Polymer degradation mathematical modelling

For the polyurethane composition considered here the maximum (adiabatic) temperature jump is equal to 25 K. This means that at ordinary working temperatures of the mold, i.e., 40 - 80°C, the maximum increase in the material temperature does not reach an unacceptable level of close to 200°C, where thermal degradation of the polymer can begin. We can restrict the maximum temperature growth Tmax by using the mathematical model based on Eqs. (4.10) - (4.13) and then constructing Tmax - vs - to curves for various mold temperatures. These provides a means of choosing the optimum process parameters when the temperature must not exceed Tmax. 

Figure 7 Principle of a Monte Carlo-based approach to mathematically model polymer degradation and drug diffusion in PLGA-based microparticles. Scheme of the iimer structure of the system (one-quarter of a spherical cross section) (A) at time t = 0 (before exposure to the release medium) and (B) during dmg release. Gray, dotted, and white pixels represent nondegraded polymer, drag and pores, respectively. Source From Ref. 48.

D.G. Duguay, R.S. Labow, J.P. Santerre, D.D. McLean, Development of a mathematical model describing the enzymatic degradation of biomedical polyurethanes. 1. Background, rationale and model formulation. Polym. Degrad. Stab. 47, 229-249 (1995)... 

Kinetic Model for Starch Digestion and Product Release. Before the comprehensive mathematical model could be constructed, some assumptions were made from prior research on polymer degradation (10) (a) the diffusion of both the enzyme and the products in the plastic matrix obeyed Pick s first law, (b) the... 

Mathematical models have also been proposed to incorporate polymer degradation kinetics as an integral part of the theoretical framework explaining drug release characteristics (51). Similarly, kinetic models have been used to explain degradation profiles of the polymer. As listed in Table 2, several pol5mier properties play an important role in their degradation behavior. 

As can be seen in this figure, a polymer behaves differently compared with substances having small molecules. There is a crystalline phase in addition to the amorphous solid and liquid phases. By the time the temperatures that are needed to vaporize the polymer are achieved, in practice they may degrade or depo-lymerize. The rest of the chapter is devoted to the study of the equations of state that can be used to describe the behavior of polymer systems. Negative pressures must be watched for in these systems. One feature that comes out clearly from the analysis presented in Sections 2.1.1 and 2.1.2 is that pressure in a box filled with gas molecules is the force exerted by the gas molecules on the walls of the container. The minimum pressure achievable is zero Nm". This can happen at very low temperatures when the velocity of the molecules reaches a state of rest or zero velocity. At this juncture, or at some time prior to this juncture, the force exerted by the molecules on the walls of the container will be zero and hence the pressure is zero. Any value of pressure lower than 0, such as negative pressure, cannot accurately describe real substances. It could be that it derives from a mathematical model that is no longer valid to describe the system in that range of conditions. 

As mentioned, the overall degradation rate is affected by numerous phenomena. Today, it is still not possible to bmld a mathematical model that predicts the final degradation rate and accounts for aU possible variables, starting from polymer processing and manufacturing to device hydrolysis. The description is even more compUcated in vivo, where polymer—tissue interactions also can play a significant role in the final behavior of bioresorbable polymers. 

Casahni, T., Rossi, F., Lazzari, S., Perale, G., Masi, M., 2014. Mathematical modeling of PLGA microparticles from polymer degradation to dmg release. Mol. Pharm. 11, 4036—4048. 

Chen, Y.H., Zhou, S.W., Li, Q., 2011. Mathematical modeling of degradation for bulk-erosive polymers applications in tissue engineering scaffolds and dmg delivery systems. Acta Biomater. 7, 1140—1149. 

Mathematical modelling of drug release from biodegradable systems requires consideration of the relative rates of polymer degradation and drug diffusion. Two defined scenarios may be established, as described next. 

The present work shows that the variation of the properties of mixtures of virgin and recycled polymers with repeated processing can be predicted with mathematical models based on experimental degradation curves. These curves also provide useful information on the mechanisms of degradation induced by reprocessing. 

Kharitonov, V. V., Psikha, B. L., Zaikov, G. E. The mathematical modelling of the inhibition mechanisms of sterically-hindered phenols in oxidizing low density polyethylene melt. Polymer Degradation and Stability, 51 (1996), p. 335 -341... 

Han X, Pan J, Buchannan F, Weir N and Farrar D (2010) Analysis of degradation data of bioresorbable polymers obtained at elevated and physiological temperatures using mathematical models. Acta Biomaterialia, 6 3882-3889. 

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