北京化工大学：《材料导论》课程阅读材料（高分子材料）Multiscale_modeling_and_simulation_of_polymer_nanocomposites.pdf_P16-P20

nanoparticle–polymer systems in which particle size is equivalent to the gyration radius. Therefore, in order to elucidate the formation of nanoparticle– polymer nanocomposites at a molecular level, some theoretical and simulation efforts have been made recently, especially on polymer nanocomposites. The simulation methods used include mean-field model [50,51], combined model of DFT and selfconsistent field (SCF) [52], and molecular dynamic model [53,54]. Table 1 presents a brief description of the theoretical studies on the thermodynamics of polymer nanocomposites. It is well recognized that the dispersion of layered clays or silicates in polymer matrix may lead to three kinds of structures, i.e., conventional immiscible microstructure, intercalated nanostructure and exfoliated/delaminated nanostructure. The formation of these equilibrium structures is believed to be determined by the interplay of entropic (i.e., intermolecular interactions) and enthalpic (i.e., configurational changes in the components) factors. Based on this consideration, Vaia and Giannelis [50,51] developed a modified mean-field model to predict the above three possible structures. Fig. 5 shows the free-energy change of polymer–organoclay mixtures as a function of clay platelet separation. In their mean-field model, the free-energy change DH associated with the platelet separation and polymer incorporation is divided into two terms: one is the internal energy change DU associated with the establishment of new intermolecular interactions, and the other is the combinatorial entropy change DS associated with configuration changes of the various components. This is DH ¼ HðhÞ Hðh0Þ ¼ DU TDS, (64) where h and h0 are the final and initial clay platelet separations and T is the temperature. Thus, DHo0 indicates the intercalation process is favorable while DH40 indicates the initial unintercalated state is favorable. Based on their calculated results, three kinds of equilibrium structures have been isolated as shown in Fig. 5. It has been shown that the entropy loss associated with polymer confinement in the clay gallery is approximately compensated by the entropy gain associated with the increased conformational freedom of the surfactants as the gallery distance increases due to the polymer intercalation. Thus, the enthalpy determines whether or not polymer intercalation will take place. From this point of view, it is possible to select potentially compatible polymer and organoclay systems to produce materials ARTICLE IN PRESS Table 1 Simulation studies on the thermodynamics of polymer nanocomposites Material system and references Simulation method Key features and findings Clay–polymer [50,51] Mean-field Evaluation of the effects of various aspects of polymer and clay/organoclay on nanocomposite formation; and Limitation of assumption, i.e., separation of configurational terms and intermolecular interaction and separation of the entropy of various components. Clay–polymer [52] Density functional theory and self-consistent field Addressing the thermodynamic and architectural requirement for intercalated and exfoliated nanostructures; Relating the particle–polymer interaction to free energy: increasing the interaction strength decreases free energy; and Coupling the conformation of polymer and that of surfactants in organoclay. Clay–nylon 6 Molecular dynamics Binding energy between various components (i.e., polymer, Clay–nylon 66 [53,54] surfactant and clay surface). Nanoparticle–polymer [13] Coarse-grained molecular dynamics Weak attractive particle–polymer interaction leads to nanoparticle aggregation; Strong attractive interaction promotes the dispersion of nanoparticles; and Repulsive nanoparticle–polymer interaction leads to an energetic contribution that dominates the interactions between two nanoparticles while the entropic is less pronounced. 206 Q.H. Zeng et al. / Prog. Polym. Sci. 33 (2008) 191–269

Q.H.Zeng et al Prog.Polym.SeL 33(2008)191-269 0.01 AH silicate layor X=0.02a) x=0.01b) x=0.005 (b) =0.0d -0.0 X=-0.01el (c) 5 -10 0.00.6101520263.0 h-h.nm Fig.6.Fre ergy change per unit area (AH)asa function of Fig.5.The clay:(a)=0 lymer in org with desirable structures.The greatest advantage of and exfoliated (curves d and e).By using an DF mode l,they [59- 62 investi aspects the polymer an effects var ite formation. an polymer the equili and in the further separation of the entropic behavior of Moreover,Balazs and co-workers found that the components,somewhat limit the usefulness of adding polymers with one reactive end group to a the model. melt of chemically identical non-functionalized To overcome some of the limitations in the above polymers can lead to the formation of exfoliated mean-field model. Balazs and co-workers have nanostructures while adding polymers with two reactive end groups (the so-called telechelic poly 56 confo mers)can pror tion of therm ally sta no longer dec nled but inste ad.th The cha n length ratio of fur nctionalized polyme conformation of one comnonent is intimately and non-functionalized polymer shows a significant influenced by the configuration of the other.For influence on the location of the phase boundaries example,they used the SCF calculation to address between the immiscible,intercalated,and exfoliated the thermodynamic and architectural requirements states.More recently,Groenewold and Fredrickson 63]carried out the theoretical calculation to explore structures dy es re in wh grafted copoly clay partic e field model [51].i.e. with th of shown in Fi found that the high mer-clay/organoclay interaction(7).the free-en ratio of the clay platelets implies a long range of change decreases from positive(curves a and b)to interaction. negative(curves d and e).This means that the final Kudryavtsev et al.[64]studied theoretically equilibrium structure of the mixtures changes from the thermodynamic equilibrium of a mixture of immiscible (curves a and b)to intercalated (curve c) homopolymer and clay modified with a diblock

with desirable structures. The greatest advantage of mean-field model is that it is able to explore the effect of various aspects of the polymer and organoclay on nanocomposite formation. However, the assumptions, such as the separation of configurational terms and intermolecular interactions and the further separation of the entropic behavior of the components, somewhat limit the usefulness of the model. To overcome some of the limitations in the above mean-field model, Balazs and co-workers have recently developed a series of models based on the theories of Scheutjens and Fleer [55,56], and Carignano and Szleifer [57] in which the conformations of polymer and tethered surfactants are no longer decoupled, but instead, the equilibrium conformation of one component is intimately influenced by the configuration of the other. For example, they used the SCF calculation to address the thermodynamic and architectural requirements necessary to achieve polymer intercalation and ultimately the exfoliated nanostructures [52,58]. Their results shown in Fig. 6 are qualitatively similar to the findings based on the above mean- field model [51], i.e., with the increase of polymer–clay/organoclay interaction (w), the free-energy change decreases from positive (curves a and b) to negative (curves d and e). This means that the final equilibrium structure of the mixtures changes from immiscible (curves a and b) to intercalated (curve c) and exfoliated (curves d and e). By using an integrated DFT–SCF model, they [59–62] investigated further the effects of various factors (e.g., surfactant-coated clay surface, end-fictionalization of polymer, block copolymer) on the equilibrium structures of polymer–clay mixtures. Moreover, Balazs and co-workers found that adding polymers with one reactive end group to a melt of chemically identical non-functionalized polymers can lead to the formation of exfoliated nanostructures while adding polymers with two reactive end groups (the so-called telechelic polymers) can promote the formation of thermodynamically stable intercalated nanostructures but not the more desirable exfoliated nanostructures [52,59]. The chain length ratio of functionalized polymer and non-functionalized polymer shows a significant influence on the location of the phase boundaries between the immiscible, intercalated, and exfoliated states. More recently, Groenewold and Fredrickson [63] carried out the theoretical calculation to explore the thermodynamic behavior of block copolymer– clay mixture in which the grafted clay particle is embedded in a lamellar block copolymer matrix as shown in Fig. 7. They found that the high aspect ratio of the clay platelets implies a long range of interaction. Kudryavtsev et al. [64] studied theoretically the thermodynamic equilibrium of a mixture of homopolymer and clay modified with a diblock ARTICLE IN PRESS Fig. 5. The free-energy change (DH) of polymer–organoclay mixtures as a function of clay gallery separation under different intercalation strength (e) between polymer–organoclay: (a) e ¼ 0; (b) e ¼ 4; (c) e ¼ 8; and (d) e ¼ 12 mJ/m2 . The inset shows the intercalation process of polymer in organoclay [51]. Reproduced from Vaia and Giannelis by permission of American Chemical Society. Fig. 6. Free-energy change per unit area (DH/A) as a function of surface separation (h) for various interaction parameter values (w), the left diagram shows the reference state where the grafted chains form a melt between the surfaces, and the right diagram shows the surfaces are separated by the intercalated polymers [58]. Reproduced from Balazs, Singh, Zhulina and Lyatskaya by permission of American Chemical Society. Q.H. Zeng et al. / Prog. Polym. Sci. 33 (2008) 191–269 207

compolymer to seek strategies for polymer melt intercalation. They concluded that a co-modification by both diblocks and surfactants is probably the best means for facilitating the intercalation. Reister and Fredrickson [65] investigated the potential of mean force between two nanoparticles surrounded by a diblock copolymer matrix. By using the SCF theory, they analyzed the energy change of the system. Above the order–disorder transition, attractive potential of the particles for one kind of monomers leads to a lamellar structure around the particles. Below the transition, they inserted particles in such a way that the axis connecting them is either perpendicular or parallel to the lamellar polymer structure. They then used the SCF theory to investigate the energy and structural change of the system with the particle distance. More recently, Kim and White [66] studied the formation of polymer–clay intercalation and nanocomposites by using statistical thermodynamical equilibrium principles. They proposed that the exothermic heat of mixing between polymer chains and organic amine on organically modified clay surface is the key to the intercalation of the polymer melt and hence the formation of polymer nanocomposites. MD simulations have also been used to investigate the thermodynamic behavior of polymer nanocomposites. For example, the binding energies between the components (i.e., polymer, surfactant and clay platelet) of nylon 6,6-clay nanocomposite and nylon 6-clay nanocomposites were calculated by Tanaka and Goettler [53] and Fermeglia et al. [54], respectively. Interestingly, both simulation studies draw the exact conclusions: (i) the binding energy between the polymer matrix and clay platelet decreases with the increase of surfactant volume while the binding energy between polymer and surfactant and that between surfactant and clay increase with the increase of surfactant volume (Fig. 8); (ii) the use of surfactant whose hydrogen atoms are substituted with polar groups (i.e., –OH, –COOH) generally results in a stronger interaction between polymer and surfactant. By using MD simulation, Toth et al. [67] studied the structure and energetic of different biocompatible polymer nanocomposites made up of two biodegradable polymers (poly (b-hydroxybutyrate) and poly (vinyl alcohol)), hydrotalcite (either in an anhydrous or in a solvated environment), and seven non-steroidal anti-inflammatory drugs. Their results showed that nanocon- fined conformations of smaller and polar drug molecules are more easily affected by the presence of water molecules in the clay gallery with respect to their larger and less polar counterparts. The binding energy between a drug and hydrotalcite layers can be increased by intercalating polymers in the gallery of the drug–pretreated hydrotalcite. In particular, the simulation results indicated that for hydrophobic drugs, the best results for a solvated environment could be obtained via intercalation with poly (vinyl alcohol) while for acidic drugs poly ARTICLE IN PRESS Fig. 8. Predicted binding energies (Ubond) as a function of surfactant molecular volume (V): Uclay–nylon 6 (circle), Unylon 6–surfactant (square) and Uclay–surfactant (triangle) [54]. Reproduced from Fermeglia, Ferrone and Pricl by permission of Elsevier Science Ltd. Fig. 7. Visualization of a clay platelet grafted with chains of type A, embedded in a lamellar matrix composed of AB block copolymers [63]. Reproduced from Groenewold and Fredrickson by permission of Springer. 208 Q.H. Zeng et al. / Prog. Polym. Sci. 33 (2008) 191–269

Q.H.Zeng et al Prog.Polym.ScL 33(2008)191-269 209 (B-hydroxybutyrate)could be the polymer of choice the nanoconfined interparticle region.Further for intercalation approach resulted in the overlap of the interfacial Smith et al.[13]used the coarse-grained MD shells and the reduction of the number of the simulation to study the interactions between two polymer beads at the nanoparticle interface. spherical nanoparticles immersed in a polymer matrix,where 3.2 Nanocomposite kinetics radius an They found tha ength of polymer are tha the dire polymer-in ticle n kin hat is nanoparticle interaction in all sys in what way such posites are formed.The formation kinetics of polymer nanocomposites is much less understood than that of formation radial distribution functions in Fig.9 show that a thermodynamics.For example,in the case of relatively weak interaction (=1)between poly- layered clays,it is still unclear how the surfactant me and nanopa prom nanoparti or polymer ge clay gallery and orm th gation indicate peak or exfo nan hinde the parat surface sp chains on the of na the vell unde promote dispersion of nanoparticles.In a further pefore manufactur study,Bedrov et al.[68]found that in systems with ing and long-term usage of clay-based polymer repulsive nanoparticle-polymer interactions the nanocomposites become possible.As an initial energetic contribution dominates the interactions stage,we should address such intercalation kinetics etween nanoparticles while the open for the accom contribut on is but not negligit ng c mns (e 0 odynamic pr roperties a (ii)by wh do the cha opa elated with the rall pol and and h polymer structure at the interface and betw do ay in teractions affect the etration of particles.In addition,as nanoparticles app roach to each other,systems gain entropy due to diffusivity of the intercalated chains compare to destabilization of the homogeneous polymers in that of bulk chains. In the past few years. some e simulation work has been done (as listed in Table 2)on such kinetics issues for polymer 80 Enp=1.0 sites [11,69 60 11.69]first investigate 1 ep=2.0 aco-workers 20 Enp =3.0 osites The 3 melt into an initially evacuated rectangular slit 2 as shown in Fig.10.They found that as the polvmer-surface aftnity increases. the flow of ed down (Fig.11). re emen the experimenta 0 ymer na 4 5 678 910 11 12 on for nde r(a) on molecular weight rather than an inverse depen rameter values (data are dence observed experimentally [74].This model, by 2.0 and however,ignores two major features of the experi- mental systems:the presence of surfactants grafted to the clay surface and the swelling of the slit during

(b-hydroxybutyrate) could be the polymer of choice for intercalation. Smith et al. [13] used the coarse-grained MD simulation to study the interactions between two spherical nanoparticles immersed in a polymer matrix, where the nanoparticle radius, the gyration radius and statistical segment length of polymer are comparable. They found that the polymer-induced interaction is greater than the direct nanoparticle– nanoparticle interaction in all systems with a range of polymer–nanoparticle interactions and polymer molecular weights. The nanoparticle–nanoparticle radial distribution functions in Fig. 9 show that a relatively weak interaction (enp ¼ 1) between polymer and nanoparticle promotes nanoparticle aggregation indicated from the sharp peak, while increased attractive nanoparticle–polymer interaction can lead to strong adsorption of the polymer chains on the surface of nanoparticles and thus promote dispersion of nanoparticles. In a further study, Bedrov et al. [68] found that in systems with repulsive nanoparticle–polymer interactions the energetic contribution dominates the interactions between two nanoparticles while the entropic contribution is less pronounced but not negligible. The dependence of the thermodynamic properties as a function of nanoparticle separation is strongly correlated with the overall polymer density, and the polymer structure at the interface and between particles. In addition, as nanoparticles approach to each other, systems gain entropy due to destabilization of the homogeneous polymers in the nanoconfined interparticle region. Further approach resulted in the overlap of the interfacial shells and the reduction of the number of the polymer beads at the nanoparticle interface. 3.2. Nanocomposite kinetics Another important issue of polymer nanocomposites is the formation kinetics, that is, how fast and in what way such nanocomposites are formed. The formation kinetics of polymer nanocomposites is much less understood than that of formation thermodynamics. For example, in the case of layered clays, it is still unclear how the surfactant or polymer get into clay gallery and form the intercalated or exfoliated structure since the gallery is initially separated by less than 1 nm and thus hinders the infusion of external species. However, the formation process must be well understood before the material design, controllable manufacturing and long-term usage of clay-based polymer nanocomposites become possible. As an initial stage, we should address such intercalation kinetics as: (i) how do the galleries open for the accommodation of intercalating chains (i.e., surfactant or polymer)? (ii) by what mechanisms do the chains enter the galleries? (iii) what are the natures of clay structure and polymer, and how do clay–clay and polymer–clay interactions affect the penetration of polymers into the galleries? (iv) how does the diffusivity of the intercalated chains compare to that of bulk chains? In the past few years, some simulation work has been done (as listed in Table 2) on such kinetics issues for polymer nanocomposites [11,69–73]. Loring and co-workers [11,69] first investigated the intercalation process of clay-based polymer nanocomposites. They employed the coarse-grained MD simulations to examine the flow of a polymer melt into an initially evacuated rectangular slit as shown in Fig. 10. They found that as the polymer–surface affinity increases, the flow of polymer into the slit is slowed down (Fig. 11), which is in agreement with the experimental observation for clay-based polymer nanocomposites. However, the effective diffusion coefficient in the simulation demonstrated a weaker dependence on molecular weight rather than an inverse dependence observed experimentally [74]. This model, however, ignores two major features of the experimental systems: the presence of surfactants grafted to the clay surface and the swelling of the slit during ARTICLE IN PRESS Fig. 9. The nanoparticle–nanoparticle radial distribution functions under different interaction parameter values (enp), data are offset vertically by 2.0 and 1.0 for enp ¼ 1.0 and enp ¼ 2.0, respectively [13]. Reproduced from Smith, Bedrov and Smith by permission of Elsevier Science Ltd. Q.H. Zeng et al. / Prog. Polym. Sci. 33 (2008) 191–269 209

the intercalation process. The surfactants undoubtedly play an important role since the intercalation process for relatively non-polar polymers does not take place in their absence. Therefore, in a more recent study [75], they introduced the two features in their simulation. The results (Figs. 12 and 13) indicated that the spontaneous intercalation and swelling of clay need a moderate polymer–clay affinity. More specifically, increasing the polymer– clay affinity would induce spontaneous intercalation and clay swelling. However, for a relatively higher polymer–clay affinity, the amount of intercalated ARTICLE IN PRESS Table 2 Simulation studies on the formation kinetics of polymer nanocomposites Material system and references Simulation method Key features and findings Clay–polymer [11,69] Coarse-grained molecular dynamics The intercalation process and interlayer swelling of clay require a moderate polymer–surface affinity; Increasing polymer–surface affinity slows down the flow of polymer into the interlayer space; and Increasing polymer molecular length leads to the decrease of flow rate. Nanoparticle–binary polymer blend [70,71] Multiscale method (coarse-grained Cahn–Hilliard approach and Brownian dynamics) Effect of shear: the domains grow initially in an isotropic manner, and in the later stage grow faster along the shear direction; Addition of solid particles significantly changes both the speed and the morphology of the phase separation; and High density of particle will destroy the shear-induced anisotropic growth. Clay–polymer [72,73] Semiphenomenological model External stress and bending of clay platelets affect clay intercalation; Strong external force is necessary to induce clay intercalation; and Intercalation kinetics is solely governed by the initial stage. Fig. 10. MD simulation scheme of intercalation process. Gray regions represent the polymer melt and striped regions represent the silicate particle: (a) reservoirs are equilibrated under constant pressure with slit closed, (b) slit is opened, and intercalation proceeds and (c) intercalation is complete [11]. Reproduced from Lee, Baljon and Loring by permission of American Institute of Physics. Fig. 11. The effect of the bead–lattice interaction on intercalation dynamics, w(t) is the number of beads at time t in the slit, normalized by its value at the equilibrium after the slit is filled, L is slit length, ebl is the bead–lattice interactions [11]. Reproduced from Lee, Baljon and Loring by permission of American Institute of Physics. 210 Q.H. Zeng et al. / Prog. Polym. Sci. 33 (2008) 191–269