Striking differences between alkyl sulfate and alkyl sulfonate when mixed with cationic surfactants

The properties of alkyl sulfate and alkyl sulfonate are similar except for their Krafft points. However, alkyl sulfate and alkyl sulfonate behave quite differently when they are mixed with cationic surfactants and show some totally unexpected results. In this work sodium alkyl sulfate (C_nH_2n+1SO₄Na,C_nSO₄)–alkyl quaternary ammonium bromide [C_nH_2n+1N(C_mH_2m+1)₃Br, C_nN, m=1–4] mixtures and sodium alkyl sulfonate (C_nH_2n+1SO₃Na, C_nSO₃)–C_nN mixtures were studied. It was found that, in contrast to the single surfactants, C_nSO₃–C_nN mixtures were much more soluble than C_nSO₄–C_nN mixtures. Besides, the two kinds of catanionic surfactant mixtures were quite different in their phase behavior and aggregate properties. The results were interpreted in terms of the interactions between surfactant molecules, which were very different in the two kinds of mixed systems owing to the distinction between alkyl sulfate and alkyl sulfonate in the molecular charge distribution.     

Synthesis of phosphate-type fluorocarbon-hydrocarbon hybrid surfactants and their adsorption onto calcium hydroxyapatite

Five novel phosphate-type hybrid surfactants, C_mF_2m+1C₆H₄CH[OPO₂(OC₆H₅)Na]C_nH_2n+1 (FmPHnPPhNa: m = 4, 6, 8; n = 3, 5), have been synthesized. When compared with sulfate-type hybrid surfactants, C_mF_2m+1C₆H₄CH(OSO₃Na)C_nH_2n+1 (C₆H₄ = p-phenylene), the new hybrid surfactants were found to have comparable abilities to lower the surface tension of water. The critical micelle concentrations of FmPHnPPhNa followed Klevens’ rule and their occupied areas per molecule increased with increasing m and n. Calcium hydroxyapatite (CaHAp) pellets modified with FmPH3PPhNa gave high hydro and lipophobic surfaces. The hybrid surfactants are expected to be useful as new dental reagents for oral hygiene.     

Synthesis of phosphate-type fluorocarbon-hydrocarbon hybrid surfactants and their adsorption onto calcium hydroxyapatite

Five novel phosphate-type hybrid surfactants, C_mF_2m+1C₆H₄CH[OPO₂(OC₆H₅)Na]C_nH_2n+1 (FmPHnPPhNa: m = 4, 6, 8; n = 3, 5; C₆H₄ = p-phenylene, C₆H₅ = phenyl), have been synthesized. When compared with sulfate-type hybrid surfactants, C_mF_2m+1C₆H₄CH(OSO₃Na)C_nH_2n+1 (C₆H₄ = p-phenylene), the new hybrid surfactants are found to have comparable abilities to lower surface tension of water. The critical micelle concentrations of FmPHnPPhNa follow Klevens rule and their occupied areas per molecule increase with increasing m and n. Calcium hydroxyapatite (CaHAp) pellets modified with FmPH3PPhNa gives high hydrophobic and lipophobic surfaces. The hybrid surfactants are expected as new dental reagents for oral hygiene.     

Synthesis and solution properties of sulfate-type hybrid surfactants with a benzene ring

Nine novel sulfate-type hybrid surfactants, C_mF_2m+1C₆H₄CH(OSO₃Na)C_nH_2n+1 (FmPHnOS: m=4, 6, 8; n=3, 5, 7; C₆H₄: p-phenylene), with a benzene ring in their molecules were synthesized. Alkanoyl chlorides were allowed to react with iodobenzene in the presence of aluminum chloride to give the corresponding aromatic ketones. The reaction of the ketones with perfluoroalkyl iodides yielded 1-[4-(perfluoroalkyl)phenyl]-1-alkanones as intermediates. The intermediates were allowed to react with methanol in tetrahydrofuran in the presence of sodium borohydride to yield 1-[4-(perfluoroalkyl)phenyl]-1-alkanols. The desired hybrid surfactants were obtained by the reaction of 1-[4-(perfluoroalkyl)phenyl-1-alkanols with sulfur trioxide/pyridine complex in pyridine and by the subsequent neutralization of the products with sodium hydroxide solution. When compared with the conventional hybrid surfactants, C_mF_2m+1C₆H₄COCH(SO₃Na)C_nH_2n+1 (FmHnS: m=4, 6; n=2, 4, 6; C₆H₄: p-phenylene), the new hybrid surfactants thus synthesized were found to have a comparable ability to lower the surface tension of water and a high hydrophilicity. The cmc of FmPHnOS obeyed Kleven’s rule and their occupied areas per molecule increased with increasing m and n with the values between 0.66 and 1.05 nm². The aggregation number for FmPHnOS micelles ranged from 6 to 45 and the hydrodynamic radius of the micelles was in the range of 1.4-3.1 nm.     

Synthesis and surface activities of organic solvent-soluble fluorinated surfactants

A variety of fluorinated surfactants soluble in organic solvent were prepared, including C₈F₁₇SO₂NHC_nH_2n+1 (n = 2, 4, 6, 8, 10), C₈F₁₇SO₂NHR (R = C₆H₁₁, C₆H₅), C₈F₁₇SO₂N(C_nH_2n+1)₂ (n = 1, 2, 3, 4) and C₈F₁₇SO₂NH(CH₂)_nNHO₂SC₈F₁₇ (n = 6, 10). Their surface activities in various organic solvents were determined by surface tension measurement. The results showed that these fluorinated surfactants can reduce the surface tension of both polar and non-polar organic solvents. In general, organic solvents with strong polarity or long alkyl chain are beneficial to increase the surface activity of these polar fluorinated surfactants. By comparing fluorinated surfactants with the same fluorocarbon segment and connecting group, C₈F₁₇SO₂N(C_nH_2n+1)₂ (n = 1, 2, 3, 4) showed lower surface activity in organic solvents than C₈F₁₇SO₂NHC_nH_2n+1 (n = 2, 4, 6, 8) with an equal carbon number of the solvophilic group. Through surface tension vs. concentration curves given for N-octyl perfluorooctanesulfonamide in various organic solvents, a break point like the critical micelle concentration of ordinary surfactants in aqueous solutions was observed, and the effect of the different types of organic solvents on adsorption and aggregation behavior was also studied.     

Self-assembly behaviors of zwitterionic heterogemini surfactant at an oil-water interface: A dissipative particle dynamics study

The self-assembly behaviors of a battery of zwitterionic heterogemini surfactants C_mH_2m+1-PO^4--(CH₂)₂-N⁺(CH₃)₂-C_nH_2n+1, abbreviated as C_m-P-N-C_n (m, n?=?9, 9; 9, 12; 9, 15; 9, 18; 12, 12; 12, 15; 12, 18; 15, 15; 15, 18; 18, 18), have been explored at an oil-water interface by means of the dissipative particle dynamics (DPD) method. Regular oil-water contact together with oil-in-water and water-in-oil emulsions has come into being. Compared with the C_m-P-N-C_n concentration and the oil-water ratio, the hydrophobic chain length plays a less important role in the self-assembly morphology of C_m-P-N-C_n molecules at the interface together with the interfacial morphology. The asymmetry in the molecular structure of C_m-P-N-C_n dominates its critical micelle concentration (CMC) and interfacial efficiency. The C_m-P-N-C_n concentration and its hydrophobic chain length work together to affect the interfacial thickness. What’s more, the dependence of CMC on the C_m-P-N-C_n molecular structure is in qualitative agreement with corresponding experimental findings.     

Alkyl polyglucoside microemulsion phase behavior

We review several key elements of alkyl polyglucoside (C_mG_n) microemulsion phase behavior. The low solubility of C_mG_n surfactants in oils such as alkanes makes producing C_mG_n microemulsions and subsequent study of their phase behavior difficult. Increasing the solubility of C_mG_n in oil is therefore helpful for the systematic study of C_mG_n-based microemulsion formulations. To this end, the role of cosurfactants in producing microemulsions with water, alkanes, and n-alkyl β-d-glucopyranosides is first discussed. Adding C₁₀βG₁ to mixtures of water–alkane–ethoxylated alcohol surfactants (C_iE_j) produces a region of the three-phase body (a ‘chimney’) that is independent of temperature; thus C_mβG₁ are not completely soluble in the co-oil formed of alkane and C_iE_j at higher temperatures. Then, through a novel approach using oxygenated ether oils (C_kOC₂OC_k), microemulsions are formed with water, C_kOC₂OC_k, and C_mβG₁ and the phase behavior studied as a function of temperature and composition. Increased C_mβG₁ solubility in the more hydrophilic ether oils produces patterns of phase behavior in water–C_kOC₂OC_k–C_mβG₁ mixtures that are identical to those observed in water–alkane–C_iE_j mixtures. Using the water–ether oil–C_mβG₁ mixtures as a base case, the role of C_mG_n surfactant structure in setting C_mG_n microemulsion phase behavior is explored. The solubility of the α-d anomer (n-alkyl α-d-glucopyranosides, C_mαG₁) in water is much less than that of the β-d surfactant, and these solubility boundaries extend to high surfactant and oil concentrations in water–C_kOC₂OC_k–C_mαG₁ mixtures. Adding C_mG₂ compounds to water–C_kOC₂OC_k–C_mβG₁ mixtures shifts the phase behavior to high temperatures, again demonstrating the extreme hydrophilic nature of the sugar headgroup. Finally, adding small amounts of ionic alkyl sulfate surfactants to water–C_kOC₂OC_k–C_mβG₁ mixtures dramatically reduces the total amount of surfactant needed to form a single-phase microemulsion.     

Synthesis and Surface Activity of Anionic Gemini Surfactants with Alkyl Spacers

A series of anionic Gemini surfactants called alkanediyl-α,ω-bis(m-octylphenoxy sulfonate) with different length of (CH₂)_x spacer, C₈C_xC₈ (x = 2, 4, 6, 8), have been synthesized from 4-n-octylphenol and their basic physicochemical properties are investigated. The results indicate that they are different from cationic Gemini surfactants called alkanediyl-α,ω-bis(dimethyldodecylammonium bromide), 12-(CH₂)_s-12, in the literature. It is found that as the carbon atom number of the spacer increases, the cmc (critical micelle concentration) decreases gradually, and the surface area per molecule (A_min) decreases initially and then increases. The breakpoints appear at number 4 of carbon atom in the spacer. Though the length of the spacer is different for the Gemini surfactants from C₈C₂C₈ to C₈C₆C₈, there is no obvious change on the micropolarity.     

Synthesis and Surface Activity of Heterogemini Imidazolium Surfactants

A series of heterogemini imidazolium surfactants with two-methylene spacer groups ([C_m-2-C_nim]Br_{2, m, n}=8, 10, 12, 14, 16; m≠n) have been synthesized and characterized by 1H NMR and ESI-MS spectroscopy. The effects of various reaction parameters, including stoichiometry, reaction temperature and time, were investigated. In addition, the surface activity study about heterogemini imidazolium surfactants was carried out and the influences of dissymmetric degree on the surface properties were also discussed.     

ESR Studies on the Micellization Behaviors of a Series of Novel Asymmetric Gemini Surfactants

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓ ,ｂｉｓ(ｑｕａｔｅｒｎａｒｙａｍｍｏｎｉｕｍ)ｓｕｒｆａｃ ｔａｎｔｓｏｒｇｅｍｉｎｉｓｕｒｆａｃｔａｎｔｓ ,ｉｎｗｈｉｃｈｔｗｏｃａｔｉｏｎｉｃｓｕｒｆａｃ ｔａｎｔｍｏｉｅｔｉｅｓａｒｅｃｏｎｎｅｃｔｅｄｗｉｔｈｔｈｅａｍｍｏｎｉｕｍｈｅａｄｇｒｏｕｐｂｙａｐｌｏｙｍｅｔｈｙｌｅｎｅｃｈａｉｎ ,ｎａｍｅｌｙ ,ａｓｐａｃｅｒｈａｖｅｂｅｃｏｍｅｏｆｉｎｔｅｒｅｓｔｄｕｅｔｏｔｈｅｉｒｅｘｃｅｐｔｉｏｎａｌｓｕｒｆａｃｅａｃｔｉｖｉｔｙａｎｄｒｅｍ…     

The Effect of Anomeric Head Groups, Surfactant Hydrophilicity, and Electrolytes onn-Alkyl Monoglucoside Microemulsions

The effects of the variables of head group structure and salt concentration on microemulsions formed in mixtures of water, alkyl ethylene glycol ethers (C_kOC₂OC_k), andn-alkyl β- -glucopyranosides (C_mβG₁) are explored. Phase behavior of mixtures containing an anomer of the surfactant (n-alkyl α- -glucopyranoside, C_mαG₁), or surfactants with long head groups (n-alkyl maltopyranosides, C_mG₂), or NaCl or NaClO₄as electrolyte are systematically reported as a function of temperature and composition. The substitution ofn-alkyl α- -glucopyranosides forn-alkyl β- -glucopyranosides causes precipitation under some conditions in all mixtures studied. These solubility boundaries begin in the water–surfactant binary mixture at the Krafft boundary, then extend to high concentrations of both surfactant and oil. Increasing the effective length of the surfactant head group by adding C_mG₂to water–C_kOC₂OC_k–C_mβG₁mixtures moves the phase behavior dramatically up in temperature when even small amounts of C_mG₂are used. Adding a lyotropic electrolyte, NaCl, to water–C_kOC₂OC_k–C_mβG₁mixtures moves the phase behavior down in temperature, while the hydrotropic electrolyte NaClO₄moves the phase behavior up in temperature.     

Synthesis and Surface Properties of Novel Cationic Gemini Surfactants

A series of novel cationic gemini surfactants, p-[C _n H_2n+1N⁺(CH₃)₂CH₂CH(OH)CH₂O]₂C₆H₄·2Cl^? [A(n = 12), B(n = 14) and C(n = 16)], containing a spacer group with two flexible and hydrophilic groups (2-hydroxy-1,3-propylene) on both sides of a rigid and hydrophobic group (1,4-dioxyphenylene) has been synthesized by the reaction of hydroquinone diglycidyl ether with N,N-dimethylalkylamine and N,N-dimethylalkylamine hydrochloride. Their surface-active properties have been investigated by surface tension measurement. The critical micelle concentration (cmc) values of the synthesized cationic gemini surfactants are one order of magnitude lower than those of their corresponding monomeric surfactants (C _n H_2n + 1N⁺(CH₃)₃·Cl^?). Both the cmc and surface tension at the cmc (γ_cmc) of A are lower than those of p-[C₁₂H₂₅N⁺(CH₃)₂CH₂]₂C₆H₄·2Cl^? (D). The novel cationic gemini surfactants A and B also show good foaming properties.     

Small-angle neutron-scattering study and micellar model of the gemini (phenylenedimethylene)bis(n-octylammonium)dibromide surfactant micelles in water

The microstructure of the micelles formed in aqueous solution by gemini surfactants with aromatic spacers, [Br(CH₃)₂N⁺(C _m H_{2 m +1})-(Ph)-(C _m H_{2 m +1})N⁺(CH₃)₂Br, m=8 and Ph = o-, m- or p-phenylenedimethylene] has been examined by small-angle neutron scattering. Aggregation of the gemini surfactants with an o-phenylenedimethylene spacer brings about formation of premicelles and small micelles at concentrations below the second critical micelle concentration, while above this concentration marked micellar growth and variation in shape occurs. It is suggested that the minimum aggregate formed at this critical micelle concentration may be the trimer or tetramer and that this result supports the mechanism of “gemini → submicelle → assembly” for micellar growth. Received: 8 September 1998 Accepted in revised form: 27 November 1998     

Mixed micellization of an anionic gemini surfactant (GA) with conventional polyethoxylated nonionic surfactants in brine solution at pH 5 and 298 K

The micellization behavior of an anionic gemini surfactant, GA with nonionic surfactants C₁₂E₈ and C₁₂E₅ in presence of 0.1 M NaCl at 298 K temperature, has been studied tensiometrically in pure and mixed states, and the related physicochemical parameters (cmc, γ _cmc, pC ₂₀, Γ _max, and A _min) have been evaluated. Tensiometric profile (γ vs log [surfactant]), for conventional surfactants, generally consists of a single point of intersection; a gradually decreasing line (normally linear, or with slight curvature) ultimately saturates in γ at a particular [surfactant], corresponding to complete monolayer saturation. The gemini, in this report, led to two unequivocal breaks in the tensiometric isotherm. An attempt to the interpretation of the two breaks from molecular point of view is provided, depending solely on the chemical structure of the surfactant. The gemini, even in mixed state with the conventional nonionic surfactants C₁₂E₅ and C₁₂E₈, manifested the dual breaks; of course, the dominance of the feature decreases with increasing mole fraction of the nonionics in the mixture. Theories of Clint, Rosen, Rubingh, Motomura, Georgiev, Maeda, and Nagarajan have been used to determine the interaction between surfactants at the interface and micellar state of aggregation, the composition of the aggregates, the theoretical cmc in pure and mixed states, and the structural parameters according to Tanford and Israelachvili. Several thermodynamic parameters have also been predicted from those theories.     

Molecular simulation study on the self-assembly behaviors of zwitterionic heterogemini surfactant in aqueous solution

The self-assembly behaviors of a series of zwitterionic heterogemini surfactants C_mH_2m+1-PO^4–(CH₂)₂-N⁺(CH₃)₂-C_nH_2n+1, abbreviated as C_m-P-N-C_n (m, n?=?9, 9; 9, 12; 9, 15; 9, 18; 12, 12; 12, 15; 12, 18; 15, 15; 15, 18; 18, 18), have been investigated in aqueous solution by the dissipative particle dynamics (DPD) method. Morphologies such as sphere (S), rod (R), planar grid (PG), lamella (L), honeycomb (H), one-, two-, and three-dimensional tunnels (1DT, 2DT, and 3DT) have been observed showing more diversities than those of the corresponding symmetric gemini surfactants C_m-N-N-C_m (m?=?9, 12, 15, 18). With the increase of surfactant concentration in the aqueous solution, a distinct transition path ‘‘S—R—PG—3DT—L—2DT—1DT’’ is proved to be common for all the C_m-P-N-C_n systems. Besides, the hydrophobic chain length has a significant influence on the self-assembly behaviors in the case of m?≠?n. Radial distribution function is an effective method to quantitatively evaluate the interaction and relationship between each functional group in the surfactant molecule and water. Results can provide a new insight into the self-assembly behaviors of zwitterionic heterogemini surfactants and the corresponding applications.     

Polyoxyethylene cholesteryl ether-based aqueous wormlike micelles

Formation of wormlike micelles (WLMs) in an aqueous mixture of polyoxyethylene cholesteryl ether (ChEO_n; where n = 20 and 30) and polyoxyethylene dodecyl ether (C₁₂EO_m; where m = 3 and 4) has been reported; rheological and small angle X-ray scattering (SAXS) measurements have been performed in the micellar solutions of ChEO_n as a function of C₁₂EO_m for the structural elucidation. When lipophilic cosurfactant, C₁₂EO_m is added to the micellar solutions of ChEO_n, it favors the sphere-to-cylinder transition due to the penetration of C₁₂EO_m in the palisade layer of ChEO_n micelle accompanying an increase in viscosity. When the concentration of C₁₂EO_m is increased, entangled network of WLMs is formed. A strong shear thinning has been observed in highly viscous samples indicating the presence of transient networks. Such samples exhibited viscoelastic behavior and could be described by the Maxwell model with a single stress relaxation mode. A maximum is observed in zero-shear viscosity-C₁₂EO_m plot. With further addition of C₁₂EO_m, viscosity declines and ultimately a phase separation occurs with the formation of turbid solution of vesicular dispersion. This decline has been interpreted in terms of micellar branching induced by an increase in endcap energy, E _c (which is compensated by the formation of branch points, having a mean curvature opposite to that of endcaps). The C₁₂EO_m induced one-dimensional micellar growth has been confirmed by SAXS.     

A mass spectrometry study of alkanes in air plasma at atmospheric pressure

The positive APCI-mass spectra in air of linear (n-pentane, n-hexane, n-heptane, n-octane), branched [2,4-dimethylpentane, 2,2-dimethylpentane and 2,2,4-trimethylpentane (i-octane)], and cyclic (cyclohexane) alkanes were analyzed at different mixing ratios and temperatures. The effect of air humidity was also investigated. Complex ion chemistry is observed as a result of the interplay of several different reagent ions, including atmospheric ions O₂^+•, NO⁺, H₃O⁺, and their hydrates, but also alkyl fragment ions derived from the alkanes. Some of these reactions are known from previous selected ion/molecule reaction studies; others are so far unreported. The major ion formed from most alkanes (M) is the species [M − H]⁺, which is accompanied by M^+• only in the case of n-octane. Ionic fragments of C _n H_2n ^+1/+ composition are also observed, particularly with branched alkanes: the relative abundance of such fragments with respect to that of [M − H]⁺ decreases with increasing concentration of M, thus suggesting that they react with M via hydride abstraction. The branched C₇ and C₈ alkanes react with NO⁺ to form a C₄H₁₀NO⁺ ion product, which upon collisional activation dissociates via HNO elimination. The structure of t-Bu⁺(HNO) is proposed for such species, which is reasonably formed from the original NO⁺(M) ion/molecule complex via hydride transfer and olefin elimination. Finally, linear alkanes C₅–C₈ give a product ion corresponding to C₄H₇⁺(M), which we suggest is attributed to addition of [M − H]⁺ to C₄H₈ olefin formed in the charge-transfer-induced fragmentation of M. The results are relevant to applications of nonthermal plasma processes in the fields of air depuration and combustion enhancement.     

ESR lineshapes and kinetic behavior of nitroxide spin probes in micellar solutions

The ESR spectrum of the nitroxide radical 2,2,6,6-tetramethylpiperidine-N-oxide (TEMPO) has been investigated in aqueous solutions of the following surfactants:n-octylammonium bromide, sodiumn-octylsulfonate,n-decylammonium bromide,n-docecyltrimethylammonium bromide, and sodiumn-dodecylsulfate. The spectra were recorded at 25° C as function of surfactant concentration in the ranges 0–0.5m for the C₁₀ and C₁₂ compounds and 0–1.0m for the others. Analysis of the spectra using computer simulation methods yields the hyperfine coupling constanta _H and the widthW _H of the partially resolved lines in the proton hyperfine structure. Changes in these variables with surfactant concentration are interpreted from medium effects on the magnetic properties of the radical, kinetics of radical-micelle interactions, and rotational dynamics of the nitroxide probe in these solutions.     

Preparation of amphiphilic organoiron(1+) complexes having two long-chain alkyl groups and their molecular assemblage characteristics

[o-, m- and p-Bis(alkylamino or alkyloxy)benzene] (cyclopentadienyl)iron(1+) hexafluorophosphates {2 and 4; [(C_nH_2n+1X)₂C₆H₄](C₅H₅)Fe⁺PF₆^?, X?NH or O} were prepared by aromatic nucleophilic substitution of the (dichlorobenzene)iron cationic complexes (1). Critical micelle concentrations of the complex chlorides (3), prepared from 2 (n=8, X?NH) by anion exchange and soluble in water, gave much smaller values than those of bis(long-chain alkyl)dimethylammonium surfactants. Furthermore, the substitution positions scarcely affected their surface activites. However, the surface pressure-molecular area isotherm of the hexafluorophosphates (2 and 4, n=18, X?NH; insoluble in water) were severely transformed by change in the substitution position of the long-chain alkyl groups on the benzene ligand in the iron cationic complexes: the o-substituted complex gave a molecularly assembled film by the Langmuir-Blodgett (LB) method, but the P-substituted one did not.     

Interfacial dilational properties of anionic gemini surfactants with polymethylene spacers

The dilational properties of anionic gemini surfactants alkanediyl-α,ω-bis(m-octylphenoxy sulfonate) (C₈C_mC₈) with polymethylene spacers at the water–air and water–decane interfaces were investigated by oscillating barriers and interfacial tension relaxation methods. The influences of oscillating frequency and bulk concentration on the dilational properties were explored. The experimental results show that the linking spacer plays an important role in the interfacial dilational properties. The moduli pass through one maximum for all three gemini surfactants at both water–air and water–decane interfaces. However, the values of moduli at the water–air interface are obviously higher than those at the water–decane interface because the sublayer formed by spacer chains will be destroyed by the insertion of oil molecules. Moreover, with the increase of spacer length, the surface adsorption film becomes more viscous at high concentration, which can be attributed to the process involving the formation of the sublayer. On the other hand, the spacers of the adsorbed C₈C₆C₈ molecules will extend into the oil phase when the interface is compressed. As a result, the interfacial film becomes more elastic with the increase of spacer length at high concentration. The experimental results obtained by the interfacial tension relaxation measurements are in accord with those obtained by the oscillating barriers method.