Dynamics of uncharged colloidal inclusions in polyelectrolyte hydrogels
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Bibliographic record
Abstract
We calculate the dynamics of an uncharged colloidal sphere embedded in a quenched polyelectrolyte hydrogel to (i) an oscillatory (optical and magnetic) force, as adopted in classical micro-rheology, and (ii) an oscillatory electric field, as adopted in electrical micro-rheology and electro-acoustics. The hydrogel is modelled as a linearly elastic porous medium with the charge fixed to the skeleton and saturated with a Newtonian electrolyte; and the colloidal inclusion is modelled as a rigid, impenetrable sphere. The dynamic micro-rheological susceptibility, defined as the ratio of the particle displacement to the strength of an applied oscillatory force, depends on the fixed-charge density and ionic strength and is bounded by the limits for incompressible and uncharged, compressible skeletons. Nevertheless, the influences of fixed charge and ionic strength vanish at frequencies above the reciprocal draining time, where the polymer and the electrolyte hydrodynamically couple as a single incompressible phase. Generally, the effects of fixed charge and ionic strength are small compared with, for example, the influences of polymer slip at the particle surface. The electrical susceptibility, defined as the ratio of the particle displacement to the strength of an applied oscillatory electric field, is directly influenced by charge at all frequencies, irrespective of skeleton compressibility. At low frequencies, polymer charge modulates the driving (electro-osmotic) and restoring (electrostatically enhanced elastic) forces, whereas charge has no influence on the restoring force at high frequencies where dilational strain is suppressed by hydrodynamic coupling with the electrolyte. In striking contrast to charged inclusions in uncharged hydrogels (Wang & Hill, J. Fluid Mech. , vol. 640, 2009, pp. 357–400), the electrical susceptibility at high frequencies is independent of electrolyte concentration. Rather, the dynamics primarily reflect the elastic modulus, charge and hydrodynamic permeability, with a relatively weak dependence on particle size. Interestingly, the dynamic mobility in the zero-momentum reference frame, which is central to the electro-acoustic response, is qualitatively different from the dynamic mobility in the skeleton-fixed reference frame. Finally, we propose a phenomenological harmonic-oscillator model to address – in an approximate manner – the dynamics of charged particles in charged hydrogels. This shows that particle dynamics at low frequencies are dominated by particle charge, whereas high-frequency dynamics are dominated by hydrogel charge.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it