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We consider the simplest representative of the class of multiply branchedpolymer macromolecules, known as a pom-pom structure. The molecule consists ofa backbone linear chain terminated by two branching points with functionalities(numbers of side chains) of $f_1$ and $f_2$, respectively. In a symmetricalcase, considered in the present study, one has $f_1=f_2=f$ with the totalnumber of chains $F=2f+1$. Whereas rheological behaviour of melts of pom-pommolecules are intensively studied so far, we turn our attention towardsconformational properties of such polymers in a regime of dilute solution. Theuniversality concept, originated in the critical phenomena and in scalingproperties of polymers, is used in this study. To be able to compare theoutcome of the direct polymer renormalization approach with that obtained viadissipative particle dynamics simulations, we concentrated on the universalratios of the shape characteristics. In this way the differences in the energyand length scales are eliminated and the universal ratios depend only on spacedimension, solvent quality and a type of molecular branching. Such universalratios were evaluated both for a whole molecule and for its individualbranches. For some shape properties, theory and simulations are in excellentagreement, for other we found the interval of $F$ where both agree reasonablywell. Combination of theoretical and simulation approaches provide thoroughquantitative description of the peculiarities of swelling effects and spatialextension of pom-pom molecules and are compared with the known results forsimpler molecular topologies.

On the swelling properties of pom-pom polymers in dilute solutions. Part 1: symmetric case