Electroneutrality and Phase Behavior of Colloidal Suspensions

Several statistical mechanical theories predict that colloidal suspensions of highly charged macroions and monovalent microions can exhibit unusual thermodynamic phase behavior when strongly deionized. Density-functional, extended Debye-H\"uckel, and response theories, within mean-field and linearization approximations, predict a spinodal phase instability of charged colloids below a critical salt concentration. Poisson-Boltzmann cell model studies of suspensions in Donnan equilibrium with a salt reservoir demonstrate that effective interactions and osmotic pressures predicted by such theories can be sensitive to the choice of reference system, e.g., whether the microion density profiles are expanded about the average potential of the suspension or about the reservoir potential. By unifying Poisson-Boltzmann and response theories within a common perturbative framework, it is shown here that the choice of reference system is dictated by the constraint of global electroneutrality. On this basis, bulk suspensions are best modeled by density-dependent effective interactions derived from a closed reference system in which the counterions are confined to the same volume as the macroions. Linearized theories then predict bulk phase separation of deionized suspensions only when expanded about a physically consistent (closed) reference system. Lower-dimensional systems (e.g., monolayers, small clusters), depending on the strength of macroion-counterion correlations, may be governed instead by density-independent effective interactions tied to an open reference system with counterions dispersed throughout the reservoir, possibly explaining observed structural crossover in colloidal monolayers and anomalous metastability of colloidal crystallites.Comment: 12 pages, 5 figures. Discussion clarified, references adde

Charge Renormalization, Effective Interactions, and Thermodynamics of Deionized Colloidal Suspensions

Thermodynamic properties of charge-stabilised colloidal suspensions depend sensitively on the effective charge of the macroions, which can be substantially lower than the bare charge in the case of strong counterion-macroion association. A theory of charge renormalization is proposed, combining an effective one-component model of charged colloids with a thermal criterion for distinguishing between free and associated counterions. The theory predicts, with minimal computational effort, osmotic pressures of deionized suspensions of highly charged colloids in close agreement with large-scale simulations of the primitive model.Comment: 15 pages, 7 figure

Poisson-Boltzmann Theory of Charged Colloids: Limits of the Cell Model for Salty Suspensions

Thermodynamic properties of charge-stabilised colloidal suspensions are commonly modeled by implementing the mean-field Poisson-Boltzmann (PB) theory within a cell model. This approach models a bulk system by a single macroion, together with counterions and salt ions, confined to a symmetrically shaped, electroneutral cell. While easing solution of the nonlinear PB equation, the cell model neglects microion-induced correlations between macroions, precluding modeling of macroion ordering phenomena. An alternative approach, avoiding artificial constraints of cell geometry, maps a macroion-microion mixture onto a one-component model of pseudo-macroions governed by effective interactions. In practice, effective-interaction models are usually based on linear screening approximations, which can accurately describe nonlinear screening only by incorporating an effective (renormalized) macroion charge. Combining charge renormalization and linearized PB theories, in both the cell model and an effective-interaction (cell-free) model, we compute osmotic pressures of highly charged colloids and monovalent microions over a range of concentrations. By comparing predictions with primitive model simulation data for salt-free suspensions, and with predictions of nonlinear PB theory for salty suspensions, we chart the limits of both the cell model and linear-screening approximations in modeling bulk thermodynamic properties. Up to moderately strong electrostatic couplings, the cell model proves accurate in predicting osmotic pressures of deionized suspensions. With increasing salt concentration, however, the relative contribution of macroion interactions grows, leading predictions of the cell and effective-interaction models to deviate. No evidence is found for a liquid-vapour phase instability driven by monovalent microions. These results may guide applications of PB theory to soft materials.Comment: 27 pages, 5 figures, special issue of Journal of Physics: Condensed Matter on "Classical density functional theory methods in soft and hard matter

Location of Pc 1–2 waves relative to the magnetopause

Spacecraft-borne and ground-based magnetome- ters frequently detect magnetospheric micropulsations in the period range 0.2–10s, termed Pc 1–2, and attributed to electromagnetic ion cyclotron waves driven by temperature anisotropy (T⊥ \u3e T∥). Previous surveys of Pc 1 occur- rence locations have been limited to L ≤ 9. We present AMPTE/IRM observations of the distribution of Pc 1 waves out to the magnetopause, for a limited region of MLT = 10–14. The probability of wave occurrence Pwav is large (\u3e 0.15) between L = 7–12, peaking at L = 8–10 (Pwav ∼ 0.25). When the L-value is normalized to the magnetopause position Lmp, however, the highest probabilities of Pc 1 wave occurrence are close to the magnetopause, with Pwav ∼ 0.25 for Lnorm ≡ L/Lmp = 0.8–1.0. These results are consis- tent with increased convective growth rate at large L and with the greater effect of magnetosphere compression close to the magnetopause. On the other hand, we only directly observe magnetic field compression for at most about 25% of the wave events

Stability of Colloidal Quasicrystals

Freezing of charge-stabilized colloidal suspensions and relative stabilities of crystals and quasicrystals are studied using thermodynamic perturbation theory. Macroion interactions are modelled by effective pair potentials combining electrostatic repulsion with polymer-depletion or van der Waals attraction. Comparing free energies -- counterion terms included -- for elementary crystals and rational approximants to icosahedral quasicrystals, parameters are identified for which one-component quasicrystals are stabilized by a compromise between packing entropy and cohesive energy.Comment: 6 pages, 4 figure

Classification of Micro-calcification in Mammograms using Scalable Linear Fisher Discriminant Analysis

Breast cancer is one of the major causes of death in women. Computer Aided Diagnosis (CAD) systems are being developed to assist radiologists in early diagnosis. Microcalcifications can be an early symptom of breast cancer. Besides detection, classification of micro-calcification as benign or malignant is essential in a complete CAD system.We have developed a novel method for the classification of benign and malignant microcalcification using an improved Fisher Linear Discriminant Analysis (LDA) approach for the linear transformation of segmented micro-calcification data in combination with a Support Vector Machine (SVM) variant to classify between the two classes. The results indicate an average accuracy equal to 96% which is comparable to state-of-the art methods in the literature.authorsversionPeer reviewe

A study of Pc-5 ULF oscillations

International audienceA study of Pc-5 magnetic pulsations using data from the Combined Release and Radiation Effects Satellite (CRRES) was carried out. Three-component dynamic magnetic field spectrograms have been used to survey ULF pulsation activity for the approximate fourteen month lifetime of CRRES. Two-hour panels of dynamic spectra were examined to find events which fall into two basic categories: 1) toroidal modes (fundamental and harmonic resonances) and 2) poloidal modes, which include compressional oscillations. The occurence rates were determined as a function of L value and local time. The main result is a comparable probability of occurence of toroidal mode oscillations on the dawn and dusk sides of the magnetosphere inside geosynchronous orbit, while poloidal mode oscillations occur predominantly along the dusk side, consistent with high azimuthal mode number excitation by ring current ions. Pc-5 pulsations following Storm Sudden Commencements (SSCs) were examined separately. The spatial distribution of modes for the SSC events was consistent with the statistical study for the lifetime of CRRES. The toroidal fundamental (and harmonic) resonances are the dominant mode seen on the dawn-side of the magnetosphere following SSCs. Power is mixed in all three components. In the 21 dusk side SSC events there were only a few examples of purely compressional (two) or radial (one) power in the CRRES study, a few more examples of purely toroidal modes (six), with all three components predominant in about half (ten) of the events. Key words. Magnetospheric physics (MHD waves and instabilities; magnetospheric configuration and dynamics) ? Space plasma physics (waves and instabilities

Density-Functional Theory of Quantum Freezing: Sensitivity to Liquid-State Structure and Statistics

Density-functional theory is applied to compute the ground-state energies of quantum hard-sphere solids. The modified weighted-density approximation is used to map both the Bose and the Fermi solid onto a corresponding uniform Bose liquid, assuming negligible exchange for the Fermi solid. The required liquid-state input data are obtained from a paired phonon analysis and the Feynman approximation, connecting the static structure factor and the linear response function. The Fermi liquid is treated by the Wu-Feenberg cluster expansion, which approximately accounts for the effects of antisymmetry. Liquid-solid transitions for both systems are obtained with no adjustment of input data. Limited quantitative agreement with simulation indicates a need for further improvement of the liquid-state input through practical alternatives to the Feynman approximation.Comment: IOP-TeX, 21 pages + 7 figures, to appear, J. Phys.: Condens. Matte