In the presence of acidic or basic catalysts, PO undergoes ring-opening and condenses with PG to form DPG. PO may also react with the produced DPG to form tripropylene glycol (TPG) and other products with higher degrees of polymerization. The reaction process is shown in Figure 1.

PG may form DPG via intermolecular dehydration condensation. PG may also react with the produced DPG to form TPG and other polymers. The reaction process is shown in Figure 2.

In short, the following reactions may be involved:

The thermodynamic parameters including $ {{H}}^{} $ (Table S2), $ {G} $ (Table S3) and $ {{S}}^{\text{}} $ (Table S4) of the reactants and products involved in reactions (1)−(4) are calculated at different states.

Then, the results are used to obtain the $ {\Delta }_{\rm{r}}{H}^{} $, $ {\Delta }_{\rm{r}}{G}^{} $ and $ K $ for the four reactions.

The effect of temperature on $ {\Delta }_{\rm{r}}{H}^{} $ of the reactions is investigated, and the results are shown in Figure 4. Under standard atmospheric pressure and the temperature ranging from 373.15 to 433.15 K, the $ {\Delta }_{\rm{r}}{H}^{} $ of reactions (1) and (2) are both negative revealing that the reactions are exothermic. While those of reactions (3) and (4) are both positive which mean that the two reactions are endothermic.

The effect of temperature on $ {\Delta }_{\rm{r}}G $ of the reactions is also studied (Figure 5). Under standard atmospheric pressure and the temperature ranging from 373.15 to 433.15 K, $ {\Delta }_{\rm{r}}G $ of reactions (1) and (2) are both negative, revealing that the two reactions are spontaneous. Moreover, as the temperature increases, the $ {\Delta }_{\rm{r}}G $ becomes larger, i.e., high temperature is unfavorable for the reaction. However, the reactions (3) and (4) cannot occur spontaneously since the $ {\Delta }_{\rm{r}}G $ of the reactions are positive.

The effect of pressure on the $ {\Delta }_{\rm{r}}G $ of the reactions is illustrated in Figure 6. For the pressure ranging from 101.325 to 506.625 kPa at 298.15, 373.15, 383.15, 393.15, 403.15, 413.15, 423.15, 433.15 K, the $ {\Delta }_{\rm{r}}G $ of reactions (1) and (2) are both negative, suggesting that these two reactions can be conducted spontaneously. As the pressure increases, the $ {\Delta }_{\rm{r}}G $ decreases, i.e. high pressure is conducive to the reaction. However, the $ {\Delta }_{\rm{r}}G $ of reactions (3) and (4) are both positive, illustrating that these two reactions cannot occur spontaneously.

In summary, under the temperature ranging from 373.15 to 433.15 K and the pressure ranging from 101.325 to 506.625 kPa, reactions (1) and (2) are both spontaneous. While reactions (3) and (4) are both non-spontaneous. In the reaction of preparing DPG from PO and PG, only the following two reactions are included (1), (2).

The effect of temperature on $ K $ of the reaction is then investigated. As illustrated in Figure 7, under standard atmospheric pressure and the temperature ranging from 373.15 to 433.15 K, the $ \mathrm{ln}K $ of reactions (1) and (2) are both positive. As the temperature increases, lnK decreases, which indicates that high temperatures reduce the extent of the reaction. However, as the temperature increases, the extent of reaction (2) is reduced more than that of reaction (1), revealing that high temperature is conducive to improving the selectivity of DPG. As is well known, increasing the temperature will accelerate the reaction rate. However, when the temperature reaches 403.15 to 413.15 K, $ \mathrm{ln}K $ of the preparation of DPG3 will be less than 5, which tends to be reversible. The result shows that the optimal temperature for the reaction is between 403.15 to 413.15 K.

The effect of pressure on the $ K $ of the reaction is illustrated in Figure 8. When the pressure is between 101.325 to 506.625 kPa and at 298.15, 373.15, 383.15, 393.15, 403.15, 413.15, 423.15, 433.15 K, the $ \mathrm{ln}K $ of reactions (1) and (2) are both positive which increase with the increasing of the pressure. It indicates that high pressure is favorable for the reaction. However, as the pressure increases, the improving extent of reaction (2) is greater than that of reaction (1), suggesting that high pressure is not conducive to promote the selectivity of DPG. So, the suitable reaction pressure is 101.325 kPa (Figure 9).

Isodesmic reaction 5 is designed to derive the calculation formulas of $ {\Delta }_{\rm{f}}{H}^{\text{θ}} $and $ {\Delta }_{\rm{f}}{G}^{\text{θ}} $(8), (9). Then, the $ {\Delta }_{\rm{f}}{H}^{\text{θ}} $and $ {\Delta }_{\rm{f}}{G}^{\text{θ}} $of DPG1, DPG2 and DPG3 are obtained respectively, which is compared with the calculation results of the group contribution method^[31] (The calculation data of the group contribution method is in Table S5) with error less than 7%. (Table 1). According to thermodynamic principle, isomer with lower $ {\Delta }_{\rm{f}}{G}^{\text{θ}} $ will be more stable^[17]. Naturally, it can be found that the thermodynamic stability of the isomers under standard conditions is in the order of: DPG1 > DPG2 > DPG3.

The accuracy of the computational results is thus verified by experiment (Figure 10). The main product of the reaction is DPG, and the by-product is mainly TPG. It can be observed that at 413.15 K, the selectivity of DPG which is the ratio of the amount of substance of DPG produced to the amount of substance of converted PO (S_DPG = $ \dfrac{{\mathop n\nolimits_{{\mathrm{DPGpro}}} }}{{\mathop n\nolimits_{{\mathrm{POcon}}} }} \times 100\% $) is the highest (Figure 10(a)), demonstrating that the computational results correspond with the experimental results. As shown in (Figure 10(b)), within the first 8 h, the product is primarily DPG. This is because the feed ratio is PG∶PO=1, which is beneficial to generate DPG. However, as the amount of DPG increases, it will continue to react with PO to form TPG and the reaction rate of DPG will increase.

When the reaction time reaches 8 h, the selectivity of DPG is maximized at 30.85%. Then the rate of DPG formation is less than the rate of DPG conversion, causing the increasing of TPG selectivity and the decreasing of DPG selectivity. When the reaction time is 16 h, the selectivity of TPG has reached 42.73%, while the selectivity of DPG has fallen to 22.85%. Combined with the results of thermodynamic calculations, when the reaction condition is at 413.15 K and 101.325 kPa, the lnK of the 2PO+PG⇌ TPG reaction is 13.60 while that of the PO+PG⇌ DPG is 4.38−7.93. This indicates that when the reaction eventually reaches equilibrium, the selectivity of TPG will be significantly higher than that of DPG. The above results show that the thermodynamic calculation results have a certain degree of accuracy and can serve as theoretical references for subsequent research on product distribution.

As shown in Figure 10(c), from 373.15 to 393.15 K, the product ratio is consistent to the thermodynamic stability of the three isomers, which is DPG1 > DPG2 > DPG3. Moreover, the difference between the ratio of DPG1 and DPG2 decreases with the increase of temperature. This is due to the low reaction temperature resulting in a low reaction rate, and the lnK is higher according to the thermodynamic calculation. So, the reaction is mainly affected by thermodynamics, DPG1 is in high proportion. However, with the increase of temperature, the lnK decreases, the reaction rate accelerates which will lead to the reduced amount of DPG1 and the increased proportion of DPG2 in the product. When the temperature reaches 403.15 K, the product distribution is influenced by kinetics, with the order of DPG2 > DPG1 > DPG3. The higher the temperature, the larger the proportion of DPG2 is. Since the unreacted PO will further react with DPG to produce TPG, it is difficult to find a equilibrium state of the target reaction. So, we predict the final state by studying the changes of DPG isomers in the reaction process. The product distribution at 413.15 K for different reaction durations are also compared (Figure 10(d)). The formation rates of the three isomers are DPG2 > DPG1 > DPG3, so the content of DPG2 is the highest, and the content of DPG3 is the lowest. As the reaction progresses, DPG will further react with PO to form TPG. The thermodynamic calculation results show that the thermodynamic stability of the three isomers is different. Thus, DPG2 and DPG3 are easier to react with PO. So, with the extension of the reaction time, it can be clearly seen that the content of DPG2 in the isomers is decreasing, and the proportion of DPG1 is increasing, which is also consistent with the thermodynamic calculation results. In summary, the yield of DPG can be improved by optimizing the reaction time and the PG/PO ratio. For the regulation of product distribution, thermodynamic factors and kinetic factors need to be considered at the same time. Low temperature is beneficial to generate DPG1 while high temperature is conducive to the formation of DPG2. The formation rate of different isomers can also be controlled by using different catalysts by tuning the activation path of the reactants.