Impact of micelles on the biocidal efficiency in a diesel–water interface

Biodegradation occurs in the diesel/water interface in petroleum product pipelines. The microbial contamination can result in inhibitor/fuel degradation, leading to unacceptable levels of turbidity, filter plugging, storage tank corrosion and stored product souring. Therefore, selection of the biocide/inhibitor plays an important role in the transportation of petroleum products through pipelines. Three biocides (cationic and nonionic) were employed to study the biodegradation in a diesel‐water interface. The biocidal efficiency against degradation of diesel was examined by employing Fourier‐transform infrared (FTIR) spectroscopy, nuclear magnetic resonance (NMR) spectroscopy and gas chromatography mass spectrometry (GC‐MS) techniques. Bronopol (2‐bromo‐2‐nitro‐propane‐1, 3‐diol) was found to have higher bactericidal efficiency than N‐cetyl‐N,N, N‐trimethyl ammonium bromide (CTAB) and cetyl pyridinum bromide (CPB). But the cationic biocides (CTAB and CPB) showed good biocidal efficiency at the interface. The data are explained in terms of a model that postulates the formation of a ‘micelle’ at the diesel‐water interface. Copyright © 2007 John Wiley & Sons, Ltd.     

The analysis of serum effects on structure, size and toxicity of DDAB-DOPE and DC-Chol-DOPE lipoplexes contributes to explain their different transfection efficiency

The effect of serum on structural properties of dimethyl-dioctadecyl-ammonium bromide (DDAB)–1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) liposomes and DDAB–DOPE/DNA lipoplexes has been investigated by energy dispersive X-ray diffraction (EDXD) technique, at different cationic lipid/DNA weight ratios (ρ). The role of serum on the size of lipoplexes has also been studied by dynamic light scattering. Lipoplex transfection efficiency (TE) as a function of ρ, and lipoplex toxicity to C6 rat glioma cells have been evaluated in Dulbecco's Modified Eagle Medium (DMEM) with and without serum. A multi-parametric analysis concerning the role of size, structure and cytotoxicity on transfection efficiency contributes to explain the experimental observation that 3β-[N-(N′,N′-dimethylaminoethane)carbamoyl]-cholesterol (DC-Chol)–DOPE/DNA transfect C6 cells better than DDAB–DOPE/DNA lipoplexes.     

The analysis of serum effects on structure,size and toxicity of DDAB–DOPE and DC-Chol–DOPE lipoplexes contributes to explain their different transfection efficiency

The effect of serum on structural properties of dimethyl-dioctadecyl-ammonium bromide (DDAB)–1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) liposomes and DDAB–DOPE/DNA lipoplexes has been investigated by energy dispersive X-ray diffraction (EDXD) technique, at different cationic lipid/DNA weight ratios (ρ). The role of serum on the size of lipoplexes has also been studied by dynamic light scattering. Lipoplex transfection efficiency (TE) as a function of ρ, and lipoplex toxicity to C6 rat glioma cells have been evaluated in Dulbecco's Modified Eagle Medium (DMEM) with and without serum. A multi-parametric analysis concerning the role of size, structure and cytotoxicity on transfection efficiency contributes to explain the experimental observation that 3β-[N-(N′,N′-dimethylaminoethane)carbamoyl]-cholesterol (DC-Chol)–DOPE/DNA transfect C6 cells better than DDAB–DOPE/DNA lipoplexes.     

Correlation between surface free energy of quartz and its wettability by aqueous solutions of nonionic, anionic and cationic surfactants

The measurements of the advancing contact angle for water, glycerol, diiodomethane and aqueous solutions of Triton X-100 (TX-100), Triton X-165 (TX-165), sodium dodecyl sulfate (SDDS), sodium hexadecyl sulfonate (SHDS), cetyltrimethylammonium bromide (CTAB) and cetylpyridinium bromide (CPyB) on quartz surface were carried out. On the basis of the contact angles values obtained for water, glycerol and diiodomethane the values of the Lifshitz–van der Waals component and electron-acceptor and electron-donor parameters of the acid–base component of the surface free energy of quartz were determined. The determined components and parameters of the quartz surface free energy were used for interpretation of the influence of nonionic, anionic and cationic surfactants on the wettability of the quartz. From obtained results it was appeared that the wettability of quartz by nonionic and anionic surfactants practically does not depend on the surfactants concentration in the range corresponding to their unsaturated monolayer at water–air interface and that there is linear dependence between adhesional and surface tension of aqueous solution of these surfactants. This dependence for TX-100, TX-165, SDDS and SHDS can be expressed by lines which slopes are positive. This slope and components of quartz surface free energy indicate that the interaction between the water molecules and quartz surface might be stronger than those between the quartz and surfactants molecules. So, the surface excess of surfactants concentration at the quartz–water interface is probably negative, and the possibility of surfactants to adsorb at the quartz/water film–water interface is higher than at the quartz–water interface. This conclusion is confirmed by the values of the adhesion work of “pure” surfactants, aqueous solutions of surfactants and water to quartz surface. In the case of the cationic surfactants the relationship between adhesional and surface tension is more complicated than that for nonionic and anionic surfactants and indicates that the relationship between the adsorption of the cationic surfactant at water–air and quartz–water interface depends on the concentration of the surfactants in the bulk phase.     

Structural behaviour of mixed cationic surfactant micelles: a small-angle neutron scattering study

Self-assembly in mixtures of two single-chain cationic surfactants, with different tail lengths (CTAB and DTAB) as well as of a single-chain (DTAB) and a double-chain (DDAB) cationic surfactant, with identical tail lengths, have been investigated with small-angle neutron scattering (SANS) and rationalised in terms of bending elasticity properties. The growth behaviour of micelles with respect to surfactant composition appears completely different in the two surfactant mixtures. DTAB form small oblate spheroidal micelles in presence of [NaBr] = 0.1 M that transform into prolate spheroidal mixed CTAB/DTAB micelles upon adding moderate amounts of CTAB, so as to give a mole fraction y = 0.20 in solution. Most unexpectedly, upon further addition of CTAB the mixed CTAB/DTAB micelles grow with an almost equal rate in both length and width directions to form tablets. In contrast to this behaviour, mixed DDAB/DTAB micelles grow virtually exclusively in the length direction, in presence of [NaBr] = 0.1 M, to form elongated ellipsoidal (tablet-shaped) and subsequently long wormlike micelles as the fraction of DDAB in the micelles increases. Mixed DDAB/DTAB micelles grow to become as long as 2000 Å before an abrupt transition to large bilayer structures occurs. This means that the micelles are much longer at the micelle-to-bilayer transition as compared to the same mixture in absence of added salt. It is found that the point of transition from micelles to bilayers is significantly shifted towards higher fractions of aggregated DTAB as an appreciable amount of salt is added to DDAB/DTAB mixtures, indicating a considerable reduction of the spontaneous curvature with an increasing [NaBr]. By means of deducing the various bending elasticity constants from our experimental results, according to a novel approach by ours, we are able to conclude that the different growth behaviours appear as a consequence of a considerably lower bending rigidity, as well as higher saddle-splay constant, for DDAB/DTAB surfactant mixtures in presence of [NaBr] = 0.1 M, as compared to mixtures of CTAB/DTAB in [NaBr] = 0.1 M and DDAB/DTAB in absence of added salt.     

Counterion Nature and Alkylammonium Halide Adsorption Thermodynamics

Two surfactants were synthesized by reacting hydrogen halides (hydrogen chloride and hydrogen bromide) with 1-dodecylamine. The resultant cationic surfactants, 1-dodecylammonium chloride (DDAC) and 1-dodecylammonium bromide (DDAB), were characterized by NMR spectrometry and FTIR spectroscopy and data related to their adsorption at the fluid liquid/gas interface were obtained employing bubble surface tensiometry, in pure water and in HCl 0.1 M. Data did not fit well to Langmuir isotherm but Frumkin isotherm did adequately describe to process of adsorption. Adsorption isotherms, as well as data related to critical micelle concentration, CMC, indicated that in HCl 0.1 M, the presence of electrolytes and a common ion to DDAC decreased chloride solvation, changing surface packing and adsorption profile for this surfactant.     

Synthesis of highly water soluble C60 end‐capped vinyl ether oligomers with well‐defined structure

Highly water soluble [60]fullerene (C₆₀) end‐capped vinyl ether (VE) oligomers with well‐defined structure were synthesized by living cationic polymerization technique. The addition reaction between 1‐octynylfulleride anion and oligomeric cationic species of VEs with pendant acetoxyl or malonic ester functions afforded the precursor C₆₀ end‐capped oligomers. The living VE oligomers were prepared by living cationic polymerization of diethyl 2‐(vinyloxy)ethylmalonate (VOEM) and 2‐acetoxyethyl vinyl ether (AcOVE) by the CH₃CH(OR)Cl/ZnI₂ [R = CH₂CH₂OCOCH₃ and CH₂CH₂CH(COOEt)₂, respectively] initiating system. The precursors were obtained as dark brown gummy solid in 33 and 72% yield for AcOVE and VOEM, respectively. UV‐vis and ¹³C NMR spectroscopy indicated the formation of 1,2‐disubstituted dihydrofullerene derivatives. Hydrolysis of the precursors proceeded quantitatively to give the water‐soluble C₆₀ end‐capped oligomers having oligo(sodium 2‐vinyloxyethylmalonate) [oligo(VOEMNa)] and oligo(2‐hydroxyethyl vinyl ether) [oligo(HOVE)] moieties. Solubility measurements revealed the water‐soluble C₆₀ end‐capped oligomer with oligo(VOEMNa) chain to have the excellent aqueous solubility compared to that of the water‐soluble C₆₀ derivatives thus far known; the maximum solubility in water is 96.6 mg/mL, which corresponds to 25.9 mg/mL of the C₆₀ moiety. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3578–3585, 2000     

Cationic double-chained surfactant as pseudostationary phase in micellar electrokinetic capillary chromatography for drug separations

The cationic double-chained surfactant didodecyldimethylammonium bromide (DDAB) was used as pseudostationary phase (PSP) in micellar electrokinetic capillary chromatography (MEKC). Its performance on the three kinds of drugs, i.e., basic, acidic, and neutral drugs, was systematically investigated. Nicotine, cotinine, caffeine, lidocaine, and procaine were selected as the model basic drugs. Good baseline separation and high efficiency were obtained under the optimal separation condition that consisted of 50mM phosphate (pH 4.0) and 0.08 mM DDAB. Three basic phenylenediamine isomers can also be well separated with DDAB in buffer. In addition, DDAB can form cationic bilayer on the capillary wall, thus the wall adsorption of basic analytes was greatly suppressed. Compared with commonly used CTAB, the separation of basic drugs was significantly improved with a much lower amount of DDAB present in the buffer. The DDAB-involved MEKC also showed superiority to CTAB upon the separation of acidic drugs, amoxicillin and ampicillin. In the case of neutral compounds, a good separation of resorcinol, 1-naphthol and 2-naphthol was achieved with 0.1mM DDAB and 30% (v/v) acetonitrile (ACN) present in buffer. Hence, it was concluded that the double-chained cationic surfactant DDAB can be a good substitute for traditional single-chained surfactant CTAB in MEKC.     

XPS and TDS study of CO interaction with Pd–AlOx systems

The metal–substrate and metal–metal interactions (MSI, MMI) represent important effects determining the properties of supported catalysts, gas sensors and gettering alloys. We investigated the MSI and MMI effects by the X-ray photoelectron spectroscopy (XPS) and temperature programmed desorption (TPD) in the case of Pd films deposited on Al₂O₃ and Al substrates. The study shows that the particle-size dependent metal–substrate interaction plays an important role in CO–Pd chemisorption, namely, in the case of “aluminium rich” Pd–aluminium oxide interface. CO chemisorption exhibits a low-temperature desorption feature at 360 K characteristic for Pd–Al and very small Pd particles. The MSI is explained by the formation of a Pd–Al intermetallic interface exhibiting a strong bimetallic Pd–Al interaction.     

Assembly of layer-by-layer films of electroactive hemoglobin and surfactant didodecyldimethylammonium bromide

When a solid substrate with negative surface charges was placed in an aqueous didodecyldimethylammonium bromide (DDAB) vesicle dispersion, the cationic surfactant DDAB with two hydrocarbon chains could be assembled into the biomembrane-like tail-to-tail double-layer structure on the solid surface with the positively charged head groups toward outside, making the surface charge reverse from negative to positive. After the solid substrate with DDAB was immersed in a hemoglobin (Hb) solution at pH 9.0, the negatively charged Hb was adsorbed on the surface of DDAB layer by electrostatic attraction, forming a DDAB/Hb film. By repeating this adsorption cycle, the {DDAB/Hb}(n) layer-by-layer films were assembled on solid surfaces, which was confirmed by UV-vis spectroscopy, quartz crystal microbalance (QCM), and cyclic voltammetry (CV). The stable {DDAB/Hb}(n) films assembled on pyrolytic graphite (PG) electrodes showed two pairs of nearly reversible redox peaks at about -0.22 and -1.14 V vs SCE in pH 7.0 buffers, characteristic of the Hb heme Fe(III)/Fe(II) and Fe(II)/Fe(I) redox couples, respectively. The direct electrochemistry of Hb in the films could be used to electrocatalyze reduction of various substrates. UV-vis and IR spectroscopic results and comparison experiments with {DDAB/hemin}(n) films indicate that Hb in the {DDAB/Hb}(n) films essentially retains its native structure. Atomic force microscopy (AFM) was used to characterize the morphology of the films with different outermost layers.     

Microemulsions with Didodecyldimethylammonium Bromide Studied by Neutron Contrast Variation

The structure of water-in-oil microemulsion droplets, stabilized by didodecyldimethylammonium bromide (DDAB), has been investigated by small-angle neutron scattering (SANS). Detailed information about the curved surfactant film has been obtained by selectively deuterating the water, DDAB, and cyclohexane components. For each surfactanth-DDAB andd-DDAB and concentration, three sets of complementary neutron contrast data were analyzed together in terms of a Schultz distribution of core–shell particles. The modeling was consistent with a simple liquid-like surfactant layer, of density 0.80 g cm⁻³, with no evidence for any solvent penetration. This film thickness was found to be 11–12 Å, about 70% of an all-transC₁₂chain length. At the water interface the area per head was 56–61 Ų, while for the alkyl chains at the outer surface it was 90–125 Ų(15–30% lower than that for a truncated cone molecular configuration). The cyclohexane–water interfacial tensions γ_o/w, measured by surface light scattering, were used along with the droplet polydispersities to find that the rigidity of the DDAB film, 2K+ is close to 1.0k_BT. This means that rather than acting as an effective parameter in the SANS analysis, the polydispersity is a natural consequence of the film rigidity. These results show that the film bending energy model accounts well for the behavior of such DDAB microemulsions.     

Characterization and Aggregation Behaviors of Mixed DDAB/SDS Solution With and Without Poly(4-styrenesulfonic Acid-Co-Maleic Acid) Sodium

Synthetic vesicles are formed by cationic and anionic surfactants, didodecyldimethylammonium bromide (DDAB), and sodium dodecylsulfate (SDS). The morphology, size, and aqueous properties of cationic/anionic mixtures are investigated at various molar ratios between cationic and anionic surfactants. The charged vesicular dispersions made of DDAB/SDS are contacted or mixed with negatively charged polyelectrolyte, poly(4-styrenesulfonic acid-co-maleic acid) sodium (PSSAMA), to form complexes. Depending on DDAB/SDS molar ratio or PSSAMA/vesicle charge ratio, complexes flocculation or precipitation occur. Characterization of the cationic/anionic vesicles or complexes formed by the catanionic vesicles and polyelectrolytes is performed by transmission electron microscope (TEM), dynamic light scattering (DLS), conductivity, turbidity, and zeta potential measurements. The size, stability, and the surface charge on the mixed cationic/anionic vesicles or complexes are determined.     

Solubilization and conformational behavior of Zein in aqueous solution of dodecyldimethylethylammonium bromide (DDAB)

The solubilization and conformational behavior of Zein in the presence of cationic surfactant, dodecyldimethylethylammonium bromide (DDAB) have been studied. The colloidal properties of DDAB in the absence and presence of Zein have also been investigated using physico-chemical and spectroscopy methods. The surfactant appears to bind to Zein at concentrations below the critical micelle concentration (cmc) and the binding becomes weaker at concentrations above the cmc. The interaction between DDAB and Zein depends on the chemical structure and molecular parameters (conformation, molar mass, charge) of the protein. The schematic sketches of the molecular mechanisms of the complex formation between like-charged proteins and surfactants have been proposed.     

Surfactant dependent morphology of polymeric capsules of perfluorooctyl bromide: influence of polymer adsorption at the dichloromethane-water interface

In a strategy to develop more stable ultrasound contrast agents (UCAs), we have designed a process to obtain nano/microcapsules with a single core of liquid perfluorocarbon within a biodegradable polymeric shell of homogeneous thickness. During the optimization of perfluorooctyl bromide (PFOB) encapsulation by solvent emulsion-evaporation, a marked influence of surfactants has been observed. While sodium cholate leads to spherical capsules of homogeneous thickness, sodium taurocholate induces to the formation of “acorn”-particles with one hemisphere of PFOB and another one of PLGA, and polyvinyl alcohol is responsible for the coexistence of both morphologies. Whereas the theoretical model proposed by Torza and Mason [J. Colloid Interface Sci. 33 (1970) 67] fails to predict the observed morphologies, microscopic observations of the evaporation and interfacial tension measurements provide an insight into the mechanism of formation of these structures. Most probably, there is a competition between PLGA and the surfactant stabilizing the emulsion at the dichloromethane–water interface. If PLGA is able to adsorb at the interface, the core–shell morphology is obtained, otherwise the acorn morphology is preferentially formed. When the surfactant rearrangement at the interface is long (>30 min), a coexistence of morphologies can be obtained.     

Competitive Self and Induced Aggregation of Calix[4]arene Ethers and Their Interaction with Pinacyanol Chloride and Methylene Blue in Nonaqueous Media

Long chain calix[4]arene ethers have been examined for aggregation in nonaqueous solvents by using UV-vis molecular absorbance spectroscopy. It has been observed that tetraalkylated (alkyl = hexadecyl and octadecyl, respectively) calix[4]arene ethers tend to aggregate in chloroform and tetrahydrofuran, possibly via π–π stacking interactions of the phenyl moieties, and the aggregation process appears to be facilitated by the alkyl chains. The analogous dialkylated compounds do not show any self-aggregation, plausibly due to strong hydrogen bonding between the –OH and the –O– of calix aryl ether which seems to disrupt the aggregation process. Addition of the anionic surfactant sodium dodecylsulfate (SDS) appears to hinder the aggregation process in nonpolar chloroform but the same surfactant facilitates aggregation in the polar tetrahydrofuran. The cationic surfactant (cetyltrimethyl ammonium bromide) and the nonionic surfactant (Brij-35) have no effect on this aggregation process. Unexpectedly, SDS induces aggregation of dialkylated calix[4]arene ethers in chloroform. It has been observed that the aggregated form of the tetraalkylated calix[4]arene ethers tend to increase the dimerization efficiency of cationic dyes (pinacyanol chloride and methylene blue) in chloroform.     

Researches on 2, 1, 3-thia- and selenadiazole

4-Hydroxy-, 4-hydroxy-5-methyl-, 4-hydroxy-7-methylbenzo-2,1,3-thiadiazoles are polymorphous.4-Hydroxybenzo-2,1,3-thiadiazole (I), 4-hydroxy-5-methyl- and 4-hydroxy-7-methylbenzo-2, 1, 3-thiadiazoles (II and III) melt at 114–115°, 110–112°, 100–102° C, respectively, after recrystallization from water [2–4], but after recrystallization from petrol ether [5] they melt at 128–129°, 124–125°, and 119–120° C [5]. In this connection we recrystallized these phenols repeatedly from petrol ether after recrystallizing them from water, and their melting points rose as expected [5]. On the other hand, the compounds with melting points 128–129°, 124–125°, 119–120° C (ex petrol ether), after repeated crystallization from water melted at 114–115°, 110–112°, 100–102° C, respectively.For Part XXXVIII see [1].     

Aroma compound analysis of Piper nigrum and Piper guineense essential oils from Cameroon using solid-phase microextraction-gas chromatography,solid-phase microextraction-gas chromatography-mass spectrometry and olfactometry

Three analytical methods were developed for the determination of toxic compounds in recirculating waters of a paper-recycling industry. Three main groups of compounds were considered: (i) wood extractives originated from the raw material; (ii) biocides added during the production process and (iii) surfactants and other adjuvants present in the formulates of these biocides. Wood extractives considered in this study included fatty and resin acids. They were analysed by liquid-liquid extraction using methyl tert.-butyl ether, followed by gas chromatography-mass spectrometry for previous formation of the respective trimethylsilyl esters. Water samples were also extracted with Oasis HLB (copolymer [poly(divinylbenzene-co-N-vinylpyrrolidone]) solid-phase extraction cartridges of 60 mg and analysed by liquid chromatography-electrospray mass spectrometry for the determination of additives and biocides. Using these two approaches levels up to 15 mg/l for total resin and fatty acids, 5 mg/l for alkylbenzene sulfonates and 2-(thiocyanomethylthio)benzotiazol, 100 microg/l for bisphenol A and 2,2-dibromo-3-nitrilepropionamide, and 300 microg/l for nonylphenol ethoxycarboxylate were detected in process waters at different production treatment stages. These levels are of relevance since poor water quality affects the paper-recycling process, the primary water treatment process and eventually, the environmental water quality.     

Didodecyldimethylammonium bromide lipid bilayer-protected gold nanoparticles: synthesis, characterization, and self-assembly

Didodecyldimethylammonium bromide (DDAB) lipid bilayer-protected gold nanoparticles (AuNPs), which were stable and hydrophilic, were synthesized by in situ reduction of HAuCl(4) with NaBH(4) in an aqueous medium in the presence of DDAB. As-prepared nanoparticles were characterized by UV-vis spectra, transmission electron microscopy, dynamic light scattering analysis, and X-ray photoelectron spectroscopy. All these data supported the formation of AuNPs. Fourier transform infrared spectroscopy (FTIR) and differential thermal analysis/thermogravimetric analysis data revealed that DDAB existed in a bilayer structure formed on the particle surface, resulting in a positively charged particle surface. The FTIR spectra also indicated that the DDAB bilayer coated on the surface of AuNPs was probably in the ordered gel phase with some end-gauche defects. On the basis of electrostatic interactions between such AuNPs and anionic polyelectrolyte poly(sodium 4-styrenesulfonate) (PSS), we successfully fabricated (PSS/AuNP)(n)() multilayers on a cationic polyelectrolyte poly(ethylenimine) coated indium tin oxide substrate via the layer-by-layer self-assembly technique and characterized as-formed multilayers with UV-vis spectra and atomic force microscopy.     

An insight into the micellization of dodecyldimethylethylammonium bromide (DDAB) in the presence of bovine serum albumin (BSA)

In this work, we report the effect of concentration of bovine serum albumin (BSA) on the micellization of a cationic surfactant, dodecyldimethylethylammonium bromide (DDAB). Several samples covering a wide range of concentrations of protein and surfactant have been investigated. The interactions between the moieties are investigated by measuring fluorescence quenching of BSA molecules. The aggregation number of DDAB micelles is found to be small in the presence of BSA. The formation of DDAB-BSA complex is confirmed by FTIR. Absorbance spectroscopy indicates that at higher concentration, the conformational stability of BSA in DDAB is higher. The viscosity data for protein-surfactant systems confirm conformational changes in protein chains induced by the surfactant. The cmc values for DDAB increase with increasing concentration of BSA. At higher temperatures the micellization-complexation becomes enthalpy-dominated.     

Conductivity of water-in-oil microemulsions stabilized by mixed surfactants

The electrical conductivity of D2O-in-n-heptane microemulsions stabilized by cationic/nonionic surfactant mixtures was studied as a function of D2O content, surfactant concentration, and surfactant mixture composition. The surfactants employed were cationic di-n-didodecyldimethylammonium bromide, DDAB, nonionic poly(oxyethylene) monododecyl ethers, C12EJ, with J=3-8 and 23, nonionic polymeric surfactants of the type PEO-PPO-PEO (Pluronic), and the reverse structure analogues (Pluronic R). Qualitative structural information was drawn from a comparison between the measured conductivity and that predicted by the charge fluctuation model for spherical droplets. The conductivity versus water content curves were found to be typical for water-in-oil systems composed of spherical droplets. From the effect of blending nonionic surfactant with DDAB on the measured conductivities, it was concluded that microemulsion conductivity is independent of the concentration of cationic surfactant (DDAB). This finding agrees well with theoretical microemulsion conductivity models.