An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

On the finite-size scalling equation for the spherical model

The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent , 0<2, is considered under periodic boundary conditions and fully finite geometry ind dimensions, when <d<2. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentumspace correlation function.On leave of absence from Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria.     

THE RING OPENING REACTION OF AN EPOXY COMPOUND ON THE TOP OF CHEMISORBED CYSTAMINE STUDIED BY THE SERS TECHNIQUE

Metal foils for Raman scattering were prepared by HNO_3 etching method. These foils werefound to exhibit a strong SERS effect and excellent thermal stability. SERS spectra of cystaminehave been taken to illustrate the usefulness of this sample preparation method in the studies ofchemisorption. The ring opening reactions of an epoxy compound have been observed on the topof chemisorbed cystamine on silver foils.     

STUDY ON THE CONCENTRATION DEPENDENCE OF ORIENTATION OF POLYSTYRENE ON SILVER BY THE SERS TECHNIQUE*

Polystyrene films were adsorbed onto a silver surface from dichloromethane solutions with concentrations of 0.1 to12 wt%, and then studied by the surface enhanced Raman technique. A critical concentration for coil interpenetration wasobserved.     

FT IR ATR Study of Molecular Interactions in the Urea/Dimethyl Sulfoxide and Urea/Diethyl Sulfoxide Binary Systems

FT IR ATR spectra of urea/dimethyl sulfoxide and urea/diethyl sulfoxide mixtures in the S=O and N—H stretching vibration regions at different molar ratios have been measured. On the basis of the band deconvolution data, various types of intermolecular associated forms, including dimers and hydrogen-bonded urea–sulfoxide complexes, have been revealed. The latter has been confirmed also by ab initio calculations.     

Equilibrium and NMR Studies of Noncovalent Interactions in Binary Systems: Uridine,Adenosine, Cytidine and Thymidine,and Adenosine (or Cytidine) 5′-Monophosphate in Aqueous Solution

The molecular complex formation reactions of uridine (Urd) with adenosine (Ado), cytidine (Cyd), thymidine (Thd), adenosine 5-monophosphate (AMP) and cytidine 5-monophosphate (CMP) have been studied at 20°C. It was found that the main positive noncovalent centers of ion–dipole and dipole–dipole type interactions are the protonated N(3) atoms of Urd, whereas the negative centers are the endocyclic atoms of the bases characterized by high electron density from the second molecule involved in the reaction. Moreover, NMR results indicate the occurrence of stacking in the complex (Urd)H(Cyd), whereas in the complex, (Urd)H₂(Thd), it is the only type of interaction. Deprotonation of the latter species brings about a change in the character of the reaction and ion–dipole interactions have been detected in the adduct, (Urd)H(Thd). Interestingly, no involvement of the phosphate groups in the formation of AMP and CMP adducts has been evidenced and the main centers of the reactions were found to be the N(7)and N(1) atoms of AMP, or the N(3) atoms of CMP and Urd. Moreover, in the Urd/CMP system the NMR results suggest stacking-type interactions.     

FT–IR microspectroscopy study of blends of ester functionalized ethylene–propylene copolymer with (vinylidene fluoride-hexafluoropropene) elastomer

An ethylene—propylene (EPR) copolymer functionalized with (1,2-dicarboethoxy)ethyl groups has been blended with a vinylidene fluoride—hexafluropropene elastomer (NML). The existence of intermolecular interactions involving mainly the carbonyl groups of the side chains of the functionalized copolymer and the methylene hydrogens of the fluoroelastomer through hydrogen bonding was shown by means of FT—IR spectroscopy. The structure and composition of some microdomains in the mixture was examined by means of FT—IR microspectroscopy.