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Effect of surfactant on the swelling of polymeric nanoparticles: toward a generalized approach

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Abstract

Tauer et al. (Colloid Polym Sci 278:814–820, 2000) claim that the well-known Morton-Kaizerman-Altier (MKA) equation fails to describe experimental swelling data of polystyrene particles with toluene in the absence of free or adsorbed surfactant. They made modifications to the MKA equation to fit their own data; however, they were not able to fit the MKA data obtained in the presence of surfactant. In this work, based on the modified MKA equation, we propose a new approach to take into account the effect of surfactant on the swelling behavior of polymer latex particles such that with only one set of parameters, it is possible to fit the Tauer et al. data and to predict the MKA data. Comparisons of model against experimental data in presence and absence of surfactant are showed and discussed.

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Acknowledgments

The authors would like to thank the National Council of Science and Technology (CONACyT-Mexico) for supporting this project (grant 62041) as well as a predoctoral scholarship for L. Farias-Cepeda. The authors gratefully acknowledge Mrs. Patricia Siller and Mr. Sion NG for their assistance in searching and securing pertinent literature and English checking, respectively.

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Authors and Affiliations

  1. Departamento de Procesos de Polimerización, Centro de Investigación en Química Aplicada (CIQA), Blvd. Enrique Reyna 140, Saltillo, Coahuila, 25253, Mexico

    L. Farias-Cepeda, J. Herrera-Ordonez & E. Saldívar-Guerra

Authors
  1. L. Farias-Cepeda
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  2. J. Herrera-Ordonez
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  3. E. Saldívar-Guerra
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Corresponding author

Correspondence to J. Herrera-Ordonez.

Appendices

Appendix 1

The value of ϕ S can be estimated as follows:

$$ {\phi_{\text{S}}} = \frac{\text{volume of surfactantvolume of particle}} = \frac{{{v_{\text{s}}}}}{v} = \frac{{a\theta {M_{\text{H}}}{Y_{\text{t}}}}}{{{a_{\text{s}}}{N_{\text{A}}}{d_{\text{H}}}v}}, $$
(17)

where v s is the volume contribution of the hydrophobic parts of the adsorbed surfactant molecules to the total volume (v) of the particles. Y t is the number of hydrophobic tails per surfactant molecule (for SDS, Y t = 1), M H is the molecular weight of a tail, N A is the Avogadro’s number, and a is the surface area of a particle. Simplifying Eq. 17 is obtained that

$$ {\phi_{\text{S}}} = \left( {\frac{{3\theta {M_{\text{H}}}{Y_{\text{t}}}}}{{{a_{\text{S}}}{N_{\text{A}}}r{d_{\text{H}}}}}} \right). $$
(18)

Appendix 2

Surfactant coverage is given by

$$ \theta = \frac{{{S_{\text{ads}}}}}{{{{\left( {{S_{^{\text{ads}}}}} \right)}^{\text{sat}}}}}, $$
(19)

where S ads and (S ads)sat are the amount of surfactant adsorbed onto the surface of the particles at non-saturation and saturation conditions, respectively.

Sads is calculated by means of a modified Langmuir adsorption isotherm [11].

$$ {S_{\text{ads}}} = \frac{{{A_{\text{p}}}}}{{{a_{\text{s}}}}}\left( {\frac{{\alpha + {\text{CMC}}}}{\text{CMC}}} \right)\left( {\frac{{{S_{\text{free}}}}}{{\alpha + {S_{\text{free}}}}}} \right). $$
(20)

Ap is the total area of particles, and CMC is the critical micelle concentration of surfactant. α is the Langmuir adsorption constant. (Sads)sat is given by

$$ {\left( {{S_{^{\text{ads}}}}} \right)^{\text{sat}}} = \frac{{{A_{\text{p}}}}}{{{a_{\text{s}}}}}. $$
(21)

Substitution of Eqs. 20 and 21 in 19 gives

$$ \theta = \left( {\frac{{\alpha + {\text{CMC}}}}{\text{CMC}}} \right)\left( {\frac{{{S_{\text{free}}}}}{{\alpha + {S_{\text{free}}}}}} \right). $$
(22)

Solving Eq. 22 for S free is obtained that

$$ {S_{\text{free}}} = \frac{{\theta \alpha }}{{\left( {\frac{{\alpha + {\text{CMC}}}}{\text{CMC}} - \theta } \right)}}. $$
(23)

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Farias-Cepeda, L., Herrera-Ordonez, J. & Saldívar-Guerra, E. Effect of surfactant on the swelling of polymeric nanoparticles: toward a generalized approach. Colloid Polym Sci 287, 1215–1220 (2009). https://doi.org/10.1007/s00396-009-2073-5

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