Types of Entanglements

Entangled systems are extended arrays, more complex than their constituents, that are comprised of individual motifs forming, via interlocking or interweaving, periodic architectures infinite in at least one dimension. Simple interdigitation is not considered here. As previously stated, most of the entangled arrays can be considered regularly repeated infinite versions of finite molecular motifs like catenanes, rotaxanes and pseudo-rotaxanes. 

Each motif is NEVER interlaced with all the others 

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Thus, the available theories are consistent with the observation that Me < Mc < Mc. There is certainly no justification for the view sometime expressed that the characteristic molecular weights differ because different types of entanglements are responsible for the properties concerned. 

The similar type of entangled state can be a starting point for internal changes leading to different quantum states sustained by the I-frame material dark states are useful in many respects. 

Figure 3.228. Types of entanglement coupling (1) temporary cross-link (2) local knot (3) long-range contour loop.

There are a number of other forms of entanglement besides interpenetration (and self-penetration), which have received considerable interest in recent times. One such class of materials is the polyrotaxane or poly-threaded structures. These entanglements show great variety, partly because there are a number of different types of entanglement which can fall under this banner. 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

The two main amphibole asbestos fibers are amosite and crocidoHte, and both are hydrated siHcates of iron, magnesium, and sodium. The appearance of these fibers and of the corresponding nonfibrous amphiboles is shown in Figure 1. Although the macroscopic visual aspect of clusters of various types of asbestos fibers is similar, significant differences between chrysotile and amphiboles appear at the microscopic level. Under the electron microscope, chrysotile fibers are seen as clusters of fibrils, often entangled, suggesting loosely bonded, flexible fibrils (Fig. 2a). Amphibole fibers, on the other hand, usually appear as individual needles with a crystalline aspect (Fig. 2b). 

In Figure 9-5 the worker is ascending a caged ladder. Notice that the worker s air pack, airline or apparatus could become entangled with the ladder protection. The worker in Figure 9-6 who is using absorbent to soak up a mock spill has no encumbrances pictured near the work area. So, besides the proper level of protection, the type of work being performed and the work area can be important. 

Coran and Patel [33] selected a series of TPEs based on different rubbers and thermoplastics. Three types of rubbers EPDM, ethylene vinyl acetate (EVA), and nitrile (NBR) were selected and the plastics include PP, PS, styrene acrylonitrile (SAN), and PA. It was shown that the ultimate mechanical properties such as stress at break, elongation, and the elastic recovery of these dynamically cured blends increased with the similarity of the rubber and plastic in respect to the critical surface tension for wetting and with the crystallinity of the plastic phase. Critical chain length of the rubber molecule, crystallinity of the hard phase (plastic), and the surface energy are a few of the parameters used in the analysis. Better results are obtained with a crystalline plastic material when the entanglement molecular length of the... 

Another type of network imperfection, resulting from cross-linking of two units not distantly related structurally, is indicated in Fig. 94. Cross-linkages such as B are wasted (except insofar as the loop may be involved in entanglements not otherwise operative). The proportion of these short path cross-linkages should be small ordinarily but could become very large if the cross-linking process were carried out in a dilute solution of the polymer. 

Gelation involves an extended structure and some type of linking between chains. The concept of salt-like crosslinks has already been described (Section 5.5). Other possibilities may be considered. Hill, Wilson Warrens (1989) examined the possibility that chain entanglements might account for the strength of polyelectrolyte cements. They used in particular... 

Simple physical entanglements can be sufficient to produce a structurally stable gel if the polymer has a sufficiently great molecular weight and if the polymer is of only modest hydrophilicity. In this case, the polymer will swell in water without dissolving, even in the absence of covalent cross-links. Poly(2-hydroxyethyl methacrylate) (PHEMA) is a prominent example of this type of hydrogel when uncross-linked, it will dissolve in 1,2-propanediol but only swell in water. 

The different length scales involve different time scales with different types of motion. For short times corresponding to spatial distances shorter than the entanglement distance, we expect entropy-determined dynamics described by the so-called Rouse model [6, 35.]. As the spatial extent of motion increases and... 

Various types of power law relaxation have been observed experimentally or predicted from models of molecular motion. Each of them is defined in its specific time window and for specific molecular structure and composition. Examples are dynamically induced glass transition [90,161], phase separated block copolymers [162,163], polymer melts with highly entangled linear molecules of uniform length [61,62], and many others. A comprehensive review on power law relaxation has been recently given by Winter [164],... 

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