| Abstract
| - The shapes and sizes of star- and comblike macromolecules in theframework of Gaussianmodels have been analytically and numerically investigated in terms ofshape factors (approximately),asphericity and prolateness parameters and factors, and shrinkingfactor. It is found that the generalsize and shape features of these macromolecules persist from twodimensions to three. For regular starsand a special class of irregular stars with f infinitelylong arms, both shape asymmetry and shrinkingfactor decrease as the number f of arms increases from 2 to12 with perfect symmetry and zero shrinkingfactor at f = ∞. For a large irregular star whosearms have two or three different lengths, the well-known “maximum shape asymmetry” effect, i.e., having greater valuesof the largest shape factor andasphericity or prolateness parameter or factor than the correspondingones for linear chains, occurs whenthe stars are chains end-linked with two or more shorter chains.For large regular combs with bothequal and unequal length arms and spacers, a “minimum shapeasymmetry” effect appears for certainvalues of f. The large shape asymmetry of theend-linked chains in three dimensions may have importantimplications for improving rheological and other shape-dependentproperties of the existing linearmacromolecules, and it is, therefore, highly desired that this findingcan also be verified for excluded-volume or rotational isomeric state models of end-linked chains and,through experiments, for real end-linked linear macomolecules.
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