BUBBLE LIFESPAN IN MOLTEN POLYMERS AND ITS ROLE IN
ROTATIONAL FOAM MOLDING
Remon Pop-Iliev, Donglai Xu, Chul B. Park, Ning Dong, and R. Fenton
Microcellular Plastics Manufacturing Laboratory
Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, Ontario, Canada M5S 3G8
Abstract
The ultimate goal in any closed-cell polyolefin
foam production is to achieve the highest possible
cell size reduction, cell size distribution uniformity,
and cell density augmentation. However, it has been
observed that the control of the cell size of
rotationally molded foams might be aggravated by
some unique inherent process limitations.
Introduction
It is inherent to the rotomolding process that, as
the melt front progresses, the air pockets that have
been entrapped inside the melt eventually become
bubbles that will be subjected to diffusion controlled
shrinkage and eventual disappearance [1]. At a high
enough melt temperature, the air in the bubbles
begins to dissolve into the polymer. Since oxygen
has about twice the solubility of nitrogen in
polyethylene, at high temperatures, the oxygen is
further depleted by direct oxidation reactions with
polyethylene. The depletion of oxygen reduces the
bubble diameter. Since the laws of surface tension
dictate that the pressure inside the bubble has to
increase as the diameter decreases, the increase in
bubble pressure forces nitrogen to dissolve in the
polymer thereby reducing the bubble diameter even
further. This repeats until the bubble disappears [2].
In deliberately developed rotationally foam
molded cellular structures using a chemical blowing
agent (CBA), a fine-celled morphology has been
closely approached, but it has not been actually
achieved yet. Perhaps this is due to the fact that the
polymer close to the internal mold surface continues
to be heated even after its foaming is completed,
simply because the interior polymer has yet to reach
the decomposition temperature of the blowing agent.
Even when cooling is applied to the mold, the
recrystallization temperature in the melt is reached
after several minutes, during which time bubble
coalescence and collapse set out and accelerate [3].
Problem Statement
It is hypothesized that in rotational foam
molding the CBA-blown bubbles having cell sizes
less than 100 m shrink and ultimately dissolve
before the time at which the non-pressurized viscous
polymer melt is cooled to its crystallization
temperature thereby precluding the formation of
fine-celled foam morphologies.
Experimental
A custom-build hot-stage optical microscopy
computerized digital imaging experimental setup
served for investigating the transformations
occurring during the cell growth of CBA-blown
bubbles in non-pressurized polyethylene (PE) melts.
Pre-compounded foamable samples (LL8556 +
3%wt Celogen OT) have been heated at a desired
rate and temperature profile.
Bubble Lifespan Observed in Hot-Stage Optical
Microscopy
The hot stage optical microscopy experimental
results revealed that the bubble lifespan consists of
three distinct phases: (i) pre-CBA, (ii) CBA, and (iii)
post-CBA decomposition governed.
The pre-CBA decomposition phase corresponds
with melt temperatures higher than the melting point
of the PE resin (e.g., 126 °C) but below the
decomposition temperature of the CBA (e.g., 158
°C). In this phase, there are some randomly
distributed bubbles throughout the melt, which
origins might be either entrapped air pockets during
sintering and polymer densification or CBA predecomposition during melt compounding, or both.
Also, it is believed that some of the initial bubbles
are being nucleated due to the presence of the CBA
particles in this phase acting as a nucleating agent.
As the temperature increases, bubbles begin to
interact, gas concentration gradient driven diffusion
takes place, and thus, some of the bubbles grow on
the account of the shrinkage and eventual
disappearance of the surrounding ones. Thereby, a
reduced number of larger bubbles live long enough
to participate in the second phase.
The CBA decomposition phase commences at
the time when the CBA becomes activated and the
CBA particles dispersed throughout the melt begin
to decompose. Since their sizes vary, and since
some are agglomerated, they have different bubble-
Modeling of the CBA-blown Phase
Based on the bubble dissolution model
developed by Kontopoulou and Vlachopoulos [4], a
simplified, single CBA-blown bubble model
assuming isothermal Newtonian non-pressurized PE
melt has been developed to simulate and quantify
bubble lifespan. Thus, the dynamics of a bubble
growth in an infinite liquid is described by a
standard group of governing equations. Eq. (1)
presents the integrated momentum equation, the
relationship expressed in Eq. (2) is the momentum
equation for Newtonian fluids, the mass balance is
described as given in Eq. (3), while the diffusion
equation is given by Eq. (4).

 rr   
2
(1)
Pg  P 
R

 2
R
r
dr  0
1
Pg  Pf R  2
R 
4

(2)
4 d Pg 3
 c 
 (
R )  4R 2 D  | r  R
3 dt R g T
 r 
(3)
c  R 2 c D   2 c 
(4)
R 2

r

t
r r r 2 r  r 
The above equations can be solved for suitable
boundary and initial conditions.
After the CBA decomposes, the gas pressure
inside the bubble can be calculated using Eq. (5):
nRT
V
Pg 
(5)
where n is the gas amount liberated by the
decomposition of the CBA (proportional to the CBA
particle size) A numerical solution method using
finite difference discretization was implemented.
Figure 1 shows the preliminary simulation of
bubble lifespan generated by CBA particles having
different sizes. The smaller the CBA particle, the
shorter life span of the bubble. The lifetime of a
~100 m bubble is less than a minute, which
prevents fine-celled foams to be preserved till the
end of rotomolding cycle.
Summary and Conclusions
Experimental results and computer simulation
are in good agreement with regards to the lifespan
time of the preferred fine-celled bubbles in rotational
foam molding.
They show that this time is
significantly shorter than the inherently lengthy
heating portion of the rotational molding process, so
that fine-celled bubbles seldom reach the
solidification stage of the cycle, thereby leaving only
the coarser-celled bubbles to participate in the final
cellular structure.
References
[1] M. Kontopoulou and J. Vlachopoulos, Polym.
Eng. Sci, 41, 155 (2001)
[2] P.Y. Kelly, Du Pont Canada Inc.(1981)
[3] J. Throne, SPE ANTEC, Technical Papers, 46,
1304 (2000)
[4] M. Kontopoulou and J. Vlachopoulos, Polym.
Eng. Sci., 39, 1189 (1999)
Bubble Diameter (micron)
generation abilities so that while some particles form
new bubbles some of them only increase the
concentration of gas in the molten polymer matrix
which busts further the growth of the surviving
bubbles from the first phase. For the newly created
bubbles, since the time of CBA gas evolution is very
short (comparable to a small explosion), the volume
of the bubble almost doesn’t change at all for this
short time period due to the resistance to bubble
volume changes caused by the viscoelastic response
of the surrounding polymer melt acting on the
bubble wall. As the time progresses, the pressuregoverned bubble overcomes this resistance. The
resulting effect is an oscillatory bubble growth. As
the bubble volume increases, the gas concentration
and inside pressure in the bubble drops until a
temporary equilibrium is reached. Then the third
and last phase of bubble growth commences.
The post-CBA decomposition phase includes the
continued rise of the temperature of the polymer
melt to the maximum process value (~220 °C) and
lasts up to the time when the polymer cools up to its
temperature of crystallization (e.g., 114 °C). The
gas diffusion in or out becomes dominant during this
phase. As a result, initially, the bubble continues to
grow thereby depleting the gas concentration of the
surrounding polymer up to the point at which the
direction of gas diffusion is directed out of the
bubble. As a consequence, the bubble shrinks. The
reduced temperature of the polymer stabilizes the
bubble after which it becomes permanently frozen at
the peak crystallization temperature of the polymer.
3X3X3 micron^3 CBA,x=0.95
6X6X6 micron^3 CBA,x=0.95
9X9X9 micron^3 CBA,x=0. 95
12X12X12 micron^3 CBA,x=0.95
15X15X15 micron^3 CBA,x= 0.95
18X18X18 micron^3 CBA,x= 0.95
160
140
120
100
80
60
40
20
0
0
10
20
30
40
50
60
70
Time (sec)
Figure 1: Effect of CBA particle size on the
lifespan of CBA-blown bubbles
80