Dimensions of Branched Molecules

Such calculations are facilitated by the use of a theorem due originally to Kramers (30). For a molecule of given structure free from rings and having a total of N units (i.e. beads in the model) joined by links of length b  

It would take much space to quote all the published results, but Table 3.1 lists the most important sources for values of g0 for a number of standard types of branched structure. 

Stars (fixed no. of branches radiating from a centre) (a) Uniform (branches equal) (b) Random (branch lengths random) (2,19-22) (16,20) 

Combs (a) Uniform (fixed number of equally-spaced equal branches) (b) Randomly spaced (fixed number of equal branches) (c) Random lengths (fixed number of branches) (d) Heterogeneous (product of random coupling between equal branches and homogeneous backbone) (19.20.21.25.29) (29) (20) (19.29) 

Randomly branched (a) All structures with fixed number of brandies (b) Product of random branching reaction, averaged over MWD (c) Fractions of homogeneous MW from product of random branching reaction (16,20) m m 

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If interactions between parts of the molecule separated by many links (the excluded volume effect ) is absent, so that the chains obey random-flight statistics, takes its unperturbed value, (s ). Theoretical calculations of the dimensions of branched molecules usually assume random flight chains, and values of the mean-square radius so obtained are estimates of . 

Zimm, B.H. and Stockmayer, W.H.J. The dimensions of chain molecules containing branches and rings, Chem. Phys., 17, 1301, 1949. 

Zimm B. H., Stockmayer W. H. Dimensions of Chain Molecules Containing Branches and Rings H J. Chem. Phys., 1949,17 (3), p. 1301-1314. 

The melt index (Ml)—also known as the melt flow index (MFl)—of a polyethylene resin refers to the rate at whieh it extrudes from a capillary die under a standard set of conditions. The method by which it is determined is described in Chapter 6. The melt index of a polyethylene resin depends on its molecular characteristics, primarily average molecular weight, molecular weight distribution, and branching characteristics—short chain versus long chain, concentration, and distribution. The melt index reflects the average dimensions of the molecules in a resin and their entanglements with one another. From a commercial point... 

Up to this point, we ve viewed molecules primarily in a two-dimensional way and have given little thought to any consequences that might arise from the spatial arrangement of atoms in molecules. Now it s time to add a third dimension to our study. Stereochemistry is the branch of chemistry concerned with the three-dimensional aspects of molecules. We ll see on many occasions in future chapters that the exact three-dimensional structure of a molecule is often crucial to determining its properties and biological behavior. 

In addition to the size of the molecules and their distribution, the shapes or structures of individual polymer molecules also play an important role in determining the properties and processability of plastics. There are those that are formed by aligning themselves into long chains of molecules and others with branches or lateral connections to form complex structures. All these forms exist in either two or three dimensions. 

Thiourea clathrates may also be applied for geochemical separations. They are similar to the molecnlar complexes of nrea bnt owing to the larger dimensions of the thiourea crystal channels, only branched alkanes, cycloalkanes, and their derivatives participate in clathrate formation. In contrast, the unbranched molecules are too small and hence cannot be held rigidly [77]. 

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-... 

Very recently, highly regular, highly controlled, dense branching has been developed. The resulting dendrimers often have a spherical shape with special interior and surface properties. The synthesis and properties of dendrimers has been reviewed (see e.g. G.R. Newkome et al. Dendritic Molecules , VCH, 1996). In this series, a chapter deals with the molecular dimensions of dendrimers and with dendrimer-polymer hybrids. One possible development of such materials may be in the fields of biochemistry and biomaterials. The less perfect hyper-branched polymers synthesized from A2B-type monomers offer a real hope for large scale commercialization. A review of the present status of research on hyperbranched polymers is included. 

If the branching density is sufficiently high to hinder segmental flexibility and impose strong excluded volume and even steric interactions, molecular dimensions become rigid. Measurements of solution and melt viscosity showed that the properties of dendritic molecules approached that of solid spheres as the... 

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