Constructing a multidimensional free energy surface like a spider weaving a web

Complete free energy surface in the collective variable space provides important information of the reaction mechanisms of the molecules. But, sufficient sampling in the collective variable space is not easy. The space expands quickly with the number of the collective variables. To solve the problem, many methods utilize artificial biasing potentials to flatten out the original free energy surface of the molecule in the simulation. Their performances are sensitive to the definitions of the biasing potentials. Fast‐growing biasing potential accelerates the sampling speed but decreases the accuracy of the free energy result. Slow‐growing biasing potential gives an optimized result but needs more simulation time. In this article, we propose an alternative method. It adds the biasing potential to a representative point of the molecule in the collective variable space to improve the conformational sampling. And the free energy surface is calculated from the free energy gradient in the constrained simulation, not given by the negative of the biasing potential as previous methods. So the presented method does not require the biasing potential to remove all the barriers and basins on the free energy surface exactly. Practical applications show that the method in this work is able to produce the accurate free energy surfaces for different molecules in a short time period. The free energy errors are small in the cases of various biasing potentials. © 2017 Wiley Periodicals, Inc.     

Hydrodynamic force on a microparticle approaching a wall in a nanoparticle dispersion: observation of a separation-dependent effective viscosity

Colloid probe atomic force microscopy was used to measure the hydrodynamic force exerted on a 30-μm-diameter silica particle being moved toward or away from a silica plate in aqueous dispersions of 22-nm-diameter silica nanoparticles (6 or 8 vol %). Upon comparing the measured force to predictions made using the well-known expression of Cox and Brenner (Cox, R. G.; Brenner, H. Chem. Eng. Sci.1967, 22, 1753-1777) assuming a constant viscosity equal to that of the bulk dispersion, the measured drag force was found to become significantly less than that predicted at smaller particle-plate separation distances (e.g., <500 nm). A recent theoretical paper by Bhattacharya and Blawzdziewicz (Bhattacharya, S.; Blawzdziewicz, J. J. Chem. Phys.2008, 128, 214704) predicted that in a solution of dispersed nanoparticles the effective viscosity characterizing the hydrodynamic force on the particle should vary from that of the solvent at contact to that of the bulk dispersion at large separations. By adjusting the viscosity in the Cox and Brenner expression to make the predicted hydrodynamic force match that measured (i.e., the effective viscosity), a curve showing these exact characteristics was obtained. The effective viscosity profile was not a function of particle speed, and changes in the effective viscosity extended to separation distances of as large as 2 μm (nearly 100 times the hard diameter of the nanoparticles). These results suggest that in the range of typical colloidal forces (on the order of 100 nm), the dynamics of particle motion in such systems are determined by the viscosity of the solvent and not that of the bulk dispersion.     

两嵌段共聚高分子链通过薄膜上纳米孑孔隙输运的研究

针对两嵌段高分子链的跨膜输运过程,分别给出与不同输运次序相对戍的高分子链的自由能,进而通过求解Fokker-Planck方程并在不同条件下对平均首次通过时间进行了数值计算.计算结果表明,当共聚高分子链由良溶剂区向不良溶剂区输运时,不能发生线团一链滴转变的链首先输运总是有利于整个高分子链的输运.而在给定输运次序的情况下,化学势、线团一链滴转变、共聚链的组成以及输运速率等因素对输运时间可产生显著影响.相关研究结果可为调控实际生物高分子链的输运时间提供可能的理论线索.     

Subdiffusion in a system with a thick membrane

We theoretically study subdiffusion in a system, in which homogeneous thick membrane separates two media; in each of them there are different subdiffusion parameters. Subdiffusion is described by the linear differential equations with fractional time derivative and the boundary conditions requiring that the ratio of substance concentrations on both sides of the membrane surface is constant in time. Starting with the Green’s functions derived for the considered system, we discuss the property of the concentrations found in the long time limit for the system where initially the membrane separates pure solvent from homogeneous solution.     

Wetting of a particle in a thin film

When a particle is placed in a thin liquid film on a planar substrate, the liquid either climbs or descends the particle surface to satisfy its wetting boundary condition. Analytical solutions for the film shape, the degree of particle immersion, and the downward force exerted by the wetting meniscus on the particle are presented in the limit of small Bond number. When line tension is significant, multiple solutions for the equilibrium meniscus position emerge. When the substrate is unyielding, a dewetting transition is predicted; that is, it is energetically favorable for the particle to rest on top of the film rather than remain immersed in it. If the substrate can bend, the energy to drive this bending is found in the limits of slow or rapid solid deflection. These results are significant in a wide array of disciplines, including controlled delivery of drugs to pulmonary airways, the probing of liquid film/particle interface properties using particles affixed to AFM tips and the positioning of small particles in thin films to create patterned media.     

Orientation of a nanocylinder at a fluid interface

A nanocylinder placed on a fluid interface can assume an end-on or side-on orientation, or it can immerse itself in the surrounding bulk phases. Any of these orientations can satisfy a mechanical force balance when the particle is small enough that gravitational effects are negligible. The orientation is determined by the surface energies of the fluid-solid, fluid-vapor, and vapor-solid surfaces. A comparison of the energy of each state allows phase diagrams to be defined in terms of the scaled aspect ratio x=2L/pir and the contact angle thetao, where L and r denote the nanocylinder length and radius, respectively. Line tension can also influence the orientations by changing the equilibrium contact angle theta and by increasing the energetic cost of the contact line. Phase diagrams accounting for positive line tensions Sigma are also constructed. These phase diagrams can be divided into two classes. In the first, over some range of x and Sigma, nanocylinders can be driven from side-on to end-on orientations with increasing Sigma. This transition terminates at a triple point where the side-on, end-on, and immersed energies are the same. In the second class, there is no triple point and, for a range of Sigma values, nanocylinders of all aspect ratios x prefer an end-on orientation. In all cases, for high enough Sigma, line tension drives a wetting transition similar to that already noted in the literature for spherical particles. The zero line tension predictions are compared favorably to experiment, in which functionalized gold nanowires made by template synthesis are spread at aqueous-gas interfaces, immobilized using a gel-fixation technique, and observed by scanning electron microscopy. The small aspect ratio particles (disks) were in an end-on configuration, while the longer nanowires were in a side-on orientation, in agreement with the theory.     

Cation-pi interactions of a thiocarbonyl group and a carbonyl group with a pyridinium nucleus

Attractive interactions between a thiocarbonyl group and a pyridinium nucleus, and between a carbonyl group and a pyridinium nucleus have been proven by (1)H and (13)C NMR studies, UV-vis spectral analyses, and X-ray crystallographic analyses of nicotinic amides 1 and 3, and pyridinium salts 2 and 4. Comparison of the Deltadelta values, which are the differences in the chemical shifts with reference compounds 5 or 6, showed that the absolute Deltadelta values of 2 and 4 are much larger than those of 1 and 3. In the UV-vis spectra, the n-->pi absorption of the C=S group of 2a exhibited a significant blue shift in CHCl(3). X-ray crystallographic analysis of 1-4 clearly showed that the C=S group of 2a and the C=O group of 4 are very close to the pyridinium moiety compared to the case of 1 and 3. In addition, the X-ray crystal packing structure of 2a showed the C=S group is sandwiched between two pyridinium rings. These experimental results strongly suggested the existence of attractive (C=S)...Py(+) and (C=O)...Py(+) interactions in solution and in crystal. The optimized geometries of 1 and 2 calculated at the HF/6-311G level are in good agreement with their X-ray geometries. MP2/6-311G calculations for the model systems of pyridinium salts 2 and 4 predicted that the electrostatic and induction energies are the major source of the attractive interactions. Since the larger contribution of electrostatic and induction interactions are characteristic features of cation-pi interactions, the (C=S)...Py(+) and (C=O)...Py(+) interactions would be classified as a cation-pi interaction.     

Influence of the electric field on a particle in a space with a disclination

We consider a quantum particle in a space with a linear topological defect, i.e., disclination. The effect of the uniform electric field in this space, on the particle, is shown to cause a translation of the wave function. In addition, the electric field is not found to be affected by the defect. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Impedance of a passive iron electrode in a solution containing a reducing agent

Frequency dependences of impedance of a passive iron electrode in 0.5 M Na₂SO₄ solutions with and without 0.01 M K₄[Fe(CN)₆] are obtained by a pulsed method and the Fourier transform. At 1–1000 Hz, the results in 0.5 M Na₂SO₄ satisfactorily agree with our previous results obtained by a lock-in method. With the [Fe(CN)₆]^4- ions present, the impedance decreases faster at lower frequencies. The impedance of the oxide film/solution interface relaxes longer the film impedance. These conclusions are similar to those obtained earlier.Translated from Elektrokhimiya, Vol. 41, No. 1, 2005, pp. 97–101.Original Russian Text Copyright © 2005 by Klyuev, Rotenberg, Batrakov.To the Centennial of B.N. Kabanov.     

Motion of a drop on a solid surface due to a wettability gradient

The hydrodynamic force experienced by a spherical-cap drop moving on a solid surface is obtained from two approximate analytical solutions and used to predict the quasi-steady speed of the drop in a wettability gradient. One solution is based on approximation of the shape of the drop as a collection of wedges, and the other is based on lubrication theory. Also, asymptotic results from both approximations for small contact angles, as well as an asymptotic result from lubrication theory that is good when the length scale of the drop is large compared with the slip length, are given. The results for the hydrodynamic force also can be used to predict the quasi-steady speed of a drop sliding down an incline.     

PHOTOSENSITIZING PROPERTIES OF BACTERIOCHLOROPHYLLIN a and BACTERIOCHLORIN a, TWO DERIVATIVES OF BACTERIOCHLOROPHYLL a

Abstract The photosensitizing properties of two water soluble derivatives of bacteriochlorophyll a , bacteriochlorophyllin a and bacteriochlorin a (lacking the central Mg-ion) were investigated and compared to those of hematoporphyrin derivatives. At physiological pH the oxygen consumption rate of histidine, tryptophan, dithiothreitol and guanosine upon illumination was 3 to 4 times higher when bacteriochlorin a was used as photosensitizer than when hematoporphyrin derivatives were used. Especially bacteriochlorin a proved to be an effective sensitizer for the killing of L929 cells. Because bacteriochlorin a has an absorption maximum at 765 nm in phosphate buffered saline (allowing a light penetration in tissue about ten times larger than at 630 nm) and a high molar absorption coefficient (32 000 M cm⁻¹) it has promising possibilities for the application in photodynamic therapy.     

Squeezing a helium nanodroplet with a Rydberg electron

We have investigated, by means of density functional theory, the structure of a "scolium", that is, an electron circulating around a positively charged 4He nanodroplet, temporarily prevented from neutralization by the helium-electron repulsion. The positive ion core resides in the center of the nanodroplet where, as a consequence of electrostriction, a strong increase in the helium density with respect to its bulk value occurs. The electron enveloping the 4He cluster exerts an additional electrostatic pressure which further increases the local 4He density around the ion core. We argue that under such pressure, sufficiently small 4He nanodroplets may turn solid. The stability of a scolium with respect to electron-ion recombination is investigated.     

Local pressure tensor of a simple fluid in a conelike cage of a solid

Asymptotic formulas are derived for distribution functions and components of the pressure tensor for a Van der Waals fluid in a conelike cage of a solid. The formulas describe the local behavior of the fluid far from the vertex of the cone and at rather large distances from solid walls. It is shown that, due to the symmetry of the system, three diagonal components and one off-diagonal component of the pressure tensor differ from zero. The effect of the deviation of conelike pore walls from a cylindrical shape on the appearance of a noticeable contribution to the local characteristics of the fluid in the pore is estimated.     

Thermal properties of a disc-like compound benzene-hexa-n-pentanoate: a precursor of a discotic mesogen

The heat capacity of a disk-like compound, benzene-hexa-n-pentanoate (BH5), a precursor of a discotic mesogen, has been measured by adiabatic calorimetry between 13 and 390 K. BH5 showed four different crystalline phases, but no liquid crystalline phase. Molar entropy and transition entropies were determined and compared with those of other homologues (BH6, BH7, and BH8). An odd-even effect with respect to the number of carbon atoms in the alkyl chain was observed for the cumulative entropies of the phase transitions occurring in the solid state. This effect is discussed by comparing with data for the n-alkanes. The molar entropies of the crystalline state, especially below 250 K, exhibited a peculiar 'pairing effect' between BH(2m- 1) and BH(2m), where m is an integer.     

Discontinuum between a thiolate and a thiol ligand

The effect of H-bond donation to the thiolate ligand of (eta(5)-C(5)H(5))Fe(CO)(2)SR (1) to give H-bond adducts (1 small middle dotHX) and eventually protonation to give [(eta(5)-C(5)H(5))Fe(CO)(2)(HSR)](+) (1H(+)()) has been investigated experimentally and computationally. The electronic structures of 1(R = Me), several derivatives of 1(R = Me) small middle dotHX, and 1(R = Me)H(+)() have been investigated using DFT (density functional theory) computational methods. As previously suggested, these calculations indicate the HOMO of 1 is Fedpi-Sppi antibonding and largely sulfur in character. The calculations indicate the electronic structure of 1 is not altered markedly by H-bond donation to the S center, but protonation results in a reorganization of the electronic structure of 1H(+)() and a HOMO that is largely metal in character. The reduction of Fe-S distances upon protonation of 1(R = Ph) to give 1(R = Ph)H(+)() small middle dotBF(4)()(-)() (2.282(2) and 2.258(2) A, respectively), as determined by single-crystal X-ray crystallography, also indicates diminished Fedpi-Sppi antibonding. Using the carbonyl stretching frequencies as a gauge of the donor ability of the thiolate ligand, we conclude that H-bonding has a continuous effect on the donor properties of the thiolate ligand of 1 (i.e., is a function of the pK(a) of the H-bond donor). A discontinuous effect results when the pK(b) of 1 is reached and the complex is protonated. For our study of 1, the maximal effect of H-bonding is about 30% of protonation. Because the position of acid-base equilibrium depends on the relative basicities of the thiolate ligand and the conjugate base of the H-bond donor (and the relative heats of solvation of the acids and their conjugate bases), a true continuum of effects can be anticipated only for systems that are pK-matched in their given environments. Thus, when the conjugate base of the H-bond donor is a stronger base than the thiolate ligand (as in the present case), H-bond donation has a relatively small effect, but protonation triggers a large, discontinuous effect on the electronic structure of 1.     

Capillary condensation in a geometrically and a chemically heterogeneous pore: a molecular simulation study

A computer simulation study has been carried out, using an extended Gibbs ensemble Monte Carlo technique, to examine the influence of so-called geometric and chemical disorder on the thermodynamic behavior of simple fluids confined in porous media. The technique allows the equilibrium coexistence of gas and liquid phases to be calculated in a single run. The phase diagram of Lennard-Jones fluid has been calculated in a perfectly cylindrical pore as a reference. Some disorder is then introduced in the porous material, first by spatially modifying the external potential of the initially cylindrical pore, to imitate the geometric disorder of a more realistic pore (undulation, constrictions, etc.) and second by modulating the amplitude of the same initially cylindrical potential to reproduce the energetic disorder of realistic pores due to chemical variations along it. It is shown that the chemical disorder has a much stronger effect on the phase diagram of the confined fluid. The complete adsorption/desorption isotherms are also calculated to help in understanding the large effects of chemical disorder.     

Electrophoresis of a rigid sphere in a Carreau fluid normal to a large charged disk

The electrophoresis of a rigid sphere in a Carreau fluid normal to a large disk is analyzed theoretically under the conditions of low surface potential and weak applied electric field. Previous analyses are extended to the case where a disk can be charged, and a more realistic electrostatic force formula is applied. We show that the qualitative behavior of a sphere depends largely on its distance from a disk, the thickness of double layer, and the nature of a fluid. In general, the presence of a disk has the effect of increasing the conventional hydrodynamic drag on a sphere, and a decrease in the thickness of the double layer surrounding a sphere has the effect of enhancing the shear-thinning effect. However, this might not be the case if a sphere is uncharged and a disk is charged, where the osmotic pressure field and the induced charge on the sphere surface can be significant. The shear-thinning effect is important only if the thickness of double layer is sufficiently thick. This result can play a significant role in practice such as in electrophoretic deposition, where the deposition electrode is charged and the fluid medium is usually of shearing-thinning nature.