Aging diffusion controlled

PVC-P materials, subjected to ageing under model and climatic conditions, have been extensively tested. Properties are lost as a result of diffusion controlled desorption of the plasticiser and a mathematical description of the ageing process has been formulated to predict lifetime (277). Plasticiser loss on ageing has also been identified in the spectroscopic investigation of roof membranes in service for a varying number of years (240). 

At early ages, da/d/ increases markedly with w/s ratio above 0.7 (B56). Moderate variations in specific surface area have little effect on the length of the induction period, but with finer grinding, da/d/ during the acceleratory period increases (K20,O12,B56). The rate of reaction increases with temperature up to the end of the acceleratory period, but is much less affected thereafter (K21), suggesting a change from chemical to diffusion control. Introduction of defects into the CjS shortens the induction period (M53,F20,O12). 

If the crystal growth process accompanying the aging phenomenon is diffusion-controlled, it can be shown (Nyvlt et al. 1985) that the size of particle in equilibrium with the solution can be obtained from the relation... 

The effective surface age has been determined on the basis of a diffusion controlled adsorption model. Similar to the maximum bubble pressure technique, where the bubble time is longer than teff, the drop formation time t is also significantly longer than the effective age teff and can be obtained as teff=3t/7 [185], This estimation assumes a radial flow inside and outside the growing drop and a homogeneous expansion of the drop surface. 

Results of the procedure are presented in Table 7.11. Ageing periods are shown as the square root of exposure hours, in the expectation that property loss would be a diffusion-controlled process due to the intrusion to the interface of water. In Table 7.11, R is defined as... 

By means of eqs. (7-49), (7-50), (7-53) and (7-54), the kinetics of ageing can be treated quantitatively. It should also be noted that it is possible, from the time-dependence of the average particle radius, to decide whether the solid state reaction is diffusion-controlled or reaction-controlled [40]. 

The relative intensity of etherification depends on curing temperature. Diffusion control of curing sets in when Tg approaches T J-g. The decrease of the rate constant is relatively steep. The decrease of segmental mobility and physical aging have been taken into account in the theoretical approach. 

Typical experiments to study the adsorption kinetics are measurements of the surface tension during the ageing of a freshly formed surface (negligible initial amount of adsorbed molecules). In this case, for a diffusion controlled process, the time evolution of the surface concentration F is described by the Ward and Tordai equation [38]... 

Most spraying processes work under dynamic conditions and improvement of their efficiency requires the use of surfactants that lower the liquid surface tension yLv under these dynamic conditions. The interfaces involved (e.g. droplets formed in a spray or impacting on a surface) are freshly formed and have only a small effective age of some seconds or even less than a millisecond. The most frequently used parameter to characterize the dynamic properties of liquid adsorption layers is the dynamic surface tension (that is a time dependent quantity). Techniques should be available to measure yLv as a function of time (ranging firom a fraction of a millisecond to minutes and hours or days). To optimize the use of surfactants, polymers and mixtures of them specific knowledge of their dynamic adsorption behavior rather than equilibrium properties is of great interest [28]. It is, therefore, necessary to describe the dynamics of surfeictant adsorption at a fundamental level. The first physically sound model for adsorption kinetics was derived by Ward and Tordai [29]. It is based on the assumption that the time dependence of surface or interfacial tension, which is directly proportional to the surface excess F (moles m ), is caused by diffusion and transport of surfeictant molecules to the interface. This is referred to as the diffusion controlled adsorption kinetics model . This diffusion controlled model assumes transport by diffusion of the surface active molecules to be the rate controlled step. The so called kinetic controlled model is based on the transfer mechanism of molecules from solution to the adsorbed state and vice versa [28]. 

During processing, only chemical, no physical aging processes occur. Processing, however, determines the physical structure of the finished part and thus influences physical aging and diffusion-controlled degradation during service. Fig. 4.1. 

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