Henry constants in polymer solutions with the van der waals equation of state

Bithas, Sotiris; Kalospiros, Nikolaos S.; Kontogeorgis, Georgios M.; Tassios, Dimitrios P.

doi:10.1002/pen.10410

Cited by 5 publications

(3 citation statements)

References 25 publications

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“…Because the gas inside the voids is assumed to be an ideal gas, the gas concentration is governed by Henry's law c = K H P G , where K H is Henry's law constant at the interface between gas and liquid underfill (see appendix B) [36][37][38]. At the infinite depleted zone of the gas concentration, the Neumann boundary condition (∂c/∂r)| t,r→∞ = 0 (gas concentration gradient) is applied because mass conservation can be expressed as a no-mass flux condition at the boundary.…”

Section: Void Growth Modelmentioning

confidence: 99%

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A numerical study of void nucleation and growth in a flip chip assembly process

Zhou

Baldwin

2010

Modelling Simul. Mater. Sci. Eng.

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In this study, we develop mathematical models and numerical simulations of void nucleation and growth induced by the chemical reaction in the flip chip package assembly process using a no-flow underfill. During the thermal assembly process, the underfill chemically reacts to the oxidation of solders I/O on the chip, achieving interconnection between chip and substrate. The chemical reaction causes a large number of voids in the thermal reflow process. The voids have been considered as a critical defect, reducing the life of the thermal reliability. This study investigates the mechanism of void nucleation and growth based on classical bubble nucleation theory and bubble dynamics, respectively. This knowledge can provide a theoretical foundation to achieve a void-free assembly process and high reliability performance.

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Section: Void Growth Modelmentioning

confidence: 99%

“…There are several reviews on models predicting the Henry's law constant [36-38, 40, 41, 62-66]. Among them, this appendix presents a predictive scheme of Henry's constant using a van der Waals equation of state [37,38]:…”

Section: Appendix B Henry's Law Constant Modelmentioning

confidence: 99%

A numerical study of void nucleation and growth in a flip chip assembly process

Zhou

Baldwin

2010

Modelling Simul. Mater. Sci. Eng.

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“…The extension to polymer solution was achieved by using the classical van der Waals one fluid mixing rule, the arithmetic mean combining rule for ij b and the Berthelot one for ij a with one binary interaction parameters, ij l . In a series of papers, this approach was applied with satisfactory results to: (1) the correlation and prediction of VLE , Harismiadis et al, 1994a; (2) the correlation and prediction of LLE in polymer solutions and blends (Harismiadis et al, 1994b, Saraiva et al, 1996; and (3) the correlation and prediction of Henry constants (Bithas et al, 1996). (Orbey and Sandler, 1994), fitted the two parameters of the PRSV equation of state for the pure polymer to its volumetric data at the temperature range of interest by assuming that its vapor pressures equal to 10 -7 MPa.…”

Section: Introductionmentioning

confidence: 99%

Modification of Sako-Wu-Prausnitz equation of state for fluid phase equilibria in polyethylene-ethylene systems at high pressures

Gharagheizi

Mehrpooya

Vatani

2006

Braz. J. Chem. Eng.

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-In order to model phase equilibria at all pressures, it is necessary to have an equation of state. We have chosen the Sako-Wu-Prausnitz cubic equation of state, which had shown some promising results. However, in order to satisfy our demands, we had to modify it slightly and fit new pure component parameters. New pure component parameters have been determined for ethylene and the n-alkane series, using vapor pressure data, saturated liquid volume and one-phase PVT-data. For higher n-alkanes, where vapor pressure data are poor or not available, determination of the pure component parameters was made in part by extrapolation and in part by fitting to one-phase PVT-data. Using one-fluid van der Waals mixing rules, with one adjustable interaction parameter, good correlation of binary hydrocarbon system was obtained, except for the critical region. The extension of the equation of state to polyethylene systems is covered in this work. Using the determined parameters, flash and cloud point calculations were performed, and treating the polymer as polydisperse. The results fit data well.

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The EoS/G^EMixing Rules for Cubic Equations of State

Kontogeorgis

Folas

2009

Thermodynamic Models for Industrial Applications

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The range of applicability of cubic equations of state (EoS) (using the standard van der Waals one-fluid mixing rules) and g E models (especially the local composition ones) is illustrated in Table 6.1 and schematically also in Figure 6.1. In a somewhat simplified way, Figure 6.1 illustrates the advantages which may be obtained by combining the strengths of both approaches (i.e. the cubic EoS and the activity coefficient models) and thus having a single model suitable for phase equilibria (at least VLE) of polar and non-polar mixtures and at both low and high pressures. This combination of EoS and g E models has been possible via the so-called EoS/G E models, which are essentially mixing rules for, typically, the energy parameter of cubic EoS. These mixing rules permit the incorporation of an expression for the excess Gibbs energy g E (i.e. an activity coefficient model) inside the EoS, permitting thus a cubic EoS to be applied to polar compounds at high pressures as well.The starting point for deriving most (but not all) EoS/G E models is the equality of the excess Gibbs energies from an EoS and from a (successful) explicit activity coefficient model at a suitable reference pressure, P:where a suitable reference pressure P can be, for example, the infinite pressure (Huron-Vidal, Wong-Sandler models) or the zero pressure (e.g. MHV2, the PSRK models), while the superscript Ã refers to the specific activity coefficient model, e.g. NRTL. The right-hand part of Equation (6.1) is the g E expression of an explicit activity coefficient model, e.g. Wilson, NRTL or UNIQUAC (see Chapters 4 and 5), whereas the g E of the EoS is obtained from classical thermodynamics when the fugacity expression is known:

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Henry constants in polymer solutions with the van der waals equation of state

Cited by 5 publications

References 25 publications

A numerical study of void nucleation and growth in a flip chip assembly process

A numerical study of void nucleation and growth in a flip chip assembly process

Modification of Sako-Wu-Prausnitz equation of state for fluid phase equilibria in polyethylene-ethylene systems at high pressures

The EoS/G^EMixing Rules for Cubic Equations of State

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Henry constants in polymer solutions with the van der waals equation of state

Cited by 5 publications

References 25 publications

A numerical study of void nucleation and growth in a flip chip assembly process

A numerical study of void nucleation and growth in a flip chip assembly process

Modification of Sako-Wu-Prausnitz equation of state for fluid phase equilibria in polyethylene-ethylene systems at high pressures

The EoS/GEMixing Rules for Cubic Equations of State

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Product

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The EoS/G^EMixing Rules for Cubic Equations of State