The temperature dependence of the heat capacity change for micellization of nonionic surfactants

The thermodynamic parameters that govern micelle formation by four different nonionic surfactants were investigated by ITC and DSC. These included n-dodecyldimethylphosphine oxide (APO12), Triton X-100 (TX-100), n-octyltetraoxyethylene (C8E4), and N,N-dimethyloctylamine-N-oxide (DAO8). All of these surfactants had been previously investigated by solution calorimetry over smaller temperature ranges with conflicting conclusions as to the temperature dependence of the heat capacity change, DeltaCp, for the process. The temperature coefficient of the heat capacity change, B (cal/mol K2), was derived from the enthalpy data that were obtained at small intervals over a broad temperature range. The values obtained for each of the surfactants at 298.2 K for DeltaCp and B were -155+/-2 and 0.50+/-0.36 (APO12), -97+/-3 and -0.24+/-0.18 (TX-100), -105+/-2 and 1.0+/-0.3 (C8E4), and -82+/-1 and 0.36+/-0.04 (DAO8), cal/mol K and cal/mol K2, respectively. The resulting B-values did not correlate with the cmc, aggregation number, or structure of the monomer in an obvious way, but they were found to reflect the relative changes in hydration of the polar and nonpolar portions of the surfactant molecule as the micelles are formed. An analysis of the data obtained from DSC scans was used to describe the temperature dependence of the critical micelle concentration, cmc. An abrupt increase in heat capacity was observed for TX-100 and C8E4 solutions of 36.5+/-0.5 and 21+/-5 cal/mol K, respectively, as the temperature of the scan passed through the cloud point. This change in heat capacity may reflect the increased monomer concentration of the solutions that accompanies phase separation, although other interpretations of this jump are possible.     

Nonmonotonic temperature dependence of heat capacity through the glass transition within a kinetic model

The heat capacity of a supercooled liquid subjected to a temperature cycle through its glass transition is studied within a kinetic model. In this model, the beta process is assumed to be thermally activated and described by a two-level system. The alpha process is described as a beta relaxation mediated cooperative transition in a double well. The overshoot of the heat capacity during the heating scan is well reproduced and is shown to be directly related to delayed energy relaxation in the double well. In addition, the calculated scan rate dependencies of the glass transition temperature T(g) and the limiting fictive temperature T(f) (L) show qualitative agreement with the known results. Heterogeneity is found to significantly reduce the overshoot of heat capacity. Furthermore, the frequency dependent heat capacity has been calculated within the present framework and found to be rather similar to the experimentally observed behavior of supercooled liquids.     

Enthalpy of solution of tigogenin saponin in dioxane and the temperature dependence of its heat capacity

The heats of solution of tigogenin C₂₇H₄₄O₃ in dioxane at dilutions equal to 1: 9000, 1: 18 000, and 1: 36 000 (mol solute/mol solvent) have been studied by isothermal calorimetry. The standard enthalpy of C₂₇H₄₄O₃ solution in dioxane at infinite dilution was derived by the mathematical processing of the calorimetric data. Dynamic calorimetry over the range 173–423 K has been used to study the heat capacity of tigogenin. The C _p ^o ～ f(T) plot has a jump at 298.15. K. The standard enthalpies of formation and combustion and the heat of melting of tigogenin have been indirectly calculated.     

Model-free temperature scaling for heat capacity

In treating the experimental data on the heat capacity of solids, the essence of any model application is in the searching for the scaling factors (k _i or 1/Θ_i) which transform a set of independent functions C _P,i(T) for every substance into a function C _P(T·k _i) universal for the particular set of substances. DSC heat capacities of I–III–VI₂ compounds at elevated temperatures exceed the upper limit of 12R (3R per mole of atoms) and make impossible application of any model. Nevertheless, the temperature scaling of heat capacity can be solved as a pure mathematical problem without any physical model (theory). The benefits of the model-free scaling are illustrated with the case of four isostructural chalcogenides (LiInS₂, LiInSe₂, LiGaS₂, and LiGaSe₂) measured recently with DSC in a temperature range from 180 to 460 K. The upper limit of C _P(T·k _i) functions was expanded up to 635 K. Low-temperature heat capacity of LiInSe₂ published in 1995 made it possible to derive the thermodynamic functions (enthalpy and entropy) for LiInS₂ (0–590 K), LiGaS₂ (0–640 K), and LiGaSe₂ (0–490 K) and expand those data for LiInSe₂ from 300 to 460 K.     

High temperature enthalpy and heat capacity of GaN

The heat capacity and the heat content of gallium nitride were measured by calvet calorimetry (320-570 K) and by drop calorimetry (670-1270 K), respectively. The temperature dependence of the heat capacity in the form C_pm=49.552+5.440×10⁻³T−2.190×10⁶T⁻²+2.460×10⁸T⁻³ was derived by the least squares method. Furthermore, thermodynamic functions calculated on the basis of our experimental results and literature data on the molar entropy and the heat of formation of GaN are given.     

Gaussian approximation for the temperature dependence of a continuous electronic spectrum

Exact expressions for the temperature dependence of the mean frequency and width of an absorption spectrum for an allowed transition between a harmonic lower state and a linear repulsive upper state potential are derived. This is sufficient information to obtain a Gaussian approximation for the absorption spectrum. The present results for the first two spectral moments are exact, and therefore represent an improvement over the Sulzer-Wieland equation in its original or modified forms.     

Low temperature heat capacity of heterocyclic polymer networks

The predicted crossover to a fractal-like vibrational regime above 8–10 K was apparently proved by precise measurements of heat capacity of a series of cross-linked heterocyclic polymers.     

On approximation of the heat capacity of substances in the gaseous state

Development of thermodynamic property databases and thermodynamic modeling algorithms require thermodynamic functions of substances presented in a functional form. In this paper we consider substances in the gaseous state only. The most known methods for approximating dependences of the thermodynamic functions on temperature are overviewed. An algorithm is proposed to fit the heat capacity with polynomials splitting the temperature range into intervals where the interval number and boundaries are optimized with respect to a given maximum approximation error. This algorithm is used in the IVTANTHERMO project and the corresponding thermodynamic modeling code.     

The phonon heat capacity of diborides: The approximation of interacting sublattices

The temperature dependence of the heat capacity of structures formed by alternating layers with different atomic compositions is described using the model of interacting three- and two-dimensional Debye sublattices. The parameters of the model are the characteristic temperatures Θ₁ and Θ₃ of the sublattices and the characteristic temperature Θ₂ corresponding to vibrations between the sublattices. (In the accepted approximation, Θ₂ equals the characteristic Debye temperature of the substance at absolute zero.) The model was used to analyze the temperature dependences of the lattice (phonon) heat capacities of transition and rare-earth metal diborides MB₂. This allowed the characteristic temperatures Θ _i and trends of their variations depending on metal atomic numbers to be determined.     

Glass transition temperature and heat capacity of heterotacticlike PMMA

The glass transition temperature and heat capacity have been determined by differential scanning calorimetry on samples of heterotacticlike monodisperse poly(methyl methacrylate) (PMMA). The nuclear magnetic resonace spectra of these samples reveal that they contain a larger percentage of mr triads (ca. 51%) than atactic polymers and that their microstructure may be predominantly stereoregular because of an abundance of mrrr sequences. We combine our T_g values with data from the literature for PMMAs of other tacticities, in order to analyze the correlation of T_g with tacticity. In this analysis, we consider PMMA as a steric copolymer formed by mm, mr, and rr triads.     

The low temperature heat capacity of some glass ceramics

The heat capacities between 1.5 and 25 K have been measured for glassy and devitrified samples of two substances: one is a commercial material (“Cer-Vit”) and the other is diopside (CaMgSi₂O₆). All samples, whether glassy or crystalline, have an “excess” heat capacity at the lowest temperatures roughly proportional to T and of similar magnitude to that found in a wide variety of inorganic glasses.     

Adiabatic microcalorimeters for heat capacity measurement at low temperature

Technical problems in the design and construction of small sample adiabatic calorimeters are pointed out and solutions to them discussed. Two calorimeters constructed on the design principle are described with illustrative examples of data obtained with them. Hard and soft wares for fully automatic operation of the two calorimeters are described in some detail.     

Low temperature heat capacity and magnetic properties of UF3

The low temperature heat capacity of UF(3) has been measured using an adiabatic low temperature calorimeter in the temperature range from 10 to 350 K. These data are complemented at the lowest temperature region with data obtained with a Quantum Design PPMS-14 device in the temperature range from 0.5 to 20 K. Good agreement between both techniques has been found, and from these experimental results the absolute entropy of UF(3) at 298.15 K has been determined as 126.8 ± 2.5 J K(-1) mol(-1). On the basis of the specific heat data and the magnetization measurements performed on a SQUID device, a transition at 1.59 K attributed to Curie temperature of a ferromagnetic transition has been found in this study. This observation makes UF(3) a unique compound with an unusually low ferromagnetic ordering temperature.     

Study of temperature profile and specific heat capacity in temperature modulated DSC with a low sample heat diffusivity

One important application of temperature modulated DSC (TMDSC) is the measurement of specific heat of materials. When the sample has very good thermal conductivity as in the case of metals, the temperature gradient is not normally an important factor and can be ignored most of the time. However, in the case of materials with poor heat transfer properties, for example, polymers, the thermal conductivity is only in the order of 1/1000 or so of that of metals. This could have a major effect on the test results. In this paper, a round analytical solution is given and a numerical model is used to analyze the effects of thermal diffusivity on temperature distribution inside the test sample and specific heat measurement by TMDSC, PET sample test results are presented to demonstrate the effects of material thermal diffusivity.     

Low temperature heat capacity and magnetic studies on DyCu5

Low temperature heat capacity studies on DyCu₅ revealed a λ-anomaly at 6.55 K. Evaluation of the entropy indicated that the ground state is not (2J + 1) fold degenerate. High field magnetization data yield a moment of 9.28 μ_B at 4.2 K and 120 kOe.