Comparison between five experimental methods to evaluate interfacial tension between molten polymers.

INTRODUCTION

When working with polymer blends, it is important to obtain at least partial compatibility between the components of the product. Polymer compatibility governs the adhesion and the condition of the interface and, therefore, the morphology and mechanical properties of the blend, i.e. the final characteristics of the blend. Interfacial tension is one of the key parameters that govern the compatibility between the components and the morphology of a polymer blend. It is the single most accessible parameter that describes the thermodynamic state and structure of an interface.

Some of the early interfacial tension measurements for polymeric materials were reported in 1969 (1). Since then, different measurements techniques have been developed. More details can be found in Wu (2). Among the various methods to measure interfacial tension, only a few are suitable for molten polymers because of their high viscosity. Most methods are based on a balance between a driving force (gravitational, centrifugal, brownian motion, shearing force) and an interfacial force that tends to minimize the contact area between the phases. In this work, five experimental methods to measure interfacial tension were used and tested for the evaluation of interfacial tension between molten polymers. The experimental methods tested included two equilibrium methods: Pendant Drop (PD) and Neumann Triangle (NT): two dynamic methods: Breaking Thread (BT) and imbedded fiber (IF); and a Rheological Method (RM) based on linear viscoelastic measurements.

MATERIALS

The pendant drop, Neumann triangle, breaking thread, imbedded fiber and rheological methods were compared and evaluated using commercial polypropylene (PP) and polystyrene (PS) at a temperature of 200[degrees]C and PP and high-density polyethylene (HDPE) at a temperature of 220[degrees]C. Table 1 shows the characteristics of the materials used in this study. Two types of PS and three types of PP were used in this work, [PP.sub.1] and [PP.sub.2] were used to evaluate the interfacial tension between PP and PS and [PP.sub.3] was used to measure interfacial tension between PP and HDPE. It was necessary to use different types of PS and PP to evaluate the interfacial tension between PP and PS to satisfy the different rheological restrictions of the different methods tested. The density of the polymers at a temperature of 200[degrees]C necessary to infer interfacial tension using the pendant drop method were inferred from equation of state (3, 4). The zero shear stress viscosity necessary to infer interfacial tensio n using the breaking thread and rheological method were inferred by fitting Carreau's model (5) to plots of the complex viscosity against frequency. These data of complex viscosity were obtained using a controlled stress rheometer (model SR-5000 from Rheometric Scientific).

Some of the methods tested to evaluate interfacial tension between molten polymers involve long experiment duration during which the polymer is kept at a temperature above its melting point. Therefore, the thermal stability of the polymers was tested by GPC. The samples were kept in an argon atmosphere at a temperature of 200[degrees]C for 10 hours (maximum duration of the experiments performed in this work). The molar mass of the samples were measured before and after this thermal treatment. It was observed that, within experimental error, neither the number average molecular weight nor the polydispersity were affected by such a treatment (6).

INTERFACIAL TENSION MEASUREMENTS

Pendant drop method: The pendant drop method involves the determination of the profile of a drop of one denser liquid suspended in a less dense liquid at mechanical equilibrium. The interfacial tension between both liquids can be Inferred from the resolution of Bashforth and Adams equation (7) that relates the surface tension to the difference of density between both liquids and the geometrical profile of the drop. More details can be found in the literature (8-11).

In this work, the interfacial tension measurements were made using a pendant drop apparatus that basically consists of three parts (6): an experimental cell where the pendant drop of the polymer was formed, an optical system to monitor the evolution of the pendant drop and a data acquisition system to infer the interfacial tension from the geometrical profile of the drop. A proportional temperature controller with a precision of [+ or -]0.5[degrees]C was used to maintain the sample at the desired temperature. The experimental cell was maintained in an argon atmosphere in order to avoid degradation. The drop insertion device consisted of a specially designed syringe to avoid problems of necking and capillary effects (9). The drop profile analysis was done using algorithms based on a robust shape comparison between the experimental profile and theoretical profile of the drop (6). More details about the experimental procedures can be found in Demarquette and Kamal (9).

Newmann Triangle: The Neumann triangle or sessile drop method is very similar to the pendant drop method, consisting of the study of the profile of a drop of one liquid resting on a flat plate surrounded by another liquid of smaller density (in the case of the determination of interfacial tension) or by air (in the case of determination of surface tension) at mechanical equilibrium. The shape of the drop is determined by a balance between gravity (or buoyancy forces) and surface forces. It is possible to infer the value of surface or interfacial tension from the shape of the drop at mechanical equilibrium. However, because of long equilibration times, it is very difficult to be used in molten polymers.

A new variation of the sessile drop method consists of using the Neumann triangle (12, 13), to evaluate the interfacial tension between two liquids. When a drop of a molten polymer rests on a plate formed by another polymer, two contact angles [[theta].sub.1] and [[theta].sub.2], can be measured as shown in Fig. 1. Using the values of these two contact angles and the values of surface tension of both polymers determined by another method it is possible to determine the interfacial tension between both polymers using the following Eq 1:

[[gamma].sub.1] = [[gamma].sub.12] cos[[theta].sub.2] + [[gamma].sub.2] cos[[theta].sub.1] (1)

where [[gamma].sub.1], [[gamma].sub.2], are the surface tension of both polymers, [[gamma].sub.12] is the interfacial tension between both polymers, [[theta].sub.1] is the contact angle formed between the horizontal line and the air/polymer surface of polymer 1 and [[theta].sub.2] is the contact angle formed between the horizontal line and the polymer 1/polymer 2 interface.

In this work, drops of polystyrene were formed on a plate of polypropylene at a temperature of 200[degrees]C. The samples were left in an argon atmosphere until mechanical equilibrium was reached (around 8 hours). The sample was then cooled, encapsulated in acrylic resin, cut with a diamond disc rotary cutter, and observed with a reflected light microscopy. The contact angles could be subsequently measured.

Breaking Thread method: The breaking thread method involves the observation of the evolution of the shape of a long fluid thread imbedded in another. Because of Brownian motion, small distortions of arbitrary wavelength are generated at the surface of the thread; this leads to a pressure difference between the inside and the outside of the thread, which induces more important deformations caused by the effect of the interfacial tension that tends to reduce the interfacial tension. It is possible to infer interfacial tension between the polymers forming the thread and the matrix from the study of the evolution of the disturbances and the zero shear stress viscosity of the polymers. Two theories have been developed to infer interfacial tension between both polymers from the study of the evolution of the thread: the theory of Tomokita (14, 15) and the theory of Tjahjadi et al (16). More details about the calculation of interfacial tension from the study of the evolution of the thread can be found in Luciani et al (17) and TJahjadi et al. (16).

In this work, based on the melting and glass transition temperatures, PS was chosen to make the films (matrix) and PP to produce fibers. PP fibers were obtained by melt spinning of molten pellets from a hot plate. Fibers diameters varied from 30 [micro]m to 110 p.m. The fibers were annealed during 12 hours at 15000 under vacuum to avoid residual stresses. The fibers used were cut in 1.0 cm pieces prior to annealing. The aspect ratio [L.sub.bf]/[D.sub.bf] (where [L.sub.bf] and [D.sub.bf] are respectively the length and diameter of the fiber) was chosen so that it would be higher than a critical value that depends on the viscosity ratio [lambda] = [[eta].sub.of]/[[eta].sub.om] (where [[eta].sub.of] is the zero shear viscosity of the fiber and [[eta].sub.om] is the zero shear viscosity of the matrix) (16). The fibers had their extremities fixed during annealing to avoid significant distortions of the diameter. The films used in the experiments were obtained by compression molding and had a thickness of 0.25 mm. This thickness was optimized to minimize eventual problems with air bubbles and to promote a melting process fast enough to avoid the fibers distortion to start before complete melting of the film. The width and length of the film were 1.5 cm. These dimensions are much larger than those of the fiber, preventing edge effects to have an influence on the capillary instability (17, 18). The experiments were carried out placing the PP fibers between two PS films. The "sandwich" formed was then placed between two glass sheets and heated in a hot stage (Mettler FP-90). The temperature was raised at a rate of 20[degrees]C/s to 150[degrees]C. The system was maintained at 150[degrees]C until all the air bubbles were able to escape. Then, the temperature was raised to the temperature at which the experiment was performed (200[degrees]C). Photos of the breakup process were taken using a CCD camera. More details about the experimental procedures can be found in another work (18).

Imbedded Fiber Retraction method: The imbedded fiber retraction method is very similar to the breaking thread method, except that the fiber is shorter. The method involves the observation of the fiber that retracts into a sphere. From the study of the evolution of the fiber and the knowledge of the zero shear viscosity of both polymers, it is possible to infer the interfacial tension between those both polymers. Two theories have been developed to infer interfacial tension between both polymers from the study of the evolution of the fiber: the theory of Carriere and Cohen (19, 20) and theory of Tjahjadi et al (16). Both theories were used in this work.

The experimental procedures to perform an Imbedded fiber retraction experiment were similar to the ones adopted for the breaking thread method except for the length of the fiber which was, In the case of the imbedded fiber method considerably shorter.

Rheological methods: A continuous effort has been applied in the last fifteen years in order to improve the understanding of the relationship between the viscoelastic properties of polymer blends, their morphology and the interfacial tension between the polymers forming the blend (21-26). In particular, it has been shown that immiscible blends have a higher elasticity, in the low frequency range, than the individual components of the blend. The higher value of elasticity of the blend results in the presence of a secondary plateau in the curve of the storage modulus G' versus frequency, [omega], for low frequencies, that can be used to infer the interfacial tension from the rheological properties of the blend (21, 22). Two emulsion models have been developed to predict the linear viscoelastic behavior of polymer blends: a) Palierne's (21); b) Bousmina's (22). Those models correlate the dynamic response of polymer blends to their morphology, composition and interfacial tension between the components. Two types of analysis can be performed to infer interfacial tension from small amplitude oscillatory shear measurements: a) comparison between the complex modulus of the blend measured experimentally to the emulsions models in the plateau region; b) Identification of a relaxation time relative to the relaxation of the dispersed phase in the relaxation spectrum of the blend (23, 27). Those two types of analysis were used here to infer interfacial tension between PP and PS and between NDPE and PP polymer.

The small amplitude oscillatory shear experiments were carried out using a controlled stress rheometer (model SR-5000 from Rheometric Scientific) under nitrogen atmosphere. A parallel-plate configuration was used. Dynamic frequency sweeps were performed for [PP.sub.1]/[PS.sub.1] blends, [HDPE.sub.1]/[PP.sub.3] blends and pure polymers.

Blends of [PP.sub.1]/[PS.sub.1] Blends were prepared in 90/10 concentration and [PP.sub.3]/[HDPE.sub.1] were prepared in six different weight concentrations ranging from 95/5 to 70/30. The blends were prepared in a Werner & Pfieiderer twin-screw extruder, model ZSK-30, with six zones of temperatures, ranging from 170 to 210[degrees]C along the barrel of the extruder. The morphology of the blend was characterized by scanning Electron Microscopy (SEM) using a Cambridge microscope, model Stereoscan 240. The samples were fractured in liquid nitrogen and then covered with gold using a Balzers sputter coater, model SCD-050. The average diameter and volume fraction of the minor phase were calculated using the SEM photomicrographs. About 300 particles were used to calculate these parameters. For the calculation of average size of the minor phase, Saltikov's correction (28) was used. This correction takes into account the polydispersity of the samples and the fact that the fracture in the sample does not always occur at the maximum diameter of the dispersed phase droplets.

RESULTS AND DISCUSSION

The interfacial tension between PP and PS was evaluated using the five different methods studied in this work. It was possible to evaluate the interfacial tension between PP and HDPE only using the rheological method; the pendant drop and dynamic methods tested in this work are based on the visualization of a drop or fiber of one of the two polymers in a matrix formed by the other. For that, both polymers should have a difference of index of refraction high enough to enable the visualization of the profile of the drop. This was not the case for PP and HDPE.

The experimental results found using each method tested are reported below. The different experimental techniques are then compared in terms of experimental duration, reliability and experimental difficulty. The advantages and limitations of each method are then discussed.

Pendant Drop

Figure 2 shows the interfacial tension calculated from the shape comparison as a function of time of a typical drop of [PS.sub.1] in [PP.sub.1] at a temperature of 200[degrees]C. It can be seen from Fig. 2 that after 10 hours, the value of interfacial tension is constant. Typically, it takes eight to ten hours for a drop of PS in a matrix of PP to reach equilibrium. The time to reach mechanical equilibrium depends on the viscosity of the samples involved in the measurement, i.e., on the temperature at which the experiment is performed and also on the molecular weight of the sample. The interfacial tension between [PP.sub.1] and [PS.sub.1] at a temperature of 20000 was found to be equal to 5.52 [+ or -] 0.2 mN/in, corroborating the values obtained by other authors (27, 29).

Neumann Triangle

Figure 3 shows a typical cut of a sessile drop of [PP.sub.1] on a plate of [PS.sub.1] imbedded in acrylic resin. The contact angles [[theta].sub.1] and [[theta].sub.2] as well as the values of surface tension of [PP.sub.1] and [PS.sub.1] at a temperature of 200[degrees]C necessary for the calculation of the interfacial tension between [PP.sub.1] and [PS.sub.1] using Eq 1 are reported in Table 2. The values of surface tension of [PP.sub.1] and [PS.sub.1] were obtained using the pendant drop method. Using the values reported in Table 2, the interfacial tension between [PP.sub.1] and [PS.sub.1] was found to be equal to 6.65 [+ or -] 1 mN/m.

Breaking Thread

In order to determine the interfacial tension between two polymers using the breaking thread method, the fiber should be formed with the material with the lower viscosity (30, 31) and with the highest melting or glass transition temperature. If the fiber is formed by the material with the highest viscosity, phenomena such as end pinching and retraction could occur. If the fiber is formed by a material with the lowest melting or glass temperature, its distortions will start before it is completely imbedded in the matrix and air bubbles will occur at the interface between both polymers (18). If both conditions are not satisfied at the same time, it is possible to use a fiber with a lower melting temperature than the matrix using appropriate thermal treatment during the experiment (18). However, the difference between the melting or glass transition temperatures should not exceed 2000. Therefore, it was not possible to measure the interfacial tension between [PP.sub.1] and [PS.sub.1] using the breaking thread me thod, in order to test the breaking thread method for polypropylene/polystyrene polymer pair, it was necessary that the zero shear viscosity of the polypropylene be lower than that of polystyrene. Therefore a higher melt index PP, [PP.sub.2]. was used. Similar procedure was necessary for the imbedded fiber experiments.

Figure 4 shows a typical evolution of a fiber of [PP.sub.2] imbedded in a matrix of [PS.sub.2] at a temperature of 200[degrees]C. It can be seen that the fiber is completely imbedded, before any significant growth of instabilities can be observed. Also during the experiments, no matrix thinning was observed. The average values of interfacial tension obtained in this work for [PP.sub.2] and [PS.sub.2] polymer pair using the theories of Tomotika (14, 15) and Tjahjadi et al. (16) were respectively 8.28 [+ or -] 0.79 mN/rn and 7.83 [+ or -] 0.57 mN/m showing that both methods lead to a similar result. It was noticed, however, that the theory of Tjahjadi et al. (16) allowed a better evaluation of the dynamic behavior of the maximum and minimum instabilities of the fiber during the breaking phenomenon, facilitating the discarding of bad experiments.

Figure 5 shows the time for complete breakup of a fiber of polystyrene ([PS.sub.2]) in polypropylene ([PP.sub.2]), as calculated by Elemans (31), at a temperature of 200[degrees]C as a function of fiber radius for different viscosity ratios, [lambda]. [lambda] = 0.059 corresponds to the viscosity ratio of the polymers used In this study. The range of fiber radius studied corresponds to the radiuses used for the different experiments. It can be seen that the time for complete breakup increases with increasing fiber radius and with increasing viscosity ratio, [lambda]. However, it can be seen that for [lambda] = 0.059 (case studied here) the time for complete breakup is less than three hours, for radiuses ranging from 15 [micro]m to 55 [micro]m. Therefore, the time to perform a breaking thread experiment is considerably smaller than the time to perform a pendant drop experiment.

Figure 6 shows the time for complete breakup of fiber of polystyrene ([PS.sub.2]) in polypropylene ([PP.sub.2]) at a temperature of 200[degrees]C as a function of matrix viscosity or fiber viscosity. When the value of either the fiber or matrix were varied, the viscosities of the complementary phases were considered as the viscosities reported in Table 1. The values of interfacial tension and fiber diameter taken in the calculation were respectively 6.5 mN/rn and 60 [micro]m. Assuming four hours as a reasonable time for an experiment without thermal degradation, it can be seen that the breaking thread suffers limitation as far as viscosity of both the matrix and fiber are concerned. For a diameter of 60 [micro]m and an Interfacial tension of 6.5 mN/m, the viscosity of the matrix should not exceed 69,200 Pa.s (when the zero shear viscosity of the fiber is 1100 Pa.s) and the viscosity of the fiber should not exceed 5590 Pa.s (when the zero shear viscosity of the matrix is 18,583 Pa.s). These upper limits of vis cosity can be increased to 110,000 Pa.s and 18,583 Pa.s respeclively if the diaxneter of the fiber is reduced to 30 [micro]m, which the lower limit for a breaking thread experiment (18). These upper limits of viscosity are lower if the interfacial tension between both polymers is lower, which is the case of compatibilized blends.

Imbedded Fiber Retraction

Figure 7 presents a typical evolution of a fiber of [PP.sub.2] imbedded in a matrix of [PS.sub.2] at a temperature of 200[degrees]C. The interfacial tension between [PP.sub.2] and [PS.sub.2] was measured using both the methods of Carriere and Cohen (20, 21) and Tjahjadi (16). According to Carriere and Cohen the evolution of an imbedded fiber as a function of time can be described by:

f([R.sub.if]/[R.sub.e]) - f([R.sub.oi f]/[R.sub.e]) = t [gamma]/[R.sub.e][[rho].sub.e][chi] (2)

where,

f(x) = 1.5Ln{[(1 + x + [x.sup.2]).sup.0.5]/1 - x}

+ 1.5[square root of (3)] [tan.sup.-1] ([square root of (3)]x/2 + x) - 0.5x - 4[x.sup.-2] (3)

where [chi] is an hydrodynamic coefficient, [R.sub.e] is the radius of a sphere having the same volume as the fiber, [R.sub.if] is the radius of the fiber as a function of time and [[eta].sub.e] is the effective viscosity, which is a function of the viscosities of both polymers, given by:

[chi][[eta].sub.e] = [[eta].sub.om] + 1.7 [[eta].sub.of]/2.7 (4)

where [[eta].sub.om] is the zero shear stress viscosity of the matrix and [[eta].sub.of] is the zero shear stress viscosity of the fiber.

Figure 8 shows f ([R.sub.if]/[R.sub.e]) - f ([R.sub.oi f]/[R.sub.e]) as a function of

time for the fiber presented in Fig. 7. It can be seen that the data lead to a straight line from which the interfacial tension can be inferred using Eq 2. Using [[eta.sub.e] defined by Eq 4 and [R.sub.oi f] = 32.01 [micro]m, the interfacial tension was found to be equal to 15.85 mN/m.

Tjahjadi et al (16) presented a method to determine the interfacial tension between two Newtonian fluids from short fiber retraction. The method uses curve-fitted polynomials to describe the decrease in length of the fiber as a function of the viscosity ratio, [lambda], and dimensionless computational time as:

L([tau])/[R.sub.e] = [summation over (4/n = 0)] [k.sub.n] ([lambda]). [[tau].sup.n] (5)

where the five coefficients, [k.sub.0] -- [k.sub.4], for different viscosity ratios and initial aspect ratios, AR, can be found in the article of Tjahjadi et al (16), L([tau]) is the half length of the fiber at time [tau], and [tau] a dimensionless computational time defined as:

[tau] = t/[t.sub.c if]

where t is the real time of the experiment and [t.sub.c if] is a characteristic time for the interfacial tension driven motions in the experiment given by:

[t.sub.cif] = [R.sub.oif] * [[eta].sub.om]/[gamma] (7)

where [gamma] is the interfacial tension, [R.sub.oif] is initial the radius of the fiber, [[eta].sub.om] is zero shear matrix viscosity.

To infer interfacial tension from the retraction of a fiber using Tjahjdi's method, two images of the evolution of the fiber at two different times [t.sub.1] and [t.sub.2] (with [DELTA][t.sub.exp], = [t.sub.2] - [t.sub.1]) are analyzed and the half length of the fiber for both images are measured. Independently, L([tau]/[R.sub.e] is plotted using Eq 5 and the coefficient [k.sub.n], for the appropriate viscosity ratio. Using the graph and the experimental values of L(t)/[R.sub.e] for both images. it is possible to determine [DELTA][[tau].sub.theo], which corresponds to the theoretical time interval between both images.

[DELTA][[tau].sub.theo] is then compared to [DELTA][t.sub.exp] and the interfacial tension can be inferred using Eqs 6 and 7.

Figure 9 presents L([tau])/[R.sub.e] as a function of time for [lambda] =

0.03. Using the experimental value of for L([tau])/[R.sub.e] = for [t.sub.1] =

540 s and [t.sub.2] = 600 s, [DELTA][[tau].sub.theo] can be measured from Fig. 9. It was found equal to 0.74. Using Eqs 6 and 7, the value of interfacial tension was found equal to 7.34 mN/in.

Figures 8 and 9 show that the values of interfacial tension obtained, from the study of the retraction of [PS.sub.2] in a matrix of [PP.sub.2]. using Carriere and Cohen's analysis is considerably larger than the one obtained using Tjahjadi's analysis using the same fibers. The values obtained using Carriere and Cohen's analysis is also considerably larger than the one obtained with the pendant drop or imbedded fiber method. Similar behavior was observed for all the experiments. These high values may be due to the use of Eq 4 to determine the effective viscosity of the polymer pair. This expression has been derived empirically for polystyrene/polymethyl methacrylate polymer pair and may be not adapted to polypropylene/polystyrene polymer pair.

Rheological Method

Figures 10 and 11 show the storage modulus for [PP.sub.1]/[PS.sub.1] (90/10) blend at a temperature of 200[degrees]C and for different [PP.sub.3]/[HDPE.sub.1] blends at a temperature of 220[degrees]C respectively as a function of frequency. It can be seen that for [PP.sub.1]/[PS.sub.1] blend, it was not possible to identify a plateau from which the interfacial tension could be determined (21, 22). In the case of [PP.sub.3]/[HDPE.sub.1] blend, it can be seen that no well defined secondary plateau can be distinguished in the storage modulus [G'([omega])) curve, for [PP.sub.3]/[HDPE.sub.1] blends with low dispersed phase concentration (5% and 10% [HDPE.sub.1]). A small shoulder can be observed for [PP.sub.3]/[HDPE.sub.1] blends with high dispersed phase concentration (25% and 30% of [HDPE.sub.1]). This behavior corroborates the predictions of Graebling et al (26), who observed that increasing the dispersed phase concentration increases both [G.sub.p], value of the storage modulus at the plateau, and the width of t he plateau. In order to infer the interfacial tension, the data of the complex modulus of the blend could be fitted to Palierne's or Bousmina's model (21, 22). This was tried in the case of both blends and it was observed that varying the interfacial tension from 1 to 20 mN/m (in the case of [PP.sub.1]/[PS.sub.1]) and from 1 to 5 mN/in (in the case of [PP.sub.3]/[HDPE.sub.1]) did not result in better fitting of the theoretical model to the experimental curves.

In order to evaluate the interfacial tension between two polymers using the linear viscoelastic behavior of the blends, It is also possible to identify a relaxation time in the relaxation spectrum of the blend that corresponds to the relaxation of the shape of the dispersed phase. The value of this relaxation time is directly proportional to the value of the interfacial tension (23). Figure 12 shows the weighted relaxation spectrum of [PP.sub.1]/[PS.sub.1] (90/10) blend and of [PP.sub.1] and [PS.sub.1] pure phases at a temperature of 200[degrees]C. The relaxation spectra were calculated using a non linear regression of the storage modulus raw data following the work of Baumgartel and Winter (32). Three relaxation times can be identified in Fig. 12: two correspond to the individual phases of the blend ([PP.sub.1] and [PS.sub.1]), since they are of the same order of magnitude as the ones of the pure phases, the remaining peak was associated with the contribution of the interface and was used to evaluate the in terfacial tension between [PP.sub.1] and [PS.sub.1]. The value obtained was 6.25 [+ or -] 0.87 mN/m. corroborating the value obtained with other methods.

Table 3 shows the value of interfacial tension between [PP.sub.3] and [HDPE.sub.1] obtained using the analysis of the relaxation spectra of the different blends of [PP.sub.3]/[HDPE.sub.1]. It can be seen that the values of interfacial tension between [PP.sub.3] and [HDPE.sub.1] vary from 1.01 to 2.32 mN/m at 220[degrees]C. It can also be seen that for composition range from 85/15 to 75/25, the interfacial tension seems to be constant. These results seem to indicate that there is a range of compositions for which it Is possible to use the rheological method to infer interfacial tension between polymers.

Comparison of the Methods

Table 4 shows a comparison of the values of surface tension between PP and PS and between HDPE and PP using the different experimental methods tested in this work. The difference between the highest and the lowest value of interfacial tension between PP and PS is around 20% but is acceptable within experimental error. The higher values obtained with the dynamic methods may be due to the fact that the theories of these methods do not take Into consideration the viscoelastic character of the polymers. Also, the values obtained using the dynamic methods are directly proportional to the zero shear stress viscosity of the polymers, which is a parameter that is difficult to measure with high accuracy. The interfacial tension between PP and HDPE could only be evaluated using RM due to a too small difference of index of refraction between both polymers.

Table 4 also shows the duration, experimental error and experimental difficulty for each method. The experimental methods are ranked from 1 to 5 according to those characteristics. Table 5 shows the advantages. limitations for each method tested in this work. It also presents the parameters necessary for the evaluation of interfacial tension. The pendant drop method is the most precise of all the methods tested in this work. Its precision is limited by the precision with which the density of the polymers is determined. Nowadays, this density can be determined with a good precision because of the development of PVT apparatus (3). The pendant drop method is, however, limited as far as duration of experiment is concerned, as the times to reach mechanical equilibrium of the drop can be up to five times the ones needed for other methods. The time for a pendant drop to reach mechanical equilibrium can reach ten hours whereas the time to perform a rheological experiment does not exceed two hours, an imbedded or brea king thread experiment three hours. The experimental precision of the breaking thread and imbedded fiber methods is limited because the interfacial tension is directly proportional to the zero shear stress of the polymers involved, a difficult parameter to be determined accurately (5). Moreover, the breaking thread and imbedded fiber experiment need to be done under a precise temperature control, owing to the large variation of viscosity with temperature. Any small variation of the temperature during the experiment could lead to erroneous results of interfacial tension. The interfacial tension, as determined using the Neumann triangle, depends on the values of surface tension of the other polymers evaluated using another method and on the preparation of the samples. At last, the rheological method is the one that involves the largest imprecision in the determination of interfacial tension, as the value obtained depends on a precise characterization of the morphology and on the values of zero shear stress of the polymers involved.

The rheological method is the simplest method to be used to measure interfacial tension between molten polymers. The main experimental difficulties encountered when using the pendant drop, breaking thread, imbedded fiber and Neumann triangle methods rely in the preparation of the samples. In the case of the pendant drop method, it is very difficult to form a polymer drop avoiding the necking and capillary effect; lots of care has to be taken in the image analysis to avoid errors such as dependence of interfacial tension with drop volume, which contradicts the Laplace equation (10); the analysis of the pendant drop is relatively complex. The Neumann triangle presents an intrinsic difficulty since the measurement of the contact angles depends on the ability of cutting the sample in the middle section of the drop and at the same time perpendicular to the base of the drop (12). In the case of the breaking thread and imbedded fiber methods, the fibers have to be annealed to avoid residual stresses that could affec t the breaking or retraction process, the thickness of the film that surrounds the drop should be carefully tailored to avoid problems such as matrix thinning. This matrix thinning squeezes the fiber and affects the dynamic phenomena (18).

CONCLUSIONS

In this work, five experimental methods were tested and compared to evaluate the interfacial tension between polypropylene and polystyrene and between high density polyethylene and polypropylene. The following conclusions could be drawn from this study:

1) The error for determining the interfacial tension between molten polymers, when using the experimental methods, increases in the following order: Pendant drop < Breaking thread < Imbedded fiber < Neumann triangle < Rheological method.

2) The time duration for determining interfacial tension, using the different methods, increases in the following order: Rheological method < Imbedded fiber < Breaking thread < Pendant drop < Neuman triangle.

3) The experimental difficulties of the different methods increase in the following order: Rheological method < Pendant drop < Neuman triangle < Imbedded fiber < Breaking thread.

4) The pendant drop, sessile drop and Neuman triangle methods are the only ones that do not make any restriction regarding the rheological nature of the polymer tested.

5) The pendant drop and dynamic methods rely on the visualization of one phase into another and therefore can be used only for polymer pairs presenting a large difference of refractive indexes of their components; the methods cannot be used either the polymer forming the matrix (lower density in the case of pendant drop method and higher viscosity in the case of dynamic methods) are opaque in the molten state.

6) The pendant drop method requires the knowledge of the density of the polymer in the molten state, a difficult parameter that can now be obtained using PVT apparatus (3), the dynamic and rheological methods require the knowledge of zero shear stress viscosity of the polymers, a difficult parameter to be determined accurately (5) the rheological method requires an accurate quantitative determination of the morphology of the blends formed by the two polymers.

7) The static and breaking thread methods are limited to low--medium range viscosities of the polymers (< [10.sup.5] Pa.s).

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Table 1

Materials Used in This Work.

                                                  ([[eta].sub.o])
              [M.sub.n]  [M.sub.w]/     MFI        200[degrees]C
Polymers       (g/mol)   [M.sub.n]   (g/10 min)  ([10.sup.4] Pa.s)

[PP.sub.1]     75.200       4.65        1.5            4.64
[PP.sub.2]                             20              0.11
[PP.sub.3]     76.000       4.5         8               --
[PS.sub.1]     91.200       2.5         2.2            3.39
[PS.sub.2]     76.600       2                          1.85
[HDPE.sub.1]   44.000       3.2         8
[HDPE.sub.2]   17.000       9.0          --           86.40

               ([[eta].sub.o])   ([[rho].sub.o])
                200[degrees]C     200[degrees]C
Polymers      ([10.sup.4] Pa.s)  (g/[cm.sup.3])   Supplier

[PP.sub.1]           --               0.751       Polibrasil
[PP.sub.2]           --               0.751       Polibrasil
[PP.sub.3]          1.07                          Polibrasil
[PS.sub.1]           --               0.970       Estireno do Brasil
[PS.sub.2]                            0.970       BASF
[HDPE.sub.1]        0.850                         Ipiranga Petroquimica
[HDPE.sub.2]                                      Aldrich

MFI: Melt Flow Index

[[eta].sup.o]: zero shear stress viscosity

[rho]: density.

Table 2

Interfacial Tension Between [PP.sub.1] and [PS.sub.1] Evaluated Using
the Sessile Drop Method.

                                                  [PP.sub.1]/[PS.sub.1]
[[gamma].sub.PS](mN/m)  [[gamma].sub.[PP.sub.1]]     [[theta].sub.1]
                                 (mN/m)                ([degrees])

23.69                            30.14                    2.16


[[gamma].sub.PS](mN/m)  [[theta].sub.2]  [[gamma].sub.12](mN/m)
                          ([degrees])

23.69                        13.78                6.65

 [[gamma].sub.PS] and [[gamma].sub.[PP.sub.1]] are the surface tension
of PS and [PP.sub.1], [[gamma].sub.12] is the interfacial tension
between [PS.sub.1] and [[theta].sub.1] and [[theta].sub.2] are defined
in Fig. 6.

Table 3

Interfacial Tension Between [PP.sub.3] and [HDPE.sub.1] at
220[degrees]C.

[PP.sub.3]/[HDPE.sub.1] Blend  Interfacial Tension
         Composition                 (mN/m)

            95/5               1.01 [+ or -] 0.26
            90/10              1.09 [+ or -] 0.24
            85/15              1.44 [+ or -] 0.27
            80/20              1.72 [+ or -] 0.31
            75/25              1.72 [+ or -] 0.22
            70/30              2.32 [+ or -] 0.26

Table 4

Summary of the Experimental Results.

                         Pendant            Neumann
                         Drop               Triangle
Polymer Pair             (P.D.)             (N.T.)

[PP.sub.1]/[PS.sub.1]    5.52 [+ or -] 0.2  6.65 [+ or -] 1
  (200[degrees]C)
[PP.sub.2]/[PS.sub.2]    5.06 [+ or -] 0.4  --
  (200[degrees]C)
[HDPE.sub.1]/[PP.sub.3]  Impossible         Not tested
  (220[degrees]C)
Duration                 4                  5
Error                    1                  4
Experimental Difficulty  2                  3

                         Breaking            Imbedded Fiber
                         Thread              Retraction
Polymer Pair             (B.T.)              (I.F.R.)

[PP.sub.1]/[PS.sub.1]    Impossible          Impossible
  (200[degrees]C)
[PP.sub.2]/[PS.sub.2]    7.83 [+ or -] 0.57  7.82 [+ or -] 0.43
  (200[degrees]C)
[HDPE.sub.1]/[PP.sub.3]  Impossible          Impossible
  (220[degrees]C)
Duration                 3                   2
Error                    3                   2
Experimental Difficulty  4                   4

                         Rheological
                         Method
Polymer Pair             (R.M.)

[PP.sub.1]/[PS.sub.1]    6.25 [+ or -] 0.87
  (200[degrees]C)
[PP.sub.2]/[PS.sub.2]    --
  (200[degrees]C)
[HDPE.sub.1]/[PP.sub.3]  1.63 [+ or -] 0.16
  (220[degrees]C)
Duration                 1
Error                    5
Experimental Difficulty  1

Table 5

Summary of the Advantages and Limitations of Each Method.

Method               Advantages

STATIC METHODS

  PD                 * Very good accuracy
                     * Theory developed for all
                       types of fluids
                     * Requires little amount of
                       material (10 mg for the drop
                       and 3 g for the other)
                     * Can be used of LCP





  NT                 * Simple experimental set-up
                       and analysis
                     * Requires small amount of
                       material (10 mg for the drop
                       and 3 g for the other)
                     * Theory developed for all
                       types of fluids


  BT                 * Short time duration of
                       experiment
                     * Requires very small amount
                       of both polymers
                       (< 20 mg of each)
                     * Simple experimental apparatus














 IFR                 * Same as breaking thread












RHEOLOGICAL METHODS

  RM                 * Theory developed for viscoelastic
                       fluids
                     * Can be used for polymers having a
                       small difference of index of regractio
                     * Can be used for polymers having high
                       viscosities
                     * Can be used for polymers having a
                       small difference of melting or glass
                       transition temperature
                     * Can be used for opaque polymers

Method                 Limitations

STATIC METHODS

  PD                 * Polymer matrix (least dense)
                       must be transparent
                     * The viscosity of the polymers
                       involved should be less than
                       5 x [10.sup.5] Pa.s
                     * The difference of index of
                       refraction of the two
                       materials should be more
                       than 0.1
                     * Materials may suffer thermal
                       degradation

  NT                 * Accuracy limited to ability
                       of cutting the sample
                       in the middle section of the
                       drop and at the same time
                       perpendicular to the base of
                       the drop
                     * Materials may suffer thermal
                       degradation

  BT                 * Theory developed for
                       Newtonian fluids
                     * Polymer matrix (with higher
                       viscosity) must be transparent
                     * The difference of melting or
                       glass transition temperature
                       between both polymers should
                       exceed 10[degrees]C
                     * The viscosity of the polymers
                       involved should not exceed an
                       upper value that depends on
                       viscosity ratio and interfacial
                       tension
                     * The difference of index of
                       refraction of the two
                       materials should be more
                       than 0.1
                     * Cannot be used for liquid
                       crystal polymers

 IFR                 * Theory developed for Newtonian fluids
                     * Theories are polymer pair dependent
                     * Polymer matrix (with higher viscosity)
                       must be transparent
                     * The difference of melting or glass
                       transition temperature between both
                       polymers should exceed 10[degrees]C
                     * The difference of index of refraction
                       of the two materials should be more
                       than 0.1
                     * Cannot be used for liquid crystal
                       polymers

RHEOLOGICAL METHODS

  RM                 * Difficulty in the visualization of
                       the plateau necessary for interfacial
                       tension evaluation
                     * Difficulty in the determination of
                       relaxation spectrum
                     * Experimental results may depend on
                       blend concentration
                     * Simple version of theory cannot be
                       used for compatibilized polymers


Method               Necessary parameters

STATIC METHODS

  PD                 * Density of both
                       polymers in the molten
                       state









  NT                 * Interfacial tension for
                       two of the three
                       polymer pairs
                       involved





  BT                 * Zero shear viscosity
                       of both polymers


















 IFR                 * Zero shear viscosity
                       of both polymers











RHEOLOGICAL METHODS

  RM                 * Quantitative morphology
                       of blend
                     * Zero shear viscosity
                       of both polymers







PD: Pendant Drop; SD: Sessile Drop; NT: Neumann Triangle; SpD: Spinning
Drop; BT: Breaking Thread; IF: Imbedded Fiber; DDRM: Deformed Drop
Retraction Method; RM: Rheological Method.

ACKNOWLEDGMENTS

The authors would like to thank FAPESP for financial support grants 94/033051-2, 97/06071-2, 00/02744-7.

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NICOLE R. DEMARQUETTE *

(*.) To whom correspondence should be sent.