(217n) Kinetics of Step-Growth Polymerization of Glycerol Into Polyglycerol Using Sulfuric Acid As Catalyst

In recent years, there are
considerable governmental incentives for using biomass as a renewable
alternative for producing fuels. As a result, there is a large amount of bio-diesel
production also resulting in large amount of Glycerol production, a co-product
of the transesterification of vegetable oils to produce bio-diesel. The
overproduction of glycerol is threating biodiesel production as a cost
effective process since it has become a waste stream [1]; therefore, new
technologies are required for using glycerol as a building block for valuable
chemicals and contribute to transform the actual biodiesel industry into a bio-refinary [2].

An approach to convert glycerol into
valuable material is to polymerize glycerol to produce polyglycerol, a
biocompatible, biodegradable and hydrophilic polymer. It consists of an inert
chain of polyether with abundant pendant hydroxyl groups. These pendant
hydroxyl groups make polyglycerol a building block for diverse polymeric
complexes [3].

The knowledge of the polymerization
kinetics is a fundamental tool to design a process of polymer production and to
tune polymer morphology and final physical and chemical properties. It was
developed a kinetic model that describes de polymerization of glycerol to
polyglicerol by an
etherification reaction. The kinetic model is based on the mathematical
description of two phenomena that occur simultaneously during the
polymerization: a chemical reaction characterized by constant activation
energy, and a transport process that is the diffusion of reactants during the
reaction. Each phenomenon is represented as a resistance, since they occur simultaneously;
the total resistance, R_t , is represented as two resistances in parallel:

R_t^-1
= R_A^-1 + R_D^-1

 The chemical resistance, R_A,
corresponds to the inverse of the specific rate of reaction, and the physical
resistance, R_D, to the inverse of the specific diffusion rate:

R_A^-1
= k_A = A e^{-Ea/RT ,}   R_D^-1
= k_D = -D

Where A is the pre-exponential factor, Ea
is the activation energy, R is the universal gas constant, T is the temperature
and D is the effective diffusion coefficient.

Reactants and water, a byproduct of
the reaction, diffuse through the polymer solution.  Diffusion resistance becomes higher as the
polymer chain growths during the reaction. 
The effective diffusion coefficient is a function of temperature. An
empirical expression, similar to others empirical correlations used by Wilke and Dymond [4],  is proposed in this
work to fix the experimental data:

k_D = B (T - C)^s

Where T is the temperature and B, C and s are
parameters that depend on heating rate and the transport phenomenon of
reactants and byproducts of the reaction through the polymer solution as will
be shown in this work.

Finally, the proposed kinetic model
is equal to the total resistance of the reaction process times a function of
concentration, f(C_A); assuming f(C_A)
=C_Aⁿ:

r_p = ( A e^-Ea/RT + B (T - C)^s
) · C_A0ⁿ
( 1 - X_A )ⁿ

Where C_A0 is the initial concentration, X_A
is the fractional conversion and n the order of the
reaction.

The developed kinetic model was
fitted with experimental data obtained by thermogravimetric analysis
using four different heating rates: 2, 3, 5 and 9 K/min. The
experimental data and the proposed model had a correlation of 0.99.  Each parameter of the proposed model is
analyzed and justified in terms of heating rate, chemical reaction and
transport phenomenon.

1.            Leoneti,
A.B., V. Aragão-Leoneti, and S.V.W.B. de Oliveira, Glycerol as a by-product of biodiesel production in Brazil:
Alternatives for the use of unrefined glycerol. Renewable Energy, 2012. 45: p. 138-145.

2.            Yuguo
Zheng, X.C., and Yinchu Shen, Commodity
chemicals derived from glycerol, an important biorefinery feedstock.
Chemical  Reviews, 2010. 108: p. 5253?5277.

3.            Wilms
D., S.-E.S., Hyperbranched Polyglycerols:
From the Controlled Synthesis of Biocompatible Polyether Polyols to
Multipurpose Applications. Accounts of chemical research, 2010. 43(1): p. 129-141.

4.            Bueno
J.L., S.J.J., Experimental binary
diffusion coeffcients of benzene and derivatives in supercritical carbon
dioxide and their comparison with the values from the classic correlations Chemical
Engineering Science, 2001. 56: p.
4309-4319.