Polymer/layered silicate nanocomposites: a review from preparation to processing

This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

The Quantitation of Aqueous Aluminum, P.R. Bloom and M.S. Erich Aqueous Equilibrium Data for Mononuclear Aluminum Species, D.K. Nordstrom and H.M. May Inorganic Aluminum Bearing Solid Phases, B.S. Hemingway and G. Sposito Aqueous Polynuclear Aluminum Species, P.M. Bertsch and D.R. Parker Environmental Chemistry of Aluminum-Organic Complexes, G.F. Vance, F.J. Stevenson, and F.J. Sikora Surface Reactions of Aqueous Aluminum Species, P.M. Jardine and L.W. Zelazny The Surface Chemistry of Aluminum Oxides and Hydroxides, S.R. Goldberg, J.A. Davis, and J.D. Hem The Solubility of Aluminum in Soils, W.L. Lindsay and P.M. Walthall The Chemistry of Aluminum in Surface Waters, C.T. Driscoll and K.M. Postek Aluminum Geochemistry at the Catchment Scale in Watersheds Influenced by Acidic Precipitation, W.H. Hendershot, F. Courchesne, and D.S. Jeffries Index

The Environmental Chemistry of Aluminum

Concerns on environmental waste problems caused by non-biodegradable petrochemical-based plastic packaging materials as well as the consumer's demand for high quality food products has caused an increasing interest in developing biodegradable packaging materials using annually renewable natural biopolymers such as polysaccharides and proteins. Inherent shortcomings of natural polymer-based packaging materials such as low mechanical properties and low water resistance can be recovered by applying a nanocomposite technology. Polymer nanocomposites, especially natural biopolymer-layered silicate nanocomposites, exhibit markedly improved packaging properties due to their nanometer size dispersion. These improvements include increased modulus and strength, decreased gas permeability, and increased water resistance. Additionally, biologically active ingredients can be added to impart the desired functional properties to the resulting packaging materials. Consequently, natural biopolymer-based nanocomposite packaging materials with bio-functional properties have a huge potential for application in the active food packaging industry. In this review, recent advances in the preparation of natural biopolymer-based films and their nanocomposites, and their potential use in packaging applications are addressed.

Natural Biopolymer-Based Nanocomposite Films for Packaging Applications

The mobility of As in soils depends on several factors including redox potential, soil mineralogy, pH, and the presence of other oxyanions that compete with As for soil retention sites. We investigated the effects of pH and competing anions on the adsorption of arsenate [As(V)] on a-FeOOH (goethite) and y-AI(OHb (gibbsite). Batch equilibrium As(V) adsorption experiments were conducted with P and MO as competing anions in order to produce single-anion [As(V), P, and MO] and binary-anion [As(V/P and As(V)/Mo] adsorption envelopes (adsorption vs. solution pH). Arsenate and P single-anion adsorption envelopes were similar with substantial adsorption occurring across a wide pH range, including pH values above the points of zero charge of the oxides. Maximum MO adsorption occurred across a narrower pH range (pH 4-6). On both oxides, equimolar P concentrations decreased As(V) adsorption within the pH range 2 to 11, whereas MO decreased As(V) adsorption only below pH 6. The constant capacitance model was used to predict competitive surface complexation behavior between As(V)/P and As(V)/Mo using intrinsic equilibrium constants [Kd, tint)] optimized from single-anion data. In addition, the model was applied using one-site (monodentate) and two-site (monodentate + bidentate) conceptualizations of the oxide surface. The two approaches gave comparable fits to experimental adsorption data and were consistent with competitive adsorption observed in binary adsorption envelopes. and MO has been described in whole soils with a competitive Freundlich-type isotherm equation (Roy et al., 1986), though the applicability o f the model was limited to cases where the As/P and As/Mo equilibrium concentration ratios were >20. Barrow (1974) investigated As(V) and P competitive adsorption in soil and found that, though As(V) desorbed some previously adsorbed P, a substantial portion o f the bound P was not displaced by As(V). Based on competitive adsorption between As(V) and P on goethite, Hingston et al. (1971) postulated that the goethite surface contains adsorption sites common to both As(V) and P anions, as well as sites that adsorb either one anion or the other. The ability to predict As(V) adsorption in complicated systems such as whole soils will require quantitative information on the adsorption of As(V) by individual soil minerals in the presence of competing anions.

Modeling competitive adsorption of arsenate with phosphate and molybdate on oxide minerals

The adsorption isotherms of quinoline from aqueous solutions by some clays and oxides varied from the S type for silica to a form somewhat similar to the Langmuir type for montmorillonite and silica- alumina. The adsorption reaction reached equilibrium in about 2 hr and was irreversible. X-ray powder diffraction studies showed that a single layer of molecules is adsorbed on montmorillonite and that the molecules lie either flat or in an upright position depending on surface coverage. The adsorption showed high sensitivity towards pH, attaining a maximum at pH 6. The decrease below pH 6 was due to competition with protons as well as to problems inherent in surface packing of positively charged quinoline molecules. The decrease above pH 6 is probably due to more exchangeable metallic cations on the surface leading to a favored sorption of water over organic molecules.

Adsorption of quinoline from aqueous solutions by some clays and oxides

Adsorption of molecules of different sizes on montmorillonite and on hydroxy-Al montmorillonite was studied to examine the effect of sorbate size on the experimental value of the surface area of the clays. For each clay the number of adsorbate units at the adsorption maximum per gram of clay produces a single hyperbolic curve, when plotted as a function of the area occupied by adsorbate, in the range of areas of 22–180 A2per sorbate. The equations of the curves are:N A= 657.7 m2/g for the clay andN A= 202.8A0.27for the hydroxy-Al montmorillonite. A dependence of the surface area of the hydroxy-Al montmorillonite on adsorbate size was observed and was attributed to surface irregularities produced by hydroxy-Al interlayering.

Surface Area Evaluation of Montmorillonite.

The adsorption of poly(vinyl alcohol) (PVA) on montmorillonites saturated with calcium (Ca-Mt) and sodium (Na-Mt) as a function of the pH value and PVA concentration in aqueous solution was studied. Owing to the binding effect of the bivalent cation, the adsorption of PVA on Ca-Mt decreases as the pH of the suspension increases, whereas adsorption on Na-Mt is unaffected by the suspension pH. The adsorption maximum of PVA (pH 6) on Ca-Mt was 151.2 mg of PVA g−1 of clay, which is considerably lower than that on Na-Mt (496.2 mg g−1). These adsorption data coincide with the basal spacings obtained for the clays: 1.72 and 2.26 nm for Ca-Mt and Na-Mt, respectively. Sodium permits a greater separation between the clay laminae than calcium, but in both clays the presence of the polymer gives rise to a material in which PVA is intercalated between the laminae and is also adsorbed on the external surface. Adsorption is a slow process and is irreversible in both clays.

Adsorption of poly(vinyl alcohol) on montmorillonite

Thermodynamic parameters of adsorption of 1,10-phenanthroline and 2,2'-bipyridyl on hematite, kaolinite and montmorillonites

The effect of interlayering montmorillonite with different amounts ofhydroxy aluminum cation on the cation exchange capacity (CEC) and the point of zero charge (PZC) of the clay was studied. The CEC decreased as the A1 content of the clay increased. Both the CEC and the loss in the CEC were linearly dependent on the A1 content, thus indicating the predominance of a single polynuclear interlayered species. Its composition is (A16(OH)16.5) LS+. Acid base titration of the interlayered montmorillonites produced values for the PZC in the range 4.5-5.9, increasing with the A1 content of the materials. The values, however, did not represent real conditions of zero charge and some samples were still negatively charged at the determined PZC. The PZC values obtained by acid-base titration are thought to be adversely affected by secondary reactions involving the interlayered material with a concomitant release of soluble A1 in amounts dependent on the pH and ionic strength.

E. A. Ferreiro

Papers

Adsorption of quinoline from aqueous solutions by some clays and oxides

Surface Area Evaluation of Montmorillonite.

Adsorption of poly(vinyl alcohol) on montmorillonite

Thermodynamic parameters of adsorption of 1,10-phenanthroline and 2,2'-bipyridyl on hematite, kaolinite and montmorillonites

Cation Exchange Capacity and Condition of Zero Charge of Hydroxy-Al Montmorillonite