Phase transition in adsorption layers at the air–water interface

Advances in Colloid and Interface Science 79 Ž1999. 19]57

Phase transition in adsorption layers at the air]water interface D. VollhardtU Max-Planck-Institut fur Rudower Chaussee 5, ¨ Kolloid- und Grenzflachenforschung, ¨ D-12489 Berlin, Germany

Abstract Conclusive evidence is presented for a first order phase transition in adsorption layers. Representative studies were performed with a special tailored amphiphile N-dodecyl-g-hydroxybutyric acid amide ŽDHBAA. although main phase transitions can occur in the adsorption layers of numerous amphiphiles. The general conditions necessary for the formation of a two-phase coexistence in adsorption layers are investigated using surface pressure Žp . transients, Brewster angle microscopy ŽBAM. and synchrotron X-ray diffraction at grazing incidence ŽGIXD.. During the adsorption kinetics, appearance and location of the phase transition point depend largely on the concentration of the amphiphile in the aqueous solution and on the temperature. In different temperature regions, various types of morphological textures of the condensed phase are formed. Lattice structure and tilt angle of the alkyl chains in the condensed phase of the adsorption layer are determined using GIXD. The main growth directions of the condensed phase textures are correlated with the lattice structure. The experimental bridging to the Langmuir monolayers supports the conclusions of a first order main transition during the adsorption kinetics. A new theoretical model is presented which describes the adsorption kinetics of the 2D first-order phase transition in an adsorption layer. The theory comprises a kinetic model for a phase transition in Langmuir and Gibbs monolayers, the adsorption from the bulk solution and the dissociation kinetics of bulk micelles. The theoretical data calculated with the new kinetic model are in agreement with the experimental results. Q 1999 Elsevier Science B.V. All rights reserved. Keywords: First order phase transition; DHBAA; Special tailored amphiphile; New theoretical model

U

Tel.: q49 30 63923150; fax: q49 30 63923102; e-mail: [email protected]

0001-8686r99r$ - see front matter Q 1999 Elsever Science B.V. All rights reserved. P I I: S 0 0 0 1 - 8 6 8 6 Ž 9 8 . 0 0 0 7 3 - 6

20

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2. Experimental section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.1. Adsorption kinetics p Ž t . and surface pressure]area Žp ]A. isotherms . . . . . . . . 24 2.2. Brewster angle microscopy ŽBAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3. Grazing incidence X-ray diffraction ŽGIXD. . . . . . . . . . . . . . . . . . . . . . . . . 25 2.4. Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3. Adsorption kinetics studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1. p Ž t . transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2. BAM studies during the adsorption kinetics . . . . . . . . . . . . . . . . . . . . . . . . . 28 4. Texture features of the condensed phase domains . . . . . . . . . . . . . . . . . . . . . . . . 32 5. Bridging between Gibbs and Langmuir monolayers . . . . . . . . . . . . . . . . . . . . . . . 34 5.1. Comparison of the phase transition points and texture features in Gibbs and Langmuir monolayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.2. Theoretical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 6. Structure features of the condensed phase of adsorption layers . . . . . . . . . . . . . . . 39 7. Other monolayer techniques for studying phase transitions in adsorption layers . . . . . 42 8. Theory for phase transition in adsorption layers ŽGibbs monolayers. . . . . . . . . . . . . 43 8.1. Equation of state for Langmuir monolayers w51x . . . . . . . . . . . . . . . . . . . . . . 43 8.2. Kinetics of two-dimensional phase transition of amphiphilic monolayers w74x . . . . 49 8.2.1. Insoluble monolayer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 8.2.2. Adsorption form solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 8.2.3. Dissociation kinetics of micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 9. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

1. Introduction Amphiphilic monolayers at the air]water interface are representative two-dimensional model systems. In principle two kinds of monolayers have to be distinguished. In one case the amphiphiles are dissolved in the aqueous solution and adsorb at the interface. Here they form an adsorption layer which is also designated as Gibbs monolayers. The well-known Langmuir monolayers are formed by spreading of long chain amphiphiles which are insoluble in water. The amphiphiles are dissolved in an organic solvent and then spread at the aqueous surface. In the last decade, rapid progress in the understanding of Langmuir monolayers has been made, particularly as the development of highly sensitive experimental techniques has provided textural and structural information on the condensed monolayer phases w1]5x. The application of sensitive optical microscopy has revealed an intriguing variety in the textures of the condensed phases formed by

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

21

Langmuir monolayers w6x. The molecular organisation of the condensed monolayer phases affects their optical properties. In particular, Brewster angle microscopy ŽBAM. w7]9x offers a powerful method to visualise the morphology of amphiphilic monolayers on a microscopic scale without requiring probe molecules. The optical anisotropy resulting from differences in the molecular tilt is the basis of contrast mechanisms. Large differences in size and shape have been found, e.g. w10]13x. The application of BAM has provided experimental evidence that a large number of the condensed phase domains of Langmuir monolayers have a well-developed inner texture which is due to the orientational order of the tilted amphiphilic molecules w14]22x. The introduction of synchrotron X-ray diffraction at grazing incidence ŽGIXD. has provided access to the lattice structure and the positional order of condensed monolayer phases on the molecular scale w23]27x. In recent papers, correlation between the microscopic crystal structure and macroscopic textural features has been demonstrated by coupling of GIXD and BAM results w28x. Recent systematic studies have shown that the textural and structural properties of the condensed phases of Langmuir monolayers are strongly affected by the chemical structure of the amphiphiles w29]31x. An important aspect for the evaluation of the phase behaviour of Langmuir monolayers is the thermodynamic characterisation. A prerequisite for the formation of well-developed condensed phase textures is that the plateau region of the surface pressure Žp . ]area Ž A. isotherm exists in an accessible temperature region. This plateau region represents a two-phase coexistence region between a fluid-like low-density phase and a condensed phase. To optimise the conditions for nucleation and growth of the domain textures, the main transition point for this first order phase transition should have a measurable surface pressure w5,32x. The success obtained in a better understanding of the physics of Langmuir monolayers has opened up the possibility also to study the Gibbs monolayers formed by adsorption of dissolved amphiphiles or surfactants using the same highly sensitive techniques. The general principles of formation and investigation of both monolayer types are presented in Fig. 1 which shows schematically the differences in the formation of Langmuir monolayers and Gibbs monolayers Žadsorption layers.. In the schematic diagram, the condensed monolayer phase is presented by a molecule aggregate at the air]water interface. During recent decades, a large number of papers has underlined the long-term interest in adsorption and adsorption kinetics of soluble amphiphiles at the air]water interface from aqueous solutions due to the importance of adsorption processes in a wide field of technical applications w33]35x. However the possibility of phase transitions in adsorption layers, i.e. the coexistence of a condensed phase and fluid-like phase, has been largely discounted. Consequently, numerous adsorption isotherms, which are available to describe theoretically the adsorption at the air]water interface, are based on a uniform distribution of the adsorbed molecules. The possibility of two-dimensional molecular clustering of adsorbed molecules has solely been considered by Ruckenstein and Bhakta w36x who in a theoretical paper

22

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

Fig. 1. Schematic presentation of the principles of Gibbs and Langmuir monolayer.

conclude an aggregation effect as a result of the competition between the entropy, which tends to disperse the molecules, and the attractive interactions between molecules, which tend to cause aggregation. For strong intermolecular interactions, conditions for a phase transition can be approximated from Frumkin’s adsorption isotherm w46x. Recently it would seem that a few papers have demonstrated the coexistence of two phases in adsorption layers w14,37,38x. However it was soon assumed that these condensed phase textures were formed by trace impurities of amphiphiles having high surface activity: Ži. dodecanol traces in the case of sodium dodecylsulfate as main component w15,39x, Žii. hexadecanoic acid traces at the sodium octanoate adsorption w15x. Nevertheless the question remained whether and under which conditions a first order phase transition can occur in adsorption layers. A precondition for the formation and evolution of morphological structures in adsorption layers ŽGibbs monolayers. is the coexistence of a condensed phase and a surrounding fluid-like phase within the adsorption layer which is analogous to the formation of the 2D structures of Langmuir monolayers. To approximate experimental conditions similar to Langmuir monolayers, but using more or less water soluble 1-alcohols ŽC 8 ]C 14 ., Berge et al. developed an experimental procedure which was based on placing an excess of the amphiphilic material on the top of a clean water surface w39,40x. In the last 2 years we have provided experimental and theoretical evidence demonstrating that a phase transition of first order can occur in adsorption layers of amphiphiles which are dissolved in water. The fundamental clarification of this problem should be based on a special tailored amphiphile having the following main features Ži. high surface activity to avoid the effect of highly surface active impurities w41]43x, Žii. solubility in the aqueous solution up to a range above the critical micelle concentration Žcmc., Žiii. solubility in the same spreading solvents to allow a comparison with corresponding Langmuir monolayers. Special attention should be paid to the pronounced effect of surface-active impurities in soluble surfactants which is determined by the ratio of the surface activity coefficients of the main and minor components. For example, traces of dodecanol can dominate in the adsorption layer of sodium dodecylsulfate ŽSDS.

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

23

due to a much higher surface activity w41,42x. Consequently condensed phase domains of dodecanol traces can be observed in the adsorption layers of aqueous SDS solutions. Therefore the experimental study of phase transitions in adsorption layers requires that a noticeable effect of surface-active impurities must be avoided. This can be achieved in the simplest way by using highly surface-active main components of optimal purity in which the presence of even higher surface active trace components is improbable. For initial fundamental studies to determine whether a first order phase transition can occur in adsorption layers of water-soluble amphiphiles we prepared a tailored amphiphile N-dodecyl-g-hydroxybutyric acid amide ŽDHBAA.. Based on the experimental results of this amphiphile we have provided first evidence that a first order phase transition can occur in adsorption layers and accordingly condensed phase domains of microscopic scale can be formed w44]46x. In this review, the key issues of the recent research concerning phase transitions in adsorption layers of water-soluble amphiphiles are surveyed. The paper is organised as follows. At first the experimental techniques and procedures used for a comprehensive characterisation of the phase transition and the characterisation of the condensed phase of the adsorption layers are briefly introduced. In the following we report on the adsorption kinetics measured by the surface pressure, the microscopic growth kinetics of the condensed phase visualised by Brewster angle microscopy ŽBAM., and structural features of the condensed phases determined by GIXD. Then it is shown that the texture features of the condensed phases can be related to the structure properties. In another section a bridging to the corresponding Langmuir monolayers provides further experimental and theoretical support for the findings obtained by adsorption of surfactants dissolved in water. The alternative procedure of Berge et al. w39x, which allows the investigation of soluble surfactants as Langmuir monolayers by placing excess material at the surface, is discussed in a following section. In the theoretical section the main features of a newly developed theoretical model are presented which describe the adsorption kinetics of the two-dimensional first-order phase transition in the adsorption layer. The theory comprises a kinetic model of the phase transition in Langmuir and Gibbs monolayers, the adsorption from the aqueous sub-solution, and the dissociation kinetics of bulk micelles. A new recently developed equation of state is presented for describing the two-dimensional phase transition of amphiphilic monolayers in equilibrium. Finally the conclusions emphasise the far-reaching consequences of the first evidence that first-order phase transitions can occur in adsorption layers.

2. Experimental section Experimental evidence for the first-order phase transition in adsorption layers has been obtained by coupling of results using the following experimental techniques. The results have been additionally corroborated by a detailed analysis of the condensed phase formed after the phase transition.

24

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

2.1. Adsorption kinetics p (t) and surface pressure]area (p ]A) isotherms The surface pressure Žp . was measured by the Wilhelmy method using a small filter paper to within 0.1 mN my1 . The p Ž t . adsorption kinetics of the amphiphiles dissolved in the aqueous sub-phase and the p ]A isotherms of amphiphiles spread at the surface were recorded with a computer-interfaced film balance. This allows not only the direct coupling with the corresponding BAM signals but also a good time resolution of the surface pressure changes during the adsorption process. Before the time-dependent surface pressure change can be measured a calibration with pure water must be performed. Afterwards the water was replaced by the amphiphile solution. Then the surface was swept off to remove already adsorbed molecules in order to ensure a water surface approximately free from adsorbed material as the initial condition Ž t s 0, G s 0. for the adsorption kinetics measurements. Recording of the p ]A isotherms of slightly soluble amphiphiles must be performed using rather high compression rates Ž D ArD t s 0.1 nm2 moleculey1 miny1 . to minimise the loss of the amphiphilic material into the subsolution by dissolution w45x. 2.2. Brewster angle microscopy (BAM) BAM is based on the fact that at the Brewster angle of incidence, a parallel Žp. polarised laser beam has a zero reflectance and the presence of a condensed monolayer phase leads to a change in the refractive index and thus to a measurable change in reflectivity w7,8x. The general principle of the method, which is presented in Fig. 2, demonstrates that not only the shape of the condensed phase domains can be visualised but also their inner texture by introducing an analyser in the reflected beam path. Fig. 3 shows a schematic diagram of the experimental set-up used w47x. The set-up consisted of a computer-interfaced film balance having a large trough area . was mounted. on which a Brewster angle microscope ŽBAM 1 q , NFT, Gottingen ¨

Fig. 2. Physical principle of Brewster angle microscopy.

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

25

Fig. 3. Schematic diagram of the experimental set-up for coupling of surface pressure measurements with Brewster angle microscopy.

Further components such as a thermostat, an x]y table, and cabinet are not presented. For vibration damping at the air]water interface, an active table ŽMOD2, JRS Scientific Instruments, Switzerland. was used. The light source was a 10 mW He]Ne laser. The microscope has a spatial resolution of ; 5 m m. A video system Žvideo recorder, video printer and monitor. was used for image formation and storage. The video signal provided from the CCD camera was recorded on a tape and was later digitised by using a frame grabber. The images were optimised using image-processing software for improving the contrast and for correcting the distortion due to the image angle. A reflectivity measurement unit allows the recording of an integral reflectivity signal. 2.3. Grazing incidence X-ray diffraction (GIXD) GIXD has been established as an effective method for studying the packing of amphiphiles at the air]water interface w24]28x. In this work, the GIXD experiments were performed using the liquid-surface diffractometer on the undulator beam-line BW1 at HASYLAB, DESY ŽHamburg, Germany.. The GIXD measurements of the adsorption layers only provided results when sufficient condensed phase was formed in the adsorption layer, i.e. after the phase transition point in the p Ž t . adsorption kinetics. The principle of GIXD experiments is presented in Fig. 4. The synchrotron beam

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

26

was made monochromatic by a beryllium Ž002. crystal and adjusted to strike the surface at grazing incidence with an incidence angle a i s 0.85a c where a i is the critical angle for total external reflection. The diffracted intensity was monitored by a linear position sensitive detector ŽPSD., ŽOED-100-M, Braun, Garching, Germany. as a function of the vertical scattering angle a f . The in-plane divergence of the diffracted beam was restricted to 0.098 by a Soller collimator in front of the PSD. The scattering vector Q consists of an in-plane component Q x y with Qx y s

2p

l

'cos a q cos a y 2cos a cos a cos2Q 2

2

i

f

i

f

Ž1.

and an out-of-plane component Q z with Qz s

2p

l

Ž sin a i q sin a f .

Ž2.

where a f and 2Q are the vertical and the horizontal scattering angle, respectively ˚ is the X-ray wavelength. and l s 1.364 A The intensities were least squares fitted as a Lorentzian parallel to the water surface and as a Gaussian normal to it. Only the lowest order peaks are observed. The lattice spacing d h k is obtained from the in-plane diffraction data by dh k s

2p Q xh yk

Ž3.

where Q xh yk is the in-plane component of the scattering vector at maximum intensity. The lattice parameters a and b are calculated from the lattice spacing d h k which provide the unit cell area A x y . According to a cylinder model the tilt angle t of the long molecular axis with respect to the normal t and the azimuthal tilt direction C h k can be calculated from the peak positions of the Bragg rods. Three non-degenerate peaks are obtained for an oblique lattice, whereas for a rectangular lattice only two peaks are observed. The adsorption layers of the amphiphiles investigated have provided only oblique lattices. Then the tilt angle t can be calculated by solution of the equation system Q zh k s Q xh yk cosC h k tant

Ž4.

with three equations resulting from each hk pair. Finally the cross-section area per chain can be obtained from molecular area parallel to the interface A x y and the tilt angle t . A 0 s A x y cost .

Ž5.

2.4. Substances The amphiphile N-dodecyl- g -hydroxybutyric acid amide ŽDHBAA . wC 12 H 25 ]NH]CO] ŽCH 2 . 2 ]CH 2 ]OHx turned out to be a good candidate for

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

27

Fig. 4. Principles of GIXD experiments.

studying the phase transition and condensed phases in adsorption layers. The preparation and purification ŽG 99%. of DHBAA is described elsewhere w45,47x. The description of the preparation and purification of another tailored amphiphile N-Žg-hydroxypropyl.tridecanoic acid amide ŽHTRAA. wC 12 H 25 ]CO]NH] ŽCH 2 . 2 ] CH 2 ]OHx is also given elsewhere w52x. The water used for the experiments was made ultra-pure by a Milli-Q system. The spreading solvent for DHBAA was chloroform Žp.a., Baker., and for the alcohols was n-heptane ŽMerck, Darmstadt..

3. Adsorption kinetics studies 3.1. p (t) transients In spite of the far-reaching meaning of the adsorption kinetics for the various applications of surfactants, a phase transition in the adsorption layer which is formed during the adsorption process has been completely discounted. Numerous experiments and their theoretical description have resulted in continuous p Ž t . transients so that a homogeneous distribution of the adsorbed material has been suggested Žsee e.g. w34x.. Encouraged by the recent experience in characterisation of the phase properties of Langmuir monolayers the question should be fundamentally clarified whether and under which conditions condensed phase structures can be formed in the homogeneous fluid-like phase of adsorption layers. The p Ž t . adsorption kinetics studies of the tailored amphiphile N-dodecyl-g-hydroxybutyric acid amide ŽDHBAA. have provided the first indication for a firstorder phase transition w44]47,49x. Similar to the equilibrium p ]A isotherms of

28

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

Langmuir monolayers, a discontinuity in the p Ž t . adsorption kinetics should indicate a phase transition in adsorption layers. For different temperatures, Fig. 5 shows the p Ž t . transients of DHBAA from a 1.5 = 10y5 M aqueous solution at the purified surface corresponding approximately to the initial conditions: t s 0, G s 0. As known from previous work, the p Ž t . transients show a continuous course over the whole time interval at higher temperatures. Below a definite temperature, however, a break in the continuity of the transients can be observed w44,45,49x. Appearance and position of an inflection point in the continuous shape of the p Ž t . transients depend not only on the temperature, but also on the bulk concentration of the amphiphile DHBAA w45x. The critical surface pressure of the phase transition point is, however, only a function on the temperature. The probability of a phase transition point in the p Ž t . adsorption kinetics increases, the lower the temperature and the higher the bulk concentration of the amphiphile. At the critical condition at which the first indication of an inflection point can be observed the adsorption layer reaches a critical state at which the formation of a new phase is expected. Beyond the inflection point, the further increase in the surface pressure is drastically reduced w44,45x. 3.2. BAM studies during the adsorption kinetics Recent studies of Langmuir monolayers have shown that two-dimensional condensed phase textures are formed above the main transition point of the p ]A isotherms. BAM studies of the adsorption layer can, therefore, provide direct information on the nature of the inflection point of the p Ž t . transients. The integral reflectivity signal of the BAM technique is a sensitive indicator for a first order phase transition in monolayers at the air]water interface as the formation of 2D condensed phase provides a strong reflectivity signal.

Fig. 5. p Ž t . adsorption kinetics of 1.5 = 10y5 M aqueous DHBAA solution at different temperatures. The coordinates of the phase transition points are a function of the temperature w45x.

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

29

All the p Ž t . transients having the usual continuous shape without an inflection point, show no remarkable change in the reflectivity. Consequently for the uniformly distributed adsorbed material, a fluid-like state without a phase transition can be expected. The situation is completely different under conditions when an inflection point occurs in the p Ž t . adsorption kinetics. Then the formation of a condensed phase in the adsorption layer is indicated by a steep increase in the integral reflectivity w44,45x. This can be clearly seen in Fig. 6, where the transients of the surface pressure and the reflectivity for a 2 = 10y5 M DHBAA solution at 108C are compared. It is interesting to note that the increase in the reflectivity starts after an induction time beyond the inflection point of the p Ž t . transient, i.e. beyond the thermodynamically-induced phase transition. The low reflectivity during the induction time may be caused by the fact that the condensed phase nuclei need a certain time to grow up to microscopic scale. During the induction time, the size of the newly formed condensed phase nuclei is not large enough to be seen microscopically by BAM. After the thermodynamic phase transition, an induction time is necessary that the dimensions of the newly formed phase reach the microscopic scale in order to affect the integrated reflectivity for BAM visualisation w45x. The increase in the integrated reflectivity is caused by the evolution and growth of condensed phase structures within the homogeneous fluid phase w44,45x. This can be convincingly demonstrated by a sequence of BAM images ŽFig. 7. taken at characteristic times after the inflection point of the thermodynamic phase transition and corresponding to the letters a]d of transients of Fig. 6 w44x. As expected,

Fig. 6. Comparison of the p Ž t . adsorption kinetics and the corresponding integrated reflectivity of 2 = 10y5 M DHBAA solutions at T s 108C. Note the induction time between the thermodynamically induced phase transition and the increase in the integrated reflectivity where the newly formed condensed phase cannot yet be observed microscopically. At the designated points Ža. ] Žd. BAM images were taken and are shown in Fig. 7 w44x.

30

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

Fig. 7. Formation and growth of the condensed phase domains in the DHBAA adsorption layer corresponding with the designated points Ža. ] Žd. of the transients of surface pressure and integrated reflectivity of Fig. 6 at T s 108C. Ža. During the induction time, the condensed phase domains are in sub-microscopic scale and cannot yet be seen. Žb. Condensed phase domains are formed within the continuous low-density fluid phase. Žc. and Žd. Growth of the condensed phase domains with three main growth directions w44x.

microscopic condensed phase textures cannot be seen before the integral reflectivity increases ŽFig. 7a.. Consequently during the induction time, condensed phase textures of microscopic size do not exist and those of sub-microscopic size cannot be determined. During the induction time, the size of nuclei formed after the thermodynamic phase transition is not large enough to be detected microscopically by BAM. Fig. 7b]d show different growth steps from microscopically small textures to extended and branched patterns at the expense of the fluid phase. At the beginning, the single condensed phase domains grow in a shape-preserving way ŽFig. 7b and c.. However, they develop side branches at a certain size ŽFig. 7d.. Finally, near the adsorption equilibrium, a large part of the accessible surface can be covered by the two-dimensional condensed phase w45x. This behaviour has also been confirmed by other amphiphiles, the adsorption layers of which show a main phase transition w48x. At higher temperature ŽT G 108C. another texture type is formed during the DHBAA adsorption w45x. Selected steps of the growth kinetics of this domain type

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

31

Fig. 8. Selected steps of the growth of a selected condensed phase domain formed during DHBAA adsorption from 1.5 = 10y5 M DHBAA solution at T s 158C. The thermodynamic phase transition, t c begins at 1160 s. Ža. t s 3220 s; Žb. t s 3250 s; Žc. t s 3280 s w45x.

32

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

from an initial state of ; 20 m m to a large size of more than 400 m m, demonstrate convincingly the growth in a shape-preserving way ŽFig. 8.. Further evidence for main phase transition in adsorption layers has been obtained for another special tailored amphiphile w48x, but also for the simple amphiphile dodecanol w50x. N-g-hydroxypropyl.tridecanoic acid amide ŽHTRAA. wC 12 H 25 ]CO]NH] ŽCH 2 . 2 ]CH 2 ]OHx dissolved in water provides similar inflection points in the p Ž t . transients as those presented for DHBAA w48x. The condensed phase domains of HTRAA grow also in different main growth directions. Different tilt directions of the molecules can be observed within different regions in the progressed growth stages of the condensed phase.

4. Texture features of the condensed phase domains The BAM experiments have shown that, depending on the temperature, different types of morphological textures of the condensed phase can exist. After the induction time, the BAM images confirm the coexistence of two phases, namely a low-density fluid-like phase Ždark regions. and a condensed phase Žbright domains.. In the case of DHBAA adsorption layers, two different types of condensed phase textures have been observed at temperatures above and below 108C ŽFig. 9. w44,45x. An effective possibility to analyze the optical anisotropy of the texture patterns results from the comparison of the texture patterns at different analyser positions. If the chains are oriented parallel to the incidence plane the p-polarised light is reflected without a change in polarisation. If the analyser is rotated, the ratio of reflected p- and s-polarised light is altered, and consequently the brightness changes with the azimuthal orientational order of the domain. Parallel polarisers cause largest brightness, whereas crossed polarisers provide lowest brightness. At temperatures F 108C the DHBAA domains have one main growth axis and two additional growth directions. Each arm of these two growth directions reflects homogeneously, but reflectivity of the arms is different. Both arms form an acute intersection angle of about 608. The main growth axis is subdivided by a straight line into two sections with different uniform reflectivity. The main axis forms an obtuse angle of about 1508C with each of the homogeneously reflecting axes. If the optical plane coincides with one of the homogeneously reflecting arms, the texture analysis of the optical anisotropy shows that at parallel positions of polarizer and analyser the bisector of the main axis subdivides the domains into two sections reflecting with different brightness, whereas for crossed polarisers the brightness of one of the sections is drastically reduced or disappears. This fact suggests an azimuthal tilt direction of the molecules parallel to the homogeneously reflecting growth axis which has an obtuse angle of 1508C with the bisector of the main axis. This is corroborated by shape and direction of some growth defects along the bisector ŽFig. 9.. The orientational order of this domain type formed at temperatures F 108C indicates that this domain type can be considered to be a contact twin. At temperatures ) 108C, the homogeneously reflecting domain textures show

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

33

Fig. 9. BAM analysis of the two condensed phase textures formed in DHBAA adsorption layers for T F 108C and T ) 108C at different analyser positions. For T F 108C Ža. at parallel polarisers the whole domain is visible having two sections of different brightness, Žb. at crossed polarisers one section disappears, Žc. schematic presentation of the orientational order of the alkyl chains. For T ) 108C Žd. at parallel polarisers the whole domain is visible, but homogeneously reflecting, Že. at crossed polarisers the whole domain disappears or the brightness is drastically reduced, Žf. schematic presentation of the orientational order of the alkyl chains.

34

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

four main growth directions with characteristic intersection angles of 60 and 1208. The homogeneous reflectivity is an indication for the same azimuthal tilt direction of the molecules ŽFig. 9, right-hand side.. Side arms can be evolved along the main axis, the direction of which is along the two adjacent main axes. Here the domains reflect with homogeneous brightness at parallel positions of polariser and analyser, whereas the domains disappear or their brightness is drastically reduced for crossed polarisers. Accordingly the azimuthal tilt direction of the molecules is parallel to one of the main growth axes, as presented by the double arrows in the right-hand side of Fig. 9.

5. Bridging between Gibbs and Langmuir monolayers 5.1. Comparison of the phase transition points and texture features in Gibbs and Langmuir monolayers The tailored amphiphiles used to prove a first order phase transition in adsorption layers, have the advantage that their solubility in some organic solvents allows a comparison with corresponding Langmuir monolayers. Traditional experiences in the field of Langmuir monolayers can provide additional support for a main phase transition. However, for soluble amphiphiles, such as DHBAA, the loss of monolayer material due to desorption and dissolution must be considered. Therefore quite high compression rates must be applied to minimise the material loss. It can be estimated that for DHBAA monolayers compressed with rates of 0.007]0.001 nm2 moleculey1 sy1 the mass losses due to desorption did not exceed 10%, even for highly compressed monolayers w51x. Langmuir monolayers of DHBAA were formed by spreading of 10y3 M solutions in CHCl 3 w45x. A sequence of p ]A isotherms recorded for a temperature range 3]258C shows clearly the main transition point at which the phase transition region starts. The following non-horizontal plateau region is due to the coexistence of a fluid-like and condensed phase. These isotherms provide clear evidence for a main phase transition of first order. As known for Langmuir monolayers of numerous other amphiphiles, the width of the plateau region decreases with increasing temperature. The main phase transition point is shifted as a function of the temperature, see e.g. w17,19,21x. It is interesting to compare the main transition points of the p ]A isotherms with the critical surface pressures for the thermodynamic phase transition points during the adsorption kinetics ŽFig. 10. w45x. The surface pressures of both transition points nearly agree and are a linear function of the temperature. The inflection point of the p Ž t . adsorption kinetics corresponds consequently to the beginning of the first order main phase transition. The textures formed in the two-phase coexistence region of the p ]A isotherms ŽFig. 11. and the p Ž t . adsorption kinetics ŽFig. 5. reveal striking similarity for comparable parameters. Shape and texture of the condensed phase domains evolved at compression of Langmuir monolayers resemble those of domains

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

35

Fig. 10. Comparison of the temperature dependence of surface pressure for the main phase transition points in adsorption layers ŽGibbs monolayers. and in Langmuir monolayers of the amphiphile DHBAA. Langmuir monolayers: B} measured values of p ]A isotherms. Gibbs monolayers: I, `, U , ^ } measured values for T - 208C and obtained for different concentrations of the sub-solution. For T s 208C the surface pressure for saturation adsorption, ps was taken w45x.

observed during the adsorption kinetics of the dissolved material. Fig. 11 shows that the characteristic domain textures formed in the two-phase coexistence region depend also on the temperature. In the corresponding temperature region, the typical textural features are comparable with those observed in the adsorption layers, but the domains are smaller and not so well developed. Two different texture types of condensed phase domains are formed. At T F 108C, the domains are also subdivided by a mirror line of a main growth axis into two different reflecting sections, each of them having an additional growth direction. Each section has the same azimuthal tilt direction of the amphiphilic molecules. At T ) 108C, the condensed phase domains with four growth directions have likewise a homogeneous inner texture. The general agreement of the condensed phase textures formed in Langmuir and Gibbs monolayers provides an essential support of the conclusion of a first order phase transition drawn from the adsorption kinetics experiments. This is also a substantial argument that highly surface-active impurities cannot be the reason for the formation of condensed phase domains in adsorption layers. In such a case, shape and texture of domains formed in adsorption layers should be completely different from those developed during the compression of the Langmuir monolayers. Although the main textural features of the condensed phase domains formed in Langmuir monolayers agree with those developed during the adsorption kinetics some minor differences exist. Generally in the Langmuir monolayers, the textures are smaller and not developed as well as in the corresponding Gibbs monolayers. This fact can be caused by the quite high compression rate, which was used in

36

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

Fig. 11. Comparison of the characteristic domain textures formed in the two-phase coexistence region of adsorption layers and Langmuir monolayers at T F 108C and T ) 108C.

Langmuir monolayers to reduce the desorption of monolayer material, and the 10 times lower growth rate of domain tips in the adsorption layers. The amphiphile HTRAA represents another example for the formation of similar textures in the corresponding two-phase coexistence regions of Gibbs and Langmuir monolayers w48x. These condensed phase domains grow in different main growth directions and form regions of different azimuthal tilt directions. 5.2. Theoretical considerations The similarities of phase transitions and texture features of Gibbs and Langmuir monolayers enable a direct comparison between the p ]A and adsorption isotherms. The transformation of the p ]t adsorption kinetics into a p ]AŽ t . adsorption kinetics allows a direct comparison with the p ]A isotherms. During the adsorption

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

37

kinetics a correlation between the surface pressure and the molecular area exists for each monolayer state. Therefore a molecular area Ž A. ]time Ž t . relationship can be calculated for the adsorbed monolayer. For the theoretical description of the adsorption kinetics, the differences of the states of the adsorption layer, which exist before and after the phase transition point, must be considered w48x. For t F t c before the phase transition point with the critical surface pressure pc , the long-time approximation ŽEq. Ž6.. w53x of the Ward]Tordai equation w54x can be used for the fitting procedure:

(

2c

G Žt. s 1q2

Dt

p

dc dG

(

Ž6.

Dt

p

where D is the bulk diffusion coefficient and c the bulk concentration. This can be considered to be the fixed G value in quasi-equilibrium. By using the relation G s 1rŽ NA = A. between surface concentration G and molecular area A which are related via Avogadro’s number NA , it holds: AŽ t . s

k ads

't

q A`

with

Ds

p = NA 4c

2

2 k ads

and

dc dG

s

A` c NA

Ž7.

where k ads is an adsorption rate constant and A` is the molecular area in the saturated state Ž t ª `.. Hence the p ]A isotherms can be directly correlated with the adsorption kinetics in the region w48x. For p - pc , the monolayer is completely in a fluid-like state, so that the molecular area during the adsorption process can be calculated before the phase transition starts. This A]t relation can be conformed to Eq. Ž7.. With these conformities, molecular areas A` of the saturated state between 0.20 nm2rmolecule and 0.25 nm2rmolecule were obtained which correspond to the areas per molecule of the condensed phase in the p ]A isotherms. For t ) t c , the long time approximation for the adsorption kinetics is no longer valid. The phase transition to an ordered condensed phase cannot be described by a diffusion-controlled process. However it is reasonable to assume that the molecules adsorb only into the fluid-like phase with a constant adsorption rate since the molecular area of the fluid-like phase of low-density remains constant during the phase transition. dA dt

s const.s

d AŽ t c . dt

for t G t c

Ž8.

In the two-phase coexistence region, the averaged area per molecule AŽ t . is

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

38

defined as AŽ t . s

FG Ž t . F0

Ž AG y AC . q AC

Ž9.

where F0 s Fg q Fc is the overall surface area, FG the ratio of the low-density fluid-like phase, FC the ratio of the condensed phase, A G the averaged molecular area occupied by the fluid-like phase, and A C the averaged molecular area occupied by the condensed phase. A small amount of freshly adsorbed molecules d Nads , causes a small change of FG which again is related to a small change of FC , as the adsorption leads to the transition to the condensed phase yd FG s A C =

`

n

AC

Ý ns0

= d Nads s A C =

ž / AG

AG AG y AC

= d Nads

Ž 10.

A small change of ratio of condensed phase can be correlated to a small change of the averaged molecular area A C = d Nads Ž t . s y

FG AG

=dA

Ž 11 .

The following differential equation can be derived by the combination of Eqs. Ž8., Ž10. and Ž11. d FG s

d AŽ t c . dt

=

FG AG y AC

dt

Ž 12 .

Integration of Eq. Ž12. and combination with Eq. Ž9. leads finally to AŽ t . s Ž A G y A C . = exp

ž

1 AG y AC

=

d AŽ t c . dt

= Ž t y t c . q AC

/

Ž 13.

For t G t c the adsorption kinetics can be described by AŽ t . according to Eq. Ž13. w48x. Fig. 12 shows an example for the direct comparison of the measured p ]A isotherms with the corresponding p ]AŽ t . adsorption isotherms of the water-soluble amphiphile N-Žg-hydroxypropyl.-tridecanoic acid amide ŽHTRAA. w48x. The p Ž t . transients measured at T s 4 and 108C show similar inflection points, as presented for the amphiphile DHBAA in Fig. 5. These p Ž t . transients were used for the transformation into the p ]AŽ t . isotherms with Eqs. Ž7. and Ž13.. Fig. 12 shows not only the good agreement with the measured p ]A isotherm of the Langmuir monolayer before the phase transition and within the two-phase coexistence region, but also similarities of the domain textures formed in the two-phase coexistence region. The reasons for the differences in the region of strong increase

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

39

Fig. 12. Comparison of measured p ]A isotherms Žthin lines. and transformed p ]AŽ t . adsorption isotherms Žthick lines. of HTRAA monolayers at T s 48C and 108C. Characteristic texture forms, as observed in the two phase coexistence region of adsorption layer as well as the Langmuir monolayer at T s 108C and p s 10 mNrm, are inserted and the corresponding points indicated by the arrows w48x.

in the surface pressure have been discussed in detail elsewhere w48,51x and can be understood as a consequence of differences between Gibbs and Langmuir monolayers at low area values, where strong external forces affect the molecular interactions in amphiphilic monolayers.

6. Structure features of the condensed phase of adsorption layers GIXD experiments can contribute to a further characterisation of the condensed phase formed in adsorption layers and thus corroborate the fact that first order phase transition can occur during the adsorption kinetics w48,55]57x. Therefore GIXD measurements on Gibbs monolayers of DHBAA were performed at the selected temperatures 5 and 158C to obtain structure data on the two texture types observed for the condensed phase of the adsorption layer w55,56x. Fig. 13 shows a characteristic contour plot of the corrected diffraction intensities as a function of the in-plane Ž Q x y . and out-of-plane Ž Q z . components of the scattering vector for adsorbed DHBAA monolayers of a 2 = 10 M DHBAA solution measured at p s 21 mNrm and T s 58C. The positions of the peak maximum and their full widths at half-maximum are compiled in Table 1 for the two characteristic texture types formed above and below 108C. The crystal structure of each type is calculated from the positions of the peak

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

40

Table 1 Scattering vector components Q x y and Q z of the diffraction peaks for an adsorption layer of a 2 = 10y5 M aqueous DHBBA solution at 58C and 158C and their full width at half-maximum Ž D Q x y and D Q z .

p T Qxy Qz Qxy Qz Qxy Qz D Qxy D Qz D Qxy D Qz D Qxy D Qz ŽmNrm. Ž8C. Ž10. Ž10. Ž01. Ž01. Ž11. Ž11. Ž10. Ž10. Ž01. Ž01. Ž11. Ž11. ˚ . Ž1rA ˚ . Ž1rA ˚ . Ž1rA ˚ . Ž1rA ˚ . Ž1rA ˚ . Ž1rA ˚ . Ž1rA ˚ . Ž1rA ˚ . Ž1rA ˚ . Ž1rA ˚ . Ž1rA ˚. Ž1rA 21 25

5 15

1.422 0.031 1.380 0.73 1.451 0.006 1.382 0.69

1.473 0.70 1.472 0.66

0.007 0.22 0.006 0.2

0.018 0.25 0.007 0.25

0.016 0.27 0.011 0.27

maximum. The indexing of the diffraction peaks to lattice planes can be seen in the contour plot of Fig. 13. The three peaks of the contour plot indicate that the condensed phase of the DHBAA adsorption layer forms an oblique lattice. The calculated lattice parameters are listed in Table 2. The molecules are strongly tilted Žt ) 278. and have a tilt direction nearly parallel to the b axis of the unit cell for both texture types. A model of the crystal structure of this oblique lattice of the condensed phase of the DHBAA adsorption layer is presented in Fig. 14. The diffraction patterns of the DHBAA adsorption layers are qualitatively unchanged below and above 108C despite the large differences of the two texture types. As expected, the cross-sectional area increases with the temperature. The small cross-sectional area values A of the amphiphilic molecule indicate a crystalline packing. It is interesting to notice that for the adsorption layers, the full widths at half-maximum of the in-plane scattering vector components of the Ž11. and Ž01. reflexes are significantly smaller than those of the corresponding Langmuir monolayers. The slower growth of the condensed phase during the adsorption causes obviously a smaller defect density which finally results in a better developed domain texture, as observed by BAM. Studies of Langmuir monolayers have shown that the positional correlation length is largest parallel to the direction of a directed bond w58x. The surface pressure dependence of the spacing parallel to this

Fig. 13. Contour plot of a Gibbs monolayer of a 2 = 10y5 M DHBAA solution Žp s 21 mNrm, T s 58C. w55x.

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

41

Table 2 Lattice parameters of the condensed phase formed in adsorbed DHBAA layers at 58C and 158C

p ŽmNrm.

˚. a ŽA

˚. b ŽA

˚. c ŽA

˚2 . Axy ŽA

˚2 . A0 ŽA

g Ž8.

ca Ž8.

t Ž8.

21 Ž58C. 25 Ž158C.

4.895 4.881

5.115 5.123

5.227 5.196

22.3 22.2

19.2 19.4

117.1 117.5

114.9 115.3

30.3 28.9

a, b, c are lattice dimensions, g is the angle between the w10x Ž a axis. and w01x Ž b axis. directions, A x y is the unit cell area per molecule, t is the tilt angle of the molecules with respect to the normal, A 0 is the chain cross section, and C is the azimuthal tilt angle of molecules with respect to the w10x direction Ž a axis..

bond is significantly smaller. Therefore, it has been suggested that hydrogen bonding between the acid amide groups should be parallel to the a axis ŽFig. 14.. ˚ is the typical distance for hydrogen The dimension of the a axis of about 4.9 A bonding between amide groups. This conclusion and the larger lattice spacings of the b and c axes are in coincidence with the three-dimensional lattice structure of comparable amphiphilic acid amides w30,31,59]62x. The availability of the results on the domain textures and 2D lattice structure of the condensed phases of DHBAA adsorption layers suggests the question whether the macroscopic texture features can be correlated with the microscopic crystal structure w55x. Fig. 15 demonstrates that for both domain textures the main or preferred growth directions of the dendritic domains are related with the low indexed lattice directions although both texture types are described by the same lattice structure. For the lower temperature region ŽT F 108C., the preferred growth directions correspond to the w01x and w12x lattice directions so that the bisector of the main domain direction is parallel to the w12x lattice direction. For T G 108C, the growth directions correspond to the w01x and w10x lattice directions for intersection angles between the growth directions of 1208 and are parallel to the w11x and w10x lattice directions for intersection angles between the growth directions of 1508.

Fig. 14. Schematic presentation of the 2D crystal structure determined from the contour plot of the Gibbs monolayer of a 2 = 10y5 M DHBAA solution ŽFig. 13.. An oblique lattice with the tilt direction of the molecules almost parallel to the b axis of the unit cell is formed. Molecule size and lattice size are not in the same proportion w55x.

42

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

Fig. 15. Correlation of the 2D crystal structure Žleft. with the domain texture Žright. DHBAA adsorption layers for T F 108C Žtop. and T ) 108C Žbottom.. The positions of the molecules are represented by filled circles. The thick grey lines in the crystal structure illustrate the growth directions in the domains. The arrows symbolize the azimuthal tilt direction of the molecules. For comparison a schema of the unit cell is inserted w55x.

7. Other monolayer techniques for studying phase transitions in adsorption layers There are two possibilities to obtain information on the phase features of water-soluble amphiphiles without studying the adsorption properties, Ži. the adsorption layer formed by a saturated or over-saturated aqueous solution of the amphiphile can be compressed using the usual monolayer technique, Žii. a droplet of the dissoluble amphiphilic substance is deposited at the air-water interface. Then an equilibrium situation results in the coexistence of a monolayer with any excess collected in a lens, which constitutes a reservoir of molecules w39x. The first possibility can be used to study the phase transition in boundary situations where it is not clear whether a phase transition can be expected for the adsorbed amphiphilic material dissolved in the aqueous sub-phase. The compression rate must be rapid enough that the compressed material of the adsorption

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

43

layers behaves as a Langmuir monolayer and cannot desorb significantly into the aqueous bulk solution during the experimental time. Under these conditions the equilibrium between the surface and the aqueous bulk phase is intentionally disturbed to study the adsorption layer when the amphiphilic material is more tightly packed. The second technique can be considered to be a modification of the classic piston oil technique w40x and has been mainly used to investigate the phase behaviour of amphiphilic alcohols w63]66x. When at the surface an excess droplet is in coexistence with a monolayer the situation should be similar to an adsorbed monolayer in the sense that the monolayer is in equilibrium with a macroscopic phase fixing the chemical potential. Using this technique for surface tension, ellipsometry and X-ray diffraction studies, phase transition in saturated alcohol monolayers, which are dissoluble in the aqueous bulk phase, can be investigated when the temperature is changed.

8. Theory for phase transition in adsorption layers (Gibbs monolayers) The experimental finding of a first-order phase transition in adsorption layers has general consequences for the field of adsorption and adsorption kinetics. So far, phase transitions as well as the coexistence of a condensed phase and a fluid-like phase have been largely discounted, see e.g. w34x. The surface-active substance of an adsorption layer has been considered to be homogeneously distributed up to the state of saturation adsorption. Consequently, the description of the adsorption at the air]water interface is based on the continuous change of the state of homogeneously distributed material. Approaches for a phase transition can be merely derived for strong interactions from Frumkin’s adsorption isotherm w46x. Therefore a theoretical model has to be introduced to take the phase transition in adsorption layers into account. Such an adsorption kinetics model also requires the development of an equation of state for the monolayer which describes the state of the monolayer after the main phase transition point with two coexisting phases and the final transition to the condensed state. 8.1. Equation of state for Langmuir monolayers [51] The plateau region of the surface pressure]area Žp ]A. isotherm is attributed to the main transition from a fluid phase of low density to a condensed phase. For this first-order phase transition, the most commonly used two-dimensional equations of state predict horizontal lines in the p ]A isotherm. However, the experimental p ]A isotherms show non-horizontal straight lines the slope of which usually increase with temperature Že.g. w17,19,21,67x.. Recently some theoretical approaches should resolve this discrepancy w68]70x, but the calculated p ]A isotherms were only in qualitative, not in quantitative agreement with the experimental data w70x. The non-horizontal plateau region was predicted for unrealisti-

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

44

cally low aggregation numbers Ž- 1000. w70x. However, the size of the experimentally observed condensed phase textures Že.g. w17,19x. allows an estimation of the aggregation numbers in the order of 10 6 and higher. The introduction of a first-order phase transition model is justified only for such high values for the aggregation number. Langmuir monolayers in the gaseous state are satisfactorily described by the general 2D equation of state kT

ps

Ayv

yB

Ž 14.

where p is the surface pressure, k the Boltzmann constant, T the temperature, A the area per molecule in the monolayer, v the net molecule area, i.e. the area actually occupied by the monolayer molecules. For B s const s p U Žcohesion pressure. Volmer’s equation w71x can be obtained, whereas for B s arA2 Ž a is a constant. Eq. Ž14. is transformed into the 2D van der Waals equation w40x. This general equation of state ŽEq. Ž14.. has been extended to further monolayer states which are formed after a main phase transition of first order. Two thermodynamic phases coexist due to the formation of 2D condensed phase. The process of formation of condensed phase is considered to be an aggregation process w51x. Monomers and aggregates Ž n-mers. are referred to as kinetic entities, so that the mean area per kinetic entity, A k , and the mean net area per kinetic entity, v k , can be expressed by Ak s

AŽ 1 q mn . 1qm

Ž 15.

and

vk s

v Ž 1 q mn . 1qm

Ž 16.

where A is the area per molecule, v k the net area actually occupied by a monomer molecule, m the number of aggregates per monomer Žin general m < 1., and n the aggregation number Ž n 4 1.. The introduction of Eqs. Ž15. and Ž16. for the corresponding kinetic entities into Eq. Ž14. leads to

ps

kT Ž A y v.K

yB

Ž 14a .

where K s Ž1 q mn.rŽ1 q m.. Since n 4 1 and m < 1, K may be approximated as K s 1 q mn. Expressions for the constant K can be obtained from the monomer]aggregate equilibrium condition in the monolayer which was treated using Buttler’s equation w72x. If the equilibrium between the aggregates and monomers is treated using

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

45

Buttler’s equation the validity of Eq. Ž14. can be extended to the two-phase coexistence region. For A - A c , the calculations have led to the following expression for the mean area per kinetic entity, A k w51x Ak s A

1 q n Ž A crA1 . 1 q Ž A crA1 .

ny 1

ny1

s KA

Ž 17 .

where A1 is the monomer area in the surface and A c the area of the thermodynamic phase transition point. Comparison with Eq. Ž15. provides the expression for the aggregate number per monomer, m m s Ž A crA1 .

ny 1

Ž 18.

In the region A - A c , the constant K can be calculated using Eqs. Ž17. and Ž18. when the correlation between the area per monomer, A1 , and the total molecule surface, A, of the monolayer is considered Ž A n is area of an n-mer. A s A1 q nA n s A1 1 q n Ž A crA1 .

ny1 y1

Ž 19.

The calculation of K as a function of ArA c for very different aggregation numbers Ž n s 10 3 ]10 6 . ŽFig. 16. has provided interesting information 1. for n ) 10 3 , the coefficient K is independent of the aggregation number, n, and is only a function of ArA c , 2. the area of the monomer, A, does not change very much and corresponds approximately to the area in the critical point Ž A1 f A c . with an accuracy of not less than 10rn, 3. the number of aggregates per monomer, m, is m < 1 Žusually m - 10rn and thus K f 1 q mn. In the region A ) A c , a similar approach can be used for the gaseous monolayer. Here the differences in the monolayer behavior with respect to that of the ideal two-dimensional gas are related to the formation of small aggregates, while intermolecular interaction is not taken into account. The non-ideality of the gaseous monolayer which made it necessary to introduce the coefficient B into Eq. Ž14., is due to the formation of small aggregates. Such aggregation of adsorbed amphiphilic molecules with cluster sizes up to 20 molecules was also concluded by modeling of adsorption isotherms using the Ising lattice gas model w73x. For such small aggregates it can be approximated that number of monomers per unit surface is equal to the number of aggregates, i.e. Gn s G 1 s G 1r2 . For small aggregation numbers, n, the following relation was derived A s A1 1 q n Ž A1r2rA1 .

ny1 y1

Ž 20 .

Fig. 17 shows the dependence of the coefficient K 1 s Ž1 q mn.rŽ1 q m. on the

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

46

Fig. 16. Dependence of the coefficient K on ArA c for different aggregation numbers n G 10 3 w51x.

ratio ArA1r2 for different small n-values Ž n s 2]15.. Here the K 1 values depend strongly on n which is different to the behaviour of K for n ) 10 3 Žsee Fig. 16.. Based on the differences in the effect of the aggregates above and below the main phase transition point which has the co-ordinates pcrA c , the following two equations of state were derived w51x. For A ) A c and the formation of small aggregates

ps

kT

Ž 21.

Ž A y v . K1

where K 1 s K U expŽypDvrkT ., Dv s n v 1 y v n , and K U is the value of the coefficient K 1 s Ž 1 q mn . r Ž 1 q m .

for p s 0,

and for A F A c at two-dimensional aggregation

ps

pc Ž A c y v . A c Ž 1 y vrA .

Ž 22.

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

47

Fig. 17. Dependence of the coefficient K 1 on ArA c for different aggregation numbers n s 2]15 w51x.

The non-horizontal plateau region can be concluded from Eq. Ž22.. This equation shows that in the region A F A c , the value of p increases with decreasing area, A, and does not remain constant. In the two-phase coexistence region the slope of the p ]A isotherm increases with the decrease in the A c value. Furthermore, it can be seen that for large n-values ŽG 10 3 ., the p ]A isotherm predicted by Eq. Ž22. is independent of the aggregation number, n. The equations of state of monolayers have been successfully verified by numerous p ]A isotherms measured over wide temperature ranges. 1-Monopalmitoylrac-glycerol ŽMPG. monolayers have a pronounced 2D phase coexistence region over a large temperature region w19,51x. In Fig. 18, the experimental curves and the calculated data for selected temperatures are compared. It can be seen that the results predicted by the theory are in good agreement with the experimental p ]A isotherms. The parameters of the phase transition for MPG monolayers are compiled in Table 3. For A F A c in the region of 2D phase transition, Eq. Ž22. generally provides a correct description of p as a function of A and pc up to the condensed monolayer

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

48

Table 3 Parameters of 2D main phase transition of 1-monopalmitoyl-rac-glycerol monolayers T Ž8C.

Ac Žnm2 rmolecule.

Pc ŽmNrm.

vf Žnm2 rmolecule.

PU ŽmNrm.

K U exp ŽyPc DvrkT .

15 17 20 23 25 27 30 35 42

0.64 0.60 0.55 0.50 0.47 0.445 0.41 0.37 0.33

0.8 1.8 3.7 5.9 8.0 9.9 13.1 18.0 26.6

0.25 0.23 0.20 0.15 0.14 0.15 0.13 0.13 0.10

8.66 8.73 8.55 8.69 8.45 8.5 8.91 10.34 12.9

11.80 5.85 3.31 2.47 2.06 1.68 1.68 1.57 1.49

Fig. 18. Surface pressure]area Žp ]A. isotherms of Langmuir monolayers of 1-monopalmitoyl-racglycerol. Experimental results w19x are presented by curves; symbols correspond to the calculations using Eq. Ž22. w51x.

state. For the region A ) A c , the values of the coefficient K 1 s K U expŽypc DvrkT . were calculated from the parameters of the critical points by using Eq. Ž21. for v s 0.22 nm2 . Whereas the coefficient K 1 decreases with the increase of pc , the values of the coefficient K U are constant. When setting the value Dv s 0.9 " 0.2 nm2 for MPG, K U s 9 is obtained. For these values of K U

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

49

and Dv , Eq. Ž21. agrees with the experimental data for gaseous monolayers, that is, in the same range where Volmer’s equation Ž B s p U in Eq. Ž14.. is valid. However, it is a disadvantage of Volmer’s equation that it cannot be used at p-values defined above for A ) 0.68 nm2 because it leads to negative p-values in this range. Such restrictions do not exist for Eq. Ž21. in the range of high A values. For the region of gaseous clusters, aggregation numbers, n, of ; n s 2]20 have been estimated using the K 1-values listed in Table 3. 8.2. Kinetics of two-dimensional phase transition of amphiphilic monolayers [74] For the analysis of the experimental results, a theoretical model has recently been developed which considers the adsorption kinetics from micellar solutions under the conditions of 2D phase transition of first order. The model is valid over a wide range of bulk concentrations and allows the calculation of the associationrdissociation kinetics in the bulk solution with the kinetics of two-dimensional association in the surface. For aggregation in the monolayer, it can be assumed w75,76x that the rate constants of direct and back reactions Ž1. are independent of the aggregate size, and thus the kinetics of a phase transition in monolayers can be described as a first-order reaction kU 1

G 1 ¡ G 1U

Ž 23.

k1

where the asterisk refers to aggregated monomers. Thus in this model, the aggregation is treated as the change of state of monomer molecule within the surface. Including the diffusion from Žand to. the bulk, the expansion]compression of the surface and the aggregate formation according to Eq. Ž23., the monomer balance in the surface layer is described by the equation d G1 dt

q uG 1 s k 1 n Gn y kU1 G 1 q D

­c

ž / ­x

Ž 24. xs0

where t is time, u s dln Vrdt the dilatation rate, V the surface area, kU1 and k 1 the rate constants for direct and back reaction ŽEq. Ž23.. respectively, Gn the surface concentration Žadsorption. of the aggregates Ž n-mers., Gn s G 1U rn and x the coordinate normal to the surface. At equilibrium Žd G 1rdt s 0, u s 0 and Ždcrd x . xs0 s 0. it follows from Eq. Ž24.

G 1o s Gno

nk 1 kU1

Ž 25.

where the superscript o refers to equilibrium. Eq. Ž24. can be reduced for small deviations from the equilibrium where the conditions G 1 s G 1o q DG 1 and Gn s Gno q DGn hold and the mass balance condition yields DGn ? n s yDG 1.

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

50

Then d DG 1 dt

q uG 1o s yk n DG 1 q D

­c

ž / ­x

Ž 26. xs0

where k n s kU1 q k 1 s k 1Ž1 q Gno ? nrG 1o .. 8.2.1. Insoluble monolayer For the conditions of the dynamic P Ž A. experiment at u s const, Eq. Ž26. becomes d DG 1 dt

s yuG 1o y k n DG 1

Ž 27.

A rigorous treatment presented in detail in Ref. w74x leads finally to

Dp s

kTA21 u Ž A1 y v . 2 A1o k n

w exp Ž yk n t . y 1 x

Ž 28.

where k is the Boltzmann constant, T the temperature, v the net monomer molecule area, A1 s 1rŽ G 1 N . the area per one monomer in the monolayer and N Avogadro’s number. For the estimation of the constant k n , Eq. Ž28. can be simplified for the conditions of the initial stage of the 2D phase transition in a compressible monolayer. Then with u s Žd Ardt .rA f Žd Ardt .rA c s constant at d Ardt s constant, and for k n t ) 1 and A c y A < A c , a simple expression is obtained w74x kn s

pgas y peq.tr pdyn y peq.tr

?

d Ardt Ž Ac y A.

Ž 29 .

where pgas is the pressure of the gaseous monolayer extrapolated to the region of 2D phase transition Ž A - A c ., A c the area per molecule in the phase transition point, peq.tr the equilibrium pressure in the region of 2D phase transition Žobtained from Eqs. Ž21. and Ž22.., and pdyn the surface pressure at A - A c under the conditions of dynamic p ]A experiments. Dynamic p ]A experiments were used to estimate the constant k n w49,74x. Theoretical and experimental results agree quite well for the sparingly soluble monolayers of the amphiphile THBAA Ž N-tetradecyl-g-hydroxybutyric acid amide. ŽFig. 19., particularly in the range A c s A ) 0.3 nm2 , where the peq.tr.Ž A. correlation was calculated from Eq. Ž22. with the critical coordinates A s 0.54 nm2 , p s 3.4 mNrm and v s 0.21 nm2 . The k n-value of the order of 1 sy1 was calculated from Eq. Ž29. by estimating the value Žpgas y peq.tr. .rŽ A c y A. f const s 30 mNrŽm nm2 ..

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

51

Fig. 19. p ]A isotherms of THBAA for different compression rates at T s 158C. The coordinates of the ˚ moleculey1 sy1 Ždotted line.; Žb. 0.5 A ˚ main phase transition point Žpc , A c . are indicated. Ža. 1.04 A ˚ moleculey1 sy1 Ždashed line.; Žd. 0.05 A ˚ moleculey1 sy1 Ždotted and dashed line.; Žc. 0.25 A moleculey1 sy1 Žfull line. w74x.

8.2.2. Adsorption from solution For adsorption of the amphiphile from the bulk solution, Eq. Ž26. becomes at Qs0 d DG 1 dt

s yk n DG 1 q D

­c

ž / ­x

Ž 30 . xs0

According to experimental results, the non-micellar bulk solution and 2D aggregates in the adsorption monolayer coexist only in a narrow range of low bulk concentrations of the amphiphile. Therefore the Ždcrd x . xs0 term in Eq. Ž30. expresses the case of micellar solutions. As phase transition within the surface takes place at sufficiently high time values an asymptotic solution of the diffusion equation for t ª ` has been used. According to w74x the kinetic Eq. Ž30. can be transformed into d DG 1 dt

s yk n DG 1 q Ž c 0 y c1 s .

(

D

t

where t is the relaxation time of the micelles association]dissociation process, c 0 the CMC Žcritical micelle concentration ., and c1 s s c 1Ž0,t y l. the concentration of the monomers near the surface. Finally one obtains for DG 1

DG 1 s

DG 1U k n Dt

w 1 y exp Ž yk n D t .x

Ž 32 .

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

52

where DG 1U Žand thus Dp U ; DG 1U . corresponds to the state of the supersaturated gaseous monolayer without a 2D phase transition. Dp ; DG 1 for small deviations from the equilibrium and Eq. Ž32. can be modified to

pdyn y peq.tr.s

pgas y peq.tr. k n Dt

w 1 y exp Ž yk n D t .x

Ž 33.

where pdyn is the dynamic surface pressure at t ) t c and t c the inflection point of the function p s p Ž t ., see Fig. 5, peq.tr the recovered equilibrium pressure at t ) t c , and pgas the pressure of gaseous monolayer extrapolated to the two-dimensional phase transition region at t ) t c . The rate constant k n can be estimated from Eq. Ž33., when the condition k n D t ) 1 is satisfied kn s

pgas y peq.tr. pdyn y peq.tr.

?

1

Ž 34 .

Dt

This equation implies a recovery in the equilibrium pressure curve for t ) t c . Assuming the equations of state ŽEqs. Ž21. and Ž22.. can also be applied for quasi-equilibrium one can determine the ratio of the derivatives dprdt at both sides of the inflection point in Fig. 5. As derived in ref. w74x, the ratio of quasi-equilibrium values of the derivatives dprdt near the phase transition point at t s t c , can be calculated as Ž dprdt . eq .tr. Ž dprdt . gas

s tst c

v Ac

exp Ž yk n ? D t .

Ž 35.

It follows from Eq. Ž35. that for k n ? D t G 2]3, the value Ždprdt .eq.tr.f 0. Consequently, the recovered equilibrium dependence of peq.tr. on t to the right of the main transition point has to be almost parallel to the abscissa axis in Fig. 5. For Gno ? n f G 1o the values of the direct and back reaction constants are almost equal to each other, i.e. k 1 f kU1 f k nr2. The 2D phase transition relaxation time, t , can be obtained due to the interdependence between the constant k n and Žaccording to
D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

53

Table 4 Kinetics of the 2D main phase transition in DHBAA adsorption layers Žp ]t experiment.

Pgas y Peq.tr

c Žmolrl.

Dt ŽmNrmrs. 10y5 2 = 10y5 2.5 = 10y5 3 = 10y5

0.006 0.01 0.02 0.025

Pdyn y Peq.tr ŽmNrm.

kn , ty1 Žsy1 .

0.07 " 0.01 0.10 " 0.02 0.14 " 0.02 0.20 " 0.04

0.09 " 0.02 0.10 " 0.02 0.14 " 0.02 0.13 " 0.03

t ª ` and trt 4 1 are satisfied y1

t

s

Ž RTG 12 .

2

c 02 D Ž ydprdty1 .

2

Ž 36.

Žii. for the fast dissociation process of micelles w76x owing to monomer exchange between micelle and from the dependence p s p Ž t . when the condition t ª 0 is replaced by condition cŽ0,t y l. s 0 and trt < 1 Ž l is the dummy integration variable.

ty1 f

s

Ž dprdt . 2

Ž 37.

Ž RTc0 . 2 D

from which also the dissociation rate constants of micelles, k s and k f , can be calculated w76x

ty1 s kf f

ž

c y c0 c0

/

Ž 38.

The conditions used to derive Eq. Ž37. are fulfilled in the time interval of about 50]250 s, i.e. for 2 F p G 8 mNrm of the p ]t adsorption kinetics of the aqueous DHBAA solutions, as presented in Fig. 5. The fast relaxation times, ty1 f , and the fast dissociation rate constants, k f , of micelles are listed in Table 5. The corresponding slow relaxation times ty1 and the s fast dissociation rate constants, k f , were calculated with Eqs. Ž36. and Ž38. and are presented in Table 6. The derivative dprdty1 based on the data presented in Fig. 5 was determined from the tangent to the curve in the immediate right of the characteristic point, that is, for maximum t values, directly before the phase transition. The value of G s Gc at 108C was assumed to be 4.5 = 10y6 molrm2 . The slow dissociation rate constant of the micelles k s was also obtained from Eq. Ž38.. A comparison of the values of k f and k s shows that under the same conditions, the k s values are significantly lower than those of k f .

54

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

Table 5 Fast dissociation kinetics of micelles in aqueous DHBBA solutions at different concentrations ŽT s 108C. dT Ž8C.

d Prdt ŽmNrmrs.

ty1 Žsy1 .

kf Žsy1 .

5 10 15 20 30

0.018 0.03 0.05 0.063 0.13

0.01 0.025 0.062 0.097 0.35

0.005 0.012 0.031 0.048 0.17

Table 6 Slow dissociation kinetics of micelles in aqueous 1.5 = 10y5 M DHBBA solutions at different temperatures c Žmolrl.

yŽd Prdt .y1 Žm srmN.

ty1 Žsy1 .

ks Žsy1 .

10y5 1.5 = 10y5 2 = 10y5 2.5 = 10y5 3 = 10y5

6.2 = 103 5.5 = 103 5.2 = 103 4.4 = 103 3.2 = 103

0.009 0.012 0.013 0.018 0.036

0.009 0.006 0.004 0.005 0.007

The data presented in Tables 4 and 5 enable the comparison of the kinetic constants and the relaxation times of the 3D Žbulk. and 2D aggregation. It is seen that the rate constant for the 2D phase transition in the monolayer is ; 10 times higher than the rate constant of the fast associationrdissociation of the micelles in the bulk solution.

9. Conclusions A review is given on recent work which has provided experimental and theoretical evidence that a phase transition of first order can occur in adsorption layers of amphiphiles which are dissolved in aqueous solution. For first fundamental studies in this new field of research, special tailored amphiphiles have to be used, which have the following features, Ži. high surface activity to avoid the effect of highly surface active impurities, Žii. solubility in aqueous solution in a certain range above the critical micelle concentration Žcmc., Žiii. solubility in some spreading solvents to allow a comparison with corresponding Langmuir monolayers. The amphiphile N-dodecyl-g-hydroxybutyric acid amide ŽDHBAA. is a good candidate to fulfil these conditions and thus, to investigate the first-order phase transition in an adsorption layer. In the mean time, first-order phase transitions in adsorption layers have been found for numerous other amphiphiles.

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

55

Effective methods for the study and characterisation of the phase transition and the condensed phase domains in adsorption layers of aqueous solutions are surface pressure Žp . measurements, Brewster angle microscopy ŽBAM. and synchrotron X-ray diffraction at grazing incidence ŽGIXD.. During the adsorption kinetics, phase transition is thermodynamically indicated by an inflection point in the continuous course of the p Ž t . transients. Appearance and location of the phase transition point depends largely on the concentration of the amphiphile in the aqueous solution and on the temperature. If a phase transition occurs in an adsorption layer the formation of condensed phase patterns surrounded by the homogeneous fluid-like phase are visualised by BAM. According to the measurements of the integral reflectivity signal, there is an induction time between the thermodynamic phase transition and the growth of condensed phase patterns on the microscopic scale. During the induction time, the size of the newly formed condensed phase nuclei is not large enough to be visualised microscopically by BAM. Different types of morphological textures of the condensed phase can be formed depending on the temperature, such as two types in DHBAA monolayers above and below 108C. Detailed information on the orientational order of the domain textures are obtained by rotating the analyser in the reflected laser beam. The lattice structure and the tilt angle of the alkyl chains can be determined by GIXD. The main growth directions of the condensed phase textures can be correlated to the lattice structure obtained by GIXD. The experimental bridging to the Langmuir monolayers supports the conclusions of a first order main phase transition drawn from the adsorption kinetics studies. The phase transition points in the p Ž t . transients correspond to the main transition points of the p ]A isotherm. In the same temperature region, the textures formed in the two-phase region of the p Ž t . transients and the plateau region of the p ]A isotherms agree completely in the major morphological properties. In the past, the possibility of first-order phase transition and the coexistence of a fluid-like and a condensed phase in adsorption layers has been largely discounted in the quantitative description of adsorption layers and adsorption kinetics. Based on the experimental findings a theoretical model has been very recently derived, which describes the adsorption kinetics of the two-dimensional first-order phase transition in an adsorption layer. The theory includes a kinetic model of the phase transition in Langmuir and Gibbs monolayers, the adsorption from the bulk solution and the dissociation kinetics of the bulk micelles. The theory allows the estimation of 2D aggregation rate constants from the p Ž t . adsorption kinetics and the dynamic p Ž A. experiments of Langmuir monolayers as well as the rate constants of the micelle formation. The analysis of the dynamic surface pressure Žp . ]area Ž A. experiments involves a description of the main phase transition between a fluid-like phase and a condensed phase and is based on new equations of state derived for monolayers. These equations consider the formation of two-dimensional aggregates and describe the non-horizontal plateau region of the p ]A isotherm for the two-phase coexistence.

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57

56

Acknowledgements Financial assistance from the Deutsche Forschungsgemeinschaft ŽSonderforschungsbereich 312, Vo 510r1-3. and the Fonds der Chemischen Industrie is gratefully acknowledged.

References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x w11x w12x w13x w14x w15x w16x w17x w18x w19x w20x w21x w22x w23x w24x w25x w26x w27x w28x w29x w30x w31x w32x w33x w34x w35x w36x w37x w38x

H. Mohwald, Annu. Rev. Phys. Chem. 41 Ž1990. 441. ¨ H.M. McConnell, Annu. Rev. Phys. Chem. 42 Ž1991. 171. C.M. Knobler, R.C. Desai, Annu. Rev. Phys. Chem. 43 Ž1992. 207. D. Jacquemain, S. Grayer Wolf, F. Leveiller, et al., Angew. Chem. 104 Ž1992. 134. D. Vollhardt, Adv. Colloid Interf. Sci. 64 Ž1996. 143. D. Mobius, Curr. Opin. Colloid Interf. Sci. 1 Ž1996. 250. ¨ S. Henon, J. Meunier, Rev. Sci. Instr. 62 Ž1991. 936. ´ D. Honig, D. Mobius, J. Phys. Chem. 95 Ž1991. 4590. ¨ ¨ D. Honig, Ph.D. Thesis, Gottingen, 1994. ¨ ¨ B. Fischer, E. Teer, C.M. Knobler, J. Chem. Phys. 103 Ž1995. 2365. M.-W. Tsao, T. Fischer, C.M. Knobler, Langmuir 11 Ž1995. 3184. D. Honig, G.A. Overbeck, D. Mobius, Adv. Mater. 4 Ž1992. 419. ¨ ¨ G. Weidemann, D. Vollhardt, Biophys. J. 70 Ž1996. 2758. S. Henon, J. Meunier, Thin Solid Films 210r211 Ž1992. 121. ´ S. Henon, J. Meunier, J. Chem. Phys. 98 Ž1993. 9148. ´ S. Riviere, J. Meunier, Phys. Rev. E 49 Ž1994. 1375. ` S. Henon, ´ D. Vollhardt, U. Gehlert, S. Siegel, Colloids Surf. A 76 Ž1993. 187. G. Weidemann, U. Gehlert, D. Vollhardt, Langmuir 11 Ž1995. 864. U. Gehlert, G. Weidemann, D. Vollhardt, J. Colloid Interf. Sci. 174 Ž1995. 392. U. Gehlert, D. Vollhardt, Progr. Colloid Polym. Sci. 97 Ž1994. 302. V. Melzer, G. Weidemann, D. Vollhardt, et al., J. Phys. Chem. B 101 Ž1997. 4752. S. Siegel, D. Vollhardt, Thin Solid Films 284r285 Ž1996. 424. G. Weidemann, D. Vollhardt, Langmuir 12 Ž1996. 5114. J. Als-Nielsen, in: W. Schommers, P. von Blanckenhagen ŽEds.., Structure and Dynamics of Surfaces, vol. 2, Springer Verlag, Berlin, 1986. J. Als-Nielsen, K. Kjaer, in: T. Riste, D. Sherrington ŽEds.., Phase Transitions in Soft Condensed Matter, NATO ASI Series B, Plenum Press, New York, 1989. K. Kjaer, Physica B 198 Ž1994. 100. J. Als-Nielsen, D. Jacquemain, K. Kjaer, M. Lahav, F. Leveiller, L. Leiserowitz, Phys. Rep. 246 Ž1994. 251. J. Als-Nielsen, H. Mohwald, in: S. Ebrashi, M. Koch, E. Rubenstein ŽEds.., Handbook on ¨ Synchrotron Radiation, Elsevier, Amsterdam, 1991. G. Brezesinski, E. Scalas, B. Struth, et al., J. Phys. Chem. 99 Ž1995. 8758. U. Gehlert, G. Weidemann, D. Vollhardt, G. Brezesinski, H. Mohwald, Langmuir 1998, in press. ¨ V. Melzer, G. Weidemann, D. Vollhardt, et al., Supramol. Sci. 4 Ž1997. 391. T. Gutberlet, D. Vollhardt, J. Colloid Interf. Sci. 173 Ž1995. 429. H.J. De Boer, The Dynamical Character of Adsorption, Oxford University Press, London, 1945. S.S. Duchin, G. Kretzschmar, R. Miller, in: D. Mobius, R. Miller ŽEds.., Dynamics of Adsorption at ¨ Liquid Interfaces, Elsevier, 1995. A.W. Adamson, Physical Chemistry of Surfaces, 5th ed., Wiley, New York, 1990. E. Ruckenstein, A. Bhakta, Langmuir 10 Ž1994. 2694. B. Berge, L. Faucheux, K. Schwab, A. Libchaber, Nature ŽLondon. 350 Ž1991. 322. J.M. Flesselles, M.O. Magnasco, A. Libchaber, Phys. Rev. Lett. 67 Ž1991. 2489.

D. Vollhardt r Ad¨ . Colloid Interface Sci. 79 (1999) 19]57 w39x w40x w41x w42x w43x w44x w45x w46x w47x w48x w49x w50x w51x w52x w53x w54x w55x w56x w57x w58x w59x w60x w61x w62x w63x w64x w65x w66x w67x w68x w69x w70x w71x w72x w73x w74x w75x w76x w77x

57

B. Berge, A. Renault, Europhys. Lett. 21 Ž1993. 773. G.L. Gaines, Insoluble Monolayers at Liquid-Gas Interfaces, Wiley, New York, 1966. D. Vollhardt, G. Czichocki, Colloids Surf. 11 Ž1984. 209. D. Vollhardt, G. Czichocki, Langmuir 2 Ž1990. 317. D. Vollhardt, M. Ziller, Colloids Surf. A 76 Ž1993. 203. V. Melzer, D. Vollhardt, Phys. Rev. Lett. 76 Ž1996. 3770. D. Vollhardt, V. Melzer, J. Phys. Chem. 101 Ž1997. 3370. V. Melzer, D. Vollhardt, Progr. Colloid Polym. Sci. 105 Ž1997. 130. V. Melzer, G. Weidemann, R. Wagner, D. Vollhardt, G. Brezesinski, H. Mohwald, Chem. Eng. ¨ Technol. 21 Ž1998. 44. V. Melzer, D. Vollhardt, G. Brezesinski, H. Mohwald, J. Phys. Chem. B 102 Ž1998. 591. ¨ D. Vollhardt, V. Melzer, V.B. Fainerman, Thin Solid Films 1998, in press. G. Emrich, S. Siegel, D. Vollhardt, Langmuir 1998, submitted. V.B. Fainerman, D. Vollhardt, V. Melzer, J. Phys. Chem. 100 Ž1996. 15478. R. Rudert, Y. Wu, D. Vollhardt, Z. Kristallogr. 211 Ž1996. 114. E. Rillaertes, P. Joos, J. Phys. Chem. 86 Ž1982. 3471. A.F.H. Ward, L. Tordai, J. Phys. Chem. 14 Ž1946. 453. V. Melzer, D. Vollhardt, G. Weidemann, G. Brezesinski, R. Wagner, H. Mohwald, Phys. Rev. E 57 ¨ Ž1998. 901. V. Melzer, G. Weidemann, D. Vollhardt, HASYLAB Annual Report, 1996, p. 459. V. Melzer, G. Weidemann, D. Vollhardt, HASYLAB Annual Report, 1997, p. 457. S.P. Weisbach, D. Jacquemain, F. Leveiller, K. Kjaer, J. Als-Nielsen, L.J. Leiserowitz, J. Am. Chem. Soc. 115 Ž1993. 11110. V. Melzer, G. Weidemann, D. Vollhardt, HASYLAB Annual Report II, 1995, p. 205. V. Melzer, G. Weidemann, D. Vollhardt, HASYLAB Annual Report II, 1995, p. 207. V. Melzer, G. Weidemann, D. Vollhardt, HASYLAB Annual Report, 1996, p. 457. V. Melzer, D. Vollhardt, G. Brezesinski, H. Mohwald, Thin Solid Films 1998, in press. ¨ A. Reneault, O. Schultz, O. Konovalov, B. Berge, Thin Solid Films 248 Ž1994. 47. B. Berge, O. Konovalov, J. Lajzerowicz, et al., Phys. Rev. Lett. 73 Ž1994. 1652. J.P. Rieu, J.F. Legrand, A. Reneault, et al., Phys. II France 4 Ž1995. 607. F. Bonosi, A. Reneault, B. Berge, Langmuir 12 Ž1996. 784. J.A. Overbeck, D. Honig, D. Mobius, Langmuir 9 Ž1993. 555. ¨ ¨ E. Ruckenstein, A. Bhakta, Langmuir 11 Ž1994. 2694. E. Ruckenstein, B. Li, Langmuir 11 Ž1995. 3510. J.N. Israelachvili, Langmuir 10 Ž1994. 3774. M. Volmer, Z. Phys. Chem. 115 Ž1925. 253. J.A.V. Buttler, Proc. R. Soc. Ser. A 138 Ž1932. 348. U. Retter, J. Electroanal. Chem. 349 Ž1993. 49. V.B. Fainerman, D. Vollhardt, V. Melzer, J. Chem. Phys. 107 Ž1997. 243. G.C. Kresheck, E. Hamori, G. Davenport, H.A. Seheraga, J. Am. Chem. Soc. 88 Ž1966. 246. E.A.G. Aniansson, S.N. Wall, J. Phys. Chem. 78 Ž1974. 1074; ibid 79 Ž1975. 857. V.B. Fainerman, G.M. Rakita, Kolloidn. Zh. 52 Ž1990. 106.