Interacting nanoparticles with functional surface groups

Functionalized nanoparticles with ionizable groups have generated a large variety of structures with important potential applications in technology. The nature of their interactions is crucial to determining their solubility and to exploring assemblies with diverse symmetries. Here, we use a molecular theory to describe the interactions between two nanoparticles coated with short polymer chains that contain ionizable (functional) end‐groups immersed in aqueous salt solution. It is shown here that the fraction of ionized functional groups in the system depends on factors such as the ionic strength and pH of solution, grafting density of polymer chains, the chain length, as well as the separation distance between the nanoparticles. The interactions between two neighboring nanoparticles influence the charge regulation of the end‐groups, which consequently induces an asymmetric distribution of these charged end‐groups on the nanoparticles, and thus confers a preferred directionality in nanoparticle–nanoparticle interactions. We show that the charge regulating system is less repulsive than an equivalent system with a fixed charge distribution. This is due to a decrease in the charge density of the weak acid end‐groups, to avoid a local increase in counterion confinement (condensation) in the region between neighboring nanoparticles, when their separation decreases. The anisotropic degree of ionization found in our results can be used to design aggregates of nanoparticles with reduced symmetries. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Analytic density-functional self-consistent-field theory of diblock copolymers near patterned surfaces

Analytical solutions are derived for the density profiles and the free energies of compressible diblock copolymer melts (or incompressible copolymer solutions) near patterned surfaces. The density-functional self-consistent-field theory is employed along with a Gaussian chain model for bonding constraints and a random mixing approximation for nonbonded interactions. An analytical solution is rendered possible by expanding the chain distribution function around an inhomogeneous reference state with a nontrivial analytical solution, by retaining the linear terms, and by requiring consistency with the homopolymer limit. The density profiles are determined by both real and complex roots of a sixth-degree polynomial that may easily be obtained by solving a generalized eigenvalue problem. This analytical formulation enables one to efficiently explore the large nine-dimensional parameter space and can serve as a first approximation to computationally intensive studies with more detailed models. Illustrative computations are provided for uniform and patterned surfaces above the order-disorder transition. The results are consistent with the previous self-consistent-field calculations in that lamellar ordering appears near the surface above the order-disorder transition and the lamella order perpendicular or parallel to the surface depending on the commensurability between the periods of the surface pattern and the density oscillations.     

Structural behavior and self-assembly of Lennard-Jones clusters on rigid surfaces

The phase behavior and surface pattern formation for intermediate size Lennard-Jones clusters on rigid surfaces are examined. We use a parallel tempering Monte Carlo algorithm, in the canonical ensemble. Tempering is done over the temperature domain in most of the calculations. A two-dimensional temperature and Hamiltonian tempering algorithm is also implemented, to examine its usefulness in investigating this type of problem. In general, we observe gas phase systems as they undergo a condensation transition on the surface, followed by a freezing transition. The final solid state pattern formed by the cluster on the surface is the result of a number of competing effects. First, there is a competition between attraction within the cluster and that between cluster and surface atoms. Second, a monolayer of Lennard-Jones atoms tends to pack in a hexadic geometry. This geometry is frustrated on a surface with a different symmetry. The molecular organization of the substrate has a serious impact on the cluster packing. The surface morphology and the size mismatch between cluster and surface atoms, along with the relative interaction strengths, determine which of the effects prevail. When the surface atoms are small enough, the interactions within the cluster determine the symmetry of the pattern. In such a case, the substrate behaves similarly to a continuous surface, and the low-temperature pattern is a hexadic monolayer. When the sizes of the surface and cluster atoms are comparable, the low-temperature adsorbed geometry mimics the substrate symmetry. On a face-centered cubic surface, face-centered cubic monolayers or droplets are obtained.     

Prevention of protein adsorption by flexible and rigid chain molecules

The ability of tethered polymer layers to reduce the non-specific adsorption of proteins is studied using a molecular theory. The protein adsorption isotherms are calculated for flexible and rigid molecules as well as for mixtures. It is found, in agreement with earlier predictions, that flexible polymers are more effective in preventing protein adsorption. The interactions of the polymer with the surface are shown to be very important in determining the ability of the polymer layer to reduce the adsorption of proteins. Further, it is found that one can tune the adsorption of a certain protein conformation by changing the interactions between the surface and the polymer segments or the composition in the case of mixtures. It is found that the optimal layers to obtain large reduction of protein adsorption and availability of functional groups for binding are obtained by using mixtures of flexible and rod-like molecules. The role of the polymer-surface interactions is shown to be different for the kinetic control of protein adsorption as compared to thermodynamic control. The application of the findings as guidelines for the molecular design of biocompatible materials is discussed.     

Critical properties of thin films of polymer solutions

The critical properties of polymer solutions confined in thin‐film environments is studied with simple scaling arguments and a molecular theory. For purely repulsive surfaces, the critical volume fraction is a universal function of x = N^1/2/L, where N is the chain length and L is the film thickness. The critical volume fraction is nonmonotonic in x and shows a deep minimum at a film thickness several times larger than the chain's radius of gyration. This nonmonotonic behavior results from the interplay between the surface–polymer entropic repulsion and the tendency of the film to avoid large density gradients. The critical temperature is a monotonically increasing function of L, as L goes from the two‐dimensional limit to the three‐dimensional limit. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1849–1853, 2005     

Selective dispersion of single-walled carbon nanotubes in the presence of polymers: the role of molecular and colloidal length scales

Dimensionality is known to play a key role in the solution behavior of nano- and mesoparticles. In particular, the shape and the range of the attractive van der Waals interparticle potential are determined by the number of microscopic versus mesoscopic dimensions. For single-walled nanotubes (SWNTs), where two of the dimensions are nanoscopic and one is mesoscopic, the intertube attraction is relatively short ranged, albeit very steep. The very large attraction (compared to the thermal energy, K(b)T) among long SWNTs leads to aggregation at different levels and constitutes a major barrier for manipulation and utilization of SWNTs. This study demonstrates that it is possible to shape the intertube potential by decorating SWNTs with end-tethered polymers. In good solvent conditions for the polymers, entropic repulsion among the tethered chains generates a free energy barrier that prevents SWNTs from approaching the attractive part of the intertube potential. Consequentially, stable dispersions of individual, well separated SWNTs can be prepared. Investigation of different chain lengths and tethering densities of the polymers as well as the interparticle potentials for nanometric versus mesoscopic particles suggests that polymer-induced steric stabilization provides a generic method for separation of SWNTs from mixtures of colloidal species, as demonstrated experimentally.     

Phase behavior and charge regulation of weak polyelectrolyte grafted layers

The stability of weak polyelectrolytes end grafted to a planar surface has been studied with a molecular theory. The effective quality of the solvent is found to depend on the interplay between polymer grafting density, acid-base equilibrium, and salt concentration. Our results reveal that increasing salt concentration results in a thermodynamically more stable layer. This reverse salt effect is due to the competition between the solvent quality and the dual role of the ionic strength in screening the electrostatic interactions (reducing stability with increasing salt concentration), and regulating the charge on the polymer (increasing charge with increasing salt concentration). Grafted weak polyelectrolyte layers are found to be thermodynamically unstable at intermediate surface coverages. Additionally, it is established that the increased solubility of the layer at low surface coverage is due to the relatively large charge of the grafted polymers. The range of stability of the film with regard to polymer surface coverage, temperature, bulk pH and salt concentration is demonstrated.     

Drop-shape analysis of receptor-ligand binding at the oil/water interface

Drop-shape analysis was used to study the binding of streptavidin to biotin at the interface between water and a pendant chloroform droplet. Polyethylene oxide molecules were synthesized with a hydrophobic tail at one end of the molecule and a hydroxyl or biotin group at the other end. The interfacial tension of the water/chloroform interface was measured before and after addition of these amphiphiles to the chloroform phase and before and after addition of streptavidin to the aqueous phase. The hydroxyl-terminated amphiphiles eliminate nonspecific adsorption of the streptavidin to the interface, while streptavidin binds irreversibly to the biotin-terminated molecules. Molecular interactions within this bound layer were studied by measuring changes in the interfacial pressure as the layer is contracted and expanded by changing the volume of the chloroform droplet. A picture of the interfacial structure was obtained from quantitative comparisons between the experimental results and a molecular theory of protein binding to tethered ligands. These comparisons suggest that protein binding is controlled by the extension of the PEO tethers away from the interface.     

Stability of superparamagnetic iron oxide nanoparticles at different pH values: experimental and theoretical analysis

The detection of superparamagnetic nanoparticles using NMR logging has the potential to provide enhanced contrast in oil reservoir rock formations. The stability of the nanoparticles is critical because the NMR relaxivity (R(2) ≡ 1/T(2)) is dependent on the particle size. Here we use a molecular theory to predict and validate experimentally the stability of citric acid-coated/PEGylated iron oxide nanoparticles under different pH conditions (pH 5, 7, 9, 11). The predicted value for the critical surface coverage required to produce a steric barrier of 5k(B)T for PEGylated nanoparticles (MW 2000) was 0.078 nm(-2), which is less than the experimental value of 0.143 nm(-2), implying that the nanoparticles should be stable at all pH values. Dynamic light scattering (DLS) measurements showed that the effective diameter did not increase at pH 7 or 9 after 30 days but increased at pH 11. The shifts in NMR relaxivity (from R(2) data) at 2 MHz agreed well with the changes in hydrodynamic diameter obtained from DLS data, indicating that the aggregation behavior of the nanoparticles can be easily and quantitatively detected by NMR. The unexpected aggregation at pH 11 is due to the desorption of the surface coating (citric acid or PEG) from the nanoparticle surface not accounted for in the theory. This study shows that the stability of the nanoparticles can be predicted by the theory and detected by NMR quantitatively, which suggests the nanoparticles to be a possible oil-field nanosensor.     

Phase diagram of a ternary mixture of cholesterol and saturated and unsaturated lipids calculated from a microscopic model

We employ a molecular model to study a ternary mixture of saturated lipid, with tails of 16 carbons, a monounsaturated lipid with tails of 18 carbons, and cholesterol. The model, solved within mean-field theory, produces several forms of phase diagrams depending upon the relative strengths of interactions, but only one that shows the coexistence of two liquid phases observed in experiment. The lipids in the phase rich in cholesterol are more ordered than those in the other. The binary cholesterol, saturated lipid system also exhibits liquid, liquid coexistence.