Hydrophobic Attraction Research Articles

The pressure difference of water, a neglected but crucial inter-surface force in aqueous solutions

In this work, thermodynamically, we demonstrate that the pressure difference of water is an essential component of the interaction pressures between surfaces in aqueous solutions due to the influence of force field generated by the surfaces on the surrounding molecules. The introduction of the essential component into the interaction pressures can provide detailed insights into hydrophobic attraction, hydrophilic repulsion, DNA condensation and de-condensation by multivalent cation salts and protein stabilization and destabilization by osmolytes and macromolecular crowding agents.

Impact of microfluidization and thermal treatment on the structure, stability and in vitro digestion of curcumin loaded zein-propylene glycol alginate complex nanoparticles

The aim of this study was to modulate the physicochemical properties, molecular interactions and microstructure of zein-propylene glycol alginate (PGA) complex nanoparticles for delivery of curcumin with the aid of high pressure microfluidization (HPM) (50–150 MPa) and thermal treatment (45–85 °C). The size of zein-PGA complex nanoparticles was decreased to around 300 nm. It was confirmed that the pressure of 100 MPa and temperature of 75 °C were the optimum parameters to provide a better protection of entrapped curcumin against environmental stresses. The electrostatic interaction, hydrogen bonding and hydrophobic attraction were the dominant driving forces in the formation of the complex nanoparticles. Field emission scanning electron microscopy (FE-SEM) revealed that HPM and thermal treatment facilitated the complex nanoparticles to form a more uniform size and spherical shape. During in vitro gastrointestinal digestion, zein-PGA complex nanoparticles showed excellent gastric stability and sustained-release of curcumin in the small intestine. HPM and thermal treatment showed a synergistic effect on enhancing the bioaccessibility of curcumin entrapped in zein-PGA complex nanoparticles. The findings revealed the influence of HPM and thermal treatment on functional attributes of the complex nanoparticles, which could be utilized to design food grade nanoparticles with desirable stability and digestive properties.

A Simple Approach for Trace Voltammetrical Determination of Itraconazole an Inhibitor of the Cytochrome P-450 14 α-demethylase Enzyme in Formulation and Human Plasma Utilizing Graphene-Carbon Paste Electrode in Situ Modified with an Anionic Surfactant

An economical graphene-carbon paste electrode (GR/CPE) in situ modified with surfactants was used for improvement the sensitivity and selectivity of the electrochemical measurement of itraconazole drug. Among the surfactants, cationic (cetyltrimethyl ammonium bromide, CTAB) and non-ionic (Triton X-100) displayed a decrease in peak current intensity, while anionic (sodium dodecyl sulfate, SDS) exhibited better change in the electrical properties of the electrode-solution interface. The adsorbed-SDS at GR/CPE interacts with itraconazole molecules through hydrophobic and electrostatic attraction which encourages the electron transmission between the drug and electrode surface. Compared with CPE and GR/CPE, SDS-GR/CPE exhibits the enhanced peak current intensity and reduces the over potential toward itraconazole oxidation as a result of the combined effect of GR and SDS. %composition of GR/CPE and SDS concentration were optimized. Wide linear dependence of the current on bulk itraconazole concentration (1.5 × 10−9–7.0 × 10−7 M) was achieved in Britton–Robinson buffer, pH 2.0 containing 0.5 mM SDS at 0.3%(w/w) GR/CPE. SDS-GR/CPE presents adequately LOD value (1.36 × 10−9 ± 1.07 × 10−10 M) for the determination of itraconazole in human plasma. SDS-GR/CPE avoids interference from important common substances in biological and pharmaceutical samples. The fabricated sensor has desirable stability and reproducibility that can be used in routine quality control and pharmacokinetic studies.

Hydrophobic Agglomeration of Fine Pyrite Particles Induced by Flotation Reagents

Flotation reagents can change the surface properties of minerals, leading to differences in the interaction between mineral particles and affecting the mutual aggregation or dispersion of particles. In this work, we studied the role of activator copper sulfate, collector butyl xanthate and frother terpineol in adjusting the potential energy of pyrite particles from the perspective of the interfacial interaction. We evaluated the surface characteristics using contact angle analysis and zeta potential measurements under different reagents. A microscope was used to observe aggregation state of particles. The hydrophobic agglomeration kinetics of pyrite was studied through the turbidity meter measurement, and the interaction energy between pyrite particles was calculated using the extended-Derjaguin-Landau-Verwey-Overbeek (extended-DLVO) theory. The results showed that the repulsive potential energy is dominant among pyrite particles in aqueous suspensions and that the particles are easy to disperse. Flotation reagents can effectively reduce the repulsive energy between pyrite particles and increase the attraction energy between particles, which is conducive to the hydrophobic agglomeration of fine pyrite. Reagent molecules can greatly reduce the electrostatic repulsion potential energy of the pyrite particles’ interface, increase the hydrophobic attraction potential energy between the particle interfaces, and its size is 2 orders of magnitude larger than the van der Waals attraction potential energy, which is the main reason for induced the agglomeration of fine pyrite and is conducive to the flotation recovery of fine pyrite. Generally, the order in which the reduction of pyrite agglomeration was affected by the additions of flotation reagents was butyl xanthate > terpineol > copper sulfate.

Role of dodecane on coal particle-bubble interaction in aqueous phase

Even if coal particles are hydrophobic, interaction between these particles and air bubbles can be enhanced by nonpolar oil in froth flotation. The role of a nonpolar liquid dodecane on coal particle-bubble interaction in aqueous phase was investigated and compared to that of a solid analogue, paraffin wax via a combined application of water contact angle and particle-bubble stability measurements, and molecular dynamics simulations. It was found both dodecane and paraffin wax can increase hydrophobicity of coal surface and attachment stability of coal particle-bubble aggregates when they covered the coal particles. Despite similar chemical structure and hydrophobicity, dodecane was more effective than paraffin wax. Molecular simulations confirmed that, comparing to the unmodified coal particle, both dodecane and paraffin wax models could increase the attachment strength of coal particle. However, different from immobile solid paraffin wax, we demonstrated that the liquid like properties of the dodecane layers present on the coal particle surfaces play an essential role in the particle-bubble interaction. When the coal particle covered by dodecane arrived at gas−water interface, the dodecane molecules will migrate and rearrange to form a new film at this interface. In addition to hydrophobic attraction of the gas bubble, the dodecane film will provide additional adhesion towards the coal particle due to oleophilicity of the coal particle, enhancing the stability of bubble-particle aggregate.

Water under extreme confinement in graphene: Oscillatory dynamics, structure, and hydration pressure explained as a function of the confinement width

Graphene nanochannels are relevant for their possible applications, as in water purification, and for the challenge of understanding how they change the properties of confined liquids. Here, we use all-atom molecular dynamics simulations to investigate water confined in an open graphene slit-pore as a function of its width w, down to sub-nm scale. We find that the water translational and rotational dynamics exhibits an oscillatory dependence on w, due to water layering. The oscillations in dynamics correlate with those in hydration pressure, which can be negative (hydrophobic attraction), or as high as ~1 GPa, as seen in the experiments. At pore widths commensurable with full layers (around 7.0 Å and 9.5 Å for one and two layers, respectively), the free energy of the system has minima, and the hydration pressure vanishes. These are the separations at which the dynamics of confined water slows down. Nevertheless, the hydration pressure vanishes also where the free energy has maxima, i.e., for those pore-widths which are incommensurable with the formation of well-separated layers, as w ≃ 8.0 Å. Around these values of w, the dynamics is faster than in bulk, with water squeezed out from the pore. This behavior has not been observed for simple liquids under confinement, either for water in closed nano-pores. The decomposition of the free energy clarifies the origins of the dynamics speedups and slowdowns. In particular, we find that the nature of the slowdown depends on the number of water layers: for two layers, it is due to the internal energy contribution, as in simple liquids, while for one layer, it has an entropic origin possibly due to the existence of a hydrogen-bond network in water. Our results shed light on the mechanisms ruling the dynamics and thermodynamics of confined water and are a guide for future experiments.

Comparison of Same Carbon Chain Length Cationic and Anionic Surfactant Adsorption on Silica

Adsorption of a cationic surfactant dodecyl pyridinium chloride (DPC) on silica was studied to show a comparison with the adsorption of an anionic surfactant sodium dodecyl sulfate (SDS), whose carbon chain length is the same and on the same silica. Results provided a better understanding of the adsorption mechanism of cationic and anionic surfactant on negatively charged silica. The experiment covered different electrolyte concentrations and pH values. Results indicated that at the same pH, the DPC adsorption amounts are higher when the electrolyte concentration is higher; at a higher DPC equilibrium concentration, the adsorption amount difference is larger than that at low DPC equilibrium concentration, and when DPC equilibrium concentration is lower than 0.1 mmol/L, the adsorption amount difference cannot be observed. At charge compensation point (CCP, 0 zeta potential), the negative surface charge of silica was compensated by DP+, a continuous increasing zeta potential indicated a bilayer adsorption of DPC on silica. The adsorption amount increased with increasing pH. The calculated lines by Gu and Zhu model show a two-step property, including a bilayer and hemi-micelle adsorption. DPC adsorbed more strongly on silica than SDS due to the combination of electrostatic and hydrophobic attraction.

Nanoscale Profiling of 2D Surface Hydrophobicity Recognition of Environmental Media via AFM Measurements In Situ.

The surface hydrophobicity and its heterogeneity are essential physicochemical properties of functional materials and environmental media, which directly influence many critical processes, such as the adsorption capacity of absorbents, water/fertilizer retention of soil and oil-water separation performances of membranes. The conventional method to characterize the surface hydrophobicity is based on the water/air/oil contact angle, which could only analyze the macroscale local hydrophobicity of the surfaces. Until now, it is impossible to profile two-dimensional surface hydrophobicity recognition in the nanoscale. Here we utilized an atomic force microscopy (AFM)-based chemical force spectroscopy to measure the topography and the local adhesion forces in the nanoscale. A novel approach is established to exploit adhesion forces to extract the hydrophobic attractions, enabling mapping of the surface hydrophobicity of environmental media in the nanoscale, which was validated by studying synthetic self-assembled monolayers of known composition. The new method was then applied to directly measure the hydrophobicity of porous biochar particles, to profile two-dimensional nanoscale hydrophobicity images of graphene oxide, and to observe the in situ variations of the graphite surface hydrophobicity in the adsorption process of benzylamine, which cannot be monitored by the conventional methods. The advantages of direct observations of the surface hydrophobicity recognition from a single AFM image dynamically and quantitatively may provide an in-depth insight into the surface hydrophobicity in the nanoscale.

Entrapment of curcumin in whey protein isolate and zein composite nanoparticles using pH-driven method

In this study, encapsulation strategy of curcumin was employed by fabricating protein-based composite nanoparticles with hydrophilic whey protein isolate (WPI) and hydrophobic zein using an alcohol-free pH-driven method. The mass ratio of WPI to zein had a great effect on WPI and zein composite properties. At the WPI to zein mass ratio of 8:2, the resulting composite nanoparticles showed a relatively small size (about 90 nm). The composite nanoparticles significantly enhanced the solubility of curcumin to be above 0.65 mg/mL and exhibited desirable storage and physical stability as well as re-dispersibility. The presence of zein significantly improved thermal stability of the composite nanoparticles and the retention rate of curcumin at a high temperature (80 °C) compared to single WPI only. X-ray diffraction confirmed that curcumin was present in an amorphous state inside the nanoparticles. Fourier transform infrared analysis revealed that hydrophobic attraction and hydrogen bonding were the major forces involved in the formation of the composite nanoparticles. Both the pH-potential curve and the transmission electron microscope images revealed that the composite nanoparticles had a core-shell structure with the zein core and WPI shell. The formation mechanism of the composite nanoparticles was also proposed. The composite nanoparticles fabricated by the simple, safe and cost-effective pH-driven method interpreted the potential for delivery of curcumin.

Quantitative Analysis of Attachment Time of Air Bubbles to Solid Surfaces in Water.

The attachment of air bubbles to solid surfaces in water is encountered in many natural processes and industrial applications. It has been established that the attachment can occur between hydrophobic surfaces and air bubbles. In this paper, we present novel experimental results to quantify the attachment in terms of the attachment time. We show that the attachment time can be determined from either the transient force curve or the transient film thickness. These techniques for determining the attachment time are based on the fact that the rupture of a thin liquid film produces a large attachment force and a rapid expansion of the three-phase contact radius in comparison with the expansion of the film radius. The experimental results are quantitatively analyzed using thin-film drainage theory and intermolecular forces, which include the advanced multilayer van der Waals force and the electrical double-layer force. The advanced van der Waals force theory allows us to incorporate the effect of interfacial gas enrichment (IGE) of dissolved gas in water at hydrophobic surfaces on the bubble-surface attachment. Critically, if the presence of IGE is ignored, the experimental results do not agree with the theory. Finally, IGE is shown to be a significant factor in controlling hydrophobic attraction between an air bubble and a hydrophobic surface and their attachment.

Adsorptive removal of Congo red by surfactant modified cellulose nanocrystals: a kinetic, equilibrium, and mechanistic investigation

A cellulose nanocrystal (CNC) based adsorbent was synthesized by modifying pristine CNC with various amounts of a positively-charged surfactant (CTAB) and was used to study the adsorption behavior of Congo red (CR) in aqueous medium. The interaction of CTAB with CNCs, and potential alterations on the chemical and physical structure of CNCs are studied, and the synthesized adsorbent, modified cellulose nanocrystal (MCNC) was characterized using Fourier transform infrared spectroscopy, X-ray diffraction, scanning electron microscopy, elemental and zeta potential analysis. The amount of surfactant used for modification was optimized to maximize the adsorption capacity of the adsorbent. Furthermore, it was found that the amount of surfactant affects the CR-MCNC interactions and determines the mechanism of adsorption. The kinetics followed a pseudo-second order and intra-particle diffusion model implying that the rate-controlling step of the adsorption process was first dominated by film-diffusion, and consequently by intra-particle diffusion. Thermodynamic studies on the system suggested that the adsorption process is spontaneous and exothermic. Characterization of the adsorbent, before and after adsorption, coupled with the kinetic and isotherm studies indicated that electrostatic attraction, hydrogen bonding, and hydrophobic attraction are the main mechanisms/interactions of adsorption. The adsorbent is highly stable in water and retains its original adsorption capacity after successive dialysis cycles.

Improved flotation of artificial galena using a new catanionic mixture

Issues related to environmental pollution and resource wastage have made the utilisation of Pb-bearing Zn residue an extremely urgent requirement. The floatability of artificial galena (AG) with a traditional xanthate collector was greatly improved by using a catanionic mixture (CM) as a collector, and the micromechanism was examined using flotation, zeta potential, adsorption, and slow positron beam measurements, together with molecular dynamics simulation. The flotation results revealed that the floatability of AG was inferior to that of natural galena (NG) when potassium amyl xanthate (KAX) was used as the collector, but it improved when using the CM. The results of zeta potential measurements, adsorption experiments, and slow positron beam detection demonstrated that the amount of KAX adsorbed on AG in the KAX/AG system was lower than that on NG in the KAX/NG system because of the greater electronegativity of surface Pb active sites resulting from the presence of S vacancy defects in AG. The molecular dynamics simulation showed that cetyl pyridine chloride and KAX promoted each other’s adsorption in the CM/AG system because of the electrostatic attraction between the sulfhydryl and pyridyl groups and the hydrophobic attraction between the amyl and cetyl groups. An adsorption model was proposed to better explain the greater floatability of AG when using the CM.

Simulation of Multiscale Hydrophobic Lipid Dynamics via Efficient Integral Equation Methods

In this paper, a mathematical model for long-range, hydrophobic attraction between amphiphilic particles is developed to quantify the macroscopic assembly and mechanics of a lipid bilayer membrane in solvents. The nonlocal interactions between amphiphilic particles are obtained from the first domain variation of a hydrophobicity functional, giving rise to forces and torques (between particles) that dictate the motion of both particles and the surrounding solvent. The functional minimizer (that accounts for hydrophobicity at molecular-aqueous interfaces) is a solution to a boundary value problem of the screened Laplace equation. We reformulate the boundary value problem as a second-kind integral equation (SKIE), discretize the SKIE using a Nyström discretization and Quadrature by Expansion (QBX), and solve the resulting linear system iteratively using GMRES. We evaluate the required layer potentials using the GIGAQBX fast algorithm, a variant of the Fast Multipole Method (FMM), yielding the required particle interactions with asymptotically optimal cost. A mobility problem formulation supplies the motion for the rigid particles in a viscous fluid. The simulated fluid-particle systems exhibit a variety of multiscale behaviors over both time and length. Over short time scales, the numerical results show self-assembly for model lipid particles. For large system simulations, the particles form realistic configurations like micelles and bilayers. Over long time scales, the bilayer shapes emerging from the simulation appear to minimize a form of bending energy.

Amphipathic design dictates self-assembly, cytotoxicity and cell uptake of arginine-rich surfactant-like peptides.

Amphiphilicity is the most critical parameter in the self-assembly of surfactant-like peptides (SLPs), regulating the way by which hydrophobic attraction holds peptides together. Its effects go beyond supramolecular assembly and may also trigger different cell responses of bioactive peptide-based nanostructures. Herein, we investigate the self-assembly and cellular effects of nanostructures based on isomeric SLPs composed by arginine (R) and phenylalanine (F). Two amphipathic designs were studied: a diblock construct F4R4 and its bolaamphiphile analog R2F4R2. A strong sequence-dependent polymorphism emerges with appearance of globules and vesicle-like assemblies, or flat nanotapes and cylindrical micelles. The diblock construct possesses good cell penetrating capabilities and effectiveness to kill SK-MEL-28 melanoma tumor cells, in contrast to reduced intracellular uptake and low cytotoxicity exhibited by the bolaamphiphilic form. Our findings demonstrate that amphipathic design is a relevant variable for self-assembling SLPs to modulate different cellular responses and may assist in optimizing the production of nanostructures based on arginine-enriched sequences in cell penetrating and antimicrobial peptides.

Self-assembly of isotropic colloids into colloidal strings, Bernal spiral-like, and tubular clusters.

We report the (spontaneous) formation of colloidal strings, Bernal spiral-like, and tubular clusters comprising spherical, isotropically functionalized colloidal particles in an aqueous environment. The formation of colloidal strings and Bernal spiral-like clusters is guided by an interplay between short-ranged hydrophobic attraction and relatively longer-ranged electrostatic repulsion acting between the colloids. When a dispersion of these colloids is densified via centrifugation, well-defined tubular aggregates were observed.

Utilizing Polymer Micelle to Control Dye J-aggregation and Enhance Its Theranostic Capability.

SummaryWe utilize polymer micelle to precisely control indocyanine green (ICG) J-aggregation in a fast and highly efficient way. In addition to simple encapsulation, the polymer micelle plays a role as a host template to drive ICG J-aggregation by the synergy of electrostatic and hydrophobic attractions. We further demonstrate that, due to the robust host-guest interaction, the intact of ICG J-aggregate will be secured by the polymer encapsulation during the intracellular and in vivo incubation. These features make this hierarchical assembly between ICG J-aggregate and the micelle polymer a promising biomedicine for cancer phototheranostics. Therefore the complex micelles are further modified by introduction of doxorubicin for chemotherapy and DNA aptamer for tumor targeting, and the final multi-functional micellar medicine shows high therapeutic efficacy for tumor, i.e., the tumor can be completely eliminated with no local reoccurrence and without long-term toxicity or side effects during a 24-day period after the treatment.

Synergistic assembly of peptide amphiphiles with varying polarities for encapsulation of camptothecin

Peptide amphiphiles (PA) are a group of peptide-based biomaterial design inspired by lipid molecules in the cell membrane. They possess distinct hydrophobic and hydrophilic regions which can self-assemble into highly ordered nanostructures based on the peptide sequence. In this work, the design strategy employed, explores the innate ability of PA to serve as a depository for hydrophobic drug camptothecin (CPT). CPT was encapsulated into two oppositely charged PA by hydrophobic attraction which develops into hybrid nanofibers by the interplay of electrostatic interactions and hydrogen bonding. This method of encapsulation averts the use of physical and chemicals factors like pH, temperature and ions to enable the self-assembly process. The CPT encapsulated PA nanofiber (PA-CPT) structure exhibits a high encapsulation efficiency of 84.83 ± 4.12%. After encapsulation, it was observed that the secondary structure of PA and active lactone conformation of CPT were perfectly retained. In vitro release studies reveal that 40% of the drug was released in the first 12 h. PA-CPT was effectively taken up by HepG2 cells with a lower IC50 value of 0.56 µM/L compared to free CPT having an IC50 of 3.75 µM/L. The developed PA-drug system enhances the bioavailability of CPT in an aqueous environment.

Co-folding of hydrophobic rice proteins and shellac in hydrophilic binary microstructures for cellular uptake of apigenin

Developing food structures that combine material properties from two or three components is intriguing as well as challenging. This study reports a simple technique for co-solvation of two hydrophobic biopolymers in a neutral aqueous solution. The process suspended rice proteins (RPs) and shellac at pH 12 with a one-step adjustment to pH 7. Results from scanning electron microscopy, polyacrylamide gel electrophoresis, and fluorescence studies showed that shellac-RP complexes (SRPs) nucleated through hydrophobic attractions between the two biopolymers. As a result, the refolding of the backbones of RPs was resisted, leading to formation of spherical SRPs with less compactness and larger sizes than untreated RPs. The nanoscale spheres were induced with Ca2+ to structural transition to ribbons or networks. The tunable structures were used to entrap and deliver apigenin for improved, controllable cellular uptake in a HepG-2 cell model compared with free apigenin.

Impact of salinity on colloidal ozone aphrons in removing phenanthrene from sediments

Polycyclic aromatic hydrocarbons (PAHs) tend to adsorb and accumulate on sediments owing to their hydrophobicity and persistence. Salinity is the predominant factor determining the PAH partition between aqueous and solid phases in freshwater, estuaries and seawater. This study focuses on the impact of salinity on the phenanthrene (PHE) removal from sediments using an in situ and targeted remediation technology – colloidal ozone aphrons (COAs). The ozone-encapsulated colloidal aphrons exhibited increasing air holdup but decreasing stability with the salinity increasing from 0.5‰ to 35‰. The hydrophobic attraction between Tween-20-coated bubbles and the hydrophobic solid surface weakened at high salinities. The presence of inorganic ions in the aqueous phase could lead to the salting-out of nonionic compounds (PHE, Tween-20 and even ozone), hindering detaching and degrading PHE from the solid phase. Anyhow, COAs achieved high efficiencies of washing (88.0–90.2%) and oxidative degradation (74.0–76.5%) particularly for the hydrophobic sediments with highly concentrated PHE (200.4 μg/kg) over the investigated salinities. The flushing effect imposed by the bubble flow played an important role, which was not greatly influenced by salinity. Although the dissolved natural organic matter competed with PHE for COAs and led to low PHE removal, the efficiency was improved by successive COA addition.

Amphiphilic hyper-crosslinked porous cyclodextrin polymer with high specific surface area for rapid removal of organic micropollutants

Amphiphilic hyper-crosslinked porous cyclodextrin polymer (PBCD-B-D) with a surface area of 1445 m2 g−1 was synthesized for rapid removal of organic micropollutants. Partially benzylated cyclodextrin was crosslinked with 4,4′-bis(chloromethyl)-1,1′-biphenyl and α,α'-dichloro-p-xylene by the Friedel–Crafts alkylation reaction. The hydrophilicity of the PBCD-B-D surface is modulated by controlling the number of hydroxyl groups on cyclodextrin. Benzylation reaction is more likely to occur at the C-2 and C-6 positions of cyclodextrin hydroxyl groups according to Gaussian computation. Four different water-soluble pollutants (3-phenylphenol, 2-naphthol, p-nitrophenol, and 4-chlorophenol) were selected for adsorption study. The adsorption rate of PBCD-B-D is extremely high, and the removal efficiency reaches above 95% in 1 min. For the adsorption of 3-phenylphenol and 2-naphthol, the rate constants of PBCD-B-D are 827–1187 and 396–413 times larger than those of granular activated carbon (GAC) and β-cyclodextrin polymer crosslinked with epichlorohydrin (EPI-CDP), respectively. The adsorption capacity of PBCD-B-D is 2 and 4 times higher than that of GAC and EPI-CDP, respectively. The combination of cyclodextrin inclusion mechanism, hydrophobic attraction, and hydrogen bonding allows PBCD-B-D to adsorb both hydrophobic and hydrophilic pollutants. PBCD-B-D can be easily regenerated at room temperature using methanol as eluent. In addition, PBCD-B-D showed excellent adsorption performance towards mixed pollutants at environmentally relevant concentrations. According to the thermodynamic study, the adsorption of organic compounds onto PBCD-B-D belongs to physical adsorption and is spontaneous. PBCD-B-D is a potential novel adsorbent for water treatment owing to its excellent adsorption performance, low cost, and good regenerability.