Distribution of molecular weight and composition in diblock copolymers
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Bibliographic record
Abstract
Abstract The distribution of molecular weight (MW) and composition of diblock copolymers is considered theoretically. Assuming that the chain end of each block is coupled randomly, the weight-average MW of the block copolymers is given by M w = w 1 (M w,1 + M n,2 ) + w 2 (M w,2 + M n,1 ), irrespective of the shape of the distribution of each block, where w i is the weight fraction, and M n,i and M w,i are the number- and weight-average MW of each block. In copolymer chains, the chemical compositions as well as the MWs cannot be identical for all polymers, and there exists a bivariate distribution of MW and composition. When the MW distribution (MWD) of both blocks follows the Schulz-Zimm distribution, the bivariate distribution can be obtained analytically. In addition to the bivariate distribution, the full MWD, the average composition as a function of MW, the composition distribution of copolymers having a specified MW, and the overall composition distribution are obtained. The composition distribution, as well as the average composition, becomes independent of MW under the condition σ 1 /M n,1 = σ 2 /M n,2 , where σ i is a parameter indicating the narrowness of the Schulz-Zimm distribution. The present theoretical analysis provides new insight into the design of diblock copolymers.
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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) | 0.000 | 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 it