To facilitate the polarized-light investigation, light was delivered from an external halogen-light source (150W at 3200K, Thorlabs Inc., NJ, USA), through a high-quality fiber-optics bundle (91 cm in length, 6.4 mm in diameter; Core Fiber Bundle, Thorlabs Inc., NJ, USA) to an aluminum housing of a silver-coated, beam-turning mirror (97.5% reflectivity, Thorlabs Inc., NJ, USA). The mirror directs the light perpendicular to the polarizer (50 mm in diameter), illuminating the cuvette in the direction of the red-dashed arrows in Fig 2B. An analyzer (12.5 mm in diameter) has been retrofitted to the tip of the borescope by means of a 3D-printed (ABS) housing. Note that the borescope setup includes an internal 45° mirror to reflect the polarized light into the axial direction of the borescope. Both polarizer and analyzer are made of a 0.3 mm-thick dichroic polarizing film sheet (>99% efficiency, Thorlabs Inc., NJ, USA), sandwiched between two protective glass windows. Each window has an antireflective coating which is optimized for the visible part of the spectrum (0.4 μm to 0.7 μm).
Following the above observations, the vitrification process is simplified to have two primary stages according to the stress level: free-of-stress large deformations (in practice, deformation under negligible stress), and significant stress which is associated with small deformations. This approach enables decoupling the heat transfer problem from the solid mechanics problem in the second stage, where results of the heat transfer solution serve as input for the solid mechanics problem. Consistently, the geometry of the cavity for the analysis in the second stage can be directly extracted from cryomacroscopy images.
Finally, the light vector to reach the analyzer is given by:(15)where the negative sign signifies that the components of and parallel to the direction of polarization of the analyzer are in opposite directions, as illustrated in Fig 4. Substituting and from Eq (12) into Eq (15) yields:(16)However, an observer standing behind the analyzer will only see the light intensity, which is proportional to the square of the light amplitude . The light intensity field is normalized in the current analysis, where the observed intensity becomes:(17)
The stress history resulting from a similar thermal history has been discussed previously [7,13], with the most relevant observation that the developed stress is insignificant under constant cooling rate conditions even when the CPA gradually becomes highly viscous. At higher temperatures, when the viscosity is very low, the CPA is free to flow, which does not permit stress buildup. At lower temperatures along the A-B segment in Fig 5, when the entire domain cools at a uniform rate, insignificant differential thermal expansion across the domain is the reason for why thermal stress does not buildup, despite the fact that the viscosity gradually becomes significant. Only when the temperature starts to equilibrate below the glass transition temperature and after the material has already gained solid-like characteristics, significant thermal stress develops. The result is residual stress at cryogenic storage, a phenomenon which is directly related to the fact that different layers in the CPA have gained solid-like behavior at different times .
Fig 7C compares the experimental and simulated light intensity field in case C, where the polarizer is oriented mid-angle between Case A and B. Results in Case C indicate a dependency of the light intensity on the orientation of the polarizer-analyzer couple setup, as is also predicted from the mathematical model applied here. The following observations can be made from Case C: (i) the cavity results in a low light intensity, similar to Cases A and B; (ii) unlike Cases A and B, a region of high light intensity is found at the wall of the cavity, but not close to its tip. A concentrated region of high light intensity is predicted below the tip of the cavity, which is not consistent with experimental results. This disagreement between the experimental and simulation results seems to be arising from reflection at the convex tip of the cavity. 2b1af7f3a8