Equilibrium polymerization in the Stockmayer fluid as a model of supermolecular self-organization

Collective motion and its connection to the energy landscape in 2D soft crystals

We examine the collective motion in computational models of a two-dimensional dusty plasma crystal and a charged colloidal suspension as they approach their respective melting transitions. To unambiguously identify rearrangement events in the crystal, we map the trajectory of configurations from an equilibrium molecular dynamics simulation to the corresponding sequence of configurations of local potential energy minima ("inherent structures"). This inherent structure (IS) trajectory eliminates the ambiguity that arises from localized vibrational motion. We find that the evolution of the IS trajectory in the crystal can be split into comparatively longer-lived ground states and shorter-lived discrete excited states. These discrete excited energy levels are a consequence of discrete numbers of defect clusters in the crystal. We find that the collective rearrangement occurs through different mechanisms: (i) small closed-loop motion in the ground states without the facilitation of defects, and (ii) much larger and complex open-ended particle motions in excited states that are facilitated by clusters of defects. In both cases, clusters of displacing particles can be separated into much smaller groups of replacing particles with a loop-like structure. In contrast to glass-forming liquids, the mass of the rearranging groups grows on heating towards the melting temperature rather than cooling. We find that crystal melting in these systems can be anticipated by the merging of the average time the crystal spends in the ground state with the average time in the excited states.

Understanding Relaxation in the Kob-Andersen Liquid Based on Entropy, String, Shoving, Localization, and Parabolic Models

We assess the validity of a range of models of glass formation based on molecular dynamics simulation results of the Kob-Andersen (KA) model system under a wide range of constant volume and constant pressure conditions. These models include the Adam-Gibbs model emphasizing configurational entropy, the string model emphasizing collective particle exchange motion, the shoving model emphasizing material elasticity, the localization model emphasizing dynamical free volume, and parabolic models based on the ideas of dynamic facilitation and, alternatively, the hypothesis that glass formation involves an avoided critical point. We demonstrate that these seemingly disparate models all provide a reasonable description of structural relaxation and diffusion data for the KA model system under all simulation conditions considered. Hence, the present study points to some unity in our understanding of the relationship between leading models of glass formation, supporting inferences drawn from previous studies of polymeric glass-forming liquids.

Theory of thermoreversible gelation and anomalous concentration fluctuations in polyzwitterion solutions

We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid-liquid, liquid-gel, and gel-gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors.

Phase separation of a magnetic fluid: Asymptotic states and nonequilibrium kinetics

We study self-assembly in a colloidal suspension of magnetic particles by performing comprehensive molecular dynamics simulations of the Stockmayer (SM) model, which comprises spherical particles decorated by a magnetic moment. The SM potential incorporates dipole-dipole interactions along with the usual Lennard-Jones interaction and exhibits a gas-liquid phase coexistence observed experimentally in magnetic fluids. When this system is quenched from the high-temperature homogeneous phase to the coexistence region, the nonequilibrium evolution to the condensed phase proceeds with the development of spatial as well as magnetic order. We observe density-dependent coarsening mechanisms-a diffusive growth law ℓ(t)∼t^{1/3} in the nucleation regime and hydrodynamics-driven inertial growth law ℓ(t)∼t^{2/3} in the spinodal regimes. [ℓ(t) is the average size of the condensate at time t after the quench.] While the spatial growth is governed by the expected conserved order parameter dynamics, the growth of magnetic order in the spinodal regime exhibits unexpected nonconserved dynamics. The asymptotic morphologies have density-dependent shapes which typically include the isotropic sphere and spherical bubble morphologies in the nucleation region, and the anisotropic cylinder, planar slab, cylindrical bubble morphologies in the spinodal region. The structures are robust and nonvolatile, and exhibit characteristic magnetic properties. For example, the oppositely magnetized hemispheres in the spherical morphology impart the characteristics of a Janus particle to it. The observed structures have versatile applications in catalysis, drug delivery systems, memory devices, and magnetic photonic crystals, to name a few.

Cation folding and the thermal stability limit of the ionic liquid [BMIM+][BF4 -] under total vacuum

Molecular dynamics simulations reveal the behavior of the bimodal distribution of cation conformations (folded/unfolded) in ionic liquids based on alkylated imidazoles, such as [BMIM+][BF4 -]. The alkyl chains of the cations can fold and block interactions between the cations and anions, thereby reducing the cohesivity of the liquid. At room temperature, the folded conformations represent less than one-third of the total conformations. In contrast to the behavior observed during the thermal denaturation of proteins, in ionic liquids, the concentration of folded cations grows when the temperature increases. At the equimolar concentration, the system reaches the reported experimental temperature of thermal stability (similar to the thermal denaturation behavior). There is an outermost layer of cations at the interface that can tilt toward the interface and cover a layer of anions adsorbed at the interface. This interfacial conformation makes the system stable in transverse directions and unstable in the normal direction at temperatures in the region of thermal instability, limiting the rate of vaporization of neutral ion pairs, which are observed as rare events at temperatures as low as 773.15 K.

Comparison of Huggins Coefficients and Osmotic Second Virial Coefficients of Buffered Solutions of Monoclonal Antibodies

The Huggins coefficient kH is a well-known metric for quantifying the increase in solution viscosity arising from intermolecular interactions in relatively dilute macromolecular solutions, and there has been much interest in this solution property in connection with developing improved antibody therapeutics. While numerous kH measurements have been reported for select monoclonal antibodies (mAbs) solutions, there has been limited study of kH in terms of the fundamental molecular interactions that determine this property. In this paper, we compare measurements of the osmotic second virial coefficient B22, a common metric of intermolecular and interparticle interaction strength, to measurements of kH for model antibody solutions. This comparison is motivated by the seminal work of Russel for hard sphere particles having a short-range "sticky" interparticle interaction, and we also compare our data with known results for uncharged flexible polymers having variable excluded volume interactions because proteins are polypeptide chains. Our observations indicate that neither the adhesive hard sphere model, a common colloidal model of globular proteins, nor the familiar uncharged flexible polymer model, an excellent model of intrinsically disordered proteins, describes the dependence of kH of these antibodies on B22. Clearly, an improved understanding of protein and ion solvation by water as well as dipole-dipole and charge-dipole effects is required to understand the significance of kH from the standpoint of fundamental protein-protein interactions. Despite shortcomings in our theoretical understanding of kH for antibody solutions, this quantity provides a useful practical measure of the strength of interprotein interactions at elevated protein concentrations that is of direct significance for the development of antibody formulations that minimize the solution viscosity.

Free energy calculations for rings and chains formed by dipolar hard spheres

We employ a method based on Monte Carlo grand-canonical simulations to precisely calculate partition functions of non-interacting chains and rings formed by dipolar hard spheres (DHS) at low temperature. The extended low temperature region offered by such cluster calculations, compared to what had been previously achieved with standard simulations, opens up the possibility of exploring a part of the DHS phase diagram which was inaccessible before. The reported results offer the unique opportunity of verifying well-established theoretical models based on the ideal gas of cluster approximation in order to clarify their range of validity. They also provide the basis for future studies in which cluster-cluster interactions will be included.

Supramolecular Self-assembly of a Model Hydrogelator: Characterization of Fiber Formation and Morphology

Hydrogels are of intense recent interest in connection with biomedical applications ranging from 3-D cell cultures and stem cell differentiation to regenerative medicine, controlled drug delivery and tissue engineering. This prototypical form of soft matter has many emerging material science applications outside the medical field. The physical processes underlying this type of solidification are incompletely understood and this limits design efforts aimed at optimizing these materials for applications. We address this general problem by applying multiple techniques (e.g., NMR, dynamic light scattering, small angle neutron scattering, rheological measurements) to the case of a peptide derivative hydrogelator (molecule 1, NapFFKYp) over a broad range of concentration and temperature to characterize both the formation of individual nanofibers and the fiber network. We believe that a better understanding of the hierarchical self-assembly process and control over the final morphology of this kind of material should have broad significance for biological and medicinal applications utilizing hydrogels.

Self-assembly of polymer-grafted nanoparticles in solvent-free conditions

Grafting of polymer chains onto the surface of spherical nanoparticles leads to a hybrid type of fluid that exhibits properties of both particle suspensions and melts of star polymers-these properties being controlled by the relative dimensions of the grafted polymer chains to the nanoparticle diameter, D, and the number of the number of chains grafted on the nanoparticle surface, f. While polymer-grafted nanoparticles (GNP) of this kind typically have a spherical average shape after grafting even a moderate number of chains, their instantaneous molecular shape can fluctuate significantly due to the deformation of the grafted chains. Both simulations and measurements have previously revealed that these "conformationally polarizable" particles can exhibit self-assembly into large scale polymeric structures in both solution and in polymer melts, and we simulate polymer-grafted nanoparticles with D and temperature (T) variations without a dispersing solvent to better understand the nature of this self-assembly process. We observe a reversible self-assembly into linear and branched dynamic GNP structures, where the extent of the assembly and geometry depend on D and T, and we constructed a map capturing the GNP structural behavior with D and T variations. Since the shape of the GNPs appeared to be correlated with the occurrence of the GNP self-assembly, we quantified the average shape and a measure of shape fluctuations to better understand how molecular shape influences their propensity to self-assemble into different structural forms. Based on this framework, we describe the clustering process of the GNPs as an equilibrium polymerization phenomenon and we calculate the order parameter governing the dynamic clustering behavior of GNPs, the average mass of the clusters, size distribution, and the apparent fractal dimension of the clusters.

Phase behavior of a binary fluid mixture of quadrupolar molecules

We propose a model molecule to investigate microscopic properties of a binary mixture with a closed-loop coexistence region. The molecule is comprised of a Lennard-Jones particle and a uniaxial quadrupole. Gibbs ensemble Monte Carlo simulations demonstrate that the high-density binary fluid of the molecules with the quadrupoles of the same magnitude but of the opposite signs can show closed-loop immiscibility. We find that an increase in the magnitude of the quadrupoles causes a shrinkage of the coexistence region. Molecular dynamics simulations also reveal that aggregates with two types of molecules arranged alternatively are formed in the stable one-phase region both above and below the coexistence region. String structures are dominant below the lower critical solution temperature, while branched aggregates are observed above the upper critical solution temperature. We conclude that the anisotropic interaction between the quadrupoles of the opposite signs plays a crucial role in controlling these properties of the phase behavior.

Self-organization of magnetic moments in dipolar chains with restricted degrees of freedom

Equilibrium behavior of a single chain of dipolar spheres is investigated by the method of molecular dynamics in a wide range of the dipolar coupling constant λ. Two cases are considered: rodlike and flexible chains. In the first case, particle centers are immovably fixed on one axis, but their magnetic moments retain absolute orientational freedom. It has been found that at λ≳1.5 particle moments are chiefly aligned parallel to the chain axis, but the total moment of the chain continuously changes its sign with some mean frequency, which exponentially decreases with the growth of λ. Such behavior of the rodlike chain is analogous to the Néel relaxation of a superparamagnetic particle with a finite energy of magnetic anisotropy. In the flexible chain particles are able to move in the three-dimensional space, but the distance between centers of the first-nearest neighbors never exceeds a given limiting value r(max). If r(max)≃d (d is the particle diameter) then the most probable shape of the chain of five or more particles at λ≳6 is that of a ring. The behavior of chains with r(max)≥2d is qualitatively different: At λ≃4 long chains collapse into dense quasispherical globules and at λ≳8 these globules take toroidal configuration with a spontaneous azimuthal ordering of magnetic dipoles. With the increase of r(max) to larger values (r(max)>10d) globules expand and break down to form separate rings.

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."

Cooperative polymerization of one-patch colloids

We numerically investigate cooperative polymerization in an off-lattice model based on a pairwise additive potential using particles with a single attractive patch that covers 30% of the colloid surface. Upon cooling, these particles self-assemble into small clusters which, below a density-dependent temperature, spontaneously reorganize into long straight tubes. We evaluate the partition functions of clusters of all sizes to provide an accurate description of the chemical reaction constants governing this process. Our calculations show that, for intermediate sizes, the partition functions retain contributions from two different structures, differing in both energy and entropy. We illustrate the microscopic mechanism behind the complex polymerization process in this system and provide a detailed evaluation of its thermodynamics.

Colloidal polymers from dipolar assembly of cobalt-tipped CdSe@CdS nanorods

The synthesis of a modular colloidal polymer system based on the dipolar assembly of CdSe@CdS nanorods functionalized with a single cobalt nanoparticle "tip" (CoNP-tip) is reported. These heterostructured nanorods spontaneously self-assembled via magnetic dipolar associations of the cobalt domains. In these assemblies, CdSe@CdS nanorods were carried as densely grafted side chain groups along the dipolar NP chain to form bottlebrush-type colloidal polymers. Nanorod side chains strongly affected the conformation of individual colloidal polymer bottlebrush chains and the morphology of thin films. Dipolar CoNP-tipped nanorods were then used as "colloidal monomers" to form mesoscopic assemblies reminiscent of traditional copolymers possessing segmented and statistical compositions. Investigation of the phase behavior of colloidal polymer blends revealed the formation of mesoscopic phase separated morphologies from segmented colloidal copolymers. These studies demonstrated the ability to control colloidal polymer composition and morphology in a manner observed for classical polymer systems by synthetic control of heterostructured nanorod structure and harnessing interparticle dipolar associations.

Molecular structure encodes nanoscale assemblies: understanding driving forces in electrostatic self-assembly

Supramolecular nanoparticles represent a key field in recent research as their synthesis through self-assembly is straightforward and they often can respond to external triggers. A fundamental understanding of structure-directing factors is highly desirable for a targeted structure design. This contribution demonstrates a quantitative relation between the size of supramolecular self-assembled nanoparticles and the free energy of association. Nanoparticles are prepared by electrostatic self-assembly of cationic polyelectrolyte dendrimers as model macroions and oppositely charged di- and trivalent organic dye molecules relying on the combination of electrostatic and π-π-interactions. A systematic set of sulfonate-group carrying azo-dyes was synthesized. Light scattering and ζ-potential measurements on the resulting nanoparticles yield hydrodynamic radii between 20 nm < R(H) < 50 nm and positive ζ-potential values indicating a positive particle charge. Studies on dye self-aggregation and dendrimer-dye association by isothermal titration calorimetry (ITC) and UV-vis spectroscopy allow for the correlation of the thermodynamic parameters of dendrimer-dye association with the size of the particles, showing that at least a free energy gain of ΔG ≈ - 32 kJ mol(-1) is necessary to induce dendrimer interconnection. Structural features of the azo dyes causing these to favor or prevent nanoparticle formation have been identified. The dye-dye-interaction was found to be the key factor in particle size control. A simple model yields a quantitative relation between the free energy and the particle sizes, allowing for predicting the latter based on thermodynamic measurements. Hence, a set of different molecular "building bricks" can be defined where the choice of building block determines the resulting assembly size.

NMR characterization of the formation kinetics and structure of di-O-benzylidene sorbitol gels self-assembled in organic solvents

The molecule 1,3:2,4-di-O-benzylidene sorbitol (DBS) is a common "gelator" that forms thermally reversible gels in diverse organic solvents. Solid-state (13)C and (1)H NMR techniques, along with electron microscopy, are utilized in an exploratory study of DBS in the gelled state where we consider both in situ and dried gels. The gels were formed in either acetone or benzene, with the former being a better solvent for DBS. We find the in situ or dried DBS gels to be composed of rigid twisted nanofibrils (∼15 to 21 nm in diameter). The fibrils show local molecular ordering, but not crystalline order, and they contain no trapped solvent. The molecular mobility at the fibril surface is modestly enhanced, and all the free hydroxyl groups of the sorbitol moiety are involved in strong hydrogen bonding. We also attempted to find a truly crystalline form of DBS whose structure, as judged by the similarity of (13)C spectra, is close to that of the fibrils. We partially succeeded in this quest, employing melt crystallization followed by slow cooling. However, this sample was a mixed crystal having small domains, where only one type of domain was structurally similar to the fibrils. We also investigated the long-time evolution of the in situ DBS gel network. Specifically, high-resolution NMR kinetic studies were performed over periods of days where the residual concentration of DBS in acetone solution was monitored during and after gel formation. The DBS concentration on these long timescales evolved slowly, and we introduce a simple mathematical model and equation to describe this phenomenon.

Clustering in polar media

Clustering prevails in water-soluble polymers and biological macromolecules. It has also been observed in polar solvent mixtures. The possible causes of clustering are discussed. A systematic investigation of clustering in poly(ethylene oxide)/d-water solutions has been undertaken using the small-angle neutron scattering method. The poly(ethylene oxide) monomer is formed of an oxygen atom and an ethylene group. Using the random phase approximation, partial Flory-Huggins interaction parameters for the three pairs (oxygen/d-water, ethylene/d-water, and oxygen/ethylene) are derived. Results show that the first two (oxygen/d-water and ethylene/d-water) are characterized by a lower critical solution temperature phase behavior (whereby phase separation occurs upon heating), while the third one (oxygen/ethylene) is characterized by an upper critical solution temperature phase diagram (whereby phase separation occurs upon cooling). It is argued that clustering is caused by the increasing repulsive interaction between oxygen and ethylene for decreasing temperature and increasing polymer volume fraction. This leads to increasing attractive interactions between ethylene groups that stick together.

Emulsion polymerization routes to chemically anisotropic particles

Methods are presented to synthesize suspensions of chemically and shape anisotropic colloids on submicrometer length scales. Particles are synthesized through seeded emulsion polymerization where a weakly cross-linked seed is swollen with monomer that phase separates at the reaction temperature resulting in a protrusion. The final particles can be considered to be composed of interpenetrating spheres. pH-sensitive anisotropy is created through the use of different surface coatings on each of the interpenetrating spheres. Dark-field imaging, dynamic light scattering, and scanning electron microscopy are used to characterize the particles.

Theoretical issues relating to thermally reversible gelation by supermolecular fiber formation

Existing models of the thermodynamics and dynamics of self-assembly are summarized to provide a context for discussing the difficulties that arise in modeling supermolecular fiber assembly and the formation of thermally reversible gels through fiber growth and branching. Challenging problems in this field, such as the physical origin of fibers of uniform diameter and fiber twisting, the kinetics of fiber growth, the hierarchical bundling of fibers into "superfibers", fiber branching, gelation through fiber impingement and the associated phenomenon of fractal fiber network and spherulite formation, and the origin and control of structural polymorphism in the fiber and superfiber geometry, are discussed from a personal perspective. Suggestions are made for integrating current research efforts into a more coherent multiscale description of fiber formation and gelation on molecular, mesoscopic, and macroscopic scales.

Metastability and sol phases: two keys for the future of molecular gels?

The future of molecular gels may rely on a deeper theoretical understanding of the gel-to-solid phase-separation process that usually limits the lifetime of molecular gels. Stable sol phases, when available, can be the appropriate vectors to transfer the 1D self-assembled and functional morphologies to solid substrates that may be used for technological devices.

Criticality of colloids with distinct interaction patches: the limits of linear chains, hyperbranched polymers, and dimers

We use a simple model of associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the bonding interactions between each pair of spots have strengths epsilon(AA), epsilon(BB), and epsilon(AB). The theory is applied over the whole range of bonding strengths and the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains (epsilon(AA) not equal to 0, epsilon(AB)=epsilon(BB)=0) , hyperbranched polymers (epsilon(AB) not equal to 0, epsilon(AA)=epsilon(B)=0) , and dimers (epsilon(BB) not equal to 0, epsilon(AA)=epsilon(AB)=0) . These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains (AA clusters connected by a few AB or BB bonds); of hyperbranched polymers (AB clusters connected by AA bonds); or of dimers (BB clusters connected by AA bonds). Interestingly, there is no critical point when in(AA) vanishes despite the fact that AA bonds alone cannot drive condensation.

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.

Direct Observation of Early-Time Hydrogelation in beta-Hairpin Peptide Self-Assembly

Triggered hydrogelation of MAX1 peptide, (VK)(4)-V(D)PPT-(KV)(4)-NH(2), proceeds through peptide intramolecular folding into beta-hairpins and concomitant self-assembly into branched clusters of well-defined (uniform, 3 nm cross section), semiflexible, beta-sheet-rich nanofibrils. Cryogenic transmission electron microscopy indicates that dangling fibrils extend from one growing cluster to another and lead to early, intercluster communication in solution. At the apparent percolation threshold, the dynamic shear modulus measured by oscillatory rheology (G'(omega), G''(omega) proportional, variant omega(n)) and the field-intensity autocorrelation function measured by dynamic light scattering (g(1)(tau) proportional, variant tau(-beta')) show power-law behavior with comparable critical dynamic exponents (n approximately 0.47 and beta' approximately 0.45). Finite interpenetration of percolating clusters with smaller clusters, along with permanent intercluster entanglements, increase the network rigidity. The self-assembly of MAX1 peptide was compared and contrasted with the assembly of other biopolymeric networks in literature.

Supramolecular self-organization in PEO-modified C60 fullerene/water solutions: influence of polymer molecular weight and nanoparticle concentration

Utilizing a first-principles-based coarse-grained implicit solvent model, we have investigated the self-association of C(60) fullerenes that have been symmetrically modified with six grafted poly(ethylene oxide) (PEO) chains in aqueous solution. Despite the highly symmetric nature of the pair interactions between PEO-grafted fullerenes, their supramolecular assemblies are highly anisotropic and resemble the linear clusters formed in Stockmayer fluids. The dipole-like interaction between these symmetrically modified fullerenes results from the shielding of the C(60) fullerenes by PEO, favoring the addition of more PEO-grafted fullerenes to the linear clusters at the relatively unprotected ends. At low nanoparticle concentrations, self-association is dominated by the formation of stable dimers and trimers resulting from fullerene-fullerene contact and favorable PEO-fullerene interactions. With increasing nanoparticle concentration, larger clusters become increasingly probable. The molecular weight of the PEO tethers can be treated as a temperature-like analogue, with a reduction in average cluster size with increasing chain length due to increased steric repulsion, which is qualitatively similar to effects observed in Stockmayer fluids with increasing temperature. The role of PEO in supramolecular self-organization in PEO-modified C(60) fullerene/water solutions is complex, contributing not only to steric stabilization but also to favorable energetic interactions, nanoparticle shielding, and depletion-driven aggregation.

Phase behavior of the Stockmayer fluid via molecular dynamics simulation

The gas-isotropic liquid-nematic liquid phase behavior of the Stockmayer fluid is studied using molecular dynamics simulation together with a mean field lattice model. We obtain coexistence curves of the Stockmayer fluid over a wide range of dipole strengths, temperatures, and densities, including the transition from the isotropic liquid to the ferroelectric liquid. In our simulations we do not observe the disappearance of the isotropic gas-isotropic liquid coexistence at high dipole strength contrary to earlier findings based on Monte Carlo techniques. Even though the formation of reversible dipole chains strongly affects the location of the critical point, it does not lead to its disappearance. These results are supported by a mean field lattice model which yields good qualitative, and in parts quantitative, agreement with our simulations. In addition, we also investigate the gas-isotropic liquid phase behavior for different polarizabilities.