Abstract: The present invention relates to sulfonated thermoplastic terpolymers which are terpolymers of p-methyl styrene, styrene and sodium styrene sulfonate wherein these sulfonated terpolymers function as viscosification agents when added to oil-based drilling muds which are the fluids used to maintain pressure, cool drill fits and lift cuttings from the holes in the drilling operation for oil an gas wells. The sulfonated thermoplastic terpolymer of the latex have about 5 to about 100 meq. of sulfonate groups per 100 grams of the sulfonated thermoplastic terpolymer, wherein the sulfonated groups are neutralized with a metallic cation or an amine or ammonium counterion. A polar cosolvent can optionally be added to the mixture of oil drilling mud and sulfonated thermoplastic polymer, wherein the polar cosolvent increases the solubility of the sulfonated thermoplastic terpolymer in the oil drilling and by decreasing the strong ionic interactions between the sulfonate groups of the sulfonated polymer.