Effects of supported metallocene catalyst active center multiplicity on antioxidant-stabilized ethylene homo- and copolymers

Abstract

A silica-supported bis(n-butylcyclopentadienyl) zirconium dichloride [(ⁿBuCp)₂ZrCl₂] catalyst was synthesized. This was used to prepare an ethylene homopolymer and an ethylene–1-hexene copolymer. The active center multiplicity of this catalyst was modeled by deconvoluting the copolymer molecular mass distribution and chemical composition distribution. Five different active site types were predicted, which matched the successive self-nucleation and annealing temperature peaks. The thermo-oxidative melt stability, with and without Irganox 1010 and Irgafos 168, of the above polyethylenes was investigated using nonisothermal differential scanning calorimetric (DSC) experiments at 150 °C. This is a temperature that ensures complete melting of the samples and avoids the diffusivity of oxygen to interfere into polyethylene crystallinity and its thermo-oxidative melt degradation. The oxidation parameters such as onset oxidation temperature, induction period, protection factor, and S-factor were determined by combining theoretical modeling with the DSC experiments. Subsequently, these findings were discussed considering catalyst active center multiplicity and polymer microstructure, particularly average ethylene sequence length. Several insightful results, which have not been reported earlier in the literature, were obtained. The antioxidant effect, for each polymer, varied as (Irganox + Irgafos) ≈ Irganox > Irgafos > Neat polymer. The as-synthesized homopolymer turned out to be almost twice as stable as the corresponding copolymer. The antioxidant(s) in the copolymer showed higher antioxidant effectiveness (AEX) than those in the homopolymer. Irganox exhibited more AEX than Irgafos. To the best of our knowledge, such findings have not been reported earlier in the literature. However, mixed with Irganox or Irgafos, their melt oxidation stability was comparable. The homopolymer, as per the calculated S-factor, showed Irganox–Irgafos synergistic effect five times that of the copolymer. This illustrates how the transition in backbone structure, from exceedingly high to low ethylene sequence length, influences antioxidant synergistic performance. Finally, this study shows a DSC-aided approach that can elucidate the effect of polyethylene structural backbone on its thermo-oxidative melt degradation as well as antioxidant synergism in a facile fashion.

Appendix: simultaneous MWD and CCD deconvolution model and computational algorithm

Single-site binary copolymer MWD and CCD

Stockmayer bivariate distributions of chain length CL and composition are assumed to apply to represent, respectively, the mass distributions of kinetic CL l _kc and chemical composition F ₁ of copolymer backbones synthesized by a given active catalyst site type. F ₁ stands for mole fraction of ethylene in the copolymer backbone. Accordingly, the Stockmayer distribution for linear binary copolymer backbones w(l _kc, F ₁) can be written as follows [46–49]:

$$ w\left( {l_{\text{kc}} ,\;F_{1} } \right) = r \times \tau^{2} \times \exp \left( { - l_{\text{kc}} \times \tau } \right) \times \frac{1}{{\sqrt {2\pi \beta /l_{\text{kc}} } }} \times \exp \left[ { - \frac{{(F_{1} - \bar{F}_{1} )^{2} }}{{2\beta /l_{\text{kc}} }}} \right], $$

(10)

where τ is the ratio of the sum of all chain transfer rates to the copolymerization propagation rate. $\bar{F}_{1}$ is the average mole fraction of monomer 1 in the copolymer. β is given by [48, 49]:

$$ \beta = \bar{F}_{1} \left( {1 - \bar{F}_{1} } \right) \times \sqrt {1 + 4\bar{F}_{1} \left( {1 - \bar{F}_{1} } \right)\;\left( {r_{1} r_{2} - 1} \right)} , $$

(11)

where r ₁ and r ₂ are the copolymerization reactivity ratios of monomers 1 and 2 (corresponding to the above catalyst active site type), respectively. r ₁ r ₂ = 1 for random copolymers produced with a typical single-site catalyst. Generally speaking, r ₁ r ₂ is a kinetic parameter of the Mayo–Lewis copolymerization equation that is used to calculate instantaneous copolymer composition (due to drift in monomer concentration with conversion) and classify copolymerization type.

Equation 10 comprises the CL distribution CLD and CCD components of Stockmayer distribution. The CLD component can be obtained by integrating Eq. 10, that is, w(l _kc, F ₁) over all chemical compositions, and this is given by Eq. 12 [48, 49]:

$$ w\left( {l_{\text{kc}} } \right) = \int\limits_{ - \infty }^{\infty } {w\left( {l,\;F_{1} } \right)} {\text{d}}\left( {F_{1} - \bar{F}_{1}} \right) = l_{\text{kc}} \times \tau^{2} \times \exp \left( { - l_{\text{kc}} \times \tau } \right). $$

(12)

Therefore, the Stockmayer binary copolymer CLD equals the most probable Flory–Schulz CLD with PDI M _w/M _n = 2 for a single active catalyst center type [48, 49].

For linear chains, the parameter τ is the reciprocal of the number average CL l _n, that is, $\tau = \frac{1}{{l_{\text{n}} }}.$ Now, we shall convert Eq. 12 into the MWD analog so that we may use the GPC-generated MWD to deconvolute it, and eventually determine the number of active catalyst site types. This is shown below.

The CLD w(l _kc) is related to the corresponding MWD w(MW) through the following expression [48]:

$$ w({\text{MW}}){\text{dMW}} = w\left( {l_{\text{kc}} } \right){\text{d}}r, $$

(13)

where MW is the instantaneous copolymer molecular mass. $\frac{\text{dMW}}{{{\text{d}}l_{\text{kc}} }}$ equals the molecular mass mw_ru of the ru (ethylene) in the polymer. Therefore, Eq. 13 becomes

$$ w({\text{MW}}) = {\text{MW}}\left( {\frac{\tau }{{{\text{mw}}_{\text{ru}} }}} \right)^{2} \exp \left( { - {\text{MW}} \times \frac{\tau }{{{\text{mw}}_{\text{ru}} }}} \right), $$

(14)

where $\frac{\tau }{{{\text{mw}}_{\text{ru}} }} = \frac{1}{{l_{\text{n}} \times {\text{mw}}_{\text{ru}} }} = \frac{1}{{M_{\text{n}} }},$ and M _n is the number average molecular mass of the polymer. Now, we shall transform Eq. 14 into the corresponding logarithmic form using the following relation:

$$ w(\log {\text{MW}}){\text{d}}\log {\text{MW}} = w({\text{MW}}){\text{dMW}} . $$

(15)

Using Eqs. 14 and 15, we can finally write the following expression that directly relates to GPC MWD:

$$ w(\log {\text{MW)}} = 2.3026 \times {\text{MW}}^{2} \times \left( {\frac{\tau }{{{\text{mw}}_{\text{ru}} }}} \right)^{2} \exp \left( { - {\text{MW}} \times \frac{\tau }{{{\text{mw}}_{\text{ru}} }}} \right). $$

(16)

As reported above, the CCD component of Stockmayer distribution can be likewise calculated by integrating Eq. 10 over all CLs. For a given catalyst site type, this is given by [48, 49]

$$ w\left( {F_{1} } \right) = \frac{3}{{4\sqrt {2\beta \tau } }} \times \left[ {1 + \frac{{(F_{1} - \bar{F}_{1} )^{2} }}{2\beta \tau }} \right]^{ - 5/2} . $$

(17)

Equation 17 correlates the CCD to instantaneous copolymer composition F ₁. However, for copolymer chains made by a given active catalyst site type, the average mole fraction of monomer 1 does not statistically depend on the kinetic CL l _kc; long and short chains have the same average chemical composition.

Multi-site binary copolymer MWD and CCD

The copolymer MWD and CCD produced by a multi-site catalyst can be considered to consist of these backbone microstructural properties generated by each catalyst active site type. Therefore, under this situation, the bivariate MWD and CCD can be obtained by superposing the corresponding Stockmayer distributions represented by Eqs. 16 and 17, respectively. Accordingly, we can write the following [48, 49]:

$$ w(\log {\text{MW}}) = \sum\limits_{{\text{i}} = 1}^{n} {m_{{\text{i}}} w_{{\text{i}}} } (\log {\text{MW}}), $$

(18)

$$ w\left( {F_{1} } \right) = \sum\limits_{{\text{i}} = 1}^{n} {m_{{\text{i}}} w_{{\text{i}}} \left( {F_{1} } \right)} , $$

(19)

where w _i(logMW), w _i(F ₁), and m _i are the MWD, CCD, and mass fraction of copolymer chains produced by catalyst site type i, respectively. w(logMW) and w(F ₁) are the corresponding overall distributions.

Combining Eqs. 16 and 18, we can write the multi-site MWD as follows [48, 49]:

$$ w(\log {\text{MW}}) = \sum\limits_{{\text{i}} = 1}^{n} {m_{{\text{i}}} \times \left[ {2.3026 \times {\text{MW}}^{2} \times \left( {\frac{{\tau_{{\text{i}}} }}{{{\text{mw}}_{\text{ru}} }}} \right)^{2} \times \exp \left( { - {\text{MW}} \times \frac{{\tau_{{\text{i}}} }}{{{\text{mw}}_{\text{ru}} }}} \right)} \right]} . $$

(20)

Similarly, considering Eqs. 17 and 19, the multi-site CCD can be written as [48, 49]

$$ w\left( {F_{1} } \right) = \sum\limits_{{\text{i}} = 1}^{n} {m_{{\text{i}}} } \frac{3}{{4\sqrt {2\beta_{{\text{i}}} \tau_{{\text{i}}} } }} \times \left[ {1 + \frac{{(F_{1} - \bar{F}_{1{\text{i}}} )^{2} }}{{2\beta_{{\text{i}}} \tau_{{\text{i}}} }}} \right]^{ - 5/2} , $$

(21)

where $\beta_{\text{i}} = \bar{F}_{1{\text{i}}} (1 - \bar{F}_{1{\text{i}}} ) \times \sqrt {1 + 4\bar{F}_{1{\text{i}}} (1 - \bar{F}_{1{\text{i}}} )\;(r_{1{\text{i}}} r_{2{\text{i}}} - 1)} ,$ and w _i(F ₁) is the CCD of copolymer chains produced by catalyst site type i. F ₁ is the instantaneous mole fraction of monomer 1 in the overall copolymer. $\bar{F}_{1{\text{i}}}$ is the average mole fraction of monomer 1; r _1i and r _2i are the reactivity ratios of monomers 1 and 2, respectively, where subscript i represents the catalyst site type. Note that $\sum\nolimits_{i = 1}^{n} {m_{{\text{i}}} = 1} .$

Computational algorithm for the simultaneous deconvolution of copolymer MWD and CCD

We outline the MWD and CCD deconvolution procedures as follows:

• (i) Formulate, using Eqs. 20 and 21, the objective function to be minimized χ ² as follows [48, 49]:

  $$ \begin{aligned} \chi^{2} = \chi_{\text{MWD}}^{2} + \chi_{\text{CCD}}^{2} & = \frac{1}{{m_{\text{MWD}} }}\sum\limits_{j = 1}^{{m_{\text{MWD}} }} {\left[ {w_{\exp } (\log {\text{MW}}) - w_{\bmod } (\log {\text{MW}})} \right]^{2} } \\ & \quad + \frac{1}{{m_{\text{CCD}} }}\sum\limits_{k = 1}^{{m_{\text{CCD}} }} {\left[ {w_{\exp } \left( {F_{1} } \right) - w_{\bmod } \left( {F_{1} } \right)} \right]}^{2} , \\ \end{aligned} $$

  (22)

  where $\chi_{\text{MWD}}^{2}$and $\chi_{\text{CCD}}^{2}$ are objective function components for MWD and CCD, respectively. m _MWD and m _CCD are, respectively, the total MWD and CCD experimental data points considered to minimize Eq. 22. Subscripts exp and mod represent experimental and model-predicted values. Note that Eq. 22 considers the simultaneous deconvolution of MWD and CCD to achieve more consistent results.

• (ii) First assume two active site types, that is, n = 2 to deconvolute the GPC MWD and Crystaf CCD. Accordingly, estimate m ₁, τ ₁, τ ₂, β ₁, β ₂, and $\bar{F}_{1i} .$ m ₂ is excluded from estimation because $\sum\nolimits_{{\text{i}} = 1}^{n} {m_{{\text{i}}} = 1} .$ For n = 2, m ₁, m ₂, τ ₁, and τ ₂ can be initially estimated using the following GPC data—number-, mass-, and z-average molecular masses—and by solving the following equations [49]:

  $$ \frac{{M_{\text{n}} }}{{{\text{mw}}_{\text{ru}} }} = \frac{1}{{m_{1} \tau_{1} + m_{2} \tau_{2} }}, $$

  (23)
  $$ \frac{{M_{\text{w}} }}{{{\text{mw}}_{\text{ru}} }} = 2\left( {\frac{{m_{1} }}{{\tau_{1} }} + \frac{{m_{2} }}{{\tau_{2} }}} \right), $$

  (24)
  $$ \frac{{M_{\text{z}} }}{{{\text{mw}}_{\text{ru}} }} = 3\left( {\frac{{m_{1} }}{{\tau_{1}^{2} }} + \frac{{m_{2} }}{{\tau_{2}^{2} }}} \right)\,\left( {\frac{{m_{1} }}{{\tau_{1} }} + \frac{{m_{2} }}{{\tau_{2} }}} \right)^{ - 1} . $$

  (25)

• (iii) For n + 1 (n ≥ 2), site types make the initial guesses for m _i and τ _i using the corresponding previous iteration converged values. Estimate τ _n+1 as the mass average of parameter τ for n site types $\left( {\tau_{n + 1} = \sum\nolimits_{{\text{i}} = 1}^{n} {m_{{\text{i}}} \tau_{{\text{i}}} } } \right).$ Assume first the parameter m for site type n + 1, that is, m _n+1 to be the average of the m _i values for the adjacent sites to τ _n+1, and then normalize the new set of parameters m so that $\sum\nolimits_{{\text{i}} = 1}^{n + 1} {m_{{\text{i}}} = 1}$ [49].

• (iv) Consider that the initial guesses for parameter $\bar{F}_{1}$ of each site type is evenly distributed within the experimental range of $\bar{F}_{1} .$ Estimate $\bar{F}_{1{\text{i}}} ,$ the value of parameter $\bar{F}_{1}$ for site type i, using the following relation [49]:

  $$ \bar{F}_{1{\text{i}}} = \bar{F}_{1\hbox{min} } + i\frac{{(\bar{F}_{1\hbox{max} } - \bar{F}_{1\hbox{min} } )}}{(n + 1)}, $$

  (26)

  where $\bar{F}_{1\hbox{max} }$ and $\bar{F}_{1\hbox{min} }$ are the maximum and minimum values of the experimental range of $\bar{F}_{1} ,$ and n is the total number of site types.

• (v) Estimate β _i, the initial guess for parameter β for site type i, by assuming that the copolymer is a perfect random copolymer (r ₁ r ₂ = 1). Then, we can write [49]

  $$ \beta_{{\text{i}}} = \bar{F}_{1{\text{i}}} \left( {1 - \bar{F}_{1{\text{i}}} } \right). $$

  (27)

• (vi) Compare the experimental MWD and CCD with the corresponding superposed Stockmayer distributions (Eqs. 20, 21), considering all the active site types. Minimize χ ² using the generalized reduced gradient (GRG2) non-linear optimization algorithm [49]. Note that in general, for n active site types, 4n − 1 parameters are to be estimated. These include m _{1, 2,…,n−1}, τ _1, 2,…,n, β _1, 2,…,n, and $\bar{F}_{1(1,\,2, \ldots ,{\text {n}})}$ and one constraint $\left( {\sum\nolimits_{{\text{i}} = 1}^{n} {m_{{\text{i}}} = 1} } \right)$[49].

• (vii) Increase the number of active site types by 1 and repeat the above calculations until the value of χ ² does not further decrease significantly.