Titration of hydrophobic polyelectrolytes using Monte Carlo simulations

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK(0) values (pK(0) represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree alpha of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK(0) value.     

Steric stabilization of spherical colloidal particles: Implicit and explicit solvent

We present the results of Monte Carlo simulations and density functional theory treatment of interactions between spherical colloidal brushes both in implicit (good) solvent and in an explicit polymeric solution. Overall, theory is seen to be in good agreement with simulations. We find that interactions between hard-sphere particles grafted with hard-sphere chains are always repulsive in implicit solvent. The range and steepness of the repulsive interaction is sensitive to the grafting density and the length of the grafted chains. When the brushes are immersed in an explicit solvent of hard-sphere chains, a weak mid-range attraction arises, provided the length of the free chains exceeds that of the grafted chains.     

Interaction between colloids with grafted diblock polyampholytes

The interaction between composite colloidal particles composed of a spherical core and grafted AB-diblock polyampholytes (diblock copolymers with oppositely charged blocks) are investigated by using a coarse-grained model solved with Monte Carlo simulations. The B block is end-grafted onto the core of the colloid and its linear charge density is varied, whereas the linear charge density of the A block is fixed. The brush structure of a single colloid, the mean force between two colloids, and the structure of solutions of such colloids have been determined for different linear charge densities of the B blocks and block lengths. Many features of the present system are controlled by the charge of the B blocks. In the limit of uncharged B blocks, (i) the grafted chains are stretched and form an extended polyelectrolyte brush, (ii) a strong repulsive force is operating between two colloids, (iii) and the solution is thermodynamic stable and displays strong spatial correlation among the colloids. In the limit where the charges of the two types of blocks exactly compensate each other, (i) the chains are collapsed and form a polyelectrolyte complex surrounding the cores, (ii) an attractive force appears between two colloids, and (iii) strong colloid clustering appears in the solution. These features become more pronounced as the length of the polymer blocks is increased, and a phase instability occurs at sufficiently long chains. A comparison with properties for other related colloidal particles is also provided.     

Anomalous potentials from inverse analyses of interfacial polydisperse attractive colloidal fluids

This paper investigates effects of using monodisperse inverse analyses to extract particle-particle and particle-surface potentials from simulated interfacial colloidal fluids of polydisperse attractive particles. Effects of polydispersity are investigated as functions of particle concentration and attractive well depth and range for van der Waals and depletion potentials. Forward Monte Carlo simulations are used to generate particle distribution functions for polydisperse interfacial colloidal fluids from which inverted potentials are obtained using an inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method. Attractive potentials are successfully recovered for monodisperse colloidal fluids, but polydispersity that is unaccounted for in inverse analyses produces (1) apparent softening of strong forces, (2) anomalous repulsive and attractive interactions, and (3) aphysical particle overlaps. This investigation provides insights into the role of polydispersity in altering the equilibrium structure and corresponding inverted potentials of attractive colloidal fluids near surfaces. These findings should assist the design and interpretation of optical microscopy experiments involving interfacial colloidal fluids similar to the simulated experiments reported here.     

Transitions of tethered polymer chains: a simulation study with the bond fluctuation lattice model

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density-of-states results have been evaluated for interaction parameters spanning the range from good- to poor-solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.     

Role of polydispersity in anomalous interactions in electrostatically levitated colloidal systems

In this paper, we investigate the effects of using inverse analyses developed for monodisperse particles to extract particle-particle and particle-surface potentials from simulated interfacial colloidal configurations having finite-size polydispersity. Forward Monte Carlo simulations are used to generate three-dimensional equilibrium configurations of log normal-distributed polydisperse particles confined by gravity near an underlying surface. Particles remain levitated above the substrate and stabilized against aggregation by repulsive electrostatic Derjaguin-Landau-Verwey-Overbeek pair potentials. An inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method are used to obtain interactions from simulated distribution functions as a function of polydispersity (sigma), relative range of repulsion (kappa a), and projected interfacial concentration (rho). Both inverse analyses successfully recover input potentials for all monodisperse cases, but fail for polydispersities often encountered in experiments. For different conditions (sigma, kappa a, and rho), our results indicate softened short-range repulsion, anomalous long-range attraction, and apparent particle overlaps, which are similar to commonly reported observations in optical microscopy measurements of quasi-two-dimensional interfacial colloidal ensembles. By demonstrating signatures of, and limitations due to, polydispersity when extracting pair potentials from measured distribution functions, our specific goal is to provide a basis to objectively interpret and resolve the effects of polydispersity in optical microscopy experiments.     

Self-diffusion in submonolayer colloidal fluids near a wall

Theoretical expressions are developed to describe self-diffusion in submonolayer colloidal fluids that require only equilibrium structural information as input. Submonolayer colloidal fluids are defined for the purpose of this work to occur when gravity confines colloids near a planar wall surface so that they behave thermodynamically as two dimensional fluids. Expressions for self-diffusion are generalized to consider different colloid and surface interaction potentials and interfacial concentrations from infinite dilution to near fluid-solid coexistence. The accuracy of these expressions is demonstrated by comparing self-diffusion coefficients predicted from Monte Carlo simulated equilibrium particle configurations with standard measures of self-diffusion evaluated from Stokesian Dynamics simulated particle trajectories. It is shown that diffusivities predicted for simulated equilibrium fluid structures via multibody hydrodynamic resistance tensors and particle distribution functions display excellent agreement with values computed from mean squared displacements and autocorrelation functions of simulated tracer particles. Results are obtained for short and long time self-diffusion both parallel and normal to underlying planar wall surfaces in fluids composed of particles having either repulsive electrostatic or attractive van der Waals interactions. The demonstrated accuracy of these expressions for self-diffusion should allow their direct application to experiments involving submonolayer colloidal fluids having a range of interaction potentials and interfacial concentrations.     

Monte Carlo simulation of structure and nanoscale interactions in polymer nanocomposites

Off-lattice Monte Carlo simulations in the canonical ensemble are used to study polymer-particle interactions in nanocomposite materials. Specifically, nanoscale interactions between long polymer chains (N=550) and strongly adsorbing colloidal particles of comparable size to the polymer coils are quantified and their influence on nanocomposite structure and dynamics investigated. In this work, polymer-particle interactions are computed from the integrated force-distance curve on a pair of particles approaching each other in an isotropic polymer medium. Two distinct contributions to the polymer-particle interaction potential are identified: a damped oscillatory component that is due to chain density fluctuations and a steric repulsive component that arises from polymer confinement between the surfaces of approaching particles. Significantly, in systems where particles are in a dense polymer melt, the latter effect is found to be much stronger than the attractive polymer bridging effect. The polymer-particle interaction potential and the van der Waals potential between particles determine the equilibrium particle structure. Under thermodynamic equilibrium, particle aggregation is observed and there exists a fully developed polymer-particle network at a particle volume fraction of 11.3%. Near-surface polymer chain configurations deduced from our simulations are in good agreement with results from previous simulation studies.     

Cascade of coil-globule conformational transitions of single flexible polyelectrolyte molecules in poor solvent

We show that hydrophobic flexible polyelectrolyte molecules of poly(2-vinylpyridine) and poly(methacryloyloxyethyl dimethylbenzylammonium chloride) are trapped and frozen due to adsorption on the mica surface, and the observed AFM single molecule structures reflect the molecular conformation in solution. An increase of the ionic strength of the solution induces the cascade of abrupt conformational transitions due to the intrachain segregation from elongated coil to compact globule conformations through intermediate pearl necklace-globule conformations with different amounts of beads per chain. The length of the necklaces and the number of beads decrease, while the diameter of beads increases with the increase of ionic strength. Coexistence at the same time of extended coils, necklaces with different amounts of beads, and compact globules indicates the cascade of the first-order-type phase transitions.     

Communication: thermodynamic signatures of cluster formation in fluids with competing interactions

Convergent theoretical evidence, based on self-consistent integral equations for the pair structure and on Monte Carlo simulations, is presented for the existence of small simultaneous jump discontinuities of several thermodynamic and structural properties of systems of colloidal particles with competing short-range attractive and long-range repulsive interactions, under physical conditions close to the onset of particle clustering. The discontinuities thus provide a signature of the transition from a homogeneous fluid phase to a locally inhomogeneous cluster phase.     

Inhomogeneous fluids of colloidal hard dumbbells: fundamental measure theory and Monte Carlo simulations

Recently, a density functional theory for hard particles with shape anisotropy was developed, the extended deconvolution fundamental measure theory (edFMT). We apply edFMT to hard dumbbells, arguably the simplest non-convex shape and readily available experimentally in the form of colloids. We obtain good agreement between edFMT and Monte Carlo simulations for fluids of dumbbells in a slit and for the same system under gravity. This indicates that edFMT can be successfully applied to nearly all colloidal shapes, not just for the convex shapes for which edFMT was originally derived. A theory, such as edFMT, that allows a fast and general way of mapping the phase behavior of anisotropic colloids, can act as a useful guide for the design of colloidal shapes for various applications.     

Internal and free energy in a pair of like-charged colloids: Monte Carlo simulations

The effective interaction between two colloidal particles in a bath of monovalent co- and counterions is studied by means of lattice Monte Carlo simulations with the primitive model. The internal electrostatic energy as a function of the colloid distance is studied fixing the position of the colloids. The free energy of the whole system is obtained introducing a bias parabolic potential, that allows us to sample efficiently small separations between the colloidal particles. For small charges, both the internal and free energy increase when the colloids approach each other, resulting in an effective repulsion driven by the electrostatic repulsion. When the colloidal charge is large enough, on the other hand, the colloid-ion coupling is strong enough to form double layers. The internal energy in this case decreases upon approaching the colloids because more ions enter the double layer. This attractive contribution to the interaction between the colloids is stronger for larger charges and larger ionic concentrations. However, the total free energy increases due to the loss of ionic entropy, and resulting finally in a repulsive interaction potential driven by the entropic contributions. The loss of ionic entropy can be almost quantitatively reproduced with the ideal contribution, the same level of approximation as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The overall behavior is captured by the DLVO theory qualitatively, and a comparison is made with the functional form predicted by the theory, showing moderate agreement.     

Influence of perpendicular external magnetic field on microstructures of monolayer composed of ferromagnetic particles: analysis by means of quasi-two-dimensional Monte Carlo simulation

We investigated the influences of the magnetic field strength and particle areal density on the microstructure of a quasi-two-dimensional monolayer composed of ferromagnetic particles by means of a Monte Carlo simulation. The magnetic field was applied along a direction perpendicular to the plane of the monolayer. Microstructures of the monolayer obtained in the simulations were analyzed in terms of radial distribution and orientational distribution functions. Formation of the microstructures is discussed from the perspective of particle-particle interaction energy and the perpendicular magnetic susceptibility of the monolayer was calculated from simulated magnetization curves. The obtained results are summarized as follows. For small areal density of particles, formation of chain-like structures is prevented by the repulsive magnetic interaction between particles due to orientations of the magnetic moments in the particles along the magnetic field direction. For intermediate areal density of particles, the chain-like structures remain even when a relatively strong magnetic field is applied, because contributions of the attractive magnetic interactions increase. For large areal density of particles, mixtures of chain-like and locally ordered structures appear due to the anisotropic attractive magnetic interactions in the absence of the magnetic field. However, when a sufficiently strong magnetic field is applied, the magnetic interactions between particles change to isotropic repulsive interactions, which results in the short-range repulsive steric interactions between particles becoming dominant with the appearance of hexagonal close packed structures.     

Interaction between small colloidal particles and molecular chains with selectively adsorbing groups: computer simulation study

Using the Monte Carlo simulation technique and the method of simulated annealing, we study interactions between small (nanometric) particles and flexible‐chain polymers with sticker groups which selectively adsorb on the particles and also can strongly attract each other. For the chains with two end stickers (telechelic polymers), we find that the colloidal particles adsorbing on the polymers play the role of junction points (locks) which bind together the ends of different chains. This direct or indirect binding leads to the formation of a web‐like structure throughout the sample: colloidal particles and chain stickers group into mixed clusters – “drops of a fog” – which are wrapped by polymer chains and connected by bridges. Analyzing static structure factors, we show that the selectively adsorbing telechelic polymers can affect the equilibrium spatially homogeneous distribution of colloidal particles that results in the appearance of a quasiregular structure on the intermediate scale related to the average intercluster distance. At sufficiently strong attraction between particles and chain end‐groups, most of the telechelic chains (>90%) adopt either a loop‐like or a stretched bridge‐like conformation, the most typical morphology of the system being a combination of these two structural elements. In the mixed clusters, the colloidal particles and the chain ends pack locally on a binary grid corresponding to a local crystal‐like arrangement. For the chains without attracting end‐groups, we observe the formation of elongated, rugby‐ball‐like clusters having alternate layers of particles and adsorbing chain groups.     

The bridging force between two plates by polyelectrolyte chains

The interaction between particles in a colloidal system can be significantly affected by their bridging by polyelectrolyte chains. In this paper, the bridging is investigated by using a self-consistent field approach which takes into account the van der Waals interactions between the segments of the polyelectrolyte molecules and the plates, as well as the electrostatic and volume exclusion interactions. A positive contribution to the force between two plates is generated by the van der Waals interactions between the segments and the plates. This positive (repulsive) contribution plays an important role in the force when the distances between the plates are small. With increasing van der Waals interaction strength between segments and plates, the force between the plates becomes more repulsive at small distances and more attractive at large distances. When the surfaces of the plates have a constant surface electrical potential and a charge sign opposite to that of the polyelectrolyte chains, the force between the two plates becomes less attractive as the bulk polyelectrolyte concentration increases. This behavior is due to a higher bulk counterion concentration dissociated from the polyelectrolyte molecules. At short distances, the force between plates is more repulsive for stiffer chains. A comparison between theoretical and experimental results regarding the contraction of the interlayer separation between the platelets of vermiculite clays against the concentration of poly(vinyl methyl ether) was made.     

Monte Carlo study of polyelectrolyte gels

The discontinuous transition between dense and dilute phases in polyelectrolyte gels is observed in Bond-Fluctuation Method Monte Carlo simulations of gels. The transition is driven by the competition between local attractive interactions of a poor-quality solvent and global repulsive interactions from counter-ion pressure. A procedure is introduced that prevents local attractive interactions from destroying ergodicity. Under good solvent conditions, lengths and volumes of gels are found to follow self-avoiding random walk scaling. © 1996 John Wiley & Sons, Inc.     

分散体系中任意形状的胶粒模型与相互作用能——Ⅲ. 园柱体型颗粒

在分散体系的研究中,也经常遇到园柱体型胶粒,例如蛋白质分子,海泡石和凸凹棒石粘土颗粒,它们都能用带电的园柱体型采近似处理。这种类型的颗粒以往研究不多,其原因大约有二,一是处理这类颗粒时,数学上的困难很大;二是这类颗粒之间的相互作用,和它们之间的取向有关。Sparnaay首先用Derjaguin法得出园柱体型颗粒处于平行和垂直位置时,相互排斥能的近似表达式。Brenner和McQuarrie(BM)对颗粒外的电位分布采     

On the behavior of the electrostatic colloidal interaction in the membrane filtration of latex suspensions

In order to investigate effects of the colloidal interaction in the membrane filtrations, the dead-end ultrafiltration of latex colloids was conducted with fully retentive membranes. Experimental results concerning the permeate flux during the filtration indicate that the void fraction of cake layer increased with the decrease of the ionic strength, due to the expanded Debye double layer thickness around the particles. The concentration dependence of the gradient diffusion coefficient of colloidal particles has been examined as a function of solution ionic strength. The NVT Monte Carlo simulation was applied on the bulk suspension so as to determine the thermodynamic coefficient, and the hydrodynamic coefficient was evaluated from the previously developed relation for an ordered system. The long-range electrostatic interactions between the particles are determined by using a singularity method, which provides accurate solutions to the linearized electrostatic field. The predictions on the variation of concentration polarization layer have been presented, from which we found that both the permeate flux and the particle diffusion are related to determine the concentration distribution above the cake layer.     

Predicting the phase diagram of two-dimensional colloidal systems with long-range interactions

The phase diagram of a two-dimensional model system for colloidal particles at the air-water interface was determined using Monte Carlo computer simulations in the isothermic-isobaric ensemble. The micrometer-range binary colloidal interaction has been modeled by hard disklike particles interacting via a secondary minimum followed by a weaker longer-range repulsive maximum, both of the order of kBT. The repulsive part of the potential drives the clustering of particles at low densities and low temperatures. Pinned voids are formed at higher densities and intermediate values of the surface pressure. The analysis of isotherms, translational and orientational correlation functions as well as structure factor gives clear evidence of the presence of a melting first-order transition. However, the melting process can be also followed by a metastable route through a hexatic phase at low surface pressures and low temperatures, before crystalization occurs at higher surface pressure.