Thermal Modeling of Polymerizing Polymethylmethacrylate, Considering Temperature-Dependent Heat Generation

Abstract

A methodology for the modeling of unsteady heat conduction in polymethylmethacrylate (PMMA) during its exothermic polymerization is presented. The emphasis is on the formulation of a model for the volumetric rate of heat generation, including its temperature-dependent characteristics. Three parameters appear in the proposed model. The empirical determination of these parameters using Differential Scanning Calorimetry is demonstrated. The incorporation of the proposed model into finite volume methods is also demonstrated, in the context of unsteady, one-dimensional, radial heat conduction in cylindrical coordinates. In addition, the application of the proposed model to two test problems is presented and discussed. The results are encouraging, and the proposed methodology appears to be applicable to the thermal modeling of exothermic polymerization processes in general.

Residual stress due to curing can initiate damage in porous bone cement: experimental and theoretical evidence

“…Meyer et al (1973), Baliga et al (1992), and Starke et al (1997). Other studies have predicted a maximum rise of 45-501C (Huiskes, 1980), 401C (Baliga et al, 1992), and 36-451C (Starke et al, 1997).…”

“…Meyer et al (1973), Baliga et al (1992), and Starke et al (1997). Other studies have predicted a maximum rise of 45-501C (Huiskes, 1980), 401C (Baliga et al, 1992), and 36-451C (Starke et al, 1997). Peak temperature rise for the observable cement of our physical model was approximately 301C; which is therefore between 61C and 201C lower than the predicted in vivo temperature rise from the aforementioned studies.…”

“…This was noted by Huiskes (1980) when comparing predictions of his model with results from an experimental study by Meyer et al (1973). Baliga et al (1992) developed an empirical model for the prediction of heat generation in polymerising cement as a function of temperature and fraction of monomer polymerised. They also showed large deviations from measured behaviour if account was not taken of the dependence of polymerisation rate on local instantaneous temperature.…”

“…The coordinates of the centroids were then transferred from the image coordinate system to a reference system, and the endpoints for each crack were calculated. The model presented here is an adaptation of that used by Baliga et al (1992) and Starke et al (1997). The polymerisation fraction p of the curing mass of cement is defined as the ratio of heat generated, Q; at time t; to the total amount of heat generated on completion of polymerisation, Q total ; i.e.…”

“…They also showed large deviations from measured behaviour if account was not taken of the dependence of polymerisation rate on local instantaneous temperature. Starke et al (1997) implemented the model of Baliga et al (1992) as an iterative numerical scheme suitable for finite element modelling and predicted that interior regions of cement experienced greater and more rapid temperature rise than regions nearer the interfaces F the temperature distribution was then used to predict thermal bone necrosis. Indeed, much analysis of polymerisation has been focussed on the prediction of thermal bone necrosis, (e.g.…”