Interfacial thickness

A fiill solution of tlie nonlinear radiation follows from the Maxwell equations. The general case of radiation from a second-order nonlinear material of finite thickness was solved by Bloembergen and Pershan in 1962 [40]. That problem reduces to the present one if we let the interfacial thickness approach zero. Other equivalent solutions involved tlie application of the boundary conditions for a polarization sheet [14] or the... 

Cakmak M. and Wang M.D., Structure development in the tubular blown film of PP/EPDM thermoplastic elastomer, Antec 89, 47th Annual Tech. Conference of SPE, New York, May 1, 1989, 1756. Hashimoto T., Todo A., Itoi H., and Kawai H. Domain boundary structure of styrene-isoprene block copolymer films cast from solution. 2. Quantitative estimation of the interfacial thickness of lamellar microphase systems. Macromolecules, 10, 377, 1977. 

Girault and Schiffrin [4] proposed an alternative model, which questioned the concept of the ion-free inner layer at the ITIES. They suggested that the interfacial region is not molecularly sharp, but consist of a mixed solvent region with a continuous change in the solvent properties [Fig. 1(b)]. Interfacial solvent mixing should lead to the mixed solvation of ions at the ITIES, which influences the surface excess of water [4]. Existence of the mixed solvent layer has been supported by theoretical calculations for the lattice-gas model of the liquid-liquid interface [23], which suggest that the thickness of this layer depends on the miscibility of the two solvents [23]. However, for solvents of experimental interest, the interfacial thickness approaches the sum of solvent radii, which is comparable with the inner-layer thickness in the MVN model. 

Figure 21 Plot of thickness values as a function of molecular weight for linear polyethylene fractions quenched to —78°C. (A), crystallite thickness, Lc (O), interlamellar thickness, La ( ), interfacial thickness, Lb. Reprinted with permission from Ref. [277]. Copyright 1990 American Chemical Society.

Figure 34. The circles show interfacial thickness as a function of resist concentration spun at 3500 rpm and prebaked at 55 C The solid dots show interfacial thickness also as a function of concentration but the spin speed is changed to maintain a constant resist thickness of 0.41 0.01 pm.

Wooster, T.J., Augustin, M.A. (2006). p-Factoglobulin-dextran Maillard conjugates their effect on interfacial thickness and emulsion stability. Journal of Colloid and Interface Science, 303, 564-572. 

Once the free energy of an inhomogeneous system is given, one can calculate by standard methods the properties of the interface—for example, the interfacial tension or the density profile perpendicular the interface [285]. Weiss and Schroer compared the various approximations within square-gradient theory discussed earlier in Section IV.F for studying the interfacial properties for pure DH and FL theory [241, 242], In theories based on local density approximations the interfacial thickness and the interfacial tension were found to differ by up to a factor of four in the various approximations. This contrasts with nonionic fluids, where the density profiles and interfacial... 

Merfeld GD, Karim A, Majumdar B, Satija SK, Paul DR (1998) Interfacial thickness in bilayers of poly(phenylene oxide) and styrenic copolymers. J Polym Sd B Polym Phys 36 3115-3125... 

Interfaces are not only present in blends, but are also a key feature of structural joints, where it is often necessary to produce interfacial strengths comparable with the cohesive strength of the bulk materials, and of laminates, where a more modest degree of adhesion may suffice [166]. The compatibility between different components can be expressed in terms of the equilibrium interfacial thickness, w, given approximately by ... 

Preliminary studies of the interphase between respective domains by Van Bogart et al. (53) indicate the thickness of this region, assuming a linear density gradient, is on the order of 10-20 A for polyester and polyether urethanes (MDI-BD based). Theoretically, the interfacial thickness is inversely related to the square root of the hard segment-soft segment interaction parameter (54). 

Fig. 12. Schematic variation of the order parameter profile /(z) of a symmetric (f=l/2) diblock copolymer melt as a function of the distance z from a wall situated at z=0. It is assumed that the wall attracts preferentially species A. Case (a) refers to the case % %v where non-linear effects are still negligible, correlation length and wavelength X are then of the same order of magnitude, and it is also assumed that the surface "field" Hj is so weak that at the surface it only induces an order parameter 0.2 n if mb is the order parameter amplitude that appears for %=%t at the first-order transition in the bulk. Case (b) refers to a case where % is only slightly smaller than %t, such that an ordered "wetting layer" of thickness 1 [Eq. (76)] much larger than the interfacial thickness which is of the same order as [Eq. (74)] is stabilized by the wall, while the bulk is still disordered. The envelope (denoted as m(z) in the figure) of the order parameter profile is then essentially identical to an interfacial profile between the coexisting ordered phase at T=Tt for (zl). The quantitative form of this profile [234] is shown in Fig. 13. From Binder [6]...

Several additional phases are observed experimentally, but are not thermodynamically stable [13]. Moreover, the synthetic nature of the copolymers implies some heterogeneity in the polymer structure and molecular weight distribution. An excellent review has recently been published [97], and the main conclusion is that the polydispersity index (PDI) influences all aspects of the self-assembly. For example, upon an increase of the PDI of one block, the lattice constant of an ordered structure or the size of microphase-separated domains increases, interfacial thickness increases, and phase transitions may be induced. In addition, macrophase-separation may occur as the PDI is increased at certain compositions and segregation strengths. 

When the interfacial thickness between the membrane and the dispersing medium is finite, a term proportional to exp( — a2q2) is multiplied by P(q) in Eqs. (1-3) at large q, where a denotes an index of the surface thickness [22,23], Thus a can be determined from the asymptotic slope of the semilogarithmic plot of P q)q (infinitely thin shell) or P q)qA (solid sphere) versus q2. 

From the results of MD simulations, the non-linear susceptibility, Xs p. can be calculated for each interfacial species of water molecule as a function of distance along the simulation cell (see Figure 2.13) to determine how each species contributes to the SF signal and to the depdi that SF intensity is generated. Although this representation is only a first approximation of the SF probe depth, it is the most relevant measure of interfacial thickness for SF experiments because it indicates the depth to which water molecules are affected by the presence of the interface. To make a direct comparison to experiment, the contribution from each OH oscillator to the total xisp is multiplied by a factor, linear in frequency, that accounts for the IR vibrational response dependency on frequency. For example, an OH vibration at 3400 cm is approximately 12 times stronger in SF intensity than the free OH. 

The molecular-level stmcture of the electrode/electrolyte interface was studied using two- and three- phase systems, including membrane/vapor, membrane/vapor/catalyst and membraneAfapor/ graphite systems. The simulations of a membraneAfapor interface show a region of dehydration near the interface. The interfacial thickness measured from the water density profile was found to decrease in width with increasing humidity. Hydronium ions displayed a preferential orientation at the interface, with the oxygen exposed to the vapor phase. 

Felton, L.A. Perry, W.L. A novel technique to quantify film-tablet interfacial thickness. Pharm. Dev. Technol. 2002, 7 (1), 1-5. 

Within the present model some semiquantltatlve measure of the Interfacial thickness can be given. Strictly speaking it is infinitely thick, but most of the density variation takes place over a distance t, obtained by extrapolation of the linear part. A simplification of the real profile would be to replace it by the linear step function. This linear part is mathematically represented by the linear term p (z) = z/ (recall tanhx = x - x /3 + 2x /15 -. ..). We find... 

Interfacial tension and interfacial thickness measurements on several quasi critical systems with salt are in agreement with this picture (18). 

Interfacial agents, such as block copolymers, are known to reduce the Interfaclal tension and hence are expected to Increase the degree of dispersion in blends. The measurement of Interfacial tension for polymer systems is not easy. Most measurements have been made by the pendant drop technique. Measurements of Interfacial thickness are also difficult. They have been made using electron microscopy and, mostly in the case of block copolymers, by x-ray and neutron scattering. Recent results using neutron reflection suggest that this will be a useful technique in the future. 

Perrin P, Prudhomme RE. SAXS measurements of interfacial thickness in amorphous polymer blends containing a diblock copolymer. Macromolecules 1994 27 1852-1860. 

The three-dimensional region of contact between phases a and j3 is called the interphase region or interfacial layer. It is generally assumed that if the ions are not present, this region is a few molecules in thickness (approximately 1-2 nm) and only an extremely small fraction of the molecules in the system are present in the interfacial region due to geometrical constraints. (If ions are present the interfacial thickness is much larger because the concentration... 

There has been some debate over the existence of an intrinsic interfacial thickness or mixed region (see below), 0, onto which the capillary waves are... 

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