Mechanics of moisture for polymers: Fundamental concepts and model study

Abstract

Reliability issues associated with moisture have become increasingly important as advanced electronic devices demand for new materials, more function integration and further miniaturization. However, the fundamentals of the mechanics of moisture transport and the subsequent failures in polymers have not been investigated extensively. This paper is devoted to some fundamental concepts of moisture absorption, diffusion, and swelling. The mathematical descriptions of moisture phase transition with temperature, and the governing equations for a deforming polymer with moisture effect are presented. The non-Fickian sorption behavior is discussed and a widely-used two-stage theory is introduced. It has been found that water sorption (immersion into liquid water bath) has very different transport mechanism at surface compared to the moisture sorption (moisture in air). The state of moisture within polymers and its interactions with polymer matrix, fillers and additives are discussed. It has been suggested that, in most of cases, the majority of absorbed water molecules neither show significant interaction with other water molecules nor with their environment. Those 'unbound' moisture stays in free-volumes and does not contribute to hygroscopic swelling. Swelling is caused by water molecules bound to the polymer matrix. Although the free volume fraction is usually in the range of 1% to 5%, the pore size is always below nanometers and not detectable by the conventional measurement techniques such as SEM and mercury intrusion. An approximate estimate of free volume fraction using weight gain data is introduced. A vapor pressure model, which allows the whole-field vapor pressure calculations, is presented. Finally the governing equations for a deforming polymer with the consideration of moisture are developed.

The Moisture Diffusion Equation for Moisture Absorption of Multiphase Symmetrical Sandwich Structures

“…To investigate moisture diffusion along the thickness direction, this moisture diffusion problem is simplified as shown in Figure 1b, where the white layer, grey layer and blue layer are defined as Phase 1, Phase 2 and Phase 3. The saturated moisture concentration C ∞ is defined as C ∞ = M ∞ /V, where M ∞ is saturated moisture uptake and V is volume of the sample [32]. The saturated moisture concentrations and diffusivities of phase 1-3 are C 1∞ , D 1 , C 2∞ , D 2 , C 3∞ and D 3 , respectively.…”

Dynamic mechanical analysis of PA 6 under hydrothermal influences and viscoelastic material modeling

“…In this context, the temperature dependence of the diffusion coefficient is often described by an Arrhenius equation. 53,54,58 However, for some polyamides, or especially in the glassy state, Fick's law is not applicable. 59 According to the findings of Arhant et al, 60 the kinetics of the diffusion coefficient in the glassy state (below glass transition temperature) can still be well described by a classical Arrhenius-type equation where the diffusion coefficient depends only on the temperature.…”

Identification of Two Commercial Pesticides by a Nanoparticle Gas-Sensing Array

“…However, the increase in sensitivity observed in Figure 3 should be mainly attributed to the polymeric coatings. Various reports indicate that polymers increase in terms of hole-free volume (volume stemming from volume relaxation and plasticization upon heating and cooling of the polymer and accessible for penetrant transport) for increasing temperature [34]; in addition, the diffusion coefficient for polymers increases for increasing temperature [35]. The overall increase in the swelling of the polymer coatings (temperature as well as vapour induced), as well as enhanced diffusion, translates to increased sensor response, in accordance with our already reported gas-sensing mechanism.…”

“…However, the increase in sensitivity observed in Figure 3 should be mainly attributed to the polymeric coatings. Various reports indicate that polymers increase in terms of hole-free volume (volume stemming from volume relaxation and plasticization upon heating and cooling of the polymer and accessible for penetrant transport) for increasing temperature [34]; in addition, the diffusion coefficient for polymers increases for increasing temperature [35].…”