A Brief Review
Rotational molding begins with -35 mesh polymer powder tumbling in a metal mold. It ends with a monolithic layer of solid polymer against the metal mold. In between, the powder tumbles against the mold until the mold temperature reaches the tack temperature of the powder, whereupon the powder begins to stick to the mold surface. Then as the powder stuck on the mold surface heats, more powder sticks to that powder, and on and on. Sometime after the first layer of powder sticks to the mold, but before the entire mass of polymer is totally liquefied on the mold surface, the air in powder bed, for the most part, “goes away”. The question for this technical minute is “Where does all the air go?”
First, we need to identify some possible mechanisms for air disappearance. I’ve put these in four general categories:
Bubble Disappearance by Molecular diffusion, and
Capillarity was the first mechanism proposed [M.A. Rao and J.L. Throne, "Principles of Rotational Molding", Polym. Eng. Sci., 12 (1972), pp. 237-264]. The coalescing bed was pictured as liquidus at the mold surface but tacked granular at the free or non-mold surface. It was proposed that when the polymer powder was fused at some point but when there was still tortuous air paths, polymer would be drawn up the air channel by simple surface tension, essentially expelling the air ahead of it toward the non-mold surface. Envisage the drawing of a liquid up a soda straw. There are several problems with capillarity. First, it depends on surface tension for the driving force, but surface tension decreases with increasing temperature. Second, the drawing effect decreases in proportion to the cross-sectional area of the flow channel. In other words, the smaller the soda straw, the higher the liquid will be drawn. And then, for capillarity to be effective in a time-dependent way, the liquid viscosity must be low. And of course, the viscosities of polymers are quite high, when compared with, say, soda. So, while there may be some capillarity effect, it is probably minimal.
Sometime after the capillarity hypothesis and after substantial observances of powder being heated on a static plate, it was decided that another mechanism was in action, that of bulk migration of the air from the powder to the non-mold surface [R.C. Progelhof, G. Cellier and J.L. Throne, "New Technology in Rotational Molding: Powder Densification", SPE ANTEC Tech. Pap., 28 (1982), pp. 627-629]. In other words, we noticed that the powder structure weakened as it heated. As a result, the ‘powder columns’ simply collapsed under their own weight. If heating was gentle, the air would be expelled toward the non-mold surface, i.e., bulk migration of air. If the heating was severe, the collapse would entrap some air, which ultimately would form into bubbles. As part of this study, it was noted that the time-dependent height of the powder bed was not altered dramatically when a substantial portion of the air was evacuated during powder bed heating. This led us to the conclusion that the underlying mechanism for air removal from the coalescing powder bed was the viscoelastic character of the polymer and not capillarity.
Bubble Disappearance via Molecular Diffusion
Recently, Dr. Roy Crawford and his team at Queen’s University at Belfast [R.J. Crawford and P.J. Nugent, "A New Process Control System for Rotational Moulding", Plast. Rubb. Compos. Process Applic., 17 (1992), pp. 23-31] have determined that the mechanism of air migration is dramatically altered once bubbles have formed. Lord Rayleigh determined that a bubble can remain stable only if the internal gas pressure is greater than the external melt pressure:
where σ is the surface tension of the polymer and r is the bubble radius. As is apparent, small stable bubbles have higher internal gas pressure than do large stable bubbles. As an example of the differential pressure required, consider a bubble 100 microns = 0.01 cm in diameter, in a polymer with the surface tension of 30 dyne/cm. The differential pressure is:
Δ P = 30 x 2/0.005 = 12000 dyne/cm2 = 1200 Pa = 0.174 psi
If the differential pressure decreases, the bubble will grow until the equation is met. If it increases, the bubble will shrink until the equation is met. [See J.L. Throne, Thermoplastic Foams, Sherwood Publishers, 1996 for more information on bubble dynamics.] Although Lord Rayleigh was right on regarding the static condition, his equation needs tampering in order to work for time-dependent events such as bubble extinction. [See J.L. Throne, "Is Your Polymer Foamable?" Foams Conference '96, Somerset NJ, 10-12 Dec 1997, for the "Second Rayleigh Equation"].
It has further been proposed that, owing to the differential pressure between the air in the bubble and that in the polymer, it simply disappears by dissolving in the polymer. Solubility is usually given by Henry’s law:
S = HP
where S is solubility in cm3(STP)/g plastic, P is pressure in atm and H is Henry’s constant, in cm3(STP)/g atm. Now for nitrogen in polyethylene, H has a value of 0.111. Therefore at the cell gas pressure calculated above:
S = 0.111 x 1.174/14.7 = 0.00887 cm3/g plastic
Assume for the moment that all the air brought in with the plastic powder becomes bubbles. Consider the bulk density of powder to be about 1/2 that of the monolithic polymer. If the density of the polymer is about 1 g/cm3, then the volume of air in the incoming powder is about 1 cm3/g plastic. [Because the polymer has some volume, the actual volume of air is somewhat less.]
Therefore, of the original air concentration of 1 cm3/g plastic, less than 1% will be dissolved in the polymer. But again, this is a static situation. We need to determine whether this very tiny concentration difference can cause the bubble dimension to decrease completely.
So… Where Does The Air Go?
Recent work at McMasters University [K. Kontopoulou and J. Vlachopoulos, "Bubble Dissolution in Molten Polymers and Its Role in Rotational Molding", paper submitted to Polym. Eng. Sci., 1998] summarizes bubble disappearance in the following way:
* From a fluid mechanics viewpoint, the rate of bubble disappearance [viz, dR/dt] is given by Lord Rayleigh’s second equation, with Newtonian viscosity, h, as a measure of polymer resistance to deflation. The greater the polymer viscosity, the more rapidly the bubble disappears. This is written as:dR/dt = [R ΔP - 2σ] / η
* From a mass transfer viewpoint, the rate of bubble disappearance is a direct function of the concentration gradient. Owing to Henry’s law, the concentration of air at the bubble interface is greater than that in the bulk polymer.
Putting these ideas together, if there is a concentration gradient owing to differential solubility, regardless of how small, the result will be diffusion of air from the bubble into the bulk polymer. This causes the bubble to decrease in radius, which in turn increases the internal bubble gas pressure, according to Lord Rayleigh, which further in turn, increases the concentration of air at the bubble interface, thereby increasing the concentration gradient. In other words, in an isothermal viscous-only world [and even in a non-isothermal viscous-only world], bubble diameter decreases slowly at first, then accelerates as the bubble gets smaller and smaller, until… POOF! The bubble is gone!
It seems fair to say that, following this logic, eventually all bubbles will go poof!, regardless of their initial size. Further it seems fair to say that the rate of extinguishment of the bubble is therefore governed primarily by polymer viscosity.
What About Applied Pressure?
Accordingly, when we apply pneumatic or air pressure to the densifying bubble, the following things happen. When we increase the hydrostatic pressure on the outside of the bubble, the volume of the bubble decreases. Remember P-V-T? Of course, the internal gas pressure increases, and since the bubble radius is now smaller, the local solubility at the bubble/polymer interface increases and therefore, so does the concentration gradient. Ergo, increasing pressure causes the bubbles to go poof! more rapidly. The only remaining question is whether someone will attempt to patent this event of nature!
So there we have it! Capillarity is apparently out of favor. Bulk migration owing to the collapse of the friable powder columns occurs but is also probably not that significant during densification. What we really have is bubble disappearance due to the differential pressure between the air in the bubble and that in the bulk polymer which triggers a concentration gradient of air between the bubble/polymer interface and the bulk polymer. Applied pneumatic pressure hastens extinction.
What’s Wrong With This Picture?
Really not a whole lot. But…
* If I can rotationally mold PS, why can’t I rotationally mold ABS?
* And, if bubbles disappear catastrophically, why are there any bubbles, at all, in some rotomolded parts?
* And, if little bubbles disappear quicker than big bubbles, why are there so many little bubbles in some rotomolded parts? Are they just formerly big bubbles on their way to extinction?
* And finally, what happens if I apply a vacuum rather than pressure? Sure, initially, the bubbles will get bigger. But the concentration gradient gets even bigger, since there’s less air in the bulk polymer. So, shouldn’t the bubbles disappear even quicker?
Here’s a thought experiment to ponder. Suppose we try to separate diffusion from dissolution. I guess I’d use the Progelhof hot plate scheme to illustrate the effect, although I might even be able to carry it out on a microscope hot stage. I’d put polyethylene powder in a glass cylinder that sits on a hot plate. Suppose that the cylinder cavity is initially filled with a gas other than air, say, carbon dioxide. Then, at the instant of coalescence completion but before densification can begin, I swap the carbon dioxide in the mold cavity for nitrogen, say. Then the concentration of carbon dioxide in the gas bubble is unity while it is zero in the mold cavity. Obviously then carbon dioxide will diffuse from the bubbles as well as the bulk polymer. But keep in mind that nitrogen will diffuse the other way, into the polymer and the bubbles. However, for most polymers, carbon dioxide permeability is about 15 times greater than that for nitrogen. So the result should be one of diminishing of bubble radii even though the polymer and gas temperatures remain isothermal. Then I’d reverse the process, this time using a gas with a low diffusional coefficient, say, dichlorotrifluoroethane [R-123], then at the same appropriate time, swapping it in the free space with carbon dioxide. And finally, I’d repeat the original Progelhof experiment, with and without one atmosphere air in the cylinder. Will I still see the same rate of bubble disappearance?
9 June 1998