Methods of capturing carbon dioxide in a wellbore (11) can include installing a sealing element (21) in the wellbore (11). The sealing element (21) swells in the presence of carbon dioxide and can be used for capturing the carbon. The sealing element (21) can include a carbon-swelling material, such as a carbon-swelling polymers, metal-based materials, or combinations of elastomeric polymers and metal-based materials. The sealing element (21) can also include combinations of different carbon-swelling materials, fillers or other compounds, and materials that are not carbon swell able. The sealing element (21) can create a seal, form an anchor, or create a seal and form an anchor in the wellbore (11) after swelling.