Concurrent polarization IR analysis to determine the 3D angles and the order parameter for molecular orientation imaging

Abstract

A non-tomographic analysis method is proposed to determine the 3D angles and the order parameter of molecular orientation using polarization-dependent infrared (IR) spectroscopy. Conventional polarization-based imaging approaches provide only 2D-projected orientational information of single vibrational modes. The newly proposed method concurrently analyses polarization angle-dependent absorptance of two non-parallel transition dipole moments. The relative phase angle and the maximum-to-minimum ratios observed from the two polarization profiles are usesd to calculate the 3D angles of the mean molecular orientation and the order parameter of the orientational distribution. Usage of those relative observables as intermediate input parameters makes the analysis results robust against variations in concentration, thickness, absorption peak, and absorption cross-section, which can occur in typical imaging conditions. This analysis is based on a single-step, non-iterative calculation that does not require any analytical model function of an orientational distribution function. This concurrent polarization analysis method is demonstrated using two simulation data examples, followed by associated error propagation analysis and discussion on the effect of absorption strength. Application of this robust spectral analysis method to polarization IR microscopy will provide a full molecular orientation image without tilting that tomographies require.

Macromolecular Orientation in Biological Tissues Using a Four-Polarization Method in FT-IR Imaging

“…A mathematical description of molecular orientation can be done utilizing orientation distribution function, which in the case of molecules with cylindrical symmetry is being approximated by a series of Legendre polynomials (with respect to the symmetry axis). 29 Depending on the mechanism of optical interaction, different measurement techniques can determine a different number of Lagrange polynomial coefficients. 29 FT-IR can provide a second-order coefficient, 29 which is also called Herman’s orientation function or in-plane orientation function, calculated as 11 , 13 where D is the dichroic ratio and α is the angle between the transition dipole moment (of a specific absorption band) and the main molecular chain axis.…”

Super-resolved 3D mapping of molecular orientation with vibrational techniques

“…where 𝐷 = 𝐴 𝑚𝑎𝑥 /𝐴 𝑚𝑖𝑛 and 𝜅 describes angle between main molecular axis and transition dipole moment. Herman's function is equal to the second order coefficient of series of Lagrange polynomials, approximating the orientation distribution function (ODF) of a molecule with cylindrical symmetry [21], [22]. Therefore, it might be used to describe level of molecular orientation of the sample.…”

“…Derivation is established on the grounds of classic electromagnetic wave theories and uses two non-parallel transition dipole moments simultaneously: primary ( 𝜇 1 ) associated with the main molecular axis (for example main molecular chain vibration) and secondary (𝜇 2 ) representing an orthogonal vibration. Based on that, absorptance (𝛼 = 1 − 𝑇) dependence from polarization direction 𝜂 for vectors 𝜇 1 and 𝜇 2 is described as [23]:…”

“…As presented in Figure 1c, following parameters pairs were later extracted from obtained experimental functions:𝛼 ratios observed in definition of 𝑀 and 𝑁, α° may be considered as a constant, thus, have no impact in further calculations. Having intermediate parameters and after equations manipulation, it is a straight way to find results for 𝜇 1 and 𝜇 2 orientations along with order parameter [23]:…”

“…The order parameter 〈𝑃 2 〉, which is equal to second-order coefficient of an ODF of molecule with cylindrical symmetry, is used as a quantity describing the breadth of ODF [23]. An example of 3D orientation results is shown in Figure 1e.…”