Synthesis and Surface Properties of Polyether-Based Silicone Surfactants with Different Siloxane Groups

A series of polyether-based silicone surfactants with different hydrophobic chains (trimethylsiloxy, triethylsiloxy, and triisopropylsiloxy) were synthesized. The molecular structures were confirmed using ¹H nuclear magnetic resonance (NMR), ¹³C NMR, ²⁹Si NMR, and fourier transform infrared spectroscopy (FT-IR). The effect of the siloxane groups on the physicochemical properties, surface tension (γ), critical micelle concentration (CMC), surface tension at the CMC (γ_CMC ), adsorption efficiency (pC₂₀), surface pressure at the CMC (π_CMC ), maximum surface excess (Γ_max ), single silicone surfactant molecule at the air/water interface (A_min ), and the standard free energy of adsorption (), of the polyether-based silicone surfactants was investigated. Results indicate that the polyether-based silicone surfactants can reduce the surface tension of water to approximately 25–31 mN m⁻¹ and the surface activity of silicone surfactants is enhanced with increasing branched trimethylsiloxyl and sterically hindered siloxane groups.     

Retracted: Synthesis,Characterization, and Surface Activities of Polymeric Cationic Thiol Surfactants in Aqueous Medium

A series of cationic polyurethane surfactants [PQ_8-18] were synthesized by the reaction of alkyl bromoacetate (namely: octyl-, decyl-, dodecyl-, tetradecyl-, hexadecyl-, and octadecyl bromoacetate) as quaternizing agents and modified polyurethane contains tertiary amine species. Modified polyurethane was prepared by the reaction of toluene diisocyanate (TDI) and triethanol amine monomercaptoacetate. The chemical structures of the prepared surfactants were confirmed using elemental analysis, Fourier transform infrared spectroscopy (FTIR), and Proton nuclear magnetic resonance (¹H NMR) spectroscopy. The molecular weight measurements of the prepared polymers showed that the segments of each polymer contain average 10 units of the urethane-triethanol amine mercaptoacetate. The surface activities of the prepared surfactants including: surface tension (γ), effectiveness ( π_cmc), concentration at micelle formation (CMC), efficiency (Pc₂₀), maximum concentration at the interface (Γ_max), and the average area occupied by each surfactant molecule at the interface at equilibrium ( A _min) of surfactants solutions were established at 25°C. The surface tension and the critical micelle concentration values of the prepared surfactants were gradually decreased by the gradual increase of their alkyl chain length. The prepared cationic surfactants showed efficient activity as inhibitors for dissolution of carbon steel in an acidic medium and also as a biocide against the growth of bacteria, fungi, and yeast.     

Surface and Aggregation Properties of Synthesized Cetyl Alcohol Based Bis-Sulfosuccinate Gemini Surfactants in Aqueous Solution

A series of cetyl alcohol based anionic bis‐sulfosuccinate gemini surfactants (BSGSCA1,4; BSGSCA1,6 and BSGSCA1,8) with different spacer lengths was prepared using dibromoalkanes. The surfactant structure was elucidated using elemental analysis, Fourier transform infrared spectroscopy (FT‐IR) and nuclear magnetic resonance spectroscopy (NMR). Surface tension measurements were used to determine the critical micelle concentration (CMC), the surface tension at the CMC (γ_CMC), surface pressure at the CMC (π_CMC) and efficiency of adsorption (pC20). On the basis of surface studies, the CMC and γ_CMC decreases with increasing length of the spacer group. The micelle aggregation number, determined by fluorescence quenching studies, increases with increasing surfactant concentration above the CMC. The micropolarity in the micelle increases with increasing length of the spacer and decreases with increasing surfactant concentration.     

Synthesis,characterization, and surface properties of phenylalanine-glycerol ether surfactants

A novel homologous series of 1-N-l-phenylalanine-glycerol ether surfactants was synthesized in satisfactory yields via reaction of epichlorohydrin with aliphatic alcohols with alkyl chains of 10–15 carbon atoms. Structural assignment of the new compounds was made on the basis of elemental analysis and spectroscopic data. Critical micelle concentration (CMC), surface tension at the CMC (γ_CMC), surfactant concentration required to reduce the surface tension of the solvent by 20 mN/m (pC₂₀), and the interfacial area occupied by the surfactant molecules (A_min) were determined from aqueous surface tension measurements using the Wilhelmy plate technique.     

Synthesis and Surface Properties of Novel Gemini Imidazolium Surfactants

Five new Gemini imidazolium surfactants were synthesized from imidazole and 1-bromoalkane (C₈, C₁₀, C₁₂, C₁₄, C₁₆) to get 1-alkylimidazole, which was further reacted with 1,3-dichloropropan-2-ol to form the surfactant molecule, 1,1′-(propane-1,3-diyl-2-ol) bis(3-alkyl-1H-imidazol-3-ium) chloride. The structures of the five new surfactants and intermediates were characterized by ¹H-NMR, ¹³C-NMR and IR spectra. Thermal properties of the five new surfactants were studied with thermogravimetric analysis and differential scanning calorimetry, the five new surfactants showed a transition from a crystalline phase to a thermotropic liquid–crystalline phase at around ca. 100 °C, which transformed to an isotropic liquid phase at around ca. 165 °C. The five new surfactants critical micelle concentrations (CMC) in the aqueous solutions were determined by surface tension and electrical conductivity methods. The surface tension measurements provided a series of parameters, including critical micelle concentration (CMC), surface tension at the CMC (γ _CMC), adsorption efficiency  (pC ₂₀), and effectiveness of surface tension reduction (π_CMC). In addition, with application of the Gibbs adsorption isotherm, maximum surface excess concentration (Γ_max) and minimum surface area/molecule (A_min) at the air–water interface were obtained. The parameters β (degree of counterion binding to micelles), ΔG _ads ^θ (Gibbs free energy of adsorption), and ΔG _mic ^θ (Gibbs free energy change of micellization) were also derived. The results indicated that the five new Gemini surfactants exhibited very low CMC and a good efficiency in lowering the surface tension of water. The foamability and foam stability of the five new surfactants were also examined at different CMC.     

Synthesis and Surface Properties of a Novel Sodium 3‐(3‐Alkyloxy‐3‐oxopropoxy)‐3‐oxopropane‐1‐sulfonate at the Air–Water Interface

The present paper describes the synthesis and evaluation of surface properties of a novel series of anionic surfactant, namely sodium 3‐(3‐alkyloxy‐3‐oxopropoxy)‐3‐oxopropane‐1‐sulfonate with varying alkyl chain length (C8–C16). Synthesis involves initial formation of the 3‐alkyloxy‐3‐oxopropyl acrylate along with fatty acrylate during the direct esterification of fatty alcohol with acrylic acid in the presence of 0.5 % NaHSO₄ at 110 °C followed by sulfonation of the terminal double bond of the 3‐alkyloxy‐3‐oxopropyl acrylate. Synthesized compounds were evaluated for surface and thermodynamic properties such as critical micelle concentration (CMC), surface tension at CMC (γ_cmc), efficiency of surface adsorption (pC₂₀), surface excess (Γ_max), minimum area per molecule at the air–water interface (A_min), free energy of adsorption (?G°_ads), free energy of micellization (?G°_mic), wetting time, emulsifying properties, foaming power and calcium tolerance. Effect of chain length on CMC follows the classic trend, i.e. decrease in CMC with the increase in alkyl chain length. High pC₂₀ (>3) value indicates higher hydrophobic character of the surfactant. These surfactants showed very poor wetting time and calcium tolerance, but exhibited good emulsion stability and excellent foamability. Foaming power and foam stability of C14‐sulfonate were found to be the best among the studied compounds. Foam stability of C14‐sulfonate was also studied at different concentrations over time and excellent foam stability was obtained at a concentration of 0.075 %. Thus this novel class of surfactant may find applications as foam boosters in combination with other suitable surfactants.     

Synthesis and Surface Tension Study of the Spacer Chain Length Effect on the Adsorption and Micellization Properties of a New Kind of Carboxylate Gemini Surfactant

A series of carboxylate gemini surfactants, which contain two hydrocarbon chains linked by amide groups, two carboxylate groups, a flexible alkane spacer were synthesized by three-step reactions and named alkylidene–bis-(N,N′-dodecyl-carboxypropylamides) (2C₁₂H₂₅CnAm; n = 2, 3, 4, 6, 8 is the number of methylene groups of the spacer), their structures were confirmed by FTIR,¹H NMR, and LC–MS/TOF, and their purity checked by HPLC. The micellar properties with increasing spacer chain length of these gemini surfactants were determined by surface tension methods. The critical micelle concentration (CMC) varies slightly with spacer chain length; surface tension at CMC(γ_CMC), the tendency of micellization versus adsorption, CMC/C₂₀, the minimum area per surfactant molecule at the air/solution interface (A_CMC), all decrease with increasing spacer chain length; surface reduction efficiency, pC₂₀, the surface excess at the air/solution interface (Г_CMC) increase with increasing spacer chain length. The results probably indicate that increasing spacer chain length of these carboxylate gemini surfactants will increase spacer incorporation into the double hydrophobic chain.     

Synthesis and Investigation of Surface Active Properties of Counterion Coupled Gemini Surfactants

Three counterion coupled gemini (cocogem) surfactants in the series 1,6‐bis(N,N‐alkyldimethylammonium) adipate, referred as n‐6‐n (n = 12, 14, 16), were synthesized, purified and characterized by ¹H NMR and ¹³C NMR. Their physicochemical properties were investigated by electrical conductivity and surface tension measurements. The degree of ionization, critical micelle concentration (CMC), surface excess at the air/solution interface (Γ_max), minimum area per surfactant molecule at the air/solution interface (A_min), surface tension at the CMC (γ_CMC), and pC₂₀ (negative log of the surfactant molar concentration, required to reduce the surface tension of water by 20 mN m^?1) were calculated. Increase in tail length of the surfactants increases the efficiency of surfactants to decrease the surface tension of water. Thermodynamic parameters, viz. molar free energy at the maximum adsorption attained at CMC (G_min), standard Gibb's energy of micellization (), and standard Gibbs energy of adsorption (), were also calculated. The and values show that the monomers were preferred to be adsorbed at the air/water interface and then in the micellar formation in the bulk. Additionally, fluorescence measurements were used to find the aggregation number. Other relevant surface properties (Krafft point, emulsion stability, foaming ability, micellar stability and dye solubilization ability) were also evaluated. These results suggest that with respect to emulsion formation, micellar stability and dye solubilization, the cocogem with a 16‐carbon chain gives better results, producing 89 % more stable foams and shows better aggregational behavior.     

Micellar and Surface Properties of Some Monomeric Surfactants and a Gemini Cationic Surfactant

The physicochemical and interfacial properties of the monomeric surfactants cetyltrimethyl ammonium bromide (CTAB), cetyltriphenyl phosphonium bromide (CTPB), tetradecyl triphenyl phosphonium bromide (TTPB), cetyldiethylethanol ammonium bromide (CDEEAB), cetyltrimethyl ammonium chloride (CTACl), tetradecyltrimethyl ammonium bromide (TTAB), and a gemini surfactant (C₁₆-3-C_16, 2Br⁻) at different pH (3.1, 7.0, and 7.75) have been investigated by conductivity and surface tension measurements at 300 K. The critical micellar concentration (CMC), degree of micellar ionization (α), surface excess concentration (Г_max), minimum surface area per molecule of surfactant (A _min), Gibbs free energy of micellization (∆G _m⁰), surface pressure at the CMC (π _CMC), and the Gibbs energy of adsorption (∆G _ads⁰) of the monomeric surfactants have also been determined. The CMC, α and Г_max, increase with increasing pH whereas A _min decreases.     

Synthesis and Self-Aggregation of a Hydroxyl-Functionalized Imidazolium-Based Ionic Liquid Surfactant in Aqueous Solution

This paper deals with the synthesis and self-aggregation of a hydroxyl-functionalized imidazolium-based ionic liquid (IL) surfactant, namely 1-hydroxyethyl-3-dodecylimidazolium chloride ([C₂OHC₁₂im]Cl). The molecular structure was confirmed by means of electrospray ionization mass spectrometry (ESI–MS), ¹H nuclear magnetic resonance (¹H NMR) and elemental analysis. Many important physicochemical parameters, such as the critical micelle concentration (CMC), the surface tension at CMC (γ_CMC), the adsorption efficiency (pC ₂₀), the surface pressure at CMC (Π_CMC), the maximum surface excess (Γ _m ), the minimum molecular cross-sectional area (A _min), the value of CMC/C ₂₀, the average number of aggregation (N _m ) and the micellar microenvironment polarity were determined by surface tension-concentration curves, fluorescence spectra, and electrical conductivity. The phenomena of the second CMC, the concentration dependence of N _m , and the critical average aggregation number (N _m,c) of imidazolium-based IL surfactants are reported for the first time in this paper.     

Polymeric surfactants for enhanced oil recovery. Part V: Prediction models for the effect of temperature and length of polyoxyethylene chain or hlb on surface and thermodynamic properties of some ethoxylated polymeric nonionics

Several equation models were investigated to find the relationship between temperature (T). number of ethylene oxide (EO) units (n) or the hydrophile-lipophile balance (HLB) and the surface and thermodynamic properties of some ethoxylated alkylphenol-formaldehyde polymeric nonionic surfactants. These properties include critical micelle concentration (CMC), free energy of micellization (ΔG_mic), surface tension at CMC (7_CMC), effectiveness (γ_CMC) and efficiency (pC₂₀) of surfactant to reduce the surface tension of water. The values of the ratio CMC/C_{2(π = 20)} were also considered. The linear multiple regression technique was employed to determine the parameters of the equations and to choose the best forms with the highest values of R² and F-ratio which reflect the goodness and the reliability of the fit.     

Undecanoic and 10-Undecenoic Acid-Based Amidobetaines and Amidoamine Oxides

Three types of undecanoic and 10-undecenoic acid-based surfactants were synthesized in the present work: amphoteric amidobetaines, cationic amidobetaine chlorides and nonionic amidoamine oxides. Structural characterizations of synthesized compounds were based on nuclear magnetic resonance (NMR) (¹H and ¹³C) and mass spectrometry. Surface properties, such as critical micelle concentration (CMC), surface tension at cmc (γ _cmc), efficiency of surface adsorption (pC20), surface excess (Γ_max) and minimum area per molecule (A _min) at the air–water interface, were determined by surface tension methods. Fluorescence probing techniques were also employed for the measurement of CMC, as well as steady state anisotropy (r) at the micellar core. The CMC of the studied surfactants follow the order: amidobetaine > amidobetaine chloride > amidoamine oxide. The influence of the terminal double bond in the hydrophobic alkyl chain on CMC was also assessed, and a significant increase in CMC was found due to the introduction of the double bond in the cases of amidobetaine chlorides and amidoamine oxides. These two types of surfactants showed higher rigidity at the micellar core compared to their corresponding unsaturated counterparts. However, such influence of unsaturation on the hydrophobic moiety was not observed in the case of amidobetaines. In all three types of surfactants, the saturated surfactant exhibited a lower γ _cmc and A _min, but higher Γ_max, r and pC20 compared to its unsaturated counterpart.     

Synthesis,Surface Activity,Thermodynamic Parameters,and Performance Evaluation of Branched Carboxylate Gemini Surfactants

Three novel carboxylate gemini surfactants (3C_ntaDA, n = 8, 10, and 12) were synthesized by two simple steps, and their structures were characterized using FT-IR and ¹H NMR. The surface activities of these surfactants were obtained from surface tension measurements at different temperatures, and the surface parameters containing the critical micelle concentration (CMC), surface tension (γ), minimum surface area per molecule ( A_min ), and maximum surface excess concentration ( Γ_max ) were obtained from surface tension measurements. The experimental results show that 3C_ntaDA surfactants have higher surface activities compared with the corresponding conventional surfactants. The thermodynamic parameters of the micellization process were investigated, and the calculated results show that it was an exothermic and spontaneous process. The emulsification and foam performance of these surfactants were also evaluated at different concentrations at 298.15 K.     

Surface Activity and Performance Properties of Gemini Salts of Linear Alkylbenzene Sulfonate in Aqueous Solution

Gemini salts of linear alkylbenzene sulfonate (LABS) were prepared by neutralization of sulfonic acid with a series of low-molecular-weight diamines in aqueous solution. The equilibrium surface activity of Gemini salts of LABS was determined by measuring the surface tension as a function of surfactant concentration to determine the critical micelle concentration (CMC), surface tension at the CMC (γ_CMC), and the area per molecule at the air-water interface (Ų). Electrical conductivity was measured as a function of surfactant concentration to determine the CMC and counterion binding. Dynamic surface tension was measured using a bubble pressure tensiometer to infer the rate at which the surfactant migrates to the air-water interface. Equilibrium interfacial tension against mineral oil was measured using a spinning drop tensiometer. Dynamic interfacial tension was measured using a drop volume tensiometer. The surface tension, CMC, and interfacial tension of Gemini salts of LABS decreased compared to monovalent organic and inorganic salts. The CMC decreases with increasing molecular weight of the diamine spacer group. Dynamic surface and interfacial tension of Gemini salts of LABS are lower than monovalent salts. The foam volume of Gemini salts of LABS was determined using a high shear blender test. The foam volume of Gemini salts of LABS is lower than monovalent salts and depends on the size of the spacer group. Hard-surface cleaning was measured using artificial soil applied to white Formica tiles. Soil removal was determined by optical reflectance as a function of abrasion cycles. Gemini salts of LABS show reduced hard-surface cleaning performance compared to monovalent salts. Detergency of different types of soils on cotton and polyester/cotton fabric was determined by optical reflectance measurements. Gemini salts of LABS show improved cleaning performance compared to monovalent salts. Cleaning performance increases with increasing molecular weight of the diamine spacer group. In situ neutralization of LABS with organic diamines is a simple and efficient way to prepare anionic Gemini surfactants for industrial scale applications.     

Effects of the Polypropylene Oxide Number on the Surface Properties of a Type of Extended Surfactant

The surface properties of 5 extended surfactant C_12–14P _mE₂S solutions in pure water and 0.1 M NaCl were investigated through surface tension and electrical conductivity measurements. The surface properties measured include the critical micelle concentration (CMC), critical surface tension (γ_cmc), maximum surface excess concentration (Γ_max), minimum area occupied per surfactant molecule (A_min), and efficiency in surface tension reduction (pC₂₀). The CMC values of the 5 surfactants decreased with increasing polypropylene oxide number (PON) and were higher than those obtained in 0.1 M NaCl. The Γ_max values showed a downward trend whereas the A_min values exhibited an upward trend with increasing PON without NaCl. The Γ_max values were higher and the A_min values were lower than those obtained without 0.1 M NaCl. The CMC values increased at elevated temperatures. The CMC values of C_12–14P₃E₂S, C_12–14P₅E₂S, and C_12–14P₈E₂S were similar but were markedly lower than those of C_12–14E₂S at different temperatures. When PON was less than 12, the log CMC value decreased linearly with increasing PON in the absence of salt, and the relationship between pC₂₀ and PON was linear. But in the presence of 0.1 M NaCl, the log CMC value decreased exponentially with increasing PON.     

Alkyl Xylosides: Physico‐Chemical Properties and Influence on Environmental Bacteria Cells

A group of four selected non‐ionic surfactants based on carbohydrates, namely octyl d ‐xyloside (C₈X), nonyl d ‐xyloside (C₉X), decyl d ‐xyloside (C₁₀X) and dodecyl d ‐xyloside (C₁₂X), have been investigated to accomplish a better understanding of their physico‐chemical properties as well as biological activities. The surface‐active properties, such as critical micelle concentration (CMC), emulsion and foam stability, the impact of the compounds on cell surface hydrophobicity and cell membrane permeability together with their toxicity on the selected bacterial strains have been determined as well. The studied group of surfactants showed high surface‐active properties allowing a decrease in the surface tension to values below 25 mN m^?1 for dodecyl d ‐xyloside at the CMC. The investigated compounds did not have any toxic influence on two Pseudomonas bacterial strains at concentrations below 25 mg L^?1. The studied long‐chain alkyl xylosides influenced both the cell inner membrane permeability and the cell surface hydrophobicity. Furthermore, the alkyl chain length, as well as the surfactant concentration, had a significant impact on the modifications of the cell surface properties. The tested non‐ionic surfactants exhibited strong surface‐active properties accompanied by the significant influence on growth and properties of Pseudomonas bacteria cells.     

Micellization and Adsorption Behaviors of New Reactive Polymerizable Surfactants Based on Modified Nonyl Phenol Ethoxylates

The synthesis and characterization of a series of polymerizable surfactants based on alkyl phenol ethoxylate backbone and carboxylic or anhydride chain ends were investigated. Surface activities of these polymerizable surfactants were investigated to correlate their structure and their performances. The new bifunctional surfmers were prepared by reacting polyoxyethylene 4-nonyl-2-propylene-phenol nonionic reactive surfactants with maleic anhydride. The chemical structure of the prepared surfactants was characterized by ¹³C and ¹H NMR analyses. The surface activities of the modified polymerizable surfactants were measured from the adsorption isotherm measurements which were determined from the relationship between the concentrations and surface tension of surfactants in aqueous medium at different temperatures. Critical micelle concentration (CMC) values were determined for water soluble surfactants. It was found that CMC decreases with the incorporation of the anhydride and acid groups in the chemical structure of polyoxyethylene 4-nonyl -2-propylene-phenol nonionic surfactant. surface-active parameters such as area per molecule at the interface (A _min), surface excess concentration (Γ_max) and the effectiveness of surface tension reduction (π_CMC) were measured from the adsorption isotherms of the modified surfactants. Some thermodynamic data for the adsorption process were calculated and discussed. The data indicated that the new surfmers are more reactive than the simple polyoxyethylene 4-nonyl-2-propylene-phenol and more adsorbed at interfaces. We have performed a preliminary experiment to explore the emulsification efficiency of the newly synthesized reactive surfactants in equal volume oil–water emulsions. Different emulsion types and stabilities were obtained.     

Synthesis and Study of the Surface Properties of Alkylnaphthalene and Alkylphenanthrene Sulfonates

Some alkylnaphthalene and alkylphenanthrene sulfonates were synthesized by means of a Wurtz–Fittig reaction. The HLB values for the prepared compounds were calculated, and the basic properties were studied in water at different temperatures, namely, 25, 35 and 45 °C. Through surface tension measurements, the following values were determined: the critical micelle concentration (CMC) and the surface tension at the CMC (γ_CMC). The following values were calculated: area per molecule at the CMC (A_CMC), standard free energy change of micellization (ΔG _mic), standard free energy of adsorption (ΔG _ad), and the efficiency of a surfactant in reducing surface tension (pC20). Furthermore, the partition coefficients of the synthesized compounds were also measured. The results show that n-alkylnaphthalene and n-alkylphenanthrene surfactants studied exhibit desirable properties that may be of value in some fields such as detergency. To confirm the detergency power of the prepared surfactants, some foam studies were performed.     

A Novel Zwitterionic Imidazolium-Based Ionic Liquid Surfactant: 1-Carboxymethyl-3-Dodecylimidazolium Inner Salt

A novel zwitterionic imidazolium-based ionic liquid (IL) surfactant, 1-carboxymethyl-3-dodecylimidazolium inner salt, was synthesized. The molecule structure was confirmed by means of electrospray ionization mass spectrometry, ¹H nuclear magnetic resonance and elemental analysis. The isoelectric point (pI) is 3.8 ± 0.1 at 35 ± 0.1 °C. The other important physicochemical parameters such as the critical micelle concentration (CMC), the surface tension at CMC (γ_CMC), the adsorption efficiency (pC ₂₀), the surface pressure at CMC (Π_CMC), the maximum surface excess (Γ_m), the minimum molecular cross-sectional area (A _min), the value of CMC/C ₂₀ and the average number of aggregation (N _m) were determined by surface tension and steady-state fluorescence probe methods, respectively.     

Synthesis and Surface Properties of Novel Carboxylic Ester-Containing Imidazolium-Based Zwitterionic Surfactants: Monoalkyl 2-(3-Methylimidazolium-1-yl) Succinate Inner Salts

A series of carboxylic ester‐containing imidazolium‐based zwitterionic surfactants, namely, monoalkyl 2‐(3‐methylimidazolium‐1‐yl) succinate inner salts (C_nMimSU, n = 8, 10, 12 and 14), have been synthesized. Their structures were confirmed by ¹H NMR, ¹³C NMR and FTIR. The typical physicochemical properties parameters such as isoelectric point, critical micelle concentration (CMC), surface tension at CMC (γ_CMC), surface pressure at CMC (Π_CMC), adsorption efficiency (pC₂₀), the maximum surface excess (Γ_m), the minimum molecular cross‐sectional area (A_min) and the value of CMC/C₂₀ were determined. The effect of the long‐chain length on the important physicochemical properties of C_nMimSU was studied. It is found that the surface activity of C_nMimSU is enhanced with the long‐chain length increases.