DFT and quantum mechanical investigation of polyethylene and polypropylene monomers

Abstract

The hydration reaction of polyethylene (PE) and polypropylene (PP) monomers was investigated by density functional theory method (DFT) and quantum mechanical calculations (QM), using various types of approximations with and without van der Waals (vdW) corrections. The transition state optimization required for computing the activation energy was validated by infrared (IR) spectra of the products and showed agreement with Markovinkov’s rule. Among all approximations tested, second order Møller-Plesset perturbation theory (MP2) provided a more accurate description of the energy profile because this theory takes into account the electron correlation which result as an energy correction. These findings demonstrate a consistent computational method that enable reliable prediction of hydrocarbon hydration and polymeric reactivity under different theoretical levels.

Introduction

Polyethylene (C$_2$H$_4$)$_n$ and polypropylene (C$_3$H$_6$)$_n$ are saturated hydrocarbon polymers derived from ethylene and propylene molecules, as shown in Fig. 1. They are thermoplastic materials^1,2 widely utilized in various applications due to their low price^3,4. They provide excellent physical and chemical resistance, good recyclability, and high rigidity at small density^1,2,5.

Fig. 1

Chemical structure of polyethylene and polypropylene.

Despite their extensive applications, investigating their chemical reactivity at the molecular scale remains an ongoing challenge. Quantum mechanical modeling of entire polymer chains is computationally demanding because of their size and complex conformational behavior. Therefore, studying their monomeric units, ethylene and propylene, offers a practical and insightful approach to examine the fundamental reactions that affect the behavior, degradation, and functionalization of polymers.

So far, there was many interesting computational and experimental studies that involve polyethylene (PE) and polypropylene (PP) that we discuss hereafter. Recently, Alexander et al.⁶ have employed density functional theory (DFT) to investigate the dehydrogenative upcycling of polyethylene (PE) with various impurities. Their findings reveal that these impurities significantly increase the activation energy of the reaction⁶. Furthermore, the study underscores the crucial function of in-chain heterogeneities in catalyzing the activation of polymer chains. The latter provides valuable insights that inform the development of efficient upcycling strategies for plastic waste, paving the way for more sustainable recycling methods⁶. Both density functional theory (DFT) and molecular dynamics simulations were employed by Chen et al.⁷ to examine how chemical defects arise in polyethylene. They identified seven distinguished atomistic pathways, providing a coherent model to understand the experimental results on polymer degradation. This multi-method strategy enhances the predictive modeling of dielectric failure in polymeric substances⁷. Juliana et al.⁸ have investigated the reaction of ethanol dehydration with $\alpha$-$Fe_2O_3$ catalyst and without a catalyst using DFT. Their results indicate that the activation energy for an uncatalyzed ethanol dehydration reaction is approximately 70% higher than that of a catalyzed reaction⁸. In addition, Zheng et al.⁹ conducted molecular dynamics (MD) simulations to study the effect of water on polypropylene surfaces. They have found that the interaction of polypropylene surfaces with water results in the formation of a hydration layer despite being hydrophobic due to its weak polarity⁹. Moreover, Xiuqin et al.¹⁰ resorted kinetic monte carlo (KMC) and periodic DFT calculations to analyze ethylene production by ethanol dehydration on the $\gamma$-$Al_2O_3$ surface. The study has investigated the adsorption properties of critical species in this reaction and has illustrated a significant reduction in system energy when Lewis acid-base pairs are co-adsorbed on the surface¹⁰. Additionally, Jingyi Li et al.¹¹ stated that plastic manufacturing continuously and improper administration of plastic waste by removing it in aqueous systems harms humans and living organisms as it carries various toxins. They have studied freshwater after purification through FTIR, pyrolysis-GC/MS, Raman spectroscopy, and liquid chromatography¹¹. They concluded that it was challenging to quantify microplastics from a freshwater sample utilizing one technique. Combining multiple approaches provides more accurate data to assess environmental risk¹¹. Hadiyanto et al.¹² investigated how Spirulina sp. interacted with microplastics made of polyethylene (PE) and polypropylene (PP) in water-based systems. They observed that exposure to microplastics caused structural damage to cells and dramatically decreased the growth rate, phycocyanin yield, and protein content of Spirulina sp. Furthermore, EDX and FTIR analyses demonstrated that Spirulina sp. may use biochemical interactions to aid in the breakdown of PE and PP microplastics¹². Dahanayake et al.¹³ investigated the conformation and hydration of polypropylene oxide (PPO) and polyethylene oxide (PEO) in aqueous solutions. According to their molecular dynamics simulation results, PEO maintains a more stable hydration shell under these circumstances, whereas PPO loses hydrogen bonds and collapses more easily. These results emphasize how crucial hydration stability and hydrogen bonding are in determining how responsive polymers are to changes in their environment¹³. Finally, Ahn et al. recently elucidated the role of alkoxy radicals in polyethylene radio-oxidation kinetics¹⁴.

Our study uses quantum-mechanical calculations and the Density Functional Theory (DFT) method to examine the chemical reaction energy for the hydration of ethylene and propylene. The analysis and interpretation of the simulation results are based on the transition state theory. The focus is on determining whether the hydration reactions of ethylene and propylene are thermodynamically favorable in the gas phase and what activation energy is required for these reactions to form the products. Additionally, the vibrational spectra of ethanol and isopropyl alcohol were analyzed to identify and characterize the vibrational modes active in their respective structures. These analysis were necessary to draw possible configurations of transition states and help in localizing the most probable ones.

Understanding the effect of water on these polymers is crucial because large-scale molecular simulations incorporating water can offer more nuanced and realistic insights into their fundamental behavior. This investigation of these molecular interactions becomes particularly compelling when analyzed under specific environmental conditions, especially at elevated temperatures. These serve as a foundational framework for our ongoing research project in understanding the water dynamics of polyethylene and polypropylene, and draw conclusions for their degradation mechanisms.

Organic reactions: hydration of alkenes and dehydration of alcohols

Polyethylene and polypropylene are hydrocarbon compounds composed exclusively of carbon and hydrogen atoms¹⁵, a feature that significantly influences their chemical stability and challenges in up-cycling processes. It is well known that polymers may undergo hydration and dehydration reactions¹⁵. However, these two polymers must contain hydrophilic groups to undergo the hydration reaction¹⁶. Examples of polyethylene and polypropylene that contain these types of groups are polyethylene and polypropylene oxides¹⁷. The hydration reaction involves the addition of water molecules to an alkene (e.g., ethylene or propylene) to form alcohols. In contrast, the dehydration reaction occurs by removing a water molecule from alcohol to produce the alkene molecule¹⁵. Therefore, these two reactions are reversible, as illustrated in Fig. 2.

Fig. 2

Comparison of hydration and dehydration mechanisms.

In particular, the hydration reaction mechanism occurs in three steps: electrophilic addition of acid to the double-bond carbon to produce the carbocation in the first step and then attaches to the water molecule in the second step. In the third step, the proton will be removed to produce alcohol since it is just a catalyst consumed during the reaction¹⁵. Moreover, the hydration reaction follows Markovnikov’s rule based on the regioselectivity feature¹⁵. This rule states that the hydrogen atom attached to the carbon is connected to more hydrogen atoms compared to other carbon in the double bond¹⁵.

In contrast, the mechanism of the dehydration reaction follows the Zaitsev rule, which states that in alcohol carbon loses a hydroxyl group (-OH). In contrast, the other carbon loses one hydrogen atom to produce water. At the same time, a double bond forms between the two carbons¹⁸.

Results and discussion

Different levels of theoretical methods, both with and without considering van der Waals (vdW) corrections, are utilized to evaluate the chemical reaction energies for both reactions discussed hereafter, aiming to investigate the effect of these corrections. The transition states are localized using the dimer method after an initial guess of the structures was constructed based on vibrational analysis. In Tables 1-3, ∆G represents the Gibbs free energy change, while ∆G^‡ denotes the Gibbs free energy of activation. The results demonstrate that the hydration mechanism of ethylene and propylene hydration is in agreement with those proposed by Markovnikov¹⁹.

Hydration of ethylene (reaction 1)

The hydration of ethylene is a reversible reaction and can be represented as follows:

$$\text {C}_{2}\text {H}_{4(g)} + \text {H}_{2}\text {O}_{(g)} \rightleftharpoons \text {C}_{2}\text {H}_{5}\text {OH}_{(g)}$$

Table 1 Comparison of chemical reaction energy in (kcal/mol) for GGA Approximations with and without vdW interactions.

Table 1 shows that the chemical reaction energies for PBE and BP are in the same range, as they used the same approximation type. This, in turn, validates our structural model and methodology. We can see that including vdW has no significant effect, yielding results that differ by approximately 1.00 kcal/mol compared to those without vdW. Figure 3 illustrates the reaction pathway for PBE and BP with and without vdW.

Fig. 3

Reaction pathway of ethylene hydration using GGA approximations (PBE and BP), (a) without vdW and (b) with vdW corrections.

Table 2 Comparison of chemical reaction energy in (kcal/mol) for AE calculations and MP2 theory with and without vdW interactions.

In addition to the GGA approximation, all-electron calculations were performed using two different basis sets (6-31G* and 6-311++G**), which vary in the number of Gaussian functions they employ. Table 2 shows a notable difference of almost 5.00 kcal/mol in the activation energy between 6-31G*and 6-311++G** with and without vdW interactions. This is because 6-311++G** includes one more valence orbital than 6-31G*, while both use six Gaussian functions for the core orbitals. Furthermore, the basis set aug-cc-pVDZ was used since it is more advanced than the above basis sets. The energy calculation for this basis set is effective with vdW, unlike without vdW. This is because the vdW correction provides a reasonable value for the activation energy of 42.20 kcal/mol. However, the calculations used these basis sets without including vdW, resulting in activation energies much higher than those for vdW. To ensure that this is not a convergence issue, other augmented basis sets were employed, such as aug-cc-pVTZ, and aug-TZV2P, which provide similar results to aug-cc-pVDZ. Moller-Plesset Perturbation Theory (MP2), based on the Hartree-Fock approximation, is applied with two different basis sets (6-31G** and aug-cc-pVDZ) to enhance the level of theory in our calculations. The chemical reaction energy with and without the vdW correction agrees with all approximations tested, except for the activation energy in MP2/6-31G**, as shown in Figs. 4 and 5. In particular, the activation energy of MP2/6-31G** with vdW correction is 12.5 kcal/mol higher than without vdW correction. Thus, the inclusion of van der Waals (vdW) correction leads to better results. The change in Gibbs free energy is negative for the GGA, AE and MP2 calculations. These results indicate consistency, as all hydration reactions are exothermic. Breaking the bonds in the reactants requires less energy than is released during product formation²⁰. From a thermodynamic perspective, exothermic reactions are characterized by a negative Gibbs free energy, as energy is released from the system to the surroundings²⁰.

Fig. 4

Reaction pathway of ethylene hydration using AE calculation for three basis sets (a) without vdW and (b) with vdW corrections.

Fig. 5

Reaction pathway of ethylene hydration using MP2 (6-31G** and aug-cc-pVDZ basis sets) (a) without vdW and (b) with vdW corrections.

Comparing the Gibbs free energy results presented in Tables 1 and 2, we observe that the change in the Gibbs free energy calculated using MP2 is more significant than those obtained from the GGA and AE calculations. We found that the activation energy, calculated using MP2/aug-ccpVDZ with vdW correction, is 85.49 kcal/mol without the use of a catalyst, which is significantly higher than the experimentally reported value of 34.1 kcal/mol²¹, measured with an acid catalyst. This difference is expected because the catalyst provides a lower-energy reaction pathway. Importantly, the MP2 method gives a more accurate and reliable estimate of the true energy barrier compared to simpler AE and GGA approaches, because it better captures essential electron correlation effects that are critical to describe energy-intensive reactions like this one.

In addition, we compare our calculated results with the data reported in the reference⁸. Our study investigates the reaction of ethylene with water, whereas the only previously reported results concern the dehydration of ethanol, which is the reverse of our reaction. Our MP2 (6-31G**) calculated reaction and activation energies appear reasonable when compared to the DFT results for ethanol dehydration. The reported chemical reaction energy for the dehydration of ethanol was 15 kcal/mol, while our calculations yield -8.66 kcal/mol with vdW interactions. Similarly, the reported activation energy for ethanol hydration was approximately 73 kcal/mol, compared to our calculated value of 83.85 kcal/mol with vdW interactions. Our results align well with those of this study, as dissociation reactions (ethanol dehydration) are endothermic because of the energy required to break the C–O bond. In contrast, synthesis reactions (ethylene hydration) are exothermic due to the energy released during bond formation⁸.

Hydration of propylene (reaction 2)

Hydration of propylene occurs naturally and leads to the formation of isopropyl alcohol, indicating that the reaction is thermodynamically favorable²². The following chemical formula represents this reaction:

$$\text {C}_{3}\text {H}_{6(g)} + \text {H}_{2}\text {O}_{(g)}\rightleftharpoons \text {C}_{3}\text {H}_{7}\text {OH}_{(g)}$$

This reaction is also simulated using the GGA, AE, and MP2 methods. Table 3 shows the calculated chemical reaction and activation energies, with and without vdW interactions.

Table 3 Chemical reaction energies in (kcal/mol) calculated using GGA, AE, and MP2 methods, with and without vdW interactions.

Table 3 illustrates that the chemical reaction and activation energies calculated using PBE and BP methods, both with and without vdW interactions, are in similar ranges. All-electron (AE) calculations with 6-31G* and 6-311++G** basis sets were used but proved inadequate for determining accurate chemical reaction and activation energies for this reaction, unlike the ethylene hydration reaction, because the propylene molecule is a bit larger than the ethylene molecule. Thus, these basis sets are more suitable for smaller systems²³. Consequently, AE calculations using the aug-cc-pVDZ basis set were employed, which yielded an activation energy of 40.86 kcal/mol with vdW correction, providing a more realistic representation than those without vdW correction. Thus, the van der Waals (vdW) correction significantly improves the computational results. Since MP2 incorporates perturbation theory with an advanced basis set, its chemical reaction and activation energies are expected to be more accurate and realistic. Although there are no DFT studies for this reaction, our results appear valid, since the negative chemical reaction energy (enthalpy) is consistent with the established principle that hydration reactions are exothermic²⁰. However, we can compare the calculated activation energy value of 85.37 kcal/mol (MP2 / aug-cc-pVDZ with vdW correction), determined in the absence of a catalyst, with the experimental value of 28.0 kcal/mol²¹, which was obtained in the presence of a catalyst. The significant difference between these values highlights the effect of the catalyst in lowering the energy barrier for the reaction. The reaction pathways calculated using the PBE, BP, AE and MP2 methods are shown in Figs. 6 and 7.

Fig. 6

Reaction pathway of propylene hydration using GGA approximations (PBE and BP), (a) without vdW and (b) with vdW corrections.

Fig. 7

Reaction pathway of propylene hydration using MP2 and AE methods for two basis sets (a) without vdW and (b) with vdW corrections.

To validate our transition state structures (Figs. 8, 9), we performed normal mode and vibrational analysis as implemented in CP2K using different DFT approximations and AE calculation as represented in Table 4. The vibrational frequencies of PBE functional for TS$_1$ (reaction 1) and TS$_2$ (reaction 2) are $-1830\ \textrm{cm}^{-1}$ and $-1748\ \textrm{cm}^{-1}$, respectively. K. B. Wiberg et al. ²⁴ reported that the TS structure in the reaction for the oxidation of ethene computed using B3LYP/6-311++G** and MP2/6-311+G* yields one imaginary frequency (1254i). We recomputed the vibrational frequencies of TS$_1$ and TS$_2$ at the same theoretical level and obtained $-2016\ \textrm{cm}^{-1}$ and $-2000\ \textrm{cm}^{-1}$, respectively. The higher vibrational frequencies of each transition state indicate that the barrier is shallow. Our calculated modes correspond to the correct reaction coordinate (bond breaking/forming) and they involved H-transfer. Recent calculations of the vibrational frequency of a transition state involved in the reaction HOSO$_2$ + O$_2$ $\rightarrow$ SO$_3$ + HO$_2$ report values of $1706i\ \textrm{cm}^{-1}$ using B3LYP/cc-pVTZ+d ²⁵ and $1038i\ \textrm{cm}^{-1}$ with r$^2$SCAN/aug-TZV2P ²⁶.

Table 4 Imaginary frequencies (cm$^{-1}$) of the two transition states calculated using different DFT approximations and AE calculation.

Fig. 8

Optimized transition state structure of Reaction 1 (ethylene hydration). Carbon atoms are shown in orange, hydrogen in gray, and oxygen in red. See Movie S1 for the full animation.

Fig. 9

Optimized transition state structure of Reaction 2 (propylene hydration). Carbon atoms are shown in orange, hydrogen in gray, and oxygen in red. See Movie S2 for the full animation.

Vibrational analysis: IR spectra

Absorption of IR radiation causes molecular bonds to bend or stretch, causing changes in bond angles (decreasing) and bond lengths (increasing)²⁷. We performed infrared spectroscopy calculations to help locate the transition states for the above reactions, as shown in Fig. 10. Vibrational analyses of the reaction products (ethanol and isopropyl alcohol molecules) using DFT with the PBE functional within the all-electron (AE) calculations framework. The aug-cc-pVDZ basis set with GTH pseudopotentials was applied to all atoms to analyze molecule vibrations and facilitate transition-state identification.

Fig. 10

Infrared spectra of ethanol and isopropyl alcohol using DFT (PBE) with AE calculations (aug-cc-pVDZ basis set).

Fig. 11

NIST infrared spectra of ethanol and isopropyl alcohol.

These spectra show vibrational patterns with varying intensities as a function of the frequency of the absorbed IR radiation. Tables 5 and 6 show the different modes of vibration of ethanol and isopropyl alcohol, representing different molecular movements at various frequencies. These tables show that the O–H bond stretches in both molecules, forming alcohol, which characterizes our products. These calculations provide an initial estimate of the transition state structure, which can then be refined by using the dimer method to locate the actual transition state. The combination of vibrational analysis and the dimer method helps accelerate the convergence and identify the most probable transition state structure.

Table 5 Bending and stretching of bonds in ethanol spectra.

Table 6 Bending and stretching of bonds in isopropyl alcohol spectra.

Fig. 12

Markovnikov’s rule.

Tables 5 and 6 also present the calculated vibrational frequencies for the two molecules and compare them with the experimental data available from NIST²⁹ as illustrated in Fig. 11. The calculations for ethanol (Table 5) predict characteristic vibration modes, including C–O stretching at two frequencies, C–H bending, and O–H stretching. The calculated frequencies for these vibrational modes align reasonably well with the experimental ranges^28,29. However, the OH stretch shows a redshift because its frequency is higher than the experimental value^28,29. For isopropyl alcohol (Table 6), the calculated vibration modes include C–C stretching, C–O stretching, C–H bending and OH stretching. The C–O stretching mode at 1122.33 cm$^{-1}$ shows excellent agreement with the experimental value of 1129 cm$^{-1}$³⁰, while other modes show some deviation from the reference values^29,30. The O–H stretching frequency exhibits a red shift compared to the experimental values^29,30. These vibrational analyses provide important structural information about both alcohols and help validate the computational methods used in this study. The presence of characteristic O–H and C–O vibrations confirms the formation of alcohol products in both reactions.

Our quantum mechanical simulations confirm that the ethylene and propylene hydration reactions follow Markovnikov’s rule¹⁹, as the transition states favor the formation of the more stable carbocation intermediate, in agreement with our theoretical predictions. Therefore, Markovnikov’s rule, which predicts the outcome of electrophilic addition reactions to alkenes, was validated in this study, as illustrated in Fig. 12.

Finally, spectroscopic analysis confirms that the transition state is driven by a proton (H) transfer from the water molecule to one of the propylene or ethylene molecules (i.e., CH$_2$).

Conclusion

The computational framework in this study provides insight into chemical reactions in polymeric systems through their monomers. The comparative analysis between the DFT method and QM calculations revealed the effect of electron correlation on the activation barriers. The inclusion of vdW corrections showed a negligible effect in computed energies, indicating a limited role in the hydration of small systems, i.e., monomers. The combination of spectroscopic analysis and quantum mechanical calculations validated the proposed Markovnikov’s mechanism and offered a detailed characterization of reaction pathways and transition state structures. Overall, these results underline the importance of selecting the appropriate theoretical level of approximation that achieves an optimal balance between computational accuracy and cost, especially when simulating polymer systems. Although the current approach provides insight into the electronic and mechanistic aspects of polymer monomer hydration, it remains limited by model simplifications that may influence the electronic properties and chemical reaction energies. Future work may further improve this model by incorporating realistic polymer chain that include periodic effect for better representation of long-range interactions and account for temperature effects, thereby linking molecular-level computational results with polymeric systems.