Mechanics of moisture for polymers: Fundamental concepts and model study

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.