Interpenetration ratio

However, the result still depends on / = u/V5, which is not an observable quantity. We can eliminate this parameter in favor of the interpenetration ratio... 

The choice of no governs r for small momenta in the dilute limit where Eq. (13.21) reduces to Nr = no- We thus should consider some universal ratio, defined for c —> 0, q -+ 0 which must be most sensitive to Nr. The interpenetration ratio ip is a good candidate, since it depends on Nr even in zero-loop approximation. From Sect. 15.4, Eq, (15.54) we take the one-loop order result... 

Fig. 18.1. Fixed point value of the interpenetration ratio as funo tion of the parameter no- Pull line, one-loop result short dashes zero-loop order long dashes xfj = 0,245...

Another startling conclusion from this study concerns the interpenetration ratio 4 (cf. eq. (2.14)), and goes to the heart of polymer theory. But this requires a brief historical digression. 

Fig. 2.15 Interpenetration ratio i versus chain length N, for SAWs in rf = 3. Error bar is one standard deviation. Data from Ref. 39.

How do highly interpenetrated random coil chains disentangle to cause fracture Disentanglement is considered to occur as shown in Fig. 14, where we depict the response of an entangled chain to a constant (step function) draw ratio X as follows ... 

Effectively, Eqs. (86) and (87) describe two interpenetrating continua which are thermally coupled. The value of the heat transfer coefficient a depends on the specific shape of the channels considered suitable correlations have been determined for circular or for rectangular channels [100]. In general, the temperature fields obtained from Eqs. (86) and (87) for the solid and the fluid phases are different, in contrast to the assumptions made in most other models for heat transfer in porous media [117]. Kim et al. [118] have used a model similar to that described here to compute the temperature distribution in a micro channel heat sink. They considered various values of the channel width (expressed in dimensionless form as the Darcy number) and various ratios of the solid and fluid thermal conductivity and determined the regimes where major deviations of the fluid temperature from the solid temperature are found. 

From CdCl2, K[Ag(CN)2] (ratio 1 2), and NH3 at pH 10 (citrate buffer), colorless crystals of [Cd(NH3)2 Ag(CN)2 2] (P42/mbc, Z= 4) are formed. Therein, /nmv-Cd(NI I3)2 entities (2/m — C2h) are linked by slightly bent NC—Ag—CN units to form a puckered 2-D network with large, 24-membered meshes. Two of these networks (transformed into each other by the 42 operation, i.e., they are perpendicular) interpenetrate.1 3 Similar corrugated sheets occur in [trans-CA (4-Mepy)2 Ag(CN)2 2] (4-Mepy) (4-Mepy = 4-methylpyridin) (Ibca, Z= 16 all atoms in general positions) but here, they are pairwise interwoven in the same layer. The intercalated 4-Mepy molecules are located in the meshes of this layer.219 From the same reaction medium, [Cd(4-Mepy)4 Ag2(CN)3 ][Ag(CN)2] (C2/m, Z = 2) crystallizes after some days. Here, the Cd(4-Mepy)4 units (2jm — C2h) are linked by almost linear NC—Ag—(C,N)—Ag CN rods to form chains, which in turn are arranged in layers. Inserted between the chains or into the layers are linear [Ag(CN)2] anions.219... 

Copolymers (graft or block) made of immiscible sequences give rise to biphasic morphologies depending on the ratio of immiscible sequences (or of their lengths). Such possible microstructures are reported in Figure 33. A minor phase can be dispersed as nodules (spheres) or filaments (cylinders) while, when concentrations of both phases get similar, lamellar (interpenetrated) structures can appear. It should be noted that rather similar morphologies could also be found in (compatibilised) polymer blends. 

So, interpenetrating polymer networks (IPNs) with a weight ratio of vinyl alcohol residue in PVA to acrylic acid monomer 4 6 exhibit positive swelling changes with temperature but IPNs 6 4 evidence negative swelling ones [48],... 

In the book by Hyde and Andersson (1989), the Nowotny phases are presented as a special case of a group of ID, columnar misfit structures which also include compounds such as Bam(Fe2S4) and other complex sulphides. Layer misfit structures, such as those of some oxide-fluorides, arseno-sulphides, etc., are also presented and classified with reference to a concept of structure commensurability based on the recognition that (along one or more axes) the ratios between the different repeat units of various interpenetrating substructures can (or cannot) be represented as ratios between integer numbers. 

Polyurethane-acrylic coatings with interpenetrating polymer networks (IPNs) were synthesized from a two-component polyurethane (PU) and an unsaturated urethane-modified acrylic copolymer. The two-component PU was prepared from hydroxyethylacrylate-butylmethacrylate copolymer with or without reacting with c-caprolactonc and cured with an aliphatic polyisocyanate. The unsaturated acrylic copolymer was made from the same hydroxy-functional acrylic copolymer modified with isocyanatoethyl methacrylate. IPNs were prepared simultaneously from the two-polymer systems at various ratios. The IPNs were characterized by their mechanical properties and glass transition temperatures. 

OP/HSP - Opaque Polymer HARP - High Aspect Ratio Polymer IPN - Interpenetrating Network PELC - Polymer Encapsulated Latex ML - Multilobe ... 

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