Three-layer film model

The accuracy of thickness measurements with this microinterferometric technique is 0.2 nm. For thinner foam films (< 30 nm) it is necessary to account also for the film structure. The three-layer film model with an aqueous core of thickness /12 and refractive index n2 and two homogenous layers of adsorbed surfactant of thickness h each and refractive index i is... 

Similar to the cases discussed above, applying DLVO-theory, the ( -potential and the surface charge density a can be estimated by the method of the equilibrium film . The equilibrium thickness hw was converted into the real film characteristics using a three-layer film model [166,191] (see also Chapter 2). Thus an aqueous core thickness equal to 3.6 nm was obtained. The algorithm [209] described in detail previously [172,194] was used for the determination of nc . 

The values of cpo for Cjo(EO)4 films was 40 mV and for NP20 films - 37 mV. Thickness hi2 was calculated employing the three-layer film model (see Chapter 2). 

To convert hw into real film thickness a three-layer film model with estimated values for the thickness and refractive index of the two adsorbed surfactant layers was assumed [159,277,278] (see Section 2.1-3). A thickness of 0.76 nm and a refractive index of 1.41 were... 

Obviously, the reliability of the above data for Y0 and Q0 depends significantly on the assumptions made to convert hw into d and on the accuracy of the Uvw evaluation. A five-layer film model that comprise the hydrophilic heads of the surfactant as separate layers may be considered as an alternative [283], This yielded d values 0.14 nm higher than those based on the three-layer model. The difference is less than the experimental scatter in the hw data used and is, as it appears from Fig. 3.45, insignificant. This, therefore, gives some supporting evidence for the assumptions made. As far as the evaluation of IIvw is concerned, no indications of considerable errors can be found through the region of the film thicknesses considered [166]. 

A snapshot of the representative configurations of the macroions in a three-layer film obtained from the simulations with and without excluded volume forces is presented on Fig. 10. The simulations without excluded volume forces (Fig. 10b) serve as a methodological example which illustrates that an adequate modelling of complex colloidal suspension should necessarily take into account the discrete nature of a primary suspending fluid. In the case of a three-layer film, the excluded volume forces play an important role in the organization of both the surface and middle-film layers. In general, the excluded volume forces become more important with a decrease of the interparticle distances this is the case for particle layers, both near the film surfaces and in the middle of the film. 

In chapter 7, section 7.2.8 an example of permeation through a functional barrier is described. Three-layered coextruded PET films were produced in which the core layer (P) was contaminated with chlorobenzene and the outer barrier layers (B) were made with virgin material. During the coextrusion process a partial contamination of the virgin layer occurred. The symmetrical structure of this film leads to a simplified treatment of it as a two layer laminate with the thickness d = a + b = 160 + 40 = 200 pm. For the modeling of this problem with numerical mathematics all parameters given in Section 7.2.8 are used. 

Since, however, each model involves some assumptions, the calculation of h2 always renders certain inaccuracy. The most important problem in the three-layer model concerns the position of the plane that divides the hydrophobic and hydrophilic parts of the adsorbed surfactant molecule. In some cases it seems reasonable to have this plane passing through the middle of the hydrophilic head of the molecule, in others the head does not enter into the aqueous core. That is why it is worth comparing film thicknesses determined by the interferometric technique using the three-layer model, to those estimated by other methods. An attempt for such a comparison is presented in [63]. Discussed are phospholipid foam films the thickness of which was determined by two optical techniques the microinterferometric and FT-IR (see Section 2.2.5). The comparison could be proceeded with the results from the X-ray Reflectivity technique that deals not only with the foam film itself but also with the lamellar structures in the solution bulk, the latter being much better studied. Undoubtedly, this would contribute to a more detailed understanding of the foam film structure. 

Fig. 2.6. A three-layer model of the foam film 1 - organic phase 2 - water phase 3 - air.

Optical measurements of foam films are very complicate. In order to have a clear and precise interpretation of the results, especially for the thinnest black films, it is necessary to make models. The simplest and the most widely used one is the three-layer model (see Section 2.1.3). 

An optical three-layer model has proved superior to a one-layer model for the interpretation of the ellipsometric data. The refractive indices of the film and surface layers are determined and it is found that the index for the surface is higher than that for the film core. A Lorenz-Lorentz type treatment of NBF reveals that there are approximately seven water molecules per molecule of surfactants in both NaDoS and NaDoBS films. The optical data obtained by the three-layer model for NBF from NaDoS indicate that the thickness of the aqueous core is zero while that of the adsorption monolayers of surfactant molecules with refractive index 1.365 is 1.8 nm, i.e. the thickness of NBF is 3.6 nm. 

Corkill et al. [56] have used for the first time the infrared spectroscopy for foam films. The measurement of the adsorption of the infrared light provides information about the water content in the foam films which is of major significance for the black foam films. These studies involved the use of dispersion type instruments. In order to obtain measurable values of adsorption, the infrared light is passed through a series of vertical films (up to 10) formed in a cylindrical tube acting as a frame. Additional information about the film structure the authors derived from the correlation between the optical infrared transmission data and the film reflectance measurements. Here a three-layer model of the film structure consisting of an aqueous core sandwiched between two adsorption layers is assumed (see Section 2.1.3). 

On the contrary the plateau values for the two copolymers are very different. Since the higher copolymer gives thicker films a surface force component of steric origin may be evoked. However, the thickness hK is an effective parameter which is too crude. As a reasonable compromise between physical relevance and tractability, the three-layer model is adopted. Within the three-layer model the foam film is viewed as a symmetric sandwich structure [159] two adsorption layers symmetrically confine an aqueous core (Fig. 3.34). 

At film thickness larger than twice the adsorption layer thickness this type of force vanishes [248], Therefore, such a mechanism is operative only at Ijtot 2Iii = 21.2 nm, i.e. hw < 28.0 nm (Table 3.5). The solid line in Fig. 3.40 is the best fit of Eq. (3.87). The van der Waals component has no practical influence on the numerical procedure. The fitted value h = 11.1 nm is in good agreement with the value of 10.6 nm used in the three layers model. Thus, de Gennes theory [248] gives a satisfactory description of the steric interactions at film thickness where brush-to-brush contact is realised. 

Note The results for the thickness of foam films according to the three-layer model depend on the place of the conditional boundary between the hydrophilic and hydrophobic parts of foam bilayer (see Section 3.4.1.2). The above values are calculated under the assumption that these boundaries are situated between the polar head groups and hydrocarbon chains of DMPC molecules. 

Lalchev et. al. [491-493] have reported results employing the FRAP method for the recovery half times (tm) and the lateral diffusion coefficients (D) of fluorophore molecules in lecithin foam films of different type. Significant differences between the values of D were obtained for very thick foam films (h 100 nm) and for grey foam films (h 30 nm) showing D values of 2210 8 and 8-10 8 cm2 s 1, respectively. A further decrease in D was observed in CBF (D = 51 O 8 cm2 s 1) and in NBF (D = 2.2-10 8 cm2 s 1) (Fig. 3.111). The CBFs have an equivalent water thickness of approximately 13 nm and consist of a free water layer between the two adsorbed layers according the three-layer model (see Chapter 2). The value of the lateral diffusion coefficient in NBF, characterised by an equivalent water thickness of approximately 7 to 8 nm (the thinnest foam bilayers in this case) and which contains no free water layer between the monolayers, was twice lower (D 210 8 cm2 s 1), than in the CBF (Fig. 3.111). Since the decrease of the film thickness reflects the decrease of the free-water... 

Taking into account the existing indications for asymmetric interactions at the interfaces (e.g., three-layer model in Ref. 4), two distinct cases must be analyzed (i) Both interfaces immobilize the chains or (ii) the chains are immobilized only at one interface while at the other one they are reflected (hard-wall behavior). In Fig. 18 the distribution of the end-to-end distance of terminal subchains is shown when both interfaces immobilize the chain segments. No shifts of the maximum position of the distribution are observed with decreasing film thickness. This result would imply that the confinement-induced mode does not exhibit thickness dependence, in contrast to the experiment. 

Summarizing, two conditions must be fulfilled in order to obtain from the simulations a confinement-induced and thickness-dependent distribution of the end-to-end distance for terminal subchains. First, a chain should be in contact with both interfaces. This happens only when the film thickness becomes comparable to the size of the chains and, obviously, explains why the confinement-induced mode does not exist in the bulk. Second, the interactions at the interfaces should be asymmetric One interface should immobilize the polymer chains, while the second one should only reflect them. This asymmetry could be induced by the nonequivalent preparation of the electrodes in the experiment While one interface is prepared by spin-coating, the other one is prepared by evaporation of aluminium on top of the polymer film (see Section II for details). A similar picture of asymmetry was found in studies on thin PS films, with a preparation procedure identical with ours. For thin PS films capped between two aluminum electrodes a three-layer model was proposed, in which, in addition to a middle-layer having bulk properties, a dead (immobilized) layer and a liquid-like layer were assumed to be present at the interfaces. 

IR Spectra. The IR spectra of the SOG film were obtained with a Perkin Elmer Model 683 Infrared Spectrophotometer in transmission mode by passing radiation through the film coated on a single crystal silicon wafer. In order to enhance the spectral signal, three layers... 

The consideration of thermal effects and non-isothermal conditions is particularly important for reactions for which mass transport through the membrane is activated and, therefore, depends strongly on temperature. This is, typically, the case for dense membranes like, for example, solid oxide membranes, where the molecular transport is due to ionic diffusion. A theoretical study of the partial oxidation of CH4 to synthesis gas in a membrane reactor utilizing a dense solid oxide membrane has been reported by Tsai et al. [5.22, 5.36]. These authors considered the catalytic membrane to consist of three layers a macroporous support layer and a dense perovskite film (Lai.xSrxCoi.yFeyOs.s) permeable only to oxygen on the top of which a porous catalytic layer is placed. To model such a reactor Tsai et al. [5.22, 5.36] developed a two-dimensional model considering the appropriate mass balance equations for the three membrane layers and the two reactor compartments. For the tubeside and shellside the equations were similar to equations (5.1) and... 

A three-layer model was found by the author to describe adequately a Shipley s phenolic XP-98248 resist, a commercially available environmentally stable chemically amplified photoresist (ESCAP) film, thus suggesting the presence of three distinct layers for each film film-substrate interface layer, bulk layer, and surface layer. This three-layer model is consistent with the results of... 

On this issue Guidelli et al. expressed the view that phase transitions take plaee when the shape of the solute molecules hinders H-bond formation between water (solvent) molecules. In this case the water molecules are squeezed out of the adsorbed layer, leaving behind a compact film of solute molecules. This view seems to be verified by the three-dimensional lattice model, which in the presence of non-polar trimeric solute molecules does predict the occurrence of a phase transition. However, due to an inappropriate statistical mechanical approach based on the use of the grand ensemble H instead of the generalized ensemble A, it is not possible to know whether this model predicts correctly or not the properties of the phase transitions. ... 

Fig. 2.6 The stratified three-phase layered optical model with optically anisotropic phases 2 and 3. where phase 1 is the electrolyte solution, phase 2 is the thin organic film of thickness d, and phase 3 is the electrode. For the optical constants, see text.

---