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Modeling of polymerization rate and microstructure in the anionic polymerization of isoprene using n-butyl lithium and N,N,N′,N′-tetramethylethylenediamine considering different reactivities of the structural units

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Abstract

A mathematical model for the anionic polymerization of isoprene using n-butyl lithium (n-BuLi) as initiator and N,N,N′,N′-tetramethylethylenediamine (TMEDA) as microstructure modifier, considering a system similar to a tetrapolymerization and a scheme of reaction that considers that the active sites are different in configuration, has been developed. Experimental data of conversion versus time and structure development (1,4-cis, 1,4-trans, vinyl or isopropenyl units) were taken from the literature. Since 1,4-cis structural units are difficult to measure, directly, we used reports based on indirect measurements for natural polyisoprene. The cis structural unit fraction was varied from 0.1 to 0.9 (referred to cis+trans content) in order to provide enough data for parameter estimation purposes. Rate expressions for monomer consumption as well as microstructure and dyad development were obtained from the proposed scheme of reaction. The fraction of active sites and dyad distribution were calculated using Markov chains theory, based on conditional probabilities. The kinetic model correctly describes the performance anionic polymerizations with and without TMEDA.

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Abbreviations

(C):

Cis active sites

(T):

Trans active sites

(D):

Isopropenyl active sites

(V):

Vinyl active sites

FC :

Cis isomer formation

FT :

Trans isomer formation

FD :

Isopropenyl isomer formation

FV :

Vinyl isomer formation

FCC :

Cis-cis dyad formation

FCT :

Cis-trans dyad formation

FCD :

Cis-isopropenyl dyad formation

FCV :

Cis-vinyl dyad formation

FTC :

Trans-cis dyad formation

FTT :

Trans-trans dyad formation

FTD :

Trans-isopropenyl dyad formation

FTV :

Trans-vinyl dyad formation

FDC :

Isopropenyl-cis dyad formation

FDT :

Isopropenyl-trans dyad formation

FDD :

Isopropenyl-isopropenyl dyad formation

FDV :

Isopropenyl-vinyl dyad formation

FVC :

Vinyl-cis dyad formation

FVT :

Vinyl-trans dyad formation

FVD :

Vinyl-isopropenyl dyad formation

FVV :

Vinyl-vinyl dyad formation

Fij:

Total quantity of the ij dyad

i:

Active site that reacts with a isoprene molecule

[I]:

Initiator concentration

j:

Terminal living isomer resulting from the propagation reaction

kij :

Propagation rate constant

kC, kT, kD, kV :

Initiation rate constants

[M]:

Isoprene concentration

MR:

[TMEDA]/[I]o ratio

Р:

\( {\text{matrix = }}\left[ {\matrix{ {{{\text{P}}_{\text{CC}}}} \hfill &{{{\text{P}}_{\text{CT}}}} \hfill &{{{\text{P}}_{\text{CD}}}} \hfill &{{{\text{P}}_{\text{CV}}}} \hfill \\ {{{\text{P}}_{\text{TC}}}} \hfill &{{{\text{P}}_{\text{TT}}}} \hfill &{{{\text{P}}_{\text{TD}}}} \hfill &{{{\text{P}}_{\text{TV}}}} \hfill \\ {{{\text{P}}_{\text{DC}}}} \hfill &{{{\text{P}}_{\text{DT}}}} \hfill &{{{\text{P}}_{\text{DD}}}} \hfill &{{{\text{P}}_{\text{DV}}}} \hfill \\ {{{\text{P}}_{\text{VC}}}} \hfill &{{{\text{P}}_{\text{VT}}}} \hfill &{{{\text{P}}_{\text{VD}}}} \hfill &{{{\text{P}}_{\text{VV}}}} \hfill \\ }<!end array> } \right] \)

Pij :

Conditional probability

[Pc], [PT] [PD], [PV]:

Concentration of active sites

Pc 1,0,0,0, PT 0,1,0,0, PD 0,0,1,0 :

Active sites with one monomeric unit with the negative

PV 0,0,0,1 :

Charge located on the cis, trans, isopropenyl and vinyl isomer units, respectively

PX a,b,f,m :

Living polymer with the negative charge located on the isomer X, (X = C, T, D or V) with a, b, f and m units of cis, trans, isopropenyl and vinyl, respectively

val:

Valvassori equality: (rCT)(rTD)(rDC) = (rCD)(rDT)(rTC)

R:

Cis/(cis+trans) ratio

rij :

Reactivity ratio

Wi :

Fraction of active sites

W :

Vector (Wc, WT, WD, WV)

XCj, XTj, XDj, XVj :

Isoprene conversion converted to the dyad Cj, Tj, Dj, Vj

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Authors and Affiliations

  1. Facultad de Ciencias Químicas, Universidad Veracruzana, Coatzacoalcos, Veracruz, Mexico

    José Alfredo Tenorio-López, Miguel Ángel Ríos-Enriquez & María Lourdes de Nieto-Peña

  2. Unidad de Desarrollo de Productos y Procesos, Resirene, S.A de C.V, Grupo Kuo. Carr. Federal Puebla-Tlaxcala Km. 15.5, Tlaxcala, Mexico

    Juan José Benvenuta-Tapia

  3. Facultad de Química, Departamento de Ingeniería Química, Universidad Nacional Autónoma de México, México D.F., Mexico

    Eduardo Vivaldo-Lima

Authors
  1. José Alfredo Tenorio-López
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  2. Juan José Benvenuta-Tapia
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  3. Eduardo Vivaldo-Lima
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  4. Miguel Ángel Ríos-Enriquez
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  5. María Lourdes de Nieto-Peña
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Correspondence to Juan José Benvenuta-Tapia.

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Tenorio-López, J.A., Benvenuta-Tapia, J.J., Vivaldo-Lima, E. et al. Modeling of polymerization rate and microstructure in the anionic polymerization of isoprene using n-butyl lithium and N,N,N′,N′-tetramethylethylenediamine considering different reactivities of the structural units. J Polym Res 19, 9909 (2012). https://doi.org/10.1007/s10965-012-9909-2

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