This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

The distribution function of relaxation times underlying the nonexponential relaxation function of Williams and Watts is derived and compared with the analogous Cole–Davidson distribution function. In order to make the comparison between the two distribution functions, a simple empirical relationship between the Cole–Davidson and Williams–Watts parameters was determined which may be used to compare data analyzed using the two fitting functions. Although the relaxation functions are similar to each other, the distribution functions are quite dissimilar. The Cole–Davidson distribution shows a sharp long time cutoff, while the Williams–Watts distribution decays approximately exponentially at long times. Finally, several useful relations between relaxation and distribution functions are summarized or derived, and the limitations of deriving distribution functions from relaxation functions are discussed.

Detailed comparison of the Williams–Watts and Cole–Davidson functions

Physical aging of polymers

Polyisocyanates, long studied as theoretical models for wormlike chains in dilute solution and liquid crystals, differ from their biological helical analogs in the absence of a pre-determined helical sense. These polymers have an unusual sensitivity to chiral effects that arises from a structure in which alternating right- and left-handed long helical blocks are separated by infrequent and mobile helical reversals. Statistical thermodynamic methods yield an exact description of the polymer and the cooperative nature of its chiral properties. Minute energies that favor one of the helical senses drive easily measurable conformational changes, even though such energies may be extremely difficult to calculate from structural theory. In addition, the chiral nature of the polymer can be used to test theoretical ideas concerned with cholesteric liquid crystals, one of which solves the problem of assigning the helical sense.

https://science.sciencemag.org/content/sci/268/5219/1860.full.pdf

A Helical Polymer with a Cooperative Response to Chiral Information

After an introduction reporting the properties and the applications of fluoropolymers, a first part deals with i) the main routes to produce vinylidene fluoride (VDF) monomer, ii) its homopolymerization, and iii) the advantages and uses of polyvinylidene fluoride (PVDF). In a second section, this review, illustrated by numerous examples, extensively reports the synthesis, properties and applications of the copolymers based on VDF with non-halogenated, fluorinated, commercially available or synthesized comonomers. These comonomers exhibit XYC=CZ-Sp-R structures where X, Y, and Z represent H, F, and CF3 groups, Sp a spacer and R a function such as OH, OAc, SAc, CO2R' (R' being a H atom or an alkyl group), CN, P(O)(OR')2 and SO3H. According to the nature and to the amount of the comonomer, the copolymers can be thermoplastic, elastomeric or thermoplastic elastomers. Introducing reactive R side groups brings complementary properties such as hydrophily, ionic exchange or surface properties, or further crosslinking of the resulting copolymers. Then, the kinetics of radical copolymerization of VDF with M comonomers led to the assessment of the reactivity ratios which are compared. Hence, a reactivity series of these M comonomers with respect to a macroradical terminated by VDF is proposed. Usually, these copolymers exhibit random structures but only three comonomers produced alternating copolymers with VDF: hexafluoroisobutylene, F2C=CFCO2CH3, and H2C=C(CF3)CO2R. The controlled radical copolymerizations of VDF with other comonomers (such as chlorotrifluoroethylene, 3,3,3-trifluoropropene, hexafluoropropylene, perfluoromethyl vinyl ether or-trifluoromethacrylic acid) either in the presence of xanthates, borinates or iodo-compounds are also reported. In addition, new VDF-containing copolymers exhibit well-defined architectures, such as block and graft copolymers. They can be synthesized either by conventional techniques or by controlled radical copolymerization. Chemical modifications of PVDF and poly(VDF-co-monomer) copolymers are also presented. Several properties and applications (such as surfactants, dielectrical polymers, thermoplastic elastomers, fuel cell and ultrafiltration membranes, or polycondensates, the fluorinated segments of which bringing softness and thermal stability) of these VDF-containing copolymers will illustrate this review.

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From vinylidene fluoride (VDF) to the applications of VDF-containing polymers and copolymers: recent developments and future trends.

Dynamics of macromolecular chains. I. Theory of motions on a tetrahedral lattice

Dynamic mechanical and 13C n.m.r. investigations of molecular motions involved in the β relaxation of epoxy networks based on DGEBA and aliphatic amines

Carbon-13 NMR investigation of local dynamics in bulk polymers at temperatures well above the glass transition temperature. 1. Poly(vinyl methyl ether)

Fluorescence anisotropy decay experiments are described for polystyrene in various ethylacetate-tripropionin mixtures. Decay curve trends agree with the proposed theoretical autocorrelation function. Study of the effects of viscosity shows that the mean relaxation time varies according to a nonlinear law for low viscosities and that the relaxation time θ, reflecting the effects of the possible departures from the motions permitted by an ideal tetrahedral lattice, obeys a law of the type: θ = α + bη. Furthermore, the effects of the direction of the fluorophore transition moment are examined.

Lucien Monnerie

Papers

Dynamics of macromolecular chains. I. Theory of motions on a tetrahedral lattice

Dynamic mechanical and 13C n.m.r. investigations of molecular motions involved in the β relaxation of epoxy networks based on DGEBA and aliphatic amines

Carbon-13 NMR investigation of local dynamics in bulk polymers at temperatures well above the glass transition temperature. 1. Poly(vinyl methyl ether)

Dynamics of macromolecular chains. III. Time-dependent fluorescence polarization studies of local motions of polystyrene in solution

Amorphous orientation and induced crystallization in uniaxially stretched poly(ethylene terephthalate glycol)