, c = 2.675 · 104 rad/g/s). Theecho-signal intensity is measured as a function of g. The plotsof ln[A(g)/A(0)] against c2g2d2(D � d/3) give a straight linewith a slope of�D when the probe molecules have single dif-fusion component. Therefore, the D value can be determinedfrom this slope, with accuracy of ca. 10%.

However, when the probe molecules have two kinds ofdiffusion components on the measurement timescale, thetotal echo attenuation is given by a superposition of thecontributions from the individual components as expressedby,

½AðgÞ=Að0Þ� ¼ f1 exp½�c2g2D1d2ðD� d=3Þ�

þ f2 exp½�c2g2D2d2ðD� d=3Þ�; ð2Þ

where Di and fi are the self-diffusion coefficient and thefraction of the ith diffusion component, respectively, wheref1 + f2 = 1. The fractions for the fast and slow diffusioncomponents can be determined from the intercept of theleast-squares fitted straight line.

2.2.2. Optical microscope experiments

The shape and size of the urea-d4/n-paraffin crystals pre-pared in this work are observed with a Keyence VH-5000digital microscope. For example, the urea-d4/n-C12H44 ureaadduct used in the NMR experiments has hexagonal crys-

slow diffusion component

fast diffusion component

ln[A

(g)/

A(0

)]

γ 2g2δ 2(Δ-δ /3)/ s /m2 (x1010 )

0 0.5 1 1.5

0

-1

-2

Fig. 2. The plots of ln[A(g)/A(0)] against c2g2d2(D � d/3) for the meth-ylene and methyl protons of n-C8H18 in urea-d4/n-C8H18 at 25 �C.

S. Kim et al. / Chemical Physics 323 (2006) 545–552 547

tals with an averaged length of ca. 10 mm and with a hex-agonal cross-section diameter of ca. 0.43 mm.

3. Results and discussion

3.1. Chain-length dependence of the diffusion coefficients ofthe n-paraffin in the urea adduct

In Fig. 1 are shown some typical spin-echo 1H NMRspectra of n-C8H18 in urea-d4 adduct at 25 �C as a functionof the field-gradient pulse strength (g) as observed by usingPFGSE 1H NMR. The broad peak at about 5 ppm can bestraightforwardly assigned to the methylene protons of n-C8H18. The minor methyl peak overlaps with the majormethylene peak as a small shoulder on the low frequencyside of the methylene peak. The origin of such a high fre-quency shift by about 3 ppm as compared with the 1Hchemical shift for the methylene protons of n-paraffins inthe solid state and the liquid state (d = about 2 ppm) maybe understood from the following. The n-paraffin chainsare in the long hexagonal channel cavities of the urea-d4

adduct which has a diameter of about 5.5 A. This is formedby hydrogen-bonds between the carbonyl �C@O groupsand the NH groups of the urea molecules. The methyleneand methyl protons of the n-paraffin are largely affectedby the magnetic anisotropy effect of the carbonyl groupsin the long channel as predicted theoretically by the mag-netic anisotropy effect/chemical shift map. When the n-par-affin molecules are placed at the center of a hexagonalchannel cavity, the intermolecular distance between themethylene protons or the methyl protons of n-C8H18 andthe carbonyl �C@O group of urea-d4 is roughly calculatedto be about 1.3 A. Thus, we can approximately calculate adeshielding by about 2–3 ppm for the protons due to themagnetic anisotropy effect/chemical shift map given byAndo and Gutowsky [47]. Thus, the 1H chemical shift ofthe methylene protons may be approximately calculatedto be about 5 ppm.

Fig. 2 shows the plots of ln[A(g)/A(0)] againstc2g2d2(D � d/3) for the methylene and methyl protons ofn-C8H18. The intensity of the corresponding peak decreaseswith an increase in g. This means that the n-C8H18 mole-

Fig. 1. Typical spin-echo 1H NMR spectra of n-C8H18 in urea-d4 adductat 25 �C as function of field-gradient pulse strength (g) as observed byusing PFGSE 1H NMR.

cules diffuse in the long channel cavity of the urea-d4

adduct. It is seen that the experimental data do not lie ona straight line but lie on a curve which can be decomposedinto two straight lines as seen in Fig. 2. This means that then-C8H18 molecules in the long channels of the urea adducthave two kinds of diffusions, a slow and a fast diffusioncomponent during the observation time of 5 ms. The diffu-sion coefficient can be determined from the slope of �D forthe individual straight lines by using Eq. (2). The deter-mined D values are listed in Table 1 together with the frac-tion of the corresponding diffusion coefficient component.

We are concerned with the origin of the two diffusioncomponents of the n-paraffin molecules with the largely dif-ferent diffusion coefficients in the long channels of the ureaadduct. As for the diffusional behavior of the n-C8H18 mol-ecules in this urea adduct system, we wish to explain theorigin of the existence of the fast and the slow diffusioncomponents.

There may be two kinds of regions in the long channelswhich include the n-C8H18 molecules in the urea adduct.Namely, there may be n-C8H18 molecules in the two exter-nal regions near the ends of the urea channel, and n-C8H18

molecules in the central inner region of the urea channel. It

Table 1Determined diffusion coefficientsa of n-paraffins in the urea adduct at25 �C

Urea adducts Diffusion coefficient, D (m2/s) Fraction

Dfast (·1010) Dslow (·1011) ffast fslow

Urea-d4/n-C8H18 7.9 10.2 0.72 0.28Urea-d4/n-C12H26 7.1 5.60 0.79 0.21Urea-d4/n-C21H44 3.0 0.70 0.67 0.33Urea-d4/n-C26H54 2.8 0.94 0.64 0.36Urea-d4/n-C28H58 2.7 1.0 0.57 0.43Urea-d4/n-C32H66 3.0 0.8 0.18 0.82

a The experimental errors for the diffusion coefficient measurements areca. 10%.

0 1 2 3

0

-1

-2

-3

uc8-exp

uc8-cal

uc12-exp

uc12-cal

uc26-exp

uc26-cal

uc28-exp

uc28-cal

uc32-exp

uc32-cal

γ 2g2δ 2(Δ-δ /3)/ s /m2 (x1010 )

ln[A

(g)/

A(0

)]

Fig. 3. The plots of ln[A(g)/A(0)] against c2g2d2(D � d/3) for the meth-ylene and methyl protons of n-paraffins with the carbon number from 8 to32 in urea-d4 adduct at 25 �C.

548 S. Kim et al. / Chemical Physics 323 (2006) 545–552

is thought that these molecules contribute to the fast diffu-sion component and the slow diffusion component, respec-tively. The shape of the n-paraffin with the extended trans

form in the urea adduct channels are roughly approxi-mated to be a rod with an average diameter of about0.4 nm, and the urea adduct channel size is 0.55 nm. Thus,the n-paraffin molecules do not experience a tight space inthe channels and are able to diffuse. From the experimentalfact that the n-C8H18 molecules in the urea channels arediffusing, it can be said that the diffusion must be coopera-tive diffusion (like the single-file diffusion model). In thediffusion, individual molecules cannot pass each other[48,49]. One n-paraffin molecule can move to the space pro-duced by movement of other n-paraffin molecules, and thena repeat diffusion and collision may occur in the inner partand the external part of the urea channels during the NMRmeasurement timescale. These displacements occur in suc-cession. In addition, as reported by Aslangul [50], the sin-gle-file diffusion model shows that at the initial timewhen n-paraffin molecules are launched in a one-dimen-sional space, each of them undergoes ordinary diffusionalmotion, but has a contact repulsive interaction with itsneighbors. As a consequence, the n-paraffin moleculeslocated at the ends of the channel can move freely on oneside and are subjected to a fluctuating boundary conditionon the other. The n-paraffin molecules located inside thechannel are subjected to such boundary conditions on bothsides. Thus n-paraffin molecules in the inner part of a ureachannel have a higher possibility of collision than thosenear the ends of a channel. Thus, the diffusion coefficient(Dinside) of the n-paraffin molecules in the inner part ismuch smaller than that of the n-paraffin molecules in theouter parts (Doutside). In the limit of large N (the numberof n-paraffins), and within a Gaussian approximation, thediffusion constant is found to behave as N�1 for the centralparaffin molecules and as (ln N)�1 for the outer ones as sug-gested by the single-file diffusion model [50]. Absolute cor-relations between the end particles increase as (ln N)2.

In the same manner, the D values of n-C12H26, n-C21H44,n-C26H54, n-C28H58 and n-C32H66 in the urea-d4 adduct at25 �C are determined. Fig. 3 shows the plots of ln[A(g)/A(0)] of these n-paraffins against c2g2d2(D � d/3) and calcu-lated curve of the superposition of the echo-signal intensi-ties from the two diffusion components. As shown in theabove-mentioned experiments, the two diffusion coeffi-cients are determined by superposition of two straightlines. The order of the diffusion coefficients of the fast dif-fusion component (Dfast) and the slow diffusion component(Dslow) are 10�10 and 10�11 m2/s, respectively. The two dif-fusion components are attributed to n-paraffin molecules inthe two end regions of the urea channel, and to n-paraffinmolecules in the central region of the urea channel asreported previously by us [21]. The determined D valuesfor all of the n-paraffins in the urea-d4 adduct are listedin Table 1.

For convenience, the diffusion coefficients of both thefast and slow diffusion components for all of the n-paraffins

are plotted against the carbon number in Fig. 4. The diffu-sion coefficients (D) decrease as the carbon numberincreases from 8 to 28 and very slowly decreases as the car-bon number increases from 28 to 32. These results are sim-ilar to those of pure n-paraffins in the rotator phase in thatthe diffusion coefficient becomes smaller as the n-paraffinmolecule becomes longer [36].

Pure n-paraffins with a large number of carbons take theall-trans zigzag form in the rotator phase [51]. Such a con-formational and dynamic behavior may be similar to thoseof the n-paraffins in the urea adducts. In the previous workon the diffusional behavior of long n-paraffins with theall-trans zigzag conformation in the rotator phase, thediffusion coefficient of n-paraffins was estimated to be ofthe order of 10�10 m2/s. For example, the diffusion coeffi-cient of pure n-C21H44 was determined to be D = 2.58 ·10�10 m2/s in the rotator phase at 37 �C. In the rotatorphase, the all-trans zigzag n-paraffin chains considered hereare hexagonally surrounded by six neighboring n-paraffinswith the all-trans zigzag form. This is roughly similar tothat for the n-paraffin chain in a long hexagonal channelof the urea adduct. Thus, the D value of n-C21H44 for thefast diffusion component along a channel of the ureaadduct is somewhat larger than that of pure n-C21H44 inthe rotator phase.

Fig. 5 shows the plots of the fraction of the two diffusioncomponents against the carbon number, as determinedfrom Eq. (2). As seen in Fig. 5, as the carbon numberincreases from 8 to 28, the fraction of the slow diffusioncomponent becomes gradually larger, and at the carbonnumber of 32 the fraction of the slow diffusion componentoccupies about 80%.

Furthermore, in order to understand more deeply thediffusion process, we can calculate the activation energy(Ea) for diffusion by using the following equation:

D ¼ A expð�Ea=kT Þ; ð3Þ

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

5 10 15 20 25 30 35

Fra

ctio

n of

the

diff

usio

n co

mpo

nent

s

Carbon numbers

Fig. 5. Dependence of the fractions of the fast (d) and slow (s) diffusioncomponents on carbon number from 8 to 32 in urea-d4 adduct at 25 �C.

-14

-13

-12

-11

-10

2.5 3 3.5 4

ln D

1/T (K–1) x10–3

Fig. 6. The Arrhenius plots of lnD against 1/T of n-C21H44 (s) in the urea/n-C21H44 adduct channels and pure n-C21H44 (d) in the rotator phase.

0

2

4

6

8

5 10 15 20 25 30 35

Dif

fusi

on c

oeff

icie

nt D

/ m

2 /s(x

10-1

0 )D

iffu

sion

coe

ffic

ient

D /

m2 /s

(x 1

0-11 )

Carbon numbers

0

2

4

6

8

10

12

5 10 15 20 25 30 35

Carbon numbers

a

b

Fig. 4. Diffusion coefficients of the fast diffusion component (d) (a) andthe slow diffusion component (s) (b) for n-paraffins with the carbonnumber from 8 to 32 in urea-d4 adduct channels at 25 �C.

S. Kim et al. / Chemical Physics 323 (2006) 545–552 549

where A is the front factor, T the absolute temperature andk the Boltzmann constant. The activation energy was ob-tained from the plots of lnD against 1/T (the Arrheniusplots) for n-C21H44 in the urea/n-C21H44 adduct channelsand pure n-C21H44 in the rotator phase [36] as shown inFig. 6. Its slope becomes �Ea/k.

The determined Ea values for the n-C21H44 in the urea/n-C21H44 adduct channels and for pure n-C21H44 in the rotatorphase are 0.6 and 4.7 kcal/mol, respectively. The Ea value ofpure n-C21H44 in the rotator phase is much larger than that ofn-C21H44 in the urea/n-C21H44 adduct channels. This indi-cates that the n-C21H44 chains in the urea adduct channelseasily diffuse as compared with the pure n-C21H44 chains inthe rotator phase. This is because the intermolecular interac-tions between the pure n-C21H44 chains in the rotator phaseare removed in the urea channels.

3.2. Diffusing-time dependence of the diffusion coefficients

The diffusion of the n-paraffins is strongly influenced byintermolecular interactions between them, and by interac-tions between the n-paraffin molecules and the wall of thechannel made by the urea molecules. Thus the diffusion coef-ficient of the n-paraffin molecules may be sensitively depen-dent on the diffusing-time D. Therefore, the diffusing-time(D) dependence of the diffusion coefficients of n-C12H26

and n-C26H54 in the urea-d4 adduct channels has been stud-ied in order to understand the diffusional behavior of then-paraffin molecules confined in the urea adduct channels.

Fig. 7 shows the plots of ln[A(g)/A(0)] against c2g2d2-(D � d/3) in the D range of 5–200 ms. It is seen that the

0 1 2 3

0

-1

-2

-3

uc8-exp

uc8-cal

uc12-exp

uc12-cal

uc26-exp

uc26-cal

uc28-exp

uc28-cal

uc32-exp

uc32-cal

γ 2g2δ 2(Δ-δ /3)/ s /m2 (x1010 )

ln[A

(g)/

A(0

)]

Fig. 7. The plots of ln[A(g)/A(0)] of urea/n-C12H26 against c2g2d2(D � d/3)at 25 �C on the gradient pulse interval D.

0

2

4

6

8

10

12

14

0 50 100 150 200 250Δ (ms)

Dif

fusi

on c

oeff

icie

nt D

/ m

2 /s(x

10-1

0 )

Fig. 8. Diffusing-time D dependence of diffusion coefficients of the fast (d)and slow (s) diffusion components of n-C12H26 in urea-d4 adduct.

-0.2

05ms

10ms

550 S. Kim et al. / Chemical Physics 323 (2006) 545–552

n-C12H26 molecules in the urea-d4 adduct have two diffu-sion components at 5–200 ms. The determined D valuesand the fractions of the corresponding diffusion compo-nents of n-C12H26 in the urea-d4 adduct are summarizedin Table 2.

For convenience, the fast and slow diffusion coefficientsof n-C12H26 in the urea-d4 adduct are plotted against thediffusing-time (D) in Fig. 8. As the diffusing time increases,both of the D values for the fast and slow diffusion compo-nents of n-C12H26 in the urea-d4 adduct decrease. Theseresults can be explained as follows. The n-paraffin mole-cules are diffusing in a channel and colliding with neighbor-ing molecules during the diffusing time. As the diffusingtime increases, the number of collisions between the n-par-affin molecules increases and the apparent diffusion coeffi-cients decrease. The D values for the two diffusioncomponents are not averaged out in the D range from 5to 200 ms and decrease continuously with an increase inD. If the n-paraffin molecules diffuse for a sufficiently longdiffusing time, D, the observed diffusion coefficient maybecome an averaged value.

In the same manner, the n-C26H54 in urea-d4 adduct hasbeen measured as a function of the diffusing-time D (that is,the field-gradient pulse interval time) by the PFGSE 1HNMR method. The diffusion coefficient measurements of

Table 2Determined diffusion coefficientsa of n-C12H26 in the urea-d4/n-C12H26

adduct channels as a function of the diffusing-time D at 25 �C

D (ms) Diffusion coefficient, D (m2/s) Fraction

Dfast (·1010) Dslow (·1011) ffast fslow

5 12.3 3.13 0.83 0.1710 9.79 1.47 0.87 0.1320 8.53 1.21 0.81 0.1950 7.07 1.0 0.72 0.28

100 3.60 0.78 0.70 0.30200 2.8 0.57 0.64 0.36

a The experimental errors for the diffusion coefficient measurements areca. 10%.

n-C26H54 in the urea-d4 adduct have been performed atD = 5 to 40 ms. Fig. 9 shows the plots of ln[A(g)/A(0)]against c2g2d2(D � d/3) in the D range of 5–40 ms. It is seenthat the n-C26H54 molecules in the urea-d4 adduct have twodiffusion components at D = 5, 10, 20 and 30 ms, but havea single diffusion component at D = 40 ms. The determinedD values and the fractions of the corresponding two diffu-sion components of n-C26H54 in the urea-d4 adduct aresummarized in Table 3.

Fig. 10 shows the diffusing-time dependence of the D val-ues for the fast diffusion component and the slow diffusioncomponent of n-C26H54 in the urea-d4 adduct, where theright-hand side is an expansion of the left-hand diagram.As the diffusing-time increases, the D values for the fastand the slow diffusion components of n-C26H54 in theurea-d4 adduct decrease. This can be explained by the fact

-1.2

-1

-0.8

-0.6

-0.4

0 0.5 1 1.5 2.5

20ms

30ms

40ms

2

ln[A

(g)/

A(0

)]

γ 2g2δ 2(Δ-δ /3)/ s /m2 (x1011 )

Fig. 9. The plots of ln[A(g)/A(0)] of urea-d4/n-C26H54 against c2g2d2-(D � d/3) at 25 �C on diffusing-time D.

Table 3Determined diffusion coefficientsa of n-C26H54 in the urea-d4/n-C26H54

adduct channels as a function of the diffusing time D at 25 �C

D (ms) Diffusion coefficient, D (m2/s) Fraction

Dfast (·1010) Dslow (·1011) ffast fslow

5 9.9 1.26 0.31 0.6910 4.4 0.61 0.30 0.7020 1.8 0.26 0.24 0.7630 0.5 0.22 0.14 0.8640 – 0.31 – 1.00

a The experimental errors for the diffusion coefficient measurements areca. 10%.

0

2

4

6

8

10

12

0 10 20 30 40 50

Δ (ms)

Dif

fusi

on c

oeff

icie

nt D

/ m

2 /s(x

10-1

0 )

Fig. 10. Diffusing-time D dependence of diffusion coefficients of the fast(d) and the slow (s) diffusion components of n-C26H54 in urea-d4 adduct.

S. Kim et al. / Chemical Physics 323 (2006) 545–552 551

that n-paraffin molecules diffusing in a channel are collidingwith neighboring molecules. The diffusion coefficients forthe two diffusion components of n-C26H54in the urea-d4

adduct become constants at D = 40 ms, thus the diffusionis described by a single diffusion component, that is, thetwo diffusion coefficients for the fast and the slow diffusioncomponents are averaged out.

The above results show evidence of restricted diffusionbecause the n-paraffin molecules are confined in the ureachannel. In the case of a short diffusing-time D, the diffu-sion of the n-paraffin molecules in the outer parts and inthe inside part of a channel are observed to be different.With a suitably long diffusing-time D, the diffusions ofthe n-paraffin molecules in the outer parts and in the insidepart of a channel are observed to be averaged out.

4. Conclusions

It is concluded that n-paraffin molecules are diffusing inthe long urea channels of the urea-d4 adduct and have twokinds of diffusion components namely the fast diffusioncomponent (D � 10�10 m2/s) and the slow diffusion com-

ponent (D � 10�11 m2/s). Further, it is found that the chainlength dependence of D for n-paraffins in the urea-d4

adduct changes abruptly at the carbon number of 26.The diffusion coefficients (D) decrease as the carbon num-ber increases from 8 to 28, and very slowly decreases asthe carbon number increases from 28 to 32. From theexperimental results on the diffusing-time dependence ofthe diffusion coefficients, it is found that the n-paraffin mol-ecules in the urea-d4 adduct channels are diffusing in colli-sion with each other. Although it has been demonstratedthat the n-paraffin molecules are diffusing in the urea chan-nel, more detailed information on the mechanism of diffu-sion may be obtained by molecular dynamics calculations.

References

[1] A.E. Smith, Acta Crystallogr. 5 (1952) 224.[2] H.L. Casal, D.G. Cameron, E.C. Kelusky, J. Chem. Phys. 80 (1984)

1407.[3] J. Schmider, K. Mueller, Mol. Cryst. Liq. Cryst. 313 (1998) 277.[4] M.S. Greenfield, R.L. Vold, R.R. Vold, J. Chem. Phys. 83 (1985)

1440.[5] F. Guilaume, C. Sourisseau, A.J. Dianoux, J. Phys. (Paris) 88 (1991)

1721.[6] S.P. Smart, F. Guillaume, K.D.M. Harris, A.J. Dianoux, J. Phys.:

Condens. Matter. 6 (1994) 2169.[7] A. El Baghdadi, F. Guillaume, J. Raman Spectrosc. 26 (1995) 155.[8] A. El Baghdadi, Thesis, University of Bordeaux I, 1993.[9] R.L. Vold, R.R. Vold, N. Heaton, Adv. Magn. Reson. 13 (1989) 17.

[10] K.-J. Lee, W.L. Mattice, R.G. Snyder, J. Chem. Phys. 96 (1992) 9138.[11] M.D. Hollingsworth, K.D.M. Harris, Compreh. Supramol. Chem. 6

(1996) 177.[12] K.D.M. Harris, J.M. Thomas, J. Chem. Soc., Faraday Trans. 86

(1990) 2985.[13] N.G. Parsonage, L.A.K. Staveley, Disorder in Crystals, Clarendon,

Oxford, 1978.[14] J.D. Bell, R.E. Richards, Trans. Faraday Soc. 65 (1969) 2529.[15] F. Guilaume, C. Sourisseau, A.J. Dianoux, J. Chem. Phys. 93 (1990)

3536.[16] Y. Cho, M. Kobayashi, H. Tadokoro, J. Chem. Phys. 84 (1986) 4636.[17] M. Kobayashi, H. Koisumi, Y. Cho, J. Chem. Phys. 93 (1990) 4659.[18] K.A. Wood, R.G. Snyder, H.L. Strauss, J. Chem. Phys. 91 (1989)

5255.[19] F. Imashiro, D. Kuwahara, T. Nakai, T. Terao, J. Chem. Phys. 90

(1989) 3356.[20] T. Nakaoki, H. Nagano, T. Yanagida, J. Mol. Struct. 699 (2004) 1.[21] S. Kim, H. Kimura, S. Kuroki, I. Ando, Chem. Phys. Lett. 367 (2003)

581.[22] O. Redlich, C.M. Gable, A.K. Dunlop, R.W. Millar, J. Am. Chem.

Soc. 72 (1950) 4153.[23] H.G. McAdie, Candian J. Chem. 40 (1962) 2195.[24] E.L. Hahn, Phys. Rev. 80 (1950) 580.[25] O.E. Stejskal, E.J. Tanner, J. Chem. Phys. 42 (1965) 288.[26] P.T. Callaghan, Principles of Nuclear Magnetic Resonance Micros-

copy, Claredon, Oxford, 1991.[27] W.S. Price, Ann. Rep. NMR Spectrosc. 32 (1996) 51.[28] H. Yasunaga, M. Kobayashi, S. Matsukawa, H. Kurosu, I. Ando,

Ann. Rep. NMR Spectrosc. 34 (1997) 39.[29] R. Kimmich, NMR: Tomography, Diffusiometry, Relaxometry,

Springler, Berlin, 1997.[30] P.T. Callaghan, K.W. Jolley, J. Lelievre, R.B.K. Wong, J. Colloid.

Interf. Sci. 92 (1983) 332.[31] P.T. Callaghan, O. Sonderman, J. Phys. Chem. 87 (1983) 1737.[32] E. Fisher, R. Kimmich, U. Beginn, M. Moeller, Phys. Rev.(E) 59

(1999) 4079.

552 S. Kim et al. / Chemical Physics 323 (2006) 545–552

[33] S. Matsukawa, I. Ando, Macromolecules 29 (1996) 7136.[34] S. Matsukawa, H. Yasunaga, C. Zhao, S. Kuroki, H. Kurosu, I.

Ando, Progress in Polymer Science 44 (1999) 995.[35] Z. Gao, S. Schlick, S. Matsukawa, I. Ando, G. Rossi, Macromole-

cules 31 (1999) 8124.[36] H. Yamakawa, S. Matsukawa, S. Kuroki, H. Kurosu, I. Ando, J.

Chem. Phys. 111 (1999) 5129.[37] Y. Yin, C. Zhao, S. Kuroki, I. Ando, J. Chem. Phys. 113 (2000) 7635.[38] Y. Yamane, M. Kobayashi, S. Kuroki, I. Ando, Macromolecules 34

(2001) 5961.[39] Y. Yamane, M. Matsui, S. Kuroki, I. Ando, Polymer 43 (2001) 1767.[40] Y. Yin, C. Zhao, S. Kuroki, I. Ando, Macromolecules 35 (2002) 2335.[41] Y. Yin, C. Zhao, S. Kuroki, I. Ando, Macromolecules 35 (2002) 5910.[42] Y. Yamane, M. Kobayashi, H. Kimura, S. Kuroki, I. Ando, J. Appl.

Polym. Sci. 89 (2003) 413.

[43] Y. Yamane, M. Matsui, S. Kuroki, I. Ando, Macromolecule 36(2003) 5655.

[44] S. Kanesaka, H. Kimura, S. Kuroki, I. Ando, S. Fujishige, Macro-molecules 37 (2004) 453.

[45] K. Nagashima, V. Strashko, P.M. Macdonald, R.D. Jenkins, D.R.Bassett, Macromolecules 33 (2000) 9329.

[46] M.A. Winnik, S.M. Bystryak, C. Chassenieux, V. Strashko, P.M.Macdonald, J. Siddiqui, Langmuir 16 (2000) 4495.

[47] I. Ando, H.S. Gutowsky, J. Magn. Reson. 31 (1978) 387.[48] J. Karger, D.M. Ruthven, Diffusion in Zeolites and Other Micropo-

rous Solids, Wiley, New York, 1992.[49] N.Y. Chen, T.F. Degnan, C.M. Smith, Molecular Transport and

Reaction in Zeolites, VCH, New York, 1994.[50] C. Aslangul, Europhys. Lett. 44 (1998) 284.[51] A. Mueller, Proc. R. Soc. London Ser. A 138 (1932) 514.