Excluded Volume Effects of Branched Molecules

Abstract

The expansion factor, ${\alpha }^2=⟨s_N^2⟩/⟨s_N^2{⟩}_0$, of branched molecules in the melt state is estimated. The equilibrium expansion factor is determined as the point in which all the inhomogeneity terms of the osmotic potential, $\Delta G_{osmotic}$, go to zero. Numerical analysis shows that $\log \alpha =0.082\log N+\text{const.}$ for $10^3\le N\le 10^7$, giving $\alpha \cong \text{const.}{N}^{1/12}$ so that $⟨s_N^2{⟩}^{1/2}\propto N^{1/3}$ which coincides with the value for the critical packing density.

5 pages, 2 figures, 1 table

References in corpus (4)

• Radius of Gyration of Randomly Branched Molecules
• Minor Amendment of the Local Free Energy
• Coil Dimensions as a Function of Concentration
• Molecular Weight Dependence of Excluded Volume Effects

Cited by in corpus (4)

• Volume Expansion of Branched Polymers
• Diffusion and Chemical Potential in Polymer Solutions
• Segment Distribution around the Center of Gravity of Branched Polymers
• Branched Polymers with Excluded Volume Effects/ Relationship between Polymer Dimensions and Generation Number