The observed optical effects were given the phenomenological names anomalous azimuthalrotation when measured by incident linearly polarized light and anomalous circularextinction when me
Tetraphenyl-X 0
Synthesis of Tetraphenylmethane 5 555555 75
Tetraphenylmethane was first synthesized in small quantities in 1897 by Moses
Gomberg.’””® The preparation given below (Scheme 2-1) was reported to have a high yield (79%).'”
CH:);CH;CH;CH;ONO me—{ (CH;);CH;CH;CH; - PhC { ) N
1 g (0.00298 mol) of p-tritylaniline (Aldrich) was dissolved in 7.5 mL (0.125 mol) of ethanol and 0.90 mL (0.0164 mol) of concentrated sulfuric acid The mixture was cooled to about -10 °C in a 25% ammonium chloride ice bath While stirring, 0.60 mL (0.00447 mol) of isopentylnitrite was added drop-wise The resulting mixture was stirred for 30 more minutes, treated with 1.5 mL of an 0.0530 M aqueous hypophosphorous acid solution, and heated to reflux After cooling to room temperature, the solid was filtered, washed with ethanol, and dried overnight in vacuo The crude product was crystallized using a dioxane/ethanol mixed solvent method from which a dark insoluble impurity was filtered A second crystallization returned a pale orange powder, colored probably from a
77 diazo by-product (Scheme 1), with an overall yield of 27% Although two spots were resolved from thin layer chromatography (Rr = 1.5, Rp = 2.3; 5:95 ethyl acetate:hexane), only four peaks were apparent in the '$C.NMR spectrum (750 MHz, CDCI3/Cr(AcAc)3, 6
= 147, 131, 127, 126 ppm), which corresponded closely to literature values (15.00 MHz,
CDCl3, ổ = 146.9, 131.2, 127.5, 126.0 ppm;®° 75 MHz, CDCh, ổ = 146.8, 131.3, 127.4,125.9 ppmẺ').
Crystal Growth and Sample Preparation
Except for tetraphenylsilane, which was grown from the melt and kindly donated by Prof Haussiihl (Institut fiir Kristallographie, Kửln), crystals were grown by slow evaporation at a constant temperature."? Covered beakers containing 100 ml of chloroform were heated to 30 °C in a water bath (Precision Scientific, 180 Series) The tetraphenyl compounds were added in amounts slightly under saturation, covered, and heated to 35 °C The solubility in 100 ml of chloroform at 30 °C is 4.00 g for SiPha, 3.75 g for GePha, and 2.50 g for SnPh¿ and PbPhy Since the available quantity of PhạC was less than 0.200 g, enough chloroform was added just to dissolve all of the material The temperature was then reduced to 30 °C, seed crystals were dropped into the solution if available, and the beakers were covered with aluminum foil pierced with several small holes Crystals were usually harvested after 6-10 days but occasionally incubated for up to three weeks The temperature of the water bath was gradually reduced to room
78 temperature to avoid thermal shock The largest crystals collected were 1 x 0.5 x 0.5 cm
(300 mg), although most were half of that size {110} and {011} faces were indexed with an optical goniometer (STOE).
Crystals were cut perpendicular to the optic axis with a wire saw (South Bay Technology, Model 750) wetted with benzene Pieces were mounted with oil onto a fiber for X-ray indexing (Nonius Kappa CCD) and the optic axis direction was oriented using the programs Collect and SCALEPACK.TM While still mounted in a known orientation within the diffractometer, the crystal was glued with a two-component epoxy to a metal post clamped onto a support stand and brought flush with the crystal The post was designed to fit into the cavity of another metal cylinder to be used for grinding and polishing a well-oriented surface The sample was smoothed on ground glass with sapphire powder and propanol and polished without solvent on 3 um and 0.3 um aluminum oxide (Al,O3) paper, and 0.3 um ferric oxide (Fe2O3) paper.®° The crystal was cut from the post with a wire saw and glued polished-side down onto a glass cover slip broken into 0.5 mm” pieces The rough side was ground to a sample thickness of about
200 lum and polished The optic axis orientation was monitored during thinning by coniscopic microscopy Despite great effort, however, the transparent crystal surfaces of optical quality were never achieved The best transparency was achieved by successive polishing on 3 um and 0.X um aluminum oxide paper, although the surfaces were then badly scratched in the process.
Refractive Index Determination ccc cceesseeseeseeteeeees 79
Refractive indices n were determined using a micron scale microscope and the three height method derived from Snell’s law of refraction (Figure 2-22): n,;, Sina =nsin ổ
"` sinB tanB dL iL, hình where 7g; is assumed to be one.
Focus inside the crystal ơ = — - % h, crystal bottom
Figure 2-22 Experimental determination of absolute refractive indices using the 3-height method derived from Snell’s law Figure reproduced from Ref 1.
The angles and / are the deviations of the light path from normal incidence at the surface and within the crystal, respectively L; is the actual length from the top of the crystal to the glass slide and L¿ is the perceived length as viewed through the crystal /; is the position of the micrometer when the glass slide is in focus, hz the focal height of a mark on the glass slide viewed through the crystal, and h; the height when the top surface of the crystal is in focus All members of the series possess negative optical character as
S0 determined in crossed polarized light with a red retardation plate.®° In coniscopic illumination, the interference colors in quadrants relative to the slow vibration direction of the retardation plate define the optical character.®’ The measured refractive indices n are given in Table 2-9.
Table 2-9 Experimental refractive indices for XPha at 650 nm Reliability is +0.01.n, and 7, are the extraordinary and ordinary refractive indices parallel and perpendicular to the crystallographic c axis, respectively An = ủ ;— Hạ.
X=C X=Si X=Ge X=Sn X=Pb ne 1446 1.706 1.602 1.757 1.730 no 1476 1.742 1.647 1.840 1.789
Curiously, Newkirk reported that the refractive indices for all the crystals in the tetraphenyl family were essentially the same at 1.58 + 0.05, and that the crystals were ail optically positive.®” Neither finding is in accord with what is reported here The purported equivalence of the refractive indices for all five compounds defies common sense.
Given below are the X-ray structure coordinates used in the optical rotation calculations for the Group 14 tetraphenyl crystals Data were collected on a NoniusKappa CCD diffractometer using Mo Kg radiation.
Table 2-10 Structure coordinates for tetraphenylmethane (P42,c): a = 10.9050(10) A, c = 7.2850(5) A; Z=2.
Table 2-1 1 Structure coordinates for tetraphenylsilane (P42:c): a = 11.4480(9) A, c= 7.0640(6) A; Z =2.
Table 2-12 Structure coordinates for tetraphenylgermane (P42)c): a = 11.6160(5) A, c = 6.9020(3) A; Z = 2.
Table 2-13 Structure coordinates for tetraphenylstannane (P42©): a = 12.0680(4) A, c = 6.5570(3) A; Z = 2.
Table 2-14 Structure coordinates for tetraphenylplumbane (P42\c): a= 12.1110(9) A, c = 6.5430(4) A; Z =2.
The electronic polarizabilities chosen for OPTACT calculations based on the coincidence of the calculated and measured refractive indices should be in proportion to the atomic electron densities The peak heights in the Fourier difference maps of the X- ray structure solution are also a measure of the electron densities around atoms and were therefore correlated to the atomic polarizabilities ** For each member of the series, the peak height of the central atom P x was normalized to the that of the phenyl carbon atom
Pc The polarizability of the central atom @x is given relative to that chosen for the phenyl carbon atom in the calculation @c (0.58 A®): ax = œc*Px/Pc These results in comparison to the polarizabilities used in the calculation are given in Table 2-15.
K-Ray Crystallography - + cv tt 1111411 cey 80
Table 2-15 Electronic polarizabilities #x of XPha derived from the electron densities measured as peak heights in the Fourier difference maps P x/ P c is the ratio of peak heights of atom X and the phenyl] carbon atom C Polarizability values are scaled to that used for the phenyl carbon atom in OPTACT calculations (œc = 0.58 A’).
X=H X=C XK=Si X=Gc K=Sn X=Pb Px/Pc 0.12 1.1 4.0 11 16 18
Pentaerythritol oe eeeesescersteceecesecseceseesesseseseseessesssesessesesseessenees 84
Sample PreparafIOn .- ác s11 11x ky 84
A truncated, tetragonal prism of crystalline pentaerythritol measuring 2.9 x 2.4 x
0.4 cm” was provided by Prof Haussiihl (Institut fiir Kristallographie, KửIn) The crystal was sectioned into approximate cubes (~ 0.5 cm per side) with a wire saw wetted with water (South Bay Technology, Model 750) as shown in Figure 2-23 The pieces from a
(101) growth sector were cleaved with a metal blade (X-Acto, No 17) perpendicular to
Figure 2-23 Preparation of pentaerythritol samples from the parent crystal Photo 1s of the remaining crystal.
Absolute Structure Determination ccccc- 85
Three-beam X-ray diffraction is an interference technique that provides direct evidence of structure-factor phases,” 90,9 and therefore resolution of enantiomorphic forms in non-centrosymmetric crystals.”?” In general, the intensity resulting from the interference of superposed coherent waves depends on the cosine of the phase difference between them:
= Ap + A; +2A,A, cos (a, — ỉ,) where A is the amplitude and # is the phase of the interacting waves In the three-beam experiment, a reflection A is brought into diffraction position after which another reflection g is simultaneously excited by a W-scan around the reciprocal lattice vector h.
Interference between the primary and secondary reflections (h and g, respectively) gives rise to the reflection +(h — g) (Figure 2-24). ơ + Rd
XXX + os, @Ó e eee pA Fa me =———-~- e h e e oo Z6 + “đ e ` ô ° â —=——.— ẽ e
Figure 2-24 Simultaneous reflections (h, g, and — g) established in the three-beam diffraction position Figure adapted from Refs 89 and 90.
The sign of the triplet phase @,ripier is Sensitive to the absolute structure:”!
LÀN = —Ô mi where the superscripts + and — denote the equal but opposite phases manifest for enantiomorphous pairs From the three beam position, rotation of the reflection g from inside to outside the Ewald sphere generates a resonance phase AC) that varies from 0° to 180° The total phase ỉ„;„„Ă aS a function of the W-scan is then given by:?
The intensity of the primary reflection # during a W-scan is recorded relative to the triplet phase so that the signal either increases as a result of constructive interference or decreases as a result of destructive interference The resulting intensity profile depends only on the sign of the initial (triplet) phase, which is opposite for different absolute
87 structures If the reflections and g are chosen such that the triplet phase is close to +90°, the intensity profile of the W-scan gives the greatest contrast as is illustrated in Figure
Figure 2-25 Dependence of the intensity 7W) of reflection h on the total phase @ ora: () as the reflection g is rotated from inside to outside the Ewald sphere A resonance phase ACP) is established that varies from 0° to 180° The primary and secondary reflections (h and g, respectively) are chosen such that the triplet phase @ripier is close to +90° at
Y = 0° The total phase ỉ„„„ C) = ai; + ACV) thereby gives rise to constructive interference and increased intensity for an initial phase of -90° or destructive interference and decreased intensity for an initial phase of +90°.
Synchrotron radiation provides minimum divergence and spectral width, which facilitates detection of the dynamical three-beam interaction occurring within a small angular range Edgar Weckert and Alexey Zozulya performed a three-beam experiment with 0.5888 A light at the Hamburger Synchrotronstrahlungslabor (HAS YLAB) facility of the Deutsches Elektronen-Synchrotron (DESY; Hamburg, Germany) for a pentaerythritol crystal marked with respect to the measured optical rotation given in
Section 2.2 The reflections (150) and g(114), referred to the coordinates in Table 2-4, were chosen so that the triplet phase yripier was Close to +90°, giving rise to destructive
88 interference The inversion related pair of reflections, h( 150) and ứ( 114), corresponded to a triplet phase @ripier close to -90° and yielded constructive interference The absolute directions were correlated to the measured optical rotation tensor in Figure 2-7.
Lai = out (deg) in-out (deg)
Figure 2-26 Intensity profiles of the reflection ? relative to that of the three-beam position as the reflection g is rotated from inside to outside the Ewald sphere for two triplet phases in crystalline pentaerythritol Left: (150) and g(114) gave a triplet phase
P iripter Close to +90° according to the coordinates in Table 2-4, yielding destructive interference Right: h( 150) and g( 1 14) gave a triplet phase @yripier Close to -90° according to the coordinates in Table 2-4, yielding constructive interference The absolute directions were correlated to the measured optical rotation tensor in Figure 2-7.
Two files are necessary for specifying the parameters of a calculation in Dalton.*!
The molecular geometry and basis set are described in a file with the extension, *.mol. For pentaerythritol, the molecule input was:
Pentaerythritol using the aug-cc-pVDZ basis
-4.17297 3.20605 -0.16366 jane ome byue Dake bine PIRGn IRC ngrs nine Pine Daze;The atom coordinates were determined by X-ray diffraction and are given in atomic units of Bohr radii ao (1 ag = 5.291071! m) The coordinates are transformed into a standard orientation that is particular to the program unless the instruction ‘Nosymmetry’ is included after the command ‘Atomtypes=3’, which additionally disables any symmetry constraints Polarizability elements were calculated both with and without the
‘Nosymmetry’ command The type of calculation and level of theory are specified in a file with the extension, *.dal For pentaerythritol, a frequency-dependent linear response calculation of the electric dipole, magnetic dipole, and electrical quadrupole moments in the length gauge was performed according to the instructions:
Elements of the position operator giving rise to an electric dipole transition moment are called DIPLEN Elements of the angular momentum operator giving rise to a magnetic dipole transition moment are called ANGMOM Elements of the operator giving rise to an electric quadrupole transition moment are called SECMOM From the values of the
Quantum CaÌCuÌatiOnS c5 5c St eerse 85
polarizability tensors given by the Dalton output, the rotatory strength of an oriented pentaerythritol molecule was computed using the Buckingham-Dunn formula.°
Absolute Orientation of Embedded Oscillators - ¿55c sec sss2 104
Introduction to Dyed CTYyS(AÌS .- án Hy HH T1 11 0g gyn 105
coordonnées par le fait méme de leur interposition entre les matériaux essentiels de l’édifice moléculaire, et tellement adaptées a sa structure, qu’elles participent à son arrangement régulier.”"*
“The agent of absorption, whatever it is, must be, to some extent, subordinate to the crystallization; and if it may reside in the non- crystalline coloring particles, it is at least necessary that their arrangement continues the crystalline medium to some extent, that they are symmetrically coordinated even by the occurrence of their interposition between the essential molecular building material, and so adapted to its structure, that they take part in its regular arrangement.”
However, without access to the diffraction and spectroscopic methods that would be available to succeeding generations of crystallographers, these questions remained outstanding Hematein doped strontium nitrate tetrahydrate crystals aptly became known as Sénarmont’s salt; few others were able to reproduce it.'”'® Pelikan noted hourglass (“sanduhrfửrmig”) inclusion along the crystallographic c direction, 'đ although this seems to be at odds with Sénarmont’s description of homogeneous (“disséminée avec continuité a l’intérieur d’un cristal”)'* coloration Regrettably, the eponymous crystals have not been reproduced since the 19" Century.!*!? p y
Hematein (1) dyed salts of potassium dihydrogen phosphate (KH›;PO¿,
I 424,921 potassium sulfate (KạSO¿, Pmcn),” ammonium dihydrogen phosphate((NH¿) H;PO¿, /422),” ? and sodium fluoride (NaF, Fm3m)TM* have been reported In a recent review, over 1,000 different dye inclusion crystals were cataloged.’ Many of these
107 host crystals admit guests only in particular facets yielding patterns of coloration that have been described as hour-glass, Maltese cross,” and bow-tie.'? The selective incorporation of impurities and the often concomitant habit change was for many years the only basis by which to infer an overgrowth mechanism Crystals of K2SO4 accommodate a great number of guests, especially sulfonated dyes, and were one of the model systems used by Buckley in his investigations of morphology change in dyed crystals He hypothesized that oxy anions, present at particular positions of the dye,”° substitute for corresponding anions on the crystal surface 282239
In 1930, the first dyed crystal was scrutinized by X-ray diffraction France and his co-workers concluded that a crystal of potassium alum (KAISOx4ằ12H;O, Pa3) was
108 unperturbed by its occluded guest, the bi-aryl azo dye, diamine sky blue (2).”' Despite the lack of structural evidence, France concurred with Buckley’s suggested recognition mechanism based on his own studies of habit modification,’ 233 but added,
“Apparently in the absence of exact information concerning the size and shape of ions and molecules and the magnitude of the forces effective at the crystal solution interfaces it is unlikely that accurate predictions can be made, at the present time, as to just what substances any given crystal will adsorb,”**
The concentrations of dyes in mixed crystals prepared by Sénarmont, Buckley, and
France were typically 1 part in 10-10”, making spectroscopy at visible frequencies a more viable method for their analysis than X-ray diffraction Qualitative observations of pleochromism in dyed crystals” were bolstered by the first spectrophotometric measurement made by Buckley in 1951.
Recently, researchers in the Kahr laboratory have done what France, in his time, could not By combining polarization spectroscopy of dyed K2SO, crystals with the calculated absorption anisotropy of dye molecules and a geometry matching routine, relative orientations of the guests were fixed in particular growth sectors The electric dipole transition moments of the dyes were determined using semi-empirical molecular orbital theory In most cases considered, sulfonate (-SO3) sulfur atoms in the dye molecules that were least squares fit to sulfate (-SO¿7) sulfur atoms in the crystal lattice yielded good fits between the computed and experimental dipole directions.*°?’ In another study, the adsorption energetics of a dyed crystal were modeled in which both the internal energy of a guest and the binding energy of the K2SO, surface were taken into
109 account While the results for most facets supported the sulfonate-sulfate substitution mechanism, at least one surface was poorly described by simple geometry matching.*®
When either the host or guest, or both the host and guest are chiral, there is an additional subtlety to the way in which a guest must be subordinate to the crystallization and adapt to the structure of the host Hematein (1), a natural derivative from logwood extract, has an absolute Š confi guration.” Kahr and co-workers recognized from photographs originally presented by Blattner et al.”” that hematein colored tetragonal
KH;PO¿ and (NH:)H;PO¿ crystals on only two of the four symmetry related prism faces.
It was further appreciated that although the host crystals are achiral (42m, Dằ¿), they possess diagonal mirror planes that generate enantiomorphous {010} and {100} faces.
These are discriminated by the chiral guest during growth.'?°!
Similarly, achiral crystals of KaSOx (mmm, Dạ„) have enantiomorphous {111} surfaces that emerge in the shape of a Maltese cross when the corresponding growth sectors are occupied by dye Crystals are stained when grown in the presence of an equilibrium mixture of conformationally chiral biaryl azo dyes.7>? In order to assess the enantioselectivity of adsorption, Kaminsky and co-workers set out to map the optical activity and circular dichroism in Evan’s blue (3) and trypan blue (4) dyed KằSO, crystals.*° Adjacent mirror image related sectors showed opposite signs of optical rotation
110 and circular dichroism, consistent with crystal symmetry However, when the crystals were turned over with respect to the light path, the sign of the signal also changed in the respective domains (Figure 3-1) This optical transformation is inconsistent with intrinsic optical rotation and circular dichroism since a simple two-fold rotation cannot
Figure 3-1 Patterns of intrinsic (top) and apparent (bottom) optical rotation and circular dichroism in crystals with sectors related by horizontal and vertical reflection planes. Blue and red represent opposite signs of the optical effects The patterns on the right hand side correspond to crystals that have been flipped 180° around a horizontal or vertical axis For intrinsic chiro-optical effects, the sign in any one sector remains constant, whereas for the anomalous effects, the sign changes. interconvert enantiomorphs.
The unanticipated optical phenomena were given the names anomalous circular extinction (ACE) when measured by differential circular polarization and anomalous azimuthal rotation (AAR) when measured in incident linearly polarized light Both effects can arise when strong oscillators are remotely separated from one another yet are oriented and rotated in the same way with respect to the eigenmodes of the host, a circumstance sometimes encountered in dyed crystals Unlike optical rotation and circular dichroism, anomalous azimuthal rotation and anomalous circular extinction are
111 insensitive to absolute molecular configuration, but are instead sensitive to the absolute orientation of adsorbed dye molecules with respect to the eigenmodes of the host crystal.” As illustrated for a two-dimensional crystal in Figure 3-2, incorporation of14 dopant within mirror-image related growth sectors (11) and (11) is selective For an equilibrium racemic mixture of adsorbate in the growth solution, the surfaces are enantioselective (Figure 3-2c,d) Moreover, the association of the dye with the crystal facets ((11) and (11)) is different in the two models; the long axis of the dye is parallel to the faces in (a) but is perpendicular in (b). ứp „09 = NI q § YW® (11) = 2D crystal with three growth
OTA 2Z ^^ sectors delineated im = Miller indices for 2D crystal (10) (19)
= chiral dye with transition moment
Figure 3-2 Schematic representations of two-dimensional crystals with three growth sectors, two of which ((11) and ( 11)) orient and overgrow dye In pair (a) and (b), it is not possible to determine the absolute orientation of the dye with respect to the eigenmodes of the host In pair (c) and (d), it is not possible to distinguish the absolute configuration of dye adsorbed onto mirror image host surfaces without a mechanism for detecting chirality in orienting media Figure reproduced from Ref 41.
Absolute Ori€n†af1ON HH TH HH HT in 120
isolated from that of the host for measurements made at appropriate wavelengths A circular extinction imaging microscope was used both for determining the absolute orientation of an embedded chromophore in a dyed crystal, and for detecting enantiomorphous twin domains in a crystal of a dye As an extension of the previous studies, the optical effects arising from chromophores that were oriented in a transparent host with well established enantiomorphous twinning were investigated Herein, anomalous circular extinction from lithium potassium sulfate (LiKSO,) crystals colored by Chicago sky blue (2/CSB; known to France as diamine sky blue), a dye with a chiral ground state conformation, is compared to those colored by pyranine (5/PYR), a dye with a rigid Z-system In addition, the dependence of anomalous circular extinction and anomalous azimuthal rotation on the linear anisotropy of the host is explored The principal tools used in assaying these effects are the tilter polarimeter (Chapter 4.2) used in the scanning mode and a circular extinction imaging microscope (Chapter 4.3).
Hexagonal crystals (P63) of LiKSO¿ are not only chiral”"”” but twin during growth, S2 859 senerating enantiomorphous {011} faces (Section 3.7.1.1) Merohedral twinning in LiKSO¿ is defined by twin planes both parallel (m // [001]) and perpendicular(m L [001]) to the unique axis, and by a 2-fold twin axis perpendicular to the unique axis(2 1 [001]), as illustrated in Figure 3-9 The effective point symmetry of the twin
122 ensemble is then 522 (Dạ,),°9 which is manifest in the hexagonal bipyramidal crystal mmm habit.
Figure 3-9 a) Idealized LiKSO, crystal habit, a consequence of enantiomorphous twinning, with shading representing the coloring by Chicago sky blue (2) and pyranine (5) b) Projection of a dyed LiKSO, crystal along the [100] (left) and [001] (right) directions Symmetry elements of the twin laws are shown in red Dotted lines indicate mirror planes and solid lines indicate 2-fold rotation axes.
The unadulterated crystals are very weakly birefringent, n, — n, = -0.0002 at 632.8 nm, and optically active, -2 °/mm measured along the [001] direction at 650 nm for an untwinned specimen.° Chicago sky blue (2) and pyranine (5) stain the {001} and {011} growth sectors of LiKSO., where the basal sectors are more darkly colored than the pyramidal ones (Figure 3-9).
From the dichroic ratio for light polarized along the extinction directions in
LiKSO¿ (n’ and n”), the relative orientation of the Chicago sky blue and pyranine electric dipole transition moments in the {011} sectors were calculated (6 = arctan[(@’/ đ”)!2I).
It is assumed that in the rigid molecule the excitation and emission dipoles are nearly
123 parallel The Chicago sky blue (2) dipoles are inclined at ~47° and the pyranine (5) dipoles at ~44° with respect to the n” vibration direction of the host However, as illustrated in Figure 3-3, we can not ordinarily determine for any one sector whether this deviation Gis clockwise, counterclockwise, or an average of the two from measurements of absorption in linearly polarized light as the electric field is constrained to projections on the eigenmodes These possibilities would lead to very different models of guest association with the surfaces of the host crystal.
The optical properties of dyed LiKSOx crystals were imaged in both linearly and circularly polarized light The assembled micrographs of Chicago sky blue (2) and pyranine (5) dyed LiKSO¿ are shown in Figure 3-9 and Figure 3-10, respectively The linear birefringence An is reported as a function of the sine of the phase factor 6, where ổ= 2Z#LAn/Â (L 1s the sample thickness; An = n’-n”, where n’” are refractive indices; A is the wavelength of incident light) The linear dichroism is given in terms of a hyperbolic tangent function that is proportional! to the scaled differential transmission 7 of linearly polarized light along the eigenmodes of the crystal (tanh(£) = (T’ - T”)(T’ + T”)) The circular extinction is recorded directly as the scaled differential transmission of right and left circularly polarized light (Up — J,)/Io).
Figure 3-10 Chicago sky blue-dyed LIKSO¿ crystals Images in the left column are made along the [100] direction (LZ = 0.68 mm); [001] is vertical Images in the right column are made along the [001] direction (Z = 0.38 mm) (a,b) Photographs in light polarized in the horizontal direction Dotted, rectangular enclosures are imaged below (c,d) Linear birefringence micrographs, ổ= 2nLAn/A (e,f) Linear dichroism micrographs, tanh(£ ) (T’-T”)\(T’ + T”) (g,h) Circular extinction micrographs, (Jp — J)/Ip Colors in (h) are not rotationally invariant and are therefore artifacts of an imperfect optical system.
Figure 3-11 Pyranine-dyed (5) LiKSO¿ crystals Images in the left column are made along the [100] direction (L = 0.58 mm); [001] is vertical Images in the right column are made along the [001] direction (ZL = 0.60 mm) (a,b) Luminescence is reproduced here because it is more illustrative than the weak yellow in transmitted light No polarizing elements were used in making these images Dotted, rectangular enclosures are imaged below (c,d) Linear birefringence micrographs, ổ= 2nmLAn/A (e,f) Linear dichroism micrographs, tanh(£) = (7 -T”)\/(T’ + T”) (g,h) Circular extinction micrographs, (7a — [,)/Io Colors in (h) are not rotationally invariant and are therefore artifacts of an imperfect optical system.
When viewed along the [001] direction, the {011} sectors showed negligible linear birefringence (Figure 3-10d and Figure 3-11d, respectively), and lacked a detectable circular extinction signal (Figure 3-10h and Figure 3-11h) Linear dichroism in the {011} sectors was modest in Figure 3-10f and ill defined in Figure 3-11f The linear dichroism, a consequence of the impurity sub-lattice, need not be constrained by the host crystal symmetry.” Along the [100] direction, the phase differences are very different in
Chicago sky blue (Figure 3-10c) and pyranine (Figure 3-11c) dyed crystals despite comparable sample thicknesses, although this is no guarantee that they are of the same order interference (see Section 3.5.2 below) Stress imposed by the dye can strongly perturb the birefringence, especially since the value in the pure material is small
(An(632.8 nm) = -0.0002°') Only when viewed along the [100] direction did the crystals showa strong differential transmission of circularly polarized light (circular extinction) near the absorption maximum of the dye (Figure 3-10g and Figure 3-11g) The resulting micrographs were divided into four regions with adjacent sectors having opposite signs, a consequence of the well-known enantiomorphous twinning both along and normal to the unique axis in LiKSQy, which has been analyzed in detail by Klapper and co-workers.”
This image was independent of rotation of the sample stage, the surest way to rule out linear biases in the optical train When the sample was inverted with respect to the light path, the sign of the effect changed, a phenomenon characteristic of anomalous circular extinction As shown in Figure 3-12, the dispersion of the signal occurs within the absorption band of the respective dye guests.
Chicago sky blue Pyranine py 0.25 0.12
Figure 3-12 Absorption (black line) and circular extinction (red and blue lines) spectra of Chicago sky blue and pyranine dyed LIKSO¿ crystals Discontinuity in the circular extinction line shapes at 485 nm for the pyranine-doped sample are a consequence of a large change in the tilt angle of the quarter-wave plate of the microscope.
Generally, an object must lack a center of symmetry to be sensitive to the handedness of light (Chapter 1.3.2) In the case of ACE-active materials, the anisotropy of the host contributes a linear component to the polarization state of light, producing orthogonal elliptically polarized states from right and left circularly polarized light The interaction of a rod-like (centrosymmetric) absorbing dipole with the two elliptical light forms need not be the same as long as the transition moment of the dye does not align
128 with an eigenmode of the medium Figure 3-13a is a schematic of an idealized case of anomalous circular extinction arising in a birefringent sample with embedded oscillators. fe) lal < i, lal, > O
Figure 3-13 Model of anomalous circular extinction (a) Crystal is treated as if it was composed of two independent portions that contribute only a 7/2 phase shift and only a strong oscillator (b) Left (blue) and right (red) circularly polarized light are converted into linearly polarized light at +45° and -45°, respectively Eigenmodes are indicated by vertical and horizontal dotted lines The fast vibration direction is assumed to be vertical. (c) Linearly polarized light is differentially attenuated from interaction with an inclined dipole, black ellipsoids inscribed with double-headed arrows, giving rise to a circular extinction signal.
Although over simplified, the model is in keeping with the formal method of R Clark
Jones for describing a crystal with simultaneous optical properties (Chapter 4.1) The crystal is modeled by two layers that contribute a phase shift and an oscillating dipole,
Experimental nh nh
3.7.1 Dyed Lithium Potassium Sulfate Crystals
Dyed, hexagonal crystals (P63) *°? of LIKSO¿ were grown by slow evaporation at room temperature from aqueous solutions (10% Min Chicago sky blue (2, Colour Index
No 24410); 10° M in pyranine (5, Colour Index No 59040)°*°) containing equimolar quantities of LiaSOa and KaSO¿a The resulting crystals grew by spontaneous nucleation such that they were oriented with their unique [001] axes perpendicular or parallel to the bottom of the crystallization dishes The hexagonal bipyramidal habit is a consequence of enantiomorphous twinning both perpendicular and parallel to [001] The Chicago sky blue-doped crystals contained an average of 8 x 10° moles of dye per mole of LiKSO¿.
The {001} growth sectors were more heavily colored whereas the {011} growth sectors were less optically dense by a factor of 4 (Amax, crystal = 604 nm) The pyranine-doped
140 crystals contained an average of 2 x 10° moles of dye per mole of LiKSOx The {001} growth sectors were more optically dense than the {011} growth sectors by a factor of 2 Both the acidic (5, Amax, crystal = 408 nm) and the basic (Amax, crystal = 488 nm) forms of pyranine were identified in the crystals grown from water.
Small as-grown crystals (0.005-0.02 g) were fixed to the end of a glass slide with a thermoplastic polymer (Crystalbond 509; Electron Microscopy Sciences) The crystal was pressed into the polymer softened over the vent of a heat gun (Master Appliance Corp., model VT-750C) Once in place, the polymer and crystal were iteratively heated and pressed with another glass slide until the crystal was evenly embedded Crystal plates were thinned to 0.4-0.7 mm by gentle abrasion on ground glass and polished with light, swift strokes across fine aluminum grit (0.3 4m) paper The polymer was then dissolved by submerging the glass slide in reagent grade acetone for about a half hour, until the crystal was free The process was repeated for the other side of the crystal.
3.7.1.3 Linear Birefringence and Linear Dichroism
Linear birefringence and linear dichroism images were made using the rotating polarizer method”? as embodied in the MetriPol microscope (described in Chapter 4.4)
141 available from Oxford Cryosystems.Š Linear birefringence images were collected at wavelengths far from the absorption maxima of the dyes, and linear dichroism images at wavelengths near the absorption maxima of the dyes to the extent it was possible with the available filters.
Anomalous circular extinction was measured as the differential transmission of right and left circularly polarized light using the circular extinction imaging microscope described in Chapter 4.3 Micrographs of stained LIKSO¿ samples were made at wavelength within the absorption band of the dye molecules Polarized absorption spectra were measured with the 4/4 plate disengaged.
Anomalous azimuthal rotation micrographs were generated using the High
Accuracy Universal Polarimetry method adapted with a translation stage, described in Chapter 4.2 Measurements were made with 635 nm and 670 nm laser sources.
3.7.2 1,8-Dihydroxyanthraquinone Crystals Ÿ http://www.metripol.com/
Large (0.5 cm x 0.5 cm x 100 Um), square, orange plates were formed by slow evaporation of 50:50 (v:v) acetone/acetonitrile solutions at room temperature The solubility of 1,8-dihydroxyanthraquinone is 4 mg/mL in acetone and 1.6 mg/mL in acetonitrile Crystals were removed from the growth solution and dried on a tissue The crystals were often raised in the center and along the borders between lateral growth sectors as seen in the optical density in Figure 3-5a, but were nevertheless well suited to optical experiments.
3.7.2.2 Linear Birefringence and Linear Dichroism
Linear birefringence images were made using the rotating polarizer method” as embodied in the MetriPol microscope (Chapter 4.4) available from Oxford Cryosystems.
Images were collected at 670 nm Polarized absorption spectra of the crystals were obtained with a SpectraCode Multipoint Absorbance Imaging (MAI-20) Microscope.
Circular dichroism was measured as the differential transmission of right and left circularly polarized light using the circular extinction imaging microscope described in
Chapter 4.3 Micrographs were measured at 515 nm, corresponding to a shoulder in the absorption spectrum.
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POLARIMETRY AND POLARIZED LIGHT MICROSCOPY
Discussed herein are contemporary methods for measuring the principal quantities comprising classical crystal optics in organized media: optical rotation, circular dichroism, linear birefringence, and linear dichroism in organized media Section 4.1 is an introduction to the matrix method of intensity analysis applied in the various techniques Section 4.2 is a description of a modified High Accuracy Universal
Polarimetry (HAUP)' method for measuring optical rotation, the ‘tilter’ method.” Section 4.3 is an introduction to a custom built microscope, U-pol,? for imaging circular dichroism Section 4.4 is an explanation of the MetriPol*? technique for imaging the magnitudes and directional dependence of signals associated with linear birefringence and linear dichroism.
4.1 INTENSITY EXPRESSIONS USING THE JONES FORMALISM
Changes in the polarization state of light transmitted through a series of optical components are difficult to evaluate al gebraically.° Fortunately, several elegant alternatives have been devised for which an explicit computation of intermediate states is avoided The Poincaré sphere’ representation employs a geometrical approach and is shown in Figure 4-1.
Figure 4-1 The Poincaré polarization sphere Linear horizontal (H) and vertical (V) states occupy opposite positions along the meridian Circular right and left states are seated at opposite poles Various admixtures of linear and circular polarization are given by intermediate elliptical forms The sphere has unit radius Figure reproduced from Ref 9.
In this polarization map, orthogonal light forms reside at opposing positions on the equator of a globe It is probably not a coincidence that Henri Poincaré invented this representation of polarized li ght while he was director of the Bureau des Longitudes.°
Linear states fall on the equator and circular states at the poles In Figure 4-1, the lower hemisphere has clockwise rotation and is defined as positive A point P on the map is specified by its longitude 22 and latitude 2@, which are correlated to the azimuth 4 and ellipticity, tan(F@pr), of an elliptical polarization state Alterations to the state at point P from interactions with a series of retardation plates can be traced, step-wise, on the surface of the sphere.” The Mueller and Jones calculi are alternative methods that employ matrices in the linear transformation of light through an optical train Both describe the incident light by a vector V and optical devices by matrices M The emergent light V’ is
152 determined by a succession of scalar products with the elements M in the order encountered:
Figure 4-2 Matrix method for tracking the polarization state of light through a series of optical elements Anjou, are vectors representing the polarization state of the incident and transmitted light forms, M, are matrices representing optical components and Myampie describes the crystal in the light path.
The Mueller calculus uses the Stokes vector definition of light, characterized by a four element column vector:
9A Ww D> where A is the intensity, B is the proportion of horizontal polarization, C the proportion polarized at +45°, and D is the proportion that is right circularly polarized Optical components in the light path are described by empirically determined parameters in 4 x 4 Mueller matrices All Mueller elements are real and have units of intensity The Jones approach is more compact as it is based on the complex phase description of light introduced by Poincaré.’ Light forms are described by two element vectors and optical