Dependence Of Relaxation Time Research Articles

Temperature Dependent Dielectric Relaxation Studies of 2-Nitrotoluene-DMSO mixture using Time Domain Relectometry from 10MHz to 50GHz

The dielectric relaxation properties of 2-Nitrotoluene (2-NT) with DMSO for 11 different concentrations has been studied in the frequency range from 10 MHz to 50 GHz using time domain reflectometry (TDR) method. In this frequency range Dielectric relaxation spectra of 2-NT-DMSO mixtures shows Debye type behavior. The temperature dependent static dielectric constant and relaxation time have been determined from 20oC to 5oC. Effective Kirkwood correlation factor is calculated to determine the effect of strong directional forces such as microwaves on heterogeneous molecules under different temperatures. The excess permittivity and excess inverse excess relaxation time is found to be negative for 2-NT-DMSO system with weak molecular interactions. The activation enthalpy have been calculated to find the energy required to rotate the molecules

Reorientation of DABCO (1,4-diazabicyclo[2.2.2]octane) in hydrogen-bonded 1:2 molecular complexes DABCO-2(SBA) with substituted benzoic acids SBA

The molecular complexes of DABCO-2(SBA) with substituted benzoic acids SBA, which have the hydrogen-bonded trimeric unit, were prepared to investigate the DABCO reorientation in the trimeric unit. By the analysis of the temperature dependence of 1H NMR spin-lattice relaxation time, the correlation time of the DABCO reorientation was determined as a function of the temperature. It is suggested that a change of potential energy of the reorientation is caused with increasing rate of reorientation resulting in a structure change of the trimeric unit to a centrosymmetric structure. The correlation between the activation energy of the DABCO reorientation and the bond nature of the hydrogen bond involved in the trimeric unit is also discussed.

Mononuclear Heptacoordinated 3d-Metal Helicates as a New Family of Single Ion Magnets

The series of Co(II), Fe(II), and Ni(II) mononuclear coordination compounds of [CoL(NCS)2]·3DMSO (1), [CoL(H2O)2](ClO4)2·DMSO (2), [CoL(H2O)(EtOH)][CoCl4]·2H2O (2a), [FeL(NCS)2]·DMSO (3), and [NiL(NCS)2]·CH3CN (4) composition (where L is 2,6-bis(1-(2-(4,6-dimethylpyrimidin-2-yl)hydrazineylidene)ethyl)pyridine), with an [MLA2] coordination unit (where A is a pair of apical monodentate ligands), was synthesized. In compounds 1, 2, 2a, and 3, the ligand L is pentadentate, and cobalt and iron ions are placed in a heavily distorted pentagonal pyramidal coordination environment, while in 4 the Ni(II) ion is hexacoordinated. Easy plane-type magnetic anisotropy (D = 13.69, 11.46, 19.5, and 6.2 cm−1 for 1, 2, 2a, and 4, respectively) was established for cobalt and nickel compounds, while easy axis-type magnetic anisotropy (D = −14.5 cm−1) was established for iron compound 3. The cobalt coordination compounds 1 and 2 show SIM behavior under a 1500 Oe external magnetic field, with effective magnetization reversal barriers of 65(1) and 60(1) K for 1 and 2, respectively. The combination of Orbach and Raman relaxation mechanisms was shown to adequately describe the temperature dependence of relaxation times for 1 and 2. CASSCF/NEVPT2 calculations were performed to model the parameters of the effective spin Hamiltonian for the compounds under study.

Improvement of extrudability and self-support of emulsion-filled starch gel for 3D printing: Increasing oil content

This work investigated the mechanism of increasing oil content in synchronously enhancing extrudability and self-support of β-carotene loaded starch-based emulsion-filled gels (S-EFG) during 3D printing in terms of gel properties. Increasing emulsion oil content enhanced the storage modulus, relaxation modulus, and hardness of gels, which indicated sodium caseinate-stabilized emulsions were active fillers in the starch gel. Thus, printed products with high oil content were less prone to collapse when selecting models with higher height. In addition, lower yield stress, relaxation time, and higher frequency dependence were observed in S-EFG with higher oil content (30–50 %) due to the lubricating/plasticizing effect of oils, which corresponded to the smoother extruded filament. Furthermore, the retention of β-carotene in high oil content gel was higher after heat treatment due to denser microstructure. These results indicated that the extrudability and self-supporting of S-EFG were simultaneously improved by increasing oil content under the active filling effect and lubricating/plasticizing effect of emulsions.

Non-Unified Constitutive Models for the Simulation of the Asymmetrical Cyclic Behavior of GH4169 at Elevated Temperatures

The tensile, creep, fatigue and creep-fatigue tests of the nickel-based superalloy GH4169 were carried out. According to the deformation characteristics of GH4169 alloy, the Ohno-Karim kinematic model (O-K model) can be used to describe the tensile behavior. The creep constitutive model presented in this paper can be used to predict the three-stage creep characteristics of the GH4169 alloy. The modified Ohno-Karim kinematic hardening model, combined with an isotropic hardening model, can well predict the cyclic softening behavior of the material under symmetric loads and the mean stress relaxation behavior under asymmetric loads. Based on the modified Ohno-Karim kinematic hardening model, isotropic hardening model and creep constitutive model, a non-unified constitutive model was established. The creep-fatigue behavior of the GH4169 alloy under symmetric and asymmetric loads is simulated by using the non-unified constitutive model. The simulation results are very close to the experimental results; however, the prediction results of the time-dependent relaxation load are relatively small.

The random first-order transition theory of active glass in the high-activity regime

Dense active matter, in the fluid or amorphous-solid form, has generated intense interest as a model for the dynamics inside living cells and multicellular systems. An extension of the random first-order transition theory (RFOT) to include activity was developed, whereby the activity of the individual particles was added to the free energy of the system in the form of the potential energy of an active particle, trapped by a harmonic potential that describes the effective confinement by the surrounding medium. This active-RFOT model was shown to successfully account for the dependence of the structural relaxation time in the active glass, extracted from simulations, as a function of the activity parameters: the magnitude of the active force (f 0) and its persistence time (τ p ). However, significant deviations were found in the limit of large activity (large f 0 and/or τ p ). Here we extend the active-RFOT model to high activity using an activity-dependent harmonic confining potential, which we solve self-consistently. The extended model predicts qualitative changes in the high activity regime, which agree with the results of simulations in both three-dimensional and two-dimensional models of active glass.

Numerical simulations of the Hebb-Wagner polarization kinetics: (I) weakly acceptor-doped perovskite oxides

The Hebb-Wagner polarization method can be used to separate the partial electronic conductivity of mixed ionic and electronic conductors (MIEC) from the partial ionic conductivity by polarizing the material between an ion-blocking and a reversible electrode using an external electric voltage. The electronic conductivity is then calculated from the steady state I-V curve where the partial current of the blocked ionic species is zero. The kinetics of the relaxation process towards the steady state and the corresponding relaxation time were, however, not investigated until now, although they are crucial to the success of the Hebb-Wagner method. In this contribution, the kinetics of the relaxation process during the Hebb-Wagner polarization of a nominally undoped perovskite-type oxide ABO3 (mixed ionic and electronic conductor) is simulated by means of numerical methods and using SrTiO3 as a model system. The simulation results show an unexpected dependence of the relaxation time of the polarization process on the applied voltage. The relaxation time first decreases until a certain voltage is reached, where it remains constant for a few voltage steps, and afterwards it increases again for higher voltage values. We show that these three different relaxation time dependencies correspond to the transition from (i) a prevailing electron hole conduction at high oxygen partial pressures to (ii) a predominant oxygen ion conduction near the p − n transition at intermediate oxygen partial pressures followed by (iii) a predominant electron conduction at low partial pressures. Additionally, the dependence on other parameters and experimental variables, such as surface exchange coefficient at the reversible electrode, acceptor concentration, temperature, and sample length, is investigated, which reveals that a slight change of one of these parameters can change the relaxation time by several orders of magnitude. The obtained insight from the numerical simulation of the electrochemical polarization process is advantageous for the experimental realization of the Hebb-Wagner polarization method, and in particular for its application to nominally undoped perovskite-type oxides, like SrTiO3.

(Invited) Unravelling Water-Ion Dynamics in Reverse Osmosis Membranes with Nuclear Magnetic Resonance Spectroscopy

Fundamental understanding of the charge (ions and water) transport in polymeric membranes used at the forefront of the water-energy nexus challenge is yet uncertain and depends on the complex interplay between polymer structure and dynamics that facilitate transport. Herein, we investigated the dynamics-transport of proton and ion transport in a rather neutrally charged organic membrane (i.e., polyamide) using solid-state NMR spectroscopy. Specifically, the role of competing ions' effect in complex ionic mixtures at the membrane interface has been explored on a molecular level. Proton and sodium ion diffusion measurements are made using pulsed-field gradient NMR diffusometry. The energy barriers for proton and ion transport within the active layer of the reverse osmosis (RO) membrane are assessed using magic angle spinning (MAS) and static NMR spectral line shape analysis. We have investigated the dynamics-transport of water and sodium ions in complex ionic mixtures of polyamide polymeric media using solid-state NMR spectroscopy. Through monitoring 13C, 23Na, and 1H NMR nuclei, quantitative insights into the diffusion of water (1H), sodium mobile ion (Na+), and polymer membrane dynamics (13C) are extrapolated. Furthermore, the spin-lattice (T1) relaxation time of sodium and water ions is investigated to obtain quantitative insight into how sodium and water ions’ rotational movements occur in the absence and presence of other competing seawater cations such as potassium. Room temperature spectra and spin-lattice relaxation times indicated the presence of both mobile and rigidly held ionic species in the membrane at different levels of relative humidity. The concentration and temperature dependence of relaxation times and chemical shifts have been investigated. NMR relaxation measurements detect how the water rotation is modified by sodium and potassium cations in the membrane. Results show that at low relative humidity and in the presence of competing ions, there are sodium ion resonances for crystalline sodium ions and rigidly held sodium ions on the surface. With increasing relative humidity and decreasing competing ions, the resonance suggests solution-like dynamic rotational movements of sodium ions in polyamide. The results confirm the change in activation energy barrier for sodium and hydrogen ion permeation in polyamide upon the presence of potassium ions.

Continuous wave and pulsed EPR study of Cd1-xMnxTe crystals with different Mn content

The cadmium manganese telluride (Cd1–xMnxTe) crystals (x < 0.001 and x = 0.02, 0.04, 0.1) grown using the Bridgman method were studied by applying continuous wave and pulsed electron paramagnetic resonance (EPR) spectroscopy in the wide temperature range. The Cd1–xMnxTe crystals with x < 0.001 revealed the EPR spectrum from isolated Mn2+ with g⊥ = g∥ = 2.0074(3), |A⊥| = |A∥| = 56.97 ⋅ 10–4 cm–1, |a| = 30.02⋅10–4 cm–1, while Cd1–xMnxTe crystals with x = 0.02…0.04 are characterized by two single broad isotropic EPR lines of Lorentzian shape (g ~ 2.009 and g ~ 1.99) due to Mn clusters of different sizes. The EPR spectrum of Cd1–xMnxTe crystals with x = 0.01 consists of the single broad line at g ~ 2.01 due to higher level of homogeneity inherent to these crystals. The temperature dependence of spin relaxation times for the isolated Mn2+ center in the Cd1–xMnxTe crystals with x < 0.001 has been described using the conceptions of Orbach process for TM–1 and two-phonon Raman process for T1–1.

Relating dynamic free volume to cooperative relaxation in a glass-forming polymer composite.

There are a variety of complementary descriptions of the temperature dependence of the structural relaxation time τ in glass-forming materials, which we interpret positively as suggesting an underlying unified description. We examine the inter-relation between the string model, an outgrowth of the Adam and Gibbs approach that emphasizes collective particle exchange motion, and the localization model, which emphasizes the volume explored by particles in their caged states, a kind of dynamic "free volume." Each model of liquid dynamics is described by a limited set of parameters that must be interrelated if both descriptions simultaneously describe the relaxation behavior. We pursue the consequences of this idea by performing coarse-grained molecular simulations of polymer melts with additives of variable size and interaction strength with the polymer matrix, thereby significantly altering the relaxation of the composite material. Both the string and localization models describe our relaxation time data well, and a comparison of the model parameters allows us to relate the local caging scale ⟨u2⟩ (the Debye-Waller parameter) to the entropy of activation for molecular rearrangements in the string model, thereby developing a bridge between these seemingly disparate approaches to liquid dynamics.

Diffusive density response of electrons in anisotropic multiband systems

We explicitly calculate the density-density response function with conserving vertex corrections for anisotropic multiband systems in the presence of impurities including long-range disorder. The direction dependence of the vertex corrections is correctly considered to obtain the diffusion constant which is given by a combination of componentwise transport relaxation times and velocities on the Fermi surface. We also investigate the diffusive density response of various anisotropic systems, propose some empirical rules for the corresponding diffusion constant, and demonstrate that it is crucial to consider the component dependence of the transport relaxation times to correctly interpret the transport properties of anisotropic systems, especially various topological materials with a different power-law dispersion in each direction.

Sensing red blood cell nano-mechanics: Toward a novel blood biomarker for Alzheimer's disease.

Red blood cells (RBCs) are characterized by a remarkable elasticity, which allows them to undergo very large deformation when passing through small vessels and capillaries. This extreme deformability is altered in various clinical conditions, suggesting that the analysis of red blood cell (RBC) mechanics has potential applications in the search for non-invasive and cost-effective blood biomarkers. Here, we provide a comparative study of the mechanical response of RBCs in patients with Alzheimer’s disease (AD) and healthy subjects. For this purpose, RBC viscoelastic response was investigated using atomic force microscopy (AFM) in the force spectroscopy mode. Two types of analyses were performed: (i) a conventional analysis of AFM force–distance (FD) curves, which allowed us to retrieve the apparent Young’s modulus, E; and (ii) a more in-depth analysis of time-dependent relaxation curves in the framework of the standard linear solid (SLS) model, which allowed us to estimate cell viscosity and elasticity, independently. Our data demonstrate that, while conventional analysis of AFM FD curves fails in distinguishing the two groups, the mechanical parameters obtained with the SLS model show a very good classification ability. The diagnostic performance of mechanical parameters was assessed using receiving operator characteristic (ROC) curves, showing very large areas under the curves (AUC) for selected biomarkers (AUC > 0.9). Taken all together, the data presented here demonstrate that RBC mechanics are significantly altered in AD, also highlighting the key role played by viscous forces. These RBC abnormalities in AD, which include both a modified elasticity and viscosity, could be considered a potential source of plasmatic biomarkers in the field of liquid biopsy to be used in combination with more established indicators of the pathology.

Estimating glass transition temperature and related dynamics of molecular glass formers combining artificial neural networks and disordered systems theory

Glass transition temperature and related dynamics play an essential role in amorphous materials research since many of their properties and functionalities depend on molecular mobility. However, the temperature dependence of the structural relaxation time for a given glass former is only experimentally accessible after synthesizing it, implying a time-consuming and costly process. In this work, we propose combining artificial neural networks and disordered systems theory to estimate the glass transition temperature and the temperature dependence of the main relaxation time based on the knowledge of the molecule's chemical structure. This approach provides a way to assess the dynamics of molecular glass formers, with reasonable accuracy, even before synthesizing them. We expect this methodology to boost industrial development, save time and resources, and accelerate the scientific understanding of structure-properties relationships. • New joint theoretical and numerical approach to estimate the molecular dynamics • Machine learning for understanding structure-property relationships • Artificial neural networks for the design and development of new materials • Combining artificial neural networks and disordered systems theory • Estimating glass transition temperature and related dynamics of molecular glass formers

Fabrication and Evaluation of Gellan Gum/Hyaluronic Acid Hydrogel for Retinal Tissue Engineering Biomaterial and the Influence of Substrate Stress Relaxation on Retinal Pigment Epithelial Cells.

Cell therapies for age-related macular degeneration (AMD) treatment have been developed by integrating hydrogel-based biomaterials. Until now, cell activity has been observed only in terms of the modulus of the hydrogel. In addition, cell behavior has only been observed in the 2D environment of the hydrogel and the 3D matrix. As time-dependent stress relaxation is considered a significant mechanical cue for the control of cellular activities, it is important to optimize hydrogels for retinal tissue engineering (TE) by applying this viewpoint. Herein, a gellan Gum (GG)/Hyaluronic acid (HA) hydrogel was fabricated using a facile physical crosslinking method. The physicochemical and mechanical properties were controlled by forming a different composition of GG and HA. The characterization was performed by conducting a mass swelling study, a sol fraction study, a weight loss test, a viscosity test, an injection force study, a compression test, and a stress relaxation analysis. The biological activity of the cells encapsulated in 3D constructs was evaluated by conducting a morphological study, a proliferation test, a live/dead analysis, histology, immunofluorescence staining, and a gene expression study to determine the most appropriate material for retinal TE biomaterial. Hydrogels with moderate amounts of HA showed improved physicochemical and mechanical properties suitable for injection into the retina. Moreover, the time-dependent stress relaxation property of the GG/HA hydrogel was enhanced when the appropriate amount of HA was loaded. In addition, the cellular compatibility of the GG/HA hydrogel in in vitro experiments was significantly improved in the fast-relaxing hydrogel. Overall, these results demonstrate the remarkable potential of GG/HA hydrogel as an injectable hydrogel for retinal TE and the importance of the stress relaxation property when designing retinal TE hydrogels. Therefore, we believe that GG/HA hydrogel is a prospective candidate for retinal TE biomaterial.

Magma pressurization sustains ongoing eruptive episode at dome-building Soufrière Hills volcano, Montserrat

Abstract Dome-building volcanoes, where long-term eruptive episodes can be interspersed with periods of intra-eruptive repose, are particularly challenging for volcanic hazard assessment. Defining the end of eruptive episodes is vitally important for the socioeconomic recovery of affected communities but highly problematic due to the potential for rapid transition from prolonged, seemingly low-risk repose to dangerous effusive or explosive activity. It is currently unclear what constitutes the end of repose and an eruptive episode. We show that analysis of surface deformation can characterize repose and help define an eruptive episode. At Soufrière Hills volcano, Montserrat, the long-term post–2010 deformation at 12 continuous GPS stations requires the pressure in the magma system to have increased with time; time-dependent stress relaxation or crustal creep cannot explain the deformation trends alone. Continued pressurization within the magmatic system during repose could initiate a renewed eruption, qualifying as sustained unrest and therefore continuation of the eruptive episode. For Soufrière Hills volcano, persistent magma pressurization highlights the need for sustained vigilance in the monitoring and management of the volcano and its surroundings, despite the last eruptive activity ending in 2010. Our results show promise for application to other dome-building volcanoes.

Magnetization loops and non-scaling behavior of flux pinning force of Fe1+y Te1−x Se x studied by numerical simulation

The magnetization of type-II superconductors has usually been described using the critical state models (CSMs). However, CSMs do not consider the time-dependent magnetic relaxation. In this work, to study the influence of magnetic relaxation on the magnetic hysteresis loops (MHLs), critical current density J c, and flux pinning force F p, a numerical method proposed by (Qin and Yao 1996 Phys. Rev. B 54 7536) was adopted and extended to the quasi-two-dimensional case. MHLs at different temperatures measured by using applied field with different sweeping rates can be well reproduced. The critical current density after relaxation J s, and F p can also fit the experimental results well. Based on the numerical simulation, the non-scaling behavior of field-dependent normalized pinning force has been proven to be due to the magnetic relaxation. By comparing the normalized pinning force with the Dew-Hughes model, the dominant pinning type in Fe1+y Te0.6Se0.4 has been confirmed to be the volume Δκ pinning. In addition, the second peak effect is found to be related to the flux lattice transition from elastic lattice to plastic lattice (E-P transition).

Resistive state relaxation time in ZrO2(Y)-based memristive devices under the influence of external noise

The effects of external digitally synthesized Gaussian noise on the resistive state relaxation time of a ZrO2(Y)-based memristive device when switching from a low resistance state to a high resistance state have been experimentally investigated. A nonmonotonic dependence of the resistive state relaxation time on the external noise intensity is found. This behavior is interpreted as a manifestation of the noise-enhanced stability effect previously observed in various complex systems with metastable states. It is shown that the experimental results agree satisfactorily with the theoretical ones. The presented results indicate the constructive role of external noise and its possible use as a mechanism for controlling the kinetics of resistive switching.

Mechanical and Microstructural Properties of Meniscus Roots Vary by Location

Background: Despite the growing awareness of the clinical significance of meniscus root tears, there are relatively limited biomechanical and microstructural data available on native meniscus roots that could improve our understanding of why they are injured and how to best treat them. Purpose/Hypothesis: The purpose of the study was to measure the material and microstructural properties of meniscus roots using mechanical testing and quantitative polarized light imaging. The hypothesis was that these properties vary by location (medial vs lateral, anterior vs posterior) and by specific root (anteromedial vs anterolateral, posteromedial vs posterolateral). Study Design: Descriptive laboratory study. Methods: Anterior and posterior meniscus roots of the medial and lateral meniscus were isolated from 22 cadavers (10 female, 12 male; mean ± SD age, 47.1 ± 5.1 years) and loaded in uniaxial tension. Quantitative polarized light imaging was used to measure collagen fiber organization and realignment under load. Samples were subjected to preconditioning, stress-relaxation, and a ramp to failure. Time-dependent relaxation behavior was quantified. Modulus values were computed in the toe and linear regions of the stress-strain curves. The degree of linear polarization (DoLP) and angle of polarization—measures of the strength and direction of collagen alignment, respectively—were calculated during the stress-relaxation test and at specific strain values throughout the ramp to failure (zero, transition, and linear strain). Results: Anterior roots had larger moduli than posterior roots in the toe (P = .007) and linear (P < .0001) regions and larger average DoLP values at all points of the ramp to failure (zero, P = .016; transition, P = .004; linear, P = .002). Posterior roots had larger values across all regions in terms of standard deviation angle of polarization (P < .001). Lateral roots had greater modulus values versus medial roots in the toe (P = .027) and linear (P = .014) regions. Across all strain points, posterolateral roots had smaller mean DoLP values than posteromedial roots. Conclusion: Posterior meniscus roots have smaller modulus values and more disorganized collagen alignment at all strain levels when compared with anterior roots. Posterolateral roots have lower strength of collagen alignment versus posteromedial roots. Clinical Relevance: These data findings may explain at least in part the relative paucity of anterior meniscus root tears and the predominance of traumatic posterolateral roots tears as compared with degenerative posteromedial root tears.

Ion-pairing equilibria and kinetics of dimethyl phosphate: A model for counter-ion binding to the phosphate backbone of nucleic acids

Dimethyl phosphate (DMP–) is the simplest model ion to assess ion-pairing phenomena between metal ions and the phosphate backbone of nucleic acids. Yet, the equilibria and dynamics of ion binding to DMP– have not been fully uncovered. Here, we study the interaction of DMP– with different cations and water in aqueous solutions of NaDMP using dielectric relaxation and nuclear magnetic resonance spectroscopies. We find DMP– to be weakly hydrated and weakly associated with Na+ in the absence of added salt. Upon addition of NaCl, MgCl2, or CaCl2 to solutions of NaDMP, we detect the formation of solvent-shared (NaDMP0) and contact (MgDMP+, CaDMP+) ion-pairs; the degree of ion association is 20–27 % at 2:1 salt:DMP molar ratio for the bivalent ions. Comparison to literature results suggests the formation constant of MgDMP+ to be a good estimate for the binding of Mg2+ to RNA. From the concentration dependence of the rotational relaxation time of the ion-pairs, we find ion-pair dissociation rates to follow the order Mg2+≪Ca2+<Na+. Strikingly, our data suggest that the overall ion-pair dissociation dynamics are governed by an ion-pair metathesis reaction, which provides a different pathway for the binding of ions by DMP–.

Rheological Properties of Purple Avocado (Persea Americana Mill.) Fruits at Different Ripening Stages

Proper postharvest handling and management of perishable horticultural commodities require the proper understanding and the need for basic information on the mechanical properties of these commodities specifically for avocados to preserve quality and reduce losses and waste. Physical characterization and compression tests were conducted on avocados to develop an understanding of the rheological properties of avocados at different ripening stages, sizes, and compression loads. An appropriate equation in predicting volume from its weight and its shape signature that specifically represents the shape of the purple fruited avocado variety in a one-dimensional function were established. The shape of avocado fruits tends toward being spherical and expected to roll not slide as indicated by the mean values of sphericity and aspect ratio. The compressive strength of avocado varied with ripeness were small size can withstand up to 5 kg of load by weight after harvest without significant internal damage and 6 kg of load for medium size. Avocado fruits had a time-dependent stress relaxation behavior like other viscoelastic material. The threeterm Maxwell model with six parameters described the stress relaxation behavior of avocado fruit at different compressive loads, ripeness and sizes based on the maximum relative difference (MRD), R2 , and residual MSE. The advancing degree of ripeness have a corresponding decrease in the decay stress value (σ1) and time of relaxation (τ1) component of the model. To minimize mechanical damage, avocado should be packed in vertical orientation with cushion (bubble wrap, foam, or paper) and can be stacked up to 10 layers for small size and 12 layers for medium size at harvest using 10 kg capacity cartons.