Towards a molecular theory of phase transitions in fatty acid monolayers

A molecular theory of phase transitions in fatty acid monolayers at the air/water interface is proposed based on rotational ordering of molecules about their longitudinal axes. The first order statistical mechanical lattice model of Bell, Mingins, and Taylor (BMT ) which is an equilibrium diluted Ising model is used to describe the monolayer behavior of some simple aliphatic carboxylic acids. The interaction energy parameters in the BMT model are adjusted to give reasonable agreement with the experimentally observed chain length dependence, and the energies thus obtained are compared with those calculated for interacting aliphatic carboxylic acid dimers by the technique of perturbative configuration interaction using localized orbitals (PCILO ). It is concluded that intermolecular rotational ordering due to the anisotropy of the intermolecular potential plays a significant role in simple fatty acid monolayer phase behavior. A possible experimental test of the model is briefly described.     

On the role of classical orbits in mesoscopic electronic systems

We discuss the semiclassical periodic orbit theory (POT) and some of its recent extensions which are applicable also to systems exhibiting a transition from integrable to chaotic behaviour. We apply the POT to give a semiclassical interpretation of shell effects in free metal clusters and semiconductor quantum dots in terms of classical periodic orbits. In particular, we study the ground-state deformations of large metal clusters and discuss the recently observed conductance oscillations in a circular quantum dot under the influence of an external magnetic field. We also predict the shell structure of a triangular quantum dot, using as models a triangular billiard and the Hénon-Heiles potential including weak magnetic fields.     

Free‐energy model of asymmetry in side‐chain liquid‐crystalline diblock copolymers

Side‐chain liquid‐crystalline‐b‐amorphous copolymers combine the thermotropic ordering of liquid crystals (LCs) with the physics of block copolymer phase segregation. In our earlier experiments, we observed that block copolymer order–order and order–disorder transitions could be induced by LC transitions. Here we report the development of a free‐energy model to understand the interplay between LC ordering and block copolymer morphology in an incompressible melt. The model considers the interaction between LC moieties, the stretching of amorphous chains from curved interfaces, interfacial surface contributions, and elastic deformation of the nematic phase. The LC block is modeled with Wang and Warner's theory, in which nematogens interact through mean‐field potentials, and the LC backbone is modeled as a wormlike chain. Free energy is estimated for various morphologies: homogeneous, lamellar, cylinder micelle, and spherical micelle. Phase diagrams were constructed by iteration over temperature and composition ranges. The resulting composition diagrams are highly asymmetric, and a variety of first‐order transitions are predicted to occur at the LC clearing temperature. Qualitatively, nematic deformation energies destabilize curved morphologies, especially when the LC block is in the center of the block copolymer micelle. The thermodynamics of diblocks with laterally attached, side‐on mesogens are also explored. Discussion focuses on how well the model captures experimental phenomena and how the predicted phase boundaries are affected by changes in polymer architecture. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2671–2691, 2001     

Isobaric volume and enthalpy recovery of glasses. II. A transparent multiparameter theory

A multiordering parameter model for glass-transition phenomena has been developed on the basis of nonequilibrium thermodynamics. In this treatment the state of the glass is determined by the values of N ordering parameters in addition to T and P; the departure from equilibrium is partitioned among the various ordering parameters, each of which is associated with a unique retardation time. These times are assumed to depend on T, P, and on the instantaneous state of the system characterized by its overall departure from equilibrium, giving rise to the well-known nonlinear effects observed in volume and enthalpy recovery. The contribution of each ordering parameter to the departure and the associated retardation times define the fundamental distribution function (the structural retardation spectrum) of the system or, equivalently, its fundamental material response function. These, together with a few experimentally measurable material constants, completely define the recovery behavior of the system when subjected to any thermal treatment. The behavior of the model is explored for various classes of thermal histories of increasing complexity, in order to simulate real experimental situations. The relevant calculations are based on a discrete retardation spectrum, extending over four time decades, and on reasonable values of the relevant material constants in order to imitate the behavior of polymer glasses. The model clearly separates the contribution of the retardation spectrum from the temperature-structure dependence of the retardation times which controls its shifts along the experimental time scale. This is achieved by using the natural time scale of the system which eliminates all the nonlinear effects, thus reducing the response function to the Boltzmann superposition equation, similar to that encountered in the linear viscoelasticity. As a consequence, the system obeys a rate (time) -temperature reduction rule which provides for generalization within each class of thermal treatment. Thus the model establishes a rational basis for comparing theory with experiment, and also various kinds of experiments between themselves. The analysis further predicts interesting features, some of which have often been overlooked. Among these are the impossibility of extraction of the spectrum (or response function) from experiments involving cooling from high temperatures at finite rate; and the appearance of two peaks in the expansion coefficient, or heat capacity, during the heating state of three-step thermal cycles starting at high temperatures. Finally, the theory also provides a rationale for interpreting the time dependence of mechanical or other structure-sensitive properties of glasses as well as for predicting their long-range behavior.     

Isobaric volume and enthalpy recovery of glasses. II. A transparent multiparameter theory

A multiordering parameter model for glass-transition phenomena has been developed on the basis of nonequilibrium thermodynamics. In this treatment the state of the glass is determined by the values of N ordering parameters in addition to T and P; the departure from equilibrium is partitioned among the various ordering parameters, each of which is associated with a unique retardation time. These times are assumed to depend on T, P, and on the instantaneous state of the system characterized by its overall departure from equilibrium, giving rise to the well-known nonlinear effects observed in volume and enthalpy recovery. The contribution of each ordering parameter to the departure and the associated retardation times define the fundamental distribution function (the structural retardation spectrum) of the system or, equivalently, its fundamental material response function. These, together with a few experimentally measurable material constants, completely define the recovery behavior of the system when subjected to any thermal treatment. The behavior of the model is explored for various classes of thermal histories of increasing complexity, in order to simulate real experimental situations. The relevant calculations are based on a discrete retardation spectrum, extending over four time decades, and on reasonable values of the relevant material constants in order to imitate the behavior of polymer glasses. The model clearly separates the contribution of the retardation spectrum from the temperature-structure dependence of the retardation times which controls its shifts along the experimental time scale. This is achieved by using the natural time scale of the system which eliminates all the nonlinear effects, thus reducing the response function to the Boltzmann superposition equation, similar to that encountered in the linear viscoelasticity. As a consequence, the system obeys a rate (time) -temperature reduction rule which provides for generalization within each class of thermal treatment. Thus the model establishes a rational basis for comparing theory with experiment, and also various kinds of experiments between themselves. The analysis further predicts interesting features, some of which have often been overlooked. Among these are the impossibility of extraction of the spectrum (or response function) from experiments involving cooling from high temperatures at finite rate; and the appearance of two peaks in the expansion coefficient, or heat capacity, during the heating stage of three-step thermal cycles starting at high temperatures. Finally, the theory also provides a rationale for interpreting the time dependence of mechanical or other structure-sensitive properties of glasses as well as for predicting their long-range behavior.     

Giving molecules an identity. On the interplay between QSARs and partial order ranking

The interplay between 'noise-deficient' QSAR and Partial Order Ranking, including analysis of average linear ranks, constitutes an effective tool in giving substances which have not been investigated experimentally an identity by comparison with experimentally well-characterized, structurally similar compounds. It is disclosed that experimentally well-characterized compounds may serve as substitutes for highly toxic compounds in experimental studies without exhibiting the same extreme toxicity, while from an overall viewpoint they exhibit analogous environmental characteristics.     

Dynamics of order formation by colloidal adsorption onto a substrate studied with Brownian dynamics

Colloidal adsorption and spontaneous ordering of adsorbed particles on a substrate was simulated using a three-dimensional simulation model for colloidal dispersion system with an adsorptive surface under a specified bulk concentration, where the particle-particle and particle-substrate interactions were modeled on the DLVO theory. The key process for order formation is considered to be the adsorption of a particle that induces the transition from incomplete order to perfect order, and is found to involve a stochastic nature due to an energy barrier which must be overcome for the system to reach ordered state. Also, a model was developed to predict the energy barrier for order formation based on direct observation of the key process. Further, a model to describe the stochastic nature of the process was developed and its quantitative validity was demonstrated. Through the examination of the key process, it is concluded that the mechanism of the order formation is composed of two successive processes and the rate-determining step varies depending on the ionic strength.     

铂/聚邻甲基苯胺/碳材料掺杂碳糊电极对甲醇的催化氧化

以石墨和液体石蜡油为主要原料,分别制备了掺杂不同量多壁碳纳米管(MWCNT)、石墨烯(GRA)、电容活性炭(YEC)和电池活性炭(YBC)的多种碳糊底电极Y-CPE(Y代表各种掺杂碳材料,CPE代表纯碳糊电极).采用恒电位法在-0.10 V(vs.Ag/Ag Cl)电位下将铂电沉积到这些电极上.结果表明,当电池碳的含量为14%时,Pt/YBC-CPE(14%)复合电极对甲醇具有最好的电催化氧化活性.采用恒电位方法在0.85 V(vs.Ag/Ag Cl)电位下将聚邻甲基苯胺(POT)电聚合沉积到纯碳糊电极CPE和含有电池碳的YBC-CPE(14%)电极上,得到复合电极POT/CPE和POT/YBC-CPE(14%),再通过恒电位方法将铂电沉积到这2个复合电极上.扫描电镜(SEM)观察结果表明,在Pt/CPE,Pt/YBC-CPE(14%),Pt/POT(6.5 mC)/CPE和Pt/POT(6.5 mC)/YBC-CPE(14%)4个复合电极中,在Pt/POT/YBC-CPE(14%)复合电极上的铂粒子的尺寸最小,并且Pt/POT(6.5 mC)/YBC-CPE(14%)复合电极电催化氧化甲醇活性最高.在POT(6.5 mC)/CPE和POT(6.5 mC)/YBC-CPE(14%)上Pt纳米颗粒的电沉积过程是一个近似的3D成核过程.研究还发现,复合电极Pt/POT/CPE和Pt/POT/YBC-CPE电催化氧化甲醇的活性随POT膜厚度的增加先增大后减少,存在一个最佳的膜厚度.     

Self-assembly of patchy particles into polymer chains: a parameter-free comparison between Wertheim theory and Monte Carlo simulation

The authors numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions based on the Wertheim perturbation theory. This comparison offers a unique framework for the analytic prediction of the properties of self-assembling particle systems in terms of molecular parameters and liquid state correlation functions. The Wertheim theory has not been previously subjected to stringent tests against simulation data for ordering across the polymerization transition. The authors numerically determine many of the thermodynamic properties governing this basic form of self-assembly (energy per particle, order parameter or average fraction of particles in the associated state, average chain length, chain length distribution, average end-to-end distance of the chains, and the static structure factor) and find that predictions of the Wertheim theory accord remarkably well with the simulation results.     

Theoretical and experimental study on phase transitions and mass fluxes of supersaturated water vapor onto different insoluble flat surfaces

The heterogeneous nucleation and condensation of water vapor onto three different surfaces (newsprint paper, Teflon, cellulose film) was studied theoretically and experimentally. The theoretical framework included the use of the classical theory of heterogeneous nucleation, diffusion theory corrected with transition regime correction factors, and the theory of heat transfer. Experiments were carried out using an environmental scanning electron microscope (ESEM). The experimental results for newsprint paper were investigated more closely. Our results show that the measured onset supersaturations were smaller than the modeled ones when the experimentally determined contact angle was used. Furthermore, the measured condensational growth rates were smaller than the modeled ones, presumably resulting from the approximations that had to be made in the calculations.     

Transferability of cocrystallization propensities between aromatic and heteroaromatic amides

New virtual cocrystal screening was proposed taking advantage of the similarities between cocrystallization landscapes of different compounds. Assuming that cocrystallization propensities can be modeled by miscibility affinities of liquid components under supercooled conditions, the quantitative rules of likeness were formulated and validated for 45 aromatic and heteroaromatic amides interacting with a variety of coformers. The most important finding comes from the observed linear trends between the values of mixing enthalpies of amides with respect to a reference molecule. Particularly isonicotinamide was found as a very convenient comparative system since it constitutes 97 binary cocrystals. Many experimentally observed cocrystals were used for supporting the analogy hypothesis, which states that a properly selected reference molecule, for which cocrystals were experimentally documented, can provide practical information about cocrystallization propensities of another compound provided that two criterions are met, namely sufficiently high similarities and high enough affinities. Hence, it is not necessary to perform experimental cocrystallization of every pair of coformers since miscibility in the solid state of one compound can be transferred to another one at least in the case of aromatic or hetero-aromatic amides.     

Solid-state energetics and electrostatics: Madelung constants and Madelung energies

The Madelung constants of ionic solids relate to their geometry and electrostatic interactions. Furthermore, because of issues in their evaluation, they are also of considerable mathematical interest. The corresponding Madelung (electrostatic, coulomb) energy is the principal contributor to the lattice energies of ionic systems, and these energies largely influence many of their physical properties. The Madelung constants are here defined and their properties considered. A difficulty with their application is that they may be defined relative to various lattice distances, and with various conventions for inclusion of the charges, leading to possible confusion in their use. Instead, the unambiguous Madelung energy, E(M), is to be preferred in chemistry. An extensive list of Madelung energies is presented. From this data set, it is observed that there is a strong linear correlation between the lattice energies of ionic solids, U(POT), and their Madelung energies: U(POT)/kJ mol(-1) = 0.8519E(M) + 293.9. This correlation establishes that the lattice energy, U(POT), for ionic solids is about 15% smaller than the attractive Madelung energy, the difference arising from the repulsions unaccounted for by the solely coulombic Madelung energy calculation. Correlations of U(POT) against E(M) for alkali metal hydrides and transition metal compounds, each having considerable covalency, show much reduced Madelung contributions to the lattice energy. These correlations permit ready estimation of lattice energies, and are the first to be based on actual data rather than a broad analysis. The independent volume-based thermodynamic (VBT) method, which relies on a separate correlation with the formula unit volume of the ionic material, complements these correlations.     

Improved estimation of the ranking probabilities in partial orders using random linear extensions by approximation of the mutual ranking probability

The application of partial order theory and Hasse diagram technique in environmental science is getting increasing attention. One of the latest developments in the field of Hasse diagram technique is the use of random linear extensions to estimate ranking probabilities. In the original algorithm for estimating the ranking probability it is assumed that the order between two incomparable pair of objects can be chosen randomly. However, if the total set of linear extensions is considered there is a specific probability that one object will be larger than another, which can be far from 50%. In this study it is investigated if an approximation of the mutual ranking probability can improve the algorithm. Applying an approximation of the mutual ranking probability the estimation of the ranking probabilities are significantly improved. Using a test set of 39 partial orders with randomly chosen values the relative mean root square difference (MRSD) decrease in average from 7.9% to 2.2% and a maximum relative improvement of 90% can be found. In the most successful case the relative MRSD goes as low as 0.77%.     

Mechanism and modeling of nanorod formation from nanodots

A population balance model based on Smoluchowski aggregation kinetics is developed to explain the formation of nanorods from a colloidal suspension of spherical nanoparticles (nanodots). Our model shows that linear pearl-chain aggregates form by the oriented attachment (OA) of nanodots during the early stages of synthesis, since it occurs with a time scale smaller than the coalescence time scale of nanodots present within an aggregate. The slower coalescence step leads to the transformation of the linear pearl-chain aggregate into a smooth nanorod over a longer time scale of many hours, as observed in experiments. The attachment kinetics is modeled by a modified Brownian collision frequency, with the latter decreasing with nanorod length, leading to the experimentally observed slower growth in nanorod length at longer times. The collision frequency also includes the effects of attractive dipole-dipole and van der Waals interactions between nanodots, which are primarily responsible for OA. Our model predictions are general, and they compare favorably with available experimental data in the literature on the distribution of the aspect ratio (length to diameter) of ZnO and ZnS nanorods over different time scales.     

Prediction of a phase transition to a hydrogen bond ordered form of ice VI

Ice VI is a hydrogen bond disordered crystal over its known region of stability. In this work, we predict that ice VI will transform into a hydrogen bond ordered phase near 108 K, and have identified the likely low-temperature phase as ferroelectric (space group Cc) with an antiferroelectric structure (space group P2(1)2(1)2(1)) close by in energy. Electronic density functional theory calculations provide input to our calculations, which are extended to cells large enough for statistical simulations by using graph invariants. A significant decrease in the configurational entropy is predicted as hydrogen bonds exhibit partial order above the transition, provided that the hydrogen bonds can equilibrate on an experimental time scale. Conversely, partial disorder is predicted at temperatures below the transition. Although some evidence for ordering of ice VI has been observed in experiments, a low-temperature proton ordered phase has not been identified experimentally.