Sedimentation equilibria of ferrofluids: II. Experimental osmotic equations of state of magnetite colloids

The first experimental osmotic equation of state is reported for well-defined magnetic colloids that interact via a dipolar hard-sphere potential. The osmotic pressures are determined from the sedimentation equilibrium concentration profiles in ultrathin capillaries using a low-velocity analytical centrifuge, which is the subject of the accompanying paper I. The pressures of the magnetic colloids, measured accurately to values as low as a few pascals, obey Van 't Hoff's law at low concentrations, whereas at increasing colloid densities non-ideality appears in the form of a negative second virial coefficient. This virial coefficient corresponds to a dipolar coupling constant that agrees with the coupling constant obtained via independent magnetization measurements. The coupling constant manifests an attractive potential of mean force that is significant but yet not quite strong enough to induce dipolar chain formation. Our results disprove van der Waals-like phase behavior of dipolar particles for reasons that are explained.     

Accelerated aging in ultrathin films of a molecular glass former

We report the thermodynamic measurement of the enthalpy released during the aging of supported films of a molecular glass former, toluene, at temperatures well below the glass transition temperature. By using microfabricated devices with very short equilibration times (below 1 s), we evidence a remarkable variation of the relaxation rate on decreasing film thickness from 100 nm down to a 7 nm thick film. Our results demonstrate that surface atoms are more efficient than bulk atoms in attaining low energy configurations within the potential energy landscape.     

Femtosecond laser writing of porous capillaries inside fused silica glass

We demonstrate that within a restricted optical pulse duration-pulse energy parameter space tightly focused femtosecond laser radiation can be used to fabricate porous capillaries in bulk fused silica glass by simply moving the laser focus through the material. We show that the rate of penetration of liquids into the porous capillaries can be controlled by the laser polarization, which determines their morphology. The fluid propagation is measured using the form birefringence of nanocrack/nanovoid structures produced inside the capillaries. We also demonstrate the nanofiltration capabilities of the capillaries by separating the relatively small molecules of Rhodamine 6G dye from their solvent.     

Analytical methods in oceanography I. Inorganic methods

Man's speculations on the nature of sea water have been recorded since the time of the ancient Greeks, but it was not until 1670, when Robert Boyle published a work entitled Observations and Experiments on the Saltiness of the Sea, that any systematic chemical measurements were carried out. Since these early days analytical chemistry has developed into the principal tool used to investigate sea water and marine processes.     

Molecular simulation of ultrathin polymeric films near the glass transition

Properties such as the glass transition temperature ( T(g)) and the diffusion coefficient of ultrathin polymeric films are shown to depend on the dimensions of the system. In this work, a hard-sphere molecular dynamics methodology has been applied to simulate such systems. We investigate the influence that substrates have on the behavior of thin polymer films; we report evidence suggesting that, depending on the strength of substrate-polymer interactions, the glass transition temperature for a thin film can be significantly lower or higher than that of the bulk.     

Superconductivity in ultrathin films I. Transition temperatures of amorphous Bi and Ga

Superconducting transition temperatures (T _c) and electron tunneling characteristics have been measured on amorphous, vapour quenched films of Ga and Bi in the thickness range 3 to 50 nm. TheT _c's are depressed and the tunnel densities of states are smeared as compared to bulk superconductors. A model considering the proximity effect between an extremely thin non-superconducting sheath (presumably due to the decrease of electron concentration at the surfaces) and a remaining bulk superconducting part gives good agreement withT _c measurements, while the predicted tunnel density of states is only in qualitative correspondence with experiments.     

New strings for old Veneziano amplitudes: I. Analytical treatment

The bosonic string theory evolved as an attempt to find a physical/quantum mechanical model capable of reproducing Euler’s beta function (Veneziano amplitude) and its multidimensional analogue. The multidimensional analogue of beta function was studied mathematically for some time from different angles by mathematicians such as Selberg, Weil and Deligne, among many others. The results of their studies apparently were not taken into account in physics literature on string theory. In a recent publication [IJMPA 19 (2004) 1655] an attempt was made to restore the missing links. The results of this publication are incomplete, however, since no attempts were made at reproduction of known spectra of both open an closed bosonic strings or at restoration of the underlying model(s) reproducing such spectra. Nevertheless, as discussed in this publication the existing mathematical interpretation of the multidimensional analogue of Euler’s beta function as one of the periods associated with the corresponding differential form “living” on the Fermat-type (hyper)surfaces, happens to be crucial for restoration of the quantum/statistical mechanical model reproducing such generalized beta function. Unlike the traditional formulations, this model is supersymmetric. Details leading to restoration of this model will be presented in the forthcoming Parts 2–4 of our work. They are devoted, respectively, to the group-theoretic, symplectic and combinatorial treatments of this model. In this paper the discussion is restricted mainly to the study of analytical properties of the multiparticle Veneziano and Veneziano-like (tachyon-free) amplitudes. In the last case, we demonstrate that the Veneziano-like amplitudes alone (with parameters adjusted accordingly) are capable of reproducing known spectra of both open and closed bosonic strings. The choice of parameters is subject to some constraints dictated by the mathematical interpretation of these amplitudes as periods of Fermat-type (hyper)surfaces considered as complex manifolds of Hodge-type.     

A model of modulated diffusion. I. Analytical results

We introduce an integrable isochronous system and perturb its frequency by an external-deterministic or purely random-noise. Under the perturbation the action variable evolves in time: the corresponding diffusion coefficient is exactly computed and its dependence on the magnitude of the perturbation is carefully investigated. Different behaviors are found and justified: the quasilinear approximation, the superlinear regime, and the ballistic motion.     

Analytical thermodynamics. Part I. Thermostatics—General theory

A new axiomatic treatment of equilibrium thermodynamics—thermostatics—is presented. The equilibrium states of a thermal system are assumed to be represented by a differentiable manifold of dimensionn + 1 (n finite). The empirical temperature is defined by the notion of thermal equilibrium. Empirical entropy is shown to exist for all systems with the property that the total work delivered along closed adiabats is zero. Absolute entropy and temperature follow from the additivity of heat and energy for two separate systems in thermal equilibrium considered as a whole. The absolute temperature is defined up to a multiplicative constant. The exterior differentiable calculus of Cartan is introduced and in a subsequent paper its use for the derivation of standard results in thermostatics will be explained.     

Yield stress in thin layers of ferrofluids

We present results of theoretical study of quasielastic behavior of ferrofluid filling a thin flat gap, placed into perpendicular magnetic field. When the field exceeds a certain critical magnitude, magnetic particles form dense discrete domains, elongated along the field, and linking the gap boundaries. Due to these bridges between the gap boundaries, the ferrofluid exhibits quasielastic properties with respect to shear strain in the plane of the gap. We estimated the elastic modules as well as the yield stress of the system, depending on magnetic field and concentration of magnetic particles in the ferrofluid. Analysis shows that there are at least two microscopical mechanisms of transition from the elastic to fluid behavior of the ferrofluid. The first one is connected with the loss of the mechanical equilibrium of the domains, slopped, under the shear stress, with respect to applied magnetic field. The second mechanism is connected with breakup of the “bridge” into two separate drops, when the shear strain exceeds some critical magnitude. Estimates show that for real ferrofluids the second mechanism is more probable.     

Invalidation of the Kelvin force in ferrofluids

Direct and unambiguous experimental evidence for the magnetic force density being of the form MnablaB in a certain geometry-rather than being the Kelvin force MnablaH--is provided for the first time. ( M is the magnetization, H is the field, and B is the flux density.)     

Segment Motion in the Reptation Model of Polymer Dynamics. I. Analytical Investigation

We analyze the motion of individual beads of a polymer chain using a discrete version of De Gennes' reptation model that describes the motion of a polymer through an ordered lattice of obstacles. The motion within the tube can be evaluated rigorously; tube renewal is taken into account in an approximation motivated by random walk theory. We find microstructure effects to be present for remarkably large times and long chains, affecting essentially all present-day computer experiments. The various asymptotic power laws commonly considered as typical for reptation hold only for extremely long chains. Furthermore, for an arbitrary segment even in a very long chain, we find a rich variety of fairly broad crossovers, which for practicably accessible chain lengths overlap and smear out the asymptotic power laws. Our analysis suggests observables specifically adapted to distinguish reptation from motions dominated by disorder of the environment.     

Infinite Compressibility States in the Hierarchical Reference Theory of Fluids. I. Analytical Considerations

In its customary formulation for one-component fluids, the Hierarchical Reference Theory yields a quasilinear partial differential equation (PDE) for an auxiliary quantity f that can be solved even arbitrarily close to the critical point, reproduces non-trivial scaling laws at the critical singularity, and directly locates the binodal without the need for a Maxwell construction. In the present contribution we present a systematic exploration of the possible types of behavior of the PDE\ for thermodynamic states of diverging isothermal compressibility _T as the renormalization group theoretical momentum cutoff approaches zero. By purely analytical means we identify three classes of asymptotic solutions compatible with infinite _T, characterized by uniform or slowly varying bounds on the curvature of f, by monotonicity of the build-up of diverging _T, and by stiffness of the PDE in part of its domain, respectively. These scenarios are analzyed and discussed with respect to their numerical properties. A seeming contradiction between two of these alternatives and an asymptotic solution derived earlier [Parola et al., Phys. Rev. E 48:3321 (1993)] is easily resolved.     

Adiabatic vs. non-adiabatic determination of specific absorption rate of ferrofluids

The measurement of temperature variations in adiabatic conditions allows the determination of the specific absorption rate of magnetic nanoparticles and ferrofluids from the correct incremental expression, SAR=(1/m_MNP)C(ΔT/Δt). However, when measurements take place in non-adiabatic conditions, one must approximate this expression by SAR≈Cβ/m_MNP, where β is the initial slope of the temperature vs. time curve during alternating field application. The errors arising from the use of this approximation were estimated through several experiments with different isolating conditions, temperature sensors and sample-sensor contacts. It is concluded that small to appreciable errors can appear, which are difficult to infer or control.     

Finite-size scaling studies of one-dimensional reaction-diffusion systems. Part I. Analytical results

We consider two single-species reaction-diffusion models on one-dimensional lattices of lengthL: the coagulation-decoagulation model and the annihilation model. For the coagulation model the system of differential equations describing the time evolution of the empty interval probabilities is derived for periodic as well as for open boundary conditions. This system of differential equations grows quadratically withL in the latter case. The equations are solved analytically and exact expressions for the concentration are derived. We investigate the finite-size behavior of the concentration and calculate the corresponding scaling functions and the leading corrections for both types of boundary conditions. We show that the scaling functions are independent of the initial conditions but do depend on the boundary conditions. A similarity transformation between the two models is derived and used to connect the corresponding scaling functions.     

Confinement and processing effects on glass transition temperature and physical aging in ultrathin polymer films: Novel fluorescence measurements

Fluorescence intensity measurements of chromophore-doped or -labeled polymers have been used for the first time to determine the effects of decreasing film thickness on glass transition temperature, T _g, the relative strength of the glass transition, and the relative rate of physical aging below T _g in supported, ultrathin polymer films. The temperature dependence of fluorescence intensity measured in the glassy state of thin and ultrathin films of pyrene-doped polystyrene (PS), poly(isobutyl methacrylate) (PiBMA), and poly(2-vinylpyridine) (P2VP) differs from that in the rubbery state with a transition at T _g. Positive deviations from bulk T _g are observed in ultrathin PiBMA and P2VP films on silica substrates while substantial negative deviations from bulk T _g are observed in ultrathin PS films on silica substrates. The relative difference in the temperature dependences of fluorescence intensity in the rubbery and glassy states is usually reduced with decreasing film thickness, indicating that the strength of the glass transition is reduced in thinner films. The temperature dependence of fluorescence intensity also provides useful information on effects of processing history as well as on the degree of polymer-substrate interaction. In addition, when used as a polymer label, a mobility-sensitive rotor chromophore is demonstrated to be useful in measuring relative rates of physical aging in films as thin as 10 nm. Received 21 August 2001