Diffusive motions in 2D phases of ethane adsorbed on graphite

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Diffusive motions in 2D phases of ethane adsorbed on graphite

J.P. Coulomb, M. Bienfait

To cite this version:

J.P. Coulomb, M. Bienfait. Diffusive motions in 2D phases of ethane adsorbed on graphite. Journal

de Physique, 1986, 47 (1), pp.89-95. �10.1051/jphys:0198600470108900�. �jpa-00210187�

Diffusive motions in 2D phases of ethane adsorbed on graphite

J. P. Coulomb and M. Bienfait

Faculté des Sciences de Luminy, Département ^de Physique (*),

Case 901, 13288 Marseille Cedex 9, ^France

(Reçu ^le 22 juillet ^1985, accepté ^{le 25} septembre 1985)

Résumé.

On étudie ici, par diffusion quasi-élastique ^{de neutrons, entre 5 et 122 K, la} mobilité diffusive rota-

tionnelle et translationnelle d’une molécule simple allongée, l’éthane ^adsorbé

^{les faces} (0001) ^du graphite. ^Le

mouvement des molécules arrangées dans deux réseaux typiques bidimensionnels (2D)

^été analysé. ^{L’un des} solides, S1’ présente

^structure

^chevrons

^{molécules couchées}

la surface du graphite. L’autre, S3,

est plus ^{dense et est} constitué de molécules debout

la surface adsorbante. Quand

augmente ^la température,

on

observe

transition rotationnelle

de laquelle ^les molécules des deux solides subissent

mouvement de rotation uniaxial autour de leur

carbone-carbone. Les temps caractéristiques ^de

^{rotations ont} été mesurés.

A plus ^haute température, ^{les solides} S1 ^et S3 fondent. Les molécules de S3 conservent leur mouvement de rotation uniaxial auquel

superpose

diffusion brownienne dont le coefficient de diffusion varie de 2 à 14 x 10-6 cm2. s-1

entre 87 et 122 K. Par contre, les molécules de S1 effectuent

mouvement de rotation isotrope auquel s’ajoute toujours

diffusion brownienne dont le coefficient de diffusion varie de 0,4 ^{à 50}

10-6 cm2. s-1 entre 71,4 ^et 122 K. L’énergie d’activation de translation correspondante ^est de l’ordre de 1,4 ^kcal. mole-1. Ces résultats sont

comparés ^à

^{décrivant la mobilité de} l’éthane dans

diverses phases tridimensionnelles.

Abstract.

The diffusive rotational and translational mobility ^of

simple ^rod-like molecule, i.e. ethane (C2H6)

adsorbed

graphite (0001), ^{has been studied} by quasi-elastic ^neutron scattering, between 5 and 122 K. The motion of the molecules packed ^{in two} typical two-dimensional (2D) solids has been investigated ^{One solid} (S1)

has

herring-bone ^{structure with molecules} lying ^down

^the graphite substrate. The second solid (S3) ^of higher density ^is made of molecules standing ^up

^the adsorbing surface. With increasing temperature,

^rotational transition is observed, between the rotationally ordered solids and 2D crystals ^{where the} C2H6 molecules exhibit uniaxial rotations about the C-C axis. The characteristic times for these rotations have been measured. At higher temperatures, ^the S1 ^and S3 ^solids melt The molecules in the higher density phase keep their uniaxial rotational motion and in addition exhibit

Brownian diffusion with diffusion coefficient ranging ^{from 2 to 14 x 10-6 cm2. s-1}

at 87 and 122 K respectively. ^{For the} S1 melted ^{solid, the} rotational motion becomes isotropic ^{and the diffusion}

coefficient ranges from 0.4

10-6 Cm2.s-1 at 71.4 K to 50

10-6 cm2 . s-1 at 122 K. The activation energy of translational diffusion is about 1.4 kcal. mole-1. These results

compared ^{with the} mobility ^of C2H6 ^{in its bulk} phases.

Classification Physics ^Abstracts

68.30

61.12

68.15

1. Introduction.

Relatively few studies of the diffusive motions (rotation

and translation) of molecules adsorbed on surfaces have been published ^{so far. Most of them deal with} mobility measurements of quasi-spherical ^molecules

like CH4 ^{[1-7] and iron or tin} tetracarbonyl compounds [8-10] ^{adsorbed on} graphite. ^{To our best} knowledge, only preliminary mobility measurements have been

performed ^{on a} rod-like molecule [11] namely ethylene

adsorbed on graphite. Here, ^we present

^obser- vations on the molecular mobility of the various

phases of ethane adsorbed on graphite ^{in the mono-} layer range. This system ^{has numerous} advantages.

Detailed structural analysis ^has been carried out and several solid and liquid-like phases ^{have been observed}

In particular, ^two solids with

low-density (Sl) ^{or a} high-density (S3) packing ^{have been} identified [12,13].

They ^exhibit structures on the surface with molecules

lying ^{down or} standing up respectively. ^{These con-} figurations ^are quite typical for rod-like adsorbed molecules [14]. Hence ethane adsorbed on graphite

is

prototype ^{for the} behaviour of non-spherical compounds condensed in surface films. In addition, hydrogen containing molecules have a strong ^inco- herent neutron cross-section and are good ^candidates

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198600470108900

90

for quasi-elastic ^neutron scattering experiments ^which probe ^the surface motions of the molecules [1-3, 11].

Finally, ^the 81 (lying ^{down) solid has}

configuration

similar to the (110) ^and (101) planes of the monoclinic

crystal ^of bulk ethane [15] whereas the S3 (standing up) ^{solid has no} corresponding ^bulk structure. These observations raise the question ^{of the} perturbation

of the molecular rotational motion (if any) by ^the

surface field of the substrate.

In this _paper, we present ^a systematic study ^{of the}

variation of the degrees of freedom of the C2H6

adsorbed molecules as

function of temperature ^and density (coverage). ^We address the problem ^{of the}

different kinds of rotational (uniaxial, isotropic)

motion of the molecule at low temperatures ^{and the} influence, ^at higher temperatures upon melting, ^{of the}

surface periodical potential ^on the translational

mobility. ^{Our aim is to} analyse the various diffusive motions of this typical rod-like molecule in the dif- ferent 2D phases which have been described in the literature and to compare them to the dynamics ^of

bulk ethane.

To clarify the aim of

study, ^we present ^the phase diagram of ethane adsorbed on graphite in the sub-

monolayer range in figure ^{1. At low} T, ^{one sees the} various stability domains of the Sl’ lying ^down, herring-bone ^structure (Fig. 2a), ^{of the} S3 standing up

packing (Fig. 2b) ^{and of an} intermediate solid (S2)’

The structure of the last phase ^{has not} yet ^been resolved. The sketches drawn in figure ² represent the static structures obtained by diffraction ^measu-

rements [12]. The rotational order of these solids is

anaiysed ^{here. Above 60-65} K, ^{the solids melt and} give

rise to the so-called 11 ^and 12 phases ^{which were once}

believed to be short _range ordered solids [12]. Very recently [13], it has been shown that I1 is instead a

lattice fluid continuously losing ^its positional ^and

bond orientational orders ^with increasing temperature.

Fig. ^1.

Proposed phase diagram ^{of ethane} monolayer

adsorbed

graphite from reference [13]. The static confi- guration ^of S1 ^and S3

represented ⁱⁿ figure ^2.

Fig. ^2.

a) ^In S,, ^the C2H, molecules lie down

the

graphite substrate in

herring-bone structure. b) ^In S,,

the C2H, molecules stand _up

graphite (0001) (from

Ref. [12]).

Hence, another motivation of this study ^{is to} specify

the nature of the 11 phase. ^{At still} higher temperatures,

a

2D isotropic liquid ^{L is stable} and, ^{above the 2D} critical temperature Tc ~ ^{130 K} [16], ^the graphite

surface is occupied by ^{a 2D} hypercritical ^{fluid F.}

Sixteen quasi-elastic ^neutron scattering ^{sets of}

measurements at different _coverages and temperatures have been carried out. They ^{are indicated} by ^{stars in}

the phase diagram ^of figure ^{1 and are} reported ^and analysed ^below.

2. Experimental.

The experimental conditions of quasi-elastic ^neutron scattering ^{studies of} hydrocarbons ^{adsorbed on} gra-

phite ^{have been} reported ^at length in several papers

[1, 3, 17] published by ^our Laboratory. ^In brief, ^the

measurements have been carried out at the Institute

Laue-Langevin (I.L.L.) ^{in Grenoble with the time-of-} flight spectrometer ^{IN5. The} incident wavelength ^was

8 A (Eo

^1.278 meV) ^{for this} experiment. ^Twelve

detectors were used at various scattering ^vectors Q

ranging from 0.34 to 1.44 A -1. The instrumental

resolution has

triangular shape ^with

^{FWHM of}

35 pev. Since the cross-section of hydrogen (~ 80 barns) ^{is more than an order of} magnitude larger ^{than that of} carbon, ^{in this} experiment

^are probing the motion of hydrogen ^atoms only.

The substrate was

powder ^of recompressed ^exfo-

liated graphite ^called papyex. Its large specific ^area (~ ²⁰ m’/cm’) makes it suitable for neutron scattering

studies of two-dimensional phases. ^{It exhibits-}

preferential alignment of the basal planes (0001) parallel ^{to the} plane of the foil. The neutron experi-

ments were performed ^{with the} scattering ^vector Q parallel ^{to this} plane.

The _coverage calibration was obtained by combining adsorption ^isotherm measurements and LEED and neutron diffraction experiments. ^{In this} paper,

follow the definition of the _coverage 0 given ^{in refe-}

rence [13], namely, ⁰⁼¹ corresponds ^{to the mono-} layer completion with the densest phase S3. ^·This

definition is used to draw the phase diagram of figure ^1.

As usual in this type ^of experiment, ^the scattering

from the adsorbed films was obtained by taking ^the

difference between counts with and without ethane in the sample cell. The spectra ^were corrected for

absorption ^and self-shielding ^and normalized with respect ^to each other by comparison ^with

^vanadium

standard

3. The models.

The scattering ^law S(Q, w)

be calculated explicitly

in the quasi-elastic region ^{if it} may be assumed that the translational motions, the molecular rotations and the various vibrational modes are uncorrelated

[18-21]. ^Then S(Q, w) ^{is the} convolution (*) ^{of the} translational St ^and rotational Sr components ^{of the} scattering law, multiplied by ^the Debye-Waller ^factor

where hm

E - Eo ^{is the} gain ^{or loss of} energy with respect ^to the incident _energy Eo, ^and

^{is the} eigen-

vector describing ^the internal molecular vibrations.

The translational component ^is

Lorentzian func- tion

whose width f(Q) ^{is model} dependent (see 3.2).

The _pure rotational scattering ^law may be written

as

where the Elastic Incoherent Structure Factor (EISF) [20-22] Ao(Q) ^{is an} important ^{term for the} experimental analysis. ^It has tractable analytical ^{forms for} simple

models. Fr(Q, ill) ^is usually

^sum of Lorentzians and

depends

^the types of rotational diffusion (uniaxial rotation, isotropic rotation,..., ^see 3.2). ^{The total}

scattering ^{is then}

In equation (4),

dropped ^the Debye-Waller ^factor

because its contribution to the total scattering ^law

is only

^few % ^{and is} comparable, ^{in our case, to the} experimental uncertainty (see ^{for instance in} figures ³

and 5, ^{the low T} data for which all diffusion motions

are frozen).

The reduction of the data is usually ^{done in two}

steps. First, ^the geometry of the bound motions is obtained from the analysis ^{of the term} Ao(Q) (EISF).

Then, ^{the whole} experimental scattering law is tested

against ^models combining rotational and transla- tional motions.

3.1 EISF.

Analysis of the Elastic Incoherent Scat-

tering ^Factor provides

powerful ^{means of distin-} guishing between different types of rotational motion.

The EISF is the fraction of the total quasi-elastic intensity ^{contained in the} purely translationally

broadened term [20-22]. When molecules undergo

rotations only, the EISF is the fraction of the intensity

contained in the central peak which is broadened by

the instrumental resolution.

Typical ^EISF corresponding ^to different diffusive rotational models are represented ⁱⁿ figures ^{3 and 5.}

As seen in the figures, appreciable difference between the uniaxial and isotropic models of rotation is apparent ^at large scattering ^vector only. ^{As an illustra-} tion, ^the analytical ^{forms for}

model where ethane molecules are allowed to perform ¹²⁰⁰ jumps ^about

their C-C axis (uniaxial rotation) ^and

model where the protons

moving ^on the surface of

sphere (isotropic rotation) ^are respectively [23, 22]

where jo ^{is the} spherical ^Bessel function of zero order and a is the appropriate ^{radius of} gyration (1.019 A

for the uniaxial rotation and 1.55 A for the isotropic rotation).

Other expressions ^{are available} for other uniaxial rotation models. For instance, ^the scattering ^{laws for}

rotation with 600 jumps

continuous rotation about the C-C axis are given in references [24] ^and [18] ^res- pectively.

3.2 SPECTRA ANALYSIS. - After’using ^the (relative) integrated ^central part ^{of the} experimental intensity (EISF), ⁱⁿ determining ^the type of rotational motion, the whole spectra ^are analysed ^to obtain the value(s)

of the diffusion coefficients) ^or of the characteristic

time(s) ^{of the} motion(s). ^In practice, ^the scattering ^law

(Eq. (4)), with the proper expression ^for S,(Q, w),

F,(Q, w) ^and Ao(Q) ^is compared ^{to the} experimental

92

data. As stated above, ^{for each} experimental ^condition ( T, 0), ^{a set of 12} spectra ^{are tested} against equation (4) averaged ^over the surface distribution of the graphite powder [17] and folded in with the instrumental resolution.

All of the models describing translational diffusion have the same limit at small Q. ^In equation (2), f(Q)

tends to D, Q2 ^with D, the translational diffusion coefficient [20-22]. ^The proton ^{is said to} obey

Brownian motion. The various models of translational motion can only be differentiated ^at large Q. ^For instance, ^{if molecules are allowed to} jump ^between

well-defined lattice sites, f(Q) ^{has first}

^maximum

and then drops ^{towards a minimum at} Q ~ ² n/d,

where d is the distance between sites [22, 25].

The contribution of rotational motions Fr(Q, w)

has different analytical expressions ^{which are model} dependent. They ^can be found in references [18, 20-24].

We do not wish to duplicate them here because they

are somewhat complicated. They depend only ^{on an} adjustable parameter ^{which is called} the rotational diffusion coefficient Dr ^{or the mean} residence time

A table with the expressions ^for Fr(Q, m) used in this paper ^can be found in reference [ 17].

4. Results.

4.1 S 1, 11 ^{AND L PHASES.}

^The mobility ^{of the low} density S1, I1 ^{and L} phases ^have already ^been analysed

in a previous paper [17]. The main results are sum-

marized here and are completed ^{with a} measurement of the temperature dependence ^of the translational diffusion coefficient for the 11 phase.

The rotational motion of the ethane molecule

depends strongly ^on temperature. ^{This is} clearly

evident from figure ³ where the EISF for various ^T and 0 are represented. ^{In the low T} regime, ^the S1 phase ^{exhibits a} herring-bone ^structure (Fig. 2) ^with

molecules lying ^{down on the} graphite ^surface. Figure ³

shows that, ^{at 10 K} (0

0.4), the ethane molecules do not exhibit _any diffusive rotational motion. The

slight decrease in intensity ^with Q corresponds ^{to an}

usual Debye-Waller ^{factor, i.e. to the} scattering

attenuation due to vibrations. At 53.5 K (0

0.54),

the variation of the EISF is consistent with an uniaxial rotation of the methyl groups about the C-C axis [17].

Three models of hindered uniaxial rotation (rotation

with jumps ^{of 600 or 120°, or rotation without} jumps)

have been tested against ^the experimental ^data. They

are all in agreement ^{with our} experimental ^{EISF at}

53.5 K. The theoretical EISF for the three models differs appreciably from each other only for Q > 2 Å-1 [23, 24],

scattering ^vector range where no measure- ment was performed because of the weakeness of the scattered intensity ^at very large Q. ^{Hence our data}

are unable to distinguish between the above models.

Still, the EISF for an isotropic ^{rotation is} significantly

different from the uniaxial rotation (Fig. 3) ^observed

within our experimental range.

Fig. ^3.

^{EISF for} 11 ^and S1 phases. The full line

ponds ^to

isotropic model of rotation (Eq. (6)) ^whereas

the dotted line corresponds ^to

uniaxial model of rotation of the C2H6 molecules about their C-C axis (Eq. (5)). 0

0.4,

T

10, ⁸⁷ K; 0

0.54, ^T

53.5, 66.4, 71.4, 76.2, ^{84.1 K.}

At 66.4, 71.4, 76.2, ^{84.1 K} (0

0.54) ^{and 87 K} (0

^{0.4 and} 0.63), i.e. in the I1 stability domain, ^the experimental ^{EISF is} consistent with an isotropic

model of rotation (and inconsistent with ^an uniaxial

rotation). Furthermore, ^{the measured} spectra ^{have a} translational component ^which obeys

jump ^trans-

lational model [17]. ^{The observed lattice} liquid ^is

consistent with LEED findings showing ^a strongly

correlated liquid ^{both in} position ^and orientation.

The broad wings of all the spectra between 66.4 and 87 K have been interpreted ^with

single ^rotational (isotropic) diffusion coefficients Dr

(5 ± 1) .010 ^s-1 (at ¹²² K, ^the translational contribution is so broad that it prevents ^{us from} extracting ^out any information from the rotational component). The translational motion can be characterized at small Q by ^{a transla-}

tional diffusion coefficient Dt whose values

given

in figure ^{4 as}

function of 1/T (see ^{also Table} I).

The uncertainty ^{at 71.4 K and below} is rather large

because the experimental broadening ^{is close to or}

smaller than the experimental resolution. However, the data at 122, 87, 84.1 and 76.2

precise enough

to estimate the activation _energy of diffusion, ^i.e.

AH* -- 1.4 kcal . mole-1,

^{value to be} compared

Table I.

Rotational diffusion coefficient Dr for ^{the isotropic motion} of ^the C2H6 ^{molecule in the} 11 phase, ^and

translational diffusion coefficient Dt ^{in the same} phase for different ^coverages and temperatures.

Fig. ^4.

Translation diffusion coefficient D, ^{in the} Ii phase

1/T .

to the latent heat of vaporization ^{of the 2D} liquid ^{in the} monolayer range [16], åHvap(2D)

^5.8 kcal . mole-1.

The obtained value is in agreement ^{with the} empirical

rule deduced from bulk data for short chain hydro-

carbons [26], namely ^the activation _energy of diffusion is about one fourth of the latent heat of vaporization AH,ap(3D).

4.2 THE S3 SOLID AND ITS CORRESPONDING LIQUID.

As recalled in the introduction, ^{molecules in the} S3

solid stand _up on the graphite ^surface (Fig. 2). ^This

structure has been studied in detail by ^{neutron dif-}

fraction [12, 27, 28] and it has been shown that its

stability domain extends

large range of _coverage above 0=1 and below - 85 K (2D melting point).

Seven sets of twelve quasi-elastic spectra ^{have been} recorded for 0 ~ 1.3 at 5, 20, 30, 57, 67, ^{87 and 122 K.}

The corresponding ^EISF

represented ⁱⁿ figure ^5.

They show that for T 57 K, the rotational motion of the molecule is frozen. At 67, ^{87 and 122} K, ^the methyl groups perform ^an uniaxial rotation about the

Fig. ^5.

^{EISF for} S3 ^{and its} corresponding ^melted phase.

The meaning ^{of the}

is indicated in figure ^3.

C-C axis. It must be pointed ^{out that the} degrees ^of

freedom of the molecule ^are limited even above the 2D

melting point (85 K). ^{This means that the} C2H6

molecules keep ^their

standing up

position ^{in the}

dense liquid film; they ^{rotate around an axis} perpen- dicular to the surface and perform

random ^trans-

lational motion. The corresponding characteristic time T for the uniaxial rotation and the associated diffusion coefficient Dt for the translational motion

can be determined from

fit of the whole measured

spectra. ^{As an} illustration, ^several among the 12 record-

ed scattering ^{laws at 87 K are} represented ⁱⁿ figure ⁶

together with the calculated spectra ^{as well. The}

rotational component ⁱⁿ equation (4) corresponds ^tao

94

Fig. ^6.

^{Set of measured} scattering ^{laws of ethane adsorbed}

on

graphite for various scattering ^vectors Q. ^T

⁸⁷ K, 0 = 1.3, Q

0.34, 0.61, ^{1.11 and 1.36} A-1. The full line represents the best fit with equation (4) folded in with the instrumental resolution. The dotted line corresponds ^{to the}

rotational component ^{of the} scattering ^law.

a

model where the methyl groups perform ^rotational jumps of 1200 about the C-C axis. The time needed to perform ^this jump is assumed to be infinitely ^short.

The molecules remain in an equilibrium position during ^an average time

At 87 K, ^our best fit is obtained for

7.5

10-12 s. Any other reasonable uniaxial model (see 4.1) gives ^also

good agreement in the entire experimental range (Q ^1.5 A-1) ^and

the obtained residence time is close to the one deter- mined above. As for the translational component,

we

use

Brownian motion model and obtain Dt

(2 ± 0.2).10-6 ^{cm2. s-1 from the fit. It} is worth notic-

ing ^two points : i) ^{our data cannot} be fitted with an

isotropic rotational model; ^as

consequence, ^our

analysis demonstrates the existence of this

uniaxial » 2D liquid ^whose properties ^are probably ^{close to those}

of liquid crystals; ii)

^{data at} large Q ^{are not} precise enough ^to decide whether the molecules

perform jumps ^{between lattice sites} (see ^{3.2 and} 4.1) because of ^a _poor correction of the counter efficiency

above Q - ¹ Å-1. _Still it seems that the experimental broadening ^{of the} spectra is smaller than the extra-

polated D, Q 2 law. This could be an indication of the existence of

strongly correlated liquid.

The values obtained for r and Dt ^{in the} temperature

range where diffusive motion has been measured are

given ^{in table II.} The absence of any measurable translational mobility ^{at 67 K} (Dt 10-’ cm2 . s- 1)

is in agreement ^{with the} observation of

narrow neutron diffraction peak ^{due to}

^{solid at this tem-}

perature [27-28].

Table II.

Rotational residence time

and transla- tional diffusion coefficient Dt for ^the S3 phase (coverage

-

1.3) ^{and its} corresponding liquid ^{at three} different

temperatures.

5. Discussion

Our quasi-elastic ^neutron scattering measurements have shown that, ^as expected, ^at very low temperature the ethane molecules condensed on graphite ^{do not} undergo any diffusive motion. Uniaxial rotational transitions occur between 57 and 67 K for the S3 ^solid (standing up molecules) and between 10 and 53.5 K for the S 1 ^solid (lying ^down molecules). The observed lower temperature for the rotational onset in the S,

solid is probably ^{related to its structure which is more}

open than that of S3 (see Fig. 2).

At higher temperature, ^when the solids

melted,

the C2H6 molecules still perform

uniaxial rotation about the C-C axis in the surface liquid corresponding

to S3 ^whereas they perform ^an isotropic ^rotational

motion in the 11 phase, i.e. in the corresponding

S1 » liquid This is also probably ^{due to the more} open nature of the S i ^solid.

In these melted films, translational mobility ^mea-

surements show that the diffusion coefficients _vary, at constant temperature, ^{with the nature of the 2D} liquid. ^For instance, ^{at 87} K, Dt changes ^{from 5}

^10-6

to 2

10-6 cm2 . s-1 in the 1, and the melted

S3 » phases respectively. ^This observation is a common-

place effect; ^the viscosity of the film increases with its

density (in passing, ^{it is} noteworthy ^{that neutron}

spectra have been also recorded in the S2 ^and 12 phases. They ^{are not} reported here because the lack of structural information makes their interpretation

less reliable).

Comparison between the observed rotational and translational mobilities in surface C2H6 films and the

corresponding motions in bulk matter is also interest-

ing. The diffusion coefficient in the liquid ^bulk é2H6

has been measured between 123 and 298 K [29, 30].

At 123 K, ^{one has} Dt = ^1.5

^{10-5 cm2 . s-1 [30]}

to be compared ^to D,

⁵

10-5 cm2 . s-1 at 122 K in the 2D liquid Hence the reduced dimensionality

and the graphite surface field do not change very much the translational mobility of the molecule.

As in S, ^and S3 ^{solids, the} C2H6 molecules lose their rotational order in bulk crystal. ^For instance,

at 54.5 K, ^the methyl groups perform 1200 rotational

jumps ^about the C-C axis. The residence time in the

equilibrium position ^{is 6 x 10- 9}

[23]. ^{The cor-} responding residence time at 53.5 K for the S, ^struc-

ture is 5

10 - 11 s [17]. As recalled in the introduction,

the S1 configuration ^{is close to the} packing ^{of the} (110)

or (101) planes ^{of bulk} crystal. Hence, the dramatic increase of the rotation rate in the Si crystal ^observed

at about the same temperature ^is probably ^related

to the fact that the motion of the ethane molecules is not hindered in the direction perpendicular ^{to the} graphite surface. On the other hand, ^{at the same} temperature, ^the S3 ^solid keeps its rotational order.

In this structure, ^the density ^is larger than in bulk and the molecular arrangement ^{has no} equivalent ^{in three}

dimensions. All of the C-C axes are aligned ^and perpendicular ^{to the} graphite ^surface (see Fig. 2b)

and the rotational motion is probably ^locked by

gear-wheel effect. This S3 ^o standing up » ^structure

seems very stable because _upon its melting ^it keeps

a

coherence length of several tens of A [27, 28] ^and

retains an uniaxial rotational motion.

The liquid I 1 corresponding ^to the melted Si ^solid

exhibits also peculiar ^{surface induced} properties.

In this 2D liquid, ethane molecules jump continuously

between graphite lattice sites thus depicting

physical

realization of a 2D lattice _gas or lattice liquid.

Acknowledgments.

The experiment ^was performed ^{at the neutron} high

flux reactor I.L.L., ^{Grenoble. We wish to thank P.}

Thorel for his help during ^the experiment ^{and the}

IN5’s staff for its technical assistance. We are also

grateful ^{to F. Volino, J.} Suzanne and J. M. Gay ^for illuminating discussions and to J. Krim and J. G. Dash for critically reading ^the manuscript.

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