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Introducing Viscoelasticity to Precollege Students Through a Composite
Bouncing Balls Hands-On Experiment
Article in Journal of Materials Education · September 2014
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Journal of Materials Education Vol. 36 (3-4): 69 - 76 (2014)
INTRODUCING VISCOELASTICITY TO PRECOLLEGE STUDENTS
THROUGH A COMPOSITE BOUNCING BALLS HANDS-ON
EXPERIMENT
Aldo Acevedo1 and Stephany Herrera-Posada
Department of Chemical Engineering, University of Puerto Rico, Mayagüez, PO Box 9000,
Mayagüez, Puerto Rico, 00680
1
Corresponding author email: aldo.acevedo@upr.edu
ABSTRACT
Understanding structure-performance relationship in materials can help engineers and scientist to
develop and optimize product and processes. This requires the integration of physics and chemistry
concepts, yet traditional education of precollege science appears to be disjointed between specialties.
In this work, a simple, safe and economic hands-on experiment is presented with the objective of
providing an engaging experience that promotes learning and integration of concepts from physics
and chemistry, allowing for the introduction of non-ideal viscoelastic materials. A viscoelastic
material is one which has both viscous and elastic properties, and do not conform to the definitions
of a perfectly elastic solid (Hooke’s law) or a simple fluid (Newton’s first law). The experiment
consists of the preparation of polymer and polymer composite balls, and the evaluation of the
bounciness to determine the energy loss and recovery. Students are then expected to provide simple
molecular arguments based on the structure and morphology to explain the macroscopically
observed physical properties. The proposed experiment was presented in a workshop for middle and
high school science teachers and their feedback, based on science standards, on where to incorporate
this experience in the curriculum is presented.
Keywords: outreach, viscoelasticity, energy dissipation, polymer composites
INTRODUCTION
Traditional education of precollege science
appears to be disjointed between the life
sciences, chemistry, and physics, and little
effort is dedicated into their integration. This
causes students to lose interest due to their
inability to relate science lessons to their
everyday life.1 Nevertheless, bridging the
classical science fields is necessary to develop a
workforce capable of tackling future engineering challenges, especially those related to the
design and optimization of materials.
Typically, introductory courses in physics study
phenomena in which the composition of the
70
Acevedo and Herrera-Posada
material in the experiment is less important than
the behavior of those materials.2 Introduction
to conservation of momentum is such an
example, where collisions are classified as
either elastic or inelastic.3 Yet, little or no
mention of the origin of elasticity or inelasticity
is found in introductory physics courses. On the
other hand, the effect of molecular structure on
mechanical properties, including elasticity, is
typically neglected from introductory chemistry
textbooks.
The mechanical properties of elastic solids are
described by the classical theory of elasticity
through Hooke’s law, which states that stress
(i.e. force per unit area) is always directly
proportional to the strain (i.e. deformation).
Meanwhile, the mechanical properties of simple
fluids are described by Newton’s law, which
states that stress is always directly proportional
to the rate of strain (i.e. rate of deformation).
Nevertheless, we are surrounded by materials
that do not conform exactly to any of these
descriptions. Instead, they combine liquid and
solid characteristics, and are aptly named
viscoelastic materials. When these materials are
deformed, molecular events, at different time
and length scales, allow for the storage (and
release) or dissipation of energy. Examples
include many food and household products,
plastics, and suspensions. Viscoelasticity is the
source for many commonly observed effects,
such as the Weissenberg or rod-climbing effect,
fluid memory, and die swell.4 Demonstrations
and experiments to evaluate these effects can be
found in the literature.5-7
In this work, we present a simple, safe, and
economic experiment to prepare composite
polymer balls with different viscoelastic
properties through the incorporation of solid
filler. Incorporation of hands-on activities into
lessons is often seen as exciting, challenging,
and uplifting. The objective of this experience
is to provide an engaging experience that
promotes learning and integration of concepts
from physics and chemistry, allowing the
introduction of non-ideal viscoelastic materials
to precollege students. As a secondary objective
students can also learn about composites and
optimization of material properties.
BACKGROUND
Viscoelasticity
A viscoelastic material is one which has both
viscous and elastic properties. When a body is
subjected to a sinusoidal stress, the strain
response will also be sinusoidal. If the material
is a perfectly elastic solid, the stress and strain
curves will be exactly in phase. If the substance
is a Newtonian fluid, the stress and strain will
be perfectly out of phase by 90°. A viscoelastic
material will have a strain response between
these two extremes. The elastic and viscous
behaviors are analogous to a mechanical spring
and dashpot, respectively, and are the basis for
the simplest Maxwell model. However, the
dynamics of real systems, such as polymer
macromolecules, show a distribution of
relaxation processes. Fast relaxation modes
correspond to portions of the molecules that can
move independently of the rest of the molecule
or system, while slow processes require the
coordinated movement of more portions. In a
branched polymer, for example, the side
branches relax faster than the polymer
backbone. Therefore, real materials behave as if
they are comprised of multiple combinations of
springs and dashpots. Irreversible movements,
such as bond rotation and chain slippage,
absorb and dissipate energy in the form of heat,
which is the molecular origin of their viscous
behavior. On the other hand, reversible events
store and release energy when they return to
their original position, and are responsible for
the elastic behavior.
Investigation of viscoelastic properties provides
(1) information about the configurational
arrangements, and short- and long-range interactions of molecules, and (2) understanding of
the mechanical properties associated with the
processing and use of materials.8 The most
common experimental techniques to characterize viscoelastic properties of materials are
performed using dynamic mechanical analyzers
(DMAs) for solid-like materials and using
dynamic oscillatory shear tests in rotational
rheometers for fluids. In-depth discussion of
these topics can be found in excellent
Journal of Materials Education Vol. 36 (3-4)
Introducing Viscoelasticity. . . . .through a Composite Bouncing Balls Hands-On Experiment
textbooks4, 9-12 or in the seminal work by Ferry
(1980)8. Understanding the relationship
between molecular structure and mechanical
properties can help engineers and scientists to
develop and optimize product formulations as
well as processes.
Bouncing Ball
If a perfectly elastic ball is dropped from an
arbitrary height, it will bounce back and reach
this initial height again. Nevertheless, this is not
observed in real life. The ball bounces back but
does not reach its initial height again. This is
due to the chemical nature of the materials. For
example, each sports ball is designed with
different materials to obtain the appropriate
bounciness required in each of them.
71
maximum. Yet, point 3 is lower than point 1.
Thus, between 1 and 3 the energy lost by the
ball is given by:
Eloss = mg(h3 - h1)
(1)
where, h1 and h3 are the position of the two
consecutive maxima in the trajectory, m is the
mass, and g is the gravitational constant. On the
other hand, the energy that is recovered or
stored within the ball is:
Estored = mgh3
(2)
The principle of energy conservation does not
allow for the creation or destruction of energy.
If the impacted surface is non-deformable the
collision can be considered inelastic and no
energy is transferred to it. Hence, where has the
energy gone?
Energy is dissipated by the internal or
molecular structure of the constituents of the
material. Thus, the energy loss and storage are
associated with the viscous and elastic
contributions of the material, respectively.
Alternatively, the elasticity can also be
expressed in terms of a recovery coefficient (R)
given by:
Recovery = h1/h0 = …. = hn+1/hn
Figure 1. Schematic representation of a bounce
cycle of viscoelastic ball
Let’s carefully consider the trajectory of a ball
as it bounces, as shown in Figure 1. The ball is
initially at rest at point 1 and all its energy is
potential. At t = 0, the ball is dropped in free
fall. As it moves down the potential energy is
converted to kinetic energy. Just before hitting
the floor at point 2, all the energy has been
converted to kinetic energy. After hitting the
horizontal surface, the ball bounces back. As it
ascends the kinetic energy is transformed into
potential energy, until it reaches a new
maximum at point 3. At point 3, kinetic energy
again is zero and potential energy is at a
(3)
where, the subscripts denote the position of the
two consecutive maxima in the trajectory.
When a material is close to ideal (or Hookean)
elastic, the recovery is close to one. Meanwhile,
for an inelastic material it is close to zero.
Viscoelastic materials can be characterized by
this coefficient of restitution or recovery, which
depends on the material itself.
EXPERIMENTAL DETAILS
Bouncing Ball Preparation
As the basis of our work we used the Super
Bouncing Ball Kits (Cat# BALL-115), a
commercially available kit to prepare round
balls from Educational Innovations, Inc.
(www.teachersource.com). The kit is comprised
of round snap-in molds and pre-measured
packages of colored poly(vinyl alcohol) (PVA)
Journal of Materials Education Vol. 36 (3-4)
72
Acevedo and Herrera-Posada
powder with specific gravity of 1.3. PVA is a
flexible polymer with a vinyl alcohol repeating
unit and with tensile elongation of up to 400%
when wet.13 The packets contain approximately
17 cm3 of polymer each. To prepare the balls
the polymer is placed into the mold and shaken
carefully to compact the polymer. The mold is
then immersed in water to allow the PVA to
swell for at least a minute. Afterwards, it is left
standing for at least three minutes over a dry
surface to remove excess water. The mold is
then carefully removed and the ball left to dry
for at least ten minutes.
To modify the viscoelastic properties of the
bouncing balls a portion of the polymer is
substituted with solid filler. In this work,
construction-grade sand from a local hardware
store was used. For simplicity, the substitution
was done volumetrically using a graded test
tube. The appropriate amounts of polymer and
filler were mixed in a beaker or plastic cup. The
balls were then prepared as described
previously. For concentrations above 50% (by
volume) of sand in solids the balls break after
being released from the mold. The weight of
filler was determined by using an analytical
balance. The molds produce a ball that
measures approximately 16.2 cm3. Figure 2
shows the mold and sample composite polymer
balls.
Methods
Place a gridded background against a flat
vertical surface and over a flat non deformable
horizontal surface. Drop each ball from a fixed
height. Make sure to use the same starting
height for all experiments. Use a video
recording device (i.e. smartphone, tablet, or
laptop with camera) to record the bouncing of
the ball until it stops. Using the playback
capabilities of the recording device scroll
through the video to determine the trajectory of
the ball or the maximum height reached after
each bounce. Repeat experiments accordingly.
At this point the student should be able to plot
the trajectory of the balls and extract the values
needed to calculate the energy loss and storage
using Eq. 1 and 2. In addition, recovery
coefficient, Eq. 3, and density can be plotted as
a function of filler concentration. Students can
also evaluate the effect of filler concentration
on density and appearance.
In a previous offering at a local science
teachers’ workshop, the analysis of the data was
done on a class-wide basis where pairs prepared
and did experiments with one or two balls each.
This way the full experience, including
discussion of results, was done in approximately one hour.
RESULTS AND DISCUSSION
Figure 3 shows the vertical displacement over
time of composite balls with sand loadings from
0 to 50%. The experiment showed good
reproducibility between balls of the same filler
loading. Nevertheless, as time progressed the
traveled distances decreased and deviated from
a completely vertical bounce making
measurements difficult causing more error in
the calculations. Experiments where the ball
deviated from a vertical bounce were not
considered.
Figure 2. Sample mold, and polymer and
composite bouncing balls
The upper plot in Figure 3 corresponds to the
polymer ball without filler which shows a
predominantly elastic character and dissipates
all its energy in 7 bouncing cycles. The visco-
Journal of Materials Education Vol. 36 (3-4)
Introducing Viscoelasticity. . . . .through a Composite Bouncing Balls Hands-On Experiment
73
and 2 in Fig. 1) and Eq. 3. For example, the
recovery coefficient of the third cycle is 0.712,
which corresponds to the energy decrease
associated with the drop from 55.6 to 39.6 cm.
As the concentration of sand is increased from
0 to 50% (from top to bottom plots in Fig. 3),
the number of cycles decreases from 7 to 2 and
the time required for the ball to lose all its
energy goes from 8 to 2.5 seconds. Figure 4
summarizes the recovery coefficient as a
function of filler concentration. Values
represent the average recovery for all bounce
cycles in the trajectory for at least two full
experiments. Error bars represent the standard
deviation from all these calculated values. The
coefficient was found to be independent of the
bounce cycle for all the studied compositions.
The latter indicates that there is no plastic or
irreversible
deformation.
The
recovery
coefficient quantifies the elastic contribution, as
depicted in Figure 4, while one minus the
coefficient (or distance from the data point to
one) indicates the viscous contribution. These
contributions would correspond to a spring and
a dashpot element in a Maxwell model, which
as mentioned previously are related to
molecular events.
Figure 3. Vertical displacement over time of
composite polymer balls as a function of sand
loadings.
elastic character can be quantified from the
trajectory as described previously using the
values of the maxima (corresponding to Point 1
Figure 4.
Recovery coefficient of composite
polymer balls as a function of sand loading
Journal of Materials Education Vol. 36 (3-4)
74
Acevedo and Herrera-Posada
A complete understanding of the molecular
origin of the viscoelastic response of PVA is
still the focus of many researchers. However,
key features have been identified. The hydroxyl
groups of the polymer allow for intermolecular
hydrogen bonding, which contribute to the
formation of a physical gel network. The
elasticity of the PVA is associated to the
reversible conformational transition from a
relaxed network to an overstretched state upon
stretching,14 or compacted state upon
compression. On the other hand, the viscous
dissipation in PVA can be attributed to
irreversible and cooperative conformational
changes. Molecular modeling has demonstrated
that conformational changes of the hydroxyl
side groups that may lead to relaxation
processes are limited, independent of tacticity.15
Meanwhile, main-chain rotation is restricted to
the three staggered conformational states with
the lowest energy. Changes between these
states are irreversible and require the
cooperative motion of neighboring molecules.
energy between polymer rich regions, a
common effect in polymer composites. Yet,
sand grains can slip around the polymer or
around each other. The second effect is
analogous to that observed in footbags or bean
bags, crocheted round bags filled with plastic
beads or seeds, which do not bounce. As energy
is transferred into the bag the beads slip around
each other dissipating the energy. Yet, little or
no deformation from its overall roundness is
observed since the surrounding bag cannot be
easily deformed. At a molecular level, the sand
grains can also disrupt the hydrogen bonding
between PVA chains, while promoting the
formation of new hydrogen bonds between the
hydroxyls of the PVA and the silanol groups on
its surface, similar to observations in
PVA/silica composites16. Thus, the PVA
network elasticity may be weakened due to the
effective reduction of crosslinks in the network.
All these effects are enhanced as the
concentration of sand increases.
In the context of the experiment, as depicted by
Figure 1, initially at point 1 the polymer
molecules are in a low energy state or
equilibrium. However, as it hits the surface,
point 2, energy is absorbed by the ball.
Internally, the energy is absorbed by the PVA
network and by the individual polymer
molecules. The network is compressed, which
is not favorable since internal stresses are
generated. Thus, the system energy that is
stored by the network is released in order to
return to a more relaxed lower energy state. On
the other hand, individual molecules can use the
energy to overcome the energetic barrier
required to change its structure and reach an
alternate propitious arrangement. The released
energy, which is lower than the absorbed,
allows the ball to bounce back until it reaches
point 3. The ball at point 1 and 3 are
macroscopically similar, although, the internal
structure has changed.
The elasticity of the ball is reduced with the
addition of sand as seen by the decrease of the
recovery coefficient. Various effects that may
reduce the elasticity of the polymer when sand
is present are plausible. First, the sand grains
cannot be deformed preventing the transfer of
Figure 5. Middle and high school teachers preparing
composite balls during the 3rd Summer Academy
organized by the UPRM Science on Wheels
program
Journal of Materials Education Vol. 36 (3-4)
Introducing Viscoelasticity. . . . .through a Composite Bouncing Balls Hands-On Experiment
This experience was presented in a workshop
for 23 science teachers from local public and
private middle and high schools. Figure 5
shows some photograph of the teachers
preparing the composite balls. This presentation originated a discussion on where to
incorporate this experience in a chemistry or
physics course using Puerto Rico Department
of Education’s Science Content Standards and
Expectations17 as a guide. There was agreement
that this experience can complement teaching
and promote the achievement of the following
expectations (translated from the original
Spanish document):
•
•
•
•
To establish the difference between elastic
and inelastic collisions, and explosions.
(Physics C.F.4.3)
To explain energy transformations based in
the law of energy conservation. (Physics
C.F.5.1)
To identify common situations where
energy is transformed, for example, from
chemical to thermal energy and from
luminous to electric energy. (Chemistry
E.Q.2.1)
To explain how intermolecular interactions
determine physical and chemical properties
of matter, like for example chemical state
and polarity. (Chemistry I.Q.2.4)
Moreover, this experiment can help to introduce
engineering principles and material design into
the curriculum. All of the above expectations
have their counterparts in the United States New
Generation Science Standards (NGSS)18 for
Physical Science, for example:
•
•
Communicate scientific and technical
information about why the molecular-level
structure is important in the functioning of
designed materials. (HS-PS2-6)
Develop and use models to illustrate that
energy at the macroscopic scales can be
accounted for as a combination of energy
associated with the motions of particles
(objects) and energy associated with the
relative position of particles. (HS-PS3-2)
75
In addition, during the discussion we were also
able to identify a general misconception that we
want to address: the more elastic a material, the
better. This is based on everyday interactions
with materials, for example, a more elastic ball
would be easier to dribble or a more elastic
bungee cord would allow us to hold more stuff.
Workshop participants expressed their concern
that making a composite ball with a more
viscous character seem counterintuitive and it
was difficult to identify applications for similar
materials. Thus, we discussed two cases, (1)
protective shields of police officers to stop
shrapnel, and (2) guides and bumpers around
conveyors in production lines to prevent glass
bottles from breaking. In both cases, dissipation
of energy is desired to prevent or minimize
motion after a collision. After discussion of
these applications the audience felt comfortable
that they could transfer the experiment to their
classrooms and engage students through the
experience.
We proposed and validated a simple hands-on
experiment to introduce the concept of
viscoelasticity using a composite bouncing ball.
Simple molecular arguments based on the
structure and morphology of the system can be
used to explain macroscopically observed
physical properties. The experiment is also
flexible allowing for modifications. Alternate
versions can evaluate composites with fillers of
different compositions, sizes, or shapes, or to
use fillers, such as conductive or magnetic
particles, that impart an additional property.
ACKNOWLEDGEMENTS
SHP was supported by the National Science
Foundation under Grant No. DMR-0934115.
We also thank the Science on Wheels Program
at the University of Puerto Rico-Mayagüez for
allowing us to present this work at their 3rd
Summer Academy, Ms. Lizzette Gómez for
help with the experiment validation, and Dr.
Barbara Calcagno for helpful discussions.
Journal of Materials Education Vol. 36 (3-4)
76
Acevedo and Herrera-Posada
REFERENCES
1. Science education in schools: Issues,
evidence and proposals; Teaching and
Learning Research Programme: London,
UK, 2006.
2. R.W. Clark, J. Chem. Ed. 80, (1), 14-15
(2003).
3. S.P. Parker, Encyclopedia of Physics. 2nd
ed.; McGraw-Hill, New York, 1993.
4. F.A. Morrison, Understanding Rheology,
Oxford University Press, New York, 2001.
5. J.H. Wiegand, J. Chem. Ed. 40, (9), 475
(1963).
6. P.M. Vilela and D. Thompson, Eur. Phys.
J., 20, 15-20 (1999).
7. V. de Zea Bermudez, P. Passos de Almeida,
and J. Feria Seita, J. Chem. Ed., 75, (11),
1410-1418 (1998).
8. J.D. Ferry, Viscoelastic Properties of
Polymers. 3rd ed., Wiley, New York, 1980.
9. R.G. Larson, The Structure and Rheology
of Complex Fluids, Oxford University
Press, New York, 1999.
11. I.M. Ward and J. Sweeney, An Introduction
to the Mechanical Properties of Solid
Polymers, 2nd ed., Wiley, West Sussex,
2004.
12. K.P. Menard, Dynamic Mechanical
Analysis: A Practical Introduction, 2nd ed.,
CRC Press, Boca Raton, FL, 2008.
13. H.P. Mark, Encyclopedia of Polymer
Science and Technology, 3rd ed., Wiley,
New Jersey, 2007.
14. H. Li, W. Zhang, W. Xu and X. Zhang,
Macromolecules 33, 465-469 (2000).
15. A. De la Rosa, L. Heux, J.Y. Cavaille, and
K. Mazeau, Polymer 43, 5665-5677
(2002).
16. Y. Zhang, and L.Ye, Composites: Part B ,
56, 749-755 (2014).
17. Estandares de Contenido y Expectativas de
Grado: Programa de Ciencias. in
Departamento de Educacion, Estado Libre
Asociado de Puerto Rico, 2007.
18. New Generation Science Standards
published by the National Science Teachers
Association - www.ngss.nsta.org.
(06/06/14) .
10. R.S. Lakes, Viscoelastic Solids, CRC
Press, Boca Raton, 1999.
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