SHAPES AND SIZES OF GAUSSIAN MACROMOLECULES .1. STARS AND COMBS IN 2 DIMENSIONS

The shapes and sizes of star- and comblike macromolecules in the frame work of Gaussian models and confined to a plane have been analytically and numerically investigated in terms of shape' factors, shape varian ce factors, asphericity parameter and factor, and shrinking factor. It is found that for regular stars and a special class of irregular star s with very long arms, both shape asymmetry and shrinking factor decre ase 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 irr egular star whose arms have two or three different lengths, the well-k nown ''maximum shape asymmetry'' effect, i.e., having greater values o f the larger shape factor and asphericity parameter or factor than the corresponding ones for linear chains, occurs when the stars are chain s 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 s hrinking factor decreases with increasing f or, for fixed f, increases with increasing length of the spacer relative to the arm. The large s hape asymmetry of the end-linked chains studied here may have importan t implications for improving rheological and other shape-dependent pro perties of the existing linear macromolecules confined to surfaces.