Aggregation behavior of latex particles in shear flow confined between two parallel plates

In this study, the aggregation and breakup behaviors of latex particles in shear flow confined between two parallel plates were investigated using an in situ observation apparatus with a laser scanning confocal microscope. To investigate the effects of shear rate and the gap width between two parallel plates on the size and structure of the aggregates in the steady state, the distributions of the projected cross-sectional area and perimeter-based fractal dimension of the aggregates were measured. As a result, the average size of the aggregates decreases as shear rate increases and the gap width decreases due to the hydrodynamic effect acting on the aggregates. The size distributions of the aggregates become narrow as the gap width decreases. In addition, the fractal dimension, that is, the structure of the aggregates, was almost independent of shear rate and the gap width and approximately 1.2, which suggests that the aggregates are relatively compact.     

Polymers confined between two parallel plane walls

Single three-dimensional polymers confined to a slab, i.e., to the region between two parallel plane walls, are studied by Monte Carlo simulations. They are described by N-step walks on a simple cubic lattice confined to the region 1< or = z < or = D. The simulations cover both regions DRF (where RF approximately Nnu is the Flory radius, with nu approximately 0.587), as well as the cross-over region in between. Chain lengths are up to N=80 000, slab widths up to D=120. In order to test the analysis program and to check for finite size corrections, we actually studied three different models: (a) ordinary random walks (mimicking Theta polymers); (b) self-avoiding walks; and (c) Domb-Joyce walks with the self-repulsion tuned to the point where finite size corrections for free (unrestricted) chains are minimal. For the simulations we employ the pruned-enriched-Rosenbluth method with Markovian anticipation. In addition to the partition sum (which gives us a direct estimate of the forces exerted onto the walls), we measure the density profiles of monomers and of end points transverse to the slab, and the radial extent of the chain parallel to the walls. All scaling laws and some of the universal amplitude ratios are compared to theoretical predictions.     

A thermodynamic analysis of charged mixed micelles in water

A thermodynamic analysis is presented for electrically charged mixed micelles in water on the basis of the Gibbs-Duhem relation proposed by Hall in combination with the information on the degree of counterion binding. The proposed analyses are shown to work well for both ionic/nonionic mixed micelles and those consisting of ionic surfactants of like charges. Conclusions for ionic/nonionic mixed micelles are as follows. (1) The contribution from counterions is significant. (2) In media of low ionic strengths, the counterion concentration varies with the micellar mole fraction of the ionic species x. The dependency of the activity coefficients and the excess free energy on x is significantly influenced by this effect, but it can be corrected to a large extent in terms of the Corrin-Harkins relation. (3) The regular solution theory (RST) is not always valid even when the excess free energy is described well with the RST expression unless the observed range of the micelle composition is wide enough. (4) The RST overestimates x and underestimates the activity coefficient of the ionic species when applied to the mixed micelles to which it is inapplicable. For the ionic mixed micelles consisting of surfactants of like charges, the Lange-Shinoda approach is shown to be consistent with the present analysis in terms of the Gibbs-Duhem relation, but Motomura's approach is found to be not exact but approximate.     

The wall and multivalent counterion effects on the electrostatic force between like-charged spherical particles confined in a charged pore

The effect of wall confinement (wall charge and wall-sphere separation distance) on the electrostatic force between two charged spheres confined in a long charged pore in symmetric and asymmetric electrolytes have been quantified by solving the nonlinear Poisson-Boltzmann equation (PBE), using adaptive finite elements combined with error minimization techniques. The computed force indicated the strong effect of the wall potential on the reduction of the repulsive force for all type of electrolytes. The influence of the wall effect was reduced when the valence of the electrolyte was increased. A significant reduction in the repulsive force between the two spheres was also observed when the distance between the pore wall and the sphere surface was reduced. A smaller long-range repulsive interaction was observed between spheres when the solutions contained multivalent counterions as compared with a monovalent solution. However, at short ranges of separation distances multivalent counterions increase the electrostatic repulsive force between the spheres. The effect of the dimensionless radius of the spheres on the electrostatic force between them has been determined and a significant reduction observed as the dimensionless radius was reduced.     

Quantitating the association of charged molecules with ionic micelles

We have studied micelles comprised of cationic (CTAB) and anionic (SDS) surfactants through the interactions of solution phase anionic disodium fluorescein (DSF) and cationic rhodamine 110 (R110) dyes with perylene sequestered within the micelles. Fluorescence lifetime measurements monitor energy transfer between the nonpolar optical donor within the micelle and ionic probes in the surrounding solution. The efficiency of this process is mediated by the extent to which the ionic dyes interact with the micelle palisade layer, and our fluorescence lifetime data allow us to determine the association constants for acceptor-micelle interactions.     

The density distributions of the counterions and the coions confined in two similarly charged plates

By using the field-theoretic method, we established a unified systematic formulation of a model of counterions and coions confined in two similarly charged plates, and calculated the density distributions of counterions and coions with various coupling parameters by the two methods: Poisson-Boltzmann (PB) approach and the strong coupling (SC) theory, respectively. We also performed Monte Carlo simulations, and obtained the density distributions of counterions and coions with several different coupling parameters. Comparing our theoretical results with those from Monte Carlo simulation, we find that the PB approach is valid when the coupling parameter Xi is smaller than 1, but, as Xi > or = 1, the results by the PB approach deviate from the corresponding Monte Carlo simulation data, and the deviation gets larger with the coupling parameter increasing. This shows that the PB approach is completely invalid when the coupling parameter is equal to 1 or larger than 1. For the latter case, the development trend of the distribution curve calculated by SC theory agrees with that from Monte Carlo simulation as the coupling parameter increases. This demonstrates that the SC theory can give a qualitative available explanation on the density distribution of the counterions in the system in which the coupling parameters are strictly confined.     

Calorimetric study on the temperature dependence of the formation of mixed ionic/nonionic micelles

The differential excess enthalpy of mixed micelle formation was measured at different temperatures by mixing nonionic hexa(ethylene glycol) mono n-dodecyl ether with anionic sodium dodecyl sulfate or cationic dodecylpyridinium chloride. The experimental data were obtained calorimetrically by titrating a concentrated surfactant solution into a micellar solution of nonionic surfactant. The composition and the size of the mixed nonionic/ionic micelles at different surfactant concentrations were also determined. Pronounced differences in both composition and excess enthalpy were found between the anionic and the cationic mixed system. For both systems, the excess enthalpies become more exothermic with increasing temperature, but for the anionic mixed system an additional exothermic contribution was found which was much less temperature dependent. Temperature dependence of the excess enthalpy was attributed to the effect of the ionic headgroup on the hydration of the ethylene oxide (EO) groups in the mixed corona. Ionic headgroups located in the ethylene oxide layer cause the dehydration of the EO chains resulting in an additional hydrophobic contribution to the enthalpy of mixing. A high affinity of sodium dodecyl sulfate for nonionic micelles and an extra exothermic and less temperature dependent contribution to the excess enthalpy found for the SDS-C(12)E(6) system might be attributed to specific interactions (hydrogen bonds) between the sulfate headgroup and the partly dehydrated EO chain.     

Synergic effects of imidazolium ionic liquids on P123 mixed micelles for inducing micro/mesoporous materials

A series of micro/mesoporous silica composites were synthesized with P123 and imidazolium ILs ([C(n)mim]X) as the co-templates. [C(n)mim]X showed notable synergic interaction with P123. By changing the alkyl chain length n in methylimidazolium, ring-like micropores were observed in the wall of the mesoporous materials when n = 4. While increasing n to 10, micropores and mesopores were found in different separated regions. Various anions of Cl(-), Br(-), and BF(4)(-) of ILs have little effect on the aggregation behavior of P123/C4X mixed micelles. The strong hydrogen bonding effect of BF(4)(-) has resulted in the ordered mesoporous channels with numerous micropores in the wall at a low temperature of 313 K. Hydrophobic C4PF(6) can only be solubilized in the core of P123 micelles, which resulted in the swelling of P123/C4PF(6) mixed aggregates and the ordered hexagonal porous silica materials at 313 K. The fundamental understanding of the synergic interaction and formation mechanisms of various porous silica materials can provide a general convenient way toward a rational design and synthesis of the micro/mesoporous composites.     

Electrostatic repulsion between two parallel plates covered with polymer brush layers

An expression for the electrostatic repulsive force is obtained for two parallel similar plates immersed in an electrolyte solution at separation h covered with a uniformly charged polymer brush layer of intact thickness d _o under compression (h<2d _o) after the two brushes come into contact. It is assumed that when the two brushes come into contact, they are squeezed against each other but do not interdigitate. The electrostatic repulsive force is found to increase with decreasing h as 1/h for highly charged brushes and as 1/h ² for weakly charged brushes. This is in contrast to the interaction force between the brush layers before contact (h≥2d _o), which is essentially proportional to exp[−κ(h−2d _o)] (where κ is the Debye–Hückel parameter). It is also shown that the interaction force for highly charged brushes, which becomes independent of the electrolyte concentration, can be comparable in magnitude to the steric repulsive forces between the brushes resulting from osmotic repulsion and the elastic energy of the brushes. Received: 21 October 1998 Accepted in revised form: 25 December 1998     

Spinodal instability and pattern formation in thin liquid films confined between two plates

The instability, morphology and pattern formation engendered by the van der Waals force in a thin liquid film of thickness h confined between two closely placed solid surfaces (at distance d > h) are investigated based on nonlinear 3D simulations. The initial and the final stages of dewetting and pattern formation are found to be crucially dependent on the volumetric (thickness) ratio of air and liquid and its deviation from the location of the maximum of the spinodal parameter versus volumetric ratio curve. On a low energy surface, relatively thinner films and wider air gaps favor initial dewetting of the lower plate by the formation of holes, whereas thicker films with thinner air gaps initially evolve by the formation of columns/bridges that join the upper plate. In the later stage of evolution, the initial holes in thinner films evolve into columns/drops, while a rapid coalescence of columns in the thicker films eventually causes formation of holes. Thus, a phase inversion, either from liquid-in-air to air-in-liquid dispersion or vice versa, occurs during the final stages of evolution. A thin film confined between two high-energy solid surfaces forms columns (bridges) only when its mean thickness, h0, is greater than a critical thickness (hc) or the air gap is smaller than a critical distance. The patterns can be aligned by using a topographically patterned confining surface. Conditions on pattern periodicity, amplitude, and the volumetric ratio of air and liquid in the gap are explored for the formation of various types of ordered patterns including annular rings of columns, concentric ripples, parallel channels and a rectangular array of complex features. The results are of significance in soft lithographies such as LISA, soft stamping and capillary force lithography.     

Screening effects on structure and diffusion in confined charged colloids

Using molecular dynamics computer simulations we investigate structural and dynamic (diffusion) properties of charged colloidal suspension confined to narrow slit pores with structureless, uncharged walls. The system is modeled on an effective level involving only the macroions, which interact via a combination of a soft-sphere and a screened Coulomb potential. The aim of our study is to identify the role of the range of the macroion-macroion interaction controlled by the inverse Debye screening length, kappa. We also compare to bulk properties at the same chemical potential as determined in parallel grand canonical Monte Carlo simulations. Our results reveal a significant influence of the interaction range which competes, however, with the influence of density. At liquidlike densities a decrease of range yields a decreasing mobility (and a corresponding enhancement of local structure) in the bulk system, whereas the reverse effect occurs in narrow slits with thickness of a few particle diameter. These differences can be traced back to the confinement-induced, and kappa-dependent, reduction of overall density compared to the bulk reservoir. We also show that an increase of kappa softens the oscillations in the normal pressure as function of the wall separation, which is consistent with experimental observations concerning the influence of addition of salt.     

Electrostatic effects on the migration rates of ions between charged micelles. Consequences for fluorescence quenching

The rate of exchange of countenons between micelles has been calculated from numerical solutions of the Poisson-Boltzmann equation for micelles in cells of spherical symmetry, and solutions of a steady-state diffusion problem for the ion in the resulting potential. The results indicate a rapid increase of the exchange rate with total amphiphilc concentration, as has been observed.     

Interaction force between two charged plates immersed in a solution of charged particles. Coupling between double layer and depletion forces

When two parallel plates are immersed in a solution of small charged particles, the center of the particles is excluded from a region of thickness D/2 near the plate, where D is their diameter. The approach which Langmuir developed for the double layer repulsion in the presence of an electrolyte with ions of negligible size is extended to the case in which one of the "ions" is a charged particle of finite, relatively small size. A general expression for the force generated between the two charged plates immersed in an electrolyte solution containing relatively small charged particles is derived. In this expression, only the electrical potential at the middle distance between the plates is required to calculate the force. A Poisson-Boltzmann equation which accounts for the volume exclusion of the charged particles in the vicinity of the surface is solved to obtain the electrical potential at the middle between the two plates. Starting from this expression, some results obtained previously for the depletion force acting between two plates or two spheres are rederived. For charged plates immersed in a solution of an electrolyte and charged small particles, the effects of the particle charge, particle charge sign, particle size, and volume fraction of the particles on the force acting between the two plates are examined.     

Rheological properties of associates of ionic monomers with micelles of oppositely charged surfactants

Rheological properties of associates formed by interaction of trimethyl[methacryl-oxyethyl]ammonium methyl sulfate with sodium octyl- and dodecyl sulfate micelles, as well as associates of sodium 4-styrenesulfonate with dodecyltrimethylammonium bromide micelles in aqueous solutions were studied by steady shear and oscillatory (dynamic) shear measurements with Fourier transform. It was shown that viscosity depends on the composition and achieves maximum value at equimolar ratio of components for two of studied systems. The extremal dependence of the viscosity vs. composition is not observed for systems with sodium octyl sulfate due to weak interactions between the components. The systems exhibiting the anomalous dependencies of concentration to viscosity are viscoelastic fluids due to the physical entanglements between the associates.     

The interaction energy between two parallel plates with constant surface charge density

On the basis of Langmuir's suggestion we simplify the Poisson-Boltzmann equation and derive the relation of surface potential, potential midway, and the plate distance. Thus we obtain the interaction force and energy equations between two dissimilar plates in the case of constant surface charge density. Agreement with the exact numerical values of the interaction of dissimilar plates is good. This method may not only apply to the cases of high constant potential but to the case of high constant charge density.     

Critical composition of ionic–nonionic mixed micelles for counterion condensation

In the mixed micelles of an ionic surfactant (sodium dodecyl sulfate) with a nonionic surfactant (N-decanoyl-N-methylglucamide, hexaoxyethylene glycol-mono-n-decylether, and hexaoxyethylene glycol-mono-n-dodecylether), the critical mole fraction, X_ic, of the ionic surfactant has been determined, below which the counterion is completely released from the micelles. The values of X_ic are 0.074, 0.11, and 0.11, for the respective nonionic surfactants. The valences, i.e., the aggregation numbers of the ionic surfactant, of the mixed micelles at X_ic are almost close to each other, around 6. At X_ic, the critical surface charge density (about 0.03 Cm^-2) for counterion condensation was tentatively calculated. In the present study, a differential conductivity method was applied.     

Three-dimensional discrete charge effects on the electrostatic interaction between two soft particles

An expression for the electrostatic interaction energy between two parallel plate-like soft particles (i.e., hard particles covered with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution is derived by using the linearized Poisson-Boltzmann equation. This expression is based on a discrete charge model in which the surface layer consists of a cubic lattice of fixed point charges. We show that the deviation of the results of the discrete charge model from those of the conventional smeared charge model becomes significant as the ratio of the lattice spacing to the Debye length becomes large. As this ratio decreases, on the other hand, the discrete charge model approaches a smeared charge model, leading to the Donnan-potential regulated interaction model.     

Conformational structures and thermodynamic properties of compact polymer chains confined between two parallel plane boundaries

In this paper, the authors investigated the adsorption phenomenon of compact chains confined between two parallel plane boundaries using a pruned‐enriched Rosenbluth method. The authors considered three cases with different adsorption energies of ε = 0, ?1, and ?3 (in units of k_BT) for the confined compact chains of different chain lengths N, respectively. Several parameters were employed to describe the size and shape of compact chain, and some special behaviors in the conformational structures were investigated for the first time. For example, the size and shape of confined compact chains undergo distinct changes in the adsorption cases of ε = ?1 and ?3, and pass through the maximum values at the characteristic distances D_c. The authors found that this characteristic distance D_c could be scaled as D_c～ (N + 1)^ν (ν = 0.56 ± 0.01) in the case of ε = ?3. In addition, the microstructures of chains were investigated, and several significant results were obtained by analyzing the segment density distribution and the mean fractions of segment in tails, trains, bridges, and loops structures. On the other hand, the thermodynamic properties were also investigated for the confined compact chains, such as average energy per bond, Helmholtz free energy per bond, and elastic force per bond. Results show that elastic forces f have different behaviors in three cases, indicating that it is not necessary to exert an external force on the boundaries in the nonadsorption case. At the same time, the average contact energy of compact chain obviously changes when the distance between the two parallel boundaries D increases, which is similar to those of the size and shape parameters. The authors also conclude that these thermodynamic properties of compact chains depend strongly on not only the adsorption energies but also the chain lengths and the confined condition. In addition, several results of the conformational and thermodynamic parameters, such as the segment density distribution and free energy, were compared with the results from the self‐consistent field theory. These investigations may help us to deepen the knowledge about the adsorption phenomenon of confined compact chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2888–2901, 2006     

Interactions between bottle-brush polyelectrolyte layers: effects of ionic strength and oppositely charged surfactant

Interactions between cationic bottle-brush polyelectrolyte layers adsorbed on mica across salt and oppositely charged surfactant solutions were investigated with the interferometric surface force apparatus, and the results were compared with what is known for similarly charged linear polyelectrolytes. Ellipsometric measurements demonstrated that the bottle-brush polyelectrolytes, which contain 45 units long poly(ethylene oxide) side chains, are more readily desorbed than linear equivalents when the ionic strength of the solution is increased. It is argued that this is due to the steric repulsion between the poly(ethylene oxide) side chains that reduces the surface affinity. The preadsorbed bottle-brush polyelectrolyte layers were also exposed to sodium dodecyl sulfate (SDS) solutions. It was found that the presence of SDS affected the force profiles less than observed for similarly charged linear polyelectrolytes. This observation was attributed to excluded volume constraints imposed by the poly(ethylene oxide) side chains that reduces the accessibility of the charged polyelectrolyte segments and counteracts formation of large aggregates within the layer.