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Review Article

A Review on Water Vapor Pressure Model for Moisture Permeable Materials Subjected to Rapid Heating

[+] Author and Article Information
Liangbiao Chen

Department of Mechanical Engineering,
Lamar University,
Beaumont, TX 77710
e-mail: goodbill2008@gmail.com

Jiang Zhou

Department of Mechanical Engineering,
Lamar University,
Beaumont, TX 77710
e-mail: zhoujx@lamar.edu

Hsing-Wei Chu

Department of Mechanical Engineering,
Lamar University,
Beaumont, TX 77710
e-mail: chuhw@lamar.edu

Guoqi Zhang

Department of Microelectronics,
Delft University of Technology,
Mekelweg 2,
Delft 2628 CD, The Netherlands
e-mail: G.Q.Zhang@tudelft.nl

Xuejun Fan

Department of Mechanical Engineering,
Lamar University,
Beaumont, TX 77710
e-mail: xuejun.fan@lamar.edu

1Corresponding authors.

Manuscript received September 6, 2017; final manuscript received March 7, 2018; published online April 23, 2018. Assoc. Editor: Rui Huang.

Appl. Mech. Rev 70(2), 020803 (Apr 23, 2018) (16 pages) Paper No: AMR-17-1062; doi: 10.1115/1.4039557 History: Received September 06, 2017; Revised March 07, 2018

This paper presents a comprehensive review and comparison of different theories and models for water vapor pressure under rapid heating in moisture permeable materials, such as polymers or polymer composites. Numerous studies have been conducted, predominately in microelectronics packaging community, to obtain the understanding of vapor pressure evolution during soldering reflow for encapsulated moisture. Henry's law-based models are introduced first. We have shown that various models can be unified to a general form of solution. Two key parameters are identified for determining vapor pressure: the initial relative humidity and the net heat of solution. For materials with nonlinear sorption isotherm, the analytical solutions for maximum vapor pressure are presented. The predicted vapor pressure, using either linear sorption isotherm (Henry's law) or nonlinear sorption isotherm, can be greater than the saturated water vapor pressure. Such an “unphysical” pressure solution needs to be further studied. The predicted maximum vapor pressure is proportional to the initial relative humidity, implying the history dependence. Furthermore, a micromechanics-based vapor pressure model is introduced, in which the vapor pressure depends on the state of moisture in voids. It is found that the maximum vapor pressure stays at the saturated vapor pressure provided that the moisture is in the mixed liquid/vapor phase in voids. And, the vapor pressure depends only on the current state of moisture condition. These results are contradictory to the model predictions with sorption isotherm theories. The capillary effects are taken into consideration for the vapor pressure model using micromechanics approach.

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Figures

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Fig. 1

Cohesive failure of polymeric thin film induced by high water vapor pressure during soldering reflow process of a microelectronic package: (a) a side view and (b) a top-down view. Adapted from Ref. [28].

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Fig. 2

(a) Strain-temperature responses and (b) the microscopy of the damage of moisture-saturated graphite/polyimidecomposites during thermal spikes. Adapted from Ref. [29] with permission of SAGE Publications, Ltd.

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Fig. 3

A schematic water vapor pressure problem representing a cavity between a moisture saturated molding compound and water-impermeable lead frame. A step change in temperature is assumed to simulate the reflow soldering process.

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Fig. 4

Water vapor pressure results based on Shirley's solutions using Eqs. (18) and (19)

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Fig. 5

Schematic 1D crack-like cavity vapor pressure problem

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Fig. 6

Results of Chen's solution in Eq. (19) matches Shirley's in Eq. (10) with RH0 = 85% and ΔHs*=−1.5 kJ/mol and returns to Hui's solution with RH0 = 100% and ΔHs*=0 kJ/mol so that kH = constant. Results are based on w = 0.2 cm, l = 0.001 cm.

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Fig. 7

Capping effect of RH0 on cavity pressure under different values of α. Material constant ΔHs*=−1.5 kJ/mol.

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Fig. 8

Normalized cavity pressure versus normalized time under three different isosteric heat of sorption (ΔHs*) with RH0 = 85% and α = 100. Capping effect exists for ΔHs*<0 while unphysical pressure occurs for ΔHs*=3.0 kJ/mol.

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Fig. 9

Maximum cavity pressure against different values of ΔHs* at different temperatures

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Fig. 10

Comparison of Chen's solution and convection-only model for the 1D problem in Fig. 3

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Fig. 11

Schematic of convection-diffusion model (Reprinted with permission from Chen et al. [44]. Copyright 2015 by Wiley.)

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Fig. 12

A comparison of the three models. Material properties: D(T) = 2.86 × 10−8e−28,268/RT m2/s for both CD model and diffusion-only model; κ is 6.9 × 10−21 m2 for CD model and 1.1 × 10−20 m2 for convection-only model. Porosity is 5% based on Ref. [44].

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Fig. 13

Schematic of different water sorption isotherms

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Fig. 14

Three distinct sorption isotherms based on Henry's law and the Ferro Fontana model at (a) T = 85 °C and (b) T = 215 °C. All the isotherms assume Qst= 38.7 kJ/mol.

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Fig. 15

Results of moisture content and pressure for different isotherms (RH0 = 100%)

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Fig. 16

Representative elementary volume describing two distinct states of moisture in the microvoids of moisture permeable materials (Reprinted with permission from Fan et al. [39]. Copyright 2005 by ASME).

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Fig. 17

A comparison between the two-phased Fan's model and Chen's unified solution with w = 0.2 cm and l = 0.01 cm. ϕeq = 5% for Fan's model in Eq. (48).

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Fig. 18

A comparison of the cavity pressure for w → ∞ based on Eq. (51) in Ref. [46], Eq. (48) in Ref. [39], and Eq. (25) in Ref.[42]

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Fig. 19

Effects of pore radius to the saturated water vapor pressure and density: (a) σ = σrm N/m and (b) σ(Τ) = 0.072 − 0.0002 (Τ − 293.15) N/m

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Fig. 20

Cavity pressure based on the modified micromechanics-based model for different radius of microvoids with T1 = 215 °C: (a) σ = 0.072 N/m and (b) σ = σ(Τ ) based on Eq. (57)

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