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Analysis of the thermal expansion behavior of oriented polyoxymethylene sheets.


Polyoxymethylene (POM) is an attractive polymer. It offers an excellent balance of properties, ease of molding, and aesthetics. It is proving successful in applications previously confined to metals, because of its mechanical and long-term properties.

Extrusion, cold and hot drawing, drawing under pressure, and microwave heating drawing processes normally increase the mechanical properties of POM (1-6). A series of complex morphological changes takes place during drawing, which produces significant changes in the linear thermal expansion. Therefore, information on the thermal expansion coefficient (TEC) is essential in understanding the overall thermomechanical response of the polymer. Thermal expansion coefficient is in itself important and plays a critical role in design considerations. It is also important when the polymer is used in conjunction with other materials to obtain dimensional and mechanical stability. Consequently, it is necessary to provide a suitable model relating the thermal expansion to the micromorphological changes occurring during drawing. This paper is an extension of previous publications (7,8) in an attempt to implement the molecular composite model for the prediction and the analysis of the thermal expansion behavior of uniaxially oriented POM.


Many models have been proposed to elucidate the effect of drawing - and, therefore, of orientation - on the mechanical and thermal behavior of polyoxymethylene (9-17). One of the earliest models used for crystalline polymers was the Takayanagi model (9). It was modified (10) to account for the presence of taut tie molecules in drawn polyoxymethylene, even though, it was not able to interpret the gradual development of anisotropy of physical properties and is only intended for highly drawn samples.

The aggregate model (11) assumed that a polymer is composed of identical transversely isotropic microscopic units and that the process of drawing only produces a preferential distribution in the orientation of these units. Unfortunately, the aggregate model can only be used at very low temperatures, when the amorphous phase is comparable in stiffness to the crystalline phase. A natural extension of the aggregate model is the Seferis model (12) applicable to two-phase systems. POM is regarded as an aggregate of crystalline and amorphous elastic, anisotropic units, whose properties remain constant, but they are gradually aligned as the polymer is drawn. The Seferis model is valid only below the [Gamma]-relaxation, because morphological changes are reduced at such low temperatures.

Choy and Nakafuku (13) proposed two models to explain the thermal expansion behavior of crystalline polymers. The intercrystalline bridge model is only applicable to the highly oriented polymer (above a draw ratio of 5). This model is also limited since it is not expected to give a good description of the thermal expansion above the glass-transition temperature, [T.sub.g], and it does not address the expansion behavior changes with uniaxial draw ratios [less than] 5. On the other hand, the dispersed crystallites model assumes that the crystallites are dispersed in an isotropic amorphous matrix. This model is suitable for the expansion in the transverse direction only because the effect of the tie molecules in this direction is of minor importance.

Ward et al. (14) adopted a three-phase model: the conventional crystalline and amorphous phases and a third phase consisting of chains that are generally aligned in the draw direction packed tightly but not in a crystalline register. Although this model seems to be the most acceptable, it does not take into consideration the change in size, shape, and geometrical arrangement of the crystallites. Any change in morphology or thermal history of the polymer can not possibly be reflected by the model.

Biswas et al. (15) used a composite model to predict the thermal expansion coefficients for polyoxymethylene and polypropylene. They included the effect of the volume fraction crystallinity and the orientation distribution of the crystalline phase, with no reference to the morphological aspects of the constituent phases during orientation and the associated possible temperature effects.

None of the models explains simply and accurately the gradual variation of the micromorphological aspects and the associated thermal expansion behavior of POM upon drawing and over a wide range of temperature. Nevertheless, the thermal expansion behavior of anisotropic polyoxymethylene can be easily interpreted and analyzed in terms of the molecular composite model (16, 17).


When supercooled from the melt, POM crystallizes in a spherulitic form (18). Halpin and Kardos (16) considered crystalline polymers as a molecular version of engineering composites. They visualized the mechanical equivalent to the crystalline polymer to be constructed as a laminate from layers of plies of orthotropic material, each of which is perfectly aligned short tape composite analogue and oriented at a particular angle with respect to the longitudinal in-plane direction. Figure 1 shows a schematic of the original physical model representing an isotropic sheet of a crystalline polymer. The model was used to predict and to analyze the mechanical and thermal expansion properties of many crystalline polymers (17, 19, 20). Furthermore, the molecular composite model has been utilized to predict precisely the thermal expansion coefficient of isotropic POM (7, 8). The polymer is regarded as a molecular composite of its own constituent crystalline and amorphous phases. The bulk POM sheet is assumed to be reconstructed as a quasi-isotropic laminate by stacking up plies, each of which contains unidirectionally oriented anisotropic POM crystallites embedded in an isotropic amorphous POM matrix. Each unidirectionally oriented ply contributes equally to the total response of the laminate.

Drawing of POM results in a gradual redistribution of crystal orientation, preferentially in the drawing direction. Molecules in the amorphous phase are oriented simultaneously. The overall macroscopic response will be anisotropic and the fractional thickness of plies oriented at different angles will not be the same. Different orientations will contribute to the overall response in proportion to their thicknesses. Once the fractional thickness of each pair of balanced plies and their mechanical properties are obtained, all the plies are stacked together to form the laminate. It is not the purpose of this paper to show the mathematics of the model, since it has been described for anisotropic crystalline polymers (20). The potential of the molecular composite model is that it combines the effect of many morphological and structural aspects governing the predicted properties at any level of orientation and in a simple manner. For instance, the morphological parameters include the longitudinal and the transverse aspect ratios l/t and w/t. Here, l, w, and t are the length, width, and thickness of the crystallites, respectively. The structural parameters involved are the volume fraction crystallinity, [V.sub.r], the amorphous phase tensile modulus, [E.sub.m], and the orientation parameter, [Lambda]. All these parameters are experimentally accessible. In addition, knowing the effect of temperature on the constituent phase properties, it can be accommodated easily in the model to obtain any variation in the macroscopic property with temperature, as well.

Properties of the Crystalline and the Amorphous Phases

The mechanical and thermal expansion properties of the constituent phases are essential to proceed with the computational format of the model. The tensile moduli of the anisotropic lamellar crystallites along the three crystallographic directions ([E.sub.a], [E.sub.b], and [E.sub.c]) are taken from the work of Sakurada et al. (21). They are consistent with those reported by Ward (22). The in-plane shear modulus of the crystalline phase, [G.sub.r], and its Poisson's ratio, [v.sub.r], are taken from the work of Leung et al. (23). The thermal expansion coefficients along the three crystallographic directions of the crystallites ([[Alpha].sub.a], [[Alpha].sub.b], and [[Alpha].sub.c]), the amorphous phase thermal expansion coefficient, [[Alpha].sub.m], and their relations to temperature are taken from the work of Choy and Nakafuku (13). The amorphous phase tensile modulus, [E.sub.m], was deduced from the work of Takeuchi et al. (24). The model also requires the ultimate properties of the amorphous phase (20). The ultimate tensile modulus for the fully aligned amorphous phase, [E.sub.m,ult], was obtained from the work of Takeuchi et al. (24), and the corresponding ultimate thermal expansion coefficient of the amorphous phase, [[Alpha].sub.m,ult], from the work of Biswas et al. (15). The effect of temperature was included not only for the thermal expansion coefficient of the constituent phases but also for their mechanical properties.

The temperature dependence of the elastic modulus of the crystalline region in the direction parallel to the chain axis, [E.sub.c], was thoroughly analyzed by Nakamae et al. (6). They have reported the observed, the estimated, and the calculated values, and they have shown that it is only below the [T.sub.g] of POM, which is -53 [degrees] C, that the modulus is a weak function of temperature; otherwise [E.sub.c] will not change with temperature. [TABULAR DATA FOR TABLE 1 OMITTED] Similar results were also obtained by Choy and Nakafuku (13). The tensile moduli transverse to the chain direction ([E.sub.a] and [E.sub.b]) are assumed to remain unchanged with temperature. On the other hand, the amorphous phase tensile and shear moduli are strong functions of temperatures, as reported by Choy et al. (25). All the required mechanical properties of both phases and their relation with temperature are shown in Table 1. Table 2 shows the thermal expansion coefficients of the constituent crystalline and amorphous phases. The orientation functions of the crystalline and amorphous phases, [f.sub.c] and [f.sub.m], appearing in Tables 1 and 2 are expressed as (26, 27):

[f.sub.c] = 2<[cos.sup.2][[Theta].sub.m]> - 1 (1)


[f.sub.m] - 2<[cos.sup.2][[Theta].sub.m]> - 1 (2)

where <[cos.sup.2][[Theta].sub.c]> and <[cos.sup.2][[Theta].sub.m]> designate the average cosine squared values of the angles [[Theta].sub.c] and [[Theta].sub.m], between the reference in-plane longitudinal direction and the c-crystallographic direction and between the polymer chain axis in the amorphous phase and the reference direction, respectively.


The analysis of the thermal expansion behavior of anisotropic POM sheets is reported as three-dimension structure-property maps. Such mapping is often useful when designing with oriented polymeric structures (28). The orthogonal in-plane thermal expansion coefficients, [[Alpha].sub.11] and [[Alpha].sub.22], are plotted as functions of selectively varied pairs of variables while keeping the others constant. The variables investigated are the orientation parameter ([Lambda]), temperature, volume fraction crystallinity ([V.sub.r]), and the longitudinal and transverse aspect ratios of the crystallites (l/t and w/t). The 1-direction is the longitudinal in-plane (draw) direction and the 2-direction is the transverse direction.

Figure 2 depicts the variation of the longitudinal and the transverse TEC with the orientation parameter and the temperature. The orientation parameter, originally introduced by Kacir et al. (29, 30) and modified [TABULAR DATA FOR TABLE 2 OMITTED] by Hosangadi (31), is given by the expression:

Y = 1 - exp(-[Lambda][[Theta].sub.c])/1 - exp(-[Lambda][Pi]/2) (3)

where Y is the cumulative fraction of crystallites aligned between the angles (-[[Theta].sub.c]) and (+[[Theta].sub.c]). For randomly aligned crystallites, or a broad distribution of crystallites (i.e., isotropic state), [Lambda] = 0; whereas, for a fully oriented texture, or a narrow distribution of crystallites, [Lambda] [approaches] [infinity]. Table 3 shows the crystallite orientation distribution within different angle intervals and the corresponding values for [Lambda]. Figure 2 shows that the alignment of crystallites in the draw direction is associated with a decrease in [[Alpha].sub.11] and a simultaneous increase in [[Alpha].sub.22]; this behavior has been reported experimentally for drawn POM (13, 15, 23, 25). Furthermore, [[Alpha].sub.11] becomes negative when the value of [Lambda] is [greater than]8. Such a behavior is expected because as the crystallites become oriented in the draw direction, the contribution of the c-axis properties in this direction increases and, in the meantime, the contribution of the properties of the a- and b-axes in the transverse direction increases. Because of the negative value of [[Alpha].sub.c] and the positive values of [[Alpha].sub.a] and [[Alpha].sub.b] (see Table 2), it is expected that higher values of [Lambda] would be associated with shrinkage in the longitudinal direction and expansion in the transverse direction, as seen from Figs. 2a and 2b, respectively. The Figures also show that as long as the value of the orientation parameter is [greater than]8, it does not have a significant effect on [[Alpha].sub.11]. On the other hand, the transverse TEC increases slightly with [Lambda], at relatively higher temperatures, as seen from Fig. 2b.

Figure 2 also shows that the orthogonal in-plane TEC of POM are significantly sensitive to temperature [TABULAR DATA FOR TABLE 3 OMITTED] fluctuations, and particularly [[Alpha].sub.11] at lower values of [Lambda]; i.e., at low to moderate draw ratios. Furthermore, a slight change in the variation of both expansion coefficients with temperature is taking place around the [T.sub.g] (-53 [degrees] C), the change being more pronounced as we approach the isotropic state. Therefore, it will be useful to analyze the thermal expansion behavior of anisotropic POM sheets below and above the [T.sub.g].

Figures 3 and 4 show the effect of the orientation parameter and the volume fraction crystallinity on [[Alpha].sub.11] and [[Alpha].sub.22], below and above the [T.sub.g], respectively. Again the effect of the orientation parameter is trivial above a value of 8, except for the transverse TEC at lower levels of crystallinity, i.e., for quenched POM. Nevertheless, a peculiar behavior is observed for the transverse expansivity above the [T.sub.g], as depicted in Figs. 2b and 4b. Above the [T.sub.g], a minimum in the transverse TEC is exhibited in the vicinity of [Lambda] = 2 for volume fraction crystallinities [less than or equal to]0.75. Such a phenomenon is a direct consequence of the response of the amorphous phase and the ratio between the crystalline phase content and that of the amorphous phase. It is assumed that thermal expansion of the amorphous phase in the transverse direction remains constant upon drawing, while it decreases in the longitudinal direction. Such approximations, however, are in the spirit of the work presented by Biswas et al. (15) and Takeuchi et al. (24). Figure 5 shows how the molecular composite model accounts for the variation of the amorphous phase thermal expansivity with the orientation parameter. The sharp decrease in the TEC in the longitudinal direction, during the early stages of drawing, will restrain the expansivity of anisotropic POM and particularly that [[Alpha].sub.1m] is [less than][[Alpha].sub.2m]. Furthermore, at this stage of drawing, [[Alpha].sub.2r] is less than air, as seen from Fig. 6. At this point it is important to note that, during the early stages of drawing, the amorphous phase thermal expansivity is from 3 to 5 times larger than that of the crystalline phase. Accordingly, the net result will be a lowered thermal expansion in both directions. Upon further drawing, e.g., as the value of [Lambda] exceeds 2, [[Alpha].sub.2r] is greater than [[Alpha].sub.1r], causing the increase in the transverse expansion and the reduction in the longitudinal TEC, as discussed earlier. It is also worthwhile to note that the inversion from positive longitudinal TEC to a negative one is directly related to the crystallites content and their alignment in the longitudinal in-plane direction, for [[Alpha].sub.1r] inverts from a positive value to a negative value around [Lambda] = 8, as seen from Fig. 6, and this is the reason for a negative [[Alpha].sub.11] as [Lambda] exceeds 8, for volume fraction crystallinity greater than 0.7, i.e., annealed structure, as shown in Figs. 2a, 3a, and 4a. From Figs. 2 through 4, we can deduce that the ultimate anisotropy in the thermal expansion behavior of oriented POM sheets can be achieved with an orientation parameter of 8, beyond which the change in both TEC is trivial. Accordingly, achieving higher levels of orientations will not affect the degree of anisotropy. Therefore, it is sufficient to align 75% of the crystallites with their c-axis at [+ or -]10 degrees to the principal in-plane (draw) direction, to attain the ultimate degree of anisotropy (see Table 3 for [Lambda] = 8).

Figures 3 and 4 depict also the effect of the volume fraction crystallinity on the expansivity of anisotropic POM sheets. Increasing the volume fraction crystallinity is associated with lowering the orthogonal TEC with the longitudinal TEC inverting from a positive value to a negative value around a volume fraction of 0.75. From a practical point, however, Figs. 3 and 4 not only show the effect of varying the extent of drawing on the anisotropic thermal expansivity of POM sheets, but they also depict the effect of varying their crystallization conditions. Increasing the crystalline phase content will stiffen the polymer structure and, therefore, increases its thermal dimensional stability; i.e., it reduces the thermal expansivity. It was mentioned earlier that the TEC of the crystalline phase are lower than those of the amorphous phase, as seen from Table 2 and Figs. 5 and 6. Accordingly, it will not be uncommon that increasing the levels of crystallinity would be associated with a lowered expansivity. For instance, annealing will produce a structure of a relatively higher crystallite content compared to quenching (32). Conceivably, such crystalline entities will constrain the expansivity of the amorphous phase, resulting in a reduced expansivity.

The combined effect of both crystallite aspect ratios (size and shape of the crystallites) and the orientation parameter (extent of drawing) on the anisotropic thermal expansion of POM sheets is illustrated in Figs. 7 through 9. Obviously the effect of the aspect ratios is trivial. Figure 7 shows that, below the [T.sub.g] at any level of orientation, both the longitudinal and the transverse TEC do not change with the longitudinal aspect ratio. The same behavior was also observed above the [T.sub.g], however. It is only at low levels of orientations that the transverse aspect ratio will have a slight effect on the orthogonal in-plane TEC of anisotropic POM, as seen from Figs. 8 and 9. At low values of [Lambda], a slight decrease in the expansivity is observed upon increasing the transverse aspect ratio from 1 to 5, i.e., as the crystallite morphology changes from a fibrillar to a lamellar structure, after which it remains constant. This is related to the stiffening effect introduced by changing the size and shape of the transverse dimensions of the crystallites during the early stages of drawing and the associated restraining of the amorphous phase. Therefore, one can say that, at a given crystallite content, i.e., given conditions of crystallization, varying the thermal history (heat treatment) of an anisotropic POM sheet will not affect its thermal expansion behavior. Nevertheless, the expansion behavior will depend strongly on the extent of orientation, again, as long as the value of the orientation parameter does not exceed 8. At this point, it is worth mentioning that, above the [T.sub.g], the observed minimum in the transverse TEC still occurs around [Lambda] = 2, regardless of the value of the transverse aspect ratio, as depicted from Fig. 9b, which shows the variation of the transverse TEC with the transverse aspect ratio and the orientation parameter.


The foregoing analysis Indicates that the molecular composite model predicts correctly the thermal expansion behavior of anisotropic POM sheets. The orientation parameter, volume fraction crystallinity, and the temperature are the prime variables affecting the orthogonal in-plane TEC of POM. On the other hand, the TEC are not sensitive to the variation of the crystallite size and geometry. Above the [T.sub.g], a minimum in the transverse TEC is exhibited in the vicinity of an orientation parameter of 2 for volume fraction crystallinities [less than or equal to]0.75, irrespective of the size and shape of the crystallites. The best achievable thermal dimensional stability is of directional dependence: in the longitudinal direction it is in the vicinity of [Lambda] = 8, while in the transverse direction it is in the vicinity of [Lambda] = 2, only [greater than][T.sub.g]. However, the ultimate anisotropy in the thermal expansion behavior of oriented POM is attainable at an orientation parameter of 8, beyond which both TEC are almost invariant to changes in levels of orientations. It is also at this value of [Lambda] that the longitudinal TEC inverts from a positive value to a negative one, provided that the volume fraction crystallinity is [greater than or equal to]0.75.


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Author:Zahran, R.R.; Shenouda, S.S.; El-Tawil, Y.A.; El-Kayar, A.
Publication:Polymer Engineering and Science
Date:May 1, 1996
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