Parameters, calculated monolayer

Table IV. Calculated Monolayer Parameters with Various Fixed Values...

The superiority of NPyT over NPAT simulations has also been claimed in a more recent 120-ps simulation of monolayers of different phospholipids, based again on the agreement of calculated order parameters with experimental data [40]. However, it was also observed that the surface area of the phospholipids did not deviate much... 

Due to the rapid development of computer performance in the last few years, the molecular dynamics simulation method can now be used in order to get more detailed information on the phase behaviour of surfactant molecules at the air/water interface, provided that the number of molecules does not exceed a certain threshold value. With these computer simulation methods, it is possible to directly calculate molecular parameters such as the average tilt angle of the surfactant molecules adsorbed in the monolayer. 

This is the equation of a straight line whose slope is the inverse of the monolayer uptake and from the intercept, it is possible to calculate the parameter K, better known as B parameter of the Langmuir model. The n parameter should be optimised according to the correlation coefficient calculated by the least squared method. In case of associative adsorption n = 1. 

This statement is supported by data for oxygen and argon isotherms measured on the same silica gel. As can be seen in Figs 27 and 28 these isotherms have measurable - identifiable from the fiinetions i /(pj.) - monolayer domains, but there are not a sufficient number of data for a fitting procedure needed to calculate the parameters of a monolayer isotherm equation. 

Shah et al. [51] demonstrated the use of a donor-receptor compartment apparatus separated by a cell monolayer to estimate membrane transport parameters. Permeability coefficients, P, were calculated as... 

The parameters K1/ K2/ and K3 are defined by the refractive indices of the crystal and sample and by the incidence angle [32]. If the sample has uniaxial symmetry, only two polarized spectra are necessary to characterize the orientation. If the optical axis is along the plane of the sample, such as for stretched polymer films, only the two s-polarized spectra are needed to determine kz and kx. These are then used to calculate a dichroic ratio or a P2) value with Equation (25) (replacing absorbance with absorption index). In contrast, a uniaxial sample with its optical axis perpendicular to the crystal surface requires the acquisition of spectra with both p- and s-polarizations, but the Z- and X-axes are now equivalent. This approach was used, through dichroic ratio measurements, to monitor the orientation of polymer chains at various depths during the drying of latex [33]. This type of symmetry is often encountered in non-polymeric samples, for instance, in ultrathin films of lipids or self-assembled monolayers. 

Figure 1. Theoretical dependence of / 0 as calculated from equations (4) and (8) solid lines ideal monolayers dashed lines non-ideal. Parameter is q.

Non-ideal solution theory is used to calculate the value of a parameter, S, that measures the interaction between two surfactants in mixed monolayer or mixed micelle formation. The value of this parameter, together with the values of relevant properties of the individual, pure surfactants, determines whether synergism will exist in a mixture of two surfactants in aqueous solution. 

EXAMPLE 7.3 Suppression of Evaporation by Monolayers. The rate of evaporation is quantified by a parameter called the transport resistance r. For water with octadecanol monolayers at surface pressures of 10, 20, 30, and 40 mN m -1, ris about 1, 2, 3, and 4 s cm 1, respectively. This resistance drops off rapidly at lower pressures and approaches 2 10 3 s cm -1 for pure water. By considering the rate of water uptake as a diffusion problem, suggest how these r values are calculated from data collected in an experiment like that described above. Use the fact that Mr is dimensionally equivalent to the diffusion coefficient D divided by a length. 

Fig. 6. Calculated ATR spectra (angle of incidence 45°) for a monolayer adsorbate (thickness tZ3 = 3 A) on a 20-nm-thick metal film in contact with a solvent as a function of the complex refractive index of the metal film. Sohd line parallel polarized light dotted line perpendicular-polarized light. The appropriate complex refractive index n2 is given at the top of each spectrum. The vertical bars indicate the scale for the absorbance, which is different for each spectrum. Parameters ni = 4.01 (Ge), n4 = 1.4 (organic solvent), rfs = 3 A, He = 1.6, S = 280000cm , Vo = 2000cm , y = 60cm . The parameters correspond to adsorbed CO. The calculations were performed by using the formalism proposed by Hansen (76), and the results are given in terms of absorbance A = —logio(7 /7 o), where 77 is the reflectivity of the system Ge/Pt/ adsorbate/solvent and Rg is the reflectivity of the system Ge/Pt/solvent (7S).

Figure 9.9 Left BET adsorption isotherms plotted as total number of moles adsorbed, n, divided by the number of moles in a complete monolayer, ri7non, versus the partial pressure, P, divided by the equilibrium vapor pressure, Po. Isotherms were calculated for different values of the parameter C. Right Adsorption isotherms of water on a sample of alumina (Baikowski CR 1) and silica (Aerosil 200) at 20°C (P0 = 2.7 kPa, redrawn from Ref. [379]). The BET curves were plotted using Eq. (9.37) with C = 28 (alumina) and C = 11 (silica). To convert from n/nmo to thickness, the factors 0.194 nm and 0.104 nm were used, which correspond to n-mon = 6.5 and 3.6 water molecules per nm2, respectively.

Fig. 6.32 Experimental I-E (a) and Q-E (b) curves obtained in CV and CVC for a mixed ferrocene monolayer (I-cO.SH — CgSH 1 20) adsorbed at a disc gold electrode of radius r = 0.001 cm in an aqueous solution 1 M NaC104 with potassium ferrocyanide lOmM. The values of the scan rate (E(t) — initial) /v (in Vs-1) appear in (b) and for (a) are the following 0.2 (solid lines), 0.4 (dotted lines), 0.6 (long-dashed lines), 0.8 (short-dashed lines), and 1 (dashed-dot-dot lines). (symbols) I-E (a) and Q-E (b) curves calculated from Eqs. (6.215) to (6.216) by using the following parameters Ef = 0.095 V, kc = 250s 1, Qv = 0.437 pC, and T = 298 K. Reproduced with permission from [71]...

The monolayer capacity, Vm, is a parameter of particular interest, since it can be used for calculating the surface area of an adsorbent if the effective area occupied by each adsorbate molecule is known. 

Another surface parameter of interest is the hysteresis area (AG), which is indicative of energy trapped in a monolayer. The hysteresis area is the difference between the free energy of compression and free energy of expansion which is calculated from the area under corresponding surface pressure - area isotherms. 

The dilatational rheology of the poly(vinylacetate) monolayer onto an aqueous subphase has been studied between 1°C and 25°C by Monroy et al. [59], These authors have used the combination of several techniques. By this way, the exploration of a broad frequency range was possible. The relaxation experiments have shown multiexponential decay curves, whose complexity increases with decreasing the temperature. A regularization technique has been used to obtain the relaxation spectra from the relaxation curves and the dilatational viscoelastic parameters have been calculated from the spectra. The shapes of the relaxation spectra agree with the predictions of the theoretical model proposed by Noskov [100],... 

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