Dynamical and statistical effects of the intrinsic curvature of internal space of molecules

The Hamilton dynamics of a molecule in a translationally and/or rotationally symmetric field is kept rigorously constrained in its phase space. The relevant dynamical laws should therefore be extracted from these constrained motions. An internal space that is induced by a projection of such a limited phase space onto configuration space is an intrinsically curved space even for a system of zero total angular momentum. In this paper we discuss the general effects of this curvedness on dynamics and structures of molecules in such a manner that is invariant with respect to the selection of coordinates. It is shown that the regular coordinate originally defined by Riemann is particularly useful to expose the curvature correction to the dynamics and statistical properties of molecules. These effects are significant both qualitatively and quantitatively and are studied in two aspects. One is the direct effect on dynamics: A trajectory receives a Lorentz-like force from the curved space as though it was placed in a magnetic field. The well-known problem of the trapping phenomenon at the transition state is analyzed from this point of view. By showing that the trapping force is explicitly described in terms of the curvature of the internal space, we clarify that the physical origin of the trapped motion is indeed originated from the curvature of the internal space and hence is not dependent of the selection of coordinate system. The other aspect is the effect of phase space volume arising from the curvedness: We formulate a general expression of the curvature correction of the classical density of states and extract its physical significance in the molecular geometry along with reaction rate in terms of the scalar curvature and volume loss (gain) due to the curvature. The transition state theory is reformulated from this point of view and it is applied to the structural transition of linear chain molecules in the so-called dihedral angle model. It is shown that the curvature effect becomes large roughly linearly with the size of molecule.     

Fine Structure of Meniscus of a Wetting Liquid

Equilibrium of a capillary meniscus near a wetting film on a solid in a gravitational field is considered. Unlike previous studies, the present study proves that the fine meniscus structure in a gravitational field is a universal feature—it takes place in a wide variety of problems. In the general case, the capillary meniscus is at a certain distance from the wetting film and does not intersect it. The relation for the minimum distance from the arbitrary meniscus to the solid generalizes the Derjaguin formula for a flat slit. An equation that optimally approximates the meniscus with due account of the contribution of the meniscus/film transition region is derived. A refined solution to the problem of a meniscus on a vertical plate is derived within the perturbation theory. Both gravity and nonuniformity of the vertical static film above a capillary–gravitational meniscus do not affect the minimum distance (the influence is less than 0.0001). A general method for solving sophisticated problems of capillary equilibrium in gravitational field is proposed.     

Investigation of some modes of flat-bed chromatography

A comparison of different chromatographic methods is presented: column liquid chromatography (CLC), thin layer chromatography (TLC), and continuous-elution flat-bed chromatography (CEFBC), which is in fact a combination of the first two methods. In CEFBC a sample is applied to a sorbent layer in a steady flow of eluent, and the components are detected directly on the layer, or immediately upon leaving it, during the separation process. It is shown that evaluation of the separation processes in CEFBC is best accomplished in terms of the parameters applicable in CLC. The reproducibility of the analytical results obtained by CEFBC is better than in the case of TLC by a factor of 6 to 10, and approaches that known for CLC.     

The evolution of nonequilibrium laser plasma of metals with the formation of structures

Processes in a plasma formed by the evaporation of material by middle power laser radiation on a metallic surface are analyzed. In the regime considered the laser radiation is not absorbed by a metallic plasma and the radiation energy is spent in the main for the atomic evaporation. As a result of the plasma relaxation, hard metallic particles of sizes of the order of 10 nm are formed. They are joined in fractal aggregates of micron sizes, and fractal aggregates may be joined in aerogel-like structures of centimeters sizes. Such a laserplasma is an example of a plasma whose evolution leads to fractal object formation. A fireball is considered as a fractal object formed as a result of the evolution of an evaporated plasma. The considered object with aerogel-like structure that is formed in a gas has both scientific and practical interest.     

A study of the reproducibility of analytical balances

The variation of balance rest point reproducibility over a wide range of sensitivities is surveyed. At low sensitivities, the reproducibility in scale units is a constant. The weighing reproducibility in milligram units in this region is limited by the readability of the scale and may be improved by increasing balance sensitivity or replacing the regular scale with a micro scale and magnifier. As the sensitivity is increased above a certain limit, control of milligram reproducibility passes from scale readability to the mechanical error of the balance. At high sensitivities, reproducibility in milligram units is practically constant and this constant is a criterion of the mechanical character of the balance.     

Effect of the sequence of the introduction of foreign substances on the action of papain

Summary In general, aniline, aniline hydrochloride, aniline sulfate, and triethylamine act as inhibitors in the hydrolysis of casein or of a suspension of flour from grain of Cicer arietinum by means of papain. The order in which the enzyme and the substrate is added to the inhibitor often has a significant effect. As a rule, there is a greater retardation when the enzyme is added last to a complex of the substrate and the inhibitor.     

Recombination of ions of a dense ion plasma in a fluorine atmosphere

A new effect leading to the slowing of recombination in a weakly nonideal ion plasma is considered. The solvation of ions is included in the explanation of the results from studying a gas discharge afterglow in a fluorine atmosphere. It is shown that recombination in such a system is slowed in comparison to the standard relationships for ideal plasma. The formation and composition of cluster ions in such a medium are considered. The relationship between the variation in the kinetics of recombination and the course of the process according to a complicated mechanism with the intermediate formation of metastable cluster pairs is established. A quantitative model is built and a formula allowing us to describe the recombination rate over a wide range of parameters of the medium is obtained. It is shown that the proposed model is in good agreement with the experimental data.     

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.     

Review of non-reactive and reactive wetting of liquids on surfaces

Wettability is a tendency for a liquid to spread on a solid substrate and is generally measured in terms of the angle (contact angle) between the tangent drawn at the triple point between the three phases (solid, liquid and vapour) and the substrate surface. A liquid spreading on a substrate with no reaction/absorption of the liquid by substrate material is known as non-reactive or inert wetting whereas the wetting process influenced by reaction between the spreading liquid and substrate material is known as reactive wetting. Young's equation gives the equilibrium contact angle in terms of interfacial tensions existing at the three-phase interface. The derivation of Young's equation is made under the assumptions of spreading of non-reactive liquid on an ideal (physically and chemically inert, smooth, homogeneous and rigid) solid, a condition that is rarely met in practical situations. Nevertheless Young's equation is the most fundamental starting point for understanding of the complex field of wetting. Reliable and reproducible measurements of contact angle from the experiments are important in order to analyze the wetting behaviour. Various methods have been developed over the years to evaluate wettability of a solid by a liquid. Among these, sessile drop and wetting balance techniques are versatile, popular and provide reliable data. Wetting is affected by large number of factors including liquid properties, substrate properties and system conditions. The effect of these factors on wettability is discussed. Thermodynamic treatment of wetting in inert systems is simple and based on free energy minimization where as that in reactive systems is quite complex. Surface energetics has to be considered while determining the driving force for spreading. Similar is the case of spreading kinetics. Inert systems follow definite flow pattern and in most cases a single function is sufficient to describe the whole kinetics. Theoretical models successfully describe the spreading in inert systems. However, it is difficult to determine the exact mechanism that controls the kinetics since reactive wetting is affected by a number of factors like interfacial reactions, diffusion of constituents, dissolution of the substrate, etc. The quantification of the effect of these interrelated factors on wettability would be useful to build a predictive model of wetting kinetics for reactive systems.     

Effect of the nature of a porogen on the porous structure of monolithic polydivinylbenzene sorbents

In quartz capillaries, macroporous monolithic sorbents based on divinylbenzene are synthesized and their porous structure is studied via inverse size-exclusion-hydrodynamic chromatography. Either a single-component porogen (a higher alcohol) or a two-component porogen (a mixture of a higher alcohol and mesitylene) is used for the synthesis of monoliths. The removal of a solvent good for a polymer from a porogen results in an increase in the size of flow-through channels and a decrease in the free-space volume inside the monolith; this space is used for the separation of polymer sorbates (the working volume of a column). At the same time, the volume of micro- and mesopores in the monolith structure is practically independent of the content of the good solvent in the porogen. It is inferred that the good porogen plays an active role in formation of the macroporous structure of monoliths. The structure of monoliths obtained on the basis of the two-component porogen with the use of nonanol and mesitylene or toluene is optimum for the molecular-mass analysis of polymers.     

Self-assembly of polymer brushes in the presence of a surfactant: A system of strands

This theoretical study is focused on the formation of a cylindrical microstructure in a planar polymer brush in the presence of a surfactant. It is assumed that the brush may be nonuniform in the direction along the grafting plane and that there are regions with constant concentrations of monomer units and regions occupied only by the surfactant. The surfactant molecule is simulated by a dimer whose parts interact in a different manner with the monomer units of the polymer. At the interface between these regions, dimer molecules are oriented mainly perpendicularly to this interface and the surface tension is reduced. If the surface energy becomes negative, the formation of a structured brush is more favorable in terms of energy than that of a uniform brush. As a result, there may appear a cylindrical microstructure in which grafted macromolecules are united into strands perpendicular to the grafting plane. The stretching of macromolecules and their interaction with the solvent within the strands are described by the Alexander-de Gennes model, whereas the surface energy is calculated with allowance for the surface curvature of strands at a high degree of amphiphilicity of the surfactant molecules. It is shown that the arising strands have radii of the order of the surfactant-molecule length, while the number of macromolecules per strand is proportional to the surface density of their grafting. With an increase in the grafting density, the strand length increases initially, while the volume fraction of the polymer in a strand remains constant. Furthermore, strands start to shorten and their density grows. Structural characteristics are calculated as a function of the parameter characterizing the degree of amphiphilicity of the solvent molecules, their sizes, and their average energy of interaction with monomer units.     

Use of molecular properties in the one-dimensional model of nonadiabatic transitions

A systematic analysis of a diabatization method proposed in a recent publication is presented for the one-dimensional linear model of nonadiabatic transitions, and the method is extended to the exponential model. The asymptotic behavior of molecular properties is studied, and the usefulness of simple properties like the kinetic energy and multipole moments is examined in detail. The method is easy to use, and provides a reliable a posteriori procedure to deal with the existence of strong radial couplings between adiabatic states, when a program to calculate the radial couplings exactly is not available.     

Shear modulus of sintered 'house of cards'-like assemblies of crystals

A cell model of a 'house of cards'-like assembly of crystals is used for the study of the evolution of the shear modulus during sintering. The crystals are assumed to have a lozenge shape. The cell model takes different crystal-crystal contacts into account. The force needed to separate two sintered crystals is calculated using the minimum surface area (MSA) approximation. By varying the thickness, long axis, and short axis of the crystals, it is possible to make space-filing configurations which have a nonzero shear modulus at crystal volume fraction that can be as low as phi = 0.03. This is significantly lower than the volume fractions phi > 0.52 that are found in studies where the MSA approximation is applied to assemblies of spherical particles. It is found that sintering may cause a nonlinear volume fraction dependence of the shear modulus, which depends on the shape of the crystals, the type of crystal-crystal contacts, and the character of the crystal assembly. The calculated shear modulus is analyzed using the phenomenological expression (phi - phi0)beta, where phi0 represents the volume fraction at the start of sintering. The exponent beta is found to vary between 1 and 2. The interpretation of the shear modulus using a fractal model is also discussed.     

Dependence of the enthalpies of formation of glycylglycinate complexes of nickel(II) on the composition of a mixed water-dimethylsulfoxide solvent

The heat effects of the complexation reactions of nickel(II) with a glycylglycinate ion in a water-dimethylsulfoxide solvent in a range of compositions of 0.00–0.60 molar parts of dimethylsulfoxide (DMSO) (an ionic strength of 0.1 was maintained using sodium perchlorate) were determined by means of calorimetry at 298.15 K. It is established that the exothermicity of complexation reactions rises by the first two steps and falls upon the addition of a third glycylglycinate anion with an increase in the concentration of DMSO. It is shown that the formation of mono- and bis-glycylglycinate complexes of nickel(II) in a water-DMSO solvent is determined mostly by the enthalpic contribution. It is concluded that the formation of tris-ligand complexes is more associated with the entropic contribution.     

Determination of the concentration dependence of polyelectrolyte diffusion coefficients by application of the Boltzmann gradient method

The concentration dependence of a polyelectrolyte diffusion coefficient in aqueous low salt solution (KCl, 1 mM) is determined from a single dynamic gradient experiment. The Boltzmann method is applied to calculate the diffusion coefficient. A special diffusion cell is constructed that minimizes aberrations in the optical detection of the polyion concentration profile. Bovine serum albumin (BSA) is chosen as a model polyion. To get information about the diffusion process down to very small polyion concentrations, the BSA molecule is fluorescently labeled. The fluorescence intensity is used as a measure of the polyion concentration. The change of the polyion net charge caused by labeling is discussed. The cell is illuminated by an LED, and the fluorescence intensity profile is detected by a CCD camera. Experiments at 5 and 17 degrees C show that the diffusion coefficient of labeled BSA remains constant in the very low polyion concentration range below a threshold of about 1.5 g/l. This is in contradiction to the linear concentration dependence of polyion diffusion coefficients at very low concentrations often postulated in the literature without reference to direct experimental evidence. Our finding is confirmed by dynamic light scattering experiments published recently. An explanation for this behavior based on a modified Donnan osmotic compressibility approach is given.     

剪切均匀性对流动诱导等规聚丙烯结晶的影响

固定应变和最终应变速率,采用瞬时和缓慢2种电机加速方式对样品施加剪切,研究了流场加载模式对样品流变和结晶行为的影响.实验结果显示缓慢加速能够消除剪切过程中流场的非均匀性,使样品取向度增加,提高流场对聚合物熔体的作用效果.同时,流动诱导结晶对于加速时间有依赖性.对于速率为17.7 s-1的剪切,加速时间为1 s时,熔体流动均匀且流动诱导的晶体取向最强,短加速时间(0.5 s)和长加速时间(1.5 s)样品的流动诱导结晶效果都弱于加速时间为1 s的样品.但是,对于不同剪切速率,其对应的最优加速时间不同.对于流动诱导结晶来说,加速时间应当作为一个重要参数来考虑,其背后的真实物理含义还需要进一步研究来说明.     

Placement of medium-sized molecular fragments into active sites of proteins

Summary We present an algorithm for placing molecular fragments into the active site of a receptor. A molecular fragment is defined as a connected part of a molecule containing only complete ring systems. The algorithm is part of a docking tool, called FlexX, which is currently under development at GMD. The overall goal is to provide means of automatically computing low-energy conformations of the ligand within the active site, with an accuracy approaching the limitations of experimental methods for resolving molecular structures and within a run time that allows for docking large sets of ligands. The methods by which we plan to achieve this goal are the explicit exploitation of molecular flexibility of the ligand and the incorporation of physicochemical properties of the molecules. The algorithm for fragment placement, which is the topic of this paper, is based on pattern recognition techniques and is able to predict a small set of possible positions of a molecular fragment with low flexibility within seconds on a workstation. In most cases, a placement with rms deviation below 1.0 Å with respect to the X-ray structure is found among the 10 highest ranking solutions, assuming that the receptor is given in the bound conformation.     

Startup of electrophoresis in a suspension of colloidal spheres

The transient electrophoretic response of a homogeneous suspension of spherical particles to the step application of an electric field is analyzed. The electric double layer encompassing each particle is assumed to be thin but finite, and the effect of dynamic electroosmosis within it is incorporated. The momentum equation for the fluid outside the double layers is solved through the use of a unit cell model. Closed‐form formulas for the time‐evolving electrophoretic and settling velocities of the particles in the Laplace transform are obtained in terms of the electrokinetic radius, relative mass density, and volume fraction of the particles. The time scale for the development of electrophoresis and sedimentation is significantly smaller for a suspension with a higher particle volume fraction or a smaller particle‐to‐fluid density ratio, and the electrophoretic mobility at any instant increases with an increase in the electrokinetic particle radius. The transient electrophoretic mobility is a decreasing function of the particle volume fraction if the particle‐to‐fluid density ratio is relatively small, but it may increase with an increase in the particle volume fraction if this density ratio is relatively large. The particle interaction effect in a suspension on the transient electrophoresis is much weaker than that on the transient sedimentation of the particles.     

Electrophoresis of a concentrated aqueous dispersion of non-Newtonian drops

The electrophoresis of a concentrated dispersion of non-Newtonian drops in an aqueous medium, which has not been investigated theoretically in the literature, is analyzed under conditions of low zeta potential and weak applied electric field. The results obtained provide a theoretical basis for the characterization of the nature of an emulsion and a microemulsion system. A Carreau fluid, which has wide applications in practice, is chosen for the non-Newtonian drops, and the unit cell model of Kuwabara is adopted to simulate a dispersion. The effects of the key parameters of a dispersion, including its concentration, the shear-thinning nature of the drop fluid, and the thickness of the double layer, on the electrophoretic behavior of a drop are discussed. In general, the more significant the shear-thinning nature of the drop fluid is, the larger the mobility is, and this effect is pronounced as the thickness of the double layer decreases. However, if the double layer is sufficiently thick, this effect becomes negligible. In general, the higher the concentration of drops is, the smaller the mobility is; however, if the double layer is either sufficiently thin or sufficiently thick, this effect becomes unimportant.     

Stability of two-dimensional growth of a packed body of proteins on a solid surface

Adsorption of proteins from the bulk is at times accompanied by a rearrangement which leads to the formation of closed packed bodies, that may or may not be crystalline. Mass transfer of protein molecules on a surface is modeled. Forced diffusion by van der Waals and electrostatic forces leads to segregation, which is eventually a different phase that is assumed to be thermodynamically favored. The net effective force in two-dimensions has been modeled approximately and shown to be much stronger and more long ranged than in the bulk: that is, under the same conditions, the protein molecules may not aggregate in the bulk they may aggregate on a surface. These forces have been used only indirectly but equivalently as an adsorption-desorption step at the interline. Eventually, a linear stability analysis of the growing body shows it to be unstable and would give rise to whiskers that are one molecule thick. This is what is observed experimentally. The conditions that give rise to the instability have been determined. The reverse case of rinsing of the protein molecules has also been studied experimentally and has been analyzed using the same mechanisms. Here it is seen that thicker inroads into the packed body cause the interline to take on a spongy appearance. It is conjectured that eventually islands will appear as seen in the experiments.