Surface diffraction studies of 2D crystals of short fatty alcohols at the air-water interface

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Surface diffraction studies of 2D crystals of short fatty alcohols at the air-water interface

A. Renault, J. Legrand, M. Goldmann, B. Berge

To cite this version:

A. Renault, J. Legrand, M. Goldmann, B. Berge. Surface diffraction studies of 2D crystals of short fatty alcohols at the air-water interface. Journal de Physique II, EDP Sciences, 1993, 3 (6), pp.761-766.

�10.1051/jp2:1993165�. �jpa-00247869�

Classification Physics Abstracts

68.00 68.42

Short Communication

Surface diffraction studies of 2D crystals of short fatty ^alcohols

at the air-water interface

A. Renault

(~),

J.F.

Legrand

_(~)~ M. Goldmann

(~)

^and B.

Berge (~)

(~) Laboratoire de Spectromdtrie Physique, URAOB, Universit6 J. Fourier, B-P. 87, 38402 Saint Martin d'Hbres, France

(~) European Synchrotron Radiation Facilities, B-P. 220, 38043 Grenoble, France

(~)

PSI, Institut Curie, II _rue P, et M. Curie, 75005 Paris, France

(Received

9 April 1993, accepted 27 April

1993)

Abstract. Using X _ray surface diffraction _we have investigated crystalline monolayers of short alcohols

(1-decanol

to

1-tetradecanol)

at the air-water interface in the vicinity of the first order transition corresponding to 2D melting

(Tm(2D)).

The diffraction patterns in the solid phase _are in agreement ^with a 2D hexagonal close-packing- The lattice parameter ^value is 5.00 1 just below

Tm(2D)

and amounts 4.90 1 _at

Tm(2D)-20

K. The resolution limited Bragg peaks indicate _a large crystalline coherence length. At the approach of the 2D melting point, the observed increase of the Debye Waller factor is attributed _to critical fluctuations.

1 Introduction.

Since _a decade

Synchroton X-Ray

Sources have enabled to

investigate

the molecular _orga- nization of

amphiphilic monolayers,

at least when there is

long

_range two-dimensional order

[Ii. Among

the _numerous

phases existing

in theses

monolayers,

the most accessible to

X-Rays

studies is the

2D-crystalline phase,

which is also of interest in view of 2D

melting

theories [2].

Unfortunately,

in most studies of

Langmuir films,

the _presence of

impurities

tends to smear out the

thermodynamical

anomalies associated with the

phase

transitions and _to mask _some

tenuous aspects of 2D order.

We have

recently

found

amphiphilic monolayers showing

_very low

sensitivity

to

impurities.

These _are short chain

fatty

alcohols

(from

I-decanol to

I-tetradecanol) spread using

_a

special technique.

A

drop

of _pure alcohol is

deposited

_on clean water surface. After spontaneous

spreading,

the

equilibrium

situation at the surface consists in the coexistence of _a

monolayer

with the

excess of alcohol collected in _a lens which constitutes _a reservoir of molecules. This

results in _a

high

lateral pressure [3]. The reservoir compensates ^for _any loss of material in the

monolayer (evaporation, dissolution, X-Ray damage..)

and thus

permits

the _use of very short chains.

Using macroscopic techniques (ellipsometry

and surface pressure

measurements),

_our inves-

tigations

_[3] of short chain

monolayer properties

_{as a} function of temperature have revealed

a clear and reversible first order transition

(without

_any detectable

impurity effect).

In the

762 JOURNAL DE

PHYSIQUE

II N°6

present _paper, we show that it

corresponds

to _a 2D

crystallization-melting

transition from results of

X-Ray grazing

incidence diffraction in the low temperature

phase (T

_<

Tm(2D)).

After

presenting

the

experimental details,

_we describe the results

concerning

the I-dodecanol at room temperature ^{and the variation of the}

Bragg peak position

for different alcohols _versus temperature. We then discuss the

original

features of these systems and

particularly

their

long

range

crystalline

order in

comparison

with the results

published

_on

longer

chain alkanes and alcohols [4, 5].

2

Experimental

_part.

Our

experiments

_were carried out at the LURE

Synchrotron facility (Orsay)

_on the D24 beam line. A monochromatic

X-Ray

beam with _a

wavelength

^of1.49

1

_is selected

by

_a vertical

Ge(ill) crystal

with

asymmetrical

cut and

slight

curvature for horizontal

focussing

with _a

divergence

of I mrad. A silica mirror is used to deflect the beam down onto the water surface at an

angle

of incidence of IA mrad. Between the mirror and the

trough,

the beam is collimated

through

Huber slits with _a vertical

height

of100 _~tm and _a width of 5 _mm and the

intensity

of the incident beam is monitored with

an ionization chamber. Scattered

X-Rays

_are counted

by

a 5 _cm wide NaI scintillation detector rotated

azimuthally

about the

sample.

^Soller slits _are used for horizontal

collimation,

their full

angle

of acceptance is 2.6 mrad.

Thus,

the resolution in _q is about

10~~l~~(FWHM),

the

integration

_range

along

_{qz is} from 0 to 0.3

l~~

_due

to the vertical size of Soller slits.

The

experiments

have been

performed

in the _same conditions _as in reference [3]. ^{The five}

alcohols

(from

I-decanol CH3

(CH2)9

^{OH to} I-tetradecanol

CH3 (CH2)13 OH)

_were

obtained from Aldrich SA and used without further

purification.

For each

coumpound

above the 2D

melting point,

both the

monolayer

and the _excess

drop

of alcohol _are

liquid. Upon cooling,

the

monolayer

first

crystallizes

and about 10-20 K

below,

the _excess

drop

also freezes in [3]. ^{The difference between 2D and 3D}

melting

temperatures ^{is almost} constant

(15 K)

when the chain

length

is

larger

^than Cio. Table I

gives Tm(3D)

and

Tm(2D)

for the different alcohols.

Table I.

Melting point

of the bulk Tm

(3D)

and

monolayer

Tm

(2D)

for the different I-alcohols.

chain carbons number

9 2.0 -5.5

10 14.5 1.0

11

12 39.0 22.0

13 48.0 30.5

14 55.0 37.7

3. Results.

The

X-Ray

diffraction pattern of

CH3 (CH2)ii

OH

(I-dodecanol)

at the air-water interface

was measured at _room temperature.

Figure

I presents the results of _a wide _scan from

Q

"

I

l~~

to

Q

₌ 2.8

l~~

_{In this}

range,

only

_one diffraction

peak

is

observed, superimposed

_on

a diffuse

scattering background

from

underlying

water whose

intensity

decreases due _to the detection

geometry

^of the Sollers slits. The

single Bragg peak

visible in

figure

I at

QBragg

"

1.477

l~~

_suggests

an

hexagonal close-packing

^{of the chains without tilt}

angle

_[5]. This value

corresponds

to _an

hexagonal

cell parameters ahex " 4.91

1. Actually

it has

appeared

^{that the}

Bragg intensity

was

fluctuating

within _a few minutes of time. This has been attributed _to slow in

plane-motions

of

large (2D) crystals

which do not

produce

_a

good powder averaging.

This

difficulty

has been _overcome in

installing

a

rotating

stage ^{under the}

trough

to obtain _an orientational

averaging by

oscillations of + 30

deg.

For all

compounds

^{from I-decanol} to

I-tetradecanol,

^the diffraction

patterns

^{of the} mono-

layer

show the _same

single

_narrow

peak

whose FWHM is

equal

to the instrumental resolution

(10~~ l~~).

12000

ioooo

j

₈₀₀₀

I 6000

(

_{4000 *}

2000

o

I 1.5 2 2.5 3

Q(h'~)

Fig. 1. X-Ray diffraction pattern of1-dodecanol measured at room temperature ^for _a ^wide scan

from Q _"

l~~

to Q

" 2.8 J~ ^~

12000

ioooo ^°

/~

(

₈₀₀₀

,.1,

°

~ ..

i

# ^~°°° '

,

"~,.,

2

'&,~__("j.

_.. ...~

)

4000

~

2000

o

.44 1.45 1.46 1.47 1.48 1.49 1.5

Qih'~₎

Fig. 2. X-Ray diffraction patterns for 1-decanol at different temperatures.

(o)

for T

= 2.5

°C; (o)

for T

= 6.0

°C; jai

for T

= 9.0

°C;

_(ZL) for T

= 12.0 °C.

764 JOURNAL DE PHYSIQUE II N°6

Table II. The

peak position

_QBragg and the

hexagonal

cell parameter

(ahex)

of the different alcohols at 20 °C.

9 5.oo

lo melt 5,oo

ii 1.468 4.94

12 1.477

13 1.485 4.88

14 1.504 4.82

5

O

4.95

~

~

il ,, ~'~~

]~~

~'~ 4 9 , ~,'

~2 ^'' ~o°'

~_$_~,__,:°° ^~ ,~£.

'

~'~~

~''

,' h

4,8

40 35 30 25 20 15 10 5 0

T-T~(2D) ^(°c)

Fig. 3. The variation of hexagonal cell parameter

(ahex)

_{as a} function of

(T Tm(2D))

for all _even

alkyl chains.

(.)

for 1-decanol; _(E3) for 1-dodecanol; _{(ZL) for} 1-tetradecanol.

Figure

² shows the diffraction patterns ^{of I-decanol} at different temperatures ^below

Tm(2D)

in the

Q-range

of the

Bragg peak.

At each temperature ^the

profile

^is fitted

by

_a Lorentzian of fixed width for _more

precise

determination of the

Bragg angle.

It is visible in

figure

2 that upon

heating

the

peak position

_QBragg shifts to low values and that the

intensity

decreases

drastically

when

approaching Tm(2D)

₌ 14.5 °C. Above this temperature, there is _no

Bragg peak.

The

same behavior has been observed for I-dodecanol and I-tetradecanol. _For I-undecanol and

I-tridecanol,

the diffraction patterns ^{have been recorded}

only

at _room temperature. Table II

displays

the

peak position

_QBragg and the

hexagonal

cell parameter

(ahex)

of the different

alcohols in solid

phase

at _room temperature.

The variation of _ahex with both temperature and

length

of the

aliphatic

chains suggests to renormalize all the available data _{as a} function of T

Tm(2D).

Figure

3 shows the results for all _even

alkyl

chains. At

high

temperature all the

experimental points

_seem to merge on the _{same curve} with _a maximum cell

parameter

_ahex of

(5.00

+

0.01) 1

at the 2D

melting point

Tm

(2D).

We observe _a linear behavior between

Tm(2D)

and

Tm(2D)

10 K. However, the

experimental points

_escape from this linear behavior below Tm 10 K for

I-decanol,

below Tm -14 K for I-dodecanol and below Tm 18 K for I-tetradecanol. At these temperatures, the lattice parameters reach _a kind of

plateau

but at lower temperature, the

large

thermal

expansion

is

apparently

recovered. It is worth

mentioning

here that the

plateau

temperatures

roughly corresponds

to

Tm(3D) (see

^Tab.

I).

At this

point

^the _excess

drop

of alcohol

undergoes

_a

phase change affecting

the chemical

potential

_as observed in surface pressure measurements [6]. ^{One should recall that these results} concern

high

lateral _pressures.

For

example,

in the _case of

I-tetradecanol,

the lateral _pressure is about 205 bars at

Tm(2D), corresponding

to ahex " 5.00

I,

_{and 230 bars at}

_Tm(2D)

_{-10 K with}

ahex " 4.93

I.

4. Discussion.

In

(3D) crystals

of I-alcohols from C12 to C20> a

high

temperature

phase (a)

exists

just

below the

melting point

with the chains

packed hexagonally perpendicular

to the basal

plane

_[7].

For

(3D) tetradecanol,

the

hexagonal

cell parameters ahex " 4.86

I

_{at 37.6}

_°C,

a value rather close to that

reported

here for

(2D)

tetradecanol

(ahex

" 4.88

I

_{at 36.8}

°C).

It is also inter-

esting

to compare these values to the

hexagonal

cell parameters of alkanes in "rotator II"

phase namely

4.77

1for (3D)

C22H46 at 43 °C [8] ^{and 4.79}

I

_for

(2D)

C20H42 at 37 °C [4]. It is remarkable that the

(3D)

and

(2D)

cell

parameters

are very similar for the _same chain

length, although

in the latter _case the

monolayer experiences high

lateral _pressure [3,

4].

^{For all these}

"rotator

[["structures,

_as in _{our case a}

single (10)

reflection is observed and neither the

(11)

not the

(20)

reflections _are detected. Calculations of the structure factor of the

rotating alkyl

chains

give only

_a ratio of the intensities

1(10)/1(11)

₌ 5 and

1(10)/1(20)

= 6.5. It should be recalled that the

intensity

at

large angles

_can be reduced

by

the

polarization

factor

(for

scattering

in horizontal

plane)

and

by

the

Debye

Waller factor. From _our measurements, _we

can estimate that the ratio

1(10)/1(11)

is

larger

than 20. This

implies

_a temperature ^factor B

(=

8~~ _< u~

>)

>

301~.

As

previously mentioned,

the width of the diffraction

peaks, being

resolution

limited, gives

a lower bound for the translational correlation

length (()

of about 2000

I.

_{For the}

_particular

case of

I-dodecanol, using

_a direct observation based _{on a} low resolution

imaging ellipsometry technique

[9], we have observed

growing crystallites

of millimeters size. This size is confirmed

by

the fact that the

monolayer

does _not realize _a

good powder averaging.

It remains that these

alcohol

monolayers

^exhibit a

high crystalline

order in _two dimensions _even close _to the

melting point

where _no

broadening

of the

Bragg peaks

is detected.

We observe several indications of critical fluctuations. First _we

already

noted the

high Debye-Waller

effect

leading

to the

suppression

of the

(11)

and

(20)

reflections. Let _us recall that in 2

dimensions,

for each temperature in the

crystal phase,

there is _a momentum transfer Q* ^above which true

Bragg scattering

is

suppressed by Debye-Waller

effect [10].

Following

these

references,

Q* can be written _as

(Q*)~

"

(kBT) /(4~Ge)

in which T is the temperature, ^G is the

in-plane

shear modulus and _e is the thickness of the

monolayer.

To estimate Q*> we determine

an order of

magnitude

of the shear elastic constant G

=

((Cl1 C12) /2) by assuming

that the variation of _{ahex comes} from the lateral _pressure variation taken from reference [3]. ^From the observed inversed

compressibility (Gil

+

C12)

_" ahex

(dp/dahex)

_" 1.8 _x 10~

N/m~,

one can

estimate _an order of

magnitude

for G. Indeed _as observed in _many alkane and

polymer crystals

the ratio of elastic constants

perpendicular

to chain axis

C12/Cii

of the order of 0.6

[1Ii.

This

gives

_a G value of the order of 0.3 _x 10~

N/m~

which

corresponds

to Q* _~J 1.4

i~~,

an order of

magnitude

which is in the

good

_range to

explain

the absence of

high

order reflections.

Second,

the

Debye-Waller

factor of the

(10)

^reflection is

strongly

temperature

dependent,

the

intensity

of the

Bragg peak decreasing

when

approaching Tm(2D), indicating again

the _presence of critical fluctuations

and/or

the decrease of the shear modulus. Note also in the

figure

I that

the

shape

of the

(10)

reflection suggests ^{thermal diffuse}

scattering by

soft transverse acoustic modes.

Third,

_we have observed fluctuation effects

by ellipsometry just

above

Tm(2D),

in the 2D

liquid

phase,

these effects

increasing

when the chain

length

is

decreasing.

766 JOURNAL DE PHYSIQUE II N°6

All this indicates that the

phase transition, although unambiguously

of first order

character,

is not far from

being

_a second order continuous

phase

transition. Current 2D

melting

theories of

point-like particles predict

continuous

phase

transitions between 2D

crystalline,

2D hexatic and 2D

liquid phases

_[2]. For the

arnphiphilic monolayers,

additionnal

degrees

of

freedom,

due to the chains

(possible

^tilt and conformational

changes),

are

coupled

to the translational

degrees

of freedom. Due to this third

dimension,

the

melting

^{also involves} a contribution of the conformational entropy ^{of the chains which} can drive the

phase

transition to the first order

one. This is consistent with the observation of _a

discontinuity

of the thickness

increasing

with the chain

length

_[3].

5 Conclusion.

We have shown in this _paper that

monolayers

of

fatty

alcohols between I-decanol to I- tetradecanol

crystallize (under

lateral

pressure)

at the air-water interface in _a

hexagonal

"ro- tator II"

phase

with

high Debye

Waller factors.

Nevertheless, they

show

large

translational

correlation

lengths

_even close to the 2D

melting point

in agreement ^with

optical

observations of the

growth

of

large crystals.

We observe _a

good

coincidence between 3D and 2D

hexagonal

structures and _{a common} temperature

dependence

of the 2D cell parameter as a function of

(T Tm(2D)), Concerning

2D

specific

aspects, _we have observed

strong

fluctuation effects like the increase of the

Debye-Waller factor,

close to the 2D

melting. Finally,

several indications

show that the first order character of the

melting

transition could be due to the

coupling

with the internal

degrees

^of freedom of the chains.

Acknowledgements.

We thank Dr C.

Williams,

M. Lemonnier

(LURE, Orsay)

and Pr. J.

Lajzerowicz (Univ.

J.

Fourier)

for fruitful discussions. We

acknowledge

Dr C.

Bourgaux

and P. Vachette and the staff of

LURE, Orsay, France,

for Beam time.

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