Random-branched chain

Within the temperature range from 10 to 40°C, both PAMAM dendrimers in EDA [5] and PPI dendrimers in water [22] showed a linear relationship between In r and /T, in good agreement with the kinetic rate theory of flow [46]. The apparent activation energies of flow (En) were constant and independent of temperature, and it was shown for PAMAM/EDA systems that the dependence of En on solution concentration was linear for all generations examined [5]. This was considerably different from the typical relationships for the solutions of linear and/or randomly branched chain polymers, where a break in the slope of... 

This leads to the conclusion that polydisperse Unear chains cannot be distinguished from randomly branched chains using only the shape of their scattering curves. Indeed, when the link probabilities are expressed in terms of the mean-square radius of gyration, the particle-scattering factor is given in both cases by... 

Similar deviations of the experimentally determined p-value from theory have been observed with branched epoxides206,207. The value of about 1.48 is close to that of monodisperse linear chains in a 6-solvent, but considerably lower than 1.73 predicted for randomly branched chains under 6-condition. Since the measurements were made in a... 

Thus, analysis of hydrodynamic properties of native lignins reveals that their behaviour in dilute solutions is different from that of linear polymers, both flexible- and rigid-chain, in any of the known conformations. Apparently, the macromolecules of soluble lignins are randomly branched chains. Branchings in a chain are known to reduce the hydrodynamic dimensions, (i.e., reduce [q]), and increase the diffusion mobility compared to the linear analog, theoretical value of b, in a 0-solvent is 0.25. The branching of the polymer also reduces the hydrodynamic invariant by 15-20% compared to the standard value 3.2 x 10 erg/(K mol ) and results in anomalous values of the Huggins parameter. 

Fig. 2.8 Branched macromolecules (a) a comb, (b) a star, (c) a randomly branched chain d) a polymer network.

Polymers are always polydisperse with a distribution in molar mass and often contain chain branches, either introduced specifically during synthesis or as a consequence of synthetic defects, and both these effects will influence the observed morphology. As we shall see later, copolymers are a special case however, the introduction of low levels of comonomers can lead to behaviour which is rather like that of random branched chains. Different molecular species crystallize in different stages indicating the thermodynamic control on the overall process, i.e. they are incorporated into the crystal structure at different temperatures and times. The intermediate and high molar mass component crystallizes early in the stacks of thick dominant crystals. Small pockets of rejected molten low molar mass material remain after crystallization... 

The primary particles exist in an aggregated form where they are fused together in a randomly branched, chain-like form described as structure . The structure is formed during the production process and is not broken down by subsequent processing operations. A secondary structure also exists, which is formed by loose attraction of black particles. This structure is easily destroyed during processing and is not described by the term structure . Structure is normally measured using dibutyl phthalate (DBP) absorption, which fills the voids between the particles. This method is also used in a modified form where the black is initially crushed to breakdown any secondary structure prior to DBP absorption. The crushed DBP is claimed to relate more closely to the way in which carbon black is found in a rubber mix [47]. 

As follows from eqn [88], by grouping the monomer units into the blobs, each containing n monomer units, the branched polymer can be envisioned as a randomly branched chain of N/n trifiinctional blobs of size or under... 

Fig. 1.3 Comparison of topological structures of a randomly branched chain and a hyperbranched chain prepared by using different types of macromonomers...

Syn. Glucose Polymers G. Polydextrosen F polydextroses These artificial low-polymeric carbohydrates are produced by a polycondensation process of - dextrose in the presence of small amounts of - sorbitol and - citric acid under vacuum at high temperatures. Randomly branched chains of D-glucose polymers result with >90% a-1,6 bonds (some sorbitol- and citric acid monoester groups) and minor amounts of D-glucose (<4%), flee sorbitol (<2%), citric acid, - le-voglucosan, - hydroxymethylfurfiiral. m.w. 162-18 000 with an average distribution 88.7%, 162-5000 5%, 5000-10000 1.2%,... 

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