Stimulated echoes and two-dimensional nuclear magnetic resonance spectra for solids with simple line shapes

Nuclear magnetic resonance (NMR) experiments on ion conductors often yield rather unstructured spectra, which are hard to interpret if the relation between the actual translational motion of the mobile species and the changes of the NMR frequencies is not known. In order to facilitate a general analysis of experiments on solids with such spectra, different models for the stochastic evolution of the NMR frequencies are considered. The treated models involve random frequency jumps, diffusive evolutions, or approximately fixed frequency jumps. Two-dimensional nuclear magnetic resonance spectra as well as stimulated-echo functions for the study of slow and ultraslow translational dynamics are calculated for Gaussian equilibrium line shapes. The results are compared with corresponding ones from rotational models and with experimental data.     

Modeling adsorption of colloids and proteins

Recent developments in the modeling of particle and protein adsorption kinetics on solid surfaces are discussed. Emphasis is focused on the coarse-grained methods, where protein molecules are treated as particles having a regular shape (spheres, spheroids) or a system of spherical beads of various sizes. Using such approaches hydrodynamic radii and diffusion coefficients of protein molecules are calculated in an exact way using the linear Stokes equation. Additionally, the surface blocking functions and jamming coverages for such molecule shapes are determined using the random sequential adsorption simulations. Theoretical results obtained in this way for various molecule shapes, including the bead models of fibrinogen are discussed. Knowing the jamming coverage and blocking functions one can formulate boundary conditions for bulk transport equations. Solutions of these equations for the convection and diffusion-controlled transport are presented. These theoretical predictions proved adequate for interpreting experimental data obtained for fibrinogen using AFM, ellipsometry and fluorescence methods. It is, therefore, concluded that these coarse grained approaches combined with solutions of the continuity equation can be efficiently used for quantitatively predicting protein adsorption kinetics for the time scale met under practical situations.     

Use of Nonlinear Frequency Response for Discriminating Adsorption Kinetics Mechanisms Resulting with Bimodal Characteristic Functions

One of the characteristic examples of the inability of the classical linear frequency response (FR) method to identify the correct kinetic mechanism is adsorption of some substances (p-xylene, 2-butane, propane or n-hexane) on silicalite-1. The linear FR resulted with bimodal FR characteristic functions, which fitted equally well to three different kinetic models: nonisothermal micropore diffusion, two independent isothermal diffusion processes, and an isothermal diffusion-rearrangement process. We show that the second order frequency response functions (FRFs), obtained from the nonlinear FR, can be used for discrimination among these three mechanisms. Starting from the nonlinear models, we derive the theoretical expressions for the first and second order FRFs corresponding to these three mechanisms and show that different shapes of the second order FRFs are obtained for each mechanism. This would enable identification of the real mechanism from nonlinear FR data.     

Combined electronic structure/molecular dynamics approach for ultrafast infrared spectroscopy of dilute HOD in liquid H2O and D2O

We present a new approach that combines electronic structure methods and molecular dynamics simulations to investigate the infrared spectroscopy of condensed phase systems. This approach is applied to the OH stretch band of dilute HOD in liquid D2O and the OD stretch band of dilute HOD in liquid H2O for two commonly employed models of water, TIP4P and SPC/E. Ab initio OH and OD anharmonic transition frequencies are calculated for 100 HOD x (D2O)n and HOD x(H2O)n (n = 4-9) clusters randomly selected from liquid water simulations. A linear empirical relationship between the ab initio frequencies and the component of the electric field from the solvent along the bond of interest is developed. This relationship is used in a molecular dynamics simulation to compute frequency fluctuation time-correlation functions and infrared absorption line shapes. The normalized frequency fluctuation time-correlation functions are in good agreement with the results of previous theoretical approaches. Their long-time decay times are 0.5 ps for the TIP4P model and 0.9 ps for the SPC/E model, both of which appear to be somewhat too fast compared to recent experiments. The calculated line shapes are in good agreement with experiment, and improve upon the results of previous theoretical approaches. The methods presented are simple, and transferable to more complicated systems.     

Intermolecular vibrational relaxation in liquids

The influence of intermolecular vibrational relaxation on dipole moment correlation functions, as obtained from IR band shapes, is discussed. It is explicitly shown that vibrational relaxation due to intermolecular interactions depends on the reorientational behaviour of the molecules in the liquid.Therefore, an a priori separation of the dipole moment correlation function into independent reorientational and vibrational factors is not generally possible. The implications for various procedures used to “correct” Raman and IR band shapes for vibrational relaxation are discussed.The expression derived for the intermolecular vibrational relaxation is used to calculate theoretically the effect of transition dipole-transition dipole coupling on dipole moment correlation functions.Experimental data obtained from isotopic dilution measurements support the interpretation of the isotopic dilution effect in terms of the transition dipole-transition dipole coupling.     

Simulation of droplet formation and coalescence using lattice Boltzmann-based single-phase model

A lattice Boltzmann method-based single-phase free surface model is developed to study the interfacial dynamics of coalescence, droplet formation and detachment phenomena related to surface tension and wetting effects. Compared with the conventional multiphase models, the lattice Boltzmann-based single-phase model has a higher computational efficiency since it is not necessary to simulate the motion of the gas phase. A perturbation, which is given in the same fashion as the perturbation step in Gunstensen's color model, is added to the distribution functions of the interface cells for incorporating the surface tension into the single-phase model. The assignment of different mass gradients along the fluid-wall interface is used to model the wetting properties of the solid surface. Implementations of the model are demonstrated for simulating the processes of the droplet coalescence, the droplet formation and detachment from ceiling and from nozzles with different shapes and different wall wetting properties.     

Quantum corrections to classical time-correlation functions: hydrogen bonding and anharmonic floppy modes

Several simple quantum correction factors for classical line shapes, connecting dipole autocorrelation functions to infrared spectra, are compared to exact quantum data in both the frequency and time domain. In addition, the performance of the centroid molecular dynamics approach to line shapes and time-correlation functions is compared to that of these a posteriori correction schemes. The focus is on a tunable model that is able to describe typical hydrogen bonding scenarios covering continuously phenomena from tunneling via low-barrier hydrogen bonds to centered hydrogen bonds with an emphasis on floppy modes and anharmonicities. For these classes of problems, the so-called "harmonic approximation" is found to perform best in most cases, being, however, outperformed by explicit centroid molecular dynamics calculations. In addition, a theoretical analysis of quantum correction factors is carried out within the framework of the fluctuation-dissipation theorem. It can be shown that the harmonic approximation not only restores the detailed balance condition like all other correction factors, but that it is the only one that also satisfies the fluctuation-dissipation theorem. Based on this analysis, it is proposed that quantum corrections of response functions in general should be based on the underlying Kubo-transformed correlation functions.     

A procedure for analysis of densitometric spectra

Computer-aided quantitative analysis of densitometric spectra is presented. The densitometric spectra are decomposed into component bands using the Powell and Marquardt minimizers. Several different functions for the component bands are utilized. It is shown that the densitometric spectra can be decomposed into component bands with high accuracy only if the proper shapes of the bands are chosen. The method described was used for quantitative analysis of densitometric spectra of DNA cleaved by neocarzinostatin. The procedure is general and can be applied to analyses of autoradiographic films and to direct scans of electrophoretic gels. It is shown that densitometric spectra which show highly overlapped bands are well approximated by asymmetric Cauchy and Gauss functions. Well separated densitometric bands which have substantial asymmetry can be fitted to more sophisticated shapes formed by combinations of symmetric and asymmetric Cauchy and Gauss functions. High accuracy fitting to asymmetric densitometric curves may only be achieved using the cosine function introduced by Mignot and Rondot, J. Appl. Cryst. 1976, 9,460-465.     

Effect of particle geometry on phase transitions in two-dimensional liquid crystals

Using a version of density-functional theory which combines Onsager approximation and fundamental-measure theory for spatially nonuniform phases, we have studied the phase diagram of freely rotating hard rectangles and hard discorectangles. We find profound differences in the phase behavior of these models, which can be attributed to their different packing properties. Interestingly, bimodal orientational distribution functions are found in the nematic phase of hard rectangles, which cause a certain degree of biaxial order, albeit metastable with respect to spatially ordered phases. This feature is absent in discorectangles, which always show unimodal behavior. This result may be relevant in the light of recent experimental results which have confirmed the existence of biaxial phases. We expect that some perturbation of the particle shapes (either a certain degree of polydispersity or even bimodal dispersity in the aspect ratios) may actually destabilize spatially ordered phases thereby stabilizing the biaxial phase.     

Statistical geometry of lattice chain polymers with voids of defined shapes: sampling with strong constraints

Proteins contain many voids, which are unfilled spaces enclosed in the interior. A few of them have shapes compatible to ligands and substrates and are important for protein functions. An important general question is how the need for maintaining functional voids is influenced by, and affects other aspects of proteins structures and properties (e.g., protein folding stability, kinetic accessibility, and evolution selection pressure). In this paper, we examine in detail the effects of maintaining voids of different shapes and sizes using two-dimensional lattice models. We study the propensity for conformations to form a void of specific shape, which is related to the entropic cost of void maintenance. We also study the location that voids of a specific shape and size tend to form, and the influence of compactness on the formation of such voids. As enumeration is infeasible for long chain polymer, a key development in this work is the design of a novel sequential Monte Carlo strategy for generating large number of sample conformations under very constraining restrictions. Our method is validated by comparing results obtained from sampling and from enumeration for short polymer chains. We succeeded in accurate estimation of entropic cost of void maintenance, with and without an increasing number of restrictive conditions, such as loops forming the wall of void with fixed length, with additionally fixed starting position in the sequence. Additionally, we have identified the key structural properties of voids that are important in determining the entropic cost of void formation. We have further developed a parametric model to predict quantitatively void entropy. Our model is highly effective, and these results indicate that voids representing functional sites can be used as an improved model for studying the evolution of protein functions and how protein function relates to protein stability.     

Collision models for spectral line shapes: explicit parity considerations

The Voigt line shape is standardly used for interpolating between gaussian and lorentzian line shapes as the gas pressure increases. This is equivalent to modelling the collision processes by one relaxation rate. Deviations from the Voigt line shape are obtained by using more detailed forms for the collision model. Here it is shown that parity considerations motivate a class of collision models, and resulting line shapes, that have not been previously considered.     

Breakthrough curves and elution profiles of single solutes in case of adsorption isotherms with two inflection points

The shape of breakthrough curves and elution profiles depends strongly on the course of the specific equilibrium functions characterizing the chromatographic system. For a highly efficient system the equilibrium theory provides a methodology how to predict the band profiles. The concept is frequently applied to analyze single component systems characterized by isotherms possessing simple shapes (Langmuir or anti-Langmuir behaviour). However, adsorption isotherms often possess more complicated shapes and have inflection points in their courses. This leads to the development of composite concentration waves and results in complex shapes of breakthrough curves and elution profiles. In this paper, the equilibrium theory is used to predict breakthrough curves for a chromatographic system characterized by an adsorption isotherm with two inflection points. The results obtained are validated by comparing with numerical solutions of the equilibrium dispersive model.     

Metric Properties of Factor Space of Molecular Shapes

Molecular shape equivalence classes defined with respect to equivalence of geometrical and topological properties are represented by logical models. Consequently, the factor space of molecular shapes is provided by a metric useful in shape comparisons.     

聚合物基微纳米功能复合材料3D打印加工的研究

高分子材料3D打印加工可制备传统加工不能制备的形状复杂的高分子制件,是近年来发展很快的先进制造技术。但适用于3D打印加工的高分子材料种类少,结构功能单一,难以制备高分子功能器件。本文介绍了我们在聚合物基微纳米功能复合材料3D打印加工方面的研究工作:通过有机/无机杂化、固相剪切碾磨、超声辐照、分子复合等技术制备适合于选择性激光烧结(SLS)和熔融沉积成型(FDM)的聚合物基微纳米功能复合材料;实现了聚合物基微纳米功能复合粉体的SLS加工和功能复合丝条的FDM加工;研究了3D打印低维构建、层层叠加、自由界面成型、复杂固-液-固转变过程;建立了功能复合粉体球形化技术,发明了直接熔融挤出新型FDM打印机;制备了常规加工方法不能制备的数种形状复杂的功能器件,如尼龙11/钛酸钡压电器件、柔性聚氨酯/碳纳米管传感器、个性化人颌骨模型等,突破了传统加工难以制备复杂形状制品和目前3D打印难以制备功能制品的局限。     

Rapid characterization of anthocyanins in red raspberry fruit by high-performance liquid chromatography coupled to single quadrupole mass spectrometry

This paper describes the results of a comparison of four peak functions in describing real chromatographic peaks. They are the empirically transformed Gaussian, polynomial modified Gaussian, generalized exponentially modified Gaussian and hybrid function of Gaussian and truncated exponential functions. Real chromatographic peaks of different shapes (fronting. symmetric, and tailing) are obtained by various separation conditions of reversed-phase liquid chromatography. They are then fitted to the peak functions via the Marquardt-Levenberg algorithm, a nonlinear least-squares curve-fitting procedure, by Microsoft Solver. The qualities of the fits are evaluated by the sum of the squares of the residuals. It is concluded in the study that the empirically transformed Gaussian function offers the highest flexibility (best fits) to all shapes of chromatographic peaks, including extremely asymmetric tailing peaks with a peak asymmetry of up to 8. The flexibility of this function should improve our ability to process chromatographic peaks such as deconvolution of overlapped peaks and smoothing noisy peaks for the determination of statistical moments.     

Methodology of predicting approximate shapes and size distribution of micelles: illustration for simple models

We propose an efficient methodology for predicting approximate shapes and size distribution of micelles. The methodology is a judicious combination of a conventional thermodynamic approach, the reference interaction site model (RISM) theory, and the Monte Carlo (MC) simulated annealing technique. Solvent effects are fully incorporated using the RISM theory with our robust and very efficient algorithm for solving the RISM equations, and the MC technique is applied only to surfactant molecules. The methodology is potentially applicable to realistic models of surfactant and solvent molecules with all-atom potentials. As the first step, however, it is illustrated for simplified models having only essential characteristics of the amphiphiles. We estimate the critical micelle concentration, approximate shapes, and size distributions at some surfactant concentrations. Roles of the solvent and effects due to the type of the surfactant molecule are discussed in detail.     

Fourier analysis of polymer x-ray diffraction patterns

In analyzing the shapes of diffraction peaks from polymers, it has been mistakenly assumed that it is possible to distinguish between models based on “microstrains” and on paracrystallinity. It is shown that either paracrystallinity or distortions due to dislocations give rise to disorder of the second kind and cannot be distinguished by current diffraction methods. Fourier analysis of shapes of peaks from polymers gives quite satisfactory results, despite comments in the literature to the contrary. The analysis can now be carried out with single peaks; multiple orders are not required.     

Dependence of the Capacity Ratio Upon Type of the Excess Adsorption Isotherm

Abstract

Model calculations of the capacity ratio for binary mobile phase “1+2” and the excess adsorption isotherm of 1-st solvent have been made by assuming nonideality of mobile and surface phases and energetic heterogeneity of the adsorbent surface. These calculations make posible the study of correlation between shapes of the folloving functions: the capacity ratio and the excess adsorption isotherm as functions of the mobile phase composition.     

Modelling and graphic interpretation of response surface in chemical analysis

The complicated effects of several factors on an analytical signal can be studied comprehensively only by an experimental design in which the additive and non-additive effects of these factors are included in one experimental run, with simultaneous variation of the values of all factors. From the law of mass action, it is shown that systems in which the analytical signal is produced by a species formed during a chemical reaction (i.e., for spectrophotometry) can be described by a model based on quasi-linear regressions with squares and products of variables. The regression coefficients can be evaluated by means of factorial designs at three levels. Interpretation of results in the case of two or three independent variables is simplified by using a graphic method in which the complex effects of factors on the dependent variable are represented as an empirical response surface. In the case of regression with three independent variables, the response surface is four-dimensional; its dimensionality is reduced to three by several three-dimensional representations. The shapes of the response surfaces described by the response functions and the adequacy of the models are discussed.