The detection of inert gases is difficult due to their inactive nature what makes preparation of the applicable gas sensor a challenging task. This work reports comprehensive first principles investigations to design inert gas sensors. Graphene (Gr) sheets decorated with palladium clusters Pd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> (n = 2-6) were optimized after which adsorption of inert gases He, Ne, Ar, Kr, Xe and Rn was carried out using density functional theory (DFT) based formalism. The reactivity of the sensors comprising of Pd cluster-decorated-defected-graphene is significantly higher than that of the sensor with bare and defect free graphene sheet. The adsorption caused redistribution of the electronic structure which provides basis for sensing of the adsorbate. The gas sensor Pd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -Gr exhibited good sensitivity towards neon and xenon while Pd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> -Gr appeared more effective in the detection of krypton gas. Helium is appropriately detected by Pd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> -Gr sensor and Pd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> -Gr sensor is found capable of sensing radon and argon gases. Pd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> -Gr sensor is not a favorable sensor for sensing of the inert gases. The findings of this work are beneficial for fabrication of inert gas sensors for small and industrial scale applications.
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