Applications of the Wormlike Chain Model in Polymer Physics: Self-consistent Field Theory
Bibliographic record
Abstract
The self-consistent field theory (SCFT) has reveived a great success in prediction of the physical properties of a variety of polymeric systems in the recent two decades. However, the traditional SCFT is based on the Gaussian chain model, completely neglecting the chain rigidity effects, which is ascribed to one of the intrinsic properties of polymer chains. This thesis concentrates on the development of SCFT in the framework of the wormlike chain model and studies the influence of the chain rigidity on the chain configuration which directly determines properties of polymer materials in the mesoscale. Firstly, considering Onsager-type, orientational-dependent repulsive interactions, we study a model for the isotropic-nematic interface in liquid-crystals. Through adjusting the ratio of total contour length L to the persistence length lambda, we consider systems consisting of molecules with various degrees of flexibility: from rods to flexible chains. Physical properties such as the surface tension, interfacial width and density- and order-parameter profiles were numerically calculated as functions of the flexibility L/lambda and tilt angle, which is defined as the angle between the interfacial normal and the nematic director. Secondly, We examine the influence of persistency on the phase diagram of AB diblock copolymers and the properties of the phase transition as a function of volume fraction, Flory-Huggins parameter and chain rigidity, covering a broad regime spanning from Gaussian chains to rigid rodlike chains. On one hand, we demonstrate that results from a Gaussian-weight based theory can be recovered in the long-chain limit, and on the other hand, we display that significant revisions to the phase diagram, due to the persistency effects, exist for shorter chains. To achieve this, an efficient numerical scheme is designed for implementing the calculations of the wormlike-chain SCFT in a full six-dimensional space.
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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".