Effect of bin time on the photon counting histogram for one-photon excitation.

We have demonstrated that our photon counting histogram (PCH) model with the correction for one-photon excitation is valid at multiple bin times. The fitted apparent brightness and concentration follow the three-dimensional diffusion model. More importantly, the semi-empirical parameter, F, introduced in the PCH model for one-photon excitation to correct for the non-Gaussian shape of the observation volume, shows small variations with different bin times. These variations are consistent with the physical interpretation of F, and they do not affect the resolving power of the PCH model for one-photon excitation. Based on these findings, we extend the time-independent PCH analysis to time-dependent photon counting multiple histograms (PCMH). This model considers the effect of bin time on the PCH parameters in a way that is similar to fluorescence intensity multiple distribution analysis (FIMDA). From the same set of data, PCMH extracts time-dependent parameters (diffusion time and triplet-state relaxation time) as well as time-independent parameters (true specific brightness and true average number of molecules). Given a three- to fourfold experimental difference in molecular brightness, we find that PCMH can resolve each species in a two-species sample and extract their respective diffusion times even when fluorescence correlation spectroscopy cannot.     

Photon Counting Histogram Analysis for Two‐Dimensional Systems

Photon counting statistics in 3D photon counting histogram analysis for one‐photon excitation is a function of the number of molecules of particular brightness in the excitation‐detection volume of a confocal microscope. In mathematical form that volume is approximated by a three‐dimensional Gaussian function which is embedded in the PCH theoretical equations. PCH theory assumes that a molecule can be found anywhere inside the excitation‐detection volume with equal probability. However, one can easily imagine systems in which this assumption is violated because molecules are constrained by the geometry of the sample. For example, molecules on a surface or in a membrane would be constrained to two dimensions. To enable the analysis of such systems by PCH, the theoretical framework requires modification. Herein, we present an extension of the PCH analysis to systems where molecules exist in thin structures that are effectively two‐dimensional. The method, aptly called two‐dimensional photon counting histogram (2D PCH), recovers the number of fluorescent particles per unit area and their molecular brightness. Both theoretical background and experimental results are presented. The theory was tested using computer‐simulated and experimental 2D PCHs obtained from confocal experiments. We demonstrate that this modification of the theoretical framework provides a tool to extract data that reveal states of aggregation, surface photophysics, and reactivity.     

Quantitative determination of the single-molecule detection regime in fluorescence fluctuation microscopy by means of photon counting histogram analysis

Fluorescence fluctuation experiments are performed in single-molecule detection regime if the fluorescence of at most one molecule is registered at a time. Although the significance of such experiments for investigations of complex nonergodic systems like those met in the biosciences has been stressed out by many scientists, the quantitative and accurate determination of the single-molecule detection regime received rather little attention. In this work we present a method based on the photon counting histogram (PCH) analysis, which enables the determination of the average number N of molecules within the observation volume, for which only the fluorescence of individual molecules is detected at a time. Thus, the accurate design of fluorescence fluctuation experiments performed in single-molecule detection regime is possible. Demonstrative fluorescence fluctuation experiments based on two-photon excitation are performed on diluted solutions of coumarin 153, in order to verify the potential of the PCH analysis in experiments on the single-molecule detection level. If the mean number N of molecules within the excitation volume is larger than 0.048, the probability to simultaneously detect the fluorescence of two or more molecules is no longer negligible, i.e., no single-molecule detection regime. If the mean number N of molecules is lower than 0.0057, the detection limit of the method is reached, i.e., the fluorescence signal cannot be distinguished from the background. Consequently, the concentration of coumarin 153 characteristic for the single-molecule detection regime lies in the range 13-110 pmol/l for the given experimental conditions. We also investigate the influence of the molecular brightness, i.e., detected photons per fluorophore molecule and sampling time, on the single-molecule detection regime.     

Elongated dihydrogen versus compressed dihydride complexes: the temperature dependence of the H-D spin-spin coupling constant as a criterion to distinguish between them

To be able to propose experimental tests to distinguish elongated dihydrogen transition-metal complexes from compressed dihydride transition-metal complexes, a thorough density functional study of the electronic structure in combination with quantum nuclear dynamics calculations have been performed for complexes [Cp*Ru(H2PCH2PCH2(H2)]+ and [CpRe(CO)2H2]. The results of this study suggest that elongated dihydrogen complexes and compressed dihydride complexes have different properties and that it should be possible to distinguish between them experimentally. In particular, different behavior is predicted with respect to 1) the sign of the isotope geometric effect on the H-H distance at 0 K, 2) the temperature dependence of the H-H distance, and 3) the temperature dependence of the H-D spin-spin coupling constant in 1H NMR spectroscopy.     

Detecting proteins complex formation using steady-state diffusion in a nanochannel

In this work, we present theoretical and experimental studies of nanofluidic channels as a potential biosensor for measuring rapid protein complex formation. Using the specific properties offered by nanofluidics, such as the decrease of effective diffusion of biomolecules in confined spaces, we are able to monitor the binding affinity of two proteins. We propose a theoretical model describing the concentration profile of proteins in a nanoslit and show that a complex composed by two bound biomolecules induces a wider diffusion profile than a single protein when driven through a nanochannel. To validate this model experimentally, we measured the increase of the fluorescent diffusion profile when specific biotinylated dextran was added to fluorescent streptavidin. We report here a direct and relatively simple technique to measure the affinity between proteins. Figure We present theoretical and experimental studies of nanofluidic channels as potential biosensors for rapidly measuring protein complex formation. Our system is based on steady-state diffusion effects which are observed inside a nanoslit.     

Extended photon counting histogram and fluorescence intensity distribution analysis approaches for optically biased photon counting statistics

A gradient potential induced by a strongly focused laser beam can perturb the diffusion dynamics of particles in solutions and result in biased photon counting statistics in fluorescence fluctuation spectroscopy (FFS). In this paper, the theories of the photon counting histogram (PCH) and fluorescence intensity distribution analysis (FIDA) approaches are extended independently to fit the biased experimental data and retrieve the unbiased parameters, i.e., the average number of the sample particles in the focal volume N, their brightness epsilon, and polarizability alpha. The extended theories are tested using Monte Carlo simulations for single- and double-component systems. It is also proved numerically and analytically that the extended PCH and FIDA approaches are completely equivalent. Practical implementations and possible applications of extended PCH and FIDA are discussed.     

Quinoline Hydrodenitrogenation over NiW/Al-MCM-41 Catalysts with Different Al Contents

Al-MCM-41 materials were prepared with different Al contents and used as supports for NiW catalysts. The supports and catalysts were characterized by XRD, N₂ adsorption-desorption, XPS, Raman, H₂-TPR techniques. The XPS result showed that the Al added to MCM-41 promoted the dispersion of W and Ni species. The Raman result showed that the Al added to MCM-41 favored the formation of the suitable W species. The H₂-TPR result showed that the Al added to MCM-41 can reduce the reduction temperature of W species on the catalysts. The hydrodenitrogenation (HDN) results showed that the HDN activity followed the order of NiW/Al-2 > NiW/Al-1 > NiW/Al-4 > NiW. Moreover, this tendency was also valid for the ratio of propylcyclohexane/propylbenzene (PCH/PB). The high HDN activity and PCH/PB ratio of NiW/Al-2 are due to the well dispersion of the W and Ni species, the suitable W species and the low reduction temperature of W species.

     

Hybrid stochastic simulations of intracellular reaction–diffusion systems

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction–diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction–diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.     

The kinetics of homogeneous and two-step nucleation during protein crystal growth from solution

Many experimental reports for the kinetics of crystal nucleation and growth, from an isothermal solution, point to a sigmoidal-like behavior for the process. Here we consider three different nucleation models from the literature and show that all lead to sigmoidal or sigmoidal-like behavior for the kinetics of nucleation. A two-step nucleation process is known to occur within certain supersaturated protein solutions, and it is demonstrated in this report how the sigmoidal law yields kinetic information for the two-step and homogeneous nucleation modes. We propose here that two-step solute-rich associates form in the solution around seed nuclei that are already present at or near the point in time when the solution is prepared. Using this hypothesis, we are able to model the time-dependent volume of the two-step phase per unit volume of solution and show that this compares well with reported experimental data. A kinetic model is given for the proposed process, which leads to a sigmoidal rate law. Additionally, a relation between the initial and final nuclei densities and the induction time is derived. As a result of this study, the conclusion is that two-step activity increases with increasing initial supersaturation or increasing salt concentration.     

Reactivity of molecularly chemisorbed oxygen on a Au/TiO2 model catalyst

We present results of an investigation into the reactivity of molecularly chemisorbed oxygen with CO on a Au/TiO2 model catalyst at 77 K. We previously discovered that exposing the model catalyst sample to a radio-frequency-generated plasma jet of oxygen results in co-population of both atomically and molecularly chemisorbed oxygen species on the sample. We tested the reactivity of the molecularly chemisorbed oxygen by comparing the CO2 produced from a sample populated with both species to the CO2 produced from a sample that has been cleared of molecularly chemisorbed oxygen employing collision-induced desorption. Samples that are populated with both species consistently result in greater CO2 produced than samples with only atomic oxygen. We interpret this result to indicate that molecularly chemisorbed oxygen on the sample can directly participate in the CO oxidation reaction. The reactivity of molecularly chemisorbed oxygen has been investigated for five different gold coverages (0.5, 0.75, 1, 1.25, and 2 ML), and we observe that there is a greater fractional difference in the CO2 produced (difference between sample populated with both molecularly and atomically adsorbed oxygen and sample populated solely with atomically adsorbed oxygen) for the 1 ML Au coverage than for the other coverages for equivalent oxygen plasma-jet exposures. However, it is not possible to unambiguously conclude that this observation is directly related to a particle size effect on the chemistry since the absolute O(2,a) and O(a) content on the various surfaces is different for all the coverages studied because of the plasma-jet technique that we employed for populating the surfaces with oxygen. Unfortunately, this precludes a direct comparison of the reactivity of molecular oxygen in the carbon monoxide oxidation reaction as a function of gold coverage and hence particle size.     

A self-consistent transport model for molecular conduction based on extended Hückel theory with full three-dimensional electrostatics

We present a transport model for molecular conduction involving an extended Hückel theoretical treatment of the molecular chemistry combined with a nonequilibrium Green's function treatment of quantum transport. The self-consistent potential is approximated by CNDO (complete neglect of differential overlap) method and the electrostatic effects of metallic leads (bias and image charges) are included through a three-dimensional finite element method. This allows us to capture spatial details of the electrostatic potential profile, including effects of charging, screening, and complicated electrode configurations employing only a single adjustable parameter to locate the Fermi energy. As this model is based on semiempirical methods it is computationally inexpensive and flexible compared to ab initio models, yet at the same time it is able to capture salient qualitative features as well as several relevant quantitative details of transport. We apply our model to investigate recent experimental data on alkane dithiol molecules obtained in a nanopore setup. We also present a comparison study of single molecule transistors and identify electronic properties that control their performance.     

On the molecular origins of volumetric data

We use a statistical thermodynamic approach and a simple thermodynamic model of hydration to examine the molecular origins of the volumetric properties of solutes. In this model, solute-solvent interactions are treated as a binding reaction. The free energy of hydration of the noninteracting solute species coincides with the free energy of cavity formation, while the free energy of solute-solvent interactions is given by the binding polynomial. By differentiating the relationship for the free energy of hydration with respect to temperature and pressure, one obtains the complete set of equations describing the thermodynamic profile of hydration, including enthalpy, entropy, volume, compressibility, expansibility, and so forth. The model enables one to rigorously define in thermodynamic terms the hydration number and the related concept of hydration shell, which are both widely used as operational definitions in experimental studies. Hydration number, nh, is the effective number of water molecules solvating the solute and represents the derivative of the free energy of hydration with respect to the logarithm of water activity. One traditional way of studying hydration relies on the use of volumetric measurements. However, microscopic interpretation of macroscopic volumetric data is complicated and currently relies on empirical models that are not backed by theory. We use our derived model to link the microscopic determinants of the volumetric properties of a solute and its statistical thermodynamic parameters. In this treatment, the partial molar volume, V degrees, of a solute depends on the cavity volume, hydration number, and the properties of waters of hydration. In contrast, the partial molar isothermal compressibility, K degrees T, and expansibility, E degrees, observables, in addition to the intrinsic compressibility and expansibility of the cavity enclosing the solute, hydration number, and the properties of waters of hydration, contain previously unappreciated relaxation terms that originate from pressure- and temperature-induced perturbation of the equilibrium between the solvated solute species. If significant, the relaxation terms may bring about a new level of nonadditivity to compressibility and expansibility group contributions that goes beyond the overlap of the hydration shells of adjacent groups. We apply our theoretical results to numerical analyses of the volume and compressibility responses to changes in the distribution of solvated species of polar compounds.     

A novel dynamic constitutive micromechanical model to predict the strain rate dependent mechanical behavior of glass/epoxy laminated composites

In the present research, a novel dynamic constitutive micromechanical (DCM) model was developed to predict the strain rate dependent mechanical behavior of laminated glass/epoxy composites. The present model is an integration of the generalized strain rate dependent constitutive model as a constitutive model for the neat polymer, the plasticity model of Huang as a micromechanical model, and dynamic progressive failure criteria. This model is able to predict the longitudinal and transverse tensile and in-plane shear behaviors of unidirectional glass/epoxy composites with arbitrary fiber volume fractions at arbitrary strain rates. The present model can also predict the stress-strain behavior of laminated composites with different layups and fiber volume fractions at arbitrary strain rates. A comparison between the results predicted by the present model and the available experimental data showed that the model predicts the strain rate dependent mechanical behavior of glass/epoxy composites with very good accuracy.     

Role of electrokinetic phenomena in the preparation of supported metal catalysts

A model accounting for the effect of electrokinetic phenomena on the prepartion of supported metal catalysts by wet impregnation is presented. The model is able to explain the dependence of catalyst distribution profile and loading on the concentration of the impregnant, on the pH and ionic strength of the impregnating solution, as well as on the presence of a co-impregnating species.     

In situ study on molecular diffusion phenomena in nanoporous catalytic solids

As an omnipresent phenomenon in nature, diffusion is among the rate-determining processes in many technological processes. This is in particular true for catalytic conversion in nanoporous materials. We provide a critical review of the possibilities of exploring diffusion phenomena over microscopic dimensions in such media by direct experimental observation. By monitoring the probability distribution of molecular displacements as a function of time, the pulsed field gradient technique of NMR (PFG NMR) records the rate of molecular re-distribution. By varying the observation time, PFG NMR is thus able to trace even hierarchies of transport resistances as occurring, e.g., in catalyst particles in the form of binder-compacted assemblages of zeolite crystallites. Alternatively, and complementary to this information, interference microscopy (IFM) and IR microscopy (IRM) are able to follow the evolution of intracrystalline concentration profiles during uptake and release. This allows, in particular, an accurate quantification of the transport resistances on the surface of the individual crystallites and of the probability that reactant molecules from the gas phase, upon colliding with the external surface, are able to penetrate through such "surface barriers" into the crystal bulk phase. Being able to distinguish between different molecular species, IRM is able to record the evolution of intracrystalline concentration profiles even during multi-component adsorption and catalytic reactions (169 references).     

Synthesis and characterization of octa- and hexanuclear polyoxomolybdate wheels: role of the inorganic template and of the counterion

Eight new compounds based on [O3PCH2PO3]4- ligands and {MoV2O4} dimeric units have been synthesized and structurally characterized. Octanuclear wheels encapsulating various guests have been isolated with different counterions. With NH4+, a single wheel was obtained, as expected, with the planar CO32- guest, (NH4)12[(MoV2O4)4(O3PCH2PO3)4(CO3)2].24H2O (1a), while with the pyramidal SO32- guest, only the syn isomer (NH4)12[(MoV2O4)4(O3PCH2PO3)4(SO3)2].26H2O (2a) was characterized. The corresponding anti isomer was obtained with Na+ as counterions, Na12[(MoV2O4)4(O3PCH2PO3)4(SO3)2]39H2O (2b), and with mixed Na+ and NH4(+) counterions, Na+(NH4)11[(MoV2O4)4(O3PCH2PO3)4(SO3)2].13H2O (2d). With [O3PCH2PO3]4- extra ligands, the octanuclear wheel Li12(NH4)2[(MoV2O4)4(O3PCH2PO3)4(HO3PCH2PO3)2].31H2O (4a) was isolated with Li+ and NH4+ counterions and Li14[(MoV2O4)4(O3PCH2PO3)4(HO3PCH2PO3)2].34H2O (4c) as a pure Li+ salt. A new rectangular anion, formed by connecting two MoV dimers and two MoVI octahedra via methylenediphosphonato ligands with NH4+ as counterions, (NH4)10[(MoV2O4)2(MoVIO3)2(O3PCH2PO3)2(HO3PCH2PO3)2].15H2)O (3a), and Li9(NH4)2Cl[(MoV2O4)2(MoVIO3)2(O3PCH2PO3)2]. 22H2O (3d) as a mixed NH4+ and Li+ salt have also been synthesized. The structural characterization of the compounds, combined with a study of their behavior in solution, investigated by 31P NMR, has allowed a discussion on the influence of the counterions on the structure of the anions and their stability. Density functional theory calculations carried out on both isomers of the [(MoV2O4)4(O3PCH2PO3)4(SO3)2]12- anion (2), either assumed isolated or embedded in a continuum solvent model, suggest that the anti form is favored by approximately 2 kcal mol(-1). Explicit insertion of two solvated counterions in the molecular cavity reverses this energy difference and reduces it to less than 1 kcal mol(-1), therefore accounting for the observed structural versatility.     

关于聚电解质单链抗衡离子浓度径向分布的研究

采用单分子荧光显微统计光谱技术,通过将pH响应型荧光探针分子精确标记于聚苯乙烯磺酸钠分子链末端,并通过不同长度的多肽链调节分子链与探针分子间的距离,有效测量了聚苯乙烯磺酸钠单分子链的抗衡离子浓度的空间分布.实验结果清晰展示了聚电解质分子链的抗衡离子云结构,并确定了抗衡离子浓度随着距离分子链末端长度的不同而发生变化的规律,为描述聚电解质抗衡离子浓度的径向分布特征提供了实验信息.     

Threshold dynamics of a stochastic Keizer’s model with stochastic incidence

In this paper, we incorporate stochastic incidence of a chemical reaction into the standard Keizer’s open chemical reaction. We prove that a positive stationary distribution (PSD) for the associated chemical master equation exists and is globally asymptotically stable. We present threshold dynamics of the stochastic Keizer’s model in term of the profile of the PSD for both finite and infinite volume size V. This establishes a sharp link between deterministic Keizer’s model and the stochastic model. In this way, we resolve Keizer’s paradox from a new perspective. This simple model reveals that such stochastic incidence incorporated, though negligible when V goes to infinity, may play an indispensable role in the stochastic formulation for irreversible biochemical reactions.     

Adsorption of gases in metal organic materials: comparison of simulations and experiments

Molecular simulations using standard force fields have been carried out to model the adsorption of various light gases on a number of different metal organic framework-type materials. The results have been compared with the available experimental data to test the validity of the model potentials. We observe good agreement between simulations and experiments for a number of different cases and very poor agreement in other cases. Possible reasons for the discrepancy in simulated and measured isotherms are discussed. We predict hydrogen adsorption isotherms at 77 and 298 K in a number of different metal organic framework materials. The importance of quantum diffraction effects and framework charges on the adsorption of hydrogen at 77 K is discussed. Our calculations indicate that at room temperature none of the materials that we have tested is able to meet the requirements for on-board hydrogen storage for fuel cell vehicles. We have calculated the volume available in a given sorbent at a specified adsorption energy (density of states). We discuss how this density of states can be used to assess the effectiveness of a sorbent material for hydrogen storage.