True Charge Research Articles

Electrochemical Interfaces with Non-Cottrellian Current-Time Scaling in Energy Storage

Researchers developing the next generation of energy storage systems are challenged to understand and analyze the different charge storage mechanisms, subsequently, use this understanding to design and control materials and devices that bridge the gap between high specific energy and power at a target cycle life. Correctly identifying and quantifying the prominent charge storage mechanism, which is either faradaic diffusion-limited, faradaic non-diffusion-limited (or pseudocapacitive), or capacitive, is of the utmost importance for understanding how the system functions and tuning material properties for specific applications. The different charge storage mechanisms are defined by a characteristic current-time scaling, that has been expressed for faradaic diffusion-limited (Cottrell relationship) and true capacitive charge storage and has been used to disentangle and determine the prominent mechanisms. However, the characteristic current-time scaling for faradaic non-diffusion-limited (or pseudocapacitive) charge storage remains unelucidated despite to date many energy storage devices, particularly those having ionic liquids, deep eutectic solvents or highly concentrated electrolytes, exhibit electrochemical interfaces with faradaic non-diffusion-limited charge storage.This talk presents the work on a theoretical intuitive framework for pseudocapacitive charge storage taking into consideration the faradaic nature of this mechanism and deviation from the classic electrochemical interface structure, which is the root cause for pseudocapacitance1. The theory will be corroborated with experimental current-time scaling using conventional variable-rate cyclic voltammetry and variable-rate AC cyclic voltammetry at higher harmonics. The results emphasize the distinct current-time scaling of pseudocapacitive charge storage mechanism and shed light on interfacial kinetics and mass transport processes in multivalent batteries with ionic liquid or deep eutectic solvents. The insights inform electrode and electrolyte material design, e.g., for fast-charging2,3and low-temperature batteries4,5.1 Schoetz, T., Gordon, L. W., Ivanov, S., Bund, A., Mandler, D. & Messinger, R. J. Disentangling faradaic, pseudocapacitive, and capacitive charge storage: A tutorial for the characterization of batteries, supercapacitors, and hybrid systems. Electrochimica Acta 412, 140072 (2022).2 Xu, J. H., Schoetz, T., McManus, J. R., Subramanian, V. R., Fields, P. W. & Messinger, R. J. Tunable Pseudocapacitive Intercalation of Chloroaluminate Anions into Graphite Electrodes for Rechargeable Aluminum Batteries. Journal of The Electrochemical Society 168, 060514 (2021).3 Leung, O. M., Gordon, L. W., Messinger, R. J., Prodromakis, T., Wharton, J. A., Ponce de León, C. & Schoetz, T. Solid Polymer Electrolytes with Enhanced Electrochemical Stability for High-Capacity Aluminum Batteries. Advanced Energy Materials 14, 2303285 (2024).4 Hawkins, B. E., Schoetz, T., Gordon, L. W., Kt, S., Wang, J. & Messinger, R. J. Reversible Zinc Electrodeposition at −60 °C Using a Deep Eutectic Electrolyte for Low-Temperature Zinc Metal Batteries. The Journal of Physical Chemistry Letters 14, 2378-2386 (2023).5 Schoetz, T., Xu, J. H. & Messinger, R. J. Ionic Liquid Electrolytes with Mixed Organic Cations for Low-Temperature Rechargeable Aluminum–Graphite Batteries. ACS Applied Energy Materials 6, 2845-2854 (2023).

Intrinsic and extrinsic contributions in the ferroelectric response of chemically synthesized BiFeO3-xPbTiO3 thin films

Multiferroic (BiFeO3)1−x-(PbTiO3)x (1−x)BF−xPT thin films exhibit very high electromechanical properties in the vicinity of the morphotropic phase boundary (MPB), making them important candidates for use in several modern device applications. However, preparing high-quality (1−x)BF−xPT thin films is challenging due to the high conductivity caused by oxygen vacancies produced during the synthesis process. This study aims to understand the effect of size and porosity density on the electrical properties of (1−x)BF−xPT thin films. A series of (1−x)BF−xPT solid solution thin films were fabricated using the spin-coating method on Pt/TiO2/SiO2/Si(100) substrates through chemical solution deposition. X-ray diffraction studies revealed a polycrystalline structure. Surface SEM images showed that the films have a uniform surface with average grain sizes ranging between 50 and 200 nm and an average film thickness of 1.5 μm. A decrease in average pore size and an increase in the number of pores were observed with the increase in PT concentration in the prepared films. Ferroelectric characterization revealed that the films exhibit room-temperature ferroelectric hysteresis loops. Sources of various contributions to polarization were extracted from hysteresis loops, including true ferroelectric switching and space charge contributions. Thin films with 0.30 < x < 0.45 show higher remanent and saturation polarization values, suggesting that these compositions exhibit the MPB. The highest remanent polarization value (PR = 16.68 μC/cm2) was observed for the thin film with x = 0.40. The correlation between the phase, composition, film morphology, and ferroelectric response is described and discussed.

Experimental research progress of charge order of nickelate based superconductors

Ever since the discovery, nickelate superconductors have attracted great attention, declaring a “nickel age” of superconductivity. Currently, there are two types of nickelate superconductors: low-valence nickelate superconductors RE<sub><i>n</i>+1</sub>Ni<sub><i>n</i></sub>O<sub>2<i>n</i>+2</sub> (RE, rare earth; <i>n</i>, number of adjacent NiO<sub>2</sub> layers) and high-pressure nickelate superconductors La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub> and La<sub>4</sub>Ni<sub>3</sub>O<sub>10</sub>. Charge order plays a crucial role in studying the strongly correlated systems, especially the cuprate superconductors, in which potential correlation between charge order and superconductivity has been indicated. Thus, great efforts have been made to explore the charge order in nickelate superconductors. In the infinite-layer nickelate RENiO<sub>2</sub>, the evidence of charge order with in-plane wavevector of <i> <b>Q</b> </i><sub>//</sub> ≈ (1/3, 0) has been found in the undoped and underdoped regime but not in the superconducting samples. However, subsequent studies have indicated that this is not the true charge order inherent in the NiO<sub>2</sub> plane,which carries unconventional superconductivity, but rather originates from the ordered excess apical oxygen in the partially reduced impurity phases. On the other hand, the overdoped low-valence nickelate La<sub>4</sub>Ni<sub>3</sub>O<sub>8</sub> shows well-defined intertwined charge and magnetic order, with an in-plane wavevector of <i> <b>Q</b> </i><sub>//</sub> = (1/3, 1/3). Resonant X-ray scattering study has found that nickel orbitals play the most important role in the multi-orbital contribution of charge order formation in this material, which is significantly different from the cuprates with oxygen orbitals dominating the charge modulation. Although the spin order in La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub> has been well established, there is still controversy over its spin structure and the existence of coexisting charge order. In La<sub>4</sub>Ni<sub>3</sub>O<sub>10</sub>, intertwined charge and spin density waves have been reported, the origin and characteristics of which remain unknown. Owing to the research on the nickelate superconductors just starting, many questions have not yet been answered, and the exploration of charge order in nickelate superconductors will still be the center of superconductor research.

Accurate determination of the shapes of granular charge distributions.

Experiments have shown that charge distributions of granular materials are non-Gaussian, with broad tails that indicate many particles with high charge. This observation has consequences for the behavior of granular materials in many settings, and may bear relevance to the underlying charge transfer mechanism. However, there is the unaddressed possibility that broad tails arise due to experimental uncertainties, as determining the shapes of tails is nontrivial. Here we show that measurement uncertainties can indeed account for most of the tail broadening previously observed. The clue that reveals this is that distributions are sensitive to the electric field at which they are measured; ones measured at low (high) fields have larger (smaller) tails. Accounting for sources of uncertainty, we reproduce this broadening in silico. Finally, we use our results to back out the true charge distribution without broadening, which we find is still non-Guassian, though with substantially different behavior at the tails and indicating significantly fewer highly charged particles. These results have implications in many natural settings where electrostatic interactions, especially among highly charged particles, strongly affect granular behavior.

Onsite and intersite electronic correlations in the Hubbard model for halide perovskites

Halide perovskites (HPs) are widely viewed as promising photovoltaic and light-emitting materials for their suitable band gaps in the visible spectrum. Density functional theory (DFT) calculations employing (semi)local exchange-correlation functionals usually underestimate the band gaps for these systems. Accurate descriptions of the electronic structures of HPs often demand higher-order levels of theory such as the Heyd-Scuseria-Ernzerhof (HSE) hybrid density functional and GW approximations that are much more computationally expensive than standard DFT. Here, we investigate three representative types of HPs, ABX3 halide perovskites, vacancy-ordered double perovskites (VODPs), and bond disproportionated halide perovskites (BDHPs), using DFT+U+V with onsite U and intersite V Hubbard parameters computed self-consistently without a priori assumption. The inclusion of Hubbard corrections improves the band gap prediction accuracy for all three types of HPs to a similar level of advanced methods. Moreover, the self-consistent Hubbard U is a meaningful indicator of the true local charge state of multivalence metal atoms in HPs. The inclusion of the intersite Hubbard V is crucial to properly capture the hybridization between valence electrons on neighboring atoms in BDHPs that have breathing-mode distortions of halide octahedra. In particular, the simultaneous convergence of both Hubbard parameters and crystal geometry enables a band gap prediction accuracy superior to HSE for BDHPs but at a fraction of the cost. Our work highlights the importance of using self-consistent Huabbard parameters when dealing with HPs that often possess intricate competitions between onsite localization and intersite hybridization.

Structural and switching ferroelectric charge density studies in BaTi0.95Sn0.05O3 prepared by microwave assisted sintering

Lead free ferroelectric perovskite compounds (ABO3) have received so much attention due to the toxic nature of lead. Among them, barium titanate is the promising lead free ferroelectric material. But this material needs more investigation to explore its technological application. To analysize the various properties such as structural and ferroelectric of polycrystalline BaTi0.95Sn0.05O3 (BTSO), it was synthesized by the Solid State method. The X-ray diffraction patterns confirmed the crystallinity of the sample. The Rietveld refinement shows that the prepared sample crystallizes to tetragonal symmetry with P4mm space group. The surface morphology of the sample was studied by using the Field Emission Scanning Electron Microscopy (FE-SEM) and the grain size of the sample was estimated with the help of Image J software. The enhancement of maximum polarization (Pmax), remnant polarization (Pr), and coercive field (Ec) with the applied electric field confirm the ferroelectric nature of the prepared sample. The Positive Up Negative Down (PUND) measurement confirms the enhanced behavior of the true switching ferroelectric charge density(QSW) concerning the applied electric field.

Diagnoses and charges of patients with ICD-10-CM environmental pollution exposure codes in Florida

PurposePollution affects both health and climate change. There is no published research on the use of four environmental pollution exposure codes new to ICD-10-CM. The purpose of this research is to provide a baseline use of the four codes in Florida, the most frequent related principal diagnoses, demographics of patients exposed to environmental pollution, total charges, and associations of total charges that are related to environmental pollution. Principal ResultsThere were 341 patients in Florida who visited an ED due to environmental pollution exposure from 2016 to 2019 and 159 patients in Florida who were hospitalized. The total charges for all patients with a documented exposure to environmental pollution were $1,379,217 for ED patients and $9,933,752 for inpatients. The independent variables that were statistically significant in the ED regression model of total charges were other insurance (-0.361 parameter estimate, 0.017 p-value, -30.3% decrease to charges); and for-profit ownership (0.376 parameter estimate, 0.0005 p-value, 45.7% increase to charges). For the inpatient regression model, the independent variables that were statistically significant were Medicare (0.317 parameter estimate, 0.027 p-value, 37.3% increase to charges); LOS (0.091 parameter estimate, <0.0001 p-value, 9.5% increase to charges); exposure to other pollution (0.407 parameter estimate, 0.002 p-value, 50.3% increase to charges); and for-profit hospital ownership (0.292 parameter estimate, 0.012 p-value, 33.9% increase to charges). Major ConclusionsPatients exposed to air pollution frequently were diagnosed with asthma or other chronic obstructive pulmonary disease. Patients with water pollution exposure frequently had open wounds or infections stemming from open wounds. For both ED and inpatient visits, $11,312,969 was charged to patients over the four year period. Due to the challenges of documenting it clinically, the true charges of healthcare due to environmental pollution are probably much higher. Education may be needed for pollution codes to be understood and used more frequently by clinicians and coders.

The Potential of Zero Charge and the Electrochemical Interface Structure of Cu(111) in Alkaline Solutions

Copper (Cu) is a unique electrocatalyst, which is able to efficiently oxidize CO at very low overpotentials and reduce CO2 to valuable fuels with reasonable Faradaic efficiencies. Yet, knowledge of its electrochemical properties at the solid/liquid interface is still scarce. Here, we present the first two-stranded correlation of the potential of zero free charge (pzfc) of Cu(111) in alkaline electrolyte at different pH values through application of nanosecond laser pulses and the corresponding interfacial structure changes by in situ electrochemical scanning tunneling microscopy imaging. The pzfc of Cu(111) at pH 13 is identified at −0.73 VSHE in the apparent double layer region, prior to the onset of hydroxide adsorption. It shifts by (88 ± 4) mV to more positive potentials per decreasing pH unit. At the pzfc, Cu(111) shows structural dynamics at both pH 13 and pH 11, which can be understood as the onset of surface restructuring. At higher potentials, full reconstruction and electric field dependent OH adsorption occurs, which causes a remarkable decrease in the atomic density of the first Cu layer. The expansion of the Cu–Cu distance to 0.3 nm generates a hexagonal Moiré pattern, on which the adsorbed OH forms a commensurate (1 × 2) adlayer structure with a steady state coverage of 0.5 monolayers at pH 13. Our experimental findings shed light on the true charge distribution and its interrelation with the atomic structure of the electrochemical interface of Cu.

Apparent and True Charges in the Partial Discharge Model at Different Defective Domain Sizes

A model of the partial discharges in a sample of solid insulation with air cavity is presented. The material of the insulation is cross-linked polyethylene. The model is based on an active-capacitive equivalent circuit, in which the resistance of the air cavity at the instant of a partial discharge ignition is shunted by the active resistance of the spark. The model takes into consideration the delay of the discharge development. The evaluation of the diagnostic value of the apparent and true charges is carried out. The results of the apparent and true charges relationship with the dimensions and proportions of the air cavity are presented. It is shown that the same magnitude of both true and apparent charges can correspond to the different volumes and shapes of the air cavities in the insulation.

The Calibration Method for Incomplete Charge Transfer in ToF Image Sensor

In this paper, a kind of calibration method for two-tap indirect time-of-flight (ToF) image sensor is proposed, which aims to reduce the distance error caused by the incomplete charge transfer. The phenomenon of two-phase charge confusion due to incomplete charge transfer makes a serious impact on the accuracy of ToF imaging especially under high modulation frequency. Current researches effort to improve the charge transfer ratio by changing pixel structure or fabrication process. The proposed method obtains a charge transfer ratio by reducing the frequency of the work timing. Then the true photon-generated charge of each phase can be calculated and the distance error can be calibrated. To verify the validity of the proposed calibration method, an accurate behavioral level model is established according to the actual ToF imaging system. The simulation results prove that the calibrated modulation contrast is improved by 60% under 100 MHz modulation and 0.1 charge transfer ratio. The calibrated modulation contrast is very close to the theoretical maximum value. When the signal strength increases or the times of charge transfer increases, the calibration effect on the distance error become more effective.

Strain-induced partial phase transition in TiO2 nanoparticles manifesting frequency dispersive pseudo-inductive switching of capacitance

The appearance of ‘negative capacitance’ (NC) in dielectric spectroscopy not always demonstrates the true reverse charge accumulation between polarizable sites in the associated system. Nonlinear transport of charge-carriers might induce an inductive growth compromising the geometrical capacitance. This sort of dispersion is investigated in mixed phase polycrystalline TiO2 powder having an initial phase ratio of anatase and rutile ~80:20, obtained through mechanical grinding up to 16 h. A significant strain-induced phase transition from anatase to rutile was affirmed from XRD and Raman analysis; whereas reduction in size was nominal. From the Energy Dispersive Analysis of X-rays (EDAX); a remarkable oxygen vacancy formation with longer duration of ball-milling has been observed. In this study, the predominant effects of oxygen vacancy formation on nonlinear hopping conduction-driven inductive response at the higher frequencies are discussed. This genre of frequency-dependent switching can provide an electrical measure of defect-density and traps present in the system. The impacts of strain-induced phase transition on the optical and electrical properties of the material are highlighted in this regard.

Abstract No. 460 Radiologists’ knowledge of procedural charges

Given rising costs of health care there have been calls to educate physicians about the cost impact of medical decisions. Interventional radiology (IR) procedures have been offered as lower cost alternatives to more traditional procedures. However, it is not known how well residents and faculty understand procedural charges or if they are receiving any training on the topic. A survey of radiology residents, IR fellows, and IR attendings at a single large academic medical center as well as at an affiliate private hospital. Subjects rated their agreement with a series of statements about procedural charges on a standard Likert scale. In addition, they provided estimates of charges for various devices and procedures. Estimates within 25% above or below the true charge were considered correct. Contingency analysis was performed to compare the cost estimate accuracy between the groups. 32 of 64 eligible participants (50%) completed the survey in its entirety, which included providing cost estimates for both procedures and devices. None of the participants endorsed having received prior training in procedural charges. Four respondents agreed with the statement, “I feel educated about device costs and RVUs;” three of these respondents were IR faculty and one was an IR fellow. All participants demonstrated poor knowledge of charges associated with procedures with overall accuracy of 15.9% and there was no significant difference in accuracy between interventional radiologists (attendings and fellows) and the radiology residents (11.8% vs. 18.1%, P = 0.2). However, in regards to charges associated with individual devices, the IRs were more accurate in estimating costs than the radiology residents (29.6% vs. 13.1%, P = 0.002). Radiologists have poor knowledge of procedural charges. None of the respondents endorsed receiving training on the subject. In addition, fellowship training in IR did not improve knowledge of procedural charges, though a certain familiarity with the charges associated with individual devices may be inferred. These findings suggest a dedicated intervention to improve knowledge about the charges of procedural health care may have significant impact.

Mechanism of partial discharges in free helium bubbles in transformer oil

Partial discharges (PD) in floating bubbles and in microspheres made from thin glass walls in transformer oil were studied experimentally and theoretically. In a test cell, the PD occurrence was a very rare event. Sometimes PD in bubbles occurred after exposure for more than 10 hours at a voltage that corresponds to a value three times the voltage in accordance with Paschen's law. In the case of a glass microsphere, PD takes place at a voltage according to Paschen's law after several hours but afterwards PD occurs more frequently. The reason for this is in the starting electrons which initiate the first avalanche. It is shown with 100 keV X-rays that PD occurs in all bubbles and its inception voltage corresponds to Paschen's law. Theoretical analysis shows that, at the conditions of PD occurrence in helium bubbles, breakdown fits the streamer mechanism. Registrations of electrical and optical signals of PD were performed to estimate apparent and true charges and the number of radiated photons. As a result of the evaluation, the number of electrons is approximately equal to the number of photons.

Simulation of partial discharge in helium filled elliptic cavity in dielectric

Partial discharge features in cavities in a condensed dielectric was studied. Two models for description of the electric charge transfer during partial discharge were used that are model of constant conductivity of a cavity and a diffusion-drift model. The numerical methods for both models were realized for parallel computations with GPU that accelerates the calculations significantly. The three-dimensional calculations of apparent and true charge in cavities of the shapes of different size spheres and prolate spheroid were conducted. The simulation of the initial stage of streamer development in elliptic helium filled cavity was performed.

Ionization electron signal processing in single phase LArTPCs. Part I. Algorithm Description and quantitative evaluation with MicroBooNE simulation

We describe the concept and procedure of drifted-charge extraction developed in the MicroBooNE experiment, a single-phase liquid argon time projection chamber (LArTPC). This technique converts the raw digitized TPC waveform to the number of ionization electrons passing through a wire plane at a given time. A robust recovery of the number of ionization electrons from both induction and collection anode wire planes will augment the 3D reconstruction, and is particularly important for tomographic reconstruction algorithms. A number of building blocks of the overall procedure are described. The performance of the signal processing is quantitatively evaluated by comparing extracted charge with the true charge through a detailed TPC detector simulation taking into account position-dependent induced current inside a single wire region and across multiple wires. Some areas for further improvement of the performance of the charge extraction procedure are also discussed.

Charge reconstruction in large-area photomultipliers

Large-area PhotoMultiplier Tubes (PMT) allow to efficiently instrument Liquid Scintillator (LS) neutrino detectors, where large target masses are pivotal to compensate for neutrinos' extremely elusive nature. Depending on the detector light yield, several scintillation photons stemming from the same neutrino interaction are likely to hit a single PMT in a few tens/hundreds of nanoseconds, resulting in several photoelectrons (PEs) to pile-up at the PMT anode. In such scenario, the signal generated by each PE is entangled to the others, and an accurate PMT charge reconstruction becomes challenging. This manuscript describes an experimental method able to address the PMT charge reconstruction in the case of large PE pile-up, providing an unbiased charge estimator at the permille level up to 15 detected PEs. The method is based on a signal filtering technique (Wiener filter) which suppresses the noise due to both PMT and readout electronics, and on a Fourier-based deconvolution able to minimize the influence of signal distortions—such as an overshoot. The analysis of simulated PMT waveforms shows that the slope of a linear regression modeling the relation between reconstructed and true charge values improves from 0.769 ± 0.001 (without deconvolution) to 0.989 ± 0.001 (with deconvolution), where unitary slope implies perfect reconstruction. A C++ implementation of the charge reconstruction algorithm is available online at [1].

An Analysis Protocol for Three-Electrode Li-Ion Battery Impedance Spectra: Part II. Analysis of a Graphite Anode Cycled vs. LNMO

Lithium-Ion batteries consisting of LNMO (LiNi0.5Mn1.5O4) cathodes and graphite anodes show severe capacity fading at elevated temperatures due to a damage of the solid electrolyte interface (SEI) on the anode. Hence, a detailed investigation of the anode with electrochemical impedance spectroscopy (EIS) can provide valuable insight into the phenomenon of anode degradation. In this study, we use a modified version of our novel impedance procedure (Part I of this study), where the anode impedance is measured at non-blocking conditions (10% SOC) and blocking conditions (0% SOC) in a graphite/LNMO full-cell with a gold wire micro-reference electrode (GWRE). We show that during cycling an ionic contact resistance (RCont.Ion) at the separator/anode interface evolves, which is most likely caused by manganese dissolution from the high-voltage cathode (LNMO). By simultaneously fitting EIS spectra in blocking and non-blocking conditions, we can deconvolute the anode impedance evolving over 86 cycles at 40°C into contributions of: a) the separator resistance (RSep.), b) the true charge transfer resistance (RCT), and, c) the ionic contact resistance (RCont.Ion) evolving at the separator/anode electrode interface. We also show that the main contributor to a rising anode impedance is the ionic contact resistance (RCont.Ion).

Simulation of apparent and true charges of partial discharges

Here it is considered partial discharges in the bubbles inserted in the fluid volume in the case of electrode systems plane-plane and point-plane. The calculated and charges show that the apparent charge is many times smaller than the true charge. Smaller bubble size leads to greater ratio of the true charge to the apparent charge. There are two cases when the values of these charges are close. First case: the size of the bubble is large enough, namely close to the value of the gap in the case of flat electrodes. Second case: the void is in contact with the electrode. The latter case is realized in the case of the electrode system point-plane. The experimental and calculated data are compared for this case.

Simulation of partial discharges in cavities and streamers with high spatial resolution

The electrical characteristics of partial discharges in cavities and streamer channels were simulated with the high spatial and temporal resolution. The parallel computations on graphic processing units were applied for the numerical solution of this system of equation. The current in an external circuit as well as the true charge during partial discharge were calculated for different positions of a single void and for two voids in electrode gap. The parallel algorithm for the stochastic growth of streamer in a dielectric was developed. The electric characteristics of the partial discharges due to the streamer growth were studied.

A simple model for electrical charge in globular macromolecules and linear polyelectrolytes in solution.

We present a model for calculating the net and effective electrical charge of globular macromolecules and linear polyelectrolytes such as proteins and DNA, given the concentration of monovalent salt and pH in solution. The calculation is based on a numerical solution of the non-linear Poisson-Boltzmann equation using a finite element discretized continuum approach. The model simultaneously addresses the phenomena of charge regulation and renormalization, both of which underpin the electrostatics of biomolecules in solution. We show that while charge regulation addresses the true electrical charge of a molecule arising from the acid-base equilibria of its ionizable groups, charge renormalization finds relevance in the context of a molecule’s interaction with another charged entity. Writing this electrostatic interaction free energy in terms of a local electrical potential, we obtain an “interaction charge” for the molecule which we demonstrate agrees closely with the “effective charge” discussed in charge renormalization and counterion-condensation theories. The predictions of this model agree well with direct high-precision measurements of effective electrical charge of polyelectrolytes such as nucleic acids and disordered proteins in solution, without tunable parameters. Including the effective interior dielectric constant for compactly folded molecules as a tunable parameter, the model captures measurements of effective charge as well as published trends of shifts in globular proteins. Our results suggest a straightforward general framework to model electrostatics in biomolecules in solution. In offering a platform that directly links theory and experiment, these calculations could foster a systematic understanding of the interrelationship between molecular 3D structure and conformation, electrical charge and electrostatic interactions in solution. The model could find particular relevance in situations where molecular crystal structures are not available or rapid, reliable predictions are desired.