The complex viscosity of Möbius macromolecules
Bibliographic record
Abstract
Using general rigid bead–rod theory, we explore the effect of twisting a macromolecule on its rheological properties in suspensions. We thus focus on macromolecules having the form of Möbius bands so that the number of twists can be incremented. We call these Möbius macromolecules. When represented in general rigid bead–rod theory, these macromolecules comprise beads whose centers all fall on a Möbius band. From first principles, we calculate the complex viscosity of twisted rings with zero to seven twists. We find that the zero-shear values of the viscosity and first normal stress coefficient increase with twisting. Furthermore, we find that the real part of the complex viscosity descends more rapidly, with frequency, with extent of twist. For the imaginary part of the complex viscosity, the more twisted, the higher the peak. For each part of the dimensionless complex viscosity and the first normal stress coefficient, the results fall on one of just three curves corresponding to zero, even, or odd numbers of twists. We also explore the effects of the length and the aspect ratio of twisted macromolecular suspensions. We close with a worked example for a suspension of triply twisted Möbius annulene.
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How this classification was reachedexpand
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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".