Control of Dispersed Polymer Domain Size Formation in Melt Processing
Eldridge M. Mount III
EMMOUNT Technologies
ABSTRACT
During the formation of cavitated films the cavitating agent needs to be completely dispersed and controlled in
average particle size. When producing cavitated films with mineral based cavitating agents this is done with particle
size reduction and dispersive mixing. However, when using incompatible polymer blends are used, the size of the
dispersed phase will impact the quality of the final film and needs to be controlled. Control of the domain size is
possible be the proper selection of the individual polymers melt viscosity, the relative compatibility of the pair in
combination with the processing conditions combine to control the domain size of the dispersed phase. Correlations
between the dispersed domain size and the capillary number can be developed
INTRODUCTION
Cavitated films are a large and growing portion of the oriented films business and are used in several segments of
the film business for both packaging and industrial applications. Key examples are: biaxially oriented
polypropylene films used for confectionary, ice cream novelties, snacks, labels and as imagining supports, biaxially
oriented polyester films for electrical insulation, eating utensils and packaging and uniaxially oriented polyolefins
for shipping labels and luggage tags.
Cavitation occurs during orientation when the adhesion between a dispersed and continuous phase fails. The failure
in adhesion causes the continuous phase to stretch while the dispersed phase remains essentially the same
dimensions as no force can be transmitted to it across the interface. This results in a cavity with two walls both of
which are sources of light scattering and this causes the haze of the film to increase proportional to the number of
voids formed. Ideally the scattering void will be 30 microns are larger in diameter1. The number of voids will
depend on the size of the dispersed particles and amount of dispersed phase in the continuous phase. Cavitating
particles may range in size from 0.1 to 10 microns but the optimum size for cavitating particles is from 0.75 microns
to 2 microns for OPP. The optimum Particle diameter will depend to some degree on the polymer being cavitated
and the stretch ratios being used. For instance OPP is produced using stretch ratios of 5 MD X 8 TD or a 40 time
area increase and a 0.75 micron particle will yield a 30 micron void. In comparison PET is stretched 3.5 MD X 3.5
TD for an area ratio of 12.3 and in this case a particle of 2.5 microns will yield a void of 30 microns diameter.
There are a wide range of materials which can be used for cavitation which include inorganic and organic materials.
Generally the effectiveness of the cavitation is determined by the particle size, the modulus (relative to the
continuous phase) and the relative compatibility of the dispersed phase to the continuous phase. In addition to the
size of the particle, the shape can have an impact on the nature of the cavitated film produced. In general the more
spherical the particle the more uniform the light scattering from the cavitation and spherical particles are to be
preferred. For large volume film applications, cost of the cavitating particle can also be important. A balance
between cost and amount of cavitating agent required to obtain the desired film properties must be kept.
The question then becomes that of obtaining a spherical particle. In general inorganic particles are obtained by
precipitation or grinding and will only be approximately spherical. Spherical inorganic particles are available e.g.
Zeeospheres® a hollow ceramic and glass spheres and microballoons and they can be hollow or solid. Spherical
inorganic particle can also be prepared from a liquid precursor which is dispersed in an incompatible liquid by
stirring and then crosslinked. Using this method spherical particle is easily made and the particle size may be
controlled by process conditions. Spherical particles used for film surface modification e.g. TOSPEARL® are
manufactured using this method2. Spherical organic particles of cross linked polymers are also available and have
been used for both cavitation and film surface modification. However, these pre-manufactured inorganic and
organic particles are relatively more expensive than simple resins and in the case of the inorganic particles can give
the film a distinct silver/gray color as opposed to the white film which is desired. Therefore, it is generally desired
to produce cavitated films using incompatible blends of polymers
Incompatible materials when mixed as liquids, at equilibrium, will yield spherical domains of the dispersed phase.
This will limit the product of the surface tension times the surface area, because a spherical particle has the minimal
surface area, of all shapes, for the volume it encloses, this spherical geometry then limits the free energy of the blend
by minimizing the surface energy at the dispersed phase/ continuous phase domain interface. Because there are
many incompatible polymer pairs, it should be straightforward to produce spherical polymer particle of one polymer
into another prior to stretching. All that is needed is a means of controlling the particle size of the dispersed
polymer.
Particle size control by liquid-liquid dispersion is well known and a dimensionless group which describes this
technology is the Capillary number (Ca)3 (Equation 1).
Ca =
Fh μcγ& R
=
Fc
σ cd
where :
Fh = hydrodynamic force
Fc = cohesive force of dispersed phase
Equation 1
μc = viscosity of continious phase
γ& = shear rate in continious phase
R = particle raduis
σ cd = interfacial surface tension
The combination of the continuous phase viscosity times the shear rate describes the shear stress applied to the
dispersed phase and this will determine the particle radius based upon the surface energy of the system. What
happens in the viscous mixing of the two phases is that the dispersed phase is elongated into a thread or fiber by the
shear field. The elongated particle is then left in an unstressed state, it will then begin to spontaneously retract and
the surface contracts pinching of particles whose surface energy matches that of the shear field. If however, the
elongated particle is kept in the shear field, then the particle will begin to break up due to the surface tractions and
the length of the broken section will be determined at the point where the rupture strength of the incompatible liquid
phase matches the surface energy of the liquid pair times the area of the elongated particle. At this point, the forces
on the surface of the dispersed phase, exceeds the strength of the dispersed liquid and the thread breaks. This
mechanism yields very regular volumes of dispersed phase which when can form spherical particles of uniform
diameter.
This drop break up has been studied by Grace4 who demonstrated that droplet formation in a shear field is limited to
viscosity ratios (Viscosity dispersed phase/viscosity of continuous phase=μd/μc) of less then 3.5 (Figure 1) and
showed that a droplet formation can be predicted from the product of a critical capillary number (Cac) times a
function of the viscosity ratio (Equation 2).
Cac f ( p ) = Cac
Where :
p=
19 p + 16
= 0.16 p −0.6
16 p + 16
Equation 2
μD
μC
This relationships permits calculation of the critical capillary number from the viscosity ratio of the continuous and
the dispersed phase, and knowledge of the critical capillary value will permit estimation of the required shear stress
in the dispersing equipment such as a single screw extruder, or a mixing head design for a given polymer pair.
Figure 1: Critical capillary number verses viscosity ratio p, redrawn from Grace4
If the incompatible polymer pair is feed into a single screw extruder, and we assume that the dispersion is limited to
the metering section, the shear stress experienced by a particle will be controlled by the screw speed and metering
depth (average shear rate= flight tip velocity/screw depth), the temperature of the continuous phase melt the
viscosity of the dispersed phase viscosity at the melt temperature. Therefore, for a fixed polymer pair and screw
design, particle size may be controlled by increasing screw speed, decreasing barrel temperatures, increasing
continuous phase viscosity (lower melt flow) or degreasing dispersed phase viscosity (increasing melt flow).
On the other hand, if dispersion is inadequate with a given screw and polymer pair, and the process conditions
cannot be adjusted to give the desired particle size, then equation 2 can be used to determine the critical capillary
number and then this value can be used in Equation 1with the desired particle radius and the polymer pair to
calculate the minimum shear rate necessary for the desired dispersion.
Figure 1 demonstrates that for a given polymer pair (i.e. fixed value of interfacial surface tension) viscosity ratio
gives the principle control of particle size generation through the capillary number and that there is a limiting value
of the viscosity ratio of 3.5. This implies that in choosing the viscosity of the two polymers, the lower the dispersed
phase viscosity the better. Also, the highest viscosity continuous phase that the extrusion system can use, based
upon torque constraints, should be the starting point for viscosity selection. This gives the best likelihood of success
in creating an extrusion process with acceptable phase dimensions for cavitation.
Currently cavitation is carried out with polypropylene, polyester and high density polyethylene (HDPE) film
production. In PP and HDPE production calcium carbonate is used extensively, but incompatible polymer cavitation
is also widely practiced for PP and PET films. Typically PP is cavitated with nylon or polybutylene terephthalate
(PBT) as the dispersed phase, and PET is cavitated with PP as the dispersed phase. PP is oriented at approximately
155 oC and requires an incompatible polymer melting higher than PP so nylon and crystallized polyesters are good
candidates. However, when orienting PET, the continuous phase is amorphous and the stretching temperatures are
approximately 80 oC and in this case the PP is a crystalline solid even though it is lower melting than crystallized
PET.
Figure 2 shows the comparison of a typical film grade PP with three nylons and a PET resin at 260 oC, an optimal
extrusion melt temperature in PP orientation processes.
If we assume the process uses a 200 mm diameter screw with a metering section of 9 mm depth and a screw speed
of 65 rpm, then we can estimate the shear rate and viscosity of each of the resins in the metering section and then the
viscosity ration for each combination. This would give a peripheral screw speed of 680 mm/sec and for a metering
depth of 9 mm an average shear rate in the metering section of approximately 80 sec-1.
Examining Figure 2 at 80 sec-1 we find that the PET has a lower viscosity than the PP and the three nylons have a
higher viscosity than the PP resin at 260 oC. Table 1 lists the Viscosity ratios for each of the resins.
Resin
Viscosity, Pa-sec
Viscosity ration μd/μc
PP
401
PET
314
0.78
Nylon 1
589
1.47
Nylon 2
825
2.05
Nylon 3
1092
2.72
Table 1: Calculated viscosity ratios of 4 potential cavitating resins relative to PP continuous phase
Table 1 shows that the best choice of cavitating resin in this instance would be the PET resin as it has a lower
viscosity relative to the PP while the nylon resins all have increasing viscosity ratios with Nylon 3 approaching the
limiting ration of 3.5 for particle formation.
Based upon Graces limit4 for tip streaming of p<0.1, particle formation with the resin combinations in Table 1
would be expected to proceed by bursting. Consequently the PET would form smaller particles more readily than all
of the three nylon resins with the suitability of the Nylons decreasing from Nylon 1 to Nylon 3. However, if the PP
were to be used to cavitate the nylon or PET the choice of PP would be poor for the PET as the viscosity ratio would
now be 1.27 while that for Nylon 3 would be 0.36.
CONCLUSIONS
Particle size control in the creation of cavitated films is critical for uniform cavitation with the need to create
particles of incompatible polymers of between 0.75 and 3.0 microns dispersed in a continuous phase. Knowledge of
the polymer viscosity as a function of temperature and shear rate in combination with the principle screw design
parameters (metering depth, screw diameter) for the metering section and/or mixer design elements will permit the
design of a robust cavitation process through the rheological control of particle size. Evaluations of resins pairs can
also aid in the determination of the best potential resin candidate for a cavitating resin in a given continuous phase.
Calculation of the final particle size range will require detailed knowledge of the interfacial tension between the
resin pairs
Ashcraft, C. R. and Park, H. C., U. S. Patent 4,377,616, “Lustrous Satin Appearing, Opaque Film
Compositions and Method for Preparing the Same”, Washington, U.S. Patent and Trademark
Office, Washington, DC, (1983)
2 Shimizu, T. et al., U.S. Patent 5,149,748, “Process of preparing surface-modified polymethylsilsesquioxane
spherical fine particles”, Washington, U.S. Patent and Trademark Office, Washington, DC, (1992)
3 Baird, D. G. and Collias, D., I., Polymer Processing Principles and Design, John Wiley & Sons, Inc,
New York, (1998), p 160-165
4 Grace, H. P., “Dispersion Phenomenon in High Viscosity Immiscible Fluid Systems and
Application of Static Mixers as Dispersion Devices in Such Systems”, Chem. Eng. Commun., 14,
(1982), pp225-277
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