Phase Behavior of Polymer Blends

1990 ◽  
Vol 63 (1) ◽  
pp. 98-109 ◽  
Author(s):  
Charles C. Han
Keyword(s):  
Free Energy ◽  
Phase Behavior ◽  
Random Copolymer ◽  
Pair Interaction ◽  
Interaction Parameters ◽  
Binary Interaction ◽  
Energy Of Mixing ◽  
Binary Interaction Parameters ◽  
Free Energy Of Mixing ◽  
Microstructure Effect

Abstract We have demonstrated in two separate cases that SANS experiments can be used to obtain binary interaction parameters effectively and accurately. With measured χ as a function of composition and temperature, the free energy of mixing can be obtained at least numerically. The phase diagram including spinodal curves and cloud-point curves can be predicted. The second derivative of free energy of mixing w.r.t. composition, ∂2ƒ/∂ϕ2, can be used directly in the kinetics studies of spinodal decomposition. In the polybutadiene/polybutadiene case, individual pair interaction parameters can be separated out. Microstructure effect is the main contribution to the incompatibility of the blends. Nevertheless, with the use of the random copolymer theory, phase behavior can be predicted.

Activity coefficients of NaNO3 in (Mg, Ca, Sr, and Ba)(NO3)2 + H2O systems at 298 K by EMF methods

1993 ◽  
Vol 71 (3) ◽  
pp. 384-389 ◽  
Author(s):  
Stephen N. Smith ◽  
S. Sarada ◽  
Ramamurthy Palepu
Keyword(s):  
Free Energy ◽  
Ionic Strength ◽  
Gibbs Free Energy ◽  
Activity Coefficients ◽  
Interaction Parameters ◽  
Excess Gibbs Free Energy ◽  
Experimental Activity ◽  
Energy Of Mixing ◽  
Total Ionic Strength ◽  
Free Energy Of Mixing

The activity coefficients of NaNO3 in Mg(NO3)2, Ca(NO3)2, Sr(NO3)2 and Ba (NO3)2 were determined at constant total ionic strength of 0.1, 0.5, 0.75, 1.0, 1.5, and 2.0 mol kg−1 at 298 K using EMF methods. The experimental activity coefficients were analyzed using four different formalisms, namely, Reilly–Wood–Robinson, Scatchard, Pitzer, and Harned equations, and the interaction parameters were evaluated. Excess Gibbs free energy of mixing and trace activity coefficients were calculated and the results are discussed.

Phase Behavior of Heavy-Oil/Propane Mixtures

SPE Journal ◽  
2018 ◽  
Vol 24 (02) ◽  
pp. 596-617 ◽  
Author(s):  
A.. Mancilla-Polanco ◽  
K.. Johnston ◽  
W. D. Richardson ◽  
F. F. Schoeggl ◽  
Y.. Zhang ◽  
...  
Keyword(s):  
High Pressure ◽  
Phase Behavior ◽  
Heavy Oil ◽  
Saturation Pressure ◽  
Interaction Parameters ◽  
Binary Interaction ◽  
Yield Data ◽  
Rich Phase ◽  
Cubic Equation ◽  
Binary Interaction Parameters

Summary The phase behavior of heavy-oil/propane mixtures was mapped from temperatures ranging from 20 to 180°C and pressures up to 10 MPa. Both vapor/liquid (VL1) and liquid/liquid (L1L2) regions were observed. Saturation pressures (VL1 boundary) were measured in a Jefri 100-cm3 pressure/volume/temperature (PVT) -cell and blind-cell apparatus. The propane content at which a light propane-rich phase and a heavy bitumen-rich (or pitch) phase formed (L1/L1L2 boundary) was visually determined with a high-pressure microscope (HPM) while titrating propane into the bitumen. High-pressure and high-temperature yield data were measured using a blind-cell apparatus. Here, yield is defined as the mass of the indicated component(s) in the pitch phase divided by the mass of bitumen in the feed. A procedure was developed and used to measure propane-rich-phase and pitch-phase compositions in a PVT cell. Pressure/temperature and pressure/composition phase diagrams were constructed from the saturation-pressure and pitch-phase-onset data. High-pressure micrographs demonstrated that, at lower temperatures and propane contents, the pitch phase appeared as glassy particles, whereas at higher propane contents and temperatures, it appeared as a liquid phase. Ternary diagrams were also constructed to present phase-composition data. The ability of a volume-translated Peng-Robinson cubic equation of state (CEOS) (Peng and Robinson 1976) to match the experimental measurements was explored. Two sets of binary-interaction parameters were tested: temperature-dependent binary-interaction parameters (SvdW) and composition-dependent binary-interaction parameters (CDvdW). Models derived from both types of binary-interaction parameters matched the saturation pressures and the L1L2 boundaries at one pressure but could not match the pressure dependency of the L1L2 boundary or the measured L1L2 phase compositions. The SvdW model could not match the yield data, whereas the CDvdW model matched yields at temperatures up to 90°C.

THERMODYNAMICS OF COMPOUND FORMING MOLTEN Cu–In ALLOYS

2008 ◽  
Vol 22 (27) ◽  
pp. 4833-4844 ◽  
Author(s):  
Y. A. ODUSOTE
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Gibbs Free Energy ◽  
Chemical Diffusion ◽  
Interaction Parameters ◽  
Ideal Behavior ◽  
Mixing Properties ◽  
Long Wavelength ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

A study of the thermodynamic properties of Cu in molten Cu – In alloys has been explained using a compound formation model. We use the model to deduce information on thermodynamic properties of the alloy such as the Gibbs free energy of mixing, the enthalpy and entropy of mixing. In this study, we first model the Gibbs free energy in terms of the interaction parameters. Sequel to this, the interaction parameters are utilized to quantify properties such as the concentration–concentration fluctuations in the long wavelength limit, the Warren–Cowley short-range order parameter, and the chemical diffusion. Both positive and negative deviations from Raoultian behavior and concentration-dependent asymmetry in the mixing properties of CuIn 4 liquid alloys were reported. Our analysis suggest that the liquid alloy undergoes a transformation from an ordered ( In -rich end) to segregating ( Cu -rich end) state. The system also exhibits ideal behavior at the Cu -rich end.

Higher Order Conditional Probabilities and Thermodynamics of Binary Molten Alloys

1997 ◽  
Vol 11 (02n03) ◽  
pp. 93-106 ◽  
Author(s):  
O. Akinlade
Keyword(s):  
Free Energy ◽  
Experimental Evidence ◽  
Cluster Model ◽  
Excess Free Energy ◽  
Higher Order ◽  
Thermodynamic Quantities ◽  
Equiatomic Composition ◽  
Conditional Probabilities ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing

The recently introduced four atom cluster model is used to obtain higher order conditional probabilities that describe the atomic correlations in some molten binary alloys. Although the excess free energy of mixing for all the systems studied are almost symmetrical about the equiatomic composition, most other thermodynamic quantities are not and thus, the study enables us to explain the subtle differences in their physical characteristics required to describe the mechanism of the observed strong heterocoordination in Au–Zn or homocoordination in Cu–Ni within the same framework. More importantly, we obtain all calculated quantities for the whole concentration range thus complimenting experimental evidence.

Diffusion-Induced Grain Boundary Migration and Role of Defects

1993 ◽  
Vol 319 ◽  
Author(s):  
T.K. Chaki
Keyword(s):  
Free Energy ◽  
Grain Boundary ◽  
Boundary Migration ◽  
Solute Concentration ◽  
Grain Boundary Migration ◽  
Thermally Activated ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Liquid Film Migration ◽  
Lattice Diffusivity

AbstractA model is presented to explain various aspects of diffusion-induced grain boundary migration (DIGM). The driving energies of DIGM are identified as the free energy of mixing and the interface free energy, the former being predominant in most cases of DIGM. The grain boundary migrates due to thermally activated motion of atoms across the interface under the influence of the driving energies. An expression for the velocity of migration is derived. It is shown that this depends parabolically on the solute concentration, in agreement with experimental observations in the case of liquid film migration (LFM), which is analogous to DIGM. Furthermore, the velocity is proportional to lattice diffusivity ahead of the boundary. Recent results of enhancement of DIGM by ion bombardment is explained by radiation-enhanced lattice diffusivity due to introduction of point defects by the ions. The model also explains that diffusion-induced recrystallization (DIR) is due to a free energy decrease associated with the transformation from the amorphous phase in the grain boundary layer to the crystalline phase.

Dolomite Decomposition to (Ca,Mg)O Solid Solutions: An X-Ray Diffraction Study.Part II.

1984 ◽  
Vol 39 (10) ◽  
pp. 981-985 ◽  
Author(s):  
G. Spinolo ◽  
U. Anselmi Tamburini
Keyword(s):  
Free Energy ◽  
Low Temperatures ◽  
Particle Sizes ◽  
Diffusional Process ◽  
X Ray Diffraction ◽  
High Iron Content ◽  
X Ray ◽  
Energy Of Mixing ◽  
Free Energy Of Mixing ◽  
Low Pressures

Abstract The full decomposition of dolomites with low and high iron content at low temperatures and low pressures is discussed with reference to the free energy of mixing of the ternary system Ca. Fe, Mg/O. The actual products of the primary step are a couple of rock salt structured oxides close to the spinodal compositions and with very small particle sizes. A subsequent diffusional process can produce large crystallites with equilibrium compositions, but it is effective only when either a low-iron dolomite is used as starting material or higher temperatures are employed.

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