synthetic swimming 
 devices possess the ability to produce enhanced 
 motion in a fluid environment , beyond the translations and rotations 
 usually present due to brownian phenomena .
these devices have potential 
 to function as targeted drug delivery systems , perform tasks such 
 as minimally invasive surgery , and transport 
 materials within microfluidic devices .
most devices currently capable of producing autonomous propulsion 
 rely on asymmetrical decomposition of dissolved fuel molecules , catalyzed 
 by an asymmetric distribution of catalyst at their surface .
this process 
 is thought to produce propulsion by a variety of mechanisms , including self - phoretic phenomena resulting from a localized concentration gradient , and 
 bubble release where nanobubbles of oxygen 
 detaching from the catalytic surface impart some of their momentum 
 to the particle .
extensively studied examples of these devices include 
 janus spheres , where one hemisphere of a colloid is coated with a 
 thin catalytic layer ( usually platinum , see figure 1 ) and also bimetallic nanorods , comprising 
 two contacting solid cylindrical segments , one of which displays catalytic 
 activity .
recently , simulations at a mesoscopic 
 level have been used to model the propulsion , including self - thermophoresis and self - diffusiophoresis .
cordova - figueroa 
 et al . modeled janus sphere swimmers 
 as a motor particle that generates a nonuniform concentration distribution 
 of reaction products via an asymmetric constant flux from the swimmer 
 surface .
the speed at which the swimmers moved was proportional to 
 the flux or the square root of the flux depending on the flux rate , 
 when the reaction products were otherwise not present in the surrounding 
 medium .
recently , research has turned attention to the challenge 
 of how 
 to control the propulsive force such materials generate in order to 
 perform useful tasks such as moving cargo within a microfluidic device . 
 achieving directional control
has mainly been achieved by the incorporation 
 of magnetic materials into the swimming device structure . to date , 
 this approach has allowed janus spheres , rods , and rolled up tubes 
 ( a third category of swimming devices which decompose fuel inside 
 a tube causing bubbles to squirt from one end ) , all to be steered by external magnetic fields , resulting in proof - of - concept 
 cargo transport demonstrations .
speed modulation independent 
 of direction control has also been achieved , for example using temperature or light stimuli .
however , considerably less experimental attention has been given 
 to the challenge of navigating swimming devices to a target with full 
 autonomy , despite the fact that external field - based methods somewhat 
 negate the benefits of the autonomous propulsion mechanism .
the first experimental report suggesting the 
 viability for full autonomy showed the slow accumulation of nanorod 
 swimmers in high fuel concentration regions , an example of synthetic 
 chemotaxis . in this scheme ,
autonomous 
 velocity changes due to a spatial fuel concentration gradient resulted 
 in statistical migration .
we have also recently investigated an extension 
 to this idea , showing that swimming devices containing responsive 
 size - changing hydrogels can also perform chemotaxis by modulating 
 their rotation rate in analogy to the run and tumble strategy used 
 by bacteria . a janus sphere consisting 
 of a thin platinum coating on one hemisphere 
 of a polymer bead .
the asymmetric decomposition of h2o2 to water and oxygen is thought to produce propulsion through 
 either a self - phoretic or nanobubble release 
 mechanism .
a survey of the literature also reveals that among these 
 navigation 
 strategies , surprisingly little or no attention has been given to 
 controlling or measuring swimming devices behavior in three 
 dimensions .
the vast majority of observations and trajectory control 
 demonstrations have instead focused on devices settled on or near 
 a planar surface and , in general , not attempted to either measure 
 or induce motion away from this plane .
this omission appears significant ; 
 as in real - world applications , the ability to control motion in all 
 three dimensions is likely to be essential .
the only notable experimental 
 example that has used an ability to control motion with respect to 
 gravity is that of externally actuated and controlled helical swimming 
 devices , which are deliberately angled upward as they swim , in order 
 to resist gravitational sedimentation .
beyond this , the potential for gravity to exert and influence swimming 
 device trajectories has been largely overlooked .
first , the most widely investigated 
 autonomous swimmer type is bimetallic nanorods , made from dense solid 
 metals which sediment rapidly and remain localized at the lowest interface . 

second , while janus spheres have been made from low density polymeric 
 materials capable of remaining in suspension , there are some practical 
 difficulties in measuring particle behavior in three - dimensions ( 3d ) 
 rapidly enough to quantify swimming behaviors . in addition , most two - dimensional 
 ( 2d ) microscopes are mounted to make observations in the xy plane .
these issues are compounded by an implicit assumption of 
 isotropic behavior contained in many theories and analysis for these 
 device behaviors .
this paucity of data was 
 addressed to a limited extent by a study 
 by palacci et al . , which used a 2d  sideways  microscope 
 to study a propulsive - sedimented janus sphere ensemble .
the work concluded that increasing swimming 
 velocity within the ensemble raises the effective temperature of the 
 sedimented state , so that faster moving ensembles are distributed 
 over a larger vertical distance above the interface .
however the influence 
 of gravity on individual swimmer trajectories was not reported , and 
 effects due to the janus sphere swimmers intrinsic mass asymmetry 
 were not described . with concern to this later point , which is the 
 focus of this current work , it has been shown that metallically coated 
 janus colloids undergoing brownian rotation in water are statistically 
 biased toward cap - down configurations due to their mass asymmetry . with a combination of this and our evidence 
 that janus spheres propulsion velocity vector points away 
 from their platinum cap , a mechanism 
 through which gravity can potentially orientate individual janus swimmer 
 trajectories emerges .
this mechanism has also been retrospectively 
 theoretically postulated to be capable of producing ensemble orientational 
 ordering phenomena in the fully sedimented state described above ; however , the required regime to observe this 
 was not achieved in the initial experimental study .
in fact , 
 in order to find examples where the role of mass asymmetry 
 has been shown to effect  swimming  behavior , it is 
 necessary to consider biological entities such as algae .
simple swimming 
 algal cells have been shown to be able to navigate upward by virtue 
 of an asymmetrical mass distribution alone , a phenomena termed  gravitaxis  .
although the mechanism for this phenomena was subject to debate , 
 it is now established that these cells are simply bottom heavy , a 
 feature which allows them to harness their ability to swim using flagella 
 to consistently move upward .
a key feature of this behavior is that 
 it demonstrates that it is possible for such cells to show gravity - guided 
 behavior without having a sophisticated gravity sensing mechanism 
 to control their flagella .
as autonomous sensing and response mechanisms 
 are very challenging to implement in synthetic systems , this immediately 
 suggests a useful new biomimetic approach to potentially add to the 
 limited existing autonomous navigation strategies described above 
 and so further motivates our work . here
then , we systematically 
 investigate the potential for low 
 density ( thin platinum coating on polystyrene colloid ) spherical janus 
 swimmers to display 
 a synthetic gravitaxis mechanism originating from the asymmetrical 
 distribution of mass at their surface .
we employ high - resolution fluorescence 
 particle tracking to measure 3d trajectories for both propulsive and 
 nonpropulsive devices in combination with  sideways  
 2d tracking .
we report and analyze the contributions of gravity to 
 the trajectories for a range of particle sizes , selected so that the 
 mass of the cap is expected to have a varying influence on the orientation 
 of the particle with respect to gravity .
this data reveals that the 
 asymmetrical weight distribution can , for larger janus swimmers , bias 
 the orientation of the janus swimmer with respect to gravity , resulting 
 in significant gravitaxis where the synthetic devices autonomously 
 swim upward via a simple  bottom-heavy mechanism similar 
 to that observed for some bacteria .
we believe the future exploitation 
 of these phenomena can lead to a wide range of new applications , including 
 autonomous sorting and cargo transport .
unless stated , all materials were used as 
 received . from sigma - aldrich ,
we obtained h2o2 puriss grade ( 30 wt% ) and platinum wire , 0.25 mm ( 99.99% ) .
we sourced 
 green fluorescent fluoro - max polystyrene microspheres from thermo 
 scientific , with a range of sphere radii ( a = 0.95 , 
 1.55 , and 2.4 m ) .
we used water from an elga purelab option 
 filtration system ( 15 m cm ) .
we prepared our catalytic 
 janus spheres by spin coating a few drops of a 0.1 wt % dispersion 
 of green fluorescent polymer microspheres in ethanol onto clean glass 
 microscope slides .
a 10 nm thick layer of platinum was evaporated 
 onto the exposed hemisphere of the monolayer of microspheres under 
 vacuum using a moorfield ( u.k . ) minilab 80 e - beam evaporator .
immediately 
 prior to use , the janus spheres were removed from the surface of the 
 slides by first moistening one edge of a 1 cm square of microscope 
 lens tissue .
the edge of the lens tissue was then dragged over the 
 surface of the slide several times , trapping the janus spheres in 
 the tissue fibers . to harvest the janus spheres ,
the lens tissue was 
 then immersed in 1.2 ml of water in a vial and shaken vigorously . 

we then diluted 1 ml of the dispersion with 1 ml of a 30 wt % solution 
 of h2o2 .
the dispersion was then sonicated for 
 5 min and allowed to rest for a further 25 min .
we have found that 
 this method serves to  clean  and fully activate the 
 catalytic surface of the janus spheres , maximizing their swimming 
 velocity . before observing the swimmers under the microscope
, an additional 
 1 ml of water was added to the dispersion to form a 10 wt % solution 
 of h2o2 .
fluorescence images measuring 170  
 170 m in the ( x , y ) plane , with an observable 
 depth of about 200 m , showed a small number of widely separated 
 particles ; from this we estimate the final particle volume fraction 
 of the swimming suspensions to be about 0.003% . by using such a low - volume 
 fraction , we avoided introducing density fluctuations which are known 
 to cause instabilities in swimming algal systems , resulting in downward flow . to observe swimmers in 2d 
 along the ( x , z ) plane , we fixed 
 a nikon lv - epiled microscope head vertically using a bespoke mounting 
 bracket .
we filled 
 an oxygen plasma cleaned cuvette ( 4  1  0.1 cm ) with the 
 swimmer dispersion , and then located and focused on one or more swimmers 
 under trans - illumination .
a sequence of 1000 images ( 800  600 
 pixels ) was recorded at 33 hz with the vertical axis of the images 
 parallel with the direction of gravity . during the recording of the 
 image sequence ,
the focal position of the objective was adjusted as 
 required to keep the swimmers in focus , appearing as a dark disc on 
 a light background .
analysis of the images using a suite of algorithms written in labview enabled us to extract the 
 swimmer trajectories and a variety of statistical information .
swimmer suspensions were prepared as 
 described and an oxygen plasma - cleaned cuvette filled with the suspension . 

the swimmers were observed in the fluorescence mode of a nikon eclipse 
 lv100 microscope using the blue excitation band of a nikon b2a filter 
 cube .
when in focus , the green fluorescent swimmers appear as solid 
 bright discs on a dark background .
however , when defocused above the 
 swimmers , their diffraction pattern forms a bright ring , the radius 
 of which is dependent upon magnification , sphere size , and the distance 
 of the sphere from the focal plane of the objective .
we recorded a sequence of 1000 images ( 730  730 pixels ) 
 using an andor neo camera at a frequency of 33 hz .
a second suite 
 of algorithms written in labview was used to analyze the images to 
 find the x- and y - coordinates from 
 the ring center and the z - coordinate from the ring 
 radius ( see the supporting information ) . 
 to quantify the positional error of the 3d tracking technique
, we 
 examined a sequence of 50 images of a 1.9 m sphere about 30 
 m from the focal plane of the 20 objective .
we found 
 that noise in the image caused a z - positional error of 25 nm , 
 with a similar degree of error in the ( x , y ) plane . 

however , the detected intensity of the fluorescence light emitted 
 by the particle drops as the distance of the spheres from the focal 
 plane is increased .
when the spheres are very far from the focal plane , 
 the signal - to - noise ratio is too low to accurately track the spheres . consequently , we tracked the 1.9 m spheres 
 over a maximum z - distance of about 100 m and 
 the 4.8 m spheres over 150 m .
for most swimmers that 
 we tracked this was not found to be a significant limitation .
tem grids were attached to 
 cleaned silicon wafers and these pieces were inserted into the evaporation 
 chamber during platinum coating .
the grids were carefully removed 
 following coating , and a vertically calibrated veeco dimension afm 
 operating in tapping mode was used to record topographic data across 
 the masked boundaries . after suitable software flattening
first , we discuss 
 the sedimentation behavior for janus spheres , with one hemisphere 
 coated with a thin layer of platinum , in pure water to allow us to 
 determine the details of the mass distribution imparted by the catalytic 
 coating and verify particle sizes and tracking procedures .
next , we 
 report trajectories for the same janus spheres following the addition 
 of hydrogen peroxide fuel to the solution , causing them to undergo 
 propulsion . finally , we demonstrate a simple model that can be used 
 to link the asymmetrical mass distribution of the janus swimmers with 
 their observed gravitational anisotropy .
3d trajectories 
 for an uncapped ( red ) and capped ( blue ) , a = 2.4 
 m janus sphere settling in water over a period 
 of 30s .
figure 2 shows two 3d trajectories for representative 
 spheres ( a = 2.4 m ) , with one sphere ( blue 
 trajectory ) coated on one hemisphere with a nominally 10 nm thick 
 platinum layer . in both cases ,
a systematic downward motion is observed , 
 indicating the spheres are sedimenting due to their greater density 
 than the surrounding aqueous medium .
qualitatively , it can be seen 
 that over the same duration , the capped sphere is undergoing more 
 rapid sedimentation due to the additional mass added by the platinum 
 layer ( pt = 21.45 g cm ) .
table 1 summarizes the experimental sedimentation rates 
 obtained from a linear fit to the z coordinate change with respect 
 to time for spheres at the three sizes investigated in this study , 
 both before and after coating with platinum ( 25 trajectories ) . for 
 a dilute suspension
, the rate of sedimentation of the uncapped spheres 
 is characterized by the stokes settling velocity1where a is the sphere radius , 
 p is the sphere density , s is 
 the density of the suspension medium , and g is the 
 gravitational constant .
comparing our experimental data for uncapped 
 spheres with this estimate ( assuming the density of polystyrene is 
 ps = 1.05 g cm ) gives good agreement , 
 suggesting we are obtaining reasonable 3d tracks ( table 1 ) .
theoretical sedimentation data 
 for the capped janus spheres assumes an ellipsoid coating shape , as 
 shown in figure 6 .
errors 
 in the experimental values are the standard deviation of the mean 
 values of 25 settling spheres .
the 
 effect of adding the thin platinum cap to our spheres can be 
 approximated as an effective increase in p , resulting 
 in an increase in vs. to predict the capped 
 janus particles , sedimentation velocity in this way consequently requires 
 accurate knowledge of the additional mass added during the coating 
 process . to estimate the added mass , first atomic force microscopy 

was performed to find the mean step height for a partially masked 
 flat silicon substrate coated with platinum in the same manner as 
 the janus swimmers .
this verified the nominal thickness value provided 
 by a quartz crystal oscillator during metal evaporation , returning 
 a consistent value of 10.04  0.6 nm . using this thickness combined 
 with a geometrical model for the cap shape allows the added mass and 
 capped sphere stokes sedimentation velocity to be estimated .
initially 
 we performed this calculation based on a uniform hemispherical overlayer ; 
 however , this gave poor agreement with the experimental data , considerably 
 overestimating the sedimentation rate .
instead , a better , more physical 
 model is used to describe the coating as an ellipsoidal shell overlayer , 
 reaching a maximal thickness of 10 nm at the pole of the janus particle 
 and with 0 nm thickness at the equatorial boundary of the coated region 
 ( figure 6 ) .
sedimentation velocities estimated 
 in this way give reasonable agreement ( 9% error ) with experimental 
 values , table 1 , although we note that the 
 prediction is poor for the smallest spheres ( 30% error ) .
the 
 small radius of curvature of the smallest spheres may be causing a 
 significant deviation from the cap weight predicted by the ellipsoidal 
 layer model ; however , despite this , the assumption of an ellipsoidal 
 layer is far more accurate than that of a hemisphere .
an ellipsoidal 
 coating distribution is also consistent with the highly directional 
 nature of the metal evaporation technique used to coat the colloids , 
 which is known to cause shadowing effects .
consequently , in the later part of this paper we use a half - ellipsoid 
 model for the asymmetric distribution of mass at the surface of the 
 janus particles .
figure 2 also shows 
 that the 3d tracks were 
 obtained with sufficient resolution to accurately resolve the stochastic 
 brownian displacements that the colloids undergo by virtue of their 
 small micrometer size .
the magnitude of brownian translational diffusion 
 is quantified by the translational diffusion coefficient , d = kbt/6a , where  is the suspension medium 
 viscosity ( water = 1 mpa s ) and kbt is the thermal energy .
a method to determine the diffusion 
 coefficient from trajectory data is to calculate the mean - squared 
 displacement , l , msd , as a function 
 of time step , which in the case of 3d trajectories is related to the 
 diffusion coefficient by l = 6dt .
we applied this analysis 
 to the ( x , y , z ) trajectories 
 for each sphere considered here in pure water ( with the addition of 
 a quadratic term to allow for the sedimentation velocity ) and returned 
 values for the diffusion coefficient which are consistent with those 
 calculated based on the nominal particle sizes for all of the capped 
 and uncapped particles ( table 2 ) . having determined 
 the nature of 
 the cap mass and asymmetry for the janus spheres under consideration , 
 we now investigate their trajectories when fueled by aqueous hydrogen 
 peroxide solutions , which should enable them to undergo propulsion
. 
 figures 3 and 4 show 
 representative 2d and 3d trajectories for the different sizes of janus 
 spheres considered . in order to establish that these janus swimmers 
 are in fact undergoing propulsion
, we calculated the 2d msd displacements 
 in the xz plane for each trajectory as a function 
 of time , which are expected to display an additional quadratic term 
 due to propulsion2where v is the propulsion 
 velocity .
the average 2d propulsion velocities 
 determined from the side on 2d trajectories for each sphere size are 
 shown in figure 5 .
as we have previously reported , 
 diffusiophoretic theory suggests an inverse relationship between swimmer 
 velocity and sphere radius ( v  1/a ) , which gives a good fit 
 to the experimental values . to further interpret the trajectory data , 

it is necessary to consider that the path followed by a given swimming 
 janus sphere will be determined by a combination of the magnitude 
 of the propulsive velocity it generates , the rate of brownian diffusion 
 phenomena , and potentially any effect the asymmetrical mass distribution 
 is exerting on the janus spheres orientation .
briefly , because 
 the janus spheres produce propulsion along a vector pointing away 
 from the catalytic cap , their trajectories 
 reflect the rate at which brownian rotational diffusion alters their 
 orientation .
rotational diffusion is characterized by rotational diffusion 
 time3which characterizes the time it 
 takes for 
 loss of orientation to occur .
the proportionality to a indicates that for larger particles , this rotational 
 diffusion process is slower , table 2 , and therefore 
 they are expected to show straighter trajectories . in consideration 
 of the 2d trajectories ( figure 3 )
, we can clearly 
 see how this interplay of brownian phenomena produces a change in 
 swimmer trajectory character as a function of size .
the a = 0.95 m trajectories show most frequent changes of direction , 
 while a = 2.4 m trajectories show very little 
 deviation over the tracking period .
the interplay of rotational diffusion 
 and propulsion velocity magnitude is most easily summarized by the 
 mean path length , the product of r , and the propulsion 
 velocity , which provides an indication of the average length a given 
 swimmer may be expected to travel in before changing direction .
good 
 qualitative agreement is seen with the theoretically predicted mean - path 
 length and the experimental trajectories ( see figure 3 caption ) .
this interplay also determines the average distance 
 a janus sphere moves from the origin in a given time period : while 
 we have seen that propulsion velocities scale as approximately 1/a , it is apparent that the difference in mean distance moved 
 from the origin is actually very similar for a = 
 0.95 m and a = 1.55 m swimmers and 
 only slightly reduced for a = 2.4 m .
this 
 is because the greater propulsion velocity for the smaller - sized swimmers 
 can not result in a significantly greater travel distance at times 
 longer than the rotational diffusion constant .
2d swimming trajectories 
 for representative janus spheres observed 
 in the ( x , z ) plane for a = 0.95 m ( black ) , a = 1.55 m ( red ) , 
 and a = 2.4 m ( blue ) spheres .
the swimmers 
 were suspended in a 10 wt % solution of h2o2 . predicted mean path lengths are 19 , 59 , and 151 m , respectively . 

3d swimming trajectories for representative 
 janus spheres ; a = 1.55 m ( left ) and a = 2.4 m 
 ( right ) . finally , we consider the distribution 
 of the trajectories with 
 respect to the direction of gravity : qualitatively , it is apparent 
 that the isotropy of motion in the z axis , in which 
 gravity acts , is lost at larger particle sizes and replaced by a pronounced 
 bias toward trajectories where the swimmers move upward ( figure 3 ) .
examination of the larger - sized sphere trajectories 
 in 3d ( figure 4 ) allows the isotropy along 
 all axes to be assessed and makes it clear that isotropic behavior 
 remains in the xy plane but is lost in the xz plane .
the degree of gravitaxis was also quantified by 
 determining the average 1d propulsion velocities resolved along the 
 x and z axis , figure 5 . the 
 ratio of these velocities assuming isotropic propulsion would be unity . 

however , at larger swimmer sizes , significantly higher velocities 
 are seen in the z direction : the ratio vz / vx increases from 1.06 for a = 0.95 m 
 to 1.55 for a = 2.4 m . taken together , this 
 data provides strong evidence that a synthetic gravitaxis mechanism 
 is being turned on as particle size increases .
on the basis of the 
 mechanism described in the introduction , a qualitative explanation 
 for this size dependency is that for larger particles , the platinum 
 caps masses are both significantly larger ( see table 1 ) and are positioned further from the center of the janus 
 swimmer and so can generate an increasing torque to constrain the 
 brownian rotations of the particles , which are limited by the available 
 thermal energy , kbt . in gravitaxis model ,
we elaborate 
 this argument to build a simple model for the expected angular distribution 
 for a freely rotating janus sphere with an asymmetrical metallic cap 
 and compare this prediction with our experimental data . we can use boltzmann statistics to 
 build a simple numerical model for the expected azimuthal angle distribution , p(a ) , of an asymmetrically platinum - coated 
 janus sphere . in order to do this
, we require an expression for the 
 energetic cost of rotating a given janus sphere from its lowest energy 
 position ( a = 0 ) ( figure 6 ) .
using the additional 
 mass values indicated by the experimental sedimentation data reported 
 above , together with the ellipsoid model for the coating shape , we 
 can use trigonometry to derive an expression for the additional gravitational 
 energy required to rotate the particles to a given angle,4where m is the experimentally 
 determined mass of the cap ( table 1 ) and
l is the distance of the center of mass of the ellipsoidal 
 shell from the center of rotation of the janus spheres ( see the supporting information ) .
the expected residency 
 time at a given angle is then given by5and the predicted normalized distribution 
 over a given range of azimuthal angles is6 the relationship between swimmer velocity ( 2d ) 
 and sphere radius . 

the solid line is a fit to the data ( see ebbens et al . ) .
inset : ratio of velocity along the z axis ( vz ) 
 to the velocity along the x axis ( vx ) .
the mass of the catalytic cap , which reaches a maximum thickness 
 max at the pole , introduces a gravitational energy 
 cost to rotating the janus spheres about its center and turning the 
 center of mass ( c.o.m . ) from its lowest energy position at  
 = 0. we measured the instantaneous velocity ( vm ) and direction ( m ) from the 2d trajectories 
 and corrected for the settling effect of gravity ( vs ) , giving the actual values va and a . in order to compare this predication with our
experimentally 
 observed 
 data , we need a method to extract equivalent angular distributions 
 from the janus swimmer trajectories .
the measured angle distributions 
 across all successive janus sphere steps for all the recorded 2d trajectories 
 are shown in figure 7 .
these plots clearly 
 illustrate a strong upward bias in the measured translational step 
 angles at larger sphere sizes .
however , these measured angles are 
 not directly comparable with the models output due to the constant 
 sedimentation velocity experienced by each janus sphere . as an illustration
, 
 an adjustment is required to allow for the case where , for example , 
 a particle is measured to have moved upward , overcoming its tendency 
 to sediment , requiring its actual orientation at the start of the 
 observed trajectory step , a , to have been angled 
 even more steeply upward to overcome sedimentation ( figure 6 ) . to generate a comparable experimental parameter 
 from this data
, we assume that a at the start of 
 each propulsive step is given by resolving the experimentally measured 
 direction of travel velocity vector ( vm ) and the downward acting constant sedimentation velocity determined 
 experimentally above ( trigonometry shows that in this case , the link 
 between the two angles is a = arctan[vm sin(m)/vm cos(m)vs ) ] . 

figure 8 compares the angle distribution predictions 
 p(a ) with the actual corrected angular distributions 
 obtained in this way < a > , showing good agreement , 
 particulary for the smaller two - sized swimmers .
the slight deviation 
 for the a = 2.4 m spheres may be due to inhomogeneities 
 in the platinum cap layer , which can introduce spin to the particle 
 trajectories resulting in a higher population of high a than predicted by the model . from the msd of the trajectories , 
 the mean angular velocities (  ) 
 for the a = 0.95 m ,  = 0.0002 rad s and a = 2.4 m ,  = 
 0.01
however , this simple model clearly shows that the mass asymmetry 
 possessed by larger janus particles is sufficient to introduce appreciable 
 gravitaxis behavior via the proposed mechanisms of biasing the janus 
 swimmers azimuthal angle toward cap - down configurations . to aid visualization 
 of the effect of the platinum cap on each janus sphere
, we have also 
 estimated the ca nt angles required to balance the sedimentation velocity 
 and produce propulsion in the horizontal plane ( i.e. , 90  
 a ) .
these are a = 0.95 m , 
 3.0 ; a = 1.55 m , 11.8 ; and a = 2.4 m , 29.8 for swimmers producing the 
 mean experimental propulsion velocities at those respective sizes . 

it is noticeable that the largest sphere requires an appreciable ca nt 
 to produce horizontal progress , illustrating the magnitude of this 
 additional factor that will to some extent reduce the amount of gravitaxis 
 biasing observed for a given cap weight .
our 
 results clearly show that for catalytic janus swimmers made 
 from polystyrene , with radii of a = 1.55 m 
 and above , the effect of gravity acting on the thin ( 10 nm ) hemispherical 
 coating used to impart propulsion is sufficient to orientate the particles 
 in a  cap down  configuration , causing them to display 
 negative gravitaxis ( i.e. , a tendency to move upward ) . to our knowledge , 

this is the first example of gravitaxis being observed for autonomous 
 synthetic swimming devices .
the mechanism driving this effect is however 
 equivalent to that present in gravitactic algae , which possess a comparable 
 asymmetrical mass distribution .
we have also tested a simple model 
 capable of predicting the extent of gravitaxis for a given sphere 
 size and coating mass , based solely on the gravitational energy required 
 to lift the masses of the asymmetric caps to allow the colloid to 
 change its azimuthal angle .
this approach shows good agreement with 
 our experimental data . in the process of developing this model ,
we 
 have also shown how these larger janus sphere swimmers are expected 
 to have a significant difference between their azimuthal angle and 
 subsequent observed step direction , for some orientations , due to 
 their relatively large sedimentation velocities .
this interplay will 
 ultimately impose a limit for the achievable degree of negative gravitaxis 
 in such devices .
while our model indicates that an even higher degree 
 of autonomous directional control can be achieved by increasing the 
 coating mass ( e.g. , by increasing the coating thickness ) and/or the 
 swimmer size , there will be limits in both of these scenarios .
increasing 
 coating mass will also increase the sedimentation rate which the propulsive 
 velocities of the particles must exceed in order to be able to move 
 upward , and increasing size also produces a reduction in intrinsic 
 velocity as previously reported and confirmed 
 again here .
however , as an indication of the scope for gravitactic 
 control beyond that reported here , a a = 1.55 m 
 particle with a nominally 50 nm thick coating is predicted to spend 
 85% of its time moving upward within 20 degrees of vertical and still 
 be capable of producing a 1 m s translational 
 rate despite having to overcome an increased sedimentation velocity .
normalized 
 angle distribution for m as a function 
 of radius for all translational steps for each recorded 2d swimmer 
 trajectory .
scatter graphs showing 
 the actual azimuthal angle , a , derived by resolving 
 the measured propulsion and sedimentation 
 velocity vectors .
solid line is p(a ) estimated from a boltzmann distribution for the gravitational energy 
 cost for rotating a solid ellipsoid overlayer of platinum . as a result of these findings
, we envisage that 
 some new applications 
 may be enabled by optimizing and exploiting this easily experimentally 
 accessible gravitaxis behavior .
for example , small scale cargo transport 
  lifts  could be constructed and made to switch between 
 lifting and sedimenting by a changing stimuli such as fuel concentration . a similar scenario could be used to effect controlled 
 release of active colloids from gravitational confinement . additionally , 
 new active separation methods may be possible , for example active 
 and passive colloids are expected to separate vertically at an enhanced 
 rate due to gravitactic propulsion , while the separation of differently 
 sized swimmers , displaying differing amounts of gravitaxis , may also 
 be envisaged .
the new observations also open up the potential for 
 some new emergent behavior in synthetic devices .
for example it is 
 well - known that algae produce flow patterns due to their gravitactic 
 accumulation at the top surface of a fluid , which causes sinking and 
 rising columns due to local densification .
in addition , the potential influence of gravitaxis behavior 
 on attempts to quantify the behavior of swimming devices in order 
 to gain theoretical insights must also be considered . in the work 
 here , we show that tracking the largest particles we considered in 
 free solution using conventional microscopy in the xy plane alone would lead to their propulsion velocities being underestimated 
 by almost a third . in conclusion , we hope that this study will lay 
 the groundwork for future exploitation of and a greater attention 
 to gravitational effects in catalytic swimming devices .
 in 
 this work , we show that the asymmetrical distribution of mass 
 at the surface of catalytic janus swimmers results in the devices 
 preferentially propelling themselves upward in a gravitational field . 
 
 we demonstrate the existence of this gravitaxis phenomenon by observing 
 the trajectories of fueled janus swimmers , which generate thrust along 
 a vector pointing away from their metallically coated half . 
 we report 
 that as the size of the spherical swimmer increases , the propulsive 
 trajectories are no longer isotropic with respect to gravity , and 
 they start to show a pronounced tendency to move in an upward direction . 
 
 we suggest that this effect is due to the platinum caps asymmetric 
 mass exerting an increasing influence on the azimuthal angle of the 
 janus sphere with size , biasing its orientation toward a configuration 
 where the heavier propulsion generating surface faces down . 
 this argument 
 is supported by the good agreement we find between the experimentally 
 observed azimuthal angle distribution for the janus swimmers and predictions 
 made by simple boltzmann statistics . 
 this gravitaxis phenomenon provides 
 a mechanism to autonomously control and direct the motion of catalytic 
 swimming devices and so enable a route to make autonomous transport 
 devices and develop new separation , sensing , and controlled release 
 applications . 
Introduction
Experimental
Details
Results
and Discussion
Conclusions