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We performed a series of simulations for a linear polymer chain in a solventusing dissipative particle dynamics to check the scaling relations for theend-to-end distance, radius of gyration and hydrodynamic radius in threedimensions. The polymer chains of up to 80 beads in explicit solvent of variousquality are studied. To extract the scaling exponent \nu, the data are analyzedusing linear fits, correction-to-scaling forms and analytical fits to thehistograms of radius of gyration distribution. For certain combinations of thepolymer characteristics and solvent quality, the correction-to-scaling termsare found to be essential while for the others these are negligibly small. Ineach particular case the final value for the exponent \nu was chosen accordingto the best least-squares fit. The values of \nu obtained in this way are foundwithin the interval \nu=0.55-0.61 but are concentrated mostly around 0.59,which is very close to the best known theoretical result \nu=0.588. Theexistence of this interval is attributed both to the peculiarities of themethod and to the moderate chain lengths being simulated. Within thisshortcoming, the polymer chain in this kind of modeling is found to satisfy thescaling relations for all three radii being considered

How does the scaling for the polymer chain in the dissipative particle dynamics hold?