Surface pressure-concentration isotherms

FIGURE 10.4 Surface pressure-concentration isotherms of Tween 20 (closed circles), P-casein + Tween 20 (open squares), and whole casein -I- Tween 20 (open triangles). The concentration of protein in the mixtures is of 0.1 g/L, and the solutions are prepared in a buffer solution at pH 7.4,1 = 16.4 mM, T = 20°C. 

We studied the surface pressure area isotherms of PS II core complex at different concentrations of NaCl in the subphase (Fig. 2). Addition of NaCl solution greatly enhanced the stability of monolayer of PS II core complex particles at the air-water interface. The n-A curves at subphases of 100 mM and 200 mM NaCl clearly demonstrated that PS II core complexes can be compressed to a relatively high surface pressure (40mN/m), before the monolayer collapses under our experimental conditions. Moreover, the average particle size calculated from tt-A curves using the total amount of protein complex is about 320 nm. This observation agrees well with the particle size directly observed using atomic force microscopy [8], and indicates that nearly all the protein complexes stay at the water surface and form a well-structured monolayer. 

FIG. 2 The surface pressure-area isotherms of PS II core complex with different concentrations of salt in the subphase. Subphase, lOmM tris-HCl, pH 8.0, 2mM sodium ascorbate and concentrations of 100, 200, and 500mM NaCl. Temperature, 23.0 0.5°C. 

Our studies on the surface pressure-area isotherms of MGDG and the mixture of PS II core complex and MGDG indicate the presence of both PS II core complex and MGDG in the monolayer. MGDG molecules diluted the PS II core complex concentration in the monolayer. MGDG lipid functions as a support for the protein complex and the resulting mixture forms higher-quality films than PS II core complex alone. 

In such an equilibrium study the surfactant is Injected beneath a monolayer, the surface is compressed in stages with equilibrium being established at each step, and the equilibrium surface pressure-area Isotherm is established. In this way, isotherms for a range of surfactant concentrations are produced. 

In contrast to this, the system neutral lipid (2J)/DSPC shows considerably smaller deviations from the additivity rule and the surface pressure/area isotherms indicate two collapse points corresponding to those of the pure components62. Photopolymerization can be carried out down to low monomer concentrations and no rate change is observed. These facts prove that the system (23)/DSPC is immiscible to a great extent. The same holds true for mixed films of diacetylenic lecithin (18, n = 12) with DSPC, as well as for dioleoylphosphatidylcholine (DOPC) as natural component. 

From the surface pressure - area isotherms of these polymers, the surface parameters could be calculated. The areas per monomer unit projected to zero surface -pressure, obtained from the linear variation of -it with the surface concentration (A0) in semidilute region [39] for the polymers, are summarized in Table 3.3. 

It should be pointed out at this juncture that strict thermodynamics treatment of the film-covered surfaces is not possible [18]. The reason is difficulty in delineation of the system. The interface, typically of the order of a 1 -2 nm thick monolayer, contains a certain amount of bound water, which is in dynamic equilibrium with the bulk water in the subphase. In a strict thermodynamic treatment, such an interface must be accounted as an open system in equilibrium with the subphase components, principally water. On the other hand, a useful conceptual framework is to regard the interface as a 2-dimensional (2D) object such as a 2D gas or 2D solution [ 19,20]. Thus, the surface pressure 77 is treated as either a 2D gas pressure or a 2D osmotic pressure. With such a perspective, an analog of either p- V isotherm of a gas or the osmotic pressure-concentration isotherm, 77-c, of a solution is adopted. It is commonly referred to as the surface pressure-area isotherm, 77-A, where A is defined as an average area per molecule on the interface, under the provision that all molecules reside in the interface without desorption into the subphase or vaporization into the air. A more direct analog of 77- c of a bulk solution is 77 - r where r is the mass per unit area, hence is the reciprocal of A, the area per unit mass. The nature of the collapsed state depends on the solubility of the surfactant. For truly insoluble films, the film collapses by forming multilayers in the upper phase. A broad illustrative sketch of a 77-r plot is given in Fig. 1. 

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. 

Fig. 30. (Top) Surface pressure-area isotherms for poly(/6-benzyl-L-aspartate) films spread on water containing small concentrations of 2-propanol (1) 0 vol% (2) 0.4 vol% (3) 0.5 vol% (4) 0.85 vol% and (5) 1.0 vol%. (Bottom) External reflection infrared spectra obtained at 40 mN/m from these films.

Fig. 10 Surface pressure— area isotherms for two different concentrations of hexylamine. The isotherms are recorded with the pendent drop technique by sucking liquid out of the droplet leading to a decrease in surface area of the droplet. The solid lines correspond to fits by (A/Aq) with exponent E as fitting parameter...

The simplest way to predict the lipid/ water partition coefficient, Kiw, of a drug is based on measurements of the surface pressure, ttd, of the drug as a function of its concentration in the aqueous subphase (Gibbs adsorption isotherm). The Gibbs adsorption isotherm provides the air/water partition coefficient, Kaw, and the cross-sectional area, Ad of the drug and allows calculation of the lipid/water partition coefficient, K]w, according to Eq. (6) [59] ... 

Fig. 20.1. Correlation between the air/water partition coefficient, Kaw, determined from measurements of the surface pressure as a function of drug concentration (Gibbs adsorption isotherm) in buffer solution (50 mM Tris/HCI, containing 114 mM NaCI) at pH 8.0 and the inverse of the Michaelis Menten constant, Km obtained from phosphate release...

The surface pressure-area (tc-A) isotherm measurements and LB film transfer were performed with the use of a KSV 5000 minitrough (KSV Instrument Co., Finland) operated at a continuous speed for two barriers of 10 cm2/min at 20°C. The buffer used in the present work was composed of 10 mM MES, 2 mM ascorbic acid sodium salt, and a given concentration of salt or polymers (pH =7.0). The accuracy of the surface pressure measurement was 0.01 mN/m. Monolayers of the PS I were transferred at 10 mN/m on hydrophobic substrate surface by horizontal lifting method. 

Now we consider the relationship between the effective concentration(reff) and the surface pressure(tt) at the air/water interface. Ideally, the surface pressure is directly proportional to the concentration of surfactants. However, as the actual it-A isotherms show several specific effects, such as limiting area and points of inflexion, we shall assume the following relationships ... 

Gibbs adsorption equation phys chem A formula for a system involving a solvent and a solute, according to which there Is an excess surface concentration of solute if the solute decreases the surface tension, and a deficient surface concentration of solute if the solute increases the surface tension. gibz ad sorp shan i.kwa-zhon Gibbs adsorption isotherm physchem An equation for the surface pressure of surface [< ... 

Virial Isotherm Equation. No isotherm equation based on idealized physical models provides a generally valid description of experimental isotherms in gas-zeolite systems (19). Instead (6, 20, 21, 22) one may make the assumption that in any gas-sorbent mixture the sorbed fluid exerts a surface pressure (adsorption thermodynamics), a mean hydrostatic stress intensity, Ps (volume filling of micropores), or that there is an osmotic pressure, w (solution thermodynamics) and that these pressures are related to the appropriate concentrations, C, by equations of polynomial (virial) form, illustrated by Equation 3 for osmotic pressure ... 

Similarly, when two or more adsorptives adsorb competitively on a surface, the adsorption isotherm for adsorptive i at a given temperature is a function of the equilibrium partial pressures of all of the adsorptives. In the case of adsorption from a liquid solution, an adsorption isotherm for any preferentially adsorbed solute may be similarly defined in terms of the equilibrium concentration of the respective solution component, but the isotherm usually... 

It is possible to control the pressures at which the phase transitions occur by fine tuning the strength of intermolecular interactions between the amphiphilic molecules. The interactions between the hydrophobic tails depend on temperature [37], while the interactions between the hydrophilic heads depend on the chemical composition of the subphase, namely its pH and ionic strength [4], For example, the fatty acid molecules in films prepared on subphase with high pH and high concentration of divalent salt, such as CaCl2 or CdCl2, are normal to the surface, i.e. are in solid state, even at low pressures. Pressure-area isotherms of such films are featureless compressed films are stable and easy to transfer [38]. 

Fig. 18 77 -< A > Isotherms for PVP/PVAc binary monolayers on water at 25 °C. Surface pressure 77 for a variety of poly(vinyl palmitate)/poly(vinyl acetate) mixtures as defined in the plot are shown as a function of area per monomer. Surface concentration was controlled by step-wise compression. The incorporation of PVP, which does not form stable monolayers alone, condenses the film and also increases the instability of the film. < A > = average area per monomer...

Equation (2.34) is often referred to as the Gibbs adsorption equation where the interdependence of r and p is given by the adsorption isotherm. TTie Gibbs adsorption equation is a surface equation of state which indicates that, for any equilibrium pressure and temperature, the spreading pressure II is dependent on the surface excess concentration r. The value of spreading pressure, for any surface excess concentration, may be calculated from the adsorption isotherm drawn with the coordinates n/p and p, by integration between the initial state (n = 0, p = 0) and an equilibrium state represented by one point on the isotherm. 

---