Linear polymers number

The structure of the linear polymer formed under a particular set of experimental conditions can be formulated in a number of cases after a detailed examination of its properties. 

The EMT analysis indicated that the stress relaxes in proportion to the number of bonds removed. The initial linear decrease of E/Eq with is intuitively appealing and is the basis for many linear constitutive theories of polymers. An example is the Doi-Edwards theory of viscoelasticity of linear polymer melts [49] in which... 

The presence of a large number of chain-ends in the fully synthesized dendrimer molecules makes them highly soluble and also readily miscible, for example with other dendrimer solutions. The solubility is controlled by the nature of the end-groups, so that dendrimers with hydrophilic groups, such as hydroxyl or carboxylic acid, at the ends of the branches are soluble in polar solvents, whereas dendrimers with hydrophobic end-groups are soluble in non-polar solvents. The density of the end-groups at the surface of the dendrimer molecule means that they have proportionately more influence on the solubility than in linear polymers. Hence a dendritic polyester has been shown to be more soluble in tetrahydrofuran than an equivalent linear polyester. 

X-ray diffraction patterns from dendrimers tend to lack sharp features and are similar to those from amorphous linear polymers. This suggests a molecular arrangement in dendrimers that is fairly disordered. There is also the problem that these molecules can exist in a large number of energetically equivalent conformations and that in solution there can be rapid interchange between these conformations. This contributes to the overall amorphous structure of dendrimers. 

The continuing success of this hook has necessitated a further revision to bring it up to date. The main chapters have not been altered, but I have introduced new material into chapters 10 and 11, and I have also added a completely new chapter, number 9, to deal with the rapidly developing subject of dendrimers. Though what I have said here is, of necessity, brief it does draw attention to the existence of these materials and to the major ways in which they differ from conventional linear polymers. 

The overall objective of this chapter is to review the fundamental issues involved in the transport of macromolecules in hydrophilic media made of synthetic or naturally occurring uncharged polymers with nanometer-scale pore structure when an electric field is applied. The physical and chemical properties and structural features of hydrophilic polymeric materials will be considered first. Although the emphasis will be on classical polymeric gels, discussion of polymeric solutions and nonclassical gels made of, for example, un-cross-linked macromolecular units such as linear polymers and micelles will also be considered in light of recent interest in these materials for a number of applications... 

Data from f.a.b.-m.s., and also f.d.-m.s., revealed the existence of naturally occurring, large cyclic polysaccharides. The first indication that a molecule may be cyclic comes from its precise molecular-weight determination. Cyclic molecules are 18 mass units less than their linear counterparts. Loss of water may, of course, occur in a number of ways, for example, by dehydration or lactonization, and conclusive evidence for the presence of a cyclic molecule can only be obtained from f.a.b.-m.s. of suitable derivatives, such as the permethyl derivative. Cyclic and dehydrated linear polymers are distinguishable after permethylation, as the cyclic polymer will incorporate one methyl group less than the linear molecule. 

Distribution curves calculated for several values of / are shown in Fig. 56. Values of p have been adjusted to give the same number average (see Eq. 23), which also locates the maxima in the curves very nearly at the same abscissa value. The sharpening of the curves with increase in / is evident. The curve for /= 1, corresponding to the most probable distribution, is included for comparison. Even for /=2, which represents the linear polymer prepared by condensing... 

The simplest, from the viewpoint of topological structure, are the linear polymers. Depending on the number m of the types of monomeric units they differentiate homopolymers (m=1) and copolymers (m>2). In the most trivial case molecules in a homopolymer are merely identified by the number l of monomeric units involved, whereas the composition of a copolymer macromolecule is defined by vector 1 with components equal to the numbers of mono-... 

In the most succinct sense, a hydrogel is simply a hydrophilic polymeric network cross-linked in some fashion to produce an elastic structure. Thus any technique which can be used to create a cross-linked polymer can be used to produce a hydrogel. Copolymerization/cross-linking free radical polymerizations are commonly used to produce hydrogels by reacting hydrophilic monomers with multifunctional cross-linkers. Water-soluble linear polymers of both natural and synthetic origin are cross-linked to form hydrogels in a number of ways ... 

---