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Previously authors have reported facts that nitrogen (N2) and oxygen solubilities in styrene is the same as those in benzene and divinylbenzene at 303 K. Though the three compounds have an atomic composition, (CH)n (n=6, 8 and 10), the gas solubilities are thought to depend on the number of aromatic carbons in the solution. Then, authors named it ‘a key group in solubility’. In this research, the key group was investigated for N2 solubility in methyl methacrylate (MMA) and its dimer, ethylene glycol dimethacrylate (EGDMA). Therefore, the calculations were carried out by Peng-Robinson (PR) equation of state based on group contribution methods. The experimental data employed were those of Lai et al., where N2 solubility are reported in MMA at 303 K. The N2 solubility in EGDMA was assumed to be double of that in MMA at 303 K, because EGDMA has two MMA units in the molecule. Two types of group contribution methods were proposed to calculate N2 solubility in EGDMA. One was for the critical temperature and pressure proposed by Joback and Reid. Using these properties, the attractive and excluded volume parameters in PR equation were evaluated for EGDMA. Other was similar to a method proposed by Orbey and Sandler. The excluded volume parameter in PR equation can be evaluated from those of MMA by multiplying the number of repeating units, and the attractive by multiplying the squared number. Instead of the method, the powers were proposed to be 3/4 and 3/2 for the excluded volume and attractive perimeters, respectively. The powers were come from a scaling theory by de Gennes. The binary parameter for N2 – EGDMA was also set to k12 = 0.224, which was the same as that for N2 –MMA. The calculated N2 solubility in EGDMA was far smaller than the hypothetical N2 solubility in EGDMA at 303 K. Otherwise, to reproduce the hypothetical N2 solubility, a quite different value, k12 = -0.044, was necessary for the method by Joback and Reid. The results suggested that a key group for gas solubility will not be accepted in MMA.

Half century has passed since the first version of Analytical Solution of Groups (ASOG) model was proposed. Now the ASOG model is well known as a group contribution method as well as UNIFAC. Although the ASOG model was designed for prediction of vapor-liquid equilibrium around the atmospheric pressure, the applications are extended to not only the phase equilibria in the wide temperature and pressure ranges but also the transport properties. The function forms in the ASOG model, basically composed of Flory-Huggins equation and Wilson equation, can be applied for the prediction of the phase equilibria (vapor-liquid, liquid-liquid, solid-liquid and vapor-solid) and the transport properties (kinematic viscosity, thermal conductivity) of the mixtures with some modifications.

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Some mixing rules were proposed with simple functional form to predict binary gas mixture solubility in pure solvent/pure gas solubility in binary solvent mixture. The experimental data employed were those of Tsuji et al. (2019) for equimolar binary gas mixture (nitrogen (N2) + oxygen (O2)) solubility in styrene at 303 K, and of Tsuji et al. (2005) for hydrogen (H2) solubility in equimolar mixture of benzene + cyclohexane at 303 K. These solubilities have a linear pressure dependence like Henry’s law at least up to 4.827 MPa. To predict gas solubilities, the mixing rules were proposed for Henry constant of gas mixtures in pure solvent and that of pure gas in solvent mixture just by using Henry constant of pure gas in pure solvent without any binary parameter. The function form was similar to that of van der Waals one fluid model, Q = ∑i ∑j zi zj Q ij for the mole ratio of constituent of gas or solvent mixture, zi. The Q = H and Q ij = (H i + H j )/2 show the best reproducibility for (N2 + O2) solubility in styrene with average absolute relative deviation (AARD) 0.667 %. Otherwise, the Q = 1/H and Q ij = (1/H i + 1/H j )/2 show the best reproducibility for H2 solubility in benzene + cyclohexane with AARD 5.605 %. The results were well described by a universality of physical properties and Lorentz-Berthelot theorem.