### Abstract

The aggregation and gelation kinetics in moderately concentrated (0.004 less than or equal to phi(0) less than or equal to 0.1) colloidal dispersions of fluorinated polymer particles has been studied. The aggregation was adjusted to proceed slowly enough to allow a convenient characterization of the kinetics through static and dynamic light scattering on quenched and diluted samples. A population balance model based on second-order aggregation rates is developed to compute the time evolution of the cluster mass distribution, from which we calculate the values of the average radii and structure factor measured by light scattering, so as to allow a direct comparison between measured and calculated quantities. The model suggests the introduction of a dimensionless time which allows the scaling of all the aggregation data on unique master curves defined by only two parameters: the exponent of the power-law aggregation kernel, lambda, and the aggregate fractal dimension, d(f). The predicted master curves were observed experimentally, which confirms the validity of the aggregation model and allows the unique determination of the kinetic and structural parameters of the aggregation process. The cluster growth behaviour, although significantly slower than DLCA, shows power-law kinetics rather than the exponential one typical of RLCA and the cluster structure is characterized by an unexpectedly small fractal dimension, d(f) = 1.7. The occurrence of gelation has been characterized using small amplitude oscillatory shearing to monitor the time evolution of the elastic modulus. It is found that also these curves, together with the gel time value, scale with the stability ratio of primary particles for a given solid volume fraction. We further use the model to calculate the cumulative occupied volume fraction of the growing aggregates and quantify in this way the increasing space filling, which is solid volume fraction dependent. The experimentally determined dimensionless gel times, which are also solid volume fraction dependent, scale then directly with the dimensionless time to reach a certain degree of the space filling in the model. This finding suggests that, like the aggregation kinetics, the gelation kinetics is governed by a second-order rate process.

Original language | English |
---|---|

Pages (from-to) | 2062-2077 |

Number of pages | 16 |

Journal | Langmuir |

Volume | 21 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Mar 2005 |

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### Keywords

- gelation kinetics
- aggregation
- gel formation

### Cite this

*Langmuir*,

*21*(5), 2062-2077. https://doi.org/10.1021/la048055s

}

*Langmuir*, vol. 21, no. 5, pp. 2062-2077. https://doi.org/10.1021/la048055s

**Scaling of the kinetics of slow aggregation and gel formation for a fluorinated polymer colloid.** / Sandkuhler, P ; Sefcik, J ; Morbidelli, M .

Research output: Contribution to journal › Article

TY - JOUR

T1 - Scaling of the kinetics of slow aggregation and gel formation for a fluorinated polymer colloid

AU - Sandkuhler, P

AU - Sefcik, J

AU - Morbidelli, M

PY - 2005/3/1

Y1 - 2005/3/1

N2 - The aggregation and gelation kinetics in moderately concentrated (0.004 less than or equal to phi(0) less than or equal to 0.1) colloidal dispersions of fluorinated polymer particles has been studied. The aggregation was adjusted to proceed slowly enough to allow a convenient characterization of the kinetics through static and dynamic light scattering on quenched and diluted samples. A population balance model based on second-order aggregation rates is developed to compute the time evolution of the cluster mass distribution, from which we calculate the values of the average radii and structure factor measured by light scattering, so as to allow a direct comparison between measured and calculated quantities. The model suggests the introduction of a dimensionless time which allows the scaling of all the aggregation data on unique master curves defined by only two parameters: the exponent of the power-law aggregation kernel, lambda, and the aggregate fractal dimension, d(f). The predicted master curves were observed experimentally, which confirms the validity of the aggregation model and allows the unique determination of the kinetic and structural parameters of the aggregation process. The cluster growth behaviour, although significantly slower than DLCA, shows power-law kinetics rather than the exponential one typical of RLCA and the cluster structure is characterized by an unexpectedly small fractal dimension, d(f) = 1.7. The occurrence of gelation has been characterized using small amplitude oscillatory shearing to monitor the time evolution of the elastic modulus. It is found that also these curves, together with the gel time value, scale with the stability ratio of primary particles for a given solid volume fraction. We further use the model to calculate the cumulative occupied volume fraction of the growing aggregates and quantify in this way the increasing space filling, which is solid volume fraction dependent. The experimentally determined dimensionless gel times, which are also solid volume fraction dependent, scale then directly with the dimensionless time to reach a certain degree of the space filling in the model. This finding suggests that, like the aggregation kinetics, the gelation kinetics is governed by a second-order rate process.

AB - The aggregation and gelation kinetics in moderately concentrated (0.004 less than or equal to phi(0) less than or equal to 0.1) colloidal dispersions of fluorinated polymer particles has been studied. The aggregation was adjusted to proceed slowly enough to allow a convenient characterization of the kinetics through static and dynamic light scattering on quenched and diluted samples. A population balance model based on second-order aggregation rates is developed to compute the time evolution of the cluster mass distribution, from which we calculate the values of the average radii and structure factor measured by light scattering, so as to allow a direct comparison between measured and calculated quantities. The model suggests the introduction of a dimensionless time which allows the scaling of all the aggregation data on unique master curves defined by only two parameters: the exponent of the power-law aggregation kernel, lambda, and the aggregate fractal dimension, d(f). The predicted master curves were observed experimentally, which confirms the validity of the aggregation model and allows the unique determination of the kinetic and structural parameters of the aggregation process. The cluster growth behaviour, although significantly slower than DLCA, shows power-law kinetics rather than the exponential one typical of RLCA and the cluster structure is characterized by an unexpectedly small fractal dimension, d(f) = 1.7. The occurrence of gelation has been characterized using small amplitude oscillatory shearing to monitor the time evolution of the elastic modulus. It is found that also these curves, together with the gel time value, scale with the stability ratio of primary particles for a given solid volume fraction. We further use the model to calculate the cumulative occupied volume fraction of the growing aggregates and quantify in this way the increasing space filling, which is solid volume fraction dependent. The experimentally determined dimensionless gel times, which are also solid volume fraction dependent, scale then directly with the dimensionless time to reach a certain degree of the space filling in the model. This finding suggests that, like the aggregation kinetics, the gelation kinetics is governed by a second-order rate process.

KW - gelation kinetics

KW - aggregation

KW - gel formation

U2 - 10.1021/la048055s

DO - 10.1021/la048055s

M3 - Article

VL - 21

SP - 2062

EP - 2077

JO - Langmuir

JF - Langmuir

SN - 0743-7463

IS - 5

ER -