A simple n-state model for water

A simple n-state configurational excitation model which takes into account the presence of weakly connected pentamer units in liquid water is proposed. The model has features of both the “continuum” and “mixture” models. Calculations based on this model satisfactorily account for the important, diagnostic thermodynamic properties of water such as the density maximum, fraction of monomers and so on.     

A simple, efficient polarizable coarse-grained water model for molecular dynamics simulations

The development of coarse-grained (CG) models that correctly represent the important features of compounds is essential to overcome the limitations in time scale and system size currently encountered in atomistic molecular dynamics simulations. Most approaches reported in the literature model one or several molecules into a single uncharged CG bead. For water, this implicit treatment of the electrostatic interactions, however, fails to mimic important properties, e.g., the dielectric screening. Therefore, a coarse-grained model for water is proposed which treats the electrostatic interactions between clusters of water molecules explicitly. Five water molecules are embedded in a spherical CG bead consisting of two oppositely charged particles which represent a dipole. The bond connecting the two particles in a bead is unconstrained, which makes the model polarizable. Experimental and all-atom simulated data of liquid water at room temperature are used for parametrization of the model. The experimental density and the relative static dielectric permittivity were chosen as primary target properties. The model properties are compared with those obtained from experiment, from clusters of simple-point-charge water molecules of appropriate size in the liquid phase, and for other CG water models if available. The comparison shows that not all atomistic properties can be reproduced by a CG model, so properties of key importance have to be selected when coarse graining is applied. Yet, the CG model reproduces the key characteristics of liquid water while being computationally 1-2 orders of magnitude more efficient than standard fine-grained atomistic water models.     

A simple,reliable model of the bending mode of water

A simple, reliable model of the bending mode vibration of the water molecule based on the Morse oscillator is presented. The model yields accurate predictions of the rotation—vibration level structure in the various ν₂ bands as well as the geometric structure of the ground state.     

A transport model for swelling of polyelectrolyte gels in simple and complex geometries

A model for the swelling of polyelectrolyte gels in salt solutions is developed and solved numerically. The model accounts for the effect of network stress, osmotic pressure, and electrical potential on the species diffusive flux. The osmotic pressure and the network stress are derived from the Helmholtz free energy of the system that is the sum of mixing, elastic, and electrostatic components. One- and two-dimensional swelling in unconstrained and constrained geometries are simulated for a salt–solvent–polymer system. The transient and equilibrium fields of electrical potential, concentrations, deformation, and stress are obtained. Transient overshoots and non-uniformities in the residual profiles are predicted.     

An accurate and simple quantum model for liquid water

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.     

A simple model for multicomponent etching

We consider the situation where a multicomponent solid is etched using one or more acids. Of fundamental interest is the rate of surface etching but when this involves multicomponent surface reactions, it becomes unclear how the overall rate can be estimated. In this paper, we sketch a simple model designed to determine the effective etching rate by means of an atomic scale model of the etching process.     

A simple model to explain the complex kinetic behavior of epoxy/anhydride systems

A survey of the literature dealing with the kinetics of epoxy/anhydride polymerizations initiated by tertiary amines, shows inconsistencies in results reported by several authors. Both first-order and autocatalytic expressions have been used to fit experimental results. In the former case, significantly different values of apparent activation energies were found in isothermal and nonisothermal experiments. A simple kinetic model is proposed to explain these inconsistencies, based on the following steps: (a) a reversible reaction transforming an inactive initiator species into an active one, (b) a propagation step, and (c) a chain transfer step regenerating the active initiator (step not relevant to the kinetic analysis). The simple model explains both the first-order and autocatalytic behaviors reported in the literature. It also leads to the experimental values of the apparent activation energies obtained under different conditions. It is also shown that isoconversional methods should not be applied to obtain fundamental kinetic parameters in systems where the reaction rate depends on the concentration of an active species that varies independently of the conversion of functional groups. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2799–2805, 1999     

A simple model for the structure of fractal aggregates

Structural properties of small aggregates containing up to 100 particles have been studied through detailed Monte Carlo cluster-cluster aggregation simulations in both diffusion-limited and reaction-limited conditions. First, the radius of gyration, the radius of the smallest sphere encompassing the cluster, and the particle-particle correlation function, g(r), have been computed based on the positions of all the particles in the cluster, and their fractal scaling has been analyzed. Then, an empirical model has been developed to simulate the g(r) function for aggregates of any size and used to determine the corresponding structural properties and scattering structure factors. Finally, in order to illustrate the application of the structural properties thus computed, two experiments on diffusion-limited aggregation have been performed, and the average scattering structure factors have been measured as a function of time using a small-angle light-scattering device. The obtained average scattering structure factors have been simulated using the Smoluchowski population balance equations, using the single aggregate structural properties and scattering structure factor predicted by the developed empirical g(r) model.     

A simple model for finitely extensible polymers

A simple model for the calculation of configurational and rheological properties of finitely extensible polymers in flow is introduced. The finite extensibility of the chain is incorporated into the common Rouse model by varying the spring constant such that a constant contour length is maintained for every flow strength. For elongational flow, a comparison with Monte Carlo simulations of a bead-rod chain with 100 links yields qualitative agreement. For shear flow, this model predicts non-Newtonian flow behaviour.     

A simple model for a reaction surface

An analytical expression, which has some claim to be the simplest possible, is proposed for the potential governing a collinear reaction. It shows the desired qualitative features but, with only one available parameter, cannot fit a given surface accurately everywhere. The quality of fitting attainable is shown using the surface for the O + H₂ reaction.Because of the simple form of this expression, it is possible to make broad generalizations about such reactions. From a plausible assumption about the parameter value the energy barrier and the transition state geometry can be predicted. These barriers agree well with those suggested by Johnston and Parr for hydrogen transfer reactions.     

A simple adsorption model for ionic surfactants

In the past, few theoretical attempts have been made to describe quantitatively the adsorption of ionic surfactants at liquid interfaces. Well-known adsorption isotherms due to Frumkin or Hill–de Boer cannot respond to the specific electrostatic and geometric properties of the surfactant molecules. Our approach is based on a combination of the Gouy–Chapman theory with a modified Frumkin isotherm. The modification implies that the system is free to choose an optimal head group area and an optimal arrangement of the surfactant molecules in the interface as a function of bulk concentration. Interaction energies between neighbouring adsorbed surfactant molecules and between surfactant and water molecules are taken into consideration. The minimum of the Gibbs free energy of the system is equivalent to a minimal interfacial tension. Thus, the thermodynamically stable isotherm can be obtained as the lower envelope of the family of σ versus ln c isotherms resulting from different choices of the model parameters, including the area per molecule. According to the Gibbs equation, the Γ versus ln c adsorption isotherm is obtained as the derivative of this envelope. By variation of the model parameters, the envelope of the calculated adsorption isotherms can be fitted to experimental data of the interfacial tension versus bulk concentration. A computer program is used to calculate the σ versus c and the Γ versus ln c curves as well as to fit the parameters. Received: 28 October 1999/Accepted: 8 February 2000     

A simple model for polysoaps' thread-like aggregates

The equilibrium polymerization, a model for one-dimensional reversible aggregates is used under conditions of theta and bad solvent to describe thread-like aggregates of polysoaps. In two dimensions, the aggregate size distribution decreases always more slowly than an exponential distribution and the dependence of the mean aggregate size L on the density φ and end-cap energy E of the polysoap cylindrical micelle is of the form L[φexp(E/KT)]^δ with δ<1/2. On the other hand, in three dimensions in the bad solvent regime, the dependence of L on φ becomes exponential explaining the high φ dependence of the viscosity in experimental results.     

A simple theoretical model for dual phosphorescence

A simple theoretical model is presented to explain the observed anomalous dual phosphorescences of certain aromatic carbonyl compounds in some rigid media. The phenomenon of dual phosphorescence for large molecules violates the well-known Kasha rule stating that the emission can occur only from the lowest excited electronic state of a given multiplicity. For a small energy gap between the second triplet state (T₂) and the first triplet state (T₁), the sparse density of T₁ vibronic levels, isoenergetic with the T₂ vibrationless level, leads to a rather slow T₂ → T₁ radiationless process which is unable to quench the T₂ emission completely. Two cases of T₁ = ³nπ^*, T₂ = ³ππ^* and T₁ = ³ππ^*, T₂ = ³nπ^* are discussed at both the low-temperature and the high-temperature limits.     

A simple colorimetric device for rapid detection of Hg(2+) in water

A 'turn-on' fluorescent colorimetric device for Hg(2+) sensing was built using a dual light-emitting diode system. Fluorescence generated from a rhodamine derivative (RHD), an indicator for Hg(2+) sensing, was combined with a background red light, and the complex light was captured by a commercial charge coupled device camera or by the naked eye.     

A simple synthesis for 2-acetonylcyclododecanone

A simple method is proposed for the alkylation of cyclododecanone by propargyl halides under phase transfer catalysis conditions with the formation of 2-propargylcyclododecanone. The hydration of 2-propargylcyclododecanone upon catalysis by mercury compounds leads to either 14-methyl-13-oxabicyclo[10.3.0]-pentadeca-1(12),14-diene or 2-acetonylcyclododecanone depending on the reaction conditions. Both these compounds are also readily obtained from 2-(2-chloropropen-2-yl)cyclododecanone which readily forms upon the alkylation of cyclododecanone by 1,2-dichloropropene under phase transfer catalysis conditions.Translated from Izvestiya Akademil Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 963–965, April, 1991.     

A simple model system for the study of carbohydrate--aromatic interactions

A molecular scaffold was identified which enables the establishment of intramolecular interactions between a monosaccharide and a nearby phenyl ring. A group of molecules containing four different monosaccharides (glucose, galactose, N-acetyl-glucosamine, and N-acetyl-galactosamine) was synthesized and used to investigate the extent and nature of this carbohydrate-arene interaction, as well as the effect on the overall 3D structure of the molecules involved. The sugar-aromatic distance was evaluated by rigorous NMR studies supported by molecular modeling and found to be constant throughout the series, independent of the nature of the sugar and of the conformational behavior of the fragment connecting the two elements. Ab initio calculations at the B3LYP/DZV(2d,p) level of theory enable the analysis of the electronic nature of the interaction. The study shows that, given the opportunity, persistent intramolecular aromatic-sugar interactions can be established and can significantly influence overall molecular shape and energetics. These results have important implications in the design of structural mimics of oligosaccharides.     

A simple microscopic model for the dynamics of adhesive failure

We consider a microscopic model for the failure of soft adhesives in tension based on ideas of bond rupture under dynamic loading. By focusing on adhesive failure under loading at constant velocity, we demonstrate that bimodal curves of stress against strain may occur due to effects of finite polymer chain or bond length and characterize the loading conditions under which such bimodal behavior is observed. The results of this analysis are in qualitative agreement with experiments performed on unconfined adhesives in which failure does not occur by cavitation.     

Reactions of the simple nitroalkanes with hydroxide ion in water. Evidence for a complex mechanism

Conventional kinetic analysis of the reactions of nitromethane (NM), nitroethane (NE) and 2-nitropropane (2-NP) with hydroxide ion in water revealed that the reactions are complex and involve kinetically significant intermediates. Kinetic experiments at the isosbestic points where changes in reactant and product absorbance cancel indicate the evolution and decay of absorbance characteristic of the formation of reactive intermediates. The deviations from 1st-order kinetics were observed to increase with increasing extent of reaction and in the reactant order: NM < NE < 2-NP. The apparent deuterium kinetic isotope effects for proton/deuteron transfer approach unity near zero time and increased with time toward plateau values as the reaction kinetics reach steady state. It is proposed that the initially formed preassociation complexes are transformed to more intimate reactant complexes which can give products by two possible pathways.     

A simple model for predicting the course of photochemical reactions

The possibility of building and using a simplified model with constant (time-invariant) reaction probabilities for rapid simulation of photochemical processes with the required reliability of the prediction has been shown. A relation between the probabilities of transformations and fundamental molecular characteristics (optical transition probabilities and quantum beat frequencies referring to a nonradiative reaction transition) that can be quantitatively determined with a good degree of certainty has been revealed. For monomolecular isomerization reactions as an example, the attainable level of the accuracy of prediction by the simple model has been estimated, which has been shown to be ～10% in most cases. It is important that the prediction of the order of magnitude of the key characteristics of photochemical processes, such as quantum yield and the reaction rate, is definitely correct as is required in most applications of photochemistry.