Power law polydispersity and fractal structure of hyperbranched polymers

Temperature-dependent structure and dynamics of highly-branched poly(N-isopropylacrylamide) in aqueous solution

Small-angle neutron scattering (SANS) and neutron spin-echo (NSE) have been used to investigate the temperature-dependent solution behaviour of highly-branched poly(N-isopropylacrylamide) (HB-PNIPAM). SANS experiments have shown that water is a good solvent for both HB-PNIPAM and a linear PNIPAM control at low temperatures where the small angle scattering is described by a single correlation length model. Increasing the temperature leads to a gradual collapse of HB-PNIPAM until above the lower critical solution temperature (LCST), at which point aggregation occurs, forming disperse spherical particles of up to 60 nm in diameter, independent of the degree of branching. However, SANS from linear PNIPAM above the LCST is described by a model that combines particulate structure and a contribution from solvated chains. NSE was used to study the internal and translational solution dynamics of HB-PNIPAM chains below the LCST. Internal HB-PNIPAM dynamics is described well by the Rouse model for non-entangled chains.

Two universality classes for random hyperbranched polymers

We grow AB2 random hyperbranched polymer structures in different ways and using different simulation methods. In particular we use a method of ad hoc construction of the connectivity matrix and the bond fluctuation model on a 3D lattice. We show that hyperbranched polymers split into two universality classes depending on the growth process. For a "slow growth" (SG) process where monomers are added sequentially to an existing molecule which strictly avoids cluster-cluster aggregation the resulting structures share all characteristic features with regular dendrimers. For a "quick growth" (QG) process which allows for cluster-cluster aggregation we obtain structures which can be identified as random fractals. Without excluded volume interactions the SG model displays a logarithmic growth of the radius of gyration with respect to the degree of polymerization while the QG model displays a power law behavior with an exponent of 1/4. By analyzing the spectral properties of the connectivity matrix we confirm the behavior of dendritic structures for the SG model and the corresponding fractal properties in the QG case. A mean field model is developed which explains the extension of the hyperbranched polymers in an athermal solvent for both cases. While the radius of gyration of the QG model shows a power-law behavior with the exponent value close to 4/5, the corresponding result for the SG model is a mixed logarithmic-power-law behavior. These different behaviors are confirmed by simulations using the bond fluctuation model. Our studies indicate that random sequential growth according to our SG model can be an alternative to the synthesis of perfect dendrimers.

Models for randomly hyperbranched polymers: Theory and simulation

We derive theoretical models for the structures of randomly hyperbranched polymers in solution, and test them against computer simulations. The models are based on the same basic approach: Building a structure by the random assembly of "simple units," which may be monomers, linear chains, or larger branched species. Comparisons to simulation reported here show that the conformations of hyperbranched species, i.e., their radii of gyration and full density profiles, are accurately described by this approach. These stringent tests complement previous tests against experiment. We include the effects of solvent quality at the mean-field level. Our model works best for hyperbranched structures, but also reproduces very well the simulated density profiles of dendrimers. The models reported here provide a simple, but realistic, picture of the physical influences that affect the conformations of hyperbranched species.