Surface pressure isotherm

Fig. 8. Surface-area/surface-pressure isotherms for spreading 1,5, and mixtures of 1 + 5 at 0.2,0.4, 0.6, and 0.8 mole fractions of 1 on aqueous S.O mM NaCl. Areas (A,) and pressures (iq) associated with the transition to a compressed state were taken by projecting the intersection of straight lines drawn to the appropriate sections of the isotherm to the surface-area and surface-pressure axes. The collapse pressure (nc) and collapse area (Ac) were taken by treating that transition, similarly. The insert shows an expansion of the isotherms between 20-40 mN/m. Temperature = 24.0 + 0.5 °C [116]...

G. Garofalakis and B. S. Murray, Surface pressure isotherms, dilatational rheology, and brewster angle microscopy of insoluble monolayers of sugar monoesters, Langmuir, 18 (2002) 4765-4774. 

Figure 4.11 shows the surface - pressure isotherms obtained in both cases. 

Keywords surface pressure isotherm, surface monolayers, nanoparticles, thermodynamic model... 

Monolayers of micro- and nanoparticles at fluid/liquid interfaces can be described in a similar way as surfactants or polymers, easily studied via surface pressure/area isotherms. Such studies provide information on the properties of particles (dimensions, interfacial contact angles), the structure of interfacial layers, interactions between the particles as well as about relaxation processes within the layers. Such type of information is important for understanding how the particles stabilize (or destabilize) emulsions and foams. The performed analysis shows that for an adequate description of II-A dependencies for nanoparticle monolayers the significant difference in size of particles and solvent molecules has be taken into account. The corresponding equations can be obtained by using a thermodynamic model developed for two-dimensional solutions. The obtained equations provide a satisfactory agreement with experimental data of surface pressure isotherms in a wide range of particle sizes between 75 pm and 7.5 nm. Moreover, the model can predict the area per particle and per solvent molecule close to real values. Similar equations were applied also to protein monolayers at liquid interfaces. 

V. B. Fainerman, V. I. Kovalchuk, D. O. Grigoriev, M. E. Leser, M. Michel, R. Miller and H. Mohwald, Surface pressure isotherms of monolayers formed by microsize and nanosize particles, Langmuir, submitted for publication. 

It is also unavoidable that sometimes the same symbol is used for different physical quantities, because we wanted to avoid excessive use of subscripts and superscripts. Mostly this does not give rise to problems, but in those places where it might, we have added a caveat. For Instance, cross-sectional areas per molecule have different meanings in lattice theories and in surface pressure Isotherms for Langmuir monolayers we explain this in sections 3.3 and 3.4. 

The increase of n(A] with decreasing A, at constant temperature, is the two-dimensional analogue of am osmotic pressure-concentration Isotherm. Such surface pressure isotherms are the prime source of information about the orientational and/or conformational properties of the molecules in the monolayer they reflect their dimensional properties as well as interactions between them. In this respect, x(A) isotherms have about the same function as adsorption Isotherms. This matter will be discussed in more detaill in secs. 3.4 and 5. 

The slope of surface pressure isotherms is a measure of their compressibility the steeper it is, the more difficult it is to compress the monolayer. Recall [2.11.4], where the isothermal bulk compressibility was defined as -(31n V/3p)j,. By analogy we introduce the two-dimensional isothermal compressibility through... 

Figure 3.8. Surface pressure isotherms for DMPA monolayers as a function of temperature. Breaks at t, a and k, a combinations are indicated. The twints M and M border the part where the isotherm is almost linear. Further discussion in the text. (Redrawn from O. Albrecht, H. Gruler and E. Sackmann, J. Fhys. (Paris) 39 (1978) 301.

Figure 3.9. Comparison of surface pressure Isotherms for fatty acids of different chain length. pH = 2. Redrawn from (1), M. Tomoaia-Cotsiel, J. Zsako, A. Mocanu, M. Lupea and E. Chifu, J. Colloid Interface Set 117 (1987) 464 (2) N. Gershfeld ibid. 85 (1982) 28 (3) M.L. Agrawal, R.D. Neumem, ibid. 121 (1988) 353.

Figure 3.10. Influence of branching on surface pressure isotherms. pH = 2 temp. 23°C. (Redrawn after F.M. Menger, M.G. Wood, S.D. Richardson, Q,Z, Zhou, A,R. Elrlngton and M.J, Sherrod, J. Am. Chem. Soc. 110 (1988) 6797.)...

Figure 3.11. Influence of the degree of saturation on surface pressure isotherms. All isotherms for Cj COOH at pH = 2 and 22°C. (Redrawn from M. Tomoaia-Cotisel, J. Colloid Interface Set, 117 (1987) 464.)...

These examples illustrate how molecular properUes affect lateral packing and, hence surface pressure isotherms. Eventually we must look for explanations in terms of molecular models, using an appropriate thermodynamic and statistical-thermodynamic framework. This is the basis of the following seetions. 

Figure 3.13. Surface pressure isotherm for cholesterol. (pH = 5.5, temperature 23.5°C) with proposed orientation at the interface. (Redrawn after C.L. Hirshfeld, M. Seul, J. Phys. (Paris) 51 (1990) 1537.)...

Figure 3.21. Monte Carlo surface pressure Isotherms for lipid-like molecules having 10 different conformational states available. 10.000 chains anchoring groups not specified. The filled circles are computed drawn lines are guides for the eye. Model parameters mimic dlpalmltoyl phosphatidyl choline (DPPC) monolayers. (Redrawn from Mouritsen et al. (1989).)...

Figure 3.31. Surface pressure isotherm (left) and generic phase diagram (right) for mono-layers of the of a Cj H-surfactants of fig. 3.30. Mean field lattice theory. Discussion in the text.

Figure 3.83. Surface pressure isotherms of stearic acid, spread from hexane temperature. 22 + 2°, no influence of compression rate. The pH is varied (using NaOM for pH > 9 and a borate buffer at pH 8) the ionic strength changes somewhat, (a) primary data, (b) corrected for losses by dissolution. Curve (1), pH 8 curve (2) pH 9.7 curve (3) pH 10.7 curve (4) Na stearate, spread at pH 10.7. (Redrawn from Tomoaia-Cotisel et al., loc. cit.)...

Figure 3.86. Surface pressure isotherms for stearic acid monolayers. Influence of bivalent counterions (1 mM), pH = 6.0. (Redrawn after Yazdanian et al.. loc. cit.)...

Surface pressure isotherms, reversibility and hysteresis studies, and pressure relaxation studies can for instance be found in two papers by Ganguli et al. - . As is the case with solid surfaces, the specificity of anions as counterions is more... 

Figure 3.97. Surface pressure isotherms for end-grafted PEO chains. SF lattice theory, iV = 700, t = 0.35 nm, two values of X (indicated).

Figure 4.12. Surface pressure Isotherms for aqueous solutions of n-C40H (a) cind n-CgOH (b). The temperature Is indicated. (Redrawn after Neam and Spaull, loc. clt.)...

Phospholipid monolayers provide useful models for studying dmg-lipid interactions as we can see from the following recent example which explores the interaction of the pheno-thiazine drugs trifluoperazine (TFP) and chlor-promazine (CPZ) with the anionic glycero-phospholipid dipalmitoylphosphatidylglycerol (DPPG). The surface pressure isotherms of... 

Figure 6.13 Surface pressure isotherms for mixed monolayers of dipalmitoylphosphatidylglycerol (DPPG) and (a) trifluoperazine (TFP) and (b) chlorpromazine (CPZ) for a range of drug/phospholipid molar ratios.

The protein concentration (C) dependence on surface pressure (tt), that is, the surface pressure isotherm, showed sigmoidal behavior (Figure 14.2) (Nino et al., 2005). At low protein concentrations, the initial solutions caused only a small increase in tt. The surface pressure increased with C and tended to a plateau. This plateau commenced at the point where tt reached its maximum value over the range of protein concentrations. The behavior of adsorbed protein films can be interpreted in terms of monolayer coverage. At the lower C, as the tt value is close to zero, the adsorbed protein residues may be considered as a two-dimensional ideal gas. Proteins at higher C, but lower than that of the plateau, form a monolayer of irreversibly adsorbed molecules. As the plateau is attained, the monolayer is saturated by protein that is irreversibly adsorbed. The protein concentration at which the plateau is attained is the adsorption efficiency (AE). At higher C, the protein molecules may form multilayers beneath the primary monolayer, but these structures do not contribute significantly to the surface pressure. The maximum tt at the plateau is the superficial activity (SA). 

Figure 5. Surface pressure isotherm for a TCA monolayer formed at 25 "C on a conventional Langmuir through in a clean room. The subphase is Milli-Q water. The Aaq, Raq, and Oaq-phase are labeled and are delimited by narrow plateaus. Reproduced from ref. 62 (Eckhardt et al.. Nature 1993, 362, 614) with permission of Macmillan Magazines.

At the end of this section, let us consider a general expression, which allows us to obtain the surface activity coefficient Yij directly from the surface pressure isotherm tt/fi). From the Gibbs adsorption isotherm, dn = T djUi, it follows that... 

Table II shows that substrate length is important up to a number of eight monomers. Ester bonds are probably less accessible for short than for long oligomers. This hypothesis agrees with the surface pressure isotherms obtained for the oligomers (Figure 8). Thus, at equal...

Further, Mann and McGregor (12) suggested that the study of the ESR spectral characteristics of labeled molecules in monolayers could lead to an experimental determination of surface viscosity numbers for expanded monolayers, While we do not report surface viscosity numbers here, we do report the spectra obtained using two ellipsoidal molecules in monomolecular films spread on water. We also report the low surface pressure isotherms for these systems and comment on the extent to which isotherms in general reflect molecular motion in monolayers. 

Figure 1.5.9 Typical surface pressure isotherm with a plateau. The arrow shows the molecular area. mN = millinewton...

Figure 2.6.3 Surface-pressure isotherms of (A) Cj sphingosine (B) Cjgdihydrosphin-gosine.

It is seen from the von Szyszkowski-Langmuir surface tension isotherm, Eq. (2.41), that at a given temperature the shape of the surface tension isotherm is determined by only one parameter cOg =cO =cd. The other parameter b enters this equation as a dimensionless variable be, in combination with the concentration. Therefore, the value of b does not affect the shape of surface tension isotherm, and only scales this curve with respect to the concentration axis. It should be noted that this dependence on b is characteristic to all the equations presented above. The dependence of the surface pressure isotherm on the molar area co is illustrated by Fig. 2.1. It is seen, that the lower ro is, hence the higher the limiting adsorption T = 1/co, the steeper is the slope of the n(c)-curve. 

Let us consider now the dependence of the shape of surface pressure isotherms on the parameters of the reorientation model. The dependence of surface pressure on the maximum area C0 is illustrated in Fig. 2.5. Here Eqs. (2.84)-(2.88) are employed with (02 = const and a = 0. All calculated curves are normalised in such a way that for the concentration 1 O " mol/1, the surface pressure is 30 mN/m. One can see in Fig. 2.5 that with the increase of (Oj the inflection of the isotherm becomes more pronounced, however, for the ratio a)i/( 2 = 4 the calculated curve almost coincides with the one calculated from the von Szyszkowski-Langmuir equation (2.41) which assumes only one adsorption state with (Oo = < = const. 

An increase of a corresponds to a sharp increase in the surface activity of the surfactant at very low concentrations. Here the surface pressure isotherm appears to consist of two curves with quite different shape. This behaviour can be attributed to the fact that in the low and medium n-range the adsorption of the surfactant molecules existing in the state with the molar surface area coi is preferred, while for high fl-values the molecules are mainly adsorbed in the state with the lower area value (02. 

Let us consider an example where the reorientation isotherm can be successfully applied to experimental data. In Fig. 2.9 the surface pressure isotherm of (N-16-alkyl-N,N-dimethylammonio)-acetic acid bromide [13,25] is presented. 

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