Linear chain macromolecules

The key parameter during the synthesis of polymer networks is the functionality / of the monomer, which is defined as the number of covalent bonds that a monomer molecule or monomeric unit in a macromolecule or oligomer molecule can form with other reactants [7], Note that there are no monofunctional monomers, as the minimum required functionality for the backbone formation is two. When/ = 2, only a linear chain macromolecule or a macrocycle can be formed. 

The concentration < omb ( / )A )comb corresponds to the overlap of long comhlike polymers and is analogous to the overlap concentration in solutions of linear-chain macromolecules. At c > c omb/ the stmcture of the solution on the large scale D coincides with that of the semidilute solution of wotmlike chains. The overall dimensions of the comhlike polymer scale as (R (c)), omb that is, decrease as a function of the... 

LAU Lau, A.C.W. and Wu, C., Thermally sensitive and biocompatible poly(A-vinylcaprolactam) synthesis and characterization of high molar mass linear chains. Macromolecules, 32, 581, 1999. 

Seo, M. et al. (2008) Polymeric nanoparticles via noncovalent cross-linking of linear chains. Macromolecules, 41,6413-6418. 

Some information concerning the intramolecular relaxation of the hyperbranched polymers can be obtained from an analysis of the viscoelastic characteristics within the range between the segmental and the terminal relaxation times. In contrast to the behavior of melts with linear chains, in the case of hyperbranched polymers, the range between the distinguished local and terminal relaxations can be characterized by the values of G and G" changing nearly in parallel and by the viscosity variation having a frequency with a considerably different exponent 0. This can be considered as an indication of the extremely broad spectrum of internal relaxations in these macromolecules. To illustrate this effect, the frequency dependences of the complex viscosities for both linear... 

Casassa, E. R and Tagami, Y. An equilibrium theory for exclusion chromatography of branched and linear polymer chains, Macromolecules, 2, 14, 1969. 

Macromolecules differ from small molecules in a number of critical properties. First, the linear chain structure confers elasticity, toughness, and strength on the solid state system. This is a consequence of the reorientational freedom of the skeletal bonds and of their ability to absorb impact or undergo elastic deformation by means of conformational changes rather than bond cleavage. 

Star shaped macromolecules are polymers, where the one end of f > 2 (f functionality of the star) linear chains is chemically attached by covalent bonds to a small central linker unit, are the simplest form of branched polymers. Modern anionic polymerization techniques allow us to synthesize star systems with a large number of nearly monodisperse arms [133, 134],... 

Tbe discussion of the semi-chlute properties remains confined mainly to the osmotic modulus which in good solvents describes the repulsive interaction among the macromolecules as a function of concentration. After scaling the concentration by the overlap concentration c = A2M.Yf) and normalizing the osmotic modulus by the molar mass, universal masteS" curves are obtained. These master curves differ characteristically for the various macromolecular architectures. The branched materials form curves which lie, as expected, in the range between hard spheres and flexible linear chains. 

The second virial coefficient is not a universal quantity but depends on the primary chemical structure and the resulting topology of their architecture. It also depends on the conformation of the macromolecules in solution. However, once these individual (i.e., non-universal) characteristics are known, the data can be used as scaling parameters for the description of semidilute solutions. Such scaling has been very successful in the past with flexible linear chains [4, 18]. It also leads for branched macromolecules to a number of universality classes which are related to the various topological classes [9-11,19]. These conclusions will be outlined in the section on semidilute solutions. 

As already outlined, star branched macromolecules resemble their linear chain analogues. The behavior becomes evident when for a given number of arms f the... 

The Schulz-Zimm distribution would be found for/end-to-end coupled linear chains which obey the most probable distribution, as well as for/of such chains which are coupled onto a star center. This behavior demonstrates once more the quasi-linear behavior of star branched macromolecules. In fact, to be sure of branching, other structural quantities have to be measured in addition to the molar mass distribution. 

Fig. 22. KMHS relationships for the fractions of end-linked 3-arm star-branched polystyrene molecules and of linear polystyrene fractions. The data refer to three samples of different in the pregel state and one from the sol fraction of a gel. The curves for the branched macromolecules coincide within experimental error in the high molar mass region. The deviations at lowM result from a different amount of non-reacted end-functionalized stars. The exponents of the end-linked and linear PS chains are a =0.42 0.02 while that of linear chains is 0.70 0.01 [95,120,123,124]. Reprinted with permission from [95]. Copyright [1997] American Society...

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