Low Angle Laser Light Scattering Research Articles

Viscosity of fractions from end‐linked polystyrene star macromolecules

AbstractA number of OH‐terminated three‐arm star molecules were prepared by anionic polymerization with a specially functionalized initiator. The stars were crosslinked over the OH groups with varying amounts of toluene‐2,4‐diisocyanate. The samples were fractionated by size exclusion chromatography (SEC) on‐line with a low angle laser light scattering (LALLS) and a viscosity (VISC) detector. The Kuhn—Mark—Houwink—Sakurada (KMHS) relationships from the various samples resulted in a common relationship. Shrinking parameters g′j≡[η]j,b/[η]j,lin were determined for each slice and could satisfactorily be interpreted on the basis of the Zimm—Stockmayer theory in connection with a suggestion by Kurata et al. The Kurata suggestion was checked with data from star molecules. The examination revealed that randomly branched and star‐branched macromolecules exhibit significantly different hydrodynamic behavior. The ratio of the Fox—Flory coefficients Φb/Φlin in the relationship [η] = Φ(R/M) increases in both cases with branching. This is a consequence of the enhanced segment density and the resulting increase in the hydrodynamic interaction.

Characterization of antigen-antibody complexes by size-exclusion chromatography coupled with low-angle light-scattering photometry and viscometry

In this paper, the molecular masses ( M rs) of the complexes of monoclonal anti-BSA (antibody to bovine serum albumin) (clone: 33) and monomer BSA were determined on-line by using size-exclusion chromatography (SEC) coupled with a low-angle laser light-scattering (LALLS) detector and two concentration detectors, ultraviolet (UV) and refractive index (RI) (SEC-LALLS/UV/RI system). Also, the size and M rs of the complexes were evaluated by the SEC-LALLS/UV/viscometer (VISC) system. This study demonstrated that, for small size macromolecules, the combination of light scattering and viscosity detection was a suitable choice for determining their M rs and sizes.

About the native and renatured conformation of xanthan exopolysaccharide

Low-angle laser light scattering (LALLS), size exclusion chromatography coupled with multi-angle light scattering (s.e.c./MALLS), low shear intrinsic viscosity and circular dichroism measurements were performed for elucidating the size and conformation changes associated with the temperature-induced denaturation and renaturation of native xanthan in different salt conditions (0.01 M and 0.1 M). Upon heating, at temperatures above the order—disorder transition temperature ( T m) the denaturation of the native ordered conformation occurs with a reduction of M w by a factor of roughly two therefore indicating a double strand conformation for the native form. The molecular weight has been found invariant after renaturation on cooling that favours the hypothesis that the restoration of the ordered form of xanthan takes place through the same molecule. The most probable conformation for the renatured form of xanthan is that of an antiparallel double stranded structure consisting of one such chain folded as a hairpin loop.

A comparison of calibration procedures for the analysis of broad molecular weight distributions using size exclusion chromatography with multiple detection

A range of well characterized broad polymer standards has been analysed using size exclusion chromatography (s.e.c.), with differential refractive index, low angle laser light scattering (LALLS) and differential viscometry (DV) as on-line detection methods. This study highlights the importance of accurate and precise estimation of the inter detector delay (IDD) parameter and shows that the conventional methods of IDD measurement will lead to errors in calculation of the molecular weight (MWT) moments and also large errors in calculated Mark—Houwink—Sakurada (MHS) parameters. The method of IDD calculation suggested by Suddaby et al. (Suddaby, K. G., Sanayei, R. A., O'Driscoll, K. F., Rudin, A., Makromol. Chem., 1993, 194, 1965) is found to be superior, and like the earlier workers we found the IDD to be MWT sensitive for both the LALLS and DV detectors. This work shows that if the MWT dependence of IDD is ignored, then this leads to a distortion in the measured relationship between intrinsic viscosity (IV) and molecular weight. This work also highlights the shortcomings of using the MHS relationship to represent the IV—MWT relationship, and we clearly show that the Stockmayer—Fixman (SF) equation is a better relationship for s.e.c. calibration over a broader MWT range. The SF equation is also recommended, as K θ can be readily estimated from group contribution calculations thus allowing the IV—MWT relationship to be defined with one adjustable parameter, K′ (or B), which itself has a thermodynamic significance. A computer program, which adds seamlessly to existing commercial software ( PL Caliber), has been written to implement these improved calibration methods. MHS constants, K and α, and SF constants, K′ and K θ , are reported for a number of polymers.

Fractionation of poly(ethylene-co-vinyl acetate) in supercritical propylene: Towards a molecular understanding of a complex macromolecule

A commercial low-density polyethylene copolymer, poly(ethylene-co-vinyl acetate) (EVA), synthesized via the high-pressure free-radical polymerization process, was fractionated with supercritical propylene by isothermal increasing pressure profiling and critical, isobaric, temperature rising elution fractionation (CITREF™). Extensive characterization of the fractions by nuclear magnetic resonance (NMR) spectroscopy, gel permeation chromatography (GPC) in combination with low-angle laser light scattering (LALLS), and differential scanning calorimetry (DSC) was used to map not only the molecular-weight and chemical composition distributions of the parent copolymer, but also its short-chain branch (SCB) and long-chain branch (LCB) distributions. Fractionation by increasing pressure profiling confirmed the broad molecular-weight distribution and the narrow acetate-branch distribution expected for this random copolymer but revealed the presence of a small amount (∼ 2 wt %) of low molecular-weight amorphous species containing a high level of alkyl SCBs (80 branches/1000 C). The LCB density estimated from the Zimm-Stockmayer relationship using the GPC data monotonically increases with increasing molecular weight above 60,000 g/mol, in agreement with the kinetics of free-radical polymerization. CITREF™ was found to fractionate this copolymer by crystallinity, which is influenced by both the alkyl SCBs and the acetate branches. Up to 18% difference in total branch density (<5% in crystallinity) between EVA molecules was identified using CITREF™. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 2015–2030, 1997

Use of laboratory robotics for gel permeation chromatography sample preparation: Automation of high‐temperature polymer dissolution

Manual preparation of polymer samples for molecular weight characterization by solution methods such as gel permeation chromatography (GPC) is a time-consuming, labor-intensive, and redundant task. Preparation of samples for high-temperature GPC characterization further complicates the procedure. A typical manual high-temperature sample preparation exposes the analyst to both hot surfaces and solvent vapors. An automated system to prepare samples for high temperature GPC analysis has been developed. The system is based on a Zymark laboratory robotic system, and custom hardware peripherals developed at The Dow Chemical Company. The automated procedure performs all the steps required to prepare samples for high-temperature GPC analysis, including the hot steps. The samples were analyzed using the Waters 150-C GPC in combination with the differential refractive index (DRI) and low-angle laser light scattering (LALLS) detectors to demonstrate the reproducibility and reliability of the automated procedure. The system hardware, software options, and performance are presented in this paper. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 1613–1623, 1997

Use of laboratory robotics for gel permeation chromatography sample preparation: Automation of high-temperature polymer dissolution

Manual preparation of polymer samples for molecular weight characterization by solution methods such as gel permeation chromatography (GPC) is a time-consuming, labor-intensive, and redundant task. Preparation of samples for high-temperature GPC characterization further complicates the procedure. A typical manual high-temperature sample preparation exposes the analyst to both hot surfaces and solvent vapors. An automated system to prepare samples for high temperature GPC analysis has been developed. The system is based on a Zymark laboratory robotic system, and custom hardware peripherals developed at The Dow Chemical Company. The automated procedure performs all the steps required to prepare samples for high-temperature GPC analysis, including the hot steps. The samples were analyzed using the Waters 150-C GPC in combination with the differential refractive index (DRI) and low-angle laser light scattering (LALLS) detectors to demonstrate the reproducibility and reliability of the automated procedure. The system hardware, software options, and performance are presented in this paper. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 1613–1623, 1997

Solution Properties of the Exopolysaccharide Produced by Pseudomonas Marginalis Strain HT041B1

The solution properties of the exopolysaccharide marginalan produced by Pseudomonas marginalis HT041B were investigated by means of low-angle laser light-scattering, capillary viscometry, and rheology. Potentiometric and viscosimetric data indicated the absence of a cooperative transition of the disorder-to-order type. The experimental findings obtained in dilute solution (Mark-Houwink coefficients, rigidity coefficient, characteristic ratio) suggested that the polymer behaves like a semiflexible chain which adopts a disordered conformation. The rheological behaviour of more concentrated marginalan solutions, as determined by means of both steady shear and oscillatory measurements, further confirmed the disordered conformational state of the polymer in solution. 1. Presented at the XVIIIth International Carbohydrate Symposium, Milan, Italy, July 21-26, 1996.

Second Virial Coefficients and Radii of Gyration for Poly(α-methylstyrene) in Cyclohexane below the ϑ Temperature

Classical and low-angle laser light-scattering experiments were performed to measure the second virial coefficient, A2, and radius of gyration, Rg, of linear poly(α-methylstyrene) (PαMS) in the poor solvent cyclohexane. The molecular weights, Mw, of the polymers used cover the range of 60 000−3 500 000, and all samples have narrow molecular weight distributions. The experimental temperatures are controlled down to about 16 °C below the ϑ temperature (36.2 °C). At this temperature, the scaling exponent of Rg with Mw is 0.414; this appears to be the lowest exponent ever reported for linear chains of synthetic polymers in solution. A strong molecular weight dependence of the measured A2 values for this PαMS/cyclohexane system is observed. These results are compared with the predictions of available theories and with other experimental results.

Characterization of an Aqueous-Dissolved Anionic Polysaccharide Using Rheology and Size-Exclusion Chromatography with a Differential Refractive-Index and Low-Angle Laser-Light Scattering Detectors

Abstract From the aqueous growth medium of Red Microalgae Porphyridium sp., anionic polysaccharide was separated by centrifugation and dialysis. Xylose, glucose, galactose, mannose, rhamnose, arabinose, methyl-pentoses, dimethyl-hexoses, glucuronic acid and sulfated sugar-units were identified as constituting monomers. By means of size-exclusion chromatography with differential refractive index and low-angle laser-light scattering (DRI/LALLS) detectors, an average molecular weight of 8.4 × 106 g/mol was determined. For the investigated sample concentrations in the range of 0.08–0.1 mg/mL, SEC separation based on decreasing molecular weight was not observed; however, decreasing particle/fragment dimensions with increasing retention volume were eluted. Rheological investigations at 20°C showed that an aqueous 0.05 M NaCl solution of the dissolved polysaccharide was non-Newtonian with high elasticity. By comparing the polymer-coil packing density of the anionic polysaccharide with three reference polysaccharides, a particle/fragment-packing similar to dextran coils was found. With information about packing density and absolute molecular weight, universal calibration enabled an estimation of dimensions for the constituting components of the anionic polysaccharide in terms of sphere-equivalent radii. The SEC-eluted polymer-coils were found in the range between ≈2–140 nm with a maximum mass occurring at ≈90 nm.

Association behavior of linear ?-functionalized polybutadienes in cyclohexane

The dilute solution properties of linear polybutadienes with dimethylamine and zwitterionic end groups were studied by membrane osmometry (MO), low-angle laser light scattering (LALLS), viscometry, and dynamic light scattering (DLS) in cyclohexane. The polymers were prepared by anionic polymerization, under high vacuum conditions using [3-(dimethylamino)propyl]lithium as initiator. The dimethylamine groups were converted to zwitterions by reaction with cyclopropane sultone. No evidence of association was found for the amine-capped polymers, whereas the zwitterionic samples exhibited strong association in cyclohexane. The degrees of association increase by decreasing molecular weight of the base polymer due to the excluded volume repulsions. These aggregation numbers are of the same order as those found for ω-functionalized polyisoprenes, with the same polar groups in the same solvent. The hydrodynamic properties, measured by viscometry and dynamic light scattering, supported the conclusions drawn by LALLS and provide strong evidence that the aggregates behave hydrodynamically as star polymers. Comparison with theoretical models shows that the association behavior is best described by the linear head packing model.

Aggregation Phenomena of Model PS/PI Super-H-Shaped Block Copolymers. Influence of the Architecture

The super-H-shaped block copolymers belong to a new class of polymeric materials, the miktoarm stars (mikto from the Greek word μικτος meaning mixed), which includes star-shaped polymers in which from one or more junction points radiate different arms. Schematically, the super-H structure can be described as two three-arm stars which are bridged with a common fourth arm. Model super-H-shaped block copolymers of the PI3(PS-d8)PI3 type, where PI is protonated polyisoprene and PS-d8 is deuterated polystyrene, were synthesized by anionic polymerization using the chlorosilane approach. These nonlinear block copolymers were characterized by size exclusion chromatography (SEC), ultraviolet (UV) spectroscopy, low-angle laser light scattering (LALLS), and membrane (MO) and vapor pressure osmometry (VPO). The micellar behavior of these stars was investigated in n-decane, which is a selective solvent for the PI part. Small angle neutron scattering (SANS), LALLS, and viscometry were used in order to characterize the micelles. SANS measurements were performed at two different contrasts, where in each case one of the monomeric units was matched to the solvent. The coherent scattering cross sections of the single cores and coronas were determined by extrapolating low-concentration data to φ = 0. A theoretically calculated cross section of an unswollen hard sphere of PS-d8 was found to fit fairly well the experimental curves for the core. A calculated cross section of a hollow sphere with a constant density profile for the PI chains was found to describe the cross sections of the corona. Experimentally, it was found that the super-H structure increases the solubility and drastically reduces the aggregation number in comparison with linear PS/PI diblocks. A scaling approach is presented to take into account the specific influence of the SH structure on the micellar properties. It was found that the derived scaling laws of an intermediate regime between the starlike and the crewcut regime are in fair agreement with the experimental observations.

8] Detection in liquid chromatography

Publisher Summary Sensitive and selective detection of biological macromolecules is the goal of almost every biotechnology laboratory and chromatography is an important tool in biopolymer characterizations. However, no one detector is capable of completely characterizing an eluting biopolymer from a chromatographic column. The detector is a tool that provides the researcher with different information based on the requirements of the sample. While numerous texts have appeared, dealing with detectors for high-performance liquid chromatography (HPLC) or biopolymer separations, most of these have not specifically emphasized biopolymer detection. This chapter discusses the detection and characterization of components in a biological sample. Each detector provides a different type of information, in terms of spectroscopic, electrochemical, light-scattering properties, molecular weight, etc. The real problem in the unambiguous identification of a given biopolymer lies in the fact that within each class of biopolymers (proteins, nucleic acids, and carbohydrates), properties are similar to one another from a detection point of view. The lack of specificity in spectroscopic and electrochemical detectors is particularly problematic in biotechnology, where minor variants of proteins are frequently the analytes of interest. Therefore, although single-wavelength ultraviolet (UV) absorbance detection is among the most universally applied detection techniques, it often does not provide the selectivity necessary to characterize a biopolymer. If more selectivity is needed, dual-wavelength or linear diode array spectra can be employed. Fluorescence (FL) and electrochemical (EC) detection can also be employed for improved selectivity of appropriate samples. Derivatization can be utilized for improved sensitivity and selectivity. Molecular weights can be determined, with mass spectrometric and light-scattering techniques. Mass spectrometry (MS) can yield further structural information about the biopolymer from fragmentation studies, while low-angle laser light-scattering (LALLS) techniques can give molecular size and may detect aggregation formation. This chapter discusses the UV, FL, EC, and LALLS detectors.

Hydroxyl-radical-induced reactions of poly (acrylic acid); a pulse radiolysis, EPR and product study. Part II. Oxygenated aqueous solutions

Hydroxyl radicals were generated radiolytically in N2O–O2(4:1)-saturated dilute aqueous solutions of poly(acrylic acid), PAA. They react with PAA by abstracting H atoms from PAA in both the α- and βpositions to the carboxy group. The resulting PAA radicals are converted by O2 into the corresponding peroxyl radicals (k= 3.1 × 108 dm33 mol–1 s–1 at pH 3.5 and k= 1 × 108 dm3 mol–1 s–1 at pH 10, as measured by pulse radiolysis). The lowering of the rate constant at high pH has been attributed to a diffusion barrier for O2 exerted by the ion cloud around the charged macroradical. Although the lifetimes of the PAA peroxyl radicals (measured by EPR spectroscopy) increase with increasing pH, they still decay much faster than the very long-lived PAA radicals formed in the absence of O2. Concomitant with an increase in the lifetime of the peroxyl radicals, O2 uptake (in units of mol per mol PAA radicals initially formed) increases from 1.7 at pH 2.5 to 17 at pH 10 as does decarboxylation (from 1.0 at pH 3.5 to 13 at pH 10), scission (from 0.05 at pH 2 to 2.4 at pH 9) and the formation of acetylacetone-like products (from 0.35 at pH 3.5 to 1.05 at pH 10). The high yield of O2 uptake at pH 10 is mainly the result of repetitive abstraction of α-hydrogens by PAA α-peroxyl radicals. The acetylacetone-like products are formed by intramolecular 1,5-H-transfer reactions followed by a decomposition of the ensuing hydroperoxides. The chain breaks are formed in the course of the bimolecular termination reactions as has been shown by pulse radiolysis with low-angle laser light-scattering detection.

Association behavior of linear ω‐functionalized polystyrenes in dilute solutions

AbstractLinear polystyrenes with dimethylamino end groups were prepared by anionic polymerization, using 3‐(dimethylamino)propyllithium as initiator and high vacuum techniques. The amino group was transformed to a sulfozwitterionic moiety by reaction with 1,3‐propanesultone. The dilute solution properties were studied by means of membrane osmometry (MO), low‐angle laser light scattering (LALLS) and viscometry in solvents with different polarity. The amine‐capped polymers, studied by LALLS in tetrahydrofuran (THF), toluene and CCI4 show no evidence of association. In contrast, the zwitterionic samples exhibited a relatively strong association in CCI4 (relative permittivity ε = 2.24), weak in THF (ε = 7.4), and intermediate in toluene (ε = 2.4). The association numbers were lower than those found for linear polyisoprenes and polybutadienes with the same end groups. Viscosity measurements supported the results drawn from LALLS. The results provide strong evidence that the micelles behave hydrodynamically as star polymers. The association behavior is best described by the linear head packing model.

Pulse radiolysis in model studies toward radiation processing

Using the pulse radiolysis technique, the OH-radical-induced reactions of poly(vinyl alcohol) PVAL, poly(acrylic acid) PAA, poly(methacrylic acid) PMA, and hyaluronic acid have been investigated in dilute aqueous solution. The reactions of the free-radical intermediates were followed by UV-spectroscopy and low-angle laser light-scattering; the scission of the charged polymers was also monitored by conductometry. For more detailed product studies, model systems such as 2,4-dihydroxypentane (for PVAL) and 2,4-dimethyl glutaric acid (for PAA) was also investigated. With PVA, OH-radicals react predominantly by abstraction of an H-atom in α-position to the hydroxyl group (70%). The observed bimolecular decay rate constant of the PVAL-radicals decreases with time. This has been interpreted as being due to an initially fast decay of proximate radicals and a decrease of the probability of such encounters with time. Intramolecular crosslinking (loop formation) predominates at high doses per pulse. In the presence of O 2, peroxyl radicals are formed which in the case of the α-hydroxyperoxyl radicals can eliminate HO 2-radicals in competition with bimolecular decay processes which lead to a fragmentation of the polymer. In PAA, radicals both in α-position (characterized by an absorption near 300 nm) and in β-position to the carboxylate groups are formed in an approximately 1:2 ratio. The lifetime of the radicals increases with increasing electrolytic dissociation of the polymer. The β-radicals undergo a slow (intra- as well as intermolecular) H-abstraction yielding α-radicals, in competition to crosslinking and scission reactions. In PMA only β-radicals are formed. Their fragmentation has been followed by conductometry. In hyaluronic acid, considerable fragmeentation is observed even in the absence of oxygen which, in fact, has some protective effect against this process. Thus free-radical attack on this important biopolymer makes it especially vulnerable with respect to a reduction of its viscosity, and in rheumatic diseases this effect may be the reason for their painfulnes.

Concentration fluctuation dynamics of concentrated aqueous hydrophobicallymodified acrylic copolymer solutions

The dynamics of concentration fluctuation in concentrated aqueous solutions of a poly(hexaethylene glycol monomethacrylate-co-acrylic acid/allyl glycidyl ether) copolymer were studied by means of the timeresolved low angle laser light scattering (LALLS). Concentrated aqueous solutions in the range 30–55% w/w showed a lower critical solution temperature behaviour (LCST). A peak was observed in the scattered light profile with time,I(q,t), when a temperature jump above the coexistence curve was performed. The peak shifted to lowerq values with time in a logarithmic mode. Only at lowq values and very short times did the solutions obeyed Cahn's linear spinodal decomposition kinetics, subsequently slowing down.

Molecular weight characterization of soluble high performance polyimides. 2. Validity of universal SEC calibration and absolute molecular weight calculation

AbstractSix different soluble high‐performance aromatic polyimides, each prepared by solution imidization to three controlled average molecular weights, were analyzed by size exclusion chromatography (SEC) using on‐line parallel coupled refractometric and viscometric detectors. N‐methylpyrrolidone (NMP) with 0.06 M LiBr and NMP stirred over P2O5 were used as mobile phase for four of the polyimides; NMP with 0.06 M LiBr and NMP stirred over P2O5 were used as mobile phases for four of the polyimides; NMP with 0.06 M LiBr tetrahydrofuran (THF) and chloroform served as mobile phases for the other two polyimides. For all the samples the stationary phase in the SEC columns was cross‐linked polystyrene beads. Molecular weight averages of the polyimides were calculated using universal SEC calibration with polystyrene standards in each solvent. The agreement of the calculated molecular weight averages in the different solvents confirms that the universal SEC calibrations are valid for these semiflexible polymers. There was good agreement with weightaverage molecular weights obtained by low‐angle laser light scattering (LALLS) performed in pure NMP. Intrinsic viscosity and molecular weight data for a series of nine samples of one polyimide covering a Mw = 20,000–70,000 g mol–1 interval were treated to obtain Mark‐Houwink‐Sakurada constants. Unperturbed chain dimensions of this polyimide were obtained by application of the Stockmayer‐Fixman extrapolation procedure to these data. ©1995 John Wiley &amp; Sons, Inc.

Model Mono-, Di-, and Tri-.omega.-Functionalized Three-Arm Star Polybutadienes. Synthesis and Association in Dilute Solutions by Membrane Osmometry and Static Light Scattering

Three-arm polybutadienes with one, two, and three functional end groups were prepared by anionic polymerization using [3-(dimethylamino)propyl]lithium and sec-butyllithium as initiators and methyltrichlorosilane as linking agent. Characterization carried out on the dimethylamine-capped polymers by SEC, in THF, low-angle laser light scattering (LALLS) in THF, and membrane osmometry (MO) in toluene indicates a high degree of molecular and structural homogeneity. The 1,2 content, determined by NMR spectroscopy, of the arms having the functional groups was higher (12-32%) than that of the arms without the functional groups (7-10%), owing to the tertiary amine group of the initiator. The dimethylamine end groups were transformed to the highly polar sulfozwitterionic ones by reaction with cyclopropanesultone. Association of the different ω-functionalized star polybutadienes was studied in dilute solutions of cyclohexane by MO and LALLS. It was found that although the dimethylamine-capped polybutadienes do not associate, the corresponding zwitterionic species associate strongly in this solvent. At fixed molecular weight of the arms, the degree of association increases with decreasing number of functional groups and, for the same number of functional groups, with decreasing molecular weight of the arms. The trifunctional species form gels at concentrations needed for MO experiments. Comparison with linear ω-zwitterionic polybutadienes in cyclohexane shows that the stars associate less strongly, maybe due to the sterically hindered star structure (monofunctional species) and to intramolecular interactions (di- and trifunctional species)

Data evaluation for unified multi‐detector size exclusion chromatography — molar mass, viscosity and radius of gyration distributions

AbstractThe output of a size exclusion chromatography (SEC) system was connected to a single capillary viscometer, a multi‐angle laser light scattering detector (MALLS) and a refractive index detector (RI). This provides absolute distributions of molar mass, radius of gyration and reduced viscosity, which are valuable both for practical polymer characterization and as tests of physical polymer theories. The instrument interfacing is described, along with the method of data analysis. A quantitative investigation of systematic and random sources of error and their influence on polymer characterization is made. An experimental example using a biopolyelectrolyte (hyaluronate), including complete error analysis, is presented, along with other data. Although the emphasis here is on aqueous SEC, most of the principles should carry over to organic phase SEC. A simultaneous, in‐line comparison of a low‐angle laser light scattering (LALLS) detector and MALLS detectors was also made. The dangers of ‘universal calibration’ for hydrosoluble polymers are also illustrated.