ABSTRACT
It is obvious, that for thermooxidative degradation processes in polymers the necessary condition is oxidant reaching of reactive center of macromolecule. This made important and often key aspect of structural stabilization a gas transport processes in polymers. Therefore, in present chapter we will give a brief description of main principles of the gas transport processes fractal model in polymer membranes. 2.1. THE MAIN PRINCIPLES OF GAS TRANSPORT PROCESSES FRACTAL MODEL
Diffusion on fractal objects, called also anomalous [1] or strange [2], has a number of specific features, the research of which begins more than twenty years ago [3] and continues up to now. These features are fully related to polymers, too which have the fractal structure. Besides, on the mentioned features polymer’s structure specific character is imposed, in which diffusion is realized through microvoids of fluctuational free volume [4, 5]. These circumstances made diffusion processes in polymer membranes complex enough and dependent on a considerable parameters number. At first we will consider the treatment of gas transport processes within the framework of classical model. Since all fluctuational free volume of polymer is concentrated in loose packed matrix [6], it should be expected, that the rise of its relative fraction cpe m. results to the increase of diffusivity D or permeability coefficient P. In reality, such correlation was obtained in paper [7], which analytically is expressed by the following simple relationship [8]:
The existence of the diffusivity D jump at melting temperature Tm of polyethylenes is a well established experimental fact [9], Authors [9] of
( 2 . 1)
fered the theoretical model for description of temperature dependence Z), which assumes two various equations for temperature intervals T<Tm and T>Tm. Let’s note, that this model does not consider structural differences of polyethylenes amorphous phase in semicrystalline (T<Tm) and viscous (T>Tm) states. In papers [10-13] the dependence D(T) description and, in particular, D jump at Tm, within the framework of cluster model was considered which considers the mentioned above structural differencies.Let’s consider the physical foundations of jump D existence at Tm in the offered treatment. The model [9] assumes the same structure of amorphous phase in semicrystalline polyethylene and its melt. In this case the role of crystalline phase reduces to D decrease proportional to crystallinity degree. Besides, the authors [9] assumed that the limiting stage of gases diffusion in semicrystalline polyethylenes is transport through crystallites contact sites that should be assumed an arbitrary enough suggestion. It is known[14] that transition of crystalline phase to amorphous is the most densely packed part of noncrystalline regions of polyethylenes and consequently it’s not reasonable to expect both crystallites direct contact and raised looseness in such contact sites if they exist [1 1 ].Within the framework of the offered treatment the structure of amorphous phase of semicrystalline polyethylene and its melt is discerned by existence in the first of local order regions (clusters), through which the gas transport processes are not also realized. The appearence of these regions at T<Tm is due to crystallization process and caused by this process chains drawing in amorphous layers [15]. At T>Tm some fraction of local order regions is also conserved, but in this case it will be dynamic with small living time [16]. The D jump at Tm within the framework of most general physical representations is due to specific character of order parameter change at critical temperature Tcr (for polyethylenes Tcr=Tm). In Fig. 2.1 the schematic temperature dependence of order parameter cp(7), is shown from which follows very fast growth (p in narrow temperature interval T<Tm [17]. As it was noted in the preceding chapter, for description of the dependence (p, ;( T) (order parameter) the thermal cluster conception can be used, where the value cp. / is given by the equation [18]:
(2.3)
where the index (32= 0 .40 [13].For accepted in the paper [9] jump D temperature range about 5 K and7,,,=403 K [19] cpc;=0.176 will be obtained, that is the cause of the mentioned jump [1 2 ],
Figure 2.1. Schematic representation of the parameter of order <p temperature dependence [17]. It’s simpler and clearer to demonstrate the jump D at T=Tm physical sense with the aid of the equations (2.1) and (2.2). Although these equations were obtained for the description of oxygen diffusion for amorphous and semicrystalline polymers number [8], nevertheless the closeness of molecule diameters for 0 2 and CH4 [5] allows to use them for pleriminary analysis of CH4 diffusion. So, for T=Tm - SK the value cpfcm. according to the model [20] is equal to about 0.827 and at T>Tm the equation (1.19) is gives cpem about 0.933. The calculation according to the equation (2.1) gives the difference of lg D for these states equal to about 0.61 and the calculation according to the equation (2.2) at f g=0.09l at T=Tm - SK and
f g=0.113 at T>Tm gives the difference lg D equal to about 0.60 for these states. These results are excellently agreed to experimental difference lg D, which is equal to about 0.63 [9].The comparison of the diffiisivity temperature dependencies for HDPE and its melt, calculated according to the equation (2 . 1) and experimentally obtained [9], in Fig. 2.2 is shown. All of a sudden good (accounting approximate character of the equation (2 . 1 ) [8]) correspondence of theory and experiment is obtained and constant value D at T> i s due to the accepted in [11] condition <pem =const=0.933 in this temperature interval. It is also important to note, that one and the same constant D0 is used, which is equal to 3.65x10'" m2/s, for both temperature intervals [10].Therefore, the cluster model allows to explain the diffusivity behaviour as a temperature function within the framework of a single structural approach both above and lower Tm. The offered by the authors [10-13] treatment explains D jump at Tm as the result of formation (decay) of local order regions (clusters) impenetrable for gas transport. The considered
treatment gives not only qualitative, but and quantitative description of D(T) dependence in the fully used temperature interval.
