Interface width

Though a powerfiil technique, Neutron Reflectivity has a number of drawbacks. Two are experimental the necessity to go to a neutron source and, because of the extreme grazing angles, a requirement that the sample be optically flat over at least a 5-cm diameter. Two drawbacks are concerned with data interpretation the reflec-tivity-versus-angle data does not directly give a a depth profile this must be obtained by calculation for an assumed model where layer thickness and interface width are parameters (cf., XRF and VASE determination of film thicknesses. Chapters 6 and 7). The second problem is that roughness at an interface produces the same effect on specular reflection as true interdiffiision. 

The toughness of interfaces between immiscible amorphous polymers without any coupling agent has been the subject of a number of recent studies [15-18]. The width of a polymer/polymer interface is known to be controlled by the Flory-Huggins interaction parameter x between the two polymers. The value of x between a random copolymer and a homopolymer can be adjusted by changing the copolymer composition, so the main experimental protocol has been to measure the interface toughness between a copolymer and a homopolymer as a function of copolymer composition. In addition, the interface width has been measured by neutron reflection. Four different experimental systems have been used, all containing styrene. Schnell et al. studied PS joined to random copolymers of styrene with bromostyrene and styrene with paramethyl styrene [17,18]. Benkoski et al. joined polystyrene to a random copolymer of styrene with vinyl pyridine (PS/PS-r-PVP) [16], whilst Brown joined PMMA to a random copolymer of styrene with methacrylate (PMMA/PS-r-PMMA) [15]. The results of the latter study are shown in Fig. 9. 

The different experimental systems all yield a similar pattern of variation of toughness with interface width. The toughness initially increases slowly with width at low interface width, and then increases rapidly with width and saturates at high width at a value close to the bulk toughness. If the density of entangled strands controlled the toughness, then the interface width at which the toughness... 

Here, d is the interface width, which according to Helfand [12] is determined by... 

FIG. 7 Log-log plots of the interface width (w ) versus the Monte Carlo time t, measured at different adsorption probabihties using channels of width L = 30. Data were obtained during the displacement of an A-poisoned phase by the reactive regime. From top to bottom the probabihties are 0.5192, 0.5202, 0.5211, 0.5215, and 0.5238. 

An ordering phase transition is characterized by a loss of symmetry the ordered phase has less symmetry than the disordered one. Hence, an ordering process leads to the coexistence of different domains of the same ordered phase. An interface forms whenever two such domains contact. The thermodynamic behavior of this interface is governed by different forces. The presence of the underlying lattice and the stability of the ordered domains tend to localize the interface and to reduce its width. On the other hand, thermal fluctuations favor an interfacial wandering and an increase of the interface width. The result of this competition depends strongly on the order of the bulk phase transition. 

X-ray reflectometry (XR) X-rays X-rays 0.1 nm heavy atoms 300 nm interface width/ profile, marker movement... 

Fig. 12. Interface width a as a function of annealing time x during initial stages of interdiffusion of PS(D)/PS(H) [95]. Data points are obtained by a fit with error function profiles of neutron reflectivity curves as shown in Fig. 11. Different symbols correspond to different samples. The interface width a0 prior to annealing is also indicated (T) and is subtracted quadratically from the data (a = [

In the following sections we describe simulation results providing new Insights Into general MOCVD reactor behavior as well as the two major practical considerations, film uniformity and Interface width. 

Using atomic force microscopy (AFM), the kinetic surface roughening in electrochemical dissolution of nickel films at a low constant current density was studied in order to reveal the scaling laws [33]. The surface measurements of AFM exhibited the oscillatory variation of the interface width with time, which made it impossible to determine the growth exponent p. The oscillatory behavior of surface... 

Small-angle scattering intensity in the high angle (q) region can be analysed to provide information on interface thickness (e.g. the lamellar interface thickness block in copolymer melts or core-corona interface widths in micelles). For a perfectly sharp interface, the scattered intensity in the POrod regime falls as q A (Porod 1951). For an interface of finite width this is modified to... 

Ellipsometry Thickness, density, defect structure, interface width Monochromatic polarized light Polarization state of polarized light — Fraction of monolayer... 

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