High Elasticity Research Articles

On the design of lignin reinforced acrylic acid/hyaluronic acid adhesive hydrogels with conductive PEDOT:HA nanoparticles

Hydrogels are of great importance in biomedical engineering. They possess the ability to mimic bodily soft tissues, and this allows exciting possibilities for applications such as tissue engineering, drug delivery and wound healing, however much work remains on stability and mechanical robustness to allow for translation to clinical applications. The work herein describes the synthesis and analysis of a biocompatible, versatile hydrogel that has tailorable swelling, high stability when swollen and thermal stability. The synthesis methods used produce a hydrogel with high elasticity, good mechanical properties and rapid crosslinking whilst displaying biocompatibility, adhesion, and conductivity. It has been shown that cell viability in the samples is above 80 % in all cases, a Young's Modulus of up to 85 kPa and high swelling degrees were achieved. These materials show potential for use in numerous applications such as adhesive sensors, skin grafts and drug delivery systems.

Fabrication of superhydrophobic all-biomass aerogels with ultralight, elasticity and degradability for efficient oily wastewater treatment

Oily wastewater has seriously threatened the water ecology and human health. Superhydrophobic biomass-based aerogels are ideal candidates to remedy the oily wastewater, but facing challenges for the usage of toxic small molecules crosslinker and the rational construction of elasticity. Herein, we employed the natural non-toxic citral as crosslinker, and then constructed a superhydrophobic chitosan/bamboo cellular fibers aerogel (S-CS/BCF-A) with ultra-light, high elasticity and degradation performances. Wherein the hydrolysis of methyltrichlorosilane produced silicon hydride and hydrogen chloride, enhanced the hydrophobicity of the aerogel surface and partially reduced rigidity of the pore walls, respectively. The S-CS/BCF-A displayed outstanding fatigue durability, which benefited for its lamellar-fiber interweaved structure. In addition, this aerogel could undergo tape-peeling, UV radiation, and organic solvents immersion without superhydrophobic variation, even in seriously abrasing that the surface still maintained high hydrophobicity. The as-made aerogel possessed high oil adsorption capacity (17.95–44.57 g/g), combined with pump-supported device for effectively recovering large-area oil spills (66,348 L·m−2·h−1). Furthermore, the resultant aerogel could efficiently separate the immiscible oil-water mixture and emulsifying wastewater (types of Oil-in-Water and Water-in-Oil emulsions). This work provides a rational design method for constructing the elastic, durable and biodegradable aerogels, used for speedy and economical separation of oil-water mixtures.

An Elastomeric Lithium-Conducting Interlayer for High-Performance LATP-Based Lithium Metal Batteries.

In response to the critical challenges of interfacial impedance and volumetric changes inLi(1+x)AlxTi(2‑x)(PO4)3 (LATP)-based lithium metal batteries, an elastomeric lithium-conducting interlayer fabricates from fluorinated hydrogenated nitrile butadiene rubber (F-HNBR) matrix is introduced herein. Owing tothe vulcanization, vapor-phase fluorination, and plasticization processes, the lithium-conducting interlayer exhibits a high elasticity of 423%, exceptional fatigue resistance (10000 compression cycles), superior ionic conductivity of 6.3×10-4 S cm-1, and favorable lithiophilicity, rendering it an ideal buffer layer. By integrating the F-HNBR interlayer, the LATP-based lithium symmetric cells demonstrate an extended cycle life of up to 1600h at 0.1mA cm-2 and can also endure deep charge/discharge cycles (0.5 mAh cm-2) for the same duration. Furthermore, the corresponding lithium metal full cells achieve 500 cycles at 0.5 C with 98.3% capacity retention and enable a high-mass-loading cathode of 11.1mg cm-2 to operate at room temperature.

Tough and elastic hydrogel thermocells for heat energy utilization

Hydrogel thermocells possess great potential in the energy conversion field as they directly absorb waste heat from the environment to drive redox reactions for continuous electricity generation. However, achieving high toughness and good elasticity simultaneously in hydrogel thermocells remains a challenge because of the inherent contradiction of energy dissipation mechanisms, severely limiting their practical applications and lifespan. To address this, a skin-like hydrogel network with a highly dense interwoven network is developed to construct hydrogel thermocells with good elasticity and high toughness. The dense network structure can effectively disperse the stress and hinder crack propagation, thus breaking the contradiction between high toughness and good elasticity. The thermocell realizes a toughness of 460 J m−2 while reaching an elastic limit strain of 350 %, far exceeding the elasticity of previous stretchable hydrogel thermocells. Meanwhile, it exhibits ultra-low hysteresis and excellent fatigue resistance under tensile and compressive cyclic loads. Moreover, the thermocell can work stably over long periods, enabling stable voltage output even under compression, bending, and stretching. In addition, the thermocell can power the LED lamp and calculator, and can also be connected in series to form large arrays, thus rendering it an ideal power source for wearable devices.

Novel PEO-based Solid Polymer Electrolyte with High Elasticity and High Ionic Conductivity for Room Temperature Lithium Metal Batteries

The development and application of polyethylene oxide (PEO) based solid polymer electrolyte (SPE) is severely constrained by its low ionic conductivity and poor tensile resistance. To improve the electrochemical performance of SPE without losing its mechanical properties, a benzene sulfonate-based additive is adopted into crosslinking system composed of -CH2-CH2-O- segments to obtain a membrane with a high ionic conductivity of 1.47 × 10−4 S cm−1 and an ionic transference number of 0.70 at room temperature. The activation energy value of 0.128 eV gives evidence for a favorable migration mechanism of PTH-SPE. Anti-dendrite growth and contact optimization can be realized by molecular structure design with a tensile elongation of 490%. The reversible overpotential of Li||Li symmetric cell within 1000 h demonstrates that the compact PTH-SPE can inhibit the growth of lithium dendrite. This work provides a new strategy for designing high-performance solid electrolytes for room temperature via a green solvent-free method.

Porous PVDF composites with ultralow percolation threshold for wide-range dynamic and static pressure sensing

Porous conductive polymer composites are very attractive for static pressure sensing due to high sensitivity and good elasticity contributed by the porous structure, while they are hard to detect dynamic pressure. Herein, we report a porous conductive poly (vinylidene fluoride) (PVDF) composite capable of detecting static and dynamic pressure over a pressure range of 0–1 MPa, which was fabricated by melt mixing PVDF, polyethylene oxide (PEO) and carbon nanofillers, followed by etching PEO with water. Such porous PVDF composites have a very low percolation threshold (0.035 wt%) of carbon nanostructures (i.e., branched carbon nanotubes) thanks to the selective distribution of conductive fillers in the pore wall after etching. At the same time, the pore size and porosity of the porous PVDF composites can be tuned by the molecular weight (Mw) and blending ratios of two polymers, leading to the kinetically-tailorable blend morphology for tunable mechanical and electrical properties. The as-fabricated porous PVDF composites with a good combination of mechanical properties and electrical conductivities, which can be used as pressure sensors toward wide-range (0–1 MPa) dynamic and static pressure sensing. Such pressure sensors demonstrate potential applications in detecting the degree of finger bending, distinguishing the walking and running, and monitoring a series of technical movements in playing soccer, i.e., static and dynamic exercises.

Fast Photoactuation and Environmental Response of Humidity-Sensitive pDAP-Silicon Nanocantilevers.

Multi-responsive nanomembranes are a new class of advanced materials that can be harnessed in complex architectures for micro and nano-manipulators, artificial muscles, energy harvesting, soft robotics, and sensors. The design and fabrication of responsive membranes must meet such challenges as trade-offs between responsiveness and mechanical durability, volumetric low-cost production ensuring low environmental impact, and compatibility with standard technologies or biological systems This work demonstrates the fabrication of multi-responsive, mechanically robust poly(1,3-diaminopropane) (pDAP) nanomembranes and their application in fast photoactuators. The pDAP films are developed using a plasma-assisted polymerization technique that offers large-scale production and versatility of potential industrial relevance. The pDAP layers exhibit high elasticity with the Young's modulus of ≈7 GPa and remarkable mechanical durability across 20-80°C temperatures. Notably, pDAP membranes reveal immediate and reversible contraction triggered by light, rising temperature, or reducing relative humidity underpinned by a reversible water sorption mechanism. These features enable the fabrication of photoactuators composed of pDAP-coated Si nanocantilevers, demonstrating ms timescale response to light, tens of µm deflections, and robust performance up to kHz frequencies. These results advance fundamental research on multi-responsive nanomembranes and hold the potential to boost versatile applications in light-to-motion conversion and sensing toward the industrial level.

Insights into the starch and proteins molecular structure changes of foxtail millet sourdough: Effect of fermentation from grains of cereal to pre-meal

This study investigated the effects of foxtail millet sourdough fermentation time (0, 8, 16, and 24 h) on the protein structural properties, thermomechanical, fermentation, dynamic rheological, starch granules crystalline regions molecular mobility, and starch microstructural characteristics. The fermentation led to a significant increase in the concentration of free amino acids from protein hydrolysis. Fourier transform infrared spectroscopy (FTIR) revealed changes in protein secondary structure and the presence of functional groups of different bioactive compounds. The result of thermomechanical properties showed a significant increase in the stability (0.70–0.79 min) and anti-retrogradation ability (2.29–3.14 Nm) of lactic acid bacteria (LAB) sourdough compared to the control dough, showing a wider processing applicability with radar profiler index. In contrast, sourdoughs with lower tan δ values had higher elasticity and strength. Scanning electron microscopy showed that the surface of the starch appeared from smooth to uneven with patchy shapes and cavities, which declined the crystallinity from 34.00 % to 21.57 %, 23.64 %, 25.09 %, and 26.34 % respectively. Fermentation changed the To, Tp, Tc, and ΔH of the starch. The results of the study will have great potential for application in the whole grain sourdough industry.

Lightweight thermoplastic polyurethane/multi-wall carbon nanotube foams with a continuous gradient cell structure for electromagnetic interference shielding

With the rapid development of portable microelectronic devices, materials with tunable electromagnetic shielding (EMI) performance and comfort of use have become urgently necessary. A lightweight, conductive thermoplastic polyurethane/multi-walled carbon nanotube (TPU/MWCNT) composite foam with a continuous gradient cell structure has been developed to impede electromagnetic wave reflection induced by excessive impedance mismatch. The continuous gradient distribution of cell structure and conductivity provides the TPU/MWCNT composite foams with distinct shielding effects of electromagnetic waves in both front and back gradient directions. The maximum front absorption coefficient (A) reached 0.93, which is higher than any foam with a uniform cell size within the cell size range of the gradient composite foams. At the same time, the gradient composite foams possess the characteristics of lightweight, high elasticity, and extensibility. The weight was decreased by 67.27–85.45 %, the elastic recovery ratio of compression reached 95 %, and the toughness was also excellent. Numerical simulation of the gradient foam model was conducted using CST Microwave Studio to uncover the gradient asymptotic dissipation mechanisms. The lightweight and stretchable continuous gradient foams show great promises for the next-generation portable electronic devices that generate no radiation pollution.

Rheology of Suspensions of TEMPO-Oxidised and Cationic Cellulose Nanofibrils-The Effect of Chemical Pre-Treatment.

Cellulose nanofibrils (CNFs) are particles with a high aspect ratio. Typically, chemically pre-treated CNFs (containing anionic or cationic charged groups) consist of long fibrils (up to 2 μm) with very low thickness (less than 10 nm). Derived from their high aspect ratio, CNFs form strong hydrogels with high elasticity at low concentrations. Thus, CNF suspensions appear as an interesting rheology modifier to be applied in cosmetics, paints, foods, and as a mineral suspending agent, among other applications. The high viscosity results from the strong 3D fibril network, which is related to the good fibrillation of the material, allowing the nanofibrils to overlap. The overlap concentration (c*) was found to vary from ca. 0.13 to ca. 0.60 wt.% depending on the type and intensity of the pre-treatment applied during the preparation of the CNFs. The results confirm the higher tendency for the fibres treated with (3-chloro-2-hydroxypropyl) trimethylammonium chloride (CHPTAC) and 2,2,6,6-tetramethylpiperidine 1-oxyl (TEMPO) to form a 3D network, resulting in the lowest c*. For the TEMPO-oxidised CNF suspensions, it was also found that aggregation is improved at acidic pH conditions due to lower charge repulsion among fibrils, leading to an increase in the suspension viscosity as well as higher apparent yield stresses. TEMPO CNF suspensions with a low content of carboxylic groups tend to precipitate at moderately acidic pH values.

Who Are the Hand-to-Mouth?

Abstract Many households hold little wealth. In standard precautionary savings models, these households should not only display higher marginal propensities to consume (MPCs) but also higher future consumption growth. In contrast, we see from the Panel Study of Income Dynamics that such “hand-to-mouth” households do not display higher growth in spending. They also exhibit greater volatility of spending and adjust their spending to a greater extent through the number of categories consumed. Consistent with a role for preference heterogeneity, the panel data show that it is persistent differences across households, not current assets, that predict low consumption growth and other spending differences for the hand-to-mouth households. To identify the extent of preference heterogeneity, we consider the model of Kaplan and Violante with both liquid and illiquid assets, but allow heterogeneity in preferences. To match the data, many poor hand-to-mouth must be relatively impatient and have a high inter-temporal elasticity of substitution. The model shows that preferences predominantly explain the higher MPCs for low-asset households. Preference heterogeneity notably increases the spending impact of fiscal transfers, but only if targeted, while reducing that from interest rate cuts.

Dual Ion Regulated Eutectogels with High Elasticity and Adhesive Strength for Accurate Strain Sensors

AbstractEutectogels have attracted increasing attention from researchers due to their broad application potential, good environmental stability, biocompatibility, and low cost. Currently reported eutectogels generally show large residue strain and hysteresis, which will cause output signal inconsistency between the loading and unloading processes and is not conducive to accurate strain monitoring. Besides, the low adhesiveness of available eutectogels brings about difficulties in the installation of the sensors and dynamic interfacial stability between the sensors and human skin. Herein, a dual ion regulation strategy is proposed to obtain eutectogels with high resilience, high adhesiveness, ultralow residue strain, wide temperature adaptability (−20–60 °C) and good environmental stability. Strain sensors based on gradient eutectogels exhibit high sensitivity, a wide linear response range, and good cycling stability. The response curve shows negligible electrical hysteresis, providing consistent output signals at the fixed strain regardless of stretch or release. Accurate micrometry with a step as minute as 50 µm is realized. Moreover, the sensors demonstrate higher signal intensity and stability in human physiological signals and motion detection due to the strong interfacial bonding.

Modified Bitumen Materials from Kazakhstani Oilfield

The oil bitumen BND 90/130, produced at the “LLP SP Caspi Bitum” with the modifier, which consists of copolymer of ethylene with butyl acrylate and glycidyl methacrylate taken in an amount of 0.5–1.6 wt%, and the tire reclaim (4–20 wt%), which is the destructate of mesh elastomers of different chemical nature, was modified; possibility of using the developed bitumen-elastomer binders in road asphalt concrete was justified. Modification of bitumen with a copolymer of ethylene with butyl acrylate and glycidyl methacrylate leads to an improvement in the properties of road bitumen: the softening point, hardness, deformability at low temperatures, elasticity, and adhesion to metal and mineral filler increase. It was shown that ethylene with butyl acrylate and glycidyl methacrylate chemically interacts with the functional groups of bitumen asphaltenes through the epoxy group of glycidyl methacrylate. Analysis of the spectra and group composition indicates an increased content of high molecular weight asphaltenes in the modified bitumen with a slight increase in structuring resins. It has been established that bitumen modified with rubber crumbs of 0.6–1.0 mm in size has high elasticity. The most effective composition of a bitumen-regenerated composite material based on tire reclaim has been determined. In terms of the totality of physicochemical and operational characteristics and comparative cost, the most acceptable is the bitumen-regenerated composition (with a regenerate content of 20%) and is superior in the complex of properties to bitumen modified with an optimal content of ethylene with butyl acrylate and glycidyl methacrylate (1.6%). The technology for modifying bitumen with tire reclaim is less time-consuming, more economically profitable, and environmentally effective, since it utilizes large-tonnage waste of worn-out tires. The resulting bitumen-polymer compositions have a high positive set of properties: softening point, hardness, elasticity, frost resistance, and low-temperature characteristics.

Development of die drawing design factor prediction models for trenchless rehabilitation of water pipes: a case study

ABSTRACT Maintenance and replacement of aging water pipes are critical for urban development. To this end, trenchless rehabilitation methods that do not require excavation offer an efficient replacement for aging water pipes. Thus, this study developed a trenchless method using die drawing, which continuously inserts polyethylene (PE) liners into the reach point while maintaining traction in the host aging pipe. If the traction is removed after a certain period, the initially contracted liner pipe undergoes expansion under natural restoration and tightly adheres to the inner wall of the host pipe to achieve structural regeneration of the aging pipe. This study aimed to determine the factors influencing the die drawing process using a rehabilitation design. Accordingly, we experimented with the die drawing method to achieve structural reinforcement using high elasticity PE liners. Thereafter, based on the experimental data, we developed prediction models to estimate traction, pipe restoration rate after traction release, and pipe restoration period. The developed models estimated the minimum required restoration period and provided deeper insights into the restoration behavior of the die drawing method employed in pre-equipment maintenance before on-site construction.

Empirical calibration method for the thermal simulation of Cu47Ti34Zr11Ni8 single tracks in laser powder bed fusion

Bulk metallic glasses (BMGs) are materials that, due to their amorphous microstructure, offer a unique combination of high strength, hardness, and elasticity, making them attractive for various applications. Using laser powder bed fusion (PBF-LB/M) enables overcoming the current limitations of BMGs in size and shape imposed by traditional manufacturing methods such as casting. Despite its potential, challenges such as porosity, (nano-) crystallization, and impurities affect the mechanical performance of additively manufactured BMGs. This study focuses on the Cu–Ti-based alloy Vit101, known for its higher strength and improved cost-effectiveness compared to Zr-based BMGs. In-situ high-speed pyrometry and thermal simulations of single tracks are employed to enhance the understanding of processing and controlling the thermal cycling of Vit101. The proposed experimental calibration is performed through an off-axis integration of the pyrometer, allowing for in-situ temperature measurements. The acquired data show sufficient congruence with the simulated cooling profiles. Minimal cooling rates in the range of 104 K/s were measured and simulated above the glass transition temperature, indicating a large leeway for further development of glass-forming alloys. Scan track widths are evaluated for validation, resulting in minor deviations between 0.47% and 3.17%. However, challenges emerge at high scanning speeds, leading to higher deviations attributed to balling phenomena, which are not considered in the numerical model.

Synthesis and Characterization of Graft Copolymers with Poly(ε-caprolactone) Side Chain Using Hydroxylated Poly(β-myrcene-co-α-methyl styrene).

Graft copolymers have unique application scenarios in the field of high-performance thermoplastic elastomers, resins and rubbers. β-myrcene (My) is a biomass monomer derived from renewable plant resources, and its homopolymer has a low glass transition temperature and high elasticity. In this work, a series of tapered copolymers P(My-co-AMS)k (k = 1, 2, 3) were first synthesized in cyclohexane by one-pot anionic polymerization of My and α-methyl styrene (AMS) using sec-BuLi as the initiator. PAMS chain would fracture when heated at high temperature and could endow the copolymer with thermal degradation property. The effect of the incorporation of AMS unit on the thermal stability and glass transition temperature of polymyrcene main chain was studied. Subsequently, the double bonds in the linear copolymers were partially epoxidized and hydroxylated into hydroxyl groups to obtain hydroxylated copolymer, which was finally used to initiate the ring-opening polymerization (ROP) of ε-caprolactone (ε-CL) to synthesize the graft copolymer with PCL as the side chain. All these copolymers before and after modifications were characterized by proton nuclear magnetic resonance (1H NMR), gel permeation chromatography (GPC), thermogravimetry analysis (TGA), and differential scanning calorimeter (DSC).

Urban traffic-parking system dynamics model with macroscopic properties: a comparative study between Shanghai and Zurich

Analyzing the dynamics of parking traffic can better represent the real dynamic states of road networks, thereby allowing for a deeper analysis of the parking system’s impact. This paper comparatively investigates the impact of parking policies on two traffic networks with different infrastructure, socio-economic, and policy characteristics. Parking space, average parking duration, and parking fee policies were analyzed as a function of cruising distances and cruising time with indirect effects on traffic emissions. Empirically, the system dynamics model application is tested and validated with the macroscopic data from two central business districts (CBDs) in Shanghai (Xujiahui area) and Zurich (Bahnhofstrasse area). Results showed Bahnhofstrasse CBD is more sensitive against the policy shifts with relatively higher elasticity and indicated greater responsiveness in aggregating traffic emissions when compared with Xujiahui CBD. The findings of this study may provide an overall framework to empirically assess the performance of different traffic conditions and strategies on urban parking systems.

Self-healing glassy hybrids based on imidazole-functionalized silica nanoparticles with zinc complexes using dynamic and reversible cross-linking

Self-healing glass materials can potentially overcome the inherent limitations of glass, such as brittleness and difficulties in repairing broken sections while maintaining its critical properties. This paper reports a structural design and synthetic strategy for preparing glassy self-healing hybrids with high silica contents. The developed hybrids exhibited excellent self-healing properties based on dynamic and reversible crosslinking owing to the high density of zinc/imidazole units on the silica surface. First, core–shell silica nanoparticles with small multifunctional imidazole/butyl units (diameter: approximately10 nm) and good processability (homogeneous colloidal dispersions in common organic solvents) were synthesized. Afterwards, imidazole-functionalized silica nanoparticles were fabricated using Zn species to obtain self-healing hybrids with high silica contents (>60 wt%). These nanoparticles served as multifunctional and reversible crosslinking sites that dissipated energy, resulting in excellent mechanical, thermal, and healing characteristics. The obtained zinc/imidazole-based silica hybrids remain solid with high storage elasticity in the temperature range of 25–160 °C and high thermal stability corresponding to a 5 wt% weight loss above 280 °C, which were critical for self-healing glass applications. They also exhibited a moderate Young’s modulus of 330 MPa and a self-healing recovery efficiency of 87%. The findings of this study provide new insights into the roles of reversible interactions (metal/ligand exchange reactions) at particle–particle interfaces and high surface functionalities that serve as non-covalent crosslinking points. The prepared hybrids with high silica contents remain solid over a wide temperature range, which can open new avenues for self-healing glass materials.

Effects of alkyl polyglucoside on the self-assembly behavior and foam properties of the thermoresponsive triblock copolymer (EO)100(PO)65(EO)100

Thermoresponsive liquid foams stabilized with the triblock copolymer (EO)100(PO)65(EO)100 (PF127) have been proved to be effective in suppressing pool fire. Understanding how the low-molecular-weight surfactants affect the properties of thermoresponsive foam stabilized by PF127 is important in the development of fluorine-free firefighting foam. In this work, the effects of the non-ionic surfactant alkyl polyglucoside (APG) on the properties of the foam stabilized by the triblock copolymer PF127 were studied. The relationships among molecular self-assembly, interfacial properties, and foam properties were investigated by conducting scattering experiments and foam aging tests. The results demonstrated that the APG molecules participated in the organization of the mixed micelles with PF127 molecules and the competition of both components in the mixed micelles affected the foaming properties. For the systems containing APG and 20 wt% PF127, APG acted as a foam inhibitor, suppressing foam generation at low concentrations. In contrast, APG acted as the foam booster at high concentrations since the mixed micelles were relatively unstable, allowing more unimers to diffuse to the interfacial region. In the absence of APG, the liquid foam from PF127 exhibited high stability and elasticity under heat due to the ordered structure formed by PF127 micelles inside the foam. As the APG concentration increased, the transition of orderly packed PF127-rich mixed micelles into disordered APG-rich mixed micelles caused the originally inhibited liquid drainage to restart rapidly, making the foams unstable upon heating. The results of this work can give theoretical guidance for the development of thermoresponsive firefighting foams.

Pricing and replenishment decision problem based on time series prediction and optimization algorithm

The pricing of vegetable products is an important research topic that involves multiple aspects such as agricultural production, market supply and demand, consumer interests, and social benefits. Vegetable products have characteristics such as short production cycles, short shelf life, large price fluctuations, and high demand elasticity, which pose challenges to pricing decisions. To develop replenishment decisions that maximize the profits of supermarkets, the author establishes a mathematical model for the total sales volume and cost add-on pricing of each vegetable category. First, the cost, cost add-on coefficient, and loss rate of individual products in the same category are summed according to the weight of sales, and the corresponding average cost, cost add-on coefficient, and average loss rate of the category are obtained. This initially achieves a negative correlation between the sales trend and the cost add-on coefficient using a function. Then, by constructing a LSTM neural network model and using known data to predict the sales of each category, the predicted sales volume of the model is used as the sales benchmark value. The relationship function between the sales trend and the cost add-on coefficient is supplemented, and the optimization algorithm is used to find the cost add-on coefficient value, the total daily replenishment quantity, and the maximum profit value that maximize the profits of supermarkets.