Lattice specific heat of carbon nanotubes

The lattice specific heat in carbon nanotubes is evaluated within the microscopic model proposed by Mahan and Jeon, published in the Physical Review B, in 2004. Phonons are considered for single wall carbon nanotubes in armchair configuration. As expected, low temperature and high temperature regions show different behaviour of specific heat. Carbon nanotubes are also displaying a very interesting lattice transport depending on the tube diameter, with high thermal conductivities for small diameters.     

Lattice gas 2D/3D equilibria: chemical potentials and adsorption isotherms with correct critical points

A priori information is used to derive the chemical potential as a function of density and temperature for 2D and 3D lattice systems. The functional form of this equation of state is general in terms of lattice type and dimensionality, though it contains critical temperature and critical density as parameters which depend on lattice type and dimensionality. The adsorption isotherm is derived from equilibrium between two-dimensional and three-dimensional phases. Theoretical predictions are in excellent agreement with grand canonical Monte Carlo simulations.     

Model studies in heterogeneous catalysis at the microscopic level: from the structure and composition of surfaces to reaction kinetics

Heterogeneous catalysis is one of the fields of modern technology, in which a characterization of structural and chemical properties of solid surfaces at the microscopic level is of enormous importance. For a long time, such insights have been precluded by the complexity of most catalytically active materials. Recently, substantial progress has been made, however, toward a microscopic-level understanding of complex catalyst surfaces. We discuss the driving factors for these advancements, which are based on the development of new well-defined model systems as well as on advances in experimental technology and theory. Scrutinizing the example of planar model catalysts, we identify the process of linking structural and chemical information to microscopic reaction kinetics as a particular challenging aspect of today’s work. We review the kinetic effects which may have an influence on the reaction kinetics on complex surfaces. As an example how structural and kinetic information can be correlated at the microscopic level we discuss the case of surface oxidation and oxygen induced restructuring of Pd nanoparticles as studied by molecular beam methods.     

Exact solution of a RNA-like polymer model on the Husimi lattice

We investigate a two-tolerant polymer model on the square Husimi lattice, which aims at describing the properties of RNA-like macromolecules. We solve the model in a numerically exact way, working out the grand-canonical phase diagram, both with and without taking into account the stacking effect. Besides a nonpolymerized phase, we observe two different polymerized phases characterized by a lower or higher density of doubly visited lattice bonds. The system exhibits three qualitatively different regimes, as a function of the monomer chemical potential. Below some T1 temperature and above some T2 temperature, the transition to the nonpolymerized phase is continuous, whereas, in the (T1,T2) temperature range, the transition is first order. In the dilute-solution limit, the high temperature regime corresponds to a swollen ("coil") state, the intermediate regime to a moderately collapsed ("molten") state, with a small fraction of paired segments, and the low temperature regime to an almost fully paired ("native") state. The molten state ends in a tricritical (Theta-like) transition at high temperature and in a critical end point at low temperature. Upon increasing the stacking energy parameter, the temperature range of the molten state turns out to be progressively reduced but never completely removed.     

Chemical sensor based on nonlinearity: principle and application.

Novel chemical sensors based on a time-dependent nonlinear response are reviewed. The strategy is to artificially mimic information transduction in living organisms. In taste and olfaction, information of chemical structure and concentration is transformed into nervous impulses in the nervous cell, i.e., time-dependent multi-dimensional information. Because the excitation and pulse generation in the nervous cell are typically nonlinear phenomena, it may be worthwhile to utilize the nonlinearity as the multi-dimensional information for molecular recognition. The principle of a "nonlinear" sensor is that a sinusoidal modulation is applied to a system, and the output signal is analyzed. The output signal of the sensor is characteristically deformed from the sinusoidal input depending on the chemical structure and concentration of the chemical stimuli. The characteristic nonlinear responses to chemical stimuli are discussed in relation to the kinetics of chemical compounds on the sensor surface. As a practical application, we introduced electrochemical sensors based on the differential capacitance, semiconductor gas sensors under the application of sinusoidal temperature or diffusion change, and a chemical sensor based on the spatio-temporal information. We demonstrated that mutli-dimensional information based on nonlinearity can provide quite useful information for the analysis of chemical species, even in the presence of another analyte or an interference with a single detector.     

A microscopic model for the fluctuations of local field and spontaneous emission of single molecules in disordered media.

We develop a microscopic model to describe the observed temporal fluctuations of the fluorescence lifetime of single molecules embedded in a polymer at room temperature. The model represents the fluorescent probe and the macromolecular matrix on the sites of a cubic lattice and introduces voids in the matrix to account for its mobility. We generalize Lorentz's approach to dielectrics by considering three domains of electrostatic interaction of the probe molecule with its nanoenvironment: (1) the probe molecule with its elongated shape and its specific polarizability, (2) the first few solvent shells with their discrete structure and their inhomogeneity, (3) the remainder of the solvent at larger distances, treated as a continuous dielectric. The model is validated by comparing its outcome for homogeneous systems with those of existing theories. When realistic inhomogeneities are introduced, the model correctly explains the observed fluctuations of the lifetimes of single molecules. Such a comparison is only possible with single-molecule observations, which provide a new access to local field effects.     

Deformability of adsorbents during adsorption and principles of the thermodynamics of solid-phase systems

A microscopic theory of adsorption, based on a discrete continuum lattice gas model for noninert (including deformable) adsorbents that change their lattice parameters during adsorption, is presented. Cases of the complete and partial equilibrium states of the adsorbent are considered. In the former, the adsorbent consists of coexisting solid and vapor phases of adsorbent components, and the adsorbate is a mobile component of the vapor phase with an arbitrary density (up to that of the liquid adsorbate phase). The adsorptive transitioning to the bound state changes the state of the near-surface region of the adsorbent. In the latter, there are no equilibrium components of the adsorbent between the solid and vapor phases. The adsorbent state is shown to be determined by its prehistory, rather than set by chemical potentials of vapor of its components. Relations between the microscopic theory and thermodynamic interpretations are discussed: (1) adsorption on an open surface, (2) two-dimensional stratification of the adsorbate mobile phase on an open homogeneous surface, (3) small microcrystals in vacuum and the gas phase, and (4) adsorption in porous systems.     

Numerical investigation of the elastic scattering of hydrogen (isotopes) and helium at graphite (0001) surfaces at beam energies of 1 to 4 eV using a split-step Fourier method

We report simulations of the elastic scattering of atomic hydrogen isotopes and helium beams from graphite (0001) surfaces in an energy range of 1–4 eV. To this aim, we numerically solve a time-dependent Schrödinger equation using a split-step Fourier method. The hydrogen- and helium-graphite potentials are derived from density functional theory calculations using a cluster model for the graphite surface. We observe that the elastic interaction of tritium and helium with graphite differs fundamentally. Whereas the wave packets in the helium beam are directed to the centers of the aromatic cycles constituting the hexagonal graphite lattice, they are directed toward the rings in case of the hydrogen beams. These observations emphasize the importance of swift chemical sputtering for the chemical erosion of graphite and provide a fundamental justification of the graphite peeling mechanism observed in molecular dynamics studies. Our investigations imply that wave packet studies, complementary to classical atomistic molecular dynamics simulations open another angle to the microscopic view on the physics underlying the sputtering of graphite exposed to hot plasma.     

Chemical input multiplicity facilitates arithmetical processing

We describe the design and function of a molecular logic system, by which a combinatorial recognition of the input signals is utilized to efficiently process chemically encoded information. Each chemical input can target simultaneously multiple domains on the same molecular platform, resulting in a unique combination of chemical states, each with its characteristic fluorescence output. Simple alteration of the input reagents changes the emitted logic pattern and enables it to perform different algebraic operations between two bits, solely in the fluorescence mode. This system exhibits parallelism in both its chemical inputs and light outputs.     

Pressure-induced local structure distortions in Cu(pyz)F2(H2O)2

We employed infrared spectroscopy along with complementary lattice dynamics and spin density calculations to investigate pressure-driven local structure distortions in the copper coordination polymer Cu(pyz)F(2)(H(2)O)(2). Here, pyz is pyrazine. Our study reveals rich and fully reversible local lattice distortions that buckle the pyrazine ring, disrupt the bc-plane O-H···F hydrogen-bonding network, and reinforce magnetic property switching. The resiliency of the soft organic ring is a major factor in the stability of this material. Interestingly, the collective character of the lattice vibrations masks direct information on the Cu-N and Cu-O linkages through the series of pressure-induced Jahn-Teller axis switching transitions, although Cu-F bond softening is clearly identified above 3 GPa. These findings illustrate the importance of combined bulk and local probe techniques for microscopic structure determination in complex materials.     

On one dimensional chemical diode and frequency generator constructed with an excitable surface reaction

The oxidation of carbon monoxide on a Pt(110) surface is considered as a medium for chemical information processing in which bits of information are represented by traveling pulses of high oxygen coverage. Using numerical simulations for a model of CO oxidation we demonstrate that in such system one dimensional chemical signal diode can be realized by setting a proper profile of temperature. We also show that a pulse splitting can occur on a temperature inhomogeneity. The phenomenon of pulse splitting can be used to construct one dimensional generator of a train of pulses with adjustable frequency.     

Towards a microscopic theory of the modulus of elasticity in crystalline covalent materials and a survey of potential superhard materials

The present report is an account of the generalization of the dynamic elasticity theory earlier proposed by Bucknum et al. and applied to the cubic diamond and tetragonal glitter lattices. It describes a theory of elasticity in which the elasticity moduli are based upon the microscopic constants of the various structure-types. Such microscopic constants include the force constants of the chemical bonds in the unit of pattern of the material, its associated lattice parameters, and the elastic chemical bond deformation parameters of the material. In developing the outward features of the dynamic elasticity model, it is shown that an integral over the force density in the unit cell of a given material; where the force is modeled based upon the elastic deformation forces of the chemical bonds in the unit of pattern of the material, and the volume is written as a function of the deformations taking place inside the unit cell of the material; generates the terms for calculating its modulus of elasticity at pressure, in components, that are directed along the principal axes of the unit cell. Several potential solutions to the problem of superhardness are discussed and illustrated.     

Thermoelectric power of superionic conductors

A technique for the calculation of the thermoelectric power in many-particle systems exhibiting hopping conduction is presented. It is shown that the combination of thermopower and conductivity data provides very useful information about the microscopic nature of the ion hopping process in solid electrolytes. There are two main qualitative features of the transport data. In most systems the heat of transport (determined from the thermopower) and the activation energy for conduction are nearly equal, and in systems exhibiting lattice gas order-disorder transitions, these parameters may change across the phase boundary. An extended polaron lattice gas model is presented which is consistent with these features of the data and which allows a determination of the relative strengths of static barrier and polaron effects on the hopping. The results of the model suggest that polaron coupling is relatively small in most materials except for those based on organic halides.     

Discrete models for chemically reacting systems

Nonequilibrium spatially distributed chemically reacting systems are usually described in terms of reaction-diffusion equations. In this article, a hierarchy of discrete models is studied that show similar spatio-temporal structure and can be used to explore the complex phenomena occurring in these systems. We consider cellular automaton models where space, time and chemical concentrations are discrete and the dynamics is embodied in a simple updating rule, coupled map lattices where space and time are discrete variables but chemical concentrations are continuous and the dynamics is given by a nonlinear function and, lastly, lattice gas cellular automaton models that view the system on a microscopic or mesoscopic level where space, time and particle velocities are discrete.     

Mean field kinetic theory for a lattice gas model of fluids confined in porous materials

We consider the mean field kinetic equations describing the relaxation dynamics of a lattice model of a fluid confined in a porous material. The dynamical theory embodied in these equations can be viewed as a mean field approximation to a Kawasaki dynamics Monte Carlo simulation of the system, as a theory of diffusion, or as a dynamical density functional theory. The solutions of the kinetic equations for long times coincide with the solutions of the static mean field equations for the inhomogeneous lattice gas. The approach is applied to a lattice gas model of a fluid confined in a finite length slit pore open at both ends and is in contact with the bulk fluid at a temperature where capillary condensation and hysteresis occur. The states emerging dynamically during irreversible changes in the chemical potential are compared with those obtained from the static mean field equations for states associated with a quasistatic progression up and down the adsorption/desorption isotherm. In the capillary transition region, the dynamics involves the appearance of undulates (adsorption) and liquid bridges (adsorption and desorption) which are unstable in the static mean field theory in the grand ensemble for the open pore but which are stable in the static mean field theory in the canonical ensemble for an infinite pore.     

Relation of the verwey transition in magnetite to an order-disorder transition of strongly correlated electrons

The principal features of the Verwey transition in magnetite have been simulated by adopting elements of order-disorder theory. In certain limiting cases we obtain the model of Strässler and Kittel which had previously been used to rationalize the electronic and thermodynamic properties of magnetite. According to the present microscopic model the discontinuous Verwey transition in magnetite is driven by a change in a highly correlated electron system with temperature from a charge-ordered small-polaron state associated with local lattice deformations to a disordered state in which electrons resonate between Fe²⁺ and Fe³⁺ ions located on the octahedral cationic sites.     

Mechanical manipulation of molecular lattice parameters in smectic elastomers

Smectic liquid crystalline elastomers (SLCE) represent unique materials that combine a 1-D molecular lattice arrangement and orientational order with rubber-elasticity mediated by a polymer network. Such materials may exhibit large thermo-mechanical, opto-mechanical and electro-mechanical effects, due to the coupling of macroscopic sample geometry and microscopic structural features. It is shown that the molecular layer dimensions in the smectic phases can be influenced reversibly by macroscopic strain of the material. We present a microscopic model on the basis of experimental results obtained by mechanical dilatation measurements, optical interferometry, X-ray scattering, (13)C NMR, FTIR and polarizing microscopy data. The model gives an explanation of the controversial results obtained in different types of smectic elastomers.     

Temperature dependence of the configurational free energy of a branched polymer

We consider a lattice model of branched polymers in dilute solution in which the polymer is modelled as an animal, weakly embeddable in the (simple cubic) lattice. In order to model the effect on the thermodynamic properties of changing the temperature or the quality of the solvent, we include an energy associated with the number of nearneighbour contacts between pairs of vertices of the animals. We show that the configurational free energy of the animal is a continuous function of the temperature and derive rigorous upper and lower bounds on the temperature dependence of the free energy. Finally, we comment on similarities between these results and corresponding ones for a model in which the energy is associated with the cyclomatic index of the animal.     

Statistical Thermodynamic Properties of Linear Protein Solutions

The thermodynamic properties of linear protein solutions are discussed by a statistical me-chanics theory with a lattice model. The numerical results show that the Gibbs function of the solution decreases, and the protein chemical potential is enhanced with increase of the protein concentration for dilute solutions. The influences of chain length and temperature on the Gibbs function of the solution as well as the protein chemical potential are analyzed.As an application of the theory, the chemical potentials of some mutants of type I antifreeze proteins are computed and discussed.     

A contribution to non-equilibrium chemical kinetics. II. Strongly non-equilibrium “hot” reactions in liquids and solids

The method proposed in part I for non-equilibrium chemical kinetics is applied to processes provoked by non-equilibrium assemblies of energetic particles in liquids and solids. The movement of such an energetic particle belonging to a certain energy group is considered as a stochastic process when the direction of the velocity is changed stochastically at each step. On the ground of this consideration a simplified model of such a process is introduced: the stochastic movement of a particle is replaced by the deterministic movement of the corresponding quasi-particle having parameters determined through corresponding averages of the stochastic process. By use of this model, group constants of kinetic equations of our abovementioned work were expressed through parameters of microscopic processes in solids and liquids, and systems of non-equilibrium chemical kinetics' equations were written for different case. The proposed approach also permits us to consider the non-equilibrium of the crystalline lattice created by energetic particles. “Hot spot” reactions were considered as an example and a method to distinguish between direct and “hot spot” reactions was indicated. The proposed approach and obtained kinetic equations can be applied to recoil atoms (ions), fission products, hot particles produced in radiation chemistry, photochemistry, by laser beams, flash-photolysis etc. The destruction of the crystalline lattice by laser beams can also be considered by use of these equations.