(217eo) Kinetics of Step-Growth Polymerization of Glycerol Into Polyglycerol Using H2SO4 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.