Comb-Like Structures

The excitation and detection of surface acoustic waves, flexural plate waves, and other plate waves on piezoelectric substrates is most readily accomplished by use of an interdigital transducer (IDT) first reported by White and Voltmer [6]. The comb-like structure of the IDT, illustrated in Figure 6.4, is typically made from a lithographically patterned thin film that has been deposited onto the surface of a piezoelectric substrate or thin film. The metal film used to make the IDT must be thick enough to offer low electrical resistance and thin enough so that it does not present an excessive mechanical load to the AW. Typical IDTs are made... 

All these properties are observed under the condition that the side chains of the graft copolymer are much shorter than the main chain, i.e. the molecules must exhibit a comb-like structure. Moreover, the higher the degree of grafting, i.e. the smaller the distance between the chains of grafted polystyrene, the more pronounced these properties. This shows that the specific properties of graft copolymer molecules, just as those of the comb-like molecules previously considered (see p. 161), are due, to a great extent, to the interactions of their side chains. 

This can be explained by the fact that in a polymer molecule (Fig. 78b) the longitudinal components of monomer unit dipoles mh are mutually compensated and the main part in the observed EB is played by normal components of monomer unit dipoles, mi, which can be parallel to the main chain of the macromolecule owing to its comb-like structure. In other words, in molecules of comb-like polymers containing mesogenic side chains, the orientations of the Mi components of the side group dipoles are correlated with each other. As a result, the macromolecule as a whole or part of it can exhibit a considerable dipole moment m in the direction of the main chain L (Fig, 78b). The existence of this dipole accounts for the orientation of the main chain in the field direction leading to negative EB. 

The use of labels makes it possible not only to distinguish a single component in a multicomponent polymer system, but also to distinguish a single part of the macromolecule the end of the main chain, the end of the side chain, the inner part of the main chain. Separate investigations of the mobility of the main chain and side chains are particularly desirable for polymers with a complex comb-like structure. 

FIGURE 10.1. DENOX catalyst The catalyst elements exhibit a honey-comb-like structure (upper photo) view into a reactor partly filled with catalyst modules (lower photo). By courtesy of Porzellanfabrik Frauenthal GmbH and Austrian Energy and Environment SGP Wagner-Biro GmbH, Austria. 

Very recently, the self-assembly of poly(y-benzyl-i,-glulamalc)-fo-poly(i,-lysine) rod-coil copolypeptide via ionic complexation was reported by Ikkala, Hadjichristidis and coworkers [65]. Complexation between the anionic surfactants dodecyl benzenesulfonic acid and the cationic poly(L-lysine) chains occurs via proton transfer from the acid group to the base, resulting in electrostatically bonded comb-like structures, and fluid-like liquid crystalline structures at room temperature due to efficient plasticization of dodecyl benzenesulfonic acid. 

If u approaches zero, a comb-like structure is obtained. The generating function of such a structure is... 

Lattice models and other discrete models are used to describe a wide variety of dynamical systems [270, 77]. In this section we study the propagation of reaction-random walk wavefronts on heterogeneous lattices that consist of a main backbone with a regular distribution of secondary branches. An example is comb-like structures, see Fig. 6.3 [53]. 

Next, we add to every site of the backbone a secondary branch of length I, to produce a comb-like structure (see Fig. 6.3). On such a stmcture, a walker that is at a given site of the backbone can spend a certain amount of time in the secondary branch before jumping to one of the nearest neighbor sites on the backbone. If we are only interested in the behavior of the system in the direction of the backbone, then the secondary branches introduce a delay time for jumps between the neighboring sites on the backbone. The random walk on the comb structure can be modeled as a CTRW with (6.27) and a new waiting PDF (p t) that includes the effect of the delay due to the secondary branches. 

The units giving rise to the liquid-crystalline behavior can be in the side chains. Although most of the polymers studied have been linear, there has been some work on hyperbranched or comb-like structures. The orientation of the mesogenic groups is important. " Frequently backbones include siloxanes and acrylates, " but a variety of other structures... 

As a result of the their -CF3 terminated side groups and comb-like structure, the typical range of surface energies for fluorinated acrylic polymers (5.6-7.S mN/m) are even lower than that of PTFE ( 20 mN/m) [35]. The p(PFDA) side chains with eight perfluorinated carbons, so-called C8, provide highly desirable iCVD surface properties but there is concern over the bioaccumulation factor of the monomer [36], suggesting that future research would benefit from utilizing monomers with shorter perfluorocarbon side chains. 

Molecular architectures can be structurally classified as being more comb-like or Cayley tree-like. Structure has impact on the radius of gyration, which is larger for linear molecules than for branched molecules of the same weight (number of monomer units), since the latter are more compact. The ratio between branched and linear radius is usually described by a contraction factor . Furthermore, Cayley tree-like structures are more compact than comb-like structures [33, 56]. We will show here how to obtain the contraction factor from the architectural information. The squared radius of gyration is expressed in monomer sizes. According to a statistical-mechanical model [55] it follows from the architecture as represented in graph theoretical terms, the KirchhofF matrix, K, which is derived from the incidence matrix, C [33] ... 

Siloxane wilii reactive Si-H groups, comb-like structure... 

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