Modeling droplet deformation in melt spinning of polymer blends.
The versatile nature of polymer blends have made them an object of research for many years. Although the properties of many polymer blends have been well documented and their morphology studied (1, 2), there remains much work to be done. The properties of polymer blends depend to a large extent on their morphology, which is mainly controlled by the melt processing conditions. Proper control of these conditions can lead to an optimization of blend properties. The study of the effects of processing conditions on polymer blend morphology is a relatively new area. Recent work done in the area of blend morphology in polymer processing (3-6) has laid a good foundation for further research of this topic.
The qualitative effects of the addition of one polymer in another during fiber spinning has been studied to a certain extent (7). However, a complete understanding of the phenomena seems to be absent. Few empirical studies have been reported and there are no reports of predictive models of the process. The development of polymer blend morphology in fiber spinning is clearly an area in polymer blend science that needs to be explored.
In this study, we report the development of a model to quantitatively predict the morphology of fibers melt spun from polymer blends of selected compositions as a function of processing parameters. An experimental verification of the model is reported by studying the fiber morphology.
2. THEORY AND MODELING OF DROPLET DEFORMATION
When two immiscible polymers are mixed, one of the components becomes dispersed into the other in the form of spherical droplets (5). In immiscible blends, there is a range of relative concentration within which the role of the two liquids inverts: the dispersed one becomes continuous and vice versa. This phenomenon is known as phase inversion (5). When the molten mix is subjected to a flow field, the strains deform the suspended droplets into ellipsoids and finally into elongated cylinders. The extent of deformation of the droplets determines, to a large extent, the rheology of the polymer blend. A fundamental knowledge of the microscale rheology of a polymer blend enables one to predict the morphology and hence the properties of the end product.
To calculate the extent of deformation and the resultant shape of the suspended droplet, the velocity and pressure fields inside and outside the droplet are calculated by solving Stoke's equation for creeping motion. Taylor (8) obtained expressions for the deformability D of the droplet for low strain conditions. The deformability D is expressed in terms of the lengths and breadths of the deformed ellipsoid as
D = (L - B) / (L + B) (1)
where L is the length and B is the breadth of the deformed ellipsoid. The expressions of droplet deformation were given in terms of two dimensionless parameters, the Capillary (Weber) Number ([Kappa]) and the Viscosity Ratio ([Lambda]). The capillary number is the ratio of the hydrostatic forces to the interfacial forces and may be expressed as,
[Kappa] = [Sigma]d/[v.sub.12] (2)
where, [Sigma] = local stress, d = droplet diameter and [v.sub.12] = interfacial tension. The viscosity ratio is merely the ratio of the viscosities of the two phases expressed as,
[Lambda] = [[Eta].sub.d] / [[Eta].sub.m] (3)
where [[Eta].sub.d] and [[Eta].sub.m] are the dispersed and matrix phase viscosities resp.
Taylor obtained the deformation expressions for two cases; viz., when interfacial forces dominate and when viscous effects dominate. When the flow is weak, [Kappa] [much less than] 1, deformation is limited by the strong surface tension,
D = ([Kappa] / 2) [(19[Lambda] + 16) / (16[Lambda] + 16)] (4)
For the case where the interfacial tension is negligibly small in comparison to viscosity,
D = 5[Kappa]/8. (5)
Taylor's analysis was limited to two cases, Cox (9) extended Taylor's analysis to systems with a full range of viscosity ratios.
D = ([Kappa] / 2) [(19[Lambda] + 16)/(16[Lambda] + 16) / ([(19[Lambda][Kappa] / 40).sup.2] + 1).sup.1/2]]
The capillary number has a critical value beyond which the droplet can no longer sustain further deformation, and it breaks up into a number of smaller droplets. The value of the critical capillary number [[Kappa].sub.crit], depends on the viscosity ratio and the type of flow field, and is expressed by empirical relationships (5).
The analysis of Taylor and Cox is restricted to the case of small deformations. For cases where the droplet is elongated into a cylindrical body, slender body mechanics was used to develop a mathematical analysis for large deformations (10). This analysis was valid only for small capillary numbers and small viscosity ratios. However, in polymer blend processing one encounters significant viscosity ratios and large capillary numbers, but one still finds clear evidence of fibrillation, implying large deformations. It was found that, for capillary numbers much greater than the critical capillary number, the deformation of the dispersed phase was affine with the matrix (6). Drop deformation and breakup depend on the reduced capillary number [[Kappa].sup.*] = [Kappa]/[[Kappa].sub.crit]. Depending upon the value of [[Kappa].sup.*] in both shear and elongation, the drops will either deform or break according to the following criteria (6):
For 0.1 [greater than] [[Kappa].sup.*]droplets do not deform.
For 0.1 [less than] [[Kappa].sup.*] [less than] 1 droplets deform, but they do not break.
For 1 [less than] [[Kappa].sup.*] [less than] 4 droplets deform, if conditions are satisfied they break.
For [[Kappa].sup.*] [greater than] 4 droplets deform affinely with the rest of the matrix and extended into long stable filaments.
Melt spinning of polymer fibers has been a widely investigated subject and fairly accurate theoretical simulations of the process are possible (11, 12). The strains and temperatures in the melt spinning process can be readily obtained with the help of these numerical simulations.
Equations 4-6 for droplet deformation presume constant temperature and strain rate. However, in the process of melt spinning, the temperature and the strain rate varies along the spin line. The variation in temperature leads to a variation in the viscosity of both the phases resulting in the variation along the spin line of the viscosity ratio. Our approach to modeling droplet deformation in melt spinning thus entails constant recalculation of the droplet shape as a consequence of these changing conditions.
Equipment and Materials
We used a blend of an isotactic polypropylene (PP) with polystyrene (PS). The PP used in this study was Himont PF 653, the PS was Styron 615 APR from Dow Chemicals. A physical mixture of the blend was extruded and spun on a laboratory scale spinning line manufactured by Hills Inc. The single screw extruder was of 1 inch (2.54 cm) diameter and 30:1 L/D ratio. A precision Zenith gear pump was used to feed the melt to the spinneret. The die used had a single hole capillary with diameter of 1.5 mm. The temperature profile set on the barrel and spin head was 170/200/ 215/230/230 [degrees] C from hopper to exit. On-line measurements of the thread line velocity were performed using a laser Doppler velocimeter. Rheological characteristics were studied on the RDS parallel plate rheometer and the Instron capillary rheometer. The parallel plate rheometer was used to characterize the low shear rate behavior of the melts, and this was used to estimate the zero shear viscosities.
The model first provides the conditions of strain rates and temperature along the spin line for a given set of process and material conditions. Knowledge of the initial droplet morphology in the polymer blend is required. The model performs droplet deformation calculations on the initial morphology utilizing the calculated strains and temperatures at each point along the spin line. The calculations of droplet deformation are continued until either droplet breakup or solidification occurs. If droplet breakup occurs, then deformation calculations are continued on the new morphology obtained due to droplet breakup. Solidification finally terminates the calculations and the final morphology of the polymer blend fiber for a certain set of conditions is obtained.
The model so derived assumes that the percentage addition of the dispersed polymer is below the level of volume percolation and so no droplet coalescence occurs. The added polymer is assumed not to significantly affect the theological properties of the matrix polymer in spinning. Stress induced crystallization and its effects are neglected.
Theoretical simulations of the process were carried at low take-up speeds, the elongational viscosity for the low strain rates was taken to be equal to three times the zero shear viscosity. A FORTRAN 77 program was written according to the algorithm illustrated in Fig. 6. The program was run on a Sun[R] Sparc 10 workstation. The theoretical simulations enabled us to obtain the strain and temperature of the spin line at each point and so the point of solidification of the thread line with varying take-up speeds could be calculated.
The spinnability of the blend was studied at different concentrations. To determine the spinnabilities of the materials, we used the measure of critical draw down ratio. By noting the gear pump rpm and the take up speed, the velocity of the melt exiting the spinneret ([V.sub.1]) and the velocity of the take up device ([V.sub.1]) could be calculated. The ratio [V.sub.1]/[V.sub.0] was the draw down ratio. The draw down ratio was noted at the point of spin line fracture and this allowed us to compute the critical draw down ratio.
Fibers were spun from the blend at various speeds to study their morphologies. A 10 wt% mixture of PP in PS was used in the morphology studies. To examine the morphology of the as-spun blend fiber, the fiber was freeze-fractured in liquid nitrogen. Fracturing the specimen in liquid nitrogen ensured the preservation of the original morphology of the fiber. The fractured surfaces were then examined in scanning electron microscopy (SEM). The electron micrograph obtained from the SEM was then scanned into an image analysis system to measure the diameters of the dispersed phase present on the form of spherical droplets or elongated fibrils.
4. RESULTS AND DISCUSSION
The rheological properties of both the materials are seen in the viscosity-shear rate plots in Figs. 1 and 2. The PS has higher viscosity than PP at 230 [degrees] C, the melt processing temperature. The viscosity ratio itself changes with the temperature as seen in Fig. 3. The spinnability of the blend at various concentrations is presented in Fig. 4. It is seen that [greater than]20% addition levels of either polymer, the spinnability drastically reduces. It is within the 20% level that the morphology of the blend is primarily that of dispersed droplets; above that, the morphology changes to co-continuous structure and goes through phase inversion (5). For addition levels [less than]20% of PS in PP, the PS forms the dispersed phase. For addition levels [greater than]80% of PS, the PP forms the dispersed phase in PS. PP alone is seen to have a higher spinnability than PS alone. However, the rate of decrease in the spinnability is greater when PS is added to PP, i.e., when PS is the minor phase, and the viscosity ratio is [greater than] 1.
The melt spinning model proposed by George (8) fits the on-line velocity data for polystyrene (PS) melt spinning well [ILLUSTRATION FOR FIGURE 5 OMITTED] and so can describe the process fairly accurately. Utilizing the strain and temperature characteristics obtained from this PS melt spinning process model, the droplet deformation of the dispersed phase is calculated according to the algorithm presented in Fig. 6. The calculated variation of drop diameter along the spin line is seen in Fig. 7 and predicted values of final drop/fibril diameter and length at different speeds are presented in Figs. 8 and 9. It is seen that the drop diameter steadily decreases with increasing take up speeds, with a corresponding increase in its length. The rate of decrease is seen to be much greater at the lower speeds and this rate decreases with increasing speeds. These simulations were conducted with a starting droplet diameter measured on the micrograph of a specimen taken at the spinneret face.
The blend is drawn at various take-up speeds and the micrographs of the samples drawn at different speeds are seen in Figs. 10 and 11. It is clearly observed that suspended PP droplets are elongated into long fibrils. The diameters of these elongated fibrils is measured and a comparison between the measured and predicted values is seen in Fig. 12.
The final diameter of the droplet in melt spinning depends on two factors, the maximum strain rate the fiber experiences at a particular speed, and the amount of time the fiber is exposed to the deformation process before it solidifies. The maximum strain rate increases linearly with Increasing take-up speeds [ILLUSTRATION FOR FIGURE 13 OMITTED], on the other hand the time to solidification varies quite non-linearly as seen in Fig. 14.
The deformation of the dispersed phase plays an important role in determining the ability of the blend to be drawn out into fibers. In the present case, where PS forms the minor phase, the viscosity ratio is higher than when PP forms the minor phase; thus the deformation of the dispersed phases is different for the two cases. When PP is the dispersed phase, the viscosity ratio is [less than]1 and the dispersed phase deforms more than when PS is the dispersed phase. This higher deformation results in enhanced spinnability of the blend, as Is seen from the spinnability data.
The droplet deformation model developed for fiber spinning is examined for the case where PP is added to PS. The validity of the theoretical predictions of the droplet deformation model has been examined by morphological investigation of the fiber structure, and the model predictions correlate well with the measured diameters. Both in the theoretical modeling and morphological investigation droplet breakup is not observed. It is thus evident that for the system under investigation, the polypropylene fibrils solidify in the threadline before capillary instabilities can induce breakup. It is clear that the final diameter of the elongated droplet depends on the maximum strain rate applied during the process. With an increase in the take-up speed there is a corresponding linear increase in the maximum strain rate. However, the droplet diameter does not decrease linearly with the increase in take-up speed. This dissonance can be attributed to the fact that with an increase in take-up speed, at a constant melt throughput, the thermodynamics of the heat transfer in the spin line reduce the time available for the deformation processes. Since the polymer solidification temperature in the spin line is nominally constant, the increase in take-up speed is equivalent to a decrease in the solidification time. Therefore, the rate of increase in the maximum applied strain rate associated with increasing take-up speeds does not directly correspond to the rate of decrease in the final droplet diameter.
A comparison between the measured and predicted values of the final droplet diameters indicates that the model tends to overestimate the deformation, One explanation for this could be the fact that the process of strain induced crystallization is not taken into account in the model. Strain induced crystallization of the PP fibrils could lead to a higher melting temperature of the fibrils in the spin line, thus delaying the onset of solidification beyond that predicted by the model.
B = Breadth of ellipsoidal droplet.
D = Droplet deformability.
d = Droplet diameter.
L = Length of ellipsoidal droplet.
[V.sub.1] = Velocity of take-up roll.
[V.sub.0] = Velocity of melt exiting the spinneret. [Alpha] = Orientation angle of deformed droplet. [Sigma] = Local stress (shear or extensional). [v.sub.12] = Interfacial tension.
[[Eta].sub.d] = Dispersed phase viscosity.
[[Eta].sub.m] = Matrix phase viscosity.[Lambda] = Viscosity ratio.
K = Capillary number.
[K.sub.crit] = Critical capillary number.
[K.sup.*] = K / [K.sub.crit].
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|Title Annotation:||International Forum on Polymers - 1996|
|Author:||Padsalgikar, A.D.; Ellison, M.S.|
|Publication:||Polymer Engineering and Science|
|Date:||Jun 1, 1997|
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