m-Fluorobenzoate (m-FBA), 2,3-difluorobenzoate (2,3-F2BA), m-methylbenzoate (m-MBA), and m-chlorobenzoate (m-ClBA) were introduced into the Cu(II) binuclear unit as bridging ligands between two Cu(II) sites, which were further connected by an axial pyrazine (pz) ligand to form one-dimensional coordination polymers of [Cu(II)2(m-FBA)4(pz)]∞ (1), [Cu(II)2(2,3-F2BA)4(pz)]∞ (2), [Cu(II)2(m-MBA)4(pz)]∞ (3), and [Cu(II)2(m-ClBA)4(pz)]∞ (4), respectively. The parallel arrangements of one-dimensional (1D) polymers result in 1D channels between the polymers that crystallization CH3CN molecules can occupy to form single crystals of 1·4CH3CN, 2·4CH3CN, 3·2CH3CN, and 4·2CH3CN. Both π-dimer and dipole-dipole interactions were simultaneously observed in the interchain interactions of m-FBA and/or 2,3-F2BA ligands in crystals 1 and 2. The sizes of the one-dimensional channels between the polymers are thus modulated according to the interchain interactions between the polar BA ligands. CH3CN molecules within the channels were easily replaced by H2O under ambient conditions. CO2 adsorption-desorption isotherms of crystals 1, 2, and 3 at 195 K indicated gate-adsorption with a hysteresis, whereas two-step gate-adsorption behavior was observed for CO2 in crystal 4. Temperature- and frequency-dependent dielectric responses were not observed in crystals 1-4 under vacuum conditions, whereas dielectric anomalies were observed around 290 K for crystals 1 and 2 with adsorbed CO2. CO2 desorption from the channels in crystals 1 and 2 activated the molecular motions of polar BA ligands and dielectric responses around 290 K, which were confirmed from CO2 adsorption-desorption isotherms around 290 K and differential scanning calorimetries under CO2 conditions.