the interaction potential 
 of spherical colloids can be tuned to 
 mimic the potentials that drive certain atomic and ionic processes . this allows for direct visualization of phase transitions and solid 
 state phenomena difficult to observe at the atomic level , such as 
 crystallization , melting , and dislocation dynamics . in analogy to colloidal atoms  the term  colloidal molecules  
 has been suggested to describe small nonspherical 
 clusters of particles that represent molecules and their interactions 
 at the mesoscale . in addition to being of interest as model systems , 
 the potential applications of these shape - anisotropic particles include 
 functional materials , such as colloidal crystals with novel optical 
 properties and self - assembly . of particular interest in this context 
 are the colloidal counterparts 
 to chiral molecules . available synthetic approaches for colloids , 
 however , generally yield particles that are either spherical or highly 
 symmetric . assembly of spherical colloid building blocks 
 is generally nonspecific , yielding a range of aggregate sizes and 
 shapes . only a few methods have been published that can produce large 
 numbers of colloids with uniform , programmable shape , and in enantiopure 
 samples . among the approaches for 
 chiral separation that are suitable for 
 study in the colloidal regime are active and passive separation techniques 
 that rely on the hydrodynamic interaction between the particles and 
 the solvent , e.g. in shear flow or using active propulsion mechanisms . the feasibility of using shear flow for enantiomer separation , which in theory should be possible but has so 
 far not been realized on the molecular scale , has been demonstrated 
 using 16 m - long , right - handed helically shaped leptospira biflexa flab bacteria . it has also recently been reported that flow through a chiral microfluidic - channel can be used to separate 
 racemic mixtures of 6-m - sized ( chiral ) particles produced 
 with photolithography . it is not yet clear whether either effect can 
 be observed at the molecular scale . in 1978 baranova and zeldovich predicted the  propeller effect  
 in which a racemic 
 mixture of chiral molecules is separated into left and right fractions 
 when subjected to a radio frequency electric field of rotating polarization . the applied electric field couples to the electric dipole moment of 
 the molecule and causes the molecules to rotate . opposite enantiomers 
 will  screw in opposite directions and thus separate 
 along the direction about which the electric field rotates . baranova 
 and zeldovich estimated the propeller effect for molecules 
 by assuming a rotating electric field of 0.3 mv / m at 100 mhz and deduced 
 that this should give rise to a 7% enantiomeric excess per centimeter 
 of sample vessel after 27 h for molecules with a permanent 
 electric dipole moment of 4 d. the propeller effect has thus far not 
 been demonstrated experimentally . herein , we demonstrate the 
 propeller effect with a colloidal model 
 system by separating a racemic mixture of magnetic dipolar chiral 
 colloids . we first describe a refinement of our previously published 
 fabrication process to obtain 10 chiral dipolar colloids . we verify the handedness of the 
 colloidal solutions with differential circular scattering experiments 
 and then describe the experimental observation of the separation of 
 a racemic mixture via the propeller effect . an exact analytical result 
 that describes the motion of dipolar propeller - shaped colloids as 
 a function of the externally applied torque is given , and we discuss 
 the significance of this study for chiral molecules . a number of strategies 
 to produce colloidal molecules have been developed , including geometrical 
 confinement ( e.g. , by microwells or emulsion droplets ) , cluster formation 
 through the application of external fields or the inclusion of magnetic 
 patches , controlled surface nucleation or phase separation approaches , 
 and use of molecular scaffolds for selectively forming bonds between 
 particles . most of these approaches tend to yield mixtures 
 of different clusters with high symmetry , due to the fact that colloids , 
 unlike atoms , generally lack directional interactions . recently , colloids 
 with up to seven chemically functionalized patches that bind selectively 
 to complementarily functionalized particles have been realized . since their production process is based on first 
 assembling clusters of small particles using the emulsion droplet 
 technique , the resulting patches still display the high symmetry characteristic 
 for syntheses employing geometric confinement . beyond its original 
 application to clusters of spheres , the term  colloidal molecule  
 has been applied to monolithic colloids in the form of rods , cubes , 
 and more complicated geometries . to this day relatively large magnetic dumbbell colloids that self - assemble into 
 helical chains as a mesoscopic counterpart to chiral polymers have 
 been produced , but to our knowledge single 
 chiral micrometer - sized colloidal particles have not been reported 
 as a model for chiral compounds . in this work we grow billions 
 of colloids with defined chirality , 
 and in - built dipole functionality , via glancing angle deposition ( glad ) . glad is a physical vapor deposition ( pvd ) technique that can grow 
 close to micrometer - sized particles with a variety of shapes and allows 
 for the inclusion of a number of different materials , and thus different 
 functionalities , in a one - step process . this technique has been used before by our group and others 
 to 
 produce magnetically actuated microhelices . in the past however , the magnetic layer was added by first releasing 
 the particles from the wafer , redepositing them on a flat surface 
 and subsequently coating them with a thin layer of cobalt by thermal 
 evaporation . in our current setup we can include a magnetic section 
 during growth , which significantly increases the yield and uniformity 
 and thus leads to reproducible samples of high monodispersity.figure 1(a ) schematic 
 of the glad technique and ( b ) sem images of a wafer 
 containing helices representative of those used in this work , as well 
 as ( c ) left- and ( d ) right - handed chiral magnetic particles and ( e ) 
 the energy - selective backscattered image ( lower right ) highlights 
 the magnetic ni inclusion . scale bar in ( b ) is 2 m ; ( c ) and 
 ( d ) are 0.5 m ; and ( e ) is 1 m . ( a ) schematic 
 of the glad technique and ( b ) sem images of a wafer 
 containing helices representative of those used in this work , as well 
 as ( c ) left- and ( d ) right - handed chiral magnetic particles and ( e ) 
 the energy - selective backscattered image ( lower right ) highlights 
 the magnetic ni inclusion . scale bar in ( b ) is 2 m ; ( c ) and 
 ( d ) are 0.5 m ; and ( e ) is 1 m . the material that is used to grow the particles is then deposited 
 onto the substrate by ( electron beam ) physical vapor deposition at 
 grazing incidence with   85 ( see figure 1a ) . the growth of helices is accomplished by azimuthal 
 rotation of the wafer during the deposition process . the chirality 
 and pitch of the particles can be easily varied by adjusting the rotation 
 direction and speed at a given vapor flux . a ferromagnetic material is incorporated by including a nickel section , which is relatively 
 stable in aqueous solution , into the growth of the colloid . chemical 
 functionality is obtained by growing the colloid from oxides that 
 permit silane coupling chemistry . the number of helices that are produced 
 in one batch in this manner is of the order of 10 on 
 a 2-in .- wafer . sonication of a wafer piece may release the particles 
 from the wafer ( into solution ) . sem images of the wafer and of released 
 right- and left - handed helices can be seen in figure 1b  e . total scattering intensity ( first row ) and the differential 
 scattering 
 signal of circular polarized light of ( a ) left- and ( b ) right - handed 
 helices , as well as ( c ) achiral rod - shaped colloids of the same size ; 
 with corresponding sem images . the dots correspond to the experimental 
 data , whereas the solid lines show the calculation results . each solution 
 had a concentration of approximatly 0.5 pm . in order to 
 characterize the handedness of the colloidal solutions , we resort 
 to scattering experiments , as the colloids do not contain a chromophore 
 or color center . the differential scattering of circularly polarized 
 light was first demonstrated experimentally in 1982 by bustamante 
 et al . who measured the polarization - sensitive 
 scattering of suspensions of helical octopus sperm heads . they showed 
 that the chirality of scatterers clearly manifests itself in circular 
 differential scattering spectra . its measure 
 is the circular differential scattering intensity ( cdsi ) , defined 
 as:1here il , r are the detected scattered 
 intensities when left- and right - circularly 
 polarized light are , respectively , incident upon the sample . because the circular differential scattering 
 intensity is a chiral observable it can 
 serve as a diagnostic to ensure that colloidal solutions obtained 
 from helices with opposite handedness grown on different wafers are 
 enantiomers . indeed , since the octopus sperm used in the previous 
 study is only available in one helicity and geometry , cdsi has previously 
 not been validated for pairs of colloidal enantiomers . tio2 screws of both helicities 
 were grown on 300 nm sio2 beads with a helical pitch of 
 250 nm and with 4 to 5 turns . as an achiral control we also 
 grew tio2 rods of the same height but produced with fast 
 azimuthal rotation . the geometrical parameters of the helices were 
 verified by scanning electron microscopy ( sem ) images of the samples 
 ( figure 2 , details in table si1 in the supporting information [ si ] ) . the results from 
 the total scattered intensity and the circular differential scattered 
 intensity measurements of the helical colloids are shown in figure 2 . the tsis decrease monotonically with increasing 
 scattering angles for angles greater than the peak position in all 
 three samples . the differences in the absolute values are mainly due 
 to slight differences in the concentrations . as expected , the total 
 scattering intensity does not differentiate between opposite helicities . in contrast the cdsi signals of the two enantiomers are approximately 
 equal in shape and opposite in sign . the cdsi signal for the achiral 
 rods vanishes for all scattering angles , as expected . ( a ) schematic of magnetic 
 dipolar colloidal helices in the presence 
 of a rotating magnetic field . the opposite enantiomers ( red and green ) 
 possess a magnetic dipole moment ( blue arrow ) that aligns and thus 
 rotates with the applied rotating magnetic field . the helices will 
 align such that their drag is reduced , and hence they propel in opposite 
 directions . ( b ) tracks of right- ( red ) and left - handed ( green ) particles 
 in a magnetic field of 20 g , rotating at a frequency of 20 hz , over 
 a time interval of 20 s. scale bar is 20 m . ( c ) relative intensity 
 change with time of the scattering intensity across the width of a 
 5 mm cuvette filled with a suspension of right- or left - handed colloids 
 in a rotating magnetic field of a strength of 50 g and a frequency 
 of 40 hz . the colloid concentrations are on the order of 10 m. in the lower left corner are representative images of a cuvette 
 containing left - handed enantiomer after 0- and 10-min field application . there is a clear decrease in intensity at the right of the cuvette 
 as the helices swim to the left . the solid lines represent theoretical calculations of the 
 scattering 
 intensity and are based on the algorithm proposed by bustamante et 
 al . which is described in the si . . discrepancies 
 between theory and experiment for small angles can be traced back 
 to the fact that , due to experimental limitations at low angle scattering 
 ( las ) , the detector observes part of the incident beam , but overall , the cdsi signals are sensitive 
 to the geometry and thus serve as a diagnostic for the chirality of 
 the solutions . in what 
 follows , racemic colloidal suspensions of magnetic chiral helical 
 colloids are prepared and used for the chiral separation experiments . 
 in our colloidal analogue of the baranova and zeldovich s 
 proposal , the electric dipolar molecule 
 driven by a rotating electric field is replaced with a magnetic dipolar 
 colloid driven by a magnetic field . the helices are magnetized orthogonally 
 to the helices long axes by placing the wafer into a strong 
 electromagnet before the helices are released from the wafer into 
 solution . figure 3a schematically shows how 
 application of a homogeneous , rotating magnetic field couples to the 
 magnetic moment of the helices and causes them to rotate in solution . because the drag on the side of the helix is larger , the 
 helices will align to minimize drag , and be propelled along the normal 
 axis of the plane defined by the rotating field . the direction of 
 translation for a helix of a given chirality is the opposite of its 
 enantiomer . for a racemic mixture tracks of screw propellers are marked in the optical images of 
 figure 3b . to distinguish both helicities under 
 bright - field illumination , right- and left - handed colloids were made 
 out of different materials with different indices of refraction ( silica 
 and titania , respectively ) , and slightly different geometries were 
 used : the left - handed screws had a slightly smaller diameter and were 
 slightly longer than the right - handed ones . the left- and right - handed 
 diametrically magnetized helices are driven by a magnetic field of 
 20 g at a frequency of 20 hz in water . although the  swimming behavior of the microhelices has already been demonstrated in previous 
 publications , this is , to our knowledge , the 
 first time that an ensemble of such colloids has been manipulated , 
 thus enabling their application as model colloidal molecules . the possibility to extend this separation principle to macroscopic 
 sample volumes was demonstrated by tracing the scattering intensity 
 across the width of a cuvette filled with a suspension of either left- 
 or right - handed colloids ( for this experiment exact enantiomers were 
 used ) which was exposed to a rotating magnetic field that should propel 
 the particles to one side of the cuvette . it is clearly visible that a reduction in intensity 
 on one side with a simultaneous slight intensity increase on the opposite 
 side takes place within a few minutes and that right - and left - handed 
 helices separate out in opposite directions . to describe the 
 motion of the helices we introduce the vector k that defines the direction and sense of the 
 driving magnetic field2 view along the axis of a helix with remnant magnetization mrem in a magnetic field b0 rotating at the rotational velocity . in this case k points out of the page . the b field illustrated in figure 4 , rotating in the xz plane such 
 that it moves 
 from + x to + z , has a k that points along the y direction , out of the page this choice of k means that right - handed helices will translate parallel 
 to k , while the left - handed particles 
 translate antiparallel to k. in the 
 images , the right - handed colloids ( red ) move in the direction of k and left - handed enantiomers ( green ) move 
 in the opposite direction . the movement perpendicular to k is due to interactions with the wall and was not 
 taken into account in the determination of the translational speeds 
 ( see figure 6 ) , since 
 it is a surface effect that causes no enantiospecific separation . the corresponding video of the chiral separation process can be found 
 in the si . overall , about 60% of colloids in a batch 
 appear to be functional , 
 i.e. they rotate with the magnetic field and exhibit translation parallel 
 to the axis of rotation . the remaining colloids are either structurally 
 incomplete or are found in clusters of more than one particle . at 
 high concentrations ( on the order of 1 pm ) the sample tends to agglomerate 
 due to magnetic interactions within less than half an hour , thus it 
 is difficult to determine the efficiency of the chiral separation 
 process over long time scales . nevertheless , within the field of view 
 ( 135 m  180 m ) , 63% of the right - handed enantiomers 
 leave the observed area through the top quarter of the frame and 9% 
 through the bottom quarter , while 54% of the left - handed enantiomer 
 exit the image through the bottom and 19% through the top quarter . diffusion is negligible in the present colloidal system , and the separation 
 process is limited solely due to structural deficiencies and agglomeration 
 effects in part of the sample , whereas in molecular systems agglomeration 
 would be negligible and diffusion is likely to be a major limiting 
 factor . the motion of the magnetic chiral colloid is dictated 
 on one hand 
 by the magnetic torque applied by the external magnetic field b acting on the particle s moment m3and on the other hand by the viscous drag 
 force that acts on the particle4where r is the colloid s 
 characteristic size , x is a scale - free geometry factor 
 that depends on the shape ( for a sphere x = 8 ) , 
  is the fluid s viscosity , and  is its speed 
 of rotation . at low velocities the particle will couple synchronously 
 with the field and maintain constant rotational speed  =  , 
 with the two torques balanced5where ( t  
  ) is the phase lag between the moment and field ( see figure 4 ) . the rotational speed at which the viscous drag 
 exceeds the magnetic torque is the step - out frequency given by6where mrem is 
 the remnant magnetization . above the step - out frequency the colloid 
 undergoes a complicated slipping motion with the applied field . using the boundary condition7 in eq 5 one obtains 
 the following analytic expression for the particles rotational 
 speed ( which is plotted in figure 5a),8where c = 
 ( x)/(mremb0 ) . the forward velocity of the colloids is 
 proportional to its angular velocity9here  is the rotation translation 
 coupling constant or propulsion efficiency and its upper limit is 
 set by the pitch of the helix . ( a ) 3d plot of the magnetic particle s 
 rotational velocity 
  with respect to the field s rotational velocity  
 and time t and ( b ) plot of the frequency - dependent 
 time - averaged value of . figure 5 shows a 3d plot and a time - averaged 
 plot of the particle s angular velocity dependence on the magnetic 
 field s rotational frequency . as one can see ,  is locked 
 to  up to the step - out frequency , beyond which the average 
 speed decreases rapidly . the result agrees well with a numerical study , that solved the corresponding problem for higher 
 reynolds numbers ( including a higher - order inertial term ) . forward velocity 
 of the chiral colloids with varying frequency 
 of the rotational magnetic field for magnetic field strengths of 20 
 g ( blue squares ) and 50 g ( red circles ) . the dotted line is a linear 
 fit of the data below the step - out - frequency ( 25 hz for 20 g and 70 
 hz for 50 g ) . figure 6 shows 
 the speed of the particles as a function of the rotational frequency f = /2 for two different magnetic field strengths , 
 20 and 50 g. the experimentally determined velocity distribution is 
 rather broad , especially near ( and beyond ) the step - out - frequency , 
 as the distance of each colloid to the wall differs in addition to 
 variations of the shape and thus the value for . however , overall , 
 the data qualitatively match the theoretical prediction shown in figure 5 . it follows that this colloidal model system can 
 thus be used to determine numerical values for several parameters 
 that baranova and zeldovich could only assume for molecules . for example , from the slope of the line in the 
 linear regime one obtains a propulsion efficiency of  = 7.0 
  0.2 nm / rad , which corresponds to about 8% of the theoretical 
 upper limit set by the helices pitch . the geometry factor x can be estimated from the 
 value of the step - out frequency according to eq 6 using the literature value for the remnant magnetization of bulk 
 nickel . taking into account that only 
 about 10% of the particles volume is ferromagnetic , this yields 
 a value of approximately x  600 . a possible explanation 
 for this is that , unlike for spheres and other highly symmetric shapes , 
 for chiral particles x includes a term for the rotation  translation 
 coupling which leads to an additional torque on the colloid . this 
 effect , however , is rather small as the relationship between x and the mobility matrix defined by the relation10shows:11c defines 
 the 
 magnitude of the translation  rotation coupling and is in all 
 practical cases considerably smaller than da . thus , the more likely reason for the discrepancy 
 between the geometry - factor for a sphere and our colloidal helices 
 is the fact that nickel microparticles have a lower remnant magnetization 
 than the bulk metal value that was used in the calculation . the effect any brownian motion has on the orientation of the colloids 
 has not been taken into account in eq 8 . an 
 estimate of thermal effects is obtained by comparing the strength 
 of the dipolar coupling to kt12which is about 10 in the present 
 experimental system . the corresponding parameter for the propulsion 
 of chiral molecules by an electric field in the baranova zeldovich model is13and has a value of 10 for 
 the parameters baranova and zeldovich assume for molecules . the difference highlights the additional challenge faced if the propeller 
 effect is to be used for the separation of chiral molecules . we have shown that glancing angle physical vapor deposition can 
 be used to produce large numbers of chiral colloids in good yields . these can be used as  colloidal molecules  to investigate 
 physical phenomena that are difficult to observe experimentally at 
 the molecular level . we were able to demonstrate that the differential 
 scattering can be used to characterize chiral colloidal suspensions . an analytical solution that describes 
 the motion of dipolar rotors as a function of the externally applied 
 torque is derived . now , that the propeller effect has been established 
 at colloidal length scales , it is of interest to pursue its realization 
 with chiral molecules . for this , the validity of continuum hydrodynamic 
 models at molecular scales as well as the randomizing force of brownian 
 motion will have to be considered . the helices are grown using glad . in 
 order to obtain well - defined regular helices across entire wafers , the shadowing growth was facilitated by first depositing a seed layer 
 of silica nanoparticles . monodisperse silica particles with a diameter 
 of about 400 nm were synthesized according to a modified stoeber method and surface - treated with allyltrimethoxysilane . a dispersion of these particles in chloroform 
 was dropped onto the surface of a langmuir the patterned wafer was then transferred 
 into the vacuum system for glad electron beam evaporation at 10 mmhg . the deposition angle was 85. 
 for the magnetic colloids a ni - layer with a thickness of about 200 
 nm was included in the structure , the helical tail was grown with 
 either silica or titania . a diode - pumped solid - state laser 
 with an optical output power of p = 100 mw ( cw ) and 
 a wavelength of  = 532 nm was used as a light source . after 
 passing an optical chopper the light was first linearly polarized 
 and then sent to a photoelastic modulator ( pem ) , which modulates between 
 left- and right - circular polarization at 50 khz , before it 
 is incident on a cylindrical scattering cell that contains the colloidal 
 solution . the scattered light was detected using a photomultiplier 
 tube mounted 
 on a precision goniometer with an angular resolution < 1. 
 the distance between the pmt and the center of the sample cell was d = 10 cm , and together with an entrance aperture of 1.5 
 mm of the pmt this resulted in an angular resolution of 0.86. the detector signal was electronically processed by two lock - in - amplifiers 
 ( lia ) locked to the modulation frequency of either the chopper or 
 the pem . while the pmt moved around the sample in an arc of 1-steps , 
 50 data points were taken for every angular position of the detector 
 and averaged . the total scattering intensity ( tsi ) can be derived 
 from the lia locked to the chopper frequency , whereas the difference 
 in the scattering between the circular polarization states is detected 
 by the second lia . the circular differential scattering intensity 
 is calculated according to:14here pem = /2 is the retardation introduced by the pem and j1(x ) the bessel function of 
 the first kind . for the measurements of the propulsion speeds and the chiral 
 separation 
 experiments , left- and right - handed colloidal particles , made out 
 of silica and/or titania and including a magnetic nickel strip with 
 a height of about 200 nm , were magnetized diametrically in an electromagnet 
 producing a magnetic field of about 1.8 t. they were dispersed in 
 water by sonicating parts of the wafer for 1 min and mixed in a ratio 
 of 1:1 for separation experiments to produce a racemic mixture . the 
 enantiomers used for imaging the separation process under the microscope 
 were grown from different materials ( silica and titania ) such that 
 the different refractive indices give rise to a distinguishable brightness 
 under bright - field illumination . for these experiments the colloidal 
 solution ( concentration roughly 10 m ) was dropped 
 into a gene frame ( thermo scientific ) on a coverslip to minimize drift 
 due to evaporation . the gene frame was then inserted into the center 
 of a custom - built three - axis water - cooled helmholtz coil which can 
 produce rotating magnetic fields in 3d of up to approximately 100 
 g. the movement of the particles was observed in a microscope ( zeiss 
 observer ) , and the paths of the left- and right - handed particles were 
 analyzed using the software imagej . for 
 the determination of swimming velocities for each setting at least 
 18 particles were tracked over a minimum time period of 20 s. for bulk experiments , enantiopure solutions of colloidal helices 
 with a concentration of roughly 10 m were used . 
 here left- and a 5 mm cuvette with a clear bottom was 
 filled with the solution and placed inside the helmholtz coils . it 
 was illuminated through the bottom with a 555 nm led . while it was 
 subjected to a rotating magnetic field ( 50 g , 40 hz ) , pictures were 
 taken from the side every minute with a canon eos 600d camera . to 
 obtain the intensity profiles shown in this work the intensity of 
 the images was integrated over the height of the cuvette for x increments ( width ) of 0.06 mm and the intensity change 
 relative to the starting value
chiral 
 molecules play an important role in biological and chemical 
 processes , but physical effects due to their symmetry - breaking are 
 generally weak . 
 several physical chiral separation schemes which could 
 potentially be useful , including the propeller effect , have therefore 
 not yet been demonstrated at the molecular scale . 
 however , it has 
 been proposed that complex nonspherical colloidal particles could 
 act as  colloidal molecules  in mesoscopic model systems 
 to permit the visualization of molecular phenomena that are otherwise 
 difficult to observe . unfortunately , it is difficult to synthesize 
 such colloids because surface minimization generally favors the growth 
 of symmetric particles . 
 here we demonstrate the production of large 
 numbers of complex colloids with glancing angle physical vapor deposition . 
 we use chiral colloids to demonstrate the baranova and zeldovich 
 ( baranovan . 
 b.zeldovichb . 
 y.chem . 
 phys . 
 lett.1978 , 57 , 435 ) propeller effect : the separation of a racemic 
 mixture by application of a rotating field that couples to the dipole 
 moment of the enantiomers and screw propels them in opposite directions . 
 the handedness of the colloidal suspensions is monitored with circular 
 differential light scattering . 
 an exact solution for the colloid s 
 propulsion is derived , and comparisons between the colloidal system 
 and the corresponding effect at the molecular scale are made .