Monte Carlo simulations of two-dimensional hard core lattice gases

Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a two-dimensional square lattice. Exclusions of one and up to five nearest neighbors (NN) are considered. These can be mapped onto hard squares of varying side length, lambda (in lattice units), tilted by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN exclusion undergoes a continuous order-disorder transition in the Ising universality class. Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors (2NN) also undergoes a continuous phase transition in the Ising universality class, while the Landau-Lifshitz theory predicts that this transition should be in the universality class of the XY model with cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau-Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous phase transition in the Ising universality class-contradicting the predictions of the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.     

Self-assembly of colloidal cubes via vertical deposition

The vertical deposition technique for creating crystalline microstructures is applied for the first time to nonspherical colloids in the form of hollow silica cubes. Controlled deposition of the cubes results in large crystalline films with variable symmetry. The microstructures are characterized in detail with scanning electron microscopy and small-angle X-ray scattering. In single layers of cubes, distorted square to hexagonal ordered arrays are formed. For multilayered crystals, the intralayer ordering is predominantly hexagonal with a hollow site stacking, similar to that of the face centered cubic lattice for spheres. Additionally, a distorted square arrangement in the layers is also found to form under certain conditions. These crystalline films are promising for various applications such as photonic materials.     

受限于两平行板间的对称星形共聚物Am Bm熔体相行为的格子自洽场理论研究

采用格子自洽场理论计算研究了受限于2个平行板间的对称星形共聚物AmBm(m=1,2,3,4,5)熔体形成的层状相结构.在给定的相互作用下(χNAB不变,χ为Flory-Huggins相互作用参数,NAB=(N?1)/m为单个聚合物分子中一对AB臂的总链节数目),针对平行板间距为体相周期的情况,系统考察了共聚物链长N和单个聚合物分子中A(或B)臂数目m对受限层结构细节及层取向的影响.由计算结果,当N或NAB不变时,受限层的归一化界面宽度随m的增大而减小.受限板为中性时,垂直层结构的单链自由能比平行层结构的低.随着板对共聚物中一种嵌段的选择作用Λ的增大,体系发生垂直层到平行层的转变,该转变为一阶相变.当m不变时,N越小,上述转变出现在越大的Λ值处,体系越容易保持垂直层结构.并且N越小,层状结构周期越小.当N或NAB不变时,m越大体系越容易保持垂直层结构.总之,星形共聚物的链长越短、臂数越多时,垂直层稳定的Λ区间越大、层状结构的界面宽度越小.这些结论可以指导刻蚀应用中对体系参数的选择.     

Polymer chains in good solvent within attracting walls

It is known that a polymer chain in an ideal solvent confined within parallel attracting walls undergoes a second-order transition at the temperature T* satisfying the equation exp[-ε/(k_BT*)]=6/5; here the model consists of a chain placed on a cubic lattice, and ε (<0) is the attractive energy experienced by a chain segment contacting a wall. We then investigate the effect induced by a good solvent upon the chain behavior. A single chain is considered; within the Gaussian approximation, we assume that its partition function may be factorized in two terms, one across the wall planes and another parallel to them. For an interplanar distance L significantly smaller than the average radius of gyration the compressed chain is assumed to reach a uniform density, so that the free energy contribution due to the intrachain atomic contacts is a function of the density alone. It may be shown that the effective value of ε/(k_BT*)(=σ) is the difference between the value to be expected “in vacuo” and β/(z-2), where z is the degree of coordination of the lattice and β is the excluded-volume parameter. As a result, for large values of L we may have an attractive effect exerted by the chain on the walls whereas at small L's we invariably have a repulsion. For the cubic lattice we have a repulsion and an attraction for large L approximatively for σ < ln(6/5)+β/(z-2) and for σ > (ln(6/5)+β/(z-2), respectively, whereas we have inversion between the two regimes at some distance L for intermediate values of σ. In the limit of an infinite molecular weight the inversion translates into a thermodynamic transition. We believe the present model may explain some important features seen in polymer adhesion.     

A density functional model for the binary crystal of hard spheres with vacancies

We study the stability of a binary mixture of hard spheres in the crystalline state in which a small fraction of lattice sites in the solid structure are vacant. The optimum vacancy concentration is obtained by minimizing the free energy of the inhomogeneous solid state. We use the modified weighted density functional approximation to compute the free energy. The necessary input for the theory is the thermodynamic properties of the homogeneous state of the mixture and is obtained from the solutions of the corresponding Percus-Yevick integral equations for the binary system. We compute the free energy for the crystal having two kinds of ordered structures in which (i) both the species lie in a disordered manner on a single face-centered-cubic lattice and (ii) each of the two species lie on a separate cubic lattice. Our theoretical model obtains equilibrium vacancy fraction of O(10(-5)) near the freezing point in both cases. The vacancy concentration decreases with the increase of density in both cases.     

One‐Pot,Template‐Free Synthesis of Pd?Pt Single‐Crystalline Hollow Cubes with Enhanced Catalytic Activity

Hollow structures have attracted ever‐growing interest owing to their various excellent properties. However, a facile strategy for their fabrication is still desired. Herein, Pd? Pt alloy with three different morphologies, that is, cubes, hollow cubes, and truncated octahedrons, is synthesized by using a one‐pot, template‐free method. The mechanism and dynamics of this system is also studied in detail. In particular, the hollow cubic structure represents enhanced catalytic activity in both coupling reactions and in the electrochemical oxidation of formic acid.     

Ba2CdMoO6及新化合物—Sr2CdMoO6晶体结构的研究

自从对Sr_2CaWO_6的相变和晶体结构研究以后,引起了我们对该类型化合物A_2~ⅡB~ⅡB~ⅥO_6的兴趣(A~Ⅱ=Ba~( 2),Sr~( 2);B~Ⅱ=Ca~( 2),Cd~( 2),Fe~( 2),Co~( 2),…;B~Ⅵ=W~( 6),Mo~( 6)),它们属于复杂的钙钛矿型结构,且具有一定的规律性。据文献[2]报导Ba_2CaWO_6属立方晶系,而文献[1]报导Sr_2CaWO_6低温相属正交晶系。在元素周期表中Mo和W同属于ⅥB族,它们的化学性质相似,二元素的离子半径也非常相近,Cd和Ca虽不同族,但离子半径很相近,化合价相同。为此,本文用Mo~( 6)代替W~( 6),Cd~( 2)代替Ca~( 2)来研究Ba_2CdMoO_6和Sr_2CdMoO_6的晶体结构。文献[3]对Ba_2CdMoO_6做了简单的报导,但Sr_2CdMoO_6则未见报导。     

Static and dynamic structures of spherical nonionic surfactant micelles during the disorder-order transition

We have investigated the static and dynamic structures of nonionic surfactant micelles, a C(12)E(8)/water binary system, during the disorder-order transition using small angle x-ray scattering, static light scattering, and dynamic light scattering techniques. In the disordered phase, the micelles have spherical shape and intermicellar interactions are governed by the hard core and weak long ranged attractive potentials. With increase of the micellar concentration, the disordered micelles transform to the three characteristic ordered micellar phases, a hexagonally close packed lattice, a body centered cubic lattice, and an A15 lattice having area-minimizing structure. The stability of these phases is well explained by balance of a close packing rule and a minimal-area rule proposed by Ziherl and Kamien [Phys. Rev. Lett. 85, 3528 (2000)]. The role of hydrodynamic interactions in surfactant micellar solutions was compared with that in hard sphere colloidal particle suspensions.     

Ordered equilibrium structures of soft particles in thin layers

Considering a system of gaussian particles confined between two hard, parallel plates, we investigate at T = 0, ordered equilibrium configurations that the system forms as the distance D between the plates gradually increases. Using a very sensitive and reliable optimization technique that is based on ideas of genetic algorithms, we are able to identify the emerging sequences of the energetically most favorable structures. Although the resulting phase diagram is rather complex, its essential features can be reduced to the discussion of two archetypes of structural transitions: (i) a continuous transformation at a fixed number of layers, leading from a square to a centered rectangular and then to a hexagonal lattice; (ii) a discontinuous transition, transforming a hexagonal to a square lattice via complex intermediate structures, i.e., the so-called buckling transition, which is encountered as the system forms a new layer. Detailed Monte Carlo simulations are able to confirm the theoretical predictions on a semiquantitative level but are not able to grasp the tiny energetic differences between competing structures.     

Monte Carlo simulation on symmetric ABA/AB copolymer blends in confined thin films

The effects of blend composition on morphology, order-disorder transition (ODT), and chain conformation of symmetric ABA/AB copolymer blends confined between two neutral hard walls have been investigated by lattice Monte Carlo simulation. Only lamellar structure is observed in all the simulation morphologies under thermodynamic equilibrium state, which is supported by theoretical prediction. When the composition of AB diblock copolymer (phi) increases, both lamellar spacing and the corresponding ODT temperature increase, which can be attributed to the variation of conformation distribution of the diblock and the triblock copolymer chains. In addition, both diblock and triblock copolymer, chains with bridge conformation extend dramatically in the direction parallel to the surface when the system is in ordered state. Finally, the copolymer chain conformation depends strongly on both the blend composition and the incompatibility parameter chiN.     

Double gyroid structures made of asymmetric dimers

Gyroid cubic phases are interesting for both scientists and engineers due to possible applications in electronic devices. New series of dimeric molecules, despite their flexible molecular structure, can display double gyroid cubic phase with Ia3d symmetry and lattice parameter corresponding to double molecular length. The cubic phase is structurally related to columnar phase and both phases often coexist in the same temperature window. Apparently, for studied compounds stronger molecular asymmetry promotes cubic structure. Interestingly, for the examined compounds the transition between two isotropic liquids was observed.     

Precise simulation of the freezing transition of supercritical Lennard-Jones

The fluid-solid transition of the Lennard-Jones model is analyzed along a supercritical isotherm. The analysis is implemented via a simulation method which is based on a modification of the constrained cell model of Hoover and Ree. In the context of hard-sphere freezing, Hoover and Ree simulated the solid phase using a constrained cell model in which each particle is confined within its own Wigner-Seitz cell. Hoover and Ree also proposed a modified cell model by considering the effect of an external field of variable strength. High-field values favor configurations with a single particle per Wigner-Seitz cell and thus stabilize the solid phase. In previous work, a simulation method for freezing transitions, based on constant-pressure simulations of the modified cell model, was developed and tested on a system of hard spheres. In the present work, this method is used to determine the freezing transition of a Lennard-Jones model system on a supercritical isotherm at a reduced temperature of 2. As in the case of hard spheres, constant-pressure simulations of the fully occupied constrained cell model of a system of Lennard-Jones particles indicate a point of mechanical instability at a density which is approximately 70% of the density at close packing. Furthermore, constant-pressure simulations of the modified cell model indicate that as the strength of the field is reduced, the transition from the solid to the fluid is continuous below the mechanical instability point and discontinuous above. The fluid-solid transition of the Lennard-Jones system is obtained by analyzing the field-induced fluid-solid transition of the modified cell model in the high-pressure, zero-field limit. The simulations are implemented under constant pressure using tempering and histogram reweighting techniques. The coexistence pressure and densities are determined through finite-size scaling techniques for first-order phase transitions which are based on analyzing the size-dependent behavior of susceptibilities and dimensionless moment ratios of the order parameter.     

Transitions in Solvate Crystals of a Tetraaryladamantane

Obtaining high-resolution structures of liquid compounds can be difficult. Encapsulating them in the lattice of a larger organic molecule acting as crystallization chaperone is one option to overcome this difficulty. Tetraaryladamantane ethers can play the role of chaperones, accommodating a range of different guest molecules in their crystals. How well-ordered crystalline arrangements for molecules of different shape are achieved is not clear. Cases in which more than one structure is found may shed light on this phenomenon. Here, we report low-order cubic crystal structures of 1,3,5,7-tetrakis(2,4-dimethoxyphenyl)adamantane (TDA) encapsulating ortho-xylene or cyclohexane, together with better ordered structures obtained after warming the crystals to 60 °C. Evidence for cubic crystal systems was also found for limonene, hexachlorobutadiene and eucalyptol, with a transition to a triclinic system for the former two, but no transition up to 70 °C for the latter. These findings indicate that some solvate structures of TDA can readily undergo structural transitions to less solvated, better ordered systems. Crystals obtained by rapid thermal crystallization may be in kinetically trapped states, and the transition to a solvate-free crystal system appears to have a kinetic barrier that depends strongly on the structure of the liquid guest molecules encapsulated in the lattice.     

On the pressure-induced phase transformation in the structure II clathrate hydrate of tetrahydrofuran

A high-pressure phase of the clathrate hydrate of tetrahydrofuran was prepared by freezing a liquid phase of overall composition THF · 7 H₂O under a pressure of 3.0 kbar, or by pressurizing the solid structure II THF hydrate of 255K to 3.4 kbar. Unfortunately, the products recovered at 77K were always mixed phase materials as shown by X-ray powder diffraction. A number of diffraction lines could be indexed in terms of the cubic structure I hydrate with a slightly expanded lattice parameter, 12.08 Å, giving some support to Dyadin's idea that the high pressure phase transition involves a conversion of Structure II to Structure I. Other phases observed in the recovered product include Ice IX and amorphous materials. The reversion of the high pressure sample to the structure II hydrate was followed by differential scanning calorimetry. At ambient pressure, the high pressure sample converts slowly back to Structure II hydrate event at 77K.NRCC No. 35786.     

Crystalline ordering in lattice models of hard rods with nearest neighbour attraction

Several lattice models for hard rods with attraction between neighbouring parallel rodes are considered. It is proved that the models for sufficiently low temperature and high fugacity exhibit a phase transition to an ordered crystalline structure. Nothing is proved about the existence of a liquid crystal state.     

In situ monitoring of structural changes during colloidal self-assembly

Reflectance spectroscopy is utilized to monitor structural changes during the self-assembly of a monodisperse colloidal system at the meniscus of a sessile drop on an inert substrate. Treating the ordered colloidal structure as a photonic crystal is equivalent to monitoring the changes in the photonic band gap (PBG) as the colloidal system self-assembles heterogeneously into a crystal through solvent evaporation in ambient conditions. Using a modified Bragg's law model of the photonic crystal, we can trace the structural evolution of the self-assembling colloidal system. After a certain induction period, a face-centered cubic (FCC) structure emerges, albeit with a lattice parameter larger than that of a true close-packed structure. This FCC structure is maintained while the lattice parameter shrinks continuously with further increase in the colloidal concentration due to drying. When the structure reaches a lattice parameter 1.09 times the size of that of a true close-packed structure, it undergoes an abrupt decrease in lattice spacing, apparently similar to those reported for lattice-distortive martensitic transformations. This abrupt final lattice shrinkage agrees well with the estimated Debye screening length of the electric double layer of charged colloids and could be the fundamental reason behind the cracking commonly seen in colloidal crystals.     

Crystallization, melting, and structure of water nanoparticles at atmospherically relevant temperatures

Water nanoparticles play an important role in atmospheric processes, yet their equilibrium and nonequilibrium liquid-ice phase transitions and the structures they form on freezing are not yet fully elucidated. Here we use molecular dynamics simulations with the mW water model to investigate the nonequilibrium freezing and equilibrium melting of water nanoparticles with radii R between 1 and 4.7 nm and the structure of the ice formed by crystallization at temperatures between 150 and 200 K. The ice crystallized in the particles is a hybrid form of ice I with stacked layers of the cubic and hexagonal ice polymorphs in a ratio approximately 2:1. The ratio of cubic ice to hexagonal ice is insensitive to the radius of the water particle and is comparable to that found in simulations of bulk water around the same temperature. Heating frozen particles that contain multiple crystallites leads to Ostwald ripening and annealing of the ice structures, accompanied by an increase in the amount of ice at the expense of the liquid water, before the particles finally melt from the hybrid ice I to liquid, without a transition to hexagonal ice. The melting temperatures T(m) of the nanoparticles are not affected by the ratio of cubic to hexagonal layers in the crystal. T(m) of the ice particles decreases from 255 to 170 K with the particle size and is well described by the Gibbs-Thomson equation, T(m)(R) = T(m)(bulk) - K(GT)/(R - d), with constant K(GT) = 82 ± 5 K·nm and a premelted liquid of width d = 0.26 ± 0.05 nm, about one monolayer. The freezing temperatures also decrease with the particles' radii. These results are important for understanding the composition, freezing, and melting properties of ice and liquid water particles under atmospheric conditions.     

DEFORMATION OF SOFT COLLOIDAL CRYSTALLINE STRUCTURE-THEORETICAL CONSIDERATIONS AND EXPERIMENTAL EVIDENCES BY SYNCHROTRON SMALL-ANGLE X-RAY SCATTERING ON TENSILE STRETCHED POLYMERIC LATEX FILM

Films obtained via drying a polymeric latex dispersion are normally colloidal crystalline where latex particles are packed into a face centered cubic (fcc) structure.Different from conventional atomic crystallites or hard sphere colloidal crystallites,the crystalline structure of these films is normally deformable due to the low glass transition temperature of the latex particles.Upon tensile deformation,depending on the drawing direction with respect to the normal of specific crystallographic plane,one ...     

Adsorption and freezing of diblock copolymers on stripe-patterned surfaces: a scaling analysis

We present the results of scaling analysis of diblock copolymers adsorbed on stripe-patterned surfaces of various widths. Our previous studies [K. Sumithra and E. Straube, J. Chem. Phys. 125, 154701 (2006)] show that the adsorption of diblock copolymer on patterned surfaces yields two peaks in the specific heat capacity, thereby indicating two transition. In the current study, we characterize these two transitions. The scaling of the adsorption energy data proves that the first peak in the heat capacity curve is, in fact, associated with the adsorption transition. We found that for this transition the classical scaling laws are obeyed and that the critical crossover exponent is unaltered with respect to the case of homogeneous polymers. However, we found a change in the scaling exponent in the case of parallel component of the radius of gyration. It is evident from the scaling analysis of the parallel component of the radius of gyration that the chain is stretched along the direction of the stripes. The scaling plot shows, for (square root )/Nnu, an exponent of approximately 0.55 which is much different from that expected of a self-avoiding chain (nud=2-nu)/phi which is 0.25. The observed value is closer to an exponent of (nud=1-nu)/phi=0.69, for a completely stretched chain in one dimension. The perpendicular component of the radius of gyration shows deviation from the power law and the slope is steeper than the expected value of -2. We have also defined an order parameter to characterize the second transition and have found that it corresponds to a freezing transition where there are only a few dominant conformations. The perpendicular component of the radius of gyration also supports this information.     

Thermodynamics of water octamer in a uniform electric field

We study the water octamer in a uniform electric field using the all-exchanges parallel tempering Monte Carlo method in the canonical ensemble. The heat capacity, quenched energy configurations, and the order parameter Q(4) are employed to understand the phase changes observed as a function of temperature and the strength of the applied electric field. At a low field strength of 0.1 V A(-1) a solidlike to liquidlike "melting" transition is detected. The corresponding heat capacity peak appears around 206 K, where Q(4) shows a significant change of slope. For E> or =0.5 V A(-1) such features are absent. However, at E=0.5 V A(-1) we find a solidlike to solidlike transition between cubic and extended structures around T approximately 25 K.