John Freudenthal

Mueller matrix polarimetry with four photoelastic modulators: theory and calibration

A spectroscopic Mueller matrix polarimeter with four photoelastic modulators (PEMs) and no moving parts is introduced. In the 4-PEM polarimeter, all the elements of the Mueller matrix are simultaneously determined from the analysis of the frequencies of the time-dependent intensity of the light beam.

The first crystal structure of a monomeric phenoxyl radical: 2,4,6-tri-tert-butylphenoxyl radical.

Crystals of the 2,4,6-tri-tert-butylphenoxyl radical have been isolated and characterized by X-ray diffraction, and calculations have been performed that give the distribution of spin density in the radical.

Reversible Twisting during Helical Hippuric Acid Crystal Growth

Crystals grow in the minds eye by the addition of small units to a monolith each part of which is in fixed translational relation to every other part. Here, it is shown that growth can induce reversible twisting and untwisting of macroscopic crystals of hippuric acid (N-benzoylglycine, C(9)H(9)NO(3)) on the scale of radians. Crystals growing in undercooled melts of hippuric acid twist about the axis of elongation. At the same time the twisting is undone by new elastic stresses that build up as the crystal thickens. The dynamic interplay of twisting and untwisting ultimately fixes the crystal morphology. A correspondence between the optical properties of hippuric acid single crystals and twisted needles measured with a Mueller matrix microscope is established. The measured crystalloptical properties are in complete accord with the optical indicatrix rotating helically along the axis of elongation at the growth front, or counter-rotating so as to unwind earlier growth. The reversible morphological changes captured here in situ are likely also found in banded spherulites of high molecular weight polymers, optically modulated chalcedony minerals, elements, proteins, and other molecular crystals for which there is evidence of helical twisting. The analysis of such systems is usually predicated on the relationship of crystalline helical pitch to a power law exponent. However, in the absence of previous considerations of untwisting, the mechanistic content of such relationships is questionable.

Twisted Mannitol Crystals Establish Homologous Growth Mechanisms for High-Polymer and Small-Molecule Ring-Banded Spherulites

D-Mannitol belongs to a large and growing family of crystals with helical morphologies (Yu, L. J. Am. Chem. Soc.2003, 125, 6380). Two polymorphs of D-mannitol, α and δ, when grown in the presence of additives such as poly(vinylpyrrolidone) (PVP) or D-sorbitol, form ring-banded spherulites composed of handed helical fibrils, where the helix axes correspond to the radial growth directions. The two polymorphs form helices with opposite senses in the presence of PVP but the same sense in the presence of D-sorbitol. The characteristic dimensions of the fibrils, including thickness, aspect ratio, and pitch, were determined by scanning probe and electron microscopies. These values must form the basis of any theory that presupposes what forces give rise to crystal twisting, a problem that has been broached but unsettled in the literature of polymer crystallization. The interdependence of the rhythmic variations of both linear and circular birefringence, as determined by Mueller matrix microscopy, informs the cooperative organization of mannitol fibers. The microstructure of mannitol ring-banded spherulites compares favorably to that of high polymers and is evaluated within the context of current theories of crystal twisting.

Imaging chiroptical artifacts

It is well-known that circular dichroism (CD) measurements of anisotropic media may contain artifacts that result from mixed linear anisotropies. Such artifacts are generally considered a nuisance. However, systematic artifacts, carefully measured, may contain valuable information. Herein, polycrystalline spherulites of D-sorbitol grown from the melt were analyzed with a Mueller matrix microscope, among other differential polarization images devices. As spherulites grew into one another they developed strong apparent optical rotation and CD signals at the boundaries between spherulites. These signals are shown not to have a chiroptical origin but rather result from the interactions of linear anisotropies in polycrystalline bodies. Such chiroptical artifacts should not be dismissed reflexively. Rather, they are comprehensible crystal-optical effects that serve to define mesoscale structure.

Reckoning electromagnetic principles with polarimetric measurements of anisotropic optically active crystals

A method is introduced to correlate electromagnetic theory and polarimetric experiments for anisotropic optically active crystals at oblique angles of incidence. It is based on the 4 × 4 algebraic descriptions of light propagation in layered anisotropic media, which can be simplified to 2 × 2 matrices when multiple reflections are disregarded. Spectroscopic Mueller matrix measurements in transmission and at oblique angles of incidence have been made on two uniaxial crystals: α-quartz and silver thiogallate. Their optical activity tensors have been spectroscopically determined using the method presented here.

Circular Birefringence of Banded Spherulites

Crystal optical properties of banded spherulites of 21 different compounds--molecular crystals, polymers, and minerals--with helically twisted fibers were analyzed with Mueller matrix polarimetry. The well-established radial oscillations in linear birefringence of many polycrystalline ensembles is accompanied by oscillations in circular birefringence that cannot be explained by the natural optical activity of corresponding compounds, some of which are centrosymmetric in the crystalline state. The circular birefringence is shown to be a consequence of misoriented, overlapping anisotropic lamellae, a kind of optical activity associated with the mesoscale stereochemistry of the refracting components. Lamellae splay as a consequence of space constraints related to simultaneous twisting of anisometric lamellae. This mechanism is supported by quantitative simulations of circular birefringence arising from crystallite twisting and splaying under confinement.

Orientational dependence of linear dichroism exemplified by dyed spherulites.

D-sorbitol forms so-called spherulites from under-cooled melts. These polycrystalline formations have optically uniaxial radii. Melts pressed between glasses crystallize as plane sections of spheres. Dyes that are soluble in molten sorbitol become oriented as the crystallization front passes through the melt so as to form disks with large linear dichroism in the absorption bands of the dyes. The dyeing of spherulites is thus a general method of solute alignment. The linear optical properties of sorbitol spherulites containing the azo dye amaranth were analyzed in detail so as to correct a persistent confusion in the literature regarding the orientational dependence of linear dichroism. In cases involving thin film dichroism of multilayered samples requiring many corrections of intensity data in non-normal incidence, some authors have taken transmittance and others absorbance as having a cosine-squared angular dependence on the plane of the electric vector of linearly polarized light. Plane sections of doped spherulites present all orientations of an electric dipole oscillator in spatially localized region in normal incidence. As such, the samples described herein are ideally suited to resolving this confusion. Images of transmittance of dyed spherulites in polarized light were recorded with a CCD camera and simulated under the assumption that both absorbance and transmittance show a cosine-squared angular dependence but with respect to different angles. Transmittance with a cosine-squared dependence follows azimuthal rotations of the spherulite radii around the wave vector, while absorbance with a cosine-squared dependence follows rotations about axes perpendicular to the wave vector, natural consequences of the properties of the optical indicatrix that are often overlooked. Spherulites obviate the substantial experimental complexities that are engendered in non-normal incidence by sample reorientation. Thus, the principles of anisotropic absorption are given in a complete and intuitive fashion.

Dendritic crystal growth, differential circular scattering, and the origin of biomolecular homochirality

Phthalic acid rapidly crystallizing in thin aqueous films is deposited radially and rhythmically as dendritic banded spherulites that have heterochiral meso-textures in hemi-circles. The chiral fields differentially scatter left and right circularly polarized light. A scenario for chiral amplification and the origin of biomolecular homochirality is thus proposed that combines the influences of crystals and light.

Imaging with photoelastic modulators

Photoelastic modulators (PEMs) are among the most robust and precise polarization modulation devices, but the high frequency free-running nature of PEMs challenges their incorporation into relatively slow CCD and CMOS imaging systems. Current methods to make PEMs compatible with imaging suffer from low light throughput or use high cost intensified CCDs. They are not ideal for some analyses (microscopy, reflectivity, fluorescence, etc.), and likely cannot be extended to polarimeters with more than two PEMs. We propose to modulate the light source with a square wave derived from particular linear combinations of the elementary PEM frequencies and phases. The real-time synthesis of the square waves can be achieved using a field programmable gate array (FPGA). Here we describe the operating principle.