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Modeling of precipitation polymerization II: calculation of macroradicals concentrations in the continuous and dispersed phases

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Abstract

According to Hunkeler model, precipitation polymerization of acrylic acid in organic media takes place simultaneously in the both dispersed and continuous phases. In this research, a model is presented based on mass balances of individual species. Hence, concentrations of macroradicals and polymer chains, in different chain lengths, were calculated in the both phases. Number- and weight-average degrees of polymerization and their distributions were concluded in the both dispersed and continuous phases. Calculation of macroradicals concentration was conducted with quasi-steady state approximation (QSSA) as well as without QSSA (based on the governing differential equations). Macroradical precipitate as soon as reaching to critical chain length. Moreover, precipitation is the main termination reaction in the continuous phase. Polymer with critical chain length is the most populated species in the dispersed phase. Comparison of theoretical and experimental results is in good agreement. QSSA theory gives better results than without QSSA theory because occlusion of macroradicals in the dispersed phase does not occur in the precipitation polymerization of water-soluble monomers in the organic media. This article has proved that the polydispersity index (PDI) of polymer product in the precipitation polymerization of acrylic acid in toluene that follows simultaneous polymerization model is less than that of PDI in the other free radical polymerization methods. Centrifugation method was used to sediment fine polymer particles. The yield of reaction was increased by sedimentation process.

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Abbreviations

c:

Continuous phase

d:

Dispersed phase

I :

Initiator

\( [I] \) :

Initiator concentration (mol/L)

k cr :

Critical chain length for solubility of macroradicals in the continuous phase

k d :

Rate constant for the thermal decomposition of initiator (min−1)

\( k_{\rm{d}}^{\prime } \) :

Rate constant for the monomer-enhanced decomposition of initiator (L/mol min)

k p :

Rate constant for the chain propagation (L/mol min)

k tc :

Rate constant for the chain termination by combination (L/mol min)

k td :

Rate constant for the chain termination by disproportionation (L/mol min)

\( k_{{\rm{tr,M}}} \) :

Rate constant for the chain transfer to the monomer (L/mol min)

\( k_{{\rm{tr,S}}} \) :

Rate constant for the chain transfer to the solvent (L/mol min)

k v :

Rate constant for the change of particle kind (min−1)

M :

Monomer

\( [M] \) :

Monomer concentration (mol/L)

\( \overline{M}_{n} \) :

Number-average molecular weight (g/mol)

\( \overline{M}_{w} \) :

Weight-average molecular weight (g/mol)

\( \rm{PDI} \) :

Polydispersity index

\( P_{i} \) :

Dead polymer containing i monomer unit

\( R_{0}^{ * } \) :

Primary radical

\( R_{i}^{ * } \) :

Macroradical containing i monomer unit

\( \Re_{i} \) :

Rate of initiation (mol/L min)

S :

Solvent

\( V_{\rm{P}}^{\prime } \) :

Molar volume of polymer (L/mol)

\( \overline{X}_{n} \) :

Number-average degree of polymerization

\( \overline{X}_{w} \) :

Weight-average degree of polymerization

\( \phi_{1} \) :

Volume fraction of primary particles

\( \phi_{2} \) :

Volume fraction of secondary particles

\( \phi_{\rm{c}} \) :

Volume fraction of continuous phase

\( \phi_{\rm{d}} \) :

Volume fraction of dispersed phase

\( \varphi \) :

Partition coefficient between continuous and dispersed phase

\( [\eta ] \) :

Intrinsic viscosity (L/g)

\( \lambda \) :

Conventional moment for macroradicals

\( \lambda^{*} \) :

Finite moment for macroradicals

\( \mu \) :

Conventional moment for dead polymers

\( \mu^{*} \) :

Finite moment for dead polymers

\( \varsigma \) :

Probability of propagation reaction

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Authors and Affiliations

  1. Iran Polymer and Petrochemical Institute, P.O. Box 14965/115, Tehran, Iran

    H. Bouhendi

  2. Polymer Engineering Department, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iran

    V. Haddadi-Asl & M. Rafizadeh

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  1. H. Bouhendi
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  2. V. Haddadi-Asl
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  3. M. Rafizadeh
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Correspondence to H. Bouhendi.

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Bouhendi, H., Haddadi-Asl, V. & Rafizadeh, M. Modeling of precipitation polymerization II: calculation of macroradicals concentrations in the continuous and dispersed phases. Polym. Bull. 68, 1603–1621 (2012). https://doi.org/10.1007/s00289-011-0640-7

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  • DOI: https://doi.org/10.1007/s00289-011-0640-7

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