When styrene-butadiene rubber"SBR" is made by anionic copolymerization of styrene & butadiene, the initiator used could be a lithium alkyl in small paraffins "the old name of alkanes" or cycloaliphatic solvent. I saw n-butyllithium supplied in n-hexane.
Therefore, I suggest trying to dissolve SBR in n-hexane or cyclopentane but take care to use a dry solvent for your research studies on viscosity.
Thank you Nizar Matar sir for your suggestion. I have tried n-hexane two days before but SBR is not soluble in it. I have also tried heating but it does not work.
To confirm that a copolymer is insoluble in a given liquid solvent, there is a need to place the solid copolymeric powder/liquid in a a stoppered test tube for 24 hours. If the amount of the solid stays unchanged, then it is insoluble.
In the strict sense of the word styrene butadiene RUBBER will not be dissolved in any solvent, it will only swell in it. Only UNCURED SBR will dissolve in a good solvent, such as benzene or toluene, see e.g. http://digital.bl.fcen.uba.ar/download/paper/paper_00143057_v43_n6_p2682_Marzocca.pdf
SBR is a commercially produced random St/But copolymer, synthesized by radical polymerization, mostly in emulsion at elevated temperature. It can be assumed, that the product is at least to some extent cured, so that it is hardly soluble. Soluble copolymer should be prepared by anionic copolymerization at low temperatue. Good Luck!