The release of CO₂ gas into the atmosphere is one of the most prolific causes of global climate change. To solve this problem, cost-effective technologies are being sought. Polymer membranes are innovative materials that can be widely used in the process of capturing and separating CO₂ gas. In this work, an amine impregnated and amidated solid sorbent (AISS) containing a copolymer (PMMA-co-AA), which consists of acrylic acid (AA) and methyl methacrylate (MMA), and PEPA (polyethylene polyamine), was synthesized. For the first time, sorbents based on homopolymers and copolymers of acrylic acid and methyl methacrylate were compared for their ability to capture CO₂ gas. Other thanthe synthesis of low swelling AISS, a calculation of its energy consumption, and a comparison of its cyclic capacity with 30% water solutions of monoethanolamine and methyldiethanolamine (MEA and MDEA) were performed. The solid sorbent PMMA-co-AAS showed a higher cyclic capacity than others, corresponding to the order PMMA-co-AAS (23 mg/g) > PAAS (16 mg/g) > MDEA (10 mg/g) > MEA (6 mg/g). The average absorption rate for these sorbents was in the sequence of MEA > PMMA-co-AAS > PAAS > MDEA at 40 °C, and the desorption rates were PMMA-co-AAS > PAAS > MDEA > MEA for these sorbents at 70 °C, correspondingly. When the amount of acrylic acid in the copolymer was varied from 0 to 100%, its water absorption capacity varied from 0.2 to 1359.63%, respectively. Among them, the swelling ability of the chosen sorbent prepared from the 10% AA-containing copolymer and PEPA was 0.64%.