화학공학소재연구정보센터
Macromolecules, Vol.30, No.7, 2125-2129, 1997
Shapes and Sizes of Gaussian Macromolecules .1. Stars and Combs in 2 Dimensions
The shapes and sizes of star- and comblike macromolecules in the framework of Gaussian models and confined to a plane have been analytically and numerically investigated in terms of shape’ factors, shape variance factors, asphericity parameter and factor, and shrinking factor. It is found that for regular stars and a special class of irregular stars with very long arms, both shape asymmetry and shrinking factor decrease as the number f of arm chains increases from 2 to 12 with perfect symmetry and zero shrinking factor at f=infinity. For a large farm irregular star whose arms have two or three different lengths, the well-known "maximum shape asymmetry" effect, i.e., having greater values of the larger shape factor and asphericity parameter or factor than the corresponding ones for linear chains, occurs when the stars are chains end-linked with two or more shorter chains. For large f-arm regular combs with both equal and unequal length arms and spacers, a "minimum shape asymmetry" effect appears for certain values of f, while the shrinking factor decreases with increasing f or, for fixed f, increases with increasing length of the spacer relative to the arm. The large shape asymmetry of the end-linked chains studied here may have important implications for improving rheological and other shape-dependent properties of the existing linear macromolecules confined to surfaces.