The hyperbranched polymers can be made by self-condensing vinyl polymerization without gelation transition. The average molecular weights, as well as the average sizes, can reach infinite values as the reaction is quantitatively completed, and the scaling forms of the molecular parameters should exist. In the paper, based on a recursion formula, the scaling form of the number fraction distribution and the number of the n-mers are given analytically as the conversion of double bonds is near 1. The mean square radius of gyration for very large hyperbranched polymers is calculated explicitly to give a scaling exponent. Finally, a scaling relation associated with the fractal dimension and the polydispersity exponent is given clearly.

In order to investigate the effect of argon introduction on the structural and physical properties of Ba 0.6 Sr 0.4 TiO 3 (BST) films, epitaxial BST films have been grown by pulsed laser deposition (PLD) on (001) oriented Nb-SrTiO 3 (STON) substrates in the ambient gas of pure oxygen and the mixture of argon and oxygen, respectively. The atomic force microscopy (AFM) reveals that the sample deposited in the mixture of argon and oxygen has a bigger grain size than that deposited in pure oxygen. The dielectric properties of two BST films have been investigated using the Pt/BST/STON parallel plate capacitors. The tunability and the figure of merit (FOM) of the BST film deposited in the mixture gas are about 41% and 7.07 at a DC bias voltage of 8 V at room temperature, which are better than 32% and 4.51, for BST film deposited in pure oxygen. On account of the introduction of argon, the leakage current density of the BST film deposited in the mixture gas has fallen by almost five times, and the leakage current mechanism is both in accordance with ohmic conductive mechanism.