Phase Volume Change Research Articles

Studies for mutual solubility of TODGA and water at 298.15 K and 0.1 MPa

Tetra-octyl diglycolic amide (TODGA) is an emerging novel solvent for flowsheet demonstrations of novel nuclear extraction processes used in nuclear fuel cycle and associated waste management activities. Mutual solubilities of extractant and water are important process parameters for modeling the mass transfer as these are vital for phase volume change calculations. Experimental results for aqueous solubility of TODGA were reported based on SCWO assisted persulphate based TOC measurements. Experimental results for solubility of water in the binary solutions of TODGA and n-dodecane were reported based on KF titration. Reported values were correlated by empirical equations.

Assessing energy balance via seismic and mechanical observations in high temperature induced crack damage in marbles

Assessing the rock physical and mechanical behavior under different temperatures has become of utmost importance. It is well known that thermal stresses induce significant crack damage in rocks due to thermal expansion or phase transformation and volume changes. Quantifying and forecasting the evolution of rock physical and mechanical parameters with temperature is thus crucial for evaluating rock integrity in many applications such as geothermal fields, nuclear waste storage, wildfire or volcanic processes. In marbles the degree of previous exposure to temperature and the chemical composition (i.e. calcite vs dolomite) plays a key role for controlling the mechanical evolution under temperature. Moreover separating out the energy contribution provided by anelastic processes driving crack damage and elastic reversible deformation under increasing temperature remains an open challenge. With these aims, three sample sets of marbles with different contents of calcite and dolomite from two Brazilian quarries were tested under different temperature conditions (from room temperature up to 600 °C). A marked increase of thermal cracking was observed after 400 °C, accompanying mass loss up to 1% and porosity increase. Moreover, a significant drop in seismic wave velocities, uniaxial compressive strength and electrical resistivity, in wet conditions, was also detected.Spectral behavior from seismic traces and energy dissipation from stress-strain curves were analyzed. A dominance of the dissipated energy compared to the elastic one was observed and related to the generation of new fracturing surfaces. This hypothesis was supported by the spectral behavior showing multiple scattering effects in the high frequency components, with an increase in attenuation. The results suggested that the percentage of dolomite has a high influence on the mechanical behavior even at low temperature, mirroring the prevalence of brittle processes in dolomitic marbles. This study represents a comprehensive benchmark for the study of effect of temperature on rocks because of its multidisciplinary and multimethod approach and the demonstrated sensitivity to subtle textural changes. Moreover, it provides a reliable tool for crack damage analysis at each thermal stress.

Corrosion Behavior of Cobalt Oxide and Lithium Carbonate on Mullite-Cordierite Saggar Used for Lithium Battery Cathode Material Sintering.

Mullite-cordierite ceramic saggar is a necessary consumable material used in the synthesis process of LiCoO2 that is easily eroded during application. In our study, we systematically investigated the characteristics and surface corrosion behavior of waste saggar samples. We divided the cross sections of waste saggar into the attached layer, hardened layer, permeability layer, and matrix layer. Then, we examined the high-temperature solid-state reactions between saggar powder and lithium carbonate or cobalt oxide to identify erosion reactants correlating with an increase in the number of recycled saggars. The results of time-of-flight secondary ion mass spectrometric analysis (TOF-SIMS) prove that the maximum erosion penetration of lithium can reach 2 mm. However, our morphology and elemental distribution analysis results show that the erosion penetration of cobalt was only 200 μm. When enough lithium carbonate reacted, lithium aluminate and lithium silicate were the main phases. Our X-ray computed tomography (X-ray CT) analysis results show that the change in phase volume before and after the reaction, including the generation of oxygen and carbon dioxide gas, led to the internal crack expansion of the material-saggar interface. Our results can contribute to improving saggar and upgrading waste saggar utilization technology.

Equilibration and thermal reversibility in mixtures of model OPV small-molecules and polymers

Following annealing at sufficiently high temperatures, well-controlled thin-film bilayers exhibit thermal changes in phase-composition, phase-volume and interfacial roughness that are reversible, irrespective of the starting layer compositions.

Experimental study in thermal expansion devices of phase-change material coupled to vapor chamber with gradient wettability wick

With the rapid development of electronics and communication technology, the applications of high-performance chips and large-scale integrated circuits have become more and more widespread. Most electronic devices have low heat generation in standby mode but large heat generation during operation, and the instantaneous temperature rise is fast. The problems of resistance to thermal shock and heat dissipation have become the bottleneck of the development of electronic technology. Phase-change thermal control technology uses phase change materials to control the temperature of electronic devices with short-term high output power. It has the advantages of reliable performance, economical and energy saving. The temperature uniformity of the bottom surface is conducive to heat expansion in the interior of the phase change material, which is promoting to the phase ratio with the finite volume phase change material. In this article, a kind of novel thermal expansion device coupled PCM (paraffin OP50E) heat sinks with vapor chambers was proposed, which were applied with gradient wettability capillary wick. The copper microcolumns clusters as the capillary wicks in these vapor chambers were grown by electroplating on copper substrate plates covered with photolithography masks using the progressive current method. By changing the characteristic scales of the microcolumn clusters from 100 μm to 10 μm, the gradient capillary pressure direction was concentrated from the periphery to the middle, and the surface wettabilities of the capillary wicks were changed from hydrophilic to superhydrophilic. From the analysis of the experimental results, the vapor chambers with gradient wettability wicks can shorten the thermal response time of the thermal expansion device by 81.7 %, and at the same time, reduce the temperature at the center of the heat source with a heat flux of 40 W/cm2 by 6.8 °C, which can be applied to effectively control the central heat source temperature of the pulsed short-time electronic device.

MoS2 with high 1T phase content enables fast reversible zinc-ion storage via pseudocapacitance

Zinc-ion batteries (ZIBs) have garnered considerable interest due to their inherent high safety, low cost, and environmental friendliness. However, the reaction mechanism of cathode material in ZIBs is not entirely clear. Herein, Mixed-phase MoS2 with a high proportion (66%) of 1T phase and 2H phase (TH-MoS2), synthesized by the hydrothermal method, is reported as the cathode material for ZIBs. Material characterizations show that TH-MoS2 have obvious two phase MoS2 with different crystal structures causes sulfur vacancies, increases interlayer spacing and intercalation water. TH-MoS2 cathode delivers excellent electrochemical performance, a satisfactory capacity of 156 mAh g−1, and an excellent cycling performance with 97.3% capacity retention after 500 cycles at 1 A g−1. The ex-situ characterizations elucidate that TH-MoS2 achieves highly reversible Zn2+ storage with negligible phase transition, volume change, and lattice distortion upon cycle. Based on kinetic analysis and first-principles calculations results, Zn2+ and H+ can be stored in TH-MoS2 and the energy storage mechanism of TH-MoS2 electrode is dominated by pseudocapacitance. Understanding the MoS2 reaction mechanism will facilitate comprehension of cathode materials for ZIBs.

Programmable shape deformation actuated bilayer hydrogel based on mixed metal ions

The intelligent hydrogel actuators that respond to temperature have great application prospects in many fields. At the same time, the intelligent hydrogel actuators still have challenges in driving force, deformation intensity, and programming deformation. Herein, we fabricated a bilayer hydrogel actuator using a two-step photopolymerization method, which consists of a poly(N-isopropylacrylamide)-chitosan-N-2-hydroxypropyl trimethylammonium chloride (PNIPAm-HACC) layer with an LCST-type volume phase change and an alginate-polyacrylamide (SA-PAm) layer. We employed mixed metal ions (trivalent/divalent cations) to cross-link alginate-based hydrogels to construct two-dimensional and three-dimensional cross-linked structure units, resulting in a synergistic effect. The Zn2+/Fe3+(1:1)-SA-PAm/PNIPAm-HACC bilayer-actuated hydrogels have excellent antibacterial properties, shape fixation (85.4 %), fatigue resistance, and reversibility, and showed rapid, reversible, and reproducible thermoresponsive bending/unbending properties, which can be prepared as an actuator, such as a gripper to capture, transport, and release an object, or a temperature-controlled device to turn on and off indicator lights. Overall, this hybrid ion-crosslinked bilayer hydrogel can provide new insights into the design and fabrication of smart actuators.

Double-buffer-phase embedded Si/TiSi2/Li2SiO3 nanocomposite lithium storage materials by phase-selective reaction of SiO with metal hydrides

Silicon monoxide (SiO)-based anode materials have been extensively investigated as high-capacity anode materials for lithium-ion batteries; however, they suffer from low initial Coulombic efficiency (ICE). Solid-state prelithiation of SiO with LiH has shown some promise to address this shortcoming, and further improvement in long-term cycle performance is a necessary step toward commercial application. Here, we propose a double-buffer-phase embedded Si/TiSi2/Li2SiO3 nanocomposite materials prepared by phase-selective reaction of SiO with metal hydrides to improve both ICE and cycle performance. The resulting Si/TiSi2/Li2SiO3 nanocomposite material outperformed prelithiated SiO with LiH composed of nanoscale Si and Li2SiO3 phase for up to 500 cycles without a significant decrease in ICE. The nano-scale TiSi2 phases formed by the reaction of Si phase in SiO with TiH2 played a key role in boosting the capacity retention of the Si/TiSi2/Li2SiO3 nanocomposite by providing a robust mechanical buffer to sustain the physical integrity of the electrode against large volume changes of Si phase during cycling. In addition to superior cycle performance, Si/TiSi2/Li2SiO3 nanocomposite demonstrated improved thermal stability at elevated temperatures and greater rate capability compared with pristine and prelithiated SiO materials, changes that can be attributed to newly introduced TiSi2 buffer phase.

Biomolecules under Pressure: Phase Diagrams, Volume Changes, and High Pressure Spectroscopic Techniques.

Pressure is an equally important thermodynamical parameter as temperature. However, its importance is often overlooked in the biophysical and biochemical investigations of biomolecules and biological systems. This review focuses on the application of high pressure (>100 MPa = 1 kbar) in biology. Studies of high pressure can give insight into the volumetric aspects of various biological systems; this information cannot be obtained otherwise. High-pressure treatment is a potentially useful alternative method to heat-treatment in food science. Elevated pressure (up to 120 MPa) is present in the deep sea, which is a considerable part of the biosphere. From a basic scientific point of view, the application of the gamut of modern spectroscopic techniques provides information about the conformational changes of biomolecules, fluctuations, and flexibility. This paper reviews first the thermodynamic aspects of pressure science, the important parameters affecting the volume of a molecule. The technical aspects of high pressure production are briefly mentioned, and the most common high-pressure-compatible spectroscopic techniques are also discussed. The last part of this paper deals with the main biomolecules, lipids, proteins, and nucleic acids: how they are affected by pressure and what information can be gained about them using pressure. I I also briefly mention a few supramolecular structures such as viruses and bacteria. Finally, a subjective view of the most promising directions of high pressure bioscience is outlined.

Efficient synthesis of furfural from xylose over HCl catalyst in slug flow microreactors promoted by NaCl addition

AbstractEfficient synthesis of furfural from xylose over the HCl catalyst in a water‐methyl isobutyl ketone biphasic system was achieved in slug flow microreactors, using NaCl as a promotor which facilitates xylose dehydration and suppresses xylose condensation. An optimized furfural yield of 93% was obtained from 1 M xylose over 0.2 M HCl with 10 wt% NaCl at 180°C within 4 min. A comprehensive kinetic model was developed from monophasic experiments in water in microreactors, by incorporating the acidity in water and kinetic constants as a function of the chloride ion concentration. The coupling of kinetic model with furfural extraction, with consideration of phase volume change as a function of temperature and partial phase miscibility, enables to predict the results of biphasic experiments in microreactors where mass‐transfer limitation was eliminated. The aqueous phase containing HCl and NaCl could be readily recycled and reused multiple times without noticeable performance loss.

Bifunctional Smart Hydrogel Dressing with Strain Sensitivity and NIR-Responsive Performance.

Smart response hydrogel has a broad application prospect in human health real-time monitoring due to its responses to a variety of stimuli. In this study, we developed a novel smart hydrogel dressing based on conductive MXene nanosheets and a temperature-sensitive PNIPAm polymer. γ-Methacryloxypropyltrimethoxysilane (KH570) was selected to functionalize the surface of MXene further to improve the interface compatibility between MXene and PNIPAm. Our prepared K-M/PNIPAm hydrogel was found to have a strain-sensitive property, as well as a respond to NIR phase change and volume change. When applied as a strain flexible sensor, this K-M/PNIPAm hydrogel exhibited a high strain sensitivity with a gauge factor (GF) of 4.491, a broad working strain range of ≈250%, a fast response of ∼160 ms, and good cycle stability (i.e., 3000 s at 20% strain). Besides, this K-M/PNIPAm hydrogel can be used as an efficient NIR light-controlled drug release carrier to achieve on-demand drug release. This work paved the way for the application of smart response hydrogel in human health real-time monitoring and NIR-controlled drug release functions.

Stabilizing the Nanosurface of LiNiO2 Electrodes by Varying the Electrolyte Concentration: Correlation with Initial Electrochemical Behaviors for Use in Aqueous Li-Ion Batteries.

This study attempted to stabilize the nanosurface of LiNiO2 (LNO) electrodes by varying the electrolyte concentration, significantly influencing its initial electrochemical behaviors for use in aqueous lithium-ion batteries. The charge/discharge capacities, reversibility, and cyclability of LNO were improved during initial cycles with an increase in the concentration of lithium bis(trifluoromethanesulfonyl)imide (LiTFSI). As determined by the galvanostatic intermittent titration technique, the superior diffusivity of Li+ ions in the LNO electrode is also obtained in the concentrated electrolyte. Nanoscale observation of the LNO surface revealed that its morphology is maintained relatively well in the concentrated electrolyte while it is destroyed in dilute electrolytes after the initial electrochemical cycles. These results are considered to be attributable to the variation of the interface condition in the electrical double layer with an increase in the electrolyte concentration, thus stabilizing the nanosurface of LNO by suppressing the dissolution of Ni ions from the surface. Additionally, in situ X-ray diffraction analysis demonstrated that LNO shows more stable phase transitions and volume changes as the electrolyte concentration increases, indicating that its structural changes in bulk can be directly related to the state of the nanosurface, which has a positive impact on the initial electrochemical behaviors in this system.

Modeling the one-way and two-way shape memory effects of semi-crystalline polymers

Polymers of two-way shape memory effects (SMEs) are of great application potential ranging from intelligent actuators to artificial muscles due to their reversible shape response on the basis of an on-off stimulus such as a cooling-heating cycle, which motivates the development of theoretical tools to support their design. In the paper, a three-dimensional phase transition finite deformation constitutive model is proposed to phenomenologically describe the underlying mechanisms of the one-way and two-way SMEs in thermal-responsive semi-crystalline polymers. A unified transition equation is proposed to depict the volume changes of crystalline phase during both crystallization and melting transitions. The crystallization-induced elongation and melting-induced contraction behaviours in two-way SMEs are assumed to be realized by an elongation-contraction element and its temperature-dependent strain evolution rules. The overall constitutive model is then implemented into Mathematica, and the model predictions are compared to and agree well with the experimental results. The paper provides an efficient method on modeling the thermal-induced two-way SMEs under stress conditions in semi-crystalline polymers and detailed discussion about the influence of several parameters such as the crosslinking density, the applied external load and the cooling/heating rate.

Grain-orientation-dependent phase transformation kinetics in austenitic stainless steel under low-temperature uniaxial loading

Deformation-induced martensites generally follow the principle on the selection of their variants in intrinsic crystallographic orientations with regard to the parent grains, which should be significantly affected by the cooperative rotation of the matrix. In this paper, the microstructural changes related to the deformation-induced transformation from metastable γ austenite to ε and α′ martensites in 304 austenitic stainless steel upon uniaxial tensile loading at 180 K was investigated by employing in-situ synchrotron-based high-energy X-ray diffraction technique. The detailed information on low-temperature phase transformation kinetics was analyzed in terms of the grain rotation and the change in phase volume, stress partitioning, and dislocation density, which were further compared with experimental observations for the room temperature deformed specimen almost without stress-induced martensite. The elastic strain measured in the newly formed α′ martensite was quite low (only ~200 μɛ) upon tensile loading due to stress relaxation, evidencing the role of α′ martensite nucleation in strain accommodation. The minor statistical evolution of texture for all constituent phases, in combination with the martensitic variant selection principle, enables us to reveal the complex interactions of deformation and transformation, finding that the ε martensite firstly originated in the [0 0 1]//LD-oriented grains of γ matrix, while α′ martensite was initially formed in the [1 1 1]//LD-oriented γ grains. Furthermore, the interplay of phases enhanced the grain rotation toward [0 0 1] during deformation at 180 K, which could be elucidated by the influence of transformed martensites on the specific selection of slip systems.

Selective fructose dehydration to 5-hydroxymethylfurfural from a fructose-glucose mixture over a sulfuric acid catalyst in a biphasic system: Experimental study and kinetic modelling

A two-step process combining the (equilibrium) glucose isomerization to fructose with selective dehydration of fructose in the obtained sugar mixture to 5-hydroxymethylfurfural (HMF), where glucose is largely unconverted and recycled, represents an attractive concept to increase the overall efficiency for HMF synthesis. This work presents experimental and modelling studies on the conversion of such fructose-glucose mixture to HMF using the sulfuric acid catalyst in a water-methyl isobutyl ketone biphasic system under a wide range of conditions (e.g., temperature, catalyst and sugar concentrations). Through detailed product analyses and ESI-MS spectroscopy, the excess formation of formic acid (together with humins) by the direct sugar/HMF degradation was confirmed and included in the reaction network (neglected in most literatures). The kinetic modelling based on batch experiments in monophasic water well describes the measurements thereof, whereas distinct deviations were found in the prediction of typical literature kinetic models. The incorporation of HMF equilibrium extraction into the developed kinetic model, with consideration of phase volume change as a function of temperature and partial phase miscibility, enables to predict reaction results in the biphasic system in batch. This kinetic model allows to optimize conditions for HMF synthesis that are favored in continuous reactors with minimized back mixing. Based on the model implications, the biphasic system was optimized with slug flow microreactors to better address process intensification and scale-up aspects. Using a simulated fructose-glucose mixture feedstock to represent commercially available high fructose corn syrups, a maximum HMF yield of 81% was obtained at 155 °C over 0.05 M H2SO4 at a residence time of 16 min in the microreactor, with 96% fructose conversion and over 95% of glucose remaining unconverted.

Highly Bidirectional Bendable Actuator Engineered by LCST-UCST Bilayer Hydrogel with Enhanced Interface.

Thermoresponsive hydrogel-based actuators are highly important for fundamental research and industrial applications, while the preparation of temperature-driven bilayer hydrogel actuators with rapid response to bend and recover properties remains a challenge. To date, most temperature-driven bilayer hydrogel actuators are based on polymers only with a lower critical solution temperature (LCST) or with an upper critical solution temperature (UCST), which need more time to bend and recover just in a small range of bending angle. Herein, we propose a new strategy to design and synthesize a fully temperature-driven bilayer hydrogel actuator, which consists of a poly(N-acryloyl glycinamide) (NAGA) layer with a UCST-type volume phase change and a poly(N-isopropyl acrylamide) (NIPAM)-Laponite nanocomposite layer with an LCST-type volume phase change. Due to the complementary UCST and LCST behavior of the two selected polymers, both layers have opposite thermoresponsive swelling and shrinkage properties at low and high temperatures; this imbues the hydrogel actuator with rapid thermoresponsive bending and recovery ability, as well as a large bending angle. In addition, the incorporation of Laponite nanosheets in PNIPAM layer not only improves the mechanical property of actuators but also provides the excellent bonding ability of the two-layer interface, which prevents delamination caused by excessive local stress on the interface during the bending process. Thanks to high-performance behavior, the actuator can act as an effective and sensitive actuator, such as a gripper to capture, transport, and release an object, or as an electrical circuit switch to turn on and off a light-emitting diode (LED). Overall, such hydrogel actuator may provide new insights for the design and fabrication of artificial intelligence materials.

Free-energy analysis of the nonhysteretic first-order phase transition of Eu2In

Binary intermetallic ${\mathrm{Eu}}_{2}\mathrm{In}$ was recently reported to exhibit a giant anhysteretic magnetocaloric effect due to a first-order magnetic phase transition between paramagnetic and ferromagnetic states. Experimentally, the transition occurs with a small phase volume change, $\mathrm{\ensuremath{\Delta}}V/V$, of approximately 0.1% around ${T}_{C}$ of $ca.$ 55 K. We represent magnetic and compute magnetocaloric properties of a ${\mathrm{Eu}}_{2}\mathrm{In}$ compound using a microscopic description based on a model Hamiltonian that takes into account magnetic exchange and magnetoelastic interactions. In the model the thermodynamic nature of the transition is conveniently represented by a single magnetoelastic interaction parameter. A good agreement between the theoretical results and earlier published experimental data confirms the effectiveness of our approach.

Dynamics and phase change heat transfer of an isolated vapor bubble traveling through a heated T-shaped branching microchannel

While flow boiling problem has been extensively investigated in the last decades, the transport details of boiling flow in heated T-shaped branching microchannels have not yet been revealed with high-fidelity simulations. The present paper reports a numerical study of the saturated boiling of an isolated vapor bubble traveling through a heated T-shaped branching microchannel. The evolution of liquid-vapor interface is captured with the volume of fluid (VOF) method, while the saturated-interface volume phase change model is employed to simulate heat and mass exchange on the interface. The numerical model is first validated with literatures, and then is utilized to simulate the bubble dynamics and phase change heat transfer. The numerical results indicate that even a very low wall heat flux can exert great influences on the bubble dynamics and heat transfer characteristics. When the bubble travels through the heated main channel (HMC), the bubble keeps growing and the heat transfer coefficient of the HMC keeps increasing. After the bubble nose leaves the HMC and enters the heated branching channel (HBC), the bubble gradually breaks into two bubbles. The bubble breakup process is found to have a great impact on the heat transfer characteristics of the HBC. As a result, the heat transfer coefficient of the HBC is improved more significantly compared with that of the HMC. At last, the influence of inlet Reynolds number (Re) on bubble dynamics and heat transfer characteristics is revealed. The bubble breakup regime is found to change significantly with Re ranging from 76 to 612. The overall heat transfer enhancement gradually decreases with increasing Re. This study provides a new insight into the bubble motion in T-shaped branching microchannels.

Thin solid electrolyte interface on chemically bonded Sb2Te3/CNT composite anodes for high performance sodium ion full cells

Nanostructured metal chalcogenides (MCs) and their composites are studied for high performance sodium-ion batteries (SIBs). Herein, we report the assembly of an emerging MC, Sb2Te3, with functionalized carbon nanotubes (CNTs) to form composite anodes. The role of oxygenated functional groups on CNTs in fostering the chemical interactions with Sb2Te3 for enhanced structural integrity of electrodes is elucidated by density functional theory combined with ab-initio molecular dynamics simulations and X-ray photoelectron spectroscopy analysis. Remarkably, cryogenic transmission electron microscopy (TEM) analysis reveals a uniform and thin solid electrolyte interface (SEI) layer of ~19.1 nm on the Sb2Te3/CNT composite while the neat Sb2Te3 presents an irregular and ~67.3 nm thick SEI. The ex-situ X-ray diffraction (XRD) and ex-situ/in-situ TEM analyses offer mechanistic explanations of phase transition and volume changes during sodiation. The Sb2Te3/CNT composite electrode with an optimal content of 10 wt% CNTs delivers excellent reversible gravimetric and volumetric capacities of 422 mA h g−1 and 1232 mA h cm−3, respectively, at 100 mA g−1 with ~97.5% capacity retention after 300 cycles. The excellent high-rate capability of 318 mA h g−1 at 6400 mA g−1 corroborates the structural robustness of the composite electrode. Sodium-ion full cells (SIFCs) are assembled by pairing the above anode with a Na3V2(PO4)2F3 cathode, which exhibit remarkable energy density of ~229 Wh kg−1 at 0.5 C and excellent cyclic stability of over 71% and 66% capacity retention at 5 C and 10 C, respectively, after 200 cycles. Even at 40 C, an ultrahigh power density of 5384 W kg−1 is delivered. Furthermore, the pouch-type SIFCs prove excellent flexibility with ~85% capacity retention after 1000 bending cycles and satisfactory operation under temperatures ranging from 40 to −20 °C. The design strategy developed here can also be employed to other electrode materials to achieve better SEI stability and excellent Na storage performance.

Calculating leakage in emulsion liquid membrane systems from pH measurements

Leakage of the internal phase droplets reduces the extraction efficiency of emulsion liquid membrane systems by spilling the stripping agent and previously extracted solute into the bulk phase. When the stripping agent is acid or base, internal phase leakage can be determined from bulk phase pH measurements. New equations for calculating leakage from these pH measurements are presented, which account for bulk phase chemistry and volume changes due to leakage and emulsion swell. We show that equations used in several studies published over more than 30 years include unidentified assumptions that can cause erroneous leakage estimates for systems with weak acid or base stripping agents or bulk phase solutions that are not initially neutral. Guidelines identifying when these approximate equations will underestimate leakage by 10% or more are presented. Based on these guidelines and calculations quantifying errors in examples from the literature, we expect that many results calculated from pH underestimate the actual leakage. The new equations use the same experimental data as the approximate equations with minimal increased complexity and are recommended whenever leakage is calculated from pH measurements in systems without solute extraction. Methods for extending the equations to systems with simultaneous solute extraction are described.