192 O.H.Zeng et al.Prog.Polym.Sci.33 (2008)191-269 2.2 oscale method Brownian dynamics 187 Dissipative particle dynamics.. attice B ndent Cinburg-Landau method. 225 Dynamie DFT method 2.3. e and macroscale methods 132 self-similar ppr 2.3.3 Finite element method. 204 3.Modeling and simulation of polymer nanocomposites.................................... 32 Nanocomposite thermodynamics........................ Nanocomposite molecular structure and dynamic properties. 213 osite morphology 342 3 Nanocomposite rheological and processing behaviors. 222 6 al properties .......... 。。。，。。。。。。 36 Continuum models 3.6.3 Equivalent-continuum and self-similar models 42 Sequential and concurrent approaches 4.3 Current research status......................... 155 Ks. References 261 1.Introduction 2 the hierarchical characteristics of the structure and dynamics of polymer nanocomposites ran- Polymer materials reinforced with nanoparticles ging from molecular scale,microscale to mesos- (e.g..nanosphere,nanotube,clay platelet)have recently cale and macroscale,in particular,the molecular received tremendous attention in both scientific and structures and dynamics at the interface between industrial communit s due to their extraordinary nanoparticles and polymer matrix: 0J.However,fror point on the ion of nanopart fabrication of polym sites.Tpu mechan ment of such materials is still largely empirical and a isms of nanoparticles in polymer nanocomposites. finer degree of control of their properties cannot be achieved so far.Therefore.computer modeling and simulation will play an ever-increasing role in predict The purpose of this review is to discuss the application of modeling and simulation techniques to ing and designing material properties,and guiding suck polymer nanocomposites.This includes a broad subject covering methodologies at various length and time ntal is We les and many aspects o for th 1.the thermodynamics and kinetics of the forma an he ughly divided int tion of polymer nanocomposites:2.2. Microscale methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 2.2.1. Brownian dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 2.2.2. Dissipative particle dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 2.2.3. Lattice Boltzmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 2.2.4. Time-dependent Ginzburg–Landau method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 2.2.5. Dynamic DFT method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 2.3. Mesoscale and macroscale methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 2.3.1. Micromechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 2.3.2. Equivalent-continuum and self-similar approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 2.3.3. Finite element method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 3. Modeling and simulation of polymer nanocomposites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 3.1. Nanocomposite thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 3.2. Nanocomposite kinetics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 3.3. Nanocomposite molecular structure and dynamic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 3.4. Nanocomposite morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 3.4.1. Homopolymer nanocomposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 3.4.2. Block copolymer nanocomposites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 3.5. Nanocomposite rheological and processing behaviors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 3.6. Nanocomposite mechanical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 3.6.1. Molecular models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 3.6.2. Continuum models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 3.6.3. Equivalent-continuum and self-similar models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 4. Multiscale strategies for modeling polymer nanocomposites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 4.1. Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 4.2. Sequential and concurrent approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 4.3. Current research status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 5. Concluding remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Acknowledgment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 1. Introduction Polymer materials reinforced with nanoparticles (e.g., nanosphere, nanotube, clay platelet) have recently received tremendous attention in both scientific and industrial communities due to their extraordinary enhanced properties [1–10]. However, from the experi￾mental point of view, it is a great challenge to characterize the structure and to manipulate the fabrication of polymer nanocomposites. The develop￾ment of such materials is still largely empirical and a finer degree of control of their properties cannot be achieved so far. Therefore, computer modeling and simulation will play an ever-increasing role in predict￾ing and designing material properties, and guiding such experimental work as synthesis and characterization. For polymer nanocomposites, computer modeling and simulation are especially useful in addressing the following fundamental issues: 1. the thermodynamics and kinetics of the forma￾tion of polymer nanocomposites; 2. the hierarchical characteristics of the structure and dynamics of polymer nanocomposites ran￾ging from molecular scale, microscale to mesos￾cale and macroscale, in particular, the molecular structures and dynamics at the interface between nanoparticles and polymer matrix; 3. the dependence of polymer rheological behavior on the addition of nanoparticles, which is useful in optimizing processing conditions; and 4. the molecular origins of the reinforcement mechan￾isms of nanoparticles in polymer nanocomposites. The purpose of this review is to discuss the application of modeling and simulation techniques to polymer nanocomposites. This includes a broad subject covering methodologies at various length and time scales and many aspects of polymer nanocomposites. We organize the review as follows. In Section 2, we introduce briefly the computational methods used so far for the systems of polymer nanocomposites which can be roughly divided into three types: molecular scale methods (e.g., molecular dynamics (MD), Monte Carlo ARTICLE IN PRESS 192 Q.H. Zeng et al. / Prog. Polym. Sci. 33 (2008) 191–269