Isothermal compressibility compressed monolayers

The electrochemical behavior of the C70 solvent-cast films was similar to that of the C60 films, in that four reduction waves were observed, but some significant differences were also evident. The peak splitting for the first reduction/oxidation cycle was larger, and only abont 25% of the C70 was rednced on the first cycle. The prolate spheroidal shape of C70 is manifested in the II-A isotherm of C70 monolayers. Two transitions were observed that gave limiting radii consistent with a transition upon compression from a state with the long molecnlar axes parallel to the water snrface to a state with the long molecnlar axes per-pendicnlar to the water surface. 

The monolayer stability limit is defined as the maximum pressure attainable in a film spread from solution before the monolayer collapses (Gaines, 1966). This limit may in some cases correspond directly to the ESP, suggesting that the mechanism of film collapse is a return to the bulk crystalline state, or may be at surface pressures higher than the ESP if the film is metastable with respect to the bulk phase. In either case, the monolayer stability limit must be known before such properties as work of compression, isothermal compressibility, or monolayer viscosity can be determined. 

The film balance may be regarded as a two-dimensional piston, and the most commonly studied property is the surface pressure (n) versus area (A) isotherm. The analogy to a PV isotherm is so appropriate that in the gaseous monolayer regime the two-dimensional analogue of the ideal gas law pertains 114 = nRT. It is therefore reasonable to relate discontinuities in n/A isotherms as the monolayer film is compressed in two dimensions to... 

The dynamic surface tension of a monolayer may be defined as the response of a film in an initial state of static quasi-equilibrium to a sudden change in surface area. If the area of the film-covered interface is altered at a rapid rate, the monolayer may not readjust to its original conformation quickly enough to maintain the quasi-equilibrium surface pressure. It is for this reason that properly reported II/A isotherms for most monolayers are repeated at several compression/expansion rates. The reasons for this lag in equilibration time are complex combinations of shear and dilational viscosities, elasticity, and isothermal compressibility (Manheimer and Schechter, 1970 Margoni, 1871 Lucassen-Reynders et al., 1974). Furthermore, consideration of dynamic surface tension in insoluble monolayers assumes that the monolayer is indeed insoluble and stable throughout the perturbation if not, a myriad of contributions from monolayer collapse to monomer dissolution may complicate the situation further. Although theoretical models of dynamic surface tension effects have been presented, there have been very few attempts at experimental investigation of these time-dependent phenomena in spread monolayer films. 

When spread from dilute hexane solution, acid-dependent enantiomeric discrimination was observed in the 11/A compression isotherms of the monolayer at 25°C (Fig. 12). It is interesting to note that at higher subphase acidities, both racemic and enantiomeric film systems become more highly expanded, and the surface pressures where enantiomeric discrimination commences occur at high (85-90 A2/molecule) average molecular areas. This may be taken as direct evidence of headgroup ionization effects. The surface... 

Given such evidences of nonthermodynamic behavior of compressed monolayers, it was important to test film stability at various points along the ir-A isotherms for the normal rate of slow compression. The racemic film maintained a steady film pressure over at least 10 min after the barrier drive was stopped, showing little or no tendency to relax from the compressed state to one of lower energy. The enantiomer film in contrast showed a tendency to relax steadily from a compressed metastable state to a more stable and better packed condition approaching the equilibrium spreading pressure. 

AFM images were obtained for films constructed, on freshly cleaved mica, from compressed monolayers of DDAB on a subphase of HMP-stabilized CdS (81). Particles, with dimensions of 8 3 nm, were seen to be evenly distributed. The determined area of 58 nm2/particle coincided well with the area per molecule determined for DDAB from its spreading isotherm, implying 1 1 particle/surfactant stoichiometry. This result is puzzling given that freshly cleaved mica is hydrophilic and therefore any particles would be buried under a layer of the hydrophobic tails of the DDAB and unaccessable to the AFM tip. 

Fig. 1 shows the surface pressure-area (n-A) isotherms of stearic acid monolayers on pure water and ion-containing subphases, respectively. The presence of bivalent cations in the subphase gives rise to condensation of the monolayers. On the Ag+-containing subphase, the isotherm shows extremely compressed characteristics with a limiting area of 0.12nm2/molecule, much smaller than the cross-sectional area of 0.20 nm2 of a saturated hydrocarbon chain, which suggests the formation of a three-dimensional structure of the compressed monolayer [48]. 

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 4. Compression isotherms for mixed monolayers of gliadin and the following surfactants Brij 35 (Curve 1), Brij 76 (Curve 2), and Brij 78 (Curve 3). The abscissa is moved to the right by 0.2 m2/mg for successive curves to avoid confusion.

A number of distinct regions are immediately apparent on examining the isotherm. When the monolayer is compressed, it can pass through several different phases, which are identified as discontinuities in the isotherm, as shown in Figure 5.6. The phase behaviour of the monolayer is mainly determined by the physical and chemical properties of the amphiphile, the subphase temperature and the subphase composition. Various monolayer states exist depending on the length of the hydrocarbon chain and the magnitude of cohe-... 

A typical effect related to surface relaxations is obtained in measurements of ti-A isotherms of insoluble monolayers. In most of the measurements with spread amphiphiles there are differences between the curve for compression and expansion of the surface films. Usually this characteristic behaviour is described as hysteresis. One experimental example of a spread dipalmitoyl lecithin is shown in Figs 3.12. This phenomenon corresponds to one or more of these surface relaxations. 

Figure 48. Semilogarithmic plot of the isothermal compressibility of N2 on boron nitride at 60.8 K as a function of the coverage in units of the complete /3 monolayer. The peak sequence starting at low coverages is attributed to the fluid to commensurate solid F-C and commensurate solid to reentrant fluid C-RF transitions and finally to second-layer growth RF-B (instead of a transition from the reentrant fluid to an incommensurate solid phase). (Adapted from Fig. 5 of Ref. 1.)...

Figure 10. Pressure-area (IT — A) isotherm for a hypothetical amphiphile organized as a monomolecular layer at the water-air interface showing a phase transition from a fluid-expanded to a solid-condensed state upon compression. The insets show cross-sectional diagrams of the Langmuir trough with the compressed monolayer in different phase states.

There is a transition point at the 11- 4 isotherm from a monolayer with crystalline chain in a tilted arrangement to a monolayer with vertical (and crystalline) chains. The monolayer phase with vertical chains is unstable which is not surprising as no stable crystal form exists with vertical chains. At variations in compression rate (Table 8.14) this transition pressure is constant whereas the collapse pressure is reduced with decreasing compression rate. The equilibrium spreading pressure of these fatty acids is equal to the transition pressure in Table 8.14. As discussed in Section 8.4 the reduction in surface tension, when crystalline fatty acids are present, is equal to the equilibrium spreading pressure. 

Considerable insight into the lateral cohesion of the floating monolayer can be obtained by examining the hysteresis of the isotherm. The greater the cohesion, the greater the hysteresis. To date, this is a rather nnderexploited approach to characterize partially compressed monolayers (i.e., at a pressure lower than jTc collapse is nsually an irreversible phenomenon). However, monolayer viscoelasticity (compression and shear moduli) has recently been determined by such an approach. ... 

For Langmuir films, surface pressure is plotted against the area per molecule (A), resulting in n-A isotherms. The pattern of such isotherms depends not only on the chemical structure of the film-forming substance, but also on experimental conditions. The increase in surface pressure corresponds to more ordered phases in the film. The n-A isotherm of a monolayer provides basic information on the material s film-forming properties and the area per molecule at different stages of film compression. Additionally, conclusions may be drawn on the presence and... 

Neumann has adapted the pendant drop experiment (see Section II-7) to measure the surface pressure of insoluble monolayers [70]. By varying the droplet volume with a motor-driven syringe, they measure the surface pressure as a function of area in both expansion and compression. In tests with octadecanol monolayers, they found excellent agreement between axisymmetric drop shape analysis and a conventional film balance. Unlike the Wilhelmy plate and film balance, the pendant drop experiment can be readily adapted to studies in a pressure cell [70]. In studies of the rate dependence of the molecular area at collapse, Neumann and co-workers found more consistent and reproducible results with the actual area at collapse rather than that determined by conventional extrapolation to zero surface pressure [71]. The collapse pressure and shape of the pressure-area isotherm change with the compression rate [72]. 

The monolayer resulting when amphiphilic molecules are introduced to the water—air interface was traditionally called a two-dimensional gas owing to what were the expected large distances between the molecules. However, it has become quite clear that amphiphiles self-organize at the air—water interface even at relatively low surface pressures (7—10). For example, x-ray diffraction data from a monolayer of heneicosanoic acid spread on a 0.5-mM CaCl2 solution at zero pressure (11) showed that once the barrier starts moving and compresses the molecules, the surface pressure, 7T, increases and the area per molecule, M, decreases. The surface pressure, ie, the force per unit length of the barrier (in N/m) is the difference between CJq, the surface tension of pure water, and O, that of the water covered with a monolayer. Where the total number of molecules and the total area that the monolayer occupies is known, the area per molecules can be calculated and a 7T-M isotherm constmcted. This isotherm (Fig. 2), which describes surface pressure as a function of the area per molecule (3,4), is rich in information on stabiUty of the monolayer at the water—air interface, the reorientation of molecules in the two-dimensional system, phase transitions, and conformational transformations. 

Traditional amphiphiles contain a hydrophilic head group and the hydrophobic hydrocarbon chain(s). The molecules are spread at molecular areas greater (-2-10 times) than that to which they will be compressed. The record of surface pressure (II) versus molecular area (A) at constant temperature as the barrier is moved forward to compress the monolayer is known as an isotherm, which is analogous to P-V isotherms for bulk substances. H-A isotherm data provide information on the molecular packing, the monolayer stability as de-... 

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