Tzu-Yu Wang

Counterion condensation and release in micellar solutions

Counterion condensation and release in micellar solutions are investigated by direct measurement of counterion concentration with ion-selective electrode. Monte Carlo simulations based on the cell model are also performed to analyze the experimental results. The degree of counterion condensation is indicated by the concentration ratio of counterions in the bulk to the total ionic surfactant added, alpha< or =1. The ionic surfactant is completely dissociated below the critical micelle concentration (cmc). However, as cmc is exceeded, the free counterion ratio alpha declines with increasing the surfactant concentration and approaches an asymptotic value owing to counterion condensation to the surface of the highly charged micelles. Micelle formation leads to much stronger electrostatic attraction between the counterion and the highly charged sphere in comparison to the attraction of single surfactant ion with its counterion. A simple model is developed to obtain the true degree of ionization, which agrees with our Monte Carlo results. Upon addition of neutral polymer or monovalent salts, some of the surfactant counterions are released to the bulk. The former is due to the decrease of the intrinsic charge (smaller aggregation number) and the degree of ionization is increased. The latter is attributed to competitive counterion condensation, which follows the Hefmeister series. This consequence indicates that the specific ion effect plays an important role next to the electrostatic attraction.

Growth of Co clusters on thin films Al2O3∕NiAl(100)

We present a scanning tunnel microscopy study of Co clusters grown through vapor deposition on Al(2)O(3) thin films over NiAl(100) at different coverages and temperatures. Formation of Co clusters was observed at 90, 300, 450, and 570 K. At the three lower temperatures, we find narrow cluster size distributions and the mean sizes (with a diameter of 2.6 nm and a height of 0.7 nm) do not change significantly with the coverage and temperature, until the clusters start to coalesce. Even on 3-4-nm-wide crystalline Al(2)O(3) strips where the deposited Co atoms are confined, the same features sustain. Only at 570 K the normal growth mode where the cluster size increases with the deposition coverage is observed, although the data are less conclusive. A simple modeling of kinetic surface processes on a strip confirms the normal growth mode, but fails to show a favored size unless additional energetic constraints are applied on the cluster sizes. Increasing Co coverages to cluster coalescence, a larger preferable size (mean diameter of 3.5 nm and height of 1.4 nm) appears for growth at 450 K. These two sizes are corroborated by morphology evolution of high Co coverages deposited at 300 K and annealed to 750 K, in which the coalescence is eliminated and the two preferable geometries appear and coexist.

Charge renormalization of charged spheres based on thermodynamic properties

At strong electrostatic coupling, counterions are accumulated in the vicinity of the surface of the charged particle with intrinsic charge Z. In order to explain the behavior of highly charged particles, effective charge Z(*) is therefore invoked in the models based on Debye-Huckel approximation, such as the Derjaguin-Landau-Verwey-Overbeek potential. For a salt-free colloidal suspension, we perform Monte Carlo simulations to obtain various thermodynamic properties omega in a spherical Wigner-Seitz cell. The effect of dielectric discontinuity is examined. We show that at the same particle volume fraction, counterions around a highly charged sphere with Z may display the same value of omega as those around a weakly charged sphere with Z(*), i.e., omega(Z)=omega(Z(*)). There exists a maximally attainable value of omega at which Z=Z(*). Defining Z(*) as the effective charge, we find that the effective charge passes through a maximum and declines again due to ion-ion correlation as the number of counterions is increased. The effective charge is even smaller if one adopts the Debye-Huckel expression omega(DH). Our results suggest that charge renormalization can be performed by chemical potential, which may be observed in osmotic pressure measurements.

Osmotic pressure and virial coefficients of star and comb polymer solutions: dissipative particle dynamics.

The effects of macromolecular architecture on the osmotic pressure pi and virial coefficients (B(2) and B(3)) of star and comb polymers in good solvents are studied by dissipative particle dynamics simulations for both dilute and semiconcentrated regimes. The dependence of the osmotic pressure on polymer concentration is directly calculated by considering two reservoirs separated by a semipermeable, fictitious membrane. Our simulation results show that the ratios A(n+1) identical with B(n+1)/R(g)(3n) are essentially constant and A(2) and A(3) are arm number (f) dependent, where R(g) is zero-density radius of gyration. The value of dimensionless virial ratio g = A(3)/A(2)(2) increases with arm number of stars whereas it is essentially arm number independent for comb polymers. In semiconcentrated regime the scaling relation between osmotic pressure and volume fraction, pi proportional to phi(lambda), still holds for both star and comb polymers. For comb polymers, the exponent lambda is close to lambda(*) (approximately = 2.73 for linear chains) and is independent of the arm number. However, for star polymers, the exponent lambda deviates from lambda(*) and actually grows with increasing the arm number. This may be attributed to the significant ternary interactions near the star core in the many-arm systems.

Equilibrium sedimentation profile of dilute, salt-free charged colloids

The sedimentation profile of a dilute colloidal solution follows the barometric distribution owing to the balance between gravitational force and thermal fluctuation. However, the electrostatic interactions may lead to significant deviation even in the low volume fraction limit (e.g., 10(-5)). On the basis of Monte Carlo simulations for a dilute, salt-free colloidal dispersion, five regimes can be identified through the resulting colloidal sedimentation profile and the counterion distribution. The electrostatic interactions depends on the Coulomb strength E(c) defined as the ratio of the Bjerrum length to the colloid size. At weak colloid-ion attractions (small E(c)), counterions tend to distribute uniformly in the container. However, both barometric and inflated profiles of colloids can be observed. On the contrary, at strong colloid-ion attraction (large E(c)), counterions accumulate in the vicinity of the colloids. Significant counterion condensation effectively decreases the strength of colloid-colloid repulsion and barometric profile of colloids can be obtained as well. As a result, the sedimentation profile and counterion distribution are indicative of the strength of effective colloid-colloid and colloid-ion interactions. It is also found that local electroneutrality condition is generally not satisfied and charge separation (or internal electric field) is neither a sufficient nor necessary condition for nonbarometric distributions.

Donnan potential of dilute colloidal dispersions: Monte Carlo simulations.

Donnan equilibrium between a salt-free colloidal dispersion and an electrolyte solution has been investigated by Monte Carlo simulations. The Donnan potential is directly calculated by considering two compartments separated by a semipermeable membrane. In order to understand the role played by colloid-ion interactions, the influences of colloidal characteristics, including particle size R, intrinsic particle charge Z, counterion valency z(c), and concentration c(p), on Donnan potential Psi(D) and effective charge Z(eff) are examined. Our simulations show that the electroneutrality condition is not followed in both compartments and the Donnan potential arises due to the net charge density. The Donnan potential grows by increasing c(p) and Z(eff) and by decreasing dielectric constant epsilon(r), i.e., Psi(D) approximately Z(eff)c(p)/epsilon(r) approximately. Note that the effective charge varies with R,Z,c(p),epsilon(r) and z(c) as well. When the salt concentration is increased, the net charge density is lowered and thus the Donnan potential decays accordingly. The validity of the classical theory based on the Nernst equation and the electroneutrality assumption is also examined. In general, the simulation results at high-salt condition can be well represented by such mean-field theory.

Effects of multivalent salt addition on effective charge of dilute colloidal solutions.

The effective charge Z* is often invoked to account for the accumulation of counterions near the colloid with intrinsic charge Z. Although the ion concentrations c(i) are not uniform in the solution due to the presence of the charged particle, their chemical potentials are uniform everywhere. Thus, on the basis of ion chemical potential, effective ion concentrations c(i)*, which can be experimentally measured by potentiometry, are defined with the pure salt solution as the reference state. The effective charge associated with the charged particle can then be determined by the global electroneutrality condition. Monte Carlo simulations are performed in a spherical Wigner-Seitz cell to obtain the effective charge of the colloid. In terms of the charge ratio alpha=Z*/Z, the effects of added salt concentration, counterion valency, and particle charge are examined. The effective charge declines with increasing salt concentration and the multivalent salt is much more efficient in reducing the effective charge of the colloidal solution. Moreover, the extent of effective charge reduction is decreased with increasing intrinsic charge for a given concentration of added salt. Those results are qualitatively consistent with experimental observations by electrophoresis.

A statistical simulation approach for early stage thin-film growth from vapor-deposited atoms

We present a statistical simulation method for the early stage of thin-film growth from vapor-deposited atoms, which simulate evolution of density, size, and spatial distribution of the growing islands on a supported substrate. The method describes surface processes of the deposited atoms by random walks and the Arrhenius form. However, we utilize the statistical behavior of the atomic surface processes over a time scale significantly larger than the typical attempt time (10(-13) s). This novel method saves enormous simulation time and thus overcomes the difficulty resulting from the remarkable gap between the typical experimental deposition rates and the attempt frequency. The statistical approach is verified by comparisons with direct step-by-step (kinetic Monte Carlo) simulations at large deposition rates. Results obtained for low deposition rates matching experimental conditions are also presented.

Effects of Multivalent Salt Addition on Effective Charge of Dilute Colloidal Solutions

The effective charge Z* is often invoked to account for the accumulation of counterions near the colloid with intrinsic charge Z. Although the ion concentrations c(i) are not uniform in the solution due to the presence of the charged particle, their chemical potentials are uniform everywhere. Thus, on the basis of ion chemical potential, effective ion concentrations c(i)*, which can be experimentally measured by potentiometry, are defined with the pure salt solution as the reference state. The effective charge associated with the charged particle can then be determined by the global electroneutrality condition. Monte Carlo simulations are performed in a spherical Wigner-Seitz cell to obtain the effective charge of the colloid. In terms of the charge ratio alpha=Z*/Z, the effects of added salt concentration, counterion valency, and particle charge are examined. The effective charge declines with increasing salt concentration and the multivalent salt is much more efficient in reducing the effective charge of the colloidal solution. Moreover, the extent of effective charge reduction is decreased with increasing intrinsic charge for a given concentration of added salt. Those results are qualitatively consistent with experimental observations by electrophoresis.