The Radius of Gyration of the Products of Hyperbranched Polymerization

Abstract

The average mean‐square radii of gyration for the products of the linear polymerization, the star‐shaped polymerization, and the hyperbranched polymerization of AB2‐type monomer in the absence or presence of a multifunctional core initiator are investigated using the Dobson‐Gordon's method. The dependence relationships between the average radii of gyration and the average degree of polymerization calculated using the Dobson‐Gordon's method for the linear polymerization products are in good agreement with those obtained from the matrix algebra method of the rotational isomeric state model. The radii of gyration of the star‐shaped and hyperbranched polymers are much smaller than those of the linear polymers if their average degrees of polymerization are equal. The conversion of groups, the core/monomer feed ratio, and the core functionality affect the average radius of gyration of the products. However, compared with the other factors, the degree of polymerization is the most influential factor on the average radii of gyration for the hyperbranched polymer system.

Step‐Growth Polymerizing Systems of General Type “AfiBgi”: Calculating the Radius of Gyration and theg‐Curve Using Generating Functions and Recurrences

“…More recently, Zhou et al discussed highly branched systems like “B3 + A1B2 + A1B1”. A recipe for such a system is given in Table .…”

“…For a slightly simpler system, namely for system “A1B1 + B3” (“stars”), we compared the results of our algorithm to those of Zhou . He derived explicit formulae for the averages {〈 R 2 〉 n , 〈 R 2 〉 w , 〈 R 2 〉 z }.…”

“…More recently, Zhou et al [24,25] www.advancedsciencenews.com for such a system is given in Table 3. A 2D picture of a typical molecule produced by this recipe is shown in Figure 7.…”

Modeling and Simulation of Complex Polymerization Reactions

“…Analytic solution, if obtainable, is the most powerful and accurate method. Zhou [9] presented the analytic equations for the radius of gyration of hyperbranched polymers, synthesized via polymerization of AB 2 -type monomer in the absence or the presence of multifunctional core initiator.…”

Can the Branching Exponent Reliably Relate the Branching Indexes?

“…The mean‐square radius of gyration, which is by definition the sum of squared distances from the center of the mass, is advantageously calculated by …”