Interfacial Tension of PBT / SAN Blends by the Drop Retraction Method

The aim of this work was to evaluate the interfacial tension from the poly(butylene terephtalate) and poly(styrene-co-acrylonitrile) (PBT/SAN) interface region using the drop retraction method. SAN filaments were sandwiched between two PBT films; the whole system was heated up to 240 °C, in a hot stage coupled to an optical microscope. The rheological parameters of the PBT/SAN system were obtained by parallel plates rheometry. An increase of the interfacial tension with the PBT molecular weight was observed with values between 0.57 and 1.06 mN/m, depending on the molecular weight. Theoretical values were calculated using the geometric-mean and harmonic-mean equations and were found to be similar to the experimental results. Viscosity measurements showed that the higher the SAN/PBT viscosity ratio, the lower the interfacial tension of these blends.


Introduction
The development of new polymeric blends is an important and creative technological way of obtaining new applications for polymeric materials, decreasing costs and optimizing properties of the final products.Most of the polymers are immiscible during their mixture with other polymers and form multiphase systems with a variety of morphologies, like: disperse droplets, fibrils, lamellar and co-continuous structures 1 .The type of blend morphology affects strongly its final properties.Therefore the morphology control is a critical factor in the optimization of the polymer blend performance.This morphology depends on the interfacial tension, among other parameters 1 .Favis and Willis 2 have pointed out that the morphology of immiscible polymer blends seems to be controlled by the following parameters, in order of importance: interfacial tension > viscosity ratio > shear stress.
Studies on toughening of PBT with other rubber modified plastics containing high amount of elastomers, like ABS and AES, have concentrated efforts on simpler systems, for a better understanding of the blend morphology establishment, due to the complexity of these multiphase systems.The adequate dispersion of both styrenic terpolymers in the PBT matrix depends strongly on the interfacial tension of the system.Usually the poly(styrene-co-acrylonitrile), SAN, matrix phase from the ABS or AES terpolymer generates the interfacial region with PBT in the PBT/ABS and PBT/AES blends.In addition, those blends have another well established interface region between the rubbery phase and the SAN phase generated by the terpolymers synthesis.Paul and his collaborators 3,4 have done many studies to understand those blends performance.However, the interfacial tension for PBT/SAN has not yet been evaluated to contribute to those studies.
Thus, the main objective of this work was to measure the interfacial tension between PBT and SAN, using the drop retraction method, developed by Mo et al. 5 and to compare the results with theoretical results.

Interfacial Tension Theoretical Background
The surface tension is a direct manifestation of intermolecular forces at any surface.The surface molecules of a liquid or solid material are influenced by the unpaired molecular forces due to the surface discontinuity, which leads to surface molecules having additional energy.When those molecules are in contact with surrounded air the surface tension increases as the intermolecular forces among the surface molecules increase.On the other hand, the contact of a material surface with other material different than air generates an additional energy in the interface region.The additional free energy at the interface between two phases is known as interfacial tension 6 .The magnitude of the interfacial tension depends on the surface tension of each contact surface.Many authors [7][8][9][10][11][12][13][14][15][16][17] have used theoretical predictions from empirical equations that correlate interfacial tension with surface tension.From these empirical equations, the interfacial tension (g) between two materials can be calculated through the harmonic mean equation (Equation 1) or through the geometric mean equation (Equation 2): (1) where g 1 is the surface tension of material 1, that is, g 1 = (g d 1 + g p 1 ), g 2 is the surface tension of material 2, or g 2 = (g d 2 + g p 2 ), where the superscript "d" refers to the non-polar contributions (dispersion contribution) and the superscript "p" to the polar contributions to the surface tension of each material.
To estimate the interfacial tension (g) through Equations 1 and 2 it is necessary to know the polar(g p i ) and the non-polar (g d i ) contributions to the surface tensions g i .Both surface tension contributions may be represented as fractions of g i , as can be observed in the Equation 3. The polar contribution fraction may be referred as the surface polarity c p i , while the non-polar contribution fraction is added to one.Therefore, if both surface tension and the surface polarity are known for each material, it is possible to find g p i and g d i , respectively.(3) The surface polarity has been considered independent of temperature, i. e., 0 c = p i d dT The surface tension can be easily obtained for any material through experimental measurements or can be found in the literature through specific handbooks.On the other hand, the surface polarity c p can be obtained as a function of the cohesive energy density ∆E or as function of the solubility parameter, as shown in Equation 4: where, ∆E p is the polar contribution to the ∆E and d p is the polar contribution to the overall solubility parameter d.The surface polarity values obtained from surface tension have been found to agree with those obtained from cohesive energy densities calculations for a high number of polymers 18 .
Hansen and Skaarup 19 assumed that the cohesive energy density, ∆E, which is proportional to d, arises from dispersive interactions (d d ), permanent dipole-dipole interactions (d p ) and hydrogen bonding forces (d h ), and is obtained as shown in Equation 5: Those parameters (d i ) are referred as Hansen parameters; however, cannot predict the overall dwith accuracy for all the materials systems.The specific interactions between groups and molecules may not be given by a simple addition rule.Even so, the estimation of the Hansen parameters can be quite useful.The Hoftyzer and van Krevelen methods 19 allow estimations of those parameters by the following expressions: where F di is the dispersive force contribution, Fpi is the polar force contribution, E hi is the hydrogen bonds energy, for each chemical group of the polymer and V molar is the molar volume.Any of the Hansen parameters can be easily calculated for any polymer if its molecular repeat unit is known.The respective values for F di , F pi and E hi are found tabulated in specific handbooks 19 .The surface polarity c p values for polymers determined through the use of interfacial properties have been observed to have good correlation with the ones determined using the cohesive densities 19 .It should be cautioned, however, that Equation 3 defines the surface polarity, while Equation 4defines the bulk polarity.These two values may not be the same, if the polymer has sufficiently long surface-active segments, which tend to preferentially adsorb on the surfaces.Therefore, from the above calculation procedures it is possible to estimate the the interfacial tension (g) between two materials of the Equations 1 and 2.
In the molten state it is very difficult to measure the interfacial tension between polymers due to their high viscosities.Therefore, numerous methods have been developed to measure this parameter, which can be classified as: thermodynamics (static), dynamics and rheological 20 .
The thermodynamics methods require long measurement times, due to the polymers high viscosities; therefore, there is a risk of polymer thermal degradation.The main thermodynamic methods are: the pendent droplet, the sessile droplet and the rotating droplet 20 .
The dynamic methods have the advantage of taking less time, thus compensating problems due to thermal perturbation.The main dynamic methods are: the breaking thread and the droplet retraction.The "breaking thread" is more complex from the experimental point of view and especially for systems were the viscosity ratio is higher than one 20 .
As a matter of fact there is not a preferential method for measuring the interfacial tension, because each one has its advantages and disadvantages.
In the three-dimensional deformation model, the drop shape is subsequently described by a symmetric, positive-definite, second rank tensor S; its eigenvalues represent the square semi-axis of an ellipsoid.The evolution of this tensor results from the action of the interfacial tension and from the hydrodynamic drag exerted by the movement and can be described by an evolution model proposed by Maffettone et al. 21, given by: ( ) ( ) where Ω is the vorticity tensor, f 1 and f 2 are coefficients which are functions of the viscosity ratio, τ is a characteristic time, I is a second order unit tensor and E is the deformation rate tensor.Assuming constant droplet volume, Mo et al. 5 developed an equation for the evolution of S in a flow field.If E and Ω are equal to zero, Equation 9 can be simplified to: where : λ 1 = L 2 , λ 2 = B 2 , L being the larger semi-axes and B the smaller semi-axes, η m is the matrix viscosity, p is the viscosity ratio = η d /η m , where η d is the viscosity of the disperse phase, R 0 is the equilibrium droplet radius and t is the measurement time in seconds.

Materials
Three different molecular weights PBT's were used in this work, named Valox 195, 325 and 315, from GE South America Plastics.The SAN, grade CN77E, was from Bayer Polymers S.A.

Melt flow index
Melf flow index was measured following ASTM D1238-00 standard procedure using a load of 1.20 kg and a temperature at 250 °C.
The PBT samples were previously dried during 16 hours at 60 °C under vacuum.PBT solutions were prepared using a concentration of 0.3 g/dL at room temperature.
The intrinsic viscosity [η] was measured at 30 ± 0.1 °C using the one point method 22,23 and the relationships given by Solomon and Ciuta (Equation 11), Rao and Yaseen (Equation 12) and Deb and Chatterjee (Equation 13).
The correlation between M n and [η] given by Borman 24 was used, as shown in Equation 14: The average molecular weight of the SAN copolymer samples was determined by gel permeation chromatography, GPC.The SAN solutions were prepared in tetrahydrofurane solvent (Vetec).The solution was filtered and injected at 40 °C at 1 mL/min in a Waters 410 chromatograph, with a refraction index detector and Ultrastyragel columns.The calibration curves were constructed with 12 PS monodisperse standard samples from Shodex Standard.

Determination of the amount of acrylonitrile in the SAN copolymer
A Fisons Instruments equipment model EA 1108 CHNS-O was used to determine the concentration of nitrogen of the SAN samples.
The amount of nitrogen (% N) measured was therefore used to calculate the % of acrylonitrile in the SAN copolymer, by using the following relationship: % 100 % 26.42

Rheological measurements
The zero shear viscosity η 0 was measured in a strain controlled rheometer, ARES, from Rheometrics, at 240 °C, under nitrogen atmosphere, using parallel plates with 25 mm diameter and gap of 1 mm.The time for measurement of η 0 was similar to the time for the droplet retraction.

Interfacial tension measurement
Films of PBT were produced by compression molding, at 240 °C, after drying the PBT at 60 °C, during 12 hours, under vacuum.SAN filaments were prepared after heating the polymer at 220 °C; the SAN was therefore drawn to produce filaments with 80~120 µm of diameter.These filaments were set between the PBT films, forming a "sandwich" structure.This "sandwich" structure was fixed between two glass slides and the whole set was heated up to 240 °C using a hot stage THMS 600 from Linkan.To avoid thermal degradation, a nitrogen saturated atmosphere was used.The thread rupture and droplet retraction was monitored using a transmitted light optical microscope, Leica Model DM RXP and image acquisition software Image-Pro Plus.The droplet aspect ratio was thus determined.

Results and Discussion
Table 1 shows the melt flow index of the polymers and the values of number average molecular weights, M n , of the PBT and SAN samples obtained as received and after the interfacial tension measurements.
Table 2 shows the values of η 0 of the polymers, at different times.The viscosity ratio p = η SAN /η PBT was calculated from those results (Table 3).
The surface tension of SAN with 25% of acrylonitrile at 20 °C was calculated by interpolation in a surface tension versus % acrylonitrile curve obtained from the literature 16 .
The values of density ρ for both SAN and PBT, shown in Table 4, were obtained from the data file of the Moldflow MPI 4.1 software.
It was verified that the majority of the (-dg/dT) values 18 for polymers is in the range between 0.06 and 0.08; therefore due to the difficulty of calculating the SAN surface tension at 240 °C, those values were used to estimate its surface tension, which is also shown in Table 5.
The value of c p for the PBT was obtained from the literature 16 while the value of c p for the SAN copolymer was calculated from the cohesive energy density, Equation 4. The values of c p , g d and g p for the PBT and the SAN are given in Table 4.
Figure 2 shows the SAN filament breaking and drop retraction in the PBT matrix.These pictures were taken after 45 minutes at 240 °C, with 30 seconds of time interval between each picture.
The change in the SAN droplet retraction dimensions, given by the difference λ 1 -λ 2 , where λ 1 = L 2 , λ 2 = B 2 , as in Equation 10, was measured as a function of time and it is shown in Figure 3.The average interfacial tension (g) was obtained from the slope of the curves at different R 0 , and it is shown in Table 5.
It can be observed that the results obtained from the drop retraction experiments reasonably agree with the calculated values from the harmonic mean and the geometric mean equations.
The empirical equations are useful for calculating the interfacial tension although there is a difference between the experimental and the calculated data because the calculation procedure has referred to the polymer as mer units and the experimental data make use of the polymer bulk to obtain the interfacial tension.However, there is no other data for PBT/SAN systems to compare with the experimental results and its can give an indication of the efficiency of the method.In addition, the experimental values stay between the harmonic  and geometric means calculated values, as already shown by Wu 16 in several polymer pair systems (PEO/PDMS, PVAc/PDMS, PCP/ PDMS, PCP/PnBMA, PCP/PS, PMMA/PNBMA, PMMA/PtBMA, PMA/PEHA, etc).It is also observed from Table 5 that the change in (-dg/dT) from 0.06 to 0.08 does not change significantly the calculated interfacial tension values.For the PBT/SAN system, it was observed an increase in the interfacial tension as a function of the increase in the PBT molecular weight, as already observed by Kamal 25 for PP/ PS systems.For that system the increase was observed up to a certain molecular weight then it leveled off for further increase.The calculated values of the interfacial tension for PBT/PS blends were obtained by Bu and He 18 at 250 °C.They used the harmonic mean equation to obtain those values and found the interfacial tension to be equal to 1.29 mN/m, which is in the same range of results for the PBT/SAN system found here.

Conclusions
The interfacial tension of the PBT/SAN system was measured at 240 °C using a modified droplet retraction method, developed by Mo et al.The experimental values have shown a reasonable agreement with the calculated ones using the harmonic and geometric averages equations.The increase in the PBT molecular weight promoted an increase in the interfacial tension for the PBT/SAN system.

Figure 2 .Figure 3 .
Figure 2. SAN filament break and droplet retraction in a PBT matrix after 45 minutes at 240 °C, where L and B are the semi-axis of the ellipsoid drop, respectively.

Table 1 .
Melt flow index and number average molecular weights of the polymers.

Table 2 .
Zero shear viscosity, η 0 , of the PBT and SAN samples, measured at 240 °C for different times.

Table 3 .
The viscosity ratio, p, of the PBT and SAN samples, measured at 240 ° C for different times.

Table 5 .
Experimental and calculated values of the interfacial tension (g) of the PBT/SAN system.