Strong Electro‐Optic Effect and Spontaneous Domain Formation in Self‐Assembled Peptide Structures

Short peptides made from repeating units of phenylalanine self‐assemble into a remarkable variety of micro‐ and nanostructures including tubes, tapes, spheres, and fibrils. These bio‐organic structures are found to possess striking mechanical, electrical, and optical properties, which are rarely seen in organic materials, and are therefore shown useful for diverse applications including regenerative medicine, targeted drug delivery, and biocompatible fluorescent probes. Consequently, finding new optical properties in these materials can significantly advance their practical use, for example, by allowing new ways to visualize, manipulate, and utilize them in new, in vivo, sensing applications. Here, by leveraging a unique electro‐optic phase microscopy technique, combined with traditional structural analysis, it is measured in di‐ and triphenylalanine peptide structures a surprisingly large electro‐optic response of the same order as the best performing inorganic crystals. In addition, spontaneous domain formation is observed in triphenylalanine tapes, and the origin of their electro‐optic activity is unveiled to be related to a porous triclinic structure, with extensive antiparallel beta‐sheet arrangement. The strong electro‐optic response of these porous peptide structures with the capability of hosting guest molecules opens the door to create new biocompatible, environmental friendly functional materials for electro‐optic applications, including biomedical imaging, sensing, and optical manipulation.

. Single domain FFF-tapes with differing orientations. Top: Bright field images of the tapes. β denotes the angle from the electrodes to the tape. Bottom: the corresponding polar plots of the same tapes. Bar size is 5 µm. Figure S5. FF structure and dipolar contributions to EO response. a. FF molecule in its zwitterionic form. Carbons are green, oxygens in red and nitrogens in blue. b. A cross section of a nanotube within the macroscopic tube structure. a and b are the crystallographic axes. c. A close up on the backbone of the nanotube inner wall. The black arrows denote the strong dipole of the charged end groups in the zwitterion. Hydrogens and aromatic side chains were omitted for clarity. Red and blue balls mark the oxygens and nitrogens of the charged end groups. d. The backbone of FF molecules comprising the tubular helix of a nanotube. Figure S6. Multi-domain structure of a tape. a) PLEOM retardance image. b) PLEOM  image. (c-d) Zoomed in retardance and  images of the area marked by a rectangle in b. e) Polar plots of the different domains in c-d.

Supplementary note 1: Estimation of FF thickness
In order to estimate the effective thickness of FF, we will look at the cross section of the tube as a ring made of two concentric circles. This is a fair approximation given the hexagonal shape of the tube. The maximal thickness of such a ring is achieved when the distance from the edge is exactly the difference between the outer and inner radii of the ring. Since the electro-optic response is linearly dependent on the thickness, we looked at the cross section of the tube and found the maximum value is achieved at a distance of 0.9 m from the tube edge. The thickness at a given distance from the edge is described by:

√( )
Where R is the radius and x is the distance from the edge. Given the radius of the analyzed tube is 1.25 m, the corresponding thickness is µm.

Supplementary note 2: FF coefficients calculation
In order to calculate the exact coefficients we must know the space group of the crystal. For the FF-tubes it is , and therefore In the crystal frame ( ) the electro-optic tensor is : in this frame the external electric field applied along y is: ( ) Figure S6. Schematic diagram of an FF tube in PLEOM and corresponding electric fields. (x,y) denotes the laboratory frame work, where x is the direction of applied AC electric field.
(X,Z) denotes the tube's framework. The double headed red arrow is the axis of the incident polarization, where α is the angle between the polarization and the x axis, and β is the angle between x and the long axis of the tube (Z). Then: Then if we assume a uniaxial crystal, based on the space group symmetry, we can call: ( ( The index ellipsoid then becomes : We will for now omit the YZ contribution in our calculation, and focus on the XZ term in order to demonstrate that cross terms effects are very small. The cross terms rotate the refractrive index ellipsoid. We therefore would like to return to an equation of the form: , by rotating the axes by an angle : With defined by: so we have the final indices : From Equation (4) it can be seen that the effect of the cross term is strongly dependent on the birefringence, , of the material, since the numerator is very small relative to the denominator even for mild birefringence, as we observed for FFF-plates, and high values of the electro-optic coefficient and the applied field. While the refractive indices of FF are unknown to date, we can estimate the response using the values for FFF-plates. using FFF's birefirngence -, the applied field -, and taking the value of of LiNBO 3 -,among the higest cross term coefficients measured, yields ( ) , corresponding to a rotation of just 1.4, and its electro-optic contribution is negligible. Therefore, we will only conisder the contributions of to the electro-optic response from here on.

The signal in PLEOM for FF-tubes
The incident field is the following, in (x,y,z) and (X,Y,Z) frameworks respectively : After going through the tube , the field is Where is the wave number of the incident laser beam, and is the effective thickness calculated above. The beam then goes through a halfwaveplate at and a polarizer along which is equivalent to projecting this field along ⃗ , the vector aligned with the incoming polarization: This can be written as the sample beam : with a modulus and a phase that will be detailed hereafter.
Under the influence of the quasistatic Electric field applied by the electrodes ⃗ , the indexes are modified.
So that the modulus is , with a phase . By mixing it with a well chosen reference beam of the form: , The total field and the intensity associated become: The balanced homodyne detection of the signal allows us direct access to the intererence term: The signal depends on and that both depend on as detailed hereafter.

The modulus
The modulus of the sample beam is: assuming , , m and nm, then ( ) , which means is a function that varies periodically with α to the tune of at most <11%.
The phase the phase of is defined by: where and are the imaginary and real parts of .
We will consider the change of with : (20) The lock in amplifier is tuned to the frequency of the applied external field, and therefore its signal is directly proportional to . From Equation (22)