SHAPES AND SIZES OF GAUSSIAN MACROMOLECULES .2. STARS AND COMBS IN 3 DIMENSIONS

The shapes and sizes of star- and comblike macromolecules in the frame work of Gaussian models have been analytically and numerically investi gated in terms of shape factors (approximately), asphericity and prola teness parameters and factors, and shrinking factor. It is found that the general size and shape features of these macromolecules persist fr om two dimensions to three. For regular stars and a special class of i rregular stars with f infinitely long arms, both shape asymmetry and s hrinking factor decrease as the number f of arms increases from 2 to 1 2 with perfect symmetry and zero shrinking factor at f = infinity. For a large irregular star whose arms have two or three different lengths , the well-known ''maximum shape asymmetry'' effect, i.e., having grea ter values of the largest shape factor and asphericity or prolateness parameter or factor than the corresponding ones for linear chains, occ urs when the stars are chains end-linked with two or more shorter chai ns. For large regular combs with both equal and unequal length arms an d spacers, a ''minimum shape asymmetry'' effect appears for certain va lues off. The large shape asymmetry of the end-linked chains in three dimensions may have important implications for improving rheological a nd other shape-dependent properties of the existing linear macromolecu les, and it is, therefore, highly desired that this finding can also b e verified for excluded-volume or rotational isomeric state models of end-linked chains and, through experiments, for real end-linked linear macomolecules.