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Polymer-layered oxide nanocomposites.

POLYMER NANOCOMPOSITES

Polymer nanocomposites are composite materials that consist of nanoscale additives dispersed in a polymer matrix where, typically, a layered material capable of exfoliation exfoliation /ex·fo·li·a·tion/ (eks-fo?le-a´shun)
1. a falling off in scales or layers.

2. the removal of scales or flakes from the surface of the skin.

3.
 into nano-sized platelets is incorporated into the polymer. Since the composites are mixed on the nanometer length scale, they often exhibit enhanced properties compared to their macroscale counterparts, such as improved strength, stiffness, thermal stability, biodegradability, flame resistance, and gas barrier (Schmidt et al. 2002). Types of polymer matrices studied include, but are not limited to, vinyl polymers (polymethacrylate, polystyrene), condensation polymers (Nylon, polyethylene terephthalate Ter`eph´tha`late

n. 1. (Chem.) A salt of terephthalic acid.
), polyolefins (polypropylene, polyethylene), epoxides, rubber, and other specialty polymers such as polypyrrole and polyaniline (Ray and Okamoto 2003). Additives that are potential candidates for polymer nanocomposites include natural, commercial, and synthetic clays, layered silicic si·lic·ic  
adj.
Relating to, resembling, containing, or derived from silica or silicon.
 acids, layered hydroxides, layered double hydroxides Layered double hydroxides (LDHs) comprise an unusual class of layered materials with positively charged layers and charge balancing anions located in the interlayer region. This is unusual in solid state chemistry: many more famililies of materials have negatively charged layers and , layered alumino-phosphonates and other metal oxides (Utracki et al. 2007). However, the vast majority of nanocomposite research is directed towards polymer matrices containing layered silicate platelets of nanometer thickness and high aspect ratio and these types of nanocomposites will be highlighted in later sections.

Nanocomposite materials are useful in a wide variety of applications in medical, automotive, fiber, textile, coatings, electronics, and packaging industries, among others. Research in this area has increased substantially after a Toyota research team developed one of the first successful montmorillonite-Nylon-6 nanocomposites in an effort to use Nylon-6 based parts in engine compartments and for automotive applications (Kojima et al. 1993, Usuki et al. 1993). Since then, layered-oxides, specifically layered silicates, have attracted a great interest as additives (Schmidt et al. 2002, Ray and Okamoto 2003, Kojima et al. 1993, Usuki et al. 1993, Alexandre et al. 2002, Alexandre and Dubois 2000, Bharadwaj et al. 2002, Carrado 2003, Chang et al. 2003, Chang and Yeong 2002, Dai and Huang 1999, Fornes et al. 2002, Garces et al. 2000, Gilman et al. 2000, Gopakumar et al. 2002, Grunlan et al. 2004, Hoffman et al. 2000, Imai et al. 2003, Jan and Lee 2004, Jordan et al. 2005, Matayabas et al. 2000, Pinnavaia and Beall 2000, Sekelik et al. 1999, Strawhecker and Manias 2000, Kim and Kim 2007, LeBaron et al. 1999, Tsai 2000).

Researchers at Eastman Chemical Company Eastman Chemical Company is a United States based chemical company, engaged in the manufacture and sale of chemicals, plastics and fibers. Eastman has 16 manufacturing sites in 10 countries, supplying its products throughout the world.  expanded on the work of Toyota, by incorporating montmorillonite Montmorillonite is a very soft phyllosilicate mineral that typically forms in microscopic crystals, forming a clay. It is named after Montmorillon in France. Montmorillonite, a member of the smectite family, is a 2:1 clay, meaning that it has 2 tetrahedral sheets sandwiching a , ion-exchanged with alkylammonium compounds, into polyethylene terephthalate (PET) via melt-blending and in-situ polymerization polymerization

Any process in which monomers combine chemically to produce a polymer. The monomer molecules—which in the polymer usually number from at least 100 to many thousands—may or may not all be the same.
 (Matayabas et al. 2000a, Matayabas et al. 2000b). They found that at even a low weight loading of montmorillonite clay, the oxygen permeability decreased dramatically. This was an important finding for Eastman, a leading producer of PET, as their motivation was to increase the gas barrier of PET for use in food and beverage F&B is a common abbreviation in the United States and Commonwealth countries, including Hong Kong. F&B is typically the widely accepted abbreviation for "Food and Beverage," which is the sector/industry that specializes in the conceptualization, the making of, and delivery of foods.  packaging. Although research in polyester-clay nanocomposites is in a relatively early stage, over 28 patents for PET-clay nanocomposites were issued between the years of 1991 and 1998, suggesting that this a thriving area of research (Tsai 2000). Earlier methods of incorporating montmorillonite clay into PET were usually based on melt-blending, or melt-intercalation by extrusion. Typically these method do not facilitate full exfoliation of the clay layers but, nonetheless, there were some successful well-exfoliated nanocomposites produced where exfoliation and enhancement in properties were achieved (Vidotti et al. 2004, Yan et al. 2004). More recently, analogous to the research developed by Eastman, layered clays like montmorillonite, talc, and mica were ionexchanged with compatibilizers or surfactants and incorporated into PET by in-situ polymerization to improve gas barrier (Sekelik et al. 1999, Ke and Yongping 2005, Ke et al. 1999, Chang et al. 2004, Tsai et al. 2005). Most recently, layered double hydroxides (LDHs) were ion-exchanged with anionic an·i·on  
n.
A negatively charged ion, especially the ion that migrates to an anode in electrolysis.



[From Greek, neuter present participle of anienai, to go up : ana-, ana-
 surfactants dodecylsulfate, dodecylbenzene sulfate, and octylsulfate and incorporated into PET by melt-extrusion (Lee et al. 2006). Only the dodecylsulfate LDH LDH -lactate dehydrogenase.

LDH
abbr.
lactate dehydrogenase



LDH

lactic acid dehydrogenase; see lactate dehydrogenase.
 was well exfoliated in the PET matrix, and consequently the thermal and mechanical properties were enhanced. This research is encouraging as only a select few PET nanocomposites are prepared with a layered oxide other than a layered silicate. However, gas barrier properties were not studied for this nanocomposite system.

Although PET is the polymer traditionally used for packaging materials, research into biodegradable packaging materials is being developed for environmental reasons. Montmorillonite was mixed into a biodegradable potato starch by melt blending (Avella et al. 2005), where complete intercalation of the starch into the interlayer galleries was achieved, as well as and increase in tensile strength and modulus. The nanocomposite films formed complied with European regulations for biodegradable materials and therefore could be used as alternative packaging materials. Gas barrier was not measured for these nanocomposites.

Epoxy-clay nanocomposites have also been well established for over a decade. Typically the clay layers are expanded with onium ions and then the epoxide epoxide /epox·ide/ (e-pok´sid) an organic compound containing a reactive group resulting from the union of an oxygen atom with two other atoms, usually carbon, that are themselves joined together. , curing agent, or a mixture of both, are intercalated into the interlayer gallery regions of the clay (Messersmith and Giannelis 1994, Wang and Pinnavaia 1998). This has been a proven method to exfoliate ex·fo·li·ate  
v. ex·fo·li·at·ed, ex·fo·li·at·ing, ex·fo·li·ates

v.tr.
1. To remove (a layer of bark or skin, for example) in flakes or scales; peel.

2.
 the clay layers into the epoxy matrix which improves mechanical properties, thermal stability, and solvent resistance.

Similarly, the most successful polystyrene-clay nanocomposites were prepared by melt-intercalating the polymer above its melting point into the interlayer galleries that had been previously expanded by quaternary alkylammonium ions (Via et al. 1996). Another polystyrene (PS) nanocomposite was prepared by covalently modifying layered mesostructured aluminosilicates (LMAS LMAS Lockheed Martin Aeronautical Systems
LMAS Lockheed Martin Assembly Services
LMAS Local Monitoring Alarm System
LMAS Laboratory for Manufacturing and Sustainability
) with hexadecyl groups and mixing the organo-alumniosilicate with polystyrene by microcompounding (Chastek et al. 2005). The PSLMAS had increased elastic modulus and strength. Although the LMAS were well dispersed, they appeared as stacks according to transmission electron microscopy images.

Poly(styrene-butadiene), a synthetic rubber copolymer copolymer: see polymer. , was intercalated into dioctadecyldimethyl ammonium exchanged montmorillonite by mixing the copolymer and the organoclay at 120[degrees]C (Laus et al. 1997, Laus et al. 1998). The nanocomposite formed showed an increased storage modulus. Natural rubber reinforced with organomontmorillonite resulted in a 350% increase in strength without sacrificing the elasticity (Arroyo et al. 2003). Other research in rubber nanocomposites has indicated that silane modified kaolinite kaolinite (kā`əlĭnīt), clay mineral crystallizing in the monoclinic system and forming the chief constituent of china clay and kaolin.  increases the compatibility between the hydrophilic hydrophilic /hy·dro·phil·ic/ (-fil´ik) readily absorbing moisture; hygroscopic; having strongly polar groups that readily interact with water.

hy·dro·phil·ic
adj.
 clay and the rubber matrix, thus reinforcing the rubber (Dai and Huang 1999).

A polypropylene-bentonite nanocomposite is a yet another example of a clay that has been organically modified with a quaternary organic salt and that was added to a polymer matrix (Dai and Huang 1999). Bentonite bentonite (bĕn`tənīt'): see clay. , a layered aluminosilicate Aluminosilicate minerals are minerals composed of aluminum, silicon, and oxygen. Andalusite, kyanite, and sillimanite are naturally occuring aluminosilicate minerals that have the composition Al2SiO5.  similar in structure to montmorillonite, was mixed with polypropylene using a batch mixer at 150-210 [degrees]C at a 1-5 wt. % loading. The main result obtained was that the nanocomposites containing organo-bentonite had a higher thermal stability than nanocomposites formed with natural clays. The authors explain this phenomenon by the formation of a nano structure that reduced diffusion of oxygen into the material.

While the above nanocomposite materials mostly utilized layered silicates to reinforce the polymer matrix, other layered oxides are being incorporated into polymer matrices for use as electrolyte materials and conducting nanocomposites, among others. An example of a PET-LDH nanocomposites was briefly presented earlier, but other LDH polymer nanocomposite systems are being studied. In contrast to silicates, LDHs have a positive charge on brucite-like Mg(OH)2 layers, which can be compensated for by anions or polymeric anions (Wilson et al. 1999). This results in an interesting layer chemistry of the materials and makes them attractive for applications such as ion-exchange, catalysis catalysis

Modification (usually acceleration) of a chemical reaction rate by addition of a catalyst, which combines with the reactants but is ultimately regenerated so that its amount remains unchanged and the chemical equilibrium of the conditions of the reaction is not
, and even as antacids (Constantino and Pinnavaia 1995, Ookubo et al. 1993, Playle et al. 1974). Early research in polymer-LDH research was based on intercalation of anionic polymers poly(styrenesulfonate) (PSS See EPSS. ) and poly(vinylsulfonate) (PVS PVS 1 Persistent vegetative state, see there 2. Pulmonary valve stenosis ) into the galleries of a carbonate-containing LDH, confirmed by an increase in the interlayer spacing by X-ray diffraction (Wilson et al. 1999). Similarly, another LDH was modified by ion-exchange with sodium dodecylsulfate or polyoxyethylene sulfate to form biocompatible biocompatible /bio·com·pat·i·ble/ (-kom-pat´i-b'l) being harmonious with life; not having toxic or injurious effects on biological function.  nanocomposites (Yang et al. 2005). Making use of the anion exchange capacity of LDHs, a poly(ethylene oxide) (PEO)-LDH was prepared for potential use as a polymer electrolyte (Liao and Ye 2004). An oligo(ethylene oxide) (OEO (Optical in Electrical processing Optical out) Refers to network devices that convert photonic transmission signals to electronic signals in order to analyze the traffic content for switching purposes. It then reconverts the signal to light for output. Contrast with OOO. ) modified LDH was made by a template method and then subsequently mixed with PEO. The LDH layers remained well exfoliated due to the compatibility between the OEO and the PEO. The PEO-LDH nanocomposite exhibited a substantial enhancement in conductivity compared to the pristine PEO.

Recently, nanosheets of layered metal oxides have attracted interest as additives for nanocomposite electrolytes because of their physicochemical properties and ability to be intercalated with various species (Pang et al. 2005). Specifically, polyaniline-vanadium oxide nanocomposites are being explored because of their mixed electronic charge-transport properties (Wu et al. 1996).

A polyaniline-V2O5 nanocomposite was formed by in-situ polymerization of aniline aniline (ăn`əlĭn), C6H5NH2, colorless, oily, basic liquid organic compound; chemically, a primary aromatic amine whose molecule is formed by replacing one hydrogen atom of a benzene molecule with an amino  intercalated into the layered V2O5 under hydrothermal conditions (Pang et al. 2005). Polyaniline- V2O5 nanocomposite sheets formed with a thickness between 10-20 nm and lateral dimensions on the range of hundreds of nanometers to several microns. Poly(ethylene oxide) (PEO) was also intercalated into a lithium trivanadate, LiV3O8, to prepare a solid polymer electrolyte with potential applications in lithium batteries.53 PEO is widely doped with lithium salts but efforts are underway to improve the conductivity of the doped-PEO. LiV3O8 is a promising material for lithium batteries because the structure allows for reversible ion-exchange of lithium cations. When the PEO is mixed with the LiV3O8 under semi-hydrothermal conditions, the PEO partially exfoliates the LiV3O8 layers. The PEO- LiV3O8 nanocomposite showed a higher ionic conductivity than LiV3O8 and other lithium salt polymer electrolytes (Yang et al. 2005). This research is a step towards the incorporation of other layered lithium containing metal oxides into polymers to form conducting nanocomposites. PEO was also introduced into the interlayer galleries of HNbWO6*1.5 H2O using melt-intercalation for another potential solid polymer electrolyte (Sairam and Viswanathan 2002). HNbWO6*1.5 H2O has a tetragonal tet·ra·gon  
n.
A four-sided polygon; a quadrilateral.



[Late Latin tetrag
 structure with layers of NbWO6 slabs made up of Nb/W oxygen octahedra, separated by interlayer water molecules. It was found that as the intercalation time (i.e. heating of a HNbWO6*1.5 H2O -PEO pressed pellet to 75[degrees]C) was increased, the conductivity also increased.

Finally, and most recently, layered zirconium zirconium (zərkō`nēəm), metallic chemical element; symbol Zr; at. no. 40; at. wt. 91.22; m.p. about 1,852°C;; b.p. 4,377°C;; sp. gr. 6.5 at 20°C;; valence +2, +3, or +4.  phosphates were synthesized and exfoliated into platelets with a high aspect ratio (>1000) for incorporation into various polymer matrices (Alberti et al. 2007, Sun et al. 2007, Zhang et al. 2007). The zirconium phosphates (ZrP) have an advantage over layered clays because of synthetic control over the dimensions and surface functionalities (Sun et al. 2007). A layered ZrP, Zr(HPO HPO

1. hyperbaric (high-pressure) oxygenation.

2. hypertrophic pulmonary osteodystrophy.
4)2*H2O was exfoliated using tetrabutylammonium hydroxide (TBA+OH-), and then the exfoliated platelets were isolated after centrifugation. These TBA+ exchanged platelets were then re-dispersed into acetone acetone (ăs`ĭtōn), dimethyl ketone (dīmĕth`əl kē`tōn), or 2-propanone (prō`pənōn), CH3COCH3  and mixed with an epoxy monomer. The acetone was evaporated and a curing agent was added to form an epoxy nanocomposite containing well exfoliated ZrP platelets with high aspect ratio (Sun et al. 2007). Similarly, ZrP was exfoliated using alkylamines and intercalated with an acrylamide acrylamide /acryl·a·mide/ (ah-kril´ah-mid) a vinyl monomer used in the production of polymers with many industrial and research uses; the monomeric form is a neurotoxin.  monomer, which was subsequently polymerized to form a polyacylamide-ZrP nanocomposite (Zhang et al. 2007). This nanocomposite had improved thermal stability, most likely from the retardant effect of the exfoliated ZrP layers. A Nafion membrane was also prepared with the addition of the same ZrP to enhance the stability of proton conductivity at higher temperatures, by increasing the stiffness of the composite membrane (Alberti et al. 2007).

These examples of successful nanocomposites reiterate the fact that research in this area is promising and a plethora of nanocomposite materials are being explored for a wide variety of applications. However, there are still obstacles present, such as incomplete exfoliation of the oxide, incompatibility of the oxide and the polymer, and the sacrifice of some properties for the enhancement of others. Ongoing research aims at finding ways to overcome these obstacles and to produce quality nanocomposites with improved gas barrier property and ideally, enhancements in mechanical properties as well. As an in-depth example of one type of polymer nanocomposite, a summary of the structure, properties, and preparation of PET based polymer nanocomposites is given below.

1.2. POLYETHYLENE TEREPHTHALATE

Polyethylene terephthalate (PET) is a polyester that is used in a variety of industrial applications, especially in the food and beverage industry as packaging material. Therefore it is imperative that the PET packaging retains a barrier to gases such as carbon dioxide and oxygen, as well as water vapor. PET has many desirable properties for a packaging material including clarity, color, processability, chemical resistance, recyclability and, most importantly for food and beverage containers, tastelessness (Matayabas and Turner 2000). However, PET alone has minimal gas barrier and, therefore, using it as packaging for foods and beverages that are sensitive to oxygen or loss of carbon dioxide is problematic. Thus, there has been a recent thrust in nanocomposite research to improve the gas barrier of PET, so that the shelf-life of products like beer, wine, and tomato-based products can be extended. Matayabas et al. 2000, Sekelik et al. 1999, Kim and Kim 2007, Matayabas and Turner 2000).

PET has been produced commercially for over 50 years, and is manufactured from ethylene glycol (EG) and terephthalic acid (TPA (Transient Program Area) See transient area.

TPA - Transient Program Area
) or dimethylterephthalate (DMT See DSL. ) (Kim and Kim 2007). The polymerization of PET requires two main steps, transesterification or direct esterification es·ter·i·fi·ca·tion
n.
A chemical reaction resulting in the formation of at least one ester product.



es·teri·fied adj.
, followed by polycondensation. Both esterification processes produce BHET, an oligomeric precursor to PET. In the final step excess EG is removed upon heating BHET to about 280[degrees]C during polycondensation to form PET. This reaction scheme is shown in Figure 1.3.

Once PET is formed, there are two main methods of dispersing the additives to prepare nanocomposites: melt-blending or in-situ polymerization (Kim and Kim 2007, LeBaron et al. 1999, Tsai 2000, Ray and Okamoto 2003). Melt-blending involves mixing the polymer and the additive above the melting point of the polymer under high shear force. Melt-blending is typically used industrially to produce large scale quantities of PET, so it is advantageous to produce nanocomposites by the same method. However, the main difficulty lies in successfully exfoliating the layered additives by shear force alone. Few have reported the successful formation of PET nanocomposites by this method (Davis et al. 2001, Lyatskaya and Balazs 1998). For in-situ polymerizations, a PET monomer is intercalated into the layered structure, and subsequently polymerized. The most important advantage of this method is the fact that exfoliation of the layers is promoted and maintained by the presence of the intercalated polymer. As discussed earlier, exfoliation is a key to producing quality nanocomposites. The main disadvantage is that large-scale production of nanocomposites by this method is a difficult and time-consuming task.

1.3. LAYERED OXIDES

As previously mentioned, layered oxides are good candidates for nanocomposite additives because their layered structure allows for exfoliation and subsequent incorporation into polymer matrices. Simply stated, layered oxides are any oxygen-containing layered material such as, cuprates, titanates, phosphonates, niobates, or silicates. However, layered silicates are the most utilized layered material in the vast majority of ongoing research in layered-oxide nanocomposites. Layered silicates, or phyllosilicates, represent a large class of clay minerals that are distinguished by layers of silicate sheets coordinated to other metal-oxygen sheets. Groups in this class include micas, kaolins, vermiculites, chlorites, talc, pyrophyllite py·ro·phyl·lite  
n.
A silvery white or pale green aluminum silicate mineral, Al2Si4O10(OH)2, occurring naturally in soft compact masses.

Noun 1.
, and smectites. Smectites are the largest and one of the most widely studied groups because they are common in temperate soils, and have a high cation exchange capacity In soil science, cation exchange capacity (CEC) is the capacity of a soil for ion exchange of positively charged ions between the soil and the soil solution. A positively-charged ion, which has fewer electrons than protons, is known as a cation due to its attraction to cathodes.  and a large aspect ratio (Carrado et al. 2001, Carrado 2004, Kloprogge et al. 1999). Two of the most researched smectites of this structure type are montmorillonite and hectorite. Montmorillonite is a readily available clay, while hectorite is an easily synthesized clay via mild conditions. Montmorillonite and hectorite are the preferred layered materials for polymer nanocomposite systems (Alexandre and Dubois 2000, Carrado 2003, Chang et al. 2003, Gopakumar et al. 2002, Loo and Gleason 2004, Maiti et al. 2002, Matayabas and Turner 2000, Nielsen 1967, Pinnavaia and Beall 2000, Strawhecker and Manias 2000).

Another layered silicate, magadiite, is a member of a class of materials known as layered hydrous hydrous

containing water.
 sodium (or alkali) polysilicates that also includes kanemite, makatite, kenyaite and octosilicate. Their structure is made up of negatively charged tetrahedral tet·ra·he·dral  
adj.
1. Of or relating to a tetrahedron.

2. Having four faces.



tet
 silicate layers balanced by sodium cations. Magadiite has an even higher cation exchange capacity and aspect ratio compared to the smectites, and is easily synthesized under semi-hydrothermal conditions (Feng and Balkus 2003, Kooli et al. 2006, Kwon et al. 1995, Kwon and Park 2004, Peng et al. 2005, Schwieger and Lagaly 2004, Wang et al. 2006, Zhang et al. 2003). Research has shown that the incorporation of exfoliated magadiite layers into epoxy nanocomposites has increased the tensile strength of the epoxy matrix, while still maintaining transparent optical properties (Wang et al. 1996, Wang and Pinnavaia 1998). To date, research of magadiite nanocomposites for improved gas barrier properties is limited.

Theoretically, based on the gas barrier models presented in the following section, these layered silicates alone should improve the gas barrier of nanocomposites. However, unfavorable interactions between the hydrophilic silicates and the hydrophobic polymer may have a negative impact on other physical and mechanical properties. Therefore, the silicates are typically modified by covalently attaching organic functionalities to the surface hydroxyl groups, or by ion-exchanging with alkylammonium cations to expand the layers, and subsequently modify the interlayer surfaces (Peng et al. 2005, Zhang et al. 2003, Fujita et al. 2003, Isoda and Kuroda 2000, Ogawa et al. 1998, Okutomo et al. 1999, Wang et al. 2004).

1.4. NANOCOMPOSITE THEORY

There are three scenarios that can occur when a layered oxide is mixed with a polymer (Figure 1.1). First, the oxide can remain ordered and unexfoliated, forming a phase-separated composite. These conventional composites might have improved rigidity, but might sacrifice other properties such as elongation and toughness (LeBaron et al. 1999). Insertion of a polymer matrix into the layered silicate structure results in an intercalated nanocomposite, where the silicate layers remain ordered, but interfacial surface area between the silicate and polymer is greatly increased. This improves chemical, structural, and thermal stabilities compared to the polymer alone (Komori and Kuroda 2000). Finally, the best-case scenario would be complete exfoliation of the silicate layers well dispersed into the polymer. In this case, the clay-polymer interactions are maximized, and thus the chemical, physical, and mechanical properties are greatly enhanced. However, complete exfoliation is often a difficult task. Variables such as choice of matrix, process of incorporating the layered additive, choice of additive, treatment of additive (organic modification), and use of dispersing aids must be carefully considered (Matayabas and Turner 2000). Since exfoliation has been determined to have a profound effect on the performance of nanocomposites, a high aspect ratio of the separated layers would further improve the performance. Therefore, nanocomposites containing well-exfoliated silicate layers with the highest aspect ratio, to maximize the clay-polymer interactions, achieve the best results.

Aspect ratio (a) is defined as the ratio of the lateral dimensions to the thickness of an exfoliated silicate platelet. Since the platelets are often irregular, the aspect ratio becomes

[alpha] = [square root of A]/Z (1)

where A is the area of the platelet face, and Z is the thickness of the platelet (Auddy 2007, Kloprogge et al. 1999, Liu 2005, Ploehn and Liu 2006). It has been found that aspect ratio is crucial for improving certain properties, such as gas barrier (Alexandre and Dubois 2000, Jang and Lee 2004, Tsai 2000, Matayabas and Turner 2000). Nielsen developed the "tortuous path" theory to explain how aspect ratio effects the permeability of gases through a polymer (Alberti et al., 2007). An approximation of the permeability ratio can be represented as

{[P.sub.n]/[P.sub.m] = [[phi].sub.p]/[tau] (2)

where Pn is the permeability of the nanocomposite and Pm is the permeability of the unfilled polymer matrix, [phi]p is the volume fraction of the polymer, and o is the tortuosity tortuosity
n.
1. The quality or condition of being tortuous; twistedness or crookedness.

2. A bent or twisted part, passage, or thing.
 factor. The tortuosity factor is defined as the distance a gas molecule must travel through a polymer film divided by the thickness of the film. This factor is dependent on the aspect ratio in the following relationship:

[tau] = 1 + [alpha][[phi].sub.f] (3)

where [phi]f is the volume fraction of filler additives and therefore equation 2 becomes

[P.sub.n]/[P.sub.m] = [[phi].sub.p]/1 + [alpha][[phi].sub.f] (4)

for ideal nanocomposite systems. This model is represented schematically in Figure 1.2, where exfoliated platelets provide a more "tortuous path" for the gas to diffuse through the polymer. A barrier improvement factor (BIF BIF

In currencies, this is the abbreviation for the Burundi Franc.

Notes:
The currency market, also known as the Foreign Exchange market, is the largest financial market in the world, with a daily average volume of over US $1 trillion.
) can be estimated from the permeabilities, where

BIF = [P.sub.m]/[P.sub.n] (5)

and the BIF is used to quantify the barrier improvement of nanocomposites (Liu 2005, Matayabas and Turner 2000, Nielsen 1967). More advanced models were also developed to account for overlapping in "semi-dilute" nanocomposites systems (Matayabas and Turner 2000, Nielsen 1967). Based on calculated aspect ratios of synthesized silicates, the barrier improvement of a nanocomposite can be predicted from this theoretical model and compared to experimental BIF values determined by various methods. More advanced models were also developed to account for overlapping in "semi-dilute" nanocomposites systems (Cussler et al., 1998).

1.5. SUMMARY

Polymer nanocomposites are an exciting and active research area that promises new materials with enhanced properties. These polymer nanocomposites consist of nanosized additives that are uniformly dispersed in a polymer host matrix, to generate substantial enhancements in physical properties relative to those of the pristine polymers. Research in nanocomposites has shifted towards layered oxides as the preferred additive, as their layered structure allows for exfoliation, or separation of layers, which increases the aspect ratio, and subsequently property enhancements.

[FIGURE 1.1 OMITTED]

[FIGURE 1.2 OMITTED]

[FIGURE 1.3 OMITTED]

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Tara J. Hansen and Hans-Conrad zur Loye

Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC1.1.
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Author:Hansen, Tara J.; zur Loye, Hans-Conrad
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