Polymerization kinetics of photocurable acrylic resins

The polymerization kinetics of photocurable compositions based on an epoxyacrylate oligomer and three analogous diacrylate monomers were investigated. The effects of the oligomer-to-monomer ratio, curing conditions, and monomer structure were considered. The polymerization is characterized by a synergistic effect observed in a wide temperature range and occurring for the polymerization rate both in air and Ar and for final conversions in air. The final conversion in Ar is determined by viscosity of a formulation. The presence of a heteroatom (S or O) in the ester group of the reactive diluent is beneficial for the polymerization course, especially in air atmosphere. The best results were obtained for the sulfur-containing monomer. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 665–673, 1998     

Functionalized acrylic polyhydroxy urethanes as molecular tool box for photocurable thermosets and 3D printing

Liquid urethane (meth)acrylates represent attractive components of photocurable thermosets for applications ranging from coatings and adhesives to 3D printing. Herein we tailor liquid polyfunctional urethane methacrylates (UMA) derived from acrylic polyhydroxy urethanes. Cyclic carbonate methacrylates react with diamines to form dihydroxy-functional urethane dimethacrylates. In an “one-pot” process the hydroxy groups are functionalized either by reaction with 2-isocyanatoethyl methacrylate (IEMA) or by esterification with methacrylic anhydride (MAA) and acetic anhydride (AA). The hydroxy group esterification substantially lowers the resin viscosity (26–156 Pa•s). Hydroxy functionalization with IEMA and MAA affords tetrafunctional methacrylates. The corresponding photo-cured thermosets exhibit higher crosslinking density and improved stiffness as reflected by increasing the Young's modulus from 2900 to 3700 MPa combined with increasing the glass temperature from 135 to 204°C. Hence, this facile molecular UMA design enables to control functionality and thermoset properties over a wide range and meets the demands of 3D printing applications.     

Thermal behaviors of electrolytes in lithium-ion batteries determined by differential scanning calorimeter

Lithium-ion batteries have been widely used in daily electric appliance, but abusive accidents occurred from time to time. Lithium-ion batteries composed of various electrolytes (containing organic solvents, inorganic salts), binder, and electrode materials, which may be unstable under some abnormal conditions. The formulation or components of electrolytes played a crucial factor in affecting reactive hazards within the cell. In order to meet safety requirements of the lithium-ion batteries on electronic device, reseachers and scholars are continuing to do further studies on the important issues in relation to the lithium-ion batteries. This study aims to apply the differential scanning calorimeter for measuring the thermal or reactive hazards of the organic solvents related to the formulation of the electrolytes. Besides, thermal instabilities of lithiated graphite or deposited lithium with electrolytes were simulated by the reactions between metallic lithium (Li) and organic carbonates of linear and cyclic structures. Exothermic onset temperatures and enthalpy changes were measured and analyzed. Results showed that the thermal behaviors of these organic carbonates themselves or with lithium hexafluorophosphate liberated less enthalpy changes. However, violent exothermic reactions were detected between the linear or cyclic carbonates and lithium metal with larger enthalpy change larger than 1,000 J g^?1 of lithium. This can be observed by Li reacted with diethyl carbonate at surprisingly lower onset temperature about 46.6 °C.     

Use of differential calorimeter for establishing temperature standards

A differential calorimeter was used to set up and critically evaluate a series of organic substances as temperature standards over the range 50–330°. The conditions for acceptance of a standard substance were a sufficient degree of purity, thermal stability, absence of polymorphism, a suitable cryoscopic constant, low volatility and ready availability.Zone refining was mentioned as a method of purification to obtain the minimum degree of required purity at 99.9 mole per cent.

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Zusammenfassung Man benützte ein Differentialkalorimeter zur Einstellung und kritischen Auswertung einer Serie von organischen Substanzen, geeignet als thermometrische Standardstoffe im Temperaturbereich von 50 bis 330°. Die Bedingungen der Annahme als solche waren ein genügender Grad von Reinheit und thermischer Stabilität, Abwesenheit von Polymorphic geeignete kryoskopische Konstanten, niedrige Flüchtigkeit und leichte Verfügbarkeit. Die Zonenreinigung erwies sich als geeignetes Verfahren, um den minimalen Grad der erforderlichen Reinheit von 99.9 Molprozenten zu erhalten.

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Résumé Emploi d'un calorimètre différentiel pour sélectionner plusieurs substances organiques comme étalons thermométriques dans le domaine de température de 50 à 330°. Les conditions requises pour retenir une substance comme étalon ont été les suivantes: degré suffisant de pureté, stabilité thermique, absence de polymorphisme, constante cryoscopique convenable, faible volatilité et disponibilité rapide. Mention de la méthode de la zone fondue comme procédé de purification pour obtenir le degré minimal de pureté nécessaire (99.9 moles pour cent).

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50–330° . , , , , . , 99,9 %.

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The authors wish to thank Prof. G. Milazzo of the Istituto Superiore di Sanità (Roma) for assistance in the work, and Dr. P. Sanmartin of the Centro Ricerche Montecatini-Edison (Porto Marghera) for the measurements and data of Table 4.     

Performance of a new differential scanning calorimeter cell

A calorimeter cell has been developed utilizing a geometry which optimizes dynamicgas flow and quantitative heat transfer to each sensing thermocouple. The basis of the cell is a sensitive thin form differential thermocouple which is symmetrically and rigidly positioned, containing a center port. The thin form differential thermocouple serves as a sample and sample container support as well as a differential detector. The dynamic gas enters through the center port permitting good contact with the sample and sample pan adjacent to it. The theoretical aspects are discussed and the necessity of having a high thermal resistance between the heat source and sample and a low thermal resistance between the sample and detecting thermocouple is demonstrated. Applications which show both qualitative and quantitative capabilities are presented.

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Zusammenfassung Es wird über eine kalorimetrische Zelle mit einer Geometrie, die einen optimalen Gasstrom und quantitative Wärmeübermittlung zu jedem Thermoelement ermöglicht, berichtet. Die Zelle besteht aus einem empfindlichen dünnen Thermoelement, das symmetrisch und fest angelagert ist und eine Öffnung in der Mitte besitzt. Das dünne Thermoelement dient zum Halten der Probe, des Probebehälters und als Differentialdetektor. Das dynamische Gas tritt durch die Öffnung ein, wodurch eine gute Berührung mit Probe und umgebendem Probebehälter ermöglicht wurde. Die theoretischen Aspekte werden erörtert und es wird bewiesen, daß zwischen der Wärmequelle und der Probe ein hoher, zwischen dem messenden Thermoelement und der Probe ein niedriger thermischer Widerstand nötig ist. Anwendungen informieren über die qualitativen und quantitativen Fähigkeiten der Zelle.

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Résumé On a mis au point une cellule calorimétrique dont la conception est favorable à la circulation d'un courant gazeux et au transfert quantitatif de la chaleur vers chaque thermocouple détecteur. Le fond de la cellule est constitué par un thermocouple différentiel fin et sensible, disposé symétriquement et d'une manière rigide, et dont le centre est muni d'un orifice. Ce fin thermocouple différentiel sert de support d'échantillon et de détecteur différentiel. La circulation du gaz s'effectue par l'orifice central qui permet un bon contact avec l'échantillon et le support d'échantillon qui lui est adjacent. Les aspects théoriques sont discutés et l'on montre la nécessité d'une résistance thermique élevée entre la source de chaleur et l'échantillon et faible entre l'échantillon et le thermocouple détecteur. Des applications illustrent les possibilités qualitatives et quantitatives de ce dispositif.

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, . , , , , . , . , , . . .

     

Applications of a new low temperature differential scanning calorimeter

A new low temperature differential scanning calorimeter is described which operates over the temperature range –150 °C to 700 °C. The equipment features a chromel heat flux DSC sensor plate located in a cobalt alloy heating chamber, enabling work to be carried out in oxidizing atmospheres to above 600 °C. Full data processing and programme control facilities are provided by an IBM compatible computer system. The performance of the instrument is illustrated by experiments on indium and poly (vinyl chloride).

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Zusammenfassung Ein neues Tieftemperatur-Differential-Scanning-Kalorimeter für den Bereich von –120 °C bis+700 °C wird beschrieben. Das Gerät enthält eine Wärmefluss-DSC-Sensorplatte aus Chromel in einer Heizkammer aus einer Kobaltlegierung, was Arbeiten in oxidierender Atmosphäre bis über 600 °C ermöglicht. Ein IBM-kompatibles Computersystem bietet alle Möglichkeiten der Datenverarbeitung und Programmregelung. Die Leistungsfähigkeit des Geräts wird an Hand von Experimenten mit Indium und Polyvinylchlorid demonstriert.

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, —150° 700°. , 600°. IBM . .

     

Acid hydrolysis of cellulose in a differential scanning calorimeter

Differential scanning calorimetry was applied to the decompositions of cellulose and D-glucose with several concentration of sulfuric acid. The heat of reaction for cellulose was slightly less than that for glucose. It suggests that the heat of hydrolysis of the (-1,4-glucosidic linkage is endothermic.The degree of reaction obtained by means of a commercial kinetic program was 1.1±0.1, which was independent of the acid concentration for both cellulose and glucose.The quantity of D-glucose produced by saccharification of cellulose was estimated using kinetic parameters obtained for cellulose and glucose, which were assumed to express the respective parameters for the successive first-order reactions cellulose to D-glucose, and glucose to decomposition products.

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Zusammenfassung Die Zersetzung von Cellulose und D-Glucose durch Schwefelsäure unterschiedlicher Konzentration wurde mittels DSC untersucht. Die Reaktionswärme ist bei Cellulose etwas geringer als bei Glucose, was zeigt, daß die Hydrolyse der-1,4-Glucosidbindung ein endothermer Vorgang ist. Der mittels eines kommerziellen kinetischen Programms erhaltene Reaktionsgrad beträgt 1.1±0.1 und erwies sich sowohl bei Cellulose als auch bei Glucose als unabhängig von der Säurekonzentration. Die durch Verzuckerung von Cellulose gebildete Menge an D-Glucose wurde unter Verwendung von für Cellulose und Glucose erhaltenen kinetischen Parametern bestimmt, für die angenommen wurde, daß sie die entsprechenden Parameter der Folgereaktionen erster Ordnung Cellulose D-Glucose und Glucose Zersetzungsprodukte darstellen.

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-. - , . , - -1,4- . , , 1.1±0.1 . -, , , , - .

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We express our sincere gratitutde to Dr. S. Tanaka for useful discussions.     

Polymerization kinetics of acrylic bone cements by differential scanning calorimetry

Bone cements are widely used for the fixation of metallic prostheses in orthopaedics and to form replacements for skull defects in neurosurgery. Acrylic bone cements are based on a mixture of methyl methacrylate (MMA) and a fine powder of polymethyl methacrylate (PMMA). The polymerization of the bone cement occurs in contact with the bone and the prosthesis which act as the boundaries of a bulk polymerization reactor. The kinetic behaviour of the bone cement plays a fundamental role for the final performance of the implant. In this paper, the isothermal and non-isothermal polymerization behaviour of a commercial bone cement is described. A simple phenomenological model, accounting for the autoacceleration ffect, for a diffusion controlled termination mechanism and for the reaction between inhibitor and initiator, is proposed. The reaction kinetics is analysed by DSC. DSC data are used for the determination of the rates of polymerization under isothermal and non-isothermal conditions. The experimental data are processed to calculate the parameters of the proposed phenomenological kinetic model. The analytical and numerical details related to the integration of the model are discussed.     

Application of the differential scanning calorimeter to purity measurements

This paper presents a new method for the calculation of the purity of organic, non-polymeric samples using the recorder trace from a Differential Scanning Calorimeter (DSC), Perkin-Elmer Corp. The entire DSC recorder trace is employed rather than only the initial portion of the curve. The previous trial and error choice of energy lost by the DSC trace has been replaced by a definite numerical value. Meaningful purity values have been obtained from a single DSC trace on samples of from 95 to 99.9% purity. This new method has been demonstrated to provide more accurate and less ambiguous results than the manufacturer's procedure.     

Characterization of solid dispersions of rofecoxib using differential scanning calorimeter

Summary Solid dispersions were prepared to enhance the dissolution rate of rofecoxib. Differential scanning calorimetry (DSC) and X-ray diffraction (XRD) were used for the characterization of solid dispersions of polyvinyl pyrrolidone (PVP):talc:drug (3:1:1) and hydroxypropyl methylcellulose (HPMC):talc:drug (4:1:1). The DSC study indicated that PVP solid dispersion showed formation of fusion solution while HPMC solid dispersion showed no intermolecular fusion during the preparation of solid dispersions by spray dry process. The dissolution profiles and the calculated times for 75 and 90% drug release showed that dissolution rate of rofecoxib was improved in solid dispersions as compared to pure drug and physical mixtures. The DSC and XRD were successfully employed to find out the crystalline state of drug in the both solid dispersions. PVP solid dispersion gave better dissolution rate than HPMC solid dispersion. The drug was transformed from crystalline to amorphous form in PVP solid dispersion which was further conformed by XRD and DSC. The PVP:talc:drug solid dispersion can be used for the dissolution enhancement and thereby bioavailability of rofecoxib.     

Determination of solidus and liquidus temperatures by means of a Perkin-Elmer 1B differential scanning calorimeter

A Perkin-Elmer 1B DSC apparatus was used to test the O'Neill expression for the melting interval of pure compounds on samples of organic compounds 1–10 mg in weight. On the basis of O'Neill's model, an expression for the melting interval of solid solutions,T, has been derived. The difference betweenT andT ₁ – T _s (T ₁ andT _s = =liquidus and solidus temperatures) is discussed. A simple procedure for the determination of solidus and liquidus temperatures from DSC data is proposed.

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Zusammenfassung Ein Perkin-Elmer DSC-Gerät 1B wurde zur Prüfung des O'Neillschen Ausdruckes für den Schmelzbereich reiner Verbindungen an Proben organischer Verbindungen von 1–10 mg eingesetzt. Auf Grund des O'Neill-schen Modells wurde ein Ausdruck für den Schmelzbereich fester Lösungen,T, abgeleitet. Der Unterschied zwischenT undT ₁ – T _s (T ₁,T _s =Flüssig- und Fest-Temperaturen) wird erörtert. Eine einfache Methode zur Bestimmung von Fest- und Flüssigphasentemperaturen aus DSC-Daten wird vorgeschlagen.

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1 — ' , 1–10 . ' . T -T , T _c — . .

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A study of sulfur-free thiuram vulcanization using differential scanning calorimeter

A number of curative mixtures without rubber and with natural rubber or polybutadiene based on binary and tertiary combinations of zinc oxide, tetramethylthiuram disulfide, and 2-mercaptobenzothiazole were treated in a differential scanning calorimeter. From the shapes of exothermal curves a zinc-accelerator complex formation has been examined. Although the experimental results can give no direct evidence for the structure of the complexes, they do contribute to an elucidation of the complex formation in the vulcanization process.     

Unusual use of the term “differential scanning calorimeter”

Derivatograph was used to investigate pseudohomogeneous ion-exchange membranes. Two membrane types were examined: a) a membrane obtained from polyethylene film modified with the copolymer of styrene and DVB; and b) membrane AMF C-311 obtained on a film of fluorinated polymeric material.Although differential thermal analysis (DTA) has been used in the investigation of polymers only recently, a large number of papers concerning different problems in this field have already appeared. Only a few of these papers, however, have been devoted to cross-linked polyelectrolytes and more exclusively to ion-exchange resins [1–5], i.e. homogeneous polyelectrolytes. Up to date no publication dealing with pseudohomogeneous ion-exchange membranes has appeared. The pseudohomogeneous membrane is a system of two phases: a polymer film (polyethylene is most often used as matrix), with a cross-linked acid (e.g.polystyrenesulphonic acid) dispersed in the polymer film. The present investigation was undertaken to find the correlation between the thermal curves of a pseudohomogeneous cation-exchange membrane and the thermal properties of both phases of the membrane.The authors wish to thank T. Grodzicka, Institute of Chemistry, N. Copernicus University, Toru>n for determinations carried out with the MOM Derivatograph.     

Enthalpies and temperatures of transformation for plutonium using a differential scanning calorimeter

The enthalpies and temperatures of transformation of high purity plutonium were measured using a differential scanning calorimeter. The results of our study are presented and compared to values obtained by previous methods.Work performed under the auspices of the U. S. Department of Energy by Lawrence Livermore Laboratory under contract No. W-7405-Eng-48.     

Enthalpy of solution of carbohydrates using a modified differential scanning calorimeter

A differential scanning calorimeter (DSC) was modified for the determination of enthalpies of solution. The measurements were performed on aqueous solutions of the deoxy- and fluoro-deoxy derivatives of D-glucopyranose (Glu) where the OH group on the C1, C2, C3, and C6 is replaced by H (1HGlu, 2HGlu, 3HGlu, and 6HGlu) and by F (1FGlu, 2FGlu, 3FGlu, and 6FGlu), 4-deoxy 4-fluoro--D-glucopyranoside (4FGlu), 1-methoxy--D-glucopyranoside (MeOGlu), 1-phenoxy--D-glucopyranoside (PheOGlu), D-mannopyranose (Man), and 3-methoxy--D-glucopyranoside (3MeOGlu), at 15.1, 25.0, 35.0, and 45.1°C. The enthalpies of solution _sH⁰(T) ranged from 1.00±0.25 kJ-mol^–1 for 6HGlu at 15.1°C to 20.4±1.4 for PhOGlu at 45.1°C and were in good agreement with literature values for Man, Glu, MeOGlu, and 3MeOGlu at 25.0 and 35.0°C and for MeOMan and 2HGlu at 35.0°C. _sH⁰(T) for the derivatives were then extrapolated up to the melting temperature T_m and compared with their enthalpies of fusion, _fH also determined from DSC measurements. If the agreement between _sH⁰(T_m) and _fH was within the 95% confidence level, then it was concluded that intermolecular interactions between the carbohydrate molecules in the liquid phase were the same as between the carbohydrate and water molecules in the solution phase. This agreement was observed for aqueous solutions of Man, Glu, MeOGlu, 3HGlu, 3FGlu, and 6FGlu.     

Comparative analysis of purity determination methods using a differential scanning calorimeter

Comparative analysis of several methods for purity determination using DSC is presented. This is based on a mathematical model including the construction of theoretical melting curves for two-component systems and the calculation of recorded melting curves with the help of a set of equations describing the formation of a DSC output signal. It is shown that the true accuracy of purity determinations in the range of impurity concentrations ¯x=0.005–0.02 does not exceed 30–50%.

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Zusammenfassung Eine Vergleichende Analyse verschiedener Methoden zur Reinheitsbestimmung mittels DSC wurde ausgeführt. Diese basiert auf einem mathematischen System, daß die Konstruktion theoretischer Schmelzkurven für Zweikomponentensysteme und die Berechnung von registrierten Schmelzkurven mit Hilfe einer Reihe die Ausbildung des DSC-Signals beschreibenden Gleichungen in sich einschließt. Es wird gezeigt, daß die Genauigkeit der Reinheitsbestimmungen bei Konzentrationen der Verunreinigungen von ¯X₂=0.005–0.02 30–50% nicht überschreitet.

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, , . , 0,005-0,02 30–50%.

     

ZnO nanoparticles and poly(acrylic) acid-based polymer gel electrolyte for photo electrochemical cell

This work presents a photo electrochemical cell based on zinc oxide (ZnO) nanoparticles and poly(acrylic) acid (PAA) doped with sodium iodide (NaI) and iodine (I₂) polymer gel electrolyte. The ZnO powders were synthesized by sol–gel storage and sol–gel centrifugation. The ZnO powder synthesized via sol–gel centrifugation showed the optimal structural properties, with largest crystallite sizes of 58 nm, average particles size between 20 and 80 nm and indirect band gap energy of 3.20 eV. The highest conductivity [(8.0 ± 0.1) × 10^?2 S cm^?1] was obtained for PAA + 0.8 M NaI + 0.02 M I₂. This sample achieved the lowest activation energy (0.029 eV) and electrochemical stability at 1.6 V. The ZnO powder synthesized via sol–gel centrifugation and PAA + 0.8 M NaI + 0.02 M I₂ was fabricated as a Cu–ZnO/PAA + 0.8 M NaI + 0.02 M I₂/C-ITO photo electrochemical cell.     

Determination of thermodynamic properties of YRhO3(s) by solid-state electrochemical cell and differential scanning calorimeter

The standard molar Gibbs free energy of formation of YRhO₃(s) has been determined using a solid-state electrochemical cell wherein calcia-stabilized zirconia was used as an electrolyte. The cell can be represented by: ( - )\textPt - Rh/{ \textY₂\textO_\text3( \texts ) + \textYRh\textO₃( \texts ) + \textRh( \texts ) }//\textCSZ//\textO₂( p( \textO₂ ) = 21.21  \textkPa )/\textPt - Rh( + ) \left( - \right){\text{Pt - Rh/}}\left\{ {{{\text{Y}}_2}{{\text{O}}_{\text{3}}}\left( {\text{s}} \right) + {\text{YRh}}{{\text{O}}_3}\left( {\text{s}} \right) + {\text{Rh}}\left( {\text{s}} \right)} \right\}//{\text{CSZ//}}{{\text{O}}_2}\left( {p\left( {{{\text{O}}_2}} \right) = 21.21\;{\text{kPa}}} \right)/{\text{Pt - Rh}}\left( + \right) . The electromotive force was measured in the temperature range from 920.0 to 1,197.3 K. The standard molar Gibbs energy of the formation of YRhO₃(s) from elements in their standard state using this electrochemical cell has been calculated and can be represented by: D_\textfG^\texto{ \textYRh\textO₃( \texts ) }/\textkJ  \textmo\textl ^{- 1}( ±1.61 ) = - 1,147.4 + 0.2815  T  ( \textK ) {\Delta_{\text{f}}}{G^{\text{o}}}\left\{ {{\text{YRh}}{{\text{O}}_3}\left( {\text{s}} \right)} \right\}/{\text{kJ}}\;{\text{mo}}{{\text{l}}^{ - 1}}\left( {\pm 1.61} \right) = - 1,147.4 + 0.2815\;T\;\left( {\text{K}} \right) . Standard molar heat capacity C^o_p,m C^{o}_{{p,m}} (T) of YRhO₃(s) was measured using a heat flux-type differential scanning calorimeter in two different temperature ranges from 127 to 299 K and 305 to 646 K. The heat capacity in the higher temperature range was fitted into a polynomial expression and can be represented by: $ {*{20}{c}} {\mathop C\nolimits_{p,m}^{\text{o}} \left( {{\text{YRh}}{{\text{O}}_3},{\text{s,}}T} \right)\left( {{\text{J}}\;{{\text{K}}^{ - 1}}{\text{mo}}{{\text{l}}^{ - 1}}} \right)} & { = 109.838 + 23.318 \times {{10}^{ - 3}}T\left( {\text{K}} \right)} & { - 12.5964 \times {{10}^5}/{T^2}\left( {\text{K}} \right).} \\ {} & {\left( {305 \leqslant T\left( {\text{K}} \right) \leqslant 646} \right)} & {} \\ $ \begin{array}{*{20}{c}} {\mathop C\nolimits_{p,m}^{\text{o}} \left( {{\text{YRh}}{{\text{O}}_3},{\text{s,}}T} \right)\left( {{\text{J}}\;{{\text{K}}^{ - 1}}{\text{mo}}{{\text{l}}^{ - 1}}} \right)} & { = 109.838 + 23.318 \times {{10}^{ - 3}}T\left( {\text{K}} \right)} & { - 12.5964 \times {{10}^5}/{T^2}\left( {\text{K}} \right).} \\ {} & {\left( {305 \leqslant T\left( {\text{K}} \right) \leqslant 646} \right)} & {} \\ \end{array} The heat capacity of YRhO₃(s) was used along with the data obtained from the electrochemical cell to calculate the standard enthalpy and entropy of formation of the compound at 298.15 K.     

Radiochemical investigations of fast neutron-induced low-yield nuclear reactions

Radiochemical separation methods for K, Mn, Cu, Ga, Sr, Y, Nb, Ag, I, Ce, Eu, Lu and Pt, employing precipitation, adsorption, distillation, solvent extraction or ion-exchange, as used in the investigations of rare nuclear reactions such as (n, t) and (n,³He) at 14. 6 MeV, are described. For studying the (n, t) reaction at 23 MeV a method for the vacuum extraction and “low-level” gas-phase counting of tritium is outlined. The measured nuclear reaction cross-section data are discussed briefly.     

Determination of heat of mixing and heat of vaporization with a differential scanning calorimeter

A simple method is presented for measuring the heat of mixing and the heat of vaporization of volatile liquids at temperatures below their boiling point. It consists in introducing liquids by a microsyringe into a nearly closed cell of the DSC. The relative standard deviation for 4 to 5 runs is ca. 5% for heat of mixing and ca. 2% for heat of vaporization.