Synthesis and properties of ionic liquid-type Gemini imidazolium surfactants

A series of ionic liquid-type Gemini imidazolium surfactants with four-methylene spacer groups were synthesized ([C(n)-4-C(n)im]Br(2), n=10, 12, 14). The surface activity and thermodynamic properties of micellization between the Gemini imidazolium surfactants and their corresponding monomers ([C(n)mim]Br, n=10, 12, 14) were compared by means of surface tension and electrical conductivity measurements. The values of cmc, gamma(cmc), pc(20), Gamma(max), and A(min) derived from surface tension measurement at 25 degrees C suggest that the surface activity of [C(n)-4-C(n)im]Br(2) is higher than that of [C(n)mim]Br. While the thermodynamic parameters of micellization (DeltaG(m)(o), DeltaH(m)(o), DeltaS(m)(o)) derived from electrical conductivity indicate that the micellization of [C(n)-4-C(n)im]Br(2) is entropy-driven, aggregation of [C(n)mim]Br is entropy-driven at low temperature but enthalpy-driven at high temperature. Finally, the activation energy of conductance (E(a)) that is associated with the effective charge is also obtained for [C(n)-4-C(n)im]Br(2) and it is constant below the cmc, but it increases above the cmc.     

Conductivities, volumes, fluorescence, and aggregation behavior of ionic liquids [C4mim][BF4] and [C(n)mim]Br (n = 4, 6, 8, 10, 12) in aqueous solutions

Densities, conductivities, and polarity indexes of pyrene for aqueous solutions of a series of ionic liquids [C(n)mim]Br (n = 4, 6, 8, 10, 12) and [C4mim][BF4] have been determined at 298.15 K as a function of ionic liquid concentrations. It was shown that possible aggregation appeared for the ionic liquids in aqueous solutions except for [C4mim]Br. The critical aggregation concentration (CAC) of the ionic liquids, the ionization degree of aggregates (beta), the standard Gibbs energy of aggregation (Delta G(m)(o)), the limiting molar conductivity (Lambda(m)(o)), and the standard partial molar volume (V(m)(o)) for the ionic liquids were derived from the experimental data. The dependence of the CAC, Delta G(m)(o), Lambda(m)(o), and V(m)(o) on the length of the alkyl chain of the cations was examined. It was further suggested from volumetric data that a micelle was formed for [C8mim]Br, [C10mim]Br, and [C12mim]Br in aqueous solutions. Their apparent molar volumes at the critical micelle concentration (V Phi,CMC), apparent molar volumes in the micelle phase (V(Phi)(mic)), and the change of their apparent molar volume upon micellization (Delta V Phi,m) were calculated by application of the pseudophase model of micellization. In addition, the average aggregation number of [C(n)mim]Br (n = 8, 10, 12) has been determined by the steady-state fluorescence quenching technique, and predicted from a simple geometrical mode. It is found that the experimental values are in good agreement with the predicted ones.     

Effect of imidazolium-based ionic liquids on the aggregation behavior of twin-tailed cationic gemini surfactant in aqueous solution

Micellization behavior of the twin-tailed surfactants can be modulated by the addition of various modifiers. Ionic liquids (ILs) are one of them and are documented here. The beauty of these environmentally benign neoteric molecules lies in their structural versatility. Here, we have investigated the effect of three ILs: 1-butyl-3-methylimidazolium bromide ([C₄mim][Br]), 1-hexyl-3-methylimidazolium bromide ([C₆mim][Br]), and 1-octyl-3-methylimidazolium bromide ([C₈mim][Br]) on the aggregation and surface adsorption behavior of cationic gemini surfactant, bis(hexadecyldimethyl ammonium)propane dibromide (16-3-16) through experimentally measured electrical conductivities, surface tensions, and by spectral methods (UV-vis absorbance and fluorescence measurements). The main focus of the study is to observe the effect of added ILs on the critical micelle concentration (cmc), various surface parameters, aggregation number, and size of the aggregates of gemini surfactant. The results show that the more hydrophobic ILs, that is, [C₆mim][Br] and [C₈mim][Br] behave as electrolyte at lower concentration and cosurfactant at higher concentration, whereas moderately hydrophobic IL [C₄mim][Br] acts as an electrolyte at all concentration ranges studied. The modulating effects of ILs were also compared with conventional electrolyte (NaBr) at similar conditions.     

Aggregation behavior of long-chain N-aryl imidazolium bromide in aqueous solution

The aggregation behavior of three long-chain N-aryl imidazolium ionic liquids (ILs), 1-(2,4,6-trimethylphenyl)-3-alkylimidazolium bromide [C(n)pim]Br (n = 10, 12, and 14), in aqueous solutions was systematically explored by surface tension, electrical conductivity, and (1)H NMR. A lower critical micelle concentration (cmc) for the N-aryl imidazolium ILs is observed compared with that for 1,3-dialkylimidazolium ILs [C(n)mim]Br, indicating that the incorporation of the 2,4,6-trimethylphenyl group into a headgroup favors micellization. The enhanced π-π interactions among the adjacent 2,4,6-trimethylphenyl groups weaken the steric hindrance of headgroups and thus lead to a dense arrangement of [C(n)pim]Br molecules at the air-water interface. An analysis of the (1)H NMR spectra revealed that the introduced 2,4,6-trimethylphenyl group may slightly bend into the hydrophobic regions upon micellization. The micelle formation process for [C(n)pim]Br (n = 10, 12, and 14) was found to be enthalpy-driven in the investigated temperature range, which is attributed to the strong electrostatic self-repulsion of the headgroups and the counterions as well as the π-π interactions among headgroups. Strong, stable fluorescence properties are presented by the new N-aryl imidazolium ILs, indicating their potential application in the field of photochemistry.     

Aggregation of ionic liquids [C(n)mim]Br (n = 4, 6, 8, 10, 12) in D2O: a NMR study

Aqueous solutions of five ionic liquids (ILs) of the 1-n-alkyl-3-methylimidazolium bromide family, [C(n)mim]Br (n = 4, 6, 8, 10, 12), were investigated by NMR measurements at 298.2 K as a function of IL concentrations. Critical aggregation concentrations and aggregation numbers of these ILs were determined by 1H NMR except for [C4mim]Br in D2O. The effects of the alkyl chain length of the cations were examined on the aggregation behavior of the ILs. 1H NMR data of the solvent D2O were used to investigate the hydration of the ILs in D2O, and it was found that the ionic hydration and the cation-anion association or aggregation of the ILs offset each other. The microenvironment of different protons of cations of the ILs in the aggregates was probed by determining the spin-lattice relaxation rate (1/T1). It is suggested that the imidazolium rings in the aggregates are exposed to water and that the molecular motion of the aggregates is more restricted than that of the monomers of the ILs. Furthermore, a stair-like microscopic aggregation structure is suggested for the [C(n)mim]Br/D2O (n = 6, 8, 10) systems from 2-D 1H-1H NOESY measurements.     

Zwitterionic heterogemini surfactants containing ammonium and carboxylate headgroups. 1. Adsorption and micellization

Zwitterionic heterogemini surfactants with two hydrocarbon chains and two different hydrophilic groups, N,N-dimethyl-N-[2-(N'-alkyl-N'-beta-carboxypropanoylamino)ethyl]-1-alkylammonium bromides (2C(n)AmCa, where n represents the hydrocarbon chain lengths of 8, 10, 12, and 14), were synthesized by N,N-dimethylethylenediamine with alkyl bromide, followed by reaction with succinic anhydride. One of the hydrophilic groups is a carboxylate anion, and the other is an ammonium cation. Their physicochemical properties were characterized by measuring equilibrium and dynamic surface tension, fluorescence intensity of pyrene, and light-scattering intensity. A relationship between a logarithm of critical micelle concentration (cmc) and hydrocarbon chain length showed a linear decrease upon increasing chain length and then a departure from linearity at n = 14. This is due to the existence of premicellar aggregations at concentrations below the cmc for n = 14. The surface tension of 2C(n)AmCa reached 27-30 mN m(-1) at each cmc, indicating efficiencies typical of hydrocarbon chain surfactants. The adsorbing rate at the air/water interface became slow with an increase of the chain length. From the fluorescence intensity ratios of 373 and 384 nm using pyrene as a probe, for n = 8, 10, and 14, the pyrene was solubilized in surfactant micelles at around the cmc, whereas for n = 12 the pyrene was solubilized from a concentration of 10-fold the cmc. The scattering intensities by dynamic light scattering also increased from around these concentrations for each chain length, showing the formation of aggregates in solution.     

Aggregation behavior of aqueous solutions of ionic liquids

The aggregation behavior in aqueous solutions of three ionic liquids based on the 1-alkyl-3-methylimidazolium cation has been investigated by means of surface tension, conductivity, and small-angle neutron scattering (SANS) measurements. From analysis of the SANS data, models for the shapes and sizes of aggregates have been proposed: the short-chain 1-butyl-3-methylimidazolium tetrafluoroborate [C4mim] [BF4] system can be best modeled by treating it as a dispersion of polydisperse spherical aggregates that form above a critical aggregation concentration, whereas the 1-octyl-3-methylimidazolium iodide, [C8mim] [I], solutions can be modeled as a system of regularly sized near-spherical charged micelles that form above a critical micelle concentration. Solutions of 1-octyl-3-methylimidazolium chloride, [C8mim]-[Cl], display weak long-range ordering of possibly disklike particles culminating in the formation of structures with distinct long-range order at higher concentrations.     

新型Gemini咪唑表面活性剂的合成及表面性能

以2,2-双(溴甲基)-1,3-丙二醇为连接基合成了新型的连接基为枝状的Gemini咪唑表面活性剂2,4-二(溴化-3-烷基咪唑)-1,3-丙二醇([Cn-P-Cnim]Br2,n=10,12,14).产物经核磁共振氢谱(1H NMR)、红外(IR)光谱和元素分析等进行了分析,证明所得产物即为目标产物.通过表面张力法和电导法测量其表面活性并计算胶束形成热力学参数(ΔG m—0,ΔH m—0,ΔS m—0).结果表明,25℃时3种表面活性剂均具有很高的表面活性,胶束的形成是自发的熵驱动过程.     

Effect of a copolymer poly(4-styrenesufonic acid-co-maleic acid) sodium salt on aggregation behavior of surface active ionic liquid 1-tetradecyl-3-methylimidazolium bromide and structurally similar conventional surfactant tetradecyltrimethylammonium bromide in aqueous media

The complex formation of anionic copolymer poly(4-styrenesufonic acid-co-maleic acid) sodium salt (PSSA-co-MA) with surfactant tetradecyltrimethylammonium bromide (TTAB) and surface active ionic liquid (SAIL) 1-tetradecyl-3-methylimidazolium bromide ([C₁₄mim][Br]) has been studied in aqueous media by utilizing various techniques such as tensiometry, conductometry and fluorimetry. Conductometric and tensiometric curve of all the investigated systems demonstrate four break points corresponding to four transition states. All the thermodynamic and surface properties of surfactant-polyelectrolyte systems have been determined by conductance and surface tension measurements respectively. The value of cmc decreases with increasing the concentration of polyelectrolyte for studied systems. But it has been observed that, the lowering in cmc values is more in [C₁₄mim][Br]-PSSA-co-MA system than TTAB-PSSA-co-MA system, although the differences in cmc are not much significant. The lowering in cmc of [C₁₄mim][Br]-PSSA-co-MA system shows that ionic attractions between cationic head group [C₁₄mim]⁺ and anionic parts (SO₃^? and COOH), are stronger than those in TTA⁺ and anionic parts (SO₃^? and COOH). The results indicated that the [C₁₄mim][Br]-PSSA-co-MA complexes are comparatively more surface active than TTAB-PSSA-co-MA complexes. The fluorescence probe behaviour also confirms cmc value and provides aggregation number (N_agg). Finally all the findings of [C₁₄mim][Br] and TTAB have been compared.     

Aggregation of quaternary ammonium gemini surfactants C12-s-C12.2Br in n-heptane/n-hexanol solution: effect of the spacer chains on the critical reverse micelle concentrations

The critical reverse micelle concentrations of C(12)-s-C(12).2Br (s=2,3,4,5,6,8,12) in n-heptane/n-hexanol solutions, cmc(I)s, have been determined by absorption spectrum method using iodine as probe. The values of cmc(I)s are smaller than those of the critical micelle concentrations (cmc(aq)s) in aqueous solution and reach a maximum at s=4, which is similar to the variation of cmc(aq) with s. The variation of cmc(I) with s is attributed to the alteration in the spacer chain conformation, i.e. when the spacer is short enough, it may adopt stretch configuration and when the spacer is long, it tends to bend towards the continuous oil phase to achieve a more densely packing of the quaternary ammonium heads on the surface of the core.     

Equilibrium and dynamic surface tension properties of partially fluorinated quaternary ammonium salt gemini surfactants

The equilibrium and dynamic surface tension properties of a partially fluorinated quaternary ammonium salt gemini surfactant 1,2-bis[dimethyl-(3-perfluoroalkyl-2-hydroxypropyl)ammonium]ethane bromide (C(n)(F)C3-2-C3C(n)F, where n represents fluorocarbon chain lengths of 4, 6, and 8) were investigated, and the effects of the fluorocarbon chain length and the number of chains on them were discussed. The plot of the logarithm of the critical micelle concentration (cmc) against the fluorocarbon chain length for C(n)(F)C3-2-C3C(n)F showed a linear decrease with an increase in chain length. On the basis of the slope of this plot, it was found that the variation in cmc with respect to the chain length is large for fluorinated gemini surfactants. The surface tension at the cmc decreased significantly; this surface tension value is lower than that of conventional fluorinated monomeric surfactants. In particular, the lowest value was 13.7 mN m(-1) for n = 8. Furthermore, it was confirmed that the kinetics of adsorption at the interface decrease with an increase in the fluorocarbon chain length and the concentration.     

全氟壬烯氧基苯磺酸钠与烷基季铵盐的相互作用

通过六氟丙烯三聚体(全氟壬烯)氧基苯磺酸钠(C₉F₁₇OC₆H₄SO₃Na, OBS)与阳离子碳氢表面活性剂C_nNR[C_nH_2n+1N(CH₃)₃Br, C_nNM, n=8, 10和C_nH_2n+1N(CH₂CH₃)₃Br, C_nNE, n=8, 10, 12]复配, 研究了OBS与C_nNR的摩尔比、 C_nNR疏水链长及C_nNR亲水基团大小对此类阴、 阳离子碳氟-碳氢表面活性剂混合体系的临界胶束浓度(cmc)、 最低表面张力(γ_cmc)、 总饱和吸附量(Γ_tm)及极限分子面积(A_min)的影响. 结果表明, 通过与C_nNR复配, OBS的cmc和γ_cmc均大幅下降, 达到了全面增效的结果. 不同摩尔比的OBS-C₈NE混合体系中, 摩尔比为1:1时表面活性最好, cmc和γ_cmc均最小; 偏离等摩尔比时, OBS过量时混合体系的cmc小于C₈NE过量时混合体系的cmc, 但γ_cmc相差不大. 与单体系相比, OBS-C₈NE混合体系的Γ_tm明显增大、 A_min明显变小. OBS与不同疏水链长的C_nNE复配时, cmc的变化规律为C₈NE>C₁₀NE>C₁₂NE, 表明C_nNE疏水链长的增加能降低混合体系的cmc. 通过比较C_nNM和C_nNE(n=8, 10)的表面活性发现, 改变混合体系中C_nNR的亲水基团大小对混合体系的表面活性无明显影响.     

Effect of additives on the surface active and morphological features of 1-octyl-3-methylimidazolium halide aggregates in aqueous media

The influence of two salts as additives namely sodium chloride and sodium sulphate and a nonelectrolyte, 2-butoxyethanol on surface chemical and aggregation characteristics of ionic liquids (IL) of 1-octyl-3-methylimidazolium chloride, [C₈mim][Cl], 1-octyl-3-methylimidazolium bromide, [C₈mim][Br], and 1-octyl-3-methylimidazolium iodide, [C₈mim][I] in aqueous media were monitored through surface tension and small angle neutron scattering measurements. The addition of salts drastically decreased the critical aggregation concentration (CAC) and increased the area per adsorbed IL molecule. The co-ions of salts modify the surface of IL molecules and aggregates through various interactions such as charge neutralization, specific interactions and dehydration The results obtained by analyzing the SANS curves in the whole Q range showed that the oblate ellipsoidal shape of the aggregates of ionic liquids is un-altered upon the addition of additives. However the additives facilitate the growth of the aggregates in to microstructures with cubic packing at high salt concentrations.     

Separation of ternary systems of hydrophilic ionic liquid with miscible organic compounds by RPLC with refractive index detection

A rapid and simple analytical method was developed for the simultaneous and quantitative determination and separation of hydrophilic imidazolium ionic liquids (ILs) (1-butyl-3-methylimidazolium chloride, [C(4)mim]Cl; 1-hexyl-3-methylimidazolium chloride, [C(6)mim]Cl; 1-octyl-3-methylimidazolium chloride, [C(8)mim]Cl; 1-allyl-3-methylimidazolium chloride, [Amim]Cl; or 1-allyl-3-methylimidazolium bromide, [Amim]Br) with miscible ethyl acetate and EtOH and their mixtures using reverse phase liquid chromatography coupled with refractive index detection (RPLC-RI). The influence of 60 to 100% (volume percentage) methanol in the mobile phase on the IL systems ([C(4)mim]Cl, [C(6)mim]Cl, [C(8)mim]Cl, [Amim]Br, or [Amim]Cl)-ethyl acetate-EtOH was investigated. The optimum mobile phase for the system [C(8)mim]Cl-ethyl acetate-EtOH, [C(4)mim]Cl-ethyl acetate-EtOH, [Amim]Br-ethyl acetate-EtOH and [Amim]Cl-ethyl acetate-EtOH was methanol/water (60:40, v/v), and methanol/water (70:30, v/v) for [C(6)mim]Cl-ethyl acetate-EtOH. Under optimum mobile phase conditions for each system, the RSD of the retention time ranged from 0.02 to 0.04%, and the RSDs of the peak area percent ranged from 0.23 to 1.85%, which showed good reproducibility of the RPLC-RI method. The RPLC-RI method can determine IL, ethyl acetate, and EtOH simultaneously in 5 min, and the analytes, especially IL, can be eluted completely. The results show that the RPLC-RI method can be used to separate and determine ILs in mixtures with organic compounds simultaneously and quantitatively.     

不等链长的碳氟、碳氢正负离子表面活性剂混合体系的表面活性

研究了全氟辛酸钠与溴化十四烷基三甲铵混合水溶液的表面活性. 测定了不同比例混合物水溶液的表面张力-浓度曲线, 得出临界胶团浓度(cmc)及监 界胶团浓度时的溶液表面张力(γcmc)值. 应用Gibbs吸附公式及吸附层中两表面活性剂分子相互作用参数法求出表面总吸附量、吸附层组成及两表面活性剂分别吸附量等. 指示此吸附层具有多分子层性质. 这可能是碳氢、碳氟正负离子混合体系的特点.     

C12-2-En-C12•2Br与SDS混合水溶液的胶团化研究

与[C12H25N＋(CH3)2CH2]2•2Br－(简记为C12-2-C12•2Br)/ C12H25SO4Na(SDS)混合水溶液相比,随着联接链上乙氧基团(E)数目增加,[C12H25N＋(CH3)2]2C2H4(OC2H4)n•2Br－(简记为C12-2-En-C12•2Br, n=2,3)与SDS混合水溶液澄清区域明显增大. C12-2-E3-C12•2Br/SDS混合胶团化过程中二组分产生了协同效应,理论预测在澄清区域所能达到的最小临界胶团总浓度(cmcT,min)= 0.0339 mmol•L－1,对应的SDS在溶液体相中的摩尔分数(x2*)=0.447.当水溶液体相中SDS摩尔分数(x2)=0.5时,混合胶团总聚集数(NT)=36,混合胶团中SDS的摩尔分数(x2M)=0.43.     

Transport Properties of Aqueous Solutions of Alkyltrimethylammonium Bromide Surfactants at 25 degrees C

Intradiffusion coefficients, D, of n-alkyltrimethylammonium bromides [CH(3)-(CH(2))(n-1)-N(CH(3))(3)Br, C(n)TAB] (n=6, 8, 10, 12) in mixtures with heavy water were measured by the PGSE-NMR technique at 25 degrees C. The experimental data permitted evaluation of the influence of the alkyl chain length on the surfactant self-aggregation process. For all the surfactants considered, the D trend showed a slope change corresponding to the critical micellar composition (cmc). In the premicellar composition range, D decreased linearly with the square root of the surfactant molality. The D values extrapolated at infinite dilution were related to the limiting mutual diffusion coefficients, determined through the Taylor dispersion technique. In the micellar composition range, solubilized tetramethylsilane (TMS) molecules were used to determine the micelle intradiffusion coefficient, D(M), from which the aggregate radii and the aggregation numbers were obtained. The decreasing trend of D(M) with increasing surfactant molality was interpreted in terms of interparticle electrostatic repulsion. D(M) values allowed evaluation of the Gouy-Chapman layer thickness. The solvent intradiffusion coefficient in the heavy water-C(n)TAB mixtures, D(w), was also measured. It decreased with increasing surfactant molality. For n=8, 10, 12 the D(w) trend presented a slope change at the cmc, which could be ascribed to the strong decrease in hydration of surfactant molecules upon micellization. Because of its short hydrophobic tail, C(6)TAB exhibited peculiar aggregation behavior. Its cmc, which is poorly marked, is lower than the value predicted by extrapolating the cmc values obtained for the other terms of the series. The C(6)TAB aggregates do not solubilize TMS molecules; the estimated aggregation number is extremely low ( approximately 3). Finally, no abrupt slope change in the solvent intradiffusion coefficient trend was detected. This evidence suggests that C(6)TAB molecules do not micellize in aqueous solution, but form trimers in which the surfactant hydrophobic tails are not hidden from contact with water molecules. Copyright 2001 Academic Press.     

Synergic effects of imidazolium ionic liquids on P123 mixed micelles for inducing micro/mesoporous materials

A series of micro/mesoporous silica composites were synthesized with P123 and imidazolium ILs ([C(n)mim]X) as the co-templates. [C(n)mim]X showed notable synergic interaction with P123. By changing the alkyl chain length n in methylimidazolium, ring-like micropores were observed in the wall of the mesoporous materials when n = 4. While increasing n to 10, micropores and mesopores were found in different separated regions. Various anions of Cl(-), Br(-), and BF(4)(-) of ILs have little effect on the aggregation behavior of P123/C4X mixed micelles. The strong hydrogen bonding effect of BF(4)(-) has resulted in the ordered mesoporous channels with numerous micropores in the wall at a low temperature of 313 K. Hydrophobic C4PF(6) can only be solubilized in the core of P123 micelles, which resulted in the swelling of P123/C4PF(6) mixed aggregates and the ordered hexagonal porous silica materials at 313 K. The fundamental understanding of the synergic interaction and formation mechanisms of various porous silica materials can provide a general convenient way toward a rational design and synthesis of the micro/mesoporous composites.     

两相催化体系中双子表面活性剂对1-十二烯氢甲酰化反应的促进作用

报道了水溶性铑膦配合物组成的复合催化体系催化1-十二烯氢甲酰化反应中,双子表面活性剂[二溴化-(N,N,N′,N′-四甲基)-N,N′-二(十六烷基)-乙二铵]形成胶束的助催化作用.结果表明,在水/有机两相中,双子表面活性剂比单链表面活性剂CTAB具有更好加速催化反应的作用,并使烯烃氢甲酰化的区域选择性显著提高.这归因于双子表面活性剂有较低的cmc,可形成更加紧密规整的胶束结构,有利于增溶在胶束中的烯烃与铑催化剂配位和生成正构醛.     

Study on the Conductivities of Pure and Aqueous Bromide-Based Ionic Liquids at Different Temperatures

Electrical conductivities were measured for the pure ionic liquids [C₆mim][Br] (1-hexyl-3-methylimidazolium bromide) and [C₈mim][Br] (1-octyl-3-methylimidazolium bromide) at 0.1 MPa from 293.15 to 333.15 K. Conductivity measurements were also made for the binary water + [C₆mim][Br] and water + [C₈mim][Br] systems and their ternary water + [C₆mim][Br] + [C₈mim][Br] system at 0.1 MPa and 293.15, 298.15, and 303.15 K. The conductivity data of the pure ionic liquids were correlated by the VFT (Vogel-Tamman-Fulcher) equation, and the fitting parameters and mean absolute deviations were determined. New explanations are presented for the molality-dependent behavior of the conductivity of the binary water + [C₆mim][Br] and water + [C₈mim][Br] systems. The generalized Young’s rule and the semi-ideal solution theory for conductivity were used to predict the conductivities of the ternary water + [C₆mim][Br] + [C₈mim][Br] system from the conductivities of its corresponding binary water + [C₆mim][Br] and water + [C₈mim][Br] subsystems. The predictions are in good agreement with the measured values.