Polymeric Materials

Polymers are a critical class of materials central to applications from advanced carbon-fiber composites and structural organics, to semiconductor and electronics manufacture and packaging.

Background

Polymers are a critical class of materials central to applications from advanced carbon-fiber composites and structural organics, to semiconductor and electronics manufacture and packaging. Advances have been made in application performance by design and commercialization of tailored polymer chemistries and network structures to balance critical properties. Development of next generation polymer systems can be enabled by Schrödinger’s Materials Science Suite capabilities for in silico design and analysis of thousands of polymer chemistries. Outside of de novo design, the selection of suitable polymeric materials for a high-performance application is greatly hindered by the lack of reliable physical and chemical data. Often, even for polymer materials reported in the literature, complete physical and chemical properties are not available. This greatly impedes the selection of appropriate polymeric materials. Additionally, there can be wide variation in the reported properties due to differences in analytical technique, sample preparation, or procedure. Atomic-scale simulation can play an important role in the selection of polymer materials by furnishing needed information; providing reliable estimates of critical properties, computed systematically so that polymer options can be compared directly.

With GPU-accelerated molecular dynamics simulations using the extremely efficient MD engine Desmond1, and the commercial OPLS3e force-field2,3, accurate prediction of polymer properties through atomistic simulation becomes feasible for even desktop computers. The Materials Science Suite provides chemical structure and polymer builders, a chemically adaptable cross-linking simulation module (Crosslink Polymers), automated thermophysical and mechanical response simulation modules (e.g. Thermophysical Properties, and Stress Strain), and analysis tools (e.g. MS MD Trajectory Analysis) allowing users to efficiently analyze single or multiple systems. Overall, the Materials Science Suite provides a unique and powerful advantage to both experienced polymer modelers and new-to-modeling scientists and engineers.

Schrӧdinger’s iterative MD-based chemical crosslinking module (Crosslink Polymers) allows the generation of realistic chemical network models. We have developed a versatile crosslinking algorithm, capable of handling different types of chemistries and reaction procedures; greatly increasing the applicability in forming polymeric networks with diverse single molecule and multi-component chemistries. Additionally, system properties can be monitored during a crosslinking simulation within a single interface, allowing the user to estimate properties like theoretical gel points and reactive group concentrations as the system evolves.

In the case of high glass transition temperature (Tg) epoxy-based thermosets, amine-based reactants are typically used. These systems are made of various epoxy and amine constituents (Scheme 1).

Scheme 1. Representative amine (DDM, 3,3-DDS, and 4,4-DDS) and epoxy (DGEBA and TGDDM) thermoset monomers.

 

The epoxide ring can react with primary and secondary amines via a ring opening process. Primary amines can react with the alpha carbon of the epoxide ring, leading to the formation of a secondary amine and a hydroxyl group. For epoxy/amine mixtures, primary and secondary amines can be treated as separate reactions in the curing procedure. Several studies have shown that reaction rates of primary versus secondary amines are different, but there is some disagreement to the relative reaction ratio.4,5Ab initio simulations of reactants, products and transition states using the Jaguar quantum mechanics engine6 can provide reliable estimates of the kinetic barriers and overall thermochemistry controlling the curing process (Figure 1). The crosslinking simulation can take into account differing reaction rates during the curing process, enabling investigation of the dependence of structure and resulting properties on reaction chemistry and kinetics.

Figure 1. Ab initio computed relative kinetic rates for the simplified primary, and secondary amine attack of an epoxide. (All ∆∆G in kcal/mol; computed using B3LYP/6-31G* at 298.15K, 1 atm)

Glass transition temperatures can be predicted for polymeric systems using long MD cooling simulations through the GPU-enabled Desmond simulation engine (Thermophysical Properties module). The speed of GPU simulations allows for rapid calculation of the equation of state, with total simulation time in excess of 1 µs. Fitting the simulated density as a function of temperature to linear or nonlinear functions allow reliable estimation of the glass-transition temperature (Tg).8 The calculated Tg values for 39 linear acrylic polymer systems are shown in Figure 2; illustrating the ability to distinguish the transition behavior for different polymers within the same chemical class, showing good quantitative agreement provided by automated MD simulation (R2 = 0.96). 

Figure 2. Predicted vs experimental glass transition temperature (Tg) data for 39 acrylic polymer systems obtained from NPT MD simulation using Desmond with the OPLS3 force-field. Experimental data from
Ref. 7.

Mechanical elastic and ultimate performance properties can also be predicted using MD simulations (Stress Strain module). At the temperature and pressure of interest, the polymer or composite material is subjected to a series of strain controlled tensile test simulations. The stress (pressure) of the system is monitored during the simulation process and the resulting stress vs. strain curve can be used to calculate mechanical response and estimate yield.

Figure 3. The uniaxial stress/strain curve for TGDDM/3,3-DDS cured to 95% calculated using Desmond MD through the Stress Strain module using the OPLS3 force-field. Grey band indicates inflection point (yield).

Figure 3 illustrates the estimation of the yield point from the induction point of the curve. The system modulus can also be calculated from the initial slope of the curve. The stress strain simulation can be performed with a varying Poisson’s ratio.9

The miscibility of reactive components, solvents, and polymer additives such as plasticizers are a critical factor in the production and formulation of commercial polymeric materials. The solubility parameter can be calculated from the cohesive energy of condensed systems. If two compounds have similar solubility parameters, they are likely miscible. The greater the difference in solubility, the more immiscible. GPU-enabled Desmond with OPLS3 force-field enables accurate Hansen and Hildebrand solubility parameters to be calculated for a large number of molecular systems.

Figure 4. Difference in solubility parameters for various solvents and styrene expressed as a separation distance. Small separation values (red shading) indicates miscibility, large separation values (purple) indicate immiscibility. Experimental data from Ref 10 was used to indicate select good and poor solvents for polystyrene.

 

Phase separation in polymer blends and copolymer systems is a critical factor in the performance of the material. The micron size scale structure resulting from the separation can be easily captured with coarse-grained simulation. With Materials Science Suite, power of GPU molecular dynamics with Desmond has been extended to coarse-grained simulation. Approaches such as dissipative particle dynamics (DPD) can be used to capture the segregation of block copolymers such as polystyrene/polyisoprene in simulations taking just minutes of clock time.

Figure 5. Cylinder structure of [polystryene]0.25/ [polyisoprene]0.75 block copolymer formed during DPD relaxation.11

Conclusion

The unparalleled efficiency, accessibility and predictive reliability provided by Schrödinger’s Materials Science Suite greatly expands the impact atomistic simulation has in the analysis, optimization and discovery of polymeric materials. Reactivity and kinetics from quantum mechanics, and component miscibility, covalent network formation, thermophysical property, and mechanical property predictions using MD simulations enables in silico analysis of known and new candidate polymer systems through physics-based simulations. Extensive workflow automation, and ground-breaking GPU MD allows for tremendous throughput, improving statistics and simulating 100’s of polymer systems. When combined with other Materials Science Suite capabilities (eg. AutoQSAR, MS Combi) the polymer development process can be greatly enhanced.
 

 

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References

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