# Stability and Rupture of Liquid Crystal Bridges under Microgravity

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## Abstract

**:**

## 1. Introduction

## 2. Setup and Materials

## 3. Results

#### 3.1. Stability Limits

#### 3.2. Bending under Lateral Acceleration

#### 3.3. Rupture Dynamics

## 4. Summary and Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Smectic bridges under normal gravity conditions in the same setup and with the same materials as in the TX55 flight, in a test run before the rocket launch. Each image shows the respective bridge within the last 20 ms before pinch-off. The TX55/Gn labels refer to the chambers of TX55/n. The scale bars mark 1 mm.

Experiment | Material | Phase | $\mathsf{\alpha}$ at Breakup |
---|---|---|---|

TX55/G1 | ST02890 | SmA | 1.14 |

TX55/G2 | ST02890 | SmA | 1.51 |

TX55/G3 | ST00554 | SmC | 2.33 |

TX55/G4 | ST00552 | SmA | 2.35 |

TX55/G5 | ST00554 | SmC | 1.81 |

TX55/G6 | ST00552 | SmA | 1.845 |

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**Figure 2.**Sketch of the TEXUS 52/TEXUS 55 liquid-crystal bridge experiment. The liquid or liquid-crystal (the bright bluish column) is initially encapsulated by a cylindrical metal hull with an inner diameter of 3 mm. This shell is pulled away from the opposing support of the bridge and a fast camera captures images of the free column at rates of 50 or 100 frames per second.

**Figure 3.**The drawing protocols for the columns in the six experiment pairs. The time counted from the start of the hull motion, which was initiated after entry into the microgravity phase. The distance L was measured from the fixed top to the upper rim of the hull that enclosed the fluid cylinders. The horizontal green line indicates the critical aspect ratio ${\alpha}_{c}$.

**Figure 4.**The isotropic bridge of ST02890 (TX52/4) at different times before pinch-off ($\alpha =2.26\pm 0.03$), where $\delta t$ is less than 10 ms. Because of a technical issue, the bridge was asymmetric and had a base diameter that was 1.5 times larger than the top diameter. The image sizes are 8 mm × 11 mm.

**Figure 5.**The nematic bridge of ST00552, 17 s before pinch-off (

**a**), 0.25 s before pinch-off (

**b**) and less than 10 ms before pinch-off (

**c**), ($\alpha =1.73$). The nematic material started to wet the hull approximately 40 s after the start of the experiment in $\mathsf{\mu}g$, which led to the instability of the cylinder radius and the premature pinch-off. The image sizes are 8 mm × 9 mm.

**Figure 6.**Smectic bridges during the deceleration phase: ST00552 in SmC at 44 ${}^{\circ}$C (

**a**) and in SmA at 53 ${}^{\circ}$C (

**b**). The inertia pulls the middle of the columns in a direction perpendicular to their axes. (

**c**) shows the columnar material in the M2 phase at the same instant and acceleration. The aspect ratios are $\alpha =4.6$ (

**b**) and 4.75 (

**a**,

**c**). The image sizes are 8 mm × 16 mm.

**Figure 7.**Deflection of two columns with aspect ratios of between 4.5 and 4.75 during the deceleration of the TX52 rocket (we measured the lateral displacements of the columns at their maximum deflections relative to the initial straight columns).

**Figure 8.**The model of the column deformation under the action of inertial lateral forces. Each slice has a circular cross-section.

**Figure 9.**Inverse radius of curvature ($1/{R}_{0}$) and the corresponding lateral acceleration a, as calculated using Equation (3). During the final 300 ms before rupture, the deformation was already asymmetric and this model did no longer apply.

**Figure 10.**The pinch-off of ST02890 during the transition from smectic A into the nematic phase at an elongation of $\alpha =4$. When the material melted, the stability provided by the yield stress was lost: The column started thinning in the center and finally pinched off (image sizes were 5 mm × 5 mm).

**Figure 11.**The pinch-off of ST02890 during the transition from smectic A into the nematic phase: Thinning of the neck diameter ${D}_{min}$ as a function of time to pinch-off at ${t}_{0}$. The dashed lines mark ${({t}_{0}-t)}^{\gamma}$ for the given exponents. Evidently, both graphs yielded qualitatively different $\gamma $ values, even though the experimental conditions were the same.

**Figure 12.**Some smectic bridges during breakup: (

**a**) ST00554 column of $L=6.0$ mm in SmC; (

**b**) ST00552 column of 6.0 mm in SmA; (

**c**) ST00554 column of 18 mm in SmC. These three columns were broken up by sideways acceleration during the re-entry of the rocket. (

**d**) The pinch-off of an ST00552 column in SmA under zero gravity conditions without acceleration (two rows). The time scale of the rupture was much longer, yet the same power law was found. Image sizes were 5 mm $\times $ 5 mm. The time $\delta t$ of the last image in each series was within 20 ms before the pinch-off. (

**e**) A summary of the thinning dynamics of the four experiments. The dashed lines indicate ${D}_{min}\propto {({t}_{0}-t)}^{0.66}$.

**Table 1.**Materials, temperatures and drawing protocols: TX52/n (n = 1...6) represent the experiments that were performed onboard TEXUS 52, and TX55/n represent those performed onboard TEXUS 55. The label ↑ indicates that the columns were only expanded, whereas $\uparrow \downarrow $ marks experiments in which the columns were expanded first and shortened later. Temperatures were kept constant, except during TX55/1,2 in which a phase transition was triggered within the bridges.

Experiment | Material | Temperature (°C) | Phase | Modus |
---|---|---|---|---|

TX52/1 | ST00552 | 44 | SmC | ↑ |

TX52/2 | ST02890 | 44 | SmA | ↑ |

TX52/3 | ST00552 | 52 | SmA | ↑ |

TX52/4 | ST02890 | 52 | Iso | ↑ |

TX52/5 | ST00552 | 60 | Nem | ↑ |

TX52/6 | ST04524 | 60 | M2 | ↑ |

TX55/1 | ST02890 | 46.5→ 53 | SmA→Iso | ↑ |

TX55/2 | ST02890 | 46.5→ 53 | SmA→Iso | ↑ |

TX55/3 | ST00554 | 53 | SmC | ↑ |

TX55/4 | ST00552 | 53 | SmA | ↑ |

TX55/5 | ST00554 | 53 | SmC | $\uparrow \downarrow $ |

TX55/6 | ST00552 | 53 | SmA | $\uparrow \downarrow $ |

**Table 2.**Chemical compositions and phase sequences of the materials that were used in the microgravity experiments. The transition temperatures are given in ${}^{\xb0}$C. The mesophases are labeled as SmC (smectic C), SmA (smectic A) and Nem (nematic). M1 and M2 represent modulated smectic phases [50].

Sample | Chemical Formula and Phase Sequence |
---|---|

ST00552 | 2-(4-n-Hexyloxyphenyl)-5-n-octylpyrimidine |

Cr 27.5 SmC 44.5 SmA 57.5 Nem 65 Iso | |

ST00554 | 2-(4-n-Decyloxyphenyl)-5-n-octylpyrimidine |

Cr 32 SmC 59.5 SmA 65.5 Nem 69.5 I | |

ST02890 | 4-n-Nonyl-biphenyl-4${}^{\prime}$-carbonitrile, 9 CB |

Cr 42 SmA 47.5 Nem 49.5 Iso | |

ST04524 | 2,3,6,7,10,11-Hexakis[dodecyloxy]triphenylene |

Cr 55 M1 58 M2 63 Iso |

Experiment | Material | Phase | Result |
---|---|---|---|

TX52/1 | ST00552 | SmC | Stable until re-entry at $\alpha =4.75$ |

TX52/2 | ST02890 | SmA | Wetted hull: breakup at $\alpha =4.4$ |

TX52/3 | ST00552 | SmA | Stable until re-entry at $\alpha =4.6$ |

TX52/4 | ST02890 | Iso | Asymmetric: breakup at $\alpha =2.26$ |

TX52/5 | ST005520 | Nem | Wetted hull: breakup at $\alpha =1.73$ |

TX52/6 | ST04524 | M2 | Stable even after re-entry |

TX55/1 | ST02890 | Nem | Breakup after melting at $\alpha =4$ |

TX55/2 | ST02890 | Nem | Breakup after melting at $\alpha =4$ |

TX55/3 | ST00554 | SmC | Stable until re-entry at $\alpha =6.5$ |

TX55/4 | ST00552 | SmA | Air bubbles: breakup at $\alpha =3.82$ |

TX55/5 | ST00554 | SmC | Stable until re-entry at $\alpha =2$ |

TX55/6 | ST00552 | SmA | Stable until re-entry at $\alpha =2$ |

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**MDPI and ACS Style**

Trittel, T.; Klopp, C.; Harth, K.; Stannarius, R.
Stability and Rupture of Liquid Crystal Bridges under Microgravity. *Crystals* **2022**, *12*, 1092.
https://doi.org/10.3390/cryst12081092

**AMA Style**

Trittel T, Klopp C, Harth K, Stannarius R.
Stability and Rupture of Liquid Crystal Bridges under Microgravity. *Crystals*. 2022; 12(8):1092.
https://doi.org/10.3390/cryst12081092

**Chicago/Turabian Style**

Trittel, Torsten, Christoph Klopp, Kirsten Harth, and Ralf Stannarius.
2022. "Stability and Rupture of Liquid Crystal Bridges under Microgravity" *Crystals* 12, no. 8: 1092.
https://doi.org/10.3390/cryst12081092