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

Liangbiao Chen, Jiang Zhou, Hsing-Wei Chu, Guoqi Zhang*, Xuejun Fan

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Article number020803
Pages (from-to)1-16
Number of pages16
JournalApplied Mechanics Reviews
Issue number2
Publication statusPublished - 2018


  • water vapor pressure
  • moisture permeable
  • moisture diffusion
  • rapid heating
  • Henry’s law
  • nonlinear sorption isotherm
  • micromechanics
  • soldering reflow
  • Electronic packaging


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