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A Molecular Dynamics Simulation Study on the Miscibility of Polyglycolide with Polyacrylonitrile

Mahamat Bichara Abderaman, Kharouna Talla, El-Hadji Oumar Gueye, Abdoulaye Ndiaye Dione, Omar Faye, Aboubaker Chedikh Beye

Abstract: Atomistic molecular dynamics and mesoscopic dynamics simulations are used to study the miscibility of polyglycolide (PGA) blended with polyacrylonitrile (PAN). Seven PGA/PAN blends (with weight ratios of 90/10, 80/20, 70/30, 60/40 and 50/50), as well as pure PGA and PAN, are examined. The Flory Huggins parameters, phase diagrams, radial distribution function, free energy, and order parameters are computed for different blends using atomistic simulations to predict blend miscibility. The simulation results show that the PGA/PAN blends have good miscibility for all the weight ratios investigated. This is further supported by the morphologies of PGA/PAN blends. The phase separation kinetics of PGA/PAN blends is then examined using density profiles calculated from the Mesodyn approach to examine the mesoscopic morphology of the blends. The results strengthen the conclusion that the blends can be miscible in the above-mentioned range of ratios, in agreement with those found in the literature.

Keywords: polyglycolide, polyacrylonitrile, miscibility, molecular dynamics, blend

Received August 11, 2018; Revised October 06, 2018; Accepted October 19, 2018

Citation: Mahamat Bichara Abderaman, Kharouna Talla, El-Hadji Oumar Gueye, Abdoulaye Ndiaye Dione, Omar Faye, Aboubaker Chedikh Beye, A Molecular Dynamics Simulation Study on the Miscibility of Polyglycolide with Polyacrylonitrile. Journal of Polymer and Biopolymer Physics Chemistry, 6 (1). 31-38. January 2018. doi:10.12691/jpbpc-6-1-4

1. Introduction

Polyglycolide (polyglycolide acid, PGA) is a thermoplastic and biodegradable polymer that can be produced from renewable resources such as sugar [1,2,3]. PGA has high mechanical strength and high gas barrier performance [4]. Its mechanical strength is greater than or equal to that of other existing plastics and resins. The resistance of PGA is approximately equivalent to that of the polyetheretherketone resin (PEEK) used for automotive parts. As a highly functional polymer, the environmentally friendly and biodegradable properties of PGA make it useful for several applications [4]. Polyacrylonitrile is a synthetic, semi-crystalline polymer which is thermoplastic in nature [5]. It is a versatile polymer used for various products and important for its properties such as low density, thermal stability, modulus of elasticity and high strength [6].

Blend polymer can lead to the development of new types of materials [7,8]. In this context, the study of miscibility between polymers is very important [9]. Generally, the goal is to produce a mixture with optimal physical and chemical properties. The miscibility of polymers has been studied by many experimental methods. Scanning electron micrograph (SEM) has been used to analyze the miscibility behavior of polystyrene/polypropylene blend [10]. The morphology, mechanical properties and thermal stability of acrylonitrile butadiene rubber (NBR)/polybutylene succinate (PBS) blend has been studied using similar method [11]. However no theoretical explanations were given in support of the experimental observations. The formation and evolution of phase structure can be predicted using Molecular Dynamics (MD) simulations. These last years, MD simulations have been widely applied in a large complex system as an effective theoretical method because they can reveal the microscopic images that are difficult to obtain or inaccessible experimentally [12,13,14,15,16,17,18]. It is one of the most promising methods for predicting the properties of materials and for investigating the microstructure [19]. The simulation results reported in the literature are in agreement with previous experimental results on samples having similar microstructure and properties [20,21]. In one of our previous paper [22], the miscibility of glycolide with different monomers (Ethylene, styrene, acrylonitrile and lactide) has been investigated by molecular dynamics simulation using Forcite and Blends Modules.

The conventional difficulty to cost-effectively manufacture high molecular weight PGA has been cleared using an original but complex process. As a matter of fact, high molecular weight PGA have been successfully manufactured by first designing and synthezing a polyalkylene glycol di-ether appropriate solvent and then developing a correct solution depolymerization process [4].

The complexity of their process is exemplified by the favorable dilution, the transfer of the glycolide to the gaz phase with the solvent which is stable at high temperature and for long period in order to form an azeotrope with the glycolide and with appropriate solubility after condensation to permit easy separation of the glycolide.

In this work, we study the thermodynamic, structural, and dynamic properties of PGA/PAN blends, as well as pure PGA and PAN, by molecular simulation using the software suite Materials Studio. Then, we study the miscibility between the two polymers. Finally, the mesoscopic dynamic (MesoDyn) simulation method is used to investigate the mesoscopic phase separation behaviour of PGA/PAN blends.

2. Simulation Methods

2.1. Molecular Dynamics (MD) Simulations

The miscibility state at the molecular level for PGA/PAN blends was investigated by MD simulations of the fully atomistic model using Materials Studio. Polymer chains are first built from repeated units of PGA and PAN and then cubic simulation boxes are constructed with the amorphous cell program [27]. Table 1 lists the PGA/PAN blends of different weight compositions (including pure polymers) examined in the MD simulations. The number of units, chains and initial densities are summarized in Table 1. The density of the PGA and PAN are fixed at 1.53g/cm³ and 1.184g/cm³ respectively [23,24]. The density of the blends is calculated from the density of individual polymers and the volume fraction of each polymer.

To eliminate the unfavorable contacts, of each system, 20 independent configurations are constructed. Then, each unit cell is initially subjected to 50 000 steps of energy minimization by the Forcite module with the energy and force convergence threshold respectively fixed to 1.10⁻⁴ kcal.mol⁻¹ and 0.005kcal.mol⁻¹. Å⁻¹. The Ewald summation method is adopted for the Coulomb interactions with an accuracy of 0.01kcal.mol⁻¹. The atom-base summation method is then applied for the Van der Waals interactions with a cutoff distance of 9.5 Å, a spline width of 1 Å, and a buffer width of 0.5 Å. For the system, the first five configurations with the lowest energy are selected for the following MD simulations. For PGA/PAN blends, the configurations with the lowest energy are examined to ensure sufficient contacts of the two polymers by calculating the inter-molecular radial distribution functions g (r) of the carbon atoms between PGA and PAN. A g (r) lower than that of pure PGA and PAN, indicates that the two polymers don’t blend. Then, this configuration is rejected and another with relatively higher energy is considered until we find the adequate configuration.

Then, molecular dynamics simulation are performed at 600K and 1bar for 1ns in the NPT ensemble. Here, the temperature was chosen at 600K to ensure that both PGA and PAN polymers are in the molten state (amorphous) the PGA melting temperature is in the 500K to 503K range [25] and the PAN melting temperature is 595K [26]. In order to further relax local hot-spots and to allow the system to reach equilibrium, these selected structures have been subjected to 10-circle thermal annealing from 300 to 1000K and then back to 300K with 50K intervals. At each temperature, 100ps NPT MD simulation was performed at a constant pressure of 1bar with a time step of 1fs. After the 10-circle annealing, 100ps NVT MD simulation equilibrium is carried out at constant volume and then 250ps NPT MD simulation at 1bar and 298K. Trajectories are saved every 5ps and the final 50ps configurations are used for analysis [27]. MD simulation parameters for PGA/PAN blends are presented in Table 1.

Table 1. PGA/PAN blends of different compositions considered in MD simulation

Then, MD simulation of this fully atomistic model is used to predict the miscibility of PGA and PAN with different compositions. The miscibility of Polymer blends, is calculated by examining the Flory-Huggins interaction parameter () calculated according to Equation 1:

[picture] | (1)

Where is the molar volume of the repeat unit, R is the molar gas constant and T is the temperature of the simulation in Kelvin. The energy mixing can be calculated according to the following equation [28]:

[picture] | (2)

Where the terms in parentheses represent the cohesive energies of the pure polymers (A and B) and the blend (mix), and represent volume fractions of PGA and PAN, respectively, in the blend where .

2.2. Blends Simulation

In Blends simulation, the Blends Module combines a modified Flory-Huggins model and molecular simulation techniques for calculating the compatibility of polymer-solvent and polymer-polymer binary mixtures [29,30,31,32]. To predict the miscibility of a polymer with two other polymers, polymer blends are used. Repeated units of PGA and PAN are constructed and then optimized with Forcite Module by adopting the Dreiding force field and charge using QEq. After making the geometry optimization, the blends calculation is carried out at 298 K using the Dreiding force field, the QEq charge and the atom-base summation-method. After calculation, the phase diagrams of PGA and PAN is obtained. Similarly, the lengths of PGA and PAN molecules of the different component composites are inserted as inputs and the binding energies in the taskbar is selected so the mixing energy () is obtained.

2.3. Mesoscopic Dynamics Simulation (MesoDyn)

For a detailed understanding of the PGA and PAN blend miscibility/immiscibility issues, Mesodyn program incorporated in Materials Studio package, is used to simulate the phase separation dynamics of the blends at the mesoscopic level. This method is based on the dynamic variant of the functional theory of mean-field density [33]. In Mesodyn, several atoms or repeating units are grouped together and presented by a single bead; a polymer chains in Mesodyn can be considered as consisting of the number of beads (Nmeso) which is calculated from the following equation :

[picture] | (3)

With N being the number of repeat units, and the characteristic ratio of the polymer. The ratio can be evaluated using the Synthia Module in the Materials Studio (MS). The for the PGA and PAN are 3.69 and 7.33, respectively. Thus, the number of beads Nmeso for PGA and PAN are found to be70 and 10, respectively. The link between the microscale and mesoscale is as follows:

[picture] | (4)

Where the parameter is calculated by atomistic simulation for each blend with different compositions. R being the molar gas constant, 8.314J/mol.K and T the temperature taken to be 298K.

Other parameters are based on the previous research work [27] in the Mesodyn simulation. Nmeso and (interacting energies between a pair of interacting bead types) are the input parameters for Mesodyn calculations. For 90/10, 80/20, 70/30, 60/40 and 50/50 blend, the values are 0.795KJ/mol, 0.832KJ/mol, 0.868KJ/mol, 0.904KJ/mol and 0.939KJ/mol, respectively. The time step for performing the simulation is chosen so that the dimensionless time step used by the program was 0.5 (i.e., between 0 and 1) to account for numerical stability and bond length was 1.1543 nm throughout and the time step is 50.0ns. The maximum number of iteration per step is 100, a total of 5000 steps being performed thereby leading to a total simulation time of 250μs for PGA/PAN mixtures at 90/10, 80/20, 70/30, 60/40 and 50/50 compositions showing miscibility. For the entire simulation a constant noise parameter of 75.02 is maintained (since too high or too low value will lead to system unstability) which is applied to shorter chains with longer statistical units [34,35]. The grid dimensions are 32x32x32 nm and the size of the mesh over which density variations are to be plotted in Mesodyn length units using the grid spacing field are 1nm.

3. Results and Discussions

3.1. Solubility and Flory-Huggins Parameters

In general, in the literature short oligomers with twenty or slightly more repeat units were used to simulate the miscibility of the polymers. Such short chains may lead to end effects and cannot represent real systems accurately. When using the actual size of the polymers, the simulations could not be performed due to the limited computer data storage spaces.

Therefore finding a minimum size that could still represent the actual polymers becomes very important for the calculation of the thermodynamic parameters. To determine such minimum size, the solubility parameters of PGA and PAN are examined as a function of the chain length as shown in Figure 1.

Figure 1. Solubility parameter as a function of chain length for PGA and PAN

Figure 1 shows the solubility parameters of PGA and PAN as a function of chain length. Analysis of this graph shows that the solubility of PGA increases with an increase of the length of the chain to 25, then decreased; similarly the solubility of PAN also increased before decreasing. When the number of monomers of PGA and PAN reaches 30, the solubility parameters are almost constant. Therefore, 30 repeat units are sufficient to stand for any longer PGA or PAN chains. To increase the accuracy of simulation calculation with 30 repeat units are used.

The two polymers can blend only if the interaction parameter is lower than a critical value given by the following relation:

[picture] | (5)

Where nA and nB represents respectively the degree of polymerization of the pure polymers A and B.

A larger or positive value of Flory-Huggins interaction parameter () indicates immiscibility for blends of high molecular weight polymers. However, if is slightly higher than the critical value, the blends are partially miscible. In this case, both phases are present, one for each component of the blend.

Thus, by comparing the values of calculated by the atomistic simulation with the critical value, the miscibility of the system can be predicted [36]. PGA and PAN unit values (nA and nB) are listed in Table 1. The calculated critical values are 0.0303, 0.0386, 0.0473, 0.0463 and 0.0364 for PGA/PAN 90/10, 80/20, 70/30, 60/40 and 50/50 blends, respectively. The results of versus the weight fraction of PGA are displayed in Figure 2.

In Figure 2, the interaction parameter as a function of the weight fraction of polyglycolide is plotted. The analysis of the graph shows that for the 90/10, 80/20, 70/30, 60/40 and 50/50 compositions, the values of are all lower than the line indicating PGA and PAN blend miscibility.

3.2. Phase Diagrams of the Binary Mixture

The Blends module combines a modified Flory–Huggins model and molecular simulation techniques to calculate the compatibility of binary mixtures. The phase diagram of PGA and PAN blends is establishes from the blends Module as shown is Figure 3. Phase diagrams are useful for illustrating the compatibility of binary mixtures, which is derived from the free energy of the blend. They give information about the temperatures at which the mixture is miscible.

Figure 2. The Flory-Huggins interaction parameter as a function of weight fraction of PGA. It can be observed that the interaction parameter for A and B polymers is lower than the critical value in all the weight fraction of PGA studied

Figure 3. Phase diagram for the binary system composed of PGA/PAN

The polyglycolide phase diagram with polyacrylonitrile calculated by the mixture is shown in Figure 3, where the composition of the mixtures is given in terms of the mole fraction of the screen component. The results show that PGA is miscible with PAN at a temperature above or at the critical point of 183K.

3.3. Radial Distribution Functions

The radial distribution function (g(r)) in a system of particles describes how density varies as a function of distance from a reference particle. It reflects the characteristics of the material’s microstructure and serves to characterize the molecular structure. It is defined as:

[picture] | (6)

Where NAB is the total number of A and B atoms in the system, k is the number of time steps, is the distance interval, is the number of B (or A) atoms between r and around an A (or B) atom, and is the bulk density [37].

In Figure 4 the intra-molecular carbon atoms and intermolecular blend systems of PGA and PAN is shown. When the peak is more than 3Å, this indicates that the molecular chains belong to the crystallization system and then have a long-range order. When the peak is less than from 3Å, the molecular chains has an amorphous structure and a short-range disorder [38].

In Figure 4a we see that pure PGA and PAN have no strong peaks between 3.95 Å and 8 Å this indicates that the constructed molecular structure is amorphous. The result of Figure 4a shows that the radial distribution function curves of PGA is close to those of PAN, which also shows that the PGA/PAN blend system has good compatibility in agreement with theoretical results on polypropylene/polyamide-11(PP/PA11) blends already reported in the literature [27]. We also calculated the radial distribution function g (r) of the inter-molecular carbon atomic pairs of PGA/PAN, PGA/PGA and PAN/PAN chains in the five blends to learn more about the miscibility (Figure 4b). The radial distribution function g(r) of the inter-molecular pairs reveals the nature and the type of the interaction for un-bonded atoms. The Van der Waals and hydrogen bonding interaction scopes are 2.5 Å ~ 4.5 Å and 2.4 Å ~ 5 Å, respectively. We see that as shown in Figure 4a, there are distinct peaks of 5.5 Å for pure PGA and PAN, indicating that the main method of molecular interaction is a Van der Waals type of interaction.

Also, the radial distribution function g (r) of PGA/PAN is higher than that of PGA/PGA and PAN/PAN in all the blends, in particular the PGA/PAN 90/10, 80/20, 70/30, 60/40 and 50/50 blends. This indicates than this two polymers can blend in any proportion [37].

3.4. Free Energy and Order Parameter

For the simulation of phase separation dynamics of the blends at the mesoscopic level, the Mesodyn program is also used as a further proof. In Mesodyn simulations, it is important to realize the system stability before getting accurate and reliable data. During the Mesodyn simulations, the free energy should asymptotically approach a stable value as the system attains dynamic equilibrium [33,39]. The evolution of the free energy is a good measure of the stability of a blend system. But the free energy density is not routinely calculated for real systems and therefore its direct comparison with experimental data was not possible [40]. But the evolution of free energy is the best measure of the stability of a system.

Figure 4. Radial distribution functions of PGA and PAN

Figure 5. Evolution of free energy density as a function to time step for PGA/PAN blend for a simulation time of 250μs

The Figure 5 shows free energy density as a function of the time step for PGA/PAN blend of composition 90/10, 80/20, 70/30, 60/40 and 50/50. The analysis of the results of graph shows that the system has reached equilibrium when it has been simulated for a higher time interval exhibiting its stability.

The order parameter, Pi, defined as the volume average of the difference between local density squared and the overall density squared, is given by the following equation: (7):

[picture] | (7)

With being the dimensionless density (volume fraction) for species i. Large values of the order parameters Pi indicate stronger phase segregation while very small values indicate blend miscibility [40]. The order parameter is an important parameter when plotted against the time step to understand aspects of miscibility/immiscibility of polymer blends.

In Figure 6, the order parameter is plotted against the time step for the different PGA/PAN blends. For the 90/10, 80/20, 70/30, 60/40 and 50/50 PGA/PAN blends, the order parameter is smaller than 0.1 indicating that all the blends systems are miscible [27,40].

3.5. Mesoscopic Morphology of PGA/PAN Blends

The morphologies of the 90/10, 80/20, 70/30, 60/40 and 50/50 blends have been shown in Figure 7. The red color represents PGA and the green color represents PAN. For some blends the surfaces of the dispersed phase appear to be very smooth, strongly suggesting poor inter-facial adhesion, while in other blends, the surfaces are not smooth and blurred, indicating good inter-facial adhesion. As Figure 7 shows, the surfaces of the dispersed phase do not appear smooth and blurred; this also validates the results obtained from the atomistic simulations discussed above.

The mesophase density profiles exhibit hardly discernable PGA/PAN interfaces characteristic of miscibility as reported in the literature in the case of PP/PA11 blends for 90/10 composition while the interface was seen very clearly for composition below [27]. In our PGA/PAN blends, the results indicate miscibility in all the composition range.

Figure 6. The order parameter as a function time step for PGA/PAN mixtures for a simulation time of 250μs

Figure 7. Mesophase density profiles for (a) 50/50, (b) 60/40, (c) 70/30, (d) 80/20 and (e) 90/10. PGA/PAN blends

4. Conclusions

In this work, Molecular Dynamique simulations using Dreiding force field and mesoscale MesoDyn simulations are used to investigate the miscibility of the PGA and PAN systems. It is found that 30 repeat units are sufficient to represent a PGA chain and a PAN chain. The Flory-Huggins parameters and the phase diagrams of blend systems for PGA and PAN are constructed, and then the radial distribution function is calculated by MD. The results show that PGA and PAN are miscible for composition varying from 50/50 to 90/10. The input parameters used in MesoDyn came from the MD simulations, which indicated the morphologies, free energy, and order parameters obtained from the MesoDyn simulations further demonstrate the miscibility of PGA and PAN.

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