## 5 Conclusions  
The absorption and recovery of dilute CO\({}_{2}\) were demonstrated using the slurry with the cross-linked thermo-responsive polymer hydrogels immobilizing tertiary amine groups. The influence of hydrophobicity of the polymer network and the amine content on the LCST, desorption behaviour of CO\({}_{2}\) and cycle capacity for CO\({}_{2}\) were investigated. The hydrophobisation of the polymer network of the hydrogel enables a large decrease in the temperature of CO\({}_{2}\) desorption without losing the cycle capacity of the gels, which is induced by the larger decrease of pK\({}_{\text{a}}\) of amine in the hydrophobic gels with cooperation of Donnan effect on the pH in the gels. This brings about a reduction in the energy consumed for the desorption of the amine. The pH in the gel is also a key condition for the effective use of the adsorption cycle capacity of the gel when Donnan equilibrium is considered. Since the pH in the gel depends on the number of amine groups and the pH in the slurry liquid phase, the balance of these factors affects the adsorption and desorption of CO\({}_{2}\) in the gel slurry system; consequently, systematic control of these factors is important for effective CO\({}_{2}\) separation and recovery.  
The equilibrium adsorption model of CO\({}_{2}\), which explains the temperature dependence of CO\({}_{2}\) adsorption/desorption and pH change in the gel slurry system, was constructed considering the Donnan equilibrium and the surface charge contribution of the gels. The model is available to estimate the  
Figure 9: pH dependence of the dissociation for the reaction of bicarbonate dissociation, carbonate dissociation, and dissociation of amine (DMAPAA).  
influence of pKa of the immobilized amine groups and solution pH on the CO\({}_{2}\) recovery performance of the gel slurry system as a function of the temperature of the slurry.  
The recovery of low concentrations of CO\({}_{2}\) by the gel system and applicability to DAC were examined by the model analysis using the constructed equilibrium adsorption model along with the adsorption data obtained in this study. It is necessary to control the water content of the slurry in order to apply the gel system to DAC. To develop the energy-saving CO\({}_{2}\) recovery process, a reduction of the water content in the slurry and in the gels is necessary. A further decrease of the specific energy requirement will be possible through (1) evaluation of the lower limit of water content in the slurry, (2) the design of the gels that function with small water contents, (3) heat utilization using a heat exchanger and heat pump, and (4) optimization of the process operation.  
The following are available online at [[http://www.mdpi.com/2073-4360/11/6/1024/s1](http://www.mdpi.com/2073-4360/11/6/1024/s1)]([http://www.mdpi.com/2073-4360/11/6/1024/s1](http://www.mdpi.com/2073-4360/11/6/1024/s1)), Table S1: Performance comparison.  
Conceptualization, Y.S.; Data curation, Y.N. and Y.S.; Formal analysis, Y.N. and Y.S.; Funding acquisition, Y.S.; Investigation, Y.N. and Y.S.; Methodology, Y.N., Y.S. and T.G.; Project administration, Y.S.; Supervision, E.F.; Validation, T.G. and E.F.; Writing--original draft, Y.S.; Writing--review & editing, Y.S.  
This research received no external funding  
NIPA and DMAPAA were supplied from KJ Chemicals Co. Japan. We would like to thank [PERSON] and [PERSON] for the FTIR data acquisition. We also would like to thank Editage (www.editage.jp) for English language editing.  
The authors declare no conflict of interest.