Theory and Modeling of Polymer Nanocomposites

This chapter is focused on Polymer Reference Interaction Site Model (PRISM) theory and its use along with molecular simulation techniques for studying polymer nanocomposites (PNCs). In the first section of this chapter, we summarize key experimental and computational studies on PNCs from the literature to show the reader the types of fundamental questions that these studies have tackled. These are the types of questions that one could also use PRISM theory to answer. Then, we describe the basics of PRISM theory with relevant equations and show how PRISM theory is linked to molecular simulations to obtain meaningful results pertaining to PNC structure and thermodynamics. We also bring to the readers’ attention the open-source package, pyPRISM, developed for both expert and novice computational researchers to easily incorporate PRISM theory into their PNC studies. We then discuss briefly past, present, and potential new directions of PNC studies using PRISM theory and conclude the chapter highlighting some of the limitations of PRISM theory.

Density functional theory (DFT) is a powerful approach utilized successfully in both quantum and classical theoretical and computational physics. Since the 1970s, DFT has been applied to predict the phase behavior of simple fluids, including the liquid-to-crystal transition in hard-sphere and Lennard–Jones fluids. Beginning in the 1990s, it was recognized that DFT can be adapted to describe the equilibrium morphologies of polymer-based nanocomposites (PNC). Here, we review various examples where DFT is applied to PNCs, from polymer–clay and polymer-nanotube mixtures to one-component hairy nanoparticle assemblies. We also discuss hybrid approaches where DFT is combined with other coarse-grained field theories, in particular, the Self-Consistent Field/Density Functional Theory (SCF-DFT) method and its applications.

For several decades polymer field theory has been an important computational and theoretical tool for predicting and interpreting the phase behavior of polymers. Many emerging applications of polymer materials involve blending polymers with nanoparticles to improve performance; however, the thermodynamics of these systems remains relatively poorly understood. In this chapter, we summarize numerous recent advances in polymer field theory with a focus on our approach to extend polymer field theory to describe polymer nanocomposites. We discuss recent applications of the methods as well as the mutual advantages and disadvantages of various implementations and conclude with a discussion of the challenges and ongoing development of the methods.

In this chapter, we focus on the polymer nanoparticle (either spherical, anisotropic or free surface) interface and specifically on polymer dynamics considering attractive interaction with the nanoparticles. We concisely report the main experimental and computer molecular simulation studies regarding the polymer mobility at the interface. We show how changes of the glass transition (\(T_\mathrm{g}\)) are correlated with segmental dynamics and relaxation at the interface.

We quantify the properties of the interfacial layers around bare nanoparticles (NPs) with variable NP diameter in model polymer-NP composites and near the solid substrate and free interfaces of supported thin polymer films using molecular simulations. These interfaces alter both the segmental packing and mobility in an interfacial layer. Variable NP diameter allows us to understand the effect of boundary curvature, where the film sets the limiting value of zero curvature. We find that the interfacial mobility scale \(\xi \) for both NPs and supported films increases on cooling, reaching a scale on the order of a few nanometers at low temperatures, regardless of the polymer-interfacial interaction strength. Additionally, we consider the related problem of the interfacial mobility scale of supported polymer films, which provides an upper limit for the interfacial scale of polymer-NP composites as the particle increases in size to macroscopic dimensions. We also characterize the interfacial density gradient scale \(\xi _\rho \) near the NP surface and find, in contrast to the length scale from dynamics \(\xi \), that \(\xi _\rho \) is even smaller and decreases on cooling in all cases simulated. In other words, the interfaces generally become more sharply defined on cooling. On the other hand, the scale of fluctuations in the interfacial density \(\sigma _{\rho }\) near solid interfaces, which reflects the degree of packing fluctuations, and thus “packing frustration”, grows on cooling and correlates in a near linear fashion with the interfacial mobility scale \(\xi \), although these characteristic thermodynamic and mobility scales have different dependences on the strength of interfacial interaction. Conversely, \(\sigma _{\rho }\) for the free interface in thin films grows on heating, similar to that of \(\xi _\rho \). Having characterized the thickness of interfacial layers from both structure and dynamics, we also examine their effect on the overall relaxation of materials and the glass transition temperature \(T_\mathrm{g}\) based on both thermodynamic and dynamic criteria. In particular, when the interfacial interaction strength is greater than the polymer-polymer interaction strength, a “bound” polymer layer forms near the interface (either the nanoparticle interface or film substrate), giving rise to an additional relaxation process in the self-intermediate scattering function. As a result, we find that \(T_\mathrm{g}\), defined from the gradient in the structural relaxation time, increases monotonically with polymer-interface interaction strength \(\varepsilon \). In contrast, the thermodynamically defined \(T_\mathrm{g}\), defined from “kinks” in the temperature dependence of quasi-thermodynamic properties, is found to saturate to a nearly constant value for \(\varepsilon \) values greater than the polymer-polymer interaction strength since this bound polymer layer effectively “cloaks” the NP or substrate from the unbound polymer from the strong interfacial interactions. Our findings emphasize the quantitative relationship between the interfacial scales in nanocomposites and thin polymer films and show that interfacial effects are rather universal in systems having significantly mobility gradients.

Renewable energy production from fuel cells and energy storage in flow batteries are becoming increasingly important in the modern energy transition. Both batteries use polyelectrolyte membranes (PEMs) to allow proton transport. In this chapter, both PEMs and PEMs-based nanocomposites have been discussed using various simulational approaches. A coarse-grained model of a Nafion film capped by the substrates with variable wettability has been used to simulate nanocomposites of PEMs by classical molecular-dynamics (MD) method. Classical MD modeling results have also been reviewed for a PEM-graphene oxide nanocomposite internal structure and dynamics. Ab-initio simulations have been implemented to describe the proton transfer pathways in anhydrous PEMs. Finally, the large-scale mesoscopic simulations have been introduced to shed light on the water domain features present in the hydrated PEMs. A brief description of polybenzimidazole membrane as electrolyte and Ionic Liquids as dopants for fuel cells is also presented.

This chapter summarizes recent investigations into the mechanical behavior of matrix-free hairy nanoparticles using molecular simulation techniques. Generic as well as systematic coarse-graining techniques are presented, highlighting emerging methods for chemistry-specific modeling of polymeric materials. Applications of coarse-graining to study assembled hairy nanoparticle systems are overviewed, with an emphasis on quantitative structure–property relationships obtained from these investigations. Comparisons of simulations with theoretical scaling relationships such as the Daoud-Cotton theory and experimental data are provided. Methods to accelerate the design space through upscaling techniques and metamodel development are briefly overviewed. Key physical insights obtained from these studies on the effects of grafting density, grafting length, and polymer chain chemistry are mentioned throughout the chapter to illustrate the importance of modeling contributions. A brief outlook into the prospects of using novel mesoscopic approaches such as those based on potentials of mean force is noted. The chapter concludes with a summary and outlook on the state of the art of the computational design of assembled hairy nanoparticles.

The mechanical properties of nano-structured materials are important field of exploration in the fields of materials science and other engineering disciplines. Thorough understanding of underlying material structure and resulting properties require a variety of tools depending on the length scales of interest. This chapter reviews continuum mechanics-based techniques, with an emphasis on micro-scale modeling techniques: analytical and computational. In addition to micro-mechanics, different approaches to multiscale modeling are presented. With the appropriate choice of techniques, models can be bridged across multiple length scales leading to mechanistic understanding of the mechanics of materials. Some illustrative examples are also discussed that utilize the techniques presented here.

In many applications (LED lighting, consumer electronics, transportation, and others), successfully managing/removing the excess (“waste”) heat is crucial to successful performance. This, in turn, requires materials with sufficiently high thermal conductivity values. However, most polymers are characterized by relatively low thermal conductivities (κ < 1 W/m K). Thus, in many applications, it is necessary to design hybrid materials (composites and nanocomposites) with the processability of polymers and thermal conductivity close to that of ceramics or other inorganics (κ ~ 1–10 W/m K). Theory and modeling are widely used to understand the design rules for the development of such composite materials. Here, we review the recent progress in this field, describing methods of predicting thermal conductivity of (nano)composites as function of their composition and the properties of the constitutive materials (matrix and fillers).

Nanoparticles are frequently combined with polymers to create polymer nanocomposite materials with enhanced electrical, optical, or transport properties. In addition to the robust suite of theoretical techniques—including molecular dynamics, Monte Carlo simulations, and polymer field theory—that exists to predict structural information of such polymer nanocomposites, there is also a sizeable selection of techniques available to predict physical properties such as optical scattering/absorption and electrical/ionic conductivity of these materials. In many instances, techniques for predicting structural information may be coupled to those used to predict physical properties. This chapter presents a survey of common approaches to modeling both the optical and electrical properties of polymer nanocomposites, explaining the foundations of each technique, limitations, and highlighting select examples from the literature using each technique.

Modern tire compound design is confronted with the simultaneous optimization of multiple performance properties, most of which have tradeoffs between the properties. In order to uncover new design principles to overcome these historical tradeoffs, multiscale compound experiment, physics, and simulation are being developed and integrated into next-generation design platforms across the tire industry. This chapter describes the efforts in our laboratories to quantify compound structures and properties at multiple scales—from nanometers to microns—and their application in compound simulations. This integration of experiment and simulation has been found to be critical to highlighting the levers in data-driven multiscale compound design. We also provide a glimpse into the next set of capabilities, particularly from data science, which will impact future compound design.