Polymer relaxation-controlled mass

Ueberreiter found that in the polymer systems he studied, the diffusion of the solvent across the gel layer is the rate-determining step (i.e., it is the slowest of all the involved steps),and in those cases solvent uptake and the inward movement of the glass-gel interface depend on the square root of time, as is characteristic of Fickian diffusion. In other systems, the processes in the glass-gel interface are rate determining, and solvent uptake and interface movement are linear functions of time. Alfrey et al. termed it case II diffusion or polymer relaxation-controlled mass transfer.Figure 11.31 shows a schematic of time-concentration profiles for the two dissolution modes. 

Many models have been suggested to describe anomalous (non-Fickian) uptake and a number of the more relevant to structural adhesives will be discussed. Diffusion-relaxation models are concerned with moisture transport when both Case I and Case II mechanisms are present. Berens and Hopfenberg (1978) assumed that the net penetrant uptake could be empirically separated into two parts, a Fickian diffusion-controlled uptake and a polymer relaxation-controlled uptake. The equation for mass uptake using Berens and Hopfenbergs model is shown below. 

Unlike classic solvent-developed negative resists such as cychzed rubber/ bisazide resist, which swell during development, the positive DNQ/novolac resists do not appreciably swell during their development in aqueous alkaline solutions. It should be emphasized that the dissolution of novolac is not exactly the same as that of the usual case II mass transfer kinetics in that it is not physical relaxation of the polymer molecules that is rate controlling. In case II dissolution, the rate-determining events occur at the polymer-gel interface. ... 

According to Kravelen,( l the fundamental characteristics of a polymer are the chemical structure and the molecular mass distribution pattern. The former includes the nature of the repeating units, end groups, composition of possible branches and cross-links, and defects in the structural sequence. The molecular mass distribution, which depends upon the synthesis method, provides information about the average molecular size and its irregularities. These characteristics are responsible, directly or indirectly, forthe polymer properties. They are directly responsible forthe cohesive force, packing density and potential crystallinity, and molecular mobility (with phase transitions). Indirectly, these properties control the morphology and relaxation phenomena (behavior of the polymer). 

---