Linear topology

Linear paraffins Linear programming Linear rollback model Linear sensor arrays Linear superelasticity Linear topology Linear units Linen... 

Similar patterns of property differentiation are clearly recognized at the macromolecular level. For example, dramatic changes in physical and chemical properties are observed by simply converting a linear topology of common composition to a cross-linked architecture. In traditional macromolecular science, these issues were considered apparent and obvious. However, as novel architectures emerged, new architecture-property relationships have not been so clearly articulated and exploited. Prompted by the synthetic accessibility of many new polymeric architectures based on common compositional monomers... 

Frechet [49, 89] was the first to compare viscosity parameters for (A) linear topologies, as well as (B) random hyperbranched polymers and (C) dendrimers. More recently, we reported such parameters for (D) dendrigraft polymers [111] as shown in Figure 1.19. It is clear that all three dendritic topologies behave differently than the linear. There is, however, a continuum of behavior wherein random hyperbranched polymers behave most nearly like the linear systems. Dendrigrafts exhibit intermediary behavior, whereas dendrimers show a completely different relationship as a function of molecular weight. 

Unique features offered by the dendritic state , that have no equivalency in the linear topologies, are found almost exclusively in the dendron/dendrimer subset or to a slightly lesser degree in the dendrigrafts. They include ... 

C. Rourke, B. Sanderson, Introduction to Piecewise-linear Topology, Ergeb. der Math. u. 

Despite the tremendous success in the development of nanomaterials, the level of control of their structure and properties is still very limited. When AuNPs are used as building blocks, monovalent, divalent, or higher valency nanoparticles would be required when aiming at the controlled and well-organized construction of 3D nanonetworks from a simple linear topology. 

From the beads-on-a-string linear topology, research moved to the mapping of genes in a chromosome, and later to the discovery that genes were nucleic acids. Their chemical constitution was then determined, first topologically according to the classic structural theory procedures by Todd, and finally in the three-dimensional structural pattern (3D) of the DNA double helix proposed by Watson and Crick in 1953. 

The relation between the structure of the reactive manifold and the exponent ( appearing in eq. (18) is still an open problem with significant theoretical and practical implications in the study of catalytic processes. The expression, eq. (23), for the exponent in the specific case study considered depends on the linear topology of the structure in... 

Similar patterns of property differentiation are clearly recognized at the macromolecular level. For example, dramatic changes in physical and chemical properties are observed by simply converting a linear topology of common... 

Let US consider a GGS that has a linear topology and that consists of Ntot = N beads connected by elastic springs, see Fig. lA. The Langevin equation of motion, Eq. 2, can be rewritten for the inner chain beads, 1 < < in the form [1,2,40,41] ... 

Use simple Hiickel MOs for butadiene to calculate to first order the change in 7T energy that would result from closing cw-butadiene to cyclobutadiene (III). Repeat the approach for closing hexatriene to benzene. (IV). Which of these two systems benefits most from cyclic as opposed to linear topology For each... 

The chains discussed so far have all a linear topology. There exists a large group of polymers with a different architecture, and some typical forms are sketched in Fig. 1.5. For example, a polymer may include short- and long-chain branches in a statistical distribution. A well-known representative of... 

Besides the shape, another important factor that affects the electronic properties and chemical reactivity of PAHs is the nature of the periphery. According to Clar s classification, the graphitic molecules with armchair and cove peripheries shown in Fig. 3.14 (A and B) are all-benzenoid PAHs. In addition to these linear topologies, Stein and Brown considered two other peripheral structures, i.e. acene-like (C) and quinoidaT (D) structures, which lie in a higher energy state and thus show higher chemical reactivity [62]. 

The chains discussed so far all have a linear topology. There exists a large group of polymers with a different architecture and some of their typical forms... 

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