Composition Of Ternary Mixtures Research Articles

An interaction-based mixing model for predicting porosity and tensile strength of directly compressed ternary blends of pharmaceutical powders

Predicting the mechanical properties of powder mixtures without extensive experimentation is important for model driven design in solid dosage form manufacture. Here, a new binary interaction-based model is proposed for predicting the compressibility and compactability of directly compressed pharmaceutical powder mixtures based on the mixture composition. The model is validated using blends of MCC, lactose and paracetamol or ibuprofen. Both compressibility and compactability profiles are predicted well for a variety of blend compositions of ternary mixtures for the two formulations. The model performs well over a wide range of compositions for both blends and better than either an ideal mixing model or a ternary interaction model. A design of experiments which reduces the amount of API required for fitting the model parameters for a new formulation is proposed to reduce amount of API required. The design requires only three blends containing API. The model gives similar performance to the well-known Reynolds et al. model (2017) when trained using the same data sets. The binary interaction model approach is generalizable to other powder mixture properties. The model presented in this work is limited to curve-fitting of empirical compaction models for mixtures of common pharmaceutical powders and is not intended to provide guidance on the practical operating space (or design space) limits.

Flammability and performance studies of eco-friendly ternary refrigerant mixtures used in vapour compression systems.

The present article analyses the refrigerant safety parameters flammability, global warming potential (GWP) and coefficient of performance (COP) for twenty-seven combinations that contain two flammable and one non-flammable (dilutant) component. The flammability of the flammable refrigerants R290, R600, R600a, R152a and R161 were investigated with different dilutants such as R245fa, R13I1 and R134a. To determine the minimum inerting concentration (which decides the flammable zone), two methods were used: thermal balance method (TBM) and the modified thermal balanced method (MTBM). The MICs estimated with both the methods are compared against the 50 experimental datapoints available in the literature (for different ternary mixtures). It was found that for all the ternary mixtures, majority of the MIC values estimated with MTBM are within ± 8% while with TBM are within ± 30%. Fifty-five ternary mixture compositions were identified (from the proposed twenty-seven mixture combinations) using the MICs predicted by MTBM. The COPs of the identified mixtures M1-M6, M8-M12, M14-M24, M26-M30, M34-M39 and M53-M54 are estimated to be less than 10% of the COP of R134a (at the same operating conditions). It is also estimated that the corresponding GWP value of the mixtures (M1 to M6, M8 to M12, M14 to M24, M26 to M30, M34 to M39, M53 and M54) are reduced by 91 to 99% when compared to R134a (GWP = 1300).

Dispersions of Zirconia Nanoparticles Close to the Phase Boundary of Surfactant-Free Ternary Mixtures.

The achievement of a homogeneous dispersion of nanoparticles is of paramount importance in supporting their technological application. In wet processing, stable dispersions were largely obtained via surfactant or surface functionalization: although effective, the use of dispersant can alter, or even impair, the functional properties of the resulting nanostructured systems. Herein, we report a novel integrated modeling and experimental approach to obtain stable ZrO2 nanoparticle (NP) dispersions at native dimensions (about 5 nm) in homogeneous ternary mixtures of solvents (i.e., water, ethanol, and 1,2-dichlorobenzene) without any further surface functionalization. A miscibility ternary diagram was computed exploiting the universal quasi-chemical functional-group activity coefficient (UNIFAC) model, which was then experimentally validated. Dynamic light scattering (DLS) on these mixtures highlights that nanometric structures, resembling nanoemulsion droplets, form close to the mixture two-phase boundary, with a size that depends on the ternary mixture composition. ZrO2–NPs were then synthesized following a classic sol–gel approach and characterized by XRD and Raman spectroscopy. ZrO2–NPs were dispersed in HCl and mixed with different mixtures of ethanol and 1,2-dichlorobenzene (DCB), obtaining homogeneous and stable dispersions. These dispersions were then studied by means of DLS as a function of DCB concentration, observing that the nanoparticles can be dispersed at their native dimensions when the mass fraction of DCB was lower than 60%, whereas the increase of the hydrophobic solvent leads to the NPs’ agglomeration and sedimentation. The proposed approach not only offers specific guidelines for the design of ZrO2–NPs dispersions in a ternary solvent mixture but can also be extended to other complex solvent mixtures in order to achieve stable dispersions of nanoparticles with no functionalization.

Selective recovery and purification of carotenoids and fatty acids from Rhodotorula glutinis using mixtures of biosolvents

Selective recovery and purification of carotenoids and lipids from oleaginous red yeast Rhodotorula glutinis require a complex integration of different downstream operations. Envisioning a future industrial application in the bioeconomy framework, an experimental planning was used to design ternary mixtures of bio-based solvents (biosolvents) for simultaneous recovery and selective separation of carotenoids (i.e., β-carotene and torularhodin) and fatty acids (i.e., margaric acid, stearic acid and pentadecylic acid) from untreated (fresh wet) and freeze/thaw pre-treated (wet and dry) biomass of Rhodotorula glutinis CCT-2186. Two ternary systems of biosolvents, (i) ethanol:ethyl lactate:water and ii) ethanol:ethyl acetate:water, were investigated in solid–liquid extraction procedures to permeabilize/disintegrate the yeast cells and to enhance the selective recovery of β-carotene, torularhodin and fatty acids from the intracellular environment. Optimization of the ternary mixture composition for recovery of carotenoids and fatty acids from the three types of biomass allowed to obtain yields higher than 75% (w/w) from pre-treated dry biomass using mixture of ethanol:ethyl acetate:water (67:33:00% w/w/w). The best systems were then integrated with a liquid–liquid extraction for the selective separation of carotenoids and fatty acids and solvent recycling. The mixtures of biosolvents were reused up to three consecutive extraction cycles, maintaining high extraction efficiency yields of both carotenoids (>45% w/w) and lipids (>30% w/w). At the end, the biological activity of the carotenoids extracts was confirmed by determining the antioxidant activity using Electron Paramagnetic Resonance (EPR) and the stable free radical 1,1‐diphenyl‐2‐picrylhydrazyl (DPPH·). The highest antioxidant activity (93%) was obtained with torularhodin (250 μg/mL). This study confirms that extraction platforms using mixed biosolvents are simple, efficient and sustainable solutions for the selective recovery and separation of carotenoids and fatty acids from microbial biomass.

The impact of Cheddar or white brined cheese with various maturity degrees on the processed cheese consistency: A comparative study

This study focussed on the dependence on different emulsifying salt ternary mixture composition [disodium hydrogenphosphate (DSP), tetrasodium diphosphate (TSPP), sodium salt of polyphosphate (P20; number of phosphate units in the chain ≈20), trisodium citrate (TSC)] of hardness and gel strength of spreadable processed cheese (PC) manufactured from Cheddar and white brined cheeses. All PC samples were stored for 60 days (6 ± 2 °C). The hardest PC and samples with the highest gel strength were those produced from DSP and TSPP in a ratio 1:1. The hardness of all examined samples increased with the extending storage period, whilst their hardness and gel strength decreased with the rising maturity degree of the raw material utilised. Furthermore, higher values of gel strength were reported for the PC samples produced with Cheddar cheese in comparison with those made from white brined cheese.

Enhanced Lycopene Extraction from Tomato Peels by Optimized Mixed-Polarity Solvent Mixtures

Mounting evidence from clinical and epidemiological studies suggests that lycopene, the most abundant carotenoid in tomatoes, may be beneficial in the prevention or treatment of some important diseases. Ripe tomato peels are the richest source of lycopene, but the use of conventional solvent extraction methods without pretreatment of the plant material results in very poor recovery. The reason lies in the localization of lycopene in the plant tissue and the low permeability of the latter to solvent molecules. In this paper, a mixture design procedure was used to formulate solvent mixtures allowing the recovery of lycopene from non-pretreated tomato peels. Two ternary systems were investigated: (a) n-hexane–ethanol–acetone and (b) ethyl lactate–ethanol–acetone. Optimization of the ternary mixture composition led to a recovery of over 90% of the lycopene present in the peels. The high extraction efficiency was explained in terms of lycopene affinity combined with the ability to swell the plant material. A tomato oleoresin with high antioxidant activity and a lycopene content of about 13% (w/w) was also produced. Overall, the results indicate that highly effective solvents for direct recovery of lycopene from tomato peels can be easily prepared by a mixture design approach.

Experimental Investigation and Thermodynamic Modeling of Glycerin/Methanol/Organic Solvent Systems

AbstractGlycerin is an important by‐product in biodiesel production. To increase its quality to be suitable for use it in other operations, e.g., the pharmaceutical industry, it needs to be purified. Therefore, the purification of glycerin by liquid‐liquid extraction of methanol using different solvents was investigated. It was shown that, in terms of separation, petroleum ether was more effective than toluene and toluene was more effective than n‐butanol. In addition to the experimental investigations, the NRTL and UNIQUAC thermodynamic models were used to predict the compositions of ternary mixtures of glycerin + methanol + organic solvent in glycerin‐rich and organic solvent‐rich phases. The results showed the high accuracy of the presented models and their consistency with the measured data.

A Generalized Ease Of Separation Index for Selection of Optimal Configuration of Ternary Distillation

The ease of separation index (ESI) that is defined by the ratio of the relative volatility between the light and middle components to that between the middle and heavy components has been adopted in the literature for the selection of optimum distillation configuration for ternary separation. The present work showed that the separation requirements (the products’ purity) have a significant impact on the economic performance of distillation systems. Then we proposed a new index, generalized ease of separation index (GESI), to include the separation requirement into consideration for the selection of the optimum ternary distillation configuration. Simple column sequences with or without heat-integration, side-rectifier, side-stripper column, and dividing wall column (DWC) were evaluated as the candidates. Triangle map of ternary mixture composition was used to show the dependence of the optimal selection on feed compositions. We showed by numerical simulation that, for a given ESI, a profound change of the partition on the triangle map occurred with the change in GESI, and on the other hand, for a given GESI, slight changes of the partition on the map could be found with the change in ESI, showing stronger dependence of the economical behaviours of the ternary distillation configurations on the proposed GESI than on the ESI. Then, the dependence of the map partition on the GESI was investigated, and we found that with the increase in GESI, the area in triangle map where DWC was the optimal configuration shrunk, while the area of direct sequence with backward heat integration (DB) expanded. We concluded that the use of the newly defined index GESI can be conductive to the optimal selection of non-azeotropic ternary distillation configuration.

MEMS for biofuel composition measurement based on thermal impedance spectroscopy

Continuous monitoring of the composition of E85 biofuel is essential for a quick start and clean and efficient operation of Flex-Fuel Vehicles. The actual ethanol concentration in E85 fuel is in the range 50%–85% and fuel-line sensors are used for ethanol-gasoline composition measurement. However, also a small amount of water is typically present, which cannot be reliably detected using state-of-the-art capacitive fuel-line sensors. Thermal impedance spectroscopy has been investigated as a non-destructive technique to determine the composition of ternary mixtures of biofuels. The principle of the thermal conductivity detector has been extended for measuring both the thermal conductivity and the thermal capacity of biofuel in the range up to 10 kHz using an AC-operated polysilicon heater for injecting a sinusoidal heat flux, and another polysilicon strip at a well-defined spacing or thermopile sensors for measuring the in-phase and quadrature components of the resulting AC temperature difference. Measurements on the components are in reasonable agreement with simulations, with a −3 dB cut-off frequency at 422.5 Hz and 340.8 Hz for ethanol and gasoline, respectively. However, the cut-off frequency of water was found to be significantly lower than simulations due to its high surface tension, thus limiting access to the detector.

You Do What in Your Microprobe?! The EPMA as a Multimode Platform for Nitride Semiconductor Characterization

While the use of electron probe microanalysis (EPMA) is widespread in the geological and metallurgical sciences, it remains less prevalent in the field of semiconductor research. For these materials, trace element (i.e. dopant) levels typically lie near or beneath the detection limit of wavelength-dispersive Xray (WDX) spectrometers, while alloy compositions of ternary mixtures and multilayer structures can more readily be determined using X-ray diffraction techniques. The electron beam measurements more commonly applied to semiconductors remain transmission electron microscopy (for structural characterization), and scanning electron microscopy (topographic, optical and electrical information). Despite this, there are many aspects of the EPMA that make it an attractive platform for all of thesetypes of semiconductor characterization, particularly when combining compositional information fromWDX with complementary and simultaneously-acquired signals. These advantages include: built-inlight optics; a stable, quantified and high-current beam; and a combined large-area and high-resolutionmapping capability. This allows the measurement of cathodoluminescence (CL), electron beam-inducedcurrent (EBIC) and electron channelling contrast imaging (ECCI) signals alongside WDX, which weapply to the investigation of visible and UV AlxInyGa1-x-yN materials, devices and nanostructures.

Liquid-Liquid Equilibrium for the Ternary Systems of Solvent+ m/o/p-Cresol+Water: Thermodynamic Modeling

In this study, NRTL and UNIQUAC thermodynamic models were used to predict the composition of ternary mixtures of solvents+ m/o/p-cresol+ water in organic and aqueous phases. Various solvents are used for the separation of cresols from water. In this study, methyl propyl ketone, methyl isopropyl ketone, methyl butyl ketone, and methyl isobutyl ketone solvents were investigated. Intermolecular interaction parameters were considered to be a function of temperature. The binary interaction parameters of water and cresols (m, o, or p) in the presence of each type of solvent were considered to be the same. Also, regardless of the type of cresol (m, o, or p), the parameters of binary interaction between water and each solvents were considered to be the same. The results proved the accuracy of the presented models, though the parameters of binary interaction parameters were considered to be the same. The root mean square deviation for NRTL and UNIQUAC models was 0.0086 and 0.0089, respectively.

Protective effects of new antioxidant compositions of 4-methylcoumarins and related compounds with dl-α-tocopherol and l-ascorbic acid.

Coumarin derivatives possess a wide range of biological activities. By functionalization of the parent coumarin skeleton that has neither antioxidant nor biological activity, a series of new bio-antioxidants has been designed. New antioxidant compositions (equimolar binary and ternary mixtures) of eight 4-methylcoumarins and three related compounds have been tested and different effects between individual components have been observed: synergism (positive effect), additivism (summary effect) and antagonism (negative effect). Higher oxidative stability of the lipid substrate was obtained in the presence of the new antioxidant compositions of the studied compounds with dl-α-tocopherol and l-ascorbic acid. The role of each component in the antioxidant compositions of ternary mixtures has been identified by using new equations composed by the authors. All ternary mixtures demonstrate synergism as a result of continuous regeneration of dl-α-tocopherol from the studied antioxidants and l-ascorbic acid. Theoretical calculations have been probed as indicators of the expected effects between the individual components in a binary mixture. © 2018 Society of Chemical Industry.

The model binary/ternary mixtures for actual EPS solution extracted from the activated sludge in MBR using dead-end membrane filtration cell.

In order to find a model solution to simulate actual extracellular polymeric substances (EPS) solution in terms of filterability behavior, a series of experiments were conducted in a dead-end unstirred cell with 0.1 μm polyvinylidene fluoride membranes using binary/ternary mixtures consisting of sodium alginate (SA), bovine serum albumin (BSA) and humic acid (HA). Three target parameters (cumulative filtrate volume (CFV), specific cake resistance (αc) and rejection (R)) were compared and the roles of mixture components were investigated. The order of degree of influence on CFV, αc and R in ternary mixture was SA (94.5%, 85.6% and 88.2%, respectively) > BSA (5.2%, 10.3% and 8.0%) > HA (0.3%, 4.1% and 3.8%). Meanwhile, when the composition of ternary mixture was SA/BSA/HA = 285.1/150.1/10.2 mg·L-1, the deviation for CFV, αc and R was 7.65%, 19.6% and 7.27%, respectively, while the corresponding values for the most suitable binary solution (SA/BSA = 140.4/50.35 mg·L-1) were -12%, 1% and 164% respectively. This indicated that the ternary solution demonstrated a more accurate estimation than the binary solution for imitating the filterability of actual EPS solution. Therefore, the ternary mixture could be employed efficiently to replace the actual EPS solution in terms of three target parameters in practice applications.

The effect of different composition of ternary mixtures of emulsifying salts on the consistency of processed cheese spreads manufactured from Swiss-type cheese with different degrees of maturity

The scope of this work was to investigate the dependence of selected textural (texture profile analysis, TPA) and viscoelastic properties of processed cheese on the composition of ternary mixtures of emulsifying salts [disodium hydrogenphosphate, DSP; tetrasodium diphosphate, TSPP; sodium salt of polyphosphate (with mean length n ≈ 20), P20; and trisodium citrate, TSC] during a 60-d storage period (6±2°C). The processed cheese samples [40% wt/wt dry matter (DM) content, 50% wt/wt fat in DM content] were manufactured using Swiss-type cheese (as the main raw material) with 4 different maturity degrees (4, 8, 12, and 16 wk of ripening). Moreover, the pH of the samples was adjusted (the target values within the range of 5.60–5.80), corresponding to the standard pH values of spreadable processed cheese. With respect to the individual application of emulsifying salts (regardless of the maturity degree of the Swiss-type cheese applied), the samples prepared with P20 were the hardest, followed by those prepared with TSPP, TSC, and DSP. Furthermore, a specific ratio of DSP:TSPP (1:1) led to a significant increase in the hardness of the samples. On the whole, the hardness of all processed cheese samples increased with the prolonging storage period, whereas their hardness significantly dropped with the rising ripening stage of the raw material utilized. In all of the cases, the trends of hardness development remained analogous, and only the absolute values differed significantly. Moreover, the findings of TPA were in accordance with those of the rheological analysis. In particular, the specific ratio of DSP:TSPP (1:1) resulted in the highest gel strength and interaction factor values, followed by P20, TSPP, TSC, and DSP (used individually), reporting the same trend which was demonstrated by TPA. The monitored values of the gel strength and interaction factor decreased with the increasing maturity degree of the Swiss-type cheese used. The intensity of the rigidity of the samples showed an analogous relationship to the intensity of the gel strength; the higher the gel strength of the sample, the more inflexible the product is expected to be.

Porous electrospun polycaprolactone (PCL) fibres by phase separation

Porous electrospun poly(ε-caprolactone) (PCL) fibres were produced through a non-solvent induced phase separation mechanism, using binary solvent systems with different properties. The effect of the solvent properties on the size and surface morphology of electrospun PCL fibres was investigated. Chloroform (CF), dichloromethane (DCM), tetrahydrofuran (THF) and formic acid (FA) were used as good solvents in mixtures with a poor solvent, dimethyl sulfoxide (DMSO), in order to generate pores on the fibre surface. The production of porous, bead free fibres with an average diameter ranging from 1470 to 2270nm was achieved using 12.5% w/v PCL in CF/DMSO solution with good/poor solvent ratios varying from 75% to 90% v/v at the applied voltage of 15kV, a spinning distance of 20cm, and the feed flow rate of 1ml/h. DCM and THF were proven to be less suitable good solvents for the process due to the formation of a solid skin on the jet surface, caused by the limited diffusivity of the polymer molecules from the jet surface to the liquid core and its subsequent collapse. FA was found to be unsuitable due to its similar evaporation rate to DMSO. The pore formation was favoured at high good/poor solvent ratios, whereas, the production of fibres with ribbon cross sections or fibres with beads was more pronounced at low good/poor solvent ratios. Data fitting was used for the development of a second order polynomial equation, correlating the produced fibre average diameter to the solution parameters (conductivity, surface tension, and viscosity), for the given polymer and solvent systems, under the specific experimental conditions used in this study. The ternary mixture compositions that lead to the formation of porous fibres were mapped on a ternary graph.

The effect of composition of ternary mixtures containing phosphate and citrate emulsifying salts on selected textural properties of spreadable processed cheese

Ternary mixtures consisting of phosphate and citrate emulsifying salts were studied for their impact on selected textural properties (especially hardness) of processed cheese spreads over a 30 day storage period at 6 ± 2 °C. Two different groups of samples were manufactured, one with pH adjustment (target values within the interval of 5.60–5.80) and one without pH adjustment. When binary mixtures with trisodium citrate (TSC) and tetrasodium diphosphate (TSPP) were used (with zero content of the other salts tested in the ternary mixture), the products consisting of TSC and TSPP at a ratio of approximately 1:1 were the hardest. Increasing the content of TSC, TSPP and/or sodium salt of polyphosphate and decreasing that of disodium hydrogen phosphate (DSP) in ternary mixtures resulted in the increasing of the hardness of processed cheese. The absolute values of processed cheese hardness significantly changed as a result of pH adjustment.

The effect of ternary emulsifying salt composition and cheese maturity on the textural properties of processed cheese

The dependence of textural parameters of processed cheeses (40%, w/w, dry matter content, 50%, w/w, fat in dry matter content) on the composition of ternary mixtures of phosphate emulsifying salts (disodium hydrogen phosphate – DSP; tetrasodium diphosphate – TSPP; sodium salt of polyphosphate – POLY) was modelled. The effects were studied in samples from cheeses with different maturity (2, 4 and 8 weeks) over a 30-day storage period at 6 °C. With a constant POLY content (below 60%) in the ternary mixtures, a rapid increase in hardness and a decrease in cohesiveness and relative adhesiveness was observed in products with a ratio of DSP to TSPP ranging in the instance of 1:1–3:4. The effect of a specific ratio of DSP to TSPP on the texture parameters decreased with increasing content of POLY in the mixtures. Neither the degree of maturity of the cheese nor a 30-day storage period affected these general trends.

Fluorescence Spectroscopic Studies of (Acetamide + Sodium/Potassium Thiocyanates) Molten Mixtures: Composition and Temperature Dependence

Steady state and time-resolved fluorescence spectroscopic techniques have been used to explore the Stokes' shift dynamics and rotational relaxation of a dipolar solute probe in molten mixtures of acetamide (CH(3)CONH(2)) with sodium and potassium thiocyanates (Na /KSCN) at T approximately 318 K and several other higher temperatures. The dipolar solute probe employed for this study is coumarin 153 (C153). Six different fractions (f) of KSCN of the following ternary mixture composition, 0.75 CH(3)CONH(2) + 0.25[(1 - f)NaSCN + fKSCN], have been considered. The estimated experimental dynamic Stokes' shift for these systems ranges between 1800 and 2200 cm(-1) (+/-250 cm(-1)), which is similar to what has been observed with the same solute probe in several imidazolium cation based room temperature ionic liquids (RTIL) and in pure amide solvents. Interestingly, this range of estimated Stokes' shift, even though not corresponding to the megavalue of static dielectric constant reported in the literature for a binary mixture of molten CH(3)CONH(2) and NaSCN, exhibits a nonmonotonic KSCN concentration dependence. The magnitudes of the dynamic Stokes' shift detected in the present experiments are significantly less than the estimated ones, as nearly 40-60% of the total shift is missed due to the limited time resolution employed (full-width at half-maximum of the instrument response function approximately 70 ps). The solvation response function, constructed from the detected shifts in these systems, exhibits triexponential decay with the fastest time constant (tau(1)) in the 10-20 ps range, which might be much shorter if measured with a better time resolution. The second time constant (tau(2)) lies in the 70-100 ps range, and the third one (tau(3)) ranges between 300 and 800 ps. Both these time constants (tau(2) and tau(3)) show alkali metal ion concentration dependence and exhibit viscosity decoupling at higher viscosity in the NaSCN-enriched region. Time dependent rotational anisotropy has been found to be biexponential at all mixture compositions studied. Both the average solvation (<tau(s)>) and rotation (<tau(r)>) times of C153 in these mixtures exhibit fractional power law dependence on medium viscosity (<tau(x)> is proportional to eta(p), x being solvation or rotation). For solvation, p is found to be 0.46, which is very different from that obtained for common polar and nonpolar solvents, and RTILs (p approximately = 1). For rotation, p approximately = 0.65, which is again different from the value (p approximately = 1) obtained for common polar solvents and RTILs but very similar to that (p approximately = 0.6) found for nonpolar solvents. In addition, experimentally measured average rotation times in these mixtures are found to exhibit slip behavior in the low eta/T region, which gradually transforms to subslip as eta/T increases. Calculations using a recently developed semimolecular theory predict a total dynamic Stokes' shift for C153 (dipolar solute) in these molten mixtures near approximately 1600 cm(-1) where the solute-solvent (dipole-dipole) and the ion-solute (ion-dipole) interactions contribute respectively approximately 80% and approximately 20% to the calculated total shift. Like in experiments, the theoretically predicted solvation response function in the overdamped limit at each mixture composition has been found to be triexponential. The calculations in the underdamped limit, however, suggest a biphasic decay where a composition independent subpicosecond component and a much slower component with the time constant spreading over 150-850 ps contribute equally to constitute the total decay. The calculated average solvation times in this limit are found to be in better agreement with experimental results than the predictions from the overdamped limit.

On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data

In this paper we present a method for determining the free energies of ternary mixtures from light scattering data. We use an approximation that is appropriate for liquid mixtures, which we formulate as a second-order nonlinear partial differential equation. This partial differential equation (PDE) relates the Hessian of the intensive free energy to the efficiency of light scattering in the forward direction. This basic equation applies in regions of the phase diagram in which the mixtures are thermodynamically stable. In regions in which the mixtures are unstable or metastable, the appropriate PDE is the nonlinear equation for the convex hull. We formulate this equation along with continuity conditions for the transition between the two equations at cloud point loci. We show how to discretize this problem to obtain a finite-difference approximation to it, and we present an iterative method for solving the discretized problem. We present the results of calculations that were done with a computer program that implements our method. These calculations show that our method is capable of reconstructing test free energy functions from simulated light scattering data. If the cloud point loci are known, the method also finds the tie lines and tie triangles that describe thermodynamic equilibrium between two or among three liquid phases. A robust method for solving this PDE problem, such as the one presented here, can be a basis for optical, noninvasive means of characterizing the thermodynamics of multicomponent mixtures.

Using Raman spectroscopy to investigate donor–acceptor reactions in the formamide/dimethylsulfoxide/acetonitrile system

AbstractRaman spectra of binary and ternary solvent systems in different concentrations were carried out. The mixtures containing equimolar quantities of dimethylsulfoxide (DMSO) and acetonitrile (ACN), or those in different compositions, do not show any spectral evidence for the formation of a Lewis acid–base adduct. On the contrary, the formamide (FA), DMSO and ACN mixtures exhibit new bands. In the S stretching region, the band at 1025 cm−1 is assigned to the FA–DMSO adduct whereas, in the C stretching region, the 2257 cm−1 band corresponds to the FA–ACN adduct. The positions of these two new bands in the present system are in agreement with our recent works. In addition, in the NH2 bending region, the 1613 cm−1 band has been described as a mixture of both adducts. Quantitative analyses performed in the S and C stretching regions show that the association extent for the FA–DMSO adduct is greater than for the FA–ACN adduct, and this is in excellent agreement with the acid–base concepts commonly used to nonaqueous solvents. Preferential interactions between FA molecules as well as their dependence on the ternary mixture composition are also discussed. The results described here open up new possibilities to study the acid–base reactions nature involving FA adducts and can be useful for a better description of biological systems in which peptide groups have a special role. Copyright © 2007 John Wiley &amp; Sons, Ltd.