JOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 21,NUMBER 4 (2000)575A MATERIALS AGING PROBELM IN THEORY AND PRACTICEPA Materials Aging Problem in Theory and PracticeLawrence W. Hunter, James W. White, Paul H. Cohen, and Paul J. Biermannolyesters are widely used in plastic objects, films, and fabrics. A recurringmechanism of polyester aging is attack by humidity (hydrolysis), whereby the longchain molecules are cleaved and the material softens. This article offers an approach formodeling the hardness/aging behavior of commercial polyesters. The model isqualitatively consistent with exposure tests on fresh polyester plastic material madefrom a commercially available resin and hardening agent. It expresses the rate ofpolyester hydrolysis in terms of the relative humidity, and then connects the degree ofhydrolysis to hardness using a relation that accounts for stabilizers that are present incommercial polymers to counter the hydrolysis. (Keywords: Balance of life, Environ-mental exposure, Ester hydrolysis, Materials aging, Polyester hydrolysis, Polyesters.)INTRODUCTIONAny model that predicts when a material will breakdown, reach the end of its service life, or stop perform-ing as required offers many benefits. With safety andperformance assured, it becomes possible to achieve themaximum service life and the most economical sched-ule for disposals and upgrades. In practice, the price canbe continuous monitoring of environmental exposureconditions like temperature, humidity, shocks, andvibrations. In addition, model accuracy is impacted bythe complexities of commercial materials.This article offers a model of the hardness/aging ofcommercial polyester materials exposed to heat andhumidity. Polyester materials have a wide range ofapplications including filter wool, photographic filmbases, packaging films, magnetic media, textiles, softdrink bottles, furniture parts, and numerous other plas-tic objects.The entanglements that occur between long molec-ular chains give a polymer its hardness. However, themolecular chains in polyesters have weak links, namely,the ester links, which can be cleaved by chemical re-action with water as follows:COO+ H2O =COHO+ HOThe first member of this equation is the weak esterlink. The chemical bonds shown as dashed lines con-nect to the remaining parts of the polymer. These partsbecome disconnected, and hence the polymer chainsbecome less entangled. The material tends to soften asa result. After the reaction, the two loose ends termi-nate, as shown on the right side of the equation, as a“carboxylic acid” group and an “alcohol” group.The literature on ester chemistry1,2 shows that thecleavage reaction is promoted (“catalyzed”) by a traceof acidity in the water. For example, the reaction goesAPPLIED RESEARCHL. W. HUNTER ET AL.576 JOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 21, NUMBER 4 (2000)much faster with a trace of hydrochloric acid (HCl) inthe water. Interestingly, one of the loose ends createdis itself acidic, i.e., the carboxylic acid group, as itsname indicates. Thus, the reaction promotes itself onceit starts (the reaction is “autocatalytic”).The preceding chemical equation is a simplificationof the sequence of molecular collisions that actuallyoccur to achieve the same net result. We will examinethe more detailed description later in the article. Mean-while, we begin with the one-step reaction as given,since it turns out that this provides a very good start.EXPOSURE TESTSWe made fresh commercial-grade polyester materialby combining a resin with a curing (hardening) agentin a mold and then applying heat. Air Products andChemicals, Inc., supplied the ingredients: Voranol 630(a trifunctional polyol) and Versathane A-8 (a toluenediisocyanate polyester prepolymer). With this newmaterial, we were able to reset our clocks back to time0 and maintain control over the complete history ofenvironmental exposures.The fresh samples were exposed to 100% relativehumidity (RH) at three temperatures (Fig. 1). Resultsshowed that higher temperatures promoted softening.The temperature effect was consistent with the hypoth-esis that the softening is caused by a chemical reactionwith water, since the rates of chemical reactions typ-ically increase as temperature increases.The data points in Fig. 1 show some fluctuations dueto experimental precision and reproducibility. It be-comes a matter of judgment to identify underlyingtrends that reflect the chemistry. Our interpretation isthat hardness tends to remain initially constant andthat the time of constant hardness decreases as temper-ature rises; then hardness starts to fall at a rate thatincreases as temperature increases; and finally, thesoftening tends to accelerate slightly with time. Similarqualitative trends have been reported in the literature.3PRELIMINARY MODEL OF AGINGThe next step is to extrapolate the results to am-bient temperatures. Our preliminary model of thetemperature dependence evolved from a simple pic-ture of the chemical reactions, since simple models arebest, if they work. Commercial polyesters like ourscontain an additive called a stabilizer that reconnectsbroken ester links until the stabilizer is depleted(Wirpsza3 lists three classes of stabilizers, including“carbodiimides” whose structure and mechanism ofaction were explained by Shoffenberger and Stew-art.4) Hence, retention of hardness depends on theamount of stabilizer present. The initial rate of reac-tion between unstabilized ester links and water atvarious temperatures was measured by Brown et al.5These results were combined with an ad hoc model ofhardness in terms of the number of ester links and theamount of stabilizer. The result is a preliminary modelof hardness versus temperature and humidity for com-mercial (stabilized) polyesters.The concentration ⑀ of ester links in an unstabilizedpolyester decreases with time according to5⑀ = ⑀0e–kRHt,in which ⑀0 is the concentration at time 0, k is the “rateconstant,” and t is time. All of the temperature depen-dence is concentrated in k, which has the “Arrhenius”formk = Ae–E/RT,where R = 1.984 ⫻ 10–3 kcal mol–1 K–1. The “frequencyfactor” A