Jacques Curély

Comments on the use of the force mode in atomic force microscopy for polymer films

Atomic force microscopy (A.F.M.) was first described as a powerful technique for studying insulating, hard surfaces. Since then, it has also been considered as an appropriate technique for investigating, at a submicromic scale, elastic and viscoelastic properties of soft materials as polymer films. An attempt is made to show how macroscopic models can be fruitfully employed in order to interpret the force curves obtained in AFM on polymer films. Through an analysis of the slope variation and the way the instability occurs at the tip‐sample contact, it is shown that a macroscopic approach is a useful way to explain most of the features of the force curves. Furthermore the importance is underlined of the initial conditions. It is shown that for polymer samples which have a stiffness within the range of the probe one, drastic changes of the force curve shape can occur when the initial conditions vary. Finally, this approach should allow one to clarify the conditions for which the macroscopic approach fails.

ANALYTICAL SOLUTION OF THE 2D CLASSICAL HEISENBERG MODEL

For the first time we exactly establish the term of higher degree in the polynomial expansion of the zero-field partition function. In the infinite-layer limit, we derive analytical expressions for the spin-spin correlations, the susceptibility and the specific heat, and we examine their respective behaviours near the critical temperature Tc = 0 K. We calculate the analytical values of critical exponents α, γ, η and ν.

Oxalate and 2,2′-bipyrimidine as bis-chelating ligands in the honeycomb layered compound {[Fe2(bpym)(ox)2]·5H2O}n

The novel two-dimensional iron(II) compound of formula {[Fe2(bpym)(ox)2]·5H2O}n (1) [bpym = 2,2′-bipyrimidine and ox = oxalate dianion] is obtained by reaction of oxalic acid, iron(II) chloride and 2,2′-bipyrimidine in aqueous solution. The structure of 1 is made up of oxalato-bridged iron(II) chains cross-linked by bischelating bpym affording a honeycomb lattice. Variable-temperature magnetic susceptibility data of 1 show the occurrence of relatively large antiferromagnetic interactions between the high spin iron(II) ions separated by more than 5.5 A through bridging bpym [Jbpym = −4.0(2) cm−1] and ox [Jox = ca. −7.8(2) cm−1] ligands. These values compare well with those obtained in the iron(II) chain [Fe(dpa)(ox)]n (2) [Jox = −8.0(2) cm−1] (dpa = 2,2′-dipyridylamine) and dinuclear {[Fe(H2O)4]2(bpym)}(SO4)2·2H2O (3) (Jbpym = −3.4 cm−1) compounds where bischelating ox (1 and 2) and bpym (1 and 3) groups and the bidentate dpa (2) ligand are present.

Thermodynamics of the 2D-Heisenberg classical square lattice : Zero-field partition function

Abstract We consider a 2D lattice composed of classical spins and characterized by a square unit cell; moreover, each classical moment interacts with its nearest neighbours by means of an isotropic alternating exchange coupling showing a regular distribution over the whole lattice. For a finite lattice, we exactly establish the beginning of the polynomial expansion of the zero-field partition function ZN(0) and we recall a numerical treatment which rapidly allows to obtain the other terms; unfortunately, it does not lead to a unique solution. However, in the infinite lattice limit, a single solution is selected and that permits to derive a closed-form expression for ZN(0). We examine its low-temperature behaviour and we show that the absolute zero plays the role of the critical temperature. Finally, in the high-temperature domain, starting from the theoretical expression of ZN(0), we directly retrieve the result obtained by Rushbrooke and Wood by means of high-temperature series expansions.

Thermodynamics of the 2D-Heisenberg classical square lattice: Part III. Study of the static susceptibility behaviours

Abstract In a previous article labelled II a closed-form expression of the dynamic and static susceptibilities has been derived (J. Curely, Physica B 254 (1998) 277, previous article in this issue). In the present one, we mainly focus on the behaviours of the static susceptibility χ . In the low-temperature domain we point out the mechanisms involved in the construction of the 2D-spin arrangement; a very simple model allows one to give a good description of the χT behaviours. For a 2D-compensated antiferromagnet, we derive a linear variation between the temperature of the maximum of the susceptibility curve T ( χ max ) and the exchange energy J / k B . In addition, above the Neel temperature, there is a remarkable agreement between the experimental and theoretical susceptibilities, for the compounds BaMnF 4 and (CH 3 NH 3 ) 2 MnCl 4 . Finally, when T decreases from the high-temperature (HT) domain, we verify on these experimental results that the HT theoretical expansion of χ leads to a value lower than the one derived from Rushbrookes HT series. In addition, it allows to fit all the experimental points belonging to the characteristic maximum of the susceptibility curve whereas the Pade method just permits to reach it before breaking down.

Thermodynamics of ferrimagnetic ising chains

The exact solutions of the so‐called ferrimagnetic Ising chain made up of two sublattices (S0,S1) are derived from a transfer matrix method. The short‐range ferrimagnetic order occurs when considering different spins and/or different Lande factors on both sublattices. Most of the physical features of interest are shown to be involved in the S0=S1=1 system including an alternation of Lande factors (g0,g1) and local anisotropies (K0,K1). Thus, in the limit K0→∞ stabilizing a Kramers doublet, Sz=±1, on even sites, the system behaves like the ferrimagnetic chain (S0=1/2, S1=1). The susceptibility and magnetization curves are discussed in various situations as a function of the significant parameters.

Role of the force of friction on curved surfaces in scanning force microscopy

Abstract Among near field microscopes, the atomic force microscope (AFM) is a powerful and versatile tool for investigating local mechanical properties, friction and adhesiveness. Especially, the knowledge of the contribution of the friction may become of primary importance to understand the structure of the objects deposited on a surface. In this paper, we show that the contribution of the force of friction lying in the tangent contact plane between the tip and the object is dependent on the geometry of the object scanned. A tip scanning a curved surface is considered and a general expression is derived describing the two contact modes in AFM: constant force and constant height.

Magnetic nanoparticles formed in glasses co-doped with iron and larger radius elements

A new type of nanoparticle-containing glasses based on borate glasses co-doped with low contents of iron and larger radius elements, Dy, Tb, Gd, Ho, Er, Y, and Bi, is studied. Heat treatment of these glasses results in formation of magnetic nanoparticles, radically changing their physical properties. Transmission electron microscopy and synchrotron radiation-based techniques: x-ray diffraction, extended x-ray absorption fine structure, x-ray absorption near-edge structure, and small-angle x-ray scattering, show a broad distribution of nanoparticle sizes with characteristics depending on the treatment regime; a crystalline structure of these nanoparticles is detected in heat treated samples. Magnetic circular dichroism (MCD) studies of samples subjected to heat treatment as well as of maghemite, magnetite, and iron garnet allow to unambiguously assign the nanoparticle structure to maghemite, independently of co-dopant nature and of heat treatment regime used. Different features observed in the MCD spectra ...

Study of the magnetic properties of two-dimensional (2D) classical square heisenberg antiferromagnets II- spin correlations and susceptibility

In this part labelled II we examine the spin correlations and the susceptibility. We use a similar method which has allowed to derive a closed-form expression of the zero-field partition function ZN(0), for 2D square lattices composed of (2N+1)2 classical spins isotropically coupled [1]. We rigorously show that the spin correlation vanishes in the zero-field limit, except at T=0 K. Thus, the critical temperature is TC=0 K, in agreement with Mermin-Wagners theorem. For calculating the spin-spin correlation, we show that it is necessary to distinguish a correlation domain in which the correlation path is confined and a wing domain (Theorem 1). In the thermodynamic limit (N→+∞), we give a general closed-form expression for the spin-spin correlation between any two lattice sites. We prove that all the possible paths have the same analytic expression and correspond to the shortest ones in agreement with the classical principle of least action and its quantum version (Theorem 2). As a result and for the first time, we derive the closed-form expression for the susceptibility, without any approximation. We finally test previous experimental fits and we show that the use of a truncated expansion for the susceptibility was totally justified.

Isotropic classical spin chains showing nearest neighbor correlated cationic distributions

A model is proposed for calculating the magnetic susceptibility of isotropic classical spin chains showing nearest neighbor correlated cationic distributions. It allows one to obtain a general closed‐form expression: This expression formally looks like previous ones obtained in the case of random chains for which the neighboring cationic species are not correlated; but here the previous intervening scalar parameters are replaced by vectorial and matricial expressions.