A non-equilibrium thermodynamics approach to model mass and heat transport for water pervaporation through a zeolite membrane

Pervaporation through zeolite membranes involves local heat effects and combined heat and mass transport. The current state-of-the-art Maxwell–Stefan (M–S) models do not take these effects into account. In this study, transport equations for the coupled heat and mass transport through a zeolite membrane are derived from the framework of non-equilibrium thermodynamics (NET). Moreover, the assumption of equilibrium between the adjacent bulk phases at the feed and permeate sides of the zeolite layer is abandoned in favor of local equilibrium. The equations have been used to model pervaporation of water through a 2 m thick NaA type zeolite membrane, deposited on an asymmetric -alumina support, at a feed temperature of 348 K. Assuming a flux of 10 kg m⁻² h⁻¹(0.15 mol m⁻² s⁻¹), the transport through the zeolite layer, as well as the liquid feed side boundary layer and the support layers is modeled. The activity, fugacity, and temperature profiles are calculated with and without taking coupling effects and surfaces into account. The profiles show distinct differences between the two cases. Including the surface effects leads to discontinuities in the activity and temperature at the membrane interfaces. A significantly higher temperature drop of 1.3 K is calculated across the zeolite, compared to 0.4 K when surface and coupling effects are not accounted for. The calculated decrease in temperature over the zeolite layer is dominated by the surfaces. This could indicate that temperature polarization is, to a large extent, a surface effect. The heat flux induces an extra driving force for mass transport, reducing the activity difference over the membrane. A positive jump in activity is observed at the interfaces, revealing the mass transport across the interfaces is governed by the coupling with the heat flux. The support layers contribute significantly to the total mass transport resistance.     

Entropy production in TMDSC

The non-equilibrium process due to irreversible heat exchanges occurring during a temperature modulated differential scanning calorimetry (TMDSC) experiment is investigated in detail. This enables us to define an experimental frequency dependent complex heat capacity from this calorimetric method. The physical meaning of this dynamic heat capacity is discussed. A relationship is clearly established between the imaginary part of this complex quantity and the net entropy created during the experimental time-scale.     

Current trends in finite-time thermodynamics

The cornerstone of finite-time thermodynamics is all about the price of haste and how to minimize it. Reversible processes may be ultimately efficient, but they are unrealistically slow. In all situations-chemical, mechanical, economical-we pay extra to get the job done quickly. Finite-time thermodynamics can be used to develop methods to limit that extra expenditure, be it in energy, entropy production, money, or something entirely different. Finite-time thermodynamics also includes methods to calculate the optimal path or mode of operation to achieve this minimal expenditure. The concept is to place the system of interest in contact with a time-varying environment which will coax the system along the desired path, much like guiding a horse along by waving a carrot in front of it.     

Evaluation of interfacial region of microphase-separated SEBS using modulated differential scanning calorimetry and dynamic mechanical thermal analysis

The continuous structural changes of Poly(styrene-b-ethylene-butylene-b-styrene) [SEBS] due to the effect of temperature are hard to evaluate using conventional differential scanning calorimetry (DSC). This paper presents an accurate and simple way to evaluate microstructural and glass transitions of SEBS using modulated differential scanning calorimetry (MDSC). The weak crystalline nature of –(CH₂-CH₂)–_n in the ethylene-butylene (EB) block melted around 36 °C. The premature molecular moment and Tg of the styrene block were at 62 °C and 96 °C, respectively. The interfacial region at high temperature was explained with respect to order-order transition (OOT) at 144 °C and a prominent Order-Disorder Transition (ODT) at around 202 °C. Dynamic mechanical thermal analysis (DMTA) and dynamic mechanical rheological testing (DMRT) measurements also revealed that the T_g of the PS transition were consistent at around 96 °C.     

Wax deposition rate model for heat and mass coupling of piped waxy crude oil based on non-equilibrium thermodynamics

In this paper, wax deposition in waxy crude oil transportation process was regarded as an irreversible process. Based on the entropy production rate equations, the linear phenomenological equations for the diffusion of wax molecules were derived by using the theory and method of non-equilibrium thermodynamics and heat-mass transfer. Combined with the mass and energy conservation laws, the differential equations of heat and mass transfer in the process of pipeline transportation were established, and the molecular diffusion rate of dissolved wax was solved. On the basis of this, the mathematical model of actual wax deposition rate was established by considering the attachment process and scouring process of the wax molecules. Taking an oil pipeline in Daqing as an example, the change law and influencing factors of the wax molecular diffusion coefficient, the wax deposition rate, and the net wax deposition rate were studied by numerical simulation. The wax deposition rate test results of the laboratory loop test were compared with the theoretical calculation results in order to analyze the accuracy and the adaptability of heat and mass coupling mechanism and to provide a theoretical basis for further study of wax deposition in the process of waxy oil pipeline transportation.     

Flexibility of enzymatic transitions as a hallmark of optimized enzyme steady-state kinetics and thermodynamics

We investigate the relations between the enzyme kinetic flexibility, the rate of entropy production, and the Shannon information entropy in a steady-state enzyme reaction. All these quantities are maximized with respect to enzyme rate constants. We show that the steady-state, which is characterized by the most flexible enzymatic transitions between the enzyme conformational states, coincides with the global maxima of the Shannon information entropy and the rate of entropy production. This steady-state of an enzyme is referred to as globally optimal. This theoretical approach is then used for the analysis of the kinetic and the thermodynamic performance of the enzyme triose-phosphate isomerase. The analysis reveals that there exist well-defined maxima of the kinetic flexibility, the rate of entropy production, and the Shannon information entropy with respect to any arbitrarily chosen rate constant of the enzyme and that these maxima, calculated from the measured kinetic rate constants for the triose-phosphate isomerase are lower, however of the same order of magnitude, as the maxima of the globally optimal state of the enzyme. This suggests that the triose-phosphate isomerase could be a well, but not fully evolved enzyme, as it was previously claimed. Herein presented theoretical investigations also provide clear evidence that the flexibility of enzymatic transitions between the enzyme conformational states is a requirement for the maximal Shannon information entropy and the maximal rate of entropy production.     

Reaction thermodynamics of amine‐cured epoxy systems: Validation of the enthalpy and heat capacity of reaction as determined by modulated temperature differential scanning calorimetry

The reaction enthalpy and reaction heat capacity of three aromatic epoxy–amine systems have been determined with modulated temperature diffential scanning calorimetry (MTDSC), mostly in quasi‐isothermal conditions, over a wide temperature range (33–140 °C) and for different mixture compositions. The reaction enthalpy is only slightly dependent on the epoxy–amine chemistry, from ?111 to ?98 kJ/mol epoxy functionality. With the model system phenyl glycidyl ether (PGE)+aniline, the reaction enthalpy of the secondary amine–epoxy reaction step is equal to that of the primary amine–epoxy reaction. Group contributions needed to calculate the reaction heat capacity with an additivity approach are evaluated, and a new value of 37.2 J mol^?1 K^?1 for the group N? (H)(C)(CB) is proposed. With this group contribution, the additivity method predicts almost equal values for the reaction heat capacity of both amine–epoxy reaction steps at 298.15 K (Δ_rC_p,prim = 15.7 J mol^?1 K^?1 and Δ_rC_p,sec = 14.6 J mol^?1 K^?1), whereas the experimental value of Δ_rC_p,sec is about three times larger than that of Δ_rC_p,prim at 100 °C. These results are confirmed experimentally for PGE+aniline as a different temperature dependence of both reaction heat capacities. MTDSC therefore is potentially interesting for differentiating between reactive species in an epoxy–amine reaction, a benefit previously assigned to spectroscopic methods only. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 594–608, 2003     

Non-equilibrium thermodynamics and kinetic theory of gas mixtures in the presence of interfaces

A broad range of the boundary value problems of the kinetic theory of gases and gas mixtures is considered based on kinetic theory and non-equilibrium thermodynamics. The interrelation of the kinetic theory and non-equilibrium thermodynamics is discussed. The balance equations at the interface are obtained for the case of the boundary layers with peculiar properties. Procedures for deriving the boundary conditions for slightly rarefied gas mixtures are outlined. The problems of calculating slip coefficients are discussed. The specificity of the kinetic effects in the boundary conditions is shown. A set of general relations related to gas mixture flows in capillaries is deduced. The possibility of non-equilibrium kinetic effects in the form of a paradoxical distribution of non-equilibrium temperature is shown. Methods of non-equilibrium thermodynamics are used to obtain the phenomenological equations describing the thermophoresis and diffusiophoresis of particles and cross phenomena. The growth and evaporation of droplets is considered based on kinetic theory and non-equilibrium thermodynamics.     

Some remarks on heat capacity measurements by temperature-modulated calorimetry

In temperature-modulated calorimetry, the condition in sample amount, especially thickness, required for high-accuracy heat capacity measurement should be made clear. We propose the condition of maximum thickness of a sample for measuring heat capacity within an accuracy of 1%. The other important factor for high-accuracy heat capacity measurement is thermal contact conductance between a sample and a sample pan and also that between a pan and a base plate of an apparatus. The conditions in these thermal contact conductances required for high-accuracy heat capacity measurement are discussed. Among them, if only thermal contact conductance between a pan and a base plate is significant, there is an ingenious method to measure heat capacity with high accuracy. Furthermore, if the thermal contact conductance between a pan and a base plate is infinite, we offer a simple method to obtain complex heat capacity.     

Modulated differential scanning calorimetry in the glass transition region

Temperature-modulated differential scanning calorimetry (TMDSC) is based on heat flow and represents a linear system for the measurement of heat capacity. As long as the measurements are carried out close to steady state and only a negligible temperature gradient exists within the sample, quantitative data can be gathered as a function of modulation frequency. Applied to the glass transition, such measurements permit the determination the kinetic parameters of the material. Based on either the hole theory of liquids or irreversible thermodynamics, the necessary equations are derived to describe the apparent heat capacity as a function of frequency.Presented in part at the 24th Conference of the Northamerican Thermal Analysis Society, San Francisco, CA, September 10–13, 1995.     

Advanced AC calorimetry of polycaprolactone in melting region

The new capabilities of AC calorimetry, when working at frequencies above the classical limit were demonstrated. The appropriate frequency range of classical AC calorimetry was substantially enlarged. It was shown that the advanced AC calorimetry can be applied for studying dynamic heat capacity of polymers in the frequency range 0.1–1 Hz. Thus, the processes with characteristic time as short as ca. 5 s was registered. The advanced AC technique was applied for investigation of the melting kinetics in polycaprolactone. It was found that melting in polycaprolactone is related to an activated process. The activation of the melting process after a step heating is described by a stretched exponent and the decay of the melting by only one exponent at short times. The dependencies of the exponent on temperature and thermal treatment were investigated at frequencies in the range 0.1–1Hz and modulation amplitudes 0.005–0.2 K.     

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.On leave from Toray Industries, Inc., Otsu, Shiga 520, Japan.This work was supported by the Division of Materials Research, National Science Foundation, Polymers Program, Grant # DMR 90-00520 and the Division of Materials Sciences, Office of Basic Energy Sciences, U. S. Department of Energy at Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corp. for the U. S. Department of Energy, under contract number DE-AC05-96OR22464. Support for instrumentation came from TA Instruments, Inc. Research support was also given by ICI Paints, and Toray Industries, Inc.     

Modulated differential scanning calorimetry in the glass transition region. V. Activation energies and relaxation times of poly(ethylene terephthalate)s

Temperature-modulated differential scanning calorimetry is used to evaluate the kinetics of the glass transition from measurement of the first harmonic of the apparent, reversing heat capacity. The data are taken from quasi-isothermal experiments with negligible instrument lag, extrapolated to zero modulation amplitude. Equations based on irreversible thermodynamics that can be understood in terms of the hole theory of liquids are applied to measurements on amorphous, semicrystalline, and biaxially drawn poly(ethylene terephthalate)s (PET). The activation energy of amorphous PET decreases from 328 to 153 kJ/mol on crystallization and to 111 kJ/mol on orientation, and is correlated with an increase in the preexponential factor. After annealing of the crystallized samples below the glass transition temperature, the activation energy of the semicrystalline PET can recover beyond the level of amorphous PET, to 387 kJ/mol. The earlier observed decrease in enthalpy relaxation on crystallization is linked to this sharp decrease in activation energy. © 1996 John Wiley & Sons, Inc.     

Thermodynamic properties of carbosilane dendrimers of the seventh and ninth generations with terminal butyl groups in the temperature range from <Emphasis Type="Italic">T</Emphasis> → 0 to 600 K

Temperature dependences of the heat capacity of carbosilane dendrimers with butyl terminal groups of the seventh and ninth generations were determined in the temperature range from 6 to 600 K by precision adiabatic vacuum calorimetry and differential scanning (dynamic) calorimetry. The physical transitions were revealed and their thermodynamic characteristics were analyzed. The experimental data obtained were used to calculate the standard thermodynamic functions C _p (T), H°(T) − H°(0), S°(T), and G°(T) − H°(0) for the temperature range from T → 0 to 600 K. The thermodynamic function-molar weight isotherms for the dendrimers of the third–ninth generations with terminal butyl groups in the glassy and highly elastic state are linear. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1924–1928, October, 2007.     

Solvation enthalpies and heat capacities of n-alkanes in four polymer phases by capillary gas chromatography

Molar solvation enthalpy (deltasol H(o)298) and molar heat capacity changes (deltasol C(o)p) were determined by gas chromatography for the C6-C12 n-alkanes on four preferred stationary phases (100% polydimethyl siloxane, 50% diphenyl-50% dimethyl polysiloxane, 50% trifluoropropyl methylsiloxane, and polyethylene glycol) in commercial FSOT. Statistical evaluation indicated the temperature independence of deltasol C(o)p in the range 303-393 K. Deltasol H(o)298 depends linearly on the number of carbon atoms in the n-alkanes, but no linearity could be established for deltasol C(o)p of higher homologues on polar columns, which may be due to a more ordered state on the liquid phase. The homologues for which a linear temperature dependence exists demonstrated that deltasol C(o)p is related linearly to the van der Waals volume and the temperature derivative of the density of the stationary phase. The results are consistent with a simple physical explanation at the molecular level.     

Thermodynamic Characteristics of Phenacetin in Solid State and Saturated Solutions in Several Neat and Binary Solvents

The thermodynamic properties of phenacetin in solid state and in saturated conditions in neat and binary solvents were characterized based on differential scanning calorimetry and spectroscopic solubility measurements. The temperature-related heat capacity values measured for both the solid and melt states were provided and used for precise determination of the values for ideal solubility, fusion thermodynamic functions, and activity coefficients in the studied solutions. Factors affecting the accuracy of these values were discussed in terms of various models of specific heat capacity difference for phenacetin in crystal and super-cooled liquid states. It was concluded that different properties have varying sensitivity in relation to the accuracy of heat capacity values. The values of temperature-related excess solubility in aqueous binary mixtures were interpreted using the Jouyban–Acree solubility equation for aqueous binary mixtures of methanol, DMSO, DMF, 1,4-dioxane, and acetonitrile. All binary solvent systems studied exhibited strong positive non-ideal deviations from an algebraic rule of mixing. Additionally, an interesting co-solvency phenomenon was observed with phenacetin solubility in aqueous mixtures with acetonitrile or 1,4-dioxane. The remaining three solvents acted as strong co-solvents.     

Modulated‐temperature differential scanning calorimetry study of temperature‐induced mixing and demixing in poly(vinylmethylether)/water

The heat capacity or reversing heat flow signal from modulated‐temperature differential scanning calorimetry can be used to measure the onset of phase separation in a poly(vinylmethylether)/water mixture, clearly showing the special type III lower critical solution temperature demixing behavior. Characteristic of this demixing behavior is a three‐phase region, which is detected in the nonreversing heat flow signal. Stepwise quasi‐isothermal measurements through the phase transition show large excess contributions in the (apparent) heat capacity signal, caused by demixing/remixing heat effects on the timescale of the modulation (fast process). These excess contributions and their time‐dependent evolutions (slow process) are useful in understanding the kinetics of phase separation and the morphology (interphase) development. Care has to be taken, however, in interpreting the heat capacity signal derived from the amplitude of the modulated heat flow because nonlinear effects lead to the occurrence of higher harmonics. Therefore, the raw heat flow signal for quasi‐isothermal demixing and remixing measurements is also examined in the time domain. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1824–1836, 2003     

Thermodynamic properties of an alternating copolymer of bicyclo[2.2.1]hepta-2,5-diene and carbon monoxide in a region from <Emphasis Type="Italic">T</Emphasis> → 0 to 550 K

The temperature dependence of the heat capacity of an alternating copolymer of bicyclo[2.2.1]hepta-2,5-diene and carbon monoxide in the temperature range 6–550 K (with an error of 0.2–0.5% at 6–350 K and 0.5–1.5% at 330–550 K) was studied by the adiabatic vacuum and dynamic calorimetry. Physical transformations of the copolymer in the studied temperature region were identified, and their thermodynamic characteristics were determined. The combustion energy of the copolymer at 298.15 K was measured in a calorimeter with a static bomb and isothermal jacket. The thermodynamic functions for a region of 0–550 K, enthalpy of combustion, and thermodynamic parameters of copolymer formation from simple substances at T = 298.15 K and p = 101.325 kPa were calculated from the obtained experimental data. The new results and earlier published data were used for the calculation of the thermodynamic characteristics of the alternate copolymerization of bicyclo[2.2.1]hepta-2,5-diene and CO under standard pressure for a region of 0–350 K for the bulk reaction. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1483–1487, June, 2005.     

Thermodynamic properties of linear polyurethanes based on 1,6-hexamethylenediisocyanate with butane-1,4-diol and hexane-1,6-diol in the temperature range from T → 0 to 460 K

The temperature dependences of the heat capacity of partially crystalline linear polyurethanes based on 1,6-hexamethylenediisocyanate with butane-1,4-diol and hexane-1,6-diol were studied for the first time in a temperature range of 6–460 K by the methods of adiabatic vacuum and dynamic calorimetry. Physical changes in the state of polyurethanes were revealed and characterized; the standard thermodynamic functions, namely, C _p °(T), H°(T)-H°(0), S°(T), and G°(T)-H°(0), were calculated from the obtained experimental data in the temperature range from T → 0 to 460 K for the polymers in the crystalline, glassy, highly elastic, and liquid states. The energies of combustion of the polymers were measured by the bomb calorimetry method, and the standard thermodynamic characteristics of their formation at 298.15 K were calculated. The thermodynamic characteristics of bulk polycondensation of 1,6-hexamethylenediisocyanate with butane-1,4-diol and hexane-1,6-diol to form linear aliphatic polyurethanes-{4,6} and-{6,6} were determined in the range from T → 0 to 350 K at p° = 0.1 MPa. The thermodynamic properties of the polyurethanes under study and polymers of isomeric structure were compared. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 817–823, May, 2006.