Phase transitions in Polymer Monolayers: Application of the Clapeyron equation to PEO in PPO-PEO Langmuir Films Louise Deschˆenes, Johannes Lyklema, Claude Danis, Franc¸ois SaintGermain PII: DOI: Reference:
S0001-8686(14)00284-X doi: 10.1016/j.cis.2014.11.002 CIS 1494
To appear in:
Advances in Colloid and Interface Science
Please cite this article as: Deschˆenes Louise, Lyklema Johannes, Danis Claude, SaintGermain Fran¸cois, Phase transitions in Polymer Monolayers: Application of the Clapeyron equation to PEO in PPO-PEO Langmuir Films, Advances in Colloid and Interface Science (2014), doi: 10.1016/j.cis.2014.11.002
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Phase transitions in Polymer Monolayers:
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Application of the Clapeyron equation to PEO in PPOPEO Langmuir Films
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Louise Deschênesa,*, Johannes Lyklemab, Claude Danisa and François Saint-Germaina
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a) Food Research and Development Centre, 3600 Casavant Blvd West, Saint-Hyacinthe, QC. Canada, J2S 8E3 b) Laboratory for Physical Chemistry and Colloid Science , Wageningen University, Dreijenplein 6, 6703 HB Wageningen, Netherlands ABSTRACT
In this paper we investigate the application of the two-dimensional Clapeyron law to polymer
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monolayers. This is a largely unexplored area of research. The main problems are (1) establishing if equilibrium is reached and (2) if so, identifying and defining phases as functions of the temperature.
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Once this is validated, the Clapeyron law allows us to obtain the entropy and enthalpy differences between two coexisting phases. In turn, this information can be used to obtain insight into the
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conformational properties of the films and changes therein. This approach has a wide potential for obtaining additional information on polymer adsorption at interfaces and the structure of their monolayer films. The 2D Clapeyron law was applied emphasizing polyethylene oxide (PEO) in
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polypropylene oxide (PPO) -PEO block copolymers, based on new well-defined data for their Langmuir films. Values for enthalpy per monomer of 0.12 and 0.23 kT were obtained for the phase transition of two different PEO chains (Neo of 2295 and 409, respectively). This enthalpy was estimated to correspond to 1.2 0.4 kT per EO monomer present in train conformation at the air/water interface. KEY WORDS: monolayers, PEO, PPO, Clapeyron, phase transition
Contents 1. Introduction........................................................................................................................... 2 2. Derivation of the two-dimensional Clapeyron equation for low-M amphiphiles .................................................. 4 3. Critical points ........................................................................................................................ 7 4. History dependence: Gibbs versus Langmuir monolayers .......................................................................... 8 1
ACCEPTED MANUSCRIPT 5. Linearity of the transition range and analogy with 3D Van der Waals gases? .................................................... 10 6. Properties of polymeric monolayers ................................................................................................ 11 7. Applying the Clapeyron equation to polymer monolayers ......................................................................... 14 8. Isotherms of spread PEO monolayers .............................................................................................. 18
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9. Investigation of other parameters affecting the isotherms ......................................................................... 20 10. Applying the Clapeyron equation to PPO-PEO block copolymer monolayers .................................................. 25 11. Establishing h per monomer and per monomer in train conformation ......................................................... 30
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12. Conclusions and outlook........................................................................................................... 33 Acknowledgements .................................................................................................................... 33 Appendix 1. Experimental ............................................................................................................. 33
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Appendix 2. Additivity of PPO and PEO at the air/water interface and A determination .......................................... 34
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References .............................................................................................................................. 36
1. Introduction
In this paper we discuss the option of using the Clapeyron equation and related expressions to
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obtain information on the entropy of phase transitions in spread, or Langmuir, monolayers of polymers. This paper serves two disparate purposes, viz. (1) it honours the internationally appreciated contributions to this field by Reinhard Miller, to whom this issue of the Advances is dedicated and (2)
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it contributes to sorting out the applicability limits of classical thermodynamics to complex real systems, whereby we bring along new experimental results. It is particularly appropriate to refer to the
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extensive work by Miller and his group because they have contributed substantially to our knowledge of monolayers, including those from polymers. Miller’s interests cover both theoretical as well as
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experimental aspects [1-14]. As a specific illustration we may cite a recent paper [9] in which the authors explicitly invoked the Clapeyron equation and one of the Maxwell relationships to obtain the entropic contribution to two-dimensional phase transitions in monolayers of lung amphiphiles. Below we shall return to this paper. For low molecular weight three-dimensional systems and simple first order phase transitions, like evaporation or freezing, the applicability of the Clapeyron equation for obtaining the entropy of this transition from its temperature dependence is beyond dispute [15]. The Clapeyron equation is a thermodynamic equation, meaning that it is derived from first principles on the assumption of equilibrium and reversibility of processes. This relationship has for long time been used and is recognized as providing important information on phase transitions for a large variety of systems [16, 17]. In the case of two-dimensional systems, the Clapeyron equation has been widely used to derive the entropy and enthalpy of liquid expanded/liquid condensed (LE-LC) phase transition for monolayers of small molecules [18-21]. Unfortunately, the extent of equilibration of these systems is not systematically investigated. Moreover, the quality of the linearity of the transition, and the 2
ACCEPTED MANUSCRIPT difficulties in determining the second transition point, remain identified as major concerns in that matter [19]. With these questions not yet answered, applying thermodynamic equations is not automatically justified. In particular, the properties of plateaus in the pressure-area isotherms π(A) must be scrutinized, because their existence is generally taken as evidence for two-dimensional phase linear stretch?
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transitions. For a quantitative evaluation a number of questions have to be solved like: how long is the Is its length reproducible upon application of successive compression/relaxation
equilibrium?
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cycles? Is it horizontal or skewed? And, if it is skewed, does its occurrence still indicate a two-phase All these questions deserve to be addressed and they appear as critical issues
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particularly when polymeric molecules are considered.
Up to date, only few examples of applications of the Clapeyron equation have been reported
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in connection with phase transitions in Langmuir films of polymeric systems. In the case of polymers, the basic issue is what the physical meaning is of such transitions, and what insight it could bring regarding the structure of the film. A comprehensive discussion on this topic is still missing. The present paper aims at contributing to fulfil this gap. It is typical for this problem that its solution entails an intrinsic circuity: physical arguments regarding the structure and conformation of the
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polymer layer are needed to establish the transition points, whereas the result of the analysis is that such information is derived from experimental facts.
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The paper is organized as follows: first, the basics of the derivation of the Clapeyron equation are introduced and discussed for the case of monolayers of small molecules. Then, considerations will
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be given regarding the history effect in the formation of polymeric Langmuir films. This is a prerequisite for establishing equilibrium. Therefore, specific issues related to the applicability of the Clapeyron relationship to polymeric monolayers will be presented, followed by a review and analysis
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of available data and findings. After that, new experimental data sets will be introduced and will be used to verify the Clapeyron relationship with PPO-PEO block copolymers, for which a pseudoplateau specific to the phase transition of PEO is present. The effects of several parameters on the linearity of the plateau as well as on the equilibrium of the monolayers have also been discussed. Although PEO-based block copolymers have been subjected to a plethora of studies and have been investigated using a large variety of experimental techniques, the thermodynamic interpretation of the transition taking place in the plateau remains obscure. Finally, a conclusion summarizes the potentials and limitations of application of the Clapeyron equation in describing the thermodynamics of phase transition in Langmuir polymer films.
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ACCEPTED MANUSCRIPT 2. Derivation of the two-dimensional Clapeyron equation for low-M amphiphiles For a general introduction and derivation of the Clapeyron relationship, as well as the description of its approximation in the shape of Clausius-Clapeyron equation, the readers could refer
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to classical textbooks on thermodynamics[15] or to Fegley (2012) [16]. For the specific purpose of our discussion, let us consider spread, or Langmuir monolayers. During the measuring time, the amphiphiles are assumed to be stably anchored to the interface and the surface concentration is
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primarily dependent on the quantity present in a defined surface area. This layer is assumed to be in thermal equilibrium with the subphase. Since the subphase composition can significantly influence the
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film organization and phase transitions [22-27], its purity and stability should be carefully controlled. Regarding the meaning of the transition to which the Clapeyron equation is usually applied for low M systems, it is usually interpreted as a first-order transition from the LE to the LC phase.
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Experimental as well as theoretical evidences have been recently reported by Vollhardt and Fainerman [28]. It depends on the nature of the systems and the experimental conditions, whether a transition is observed. Sometimes more than one phase change is observed. When a transition is found, its length can be short or long, depending on the chemical structure of the molecule [21, 29-
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32]. Just a small variation in the size of the polar head, the addition of a small methyl segment close to it [33] or modification of the length of the alkyl chain [30, 31] can inhibit its presence It was also
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observed to be temperature-dependent [21]. The temperature at which the phase transition vanishes is identified as the critical point [34, 35] or sometimes a tricritical point [19, 36, 37], a notion that will
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be shortly discussed in the next section. In many cases, the beginning of the plateau corresponds to the formation of domains observable by Brewster angle microscopy (BAM) [33, 38, 39]. However, it should be kept in mind
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that the determination of the beginning of this transition based on BAM is limited to the detection of domains of microscopic size. As a complementary analytical approach, grazing incidence X-ray diffraction (GIXD) has also been proven a successful technique in determining the nature and the structure of these surface self-assemblies [28, 40-42]. At given p and T, the Gibbs energy is the most convenient and most encompassing characteristic function because, when this quantity is known as a function of the temperature, it is possible to derive the corresponding surface excess entropy and enthalpy using the appropriate GibbsDuhem relation. For Langmuir monolayers, this approach mostly does not work because it is difficult to obtain the surface excess Gibbs energy. In fact, once this function is known, it implies that the enthalpy and entropy are also known. However, even if the surface excess Gibbs energy of the monolayer is not easily available it is still possible to use the differential of this quantity to analyse the thermodynamics of phase transitions using the propensity of cross-differentiation. This option is available because the excess Gibbs energy is a function of state. 4
ACCEPTED MANUSCRIPT This takes us to the derivation of the two-dimensional Clapeyron equation. For Langmuir monolayers, the most direct way is starting with the differential form of the surface excess Gibbs energy G(σ) (see Appendix 5 in ref. [43]), which for a monolayer at fixed composition can be expressed in terms of
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entropy and surface tension by the following relationship
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(1)
where the upper index (σ) refers to the Gibbs surface excess and A is the interfacial area.. This equation can also be found in the IUPAC recommendations [44]. Here, S(σ) is the sought surface
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excess entropy. This is a total differential, implying that changes in the surface excess Gibbs energy are completely described by the two terms on the right hand side of the relationship. The equation
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applies to one monolayer of area A, but in a Langmuir trough the difference between two monolayers is measured, say between the monolayer and the reference. The required value of Gσ is really Gσ (film) = G -
with
referring to the Gibbs energy of the reference (subphase without any
amphiphilic molecules at its air/fluid interface). Similarly for the entropy term and the surface tension,
.
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So for the film it leads to
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where because of the definition of the surface pressure (Eq. (2)), a minus sign is needed. (2)
(3)
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In order to obtain the excess entropy as a function of A, we introduce the new function of state (4)
Cross-differentiation gives
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This equation can be used at any point of a (A) curve. The excess entropy obtained this way is that of the entire monolayer. Eq (1) can also be used to derive the two-dimensional Clapeyron equation. To that end, consider a reversible phase transition occurring between two positions 1 and 2 in the π(A) curves (Fig. 1). 5
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Fig. 1. Idealized isotherm.
Let the areas be A1 and A2 and the corresponding surface excess entropies S1 and S2. As the
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we may write
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equilibrium between these two points is characterized by identical Gibbs energies and identical dG(σ)
(A1 – A2)dπ = (S1 – S2)dT
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Here, we have omitted the superscripts (σ) because both entropies are referred to the same reference liquid. Introducing the symbol Δ to indicate the macroscopic difference between states 1 and 2, for n adsorbing molecules Eq. (4) can be rewritten as
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This, or very similar expressions, have also been used by, for instance, Grigoriev et al. [18], and by several other authors [19, 20, 45]. Interpretation of Eq. (2) to obtain (S1 – S2) involves two steps. The first one is of an experimental nature, viz. establishing the transition values of π and A as a function of T. The second is the molecular interpretation of the obtained entropy shifts. For low-M amphiphiles establishing point 1 (Fig. 1) is usually believed to be straightforward. It is the two6
ACCEPTED MANUSCRIPT dimensional equivalent of the corresponding onset of condensation of a vapour. Upon further compression a linear stretch is expected. It is not always horizontal, but even if it is skewed, point 2 can in principle be obtained from the crossing point of the (either or not extrapolated) linear part and the rapidly ascending branch to the left. Information about these determination approaches can be
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found in more details in Yue et al. [46]. In ambiguous situations, where the position of the ascending branch cannot be fixed with certainty, non-thermodynamic arguments could be needed. For
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amphiphiles like lipids, experimental techniques such as Brewster angle microscopy (BAM) and grazing incidence X-ray diffraction (GIXD) could be particularly helpful. Other procedures based on graphical analyses have also been proposed [18, 19]. Execution of such a procedure gives
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automatically some feeling for the incurred inaccuracies. The ΔS obtained is that of the entire monolayer but in the case of Langmuir films, it can be reduced to an entropy change per molecule. All
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of this becomes more challenging for polymeric amphiphiles.
In fact, few studies deal with the full thermodynamical approach required for the determination of the molecular area range in which the believed LE-LC transition is taking place. Most of the available data concern the determination of the entropy at the beginning of the transition range (A1). The results obtained are usually considered as easily accessible information on the
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thermodynamics of the transition. However, this approach does not allow for the determination of entropy and enthalpy parameters of the whole transition. At its best, it supplies information about the
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entropy status of the system at the beginning of the phase change, giving insights into the driving forces influencing its initiation. Kellner et al. [47] produced an impressive compilation of the d/dT
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(entropy) values at the onset of transition for a large number of small molecules from fatty acids to phospholipids. Most of the values are positive, indicating that the condensation is favoured by decreasing temperature. Few examples were given, showing a reverse trend, namely for D(+)-
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tetracosanol-2 acetate, hexa and octadecyl urea and 2-(10-carboxydecyl-2-hexyl-4,4-dimethyl-3-oxazolidinyloxyl)12-doxyl octadecanoic acid, indicating a kinetically controlled process, which is quite unusual for small molecules.
3. Critical points In the phase diagrams considered when applying the Clapeyron equation in monolayers of small molecules at the air/water interface, the temperature dependence usually shows a specific value (Tc) at which the phase transition vanishes. As previously mentioned, these points are referred to as critical points. The molecular area associated with the phase transition, A1 – A2, usually decreases as the temperature reaches values closer to Tc. The change of the heat of transition with temperature is usually reported to be linear [19, 34]. At the critical temperature, the latent heat of transition is basically zero. However, there is no consensus about its interpretation. In some cases, it has also been 7
ACCEPTED MANUSCRIPT proposed that the physical nature of this point could be, in fact, a tricritical point between the original phase (low concentration) and two other phases, one corresponding to the first-order transition and the other one associated to a second order transition. The existence of such a tricritical point has been suggested by Albretch et al. [37] to explain the behaviour of phospholipids at the air/water interface,
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a condition not encountered for van des Waals gases. Albrecht et al. based their interpretation of the existence of such a tricritical point in monolayers of -dipalmitoyllecithin on evidence of the
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coexistence of three phases. In addition to the usual isotropic liquid expanded fluid (let’s call it LEi) and the crystalline tilted condensed phase (LC), they proposed the formation of a mesophase of the shape of an anisotropic fluid (LEa), the LEi LEa transition being of second order. This transition
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was accompanied by a substantial decrease in viscosity and could be described by the Landau theory.
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Recent findings from Brezesinski et al. [48] point out the presence of a second transition in the monolayers of n-acylated ethanolamine. From combining BAM and GIXD, the authors concluded that a second first order transition exist at temperatures below 10°C for that system. At low temperature, the first obtained oblique lattice develops into an orthorhombic morphology. In this morphology, the change in the tilt angle contributes to lowering the molecular area occupied.
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In the case of the LE-LC transition of benzene-hexa-n-alkanoates Langmuir films, it was concluded that at temperatures above Tc, the liquid expanded phase of small molecules simple
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persists. In that particular case, the estimated heat of transition obtained from applying the Clapeyron equation decreased with the length of alkyl chains [34] in contradiction to what is usually observed in
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monolayers of fatty acids. However, as it is not possible to generalize these trends to all types of small
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molecules, we shall not further discuss them.
4. History dependence: Gibbs versus Langmuir monolayers For the purpose of the present paper, molecules adsorbing at interfaces will be called amphiphiles. They can be low-M amphiphiles, or polymeric. They can arrive at the air-water interface either by adsorption, by spreading or an alternative way of deposition. Adsorption from solution requires the amphiphile to be water-soluble whereas for spreading solubility should be insignificant or, for that matter, dissolution should be negligible. Adsorption leads to Gibbs monolayers, spreading to Langmuir monolayers, to which the present paper will be mainly devoted. The distinction between these two types of monolayers is important because different types of boundary conditions apply in the thermodynamics. Details in that matter can be found in the extensive development described by Motomura[49]. In practice, it is not always obvious to what extent these ideal limiting cases have been attained.
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ACCEPTED MANUSCRIPT In the ideal limiting situation, the molecules in a Langmuir monolayer behave as if they are fully insoluble into the subphase, in our case water. Strictly speaking, zero solubility does not exist, but the amount of amphiphile that upon spreading and/or compression disappears into the substrate can be neglected in many cases, particularly for polymers with anchoring groups. If this condition is
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fulfilled, the spread layer may be considered a closed two-dimensional system. The condition ― twodimensional‖ is interpreted in the Gibbs sense of the definition of the surface concentration of
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amphiphile molecules with a finite volume. Physically, the Langmuir layers have a non-zero thickness, which is dependent on the surface concentration. For fatty acids and phospholipids parts of the molecules stick out into one of the phases. For polymers loops and tails do the same and that is
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clearly also the case for 3D brushes anchored to the surface by insoluble moieties. Similar reasoning applies to diffuse double layers, where the ions in the diffuse part of the double layer contribute
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equally well to the thermodynamic surface excess. Thermodynamically all excess amounts are counted with respect to the Gibbs dividing plane, so that two-dimensional thermodynamics can be applied regardless the molecular lay-out at the surface [50]. The only respect in which the water subphase exerts its influence is that it acts as the surroundings of the Langmuir monolayer, in this way
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defining the temperature of the monolayer.
Conditions can be encountered where the solubility of the amphiphile in the substrate is non-
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zero but where nevertheless dissolution upon compressing is negligible. Several causes for that can be envisaged. One of these is that the initial part of the adsorption isotherm is extremely steep, leading to
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a high-affinity isotherm. This is typical for polymers. It means that desorption of only a very few molecules from the Langmuir layer suffice to makes the bulk concentration so high in the subphase proximal layer that at a certain point, no further desorption takes place [51]. Another option is that the
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desorption process is kinetically arrested (frozen) so as to look virtually irreversible. This, however, would not prevent us from applying thermodynamic concepts to frozen non-equilibrium systems, as long as the rate of desorption is slow as compared to the rate of measurement or, for that matter, if the Deborah number De
