rheology of polymer/layered silicate nanocompositesin this article, recent advances in melt-state...

J. Ind. Eng. Chem., Vol. 12, No. 6, (2006) 811-842

REVIEW

Rheology of Polymer/Layered Silicate Nanocomposites Suprakas Sinha Ray†

Macromolecular Nanotechnology Research Group, Nanoscience Research Centre, CSIR Materials Science and Manufacturing, PO Box 395, Pretoria 0001, Republic of South Africa

Received November 14, 2006

Abstract: Over the last few years, polymer/layered silicate (PLS) nanocomposites have been an area of intense academic and industrial research. No matter the measure-journal articles, patents, and industry research and development (R&D) funding-efforts in PLS-nanocomposite have been exponentially growing worldwide for the last ten years. Aside from the understanding in fabrication, characterization, and improved mechanical and other properties, the measurement of rheological properties of PLS-nanocomposites under molten state is crucial to gain fundamental understanding of the processability of these materials. In the case of PLS- nanocomposites, the measurements of rheological properties are also helpful to find out the strength of polymer-layered silicate interactions and the structure-property relationship in nanocomposites. This is because rheological behaviors are strongly influenced by their nanoscale structure and interfacial characteristics. In this article, recent advances in melt-state rheological properties of PLS-nanocomposites are highlighted. To begin this a very brief description of structure and dynamics of PLS-nanocomposites are also described.

Keywords: polymer/layered silicate nanocomposite, structure, thermodynamics, melt rheology

Introduction

1)

The word composite is generally used to define any ma-terial made of more than one component. Depending on the matrix nature, composite materials can be broadly divided into three categories such as polymeric, metallic, and ceramic. In most of the commercially available com-posite materials the structural unit is on the micrometer (10‐6 m) length scale and is used mostly to improve the mechanical properties of matrix material. Now one can change the dimension of the structural building block to the nanometer (10‐9 m) scale, the resulting composite ma-terial is called a Nanocomposite. The nanometer is one billionth of meter and ∼10,000 times finer than a human hair. Figure 1 compares the morphology of classical- and nano-filler filled composite. Here we are interested on polymer nanocomposites that means nanocomposite made with polymer and nanoscale filler. Over the last few years, various types of nano-fillers are in development such as layered silicates

† To whom all correspondence should be addressed.(e-mail: [email protected])

[1], metal oxide nanoparticles [2,3], inorganic nanotubes [4], expandable graphite [5-7], layered titanate [8], cellu-lose nanowhiskers [9], polyhedral oligomeric silses-quioxanes (POSS) [10], carbon nanotubes [11-17], etc. Polymer nanocomposites based on layered silicates have attracted great interest in today’s materials research, as it is possible to achieve impressive enhancements of prop-erties when compared with virgin polymer [1,18-20]. These improvements can include high moduli [1,18], in-creased strength and heat resistance [1,18], decreased gas permeability [21-23] and flammability [24-27], and in-creased degradability of biodegradable polymers [28-30]. On the other hand, there has been considerable interest in theory and simulations addressing the preparation and properties of these materials [31], and they are also con-sidered to be unique model systems to study the structure and dynamics of polymers in confined environments [32]. The main reason for these improved properties in nanocomposites is the interfacial interaction between the matrix and layered silicate, as opposed to conventional composites [1]. Layered silicates have layer thickness on

Suprakas Sinha Ray812

Figure 1. Schematic comparison between microcomposite (classical filler filled) and “Nanocomposite. Reproduced with permission from Elsevier Science Ltd., UK.

Figure 2. Schematic illustration of three different types of ther-modynamically achievable polymer/layered silicate composites.

the order of 1 nm, and very high aspect ratios (e.g. 10∼ 1,000). A few weight percent of layered silicate particles that are properly dispersed throughout the matrix can thus create a much larger surface area for polymer filler interactions than do conventional composites. On the basis of the strength of the polymer/layered silicate interfacial interaction, three structurally different types of composites are achievable (see Figure 2): (1) phase- separated composite, when polymer matrix has no interaction with layered silicate, (2) intercalated nanoco- posites, where insertion of polymer chains into the silicate structure occurs in a crystallographically regular fashion, regardless of the polymer-to-layered silicate

ratio, and a repeat distance of few nanometers, and (3) exfoliated nanocomposites, in which the individual silicate layers are separated in the polymer matrix by average distances that totally depend on the layered silicate loading. This article highlights recent advances in melt-state rheological properties of PLS nanocomposites. To begin this a brief description on structure and properties of layered silicates, nanocomposites preparation techniques and thermodynamics are described. Finally, attention is drawn to how rheological behavior of PLS nanocomposites can be understood directly from their structure.

Structure and Properties of Layered Silicates

The commonly used layered silicates for the preparation of PLS nanocomposites belong to the same general family of 2 : 1 layered- or phyllosilicates [33]. Their crystal structure consists of layers made up of two tetrahedrally coordinated silicon atoms fused to an edge-shared octahedral sheet of either aluminum or magnesium hydroxide. The layer thickness is around 1 nm, and the lateral dimensions of these layers may vary from 30 nm to several microns or larger, depending on the particular layered silicate. Stacking of the layers leads to a regular van der Waal’s gap between the layers called the interlayer or gallery. Isomorphic substitution within the layers (for example, Al+3 replaced by Mg+2 or Fe+2, or Mg+2 replaced by Li+1) generates negative charges that are counterbalanced by alkali and alkaline earth cations situated inside the galleries. This type of layered silicate

Rheology of Polymer/Layered Silicate Nanocomposites 813

Figure 3. Structure of 2:1 phyllosilicates. Reproduced from ref. [1] by permission of Elsevier Science Ltd., UK.

is characterized by a moderate surface charge known as the cation exchange capacity (CEC), and generally expressed as mequiv/100 gm. This charge is not locally constant, but varies from layer to layer, and must be considered as an average value over the whole crystal. Layered silicates have two types of structure: tetrahedrally substituted and octahedrally substituted. In the case of tetrahedrally substituted layered silicates, the negative charge is located on the surface of silicate layers and, hence, the polymer matrices can interact more readily with these than with octahedrally substituted material. Generally, layered silicate minerals are divided into three major groups: (a) the kaolinite group, (b) the semc-tite group and (c) the illite or the mica-clay group. Among the three major groups, smectite types or more precisely montmorillonite, saponite and hectorite are the most commonly used layered silicates in the filed of pol-ymer nanocomposite technology. Again, among mont-morillonite, saponite, hectorite, montmorillonite (MMT) is the most commonly used layered silicates for the fab-rication of PLS nanocomposites, because it is highly abundant and inexpensive. MMT is the name given to the layered silicate found near montmorillonite in France, where MMT was first identified by Knight in 1896. The chemical formula of MMT is Mx(Al4‐xMgx)Si8O20(OH)4. The CEC (generally 90∼110 meq/100 g) and particle length of MMT (100∼150 nm) depends on the source. The specific surface area of MMT is equal to 750∼800 m2/g and the modulus of each MMT sheet is around 170 GPa [34]. The interlayer thickness of hydrated MMT is equal to 1.45 nm and the average density ρ= 2.385 g/mL. Drying MMT at 150 °C reduces the gallery height to 0.28 nm which corresponds to a water monolayer and hence the interlayer spacing decreases to 0.94 nm and the average density increases to 3.138 g/mL [35]. The unit structure of MMT is presented in Figure 3.

Two particular characteristics of layered silicates are generally considered for PLS nanocomposites fabrication. The first is the ability of the silicate particles to disperse into individual layers inside the polymer matrix. The second characteristic is the ability to fine-tune their surface chemistry through ion exchange reactions with organic and inorganic cations. These two characteristics are, of course, interrelated, since the degree of dispersion of layered silicate in a particular polymer matrix depends on the interlayer cation. Pristine layered silicates usually contain hydrated Na+ or K+ ions [1]. Obviously, in this pristine state, layered silicates are only miscible with hy-drophilic polymers such as poly(ethylene oxide) (PEO) [36] or poly(vinyl alcohol) (PVA) [37]. To render lay-ered silicates miscible with various polymer matrices, one must convert the normally hydrophilic silicate sur-face to an organophilic one, making the intercalation of many polymers possible. Generally, this can be done by ion-exchange reactions with cationic surfactants includ-ing primary, secondary, tertiary, and quaternary alky-lammonium or alkylphosphonium cations. Alkylam- monium or alkylphosphonium cations in the organo-silicates lower the surface energy of the inorganic host and improve the wetting characteristics of the polymer matrix, and result in a larger interlayer spacing. Additionally, the alkylammonium or alkylphosphonium cations can provide functional groups that can react with the polymer matrix, or in some cases initiate the poly-merization of monomers to improve the strength of the interface between the inorganic and the polymer matrix [1].

Preparative Methods

Intercalation of polymer chains inside layered silicate galleries has proven to be a successful approach to fab-ricate PLS-nanocomposites. Thermoplastic polymers based PLS-nanocomposites may be prepared by one of the three following routes: (i) in-situ intercalative poly-merization of monomer, (ii) intercalation of polymer or pre-polymer from solution, and (iii) melt-intercalation. The second method may be processed using emulsion, whereas when the good solvent is not available, re-searchers have to choose either in-situ polymerization method (i) or direct melt blending (iii). The direct melt-intercalation process involves annealing a mixture of the polymer and layered silicate (organically modified or not) above the softening point of the poly-mer, statically or under shear. While annealing, the poly-mer chains diffuse from the bulk polymer melt into the galleries between the silicate layers. A range of nano-composites with structures from intercalated to exfoliate can be obtained, depending on the degree of penetration


of the polymer chains into the silicate galleries. This process was found to be completely reversible in the pol-ystyrene (PS) based nanocomposite because PS has al-most no interaction with the organically modified layered silicate (OMLS) surface, but when polymer chains have some favorable interaction with silicate surface, this process found to be irreversible. However, for a large va-riety of nanocomposites, this method requires often the use of extrusion process in order to get a homogeneous dispersion of intercalated silicate layers in the polymer matrix.

Thermodynamics and Molecular Modelling of PLS Nanocomposite Formation

The solution intercalation method is based on a solvent system in which the polymer or pre-polymer is soluble and the silicate layers are swellable. The layered silicate is first swollen in a solvent, such as water, chloroform, or toluene. When the polymer and layered silicate solutions are mixed, the polymer chains intercalate and displace the solvent within the interlayer of the silicate. Upon sol-vent removal, the intercalated structure remains, resulting in polymer/layered silicate nanocomposite. For the overall process, in which polymer is exchanged with the previously intercalated solvent in the gallery, a negative variation in the Gibbs free energy is required. The driving force for the polymer intercalation into lay-ered silicate from solution is the entropy gained by de-sorption of solvent molecules, which compensates for the decreased entropy of the confined, intercalated chains. Using this method, intercalation only occurs for certain polymer/solvent pairs. This method is good for the inter-calation of polymers with little or no polarity into layered structures, and facilitates production of thin films with polymer-oriented clay intercalated layers. In recent years, the melt intercalation technique has be-come the standard for the preparation of PLS-nanocomposites. During polymer intercalation from solution, a relatively large number of solvent molecules have to be desorbed from the host to accommodate the incoming polymer chains. The desorbed solvent molecules gain one translational degree of freedom, and the resulting en-tropic gain compensates for the decrease in conforma-tional entropy of the confined polymer chains. Therefore, there are many advantages to direct melt intercalation over solution intercalation. For example, direct melt in-tercalation is highly specific for the polymer, leading to new hybrids that were previously inaccessible. So far, experimental results indicate that the outcome of polymer chains intercalation into two dimensional sili-cate galleries depends critically on layered silicate sur-face functionalization and constituent interactions. Pre-

sent author observes that (a) an optimal interlayer struc-ture on the OMLS, with respect to the number per unit area and size of surfactant chains, is most favorable for nanocomposite formation, and (b) polymer intercalation depends on the existence of polar interactions between the OMLS and the polymer matrix. In order to understand the thermodynamic issue asso-ciated with nanocomposite formation during melt-inter-calation, Vaia and coworkers [38,39] applied a mean‐field statistical lattice model, reporting that calculations based on the mean field theory agree well with ex-perimental results. Although there is entropy losses asso-ciated with the confinement of a polymer melt during nanocomposite formation, this process is allowed be-cause there is an entropy gain associated with the layer separation, resulting in a net entropy change near to zero. Thus, from the theoretical model, the outcome of nano-composite formation via polymer melt intercalation de-pends primarily on energetic factors, which may be de-termined from the surface energies of the polymer and OMLS. Based on the Vaia and coworkers [38,39] study and the construction of product maps, general guidelines may be established for selecting potentially compatible poly-mer/OMLS systems. Initially, the interlayer structure of the OMLS should be optimized in order to maximize the configurational freedom of the functionalizing chains upon layer separation, and to maximize potential inter-action sites at the interlayer surface. For these systems, the optimal structures exhibit a slightly more extensive chain arrangement than with a pseudo-bilayer. Polymers containing polar groups capable of associative inter-actions, such as Lewis-acid/base interactions or hydrogen bonding, lead to intercalation. The greater the polar-izability or hydrophilicity of the polymer, the shorter the functional groups in the OMLS should be in order to minimize unfavorable interactions between the aliphatic chains and the polymer. One of the great advantages of the Vaia mean-field stat-istical lattice model is the ability to determine analyti-cally the effect of various aspects of the nanocomposite formation. According to this model, the variation of the free energy of mixing and subsequent dependence on en-thalpic and entropic factor, suggest the formation of three possible structures-phase separated, intercalated and exfoliated. Although, Vaia model able to address some of the fundamental and qualitative thermodynamic issues associated with the nanocomposite formation, however, some of the assumptions such as the separation of con-figurational terms and intermolecular interaction and the further separation of the entropic behavior of the con-stituents, somewhat limit the usefulness of the model. Not only that, this model is based on nanocomposites where polymer chains are completely tethered with the


silicate surface, which is not the case for most of the pol-ymer nanocomposites. To overcome the limitation of Vaia model, Balazs and coworkers [40] proposed a model based on a self-con-sistent field (SCF) calculation, such as the Fleer and Scheutjens theory [41]. In the Fleer and Scheutjens theo-ry, the phase behavior of polymer systems is modeled by combining Markov chain statistics with a mean field approximation. These calculations involve a planar lat-tice where lattice spacing represents the length of a stat-istical segment within a polymer chain. Details regarding this theory can be found in ref. [41]. Using this method Balazs and coworkers tried to calculate the interactions between two surfactant-coated surfaces and a polymer melt. They considered two planar surfaces that lie paral-lel to each other in the xy-plane and investigated the ef-fect of increasing the separation between the surfaces in the z-direction. The two surfaces are effectively im-mersed within a polymer melt. As the separation between the surfaces is increased, polymer from the surrounding bath penetrates the gap between these walls. Each surface is covered with monodispersed end-grafted chains, i.e. surfactants. Now if χsurf represents the Flory-Huggins in-teraction parameter between the polymers and the under-lying solid substrate and χssurf represents the Flory‐Huggins interaction between the surfactant and surface. Therefore, χsurf -χssurf = 0. It should be noted here; in their calculation Balazs and coworkers did not consider electrostatic interaction. Their calculations show that on increasing the attraction between the polymers and the modified surfaces are qualitatively similar to observation as made by Vaia and coworkers [38,39]. However, Balazs and coworkers found that the actual phase behavior and morphology of the mixer can be affected by the kinetics of the polymers penetrate the gap between the plates. At the beginning, the polymer chains have to penetrate the space between the silicate layers from an outer edge and then diffuse to-ward the centre of the gallery. Now if we consider the case where χsurf < 0 and thus, the polymer and surface experience an attractive interaction. In this case as the polymer diffuses through the energetically favorable gal-lery, it maximizes contact with the two confining layers. As a results, the polymer ‘glues’ the two surfaces togeth-er as it moves through the interlayer. This ‘fused’ con-dition could represent a kinetically trapped state and con-sequently, increasing the attraction between the polymer and layered silicate sheets would only lead to interca-lated, rather than exfoliated structures. On the other hand, in the case where χsurf > 0, the polymer can separate the sheets, as the chain tries to retain its coil-like con-formation and gain entropy. However, recent literatures revealed that the melt mixing of organically modified layered silicates and almost no attractive polymer ma-

trices always lead to the formation of phase separated structure. The SCF calculations and phase diagrams lead to the same conclusion. To overcome this problem, Balazs and coworkers then proposed the scheme of using a mixture of functionalized and non-functionalized polymers for the melts [42]. While the stickers at the chain ends are highly attracted to the surface, the remainder of polymer does not react with the substrate. Thus, as the polymer chain penetrate the sheets, the majority of the chain is not likely to glue the surfaces together. Balazs and coworkers [43,44] also proposed a simple model that describes the nematic ordering in the poly-mer-layered silicate systems. Because of the very high degree of anisotropy (a typical layered silicate platelet is ∼1 nm in thickness and 100∼200 nm in diameter), lay-ered silicate particles experience strong orientational or-dering at low volume fractions and can form liquid crys-talline phases such as nematic, smectic, or columnar, in addition to traditional liquid and solid phases (see Figure 4). Starting from the Onsager free energy functional for the nematic ordering of rigid rods, they developed a modified expression to combine the disk orientational and positional entropy, steric excluded-volume effects, translational entropy of the polymer, and finally the Flory-Huggins enthalpic interaction. The resulting iso-thropic-nematic phase diagram correctly represents many important features, such as the role of shape anisotropy in depressing the ordering transition and the increase in the size of the immiscibility region with increases in the polymer chain length. Unlike most of the phenomeno-logical theories of polymer-liquid crystal systems [45- 48], in the Onsager-type model the features of the phase diagram are directly derived from the geometric charac-teristics of the anisotropic component. Balazs and coworkers first modified and expanded Onsager theory by including nematic, smectic and columnar crystalline phases. To do calculation, they also adopted Somoza-Tarazona formalism of density functional theory (DFT) and then incorporated expressions that describe the entropy of mixing between the different components and the enthalphic interaction between the platelets [34,49]. The resulting free energy function can be minimized with respect to both the orientational and positional single-particle distribution function of the platelets, and thus, potentially, all phases and coexistence regions can be determined. The resulting phase diagram was shown to exhibit a strong dependence on the shape anisotropy of the layered silicate particles, the polymer chain length, and the strength of the interparticle interaction. In particular, an increase in the shape anisotropy for oblate ellipsoidal filler particles leads to the broadening of the nematic phase at the expense of the isotropic region. The increase in the polymer chain


Figure 4. Possible mesophases of oblate uniaxial particles dispersed in a polymer: (a) isotropic, (b) nematic, (c) smectic A, (d) col-umnar, and (e) crystal. The nematic director n in ordered phases is aligned along Z axis; the disks lie in the XY plane. Dashed lines show smectic layers (c) and columns (d). Reprinted from ref. [44] with permission from American Chemical Society, USA.

length leads to the formation of the crystalline and/or liquid crystalline mesophases and promotes segregation between polymerrich regions and filler particles. Finally, an increase in the strength of the interparticle potential leads to the complete elimination of the nematic phase and to the direct coexistence between isotropic and crystal or columnar phases. The only limitation of this model is that this model cannot determine the topology of the phase diagram and the nature of the ordered phases for intermediate and high volume fractions of colloidal particles. The huge interfacial area and the nanoscopic di-mensions between nanoelements differentiate PLS-nano-composites from conventional composites and filled

plastics. The dominance of interfacial regions resulting from the nanoscopic phase dimensions implies that the behavior of PLS nanocomposites cannot be understood by simple scaling arguments that begin with the behavior of conventional polymer composites. Since an interface limits the number of conformations that polymer mole-cules can adopt, the free energy of the polymer at the in-terfacial region is fundamentally different from that of polymer molecules far away from the interface i.e. bulk. The influence of interface always depends on the funda-mental length scale of the adjacent matrix. In the case of polymer molecules, this is of the order of the radius of gyration of a polymer chain, Rg and this is equal to 5∼10 nm. For this reason, in nanocomposites with a very few


volume percent of dispersed nanofillers in polymer ma-trix, the entire matrix may be considered to be a nano-scopically confined interfacial polymer. The restrictions in chain conformations will alter molecular mobility, re-laxation behavior, free volume, and thermal transition such as the glass transition temperature. Recent molecular dynamics simulation studies have shown that the dynamics of the polymer chains undergo radical changes at the interfacial region. For example, both the chain mobility and the chain relaxation times can be slowed by three orders of magnitude near phys-isorbing surfaces. Not only that, extensive surface forces apparatus experiments report how these novel dynamics of nanoconfined polymers are manifested through vis-cosity increases, two values orders of magnitude higher than the bulk values solid-like responses to imposed shear, and confinement induced ‘sluggish’ dynamics that suggest the existence of a ‘pinned’, ‘immobilized’ layer adjacent to the confining mica surface. The kinetics of intercalation of polymer chains into the silicate galleries to form layered nanocomposites has been studied by Vaia and coworkers [50]. They have in-vestigated the kinetics of the intercalation of PS above its entanglement molecular weight into octadecylammonium exchanged fluorohectorite. XRD reveals the average lay-er spacing in the unintercalated silicate to be 2.13 nm. During intercalation, this spacing increases to 3.13 nm. Measurement of this layer spacing as a function of time during intercalation yields a time-dependent fraction of intercalated silicate that is directly comparable to the time dependent number of beads in the slit, χ(t) and it is well fit by the prediction of a continuum diffusion model. In their model Vaia and coworkers considered the dif-fusion of polymer chains into an empty cylinder with a permeable wall and impermeable caps. The diffusion co-efficient determined by fitting χ(t) to this model, effec-tive diffusion coefficient, Deff, is large compared to the equilibrium self-diffusion coefficient in bulk polystyrene of the appropriate molecular weight. These results sug-gested that the process of intercalation of polymer chains into the two dimensional silicate galleries is limited by the transport of the polymer chains into the primary par-ticles of the silicate and not specifically by transport of polymer chains inside the silicate galleries. Now to understand the detail formation kinetics and physical properties of PLS-nanocomposites we need a clear molecular picture of the structure and dynamics of confined polymers. Researchers generally used the surfa-ces force apparatus [51-55] and computation studies [56- 67] to understand the behavior of confined fluids. Confinement of a fluid on length scales comparable to the molecular size has been demonstrated to dramatically alter its structure and dynamical pictures [51-67]. For ex-ample, confined fluids have been shown to solidify or

vertify at temperatures well above the bulk transition temperature [65]. Because of the strong interactions be-tween the confined molecules and the atoms or mole-cules of the confining medium, the mobility of the mole-cules in the confined environment is greatly reduced compared to the bulk [51,68-71]. Molecules in films of nanometer thickness organize in layers parallel to the surface. However, the confining medium induces two di-mensional orders in these layers [67]. On the other hand, in certain circumstances, confinement phenomenon may also have opposite effect of enhancing molecular mobi-lities in a supercooled thin film, relative to the bulk. Lee and coworkers [72] have presented an investigation of the molecular mechanism of polymer melt inter-calation using molecular dynamics simulations. They tried to find out the motion of polymer chains from a bulk melt into a confined volume. In their model they represented macromolecules by bead-spring chains, leave a reservoir of bulk melt to enter a slit of rectangular cross section and fixed dimension. They adopted a coarse- grained description of polymers, because such a picture has been demonstrated to provide a useful description of melt dynamics over longer time scales than would be ac-cessible with an atomistic model [73,74]. They also con-sidered a slit of fixed dimension to understand the trans-port of a polymer melt from the bulk into a confined vol-ume of fixed dimension. However, they did not consider the presence of surfactant molecules in the slit and the swelling of the slit during intercalation. They found that the intercalation process can be approx-imately characterized by an effective diffusion co-efficient that is twice as large as the equilibrium self-con-sistence in the bulk melt. Increasing the polymer-silicate interactions is found to induce spontaneous intercalation, but for a high-polymer silicate affinity, the amount of in-tercalated material at a given time is reduced compared to the case of a weaker polymer-silicate attraction. The crossover from polymer-silicate miscibility to interca-lated structures with increasing polymer-surface affinity has already been mentioned by Vaia and coworkers [50]. However, their study suggested that an important role may be played by the relaxations of polymer bridges that connect the two silicate surfaces. The number of these bridges, as well as their dynamical properties, will be controlled by chain length [75]. Manias and coworkers [76] extended Vaia and cow-orkers studies and presented a systematic study of the ki-netics of polymers entering 2 nm wide galleries of mica- type silicates as a function of polymer molecular weight and polymer-surface interactions. They varied the poly-mer-surface interactions in two ways: either through changing the surface modification, i.e. by varying the or-ganic coverage or through attaching strongly interacting sites-sticky groups-along the polymer chain. The poly-


mer-surface affinity is the one of the most crucial param-eters during nanocomposite preparation, since it controls the polymer-surface monomeric friction coefficient and thus determines the motion of the polymer next to a solid surface. The interaction between the polymer and silicate surface can be controlled in two novel and well-con-trolled ways: (i) keeping the polymer the same and mod-ifying the silicate surface, via controlled surface covering by surfactants of varying length at the same grafting den-sity, and (ii) keeping the organically modified surface the same and modifying the polymer friction coefficient, by attaching along the polymer chain a controlled amount of groups that interact strongly with the silicate surface. They [76] used the PS as polymer and the same octade-cylammonium modified fluorohectorite to study the in-tercalation process. While Vaia and coworkers [50] made all XRD measurements on similar hybrids during in-situ annealing; Manias and coworkers [76] used ex-situ sam-ple for XRD and other measurements. The ex-situ meth-od has several advantages over the in-situ method: First, one can able to anneal the sample under vacuum, thus re-ducing any polymer chain degradation. Second, one can heat and subsequently investigate the same side/surface of the pellet sample by XRD, a procedure that provides a much more accurate control of the annealing temperature than in-situ case, where pellet is heated in one side and is studied by XRD on the opposite side. They made several comparative studies by using concurrent in-situ small-an-gle neutron scattering (SANS) and intermediate-angle neutron scattering (IANS) to monitor the changes in di-mensions of the polymer, i.e. Rg, and also to follow the changes in the single chain scattering function during intercalation. Results of concurrent SANS and IANS studies shown that during intercalation the silicate gallery expansion di-rectly reflects the motion inside the 2 nm slit pore of the polymer chains. For the same polymer and the same an-nealing temperature, they found the experimentally measured effective diffusion coefficient depends strongly on the surfactant used for the modification of fluorohectorite. For several different polymer molecular weights and annealing temperatures they observed that Deff in-creases markedly with longer surfactant lengths and much more than is expected just from the enhancement of polymer mobility resulting from the polymer dilution by small hydrocarbon oligomers. Longer surfactants re-sult in less silicate surface area exposed to the polymer, thus effectively reduced the density attraction sites. On the other hand, introducing controlled amount of groups along the polymer chain that interact strongly with the silicate surface, resulting in a strong decrease of Deff. Therefore, increasing either the density or the strength of these attractive sites leads to much slower intercalation kinetics. However, an increase in site density or strength

must also increase the driving force for intercalation; evi-dently such increases depress the friction coefficient ζ much more strongly. To understand the atomistic details of the structure of the confined-intercalated-polystyrene chains inside the two dimensional silicate gallery, Manias and coworkers also carried out molecular dynamic simulation. Details regarding simulation can be found in ref. [76]. They used the rotational-isomeric-state (RIS) model to create initial polymer conformations of PS oligomers. Conformations that fit in the interlayer gallery were chosen, and the PS chains were equilibrated by an off-lattice Monte Carlo scheme that employed small random displacements of the backbone atoms and orientational biased Monte Carlo rotations of the phenyl rings; at the same time, the surfactants were equilibrated by a configurational biased scheme in coexistence with the polymer chains. After equilibrium, MD simulations were used to obtain the structure and density profiles of the intercalated poly-mer/surfactant films. The numbers of polymer chains and alkylammonium surfactants were chosen so as to match the densities found in the experimental studies. The re-sults suggested that the confined film adopts a layered structure normal to the solid surfaces, with the polar phe-nyls dominating the organic materials adsorbed on the walls, and the aliphatic groups predominantly in the cen-ter of the pore. 1H‐29Si cross-polarized nuclear magnetic resonance (NMR) measurements revealed a coexistence of ultra-fast and solid-like slow segmental dynamics throughout a wide temperature range, below and above Tg, for both the styrene phenyl and the backbone groups. The mobile moieties concentrate at the center of the slit pore, especially for the higher temperatures. This leads to a strong density inhomogeneity in the direction normal to the surface. Fast dynamics occur in the lower density re-gions, whereas slower dynamics occur in high-segment‐density regions close to the surface. This heterogeneous mobility combined with an observed persistence of mo-bility below the bulk glass transition temperature has im-plications to nanocomposite properties.

Rheology

Let us begin with‐what is rheology? Rheology is the study of the flow of matter. The name derives from the greek word “rheo” which means “to flow”. A solid will usually respond to a stress force by deforming and storing energy elastically. A liquid, however, will flow and dissipate energy continuously in viscous losses. A Newtonian liquid has a linear relationship between the shear rate and stress. Complex fluids are interesting because they exhibit both an elastic and viscous responses and exhibit a non‐linear relationship between


Figure 5. Schematic diagram describing the end‐tethered nanocomposites. The layered silicates are highly anisotropic with a thickness of 1nm and lateral dimensions (length and width) ranging from ∼100 nm to a few microns. The polymer chains are tethered to the surface via ionic interactions between the silicate layer and the polymer-end. Reproduced from ref [78] by permission of American Chemical Society.

the shear rate and strain. One of the properties often dealt within rheology is viscosity which measures how thick a fluid is. Some materials are intermediate between solids and fluids and the viscosity is not enough to characterize them. A solid material can be described by its elasticity or resilience: when it is deformed it will store the energy and fight back. Imagine a spring that regains its original shape after being deformed. The other extreme is a fluid which stores no energy while deformed and just flows. A viscoelastic material is intermediate and stores some energy and flows a little when deformed. Consider a system where a micron-sized probe particle is doped inside a rheologically complex fluid such as polymer network and Brownian fluctuations are recorded. Now question is how to predict the mechanical properties of the medium from the observed Brownian motion of the particle. If the fluid is Newtonian and the probe molecule is spherical, one can easily determine the viscosity of the medium from the measured diffusion coefficient by using the standard Stokes-Einstein (SE) relation. How- ever, a polymer network is generally viscoelastic, with a complex shear modulus having both elastic i.e. solid-like and viscos i.e. liquid-like components of similar magni- tudes over a large range of frequencies. Now question is- is it possible to extend the SE relation to determine shear complex modulus for such a system? An affirmative answer would allow one to measure the local rheological

properties not only in inhomogeneous materials but also at high frequencies that are inaccessible using mechanical rheometer. This subject is known as ‘microrheology’ [77]. Now consider a similar system where nanoscopic-sized particles are dispersed in polymer network, enjoying rap-id development in recent years, known as ‘nanorheol- ogy’. Here we are going to discuss about the melt-rheo-logical behavior of polymer materials where nanometer- size highly anisotropic particles are dispersed, known as polymer nanocomposites. In this section author survey some of the current development in the melt-state rheo-logical behavior of polymer nanocomposites based on layered silicates. The measurement of rheological behavior of any poly-meric material under molten state is crucial to gain fun-damental understanding of its processability. In the case of PLS-nanocomposites, the melt-rheological properties are also helpful to find out the degree of polymer-filler interactions and the structure-property relationship in nanocomposites. This is because rheological material functions are strongly influenced by the structure and the interfacial properties.

Linear Dynamic Rheological Properties Small deformation amplitude oscillatory shear measure-ments of polymeric materials are generally performed by applying a time dependent strain

γ(t) = γ0 sin(ωt) (1)

and measuring the resultant shear stress

σ(t) = γ0 [G'sin(ωt) + G"cos(ωt) ] (2)

where G' and G" are the storage and loss moduli, re-spectively and ω is the frequency. Krishnamoorti and coworkers [78] first described the flow behavior of delaminated nanocomposites based on poly(ε-caprolactone) (PCL) and nylon 6 (N6). Both nanocomposites were prepared by in-situ polymerization method in the presence of organically modified MMT, which engendered direct grafting of macromolecular chains on the MMT surface-a hairy layered silicate platelets structure (see Figure 5). The authors coded these nanocomposites as ‘end-tethered polymer layered silicate nanocomposites’. Figure 6 represents the rheological master curves based on linear viscoelastic measurements for a series of end-tethered PCL-MMT nanocomposites. The flow behavior of PCL nanocomposites differed significantly from that of the corresponding neat matrices, whereas the thermorheological properties of the nanocomposites were entirely determined by the behavior of the matrices. The slopes of log G'(ω) and


Figure 6. Storage modulus (G') for PCL‐based silicate nanocomposites. Silicate loadings are indicated in the figure. Master-curves were obtained by application of time-temper-ature superposition and shifted to T0 = 55 oC. Reproduced from ref. [78] by permission of American Chemical Society.

G"(ω) versus log aTω are much smaller than 2 and 1, respectively. Values of 2 and 1 are expected for non- crosslinked polymer melts, but large deviations occur, especially in the presence of a very large amount of layered silicate loading, which may be due to the formation of a network structure in the molten state. However, nanocomposites based on the in-situ polymerization technique exhibit a fairly broad molar mass distribution in the polymer matrix, which hides the relevant structural information and impedes the inter- pretation of the results. The similar behavior was also observed in the case of end-tethered N6-MMT nanocomposites. Ren and Krishnamoorti [79] then showed significant modification of flow behavior of nanocomposites when polymer chains are not tethered on the silicate surface. The nanocmposites of polystyrene-1, 4-polyisoprene (7 mol% 3, 4 and 93 mol% 1, 4) diblock copolymer (PSPI 18) were prepared with (0.7, 2.1, 3.5, 6.7, and 9.5 wt%) dimethyl dioctadecyl ammonium modified MMT by solution mixing in toluene. The homogeneous solution was dried extensively at room temperature and subsequently annealed at 100 oC in a vacuum oven for ∼12 h to remove any remaining solvent and to facilitate complete polymer intercalation between the silicate layers. The XRD patterns of PSPI18/2C18-MMT and PS/2C18-MMT clearly indicates the formation of intercalated structures, whereas the composite prepared with 1, 4-polyisoprene (PI) showed no change in gallery height. The intercalation of 2C18-MMT by PS and not by PI is consistent with the results of previous experimental work and theories of Vaia and coworkers [37,38] and of Balazs and coworkers [39,40]. The

Figure 7. Time-temperature superposed linear storage modulus (a, top) and loss modulus (b, bottom) for the series of 2C18M-based PSPI18 intercalated hybrids. As expected, the moduli increase with increasing silicate loading at all frequencies. At high frequencies, the qualitative behavior of the storage and loss moduli are essentially unaffected. However, at low frequencies the frequency dependence of the moduli grad-ually changes from liquidlike to solidlike for nanocomposites with 6.7 and 9.5 wt% silicate. Reproduced from ref. [79] by permission of American Chemical Society.

intercalation of PS into the silicate layers may be due to the slight Lewis base character imparted by the phenyl ring in PS, leading to the favorable interactions with the 2C18-MMT layers. All rheological measurements were conducted in the temperature range of 80∼105 °C. The time-temperature master curves for neat PSPI and various nanocomposites are presented in Figure 7. It is clear from the figures that viscoelastic behavior of PSPI significantly modified after nanocomposite formation. At high frequency region (where frequency > 10 rad.s), viscoelastic properties of PSPI were unaffected by the presence of silicate particle, while at the low frequency region (region where fre-quency < 10 rad.s), both G' and G" for the nano-composites exhibited a significant diminished frequency


dependence and this behavior was more prominent with higher loading of silicate layers, similar behavior as ob-served in the case of end-tethered nanocomposite. Similar behavior has also been noted for carbon black [80], calcium carbonate [81], and talc [82] filled polymers. However, in those cases the particle volume fractions were substantially higher, 5∼10 wt% for which strong frequency independent behavior is seen for PLS‐nanocomposites. Time-temperature superposition required simultaneous horizontal and vertical shifting of the shear moduli: bT G' and bT G" versus aTω, where aT is the horizontal shift factor, bT is the vertical shift factor and ω is the frequency. While aT for all nanocomposites followed the same WLF (Williama-Landel-Ferry) [83] dependence but bT did not. The authors attributed this could be the block architecture of the polymer examined, and the relative proximity of the order-disorder temperature to the tem-perature of the experimental measurements or may be due to formation of different types of structural ori-entation in the presence of organocaly. To understand the viscoelastic behavior observed at low frequencies region in the dynamic measurements for the nanocomposites, they conducted stress relaxation measurements. The stress relaxation data of these nano-composites in the terminal region showed a solid-like behavior. Like G', the effect was particularly pronounced at ≥ 6.7 wt% silicate loading. The authors attributed this behavior is due to the presence of stacks of intercalated silicate layers and those are randomly oriented in the pol-ymer matrix, forming three dimension network structure. These stacked intercalated silicate layers have only trans-lational motion. A large-amplitude oscillatory shear is able to orient these structures and reduce the solid like behavior. Another explanation may be the formation of PI micro-domains. Results of XRD revealed that only PS block diffused into the interlayer galleries, leaving the PI block out of the silicate galleries. These PI blocks can form phase-separated micro-domain structures, which ac-tually hinder the orientation of stack intercalated silicate layers under small-amplitude shear. Another explanation is the physical jamming of the dis-persed stack intercalated silicate layers owing to their highly anisotropic nature. Transmission electron micro-scopy image revealed the formation of intercalated struc-ture for the PSPI-based nanocomposites. On the basis of this mesoscopic structure and at low silicate loadings, au-thors suggested that, beyond a critical volume fraction, the tactoids and the individual layers are incapable of freely rotating and when subjected to shear are prevented from relaxing completely. This incomplete relaxation due to the physical jamming or percolation of the nano-scopic fillers leads to the presence of the pseudo-solid- like behavior observed in both the intercalated and ex-

foliated hybrids. To verify above percolation theory, Krishnamoorti and coworkers estimated the percolation threshold for these hybrids on the basis of stack size of the intercalated sili-cate layers. They assumed a hypothetical hydrodynamic sphere surrounding each tactoid and the percolation of these hydrodynamic spheres to signify the onset of in-complete relaxation and the presence of pseudo-solid- like behavior in the intercalated nanocomposites. To find out the relation between the number of silicate layers per tactoid, nper and the layered silicate weight fraction at percolation, wsil, per, as

(3)

where Rh is the radius of the hydrodynamic volume (in this case equivalent to the radius of the disk-like layered silicates), øper is the percolation volume fraction, hsil is the thickness of the silicate layers (generally 1 nm), ρorg and ρsil are the densities of the organic component and layered silicate respectively. By considering the uniform disks diameter (2Rh) of 0.5 µm and the wsil, per to be 0.067, they calculated the average tactoid size to be around 30 layers. This calculated value was well matched with the value calculated from XRD pattern and TEM measurement. Furthermore, this tactoid size implies that the effective anisotropy associated with the filler is 5∼10. It is this anisotropy, along with the random relative arrangement of the tactoids that leads to the observation of the percolation phenomenon at extremely low loading of the silicate. Krishnamoorti and coworkers also used above equation to estimate the percolation threshold for the exfoliated nanocomposites by assuming the same geometrical pa-rameters as considered previously. They suggested that in the case of exfoliated nanocomposites, there exist con-siderable local orientational order which has enormous consequences for the physical and mechanical properties of the hybrids. This orientational ordering along with the end-tethering of the polymer chains on the layered sili-cate surface in fact responsible for the non-terminal inter-mediate frequency response in the PCL and N6-based nanocomposites. Over the last few years, the linear dynamic and steady rheological properties of several nanocomposites have been examined for a wide range of polymer matrices including N6 with various matrix molecular weights [84], polyamides [85-91], polystyrene [92-96], polypropylene [97-102], polyethylene [103], ethylene vinyl copolymers [104-106], polycarbonate [107-109], poly (ethylene oxide) [110-112], poly(ε-caprolactone) [113, 114], poly(ethylene terephthalate) [115], polylactide


Figure 8. Complex viscosity versus frequency from a dynamic parallel plate rheometer (solid points) and steady shear viscosity ver-sus shear rate from a capillary rheometer (open points) at 240 °C for (a) pure HMW and its (HE)2M1R1 organoclay nanocomposite, (b) pure MMW and its (HE)2M1R1 organoclay nanocomposite. The nanocomposites contain ∼3.0 wt% MMT. Reproduced from ref. [84] by permission of Elsevier Science Ltd., UK.

[116-118], poly(butylene succinate) [119-121], poly [(butylene succinate)-co-adipate] [122,123], synthetic biodegradable aliphatic polyester (BAP) [124,125], liquid crystal polymer [126,127], PLS-nanocomposites based on immiscible and miscible polymers blend [128, 129], etc. Choi and coworers described the melt-state rheological behavior of a series of PEO/organoclay nanocomposites [111,112]. To understand both the effect of degree of dis-persion of silicate layers and the interaction between the organoclay surface and polymer matrix, they used three types of surfactants modified montmorillonite. First, they selected two different organoclays, which have different modifier concentration but the same alkylamonium salt. Second, they differentiated the types of alkylamonium salts having the same organic modifier. All nanocomposites were prepared via solvent casting method using chloroform as a co-solvent. XRD patterns and TEM ob-servations revealed the formation of intercalated nanocomposites. Rheological properties measurements

under molten state revealed that an increase in shear vis-cosity and storage and loss moduli of nanocomposites with clay content. Like other properties, they also fond that rheological properties of nanocomposites directly re-lated to the degree of dispersion of silicate layers in the polymer matrix and also the level of interfacial inter-actions between the layered silicate surface and polymer chains. They concluded that linear rheological properties are strongly correlated with the mesoscopic structure and it was postulated that the molecular weight and inter-action strength would affect the mesoscopic structure and the rheological properties of these nanocomposites. Fornes and coworkers [84] have conducted dynamic and steady shear capillary experiments over a large range of frequencies and shear rates of pure N6 with different molecular weights, and their nanocomposites with OMLS. Figure 8 shows bilogarithmic plots of the complex viscosity, |η*| vs. ω at 240 oC for pure N6 and (HE)2M1R1 nanocomposites based on (a) high molecular weight (HMW), (b) medium molecular weight (MMW),


Figure 9. Influence of frequency on shear storage modulus for pure LMW, and for LMW, MMW and HMW based nanocomposites. Reproduced from ref. [84] by permission of Elsevier Science Ltd., UK.

and (c) low molecular weight (LMW), obtained using the parallel plate oscillating rheometer. Figure 8 also shows a bilogarithmic plot of the steady-state shear viscosity η versus shear rate , obtained using a capillary rheometer. Inspection of these figures reveals a significant differ-ence between the nanocomposites, particularly at low frequencies. The HMW-based nanocomposites show very strong non-Newtonian behavior, and this is more pronounced at low frequencies. On the other hand, the magnitude of the non-Newtonian behavior gradually de-creases with decreasing molecular weight of the matrix, and with LMW it behaves like pure polymer. This trend is more clearly observed in the plot of G' vs. ω, due to the extreme sensitivity of G' towards dispersed morphol-ogy in the molten state (see Figure 9). The difference in the terminal zone behavior may be due to different ex-tents of exfoliation of the clay particles in the three types of matrices. At the other extreme, the steady shear capillary rheol-ogy shows a trend with respect to the matrix molecular weight. The HMW and MMW-based nanocomposites exhibit lower viscosities compared to that of their corre-sponding matrices, whereas the viscosities of LMW- based nanocomposites are higher than the pure matrix. This behavior is also due the higher degree of exfoliation in the case of HMW and MMW-based nanocomposites compared to the LMW-based nanocomposite. Finally they considered the differences in the melt vis-cosity among the three systems. Over the range of fre-quencies and shear rates tested, the melt viscosity of the

three systems follows the order HMW > MMW > LMW, and hence the resulting shear stresses exerted by the pure polymers also follow the same order. Therefore, during melt mixing the level of stress exerted on the OMLS by the LMW polyamide is significantly lower than those de-veloped in the presence of HMW or MMW polyamides. As a result, the break-up of layered silicate particles is much easier in the case of HMW polyamides, and lay-ered silicate particle dispersion is ultimately improved. The role of polymer molecular weight is believed to stem from an increase in the melt viscosity, facilitating the degradation of the taller stacks into shorter ones. The fi-nal step in exfoliation involves peeling away the platelets of the stacks one by one, and this takes time and requires the strong matrix-OMLS interaction to cause sponta-neous wetting. Aubry and coworkers were studied the dynamaic and steady flow properties of a polyamide-12 (PA12) melt layered silicate nanocomposites as a function of the sili-cate volume fraction, ø [88]. They found above a vol-ume fraction threshold øp is equal to 1.5 %, and below a critical strain γc, the storage (G') and loss moduli (G") were shown to exhibit a low-frequency plateau and the flow curve was shown to exhibit a stress, τy. The study of G', γc, and τy as a function of ø showed the energy needed for removing connectivity on a mesoscale did not depend on the silicate loading. These original properties were attributed to the existence, in the quiescent state, of mesoscopic domains composed of correlated silicate layers. Moreover, the steady shear response of all sam-ples at solid volume fractions above øp showed the ex-istence of a critical shear rate is equal to 1/s, separating a behavior governed by the networked domains from a be-havior dominated by the polymer matrix. Gelfer and coworkers have investigated the particular relationship among the molecular structure of polymer chains, morphology, and rheology of nanocomposites prepared by melt-blending of Cloisite organoclays and ethylene-co-vinyl acetate (EVA) and ethylene-co-methyl acrylate (EMA) random copolymers [104,106]. TEM ob-servation confirmed the mixed intercalated-exfoliated morphology in these nanocomposite systems. The melt- state rheological properties were very similar in EVA- and EMA-based nanocomposites. These materials ex-hibited a pseudo-solid like rheological behavior, which became more pronounced upon heating, especially at temperature above 180∼200 °C. Authors attributed this behavior is due to the physical gelation due to the for-mation of 3D tactoid network in the polymer matrix. They found that this gelation behavior is directly related to the overall content of organoclay and the extent of miscibility between the organoclay and polymer matrix. The SAXS data indicated that the silicate gallery spacing (d001), intercalated by EVA and EMA chains,


Figure 10. G' vs. reduced frequency for PS100 matrix (black line), CPS (A), and C-PEA (W). Silicate loading: 5 wt%. Reproduced from ref. [89] by permission of Wiley-VCH, Germany.

decreases with increasing temperature. At temperature above 200 °C, the desorption of surfactant in organoclay decreases the compability between the clay surface and the polymer matrix, which finally exhibited a LCST (lower critical solution temperature) type behavior between organoclays and polymer, enhancing the state of gelation. This behavior manifested itself by a reverse temperature dependence of viscoelastic properties and strong deviation of rheological behavior from the time‐temperature superposition principle. Hoffmann and coworkers [89] recently conducted rheo-logical measurements of nanocomposites of polystyrene (PS100) with synthetic mica (ME100) modified with amine-terminated polystyrene (AT-PS8) and 2-phenyl-ethylamine (PEA) respectively, in order to verify the presence of a particle network formation via inter-par-ticle interaction and self-assembly. Figure 10 represents G'(ω) vs. aTω for PS100 and its corresponding nano-composites prepared with AT-PS8 modified ME100 (C- PS) and PEA modified ME100 (C-PEA). The rheological responses of PS100 and C-PEA are the same, whereas the rheological response of C-PS is completely different. At the lowest frequencies, which correspond to the marked region III, G'(ω) strongly increases, and the slope approaches to zero. Such behavior is an indication of network formation involving the assembly of in-dividual plates composed of silicate layers. In the regime of intermediate frequencies (region II, see Figure 10) the G'(ω) value is lower in comparison to that of PS100. This might be due to dilution of the amine-terminated PS being below the entanglement molecular weight. On the other hand, in high frequency region (region I, Figure 10) the rheological behavior is the same for all systems. Sinha Ray and coworkers [116-118] have conducted the

Figure 11. Reduced frequency dependence of storage modulus, G' and loss modulus, G" of PLA and various PLACNs. Reprinted from ref. [118] by permission of Wiley-VCH, Germany.

dynamic oscillatory shear measurements of PLA nanocomposites with intercalated structure. Melt rheological measurements were conducted on Rheometric Dynamic Analyzer (RDAII) instrument using 25 mm diameter parallel plates with a sample thickness of ca. 1.5 mm and in the temperature range of 175∼205 °C. To avoid nonlinear response, the strain amplitude was fixed to 5 % to obtain reasonable signal intensities even at elevated temperature or low w. For each nanacomposite investigated, the limits of linear viscoelasticity were determined by performing strain sweeps at a series of fixed frequencies. The master curves were generated using the principle of time-temperature superposition and shifted to a reference temperature (Tref) of 175 °C, which was chosen as the most representative of a typical processing temperature of PLA. The master curves for G' and G" of pure PLA and various nanocomposites with different weight percenta- ges of C18 MMT loading are presented in Figure 11. At high frequencies (aT.ω > 10), the viscoelastic behavior of all nanocomposites was the same. On the other hand, at low frequencies (aTω < 10), both moduli exhibited weak frequency dependence with increasing C18MMT content, with a gradual change of behavior from liquid- like [G' ∝ ω2 and G" ∝ ω] to solid-like ( G' ≥ G") with


Figure 12. Flow activation energy as a function of C18- MMTcontent. Reprinted from ref. [118] by permission of Wiley-VCH, Germany.

increasing C18MMT content. The slope of G' and G" in the terminal region of the master curves of PLA matrix was 1.85 and 1 respectively. On the other hand, the slopes of G' and G" were considerably lower for all PLACNs compared to those of pure PLA. In fact, for PLACNs with high C18MMT content, G' becomes nearly independent at low aTω and exceeds G", characteristic of materials exhibit-ing a pseudo-solid-like behavior. Figure 12 represents the C18MMT content dependent (wt%) flow activation energy (Ea) of pure PLA and vari-ous nanocomposites obtained from an Arrhenius fit of master curves [118]. There was a significant increase of Ea for PLA/C18 MMT3 compared to that of pure PLA followed by a much slower increase with C18MMT content. This behavior may be due to the dispersion of intercalated and stacked C18MMT silicate layers in the PLA matrix. The dynamic complex viscosity (｜η*｜) master curves for the pure PLA and nanocomposites, based on linear dynamic oscillatory shear measurements, are presented in Figure 13 [118]. At low aTω region ( < 10 rad.s‐1), pure PLA exhibited almost Newtonian behavior while all nanocomposites showed very strong shear-thinning tendency. On the other hand, Mw and PDI of pure PLA and various nanocomposites were almost the same, thus the high viscosity of PLACNs were explained by the flow restrictions of polymer chains in the molten state due to the presence of MMT particles. Figure 14 represents the master curves for G' and G" of neat PBS and various PBSCNs prepared with two different types of OMLS [120]. At all frequencies, both G' and G" of nanocomposites increased monotonically with increasing OMLS loading with the exception of PBS/C18MMT1 and PBS/qC16SAP1 for which viscoe-

Figure 13. Reduced frequency dependence of complex vis-cosity (｜η*｜) of PLA and various PLACNs. Reprinted from ref. [118] by permission of Wiley-VCH, Germany.

lastic behavior was almost identical to that obtained for neat PBS. At high frequencies (aTω< 5), both moduli exhibited weak frequency dependence with increasing clay content, which means that there are gradual changes of behavior from liquid-like to solid-like with increasing clay content. Lepoittevin and coworkers [113] reported the melt rheo-logical properties of PCL-based nanocomposites pre-pared by melt intercalation method. G' and G" of unfilled PCL and PCL filled with 3 wt% of MMA-Na+, MMT‐Alk or MMT-(OH)2 were measured at 80 ºC in the fre-quency range from 16 to 10‐2 Hz. The rheological behav-ior of the PCL filled with 3 wt% of MMT-Alk and MMT-(OH)2 was significantly different compared to un-filled PCL and PCL/MMT-Na composites. The fre-quency dependence of G' and G" was, however, per-turbed by organically modified MMT. The effect was dramatic in the slope of G' which drops from 2 to 0.14 and 0.24 for MMT-(OH)2 and MMT‐Alk, respectively. The dependence of G' and G" on frequency with the filler content is presented in Figure 15 for the MMT- (OH)2 clay. When the clay content exceeded 1 wt%, not only the classical power laws for the frequency depend-ence of G' and G" were deeply modified, particularly in the case of G' but the moduli increased dramatically at low frequency. This is a characteristic of pseudo-solid- like behavior due to the formation of a network percolat-ing clay lamellae. The same behavior was also observed in the case of PLA or PBS-based nanocomposites [118, 120,121]. Sinha Ray and his coworker recently described the melt-state rheological properties of poly[(butylene succinate)-co-adipate] (PBSA) nanocomposites [122]. Cloisite® 30B (C30B) organoclay was used for the preparation of nanocomposites. Nanocomposites were


Figure 14. (a) Reduced frequency dependence of the storage modulus,G'(ω), and the loss modulus, G"(ω), of PBS and various PBSCNs prepared with C18-mmt clay. Tref ) 120 °C. (b) Reduced frequency dependence of the storage modulus, G'(ω), and the loss modulus, G"(ω), of PBS and various PBSCNs prepared with qC16‐sap. Tref ) 120 °C. Reproduced from ref. [120] with permis-sion of American Chemical Society, USA.

prepared at 135 oC in a batch mixer. Nanocomposites (PBSACNs) prepared with three different amount of C30B of 3, 6, and 9 wt% were correspondingly abbreviated as PBSACN3, PBSACN6, and PBSACN9. The structure of the nanocomposites was studied using XRD and TEM that revealed a coexistence of exfoliated and intercalated silicate layers dispersed in the PBSA matrix, regardless of the silicate loading. The angular ω dependence of storage, G'(ω) and loss modulus, G"(ω) of neat PBSA and PBSACNs with three different wt% of C30B loading are presented in Figure 16, parts a and b, respectively. At all frequencies, both G'(ω) and G"(ω) for PBSACN6 and PBSACN9 in-crease with increasing C30B content with the exception of PBSACN3 for which the viscoelastic response is al-most identical to that observed for neat PBSA. At high-ω region, the viscoelastic behavior of all PBSACNs is quite the same, with only a small systematic increase in G'(ω) with the C30B loading, indicating that the ob-served chain relaxation modes are almost unaffected by the presence of the layered silicate particles (Figure 16a and b). However, at the low-ω region, both dynamic moduli exhibit weak frequency dependence with C30B loading. For the 9 wt% of C30B loading, G'(ω) exceeds G"(ω) and becomes nearly independent of ω. To verify the interesting viscoelastic behavior observed at low frequency region in the dynamic oscillatory shear measurements for the nanocomposites with high wt% C30B loading, the linear stress relaxation measurements

were conducted. Results of linear relaxation behaviors of neat PBSA and PBSACNs are presented in Figure 17. For any fixed time after imposition of strain, the relaxa-tion modulus, G(t) increases with increasing C30B load-ing, similar to that observed in the dynamic oscillatory shear measurements. Similar to the behavior observed at high frequencies in dynamic mode (Figure 16a and b), the stress relaxation modulus of all PBSACNs is quite of the same magnitude as that of the neat PBSA at short times, with only a slight increase with C30B content (Figure 17). However, at long time periods, the pure PBSA and PBSACN3 relaxes like a viscoelastic liquid, while the PBSACNs with 6 and 9 wt% of C30B loading behave like a pseudo-solid-like material. Therefore, on the basis of both the dynamic oscillatory shear (Figure 16a and b) and linear stress relaxation measurements (see Figure 17), it is clear that C30B lay-ered silicate has a profound effect on the long relaxation time of the nanocomposites. For PBSACNs with C30B loading in excess of 3 wt% , the liquid-like behavior ob-served in the case of pure PBSA gradually changes to pseudo-solid-like behavior. A reasonable explanation for this low frequency viscoelastic behavior of PBSACNs is that the moderate interactions of the PBSA backbone with C30B surface lead to the high degree of confinement of polymer chains inside the silicate layers. As a result anisotropic silicate layers are fully dispersed in the PBSA matrix, as


Figure 15. Storage modulus (G0) and loss modulus (G00) for unfilled PCL and PCL modified by 3 wt% of MMT-Na, MMT-Alk, MMT-(OH)2 at 80 C [160]. Reproduced from ref. [113] by permission of Elsevier Ltd., UK.

observed in XRD patterns and TEM images [122]. Because of their highly anisotropic nature, the dispersed layered silicate particles would exhibit local correlations that finally cause the formation of micro-domains or mesoscopic structure [116,124,125]. Like in liquid crystalline and ordered block copolymer systems [130- 133] the presence of these micro-domains or mesoscopic structure causes only a slight increase of the low-ω elastic modulus that varies in low power-law fashion. This is the case for low C30B concentration (∼3 %). However, beyond this concentration, exfoliated and or disordered intercalated silicate layers form a network- type structure rendering the system highly elastic as revealed by the low frequency plateau. Such a plateau is similar to the one observed in rubber-toughened polymers [134,135] where rubber particles form a

Figure 16. Frequency dependence of (a) dynamic storage, G'(ω) and (b) loss, G"(ω) moduli of neat PBSA and various PBSACNs. Reprinted from ref. [122] by permission of Wiley‐VCH, Germany.

percolating network that imparts the blend with solid-like behavior. Such a behavior can also be seen on the dynamic complex viscosity, η*(ω), shown in Figure 18. Little effect of C30B addition is observed at high frequencies, where the relaxation mechanism is mainly dominated by that of the PBSA matrix, whereas at low frequencies, the relaxation is that of particle-particle interactions inside the percolating network of the silicate layers. In a recent literature Huang and Han reported the melt- state rheological behavior of PLS nanocomposites based on thermotropic liquid-crystalline polymers (TLCP) [126]. In their study they used two different types of TLCPs such as TLCP having pendent pyridyl group (PyHQ12) and TLCP having pendent phenylsulphonyl group (PSHQ12). They also used two different types of


Table 1. Characteristics of Organically Modified Layered Silicates (OMLS) used in this Research

Organoclay Type Code Modifier Concentration(meq/ 100 g) Chemical Structure of Organic Modifiera δ of Organic Modifierb, c

Cloisite 15 A C15 A 125 H3C HTN+

HT

CH3

H3C HTN+

HT

CH3

16.94

Cloisite 93 A C93 A 90 H3C HTN+

HT

H

H3C HTN+

HT

H

17.96

Cloisite 30 B C30 B 90

CH2CH2OH

CH2CH2OH

H3C HTN+

CH2CH2OH

CH2CH2OH

H3C HTN+ 21.08

a HT is hydrogenated tallow (∼65 % C18; ∼30 % C16; ∼5 % C14)b δ is the solubility parameter calculated by group contribution method of Fedorsc δ value of neat PBSA is 23.8

Figure 17. Stress relaxation behavior of Neat PBSA and vari-ous PBSACNs. Reprinted from ref. [122] by permission of Wiley-VCH, Germany.

OMLS such as C30B and C20A for the preparation of nanocomposites. Nanocomposites were prepared by solution blending method using pyridine as a co-solvent. XRD patterns and TEM revealed the high degree of dispersion of silicate layers in PyHQ12/C30B nanocomposites, whereas silicate layers formed aggregates in PyHQ12/C20A and PSHQ12/C30B nanocomposites.

Authors presented dramatic differences in linear dy-namic viscoelastic properties between PyHQ12/C30B and PSHQ12/C30B nanocomposites. They attributed that the presence of strong interaction between PyHQ12 poly-mer chains with C30B surface through hydrogen bond is main responsible factor for significant improvement in rheological properties in case of PyHQ12/C30B nanocomposite. Authors also observed a considerable amount of loss in the degree in liquid crystallinity of PyHQ12 matrix in PyHQ12/C30B nanocomposite, although it has intercalated structure. This is due to the strong interaction between polymer backbone and clay surface, which fi-nally lead to the highly restricted movement of the poly-mer chains in nanocomposite. The same type of con-clusion has been made by this group of researchers in case of PC/C30B nanocomposite, but they did not con-sider the degradation of matrix or C30B at the processing temperature (260 oC) [109]. To find out the direct relation between the structure and melt-state rheological properties in case of nanocomposites, Sinha Ray and coworkers prepared a series of PLS nanocomposites based on PBSA [123]. Three different types of commercially available organically modified montmorillonite (OMMT) were used for the preparation of nanocomposites. By varying the hydrophobicity, and consequently the favorable interactions of the surfactant with the polymer matrix, a spectrum of structures including phase-separated, intercalated, disordered inter-


Figure 18. Frequency dependence of dynamic complex vis-cosity (η*) of neat PBSA and various PBSACNs. Reprinted from ref. [122] by permission of Wiley-VCH, Germany.

calated, and intercalated-exfoliated were obtained (Fig- ure 19). The chemical structure of the specific surfactant and the cation exchange capacity of each of the OMMT used in this research are presented in Table 1. The small amplitude oscillatory shear storage modulus, G'(ω), of the neat PBSA and the three nanocomposites

is presented in Figure 20. As expected, G'(ω) of the nanocomposites increases with increasing the degree of dispersion of the silicate layers in the PBSA matrix over all frequency range. At high frequencies, only a slight in-crease in modulus with respect to that of the pure PBSA is observed. G'(ω) of the matrix and the nanocomposites decreases linearly with lowering of frequency. However, at very low frequencies a significant increase in G'(ω) is observed in the case of PBSA/C30B nanocomposite, in-dicating that C30B silicate layers have strong effect on the chain relaxation of PBSA. Upon increase in the fa-vorable specific interactions between the surfactant and PBSA matrix, G'(ω) becomes a weak function of fre-quency and exhibits a pseudo-plateau in the terminal zone of the pure PBSA. This gradual change of behavior from liquid-like to solid-like is mainly attributed to the extent of dispersion and distribution of the clay lamellae that form three dimensional percolating networks [116]. This of course depends on the extent of enthalpic interactions between the PBSA backbone and the surface of OMMTs, which finally leads to the confinement of polymer chains inside the silicate galleries. Because of their highly anisotropic nature, the fully dispersed silicate layers would exhibit local correlations, which finally lead to the formation of three dimensional mesoscopic structures [123] and the tendency of formation of this mesoscopic structure gradually decreases with decreasing

Figure 19. TEM bright field images of (a) PBSA/6CNa hybrid, (b) PBSA/6C15A nanocomposite, (c) PBSA/6C93A nanocomposite, and (d) PBSA/6C30B nanocomposite. Reproduced from ref. [123] by permission of Elsevier Science Ltd., UK.


Figure 20. Frequency dependence of dynamic storage modulus, (G'(ω)), of neat PBSA and various nanocomposites. Repro- duced from ref. [123] by permission of Elsevier Science Ltd., UK.

the degree of dispersion of intercalated silicate layers in the polymer matrix. Among the three OMMTs used for the preparation of PBSA nanocomposites, C30B has the higher degree of interactions with PBSA matrix and as a result intercalated silicate layers are relatively well dispersed in the PBSA matrix (see Figure 19). Conse- quently, silicate layers are highly correlated in the PBSA/C30B nanocomposite. With decreasing the degree of dispersion of intercalated layers in the PBSA matrix, the tendency of formation of this type of correlated structure is also decreased and thus the increment in modulus systematically decreases from PBSA/C30B nanocomposite to PBSA/C15A nanocomposite. The solidlike behavior can also be evidenced by the sharp increase in viscosity in the low frequency region for nanocomposites, where the pure PBSA shows rather a Newtonian behavior (see Figure 21). Parts a and b of Figure 22 show the time dependent evolution of the storage and loss moduli for PPCH8 (PP = 91 wt%, MMT = 9 wt%) and PPCH9 (PP = 82 wt%, MA = 9 wt% and MMT = 9 wt%) samples, subjected to small strain oscillatory shear tests every 10 min during their total annealing time of 3 h at 200 oC [97]. At high frequencies the elastic moduli of PPCH8 and PPCH9 are comparable at similar annealing times, and both decrease with annealing due to possible degradation of the PP- matrix. At low frequencies the elastic modulus of PPCH 9 is qualitatively different than that of PPCH 8. The low-frequency elastic modulus of as-extruded PPCH9 is always higher than that of PPCH8, indicating that most of the micro-structural development in PPCH9 has already occurred during the extrusion process, while only subtle micro-structural changes occurred during annealing.

Figure 21. Frequency dependence of dynamic complex vis-cosity (η*) of neat PBSA and various nanocomposites. Reproduced from ref. [123] by permission of Elsevier Science Ltd., UK.

Furthermore, the elastic modulus of PPCH8 at low fre-quency decreases with annealing time, but that of PPCH9 remains more or less unchanged. Thus at high frequency, the response of the PPCH9 hybrid is dominated by the matrix, while at lower frequencies its solid-like response is strongly influenced by the presence of clay. On the other hand, the low frequency response of PPCH8 is not dominated by the presence of clay, which highlights the important role played by PP-MA in the formation of the hybrids. The above results show that the solid-like rheological behavior of nanocomposites at lower frequencies is com-pletely independent on the fine structure of the nano-composites i.e., whether it is end-tethered or stacked in-tercalated, but it is depends primarily upon the amount of clay loading in the nanocomposites. Galgali and cow-orkers [97] have also shown that the typical rheological response in nanocomposites arises from frictional inter-actions between the silicate layers and not due to the im-mobilization of confined polymer chains between the sil-icate layers. They have also shown a dramatic decrease in the creep compliance for the PPCH prepared with MA modified PP and 6 wt% MMT. In contrast, for PPCH prepared with MA modified PP and 9 wt% of MMT, they show a dramatic three-order of magnitude drop in the zero shear viscosity beyond the apparent yield stress, suggesting that the solid‐like behavior in the quiescent state is a result of the percolated structure of the layered- silicate. In order to characterize the viscoelastic properties of the so-called network formation, Aubry and coworkers [88] measured G' as a function of the layered silicates volume fraction, ø. Parts a and b of Figure 23 respectively


Figure 22. Zero shear viscosity as a function of annealing time for several PPCH samples in the presence (denoted by filled symbols) and absence (denoted by open symbols) of PP-MA. (b) Zero-shear viscosity as a function of clay content for sam-ples with and without compatibilizer. Reproduced from ref. [97] by permission of American Chemical Society.

represents G' and G" of PA12‐based nanocomposites. The ø dependence of G' is presented in Figure 24, which is rather well fitted by a quadratic equation:

G' ∝ø (4)

According to them the appearance of nonlinearities in the viscoelastic response of nanocomposites at a strain γc (see Figure 25) is due to partial rupture of connectivity within the system and it is found that γc is inversely re-lated to the volume fraction of layered silicate added (ø), i.e. γc ∝ø‐1 (5)

The amount of elastic energy stored in the nanocomposite at γc is the energy needed (termed as yield energy, Ey) to break some crucial connections between silicate entities and allowing the system to yield, but not to disturb, as shown by the relatively smooth decrease of both viscoelastic moduli above γc (see Figure 25).

Figure 23. (a) Storage modulus G' as a function of frequency at (●) 0 %, (O) 0.5 %, (■) 1 %, (□) 1.5 %, (∆) 2.5 %, (▲) 5 %, and (▼) 10 %. (b) Loss modulus G" as a function of fre-quency at (●) 0 %, (O) 0.5 %, (■) 1 %, (□) 1.5 %, (∆) 2.5 %, (▲) 5 %, and (▼) 10 %. Reproduced from ref. [88] by per-mission of The Society of Rheological, USA.

This yield energy, Ey can be defined as follows:

′ (6)

where τis the shear stress. Combining the equations (5) and (6), the yield energy, Ey is found to be independent of the layered silicate vol-ume fraction, ø:

∝ø0 (7)

Now it will be very interesting if we compa0re this yield energy data with the “cohesive” energy (Ec) data for aqueous clay suspensions. Ramsay in 1986 [130,131] and Sohm and Tadors in 1989 [132] respectively determined the ø dependence of Ec for laponite dispersion (Ec ∝ø1.8) and for MMT suspensions (Ec ∝ ø3.1) in the gel structure. However, the concept of cohesive energy, although defined by the same equation as (6), still differs from the concept of yield energy


Figure 24. Plateau storage modulus G' as a function of nano-filler volume fraction. The solid line corresponds to Eq. (4). The square of the correlation coefficient r2 is 0.95. Reproduced from ref. [88] by permission of The Society of Rheological, USA.

discussed here. Indeed the term cohesive energy is appropriate for sys-tems which extensively disrupt at a critical strain γc due to rupture of all elastic links, as observed in clay gels [130], whereas the term yield energy is more appropriate for systems which yield above γc due to the rupture of some crucial elastic links, as generally observed in the case of layered silicate-based nanocomposites as dis-cussed here. The difference in scalling behavior of the elastic energy stored at γc means that the structure of the percolated network in layered silicate nanocomposites differs significantly from that of the gel in concentrated aqueous swelling layered silicate suspensions. Recently, Okamoto and coworkers completely disagree with these interpretations. In the former structure, adding clay par-ticles seems to have no significant effect on the average connectivity of the network as Ey ∝ø0, whereas increas-ing the layered silicate loading in the latter increases the number of network links as Ec depends strongly on ø. The peculiar feature of the scaling behavior of the Ey of the percolated network guggests that the entities respon-sible for the yield properties of the nanocomposites are not individual layered silicate particles, rather, silicate domains, whose characteristic size independent of lay-ered silicate loading, as mentioned by Solomon and cow-orkers [98] to interpret results from flow reversal experiments. However, Mederic et al. proposed that the existence of a unique characteristic fc ∼ 0.2 Hz, making a change in the power-law frequency dependency of G' for all nanocomposites samples, is another macroscopic time signature of these domains. Not only that, it should be noted here that for a given

Figure 25. (a) Storage modulus G' as a function of strain γ at (●) 0 %, (O) 0.5 %, (■) 1 %, (□) 1.5 %, (∆) 2.5 %, (▲) 5 %, and (▼) 10 %. (b) Loss modulus G"(ω) as a function of strain γ at (●) 0 %, (O) 0.5 %, (■) 1 %, (□) 1.5 %, (∆) 2.5 %, (▲) 5 %, and (▼) 10 %. Reproduced from ref. [88] by per-mission of The Society of Rheological, USA.

sample at a given frequency, G' and G" have the same or-der of magnitude showing that dissipative phenomena are as important as elastic phenomena in the behavior of nanocomposites. This point is all the more important to be emphasized since G" results are scarcely presented and discussed in the leature dealing with the rheology of layered silicate nanocomposites. The ø dependence of the low-frequency plateau value of G", presented in Figure 26, shows that

G' ∝ø 2.4 (8)

This observation tends to show that, contrary to elastic contributions, viscous contribution depend on the layered silicate loading in a more significant way. It is also confirmed by the ø dependence of the frequency marking


Figure 26. Plateau storage modulus G" as a function of nano-filler volume fraction. The solid line corresponds to Eq. (8). The square of the correlation coefficient r2 is 0.95. Reproduced from ref. [88] by permission of The Society of Rheological, USA.

Figure 27. The steady-shear rheological behavior for a series of intercalated nanocomposites of poly(dimethyl 0.95-diphenyl 0.05 siloxane) with layered silicate (dimethyl ditallow mont-morillonite) at 25 °C. The silicate loading is varied and are not-ed in the legend. Reproduced from ref. [130] with permission of Springer‐Verlag Berlin Heidelberg.

the change in the power-law dependency of the loss modulus. The solid content dependence of the dissipative properties could be assigned to the multiscale origin of the viscous dissipation. However, viscous dissipation comes from many contributions such as from viscous dissipation due to relative motions of domains on a mesoscopic length scale but also from relative motions of exfoliated dispersed layered silicate particles on nano- or micro-scopic length scales.

Steady Shear Rheology In 1996, Krishnamoorti and coworkers [77] first described the steady shear rheological behavior of nano-

Figure 28. The steady-shear rheological behavior for a series of delaminated nanocomposites of polydimethylsiloxane with di-methyl ditallow montmorillonite at 25 °C. The steady-shear viscosity shows an increase with respect to that of the pure-pol-ymer at low shear rates but still obeys Newtonian type behav-ior, even at the highest silicate loadings examined. Reproduced from ref. [130] with permission of Springer-Verlag Berlin Heidelberg.

composites based on poly(dimethyldiphenyl siloxane) (PDS) and dimethyl ditallow ammonium modified montmorillonite (2M2T-MMT). Figure 27 represents the steady-shear rheological behavior of a series of intercalated poly(dimethyldiphenyl siloxane) [it is a copolymer of poly(dimethyl siloxane) and poly (diphenyl siloxane)]/2M2T‐MMT nanocomposites with varying silicate contents at 28 °C. The viscosity of nanocomposites was increased considerably and for a fixed shear rate, increases monotonically with silicate loadings. In the low-shear rate region ( < 2 s‐1) neat polymer showed Newtonian behavior, whereas intercalated nanocomposites showed shear thinning behavior and this shear thinning behavior was more prominent with higher silicate loading. At high shear rate both neat polymer and nanocomposites displayed strong shear thinning behavior. This observation indicates highly anisotropic intercalated layered silicate particles alter the relaxation dynamics of the polymer, leading to the non-Newtonian viscosity behavior of nanocomposites at all shear rates. More interesting behavior was observed in the case of poly(dimethyl siloxane)/2M2T-MMT nanocomposites, where layered silicates are fully delaminated in the polymer matrix, the steady-shear viscosity behavior of nanocomposites systematically increased with silicate loading but still obeys the Newtonian behavior in the lower shearrate region. Figure 28 represents the steady- shear rheological behavior of a series of intercalated poly(dimethyl siloxane)/2M2T‐MMT nanocomposites with varying silicate contents at 28 °C This indicates delaminated silicate layers have no effect on the relaxation dynamics of poly(dimethyl siloxane). There- fore, the rheological behavior of these nanocomposite


Figure 29. shear rates dependent viscosity of pure PLA and various PLACNs measured at 175 oC.

systems is similar to the rheological behavior of conventional filler filled systems. Figure 29 represents the shear rates dependent viscosity of pure PLA and various PLACNs measured at 175 oC. While the pure PLA exhibits almost Newtonian behavior at all shear rates, PLACNs exhibited a non-Newtonian behavior. All PLACNs showed a very strong shear-thin-ning behavior at all measured shear rates and this behav-ior is analogous to the results obtained in the case of os-cillatory shear measurements (see Figure 13). Additio- nally, at very high shear rates, the steady shear vis-cosities of PLACNs were comparable to that of pure PLA. These observations suggest that the silicate layers are strongly oriented towards the flow direction at high shear rates. Like PLA-based nanocomposite systems, all PBSCNs show very strong shear thinning behavior at all shear rates whereas neat PBS exhibits Newtonian behavior. At very high shear rates the viscosities of the nano-composites are comparable to that of pure PBS. The shear viscosity as a function of shear rate for BAP/OMMT and BAP is presented in Figure 30 [124,125]. Like previous systems, the viscosity of the BAP/OMMT nanocomposites were also decreased with increasing shear rate, however, at very low shear rates, the shear viscosity data exhibited a Newtonian plateau even for high OMMT content. With increasing shear rate, the nanocomposites exhibit higher degrees of shear- thinning behavior compared to the pure polymer. A similar behavior was also observed by Krishnamoorti and coworkers [78] in the case of delaminated PCL- based nanocomposites with several silicate loadings. These observations suggest that the silicate layers are strongly oriented towards the flow direction at high shear rates, and that the shear thinning behavior observed at high shear rates is dominated by that of pure polymer.

Figure 30. Shear viscosity vs. shear rate of BAP/OMMT nano-composites for various OMMT loadings at 140 ºC. Reproduced from ref. [124] with permission of American Chemical Society, USA.

Like dynamic viscoelastic properties, steady shear vis-cosity of nanocomposites also systematically increased with increasing favorable interaction between the PBSA matrix and organic modifier. For comparison purposes, the small amplitude oscillatory shear viscosity is also re-ported on the Figure 31. As can be expected, the steady shear viscosity and the dynamic viscosity overlap very well for the pure PBSA for ω = (Cox-Merz rule holds). However, for the nanocomposites, such a rule fails. The steady shear viscosity becomes lower than the dynamic shear viscosity. At high shear rate, the nano-composites loose their solid‐like behavior and a rather classical. Newtonian behavior is observed for the three nanocomposites. This might be due to the destruction of the percolating network and the alignment of the silicate layers in the direction of flow. The polymeric chains en-trapped between these thin channels of silicate layers are highly oriented and flow easily due to the loss of the den-sity of their entanglements with the neighbouring chains. This loss of local entropy decreases the local frictions and thus facilitates the chain movements in the direction of flow. Such behavior is similar to that of layered poly-mer blends or reinforced polymers that show a dramatic decrease in their viscosity when submitted to a strong shear flow [38-40]. The increase in shear viscosity of the PLS-nanocomposites was recently analyzed using a mean- field theory [111]. The viscosity at high shear rates showed more decreased values from the zero-shear viscosities with increasing clay loading, and the values were identical to those of virgin polymer. Although the exact mechanism which causes the shear-thinning behavior still is not clear, however, it can be deduced that the orientation of the silicate layers under shear is the main


Figure 31. Steady shear viscosity of neat PBSA and various nanocomposites as a function of shear rate. Reproduced from ref. [123] with permission of Elsevier Science Ltd.

cause. With increasing shear rate, the intercalated polymer chain conformations change as the coils align parallel to the flow [133]. Nevertheless, because of this shear-thinning property, the nanocomposites can be processed in the melt state using the conventional equipment available in a manufacturing line. PLS nanocomposites [1] always exhibit significant de-viations from the empirical Cox-Merz relation [134], while all neat polymers obey the empirical relation, which stipulated that, for = ω, the viscoelastic data obeys the relationship

η() = ｜η*(ω)｜ (9)

Typically, the quiescent state linear dynamic oscillatory η*(ω) exceeds the steady shear η(), with the discrepancy being largest at low shear rates. Furthermore, a comparison of the steady shear η() with the aligned state ηal*(ω) clearly demonstrates that η() ≥ηal*(ω), with the values at high shear rates being comparable. These results suggest that even at low shear rates, the application of steady shear results in at least some alignment of the silicate layers. The first normal stress difference (N12=σ11 - σ22), a measure of the elasticity, for the disordered PS-PI based nanocomposites when compared at the same shear stress (σ12), is independent of silicate loading and identical to that of the unfilled polymer [135]. Those measurements were typically restricted to high shear rates (to obtain reliable values of N12), where the silicate layers are believed to be oriented and only relatively small changes are observed in the viscosity data. It has been suggested that the near independence of the recoverable strain (=N12/σ12) on the silicate loading and the near equivalence to that of

Figure 32. Steady shear viscosityηas a function of shear rate at (●) 0 %, (O) 0.25 %, (■) 0.5 %, (□) 0.75 %, and (∆) 1 %. Reproduced from ref. [88] by permission of The Society of Rheological, USA.

the unfilled polymer melt, is a result of the ability of the two-dimensional silicate layers to be preferentially oriented by shear flow [135]. Solomon and coworkers [89] have performed flow re-versal experiments to examine changes in structure due to flow in PP based nanocomposites. The transient flow- reversal stress response exhibits a stress overshoot, whose magnitude increases with increased quiescent waiting time between flow reversals. While a scaling of the stress overshoot by 1/c (c being the concentration) leads to the development of a mastercurve with respect to time, the start-up transient stress exhibits a simple strain scaling. These results are interpreted in the context of the silicate layers being non-Brownian and the stress re-sponse being dictated by hydrodynamics alone. Figure 32 represents the steady shear apparent viscosity η, for PA12-based nanocomposite samples at low load-ings, from 0 wt% up to 1 wt%. On the basis these data, Aubry and coworkers tried to determine an intrinsic vis-cosity [η] and an interaction constant k, by fitting the curve to the second‐order Einstein‐type equation:

η0 = 1+[η]ø + k([η]ø)2 (10)

The least-squares fit leads to [η] ∼100 and k ∼0.5, which confirms the same results obtained by Utracki and coworkers [136] for the similar organoclay based nano-composite systems. In 2003 Jeon and coworkers [110,111] proposed an alternative method to calculate the [η] by fitting the relative viscosity versus volume fraction plot using a modified Krieger’s empirical equation, replacing the effective maximum packing volume fraction by the


Figure 33. (a) Relative Newtonian viscosity as a function of nanofiller volume fraction, ø. The solid line corresponds to Eq. (10), with [η] = 100 and k = 0.5. The square of the corre-lation coefficient r2 in 0.83. (b) Relative Newtonian viscosity as a function of normalized nanofiller volume fraction. The line corresponds to Eq. (11), with øvp = 1 % and [η] = 65. The square correlation coefficient r2 = 0.85. Reproduced from ref. [88] by permission of The Society of Rheological, USA.

viscosity percolation threshold øvp as

[ ] vp

vpr

φη

φφη

−

⎥⎥⎦

⎤

⎢⎢⎣

⎡−= 10 (11)

On the basis of Figure 32, they considered øvp is equal to 1 wt% is the viscosity percolation threshold corre-sponds to the critical volume fraction at which the vis-cosity tends to diverge, showing no Newtonian plateau at low shear rates. Figure 33b shows that the relative vis-cosity versus volume fraction plot can be well fitted by Eq. (11); [η] obtained from the beast least-squares fit is ∼ 65. This result is in good agreement with the result

obtained from equation 5, given the uncertainty in the de-termination of the critical volume fraction øvp. By knowing the value of [η] and the aspect ratio p (ratio of diameter and thickness) of the disk-like layered silicate particles can be inferred:

[η] = 2.5 + 0.025 (1 + p1.47) (12)

Again by considering the value of [η] in between 65 to 100, p is shown ti lie between 200 and 260. This result is about one-half of the average aspect ratio of individual MMT particles [135]. This indicates exfoliation of lay-ered silicates particles is not perfectly achieved, even at very low layered silicate content. The volume fraction of freely rotating disks with radius r and thickness e (aspect ratio, p = 2r/e) isπr2e/4 = 3/2p (3πr3) times the volume fraction of equivalent of hard spheres. Assuming a hard sphere random close packing ∼64 %, they calculated the maximum packing volume fraction of disk-like particles (ømcalc) with an aspect ratio 200 and 260 respectively and this value is about 0.48 % and 0.38 % respectively. Further, assuming a critical vol-ume fraction of spherical particles at percolation to be ∼30 %, the freely rotating disk-like layered silicate par-ticles are expected to be percolated at ømcalc ∼0.23 % and 0.18 % respectively. All of these calculations are ap-proximate, insofar as they do not take into account the presence of large aggregates. Present author believe that the real close packing volume fraction and percolation threshold most likely occur at higher volume fractions, possibly explaining the relatively “high” value of øvp.

Elongation Flow Rheology Okamoto and coworkers [137] first conducted elonga-tion tests of polypropylene based nanocomposite (PPCN4) in the molten state at constant Hencky strain rate, ‧ε0 using elongation flow rheometer. Figure 34 shows double-logarithmic plots of the transient elonga-tion viscosity ηE( ‧ε0 ; t) versus time t, observed for PPCN4 (4 wt% of MMT) at 150 oC with different ‧ε0 values ranging from 0.001 to 1.0 s‐1. The solid line on the curve ‧ε0 represents 3η0(; t), the 3-fold shear viscosity of PPCN4, measured with a constant of 0.001 s‐1 at 150 oC. At short times, ηE( ‧ε0 ; t) gradually increases with time, but is independent of ‧ε0 ; this is generally called the linear region of the ηE ( ‧ε0 ; t) curve. After a certain time tηE, generally called the up-rising time (marked with the upward arrows), there is a rapid upward deviation of ηE ( ‧ε0 ; t) from the curves of the linear region. On the other hand, the shear viscosity curve shows two distinctive features: first, the extended Trouton rule is not valid in this case and second, the shear viscosity of PPCN4 increases continuously with time within the ex-perimental time span. This time-dependent thickening


Figure 34. Time dependence of elongation viscosity for PP/clay (4) (PPCN4) melt at 150 ºC. The upward arrows in-dicate up-rising time for different strain rate. The solid line shows three times the shear viscosity, taken at a low shear rate of 0.001 s‐1 on a cone plate. Reproduced from from ref. [137] with permission of American Chemical Society, USA.

behavior, as mentioned before, is called rheopexy. These

Figure 36. Double‐logarithmic plots of the transient elongationviscosity ηE( ‧ε0 ; t) versus time t, observed for PLACN5 at 170 oC with different 0ε& values ranging from 0.01 to 1.0 s‐1.

differences in the time-dependent responses reflect differences in the shear flow-induced versus elongation- induced internal structure formation in the case of

Figure 35. TEM micrographs showing PPCN4 elongated at 150 ºC with (a) ε0 = 1.0 s‐1 up to ε0 = 1.3 s‐1 (λ = 3.7) and (b) ε0 = 0.001 s‐1 up to ε0 = 0.5 s‐1 (λ = 1.7); respectively. Upper pictures are in the x-y plane, and lower are in x-z plane along the stretch-ing direction. Reproduced from from ref. [138] by permission of American Chemical Society, USA.


Figure 37. Hencky strain rate dependence of the up-rising Hencky strain (εηE) = ‧ε0 × tηE taken for PLACN3 at 170 oC.

PPCN4 in the molten state. The same experiments conducted with a PP-MA matrix without clay did not exhibit any strain-induced hardening or rheopexy behavior in the molten state. Figure 35 represents typical TEM photographs of the center portions of the recovered samples after elongation. The x- and y-axes of the elongated specimen correspond to directions parallel and perpendicular to the stretching direction, respectively. A converging flow is applied to the thickness direction (y- and z-axis) with stretching if the assumption of an affine deformation without volume change is valid. Interestingly, for the specimen elongated with a high strain rate, there is perpendicular alignment of the silicate layers (edges) along the stretching direction (x-axis) in the x-y plane. For the x-z plane, the silicate layers (edges) disperse into the PP-MA matrix along the z-axis direction rather than randomly, but these faces cannot be seen in this plane. On the basis of experimental results and two-directional TEM observations, the authors concluded that the formation of a “house-of- cards” like structure was observed under slow elongational flow. Details regarding the data collection and explanations are presented in reference [137]. Sinha Ray and coworkers [118] conducted elongation tests of PLACN5 (PLA nanocomposites prepared with 5 wt% of C18MMT) in the molten state at constant Hencky strain rate, ‧ε0 using elongation flow rheometry [138]. On each run of the elongation test, samples of 60 × 7 × 1 mm3 size were annealed at a predetermined tem-perature for 3 min before starting the run in the rhe-ometer, and uniaxial elongation experiments were con-ducted at various ‧ε0 ranging from 0.01 to 1 s‐1. Figure 36 shows double-logarithmic plots of the transient elonga-tion viscosity ηE( ‧ε0 ; t) versus time t, observed for PLACN5 at 170 oC with different ‧ε0 values ranging from 0.01 to 1.0 s‐1. Figure shows a strong strain-induced

hardening behavior for PLACN5. In the early stage, ηE gradually increases with t but almost independent of ‧ε0 . This is generally calling the linear region of the viscosity curve. After a certain time, tηE which is the up-rising time (marked with the upward arrows in figure), was strongly dependent on ‧ε0 , and a rapid upward deviation of ηE from the curves of the linear region was observed. On the other hand, Sinha Ray and coworkers [118] tried to measure the elongational viscosity of pure PLA but they failed to do that accurately. Low viscosity of pure PLA may be the main reason. However, they confirmed that neither strain‐induced hardening in elongation nor rheopexy in shear flow took place in the case of pure PLA having the same molecular weights and poly-dispersity with that of PLACN3 [118]. Like polypropylene/OMLS systems, the extended Trou- ton rule, 3η0 (; t) ≅ ηE ( ‧ε0 ; t), does not hold for PLACN5 melt, as opposed to the melt of pure polymers [138]. These results indicate that in the case of PLACN5, the flow induced internal structural changes also occurred in elongation flow, but the changes were quite different from shear flow. The strong rheopexy observed in shear measurements for PLACN5 at very slow shear rate reflected a fact that the shear-induced structural change involved a process with an extremely long relaxation time. As to the elongation‐induced structure development, Figure 37 represents the Hencky strain rate dependence of the up‐rising Hencky strain (εηE) = ‧ε0 × tηE taken for PLACN3 at 170 oC. The εηE values increased systematically with the ‧ε0 . The lower the value of ‧ε0 , the smaller is the value of εηE. This tendency probably corresponds to the rheopexy of PLACN5 under slow shear flow.

Conclusions

Rheological properties of several polymer nano-composites with layered silicates have been discussed herein. On a global scale, the linear viscoelastic behavior of the polymer chains in the nanocomposites, as detected by conventional rheometry, is dramatically altered after nanocomposites formation. Linear rheological material functions showed that the nanocomposites are charac-terized by a solid-like behavior as revealed by the pres-ence of a low-frequency plateau on storage modulus. The magnitude of such plateau or pseudo-plateau is found to strongly depend on the level of interactions between the polymer matrix and the surfactant of the modified lay-ered silicate. Such specific interactions favour the state of dispersion-distribution of the layered silicate lamellae within the polymeric matrix that lead to the formation of a long range or short range percolating network. However, such a network does not seem very stable


vis-a-vis of steady shear flow. In fact steady shear flow destroys such connectivity and imparts the material with a rather Newtonian behavior in the high-shear rate region. For the moment it is not clear whether or not such percolating network can be maintained when the nano-composites are reprocessed in machines such as ex-truders and injection moldings, where the flow has a complex pattern combining shear, elongational, hyper-bolic and eventually chaotic flows. However, some of these systems show close analogies to other intrinsically anisotropic materials such as block copolymers and smectic liquid crystalline polymers and provide model systems to understand the dynamics of polymer brushes. Under uniaxial elongational flow, the nanocomposites generally exhibit very high viscosity and a tendency to strong strain‐induced hardening, which author believes originate from the perpendicular alignment of the silicate layers towards the stretching direction. Although a significant amount of work has already been reported on rheological properties of PLA-nanocomposites, much research still remains in order to under-stand the complex structure-property relationships in var-ious PLA-nanocomposites.

Abbreviations

BPA, biodegradable aliphatic polyester; CEC, cation exchange capacity; Deff, effective diffusion coefficient; EMA, ethylene-co-methyl acrylate; EVA, ethylene-co- vinyl acetate; HMW, high molecular weight; IANS, in-termediate-angle neutron scattering; LCST, lower critical solution temperature; LMW, low molecular weight; MD, molecular dynamics; MMT, montmorillonite; 2M2T- MMT, dimethyl ditallow ammonium modified montmor-illonite; MMW, medium molecular weight; N6, nylon 6; NMR, nuclear magnetic resonance; OMLS, organically modified layered silicate; PA12, polyamide 12; PBS, poly(butylene succinate); PBSA, poly[(butylene succi-nate)-co-adipate]; PCL, poly(ε-caprolacton); PEO, poly (ethylene oxide); PDS, poly(dimethyl siloxane); PLA, polylactide; PLS, polymer layered silicate; PP, poly-propylene; PPCH, polypropylene hybride; PS, poly-styrene; QA+, quaternary ammonium cation; Rg, radius of gyration; RIS, rotational-isomeric-state; SE, Stokes- Einstein; SFM, synthetic fluorine mica; TEM, trans-mission electron microscopy, XRD, x-ray diffraction, POSS, polyhedral oligomeric silsesquioxanes; PVA, poly (vinyl alcohol); SCF; self-consistent field; SANS, small- angle neutron scattering.

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