Model for reversible nanoparticle assembly in a polymer matrix

Nanoparticle Assembly as a Materials Development Tool

Nanoparticle assembly is a complex and versatile method of generating new materials, capable of using thousands of different combinations of particle size, shape, composition, and ligand chemistry to generate a library of unique structures. Here, a history of particle self-assembly as a strategy for materials discovery is presented, focusing on key advances in both synthesis and measurement of emergent properties to describe the current state of the field. Several key challenges for further advancement of nanoparticle assembly are also outlined, establishing a roadmap of critical research areas to enable the next generation of nanoparticle-based materials synthesis.

Perspective: Outstanding theoretical questions in polymer-nanoparticle hybrids

This topical review discusses the theoretical progress made in the field of polymer nanocomposites, i.e., hybrid materials created by mixing (typically inorganic) nanoparticles (NPs) with organic polymers. It primarily focuses on the outstanding issues in this field and is structured around five separate topics: (i) the synthesis of functionalized nanoparticles; (ii) their phase behavior when mixed with a homopolymer matrix and their assembly into well-defined superstructures; (iii) the role of processing on the structures realized by these hybrid materials and the role of the mobilities of the different constituents; (iv) the role of external fields (electric, magnetic) in the active assembly of the NPs; and (v) the engineering properties that result and the factors that control them. While the most is known about topic (ii), we believe that significant progress needs to be made in the other four topics before the practical promise offered by these materials can be realized. This review delineates the most pressing issues on these topics and poses specific questions that we believe need to be addressed in the immediate future.

How the flow affects the phase behaviour and microstructure of polymer nanocomposites

We address the issue of flow effects on the phase behaviour of polymer nanocomposite melts by making use of a recently reported Hamiltonian set of evolution equations developed on principles of non-equilibrium thermodynamics. To this end, we calculate the spinodal curve, by computing values for the nanoparticle radius as a function of the polymer radius-of-gyration for which the second derivative of the generalized free energy of the system becomes zero. Under equilibrium conditions, we recover the phase diagram predicted by Mackay et al. [Science 311, 1740 (2006)]. Under non-equilibrium conditions, we account for the extra terms in the free energy due to changes in the conformations of polymer chains by the shear flow. Overall, our model predicts that flow enhances miscibility, since the corresponding miscibility window opens up for non-zero shear rate values.

String model for the dynamics of glass-forming liquids

We test the applicability of a living polymerization theory to describe cooperative string-like particle rearrangement clusters (strings) observed in simulations of a coarse-grained polymer melt. The theory quantitatively describes the interrelation between the average string length L, configurational entropy Sconf, and the order parameter for string assembly Φ without free parameters. Combining this theory with the Adam-Gibbs model allows us to predict the relaxation time τ in a lower temperature T range than accessible by current simulations. In particular, the combined theories suggest a return to Arrhenius behavior near Tg and a low T residual entropy, thus avoiding a Kauzmann "entropy crisis."

Hierarchical self-assembly: Self-organized nanostructures in a nematically ordered matrix of self-assembled polymeric chains

We report many different nanostructures which are formed when model nanoparticles of different sizes (diameter σn) are allowed to aggregate in a background matrix of semiflexible self-assembled polymeric wormlike micellar chains. The different nanostructures are formed by the dynamical arrest of phase-separating mixtures of micellar monomers and nanoparticles. The different morphologies obtained are the result of an interplay of the available free volume, the elastic energy of deformation of polymers, the density (chemical potential) of the nanoparticles in the polymer matrix, and, of course, the ratio of the size of self-assembling nanoparticles and self-avoidance diameter of polymeric chains. We have used a hybrid semi-grand-canonical Monte Carlo simulation scheme to obtain the (nonequilibrium) phase diagram of the self-assembled nanostructures. We observe rodlike structures of nanoparticles which get self-assembled in the gaps between the nematically ordered chains, as well as percolating gel-like network of conjoined nanotubes. We also find a totally unexpected interlocked crystalline phase of nanoparticles and monomers, in which each crystal plane of nanoparticles is separated by planes of perfectly organized polymer chains. We identified the condition which leads to such interlocked crystal structure. We suggest experimental possibilities of how the results presented in this paper could be used to obtain different nanostructures in the laboratory.

Photoluminescence Studies in II-VI Nanoparticles Embedded in Polymer Matrix

Recently, organic-inorganic hybrid nanocomposite materials have been of great interest for their extraordinary performances due to the combination of the advantageous properties of polymers and the size dependent properties of nanocrystals (NCs). Interaction between the polymer matrix and nanocrystalline fillers produces wonderful features, viz. thermal, magnetic, mechanical, electrical and optical properties to these materials. Modern applications require a new design of responsive functional coatings which is capable of changing their properties in a controlled way. However, the synthesis of II-VI nanoparticles into the polymer matrix of its nanocomposites with adjustable sizes and protected from photo-oxidation is a big challenge to the scientific community. It is difficult to synthesize the highly enhanced luminescence in polymers and its semiconductor nanocomposite systems. Luminescence from the polymer embedded II-VI nanoparticles is greatly enhanced and better stability can be achieved from the composite compared to bulk materials. The formation of nanocomposites can be confirmed by photoluminescence (PL) spectroscopy. It is an important technique for determining the optical gap, purity, crystalline quality defects and analysis of the quantum confinement in these nanocomposite materials. In this paper, we have reviewed the present status of II-VI polymer nanocomposites from the photoluminescence studies point of view. We have also shown the results of the PL of these nanocomposite materials and the results will be compared with the reported literature by other groups.Contents of Paper

Nanoparticle self-assembly assisted by polymers: the role of shear stress in the nanoparticle arrangement of Langmuir and Langmuir-Blodgett films

We propose to use the self-assembly ability of a block copolymer combined with compression-expansion cycles to obtain CdSe quantum dots (QDs) structures of different morphology. The methodology proposed consists in transferring onto mica mixed Langmuir monolayers of QDs and the polymer poly(styrene-co-maleic anhydride) partial 2-butoxyethyl ester cumene terminated, PS-MA-BEE, previously sheared by 50 compression-expansion cycles. Results indicate that the shear stress takes out nanoparticles at the air-water interface from metastable states and promotes a new equilibrium state of the Langmuir monolayer. This new state was transferred onto mica by the Langmuir-Blodgett (LB) methodology, and the morphology of the LB films was analyzed by atomic force microscopy and transmission electron microscopy measurements. Our results show that when the amplitude strain increases, the QDs domain size decreases and the QDs LB film arrangement becomes more ordered. The dynamics of the monolayer relaxation after cycling involves at least three time scales which are related to the damping of surface fluctuation, raft rearrangement, and component movements inside each raft. Brewster angle microscopy allowed visualizing in situ the raft rearrangement at the air-water interface.

Anisotropic aggregation in a simple model of isotropically polymer-coated nanoparticles

We report a numerical study of a simple, modified Asakura-Oosawa model for nanoparticles that are isotropically grafted with polymer chains. We perform canonical and grand-canonical Monte Carlo simulations to establish a qualitative morphology diagram, as well as quantitative phase diagrams. The morphology diagram qualitatively reproduces experimental observations and theoretical approaches employing more complex models. In addition, we establish the transition lines for a microphase separation and show that the phase behavior saturates for larger polymer sizes. An analytical treatment on the level of the second virial coefficient indicates that this saturation effect is caused by less effective shielding of nanoparticles by longer polymers. Our simple model enables large-scale particle-based simulations of self-assembly of polymer-coated particles.

A general method for spatially coarse-graining Metropolis Monte Carlo simulations onto a lattice

A recently introduced method for coarse-graining standard continuous Metropolis Monte Carlo simulations of atomic or molecular fluids onto a rigid lattice of variable scale [X. Liu, W. D. Seider, and T. Sinno, Phys. Rev. E 86, 026708 (2012)] is further analyzed and extended. The coarse-grained Metropolis Monte Carlo technique is demonstrated to be highly consistent with the underlying full-resolution problem using a series of detailed comparisons, including vapor-liquid equilibrium phase envelopes and spatial density distributions for the Lennard-Jones argon and simple point charge water models. In addition, the principal computational bottleneck associated with computing a coarse-grained interaction function for evolving particle positions on the discretized domain is addressed by the introduction of new closure approximations. In particular, it is shown that the coarse-grained potential, which is generally a function of temperature and coarse-graining level, can be computed at multiple temperatures and scales using a single set of free energy calculations. The computational performance of the method relative to standard Monte Carlo simulation is also discussed.

Nanocomposites: structure, phase behavior, and properties

It is well recognized that nanocomposites formed by adding nanoparticles to polymers can have significantly enhanced properties relative to the native polymer. This review focuses on three aspects that are central to the outstanding problem of realizing these promised property improvements. First, we ask if there exist general strategies to control nanoparticle spatial distribution. This is an important question because it is commonly accepted that the nanoparticle dispersion state crucially affects property improvements. Because ideas on macroscale composites suggest that optimizing different properties requires different dispersion states, we next ask if we can predict a priori the particle dispersion and organization state that can optimize one (or more) properties of the resulting nanocomposite. Finally, we examine the role that particle shape plays in affecting dispersion and hence property control. This review focuses on recent advances concerning these underpinning points and how they affect measurable properties relevant to engineering applications.

Atomic force microscopy nanomanipulation of shape persistent, spherical, self-assembled aggregates of gold nanoparticles

Gold (Au) nanoparticles have been synthesized that are stabilized by an organic ligand bearing a dithiolane functional group for binding to Au, an oligo(p-phenylene vinylene) (OPV) chromophoric group to drive self-assembly via π-π interactions, and a hydroxy functionality for interparticle hydrogen bonding. The OPV-Au particles reversibly self-assemble in n-heptane solution, forming shape persistent, spherical, nanometer-sized aggregates that do not collapse on a substrate. Optical absorption and transmission electron microscopy tomography studies show that the size and shape persistency can be tuned by modification of the ligands, adjustment of the core size, and variation of the concentration. The spherical assemblies can be manipulated with the tip of an atomic force microscope: an aggregate can be pushed over the surface for at least 20 times with nanometer precision and without substantial loss of material.

Nanoparticle Network Formation in Nanostructured and Disordered Block Copolymer Matrices

Incorporation of nanoparticles composed of surface-functionalized fumed silica (FS) or native colloidal silica (CS) into a nanostructured block copolymer yields hybrid nanocomposites whose mechanical properties can be tuned by nanoparticle concentration and surface chemistry. In this work, dynamic rheology is used to probe the frequency and thermal responses of nanocomposites composed of a symmetric poly(styrene-b-methyl methacrylate) (SM) diblock copolymer and varying in nanoparticle concentration and surface functionality. At sufficiently high loading levels, FS nanoparticle aggregates establish a load-bearing colloidal network within the copolymer matrix. Transmission electron microscopy images reveal the morphological characteristics of the nanocomposites under these conditions.

Dispersing nanoparticles in a polymer matrix: are long, dense polymer tethers really necessary?

Dispersing nanoparticles in a polymer matrix is intrinsically challenging because of unfavorable entropic interactions between the matrix and the nanoparticle. Similar to suspensions of larger colloidal particles, it has been found that thermodynamically stable dispersions of nanoparticles can be achieved in polymer matrices when the nanoparticles are decorated with dense layers of polymer tethers whose molecular weight is comparable to or greater than that of the matrix. Utilizing molecular dynamics simulations, we demonstrate that, in contrast to larger colloidal particles, repulsive interactions between nanoparticles can be achieved with tethered polymers much shorter than the polymer matrix when relatively sparse grafting is employed.

Lattice model of equilibrium polymerization. VII. Understanding the role of "cooperativity" in self-assembly

Cooperativity is an emergent many-body phenomenon related to the degree to which elementary entities (particles, molecules, organisms) collectively interact to form larger scale structures. From the standpoint of a formal mean field description of chemical reactions, the cooperativity index m, describing the number of elements involved in this structural self-organization, is the order of the reaction. Thus, m for molecular self-assembly is the number of molecules in the final organized structure, e.g., spherical micelles. Although cooperativity is crucial for regulating the thermodynamics and dynamics of self-assembly, there is a limited understanding of this aspect of self-assembly. We analyze the cooperativity by calculating essential thermodynamic properties of the classical mth order reaction model of self-assembly (FAm model), including universal scaling functions describing the temperature and concentration dependence of the order parameter and average cluster size. The competition between self-assembly and phase separation is also described. We demonstrate that a sequential model of thermally activated equilibrium polymerization can quantitatively be related to the FAm model. Our analysis indicates that the essential requirement for "cooperative" self-assembly is the introduction of constraints (often nonlocal) acting on the individual assembly events to regulate the thermodynamic free energy landscape and, thus, the thermodynamic sharpness of the assembly transition. An effective value of m is defined for general self-assembly transitions, and we find a general tendency for self-assembly to become a true phase transition as m-->infinity. Finally, various quantitative measures of self-assembly cooperativity are discussed in order to identify experimental signatures of cooperativity in self-assembling systems and to provide a reliable metric for the degree of transition cooperativity.

Third-order thermodynamic perturbation theory for effective potentials that model complex fluids

We have performed Monte Carlo simulations to obtain the thermodynamic properties of fluids with two kinds of hard-core plus attractive-tail or oscillatory potentials. One of them is the square-well potential with small well width. The other is a model potential with oscillatory and decaying tail. Both model potentials are suitable for modeling the effective potential arising in complex fluids and fluid mixtures with extremely-large-size asymmetry, as is the case of the solvent-induced depletion interactions in colloidal dispersions. For the former potential, the compressibility factor, the excess energy, the constant-volume excess heat capacity, and the chemical potential have been obtained. For the second model potential only the first two of these quantities have been obtained. The simulations cover the whole density range for the fluid phase and several temperatures. These simulation data have been used to test the performance of a third-order thermodynamic perturbation theory (TPT) recently developed by one of us [S. Zhou, Phys. Rev. E 74, 031119 (2006)] as compared with the well-known second-order TPT based on the macroscopic compressibility approximation due to Barker and Henderson. It is found that the first of these theories provides much better accuracy than the second one for all thermodynamic properties analyzed for the two effective potential models.

Nanoparticle-regulated phase behavior of ordered block copolymers

Although block copolymer motifs have received considerable attention as supramolecular templates for inorganic nanoparticles, experimental observations of a nanostructured diblock copolymer containing inorganic nanoparticles-supported by theoretical trends predicted from a hybrid self-consistent field/density functional theory-confirm that nanoparticle size and selectivity can likewise stabilize the copolymer nanostructure by increasing its order-disorder transition temperature.