Tree-like molecules

Finally, the applicability of the cascade theory to rather complicated systems with unequal functional groups, substitution effect, vulcanization of chains and long rang correlation as a result of directed chain reactions is shown. The limitation of the theory to essentially tree-like molecules and their unperturbed dimensions is outlined and the consequence of this error for the prediction of reed systems is discussed. 

Lipids form membranes inside and around the cell. Carbohydrates form complex tree-like molecules that become attached to the surface of proteins and cellular membranes. In both cases, the three-dimensional molecular structure is not unique, but the molecular assemblies are highly flexible. Thus, analyzing the molecular structure involves the inspection of a process in time. Molecular dynamics is the only available computer-based method for doing so. Compared with protein structures there are relatively few results on lipids and carbohydrates. The book does not detail this topic. 

Starch is a plant polysaccharide that we encounter in our food, but we in fact manufacture a very similar substance ourselves in our liver and in our muscles we have our own carbohydrate energy store, glycogen. This is closely similar to plant amylopectin, with a branched, tree-like molecule, the only difference being that glycogen is more highly branched. 

Glycogen A storage polysaccharide in muscle and liver made of hundreds of glucose units joined to form tree-like molecules. 

The last two models have been investigated extensively by Flory He considered networks forming part of a larger network with fixed jimctions outside the network under consideration. The crosslinking points of the inner network were assumed to fluctuate freely, or to have fixed positions in space. In both cases, the inner network can be considered as localized by boundary conditions. In particular, Flory considered a network formed in two hypothetical steps. First, a giant acyclic molecule is formed by joining all chains via the available multifunctional junctions such a tree-like molecule can be characterized by v -H 1 v junctions plus chain ends (i.e. number of labelled points). Figure 3 shows an example of the network after the first step. In the second step additional connections are formed by the reaction of 2 unreacted functionalities, which reduces the number of labelled points to approximately The number is called the cycle rank, which can be defined... 

In some cases we encourage branching. For example, model molecules can be synthesized with the geometry of stars or combs (Fig. 0.1). More often, branching takes place statistically. It may lead either to tree-like molecules, or, at a higher level, to network structures (discussed in Chapter V). In summary, we can obtain chains that are strictly linear (when is not too large) we can also insert on a chain a controlled number of branch points. 

The accepted model of a gel for purposes of sol-gel analysis or elasticity parameters is the ring-free infinite tree-like molecule. It is successful, even though such a molecule could not be packed into three-dimensional space after the gel point, i.e. when its relative conversion a/a shall denote this... 

Recent developments in the design of dendritic molecules has provided both new methodology and molecular architecture which are structure controlled macromolecules, globular-shaped, dendritic-branched tree-like structures with nanoscscale dimensions [1], Dendrimers generally consist of a focal core, many building blocks (monomer units) and a mathematically defined number of ex-... 

A feature of theories for tree-like polymers is the disentanglement transition , which occurs when the tube dilation becomes faster than the arm-retraction within it. In fact this will happen even for simple star polymers, but very close to the terminal time itself when very little orientation remains in the polymers. In tree-like polymers, it is possible that several levels of molecule near the core are not effectively entangled, and instead relax via renormalised Rouse dynamics (in other words the criterion for dynamic dilution of Sect. 3.2.5 occurs before the topology of the tree becomes trivial). In extreme cases the cores may relax by Zimm dynamics, when the surroundings fail to screen even the hydro-dynamic interactions between the slowest sections of the molecules. 

Unlike amylose, amylopectin, which is practically insoluble, is branched. On average, one in 20-25 glucose residues is linked to another chain via an al 6 bond. This leads to an extended tree-like structure, which— like amylose—contains only one anomeric OH group (a reducing end ). Amylopectin molecules can contain hundreds of thousands of glucose residues their mass can be more than 10 Da. 

In this context, much attention is currently devoted to the preparation of highly branched tree-like species, variously called cascade molecules, arborols, or dendrimers. The reasons why such compounds are interesting from a fundamental viewpoint and promising for a variety of applications have been reviewed and highlighted by several authors. Many of the dendrimers obtained so far are organic in nature. This review describes a novel family of dendrimers containing metal ions, prepared in our laboratories over the last few years. 

Dendrimers (Newkome et al., 1996) and hyperbranched polymers, HBP, look like functional microgels in their compactness but they differ in two aspects they do not contain cyclic structures and, more importantly, they are much smaller, in the range of a few nanometers in size. They are prepared stepwise in successive generations (dendrimers) or they are obtained by the polyaddition/polycondensation of ABf monomers, where only the A + B reaction is possible (HBP Voit, 2000). Both molecules have tree-like structures, but a large distribution of molar masses exists in the case of HBP. 

The name dendrimers, which has meanwhile largely displaced the original designation of cascade molecules, is derived from the Greek words dendron and meros, and is meant to underscore the tree-like branched structure of this class of compounds (see Section 1.1). 

---