Evaluation of CO2-philicity of poly(vinyl acetate) and poly(vinyl acetate-alt-maleate) copolymers through molecular modeling and dissolution behavior measurement.

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Evaluation of CO-Philicity of Poly(vinyl acetate) and Poly(vinyl acetate-alt-maleate) Copolymers through Molecular Modeling and Dissolution Behavior Measurement Dongdong Hu, Shaojun Sun, Pei-Qing Yuan, Ling Zhao, and Tao Liu J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp5130052 • Publication Date (Web): 19 Jan 2015 Downloaded from http://pubs.acs.org on January 27, 2015

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The Journal of Physical Chemistry

Evaluation of CO2-philicity of poly(vinyl acetate) and poly(vinyl acetate-alt-maleate) copolymers through molecular modeling and dissolution behavior measurement Dongdong Hu, Shaojun Sun, Peiqing Yuan, Ling Zhao, Tao Liu* State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, P. R. China. *

Corresponding author. Tel.: +86 21 64253470; fax: +86 21 64253528.

E-mail address: [email protected] (T. Liu).

1

ACS Paragon Plus Environment


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Abstract Multi-scale molecular modeling and dissolution behavior measurement were both used to evaluate the factors conclusive on the CO2-philicity of poly(vinyl acetate) (PVAc) homopolymer and poly(vinyl acetate-alt-maleate) copolymers. The ab initio calculated interaction energies of the candidate CO2-philic molecule models with CO2, including vinyl acetate dimer (VAc), dimethyl maleate (DMM), diethyl maleate (DEM) and dibutyl maleate (DBM), showed VAc was the most CO2-philc segment. However, the cohesive energy density, solubility parameter, Flory-Huggins parameter and radial distribution functions calculated by using the molecular dynamics simulations for the four polymer and polymer/CO2 systems indicated that poly(VAc-alt-DBM) had the most CO2-philicity. The corresponding polymers were synthesized by using free radical polymerization. The measurement of cloud point pressures of the four polymers in CO2 also demonstrated poly(VAc-alt-DBM) had the most CO2-philicity. Although copolymerization of maleate, such as DEM or DBM, with PVAc reduced the polymer-CO2 interactions, the weakened polymer-polymer interaction increased the CO2-philicity of the copolymers. The polymer-polymer interaction had a significant influence on the CO2-philicity of the polymer. Reduction of the polymer-polymer interaction might be a promising strategy to prepare the high CO2-philic polymers on the premise that the strong polymer-CO2 interaction could be maintained. Key words: CO2-philicity; poly(vinyl acetate-alt-maleate); copolymer; molecular modeling; cloud point pressure

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1. Introduction The environmental impacts posed by industrial development have received growing attention. The waste water caused by the extensive use of organic solvents leads to huge environmental damage and threat. Supercritical carbon dioxide (scCO2) is of interest and well suited as an alternative green solvent to conventional organic solvents employed in many industrial processes,1 particularly in food and pharmaceutical industries. It is worth to mention that scCO2 is a non-flammable, non-toxic, inexpensive and environmentally friendly solvent2-4 with the moderate critical temperature and pressure (Tc = 31.1 oC, Pc = 7.38 MPa). Moreover, at the supercritical state, the fluid properties can be adjusted by easily changing its temperature or pressure. Substantial efforts have been devoted to develop scCO2 as a green solvent.4-18 Unfortunately, due to the fact of weak polar and low dielectric constant, scCO2 is a poor solvent for the vast majority of polar substances and polymers. The solubility of them in scCO2 is very low and extremely limited,4,10 which restricts their use in many processes such as being thickeners to control the CO2 mobility in CO2 flooding15,16 or chelating agents in metal processing in scCO2.19,20 Although it remains a great challenge to address this thorny problem, in recent years, lots of efforts have been made in the design of CO2-philes to modify the solvent character of CO2 and improve the solubility of solutes in scCO2.4-16,21-25 Fluoropolymers7,26 and silicone-based polymers5 have shown relatively good compatibility with CO2. However, both of them are expensive and fluorinated additives can cause the environmental issues,4 making them unsuitable to apply on a large scale. Non-fluorous hydrocarbon polymers have been attracted widespread attentions and some of them have been

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identified relatively high solubility in scCO2.8,9,22-25 Poly(vinyl acetate) (PVAc) was reported as one of the most CO2-philic hydrocarbon homopolymers,8 which was a significant step forward. But even so, the solubility of PVAc is far lower than that of fluoropolymers. Understanding of the intermolecular interactions in the hydrocarbon polymer/CO2 system is greatly helpful to design the more CO2-philic materials and expand the application range of CO2. In a solute-solvent system, the dissolution process depends on three kinds of intermolecular forces, i.e., the attraction forces between solute-solute, solvent-solvent and solute-solvent in the solution.27 The former two will prevent the formation of a solution system while the latter is the only one favorable to promote the formation of the solution. The relative values of these three attraction forces will notably affect or even determine the solubility of solute in a specific solvent.18,22,28 Therefore, in a polymer/CO2 system, the three factors containing CO2-CO2, polymer-CO2 and polymer-polymer interactions, should be all taken into account to understand the dissolution of the polymer in CO2. It is difficult to have a big change in solvent-solvent interactions without cosolvent so that exploration of the polymer-CO2 and polymer-polymer interactions is the key to screen suitable CO2-philic polymers. The appropriate functional groups introduced into the polymer will bring favorable polymer-CO2 interactions. Although CO2 is a weak polar solvent, it may act as a Lewis acid when interacting with polymers. CO2 also exhibited the potential acting as a Lewis base when interacting with specific groups, which was identified by DeSimone et al.29 Using

19

F NMR

spectroscopy, they identified the specific interactions between F atoms and CO2. Kazarian et

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al.30 found weak attractive interactions between carbonyl-containing compounds and CO2 using FT-IR. Furthermore, Beckman et al.31 confirmed the O atom in carbonyl group would enhance the compatibility of polymers with CO2 through weak Lewis acid-Lewis base (LA-LB) interactions. Molecular modeling is another feasible approach used by several research groups to qualitatively study the interactions between polymers and CO2. McHugh et al.32 identified that CO2 could act simultaneously as a Lewis acid and a Lewis base as well using ab initio calculations. Modeling by Raveendran et al.33 revealed the existence of a weak cooperative hydrogen bond between H atom of CO2-philic molecule and the O atom in CO2, which enhanced the binding energy with CO2 and increased the solubility in CO2. Wang et al.23 also used ab initio simulations to calculate the interactions between the representative moieties of candidate polymers and CO2 to design and explore non-fluorous polymers that might have high solubility in scCO2. The sites of LA and LB on the target moieties and CO2 should have favorable positions that contributed to the formation of binding between polymer moieties and CO2, which was the “multi-dentate” binding that could increase the interaction energy. In principle, due to limited computing resource, only could the binding energy between CO2 and the target polymer moieties with low molecular weight be calculated accurately by using quantum mechanical method. Fortunately, the favorable moieties and functional groups can be discovered by calculating the interaction energy using the quantum simulations. In addition to favorable polymer-CO2 interactions, moderate polymer-polymer interactions are essential to their dissolution in CO2. O'Neill and coworkers28 correlated the polymers solubility in scCO2 to their surface tension. They found that the lower surface

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tension was due to a weaker polymer-polymer interaction, which promoted the higher solubility in scCO2. It could be concluded that the material with low cohesive energy density was conducive to weak the solute-solute interaction and tended to be more CO2-philic, which was evidenced by the high CO2-philicity of fluorinated polymers and poly(dimethylsiloxane) with low solubility parameter.4,28 For this reason, strong chain interactions of PVAc resulted in relatively low solubility in scCO2 in comparison with the fluorinated and silicon materials. Hence, based on the comparison of the aforementioned polymers, it was suggested that reduction of polymer-polymer interaction might be the main driving force that could enhance the solubility of polymers in scCO2. In the case of preserving relative strong solute-solvent interaction, it was a promising strategy to introduce another monomer into the polymer backbone for decreasing the strength of solute-solute interaction and enhancing its CO2-philicity. In this regard, a series of attempts were made. According to the work of Howdle et al., Poly(vinyl acetate-co-vinyl butyrate)11 and poly(vinyl acetate-alt-dibutyl maleate)12 exhibited higher solubilities in scCO2 than PVAc homopolymer at the same condition. They surmised adding carbonyl groups in the side chains of copolymer might have a favorable specific interaction with CO2, and elevated chain flexibility leaded to low polymer-polymer interactions. Destarac et al. introduced fluorinated vinyl ester monomers (vinyl trifluoroacetate17 or 1-(trifluoromethyl) vinyl acetate18) into PVAc backbone by RAFT copolymerization. They demonstrated that the solubility of the copolymers in scCO2 was enhanced in comparison with PVAc homopolymer, and surmised that polymer-polymer interaction was the key lever to increase the solubilities of PVAc copolymers in scCO2 by measuring the surface tensions of PVAc and its copolymers. As we have known, the surface

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tension of a polymer is correlated with its cohesive energy density or solubility parameter which can be estimated from the statistical mechanics simulation, providing the possibility to predict the thermodynamic properties related to the solubility in a polymer-CO2 system. Although molecular modeling had been used to compute the energy properties of polymer-CO2 systems, the vast majority of simulations were based on small molecular segments of polymers and hardly had any attempts been made to compute the interactions between polymer chains and CO2 in a polymer-CO2 system. This work aims at investigating the key factors which influence and even decide the CO2-philicity of non-fluorous hydrocarbon polymer from the viewpoints of polymer-CO2 and polymer-polymer interactions through both multi-scale molecular modeling and experimental solubility measurements, which will help to design high CO2-soluble polymer and develop the applications of CO2. Ab initio method was used to calculate the binding energies between small model molecular structures and CO2 to characterize the polymer segment-CO2 interactions, including vinyl acetate dimer (VAc dimer), dimethyl maleate (DMM), diethyl maleate (DEM) and dibutyl maleate (DBM). Taking into account the impact of complex polymer chain structure, molecular dynamics simulations (MD) were introduced to estimate the interaction energies of CO2 with the four polymer chains, i.e., pure PVAc, poly(VAc-alt-DMM), poly(VAc-alt-DEM) and poly(VAc-alt-DBM), in COMPASS force field. The cohesive energy density and solubility parameter of the four polymers and CO2 were also evaluated by the construction of the polymer chain models in the MD simulations. Furthermore, the suppositional polymer-CO2 systems were constructed to analyze and compare the radial distribution functions for understanding the inter-molecular interactions.

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PVAc homopolymer and several poly(vinyl acetate-alt-maleate) copolymers were synthesized by using free radical polymerization for measurement of their cloud point pressures in scCO2. By comparing the results of computer simulations and experiments, CO2-philes with high solubility in CO2 might be found and screened. The factors conclusive for the design of CO2-philic polymers were explored. 2. Computational Section 2.1 Ab initio method To identify the CO2-philic structures and quantify their affinities with CO2, ab initio method was used to calculate the interaction energies between model structures and CO2. It was carried out in the Gaussian 09 software package.34 Four modeling molecules shown in Figure 1 were chosen to represent the dimer of VAc, the chain units of DMM, DEM and DBM in polymer chains, respectively. For each case, an initial configuration contained a CO2 molecule and a modeling molecule was guessed by placing the CO2 close to the oxygen atom of the target molecule. The second-order Møller-Plesset theory (MP2) with the 6-31+g(d) basis set were implemented to optimize the configuration of the bimolecular system in order to achieve the minimum energy position of CO2. Then, a larger basis set, 6-311++g(d), was used to calculate the single point energy of the optimized structure in MP2 level. Also, the basis set superposition error (BSSE) was corrected by the counterpoise correction35 in order to obtain more accurate binding energy. The details of a similar calculation procedure had been presented in Wang et al. work.23 The binding energy reported in this work was the average value of the raw energy and the corrected one. In addition, the charge analysis was performed by using the full natural bond orbital method (NBO)36 to gain a further understanding of the

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calculated result of binging energy.

O

O

O

O

O

O

O

O O

O

O

(a) VAc Dimer

O

O

O O

O

(b) m-DMM

(c) m-DEM

(d) m-DBM

Figure 1. Four modeling structures used to calculate the interaction energies with CO2. (a), (b), (c) and (d) represent the models for the VAc dimer, DMM, DEM and DBM, respectively.

2.2 Molecular dynamics MD calculations were carried out to study the models of polymers and polymer-CO2 solutions by using Material Studio 6.1 package from Accelrys Inc. All the calculations were carried out with the COMPASS force field.37 The detailed force field parameters used are shown in the supporting information. Polymer chains were built from repeat units to construct modeling structures and the geometries were optimized by Smart Minimizer in Discover module. Then, the cubic boxes were constructed by using Amorphous Cell module with periodic boundary conditions38 and ten configurations were generated. The configuration with the lowest energy was chosen in subsequent calculations for equilibration using Forcite programme. The simulation procedures are presented as follows: (1) 5-circle annealing from 300 to 500 K with 4 heating ramps per cycle and then back to 300 K so that the local hotspots were more relaxed and the system could achieve equilibrium. (2) 300 ps NPT MD simulation (at 20 MPa and 298 K) with the time step of 1fs. Trajectories were saved with 5 ps intervals and the configurations of final 50 ps were used for data analysis. The pressure and temperature in the MD simulations were all controlled by Berendsen method.39 The

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interactions of electrostatic terms were calculated by Ewald summation while the interactions of van der Waals terms were estimated by atom based summation with the buffer width of 0.5 Å, a spline width of 1 Å and cutoff distance of 15.5 Å. Three kinds of systems were calculated by MD simulation, namely, pure polymer system with six polymer chains, polymer-CO2 system with one polymer chain and 1000 CO2 molecules, and polymer-CO2 system with six polymer chains and 1000 CO2 molecules. The molecular weight of polymer chain has a significant effect on the thermodynamic parameters containing the cohesive energy density and the solubility parameter in many polymer systems. Thus, the number of monomer repeat-units is an important factor that must be considered in the MD calculations. Theoretically, the results of thermodynamic parameters are closer to the actual situation by increasing the number of repeat-units and polymer chains. However, MD simulations cannot be performed effectively in real polymer systems because of the limitation of computing resource. Previous work40,41 has shown that the cohesive energy density becomes insensitive to the chain length of polymer and reaches a nearly constant when the repeat units reach a certain size. Considering these two factors together, the polymer chain of PVAc was constructed with 50 repeat-units which is corresponding to a molecular weight of 4300 g/mol. The other three polymers were built by using substantially the same molecular weight of the PVAc chain. The different compositions of simulation boxes are listed in Table 1. The abbreviations of PVDMM, PVDEM and PVDBM refer to poly(VAc-alt-DMM), poly(VAc-alt-DEM) and poly(VAc-alt-DBM), respectively.

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Table 1. Systems of different compositions considered in molecular dynamics simulations Mn of Number Number of Number of Number System Composition a chain of chains VAc units Maleate units of CO2 1 CO2 1000 2 3 4 5

PVAc PVDMM PVDEM PVDBM

4302 4286 4302 4312

1 1 1 1

50 18 16 13

0 19 17 14

-

6 7 8 9

PVAc-CO2 PVDMM-CO2 PVDEM-CO2 PVDBM-CO2

4302 4286 4302 4312

1 1 1 1

50 18 16 13

0 19 17 14

1000 1000 1000 1000

10 11 12 13


4302 4286 4302 4312

6 6 6 6

50 18 16 13

0 19 17 14

-

14 15 16 17

PVAc-CO2 PVDMM-CO2 PVDEM-CO2 PVDBM-CO2

4302 4286 4302 4312

6 6 6 6

50 18 16 13

0 19 17 14

1000 1000 1000 1000

3. Experimental 3.1 Materials Vinyl acetate (VAc, 99%, Aldrich) was washed by using saturated NaHSO3 aqueous solution and Na2CO3 aqueous solution, dried with CaCl2 for 6 h, and distilled under nitrogen. Dimethyl maleate (DMM, 99.5%), diethyl maleate (DEM, 99.5%) and dibutyl maleate (DBM, 99.5%)

were

purchased

from

Shanghai

Aladdin

Industrial

Corporation.

2,2'-Azobis(isobutyronitrile) (AIBN, Sinopharm Chemical Reagent) was recrystallized from ethanol and vacuum dried for 24 h. CO2 (99.99 wt%) was supplied by Shanghai Baogang Praxair Application Gas Co., Ltd. The solvent toluene was distilled before used, and the other chemicals were used as received. 3.2 Synthesis of poly(vinyl acetate-alt-maleate) copolymers The alternating copolymers, poly(vinyl acetate-alt-dimethyl maleate) (PVDMM), 11



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Poly(vinyl acetate-alt-diethyl maleate) (PVDEM) and Poly(vinyl acetate-alt-dibutyl maleate) (PVDBM), were synthesized by using free radical polymerization in toluene, as illustrated in Figure 2. A typical experimental procedure was presented as follows: 8.08 mL DEM (0.05 mol), 5.31 mL VAc (0.05 mol) and 0.15g AIBN (1 wt% based on the total weight of monomer) were added and followed by 10 mL toluene as solvent into a 100 mL begoon-shape flask with a polytetrafluoroethylene valve. After being degassed by three freeze-pump-thaw cycles, the mixture was sealed under vacuum and then heated to 75 oC in an oil bath with stirring. After 24 h, the reaction flask was rapidly cooled to room temperature. The polymer was precipitated from the solution through addition of n-hexane. The product was further purified by using 10 MPa CO2 in a high-pressure autoclave to remove the less volatile small molecules (DMM, DEM and DBM)12, and then dried under vacuum to constant weight at 40 o

C. O

O

+ O

O

AIBN

O

75oC

x

y

O

O

O O O

O

O

VAc

DMM

PVDMM

Figure 2. Polymerization of VAc and DMM at 75 oC.

3.3 Structure characterization The molecular weight averages and polydispersity index of the products were determined by using gel permeation chromatograph (GPC, Agilent, PL-GPC50) in a THF mobile phase at a flow rate of 1 mL/min with mono-dispersed polystyrene as a calibration standard. The products were also analyzed by using 1H NMR spectra which was carried out on a nuclear magnetic resonance instrument (BRUKER, AVANCE 500) in CDCl3. The

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copolymer composition and the content of VAc could be estimated by the analysis of peak position and intensity in NMR spectra. 3.4 Experimental solubility measurements in scCO2 The cloud points of the polymers in scCO2 were observed by using a high-pressure variable volume view cell (from 25.0 mL to 50.0 mL) equipped with two sapphire windows. The temperature of the system was controlled by a thermostat and determined by a thermocouple (T type, the measurement accuracy of ±0.1 oC), while the pressure was measured by a pressure sensor (YMC-1N, precision of ±0.035 MPa) equipped with a numerical display. In a typical measurement, 47.7 mg sample (0.2 wt% based on the weight of injected CO2 at 35 MPa) was placed at the bottom platform in the cell. The cell was sealed and heated to 35 °C. The cell was then flushed three times with CO2 at 0.2 MPa for the removal of air. Thereafter, the system was pressurized to 35 MPa by injecting CO2 using a booster pump. The polymer would dissolve gradually in CO2 while stirring. After complete dissolution of the sample, the polymer-CO2 solution was equilibrated for 30 min. The cloud point was measured by slowly reducing the autoclave pressure, which was adjusted through the change of cell piston position. The cloud point pressure refers to the point when the single-phase, translucent and clear solution becomes cloudy. The phase transition was observed and recorded by using a CCD camera connected to a computer. At least three times were carried out to ensure the repeatability for each measurement. The deviation of the cloud point pressure was usually no more than ±0.5 MPa 4. Results and Discussion 4.1 Models and simulations 13



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4.1.1 Polymer segment-CO2 interaction Polymer-CO2 interactions were preliminarily evaluated using model molecules, namely, VAc dimer, m-DMM, m-DEM and m-DBM, which were representative of the backbone of PVAc and the three maleates. Several optimized structures of the complexes are obtained at the MP2/6-31+g(d) level and the typical binding modes are illustrated in Figure 3. Only one stable binding mode was found and optimized for the VAc dimer-CO2 system, as shown in Figure 3(a). The carbon atom of CO2 was placed between carbonyl oxygen in one carboxyl group and ether oxygen in the other carboxyl group while m-DMM, m-DEM and m-DBM all had three stable configurations, which were the CO2 positions placed between two carbonyl oxygen as shown in Figure 3(b), only close to one carbonyl oxygen as shown in Figure 3(c) and only close to one ether oxygen as shown in Figure 3(d), respectively .

Figure 3. Binding modes of optimized configurations for VAc dimer/CO2 and m-DMM/CO2 systems. (a) mode of VAc dimer; (b) mode A of m-DMM; (c) mode B of m-DMM; (d) mode C of m-DMM.

The calculated interaction energies are gathered in Table 2. It is shown that the binding energies of these systems are in the same order of magnitude and the binding energy of VAc dimer/CO2 is significantly larger than those of the other three systems, indicating VAc dimer/CO2 is a more stable structure from the energy point of view and the ester-containing polymers with the backbone of alcohol groups have more favorable sites for the polymer-CO2 interaction. Comparing the interaction of CO2 with m-DMM, m-DEM and m-DBM, it could

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be seen that m-DEM/CO2 system provided stronger CO2-polymer binding which was attributed to the interaction between CO2 and more acidic hydrogen atoms that were three bonds away from an electronegative atom (oxygen)23 This phenomenon was related to the anomeric effect or hyperconjugation. Also, the most stable configurations of all the four systems are presented in Figure 3(a), (b) and Figure 4, respectively. It can be seen that binding modes with four or five interaction points represented with dashed lines (the inter-atomic distance is roughly less than 3 Å) in Figures 3 and 4 involve larger binding energies than those with less interaction points. Taking VAc dimer as an example, the structure of the O atoms of VAc interacted with the C atom of CO2 could appear a Lewis acid-Lewis bases (LA-LB) interaction where O atoms acted as Lewis bases for binding with the Lewis acid CO2. Correspondingly, a weak hydrogen bond formed between the O atoms of CO2 and the H atoms of VAc in the system. Combination of the two factors resulted in the formation of a relatively stable six-membered ring. The most stable modes in the four systems all had many six-membered rings, which explained the stability to some extent.

Figure 4. Most stable mode in m-DEM/CO2 and m-DBM/CO2 systems. (a) m-DEM/CO2; (b) m-DBM/CO2. The other most stable modes of VAc dimer and m-DMM systems are shown in Figure 3 (a) and (b).

Table 2 shows the shortest distance between the C atom of CO2 and the O atom of carboxyl group in the target molecule. The NBO charges of the carboxyl O atom for the mode with maximum binging energy in the four systems were also demonstrated. From the

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comparison of the four most stable modes in the different systems, carbonyl O atom of VAc dimer had the maximum NBO charges and the minimum distance with C atom of CO2, indicating that the interaction between VAc dimer and CO2 was stronger than the other three ones. It was consistent with the conclusion that PVAc was the most CO2-soluble homopolymer containing only C, H and O to the best of our knowledge. The details of charge distributions computed for the most stable modes of four molecules can be found in the supporting information. Table 2. Interaction energies of CO2 with the models of VAc dimer, DMM, DEM and DBM Complex

Interaction energy Einter (kJ/mol)

dC

O

(Å)

qO (e)

(A)

(B)

(C)

average

in mode A

in mode A

VAc dimer

-16.37

-

-

-16.37

2.860

-0.744

m-DMM

-15.31

-11.79

-7.59

-11.56

2.892

-0.727

m-DEM

-15.47

-11.74

-7.68

-11.63

2.875

-0.735

m-DBM

-15.77

-11.08

-7.91

-11.59

2.864

-0.737

4.1.2 Polymer chain-CO2 interaction Although the ab initio calculations could identify accurately the affinities of functional groups with CO2, it was only part of the simulation that the self- and cross-interaction energies had not been reflected and the interactions between polymers and CO2 were still difficult to calculate because of the multi-scale structures of polymer and time-consuming calculation for ab initio method. Considering the impact of polymer chain on the interaction with CO2, MD simulations were introduced to evaluate the polymer-polymer and polymer-CO2 interactions for a better understanding of the compatibility of the polymer with CO2. The NPT ensemble method was used to calculate the energies of systems 1 to 9 in Table 1, containing a system of 1000 CO2 molecules, the systems of single-chain polymers (PVAc, 16


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PVDMM, PVDEM and PVDBM) and the systems of single-chain polymers and 1000 CO2 molecules (PVAc/CO2, PVDMM/CO2, PVDEM/CO2 and PVDBM/CO2). The intermolecular interactions could be quantitatively characterized by the intermolecular interaction energy (the binding energy) to predict the compatibility of the system components. The total energy of each system at stable structure was simulated to calculate the interaction energy between polymer chain and CO2, expressed as following:

Einter = − Ebinding = Echain/CO2 − ( Echain +ECO2 )

(1)

where Einter was the interaction energy between a polymer chain and CO2, and its value was equal to the negative of the binging energy Ebinding. Echain/CO2 referred to the total energy of polymer chain/CO2 system, and Echain and ECO2 were the energies of the systems with the polymer and CO2, respectively. The simulated results of ECO2, Echain and Echain/CO2 are shown in Table S5 and S6 in the supporting information. The interaction energies between a polymer chain and CO2, containing the total and non-bond interaction energy part, are shown in Table 3. The difference between Einter and ENon-bond was attributed to the change of valence (or bond) energies and cross term interaction energies because of the addition of polymer chain into the pure CO2 system. The binding energy of the PVAc chain with CO2 (2391.4 kJ/mol) was significantly larger than the other three polymer chains (1911.3, 2027.1 and 1949.5 kJ/mol for PVDMM, PVDEM and PVDBM, respectively). The non-bond energy (ENon-bond) of PVAc with CO2 was also the largest one in the four systems. Copolymerization of maleate, i.e., DMM, DEM and DBM, with PVAc reduced the polymer-CO2 interactions. Comparing the Einter and ENon-bond of different polymer chains with CO2, the variation tendency was consistent with the ab initio calculation results because the two simulations both focused on the 17



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Page 18 of 36

non-bonding affinity between the CO2-soluble candidates and CO2. However, in MD simulations, the influences of polymer chain structure and CO2 self-interactions were considered, and the molecular scale was larger in comparison with the ab initio calculations, which conduced to a more accurate prediction on the compatibility of polymers with CO2. Table 3. Interaction energy between a single polymer chain and 1000 CO2 molecules. (energy unit: kJ/mol) System

Echain/CO2

Echain

ECO2

Einter

ENon-bond

PVAc/CO2

-9094.8

-5175.5

-1527.9

-2391.4

-3043.2

PVDMM/CO2

-2388.8

1050.4

-1527.9

-1911.3

-2284.5

PVDEM/CO2

-4078.7

-523.7

-1527.9

-2027.1

-2642.5

PVDBM/CO2

-3601.5

-124.1

-1527.9

-1949.5

-2402.0

4.1.3 Polymer-polymer interaction The impact of the polymer-polymer interactions on its compatibility with CO2 should also be considered. The polymer-polymer interactions played an important role in cohesive energy, solubility parameter, mixing entropy, free volume and so on. The cohesive energy (Ecoh) was a widely accepted criterion to evaluate the intermolecular force of condensed matters, which referred to the energy needed to eliminate all the intermolecular forces for per mole material. The cohesive energy density was defined as the quotient value obtained from the cohesive energy divided by the volume of the cell. The expression of the cohesive energy is described as following: (2)

ecoh = E coh V

where ecoh represents the cohesive energy density (CED) and V the cell volume of polymer in calculation. In addition, the solubility parameter (δ) is defined as the square root of the cohesive energy density and given by the following equation:

δ = ecoh = Ecoh V

(3) 18


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The values of ecoh or δ could describe quantitatively the attractive strength between the molecule chains of the polymer to reflect the intermolecular forces, which had a consistent trend with the intermolecular forces in general and exerted a huge impact on the miscibility of polymers in CO2. To consider the effect of the polymer-polymer interactions on the compatibility of polymers with CO2, the PVAc homopolymer and three alternate copolymers (PVDMM, PVDEM and PVDBM) were calculated by using MD simulations. Each system had six polymer chains. The components of the four systems are listed as systems 10 to 13 in Table 1 and optimized structures are shown in Figure S1 in the supporting information. The trajectory files saved in the last 50 ps were applied to calculate the thermal properties of the simulated system containing ecoh and δ. Table 4 shows the statistics results of cohesive energy density and solubility parameter values for the four polymers and CO2. As can be seen, the δ calculated of PVAc was slightly lower than the experimental result (19.2 (J/cm3)1/2) provided by aldrich 42, and had the maximum values of ecoh and δ, indicating that the PVAc preserved stronger polymer-polymer interactions between molecular chains than the other three systems did. The powerful intermolecular forces might obstruct the formation of the polymer-CO2 solution and decrease the solubility in CO2. In contrast, copolymerization of maleate, i.e., DMM, DEM and DBM, with PVAc weakened polymer-polymer interaction. The moderate intermolecular interactions in PVDBM brought about low surface tension, promoted the thermodynamic stabilities of the polymer-CO2 complexes and lowered the cloud point pressure. In addition, dihexyl maleate (DHM) with longer side chain than DBM were also introduced to build the copolymers with VAc, i.e., poly(VAc-alt-DHM) (PVDHM). The ecoh

19



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was calculated by using MD simulation, which was 2.43E+08 J/m3 similar with that of PVDBM. However, the interaction of PVDHM with CO2 was lower than that of PVDBM, indicating that the compatibility of PVDHM with CO2 might be inferior to PVDBM. From the viewpoint of polymer-polymer interactions, the copolymers might have a better compatibility with CO2 than PVAc, in which PVDBM should be a most favorable candidate for enhancing the solubility and decrease the cloud point pressure in CO2. According to the theory of similarity and inter-miscibility, the solubility parameter was a relatively simple theoretical criterion to predict the miscibility between two materials in the absence of experimental data. Certainly, there were some necessary prerequisites when using this judging method that strong polar groups and hydrogen-bonding interactions did not have a dominant influence to the intermolecular interactions in the binary system. The systems calculated in this work met these requirements. The difference in solubility parameters (∆δ) between the polymer and CO2 was used to judge the miscibility between the polymer-CO2 mixture. In general, if the polymer had similar value of δ with CO2, they would tend to have a good miscibility. The δ value of CO2 was calculated by MD simulations at 20 MPa and 298 K. It was 13.15 under the simulation conditions and slightly lower than the results of Ohashi's work (14.3 in 318 K).43 As shown in Table 4, it can be seen that the solubility parameter of PVDBM was closest to that of CO2, indicating that the miscibility was most outstanding in the PVDBM/CO2 system from the point of view in similar polarity. Nevertheless, it was noteworthy that, dissolving or swelling of the solute would carry out when |∆δ| was less than the critical value about 1.7~2.044 when mixing the amorphous polymers into a non-polar solvent. As the simulated data of |∆δ| in this work were all larger than 2.0, the four polymers 20


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should have a poor compatibility in CO2 which in a good agreement with the fact that CO2 was a feeble solvent to the materials with high molecular weight. Table 4. Simulated cohesive energy density and solubility parameter System

Density (g/cm3)

ecoh (J/m3)

δ ((J/cm3)1/2)

PVAc

1.154

3.41E+08

18.72

PVDMM

1.207

3.19E+08

17.86

PVDEM

1.161

2.99E+08

17.28

PVDBM

1.088

2.47E+08

15.70

CO2

0.872

1.73E+08

13.15

4.1.4 Flory–Huggins interaction parameter The Flory-Huggins interaction parameter χ12 was another useful criterion to predict and understand the miscibility of polymer and the small molecule solvent. Especially, it was more suitable than the solubility parameter method for the system involving electrostatic force and H-bonding interactions. χ12 can be calculated from the equation as following45:

χ12 =(

∆Emix )Vm RTϕ Aϕ B

(4)

where R refers to the molar gas constant and T the temperature in Kelvin. Vm is the reference mole volume used for χ12, ∆Emix represents the energy of mixing, and φA and φB are the volume fractions of components A and B in the binary system. When the dispersive interaction is a dominant force in the system, a common approximation of χ12 proposed by Hildebrand46 is expressed according to Eq. (5):

Vm (δ1 − δ 2 ) 2 χ12 = RT

(5)

where the value of Vm is calculated by using the average mole volume of repeat unit, and δ1 and δ2 are the solubility parameters of polymer and CO2, respectively. In general, the critical value of miscibility criterion χc can be calculated by Eq. (6): 21



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1 2

χ c = (1 +

Page 22 of 36

1 2 ) n

(6)

where n is the number of polymerization degree in polymer chains. When χ12 of the mixture is smaller than χc, the system is considered to be miscible. Otherwise, if the value of χ12 is sufficiently larger than χc, the components would be immiscible completely in the system. If χ12 is slightly larger than χc, the system exhibits partial miscibility. Thus, it provides a good proposal for predicting the extent of polymer-solvent miscibility and phase behaviors by comparing the value of χ12 calculated by simulations with the critical value χc. Table 5 lists the calculated values of Vm, χ12 and χc using the simulated results of system 1 and systems 10-13. The results indicated that only was the χ12 of the PVDBM/CO2 system smaller than the χc and might form a single phase solution. The χ12 of the other three systems were all larger than the χc, proposing that they were difficult to be miscible and might be partial miscible or immiscible. Through the comparison of χ12, PVDBM was found to be the most CO2-philic material and have a strongest interaction with CO2 in the four systems, which was consistent with the results of polymer-polymer interactions evaluated by MD simulations. Table 5. Flory-Huggins parameter and critical value of miscibility calculated from MD simulations System

Vm (cm3/mol)

χ12

χc

PVAc/CO2

92.6

1.37

0.65

PVDMM/CO2

109.4

1.15

0.68

PVDEM/CO2

128.2

1.12

0.69

PVDBM/CO2

164.1

0.48

0.71

4.1.5 Radial distribution functions To provide a deeper understanding of the variation of polymer-CO2 interaction, the radial distribution functions (RDF) were analyzed in the equilibrium configuration after MD simulation using the Forcite module. RDF analysis was a common and useful characterization 22


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method in molecular structure to reflect the micro-structural characteristics and study the regularity of specific interactions in the system. It proposed the probability about the appearance of a pair of atoms at a distance r relative to the bulk phase for a completely random distribution. The function of RDF is defined as following: N AB

g AB (r ) =

1

ρ AB ⋅ 4π r 2 ⋅ ∆r

∑ ∆N

AB

(r → r + ∆r )

j =1

(7)

N AB

where gAB(r) is the intensity of RDF, the subscripts A and B denote two kinds of atoms or groups, ρAB is the bulk density of the system, NAB represents the number of atoms containing A and B, and ∆NAB refers to the atomic number of A (or B) within a distance interval ∆r from r to r+∆r around B (or A). The function of g(r) could be roughly divided into two contributions, i.e., the intra-molecular RDF and the inter-molecular RDF. The former was related to correlations between atoms of the same molecule or chain to characterize the molecular structure while the latter represented the correlations of molecular arrangement among the atoms on different molecules or chains to assess miscibility47. Figure 5 shows the intra-molecular and inter-molecular distribution functions calculated by Forcite analysis for the carbon-carbon pairs of the four polymer systems (systems 10 to 13 in Table 1). In Figure 5(a), the g(r) curves of intra-molecular carbon atoms in PVAc and the copolymers showed the analogous plots and same variation trend, indicating that their atom connectivity methods were very similar and the whole chain structures were no significant changes in the four polymer systems. For the polymer chains, the observed strongest peak appeared at near 1.53 Å, which simply proposed the characteristic peak of C-C bond connectivity. The peak at near 2.57 Å was the response of the atomic pairs without bond

23



connectivity in the ortho position, and the responsible peaks of other positions were at 3.25 Å, 3.65 Å and 3.95 Å, respectively. When the distance was greater than 4 Å, the value of g(r) tended towards 0, indicating that long-range order was not established in the simulated polymer chain systems. In the g(r) curves of intermolecular carbon atoms in PVAc and the copolymers, as shown in Figure 5(b), the variation tendencies were similar in the four polymer systems. No sharp peaks could be observed in the curves of Figure 5(b). These phenomenon proposed clearly that the carbon atom pairs from different molecules were not systematically at a distance of r, which were in good agreement with the amorphous structure of the polymers in this work. However, the intensities of g(r) curves had significant differences. The g(r) values of intermolecular C-C atom pairs were highest in PVAc followed sequentially by PVDMM, PVDEM and PVDBM. It was proposed that the chain interaction of PVAc was strongest as well as the C-C interactions between PVAc chains. The results were highly consistent with the variation tendencies of cohesive energy density, which was self-consistent and in good agreement with the inherent logic of chain interactions. 6

1.0

(b)

(a) 0.8 (r)

0.4

inter

0.6

gC-C

4

gC-Cintra(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 36


2


0.2

0

0.0 0

2

4

6 r (Å)

8

10

12

0

4

8

12

16

20

r (Å)

Figure 5. Radial distribution functions of the intra-molecular and inter-molecular carbon-carbon pairs of four polymers. (a) intra-molecular distribution; (b) inter-molecular distribution.

The g(r) of intermolecular C-C pairs of chain-chain, chain-CO2 and CO2-CO2 in the systems 14 to 17 in Table 1, containing six polymer chains and 1000 CO2 molecules, was also 24


Page 25 of 36

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analyzed by using the same method for the pure polymer systems. The results are shown in Figure 6. The g(r) functions appeared values greater than zero at the distance of about 3 Å, which indicated the molecular interactions in these systems were mainly based on the van der Waals forces (interactions distance 3-5 Å). Recently, researches for polymer miscibility were assessed by comparing the g(r) functions for intermolecular distributions between different components41,47,48 to ascertain the miscibility. A miscibility criterion was proposed that the two components in the system would show a good miscibility tendency when the values of g(r) for the atom pairs belonging to two different components were higher than those in one-component contact. In this work, three kinds of g(r) functions for C-C atomic pairs were calculated, i.e., C-C pairs between polymer chains, C-C pairs between CO2 molecules and C-C pairs between polymer chains and CO2 molecules. For the PVAc-CO2 system, as shown in Figure 6(a), both homo-contact (PVAc-PVAc and CO2-CO2) curves are higher than that of the hetero PVAc-CO2 contacts, indicating that PVAc and CO2 have poor miscibility. Nevertheless, for the PVDBM-CO2 system, as shown in Figure 6(d), the values of g(r) in hetero PVDBM-CO2 contacts are higher than the homo-contact curves of PVDBM-PVDBM but lower than the g(r) of CO2-CO2 contacts, indicating that the carbon atoms of PVDBM chain are more preferentially surrounded by the carbon atoms of CO2 molecules than those of other PVDBM chains. Thus, a slight miscibility between PVDBM and CO2 might exist under the simulation condition. In Figure 6(b) and (c), for the PVDMM-CO2 and PVDEM-CO2 systems, the comparisons of g(r) values show a better miscibility than PVAc but a worse miscibility than PVDBM, which has a good agreement with the simulated results of solubility parameter analysis and the changing trends of the Flory-Huggins interaction parameter.

25


2.4

2.0

CO2-CO2

2.0 1.6 1.2

inter

1.6

(r)

PVAc-PVAc PVAc-CO2

gC-C

inter

gC-C

2.4

1.2 0.8

Page 26 of 36

PVDMM-PVDMM PVDMM-CO2 CO2-CO2

0.8

0.4

0.4

(a)

0.0

(b)

0.0

0

4

8

12

16

20

0

4

8

r (Å)

16

20

PVDBM-PVDBM PVDBM-CO2

2.0

CO2-CO2 inter

(r)

1.6 1.2

gC-C

(r)

2.4

PVDEM-PVDEM PVDEM-CO2

2.0

inter

12 r (Å)

2.4

gC-C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(r)


0.8

CO2-CO2

1.6 1.2 0.8

0.4

0.4

(c)

(d)

0.0

0.0

0

4

8

12

16

20

0

4

r (Å)

8

r (Å)

12

16

20

Figure 6. Pair correlation functions of the inter-molecular carbon-carbon pairs between four polymers and CO2. (a) PVAc-CO2; (b) PVDMM-CO2; (C) PVDEM-CO2; (D) PVDBM-CO2.

4.2 Dissolution behaviors of PVAc and poly(VAc-alt-maleate) in CO2 4.2.1 Synthesis and characterization of PVAc and poly(VAc-alt-maleate) copolymers The PVAc homopolymer and poly(VAc-alt-maleate) copolymers were synthesized in toluene by using free radical polymerization at 75 oC with AIBN as the initiator. After purifying the polymers with supercritical CO2 extraction, the molecular weight and molecular weight distribution of the samples were characterized by using GPC. The results are shown in Table 6 and the GPC traces are represented in the Figure S2 in the supporting information. The polymers had the number average molecular weight ranging from 4000 to 7600 g/mol and a relatively wide molecular weight distribution. The comparisons of the polymers’ cloud points in CO2 depended on the two classes of molecular weight, i.e., ranging from 6500 to 7600 and close to 4000. 26


Page 27 of 36

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Table 6. Synthesis of PVAc and poly(VAc-alt-maleate) copolymers using 1wt % AIBN as initiator Sample

System

Molar ratio of monomers

Reaction Time (h)

Mn (g/mol)

PDI

1

PVAc

-

6

3976

1.15

2

PVAc

-

12

6730

1.24

3

PVDMM

1:1

24

6556

1.63

4

PVDEM

1:1

24

7212

1.79

5

PVDBM

1:1

24

7536

1.76

6

PVDBM

1:1

8

4423

1.28

The maleate esters have symmetrical non-polar structures and structural hindrance, making their self-polymerization hardly occur. The reactivity ratio of VAc, i.e., r1(VAc) = 0.17, and that of DEM, i.e., r2(DEM) = 0.043. Their product is approximately zero, indicating that the copolymer tends to form an alternating structure during the copolymerization between DEM and VAc. The similar phenomenon would occur in the copolymerization between the other two maleate esters and VAc due to the analog structures. The 1H NMR spectrum was employed to confirm the structure and composition of samples. Herein we only show the 1H NMR spectrum of purified PVDEM for the analysis of structure and composition, as demonstrated in Figure 7. The other detailed results of 1H NMR spectrum can be found in Figure S3 and Figure S4 in the supporting information. As can be seen, the chemical shift of H atom belonging to VAC in the point b was in the range of 4.6-5.5 ppm while that belonging to DEM in the point d and e was in the range of 2.4-3.2 ppm. The composition of the sample could be determined with the peak intensity of these two kinds of H atom from two different monomers. The ratio of the area in the two peaks was 1:1.84 so that the mole ratio of VAc:DEM = b:(d+e)/2 = 1:1.84/2 = 52:48, which was approximately 1:1 and consistent with the expected alternating structure of PVDEM. The mole ratios of VAc over maleate ester in PVDMM and PVDBM calculated by using the same method were 52:48 and 54:46,

27



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Page 28 of 36

respectively.

b e

d x

O

O

O O

a y O

O

f

d+e

b 8

7

6

a+c

f

c

5 4 Chem ical shift (ppm)

3

2

1

Figure 7. 1H NMR spectrum for a purified poly(VAc-alt-DEM) copolymer.

4.2.2 Cloud point pressures of PVAc and poly(VAc-alt-maleate) copolymers in CO2 In the high-pressure variable volume view cell, the cloud point pressures of the samples in CO2 were determined at a concentration of 0.2 wt% CO2 and temperatures ranging from 35 o

C to 65 oC. Compared the PVAc and PVDMM, the polymer chain-CO2 interaction of PVAc

was conducive to its CO2-philicity while the polymer-polymer interaction of PVDMM was positive. The PVDMM had a similar cloud point pressure with the PVAc of similar molecular weight, indicating that the negative polymer chain-CO2 interaction and the positive polymer-polymer interaction offset each other. From comparison of the cloud point pressures of the PVDEM, PVDBM and PVAc with the molecular weight in the range of 6500-7600 g/mol, as shown in Figure 8, the PVDBM with molecular weight of 7600 g/mol, which was nearly twice of 4000 g/mol of the PVAc, still had the lower cloud point pressure of 26.1 MPa at 35 oC, similar with that of PVAc-4000, i.e., 25.4 MPa at 35 oC. Compared PVDBM-4400 with PVAc-4000, the PVDBM showed an much higher CO2-philicity (18.5 MPa at 35 oC) than PVAc. Moreover, the variation tendency of CO2-philicity of the four polymers was consistent with the calculated results of cohesive energy density, solubility parameter, 28


Page 29 of 36

Flory-Huggins parameter and radial distribution functions due to the different chain flexibility provided by the side chain groups. It could be summarized copolymerization of maleate with PVAc weakened the polymer-polymer interaction which increased the CO2-philicity of the copolymers. By using multi-scale molecular modeling, the viewpoints of Howdle et al.12 and Destarac et al.17-18 were verified that the polymer-polymer interaction had a very important and significant influence on the CO2-philicity of the polymer, and sometimes might be even a key factor to decide whether the polymer could be dissolved in CO2. Therefore, reduction of the polymer-polymer interaction was a promising strategy to select the CO2-philes and obtain the high CO2-philic polymers on the premise that the strong polymer-CO2 interaction could be maintained. 50 Cloud point pressure (MPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


45

PVDBM 7600 PVDEM 7200 PVDMM 6600 PVAc 6700

PVDBM 4400 PVAc 4000 PVAc 6000

40 35 30 25 20 15 30

40

50 o Temperature ( C)

60

70

Figure 8. Cloud point pressures of the PVAc and poly(VAc-alt-maleate) copolymers in CO2 at different temperatures (polymer concentration: 0.2 wt% CO2).

5. Conclusion This work aims at evaluating the factors conclusive on the CO2-philicity of PVAc and poly(VAc-alt-maleate) copolymers through multi-scale molecular modeling and dissolution behavior measurement. Ab initio method was applied to calculate the interaction energies of the candidate CO2-philic molecule models with CO2, including VAc dimer, DMM, DEM and 29



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

DBM. It was found that VAc was the most CO2-philc segment and had strongest interaction with CO2 in the four simulated systems, in which the carbonyl O atom had the maximum NBO charges and the minimum distance with the C atom in CO2. MD simulations were then used to estimate the interaction energies of CO2 with the PVAc and the other three poly(VAc-alt-maleate) copolymer chains, which was also consistent with the conclusion that the interaction of PVAc with CO2 was strongest in the four polymers. Therefore, VAc was a favourable candidate for designing the CO2-soluble hydrocarbon polymers. The cohesive energy density ecoh and solubility parameter δ of the four polymers and CO2 were simulated for characterization of the polymer-polymer interaction, and the Flory-Huggins interaction parameter χ12 was obtained simultaneously according to the simulated results. The radial distribution function of the four polymers was also analyzed from the MD simulations for the four polymer/CO2 systems. The results indicated that PVDBM with the lowest values of ecoh and δ should have the most favorable CO2-philicity in the four polymers. The PVAc and the other three poly(VAc-alt-maleate) copolymers were synthesized by using free radical polymerization for measurement of cloud point pressures in scCO2. In the four polymers, PVDBM showed the best CO2-philicity consistent with the calculated results that it had the lowest values of ecoh. It was suggested that the polymer-polymer interaction influenced significantly and even decided the CO2-philicity of the PVAc and poly(VAc-alt-maleate) copolymers. Although copolymerization of maleate, such as DEM or DBM, with PVAc reduced the polymer-CO2 interactions, the weakened polymer-polymer interaction increased the CO2-philicity of the copolymers. Reduction of the polymer-polymer interaction might be a promising strategy to prepare the high CO2-philic polymers on the 30


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premise that the strong polymer-CO2 interaction could be maintained.

Acknowledgment. The authors are grateful to the National Science Foundation of China (21376087), the 111 Project (B08021) and the Fundamental Research Funds for the Central Universities. Prof. Liu H.L. and Prof. Sun W.Z., East China University of Science and Technology, are thanked for making a useful discussion with us on the manuscript.

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Captions Figure 1. Four modeling structures used to calculate the interaction energies with CO2. (a), (b), (c) and (d) represent the models for the VAc dimer, DMM, DEM and DBM, respectively.

Figure 2. Polymerization of VAc and DMM at 75 oC. Figure 3. Binding modes of optimized configurations for VAc dimer/CO2 and m-DMM/CO2 systems. (a) mode of VAc dimer; (b) mode A of m-DMM; (c) mode B of m-DMM; (d) mode C of m-DMM.

Figure 4. Most stable mode in m-DEM/CO2 and m-DBM/CO2 systems. (a) m-DEM/CO2; (b) m-DBM/CO2. The other most stable modes of VAc dimer and m-DMM systems are shown in Figure 3 (a) and (b).

Figure 5. Radial distribution functions of the intra-molecular and inter-molecular carbon-carbon pairs of four polymers. (a) intra-molecular distribution; (b) inter-molecular distribution.

Figure 6. Pair correlation functions of the inter-molecular carbon-carbon pairs between four polymers and CO2. (a) PVAc-CO2; (b) PVDMM-CO2; (C) PVDEM-CO2; (D) PVDBM-CO2.

Figure 7. 1H NMR spectrum for a purified poly(VAc-alt-DEM) copolymer. Figure 8. Cloud point pressures of the PVAc and poly(VAc-alt-maleate) copolymers in CO2 at different temperatures (polymer concentration: 0.2 wt% CO2).

Table 1. Systems of different compositions considered in molecular dynamics simulations. Table 2. Interaction energies of CO2 with the models of VAc dimer, DMM, DEM and DBM. Table 3. Interaction energy between a single polymer chain and 1000 CO2 molecules. (energy unit: kJ/mol) Table 4. Simulated cohesive energy density and solubility parameter.

Table 5. Flory-Huggins parameter and critical value of miscibility calculated from MD simulations.

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Graphic Abstract

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Polyvinyl Alcohol Electrospun Nanofibers Containing Mafenide Acetate.

The properties of enteric tablet coatings made from polyvinyl acetate-phthalate and cellulose acetate-phthalate [proceedings].

Linear drug release from laminated hydroxypropyl cellulose-polyvinyl acetate films.

A systematic study of the effect of molecular weights of polyvinyl alcohol on polyvinyl alcohol-graphene oxide composite hydrogels.

A visco-hyperelastic constitutive approach for modeling polyvinyl alcohol sponge.

Oral 4-week and 13-week toxicity studies of polyvinyl acetate vinyl laurate copolymer in rats.

Evaluation of phenylephrine stability in polyvinyl chloride bags.

Improvement of vibrodamping properties of polyvinyl acetate-graphite composites by electron beam processing of the filler.

The use of vacuum-molded polyvinyl acetate-polyethylene copolymer (PVAC.PE) for a handicapped patient.

Evaluation of dimensional stability and accuracy of autoclavable polyvinyl siloxane impression material.

The chemical stability of polyvinyl alcohols [proceedings].

Preparation and thrombogenicity of alkylated polyvinyl alcohol coated tubing.

Polyvinyl siloxane impression materials: a review of properties and techniques.

Evaluation of polyvinyl alcohol composite membranes containing collagen and bone particles.

Comparative Study on the Efficacy of Gingival Retraction using Polyvinyl Acetate Strips and Conventional Retraction Cord - An in Vivo Study.

Chitosan and polyvinyl alcohol composite films containing nitrofurazone: preparation and evaluation.

Artificial Auricular Cartilage Using Silk Fibroin and Polyvinyl Alcohol Hydrogel.

Polyvinyl siloxane as a disclosing medium.

Polyvinyl alcohol (Ivalon)--a new embolic material.

Comparative evaluation of dimensional accuracy of different polyvinyl siloxane putty-wash impression techniques-in vitro study.

Vitamin A sorption to polyvinyl and polyolefin intravenous tubing.

Early malfunction of polyvinyl alcohol membrane of septal occluder.

External reinforcement of tracheal tube by using polyvinyl chloride tube.

Structural insights into enzymatic degradation of oxidized polyvinyl alcohol.