Electron transport and recombination in dye-sensitized mesoporous TiO2 probed by photoinduced charge-conductivity modulation spectroscopy with Monte Carlo modeling

We present a combined experimental and theoretical investigation into the charge transport and recombination in dye-sensitized mesoporous TiO2. We electronically probe the photoinduced change in conductivity through in-plane devices while simultaneously optically probing signatures of the charge species. Our quasi-continuous wave technique allows us to build data sets of electron mobility and recombination versus charge density over a wide temperature range. We observe that the charge density dependence of mobility in TiO2 is strong at high temperatures and gradually reduces with reducing temperature, to an extent where at temperatures below 260 K the mobility is almost independent of charge density. The mobility first increases and then decreases with reducing temperature at any given charge density. These observed trends are surprising and consistent with the multiple-trapping model for charge transport only if the trap density-of-states (DoS) is allowed to become less deep and narrower as the temperature reduces. Our recombination measurements and simulations over a broad range of charge density and temperature are also consistent with the above-mentioned varying DoS function when the recombination rate constant is allowed to increase with temperature, itself consistent with a thermally activated charge-transfer process. Further to using the Monte Carlo simulations to model the experimental data, we use the simulations to aid our understanding of the limiting factors to charge transport and recombination. According to our model, we find that the charge recombination is mainly governed by the recombination reaction rate constant and the charge density dependence is mainly a result of the bimolecular nature of the recombination process. The implication to future material design is that if the mobility can be enhanced without increasing the charge density in the film, for instance by reducing the average trap depth, then this will not be at the sacrifice of comparably enhanced recombination and it will greatly increase the charge carrier diffusion lengths in dye-sensitized or mesoscopic solar cells.     

Electrophoretic mobility of a particle covered with an ion-penetrable membrane

The electrophoretic behavior of a planar particle covered by an ion-penetrable membrane, which simulates a biological entity, is investigated. We show that, in general, a point charge model will overestimate the electrophoretic mobility of a particle and the deviation increases with the increase in the concentration of fixed charge and with the decrease in the thickness of membrane layer. As in the case of a point charge model, the present model also predicts a local maximum in the absolute mobility as the thickness of membrane layer varies. If the sizes of counterions of various valences are the same, then the lower the valence of counterions, the larger the mobility, and the larger the counterions, the greater the mobility. The latter is consistent with the experimental observations in the literature. For the level of the concentration of fixed charge examined, the effect of coions on the mobility is negligible.     

A time-dependent quantal analysis of vibronic excitation via charge transfer in ion-molecule collisions

A semi-classical multiple state model describing charge transfer in ion-molecule system is presented. Analytical expressions for the state-to-state transition probabilities are given for both the weak-coupling and the high-velocity limits. The expressions are compared to a two-state model describing charge transfer in ion-atom systems. Some numerical calculations are presented to illustrate the various phenomena which can occur in multiple state charge transfer processes. These numerical calculations will be based upon a simple system derived from the system (Ar + N₂)⁺.     

Gaussian induced dipole polarization model

A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The Gaussian polarization model is compared with the damped Thole-induced dipole model and the point dipole model. It will be shown that the Gaussian polarization model performs slightly better than the Thole model in terms of fitting to molecular polarizability tensors. An advantage of the model based on Gaussian charge distribution is that it can be easily generalized to other multipole moments and provide effective damping for both permanent electrostatic and polarization models. Finally, a method of parameterizing polarizabilities is presented. This method is based on probing a molecule with point charges and fitting polarizabilities to electrostatic potential. In contrast to the generic atom type polarizabilities fit to molecular polarizability tensors, probed polarizabilities are significantly more accurate in terms of reproducing molecular polarizability tensors and electrostatic potential, while retaining conformational transferability.     

An Electrostatic Charge Partitioning Model for the Dissociation of Protein Complexes in the Gas Phase

Electrosprayed multi-protein complexes can be dissociated by collisional activation in the gas phase. Typically, these processes follow a mechanism whereby a single subunit gets ejected with a disproportionately high amount of charge relative to its mass. This asymmetric behavior suggests that the departing subunit undergoes some degree of unfolding prior to being separated from the residual complex. These structural changes occur concomitantly with charge (proton) transfer towards the subunit that is being unraveled. Charge accumulation takes place up to the point where the subunit loses physical contact with the residual complex. This work develops a simple electrostatic model for studying the relationship between conformational changes and charge enrichment during collisional activation. Folded subunits are described as spheres that carry continuum surface charge. The unfolded chain is envisioned as random coil bead string. Simulations are guided by the principle that the system will adopt the charge configuration with the lowest potential energy for any backbone conformation. A finite-difference gradient algorithm is used to determine the charge on each subunit throughout the dissociation process. Both dimeric and tetrameric protein complexes are investigated. The model reproduces the occurrence of asymmetric charge partitioning for dissociation events that are preceded by subunit unfolding. Quantitative comparisons of experimental MS/MS data with model predictions yield estimates of the structural changes that occur during collisional activation. Our findings suggest that subunit separation can occur over a wide range of scission point structures that correspond to different degrees of unfolding.     

Surface charging behaviors of electrocatalytic interfaces with partially charged chemisorbates

The surface charge is a key concept in electrochemistry. Mathematically, the surface charge is obtained from a spatial integration of the volume charge along a particular direction. Ambiguities thus arise in choosing the starting and ending points of the integration. As for electrocatalytic interfaces, the presence of chemisorbates further complicates the situation. In this minireview, I adopt a definition of the surface charge within a continuum picture of the electric double layer. I will introduce surface charging behaviors of firstly ordinary electrochemical interfaces and then electrocatalytic interfaces featuring partially charged chemisorbates. Particularly, the origin of nonmonotonic surface charging behaviors of electrocatalytic interfaces is explained using a primitive model. Finally, a brief account of previous studies on the nonmonotonic surface charging behavior is presented, as a subline of the spectacular history of electric double layer.     

Charge state of the fast gate in chloride channels: insights from electrostatic calculations in a schematic model

Fast gating is a unique property of chloride channels, where a permeating Cl(-) ion acts as its own ligand in opening the channel. The glutamate residue implicated in fast gating normally carries a unit negative charge. Whether this charge needs to be protonated to enable permeation of a Cl(-) ion is an important question that will affect how models of chloride channels are constructed. We investigate the energetic consequences of the charge state of this glutamate residue from continuum electrostatics using a schematic cylindrical channel model. Both analytical solutions of the Poisson equation for an infinite cylinder and numerical ones for a finite cylinder are employed in the calculations.     

An intramolecular induction correction model of the molecular dipole moment

A model for intramolecular polarization is presented. It is used to describe the changes in the molecular charge distribution occurring as a response to changes of dihedral angles in the molecule. The model is based on a multicenter multipole distribution of the molecular charge distribution. The electric field from this charge distribution induce dipole moments in the same molecule. The model contains atom type parameters to describe the damping of the electric field. A total of four atom types are used. The parameters are fitted to a calibration set with various functional groups, and tested against a validation set. The error obtained for the calibration set is reduced by 92% and by 88% for the validation set, if compared to an accurate state-of-the-art force field. It is shown that rotating the non-polarizable multicenter multipole distribution for the equilibrium geometry gives too large dipole moments for dihedral angles deviating from the equilibrium geometry. This will lead to too large long-range attractions in simulations. This problem is overcome by using the dipole polarizability correction suggested here, which gives dipole moments very close to the Hartree-Fock dipole moments obtained from reference calculations.     

Activity coefficients and Donnan coion exclusion in charged membranes with weak-acid fixed charge groups

We have studied theoretically the effects that the dissociation equilibrium of weak-acid fixed charge groups (e.g. carboxyl groups) exerts on the mean activity coefficients in charged membranes using a Donnan formalism. The model calculations indicate that unless carbon dioxide is excluded from the external aqueous solution, the pH of the membrane solution can be low enough to affect significantly the effective fixed charge concentration and the coion exclusion when the membrane fixed charge concentration is high compared with the external solution salt concentration. Although this problem was already pointed out in previous studies, the possibility that the pH and salt concentration effects appeared in the mean activity coefficient was not considered. We have analyzed quantitatively these effects here and shown that they will eventually be reflected in the effective mean activity coefficients obtained experimentally unless an appropriate theoretical model incorporating the dissociation equilibrium equation explicitly is used to analyze the experimental data.     

“One dimensional” double layer. The effect of size asymmetry of cations and anions on charge-storage in ultranarrow nanopores—an Ising model theory

We develop a statistical mechanical theory of charge storage in quasi-single-file ionophilic nanopores with pure room temperature ionic liquid cations and anions of different size. The theory is mapped to an extension of the Ising model exploited earlier for the case of cations and anions of the same size. We calculate the differential capacitance and the stored energy density per unit surface area of the pore. Both show asymmetry in the dependence on electrode potential with respect to the potential of zero charge, related to the difference in the size of the ions, which will be interesting to investigate experimentally. It also approves the increase of charge storage capacity via obstructed charging, which in these systems emerges for charging nanopores with smaller ions.     

Electrokinetic transport of nanoparticles in functional group modified nanopores

Nanopore detection is a hot issue in current research. One of the challenges is how to slow down the transport velocity of nanoparticles in nanopores. In this paper, we propose a functional group modified nanopore. That means a polyelectrolyte brush layer is grafted on the surface of the nanopore to change the surface charge properties. The existing studies generally set the charge density of the brush layer to a fixed value. On the contrary, in this paper, we consider an essential property of the brush layer: the volume charge density is adjustable with pH. Thus, the charge property of the brush layer will change with the local H⁺ concentration. Based on this, we established a mathematical model to study the transport of nanoparticles in polyelectrolyte brush layer modified nanopores. We found that pH can effectively adjust the charge density and even the polarity of the brush layer. A larger pH can reduce the transport velocity of nanoparticles and improve the blockade degree of ion current. The grafting density does not change the polarity of the brush charge. The larger the grafting density, the greater the charge density of the brush layer, and the blockade degree of ion current is also more obvious. The polyelectrolyte brush layer modified nanopores in this paper can effectively reduce the nanoparticle transport velocity and retain the essential ion current characteristics, such as ion current blockade and enhancement.     

Cell model of the direct current electrokinetics in salt-free concentrated suspensions: the role of boundary conditions

In this paper, a general electrokinetic theory for concentrated suspensions in salt-free media is derived. Our model predicts the electrical conductivity and the electrophoretic mobility of spherical particles in salt-free suspensions for arbitrary conditions regarding particle charge, volume fraction, counterion properties, and overlapping of double layers of adjacent particles. For brevity, hydrolysis effects and parasitic effects from dissolved carbon dioxide, which are present to some extent in more "realistic" salt-free suspensions, will not be addressed in this paper. These issues will be analyzed in a forthcoming extension. However, previous models are revised, and different sets of boundary conditions, frequently found in the literature, are extensively analyzed. Our results confirm the so-called counterion condensation effect and clearly display its influence on electrokinetic properties such as electrical conductivity and electrophoretic mobility for different theoretical conditions. We show that the electrophoretic mobility increases as particle charge increases for a given particle volume fraction until the charge region where counterion condensation takes place is attained, for the above-mentioned sets of boundary conditions. However, it decreases as particle volume fraction increases for a given particle charge. Instead, the electrical conductivity always increases with either particle charge for fixed particle volume fraction or volume fraction for fixed particle charge, whatever the set of boundary conditions previously referred. In addition, the influence of the electric permittivity of the particles on their electrokinetic properties in salt-free media is examined for those frames of boundary conditions.     

Computational investigation of amine-oxygen exciplex formation

It has been suggested that fluorescence from amine-containing dendrimer compounds could be the result of a charge transfer between amine groups and molecular oxygen [Chu, C.-C.; Imae, T. Macromol. Rapid Commun. 2009, 30, 89.]. In this paper we employ equation-of-motion coupled cluster computational methods to study the electronic structure of an ammonia-oxygen model complex to examine this possibility. The results reveal several bound electronic states with charge transfer character with emission energies generally consistent with previous observations. However, further work involving confinement, solvent, and amine structure effects will be necessary for more rigorous examination of the charge transfer fluorescence hypothesis.     

电极/溶液界面单分子吸附层的统计力学处理 I. 非水溶液中汞电极的内层微分电容

本文提出电极/溶液界面溶剂化层偶极取向分布模型, 应用统计力学方法及热力学平衡条件导出普遍化的单层吸附等温方程, 其电解质溶液的溶剂组成可以是纯态的或混合物(多组份)的. 文中分别以甲酰胺、碳酸亚乙酯和甲醇等三种纯溶剂的汞/溶液界面为例, 采用曲线拟合计算内层微分电容随表面电荷变化关系。预计本模型处理对汞/水溶液或汞/(混合溶剂)溶液界面仍可适用。     

Theoretical investigations of the dissociation of charged protein complexes in the gas phase

A series of calculations, varying from simple electrostatic to more detailed semi-empirical based molecular dynamics ones, were carried out on charged gas phase ions of the cytochrome c(') dimer. The energetics of differing charge states, charge partitionings, and charge configurations were examined in both the low and high charge regimes. As well, preliminary free energy calculations of dissociation barriers are presented. It is shown that one must always consider distributions of charge configurations, once protein relaxation effects are taken into account, and that no single configuration dominates. All these results also indicate that in the high charge limit, the dissociation of protein complex ions is governed by electrostatic repulsion from the net charges, the consequences of which are enumerated and discussed. There are two main trends deriving from this, namely that charges will move so as to approximately maintain constant surface charge density, and that the lowest barrier to dissociation is the one that produces fragment ions with equal charges. In particular, it is shown that the charge-to-mass ratio of a fragment ion is not the key physical parameter in predicting dissociation products. In fact, from the perspective of the division of total charge, many dissociation pathways reported to be "asymmetric" in the literature should be more properly labelled as "symmetric" or "near-symmetric". The Coulomb repulsion model assumes that the timescale for charge transfer is faster than that for protein structural changes, which in turn is faster than that for complex dissociation.     

Behavior of mixtures of symmetric and asymmetric electrolytes near discretely charged planar surfaces: a Monte Carlo study

Canonical Monte Carlo (CMC) simulations are employed in this work in order to study the structure of the electrical double layer (EDL) near discretely charged planar surfaces in the presence of symmetric and asymmetric indifferent electrolytes within the framework of a primitive model. The effects of discreteness and strength of surface charge, charge asymmetry, and size asymmetry are specific focuses of this work. The CMC simulation protocol is initially tested against the classical theory, the modified Gouy-Chapman (GC) theory, in order to assess the reliability of the simulation results. The CMC simulation results and the predictions of the classical theory show good agreement for 1:1 electrolytes and low surface charge, at which conditions the GC theory is valid. Simulations with symmetric and asymmetric electrolytes and mixtures of the two demonstrate that size plays an important role in determining the species present in the EDL and how the surface charge is screened. A size-exclusion effect could be consistently detected. Although it is energetically favorable that higher-valence ions screen the surface charge, their larger size prevents them from getting close to the surface. Smaller ions with lower valences perform the screening of the charge, resulting in higher local concentrations of small ions close to the surface. The simulations also showed that the strength of the surface charge enhances the size-exclusion effect. This effect will definitely affect the magnitude of the forces between interacting charged surfaces.     

Can nanofiltration be fully predicted by a model?

There is an increasing need for model-based tools to design membrane processes for new industrial applications or to optimise existing membrane installations. The advantage of such tools is that costs can be saved by reducing the number of expermiments. In this study, the requirements for a membrane filtration model, suitable for practical use, are summarised. It is investigated to what extent it is possible to set-up such a model with the current available literature and knowledge. A membrane filtration model has been set-up based on the Maxwell–Stefan transport equations. A Freundlich equation is used to describe the membrane charge by means of adsorption of ions. With the model the permeate flux and rejections of multi-component liquid feeds can be calculated as a function of membrane properties (mean pore size, porosity, thickness, surface charge characteristic) and feed pressure. With two NF-membranes (Desal 5DK and a prototype capillary type 2 membrane) rejection experiments have been carried out with glucose, single salt solutions (NaCl, CaCl₂, Na₂SO₄) and ternary ion mixtures of these salts. With the model the experimental flux-rejection curves can be fitted reasonably well. However, each salt mixture needs its own set of fitted parameters for the membrane charge isotherms. Furthermore, the fitted membrane charges are in contradiction with values from the literature obtained by electrokinetic measurements. Obviously, the membrane charge parameters have lost their physical meaning and are used to compensate for physical phenomena not included in the model. Extending the model with an electrostatic free energy term will be a step forward in development. Further research is needed to fulfil all requirements for the wide scope of industrial applications.     

二元类水滑石层板组成、结构与性能的理论研究

采用晶体学理论建立二元类水滑石(LDHs)微观结构模型与静电势能模型，将层板金属离子间距、层板电荷密度、层间阴离子间距等微观结构参数定量化，并将层间阴离子的静电势能表示成层板金属离子半径和物质的量之比、插层阴离子尺寸和电荷的函数。研究结果表明：LDHs层板金属离子间距应用离子紧密堆积来估算和孔径按阴离子平面六方点阵分布来计算是可行的；调变层板金属离子种类与物质的量之比影响层间阴离子的稳定性，势能计算值与文献报道的LDHs热稳定性次序一致。所以该模型可用于预测LDHs的微观结构参数以及热稳定性，为新型层状双羟基材料的定向合成提供思路。     

Theoretical investigation of charge transfer excitation and charge recombination in acenaphthylene–tetracyanoethylene complex

Ab initio calculations were performed to investigate the charge separation and charge recombination processes in the photoinduced electron transfer reaction between tetracyanoethylene and acenaphthylene. The excited states of the charge‐balanced electron donor–acceptor complex and the singlet state of ion pair complex were studied by employing configuration interaction singles method. The equilibrium geometry of electron donor–acceptor complex was obtained by the second‐order Møller–Plesset method, with the interaction energy corrected by the counterpoise method. The theoretical study of ground state and excited states of electron donor–acceptor complex in this work reveals that the S₁ and S₂ states of the electron donor–acceptor complexes are excited charge transfer states, and charge transfer absorptions that corresponds to the S₀ → S₁ and S₀ → S₂ transitions arise from π–π* excitations. The charge recombination in the ion pair complex will produce the charge‐balanced ground state or excited triplet state. According to the generalized Mulliken–Hush model, the electron coupling matrix elements of the charge separation process and the charge recombination process were obtained. Based on the continuum model, charge transfer absorption and charge transfer emission in the polar solvent of 1,2‐dichloroethane were investigated. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 23–35, 2003     

The interaction between silica flat substrate and functional group–modified nanoparticles

Inspired by nature, the research of functionalized nanoparticles and nanodevices has been in-depth developed in recent years. In this paper, we theoretically studied the interaction between functional polyelectrolyte brush layer–modified nanoparticles and a silica flat substrate. Based on the Poisson–Nernst–Planck equations, the mathematical model is established. The changes of the volume charge density and electric field energy density when the nanoparticle interacts with the silica flat substrate under multi-ions regulation were investigated. The results show that when there is a strong interaction between the silica flat substrate and nanoparticles, such as the distances between the nanoparticle and silica flat substrate, which are 2 or 5 nm, the isoelectric point shift under the influence of silica flat substrate and the total charge density in the brush layer is jointly controlled by the cations in the solution and the volume charge density of the brush layer. With the increase of the distances between the nanoparticle and silica flat substrate, the regulation of the volume charge density of the brush layer dominates. These results will provide guidance for the movement mechanism of functionalized nanoparticles in silica nanochannels.