Spherical colloidal particles generally self-assemble into hexagonal lattices in two dimensions. However, more complex, non-hexagonal phases have been predicted theoretically for isotropic particles with a soft repulsive shoulder but have not been experimentally realized. We study the phase behavior of microspheres in the presence of poly(N-isopropylacrylamide) (PNiPAm) microgels at the air/water interface. We observe a complex phase diagram, including phases with chain and square arrangements, which exclusively form in the presence of the microgels. Our experimental data suggests that the microgels form a corona around the microspheres and induce a soft repulsive shoulder that governs the self-assembly in this system. The observed structures are fully reproduced by both minimum energy calculations and finite temperature Monte Carlo simulations of hard core-soft shoulder particles with experimentally realistic interaction parameters. Our results demonstrate how complex, anisotropic assembly patterns can be realized from entirely isotropic building blocks by control of the interaction potential.

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We study both experimentally and theoretically the self-assembly of binary polycaprolactonepolyethyleneoxide (PCL-PEO) block copolymers in dilute solution, where self-assembly is triggered by changing the solvent from the common good solvent THF to the selective solvent water, and where the two species on their own in water form vesicles and spherical micelles respectively. We find that in water the inter-micellar exchange of these block copolymers is extremely slow so that the resultant selfassembled structures are in local but not global equilibrium (i.e., they are non-ergodic). This opens up the possibility of controlling micelle morphology both thermodynamically and kinetically. Specifically, when the two species are first molecularly dissolved in THF before mixing and self-assembly ('premixing') by dilution with water, the morphology of the formed structures is found to depend on the mixing ratio of the two species, going gradually on a route of decreasing surface curvature from vesicles via an intermediate regime of micelles in the shape of 'bulbed' rods, rings, Y-junctions finally to spherical micelles as we increase the proportion of the "sphere formers". On the other hand, if the two species are first partially self-assembled (by partial exchange of the solvent with water) before mixing and further self-assembly ('intermediate mixing'), novel metastable structures, including nanoscopic 'pouches', emerge. These experimental results are corroborated by self-consistent field theory

Articles you may be interested inEffect of surface tension and surface elasticity of a fluid-fluid interface on the motion of a particle immersed near the interface Structure of the nonionic surfactant triethoxy monooctylether C 8 E 3 adsorbed at the free water surface, as seen from surface tension measurements and Monte Carlo simulations Effects of viscoelasticity of bulk polymer solution on the surface modes as probed by laser light scatteringWe present a microscopic theory for the interfacial rheology of a fluid-fluid interface with adsorbed surfactant and calculate the effect of this on surface light scattering from the interface. We model the head and tail groups of the surfactant as polymer chains, a description that becomes increasingly accurate for large molecular weight surfactants, i.e., polymeric surfactants. Assuming high surface concentrations so that we have a double-sided polymer brush monolayer, we derive microscopic scaling expressions for the surface viscoelastic constants using the Alexander-deGennes model. Our results for the surface elastic constants agree with those in the literature, while the results for the viscous constants are new. We find that four elastic constants, i.e., ␥ ͑surface tension͒, ⑀ ͑dilational elasticity͒, ͑bending modulus͒, ͑coupling constant͒, and three viscous constants, i.e., ⑀Ј,Ј,Ј ͑the viscous counterparts of ⑀, , and , respectively͒ are required for a general description of interfacial viscoelasticity ͑neglecting in-plane shear͒. In contrast to current phenomenological models, we find ͑1͒ there is no viscous counterpart to ␥, i.e., ␥Јϵ0; ͑2͒ there are two additional complex surface constants ͑i.e., ϩiЈ and ϩiЈ) due to the finite thickness of the monolayer. Excellent agreement is found comparing our microscopic theory with measurements on diblock copolymer monolayers. We further derive the dispersion relation governing surface hydrodynamic modes and the power spectrum for surface quasielastic light scattering ͑SQELS͒ for a general interface parameterized by all the surface viscoelastic constants. Limiting results are presented for ͑1͒ liquid-air interfaces; ͑2͒ liquid-liquid interfaces with ultralow ␥. The significant contribution of in the latter case opens up the possibility for a direct measurement of using SQELS for polymeric surfactant monolayers. Finally, we show that the coupling constant can lead to apparent negative values of ⑀Ј, as observed in many experimental systems. This is the first time that this result has been explained for insoluble monolayers using a physically realistic model. Based on our theory, we speculate the existence of a thick sublayer ͑on the length scale of a micron͒ in recent experiments on insoluble copolymer systems where negative surface viscosities have been found. We also suggest methods to detect the presence of such a sublayer if it does exist.

Using a molecular dynamics and mean field theory approach which explicitly accounts for free ions, we study the conformation of polyelectrolyte dendrimers for different generation numbers, spacer lengths, charge distributions and ionic strengths. We find that, due to local charge neutrality, electrostatic interactions are strongly screened under all the conditions studied (including salt free conditions). This leads to the cores of the dendrimers being filled and to a very weak dependence of dendrimer conformations on ionic strength. These results are contrary the predictions of Debye-Hu ¨ckel theory and highlight the limitations of Debye-Hu ¨ckel theory in modeling the properties of highly charged macromolecular systems. However, our simulations suggest that some responsiveness to ionic strength may be recovered for more weakly charged dendrimers.

We study the structure of mixed monolayers of large (3 μm diameter) and small (1 μm diameter) very hydrophobic silica particles at an octane-water interface as a function of the number fraction of small particles ξ. We find that a rich variety of two-dimensional hexagonal super-lattices of large (A) and small (B) particles can be obtained in this system due to strong and long-range electrostatic repulsions through the nonpolar octane phase. The structures obtained for the different compositions are in good agreement with zero temperature calculations and finite temperature computer simulations.

We study via lattice Monte Carlo simulation and Flory theory the properties of g=1-6 dendrimers in variable solvent quality. For all the generations studied, we find that the radius of gyration R(g) collapses significantly (factor of 2) going from athermal to extreme poor solvent conditions, indicating that varying solvent quality is an effective means of controlling dendrimer size. We also find that in athermal, theta, and extreme poor solvent conditions, the radius of gyration of dendrimers scales with the total number of monomers roughly as R(g) approximately N(1/3). However, a more careful analysis shows that in athermal and theta solvents, there is, in fact, a small but systematic deviation of R(g) from R(g) approximately N(1/3) scaling and the simulation data is described better by the Flory theory prediction of R(g) approximately N(1/5)[(g+1)m](2/5) in athermal solvents and R(g) approximately N(1/4)[(g+1)m](1/4) in theta solvents. We also find for our simulation data that stronger deviations from constant density scaling are possible, with scaling behavior as shallow as R(g) approximately N(0.26) possible for solvent conditions in between theta and the completely collapsed state. It is evident therefore that dendrimers do not obey (or even approximately obey) R(g) approximately N(1/3) scaling under all solvent conditions. Under all solvent conditions, we find that the intramolecular density is dense corelike (i.e., the density maximum is in the interior of the dendrimer) and terminal groups are delocalized throughout the dendrimer.

We present a configurational-biased lattice Monte Carlo scheme for simulating nonideal dendrimers that satisfies detailed balance. This corrects an important shortcoming in a previous lattice Monte Carlo scheme by Mansfield and Klushin: in a previous publication, we showed that the Mansfield and Klushin scheme did not obey detailed balance, and that this led to surprisingly large errors in the radius of gyration R g and scattering form factor P(q) for ideal dendrimers. In this paper, we have calculated the radius of gyration, the form factor, and the intramolecular density profile for g ) 1-8 self-avoiding dendrimers and find that our results are qualitatively the same as previous results obtained by Mansfield and Klushin (g is the generation number). This indicates that the error in the Mansfield and Klushin scheme due to detailed balance violation is much smaller for self-avoiding dendrimers. Our other key conclusions concerning the equilibrium properties of self-avoiding dendrimers are the following: (1) The radius of gyration scales with the total number of monomers roughly as Rg ∝ N 1/3 . A more careful analysis however shows that there is a small (∼30%) and nonmonotonic variation in the internal density of the dendrimer with N, the form and magnitude of which are consistent with previous intrinsic viscosity results on dendrimers. (2) The intramolecular density profile is dense core like at low dendrimer generations (g < 5) and solid sphere like at high generations (g g 5).(3) There is some "hollowness" in the core region of the dendrimer for higher generation dendrimers (g g 5), though the depth and extent of the hollowness are much smaller than that predicted by the dense shell model. (4) Terminal groups of the dendrimer are not localized at the periphery but delocalized throughout the dendrimer. The relationship between our findings and previous theoretical and experimental studies, especially recent scattering studies on dendrimers, is discussed.