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Tutorial: Liquid crystals

Contributors: Shinji Kihara & Jacob Judas Kain Kirkensgaard


Lipid molecules can adopt many liquid crystalline phases within biological settings (e.g., lamellar, hexagonal, and inverse hexagonal phases).

Before you start

  • Knowledge of Bragg's law and basic understanding of molecular self-assembly are assumed.

Learning outcomes

At the end of this tutorial you are expected to be able to:
  • Identify some of the liquid crystalline structures within soft matter research.

Introductory remarks

Many biological amphiphilic molecules (a prominent example being lipids) can self-assemble into interesting geometries. In this tutorial, you are tasked to identify some of the major mesophases which lipids form.

Part 1: Identifying a single phase system

Lipids are known to form liquid crystalline phases even in the food we consume (Salentinig et al., ACS Nano 2013). Small-angle scattering techniques provide insight into specific types of phases which lipids can form.

Scenario: you measured a mixture of lipids at a synchrotron SAXS. Work your way through to identify which phase(s) are present in your sample. In the figure below, you can immediately identify three diffraction peaks positioned at q = 0.062, 0.088, and 0.112 Å-1.


SAXS pattern of a lipid sample A.

In the table below, you can find the respective peak positions of the diffraction peaks (i.e., first order, second order, third order, ... fifth order diffractions) which belong to different crystallographic phases. For more detailed explanation, we recommend Tyler et al., Methods in lipids, 199-225. The phases described in the table includes lamellar stacks (Lα), 2-dimentional hexagonal phase (H2 or p6mm), inverse bicontinuous hexagonal phase (Im3m), and a discontinuous cubic phase (Fd3m).


Table 1. Relative postions (on the q-axis) of Bragg peaks in four different lipid phases.

The most obvious one you can test is the Lα phase, as the diffraction peaks are separated by simple integer multiplication (i.e. the q position of the peaks are either 2 times, 3 times, 4 times, etc the q-value of the first-order diffraction peak). The liquid crystalline phase which adopts Lα phase, thus, follows the scenario where the first diffraction position is at $q=0.062$ Å-1, the second and third peaks should be at $q = 0.124$ and $q=0.186$ Å-1, respectively. We can therefore exclude Lα phase. A similar process can be followed by inserting the $q$-value of the first-order diffraction peak and calculate the expected positions of the subsequent diffraction peaks (see below).


Table 2. Theoretical positions of Bragg peaks ($q$ values), relating to different phases, assuming first-order peak at $q=0.062$ Å-1.

Give a try at filling the table for the other phases. You should be able to find the Im3m phase to be the hit, where you have the match between the expected $q$-values and the actual positions of the diffraction peaks.

Challenges

In the challenges, you should identify unknown phase(s) from SAXS data (try solving the challenges without using the hints)

  • Challenge 1: Identify the phase(s) from the SAXS pattern below (note that the first diffraction peak is positioned at 0.072 Å-1).

    SAXS pattern of a lipid sample B.

  • Challenge 2: Identify the liquid phase(s) from the SAXS pattern below (first hint,second hint).

    SAXS pattern of a lipid sample C.

Feedback

Help us improve the tutorials by
  • Reporting issues and bugs via our GitHub page. This could be typos, dead links etc., but also insufficient information or unclear instructions.
  • Suggesting new tutorials/additions/improvements in the SAStutorials forum.
  • Posting or answering questions in the SAStutorials forum.

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