A light scattering study of thermotropic transitions of monoglyceride monolayers : influence of molecular area fluctuations

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A light scattering study of thermotropic transitions of monoglyceride monolayers : influence of molecular area

fluctuations

J.F. Crilly, J.C. Earnshaw

To cite this version:

J.F. Crilly, J.C. Earnshaw. A light scattering study of thermotropic transitions of monoglyceride monolayers : influence of molecular area fluctuations. Journal de Physique, 1987, 48 (3), pp.485-494.

�10.1051/jphys:01987004803048500�. �jpa-00210464�

485

A light scattering study ^of thermotropic transitions ^of monoglyceride monolayers : influence of molecular area fluctuations

J. F. Crilly (*) ^{and J. C. Earnshaw} (+)

Department of Pure and Applied Physics, ^{The Queen’s} University ^of Belfast, ^{Belfast BT7 1} NN,

Northern Ireland

(Reçu ^{le 11} juin 1986, révisé le 6 octobre, accepté le 6 octobre 1986)

Résumé.

On étudie la viscoélasticité de surfaces liquides supportant des monocouches d’oléate de glycérol par

spectroscopie de corrélation de photons. ^Les transitions de monocouches entièrement comprimées ^{sont étudiées en}

détail. En mesurant les variations de la tension superficielle ^et du module de dilatation, ^on peut évaluer les

amplitudes relatives des fluctuations d’aire moléculaire. Les monocouches se comportent différemment suivant

qu’elles ^{ont été} formées à des températures supérieures ^ou inférieures à la transition thermotrope. ^{Pour une}

monocouche complètement comprimée dans l’état basse température, ^les changements ^{à la} transition sont faibles

(fluctuation 2014 ^{8,4 % de l’aire} moyenne). ^{Pour un} film entièrement comprimé ^{à des} températures supérieures ^{à la}

transition des lipides, ^les changements ^sont beaucoup plus importants (fluctuation jusqu’à ^{95 % de l’aire} moyenne).

Les variations en température ^{sont aussi} quelque peu différentes, quoique dans les deux cas les transitions aient lieu entre 15,3 ^et 16,5 °C. On discute l’origine moléculaire de ces différences, ^{et on} compare ^ces résultats avec les études récentes des transitions des films noirs sans solvant du même lipide.

Abstract.

Photon correlation spectroscopy has been used to investigate ^the viscoelasticity ^of liquid ^surfaces supporting monolayers ^of glycerol monooleate. Thermotropic transitions of fully compressed monolayers ^were

studied in detail. From the observed changes in surface tension and dilational modulus, the relative amplitudes ^{of the}

fluctuations in molecular area were evaluated. Monolayers ^{formed at} temperatures above and below the transition behaved differently. ^{For a} monolayer fully compressed in the low temperature state, the transitional changes ^were

small (fluctuations ~ ^{8.4 % of} A>). ^{For a film} fully compressed ^at temperatures ^{above the} lipid transition the

changes ^{were much} larger (fluctuations up ^to 95 % of A>). ^The temperature variations also were somewhat

different, although ^{in both cases} the transitions occurred between about 15.3 and 16.5 °C. The molecular bases of the differences are discussed. Some comparisons ^are drawn with recent studies of the transitions of

solvent-free

black membranes of the same lipid.

J. Physique ⁴⁸ (1987) ^{485-494 MARS 1987,}

Classification

Physics ^Abstracts

68.10

87.20

05.40

64.90

78.35

1. Introduction.

The transitions of amphiphilic substances are of consid- erable interest, ^both physico-chemically, ^as molecularly

ordered phases ^{which can be} restricted to two dimen-

sions, ^and biologically, ^{as models of the} lipid ^{matrix of}

biomembranes. Various systems have been studied, including monolayers spread ^{at air-water or oil-water} interfaces, single planar bilayers (black lipid ^mem- branes), multi-lamellar aggregates and vesicles. The different models provide ^certain advantages ^for particu-

lar experimental approaches. Multi-lamellae or vesicles have been widely ^studied by ^various spectroscopic techniques, ^{as the} multiplicity of interfaces yields ^a

(*) ^{Present address : Unilever} Research, Colworth

Laboratory, Sharnbrook, Bedford, MK44 lLQ, ^U.K.

(+) ^{To whom} reprint requests should be addressed.

large signal. Conversely, ^a spread monolayer ^{is not} easily ^studied spectroscopically [1] ^{but is rather} easily manipulated experimentally, permitting control of

extrathermodynamic ^variables (e.g. surface pressure, molecular area). ^{In the various model} systems ^the

amphiphilic ^{molecules are} subject ^{to different} physical

constraints which influence the nature of the transition

perceived [2]. Thus studies of the same molecular

species ^{in different} systems ^can provide complementary

information _{upon the} inter-molecular or inter-aggre-

gate forces involved.

The present ^{aim was to} investigate ^the thermotropic

transition in monoglyceride monolayers ^at the air-water interface. The results are compared with those obtained in a parallel study ^{of black} lipid ^membranes (BLM) ^of

the same lipid [3]. ^The validity of any correspondence

between monolayers ^and bilayers, particularly ^{at their}

transitions is still open ^to discussion [4, 5]. It is gener-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01987004803048500

ally argued ^{that as the} temperature ( T) is varied the

bilayer ^{state will trace out a locus on the} monolayer

7r-A plot. ^{The nature of the} appropriate locus is still debated : it seems reasonable to think that it must

depend upon the bilayer system of interest. The choice of constant 7r( - ⁵⁰ nM/m) [4] may be valid for ^ten- sion-free bilayers ^{such as} flaccid vesicles or lamellae in

lipid-water dispersions, ^{but seems} inappropriate ^for

BLM. These exist in a state of tension [3], the tension

increasing ^{with T. A constant 7r locus,} implying ^tension falling ^with increasing ^{T, cannot be an} appropriate comparison. We have chosen a constant A locus for

fully compressed monolayers. ^{In such} monolayers ^the

molecular packing density ^is comparable ^{to that in}

BLM. This choice probably ^{does not} yield perfect correspondence ^{with BLM.} However, ^{the transition} temperatures ^{of the two} systems ^{are close} (2013 ¹ K ) .

The differences between the two systems ^{will be} discussed below. The constant A locus on the IT-A

diagram ^{also shows} monolayer transitions in a rather

new light compared ^{to the usual} isothermal variation of molecular area.

This paper presents ^{data on} changes ⁱⁿ viscoelastic

properties ^for fully ^condensed monolayers ^observed

over the transitional region. The results show that the thermal behaviour is distinctly ^{different for} monolayers

formed above and below the transition. These differ-

ences have been interpreted ^{in terms of} differences in fluctuations in molecular packing.

Considerable transitional changes ^{have been ob-}

served in membrane properties [6] (such ^as per-

meability) which arise from the fluctuations within membranes at or near the lipid transitions. Various theories have treated these fluctuations, ranging ^from Ginzburg-Landau treatments based _upon a two-state

Ising ^model [7] ^to Monte-Carlo simulations involving lipid ^molecules having ^two chains with up ^{to ten} separate ^states [8]. The latter approach demonstrates the existence of considerable clumping ^{in the} bilayer, phase separated ^areas being apparent ⁱⁿ Monte-Carlo

«

snap-shots ^». Rather easy exchange ^of lipid ^between gel ^{and fluid} regions ^seems possible. ^The theory [8]

predicts ^the temperature variation of the amplitude ^of

the fluctuations of the molecular packing density ^{in the} bilayer ^{close to the} transition.

Unfortunately ^our experiments ^{are not} directly ^com- parable with these simulations. In the simulations, ^{as in}

most experiments ^on bilayers, ^{the mean molecular area} ( (A») ^{is free to} change ^with temperature, ^whereas the fixed monolayer ^{area in the} present experiments imposed ^an additional constraint upon the system.

Basically the simulations concentrate upon fixed N

(particle number) ^{whereas our} experiments entail both fixed N and fixed (A).

The lipid ^{studied was} glycerol monooleate (GMO).

The transitions of GMO have been investigated ^for

BLM [3, ^9, 12], ^{and for} monolayers ^at the oil-water interface [10]. Major transitional changes occur over

the range 12-17 °C : _{there may} not be a unique ^transi-

tion temperature ( Tt ) . ^{The variation in reported}

values of T, may arise from the specific temperature

variation of the property probed, ^{from the nature of the}

membrane system (monolayer,

solvent-free » BLM

etc.) ^or from the presence of impurities (such ^{as solvent}

in some BLM cases). ^The present results will be

compared ^{to those of a detailed} light scattering study ^of

BLM formed from GMO [3]. ^The transitional changes

observed in several membrane properties ^{for a}

«

solvent-free

BLM in that study ^{tended to cluster}

about two temperatures : ^{12.5 and} 16.6 °C. Rather than

considering ^{this as evidence of a} two-stage transition,

these temperatures might ^be interpreted ^{as the extre-}

mes of a single broad transition involving ^{the existence}

of mesophases ^{or molecular} complexes. ^The transitional

changes about 16.6 °C appeared ^{to involve an increase}

in the probability ^of gauche conformations in the acyl

chains of the lipid ^molecules (« chain-melting »).

Although ^exact agreement with this value of Tt (16.6 °C) ^{has not been} found, the results of the present work are consistent with a chain-melting transition.

Oleic acid shows transitional effects [13] ^{between 14}

and 18 °C, ^further supporting the association of these

changes in GMO with the oleyl ^chain.

Laser light scattering has been used here as non-

perturbing probe of surface dynamics. ^This technique ^is uniquely non-perturbative. ^{Even in} thermodynamic equilibrium ^{there are} fluctuations at the air-water interface : a complete ^{set of} capillary modes will be

thermally excited. These scatter light, ^the spectrum

reflecting ^the temporal evolution of capillary ^{waves of} given wave-number ( q

² ’IT I A) , ^{which is influenced} by ^the viscoelastic properties ^{which a} monolayer ^confers

upon the surface. Several light scattering studies of insoluble monolayers have been reported [14, 16].

However, ⁱⁿ nearly ^{all cases the data} analysis ^has

involved essentially arbitrary assumptions. ^{To our} knowledge, this paper contains the first experimental

demonstration that the accessible surface properties

can be inferred directly ^{from the} form of the light scattering spectrum (cf. ^{the case of} simulated data [17]).

2. Theoretical background.

A brief summary of theoretical treatments of light scattering [15] from thermal excitations of a liquid

surface supporting ^a monolayer ^is given.

Thermal agitation continually roughens ^{a fluid sur-}

face. The rough ^{surface can} be Fourier decomposed

into a complete ^{set of} capillary modes, each of which

can be described by ^a displacement ^{from the mean}

interface plane :

The temporal ^{evolution of waves of} fixed q is studied

through the correlation function of the scattered light

487

field. The frequency Cù ( = Cùo + i r) is ^{related to q via}

a dispersion ^relation [15] :

were 17 ^and p ^are the viscosity ^and density ^{of the} subphase fluid and m is defined by

The surface affects the dispersion ^{relation via the}

surface tension y and the dilational modulus

The spectrum ^{of the scattered} light ^{for waves of} given q

can be written as [15]

where D ( w )

^{0 is the} dispersion equation (Eq. (2)).

This spectrum ^{is used to} analyse ^our experimental

observations (see below).

Goodrich has shown that up ^to four separate ^interfa- cial viscosities may exist [18]. ^{The nature of these}

viscosities is not as yet fully understood. They ^are perhaps ^best regarded ^{as surface excess} quantities.

Each forms the dissipative portion ^{of a} viscoelastic modulus. Two of these moduli couple ^to the disturb-

ances studied here : one affects shear normal to the

surface, equivalent ^{to surface tension}

while the other governs dilatation within the interfacial

plane

The elastic moduli yo and eo ^are identified with the

classically measurable surface tension and dilational

modulus, ^while y’ ^{and E’ are} separate specifically

defined surface viscosities. Neither corresponds ^{to the}

conventional

surface viscosity » which governs shear within the surface plane. (N.B. ^{there is as} yet ^no uniform notation for this field.) These four surface

properties just defined have effects _{upon the} propaga- tion of capillary ^waves which have been discussed fully

elsewhere. In particular their effects upon P ( w )

differ, leading ^to variations in the sensitivity ^of light scattering observations to the values of the surface

properties [17].

3. Experimental ^methods.

The methods used in this work, apart ^{from the data} analysis procedures, ^{have been described}

elsewhere [19] ^and only essential details need be given.

3.1 LIGHT SCATTERING. - Our light scattering spec-

trometer has been described elsewhere [19]. ^{The essen-}

tial feature is the use of a coarse diffraction grating [20]

to generate ^{a reference beam for} optical heterodyning.

The scattered light (at scattering angles 1") ^and

reference light ^{are mixed at the} photomultiplier, ^the

output ^{of which is} processed by ^{a multi-bit correlator} having ^{128 channels} (Malvern K7025). ^{The entire} ap- paratus ^{was mounted on a massive} vibration-isolated table to avoid large-scale ^{motions of the} liquid ^surface.

3.2 MONOLAYERS. - Our Langmuir trough ^has

been described elsewhere [19]. ^{It was enclosed for}

acoustic isolation and to avoid evaporation. ^The subph-

ase was 0.1 M NaCI made up in « polished

^{water from}

a Millipore (Milli-Q) ultrafiltration system. ^Thermos-

tatted water circulating ^{in a} glass ^coil permitted ^tem-

perature ^{control of this} subphase ^{to ± 0.1 °C, the}

temperature being ^measured by ^a thermocouple placed

close to the monolayer ^{surface. Before} spreading ^a monolayer ^{the surface was} repeatedly swept, ^contami- nation being ^removed by suction with a Pasteur pipette

connected to a low vacuum.

Glycerol-1,2-mono-oleate (Sigma Ltd, Sigma ^Grade

> 99 %, ^{ca 95 %} 1-isomer, ^{ca 4 %} 2-isomer) ^{was used}

without further purification. ^Each sample ^{of GMO was}

dissolved in n-hexane and a small precise quantity dispensed ^{on to the} aqueous surface ^{with a mic-}

ropipette. Following ^{a short time to} permit evaporation

of the solvent and equilibration, ^{the monolayer was} quasi-statically compressed ^{to the} fully ^condensed

state, determined as that area at which the capillary

wave frequency (i.e. tension) ^{ceased to} change. ^The

molecular areas at which this occurred agreed ^with

values quoted by ^White [10] : ^{25 A2 below and 37 A2}

above the lipid transition [19]. The values of surface tension in the condensed state were concordapt ^with

literature values (see below). Light scattering experi-

ments were then initiated, measurements being ^made

as the system ^{was heated or cooled} through ^the

temperature range of interest.

3.3 DATA ANALYSIS.

Capillary ^{waves can be af-}

fected by ^four separate monolayer properties. ^The spectrum ^of light ^scattered by ^{the waves is} implicitly ^a

function of these four properties. ^A rigorous ^data fitting procedure ^{is thus} required to extract all of the

properties ^{from the} spectrum. ^The spectrum ^has usually

been analysed ^{in terms} of wo and T, using ^{a Lorentzian} approximation. Extraction of four physical properties

from two observables poses difficulties in terms of the

uniqueness ^and reliability of values [21, 22]. ^{It is,} however, possible ^{to extract} the interfacial properties directly ^{from a} single light scattering observation [17].

Basically ^the spectrum of the scattered light ^{is not} exactly Lorentzian and the deviations from that form

are systematic ^{functions of the} interfacial properties.

This method, ^which involves considerable computation,

is here applied for the first time to experimental ^data.

The observed correlation functions are analysed by

non-linear least-squares fitting using ^an objective ^func-

tion based on the power spectrum ^P ( w ) (Eq. (5)).

This is evaluated for initial estimates of

Y(= YO+i-Y’) ^and e ( = E0 + iw E, )

^assuming

that the subphase ^{p and q} both have their accepted

values. The Fourier transform of P ( w ) ^convoluted

with a Gaussian instrumental function (appropriate ^for

our Gaussian laser beam profile) ^{forms the} correlation function

This is extended to include the possibility ^{of a self-beat}

contribution to the observed correlation function

as [23]

where A is the amplitude ^{of the} time-dependent

modulation and B is a background. ^The parameter ^k

was always small in fits to our data, ^but apparently improved ^{the fit.}

The validity ^{of the method of data} analysis ^outlined

above has been demonstrated for simulated data [17]

-

theoretically generated correlation functions with random noise superimposed. ^The sensitivity ^and preci-

sion of this approach depends upon the magnitudes ^of

the several surface parameters (due ^{to their} varying

effects upon capillary ^wave propagation) and upon the random noise upon the correlation functions. It ^has

been shown [17] ^that yo and Eo ^{are most} precisely

determined and least affected by noise. However the

precision ^of Eo varies with its value (relative ^to yo) : large Eo values ^are very uncertain. The surface vis- cosities y’ ^and cB ^{which are less} reliably determined,

are not used in the interpretation ^{of the} present ^results.

In the experiment described here the results of the

light scattering observations were not compared ^with

tensions derived from classical techniques (e.g. ^Wilhel-

my plate). ^Such comparisons ^are presently being ^carried

out as part ^{of a wider} study. However, ^{we can state for}

the free subphase surface, for very expanded ^GMO monolayers ( 1T --1. 0 ) ^{and for} fully compressed ^mono- layers the tension values deduced from the light ^scat- tering ^{data are} in excellent accord with accepted ^values.

The analysis ^{involves a} highly non-linear optimization problem. ^A comprehensive quasi-Newton algo-

rithm [24] ^was used for its convergence in such non-

linear situations ; ^no function derivatives were required.

The uniqueness ^{of the} solution obtained was investi-

gated using various different starting points. ^{Points as}

different as Eo

0 and 100 mN/m were included, ^to check ambiguities ^{due to} the double-valued nature of EO ^{as a} function of w. In nearly ^{all cases} these different

starting points gave final solutions which were essen-

tially identical. Occasional different results usually

were associated with ambiguities ⁱⁿ Eo* Comparisons ^of

the magnitude and covariance of the residuals afforded

reliable statistical criteria on which the various solutions

were assessed. Solutions selected on the basis of these statistics showed continuity with results of neighbouring

observations.

The manner of including ^the instrumental line-

broadening ⁱⁿ equation (8) ^seems satisfactory. ^Data analysis returned consistent values of 0, which showed

no dependence upon the values of the interfacial

properties. The values found (e.g. (f3)

^{2 800 s-1 at}

q

716.3 cm- 1) agreed reasonably ^well with theoreti- cal expectation [20]. ^{When the} instrumental linewidth f3 ^{is not} large compared ^{with the width of P} ( w ) (Eq. (5)), ^{as was the case in all of the} present ^ex- periments, ^the formulation of equation (8) ^{should be} essentially ^exact [25].

4. Results.

4.1 MONOLAYER DATA. - Data are presented ^here

for two fully compressed monolayers ^{of GMO. One}

film was formed at 11.6 °C, well below the reported

transition of GMO (referred ^{to below as « LOW} T»). ^{The other was formed at} 18 °C, ^above T, (« ^HIGH

T» below). ^{In both cases} preliminary light scattering

from the free subphase ^surface yielded yo ^{values in}

acceptable agreement with literature results.

The tension for the LOW T data remained essentially

constant from 11.8 to 15.3 °C, ^{then rose} by ^{1.76 mN/m}

over about 1 °C and thereafter became sensibly ^constant again (Fig. 1). ^The spread of the measured yo ^values evident below 15.3 °C gives ^a good indication of the

precision of determination of yo ^{in these} experiments.

The standard deviation of these values was 0.14 mN/m.

This will be taken below as the precision ^{of a} single (unaveraged) yo ^value.

Fig. ^1.

The variation of surface tension with temperature for the LOW T data (q

^{716.3 cm-} 1). The line is a cubic

spline approximation ^{to the data to} guide the eye.

At low temperatures (i.e. ^below 15.3°C) /yoB =

28.93 ± 0.02 mN . m, while above 16.3 °C yo -

30.69 ± 0.04 mN/m. The mid-point ^of the transitional

489

change (TlIz ) ^of these data depended only slightly

upon the line drawn through ^{them. We estimate} Tlt2 ^{= 15.86 °C.}

Other interfacial properties ^{were less} precisely ^deter-

mined. Again, ^for temperatures less than 15.3 °C 60 ^{was too} large (y 0) ^{for precise} determination.

For r> 15.5 *C Eo ^was lower, ^{but showed} quite large

scatter. In this region ^{we feel that it is} only ^{safe to state}

that EO)

^{21 ±} 11 mN/m. The viscosities are men-

tioned here for completeness, ^{but are not} used in the

subsequent interpretation. y’ (the transverse shear

viscosity) ^showed large ^{scatter but was} apparently ^non-

zero at all temperatures. Below 15.3 *C ^{= 7.9 ±}

0.5 nN . s/m whereas above 16.3 °C y ’ ) ^{= 5.8 :t}

1.3 nN . s/m. We regard neither the difference between these values nor an apparent slight ^T dependence ^of y’ ^as significant. Values of E’ (lateral dilational vis-

cosity) ^were very scattered : the average value, ^while large in absolute terms, ^was compatible ^{with zero. No}

great precision of determination of either E’ or Eo would be expected in view of the size of (EO) ^relative

to (y 0) .

The HIGH T data behave very differently (Fig. 2).

Here some data are averages of the results from several correlation observations at a given temperature. ^Such

cases served to provide estimates of the errors upon Yo (generally agreeing ^with the standard deviation

quoted above) and upon Eo* The latter error was

estimated to be ( ± 2.1) ^mN/m.

Fig. ^2.

The variation of yo with T for the HIGH T data

(q

^{292.2 cm} 1). The line is a cubic spline ^{fit as in} figure ^{1 :}

note that there are three knots at 15.3 *C.

From 17.8 *C yo ^{falls to an} approximately ^constant

value ( ( yo)

25.43 ± 0.07 mN/m) ^{between about}

17.3 and 16.5 *C. On further cooling yo ^increased

steadily ^{until a} very rapid ^increase about 15.3 °C lead to a reversion to near constancy. ^The variation in tension is opposite ^{in sense and of much} greater

magnitude than for the LOW T data. The range of yo is 17 mN/m for the HIGH T _case, compared ^to

1.76 mN/m for the LOW T data. The T1f2 values also differ somewhat: for the HIGH T data we estimate

Tl/2 ^{= 15.44 °C. We} emphasize ^{that no} hysteresis ^is

involved. The monolayers ^were prepared ^{under com-} pletely different conditions and at no temperature could they have been similar at the molecular level.

The variation of Eo for the HIGH T data is shown in

figure 3, ^{where a vertical arrow denotes a} large (indeterminate) value. Between 16.6 and 17.3 °C (the region ^of apparent constancy ⁱⁿ yo) eo ^{is seen to be} large : ^the monolayer ^is incompressible. ^{Outside that}

range Eo varied somewhat.

Fig. ^3.

Surface dilational modulus as a function of temperature for the HIGH T data. A vertical arrow indicates

an indeterminate, large value of EO.

Between 16 and 15 °C it rose smoothly. ^Above

16.2 °C occasional values were indeterminately large (see Fig. 3). ^This may reflect local inhomogeneities ⁱⁿ

the film which have sizes comparable ^{with the area}

illuminated by ^the laser beam [26], ^{but this} requires

confirmation.

Both monolayer viscosities were zero for the HIGH T data: the occasional non-zero values of E’ found

were invariably associated with large ^values of -09 and

were consistent with E’

0.

4.2 MOLECULAR AREA FLUCTUATIONS. - In both sets of data described above there is a temperature

range (T -- ^{15.3 °C for LOW T and} 16.6 -- T -- 17.3 °C for HIGH 1) ^over which the tension remains essentially

constant. In both cases as T is scanned through ^the

transition region the tension rises. Within these regions

of constant, low tension the monolayer ^dilational

modulus is _very large ^{indeed. A} large eo implies ^that

the thermally ^excited longitudinal (or compression)

waves within the monolayer ^{are of small} ampli-

tude [15]: as Eo falls these ^waves will grow in magni-

tude. The transitional increases in yo observed ^for fully

compressed ^GMO monolayers ^{are thus} accompanied (in ^{both data} sets) by increases in the amplitudes ^of

these longitudinal ^waves. This connection permits ^the

transitional changes ^{in the} fluctuations in molecular

area to be estimated.

Within a monolayer ^the amphiphile packing density

is a random function of position, ^{due to} thermally

excited fluctuations in molecular area. These form a

complete ^{set of} longitudinal ^{waves. Such waves} periodi- cally change ^{the local tension at} any given point ^{in the} monolayer. ^{These effects have} been demonstrated for

mechanically generated longitudinal ^waves upon ^mono-

layers [27] ^{and surfaces of} surfactant solutions [28].

A change ^{dA in molecular area will} change ^the

tension yo from that value (’Y A) appropriate ^{to a} monolayer ^{of uniform molecular} packing (mean ^area

W) [29]

To first order (neglecting ^the higher terms) ^a longitudi-

nal wave involving ^a periodic variation dA will, ⁱⁿ general, ^{cause a} symmetric variation of yo ^about yA.

The average local tension will thus ^not be changed ^from

yA. ^However (E. ^{A. Evans,} private communication)

this symmetry may fail in ^some situations. In particular,

this will be the case for a monolayer fully compressed ^to

the collapse point (as ^{in the} present experiments).

In this _case, fluctuations involving ^{an increase in}

molecular area ( AA + ) ^{will be} accompanied by ^an

increase in tension :

However, fluctuations which attempt ^{to decrease the} molecular area in the equilibrium ^surface plane

(AA- ) ^{will result in transient buckling or bulging of}

the film as a precursor ^to collapse. During ^this buckling

the local molecular area within the film remains un-

changed (the ^molecular packing per unit area of trough increases) ^{and the} local tension is thus unchanged.

Thus AA+ involves an increase in yo whereas DA - does not, and the average local tension will be raised from the equilibrium ^value expected ^{for a uniform film}

of the same mean molecular area :

where the fluctuations are averaged ^over all longitudi-

nal wave-vectors ( qL ) . ^{For brevity} (åA + ) I (A> ^is

below written as AA/A.

It seems unlikely ^that thermal fluctuations will cause

collapse ^{of a film in} equilibrium. ^The longitudinal ^wave frequencies ^{will exceed} the inverse times (- minutes)

for relaxation of the overcompressed monolayer ^{to the}

bulk lipid phase [30]. ^{The wave} frequencies ^are given by (15)

Using EO 2: ^{10 mN/m} (as here), wavelengths ^{less than}

the dimensions of the trough (qL -’5 ¹⁰ cm) ^{will corre-} spond ^to w L > ^{10 Hz.}

Light scattering ^from capillary ^{waves has been}

shown [26] ^{to be sensitive to} interfacial or surface

properties averaged ^over local values across the illumi- nated area. Thus to compare ^with the present exper- imental data, ^the average of AA’ in equation (12) ^must

be taken in a manner appropriate ^{to the} light scattering

response ^to yo. ^{It is not} necessary ^to specify ^this averaging process precisely ^here.

Thermally ^{excited area} fluctuations will occur at all T : the data of figures ^{1 to 3} permit ^the changes ^{in these}

fluctuations which arise as the system ^{is taken} through

the lipid transition temperature ^{to be} estimated. In the LOW T data (Fig. 1) ^{the tension} is low and constant at T:> 15.3 °C «( ’Yo)

^{28.93 mN/m),} where Eo is very

large. ^{In this} temperature region ^the fluctuations in A will be small. We thus take /yo) ^{in this}

^reference

state » as yA. ^{Above the} transition Eo, while still quite large, is reduced. From the difference in /yoB ^across

the transition (1.86 ± 0.04 mN/m) using EO) ^{= 21 ±}

11 mN/m for T::. 16.3 °C we find from equation (12)

the relative amplitude ^{of the} fluctuations above the transition to be

The large ^{error in} AA/A entirely ^{arises from the error}

upon (EO) ; the increase in yo is very well defined.

To the extent that small amplitude fluctuations will

occur for T 15.3 °C, despite the very large ^dilational modulus, ^this result will underestimate the absolute size of the fluctuations.

Turning ^to the HIGH T data (Figs. ^{2 and} 3), again ^a region of low and constant yo coincides ^{with a} region ^of

very large Eo* ^We thus take the range 16.6 -- T ,17.3 *C as the « reference state » of minimum fluctuation in A and identify /7oB ^there

( ^{= 25.43} mN/m) ^with yA ⁱⁿ equation (12). ^{From the}

behaviour of yo and -o ^outside this range the tempera-

ture variation of AA/A ^{shown in figure 4 is derived.}

Cases of indeterminately large Eo ^{have been omitted}

from this plot. ^{The errors} upon AA/A ^{are dominated} by ^{the errors in} so.

A somewhat unexpected feature of figure ^{4 is the}

increase in fluctuations in area at T > 17.3 °C. This

seems to be a real feature of the data, arising ^{from the}

increase in yo ^and the decrease in Eo ^{at these tempera-}

tures compared ^to the reference state. Similar trends

appear in several other data ^sets. The tension at

491

Fig. ^4.

The relative fluctuations in molecular area for the HIGH T film, deduced from the data of figures ^{2 and 3.}

T > 17.5 °C is consistent with literature val-

ues [19, ^31, 32] ^for the surface pressure of fully ^com- pressed monolayers ^{of GMO at the} air-water interface.

We have as yet ^{no clear} explanation ^{of this effect.}

In addition to the random errors quoted ^{above, the} DAIA values will be subject ^to systematic ^{errors. The}

dilational modulus 80 ^{is not} independent ^{of A : in a}

fluctuation dA the value appropriate ^to the instantane-

ous area will vary. These effects are essentially ^reflected

in the higher ^{order terms of} equation (10), ^here neglec-

ted. For small dA/A (as for the LOW T case) 80 ^will

not change ^{much and} neglect ^{of these} higher ^{terms will}

not introduce great ^{error. For} large dA/A (as ^for

HIGH 1) ^{these terms} may have non-negligible ^effects.

However the error will be less than at first _{appears :}

just ^as yo deduced from light scattering ^{is an} average

over the fluctuations within the illuminated _area, so

E0 ^{will be} averaged. ^Thus the Eo ^values quoted ^{here and}

used in evaluating dA/A ^from equation (12) ^{are not}

those appropriate ^to (A ) ^but will be averages ^over the molecular area fluctuations concerned. To estimate the

magnitude ^{of these} systematic ^{errors in} dA /A ^would require ^a deeper understanding ^{than is} presently ^avail-

able of the response of the light scattering ^from capillary ^{waves to local} fluctuations in packing.

5. Discussion.

The thermotropic ^{behaviour of the two different films}

described above can be understood in terms of a

transition involving lipid ^chain melting. ^{However such}

a model is not essential to the present ^{data as other} processes involving substantial changes in surface area

occupied by ^a molecule could equally ^{be invoked} (e.g.

molecular tilt). ^The discussion is restricted to a chain-

melting model for definiteness and because parallel

studies of thermotropic transitions of GMO in

«

solvent-free » bilayer membranes favour this _process.

The LOW T film displays fluctuations in molecular

area above the transition which are not of large

amplitude. This accords with expectation ^{for a mono-} layer formed from GMO molecules predominantly ⁱⁿ

the all-trans state. The mean molecular area of such a

monolayer ^is

^{27 A2 : the} packing is very close. In this state steric repulsions between the GMO molecules will tend to inhibit the formation of gauche conformations above the transition. Such molecular conformations could only ^be accommodated by ^local deformations of the packing ^of the all-trans molecules. Only fluctuations of small amplitude ^{could be} expected ^{in this} very constrained case.

The HIGH T data clearly ^show fluctuations in molecular area throughout the transitional region,

which reach _very large amplitudes. ^This again ^is

consistent with a model involving chain-melting. ^The

film is fully compressed ^{to a state} (above Tt) ^corre- sponding ^{to mean molecular area of 37 A 2 due to the}

presence, ^on average, of several gauche ^bonds (or kinks) per molecule. On cooling, ^some molecules will

adopt ^{an all-trans} form, with much lower molecular

area. The consequent fluctuations are opposed by ^no strong ^steric repulsion and involve no strain in a quasi- crystalline ^{lattice of} lipid ^molecules.

The changes ^{in y for both} monolayers ^{extend over}

almost exactly ^{the same} temperature range. This is

emphasized ⁱⁿ figure 5, showing ^{the variation} through

the transition of the

order parameter

.0, ^{defined as}

the relative change ^{in each case from the}

^reference

state » to the subsequent ^{state of} apparent ^constant

Fig. ^5.

^A comparison of the relative variation of yo through the transition region ^{for the two} monolayers (8 LOW ^{T, x HIGH} TJ. ^{The lines are the} spline ^functions

from figures ¹ and 2. See text for definition of 0 (Eq. (14)).

We reiterate ^{that no} hysteresis ^is involved here : the two monolayers ^{were formed in} completely ^different

initial states. The similarity ^{of the} temperature ranges covered by the transition in the two cases implies ^that

the same physical ^{effects must be} operative ^{in both}

cases. The physico-chemical constraints _are, as already discussed, very different in the two cases, reflected in the distinctly ^different temperature dependences ^of 0.

The HIGH T data changes quite sharply, ^{60 % of the} change ⁱⁿ yo occurring ^over only ^{0.2 °C. This} abrupt change ^{reflects the} increasing ^{ease of} cooperative change ^{as more « free area »} is created by ^molecular changes ^as the transition proceeds. Conversely ^the

rather small and less cooperative changes ^{in the LOW}

T case result from the resistance of the close-packed

molecular chains to increased chain disorder. Only ^at

rather high temperatures within the transition are the forces driving ^the change sufficient to substantially

overcome this resistance.

The changes ⁱⁿ yo ^{do not} linearly map ^to AA/A as Eo also changes through ^the transition region. AA/A ^must

increase faster than yo, whatever the details of the transitional variation of Eo. These arguments ^rather naturally explain ^the differences in Tl/2 ^{values estimated}

from the variations in yo - 15.86 ^{°C in the LOW T case}

and 15.44 °C for the HIGH T data.

The films examined in this work somewhat resemble GMO bilayers, ^whose transitions have recently ^been

the subject ^{of a detailed} light scattering study [3].

There are also other reports of various transitional

changes ^{in GMO membranes} [9, 12]. ^{We do not wish to}

make detailed comparisons with these studies, ^but

rather note one or two salient points referring ^{to the} bilayer light scattering ^work [3]. The main transitional

changes ⁱⁿ

solvent-free » BLM centred upon 16.6 *C,

rather above the TlIZ values found here. The transition

was most apparent ^{in membrane} thickness but was also evident in the membrane tension and viscosity. ^The

difference between the present Tl/2 values and 16.6 °C is well outside errors. There may be several ^causes of these differences.

The systems ^involved have rather different physical

natures. BLM are thermodynamically open systems, the Plateau-Gibbs border providing ^{a reservoir of} lipid.

Insoluble monolayers ^{are closed,} containing ^{a well-}

defined number of lipid molecules. Again, ^{in the} present study ^{the mean molecular area is held constant}

whereas in a bilayer ^{it is} quite uncontrolled. The BLM transition at 16.6 °C showed a width A Tl/2 - ^{1.5 °C . At}

the lower side of this transitional region ^a combination of the anisotropic part ^{of the} bilayer dielectric constant

( E,,) ^{and a molecular order} parameter (So) ^was

found to drop very rapidly ^at about 15.5 °C. Both the

present Tl/2 ^{values are} rather close to this temperature.

Nagle ^has argued ^that bilayers ^and monolayers may be different microscopically ^{as well as} thermodynami- cally [4]. ^An isolated all-trans acyl ^{chain in a} monolayer

extends into an energetically unfavourable environ- ment, whereas ^{in a} bilayer ^{it would be} surrounded by hydrocarbon chains from the apposing monolayer. ^The

energy penalty ^{involved could} explain ^the observation

of transitional changes ⁱⁿ monolayers ^at rather lower

temperatures than in the BLM case. At lower tempera-

tures the increased probability ^{of all-trans molecular} configurations will reduce the probability ^{of such}

extended chains being ^{isolated in} this way.

Further, ^{the nature of the} transitional change ⁱⁿ

membrane models depends strongly upon the ^mem- brane property probed [33]. ^A property ^{biassed towards} the low-temperature ^{state will} suggest ^{a lower} T, ^than

one dominated by ^the high-temperature ^{state. As} noted, ^{the BLM} Tt ^was largely ^based upon membrane thickness. The elongation ^of lipid ^{molecules as the} acyl

chains adopt all-trans conformations _{may well} not show the same temperature ^{course as the} changes ^{in tension}

due to fluctuations in molecular packing ^driven by ^the

conformational change.

In practice ^{these causes} probably ^all contribute to the differences observed between the transitions in bi- and monolayers. ^{The effects of} physical constraints upon the molecules is illustrated by the lack of convergence of Tln ^{for the LOW T and HIGH T} monolayers.

Detailed comparisons ^{of the} present monolayer ^results

with bilayer ^{data would be} misleading ^{due to these}

various differences. It may well be that such differences will limit exact correspondence being ^{drawn between} monolayer ^{states and} bilayers.

While the present ^{results are} consistent with a chain-

melting picture ^{of the} transition, other models are not excluded. However, the closeness of the TlIZ ^{values for}

both HIGH T and LOW T cases to the temperature ^at which the combined molecular order and dielectric

anisotropy abruptly changed ⁱⁿ

solvent-free

BLM

[3] ^are suggestive ^{of this} explanation. ^Further experi-

ments to investigate ^{the behaviour} of ea ^{in this} tempera-

ture range could substantiate the chain-melting ^model

for the present ^data.

The analysis ^{of the} present ^{data could be extended in} several _ways, motivating further studies. In particular

examination of a wider _range of temperature, ^{with data}

taken at finer intervals (especially in the transitional

region) ^{would be most useful.} Two illustrative areas of

potential ^{interest are} noted here.

a) ^The derivatives of yo ^with respect ^{to T should}

yield significant thermodynamic properties ^{of the} monolayer. ^However, differentiation of experimental

data is very inaccurate, requiring closely spaced ^{data of} high precision. ^{Here we} simply ^{show the} entropy ^of formation [34] ^{of the two films} (Fig. 6) derived from the derivatives of the cubic spline fits shown in figures ¹

and 2 :

(where yW is the tension of the free water surface). ^The variations ^shown depend upon the position ^{of the knots}

on which the splines ^{are based} [35] ^{and excessive}

significance should therefore not be placed upon ^the

detailed behaviour shown. However the two cases are

493

Fig. ^6.

^The entropy of formation of the monolayer (Eq. (15)) ^{as a} function of T for the two films. The variations derive from the temperature derivatives of the spline ^{fits of} figures ^{1 and 2.}

evidently quite different: the LOW T data show a

small transitional minimum in S just ^at the relevant

Tl,2, whereas the HIGH T data show a much sharper

and larger maximum rather below the relevant T112’

The entropies shown refer only ^{to formation of the}

monomolecular film and so negative ^{values are} quite acceptable.

b) Theoretical predictions of molecular clustering

close to transitions in lipid ^films [8] ^{have been men-}

tioned. These results are not directly comparable ^{to the} present ^{data. In} general the theories treat lecithins,

which have recently been shown to display first-order transitions at the air-water interface [36]. Secondly ^the

theories do not address the situation of constant molecular area. Nevertheless, ^{data such as the} present

(Fig. 4), ^{over a} wider T range and with better resol-

ution, ^could usefully ^be compared with the results of

suitably ^amended simulations. It should be possible ^to

observe hysteresis in the transitions. The possible

measurements of surface viscosities could be useful in

elucidating ^{the nature of the} monolayer phases.

The interfacial properties ^measured by light ^scat- tering ^are averages ^over the illuminated area of the interface. The consistency ^{of the} present monolayer properties ^at adjacent temperatures indicates that the fluctuations in molecular area involved are predomi- nantly ^{local in nature} (or ^{at least} large scale fluctuations do not persist for times comparable ^to experimental

durations - - 30 s). ^{This contrasts} with the fluctuations inferred in the co-existence region ^of highly purified fatty ^{acids which} apparently ranged up ^{to mm} in size

[37]. Laser beams of different diameter could be used

(with ^a certain caution regarding instrumental line-

broadening [20]) ^to probe ^the spatial ^{extent of the} present fluctuations.

The fluctuations in molecular area apparent ^{for even}

a close-packed monolayer may have ^a variety ^of

consequences. ^For example, the electrical behaviour of pure GMO bilayers [38] ^must rely upon ^the creation of pores through ^the membrane, ^{which would} require

fluctuations in molecular packing ^{in the two} apposing monolayers. Again, ^the appearance ^{of such} fluctuations may effect the ^rate of evaporation ^{of water} through ^an

insoluble monolayer [39].

Acknowledgments.

This work was supported by ^{the Science and} Engineer- ing ^{Research Council} of the UK. Discussions with Pr.

E. Evans are gratefully acknowledged.

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