(289g) Gel Time Prediction in Multifunctional Acrylates

Gel time prediction in
multifunctional acrylates

The photopolymerization kinetics of multifunctional acrylates
have been studied extensively since these polymers are used in a wide range of
applications from lithography and coatings, to biologically related uses such
as dental composites and contact lenses¹. The vinyl bonds on acrylates react
readily in the presence of radicals, and in the case of multifunctional
acrylates, which have multiple vinyl groups per monomer, reactions between
distinct chains are also possible. These types of reactions, known as
cross-linking, bind different polymer chains in the reaction volume into an
insoluble network. Cross-linking does not occur during photopolymerization of monofunctional
monomers, thus resulting in a soluble network of linear chains. In contrast,
the cross-linked networks formed by multifunctional monomers are insoluble and
this is known as the gel state. It is important to correctly identify the point
at which gel occurs because it is an important parameter which will determine
the durability of the resulting polymer^2-4.

The time at which the liquid resin transitions to a crosslinked
gel is called the gel time, and it can be quantified experimentally using
microrheology⁵.  In this work we study gelation
behavior of the trifunctional monomer trimethylolpropane triacrylate with the photoinitiator
DMPA.  To predict the gel time and thus the part height, we construct a reaction-diffusion
model to predict gel time based on resin composition, exposure intensity, and
exposure time.  Unknown coefficients in the model are estimated using
experimental data from microrheology^{6, 7} and Fourier transform infrared spectroscopy
(FTIR).  Specifically, the FTIR data is used to build the reaction-diffusion
model for the polymerization kinetics, and the microrheology data is used to
estimate a single critical value of double bond conversion that indicates the
onset of gelation. 

Across the entire broad range of polymerization conditions
considered, the experimentally measured gel time occurs at a double bond
conversion of 12%.  Moreover, we find that the local rate of radical generation
is the single model variable needed to predict the gel time.  Because our model
is based on polymerization kinetics, rather than empirical fits that are
typically used in stereolithography, it also can be modified for gel time
predictions with different resin formulations or different exposure
intensities. 

1.         Bowman, C. N.; Peppas, N. A., A kinetic gelation
method for the simulation of free-radical polymerizations. Chemical
Engineering Science 1992, 47, (6), 1411-1419.

2.         Lee, J. H.; Prud'homme, R. K.; Aksay, I. A., Cure
depth in photopolymerization: Experiments and theory. Journal of Materials
Research 2001, 16, (12), 3536-3544.

3.         Tang, Y. Y.; Henderson, C.; Muzzy, J.; Rosen, D.
W., Stereolithography cure modelling and simulation. International Journal
of Materials & Product Technology 2004, 21, (4), 255-272.

4.         Zhang, X.; Jiang, X. N.; Sun, C., Micro-stereolithography
of polymeric and ceramic microstructures. Sensors and Actuators a-Physical 1999,
77, (2), 149-156.

5.         Winter, H. H.; Chambon, F., Analysis of linear viscoelasticity
of a cross-linking polymer at the gel point. Journal of Rheology 1986,
30, (2), 367-382.

6.         Slopek, R. P.; McKinley, H. K.; Henderson, C. L.; Breedveld,
V., In situ monitoring of mechanical properties during photopolymerization with
particle tracking microrheology. Polymer 2006, 47, (7),
2263-2268.

7.         Slopek, R. In-Situ  Monitoring of the Mechanical
Properties During the Photopolymerization of Acrylate Resins Using Particle
Tracking Microrheology. Georgia Institute of Technology, Atlanta, 2008.