Transition layer thickness

In a recent study, Shilov et employed a small-angle x-ray 

Values of 4 and R are shown in Table 6.13. The values average between a few hundred and several hundred angstroms, with a maximum at midrange compositions, corroborating the results of electron microscope studies shown on other materials. 

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In our previous paper (H), we introduced a novel experimental method to study the mechanistic details of solvent permeation into thin polymer films. This method incorporates a fluorescence quenching technique (19-20) and laser interferometry ( ). The former, in effect, monitors the movement of vanguard solvent molecules the latter monitors the dissolution process. We took the time differences between these two techniques to estimate both the nascent and the steady-state transition layer thicknesses of PMMA film undergoing dissolution in 1 1 MEK-isoproanol solution. The steady-state thickness was in good agreement with the estimate of Krasicky et al. (IS.). ... 

Despic AR, Trisovic T (1993) Transition layer thickness in microlaminar deposits. J Appl Electrochem 23 662-668... 

Plastic Fluid layer thickness (mm) Elastic (transitional) layer thickness (mm) Frozen layer thickness (mm)... 

For understanding the properties of IPNs, it is important to know the transition layer thickness. Using small-angle X-ray scattering technique, this value... 

They indicate that as the short-chain branching content increases from 2.9 to 28.2 branches per 1000 C atoms, the crystal core thickness decreases from 97 to 18 A and the transition layer thickness increases from 8 to 21 A. These results are in qualitative agreement with Flory s prediction that crystal core thickness... 

Figure 11.5 SAXS-determined morphology data for compositional fractions of ethylene-octene copolymers number-averaged lamellar thickness (open squares), crystal core thickness (open circles), transition layer thickness (stars). Reprinted with permission from Reference [28]. Copyright 1993 American Chemical Society.

Kim MH (2004) Modified Porod s law estimate of the transition-layer thickness between two phases test of triangular smoothing function. J Appl Crystallogr 37 643-651. doi 10.1107/ S0021889804013196... 

Figure B3.6.3. Sketch of the coarse-grained description of a binary blend in contact with a wall, (a) Composition profile at the wall, (b) Effective interaction g(l) between the interface and the wall. The different potentials correspond to complete wettmg, a first-order wetting transition and the non-wet state (from above to below). In case of a second-order transition there is no double-well structure close to the transition, but g(l) exhibits a single minimum which moves to larger distances as the wetting transition temperature is approached from below, (c) Temperature dependence of the thickness / of the enriclnnent layer at the wall. The jump of the layer thickness indicates a first-order wetting transition. In the case of a conthuious transition the layer thickness would diverge continuously upon approaching from below.

However, the transition Reynolds number depends on free-stream turbulence and may range from 3 X 10 to 3 X lO ". The laminar boundary layer thickness 8 is a function of distance from the leading edge ... 

Figure 12 shows the dependence of the average aspect ratio and the TLCP volume fraction on the relative sample thickness for the four processing conditions in the core layer, transition layer and skin layer, respectively, by a morphological examination [13]. Generally, the aspect ratio increases from core to skin layer, whereas the situation is reversed for the volume fraction. An average volume fraction about 20% can be clearly seen. 

When a fluid flowing at a uniform velocity enters a pipe, the layers of fluid adjacent to the walls are slowed down as they are on a plane surface and a boundary layer forms at the entrance. This builds up in thickness as the fluid passes into the pipe. At some distance downstream from the entrance, the boundary layer thickness equals the pipe radius, after which conditions remain constant and fully developed flow exists. If the flow in the boundary layers is streamline where they meet, laminar flow exists in the pipe. If the transition has already taken place before they meet, turbulent flow will persist in the... 

Let us consider now a transition from a layer with a finite thickness to a plane of surface masses, where z = 0. Suppose that the layer thickness tends to zero, but the volume density increases in such way that their product, a — 6h remains constant. Then, the field outside the layer does not change and equals its original value, while... 

Diffusion in a convective flow is called convective diffusion. The layer within which diffnsional transport is effective (the diffnsion iayer) does not coincide with the hydrodynamic bonndary layer. It is an important theoretical problem to calcnlate the diffnsion-layer thickness 5. Since the transition from convection to diffnsion is gradnal, the concept of diffusion-layer thickness is somewhat vagne. In practice, this thickness is defined so that Acjl8 = (dCj/ff) Q. This calcniated distance 5 (or the valne of k ) can then be used to And the relation between cnrrent density and concentration difference. 

At the interface between two similar solutions (a) and (p) merely differing in their composition, a transition layer will develop within which the concentrations of each component j exhibit a smooth change from their values cj in phase (a) to the values cf in phase (p). The thickness of this transition layer depends on how this boundary has been realized and stabilized. When a porous diaphragm is used, it corresponds to the thickness of this diaphragm, since within each of the phases outside the diaphragm, the concentrations are practically constant, owing to the liquid flows. 

This equation holds only at short times when thickness 5. is small compared to the steady-state dilfnsion-layer thickness 5j.(, which will be attained under given experimental conditions, particularly when the solntion is stirred. As soon as attains the value of 5,.(, the transitory processes end and a steady state is attained there is no fnr-ther change in concentration distribution with time (Fig. 11.3a). It follows from Eq. (11.7) that the transition time of the transient process... 

Figure 8.10. The real two-phase system (a) and the transition into an ideal system (c) by removal of the density fluctuation background, Ipi, and of a transition layer of thickness dz between the hard and the soft domains. The elongated white region indicates a void...

Figure 8.40. Computer-simulated IDFs gi (u) of ID two-phase structure formed by the iterated stochastic structure formation process. tt is the thickness of the transition layer at the phase boundary. o> is the standard deviation of a Gaussian crystallite thickness distribution... 

Van der Waals further finds a relation between the temperature coefficient of surface tension and the molecular surface energy which is in substantial agreement with the Eotvos-Ramsay-Shields formula (see Chapter V.). He also arrives at a value for the thickness of the transition layer which is of the order of magnitude of the molecular radius, as deduced from the kinetic theory, and accounts qualitatively for the optical effects described on p. 33. Finally, it should be mentioned that Van der Waals theory leads directly to the conclusion that the existence of a transition layer at the boundary of two media reduces the surface tension, i.e., makes it smaller than it would be if the transition were abrupt—a result obtained independently by Lord Rayleigh. 

The boundary layer thickness gradually increases until a critical point is reached at which there is a sudden thickening of the boundary layer this reflects the transition from a laminar boundary layer to a turbulent boundary layer. For both types, the flow outside the boundary layer is completely turbulent. In that part of the boundary layer near the leading edge of the plate the flow is laminar and consequently this is known as a... 

Transition layer is found to exist for all types of silicon.7,16 20,24 25 80 The pores in the transition layer are generally much smaller than those in the bulk. There is not a clearly definable boundary that separates the surface layer and the bulk. The thickness of the transition layer is related to the size of pores the smaller the pores the thinner the surface transition layer. For n-Si, the transition layer can be clearly seen as for example shown in Figures 11 and 16.24 On the other hand, for p-Si this surface layer is very thin (near zero) for some PS with extremely small pores. Such thin layer may not be observed because it may be removed due to chemical dissolution during its exposure in solution. 

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