Simulation studies of self-assembly of end-tethered nanorods in solution and role of rod aspect ratio and tether length

We present temperature versus concentration phase diagrams for "shape amphiphiles" comprised of tethered moderate and low aspect ratio rods. Simulations of moderate aspect ratio rods (first reported by Horsch et al. [Phys. Rev. Lett. 95, 056105 (2005)]) predict their self-assembly into spherical micelles with bcc order, long micelles with nematic order, a racemic mixture of hexagonally ordered chiral cylinders, two perforated phases: one with tetragonal order and one with hexagonal order, and a smectic C lamellar phase. In contrast, we predict here that small aspect ratio tethered rods self-assemble into bcc ordered spherical micelles, hexagonally ordered cylinders, and a smectic C lamellar phase. We compare and contrast the phases obtained for the two aspect ratios and examine in further detail several unusual phases. Our simulations also reveal that for moderate aspect ratio rods there is a tendency toward phases with decreasing interfacial curvature with decreasing coil size, including a double gyroid phase. In addition, we investigate the role of tether length on the assembled structures. Our results are applicable to short rod-coil block copolymers and rodlike nanoparticles with polymer tethers, and to colloidal building blocks comprised of a flexible string of colloids tethered to a rigid string of colloids, with the interactions scaled appropriately.     

Ivar Waller 90 years on June 11, 1988

Linkage properties of the diagrammatic representation of the energies obtained in the multireference many-body perturbation calculations with respect to the incompleteness or completeness of the model space are discussed. The case of not completely degenerate model space is considered for which a comparison with the standard single-reference many-body perturbation expansion is possible. The Hose–Kaldor type of graphical representation of the perturbation expansion for the effective Hamiltonian is used in this comparison. It is shown that for an incomplete model space the perturbation expansion is not size-extensive. In this case, for a truncated expansion of the effective Hamiltonian, the energies obtained by diagonalization of the effective Hamiltonian matrix are represented by both linked and unlinked irreducible contributions. The unlinked ones do not appear when the complete model space is used.     

用重整化群理论研究胶体模型体系的相行为

用yukawa势能函数表达胶体颗粒之间的吸引作用。用Duh-Mier-Y-Teran状态方 程表达液相Helmholtz自由能。用一阶微扰理论、固体硬球径向分布函数解析式和 改进的胞腔模型建立固相状态方程，结合建立的状态方程和重整化群理论。研究了 胶体模型体系的液-液相平衡和液-固相平衡。研究表明，颗粒之间色散作用量程参 数的变化对胶休到本世纪末茶杯 系的相行为有特殊需要影响。所得结果与分子模 拟数据吻合良好。     

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.     

Improved perturbative treatment of electronic energies from a minimal-norm approach to many-body perturbation theory

We propose a zeroth-order Hamiltonian for many-body perturbation theory based on the unitary decomposition of the two-particle reduced Hamiltonian. For the zeroth-order Hamiltonian constrained to be diagonal in the Hartree-Fock basis set, the two-particle reduced perturbation matrix is chosen to have a minimal Frobenius norm. When compared with the M?ller-Plesset partitioning, the method yields more accurate second-order energies.     

Density-functional study of interfacial properties of colloid-polymer mixtures

Interfacial properties of colloid-polymer mixtures are examined within an effective one-component representation, where the polymer degrees of freedom are traced out, leaving a fluid of colloidal particles interacting via polymer-induced depletion forces. Restriction is made to zero-, one-, and two-body effective potentials, and a free energy functional is used that treats colloid excluded volume correlations within Rosenfeld's fundamental measure theory, and depletion-induced attraction within first-order perturbation theory. This functional allows a consistent treatment of both ideal and interacting polymers. The theory is applied to surface properties near a hard wall, to the depletion interaction between two walls, and to the fluid-fluid interface of demixed colloid-polymer mixtures. The results of the present theory compare well with predictions of a fully two-component representation of mixtures of colloids and ideal polymers (the Asakura-Oosawa model) and allow a systematic investigation of the effects of polymer-polymer interactions on interfacial properties. In particular, the wall surface tension is found to be significantly larger for interacting than for ideal polymers, whereas the opposite trend is predicted for the fluid-fluid interfacial tension.     

On multireference superdirect configuration interaction in third order

The superdirect configuration interaction (Sup-CI ) method has the usual versatility and stability of the CI methods with computational efficiency typical to that of the many-body methods, such as the many-body perturbation theory (MBPT ). The Hamilton operator is projected into a space of a few trial vectors, such as Krylov, Nesbet, or Møller–Plesset correction vectors. In this space, Hamiltonian matrix elements may be directly computed in the many-body fashion, as weighted sums of integral products over orbital indices. The variation-perturbation method based on the first-order wave function is equivalent to the Sup-CI method with a single correction vector of the Møller–Plesset type. Different points of view on the superdirect CI method are discussed and a version in which third-order contributions are computed for a relatively small (10–100) space of reference and correction vectors is tested. Selection of the best “effective first-order spaces” and size-extensivity corrections in Sup-CI are briefly discussed. Møoller–Plesset, Epstein–Nesbet, and other correction vectors are included in the model calculations on the symmetric stretch of bonds in water, acetylene, and the NH₂ molecule. Errors are almost independent of molecular geometry and the method appears to be superior than the multireference second-order perturbation methods. © 1994 John Wiley & Sons, Inc.     

Measurement of density distributions for colloidal beta-FeOOH rods in suspensions exhibiting phase separation: the role of long-range forces in smectic ordering

We prepared monodisperse colloidal beta-FeOOH rods with length-to-width ratios L/W of 3.6-7.0 (L=210-330 nm and W=40-58 nm). Density gradients of the rods occurred in the suspensions by gravity, inducing a phase separation. The denser phase showed smectic (Sm) liquid crystalline structures exhibiting iridescent colors in a wide range of pH from 1.2 (at which the rods interact attractively) to 4.7 (repulsively). The lower density phase was disordered, but frequently emitted diffuse colors locally (at pH>2.6), implying the occurrence of short-range order. The nematic phase was not observed in the beta-FeOOH systems, being consistent with theoretical predictions. The particle density distributions were measured over the whole region of the suspensions (separated into two phases) at various pH values using a rapid freezing method. A phase diagram was determined thereby, where the critical (minimal) packing fraction of the particles for the Sm phase showed a nonlinear decrease from 0.43 to 0.12 with increasing pH. Rod-rod spacings in the Sm phase estimated experimentally at various pH were well explained using Derjaguin-Landau-Verwey-Overbeek (DLVO) type pair potentials. It is suggested that Sm ordering can be induced by attractive minima at pH<2.2, while driven by soft repulsions at pH>2.6. The former Sm ordering is expected to be the condensation-type phase transition and the latter the disorder-order transition.     

Thermodynamic stability of fluid-fluid phase separation in binary athermal mixtures: the role of nonadditivity

We studied the thermodynamic stability of fluid-fluid phase separation in binary nonadditive mixtures of hard-spheres for moderate size ratios. We are interested in elucidating the role played by small amounts of nonadditivity in determining the stability of fluid-fluid phase separation with respect to the fluid-solid phase transition. The demixing curves are built in the framework of the modified-hypernetted chain and of the Rogers-Young integral equation theories through the calculation of the Gibbs free energy. We also evaluated fluid-fluid phase equilibria within a first-order thermodynamic perturbation theory applied to an effective one-component potential obtained by integrating out the degrees of freedom of the small spheres. A qualitative agreement emerges between the two different approaches. We also addressed the determination of the freezing line by applying the first-order thermodynamic perturbation theory to the effective interaction between large spheres. Our results suggest that for intermediate size ratios a modest amount of nonadditivity, smaller than earlier thought, can be sufficient to drive the fluid-fluid critical point into the thermodinamically stable region of the phase diagram. These findings could be significant for rare-gas mixtures in extreme pressure and temperature conditions, where nonadditivity is expected to be rather small.     

Polymer-induced phase separation and crystallization in immunoglobulin G solutions

We study the effects of the size of polymer additives and ionic strength on the phase behavior of a nonglobular protein-immunoglobulin G (IgG)-by using a simple four-site model to mimic the shape of IgG. The interaction potential between the protein molecules consists of a Derjaguin-Landau-Verwey-Overbeek-type colloidal potential and an Asakura-Oosawa depletion potential arising from the addition of polymer. Liquid-liquid equilibria and fluid-solid equilibria are calculated by using the Gibbs ensemble Monte Carlo technique and the Gibbs-Duhem integration (GDI) method, respectively. Absolute Helmholtz energy is also calculated to get an initial coexisting point as required by GDI. The results reveal a nonmonotonic dependence of the critical polymer concentration rho(PEG) (*) (i.e., the minimum polymer concentration needed to induce liquid-liquid phase separation) on the polymer-to-protein size ratio q (equivalently, the range of the polymer-induced depletion interaction potential). We have developed a simple equation for estimating the minimum amount of polymer needed to induce the liquid-liquid phase separation and show that rho(PEG) (*) approximately [q(1+q)(3)]. The results also show that the liquid-liquid phase separation is metastable for low-molecular weight polymers (q=0.2) but stable at large molecular weights (q=1.0), thereby indicating that small sizes of polymer are required for protein crystallization. The simulation results provide practical guidelines for the selection of polymer size and ionic strength for protein phase separation and crystallization.     

Phase Transitions of the Liquid–Liquid Type and a Change in the Particle Charge in Colloidal Solutions

The thermodynamic properties are studied for the solutions of charged colloidal particles with ionizable surface groups. The microscopic mechanism of microion binding at surface groups is considered. The free energy of the system in the parameter range where the usual theory of such solutions is inadequate (a range of practical interest) is calculated using the method of the thermodynamic perturbation theory. The first-order phase transition of the liquid–liquid type is shown to be possible; in this phase transition, a phase with a high concentration of colloidal particles that have a higher charge coexists with a phase with a lower concentration of particles that have a lower charge.     

Potential energy surfaces and dynamics of Ni2+ ion aqueous solution: molecular dynamics simulation of the electronic absorption spectrum

We develop a model effective Hamiltonian for describing the electronic structures of first-row transition metals in aqueous solutions using a quasidegenerate perturbation theory. All the states consisting of 3d(n) electronic configurations are determined by diagonalizing a small effective Hamiltonian matrix, where various intermolecular interaction terms such as the electrostatic, polarization, exchange, charge transfer, and three-body interactions are effectively incorporated. This model Hamiltonian is applied to constructing the ground and triplet excited states potential energy functions of Ni(2+) in aqueous solution, based on the ab initio multiconfiguration quasidegenerate perturbation theory calculations. We perform molecular dynamics simulation calculations for the ground state of Ni(2+) aqueous solution to calculate the electronic absorption spectral shape as well as the ground state properties. Agreement between the simulation and experimental spectra is satisfactory, indicating that the present model can well describe the Ni(2+) excited state potential surfaces in aqueous solution.     

Depletion interaction mediated by polydisperse rods

The interaction between a colloidal hard sphere of radius R and a wall or between two spheres in a dilute suspension of infinitely thin rods of length L is calculated numerically. The method allows the study of depletion potentials for any value of LR and, consequently, the influence of rod length polydispersity can be investigated. It was observed that both the depth and the range of the potential increase drastically if the relative standard deviation sigma of the length distribution is larger than 0.25, while the potential is virtually indistinguishable from that caused by monodisperse rods, if sigma < or similar to 0.1.     

Effect of polydispersity and soft interactions on the nematic versus smectic phase stability in platelet suspensions

We theoretically discuss, using density-functional theory, the phase stability of nematic and smectic ordering in a suspension of platelets of the same thickness but with a high polydispersity in diameter, and study the influence of polydispersity on this stability. The platelets are assumed to interact like hard objects, but additional soft attractive and repulsive interactions, meant to represent the effect of depletion interactions due to the addition of nonabsorbing polymer, or of screened Coulomb interactions between charged platelets in an aqueous solvent, respectively, are also considered. The aspect (diameter-to-thickness) ratio is taken to be very high, in order to model solutions of mineral platelets recently explored experimentally. In this regime a high degree of orientational ordering occurs; therefore, the model platelets can be taken as completely parallel and are amenable to analysis via a fundamental-measure theory. Our focus is on the nematic versus smectic phase interplay, since a high degree of polydispersity in diameter suppresses the formation of the columnar phase. When interactions are purely hard, the theory predicts a continuous nematic-to-smectic transition, regardless of the degree of diameter polydispersity. However, polydispersity enhances the stability of the smectic phase against the nematic phase. Predictions for the case where an additional soft interaction is added are obtained using mean-field perturbation theory. In the case of the one-component fluid, the transition remains continuous for repulsive forces, and the smectic phase becomes more stable as the range of the interaction is decreased. The opposite behavior with respect to the range is observed for attractive forces, and in fact the transition becomes of first order below a tricritical point. Also, for attractive interactions, nematic demixing appears, with an associated critical point. When platelet polydispersity is introduced the tricritical temperature shifts to very high values.     

Depletion potentials induced by charged colloidal rods

We present direct depletion potential measurements for a single colloidal sphere close to a wall in suspensions of charged colloidal rods. In contrast to earlier studies of purely entropic systems (Helden et al. Phys. Rev. Lett. 2003, 90, 048301), here electrostatic interactions are important. These enhance the depletion attraction and lead to repulsive parts in the interaction potentials, indicating correlation effects between the rods.     

Self-assembly of rod-coil block copolymers

We present a self-consistent field theory model for the self-assembly behavior of rod-coil block copolymers. The orientational interactions between the rods were modeled through a Maier-Saupe interaction, while the enthalpic interactions between rods and coils were modeled through a standard Flory-Huggins approach. We outline a "real-space" numerical approach to solve the self-consistent field equations for such rod-coil block copolymers. A major focus of our work is upon the nonlamellar phases observed in the experiments on such polymers. To develop a physical understanding of these phases and their regimes of occurrence, we compute the two-dimensional phase diagram for our model. The latter shows significant departures from the one-dimensional phase diagram, but matches qualitatively with the existing experimental results. We also present scaling arguments that rationalize the numerical results for the self-assembly behavior.     

Stability of nematic and smectic phases in rod-like mesogens with orientation-dependent attractive interactions

The stability of isotropic (I), nematic (N), smectic A (Sm A), and hexatic (Hex) liquid crystalline phases is studied for a fluid of molecules with a rod-like shape and dispersive interactions dependent on orientation. The fluid is modeled with the spherocylindrical Gay-Berne-Kihara interaction potential proposed in a recent work, with parameters favoring parallel pair orientations. The liquid crystal phase diagram is characterized for different molecular aspect ratios by means of Monte Carlo simulations in the isobaric-isothermal ensemble. Three types of triple points are observed, namely, I-Sm A-Hex, I-N-Sm A, and N-Sm A-Hex, leading to island-shape domains for the smectic A phase. The resulting phase diagrams are compared with those derived previously for prolate fluids of ellipsoidal and spherocylindrical symmetry. It is concluded that the stability of the layered phases with respect to the nematic phase is enhanced in the spherocylindrical fluids due to geometrical constraints. Furthermore, the anisotropy of the dispersive interactions induces a stronger dependence of the overall phase diagram on temperature and aids in the energetic stabilization of the hexatic crystalline phase with respect to the fluid smectic A phase.     

Study of the isotropic to smectic-A phase transition in liquid crystal and acetone binary mixtures

The first-order transition from the isotropic (I) to smectic-A (Sm?A) phase in the liquid crystal 4-cyano-4(')-decylbiphenyl (10CB) doped with the polar solvent acetone (ace) has been studied as a function of solvent concentration by high-resolution ac-calorimetry. Heating and cooling scans were performed for miscible 10CB+ace samples having acetone mole fractions from x(ace)=0.05 (1 wt?%) to 0.36 (10%) over a wide temperature range from 310 to 327 K. Two distinct first-order phase transition features are observed in the mixture whereas there is only one transition (I-Sm?A) in the pure 10CB for that particular temperature range. Both calorimetric features reproduce on repeated heating and cooling scans and evolve with increasing x(ace) with the high-temperature feature relatively stable in temperature but reduced in size while the low-temperature feature shifts dramatically to lower temperature and exhibits increased dispersion. The coexistence region increases for the low-temperature feature but remains fairly constant for the high-temperature feature as a function of x(ace). Polarizing optical microscopy supports the identification of a smectic phase below the high-temperature heat capacity signature indicating that the low-temperature feature represents an injected smectic-smectic phase transition. These effects may be the consequence of screening the intermolecular potential of the liquid crystals by the solvent that stabilizes a weak smectic phase intermediate of the isotropic and pure smectic-A.     

Structure and phase behavior of a confined nanodroplet composed of the flexible chain molecules

A polymer density functional theory has been employed for investigating the structure and phase behaviors of the chain polymer, which is modelled as the tangentially connected sphere chain with an attractive interaction, inside the nanosized pores. The excess free energy of the chain polymer has been approximated as the modified fundamental measure-theory for the hard spheres, the Wertheim's first-order perturbation for the chain connectivity, and the mean-field approximation for the van der Waals contribution. For the value of the chemical potential corresponding to a stable liquid phase in the bulk system and a metastable vapor phase, the flexible chain molecules undergo the liquid-vapor transition as the pore size is reduced; the vapor is the stable phase at small volume, whereas the liquid is the stable phase at large volume. The wide liquid-vapor coexistence curve, which explains the wide range of metastable liquid-vapor states, is observed at low temperature. The increase of temperature and decrease of pore size result in a narrowing of liquid-vapor coexistence curves. The increase of chain length leads to a shift of the liquid-vapor coexistence curve towards lower values of chemical potential. The coexistence curves for the confined phase diagram are contained within the corresponding bulk liquid-vapor coexistence curve. The equilibrium capillary phase transition occurs at a higher chemical potential than in the bulk phase.