Article pubs.acs.org/IECR
Molecular Dynamics Simulation on the Binder of Ethylene Oxide− Tetrahydrofuran Copolyether Cross-Linked with N100 Yanhua Lan, Dinghua Li,* Jinxian Zhai, and Rongjie Yang School of Materials Science and Engineering, Beijing Institute of Technology, Beijing, 100081, China S Supporting Information *
ABSTRACT: Ethylene oxide−tetrahydrofuran copolyether (P(E-co-T)) crosslinked with isocyanate Desmodur (N100) is widely used as the binder system in solid energetic propellant. The effect of its cross-linking degree on the physical properties is important for the evaluation of the propellant binders. In this work, an efficient method was presented for simulating the crosslinking process, predicting the microscopic behaviors and macroperformances of cross-linked P(E-co-T)−N100 binder systems. During the simulation of cross-linking network forming, the initial physical mixture model of P(E-co-T)/N100 was firstly constructed and optimized through molecular dynamics. Then the possible cross-linking topology was generated by means of the identification of the reactive site pairs. In this way, the P(E-co-T)−N100 cross-linking pathway was realized by alternate structure optimization and junction reaction. The cross-linking intermediate models were analyzed, and the density and mechanical property profiles have revealed the increasing tendency with cross-linking progressing, which is corresponding to the experimental results. Moreover, volume−temperature behaviors of P(E-co-T) and cross-linked P(E-co-T)−N100 systems were simulated to study the cold resistance characterized by glass transition temperature. The mean-squared displacements and free volume data have verified that the cross-linking structure of P(E-co-T)−N100 restricts the molecular mobility, which is helpful to explain the higher glass transition temperature and stronger mechanical properties.
1. INTRODUCTION The hydroxyl-terminated polyether binder plays an essential role in binding the filler particles and other additives together to form a grain composite material with satisfactory mechanical behaviors.1 Ethylene oxide−tetrahydrofuran copolyether P(Eco-T) (shown in Figure 1) is widely used in nitrate ester
As for solid composite propellants, specimen preparation and formulation optimization usually spend much time and money with high danger.10 So it is important to predict the properties of composite propellants before experiments by means of molecular simulation. Among the literature related to the crosslinking simulation, most of the simulated works have focused on epoxy systems11−16 while the cross-linking process of propellant binder is scarcely studied. Furthermore, almost all of simulated precursors are monomers,11−17 while the common propellant binders are the elastomer systems of prepolymer/cross-linker.2,8,9 The prepolymers with long chain molecules decrease the possibility of contact between functional groups of cross-linking system. So it is necessary to simulate the cross-linking process of longchain prepolymer with cross-linker, which can contribute to the formula development theoretically. For the propellant application, a good binder is required to have low glass transition temperature, good mechanical properties, and proper density. In this work, the molecular models of the cross-linked P(E-co-T)−N100 system were constructed by stepwise junction reaction and structure optimization. Density and mechanical properties of P(E-coT)−N100 in different cross-linking degree were calculated to study the effect of microscopic structure on the macroperformances. Volume−temperature (V−T) behaviors, meansquared displacements, and free volumes of cross-linked P(E-
Figure 1. Molecular formula of P(E-co-T) binder.
plasticized polyether (NEPE) energetic propellants because of its uncrystallizable behavior at room temperature and good compatibility with other propellant ingredients.2−4 The cross-linked P(E-co-T) network is the principal factor in determining the ultimate physical and mechanical properties of NEPE propellant.5,6 The P(E-co-T) prepolymer usually reacts with a trifunctional isocyanate curing agent Desmodur N100, whose representative structure is shown in Figure 2.7 Many research studies have focused on the formula and physical properties of cross-linked P(E-co-T)−N100,8,9 while little attention is paid to the change in the cross-linking process.
Received: Revised: Accepted: Published:
Figure 2. Molecular structure of Desmodur N-100. © 2015 American Chemical Society
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January 14, 2015 March 24, 2015 March 26, 2015 March 26, 2015 DOI: 10.1021/acs.iecr.5b00187 Ind. Eng. Chem. Res. 2015, 54, 3563−3569
Article
Industrial & Engineering Chemistry Research co-T)−N100 system were simulated and used to explain the predicted glass transition temperature.
2. MODELS AND COMPUTATIONAL DETAILS 2.1. Model Construction. All simulations were performed using the software modules, Amorphous builder and Forcite, as implemented in the commercial platform Materials Studio (version 6.0, Accelrys, San Diego, CA, USA). The structure of P(E-co-T) (molecular weight of 4098 g·mol−1) and crosslinking agent N100 are respectively shown in Figures 1 and 2. As for the modeling, P(E-co-T) amorphous cell contained 2 P(E-co-T) chains with 40 repeat units, while P(E-co-T)/N100 blends consisted of 6 P(E-co-T) chains and 8 N100 molecules, so the mass ratio of P(E-co-T) to N100 could be pinned to 22:3, corresponding to the mixture composition in the experiments.18 R is defined as the equivalent ratio of the cross-linker functional group and the prepolymer functional group;8 therefore, the molar ratio (R) of isocyanate (NCO) to hydroxyl (OH) is 2 in this simulation. The structures of two amorphous systems are illustrated in Figure 3.
Figure 4. Geometry energy-minimization algorithm.
final 50 ps should be equilibrated. The data of final 50 ps of NPT MD simulation are used to analyze the volume− temperature (V−T), free volume−temperature (FV−T) behavior, and the mean-squared displacements (MSD) of the model are analyzed through a full 1000 ps NVT simulation. Furthermore, the cold resistance is evaluated through glass transition temperature on the basis of the above V−T, FV−T, and MSD−T data.19 The Coulomb and nonbond interactions are handled by the standard Ewald and atom-based summation methods, respectively. Nonbond interactions, spline width, and buffer width are specified to be 9.5, 1.0, and 0.5 Å, respectively. The Andersen20 and Berendsen21 algorithm are respectively used for temperature (thermostat) and pressure (barostat) control, under a collision rate of 1.0 and a decay cutoff of 0.1 ps. The COMPASS force field is applied to study the structures and properties of all systems in the whole MD simulation. Its parameters are debugged and ascertained from the ab initio calculations, optimized according to the experimental values, and parametrized using extensive data for molecules in the condensed phase. Its nonbond parameters are further amended and validated by the thermophysical properties of the molecules in liquid and solid phases. COMPASS is able to accurately predict the structure, conformation, vibration, and thermophysical properties for a broad range of compounds in both isolation and condensed phases.22−26 That is the reason why we perform MD simulations of P(E-co-T) and cross-linked P(E-coT)−N100 systems with COMPASS. 2.3. Cross-Linking Reaction. The functional groups of P(E-co-T) and N100 involved in the cross-linking reaction are hydroxyl and isocyanate, respectively. Considering that the molar ratio (R) of isocyanate (NCO) to hydroxyl (OH) is 2, there are 12 OH groups and 24 NCO groups in the system to make sure the cross-linking reaction of OH groups complete. The cross-linking occurs at a temperature of 333 K (60 °C) following the reaction route in Figure 5, where hydroxyl and isocyanate groups generate amino methyl ester group that contributed to form the cross-linking network. Figure 6 shows the cross-linking process algorithm, and some simulation details in cross-linking reaction of P(E-co-T) and N100 are presented as follows.
Figure 3. Molecular module of P(E-co-T) (a) and P(E-co-T)/N100 (b): C, gray; H, white; N, blue; O, red; N100 in CPK molecular style.
2.2. Geometry Energy Minimization and Property Prediction. Usually, the initial established amorphous structure is in a relatively high-energy state, so it is necessary to optimize the initial structure before the performance prediction. Figure 4 displays the detail geometry energyminimization algorithm. Before annealing calculations, 5000 steps of energy minimization are performed to relax the structure based on the smart minimizer method. Then the relaxed structure is subjected to 5-repeated-cycle annealing from 300 to 600 K and back to 300 K with 50 K intervals in order to overcome the local energy barriers, and a total of 1200 ps simulation is performed at constant temperature and pressure (NPT) ensemble. At the end of each annealing cycle, the structure is always energy-minimized again. As the geometry optimization is completed, the final conformation is extracted for further simulation. Subsequently, the structure model is heated to temperature of 400 K, which is well above the glass transition temperature and then cooled to 100 K with 25 K intervals. At each temperature, the system is relaxed by means of 1000 ps of NPT molecular dynamics simulation, followed by 1000 ps of constant temperature and volume (NVT) simulation. In order to ensure that the simulation time is sufficiently long for the geometry equilibrium, it is used as criterion that the density of 3564
DOI: 10.1021/acs.iecr.5b00187 Ind. Eng. Chem. Res. 2015, 54, 3563−3569
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Industrial & Engineering Chemistry Research
double bonds of CN in N100 were opened to form C−N single bond. Subsequently, new chemical bonds C−O and N− H were respectively created. After such one step cross-linking reaction, the P(E-co-T)/N100 model was modified as the initial state of updated cross-linked molecular system. (5) As the stepwise cross-linking reaction goes on, it is necessary to judge the cross-linking end. If the cross-linking degree did not reach 100%, the algorithm jumped to step 2. Otherwise, the new cross-linked geometry would be relaxed according to the method in step 2 and then stopped. Figure 7 has displayed the final fully cross-linked P(E-co-T)−N100 molecular system model.
Figure 5. Reaction route between P(E-co-T) and N100.
Figure 7. Fully cross-linked P(E-co-T)−N100 molecular system model.
(6) The conformation with minimum energy, relaxed in step 2, was studied in stepwise cross-linking process, while the density and mechanical properties were analyzed by the data of the final 50 ps in the statistical methods.
Figure 6. Cross-linking process algorithm.
(1) Initial cutoff distances as well as cross-linking limits (in terms of %) are defined for the cross-linking algorithm. The interatomic distance of 9.5 Å is taken as a reaction cutoff distance; that is to say, the groups separated by the longer distance are considered nonreactive. The cross-linking limit is set to be 100%. (2) The energy minimization of P(E-co-T)/N100 amorphous cell was carried out according to the algorithm in Figure 4. After the annealing, the system was equilibrated at 333 K through 1000 ps of NPT and 1000 ps of NVT MD simulation. With density used to evaluate the system equilibration, the P(Eco-T)/N100 system achieved the idealistic conformation with the lowest energy. (3) Subsequently, the resulting model of the P(E-co-T)/ N100 physical mixture was analyzed to identify the potential reactive sites in close proximity. The sites were considered to be the most probable to participate in the cross-linking reactions according to the steric effects. The cross-linking reactivity order has been taken into account, and the priority to react has been scheduled for the closest interatomic distance. In order to avoid the strain increase of the molecular system, only the closest active sites were chosen to react at every turn. If there was no such pair within cutoff distance, the simulation should go back to step 2 for further geometry minimization. (4) The reaction sites identified in the previous step were chemically reacted by hand operation, shown in Figure 5. Single bonds of H−O in P(E-co-T) molecules were eliminated, and
3. RESULTS AND DISCUSSION 3.1. Density Change of P(E-co-T)−N100 in the CrossLinking Process. The density of the cross-linked P(E-co-T)/ N100 binder system is an important factor for the preparation of propellants due to different cross-linking degree.27 The density gives us an indication to know how tightly or loosely
Figure 8. Density change of P(E-co-T)−N100 along with cross-linking degree. 3565
DOI: 10.1021/acs.iecr.5b00187 Ind. Eng. Chem. Res. 2015, 54, 3563−3569
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Industrial & Engineering Chemistry Research Table 1. Mechanical Properties of Cross-Linked P(E-co-T)− N100 Systems system
E, GPa
K, GPa
G, GPa
K/G
not cross-linked P(E-co-T)/N100 50% cross-linked P(E-co-T)−N100 100% cross-linked P(E-co-T)−N100
0.72 0.92 1.21
2.87 4.65 8.98
0.44 0.59 0.80
6.52 7.88 11.23
the molecules are packed in the network structure. Figure 8 displays the density curves of P(E-co-T) cross-linked by N100 along with cross-linking degree, while cross-linking degree is defined as the ratio of the number of cross-linked hydroxyl groups to that of the initial hydroxyl groups. The density of cross-linked P(E-co-T)−N100 increases in linear tendency with cross-linking reaction progressing, which reveals that the P(E-co-T)−N100 network structure is more compact than the un-cross-linked P(E-co-T)/N100 mixture. As the first cross-linking site is formed, the density of the system is 1.031 g/cm3, and the density increases to 1.047 g/cm3 as all the OH groups are transferred to urethane groups. The calculated density value of fully cross-linked P(E-co-T)−N100 is a little lower than the experimental data (1.052 g/cm3) tested by Archimedes principle methods. The difference is mainly owing to more un-cross-linked N100 dangling chains in the simulation system, since the molar ratio of OH group and NCO group is 1:2 in our cross-linking system model and the molar ratio is 1:1.2 in the experiments. Reference 28 also observed a similar phenomenon in the cross-linked epoxy simulation. In other words, the density of cross-linked P(E-co-T)−N100 depends on both the cross-linking degree and the un-crosslinked dangling groups. 3.2. Mechanical Property of P(E-co-T)−N100 in the Cross-Linking Process. Material stress and strain tensors are denoted by σ and ε, respectively. They are applicable for materials exhibiting small deformations when subjected to external forces. Thus, constant stress molecular dynamics was used to study the elastic moduli, which can be calculated from the stress−strain behavior of a material subjected to an applied load. The dependence of the stress on the strain for elastic materials can be written as in eq 1.29 σij = Cijklεkl
Figure 10. Volume−temperature results of P(E-co-T) and fully crosslinked P(E-co-T)−N100 structures.
fully describe the stress−strain behavior of an arbitrary material.29 Thus, σ and ε are expressed by eqs 2 and 3: N
σ=−
ε=
1 T T [(∑ mi(vv i i )) + (∑ rijfij )] V0 i = 1 i
