Switchable Wettability Research Articles

Mechanically Induced Hydrophobic Recovery of Poly(dimethylsiloxane) (PDMS) for the Generation of Surfaces with Patterned Wettability.

Silicone elastomers are used in a variety of "stretchable" technologies (e.g., wearable electronics and soft robotics) that require the elastomeric components to accommodate varying magnitudes of mechanical stress during operation; however, there is limited understanding of how mechanical stress influences the surface chemistry of these elastomeric components despite the potential importance of this property with regards to overall function. In this study, plasma-oxidized silicone (poly(dimethylsiloxane)) films were systematically subjected to various amounts of tensile stress and the resulting surface chemical changes were monitored using contact angle measurements, X-ray photoelectron spectroscopy, and gas chromatography-mass spectrometry. Understanding the influence of mechanical stress on these materials made possible the development of a facile method for the rapid, on-demand switching of surface wettability and the generation of surface wettability patterns and gradients. The use of mechanical stress to control surface wettability is broadly applicable to the fields of microfluidics, soft robotics, printing, and to the design of adaptable materials and sensors.

Visual detection of the prostate specific antigen via a sandwich immunoassay and by using a superwettable chip coated with pH-responsive silica nanoparticles.

A pH-responsive superwettable chip is described whose surface can switch between superhydrophobic and superhydrophilic. It can be used for the visual detection of the prostate specific antigen (PSA) based on contact angle readout. Magnetic beads were modified with primary antibody against PSA. After immunobinding, gold nanoparticles loaded with secondary antibody labeled with glucose oxidase is added. On addition of glucose, gluconic acid is formed which causes a drop in the local pH value. This results in a wettability switch of the pH-responsive superwettable chip from hydrophobic to hydrophilic. Under the optimized conditions, PSA can be quantified with a 3.2pgmL-1 limit of detection by analyzing the contact angle and the related color that changes from blue via orange to red. The method is applicable to PSA detection in serum samples and for visual classification by cancer patients and healthy persons. It is also suitable for color-blind and color-weak individuals. Conceivably, this kind of assay can be transferred to the determination of various kinds of other bioanalytes including nucleotide, proteins, and even of ions and small organic molecules, and thus is has a wide scope. Graphical abstract Schematic presentation of a pH-responsive superwettable chip coated with silica nanoparticles for the visual detection of prostate specific antigen (PSA) by reading the contact angle. The superwettable chip achieves reliable clinical detection of serum PSA from prostate cancer patients.

Multistimuli-Responsive Microstructured Superamphiphobic Surfaces with Large-Range, Reversible Switchable Wettability for Oil.

The switchable wettability is essential for widespread applications in droplet manipulation, rewritable liquid patterning, fluid carrying, and so forth. However, it remains difficult to achieve the multistimuli-responsive, large-range, and reversible wetting switching especially for liquids with low surface tensions through surface topographical management. Here, we apply a simple and effective template-free self-assembly strategy to fabricate microstructured superamphiphobic surfaces that can reversibly switch the wetting performance for oil by transforming the surface morphology in response to multiple stimuli of magnetic fields and mechanical strains. Notably, the noticeably different wetting switching of oil triggered by different stimuli is demonstrated. The contact angles of hexadecane droplets on the as-prepared surfaces can be reversibly switched between 150 ± 1° and 38 ± 2° in response to mechanical strains. Furthermore, the underlying mechanism of wetting switching has been further elucidated using mathematical models. Interestingly, these switchable surfaces dramatically demonstrate the ability to transport oil droplets, without requiring lubricating liquid films. This work not only achieves the large-range and reversible wetting switching for oil but also opens new avenues for fabricating tunable superamphiphobic surfaces with transformable mushroom-like microstructures that can be easily extended to microstructure-dependent friction or adhesion control and used in other fields.

Lattice Boltzmann simulation of liquid water transport inside and at interface of gas diffusion and micro-porous layers of PEM fuel cells

In this study, an optimized stochastic model is developed to reconstruct the realistic 3D microstructure of gas diffusion layer (GDL) and micro porous layer (MPL). With considering GDL and MPL microstructure simultaneously, a 3D lattice Boltzmann (LB) model is developed to study the role of MPL macro crack in liquid water transport and redistribution at GDL/MPL interface. The proposed model is validated with visualization experiment in literature, and then the effects of different Poly Tetra Fluoroethylene (PTFE) distributions and pressure differences are investigated. The results show that PTFE distribution under vacuum-drying is almost uniform inside GDL, and the continuous switching of wettability between carbon fiber and PTFE can accelerate the liquid water permeation. PTFE under air-drying will accumulate at one side of GDL and reduce the porosity in this region, and thus the larger pressure difference or longer time is needed for liquid water break-through. As the pressure difference increases, the retaining amount of liquid water inside the narrow pore is increased. Inserting of MPL only latches the liquid water in GDL region close to macro crack, which helps reduce the water flooding and improve the gas transport to active sites.

Recent advance of two-dimensional carbon-based films and their polymer functionalized membranes for oil/water separation

<p indent=0mm>Oily water treatment has become an urgent task in our daily life because of the environmental and economic demands. Traditionally, gravity separation, flotation and filtration are used to separate oil/water mixtures successfully, but these methods have some drawbacks, including energy waste, low efficiency and secondary environmental pollution. In recent years, advanced materials with superwetting property involving superhydrophobic/superoleophilic separation materials, superhydrophilic and under-water superoleophobic separation materials, Janus separation materials, smart separation materials with switchable wettability emerge as a new research direction to address these problems. Because of the convenient separation and low-energy consumption, membrane separation material shows great advantages over conventional separation materials, which has a promising choice in the area of oily water treatment. Despite all these progress, most of the membranes separation materials are suffered from several limits for separating surfactant-stabilized oil/water emulsions and surfactant-free oil/water emulsions with micron or nanometer size, which may bring long-term damage to the natural environment. Furthermore, due to the presence of various harmful substances involving organic solvents, bacterial, heavy metal ions in real sewage system, the water pollution has become more serious and thus the resultant water phase is not suitable to put into the water system even after several separation cycles. From this perspective, to construct novel separation membrane materials with multifunction, good separation efficiency, high recyclability and convenient separation process for the separation of oil/water emulsions is passionately desired. Carbon-based (graphene and carbon nanotubes) membranes materials, especially polymer-functionalized carbon-based membrane materials, have gained increasingly attentions attributing to their outstanding physical and chemical properties, therefore are considered as an important choice for the separation of oily wastewater. Until now, there are tremendous advances on the carbon-based materials for oil/water separation, but most of them are focused on the development of three dimensional carbon-based separation materials, whereas the carbon-based membranes which play an important role on the treatment of oily wastewater have been almost neglected. Based on these, the research progress of polymer modified carbon-based films in wastewater treatment in recent years is reviewed in this paper. According to wettability and functions, the carbon-based membranes are divided into five parts: (1) Superhydrophobic carbon-based separation membranes, (2) superhydrophilic carbon-based separation membranes, (3) Janus carbon-based separation membranes, (4) smart carbon-based separation membranes, and (5) multi-functional carbon-based separation membranes. In each part, the influences of design routes, preparation methods and wetting behaviors on the separation efficiency of oily wastewater are discussed in detail. Finally, the development prospects and challenges of carbon-based membranes used for oil-containing wastewater purification are comprehensively discussed.

Smart Copolymer-Functionalized Flexible Surfaces with Photoswitchable Wettability: From Superhydrophobicity with "Rose Petal" Effect to Superhydrophilicity.

Realizing smart surfaces with switchable wettability inspired by nature continues to be fascinating as well as challenging. Herein, we present a versatile dip-coating approach to fabricate smart polymer-functionalized flexible surfaces with photoswitchable superwettability. Decorated with novel acrylate copolymers bearing a trifluoromethyl side chain and fluorine-containing azobenzene derivative moieties, the modified cotton fabric possesses a rose petal-like superhydrophobicity with contact angles larger than 150° and high water adhesion. This smart surface exhibits rapid phototriggered wettability transformation between superhydrophobicity and superhydrophilicity via alternate irradiation with ultraviolet and visible light, respectively. Meanwhile, the as-prepared flexible smart surfaces have excellent chemical and physical stabilities, which could tolerate harsh environmental conditions and repetitive mechanical deformation (e.g., stretching, curling, folding, and twisting) as well as multiple washing. More importantly, based on the excellent photocontrollability, various erasable and rewritable patterns with distinct wetting properties upon selective photoirradiation can be obtained. This simple strategy and the developed smart surface may find more advanced potential applications in controllable liquid transport, patterning droplet microarrays, and microfluidic devices.

Wettability of quartz controlled by UV light irradiation using an azobenzene surfactant

Solids having controllable wettabilty have received much attention due to their great importance in many industrial fields. In this paper, the quartz surfaces and particles with reversibly switchable wettability have been studied. The wettability of quartz can be controlled by UV light irradiation in the presence of an azobenzene surfactant (AZO). The adsorption behavior of AZO at the quartz-liquid interface was investigated by the measurements of the surface tension, contact angle and Zeta potential. The adsorption process was monitored by the quartz crystal microbalance with dissipation (QCM-D).The results show that AZO has a strong tendency to adsorb at the quartz–liquid interface. UV light irradiation causes the quartz-liquid interfacial tension (γsl) to decrease. The results from the QCM-D measurements show that the frequency change (Δf) decreases and the dissipation loss (ΔD) increases when AZO adsorbs onto the quartz surface. The dissipation changes are very small and the adsorption layer is rigid. After UV light irradiation, the adsorbed surfactants are desorbed from the quartz surface and the adsorption layer partly decomposes, causing the thickness of the adsorption layer to decrease.

Colorful nanostructured TiO2 film with superhydrophobic–superhydrophilic switchable wettability and anti-fouling property

Superhydrophobic nanostructured TiO2 film was successfully fabricated on the Ti plate by anodic oxidation and lauric acid modification. By varying the applied voltage, TiO2 films with various nanostructures and colors were prepared. The water contact angles (WCA) on the modified TiO2 film increased as the applied voltage increased, and the highest WCA on the TiO2 nanovesuvianite film was about 161.23°. When the applied voltage was 5 V and 20 V, the obtained TiO2 nanopores and TiO2 nanotubes could be used to build two improved Cassie models for designing superhydrophobic surface. Moreover, the superhydrophobic TiO2 film showed good anti-fouling property, particularly it could maintain superhydrophobicity both when immersed in and taken out from the organic solvents. The superhydrophobic film could be changed into superhydrophilic under ultraviolet (UV) irradiation, and the superhydrophilic film recovered to hydrophobic or superhydrophobic gradually at 60 °C in the dark. Additionally, the superhydrophilic film showed underwater superoleophobicity, which exhibited excellent anti-fouling property by degrading the oil under UV light.

In Situ Reversible Control between Sliding and Pinning for Diverse Liquids under Ultra-Low Voltage.

Thermally responsive paraffin-infused slippery surfaces have demonstrated intriguing performance in manipulating the behaviors of versatile droplets. However, present methods have been limited to ex situ rigid heat sources with a high voltage of 220 V or certain specific photothermal materials, which greatly hinders its practical applications. To solve this problem, an intelligent droplet motion control actuator (DMCA) composed of paraffin wax, hydrophobic micropillar-arrayed ZnO film, and a flexible transparent silver nanowire heater (SNWH) is reported in this work. Due to the good portability of DMCA, in situ switchable wettability for several liquid droplets with different surface tensions can be achieved by simply loading and unloading Joule heat at an ultra-low voltage (12 V). The relationship among sliding velocity and droplet volume and inclined angles was quantitatively investigated. By virtue of the flexible and mechanical endurance, this smart DMCA is dramatically functional for droplet motion manipulation ( e.g., reversible control between sliding and pinning) on complex 3D surfaces. Significantly, an impressive self-healing ability within 22 s is also demonstrated through the in situ application of Joule heat on the scratched DMCA, which renders its practical usability in various harsh conditions. This work provides insights for designing intelligent, flexible, and portable actuators dealing with the challenges of smart temperature-responsive surfaces.

Magnetic textile with pH-responsive wettability for controllable oil/water separation

More and more attention has been paid to materials with special wettability for the potential application in oil/water separation and oil-spill treatment. In this work, we presented a simple, efficient, and environmentally friendly method to develop a magnetic textile that could achieve switchable wettability by changing the pH value of the surface. The textile was fabricated by a mixture of Fe3O4 nanoparticles and dodecylamine (DDA)-modified TiO2 with high permeate flux, high separation efficiency and good stability. The Fe3O4/DDA-TiO2 textile showed its superhydrophobicity and superoleophilicity for neutral water (pH = 7), while the textile became superhydrophilic and underwater superoleophobic for acidic water (pH = 2).The as-prepared textile was investigated using eight different density oil/water mixtures. The results showed that the as-prepared textile possessed excellent separation efficiency (>99%) and high oil flux of about 9400–13,000 L h−1 m-2, water flux of about 6400–6700 L h−1 m-2 and good reusability. Meanwhile, the textile can maintain superhydrophobic under high temperature (˜170 °C), which significantly indicated its practical application in harsh environment. Because of its magnetism, the textile can be recovered and removed by magnets. We believe that this work may provide a number of potential application, such as microfluidic device, oil recovery and sewage purification.

A fully bio-based composite coating with mechanical robustness and dual superlyophobicity for efficient two-way oil/water separation

Recently, two-way oil/water separation materials bearing both “water-removing” and “oil-removing” functions are of great interest for treating environmental water pollution. Despite having switchable surface wettability, these materials are generally designed to possess superhydrophilicity in air, which, standing on the viewpoint of thermodynamics, is unstable and easy to lose the superwetting property. Concerning the full exploitation of sustainable biomass resources, herein, we use soy protein and ramie fiber to fabricate a cross-linked biocomposite whose amphiphilicity can be tuned by introducing a low surface-energy agent, octadecylamine. The resultant composite can be used as a coating for stainless steel meshes, preparing stably hydrophobic surface in air as well as achieving dual superlyophobicity under liquid that is required for efficiently separating light and heavy oils from water. Furthermore, a high separation efficiency is acquired for both light oil/water and heavy oil/water mixtures during cyclicusage. Notably, the fully bio-based coating displays high resistance against mechanical abrasion and harsh chemical corrosions (acid, alkaline, and salt) without losing high separation efficiency, indicating the potential application of such material in oily wastewater treatment.

In-Channel Responsive Surface Wettability for Reversible and Multiform Emulsion Droplet Preparation and Applications.

We report on a simple approach for in-channel functionalization of a polydimethylsiloxane (PDMS) surface to obtain a switchable and reversible wettability change between hydrophilic and hydrophobic states. The thermally responsive polymer, poly( N-Isopropylacrylamide) (PNIPAAm), was grafted on the surface of PDMS channels by UV-induced surface grafting. PNIPAAm-grafted PDMS (PNIPAAm-g-PDMS) surface wettability can be thermally tuned to obtain water contact angles varying in the range of 24.3 to 106.1° by varying temperature at 25-38 °C. By selectively modifying the functionalized area in the microfluidic channels, multiform emulsion droplets of oil-in-water (O/W), water-in-oil (W/O), oil-in-water-in-oil (O/W/O), and water-in-oil-in-water (W/O/W) could be created on-demand. Combining solid surface wettability and liquid-liquid interfacial properties, tunable generation of O/W and W/O droplet and stratified flows were enabled in the same microfluidic device with either different or the same two-phase fluidic systems, by properly heating/cooling thermal-responsive microfluidic channels and choosing suitable surfactants. Controllable creation of O/W/O and W/O/W droplets was also achieved in the same microfluidic device, by locally heating or cooling the droplet generation areas with integrated electric heaters to achieve opposite surface wettability. Hollow microcapsules were prepared using double emulsion droplets as templates in the microfluidic device with sequential hydrophobic and hydrophilic channel segments, demonstrating the strength of the proposed approach in practical applications.

Rapid, ultraviolet-induced, reversibly switchable wettability of superhydrophobic/superhydrophilic surfaces.

Controllable wettability is important for a wide range of applications, including intelligent switching, self-cleaning and oil/water separation. In this work, rapid switching and extreme wettability changes upon ultraviolet (UV) illumination were investigated. TiO2 nanoparticles were modified in solutions of trimethoxy(alkyl)silane, and the suspensions were sprayed on glass substrates. For such samples, the water contact angle (WCA) was shown to transition from a superhydrophobic (WCA ≈ 165°) to a superhydrophilic (WCA ≈ 0°) state within 10 min upon UV illumination and subsequent recovery to superhydrophobicity occurred after heat treatment. It was found that the changes in the trimethoxy(alkyl)silane upon UV illumination can explain the rapid decrease of the WCA from more than 165° to almost 0°. To further investigate the wettability transition, trimethoxy(alkyl)silane and Al2O3 nanoparticles (which are not photocatalytic) were mixed and spray-coated onto the glass substrates as the control samples. Then the unrecoverable change of trimethoxy(alkyl)silane under UV illumination can be confirmed. It was found that the presence of trimethoxy(alkyl)silane in the TiO2–trimethoxy(alkyl)silane coating served to speed up the super-wettability transition time from superhydrophobicity to superhydrophilicity, but also limited the number of wettability recycle times. With this understanding, the effect of the trimethoxy(alkyl)silane concentration on the number of recycle cycles was investigated.

Smart carbon foams with switchable wettability for fast oil recovery

The adsorption and recovery of crude-oil from oily water using oil-selective adsorbents is a highly promising solution for the increasing worldwide oil pollution, but remain a challenge. Herein, we reported a carbon foam (CF) with switchable wettability as smart materials for fast oil adsorption and recovery. By grafting poly(4-vinylpyridine) (P4VP) onto the surface of CF, the obtained smart foam presented a pH responsiveness and could change superhydrophilic and superhydrophobic surface according to the pH value. Thus, the smart responsive carbon foam could fast adsorb the oil in neutral solution (pH = 7) with high oil adsorption capacity of 62–120 g g−1 and desorb all the adsorbed oil in acidic solution (pH = 1) within 1.5 min. In addition, only 3% loss was observed for oil (chloroform) adsorption and recovery after successive reuses of up to 15 cycles, which demonstrated great recyclability of the materials.

Novel reversibly switchable wettability of superhydrophobic-superhydrophilic surfaces induced by charge injection and heating.

Reversibly switching wettability between superhydrophobicity and superhydrophilicity has attracted widespread interest because of its important applications. In this work, we propose a reversible superhydrophobic–superhydrophilic conversion induced by charge injection and heating. Different from the conventional electrowetting phenomenon caused by the accumulation of solid–liquid interfacial charges, we discovered a phenomenon where charge injection and accumulation at the solid surface results in a sharp increase in wettability. The wettability of a sprayed SiO2 nanoparticle coating on a glass slide was shown to change from superhydrophobic to superhydrophilic by charge injection and heating, and the superhydrophobicity was restored by heating, verifying a reversible superhydrophobic–superhydrophilic conversion. The influence of voltage, temperature, and time on the coating wettability and its durability under reversible conversion have been studied.

Conversion of skin collagen fibrous material waste to an oil sorbent with pH-responsive switchable wettability for high-efficiency separation of oil/water emulsions

Collagen fibrous material waste is an undervalued sustainable resource with many potential applications. Herein, a three-dimensional collagen fiber matrix (CFM), derived from skin collagen fiber waste generated in the leather industry, was modified by pH-responsive copolymer P(MAA-co-GMA) terminated with dodecyl hydrocarbon chains via an in situ free radical polymerization. The functionalized CFM possesses an appropriate porous structure, and shows switchable hydrophobicity/hydrophilicity for different pH values. It displayed high separation efficiency (∼99.93 ± 0.03%) for separating surfactant-free oil-in-water emulsion (10 cycles) as well as surfactant-stabilized oil-in-water emulsion (3 cycles). More importantly, the functionalized CFM displayed excellent self-cleaning performance. In other words, the absorbed oil was released after treatment in basic aqueous medium. The attractive properties of the functionalized smart collagen fiber matrix make it an excellent prospect for potential application in oily emulsion treatment from the reusable resource and environmentally friendly perspectives.

A nanoneedle-based reactional wettability variation sensor array for on-site detection of metal ions with a smartphone

An enhancement of the reactional wettability variation (RWV) sensing strategy is achieved based on the wettability switch of a nanoneedle surface. The sensor unit is formed by coating hydrophobic azoimidazole compounds, as the responder compounds onto the originally hydrophilic surface of cobalt hydroxide nanoneedles. The complexation reaction between metal ions and azoimidazole ligands etches the hydrophobic coating and switches the surface wettability, making the surface hydrophilic again. This switch is revealed by a decrease in the static contact angle (CA) and an increase in the sliding angle of the surface. The reactivity is tuned by the derivatization and conformational manipulation of the azoimidazole compounds. A sensor array composed of six as-tuned sensor units is constructed to distinguish among the species and concentrations of Fe3+, Ni2+ and La3+ at a low limit of 10−6 M using the chemometric method of principal component analysis (PCA). In addition, a new on-site detection strategy is developed based on PCA of the sliding angle, which can be measured conveniently and swiftly with a smartphone app and a commercially available setup. The application of the general RWV strategy is envisioned to open new possibilities for on-site detection.

ZnO nanoparticles coated mesh with switchable wettability for on-demand ultrafast separation of emulsified oil/water mixtures

Due to frequent discharge of oily wastewater and oils spill accident, oil/water separation has attracted worldwide attention. Nowadays, the on-demand separation of emulsified oil/water mixtures is urgent. Herein, the ZnO nanoparticles (NPs) coated mesh was prepared successfully by a simple spraying method. Reversible wettability conversion of the coated mesh between superhydrophobicity/superoleophilicity and superhydrophilicity/underwater superhydrophobicity was rapidly achieved by the alternation treated the coated mesh with stearic acid ethanol and NaOH solution for 15 min. Combined with the nanoscale pore size (smaller than the emulsion), the coated mesh could separate various kinds of emulsions whether water or oil is the continuous phase. Gravity is the only driving force for the entire separation process. The separation efficiency of emulsified oil/water mixtures was larger than 99.0%. Moreover, the coated mesh still showed high separation efficiency greater than 98.0% after 8 times cycle operations of wettability transition and separation, indicating a good stability and excellent recyclability. The developed ZnO NPs coated mesh should be a potential candidate for on-demand emulsions separation.

Superwetting rape pollen layer for emulsion switchable separation with high flux

The treatment of various kinds of oil-in-water and water-in-oil emulsions is increasingly desired but is still a considerable challenge. Although traditional two-dimensional superwetting separation materials have been widely studied, they still suffer from disadvantages such as single wettability and low separation flux. In this work, three-dimensional hollow porous rape pollen with switchable wettability was fabricated via simple solvent extraction and subsequent calcination using the pristine rape pollen as starting material. The obtained rape pollen was developed into a superwetting rape pollen layer, which achieves controllable wettability transition between hydrophobicity/underwater superoleophilicity and superhydrophilicity/underoil superhydrophilicity via calcination and steam modification alternately, without the addition of toxic modification reagents. Moreover, the wettability of rape pollens could be reversibly switched for many times. The obtained rape pollen layer can be used for on-demand separation of various oil-in-water and water-in-oil emulsions in one single device. After calcination, the hydrophobic/underwater superoleophilic rape pollen layer can absorb tiny oil droplets from oil-in-water emulsion, and the wetting properties can be rapidly switched to be superhydrophilicity/underoil superhydrophilicity to capture the water droplets from water-in-oil emulsion, with both high separation efficiency and separation flux. This work not only provides a novel emulsion separation approach that is different from membrane separation, but also has high potential in practical applications relating to wastewater treatment, fuel purification, microfluidics, and so on.

A Potential Amphiprotic Sponge with a Controlled Release Characteristic of Protons on Demand for Oil/Water Separation and Acid/Base Neutralization

AbstractUltralight sponges with the ability to release protons on demand, namely, superhydrophobic melamine formaldehyde sponges (SHpho‐MFSs), which are characterized as being safe‐to‐handle, convenient‐to‐use, easy‐to‐store, easy‐to‐carry, and easy‐to‐collect, are switched from superhydrophilic MFSs (SHphi‐MFSs) by a one‐step ultrasound treatment at a low pH. The wettability of the SHphi‐MFS is completely switched from the outside to the inside of the MFS. After wettability switching is achieved, the SHpho‐MFS that is prewetted with water and oil is able to selectively separate both water and oil, respectively. A compressed SHpho‐MFS also exhibits excellent separation performance of a water‐in‐oil emulsion. Furthermore, since the SHpho‐MFS can linearly release protons in an aqueous solution, during the oil/water separation (water‐removing), an aqueous solution of a strong base is neutralized or changed into a certain solution with a tailored pH by a simple filtration step using an appropriately sized SHpho‐MFS. The SHpho‐MFS can maintain a slow reaction rate and reduce the sudden release of heat during neutralization. Controlled release of the SHpho‐MFS capable of the ordered production of protons on demand is also achieved because the release “on and off” behavior of protons is repeatedly observed for every cycle.