Volume Expansion of Branched Polymers

The excluded volume effects of randomly branched polymers are investigated. To approach this problem we assume the Gaussian distribution of segments around the center of gravity. Once this approximation is introduced, we can make use of the same method as employed for linear molecules. By simulating a model-polymer system, it is found that the excluded volume effects of branched polymers are manifested pronouncedly under any conditions from the dilution limit to the melt, including the $\Theta$ state; every result satisfies the restraining condition: $\langle s^2\rangle^{1/2} \ge N^{1/d}$ in accord with our experiences. As a result the Gaussian approximation extracts the essential features of the excluded volume effects of branched molecules.