Apparent Heat Capacities Research Articles

Differential scanning calorimetry of mixtures of EVA and PE. Kinetic modeling

Mixtures of commercial EVA and different concentration of PE have been prepared and the heat evolution during two successive heating experiments has been studied by means of differential scanning calorimetry (DSC). A kinetic model has been suggested and applied, involving the different intrinsic fractions susceptible of undergoing transitions during the experiment, and also the concentration of PE in the initial binary mixture. Moreover, the variation of the apparent heat capacities of the different fractions and components with the temperature has been considered, yielding a remarkable improvement in the fitting of the DSC curves in the whole range of temperature studied. The models applied are capable of representing all the different processes observed and can be of great interest in the understanding of such phenomena, as well as in modeling the heat involved in the industrial processing of these types of products.

An Aqueous Thermodynamic Model for the Complexation of Sodium and Strontium with Organic Chelates valid to High Ionic Strength. I. Ethylenedinitrilotetraacetic acid (EDTA)

An aqueous thermodynamic model is developed, which accurately describes the effects of Na+ complexation, ionic strength, carbonate concentration, and temperature on the complexation of Sr2+ by ethylenedinitrilotetraacetic acid (EDTA) under basic conditions. The model is developed from the analysis of literature data on apparent equilibrium constants, enthalpies, and heat capacities, as well as on an extensive set of solubility data on SrCO3(c) in the presence of EDTA obtained as part of this study. The solubility data for SrCO3(c) were obtained in solutions ranging in Na2CO3 concentration from 0.01 to 1.8 m, in NaNO3 concentration from 0 to 5 m, and at temperatures extending to 75○C. The final aqueous thermodynamic model is based upon the equations of Pitzer and requires the inclusion of a NaEDTA3− species. An accurate model for the ionic strength dependence of the ion-interaction coefficients for the SrEDTA2− and NaEDTA3−aqueous species allows the extrapolation of standard state equilibrium constants for these species, which are significantly different from the 0.1 m reference state values available in the literature. The final model is tested by application to chemical systems containing competing metal ions (i.e., Ca2+) to further verify the proposed model and indicate the applicability of the model parameters to chemical systems containing other divalent metal-EDTA complexes.

Heat capacity analysis of oxidized Escherichia coli thioredoxin fragments (1–73, 74–108) and their noncovalent complex

We have calculated the absolute heat capacities of fragments 1--73 (N fragment) and 74--108 (C fragment) from thioredoxin, their complex and the uncleaved protein, from the concentration dependence of the apparent heat capacities of the solutions determined by differential scanning calorimetry. We find that, while the absolute heat capacities of uncleaved, unfolded thioredoxin and the C fragment are in good agreement with the theoretical values expected for fully solvated chains (calculated as the sum of the contributions of the constituent amino acids), the absolute heat capacities of the N fragment and the unfolded complex are about 2 kJ x K(-1) x mol(-1) lower than the fully solvated-chain values. We attribute this discrepancy to burial of the apolar surface in the N fragment (as burial of the polar area is expected to lead to an increase in heat capacity). Illustrative calculations suggest that burial of about 1000--1600 A(2) of apolar surface takes place in the N fragment (probably accompanied by the burial of a smaller amount of polar surface). In general, this work is supportive of heat capacity measurements on protein fragments being useful as probes of surface burial in studies to characterize protein unfolded states and the high regions of protein folding landscapes.

Molar Volumes and Heat Capacities of Electrolytes and Ions in Nonaqueous Solvents: 1. Formamide

Apparent molar volumes and heat capacities of 27 electrolytes have been measured as a function of concentration in formamide at 25°C using a series-connected flow densimeter and Picker calorimeter system. These data were extrapolated to infinite dilution using the appropriate Debye–Huckel limiting slopes to give the corresponding standard partial molar quantities. Ionic volumes and heat capacities at infinite dilution were obtained by an appropriate assumption based on the reference electrolyte Ph4PBPh4 (TPTB). The ionic volumes, but not the heat capacities, agree reasonably well with previously published statistically based predictions. The values obtained are discussed in terms of simple models of electrolyte solution behavior and a number of interesting features are noted, including, possible dependencies of ionic volumes on solvent isothermal compressibility and of ionic heat capacities on solvent electron acceptor abilities.

Measurement of thermodynamic quantities in the heating-rate dependent thermal transitions of sequenced polytripeptides

The apparent excess heat capacities ( C p ) of sequenced polytripeptides, (Pro-Pro-Gly) 10 and (Pro-Hyp-Gly) 10 in various solutions were measured using a differential scanning calorimeter. The dependence of the peaks of the C p curves on heating rates was identical for all solutions studied. The apparent enthalpy changes of the transition did not depend on the heating rate. The equilibrium thermodynamic data, Δ H and Δ S of the transition, obtained calorimetrically in this system, are found to be linear to each other, indicating an enthalpy–entropy compensation. These results are discussed in terms of the phase transition.

Heat-capacity determination by temperature-modulated DSC and its separation from transition effects

Temperature-modulated calorimetry offers three methods of establishing heat capacity: (1) the traditional method of scanning thermal analysis by finding the heat flow into the sample during a measured temperature increase: (2) the quasi-isothermal method by finding the maximum amplitude of the periodic heat flow in response to a temperature modulation at a constant base temperature; and (3) the pseudo-isothermal analysis of a temperature-modulated scanning experiment by subtracting the effect due to the underlying (usually constant) heating rate and evaluating the effect due to the modulation as in a quasi-isothermal experiment. The background, advantages, and limitations of the three methods are discussed along with the possibility of establishing apparent heat capacities in dynamic systems, and the separation of heat capacities from phase transitions.

Modulated differential scanning calorimetry in the glass transition region

Temperature-modulated calorimetry (TMC) allows the experimental evaluation of the kinetic parameters of the glass transition from quasi-isothermal experiments. In this paper, model calculations based on experimental data are presented for the total and reversing apparent heat capacities on heating and cooling through the glass transition region as a function of heating rate and modulation frequency for the modulated differential scanning calorimeter (MDSC). Amorphous poly(ethylene terephthalate) (PET) is used as the example polymer and a simple first-order kinetics is fitted to the data. The total heat flow carries the hysteresis information (enthalpy relaxation, thermal history) and indications of changes in modulation frequency due to the glass transition. The reversing heat flow permits the assessment of the first and higher harmonics of the apparent heat capacities. The computations are carried out by numerical integrations with up to 5000 steps. Comparisons of the calculations with experiments are possible. As one moves further from equilibrium, i.e. the liquid state, cooperative kinetics must be used to match model and experiment.

Self-association of 1,2-diols Apparent heat capacities of 1,2-diols in n-heptaneand carbon tetrachloride

Apparent molar heat capacities at constant pressure, Cmapp, have been measured for several 1,2-diols in dilute n-heptane and carbon tetrachloride solutions at 25 °C. The systems were: hexane-1,2-diol, octane-1,2-diol and decane-1,2-diol in n-heptane and butane-1,2-diol, pentane-1,2-diol, hexane-1,2-diol, octane-1,2-diol, decane-1,2-diol and dodecane-1,2-diol in carbon tetrachloride; in addition, values of Cmapp for hexan-1-ol and decan-1-ol in carbon tetrachloride were determined. The experimental values of Cmapp show a maximum against diol concentration which is larger and shifted to smaller concentrations than that for the equal carbon number 1-alcohol, indicating that the self-association capability of the 1,2-diols is greater than that of the monoalcohols. The contribution to Cmapp arising from intramolecular H-bonding is small compared to that arising from the intermolecular H-bonds. Diol and monoalcohol self-association is reduced in going from the inert n-heptane to CCl4, which acts as a weak proton acceptor. The data for 1,2-diols when plotted against ψ1, the concentration of hydroxy groups in the mixture, follow a single, corresponding states curve for each of the solvents. To interpret these heat capacity data, an extension of the Treszczanowicz–Kehiaian (TK) model for associated liquids has been undertaken. This extension takes into account the formation of intramolecular H-bonds. The parameters of the model, i.e. equilibrium constants and enthalpies of association, have been fitted to the data. It is concluded that at the dilute 1,2-diol concentrations used here, the heat capacity data can be well explained considering that there is only one predominant species in the solution, viz. pentamers or hexamers.

Thermodynamic studies on N,N,N-octyloctyldimethyl ammonium chloride in water-urea mixtures

The densities, heat capacities and enthalpies of dilution at 298 K and the osmotic coefficients at 310 K were measured for N,N,N-octyloctyldimethylammonium chloride (OOAC) in aqueous urea solution as a function of urea ( m u) and surfactant ( m s) concentrations in order to determine, in comparison with the lower homologue N,N,N-pentyloctyldimethylammonium chloride, OPAC, the influence of the hydrophobic tail on the properties of a double-chain surfactant in the presence of an additive like urea. From specific conductivity data, the critical micelle concentration (cmc) and the degree of the counterion dissociation (β) have been calculated. From the thermodynamic data, the molar apparent volumes, V φ , heat capacities, C φ , and apparent molar relative enthalpies, L φ , were derived as a function of m u and m s at 298 K.

Calorimetric investigation of DNA in the native and denatured states

The results of determination of apparent heat capacities of naturally occurring DNA in native (helix) and denatured (coils) states in dilute aqueous solutions have been reported. These results, supplemented by direct heat capacity measurements as a function of temperature, using a capillary scanning calorimeter, clearly show that the apparent heat capacity of polynucleotide chains of DNA in aqueous solution is strongly dependent upon the conformational state of the macromolecule. Comparison of data obtained for DNA in the “solid state”, at different levels of hydration and for DNA in H 2O and D 2O solutions reveals the possibility that the heat capacity increment ( Δc p = 0.36 ± 0.04 J g −1 K −1) is determined by an increase in the number of vibrational degrees of freedom, by hydrophobic effects and as a result of hydrogen bond destruction in water (including the ordered water clusters in the hydration shells of double helix of DNA).

Modeling the Heat Capacities of Aqueous 1−1 Electrolyte Solutions with Pitzer's Equations

The apparent molal heat capacities (φCp) of 1−1 electrolytes at 25 °C have been fitted to the Pitzer equation φCp = Cp,2° + (AJ/1.2) ln(1 + 1.2I1/2) − 2RT2[mBJMX + m2CJMX], where Cp,2° is the partial molal heat capacity of at infinite dilution and BJMX and CJMX are empirical constants related to ion−ion interactions. The values of Cp,2° of the electrolytes have been used to determine partial molal heat capacities of ions. The coefficients BJMX and CJMX have been combined with Pitzer coefficients for enthalpies and osmotic coefficients to develop equations that can be used to determine activity coefficients of these electrolytes from 10 to 70 °C and from 0.1 to 2 m to within 1%.

Salt Effect on Postmicellar Transitions: Heat Capacities and Volumes of Ternary System Water + Sodium Dodecylsulfate + Salt at 25°C

Densities and heat capacities of the ternary system water + sodium dodecylsulfate (SDS) + NaCl have been measured in the aqueous domain as a function of NaCl and surfactant concentrations. Apparent molar volumes and heat capacities of both solutes, SDS and NaCl, have been obtained therefrom and analyzed as functions of the concentrations of the two solutes. In the micellar domain, for peculiar concentrations of surfactant or salt, marked variations of the apparent heat capacity of the solute are observed. It is shown they are related to transitions occurring in the micellar solution and influenced by the presence of salt. Particularly, the post-micellar transition, revealed at 0.2 m in SDS solutions from the study of the transfer of alcohols, is enhanced in the presence of the salt and a drastic variation of the transfer heat capacity of NaCl occurred between 0.15 and 0.2 m. Moreover, the "second CMC" which had been suggested from conductivity measurements is also evidenced here through apparent heat capacities of the salt at 0.05 m in SDS. It is shown that these two transitions are very sensitive to NaCl, revealing thus their electrostatic nature. The latter, at 0.05 m, is due to the variation of the ionicity of small spherical micelles whereas the former, at 0.2 m, is certainly associated with the variation of β, the ratio of bound counterions to micelles, preceding the sphere-to-rod transition. Moreover, the identical values of heat capacities of transfer obtained with NaCl and Nal and their similar variations with the SDS concentration are also additional evidence of the pure electrostatic nature of the observed transitions.

Volume and heat capacity of model non-aqueous self-assembly systems

Blends of immiscible polymers are often stabilized by block copolymers which can form non-aqueous micelles and microemulsions in the liquid polymers. The phase diagrans, apparent volumes and apparent heat capacities of model non-aqueous binary and ternary systems were studied in order to investigate the conditions under which such self-assembly systems could form. 1,2-Hexanediol, which can cosolubilize hexane and ethyleneglycol, forms inverse micelles in hexane and weak microaggregates in ethyleneglycol. Genapol X-060, a commercial alcoholic surfactant containing on the average an aliphatic chain of 13 carbons and 6 oxyethylenes (C13E6), forms microaggregates in poly(ethyleneglycol) 400. These self-assembly systems are strengthen in the presence of a third component which has an affinity for the inner phase.

Microcalorimetric titration of α-cyclodextrin with some straight-chain α,ω-dicarboxylates in aqueous solution at different temperatures

The complex formation of α-cyclodextrin and straight-chain aliphatic α,ω-dicarboxylates, –O2C(CH2)nCO2–(n= 6, 7, 8), in aqueous solution has been studied by titration microcalorimetry at 288.15, 298.15 and 308.15 K. Apparent Gibbs energies, enthalpies, entropies and heat capacities for the 1 : 1 complex formations were derived from the calorimetric data. The thermodynamics of binding show typical enthalpy–entropy compensation effects, which result in weak temperature dependences of the Gibbs energies. The heat capacities of binding are large and negative. This confirms the view that the binding of non-polar moieties to cyclodextrins is to a large extent a result of hydrophobic dehydration. Experimental conditions causing deviations from the 1 : 1 model, are also discussed.

Model system for concentrated electrolyte solutions: Thermodynamic and transport properties of ethylammonium nitrate in acetonitrile and in water

Ethylammonium nitrate (ETAN), a low melting fused salt which is completely miscile in water and in many non-aqueous solvents, was used as a model system for the study of concentrated non-aqueous electrolyte solutions. Acetonitrile (AN) was chosen as a representative aprotic solvent. Some data were also obtained for water as solvent. The properties investigated over the whole mole fraction range, many as a function of temperature, were solid-liquid phase diagram, volume, heat capacity, conductivity and viscosity. Most properties in both solvents vary in a regular fashion over the whole mole fraction range and the properties at high concentration rapidly tend to those of the molten salt. The apparent volumes and heat capacities vary linearly with lnX2 over a large mole fraction range. There is evidence of significant association in AN (K A =1094 l-mol−) but not in water. The low concentration thermodynamic data were fitted with an association model using the above K A to obtain the partial molar quantities of ETAN at infinite dilution and in the associated state. These latter values are of the same magnitude as the molar quantities of the molten electrolyte.

Self-association of cyclohexanols in inert solvents. Apparent heat capacities of cyclohexanol and substituted cyclohexanols in n-heptane and n-decane

Apparent heat capacities have been measured for cyclohexanol and substituted cyclohexanols in dilute n-heptane and n-decane at 25 °C. The alcohols are cyclohexanol, 2-ethylcyclohexanol, 2-tert-butylcyclohexanol, trans-2-phenylcyclohexanol, 2,6-dimethylcyclohexanol, 2,3-dimethylcyclohexanol, 3,4-dimethylcyclohexanol, 3,3,5-trimethylcyclohexanol and 3,3,5,5-tetramethylcyclohexanol. The associational part of the apparent molar heat capacity, ϕc(assoc), shows a maximum against concentration which decreases and moves to higher alcohol concentration as the hydroxyl group on the alcohol becomes increasingly hindered, effectively reducing the self-association capability. A comparison between cyclohexanols and the previously reported phenols (J. Chem. Soc., Faraday Trans., 1991, 87, 1733) indicates that cyclohexanols show a higher ability to self-associate owing to the larger flexibility of the cyclohexanol ring as compared to the rigid aromatic ring. Treszczanowicz–Kehiaian theory for associated liquids was used to obtain the volumetric equilibrium constants and the enthalpy change for the formation of hydrogen bonds, ΔH0. For cyclohexanols ΔH0 is higher than for the corresponding phenols. As with the phenols, the tetramer population is severely reduced, dimers and trimers being more important.

Self-association of phenols in inert solvents. Apparent heat capacities of phenol, substituted phenols and aromatic alcohols in n-heptane

Download options Please wait... Article information DOI https://doi.org/10.1039/FT9918701733 Article type Paper Download Citation J. Chem. Soc., Faraday Trans., 1991,87, 1733-1738 BibTex EndNote MEDLINE ProCite ReferenceManager RefWorks RIS Permissions Request permissions Self-association of phenols in inert solvents. Apparent heat capacities of phenol, substituted phenols and aromatic alcohols in n-heptane S. Pérez-Casas, L. M. Trejo and M. Costas, J. Chem. Soc., Faraday Trans., 1991, 87, 1733 DOI: 10.1039/FT9918701733 To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page. If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given. If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page. Read more about how to correctly acknowledge RSC content. Search articles by author Silvia Pérez-Casas Luis M. Trejo Miguel Costas

Equilibrium partial pressures and mean activity and osmotic coefficients of 0-100% nitric acid as a function of temperature

Rational activity and osmotic coefficients and Henry's law constants K{sub Hx} (for the reaction HNO{sub 3(g)} = H{sup +}{sub (aq)} + NO{sub 3}{sup {minus}}{sub (aq)}), given as functions of temperature, enable p(H{sub 2}O) and p(HNO{sub 3}) to be calculated from {minus}60 to 120{degree}C, 0-100% HNO{sub 3}. Apparent molal enthalpies, heat capacities, and activity coefficients (derived from electromotive force (emf), freezing point, and partial pressure data) are represented with the use of the species-interaction models of Pitzer. Equations for the partial molal functions are given. The Henry's law constant is evaluated from p(HNO{sub 3}) data at 298.15 K, tabulated heats of formation, and heat capacities. Calculated p(H{sub 2}O) and p(HNO{sub 3}) over the entire concentration range agree with available data over 5 orders of magnitude of p(H{sub 2}O) and 7 orders of magnitude of p(HNO{sub 3}).

Calculation of the thermodynamic properties of aqueous electrolytes to 1000.degree.C and 5000 bar from a semicontinuum model for ion hydration

A semicontinuum approach for prediction of standard-state Gibbs free energies of ionic hydration, {Delta}{sub h}G, at high temperature steam conditions has been revised to permit predictions at temperatures from 0 to 1000{degree}C and any pressure up to 5 kbar. The revised semicontinuum model provides for a more realistic identification of inner-shell and outer-shell contributions. The inner-shell term accounts for contributions to {Delta}{sub h}G from the first six H{sub 2}O molecules of hydration. Inner-shell contributions are calculated by using available experimental equilibrium constants for successive ionic hydration reactions and an empirical parameter that represents the effective volume increment per H{sub 2}O of hydration. The outer-shell term accounts for contributions to {Delta}{sub h}G from H{sub 2}O molecules outside the inner-shell region. Outer-shell contributions are obtained from the Born equation using the bulk solvent dielectric constant and an empirical parameter that represents the effective Born radius. The empirical parameters in the revised model are characterized in a manner that ensures reasonable consistency with experimental standard-state volumes and heat capacities for aqueous electrolytes. Calculations on alkali-metal halide and alkali-metal hydroxide electrolytes are considered, and the results for NaCl are used to illustrate the pressure and temperature behavior of standard-state properties. Evaluation of uncertainties inmore » predicted values for {Delta}{sub h}G supports application of the revised model for rough quantitative estimation of standard-state properties at supercritical conditions. The validity of the revised model at supercritical conditions is also supported by a comparison of calculated and experimental apparent molal heat capacities for NaCl.« less

Complex formation and self-association in ternary mixtures. Apparent heat capacities for alcohol–methyl acetate–hydrocarbon and acetone–chloroform–cyclohexane

Apparent molar heat capacities, ϕc, have been measured for hexan-1-ol and 2-methylcyclohexanol at 25 °C in their binary mixtures with methyl acetate (MA) and the following ternary mixtures: hexan-1-ol–(p wt % of MA–n-dodecane) where p= 2, 4.3, 10.2 and 30 and 2-methylcyclohexanol–(p wt % of MA–n-decane) where p= 1.5, 5 and 50. The measurements were made from extreme dilution up to 10 wt % of alcohol. The ternaries acetone–(p wt % of chloroform–cyclohexane) where p= 4.5 and 7.4 are also reported. Plots of ϕc against alcohol concentration show that the high maximum obtained for the binary alcohol–hydrocarbon mixture (OH–I) is progressively decreased for the ternary mixtures as the concentration of MA increases until, for the binary alcohol–MA mixture (OH–MA) the ϕc curve has been flattened. This behaviour is explained quantitatively by the Treszczanowicz–Kehiaian (TK) model for associated mixtures extended to include the possibility of complex formation between the alcohol and the proton-acceptor, MA. In a MA–hydrocarbon environment, ϕc drops owing to the partial destruction of hydrogen bonds between alcohol molecules and the corresponding formation of a hydrogen-bonded complex between the alcohol and MA. At low alcohol concentrations, ΔCp of mixing is negative for the OH–I binary, turning positive when the hydrocarbon is replaced by a mixture of hydrocarbon with an increasing amount of MA. Further increase in MA concentrations decreases ΔCp until for the binary OH–MA it is again negative. These changes are explained by the TK model in terms of the different amounts of self-associated and complex species in solution. The TK model has been applied to ϕc data for the mixture acetone–chloroform–cyclohexane, where only complex formation is present in solution, and found to be qualitatively successful.