Some issues in polymer nanocomposites: Theoretical and modeling opportunities for polymer physics

Authors


Addition of fillers to polymers has long been used as a strategy to enhance the properties of polymers. In the last two decades, however, a class of materials termed as “polymer nanocomposites” (PNC) has evolved to refer to blends of polymers and inorganic fillers in which the inorganic component has one or more dimensions below 100 nm.1–3 Examples of such materials include mixtures of a variety of homopolymers and multicomponent polymers blended with fillers such as clays, nanotubes, Fullerenes, polyhedral oligomeric silsesquioxanes (POSS), nanoscopic silica particles, and so forth.2–7 Initial interest and research in such materials arose from the significant property enhancements reported for extremely low loadings of nanofillers. These reports fueled intense research into the mechanical, electrical, barrier, and fire retardancy properties of PNCs and have led to some notable commercial technologies utilizing PNCs.1, 8–10 More recent efforts have expanded the above class of studies and materials by examining the properties of nanocomposites involving polymer blends and block copolymers, where the potential to create multifunctional materials possessing novel electrical, magnetic, and optical properties have been reported.11, 12 However, despite the scale of intense research on PNCs, much of the initial promise of PNCs has not yet borne out. In this viewpoint article, I present an (admittedly) personal perspective of some of the issues confronting the field of PNCs, focusing especially on the opportunities by which theory, modeling, and computer simulations from polymer physics may aid in realizing the full potential of PNCs.

STRUCTURE AND DISPERSION CHARACTERISTICS OF PNCs

Many of the common nanofillers used in PNCs are unfortunately characterized by strong van der waals interparticle attractions, which promote their agglomeration.13 Moreover, the effective interactions between nanofillers are also influenced by the polymer-filler interactions, and if the latter are unfavorable, it leads to conditions conducive to the aggregation of the fillers. Aggregation and clustering of the fillers typically leads to a significant reduction in the interfacial contact between the fillers and the polymer and hence a deterioration of the property enhancements that can be attained in PNCs. Consequently, achieving stable, dispersed configurations of nanofillers in the polymer matrix is a prime requirement to realize the full property potential of PNCs.

Many experimental strategies have been explo-red to overcome the above challenge.14 These have ranged from using polymer-filler combinations, which are known to exhibit favorable affinities to functionalizing the fillers by self-assembling surfactant and grafting polymers to promote favorable polymer-filler interactions (and provide a steric barrier against agglomeration). Also, successful strategies using external fields to promote nonequilibrium dispersion of the nanofiller have been demonstrated.15 From a theoretical perspective, the outstanding question confronting the design of such strategies is “For specified combination of matrix polymer(s), filler(s), the functionalizing moieties and/or external fields, can we predict the equilibrium and nonequilibrium structural characteristics of the PNC dispersion?”

There has been significant progress in theories, models, and simulation approaches, which have addressed different aspects of the above question. Most such theories and models use a coarse-grained perspective where simple micromechanical representations are used for the polymers and fillers, with their interactions represented by few coarse-grained parameters. Using such representations, theories and simulations based on PRISM,16–18 self-consistent field approaches,19–22 field-theoretic,23 and molecular dynamics simulations24–26 have addressed the equilibrium structure and phase behavior of mixtures of (mostly) spherical nanofiller units dispersed in homopolymers, polymer blends, and block copolymers. Despite these advances, a number of open issues relevant to PNCs still remain:

  • (a)Anisotropy of fillers: Most of the PNCs explored for applications involve filler particles such as clays, carbon nanotubes, nanofibers, and so forth, which exhibit considerable shape anisotropy. Indeed, such fillers prove most suitable for exploiting significant polymer-filler interfacial contact at even extremely low loadings of the filler. In contrast, very few of the aforementioned theories and simulations deal with the phase behavior and structure of mixtures of anisotropic fillers dispersed in single and multicomponent polymers.27–29 The rich literature of colloidal physics suggests that the equilibrium characteristics of anisotropic colloids can be expected to be significantly different and richer compared with their isotropic counterparts.30 Moreover, situations combining anisotropic fillers with multicomponent polymers such as block copolymers can be expected to reveal a rich interplay between polymer self-assembly and colloidal phase behavior. It will be of significant interest to PNC research to translate some of the theoretical advances achieved in the context of spherical fillers to the corresponding situations involving anisotropic fillers.
  • (b)Role of Functionalization: As mentioned earlier, functionalization of the fillers is a common strategy to overcome the issue of agglomeration of fillers. However, in much of the existing theories, the role of functionalization is treated either empirically as a modified polymer-filler interaction18, 23 or in more detailed formalism as a modification of the effective polymer-mediated potentials between the fillers. The first approach can be deemed reasonable for small oligomeric or surfactant-like functionalizers, but suffers from the drawback that it leaves open the question of the relationship between the polymer-filler interaction and the physicochemical properties of the functionalizing group. The second approach has typically been effected for the situation of grafted polymer functionalizers.31 It is, however, a pairwise interaction approach that works only for the homogeneous phase of the polymer matrix and in addition neglects multibody effects, which may become important when either long grafting polymers or higher concentrations of fillers are used. Overall, it would be desirable to develop a suite of simulations and/or modeling tools that, similar to the nongrafted case, can obviate such assumptions while still being able to predict the structure of the PNC dispersion.
  • (c)Structure under nonequilibrium and external field conditions: Despite the best experimental strategies, nonequilibrium effects resulting from filler aggregation and/or external fields are bound to remain important for many applications of PNCs, especially for situations involving anisotropic fillers. Some unresolved questions include: “How does the structure of a PNC dispersion evolve upon dispersing the fillers in the polymer matrix?,” “Can quantities such as the fractal dimension and cluster size distributions be predicted for specified polymer-filler combinations?,” “How does externally applied shear, electric, and magnetic fields (and combinations thereof) impact upon the nonequilibrium state of the dispersion?” Although computer simulations may shed light on some of the relevant issues, the time and length scales, which can be probed by such means may not necessarily overlap with experimental regimes, and there is a need for development of appropriate theoretical models to address pertinent issues. There have been some notable theoretical advances in this regard in the context of colloidal science,32, 33 and a preliminary assessment of their applicability to the field of PNCs would be extremely beneficial. However, issues unique to PNCs, such as the significant anisotropy of the fillers, potentially long-ranged interparticle interactions (mediated by the polymers), the dynamical and rheological response of the polymer matrix, are expected to prove important and provide fertile and challenging areas for theoretical research.
  • (d)Detailed structural characteristics: Many experimental studies of the mechanical, electrical, and rheological behavior of PNCs have suggested an intimate connection between enhanced macroscopic properties and the percolation behavior of the fillers.10, 34–36 Although such features can be directly extracted in computer simulations, existing theoretical frameworks mostly concern with the phase behavior and/or structural features at a pair correlation level. It may be of interest to the PNC experimental community to develop a theoretical framework, which can predict the the influence of different interactions, functionalization, and external fields upon more detailed structural characteristics such as the percolation characteristics37, 38 fractal and cluster dimensions of the fillers in the polymer matrix.
  • (e)Connection to atomistic details: Much of the above discussion focused on some open questions in the context of structure of PNCs as examined from a “coarse-grained” polymer physics perspective. Although such efforts are valuable for providing design guidelines, deducing mechanistic underpinnings and suggesting new experimental strategies, questions involving the detailed chemistry of the filler, polymer and functional groups cannot typically be answered in such frameworks. This situation is compounded by the fact that much of the coarse-grained modeling of PNCs use potentials and interaction parameters, which cannot also be directly determined from experimental measurements. The latter contrasts with the analogous situation in multicomponent polymer melts and solutions where experimental solubility measurements provide direct information on the parameters used in the corresponding coarse-grained theories.39 Addressing this shortcoming in the context of PNCs requires the development of efficient computer simulation tools and methodologies, which can render the connection between the chemistry of the components and the coarse-grained parameters more quantitative. The research field of “coarse-graining methodologies” is undergoing intense development in the context of simple and polymeric fluids.40–42 Although some notable “multiscale” efforts have also occurred in the context of PNCs,43, 44 much work remains to be done in surmounting the time, length scale challenges accompanying the interactions, structure, and properties of PNCs.

CONNECTING THE STRUCTURE TO PROPERTIES

Ultimately, PNCs are designed to exploit the value addition in properties that result over and above that of the pure polymer matrix alone. Because it is commonly acknowledged that the underlying structure of the polymer(s) and fillers influence the macroscopic properties, controlling the structure of the PNC provides an indirect means to control the properties of PNCs. However, achieving success in this effort requires knowledge of an equally, if not more important component, viz., the quantitative connection between the structure and the property of interest. Unfortunately, establishing such connections and models have remained somewhat elusive for PNCs. This might seem somewhat surprising, considering that theories for macroscopic mechanical, electrical, and optical properties of two (or more) phase dispersed media have had a long history of development and experimental validation.45 However, many experimental studies have reported that such theories prove less than satisfactory in their ability to model the macroscopic properties of interest in the context of PNCs.9, 46 Two issues can be identified as partially responsible for this situation:

  • (i)Detailed structural information: Much of the aforementioned macroscopic theories were developed for model structural representations such as random or completely aligned dispersions while ignoring PNC specific features such as aggregation and/or complex structural arrangement of the fillers. Consequently, it is not surprising that such ideal models cannot quantitatively predict the properties of PNCs. One potential area for future research is the development of macroscopic models capable of accommodating detailed structural information, such as experimentally obtainable pair correlation functions of the fillers or cluster sizes and fractal dimension of aggregates, while rendering quantitative predictions regarding the macroscopic properties of PNCs. This area has recently seen some notable advances, especially arising from numerical continuum mechanical approaches.47–49 It may be envisioned that the results of such efforts can be used to guide the refinement of classical models to accommodate the PNC specific features.
  • (ii)Interfacial effects: An important feature that distinguishes PNCs from traditional composites is the presence of significant amounts of polymer-filler interfaces and its influence upon the macroscopic properties. To highlight the resulting issues, I point out the status with respect to the “simpler” situation of polymer films supported on a solid substrate. In such contexts, experiments have clearly demonstrated that the polymer-surface interactions can lead to properties for the polymer layer, which are in general markedly different from that of the bulk polymeric material.50 Moreover, for properties such as glass transition temperatures,51 aging dynamics,52, 53 and elastic moduli,54 the interfacial effects have been shown to persist to extremely long length scales relative to the physical dimensions of the polymer.

Most of the existing macroscopic models for dispersed media and composites do not satisfactorily account for the above interfacial effects. Indeed, classical models treat the interface between dispersed media either as a boundary condition for the field equations or by incorporating a fictitious “interfacial” phase characterized by properties different that of the bulk polymer. Such a framework is usually expected to be reasonable for situations where the length scale of variation of the interfacial properties is much smaller than both the radii of the fillers and the variations in the macroscopic fields (stress, electrical fields etc.) set up due to the introduction of the filler. For PNC systems, two major shortcomings need to be addressed for successful application of such models to property predictions:

  • (a)In the context of properties that exhibit only a short ranged interfacial effects (such as solubility of penetrants and mechanical properties), the aforementioned approaches may suffice to accommodate the influence of polymer-filler interfaces upon macroscopic properties. However, to endow a predictive value to theories, quantitative connections between the physicochemical polymer-filler interactions and the properties of the interfacial layer (or the parameters in the boundary conditions) in such models needs to be established. Although computer simulations may aid in this effort, in many cases, new formalisms may be necessary to discern quantities such as “local” mechanical properties,55 “local” conductivities, “local” penetrant diffusivities, and so forth, in such efforts. Once the connections between polymer-filler interactions and the interfacial properties are firmly established, “homogenization theories” similar to that used for the macroscopic properties of composites and dispersed media may be pursued. However, such approaches still need to be augmented to account for the possibility of complex structural arrangement of the fillers (an issue discussed earlier) and the overlap of interfacial layers which may consequently arise.
  • (b)As discussed earlier, some interfacial properties (such as the glass transition temperatures) are known to display long ranged variations influenced by the surface of the fillers, and in such cases, boundary condition and/or three-phase model approaches are likely to prove inadequate for capturing the influence of polymer-filler interfaces upon the macroscopic properties of the system. Refining the existing models to account for such properties represents an extremely challenging task, because in many cases there is a lack of understanding of the physics underlying such long ranged variations in polymer thin films. Moving to PNCs brings even more complications, such as the possibility for overlap of interfacial layers arising from different particles (such overlaps become very likely for long-ranged effects), leading to significant multibody interaction effects. Overall, this is an area for which the directions of theoretical modeling are far less clear (to me), suggesting that radically new ideas may be necessary to make progress in understanding and predicting the properties of polymer thin films and PNCs.

CONCLUSIONS

The above represents an opinionated selection of some of the open questions confronting theoretical modeling of polymer nanocomposite systems. While active research is in progress in a number of the above-mentioned areas, successful fruition in many of the issues requires a confluence of ideas from different fields, viz., colloid and polymer physics, statistical and continuum mechanics, modeling and simulation approaches, and most importantly, experiments and theories. While technology and experiments are likely to provide more focus to the issues and theoretical efforts, progress in the above delineated issues is expected to have significant fundamental implications for many related areas of polymer and colloidal science, and may also potentially lead to uses and applications of PNCs above and beyond what has been realized or even dreamed about.

Acknowledgements

This research program on polymer nanocomposites has been graciously supported by research grants from the National Science Foundation, American Chemical Society, Air Force Research Laboratories, Robert A. Welch Foundation, and the US Army Research Office under grant W911NF-07-1-0268. The author thanks Dr. Victor Pryamitsyn for useful comments which helped to shape the ideas expressed in this viewpoint. The author also acknowledges Profs. Glenn Fredrickson, Kenneth Schweizer, John Torkelson, Peter Green, Donald Paul, Jack Douglas, Sanat Kumar, Richard Vaia, and Ramanan Krishnamoorti for many discussions over the years while patiently educating him on the issues in polymer nanocomposites.