Volmer Equation Research Articles

Preparation of lucigenin-doped silica nanoparticles and their application in fiber optic chloride ion sensor

A novel fiber optic sensor was developed to detect chloride ion by means of a cellulose acetate (CA) sensitive film, in which the lucigenin-doped silica nanoparticles were synthesized by the reverse microemulsion method and immobilized into sensitive membrane via physical embedding and. The morphology, structure and fluorescence performance of the lucigenin-doped silica nanocomposite particles were characterized by scanning electron microscope (SEM), Brunauer-Emmett-Teller (BET) nitrogen adsorption-desorption isotherms, Fourier transforming infrared (FT-IR), Ultraviolet absorption spectrometer and Fluorescence spectrometer, respectively. The results show that the lucigenin-doped silica nanocomposite particles still had excellent fluorescence performance and high sensitivity for chloride detection, even fluorescence stability was improved compared with single lucigenin. Based on the principle of fluorescence quenching, that is the fluorescence intensity of lucigenin-doped silica nanoparticles will decrease with increasing of the chloride ion concentrations, the chloride concentrations were detected by the fiber optic sensor, in which the end face of optic fiber was coated with the CA sensitive film. The relationship between the intensity of lucigenin-doped silica nanoparticles and the concentrations of chloride ion followed the Stern–Volmer equation, and a linear relationship formula of I0I=1.623+49.845[Cl−](R2=0.995) was obtained with the concentration range from 0.02 M to 0.06 M.

Extracellular Oxygen Sensors Based on PtTFPP and Four-Arm Block Copolymers

Three four-arm amphiphilic block copolymers with different chain lengths, consisting of a hydrophilic chain of polyethylene glycol (PEG) and hydrophobic segment of polycaprolactam (PCL), were synthesized and used to encapsulate the high-efficient and hydrophobic oxygen probe of platinum(II)-5,10,15,20-tetrakis-(2,3,4,5,6-pentafluorophenyl)-porphyrin (PtTFPP) to form polymer micelles. This approach enabled the use of PtTFPP in aqueous solution for biosensing. Experimental results demonstrated that the particle sizes of these nano-oxygen sensors between 40.0 and 203.8 nm depend on the structures of block copolymers. PtTFPP in these micelles showed an effective quantum yield under nitrogen environment, ranging from 0.06 to 0.159. The new sensors are suitable for analyzing dissolved oxygen concentrations in the range of 0.04–39.3 mg/L by using the linear Stern–Volmer equation at room temperature. In addition, it has been shown that these sensors are capable of in situ monitoring the dissolved oxygens in the culture medium of E. coli and Romas cells during the respiration process, and distinguishing the drug activity of antibiotic ampicillin from that of antimycin A. This study showed that the use of these nanostructured multi-arm block copolymer micelles can achieve efficient biological applications without specific structural modification of the hydrophobic PtTFPP probe, which is expected to have broad prospects.

Dislocation based stresses during electrochemical cycling and phase transformation in lithium-ion batteries

Lithium iron phosphate (LiFePO4) contains defects that play an important role in structural degradation of batteries. Linear defects called dislocations are introduced inside the lithium ion battery material during fabrication process accompanied by distortion produced stress fields around them. The present study deals with these mechanical stresses around dislocations in lithium iron phosphate and the change in stress field during phase transformation of lithium iron phosphate electrode material. A model consisting of multiple dislocations inside a lithium iron phosphate material incorporating anisotropic material properties is used to calculate stress fields using linear elastic theory and the superposition method. The stress fields around dislocations during phase transformation of lithium-iron phosphate are numerically calculated by incorporating the anisotropic properties of the material. The change in electrochemical behaviour of material due to change in stress field during phase transformation is also studied, where a modified electrochemical kinetics equation (i.e., Butler Volmer equation) is derived and used to account for dislocation induced stresses during the reversible cyclic voltammatery of the lithium iron phosphate. The results shows the stress inside material does not remain constant during phase transformation and its variations are dislocation orientation dependent. In addition, the result shows that the presence of stress fields around dislocations changes the electrochemical behaviour of the material as suggested by the shift in the cyclic voltammograms. The effect of increasing scan rate on cyclic voltammogram is also studied for lithium iron phosphate. The results show that the increase in current at peaks is independent of the orientation of dislocations studied. Moreover, the decrease in current corresponding to a particular overvoltage value before anodic peak and increase in current after the anodic peak is found to be somehow proportional to the scan rate. Increased scan rates show increased deviation of current from a cyclic voltammogram for material in which there is no phase transformation. The results provide an insight into how presence of defects and phase transformation changes the electrochemical behaviour of the material. It is concluded that the combined effect of the stresses induced around dislocations during phase transformation and high scan rate can be used for modifying battery materials for various applications by changing electrochemistry of electrodes. The present study incorporates electrochemistry, defects and phase transformation into one battery chemistry and thus is important in our understanding of the Li-ion batteries.

A new single-particle model to evaluate the Li-ions diffusion coefficients of LiMn1−xFexPO4

It remains a challenge to evaluate the Li-ions diffusion coefficients of LiMn[Formula: see text]FexPO4 due to the presence of two voltage platforms upon charge/discharge. In this paper, a new single-particle model based on Butler–Volmer (BV) equation and one-dimensional diffusion equation is established. Using this model, the cyclic voltammogram curves of LiMn[Formula: see text]FexPO4 single-particle electrodes are successfully fitted and their Li-ion diffusion coefficients in organic electrolyte are obtained. Through analyzing the diffusion coefficients, it is found that the Li-ions diffusion coefficients for both Fe and Mn redox processes in LiMn[Formula: see text]FexPO4 reach the maximum when [Formula: see text]. In addition, the values for oxidation processes are much larger than those for reduction processes.

Ratiometric Luminescent Nanoprobes Based on Ruthenium and Terbium-Containing Metallopolymers for Intracellular Oxygen Sensing.

A collection of luminescent metal complexes have been widely used as oxygen probes in the biomedical field. However, single intensity-based detection approach usually suffered from errors caused by the signal heterogeneity or fluctuation of the optoelectronic system. In this work, respective ruthenium (II) and terbium (III) complexes were chosen to coordinate a bipyridine-branched copolymer, so that to produce oxygen-sensitive metallopolymer (Ru-Poly) and oxygen-insensitive metallopolymer (Tb-Poly). Based on the hydrophobic Ru-Poly and Tb-Poly, a ratiometric luminescent oxygen nanoprobe was facilely prepared by a nanoprecipitation method. The nanoprobes have a typical size of ~100 nm in aqueous solution, exhibiting a green-red dual-wavelength emission under the excitation of 300 nm and 460 nm, respectively. The red emission is strongly quenched by dissolved oxygen while the green one is rather stable, and the ratiometric luminescence was well fitted by a linear Stern–Volmer equation. Using the ratiometric biocompatible nanoprobes, the distribution of intracellular oxygen within three-dimensional multi-cellular tumor spheroids was successfully imaged.

Machine Learning Approaches for Designing Mesoscale Structure of Li-Ion Battery Electrodes

We have proposed a data-driven approach for designing the mesoscale porous structures of Li-ion battery electrodes, using three-dimensional virtual structures and machine learning techniques. Over 2000 artificial 3D structures, assuming a positive electrode composed of randomly packed spheres as the active material particles, are generated, and the charge/discharge specific resistance has been evaluated using a simplified physico-chemical model. The specific resistance from Li diffusion in the active material particles (diffusion resistance), the transfer specific resistance of Li+ in the electrolyte (electrolyte resistance), and the reaction resistance on the interface between the active material and electrolyte are simulated, based on the mass balance of Li, Ohm’s law, and the linearized Butler–Volmer equation, respectively. Using these simulation results, regression models, using an artificial neural network (ANN), have been created in order to predict the charge/discharge specific resistance from porous structure features. In this study, porosity, active material particle size and volume fraction, pressure in the compaction process, electrolyte conductivity, and binder/additives volume fraction are adopted, as features associated with controllable process parameters for manufacturing the battery electrode. As a result, the predicted electrode specific resistance by the ANN regression model is in good agreement with the simulated values. Furthermore, sensitivity analyses and an optimization of the process parameters have been carried out. Although the proposed approach is based only on the simulation results, it could serve as a reference for the determination of process parameters in battery electrode manufacturing.

Separation of Protein-Binding Anthraquinones from Semen Cassiae Using Two-Stage Foam Fractionation

Anthraquinones are compounds of high medicinal value in many plants. Based on their good protein binding affinity, foam fractionation was attempted to separate them using proteins in the aqueous extract of Semen Cassiae as collectors. Firstly, the interaction between anthraquinones and Semen Cassiae proteins has been analyzed by the Stem–Volmer equation with physcion as a standard. The results show that physcion had good interaction with the proteins via hydrophobic forces. More importantly, the proteins effectively assisted the foam fractionation of several anthraquinones including aurantio-obtusifolin, aloe-emodin, rhein, emodin, chrysophanol, and physcion. On this basis, a two-stage foam fractionation technology was developed for process intensification using a foam fractionation with vertical sieve trays (VSTs). VSTs, initial feed concentration of total anthraquinones, temperature, volumetric air flow rate and pore diameter of gas distributor had significant effects on enrichment ratio and recovery yield of anthraquinones. Under suitable conditions, the enrichment ratio of total anthraquinones reached 47.0 ± 4.5 with a concentration of 939 ± 94 mg/L in the foamate while their total recovery percentage reached more than 47.7%. In addition, foam fractionation also increased the purity and hydroxyl radical scavenging activity of total anthraquinones. The results had significant implications for the separation of anthraquinones from Semen Cassiae.

Investigating erythrosine B as a fluorimetric probe for the determination of benzimidazole drugs via facile complexation reaction

Two benzimidazole anthelmintic drugs; flubendazole (FBZ) and mebendazole (MBZ), were determined by simple spectrofluorimetric method through complex formation with erythrosine B. The ion-pair formation between the dye and the studied drugs quench the fluorescence activity of the dye which was monitored at 554 nm (λex = 527 nm). The reaction was performed in Teorell - Stenhagen buffer solution (pH 2.9). The reduction in the emission value of the fluorescence was proportional to the added drug in a linear range of 0.1–3.5 μg mL−1 for both drugs. The detection limits were 34 and 30 ng mL−1 for FBZ and MBZ respectively. The suggested procedure was validated in accordance with ICH guidelines, with satisfactory results. Several commercially available pharmaceutical formulations containing the drugs were successfully analyzed with no significant interference due the commonly used excipients. In addition, the quenching mechanism was explored with Stern Volmer equation and the quenching of the fluorescence was assumed to proceed through static process. Moreover, the free energy change, ∆G°, for the complex formation reactions were −25.6 and −30.1 KJ mol−1 for FBZ and MBZ, respectively.

Studies on Pitting Corrosion of Al-Cu-Li Alloys Part III: Passivation Kinetics of AA2098-T851 Based on the Point Defect Model.

In this paper, the passivation kinetics of AA2098–T851 was investigated by a fundamental theoretical interpretation of experimental results based on the mixed potential model (MPM). The steady state passive layer formed on the AA2098–T851 in NaHCO3 solution in a CO2 atmosphere upon potentiostatic stepping in the anodic direction followed by stepping in the opposite direction was explored. Potentials were selected in a way that both anodic passive dissolution of the metal and hydrogen evolution reaction (HER) occur, thereby requiring the MPM for interpretation. Optimization of the MPM on the experimental electrochemical impedance spectroscopy (EIS) data measured after each potentiostatic step revealed the important role of the migration of Al interstitials in determining the kinetics of passive layer formation and dissolution. More importantly, it is shown that the inequalities of the kinetics of formation and dissolution of the passive layer as observed in opposite potential stepping directions lead to the irreversibility of the passivation process. Finally, by considering the Butler–Volmer (B–V) equation for the cathodic reaction (HER) in the MPM, and assuming the quantum mechanical tunneling of the charge carriers across the barrier layer of the passive film, it was shown that the HER was primarily controlled by the slow electrochemical discharge of protons at the barrier layer/solution (outer layer) interface.

Mechanistic and Conformational Studies on the Interaction Between Myriocin and Human Serum Albumin by Fluorescence Spectroscopy and Molecular Docking

The interactions between myriocin (ISP-1) and human serum albumin (HSA) were studied by fluorescence spectroscopy, synchronous fluorescence spectroscopy, three-dimensional fluorescence spectroscopy and molecular docking approach. The intrinsic fluorescence of HSA was quenched through a combination of static and dynamic quenching. The binding constants and the number of binding sites were evaluated according to the Stern–Volmer equation. ISP-1 could not bind efficiently to HSA at higher temperatures. The electrostatic force, hydrogen bonding and hydrophobic force were dominant for the binding ISP-1 and HSA. The site I was the primary binding site for the binding ISP-1 and HSA. What’s more, the conformational and microenvironmental changes of HSA during the binding process were studied by synchronous fluorescence spectroscopy and three-dimensional fluorescence spectroscopy. Lys-195, Arg-218, Arg-222 and Val-293 were the important amino acid residues involved in the binding process.

A Novel Fractional Order Model for State of Charge Estimation in Lithium Ion Batteries

Battery models are the cornerstone to battery state of charge (SOC) estimation and battery management systems in electric vehicles. This paper proposes a novel fractional-order model for a battery, which considers both Butler–Volmer equation and fractional calculus of constant phase element. The structure characteristics of the proposed model are then analyzed, and a novel identification method, which combines least squares and nonlinear optimization algorithm, is proposed. The method is proven to be efficient and accurate. Based on the proposed model, a fractional-order unscented Kalman filter is developed to estimate SOC, while singular value decomposition is applied to tackle the nonlinearity of Butler–Volmer equation and fractional calculus of constant phase element. The systematic comparison between the proposed model and traditional fractional order model is carried out on two LiNiMnCo lithium-ion batteries at different temperatures, ageing levels, and electric vehicle current profiles. The comparison results show that the proposed model has higher estimation accuracy in battery terminal voltage and SOC than the traditional model over wide range of temperature and ageing level under electric vehicle operation conditions. Furthermore, the hardware-in-the-loop test validates that the proposed SOC estimation method is suitable for SOC estimation in electric vehicles.

Synthesis, X-ray structural analysis, antibacterial and DNA-binding studies of a lanthanum bis-(5,5′-dimethyl-2,2′-bipyridine) complex

A new complex with the formula [La(5,5′-dmbpy)2(NO3)3] (a) [where (5,5′-dmbpy = 5,5′-dimethyl-2,2′-bipyridine)] has been synthesized. The compound was characterized by cyclic voltammetry, elemental analysis and spectroscopic methods (IR, UV–Vis, 1H-NMR). Single crystals adapted for X-ray diffraction analysis were recorded by slow crystallization from a methanol solution. The complex is neutral being the lanthanum cation chelated by two bipyridine derivative neutral ligands and three bidentate nitrate groups. Electronic spectra show the transition of both ligand field and charge transfer bands. The fluorescence properties of the compound have been studied. The interactions of complex with FS-DNA (salmon sperm DNA) have been studied using UV–Vis, fluorescence spectroscopies and gel electrophoresis. The above-mentioned techniques were used in physiological buffer having pH 7.2. The binding constant (Kb) for interaction in (a) with DNA was obtained using UV–Vis spectroscopies (Kb= 1.2 × 105) and fluorescence spectroscopies (Kb= 1.50 × 105). The binding constant (Kb), the number of binding sites for each 1000 nucleotides (n) and the apparent bio molecular quenching constant (kq) for FS-DNA were obtained through Stern–Volmer equation. Thermodynamic parameters data (∆H°, ΔS° and ΔG°) showed that hydrogen bonding and van der Waals interactions have an important function in the interaction of DNA–La(III) complex, and the binding mode is the groove binding. The DNA binding of La(III) complex is spontaneous as suggested by the negative ΔG°. Moreover, the DNA cleavage has been studied using agarose gel electrophoresis. The antibacterial effects of complex (a) have also been examined in vitro against standard bacterial strains.

The electrochemical properties of alloy 690 in simulated pressurized water reactor primary water: Effect of temperature

By anodic potentiostatic polarization and electrochemical impedance spectroscopy (EIS) measurements, the effect of temperature (200 °C, 250 °C, and 300 °C) on the electrochemical behavior of Alloy 690 was investigated in oxygenated borate buffer solution containing H3BO3 (2000 ppm B) + LiOH (2 ppm Li). The steady state passive current density was independent of the film formation potential at each temperature, indicating that the passive film is n-type in electronic character based on the predictions of the Point Defect Model (PDM). The passive current density increased and the absolute value of impedance decreased with increasing temperature, indicating a corresponding decrease in corrosion resistance. A mixed potential model (MPM), containing the PDM for describing the anodic passive dissolution of the alloy and the generalized Butler–Volmer equation for the cathodic oxygen reduction reaction was optimized on the experimental EIS data in order to extract model parameters, including kinetic parameters for the generation and annihilation of point defects in the barrier layer of the passive film. Metal (Cr,Ni,Fe) interstitials, which were found to have a higher concentration than oxygen vacancies, dominate the point defect structure of the barrier layer of the passive film at each temperature, thereby accounting for the n-type behavior of the passive film. With increasing temperature, the film thickness and defect density also increased, resulting in the decreased corrosion resistance of film. This indicates that the defect density of passive film plays a more important role on corrosion behavior of alloy than the film thickness.

One step synthesis of AgClNPs/PANI/D-dextrose nanocomposite by interfacial polymerization method and its catalytic and photocatalytic applications

A new approach was used to prepare a hybrid material of silver chloride nanoparticles incorporated into a polyaniline-grafted D-dextrose nanocomposite (AgClNPs/PANI/D-Dex) by an interfacial polymerization method. The AgClNPs/PANI/D-Dex nanocomposite was characterized with distinct instrumental methods such as Fourier Transform Infrared Spectroscopy (FT-IR), UV–visible Spectroscopy (UV–Vis), Fluorescence spectroscopy, X-ray Powder Diffraction (XRD), Raman spectroscopy, Thermal Gravimetric Analysis (TGA), Zeta sizer analyzer, Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), Electrochemical Impedance Spectroscopy (EIS) and Cyclic Voltammetry (CV). This nanocomposite was used in the catalytic reduction of 4-nitrophenol (4-NP) with NaBH4 as the reducing agent and photocatalytic degradation of methylene blue (MB) under visible light irradiation. The catalytic reduction of 4-NP was also investigated with different catalyst dosages of the AgClNPs/PANI/D-Dex nanocomposite. This nanocomposite proved to be an excellent catalyst for the reduction of 4-NP to 4-AP with a reaction rate of 0.365 min−1. The AgClNPs/PANI/D-Dex nanocomposite catalyst was additionally reused for the reduction of 4-NP after four cycles. AgClNPs/PANI/D-Dex nanocomposite was also applied as a photocatalyst for the degradation of MB under visible light irradiation. The extent of photocatalytic degradation of MB was determined as a function of various parameters such as dosage, pH of MB solution and different initial concentrations of MB solution under visible light irradiation. This hybrid AgClNPs/PANI/D-Dex nanocomposite enhanced the electron-hole separation, provided a high surface area and improved the photocatalytic activity under visible light irradiation because of the synergetic effect of AgClNPs and PANI/D-Dex to enhance the photocatalytic reaction with a reaction rate constant of 0.0298 min−1. Further, the fluorescence quenching for calculated the binding interaction between MB dye and AgClNPs/PANI/D-Dex nanocomposite was also studied. The binding interaction constant (Ka) was calculated by using the Stern–Volmer equation. Finally, AgClNPs/PANI/D-Dex nanocomposite exhibited good catalytic and photocatalytic properties.

A novel star-shaped triazine-triphenylamine–based fluorescent chemosensor for the selective detection of picric acid

This work reports development of a new donor-acceptor–type star-shaped 4,4′,4″-(1,3,5-triazine-2,4,6-triyl)tris(N,N-diphenylaniline) (TRZDPA) molecule towards detection of an ultratrace amount of picric acid (PA). TRZDPA showed solvent-dependent fluorescence spectra in an excited state owing to its strong intramolecular charge-transfer properties. As a fluorescent probe, TRZDPA shows remarkable sensitivity towards the PA in a highly selective manner compared with other nitroaromatic compounds. Furthermore, efficiency of the quenching process was evaluated by the Stern–Volmer equation. The fluorescence quenching mechanism of the probe during PA detection was evaluated from the photophysical and other spectral characterizations. The detection limit of PA was 0.37 nM, confirming the detection of PA in aqueous media at a trace level. To facilitate easy detection of PA, TRZDPA-modified fluorescent thin-layer chromatography (TLC) strips were developed as ‘turn-off’ sensors which can be visualized by the naked eye.

Calix[4]pyrrole virtuous sensor: a selective and sensitive recognition for Pb(II) ions by spectroscopic and computational study

ABSTRACTA novel supramolecular sensor derived from calix[4]pyrrole system i.e. calix[4]pyrrole bearing aminoanthraquinone derivative (CAAQ) have been designed and synthesized. The complexation behavior of metal cations [Ag(I), Ba(II), Ca(II), Ni(II), Co(II), Fe(III), Hg(II), Cu(II), Cr(II), Pb(II), Zn(II), (1 × 10−4 M)] with CAAQ (1 × 10−6 M) was studied by spectrophotometry and spectrofluorometry. Metal ion like Pb(II) produces red shift in absorption spectra and quenching in emission spectra likelihood of strong complexation of Pb(II) ions with CAAQ. Fluorescence cell imaging also supports the complexation of Pb(II) ions with CAAQ. The binding constants, quantum yield, stoichiometry of complex, mechanism of quenching by Stern–Volmer equation and Density functional theory calculation have been determined.

Plasma-modified C-doped Co3O4 nanosheets for the oxygen evolution reaction designed by Butler–Volmer and first-principle calculations

Electrocatalysts serving in electrochemical cells differ from general chemical catalysts by way of their special double-layer structure and a rarely discussed interface potential drop as described by the Butler–Volmer (BV) equation.

A fresh look at depolarisation criteria for cathodic protection of steel reinforcement in concrete

Criteria for the successful application of cathodic protection (CP) for steel reinforced concrete have been fixed for decades and form part of ISO EN12696. The most used criterion is the achievement of 100 mV depolarization over a period not exceeding 24 hours after discontinuation of the applied current. Although more empirical than theoretically based, the criterion has served the CP industry well. It does, however, exclude any systems that may not always achieve that level of depolarization but have been shown to offer adequate protection, and so there is a need to explore ways of assessing depolarisation data more effectively. On a fundamental level, non-linear polarisation, as described by the Butler Volmer equation, relates corrosion rate to polarisation for a given applied current density and shows that at low current densities, estimated corrosion rates can be shown to be still insignificant at less than 100 mV polarisations. This paper explores the use of non-linear polarisation as an additional supportive criterion based on the measured 24-hour depolarisation level for a known applied current density and tests its applicability in the laboratory and in the field. It speculates that a reducing apparent corrosion current density trend in combination with a depolarised potential moving in a more noble direction is likely to be a suitable alternative criterion, where 100 mV depolarisation is not achieved.

Predicting the corrosion rate of steel in cathodically protected concrete using potential shift

The commonly accepted Cathodic Protection (CP) criterion i.e. 100 mV decay evolves from experimental investigations and may not always be accurate. Alternatively, corrosion rate monitoring can assess the adequacy of CP. This work examines the possibility of predicting the corrosion rate of steel in concrete using polarization data induced by known applied current density using Butler Volmer equation. For this, the value of cathodic Tafel slope (βc) plays an important role; decreasing βc from 210 to 60 mV, decreases the corrosion rate by 92% at 20 mA/m2 current density.The adequacy of the proposed method is evaluated by applying Impressed Current Cathodic Protection (ICCP) to concrete specimens which have a zinc rich paint (ZRP) as an external anode for a short duration of time. Results showed that to achieve at least 100 mV of depolarization, the applied current density should be at least 7 times the corrosion rate for the ZRP anode. However, this holds true, considering the short duration of the tests. Prediction of the corrosion rate of steel from potential shift forms the basis for the improved CP performance criterion for reinforced concrete structures.

Modeling Power Generation and Energy Efficiencies in Air-Cathode Microbial Fuel Cells Based on Freter Equations

The model proposed in this study was based on the assumption that the biomass attached to the anode served as biocatalysts for microbial fuel cell (MFC) exoelectrogenesis, and this catalytic effect was quantified by the exchange current density of anode. By modifying the Freter model and combining it with the Butler–Volmer equation, this model could adequately describe the processes of electricity generation, substrate utilization, and the suspended and attached biomass concentrations, at both batch and continuous operating modes. MFC performance is affected by the operating variables such as initial substrate concentration, external resistor, influent substrate concentration, and dilution rate, and these variables were revealed to have complex interactions by data simulation. The external power generation and energy efficiency were considered as indices for MFC performance. The simulated results explained that an intermediate initial substrate concentration (about 100 mg/L under this reactor configuration) needed to be chosen to achieve maximum overall energy efficiency from substrate in the batch mode. An external resistor with the value approximately that of the internal resistance, boosted the power generation, and a resistor with several times of that of the internal resistance achieved better overall energy efficiency. At continuous mode, dilution rate significantly impacted the steady-state substrate concentration level (thus substrate removal efficiency and rate), and attached biomass could be fully developed when the influent substrate concentration was equal to or higher than 100 mg/L at any dilution rate of the tested range. Overall, this relatively simple model provided a convenient way for evaluating and optimizing the performance of MFC reactors by regulating operating parameters.