Interphase distribution function

Important morphological parameters such as the long period (I), crystal thickness (Ic), and amorphous layer thickness (la) of semipolymer melts and blends can be determined using SAXS via two different approaches. In the first approach, standard models such as the Hosemarm-Tsvankin [23] and the Vonk-Kortleve [24,25] for lamellar stacks are fitted to data obtained for the SAXS profile. The second approach is based on performing a Fourier transform for the SAXS profile to produce a one-dimensional correlation function, y(z) (which is Fourier transform of the measured I(q) in SAXS) or an interphase distribution function (IDF) in real space. 

Interphase Distribution Function (IDF) Method The IDF, g (z), is equal to the second derivative of the correlation function, y(z), and is given by... 

Figure 6.7 (a) The interphase distribution function (IDF) for the listed compositions of PCL/PVC blends (b) Morphological parameters obtained from the deconvolution of the... 

Fig. 7 Appearance of the composition distribution function/0 ( 1) typical of the products of interphase (1) as well as hypothetical (2) and real (3) homophase copolymerization at...

Equations (11) and (12) are the linear momentum balances in the flow direction. Here the total pressure head has been partitioned into partial pressure components through the use of the solid volume distribution function . Equation (13) is the balance of linear momentum for the solid phase (the fluid phase is the same but of opposite sign) in the y direction. In this equation, we have allowed for an interphase pressure effect (incorporated in the parameter E) to ensure that the mixture remains saturated at all times [8]. Equations (14) and (15) account for the angular momentum balance in the binormal direction for the two constituents. Finally, the primes imply differentiation with respect to 3 ... 

Static mixing of immiscible Hquids can provide exceUent enhancement of the interphase area for increasing mass-transfer rate. The drop size distribution is relatively narrow compared to agitated tanks. Three forces are known to influence the formation of drops in a static mixer shear stress, surface tension, and viscous stress in the dispersed phase. Dimensional analysis shows that the drop size of the dispersed phase is controUed by the Weber number. The average drop size, in a Kenics mixer is a function of Weber number We = df /a, and the ratio of dispersed to continuous-phase viscosities (Eig. 32). 

Liquid chromatography (LC) and, in particular, high performance liquid chromatography (HPLC), is at present the most popular and widely used separation procedure based on a quasi-equilibrium -type of molecular distribution between two phases. Officially, LC is defined as a physical method... in which the components to be separated are distributed between two phases, one of which is stationary (stationary phase) while the other (the mobile phase) moves in a definite direction [ 1 ]. In other words, all chromatographic methods have one thing in common and that is the dynamic separation of a substance mixture in a flow system. Since the interphase molecular distribution of the respective substances is the main condition of the separation layer functionality in this method, chromatography can be considered as an excellent model of other methods based on similar distributions and carried out at dynamic conditions. 

There is a functional relationship between the charge on each phase (or the potential difference across the interface) and the structure of the interphase region. The fundamental problem of double-layer studies is to unravel this functional relationship. One has understood a particular electrified interface if, on the basis of a model (i.e., an assumed type of arrangement of the particles in the interphase), one can predict the distribution of charge (or variation of potential) across the interphase. 

Consider the relation between the correlation function and its spectral density. Slower and faster decays of the correlation function (i.e. slower and faster motions) give narrower and wider distributions of the spectral density, respectively. Figure 11 (a) shows some decay curves of the correlation function for motions with different xc values and (b) indicates the distributions of their respective spectral densities that are obtained by Fourier transform of the decay curves. Here A, B, C in (a) are the decay curves with xca> tcb> and A, B, C in (b) are the distribution of their respective spectral densities. As can be seen, the decay becomes slower and the spectral density distribution becomes narrower as the Xc increases. Assume here that xca cb i cc and the amorphous phase involves two independent motions dictated by xca and xcb whereas the crystalline-amorphous interphase involves two motions dictated by xca and Xcc-Here, xca characterizes a local molecular motion with relation to few carbon atoms in the main molecular chain, and xcb>tcc a somewhat long-ranged motion with relation to a conformational change of ca. 10-20 carbon atoms. In other words, it is assumed that somewhat long-ranged motion is different between the two phases but local motion is the same, the former is dictated by xcb or Xcc and the latter by a common relaxation time xca-... 

The properties of filled materials are eritieally dependent on the interphase between the filler and the matrix polymer. The type of interphase depends on the character of the interaction which may be either a physical force or a chemical reaction. Both types of interaction contribute to the reinforcement of polymeric materials. Formation of chemical bonds in filled materials generates much of their physical properties. An interfacial bond improves interlaminar adhesion, delamination resistance, fatigue resistance, and corrosion resistance. These properties must be considered in the design of filled materials, composites, and in tailoring the properties of the final product. Other consequences of filler reactivity can be explained based on the properties of monodisperse inorganic materials having small particle sizes. The controlled shape, size and functional group distribution of these materials develop a controlled, ordered structure in the material. The filler surface acts as a template for interface formation which allows the reactivity of the filler surface to come into play. Here are examples ... 

From the economic as well as the performance points of view, the reactive compatibUization is most interesting (see Chapter 5). The process involves (i) sufficient dispersive and distributive mixing to ascertain required renewal of the interface, (ii) presence of a reactive functionality, suitable to react across the interphase, (iii) sufficient reaction rate making it possible to produce sufficient quantity of the compatibiUzing copolymer within the residence time of the processing unit The method leads to particularly thick interphase, thus good stability of morphology. 

The conformer distribution estimated above leads to the configurational partition function Zn for the nematic state. Since the partition function Zj for the isotropic state is available from the conventional RIS calculation, the conformational entropy change 5 at the NI interphase may be obtained as... 

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