Thermodynamic study of a pressure‐temperature phase diagram for poly(N‐isopropylacrylamide) gels

The volume change, ΔV_h,_, accompanying the hydrophobic hydration associated with the volume phase transition in Poly(N‐isopropylacrylamide) gels was measured by a simple method. The hydration accompanies a negative ΔV_h′?2.5 cm³/mol. The P‐T phase diagram, the coexistence curve, for the gels was determined from the swelling ratio‐pressure curves up to 350 MPa for various constant temperatures. The contour of the coexistence curve is shaped like an ellipsoid on the P‐T plain, which is a feature peculiar to the reversible pressure‐temperature denaturation of a protein. The thermodynamic analysis of the Clausius–Clapeyron relation for the measured ΔV_h elucidates that the obtained coexistence curve represents the phase boundary between thermodynamic different phases like the two phases, native and denatured, of a protein and gives the transition enthalpy, ΔH, 5.2kJ/mol by estimate, which well coincides with the transition heat measured by a calorimetric method. Considering the volume‐dependent free energy, Δv_mi · P, for the mixing free energy of the gel, we can fit the calculated curve to the measured swelling ratio‐pressure curve of PNIPA gels. The value of Δv_mi changes the sign from negative to positive above around 100MPa. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 405–412, 2005     

A method for estimating both the solubility parameters and molar volumes of liquids

The solubility parameters and molar volumes of substances can be used, in conjunction with suitable theory, to provide estimates of the thermodynamic properties of solutions; the solubility characteristics of polymer-solvent systems and the estimation of the equilibrium uptake of liquids by polymers are examples of the type of practical problems that are amenable to treatment. For low molecular weight liquids, the solubility parameter, δ, is conveniently calculated using the expression δ = (ΔE_v/V)½, where ΔE_v is the energy of vaporization at a given temperature and V is the corresponding molar volume which is calculated from the known values of molecular weight and density. For high molecular weight polymers, the volatility is much too low for ΔE_v to be obtained directly and hence recourse must be made to indirect methods for estimating δ for these materials. One such widely used method is based on Small's additive group “molar-attraction constants” which when summed allow the estimation of δ from a knowledge of the structural formula of the material; however, the density must still be determined experimentally. The proposed method of estimating δ, also based on group additive constants is believed to be superior to Small's method for two reasons: (1) the contribution of a much larger number of functional groups have been evaluated, and (2) the method requires only a knowledge of the structural formula of the compound.     

Thermodynamic modeling of YO1.5-TaO2.5 system and the effects of elastic strain energy and diffusion on phase transformation of YTaO4

Thermodynamic parameters of the YO_1.5-TaO_2.5 system were obtained, and the effects of elastic strain energy and diffusion on phase transformation of YTaO₄ were analyzed in this work. The YO_1.5-TaO_2.5 system was critically modeled using the CALPHAD technique based on our calculated formation energies by DFT and available experimental data. According to DFT calculations, M′-YTaO₄ was suggested to be the thermodynamically stable phase at low temperature. For a displacive transformation of T→M between the equilibrium tetragonal and monoclinic YTaO₄, our calculations suggested it cannot be hindered by elastic strain energy. For a diffusive transformation of T→M′, it can be divided into T→M and M→M′. Diffusive transition of M→M′ was likely to be impeded due to large diffusion energy barrier, which was calculated to be 3.260 eV. However, the driving force ΔG _M→M′ is about -0.121 kJ/mol. The large diffusion energy barrier and small driving force may be the main reason that T cannot transform to M′ after cooling.     

Isothermal and nonisothermal melt‐crystallization kinetics of syndiotactic polystyrene

Analyses of the isothermal and nonisothermal melt kinetics for syndiotactic polystyrene have been performed with differential scanning calorimetry, and several kinetic analyses have been used to describe the crystallization process. The regime II→III transition, at a crystallization temperature of 239°, is found. The values of the nucleation parameter K_g for regimes II and III are estimated. The lateral‐surface free energy, σ = 3.24 erg cm^?2, the fold‐surface free energy, σ_e = 52.3 ± 4.2 erg cm^?2, and the average work of chain folding, q = 4.49 ± 0.38 kcal/mol, are determined with the (040) plane assumed to be the growth plane. The observed crystallization characteristics of syndiotactic polystyrene are compared with those of isotactic polystyrene. The activation energies of isothermal and nonisothermal melt crystallization are determined to be ΔE = ?830.7 kJ/mol and ΔE = ?315.9 kJ/mol, respectively. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 2528–2538, 2002     

On the pressure of water of crystallization at filler inclusions

On water uptake, plaster of Paris sets to gypsum, and the volume expansion associated with this particular hydration reaction has been long exploited to make casts for statuary. Immobilization of molecules of liquid water into the crystal lattice of water of crystallization gives rise to a decrease of entropy, and this is manifested by the so-called heat of hydration. When it occurs at a calcium sulfate inclusion inside a polymer, the plaster of Paris → gypsum reaction generates a pressure, and the dependence of the equilibrium value of this pressure on temperature is expressed by Clapeyron's equation. From published data for the volume expansion ΔV and entropy decrease ΔS, it is shown that Using as a benchmark the fact that p is zero at 100°C, the temperature at which plaster of Paris, gypsum, and liquid solution can exist in thermodynamic equilibrium (1), we find that hydration at ambient temperatures of a typical calcium sulfate filler composition will, under conditions of thermodynamic equilibrium, generate sufficient pressure to cause internal cracking. Attention is drawn to the fact that creation of water of crystallization pressures of similar magnitude can be expected for any other filler that can exist in more than one state of hydration. As a corollary, the Clapeyron equation is used to make a similar analysis of the phenomenon of frost shattering in polymeric materials that contain free water.     

Optimization of elution conditions of chitosan gel and the study of its adsorbent mechanism

Chitosan gel was prepared by crosslinking method. To make use of chitosan gel, the optimization of elution conditions and the adsorbent characteristics of chitosan gel were discussed in this article. The optimum elution conditions were c (NaCl) = 0.05 mol/L in Tris‐HCl (pH, 9.05) at the flow rate of 2.0–3.0 mL/min with chitosan gel (particle sizes, 120–140 μm). The effects of contact time, pH, initial BSA concentration, and temperature on adsorption were studied. The equilibrium data could be described well by Langmuir, Freundlich, and Redlich–Peterson models. Adsorption dynamics had been successfully studied by Langergren, intraparticle diffusion model and Avrami model. The thermodynamics parameters ΔG°, ΔH°, and ΔS° were calculated. The spectra studies indicated that the interaction between gel and protein was chiefly through electrostatic attraction in the shape of hydrogen bond. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1495–1506, 2007     

Estimates of the Properties of Liquids

An equation which relates the volume term (V=M/_(ρL-ρg)) of unassociated liquids to pressure P and temperature T has been obtained by the combination of (a) 03V(?I/?V)_P→0=T_x-T for the effect of temperature on V at low (atmospheric) pressure and (b) - V(?P/?V)_T = P_x V_x/⁶/V⁶ _p→0+9(P-p) for the effect of pressure on volume at constant temperature. In the equations, p is the vapour pressure; pL the density of the liquid and pg the vapour density. Often pg can be neglected compared with pL and p is small compared with the large pressures required to affect the densities of liquids appreciably. There are three constants: Tx, Px, which equals 4.455 × 10⁹ N m², and Vx which can be calculated by the addition of atomic values for all the atoms in the molecule and subtraction of a value (6.56 × 10⁶ m³ mol¹) for each bond. When V approximates to M/ρL, the molar volume, the equation can be integrated to give the work and heat of isothermal compression. The viscosity of a liquid is related to the work of compression and solubilities in a liquid to the work required to bring the solute to the compressibility of the liquid. Many relationships can be derived and can be used to estimate properties of unassociated liquids.     

Adiabatic compressibility of polyelectrolytes: The influence of solvents on ionic and nonionic polymers

The adiabatic compressibility of two ionic polymers; namely, poly(acrylic acid) (PAA) and poly(N-dimethylaminoethyl methacrylate) (PDAM) in methanol and dioxane solutions and of a nonionic polymer, poly(vinyl pyrrolidone) (PVP) in aqueous, methanol, and dioxane solutions has been studied. The φV₂ and φK₂ values for the three polymers and their corresponding monomers in methanol and dioxane solutions are found to be concentration independent. There is a marked difference in φK⁰₂ and φV⁰₂ values between monomer and polymer in all three solvents. In aqueous solution, the difference in φV⁰₂ is, on an average, 16.1 cm³/mol, while in methanol and dioxane solution, the same is 24.0 and 20.5 cm³/mol (average), respectively. All three monomers in dilute aqueous solution show a contraction of volume and decrease of adiabatic compressibility which are comparatively small in methanol and dioxane solutions. The φV⁰₂ for PAA, PDAM, and PVP were found to have increased by 0.8, 11.0, and 1.5 cm³/mol, respectively, in dioxane solution over that of the value of the aqueous solution. It is interesting to note that in methanol solution, PAA, PDAM, and PVP show a decrease of φK⁰₂ and φV⁰₂ values by 68.8 cm³/bar/mol and 8.2 cm³/bar/mol, 32.7 cm³/bar/mol, and 4.3 cm³/mol, and 36.6 cm³/bar/mol and 5.8 cm³/mol, respectively, compared to the values obtained from aqueous solution. This has been ascribed to geometric effect since the void space around the molecules is smaller in methanol than in water.     

Solid-liquid phase equilibria,excess molar volume,and molar refraction deviation for the mixtures of ethanoic acid with propanoic,butanoic, and pentanoic acid

The paper reports the solid-liquid phase equilibria (SLE), excess molar volume (V^E), and molar refraction deviation (ΔR) for binary systems of ethanoic acid with the C₃ to C₅ carboxylic acids, propanoic, butanoic, and pentanoic acid, which are the main constituents of bio-butanol fermentation broth. The SLE was determined via a synthetic method using a custom-built glass tube at atmospheric pressure, whereas the thermodynamic mixture properties, V^E and ΔR were obtained from directly measured density and refractive index using a precision densitometer and refractometer, respectively. All of the SLE that were determined for binary mixtures of ethanoic acid+C₃-C₅ carboxylic acids showed a single eutectic point and regressed well with the NRTL activity model within 0.6 K of RMSD. The V^E values for the same binaries were positive for the entire composition ranges of all the systems, whereas the ΔR values were negative for all the systems. The V^E and ΔR were well regressed by polynomial equations, namely Redlich-Kister within 0.006 cm³·mol^?1 of the standard deviation for V^E and 0.02 cm³·mol^?1 for ΔR.     

Free volume of liquids and polymers from internal pressure studies

The free volume, v_f, of liquids is defined in many ways. Comparison of solid and liquid behavior indicates that the definition for free volume in terms of the internal pressure of the liquid (?E/?V)_T, is physically reasonable. Application of the definition of free volume, v_f = RT/(?E/?V)_T, to polymethylenes, coupled with surface energy values, leads to an evaluation of both polymer segmental volume, ?_s, and free volume per segment, (v_f)_s, as a function of temperature. These equilibrium thermodynamic measurements of ?_s and (v_f)_s lead to an energy of activation for viscous flow in good agreement with viscosity studies. Information of this type could be of great use in considering many current problems in polymer flow such as the effect of pressure on viscosity.     

Homogeneous liquid–liquid extraction using perfluorooctanesulfonic acid and calcium and its application to the separation and recovery of vitamin B12

A new phase separation phenomenon was observed in which the perfluorooctanesulfonate ion (PFOS⁻) and calcium ion form an ion‐pair associator and the sedimented liquid phase occurs from the homogeneous aqueous solution. This phenomenon was observed in the neutral pH region at room temperature (25 °C). The optimum concentration conditions for the reagents were [PFOS⁻]_T = 7 × 10⁻³ mol dm^‐3 and [Ca²⁺]_T = 1.1 mol dm^‐3. When these findings were applied to the homogeneous liquid–liquid extraction of vitamin B₁₂, the extraction percentage (E) was 83% and the concentration ratio (ie V_a/V_s, where V_a is the volume of the aqueous phase and V_s is the volume of the sedimented liquid phase) was a maximum of 149. The recovery of vitamin B₁₂ was achieved by adding the propanol–acetone (20 : 80 v/v%) mixed solvent to the sedimented liquid phase; the vitamin B₁₂ precipitated and was filtered. Both the PFOS⁻ and Ca²⁺ were removed by dissolution in the mixed solvent. The recovery percentage of vitamin B₁₂ was 78%. © 1999 Society of Chemical Industry     

Density,refractive index,excess molar volumes and deviations in molar refraction at 298.15 K for binary and ternary mixtures of DIPE (OR TAME) + 1‐methanol (or 1‐propanol) + trihexyltetra‐decylphosphonium bis (2,4,4‐trimethylpentyl) phosphinate

The excess molar volumes (V^E) and the deviations in molar refraction (ΔR) at 298.15 K were determined for the binary systems {diisopropyl ether (DIPE) + 1‐propanol}, {Tert‐amyl methyl ether (TAME) + methanol}, {DIPE + trihexyltetradecylphosphonium bis(2,4,4‐trimethylpentyl)phosphinate ([P_666,14][TMPP])}, {TAME + [P_666,14][TMPP]}, {methanol + [P_666,14][TMPP]} and {1‐propanol + [P_666,14][TMPP]} using a digital vibrating‐tube densimeter and a precision digital refractometer. The V^E and ΔR were correlated with the Redlich–Kister equation for binary systems. In addition, the ternary V^E and ΔR data at 298.15 K were predicted for the ternary systems {DIPE + 1‐propanol + [P_666,14][TMPP]} and {TAME + methanol + [P_666,14][TMPP]} by using the binary contribution model of Radojkovi? with correlated sub‐binary Redlich–Kister parameters. © 2011 Canadian Society for Chemical Engineering     

Silica masterbatches produced with liquid phase mixing Part IV. Volume variation and SEM observations upon stretching

The volume of vulcanizates changes slightly during stretching. Generally, dilatometry and hydrostatic weighing methods are used to measure volume change. Vacuole formation and polymer crystallization are the two main causes of the volume changes, and these are attributed to the separation of polymer from the filler surface and the alignment of polymer molecules, respectively. The relative volume change, ΔV/V, of four different vulcanizates based on a blend of SSBR (solution polymerized styrene-butadiene rubber) and BR (cis-polybutadiene rubber) has been plotted against elongation, ε. The relative volume change of an eco-visco-elastomer-composite (EVEC) compound produced by a continuous liquid phase mixing process was much less than that of a dry-mixed counterpart, especially after normalizing by stress, σ. Scanning electron microscopy (SEM) was utilized to observe the emergence of vacuoles during stretching, and obtain information on their relative size and distribution without the need for replication or ion sputter coating. SEM images also showed that the dispersion of silica in EVEC is better and the number of vacuoles is much less than in the dry-mixed compounds, characterizing a “denser” vulcanizate.     

Free volume in poly(n-alkyl methacrylate)s from positron lifetime and PVT experiments and its relation to the structural relaxation

Free volume data from positron annihilation lifetime spectroscopy (PALS) experiments are combined with a Simha-Somcynsky (S-S) equation of state analysis of pressure-volume-temperature (PVT) data to model free volume contributions to structural mobility in a series of poly(n-alkyl methacrylate)s. From the PALS data the glass transition temperature, T_g, decreases (from 382 to 224 ± 5 K) and a given mean free volume is observed at lower temperatures as the side-chain length increases (going from methyl- to hexyl-). This is evidence of an internal plasticization whereby the side-chains reduce effective packing of molecules. By comparing PALS and PVT data, the hole number per mass unit, N_h′, is calculated using different methods; this varies between 0.54 and 0.86 × 10²¹ g⁻¹. It is found that the extrapolated free volume becomes zero at a temperature T₀′ that is smaller than the Vogel temperature T₀ of the α-relaxation. The α-relaxation frequencies can be fitted by the free volume theory of Cohen and Turnbull, but only when the free volume V_f is replaced by (V_f − ΔV) where ΔV( = E_f(T₀ − T₀′), E_f is the thermal expansivity of V_f) varies between 0.060 and 0.027 ± 0.003 cm³/g, decreasing with side-chain length, apart from poly(n-hexyl methacrylate) where ΔV increases to 0.043 ± 0.003 cm³/g. One possible interpretation of this is that the α-relaxation only occurs when, due to statistical reasons, a group of m or more unoccupied S-S cells are located adjacent to one another. m is found to vary between 8 and 2 for poly(methyl methacrylate) and poly(n-butyl methacrylate), respectively. We found that no specific feature in the free volume expansion was consistently in coincidence with the dynamic crossover.     

Chemistry and kinetics of chemical vapour deposition of pyrocarbon: VII. Confirmation of the influence of the substrate surface area/reactor volume ratio

Carbon deposition from a methane–hydrogen mixture (p_CH4=17.5 kPa, p_H2=2.5 kPa) was studied at an ambient pressure of about 100 kPa and a temperature of 1100°C, using deposition arrangements with surface area/reactor volume ratios, [A_S/V_R], of 10, 20, 40 and 80 cm⁻¹. Steady-state deposition rates and corresponding compositions of the gas phase as a function of residence were determined. The deposition rates in mol/h increase with increasing [A_S/V_R] ratio at all investigated residence times up to 1 s. However, surface-related deposition rates in mol/m²h decreased. As the same results have been obtained in a preceding study using pure methane at a partial pressure of 10 kPa, it has been confirmed that all the kinetics can be determined by changing the [A_S/V_R] ratio.     

Prediction of adsorption equilibrium using a modified D-R equation: pure organic compounds on BPL carbon

A method for predicting adsorption equilibrium using a modified Dubinin-Radushkevich (D-R) equation is presented in this paper. We focus on adsorption of pure organic compounds on BPL-activated carbon. We introduce a new variable k_v, a volume adjusting coefficient, and simply use V_b, the constant molar volume of the adsorbate at its normal boiling temperature, instead of V_m, the temperature-dependent molar volume of the adsorbate at the adsorption temperature. The model parameters in the modified D-R equation for an adsorbate are predicted from V_b. Overall, the modified D-R equation gives more accurate results than the traditional one.     

Thermodynamic aspects of the bovine serum albumin adsorption onto N,N′‐ diethylaminoethyl dextran microbeads

Adsorption of proteins on solid surfaces is widely studied because of its importance in various biotechnological, medical, and technical applications, e.g., biosensor cardiovascular implants and chromatography. Adsorption thermodynamics has been studied on the microbeads of N,N′‐diethylaminoethyl (DEAE) dextran anion exchanger for bovine serum albumin at 25, 30, 35 40, and 45°C. As a result some thermodynamic parameters like Freundlich constants, thermodynamic equilibrium constant (K_D), standard free energy changes (ΔG_assoc), standard entropy changes (ΔS_assoc), and standard enthalpy change (ΔH_assoc) have been evaluated. Using the linear Van't Hoff plot, the ΔH_assoc value of the system for the interaction of BSA adsorbed crosslinked DEAE dextran microbeads was determined as 12.5 kJ/mol. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci, 2006     

Hydrophobic–hydrophilic polydivinylbenzene/polyacryldiethylenetriamine interpenetrating polymer networks and its adsorption performance toward salicylic acid from aqueous solutions

Hydrophobic–hydrophilic interpenetrating polymer networks (IPNs) composed of polydivinylbenzene (PDVB) and polyacryldiethylenetriamine (PADETA) were prepared and its adsorption performance toward salicylic acid was studied from aqueous solutions. The structure of PDVB/PADETA IPNs was characterized by Fourier transform infrared spectroscopy, N₂ adsorption–desorption isotherms, weak basic exchange capacity, and swelling ratio, respectively. The results indicated that PDVB/PADETA IPNs possessed both hydrophobic and hydrophilic properties and they were much superior to the hydrophobic PDVB and the hydrophilic PADETA in adsorption of salicylic acid from aqueous solutions. The Freundlich model was more appropriate for fitting the equilibrium data than the Langmuir model and the isosteric enthalpy decreased with increment of the equilibrium uptakes. The breakthrough dynamic capacity of salicylic acid on PDVB/PADETA IPNs was 77.27 mg/mL wet resin at an initial concentration of 650.4 mg/L and a flow rate of 7.2 BV/h (bed volume, 1 BV = 10 mL) and the saturated dynamic capacity was calculated to be 93.28 mg/mL wet resin. One hundred and forty milliliter of 0.01 mol/L of sodium hydroxide (w/v) and 40% of ethanol (v/v) could regenerate the resin column completely. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2636–2643, 2014     

Glass Formation and Characterization Studies in the TeO2–WO3–Na2O System

Glass formation behavior of the TeO₂–WO₃–Na₂O system was studied by using conventional melt‐quenching technique. A wide glass formation range was determined for the first time in the literature and thermal, physical, and structural characterization of sodium‐tungsten‐tellurite glasses were realized using differential scanning calorimetry (DSC) and Fourier transform infrared (FTIR) spectroscopy techniques. Glass transition (T_g) and crystallization (T_c/T_p) temperatures, glass stability (?T), density (ρ), molar volume (V_M), oxygen molar volume (V_O), and oxygen packing density (OPD) values and structural transformations in the glass network were investigated according to the equimolar substitution of TeO₂ by Na₂O+WO₃ and changing Na₂O or WO₃ at constant TeO₂.