Kramers-Kronig Relations Research Articles

Driving deep-learning-based metasurface design with Kramers-Kronig relations

Driving deep-learning-based metasurface design with Kramers-Kronig relations

Nonminimal coupling holographic superconductors

We explore a holographic superconductor model in which a real scalar field is nonminimally coupled to a gauge field. We consider several types of the nonminimal coupling function h(ψ) including exponential, hyperbolic (cosh), power-law, and fractional forms. We investigate the influences of the nonminimal coupling parameter α on condensation, critical temperature, and conductivity. We can categorize our results in two groups. In the first group, conductor/superconductor phase transition is easier to occur for larger values of α, while in the second group stronger effects of the nonminimal coupling makes the formation of scalar hair harder. Although the real and imaginary parts of conductivity are impressed by different forms of h(ψ), they follow some universal behaviors such as connecting with each other through Kramers–Kronig relation in ω → 0 limit or the appearance of gap frequency at low temperatures around ωg ∼ 8 Tc, which shifts to larger values by increasing the strength of α. Among all forms of h(ψ) we observe that h(ψ) = 1 + αψ2 gives us better information in wide range of nonminimal coupling constant and temperature. Choosing the best form of h(ψ), we construct a family of solutions for holographic conductor/superconductor phase transitions to discover the effect of the hyperscaling violation when the gauge and scalar fields are nonminimally coupled. we find that the critical temperature increases for higher effects of hyperscaling violation θ and nonminimal coupling constant α. By increasing these two parameters, we obtain lower values of condensation which means that conductor/superconductor phase transition will acquire easier. Furthermore, we understand that the hyperscaling violation affects the conductivity σ of the holographic superconductors and changes the expected relation in the gap frequency. Some universal behaviors like infinite DC conductivity are observed. In addition, we consider a five-dimensional Gauss–Bonnet (GB) black hole with a flat horizon. We find out that the critical temperature decreases for larger values of GB coupling constant, λ, or smaller values of nonminimal coupling constant, α, which means that the condensation is harder to form. Moreover, we study the electrical conductivity in the holographic setup. We observe that the gap frequency shifts to larger values for stronger λ, and becomes flat by increasing α.

Direct extraction of optical constants of organic semiconductors in ultrastrongly coupled microcavities and their application in antireflection design for polariton devices

The strongly bound Frenkel excitons in organic semiconductors enable strong or even ultrastrong exciton-photon coupling in room-temperature cavities, with the resulting polariton states typically resolved through reflectance measurements. This paper demonstrates that the distinct features of exciton and polariton modes in the reflectance spectra of strongly/ultrastrongly coupled organic microcavities can be effectively utilized to extract the optical constants and physical thickness of the embedded organic semiconductor. We investigate metal-clad microcavities based on two prototype conjugated polymers, poly[2-methoxy-5-(3,7-dimethyloctyloxy)-1,4-phenylenevinylene] (MDMO-PPV) and poly(3-hexylthiophene) (P3HT), both exhibiting ultrastrong coupling characteristics. The (n,k) spectra and thickness of these polymer films are determined by fitting the normal incidence reflectance spectra of organic microcavities, using Kramers-Kronig transformation and transfer-matrix calculations with varying optical and thickness parameters. We also examine the individual effects of the main fitting parameters on the spectrum, establishing a close correlation with the underlying polariton properties. Moreover, we analyze the optical admittance at exciton and polariton modes to understand reflectance variations with different parameters, which facilitates precise control of optical properties at specific modes through cavity design. Finally, using the extracted optical constants of MDMO-PPV and P3HT, we propose optimized microcavity designs that exhibit antireflection at the lower polariton mode for potential luminescence and photodetection device applications.

Study of Dynamic Modulus of Asphalt Mix after Reinforcement of Sandstone

Sandstone has poor mechanical properties. To facilitate the application of sandstone into asphalt mixtures, sandstone was treated by immersion in sodium silicate solution, and the dynamic modulus after reinforcement was used as a criterion. The results showed that the mechanical properties of the sandstone aggregate treated with sodium silicate were improved, and the dynamic modulus was increased by 18.2%, which will help to reduce rutting. The dynamic modulus and phase angle can be effectively predicted over a wide frequency range using the sigma function and the Kramers–Kronig relationship. Sandstone asphalt mixtures basically conform to linear viscoelasticity, but the phase angle changes are more complicated at high temperatures and do not vary monotonically with frequency. By calculating the rutting coefficient, fatigue coefficient, and DSRFn parameters for performance prediction, it was found that an increase in dynamic modulus resulted in a significant increase in the rutting coefficient but a decrease in the cracking resistance.

An alternative approach for characterization of the linear viscoelastic behavior of asphalt binders

This study aimed to develop an alternative approach to characterise the linear viscoelastic behaviour of asphalt binders. A rheogram model was firstly proposed based on the Carreau–Yasuda model; its accuracy was substantiated by high R 2 values. The dynamic shear modulus master curve model was then obtained using the relationship between the magnitude of complex viscosity and dynamic shear modulus and the two definitions of the time-temperature shift factor. Afterwards, the phase angle master curve model was derived according to the approximate Kramers–Kronig relation. The proposed approach was demonstrated to be capable of accurately characterising the linear viscoelastic behaviour of selected asphalt binders. In addition, the predicted zero shear viscosity (ZSV) could be potentially employed to evaluate the asphalt binder rutting resistance. Compared with the widely-used Christensen-Anderson-Marasteanu (CAM) model, the developed master curves models were better at constructing the phase angle master curves of selected asphalt binders.

DFT insight into the phase stability, optoelectronic, elastic, vibrational, and thermodynamic properties of metal chalcogenides RbKM (M = S, Se, Te) for energy harvesting technology

In this manuscript, the structural, optoelectronic, elastic, vibrational, and thermodynamic properties of RbKM (M = S, Se, Te) chalcogenides are explored via first principles approach. The estimated equilibrium lattice parameters a(c) through the TB-mBJ functional are 5.3876 Å (8.2810 Å), 5.2700 Å (8.6550 Å) and 5.2656 Å (8.7707 Å) for RbKS, RbKSe and RbKTe, respectively. The large value of the cohesive (Ecoh) and formation energy (Eform) reveals that all these compounds are stable at 0 K that may be difficult to decompose at ambient conditions. The direct band gap for RbKS, RbKSe and RbKTe is noted as 4.05 eV, 3.71 eV and 3.63 eV, respectively that is sufficient to declare them as semiconducting materials. So far as, the projected density of states (PDOS), pseudo electrons residing in d orbitals of the rubidium atoms contribute in the conduction region and p orbitals of chalcogen elements partake in the valence band. The optical parameters are determined by Kramers-Kronig relations. The elastic constants unveil that all compounds are mechanically stable and hold anisotropic nature. Here the vibrational properties of RbKM (M = S, Se, Te) are examined through Density functional perturbation theory (DFPT) technique. The Harmonic Approximation Method (HAM) is utilized to seek thermodynamic stability that is ensured due to the observance of negative free energy for all cases. Our theoretical outcomes for RbKM (M = S, Se, Te) can contribute significantly to amelioration for future research in devising optoelectronic and energy harvesting like appliances.

Thermal radiation characteristic parameters of biomass mixed feedstock for concentrating solar gasification reaction

Solar energy and biomass are both important renewable energy, and the studies on them contribute to current goal of global carbon neutral. The solar gasification process directly employs solar radiation to drive the conversion from biomass to syngas via endothermic gasification reactions. This process relies on the biomass feedstock absorbing incident solar irradiation to sustain these reactions. The thermal radiation characteristics of biomass materials, such as spectral emissivity and absorptivity, determine its capacity for solar energy absorption versus losses from self-emission. Thus, these parameters are critical inputs for accurate thermal-balance modeling of the solar reactor. In this study, the reflectance of 9 biomass samples were experimentally measured in the main solar spectrum range of 200–2500 nm. Based on measurement results, the refractive index (n) and extinction coefficient (k) of each biomass materials are obtained via Kramers-Kronig relations. Besides, the dielectric function of the 9 biomass samples are also modeled using a 5-th Lorentz oscillator model and the model parameters are determined. The results indicate that the 5-th Lorentz oscillator model adequately characterizes the thermal radiation properties of diverse biomass feedstocks over the measured spectrum. This work contributes important spectral property data to enable accurate modeling and optimization of solar thermochemical conversion based on biomass gasification processes.

Comparison of Approaches for Assessing Linearity of Impedance Measurements

There are two experimental methods available to assess the linearity of electrochemical impedance measurements. Observation of current as a function of potential, known as Lissajous plots, provides an instantaneous visual representation of the data.1 Deviation from an elliptical shape suggests a perturbation amplitude that is too large, resulting in nonlinear impedance data. A second approach is to measure, along with the fundamental, the higher harmonics of the measurement signal. Under potentiostatic control, the harmonics of current that exceed the noise level suggest nonlinear behavior. These harmonics may be expressed in terms of a frequency-dependent total harmonic distortion, THD, written as the ratio between the sum of the root mean square of the harmonic magnitude and fundamental frequency magnitude for electrochemical applications.The impedance was measured for a model system consisting of a Pt disk immersed in an electrolyte containing 0.01 M potassium ferricyanide, 0.01 M potassium ferrocyanide, and 1 M KCl. Measurements were performed using a Gamry Reference 3000 with THD measurement enabled and disabled. Low-frequency (10 mHz) Lissajous plots were recorded to facilitate comparison of the two methods for assessing linearity. The impedance measurements with THD enabled or disabled were in good agreement, including the frequency-dependent stochastic error structure, the shapes of Lissajous curves, and the values of the impedance. Both the low-frequency THD and the low-frequency Lissajous plots gave similar sensitivity to nonlinear behavior. Perturbation amplitudes of 1, 5, and 10 mV rms yielded elliptical Lissajous plots with THD values on the order of the background noise. Interestingly, the THD for the 10 mV perturbation was slightly above the background noise with a value of 0.01 (or 1 % of the fundamental). Perturbation amplitudes of 20, 60, and 100 mV rms yielded both non-elliptical Lissajous plots and low-frequency THD values much larger than the background noise.The regression of the measurement model 2 to the imaginary part of the impedance was applied to assess the consistency of the measured data to the Kramers-Kronig relations.3 Data measured at amplitudes of 1, 5, 10, and 20 mV rms were found to be consistent with the Kramers-Kronig relations, and data collected with amplitudes of 60 or 100 mV rms were found to be inconsistent with the Kramers-Kronig relations. As the measurement with a 20 mV rms amplitude was found to be nonlinear by observation of non-elliptical Lissajous plots and a THD of 4.2% at a frequency of 10 mHz, the post-measurement analysis of consistency with the Kramers-Kronig relations was found to be less sensitive than experimental observation of Lissajous plots and calculation of THD. Comparison of Lissajous plots to THD values suggests that experiments with THD less than 1% of the fundamental may be considered to be linear.

On the Correlation of Kramers-Kronig (KK) Analysis and Non-Linear Harmonic Analysis (NHA)

Primary lithium batteries are known for their elevated volumetric and gravimetric energy densities and production cost efficiency. Within this category, lithium thionyl chloride (Li/SOCl2) batteries exhibit a constant discharge voltage (~3.6 V) and a broad operational temperature range (-50ᵒC to 80ᵒC). Moreover, forming a LiCl passivation layer on the metallic Li anode can extend its shelf-life up to 20 years at optimal storage temperature. These characteristics render lithium thionyl chloride batteries applicable in military and security applications, microcomputers, measurement devices, and medical instruments. Therefore, the characterization of lithium thionyl chloride batteries accurately has the utmost importance. Understanding the critical electrochemical processes that occur inside the battery without damaging or disassembling the cell requires delicate techniques.EIS has emerged as a non-destructive and in-situ measurement technique with increasing popularity. Essential battery properties can be derived from EIS data. The credibility of EIS data, considering linearity, causality, and stability, can be verified through Kramers-Kronig relations. The obtained spectrum is fitted with an optimal number of Voigt elements (RC components in parallel)[1]. Given the linearity and stability of these individual Voigt elements, the entire spectrum should exhibit linearity if it is Kramers-Kronig compatible[2].Non-linear harmonic analysis (NHA) is a complementary technique to EIS, wherein the response signal undergoes conversion from the time domain to the frequency domain through Fast Fourier Transformation (FFT). While EIS employs a single-phased pure sinusoidal signal as the input, the response includes a fundamental frequency and harmonics at integer frequencies of this fundamental response signal. NHA can be utilized in the diagnosis of non-linear, non-stationary situations alongside the identification of drift and initial transients.This study first explains a new EIS measurement method for Li/SOCl2 batteries and Li/SOCl2/SO2Cl2 mixture batteries. The new method describes the solid electrolyte interface (SEI) stability of the batteries and the modifications needed to get KK-compatible results. After that, the equivalent circuit fits applied to the acquired spectra. Essential battery parameters such as solution resistance, charge transfer resistance, and double-layer capacitance were calculated. Kramers-Kronig analysis of the batteries was conducted, and the residuals of the fits were investigated. Subsequently, the NHA of the batteries was examined and compared to the Kramers-Kronig residuals. A correlation between the residuals and NHA of the batteries was extended based on the terms "KK-compatible" and "non-KK-compatible" in comparing KK-residuals and NHA results.[1] Boukamp, B. A. , Journal of the Electrochemical Society 142.6 (1995): 1885.[2] Agarwal, et al., Journal of the Electrochemical Society 142.12 (1995): 4159. Figure 1

Joint Time-Frequency Signal Analysis of Li-Ion Batteries

Measurements acquired from batteries, such as voltage-time and capacity-time signals, offer valuable insights into their cyclability performance. While analyzing these signals in the time domain provides an understanding of global characteristics, scrutinizing local behavior is crucial for detecting issues like battery fading. In this context, we delve into the application of short-time Fourier transform for time-frequency deconstruction of galvanostatic charge/discharge signals, using lithium-sulfur batteries as an illustrative example. Spectrograms resulting from this analysis unveil the evolving frequency content of signals throughout the battery's lifespan, facilitating the identification of critical changes in the response and early detection of issues leading to fading and potential default. Simultaneously, the stability analysis of the dynamic response of red phosphorus and sulfide polyacrylonitrile (RP-SPAN) composite, a promising anode material for lithium batteries, can also be studied using Fourier transform analysis. Our study employs transfer function stability analysis, Kramers-Kronig integral relations, and differential capacity analysis to assess the cell's behavior in both frequency and time domains. Parameters such as stationarity, stability, linearity, dissipation, and degradation are scrutinized over extended charge/discharge cycles. Results reveal a highly nonlinear and time-variant system at low frequencies, aligning with the observed 0.21% average capacity loss per cycle. Our results indicate that short-time Fourier transform could provide insightful information for analyzing battery health.

Indirect measurement of atomic magneto-optical rotation via Hilbert transform

Abstract The Kramers–Kronig relations are a pivotal foundation of linear optics and atomic physics, embedding a physical connection between the real and imaginary components of any causal response function. A mathematically equivalent, but simpler, approach instead utilises the Hilbert transform. In a previous study, the Hilbert transform was applied to absorption spectra in order to infer the sole refractive index of an atomic medium in the absence of an external magnetic field. The presence of a magnetic field causes the medium to become birefringent and dichroic, and therefore it is instead characterised by two refractive indices. In this study, we apply the same Hilbert transform technique to independently measure both refractive indices of a birefringent atomic medium, leading to an indirect measurement of atomic magneto-optical rotation. Key to this measurement is the insight that inputting specific light polarisations into an atomic medium induces absorption associated with only one of the refractive indices. We show this is true in two configurations, commonly referred to in literature as the Faraday and Voigt geometries, which differ by the magnetic field orientation with respect to the light wavevector. For both cases, we measure the two refractive indices independently for a Rb thermal vapour in a 0.6 T magnetic field, finding excellent agreement with theory. This study further emphasises the application of the Hilbert transform to the field of quantum and atomic optics in the linear regime.

Investigating 3D microbial community dynamics of the rhizosphere using quantitative phase and fluorescence microscopy

Microbial interactions in the rhizosphere contribute to soil health, making understanding these interactions crucial for sustainable agriculture and ecosystem management. Yet it is difficult to understand what we cannot see; among the limitations in rhizosphere imaging are challenges associated with rapidly and noninvasively imaging microbial cells over field depths relevant to plant roots. Here, we present a bimodal imaging technique called complex-field and fluorescence microscopy using the aperture scanning technique (CFAST) that addresses these limitations. CFAST integrates quantitative phase imaging using synthetic aperture imaging based on Kramers–Kronig relations, along with three-dimensional (3D) fluorescence imaging using an engineered point spread function. We showcase CFAST’s practicality and versatility in two ways. First, by harnessing its depth of field of more than 100 μm, we significantly reduce the number of captures required for 3D imaging of plant roots and bacteria in the rhizoplane. This minimizes potential photobleaching and phototoxicity issues. Second, by leveraging CFAST’s phase sensitivity and fluorescence specificity, we track microbial growth, competition, and gene expression at early stages of colony biofilm development. Specifically, we resolve bacterial growth dynamics of mixed populations without the need for genetically labeling environmental isolates. Moreover, we find that gene expression related to phosphorus sensing and antibiotic production varies spatiotemporally within microbial populations that are surface attached and appears distinct from their expression in planktonic cultures. Together, CFAST’s attributes overcome commercial imaging platform limitations and enable insights to be gained into microbial behavioral dynamics in experimental systems of relevance to the rhizosphere.

Investigating the optical and magnetic properties of engineered multifunctional graphene oxide and potential application in medical physics and nonlinear optics‏

Herein, the synthesis of multifunctional engineered GOs with the structure of GO@Fe3O4-ligands-CdTe quantum dots (QDs) by an environment-friendly aqueous method was reported. l-cystein (Cys), 3-trimethoxysilyl-propanethiol (TMSP), and glutathione (GSH) were selected as ligands. The as-prepared GO@Fe3O4-ligands-CdTe QDs hybrid nanostructures were characterized by different methods. The findings indicate that the nanocomposites of GO@Fe3O4–ligands–CdTe QDs demonstrate superparamagnetic properties at room temperature. The saturation magnetization values for GO@Fe3O4, GO@Fe3O4-Cys-CdTe, GO@Fe3O4-GSH-CdTe, and GO@Fe3O4-TMSP-CdTe, are 25, 14, 16, and 2 emu g−1, respectively. These nanocomposites show stable and strong luminescence at 580-600 nm. The magnetic nanostructures also reveal the absorption wavelength at 300-490 nm. Using TMSP ligand as a bridge between QDs and magnetic GOs, the luminescence of the nanostructure has not decreased much compared to CdTe QDs. The use of Cys ligand preserves the saturation magnetism of the nanocomposite more than magnetic GO, and the dispersed nanostructure is stable in water. Furthermore, the transverse and longitudinal optical (TO and LO) phonon modes of prepared GO@Fe3O4–ligands–CdTe QDs were obtained by Kramers-Kronig (KK) relations based on fourier-transform infrared (FTIR) spectroscopy. The Z-scan results show that the type of used ligand has a great effect on the nonlinear optical (NLO) properties of the final product. The largest NLO parameters are related to GO@Fe3O4- TMSP -CdTe QDs, and the values of nonlinear absorption coefficient and nonlinear refractive index were obtained as 2.17×10−3(cm/W) and10.27×10−8(cm2/W), respectively. As a result, GO@Fe3O4–ligands–CdTe QDs nanostructures can be considered as promising multifunctional nanostructures for various biomedical applications and NLO devices.

Multiple micro-cavity vibro-polaritons formation with different vibrational bands of the methylene group

We present an experimental technique to accurately predict the formation of vibro-polaritons from a molecular polymeric film embedded in a resonant mid-infrared cavity. Using simple Fourier-transform reflectance measurement, we extract the complex dielectric function of a polyethylene film using Kramers-Kronig relations. The fitted dielectric function can be plugged into a numerical code to predict the strength and dispersion of the strong light-matter coupling regime between the quantized electromagnetic modes of a microcavity and the vibrational bands of the molecules. As a demonstration, we experimentally resolve the simultaneous formation of multiple vibro-polariton modes issued from the strong coupling of some vibrational bands of the methylene group (CH2) in a 2.5-μm-thick polyethylene film embedded in a microcavity. We measure a Rabi splitting of 6.3 THz for the stretching doublet around 87.5 THz and a Rabi splitting of 1.1 THz for the scissoring doublet around 43.7 THz, in excellent agreement with numerical predictions.

Harnessing the Missing Spectral Correlation for Metasurface Inverse Design.

A long-held tenet in computer science asserts that the training of deep learning is analogous to an alchemical furnace, and its "black box" signature brings forth inexplicability. For electromagnetic metasurfaces, the related intelligent applications also get stuck into such a dilemma. Although the past 5 years have witnessed a proliferation of deep learning-based works across complex photonic scenarios, they neglect the already existing but untapped physical laws. Here, the intrinsic correlation between the real and imaginary parts of the spectra are revealed using Kramers-Kronig relations, which is then mimicked by bidirectional information flow in neural network space. Such consideration harnesses the missing spectral connection to extract crucial features effectively. The bidirectional recurrent neural network is benchmarked in metasurface inverse design and compare it with a fully-connected neural network, unidirectional recurrent neural network, and attention-based transformer. Beyond the improved accuracy, the study examines the intermediate information products and physically explains why different network structures yield different performances. The work offers explicable perspectives to utilize physical information in the deep learning field and facilitates many data-intensive research endeavors.

On the Applicability of Kramers–Kronig Dispersion Relations to Guided and Surface Waves

In unbounded media, the acoustic attenuation as function of frequency is related to the frequency-dependent sound velocity (dispersion) via Kramers–Kronig dispersion relations. These relations are fundamentally important for better understanding of the nature of attenuation and dispersion and as a tool in physical acoustics measurements, where they can be used for control purposes. However, physical acoustic measurements are frequently carried out not in unbounded media but in acoustic waveguides, e.g., inside liquid-filled pipes. Surface acoustic waves are also often used for physical acoustics measurements. In the present work, the applicability of Kramers–Kronig relations to guided and surface waves is investigated using the approach based on the theory of functions of complex variables. It is demonstrated that Kramers–Kronig relations have limited applicability to guided and surface waves. In particular, they are not applicable to waves propagating in waveguides characterised by the possibility of wave energy leakage from the waveguides into the surrounding medium. For waveguides without leakages, e.g., those formed by rigid walls, Kramers–Kronig relations remain valid for both ideal and viscous liquids. Examples of numerical calculations of wave dispersion and attenuation using Kramers–Kronig relations, where applicable, are presented for unbounded media and for waveguides formed by two rigid walls.

Temperature-dependent optical constants of vanadium dioxide thin films deposited on polar dielectrics

Coating polar dielectrics with thin film vanadium dioxide (VO2) enables one to exploit the temperature-dependent phase transition within VO2 to actively tune and modulate surface phonon polaritons at mid-infrared. However, controlling the behavior of such systems requires intimate knowledge of the temperature-dependent optical constants of VO2, which depend greatly on the growth conditions and substrate material. Here, we accurately determine the complex optical constants of VO2 on polar dielectrics across the insulator-to-metal phase transition (IMT) using only normal incident reflectance spectra by analyzing the reflectance with Kramers–Kronig relations and thin film Fresnel equations. This non-ellipsometry technique offers an advantage in determining the refractive index using a standard infrared spectrometer.

Full-angle single-shot quantitative phase imaging based on Kramers-Kronig relations.

As a non-interference and non-iterative method, annular-illumination quantitative phase imaging based on Kramers-Kronig relations (AIKK) can realize phase measurement with full-angle resolution enhancement under multiple exposures. In order to completely record the object spectrum with a single shot, we proposed a colorful complementary illumination method in the recording process. The angle of this illumination mode is not symmetrical with each other, so the spectrum between the three channels can complement each other to avoid spectrum loss caused by spectrum conjugation. Meanwhile, the three spectral segments of full-angle information spectrum respectively carried by three wavelengths can be recorded. Additionally, the numerical filter is applied to correct the overlapped spectrum in the reconstruction process. Simulation and experimental results show that this method can achieve high spatiotemporal resolution quantitative phase measurement.

Study on the Application of Kramers-Kronig Relation for Polyurethane Mixture.

Polyurethane (PU) mixture, which is a new pavement mixture, exhibits different dynamic properties compared to a hot-mixed asphalt mixture (HMA). This paper analyzed whether the Kramers-Kronig (K-K) relation and thermorheologically simple properties applied to the PU mixture. Based on the results, the PU mixture exhibited thermorheologically simple properties within the test conditions. The time-temperature superposition principle (TTSP) was applicable for the PU mixture to construct a dynamic modulus master curve using the standard logistic sigmoidal (SLS) model, the generalized logistic sigmoidal (GLS) model, and the Havriliak-Negami (HN) model. The Hilbert integral transformed SLS and GLS models for the phase angle can accurately fit the measured phase angle data with newly fitted shift factors and predict the phase angle within the viscoelastic range. The core-core and black space diagrams both displayed single continuous smooth curves, which can be utilized to characterize the viscoelastic property of the PU mixture. The K-K relation is applicable for the PU mixture to obtain the phase angle master curve model, storage modulus, and loss modulus from the complex modulus test results with the test temperatures and loading frequencies. The phase angle of the PU mixture at extremely high or low test temperatures cannot be derived from the dynamic modulus data.

Electrical rejuvenation of chronically implanted macroelectrodes in nonhuman primates

Objective. Electrodes chronically implanted in the brain undergo complex changes over time that can lower the signal to noise ratio (SNR) of recorded signals and reduce the amount of energy delivered to the tissue during therapeutic stimulation, both of which are relevant for the development of robust, closed-loop control systems. Several factors have been identified that link changes in the electrode-tissue interface (ETI) to increased impedance and degraded performance in micro- and macro-electrodes. Previous studies have demonstrated that brief pulses applied every few days can restore SNR to near baseline levels during microelectrode recordings in rodents, a process referred to as electrical rejuvenation. However, electrical rejuvenation has not been tested in clinically relevant macroelectrode designs in large animal models, which could serve as preliminary data for translation of this technique. Here, several variations of this approach were tested to characterize parameters for optimization. Approach. Alternating-current (AC) and direct-current (DC) electrical rejuvenation methods were explored in three electrode types, chronically implanted in two adult male nonhuman primates (NHP) (Macaca mulatta), which included epidural electrocorticography (ECoG) electrodes and penetrating deep-brain stimulation (DBS) electrodes. Electrochemical impedance spectroscopy (EIS) was performed before and after each rejuvenation paradigm as a gold standard measure of impedance, as well as at subsequent intervals to longitudinally track the evolution of the ETI. Stochastic error modeling was performed to assess the standard deviation of the impedance data, and consistency with the Kramers–Kronig relations was assessed to evaluate the stationarity of EIS measurement. Main results. AC and DC rejuvenation were found to quickly reduce impedance and minimize the tissue component of the ETI on all three electrode types, with DC and low-frequency AC producing the largest impedance drops and reduction of the tissue component in Nyquist plots. The effects of a single rejuvenation session were found to last from several days to over 1 week, and all rejuvenation pulses induced no observable changes to the animals’ behavior. Significance. These results demonstrate the effectiveness of electrical rejuvenation for diminishing the impact of chronic ETI changes in NHP with clinically relevant macroelectrode designs.