Axisymmetric Drop Shape Analysis-profile Research Articles

Effects of starch nanoparticles on phase inversion of Pickering emulsions

AbstractUnderstanding the effects of interfacial additives such as surface‐active nanoparticles on phase inversion of Pickering emulsions is important from a practical point of view. In this work, we studied the effects of surface‐active starch nanoparticles on catastrophic phase inversion of Pickering emulsions by continuous addition of a dispersed phase. Two types of experimental‐grade starch nanoparticles were used: hydrophilic starch nanoparticles (HSNP) and hydrophobic starch nanoparticles (HOSNP). The dynamic oil‐water interfacial tension was measured using the pendant drop method at varying starch concentrations in the aqueous phase while the contact angles were measured using the sessile drop method of the Axisymmetric Drop Shape Analysis‐Profile (ADSA‐P). Both types of starch nanoparticles (HSNP and HOSNP) were effective in delaying the phase inversion of emulsions from water‐in‐oil (W/O) type to oil‐in‐water (O/W) type. This delay in phase inversion was directly correlated with the concentration of starch nanoparticles. The interfacial tension decreased as the drop aged at a given starch nanoparticle concentration. The contact angles for both types of starch nanoparticles were within the intermediate wettability range that confirmed the irreversible adsorption of starch nanoparticles at the oil/water interface leading to an increased stability of emulsions.

Spreading of a distilled water droplet over polished and laser-treated aluminum surfaces

Spreading of a distilled water droplet over polished and laser-treated aluminum surfaces is studied experimentally. We present an attempt to apply the molecular-kinetic theory to the experimental dependences of the dynamic contact angle on the contact line speed. Advancing and receding contact angles at different liquid flow rates are obtained experimentally, and their values are used to calculate the contact angle hysteresis on each substrate. The bottom-up approach is used to form a droplet on the surface when liquid is supplied through an opening in the substrate. This makes it possible to control wetting and dewetting by increasing and decreasing the droplet volume. The main geometrical parameters are obtained using the shadow method by Axisymmetric Drop Shape Analysis-Profile. Experimental data on the dynamic contact angle on a laser-treated surface are found to be a better fit to the theoretical equation in comparison with the results on a smooth polished surface. We have formulated a hypothesis that the theoretical and experimental values of the dynamic contact angle are in good agreement due to the physics of the process (smaller hysteresis on the laser-treated surface).

Solubility and interfacial tension of thermoplastic polyurethane melt in supercritical carbon dioxide and nitrogen

Various industries, such as automotive and leisure, show a great interest in foaming thermoplastic polyurethane (TPU) with physical blowing agents. Hence, this study aims to investigate the effects of absorption of carbon dioxide and nitrogen by melt TPU on solubility and interfacial tension. Using a pressure–volume–temperature apparatus for high pressure and temperature combined with a magnetic suspension balance, the solubility of carbon dioxide and nitrogen in thermoplastic polyurethane melt was measured at temperatures from 190°C to 220°C and at pressures to 25MPa. The solubility of both supercritical fluids (SCF) in the TPU melt was then compared with semiempirical data and theoretical values calculated from the Sanchez–Lacombe equations of state (S-L EOS). The surface tension of the TPU/SCF interface was measured using the axisymmetric drop shape analysis profile. It was observed that the dependency of interfacial tension on temperature at high pressures decreases because of a reduction in SCF solubility at high temperatures. The relationship between the interfacial tension and the density difference of polymer-supercritical fluid was also examined using the generalized Macleod's equation.

Adsorption of Surface-Modified Silica Nanoparticles to the Interface of Melt Poly(lactic acid) and Supercritical Carbon Dioxide.

With the purpose of fabricating polymer nanocomposite foams and preventing coalescence in foaming processes, the interfacial tension of poly(lactic acid) (PLA)-silica composites is investigated in this work. Synthesized silica nanoparticles (SNs) with a CO2-philic surface modification are used as the dispersed nanoparticles. Interfacial tension is a key parameter in processing of polymer foams since it directly affects the final foam properties, such as cell size and cell density. Interfacial tension of silica-containing PLA and supercritical carbon dioxide (CO2) is measured using axisymmetric drop shape analysis profile (ADSA-P) pendant drop method at high pressures and high temperatures. The interfacial tension between PLA and supercritical CO2 is observed to decrease as a result of the nanoparticles' adsorption to the interface. These results indicate that the reduction in interfacial tension with increasing silica content significantly deviates from a linear trend; there is a minimum at 2 wt % loading of the SNs and then the interfacial tension curve reaches a plateau. Contact angle measurements show an affinity of the SNs for the polymer-supercritical CO2 interface, and these obtained results are used to calculate the binding energy of the nanoparticles to the PLA/CO2 interface. In addition to interfacial properties, the adsorption of silica nanoparticles at the interface is also studied in detail with scanning electron microscopy.

Effect of pressure and temperature on interfacial tension of poly lactic acid melt in supercritical carbon dioxide

The interfacial tension of poly lactic acid (PLA) melt is measured in supercritical carbon dioxide (CO2) at the temperature range of 143°C to 168°C and CO2 pressures up to 13,790kPa, using axisymmetric drop shape analysis profile (ADSA-P). The results show a decrease in interfacial tension with increasing temperature and pressure. However, the interfacial tension dependency on temperature at high pressures decreases because of a reduction in CO2 solubility at high temperatures. The relationship between the interfacial tension and the density-difference of polymer-supercritical CO2 mixtures is also examined by the generalized Macleod’s equation. Moreover, the range of stability for the melted drop, in interfacial tension measurements, is obtained by dimensionless Bond number. The results indicate the validity of the measurements for Bond number between 0.36 and 0.48.

An algorithm for selecting the most accurate protocol for contact angle measurement by drop shape analysis.

In this study, an error analysis is performed to study real water drop images and the corresponding numerically generated water drop profiles for three widely used static contact angle algorithms: the circle- and ellipse-fitting algorithms and the axisymmetric drop shape analysis-profile (ADSA-P) algorithm. The results demonstrate the accuracy of the numerically generated drop profiles based on the Laplace equation. A significant number of water drop profiles with different volumes, contact angles, and noise levels are generated, and the influences of the three factors on the accuracies of the three algorithms are systematically investigated. The results reveal that the above-mentioned three algorithms are complementary. In fact, the circle- and ellipse-fitting algorithms show low errors and are highly resistant to noise for water drops with small/medium volumes and contact angles, while for water drop with large volumes and contact angles just the ADSA-P algorithm can meet accuracy requirement. However, this algorithm introduces significant errors in the case of small volumes and contact angles because of its high sensitivity to noise. The critical water drop volumes of the circle- and ellipse-fitting algorithms corresponding to a certain contact angle error are obtained through a significant amount of computation. To improve the precision of the static contact angle measurement, a more accurate algorithm based on a combination of the three algorithms is proposed. Following a systematic investigation, the algorithm selection rule is described in detail, while maintaining the advantages of the three algorithms and overcoming their deficiencies. In general, static contact angles over the entire hydrophobicity range can be accurately evaluated using the proposed algorithm. The ease of erroneous judgment in static contact angle measurements is avoided. The proposed algorithm is validated by a static contact angle evaluation of real and numerically generated water drop images with different hydrophobicity values and volumes.

Static contact angle algorithm selection for superhydrophobic surface hydrophobicity detection

The static contact angle calculation for superhydrophobic surfaces is systematically investigated. The water drop profiles with different volumes, contact angles, rotational angles and apex coordinates are numerically generated based on the Laplace equation. Thereafter, the goniometry, θ/2 method, circle and ellipse fitting algorithms and an improved axisymmetric drop shape analysis-profile (ADSA-P) algorithm are used to calculate the static contact angle. The results reveal that the contact angle errors by the θ/2 method, circle and ellipse fitting algorithms increase with the drop volume/contact angle. The goniometry will introduce significant error. The ADSA-P algorithm can accurately obtain the contact angles (error < 0.3°) for the drop profiles regardless of the water drop volume, contact angle, rotational angle and apex coordinate. The ADSA-P algorithm should be selected to calculate the static contact angles for the superhydrophobic surfaces. Static contact angle measurements of the superhydrophobic surfaces validate the aforementioned analysis.

A static contact angle algorithm and its application to hydrophobicity measurement in silicone rubber corona aging test

To improve the accuracy of the static contact angle measurement for the corona aged silicone rubber, a static contact angle algorithm based on the least-squares circle fitting is presented, and the least-squares model, the optimization algorithm, the determination of initial values and the convergence criterion are introduced in a systematic way and at the same time the best selections are given by the systematical comparison. With regards to the numerically generated water drop profiles and the water drop images of the corona aged silicone rubber, the accuracy and the computation time of the goniometry, the θ/2 method, the circle fitting algorithm and the ADSA-P (axisymmetric drop shape analysis-profile) algorithm are analyzed and compared. The influence of the water drop volume/contact angle/profile point number on the accuracy of the circle fitting algorithm is analyzed. The results reveal that the contact angle errors increase with the water drop volume/contact angle/noise. The goniometry has the characteristics of relative low accuracy, expensive computation and large workload. The computed result of the circle fitting algorithm is very close to that of the θ/2 method, and both the two methods have relative less computation time. In the meantime, the fitted water drop edges can be obtained by the circle fitting algorithm, which can be taken as an indicator of the computation accuracy, while the θ/2 method cannot give such indicator. The ADSA-P algorithm has high accuracy and high computational complexity, and is very easy to be interfered by the noise. Therefore, it is not suited to the case of small contact angle and volume, and high interference. The circle fitting algorithm has less computation time, and is intrinsically resistant to noise. Therefore, for the case of small contact angle and volume, not the ADSA-P algorithm but the circle fitting algorithm should be selected. Therefore, the circle fitting algorithm is selected to measure the static contact angle of the corona aged silicone rubber. The critical water drop volumes and the critical contact angles of different liquids are given, which can be guaranteed for high accuracy of the static contact angle measurement.

A Robust Polynomial Fitting Approach for Contact Angle Measurements

Polynomial fitting to drop profile offers an alternative to well-established drop shape techniques for contact angle measurements from sessile drops without a need for liquid physical properties. Here, we evaluate the accuracy of contact angles resulting from fitting polynomials of various orders to drop profiles in a Cartesian coordinate system, over a wide range of contact angles. We develop a differentiator mask to automatically find a range of required number of pixels from a drop profile over which a stable contact angle is obtained. The polynomial order that results in the longest stable regime and returns the lowest standard error and the highest correlation coefficient is selected to determine drop contact angles. We find that, unlike previous reports, a single polynomial order cannot be used to accurately estimate a wide range of contact angles and that a larger order polynomial is needed for drops with larger contact angles. Our method returns contact angles with an accuracy of <0.4° for solid-liquid systems with θ < ~60°. This compares well with the axisymmetric drop shape analysis-profile (ADSA-P) methodology results. Above about 60°, we observe significant deviations from ADSA-P results, most likely because a polynomial cannot trace the profile of drops with close-to-vertical and vertical segments. To overcome this limitation, we implement a new polynomial fitting scheme by transforming drop profiles into polar coordinate system. This eliminates the well-known problem with high curvature drops and enables estimating contact angles in a wide range with a fourth-order polynomial. We show that this approach returns dynamic contact angles with less than 0.7° error as compared to ADSA-P, for the solid-liquid systems tested. This new approach is a powerful alternative to drop shape techniques for estimating contact angles of drops regardless of drop symmetry and without a need for liquid properties.

Surface tension of high density polyethylene (HDPE) in supercritical nitrogen: Effect of polymer crystallization

Surface tension of a polymer melt in a supercritical fluid is a principal factor in determining cell nucleation and growth in microcellular foaming. This work focuses on the surface tension of a crystalline polymer, high density polyethylene (HDPE), in supercritical nitrogen under various temperatures and pressures. The surface tension was determined by Axisymmetric Drop Shape Analysis-Profile (ADSA-P). The dependence of the surface tension on temperature and pressure, at temperatures above the HDPE melting point, ∼125 °C, was found to be similar to that of the amorphous polymer polystyrene (PS) in supercritical CO 2, previously reported, i.e., the surface tension decreased with increasing temperature and gas content. Below 125 °C and above 100 °C, HDPE underwent the process of crystallization, where the surface tension dependence on temperature was different from that above the melting point, and decreased with decreasing temperature. Differential scanning calorimetry (DSC) characterization of the polymer was carried out to reveal the process of HDPE crystallization and relate this to surface tension behavior. It was found that the amount of the decrease in surface tension was related to the rate of temperature change and hence the extent of polymer crystallization.

ADSA-TRIS: a new method to study interfacial phenomena at polymer–aqueous solution interfaces

Axisymmetric drop shape analysis-profile (ADSA-P) was combined with total reflectometric interference spectroscopy (TRIS) in one experimental setup to study the interfacial phenomena at solid-liquid and liquid-vapor interfaces caused by adsorption/desorption (dissolution) of surface-active substances. Using sessile liquid droplets on polymer film/chromium-coated glass substrates that were optically matched with an immersion oil to a TRIS reflection prism, the optical thickness (product of physical thickness d and refractive index n) of the polymer film can be estimated by evaluating the wavelength-dependent intensity of reflected light. The sessile droplet is analyzed simultaneously by an ADSA setup arranged in a transverse direction to the path of the white-light beam of TRIS. From this analysis, the solid-vapor interfacial tension gamma (lv)(t), contact angle theta(t), contact radius r(t), drop volume V(t), and solid-liquid interfacial tension gamma (sl)(t) can be monitored as a function of time. The new method was applied to study polystyrene and poly(4-hydroxystyrene) surfaces in contact with aqueous buffer solutions and with protein solutions. The time-dependent changes in the optical film thickness caused by the adsorption of human serum albumin (HSA) and lysozyme (LSZ) were accompanied by changes in the solid-liquid interfacial tension. From the detailed study of both parameters, conclusions can be drawn with regard to the adsorption kinetics of the proteins on the hydrophobic polystyrene surfaces and to conformational changes occurring within the adsorbed protein layers.

Effect of Molecular Weight on the Surface Tension of Polystyrene Melt in Supercritical Nitrogen

This paper presents experimental results on the effect of molecular weight on the surface tension of polystyrene melt in supercritical nitrogen. The surface tension was determined by the axisymmetric drop shape analysis-profile (ADSA-P) method, for which a high-pressure and high-temperature cell was used to form pendant drops of the polystyrene melt. For two monodisperse polystyrenes of Mw ∼ 100 000 and 400 000 and one polydisperse polystyrene, a linear relationship was found between surface tension and temperature and between surface tension and pressure within a temperature range of 170−210 °C and a pressure range of 500−2000 psi. With an increase in pressure or temperature, the surface tension of all three polystyrenes decreases. Monodisperse polystyrene of a higher molecular weight has a higher surface tension by 6−9 mJ/m2 under all experimental conditions. The surface tension dependence on temperature and on pressure is more significant for the higher molecular weight polystyrene. For the polydisperse polystyrene, high surface tension values seem to be related predominantly to its high molecular weight portion of polystyrene molecules. An empirical equation, the Mecleod relation, was used to relate surface tension with the density difference between the polymer and supercritical nitrogen satisfactorily.

Effect of Temperature and Pressure on Surface Tension of Polystyrene in Supercritical Carbon Dioxide

The surface tension of polymers in a supercritical fluid is one of the most important physicochemical parameters in many engineering processes, such as microcellular foaming where the surface tension between a polymer melt and a fluid is a principal factor in determining cell nucleation and growth. This paper presents experimental results of the surface tension of polystyrene in supercritical carbon dioxide, together with theoretical calculations for a corresponding system. The surface tension is determined by Axisymmetric Drop Shape Analysis-Profile (ADSA-P), where a high pressure and temperature cell is designed and constructed to facilitate the formation of a pendent drop of polystyrene melt. Self-consistent field theory (SCFT) calculations are applied to simulate the surface tension of a corresponding system, and good qualitative agreement with experiment is obtained. The physical mechanisms for three main experimental trends are explained by using SCFT, and none of the explanations quantitatively depend on the configurational entropy of the polymer constituents. These calculations therefore rationalize the use of simple liquid models for the quantitative prediction of surface tensions of polymers. As pressure and temperature increase, the surface tension of polystyrene decreases. A linear relationship is found between surface tension and temperature, and between surface tension and pressure; the slope of surface tension change with temperature is dependent on pressure.

Anion Effect on the Nanostructure of a Metal Ion Binding Self-Assembling Peptide

Effects of copper salts containing different anions (SO(4)(2)(-), Cl(-), and NO(3)(-)) on the self-assembly of a designed peptide EAK16(II)GGH with affinity for Cu(2+) have been investigated. The peptide secondary structure, self-assembled nanostructures, and surface activity were observed to depend strongly on the type of anion. Over a salt concentration range from 0.05 to 10.0 mM, SO(4)(2)(-) induced long fiber formation, whereas Cl(-) and NO(3)(-) caused short fiber formation. The fiber length increased with copper sulfate concentration, but the concentration of copper chloride and copper nitrate did not affect the peptide nanostructures significantly. Analysis by Fourier transform infrared spectroscopy (FTIR) revealed that the addition of the copper salts tended to cause the peptide conformation to change from alpha-helix/random coil to beta-sheet, the extent to which depended on the anion type. This evidence of the anion effect was also supported by surface tension measurements using the axisymmetric drop shape analysis-profile (ADSA-P) technique. An explanation for the effect of anions on the peptide self-assembly was proposed. The divalent anion SO(4)(2)(-) might serve as a bridge by electrostatically interacting with two lysine residues from different peptide molecules, promoting beta-sheet formation. The extensive beta-sheet formation may further promote peptide self-assembly into long fibers. On the other hand, monovalent anions Cl(-) and NO(3)(-) may only electrostatically interact with one charged residue of the peptide; hence, a mixed secondary structure of alpha-helix/random coil and beta-sheet was observed. This observation might explain the predominant formation of short fibers in copper chloride and copper nitrate solutions.

Surface Tension Measurement of Polystyrene Melts in Supercritical Carbon Dioxide

This paper introduces an experimental method that uses Axisymmetric Drop Shape Analysis-Profile (ADSA-P) to measure the surface tension of polymer melts in supercritical carbon dioxide. The method is verified by experiments in air and nitrogen, where reproducibility tests and statistical analyses are performed. The surface tension of polystyrene (PS) melts in supercritical carbon dioxide is obtained, while the gas solubility is correlated with the surface tension value determined under various pressures. The Sanchez−Lacombe (S−L) equation of state (EOS) is applied to estimate the pressure−volume−temperature (PVT) data of the PS/supercritical-carbon-dioxide mixtures, which gives density data. The relationship between surface tension and density is described by the empirical Macleod equation. To characterize the stability of pendant drops formed by the polymer melt, the Bond number is determined to be useful; in particular, a stable pendant drop is obtained when the Bond number is in the range of 0.4−0.8.

Effect of NaCl and peptide concentration on the self-assembly of an ionic-complementary peptide EAK16-II

Previous work has examined the effects of such factors as pH and peptide concentration on the self-assembly of ionic-complementary peptides. This work focused on the effect of sodium chloride on the molecular self-assembly of an ionic-complementary peptide EAK16-II (AEAEAKAKAEAEAKAK). Surface tensions and dimensions of the self-assembled nanostructures were determined for a wide range of peptide and sodium chloride concentrations using axisymmetric drop shape analysis-profile (ADSA-P) and atomic force microscopy (AFM), respectively. The critical aggregation concentration, or critical self-assembly concentration (CSAC), of EAK16-II was not significantly affected by the presence of NaCl. However, the analysis of size variations in self-assembled nanostructures in response to changes in NaCl concentration indicated that the presence of NaCl does influence the resulting dimensions of the peptide nanostructures when the peptide concentration is below its CSAC. A critical NaCl concentration was identified at ∼20 mM, below which the equivalent radius of the peptide fibrils increased with increasing salt concentration, and above which the opposite response was observed. This critical NaCl concentration was further confirmed in the surface tension measurements, where the equilibrium surface tension and induction time of the peptide at low concentrations (<CSAC) decreased with increasing NaCl concentration up to approximately 20 mM and a further increase caused the opposite trend.

The dynamics of impacting water droplets on alkanethiol self-assembled monolayers with co-adsorbed CH 3 and CO 2H terminal groups

The impact of water droplets (diameter 3.6 mm) at a fixed Weber number of 59 on solid surfaces with precisely tailored surface wettabilities was studied experimentally using a high-speed imaging camera at 2500 frames per second. Solid surface wettability was varied using four fractional mixtures of self-assembled monolayers of 1-octadecanethiol and 16-mercaptohexadecanoic acid. The surfaces so obtained are characterized for contact angle and chemical functionality using the axisymmetric drop shape analysis profile (ADSA-P) technique and Fourier transform infrared spectroscopy (FT-IR). Our results correlate the wetting effects of the impacting droplets with the surface energy and contact angle measurements of the tailored surfaces. Literature models for the maximum spreading diameter are employed and compared with those from our experiments. An equation is also proposed for the maximum spreading diameter which makes use of the correct contact angles and results in the least error among the models considered. As a consequence of Young's equation, the correct contact angles to be used for droplet impact dynamics should be the corresponding advancing angles on a smooth substrate of interest. We also conclude that accurate examination of literature models requires careful experimentation on impact dynamic data on well-prepared and characterized surfaces such as those presented here.

CRITERIA FOR EVALUATING THE ACCURACY OF SURFACE TENSION VALUES FROM DIGITAL VISION SYSTEMS

Experimental techniques for measuring surface tension using the shape of either axisymmetric sessile or pendant drops have existed for many years. Recent developments in digital image acquisition and processing have permitted the computerization of the process, by which the coordinates of the drop’s edge profile are obtained. Algorithms like the axisymmetric drop shape analysis–profile (ADSA–P) program use the edge profile coordinates to estimate quantities such as the surface tension, drop volume, and contact angle. The precision of these estimated quantities depends on various effects that influence the accuracy by which the edge profile coordinates are acquired. We have modeled this uncertainty in coordinate information as a perturbation effect and related the size of the perturbation to the surface tension accuracy. Two analogous relations were used to set regions of surface tension accuracy, e.g.,oras functions of the magnification of the drop, CCD camera array size, pixel size, drop shape, and drop edge precision. An algorithm for the design of various vision systems based on these criteria will be discussed and illustrated.

Surface characteristics of hydrosilylated polypropylenes: Effect of co‐catalyst and reaction temperature

AbstractPolypropylene (PP) was modified through a peroxide‐induced degradation and a catalytic hydrosilylation reaction in the melt phase. The effects of temperature and co‐catalysts on the reaction and the surface characteristics of the hydrosilylated polypropylene (SiPP) were studied. Axisymmetric Drop Shape Analysis‐Profile (ADSA‐P) was used to characterize the surface wettability. The morphology, roughness and heterogeneity of the surface were investigated by the lateral force mode of atomic force microscopy (LFM). Proton nuclear magnetic resonance (1H NMR) spectroscopy was employed to quantify the conversion of terminal double bonds. X‐ray photoelectron spectroscopy (XPS) was used to quantify the surface chemical composition. LFM images showed that the surfaces of the PP and DPP samples were rough but heterogeneous and that the surfaces of the SiPP samples appeared rough but homogeneous. The surface wettability was well correlated to the surface microstructure and surface chemical composition. The surfaces investigated were modeled based on the microstructure observed, and a new scheme was developed to calculate surface free energy and adhesion work. Results showed that there is an optimum reaction temperature in terms of the conversion of double bonds, and that increasing the amount of co‐catalyst promotes the conversion.

Effect of amino acid sequence and pH on nanofiber formation of self-assembling peptides EAK16-II and EAK16-IV.

Atomic force microscopy (AFM) and axisymmetric drop shape analysis-profile (ASDA-P) were used to investigate the mechanism of self-assembly of peptides. The peptides chosen consisted of 16 alternating hydrophobic and hydrophilic amino acids, where the hydrophilic residues possess alternating negative and positive charges. Two types of peptides, AEAEAKAKAEAEAKAK (EAK16-II) and AEAEAEAEAKAKAKAK (EAK16-IV), were investigated in terms of nanostructure formation through self-assembly. The experimental results, which focused on the effects of the amino acid sequence and pH, show that the nanostructures formed by the peptides are dependent on the amino acid sequence and the pH of the solution. For pH conditions around neutrality, one of the peptides used in this study, EAK16-IV, forms globular assemblies and has lower surface tension at air-water interfaces than another peptide, EAK16-II, which forms fibrillar assemblies at the same pH. When the pH is lowered below 6.5 or raised above 7.5, there is a transition from globular to fibrillar structures for EAK16-IV, but EAK16-II does not show any structural transition. Surface tension measurements using ADSA-P showed different surface activities of peptides at air-water interfaces. EAK16-II does not show a significant difference in surface tension for the pH range between 4 and 9. However, EAK16-IV shows a noticeable decrease in surface tension at pH around neutrality, indicating that the formation of globular assemblies is related to the molecular hydrophobicity.