aqueous dispersions 
 of micrometer - sized droplets of thermotropic 
 liquid crystals ( lcs ) provide versatile platforms for the design of 
 stimuli - responsive soft matter systems .
the responsiveness of these droplet - based lc systems to various 
 types of stimuli results from the fine scale of energetics that controls 
 the equilibrium ordering of lcs .
specifically , past studies have established 
 that the ordering of lcs within micrometer - sized droplets reflects 
 contributions to the free energy that arise from orientation - dependent 
 anchoring of the lc at the surfaces of the droplets , elastic strain 
 of the lc associated with the accommodation of surface anchoring , 
 and the formation of topological defects .
recent studies , however , have also led to observations involving 
 lc droplets in aqueous dispersions that reveal our understanding of 
 factors controlling the ordering of lc droplets to be incomplete . 
 in particular , existing theories of lc droplets can not account for 
 ( i ) changes in the internal configurations of the lc droplets that 
 occur with changes in droplet size , ( ii ) the effects of simple salts on the ordering 
 of the lcs , or ( iii ) the partitioning 
 of amphiphiles to the defects of lc droplets . in this paper
, we seek to advance our understanding 
 and ability to design aqueous dispersions of stimuli - responsive lc 
 droplets by exploring the properties of lc droplets encapsulated ( or 
  caged  ) inside thin and porous polymeric membranes . 

our results reveal that the interactions of the lc droplets with the 
 interfaces of the polymeric cages give rise to surfactant - triggered 
 shape changes and resulting internal ordering transitions that are 
 not seen in free lc droplets .
of particular relevance to this 
 article are recent studies that 
 have investigated the ordering of spherical lc droplets encapsulated 
 in capsules composed of polyelectrolyte multilayers ( pems ) . in those studies ,
the spherical polymeric capsules were formed using 
 noncovalent interactions ( e.g. , electrostatic interactions or hydrogen 
 bonding ) , and the lcs were observed to fill the interiors of the capsules 
 completely . the study reported in this article moves to investigate 
 the ordering of lcs within multilayer capsules prepared by covalent 
 reactions of branched polyethylenimine ( pei ) and poly(2-vinyl-4,4-dimethylazlactone ) 
 ( pvdma ) .
in contrast to capsules formed from pems , multilayer capsules 
 formed using pei and pvdma have been found to fill only partially 
 with lc , resulting in the formation of micrometer - sized lc droplets 
 that are trapped or caged in aqueous solutions contained within the 
 polymer capsule .
these systems are a 
 particularly interesting class of responsive soft matter , as the capsules 
 can be designed to bind to the surfaces of mammalian cells , with the 
 caged lc droplets undergoing changes in optical appearance upon exposure 
 to cytotoxic analytes ( thus providing the basis for sensors of local 
 concentrations of toxic analytes near cells , etc . ) .
the work reported here sought to provide insight 
 into some of the 
 observations reported above and explore further the properties of 
 caged lc droplets in the presence of aqueous solutions of surfactants . 

first , we report on the origins of the partial filling of pei / pvdma 
 capsules by the nematic lc e7 . in this context
, we describe the design 
 of new amphiphilic polymeric capsules that were prepared to present 
 a hydrophobic inner surface to the lc droplet ( to promote filling ) 
 and a charged ( cationic ) outer surface to promote the dispersal of 
 the capsules in water .
we establish that the partial filling of the 
 capsules by e7 is also observed with amphiphilic capsules and that 
 it arises largely from the swelling of the capsules upon transfer 
 into water from the bulk lc phase after filling of the capsules with 
 lc .
second , because the capsules are partially filled by lc ( the remainder 
 of the internal volume of the capsule is an aqueous solution ) , we 
 explore changes in the shapes of the caged lc droplets that are driven 
 by surfactant - induced changes in the wetting of the lc on the inner 
 surfaces of the capsules . as detailed below , we observed the addition 
 of surfactants to aqueous solutions of caged lc droplets to promote 
 wetting and ordering transitions of a complexity not observed in free 
 lc droplets , which may permit new designs of stimuli - responsive lc - droplet - based 
 systems .
the 
 fabrication of hollow polymer microcapsules was performed according 
 to a previously published procedure for the layer - by - layer ( lbl ) formation 
 of covalently assembled polymeric capsules . on the basis of a past report , we used 
 monodisperse silica microspheres with a diameter of 4.99  0.22 
 m as a template for the polymer microcapsules to produce lc 
 droplets of a size that is sensitive to amphiphilic adsorbates .
solutions 
 of pei and pvdma ( or pvdmafl labeled with 6-aminofluorescein 
 to facilitate fluorescence - based imaging ) ( figure 1a ) were prepared in acetone ( 20 mm with respect to the molecular 
 weight of the polymer repeat unit ) .
sio2 microparticles 
 ( 100 l in plastic microcentrifuge tubes ) were rinsed with 1 
 ml of acetone and centrifuged prior to the addition of polymer . in 
 brief ( see si and past reports for details ) , an initial layer of pei was adsorbed onto the silica 
 microparticles through electrostatic interactions , and subsequent 
 layers of pvdma ( or pvdmafl ) and pei were sequentially 
 added , layer - by - layer , to build up a covalently cross - linked multilayer 
 film . between the addition of each polymer layer , particles were rinsed 
 three times by centrifugation ( 2 min at 1500 rpm ) and resuspension 
 in acetone .
films fabricated using this method have been shown 
 previously to contain residual azlactone groups , providing a reactive 
 handle for postfabrication functionalization with other chemical functionalities . 

we selected two different structural motifs , shown in figure 1b ; further discussion is included below .
after the 
 fabrication of two pei / pvdma bilayers , the coated microparticles were 
 rinsed with tetrahydrofuran ( thf ) and functionalized by adding 1 ml 
 of decylamine ( da , figure 1b ) in thf ( 20 mm ) 
 for 1 h to install the hydrophobic functionality .
these da - functionalized 
 coated microparticles were then rinsed with thf three times and dispersed 
 in acetone prior to resuming the fabrication of an additional 2.5 
 bilayers of pei and pvdma .
finally , to functionalize these outer 2.5 
 bilayers with protonatable hydrophilic functional groups , the microparticles 
 were washed with thf three times and then dispersed in 1 ml of 3-(dimethylamino)propylamine 
 ( dm ) in thf ( 20 mm ) for 1 h. polymer - coated silica microparticles 
 were rinsed with thf three 
 times by centrifugation and then suspended in a small volume of water 
 ( 100 l ) in preparation for aqueous etching . the silica 
 core was removed from the polymer membrane by treatment with a commercially 
 available buffered oxide etching ( boe , 10:1 ) solution containing hydrofluoric 
 acid ( hf ) ; see materials section in si . 

hf solutions and vapors are extremely poisonous and corrosive 
 and may cause extreme burns that are not immediately painful . handle 
 with extreme caution in a chemical fume hood , and use appropriate 
 protective equipment ( gloves , face / eye protection , laboratory coat , 
 etc . ) , and neutralize waste appropriately . ) the samples were 
 incubated with 800 l of boe at room temperature for 510 
 min .
the resulting hollow capsules were centrifuged ( 4500 rpm for 
 5 min ) and rinsed five times in 1 ml of water .
after the silica 
 template was removed to obtain hollow polymeric microcapsules , the 
 microcapsules were filled with lc following a previously reported 
 protocol . in brief , 
 the capsules were rinsed with ethanol twice , centrifuged to remove 
 as much of the supernatant ethanol as possible , and suspended in a 
 mixture of 5% ethanol and 95% e7 .
this mixture of ethanol and e7 forms 
 an isotropic phase that can infiltrate the polymeric capsules .
the 
 ethanol was slowly evaporated from the sample by leaving the tube 
 containing the sample uncapped on a shaker plate for 24 h , resulting 
 in a nematic phase containing the capsules .
the capsules were then 
 extracted into an aqueous phase by removing excess e7 by centrifugation , 
 contacting the sample with water , and shaking gently .
this procedure 
 resulted in the spontaneous transfer of capsules containing lc droplets 
 to the aqueous phase .
dispersions of either bare or coated 
 microparticles , hollow capsules , 
 and lc - containing capsules were placed on a coverslip and optically 
 imaged in bright - field polarized light ( crossed polarizers ) using 
 fluorescence modes with an olympus ix-71 inverted microscope ( center 
 valley , pa ) with a 100 oil - immersion objective ( with or without 
 an additional 1.6 optical zoom ) and equipped with a 100 w mercury 
 lamp . for fluorescence - based imaging of capsules fabricated using 
 pvdmafl ,
an olympus u - mnb2 fluorescence filter cube was 
 used with a 470490 nm excitation filter and a 520 nm emission 
 filter .
a monochrome hamamatsu 1394 orca - er ccd camera ( bridgewater , 
 nj ) was controlled with simplepci software ( compix , inc .
images were later analyzed using imagej software ( nih , 
 bethesda , md ) .
for each sample , the bulk solution was imaged using 
 polarized light microscopy to determine the ordering of lc droplets 
 in capsules that were freely diffusing .
however , since the diffusion 
 quickly moved the capsules out of the plane of focus or the field 
 of view , capsules could be imaged in all three imaging modes ( bright 
 field , crossed polarizers , and fluorescence ) only after sedimentation 
 onto the coverslip surface . in our experiments
, we did not observe 
 any orienting effect on the lc resulting from contact with the coverslip , 
 as reported in a past study .
( a ) chemical 
 structure of branched pei and pvdma used for the covalent 
 layer - by - layer assembly of multilayer films .
chemical functional groups : decylamine 
 ( denoted r1 or da ) was used to functionalize the first 
 two bilayers , and dimethylaminopropylamine ( denoted r2 or 
 dm ) was used to functionalize the outer 2.5 bilayers ( see text ) .
in contrast 
 to prior studies described in the introduction , the capsules used in this current investigation were prepared to 
 have walls with hydrophobic functionality facing the interior of the 
 capsule and hydrophilic functionality on the outer surface .
this was 
 accomplished by functionalizing the interior with decylamine ( da ) 
 and the exterior with dimethylaminopropylamine ( dm ) such that the 
 hydrophobic interior contacted the lc and the hydrophilic exterior 
 surface contacted the bulk aqueous phase .
( see figure 1 and the experimental section for 
 details . ) in the remainder of this article , we refer to these capsules 
 as having an amphiphilic structure and by using the acronym dadm to 
 identify the da and dm motifs decorating the interior and exterior 
 walls of the capsules . in the interest of brevity ,
the confirmation 
 of the successful synthesis of these dadm capsules is detailed in 
 the supporting information ( si ) . specifically , 
 we present evidence of the incorporation of the da and dm into the 
 capsule walls ( figure s1 ) and show scanning 
 electron micrographs of polymer - coated microparticles and hollow capsules 
 ( figure s2 ) .
measurements made using the 
 scanning electron micrographs reveal the size of the dried , polymer - coated 
 microparticles to be 4.9  0.2 m . after treatment 
 with lc using methods that lead to the complete filling of pem - based 
 capsules in past studies , we observed the dadm - functionalized pei / pvdma 
 capsules used here to be only partially filled with lc ( see figure 2f , middle row ) .
specifically , we measured the average 
 diameters of the dadm capsules and the lc droplets to be 6.7  
 0.3 and 4.9  0.5 m , respectively ; that is , the lc filled 
 approximately 40% of the internal volume of the capsules . to provide 
 insight into the reasons underlying partial filling , we imaged the 
 film - coated microparticle precursors and the hollow capsules in each 
 step of the synthesis ( figure 2 ) .
the images 
 in the middle row of figure 2 are bright - field 
 micrographs , and images in the bottom row are fluorescence micrographs 
 of fluorescein - labeled capsules that clearly define the sizes and 
 shapes of the capsules .
first , the dadm - coated silica microparticles 
 in water were measured to have a diameter of 5.3  0.3 m 
 ( figure 2b ) , a value that is indistinguishable 
 from the diameter measured for the bare silica microparticles in water 
 ( 5.2  0.3 m as in figure 2a ) . 

second , after etching of the silica templates , we measured the diameter 
 of the resulting hollow capsules to vary significantly depending upon 
 the solvent in which they were suspended ( figure 2c  e ) .
specifically , we measured capsule diameters to 
 be 6.7  0.3 m in water , 5.6  0.3 m in 90% 
 acetone/10% water , and 4.7  0.2 m in nematic e7 .
third , 
 upon extraction of lc - containing dadm capsules into an aqueous phase , 
 the capsule diameter was again measured to be 6.7  0.3 m 
 ( figure 2f ) , a value that is indistinguishable 
 from that of empty capsules in water .
overall , these observations 
 reveal that the volume of the lc encapsulated within the polymeric 
 shell is determined by the size of the capsule when it is present 
 in the nematic lc ( i.e. , during filling ; compare panels e and f of 
 figure 2 ) . when lc - filled capsules are extracted 
 into an aqueous phase , the capsules swell , thus resulting in capsules 
 that are only partially filled .
we emphasize that the volume of the 
 lc droplets caged within the polymer capsules when dispersed in water 
 is roughly equal to the interior volume of the capsules when they 
 are dispersed in nematic lc during filling .
the top row shows a cartoon 
 of the sample composition , the middle 
 row consists of bright - field images , and the bottom row contains the 
 corresponding fluorescence microscopy images of ( a ) bare silica microparticles 
 in water , ( b ) dadm - coated silica microparticles in water , ( c ) empty 
 dadm capsules in water ( after hf treatment and rinsing ) , ( d ) empty 
 dadm capsules in a solution of 90% acetone and 10% 
 water , ( e ) dadm capsules in nematic e7 , and ( f ) dadm capsules partially 
 filled with e7 in water .
the average capsule size is noted below the 
 fluorescence microscopy image , and the lc droplet size is also denoted 
 below ( f ) .
bright - field and fluorescence microscopy images are not 
 shown for all states , e.g. , where the sample was not in focus or not 
 fluorescent .
( a , b ) micrographs of the same group of capsules imaged with different 
 locations of the focal plane such that in ( a ) the circular capsule 
 on the right of the image was in focus and in ( b ) the crescent - shaped 
 capsule in the center of the group was in focus .
( c ) micrograph of 
 a separate region showing a group of capsules with more spherical 
 than nonspherical capsules .
finally , we comment that a fraction of capsules 
 observed in nematic 
 e7 ( approximately one in six capsules prior to extraction into water ) 
 possessed nonspherical crescent shapes , consistent with a buckling 
 instability in the capsule wall ( figure 3 ) . for these nonspherical capsules , we measured 
 the long axis ( i.e. , the largest diameter that could be measured ) 
 to be 4.5  0.3 m , corresponding to a diameter similar 
 to that of the spherical capsules ( 4.9  0.5 m ) , and the 
 short axis ( perpendicular to the long axis ) was measured to be 2.3 
  0.6 m .
this small subpopulation impacted the underfilling 
 of the capsules with lc and contributed to heterogeneity in the size 
 and shape of the capsules and droplets .
we note that the majority 
 of capsules that we observed to be nonspherical in the e7 phase returned 
 to a spherical shape when transferred to the aqueous phase ; a very 
 small percentage of capsules ( approximately 2% ) remained nonspherical 
 in shape .
figure 4a  c shows representative caged lc droplets imaged in 
 bright - field and polarized light modes as well as schematic illustrations 
 of the ordering of the lc in the droplets .
a number of features of 
 the droplets imaged between crossed polarizers led us to conclude 
 that the orientational ordering of the lc within these droplets corresponds 
 to a so - called bipolar configuration . in this configuration ,
aqueous interface with two point 
 defects at diametrically opposite poles , as depicted schematically 
 in the right column of figure 4 .
in figure 4a , the key identifying features are the two dark spots on the left 
 and right sides of the droplet , bright lobes above and below these 
 spots , and a relatively dark center of the droplet , indicating that 
 the lc in the center is aligned with either the polarizer or analyzer . 

the narrow dark spots correspond to point defects on the droplet surface 
 known as boojums that define the poles and , thus , the symmetry axis 
 of the bipolar nematic droplet .
( the angle that this symmetry axis 
 makes with the polarizer is indicated on the polarized light images . ) 

typically , boojum defects can be seen in bright - field images as dark 
 regions because they possess a local refractive index environment 
 that is distinct from that of the rest of the lc droplet and thus 
 scatter light . however , optical distortions resulting from the polymer 
 capsule prevented us from identifying the boojums in many of our bright - field 
 images .
bright - field and polarized light micrographs of dadm capsules in 
 water ( left and center columns , crossed polarizers indicated by white 
 arrows ) .
corresponding schematic illustrations of the lc director 
 profiles are shown in the right column .
the angle that the axis of 
 symmetry of the droplet makes with the polarizer is 0 in ( a ) , 
 14 in ( b ) , and 43 in ( c ) .
( d ) two droplets with asymmetric 
 shapes also exhibit signature features of bipolar ordering with arrows 
 indicating the locations of boojum defects .
figure 4b shows a droplet that has 
 its symmetry 
 axis , defined again by dark spots that correspond to the boojums , 
 at an angle between the polarizer and analyzer .
the rotation of the 
 symmetry axis away from the polarizer / analyzer results in a birefringent 
 texture within the droplet that is brighter than that shown in figure 4a .
this droplet also has curved dark bands within 
 the bright central region in a baseball - like pattern , a characteristic 
 that is frequently used to identify bipolar droplets .
figure 4c shows a bipolar lc droplet within 
 a capsule aligned with its axis of symmetry at an angle of 43 
 from the polarizer and analyzer . in this image
, we observed only one 
 bright region next to each boojum , as the other lobe is more closely 
 aligned with a polarizer . in summary ,
the observations reported above 
 are consistent with a bipolar configuration of roughly spherical lc 
 droplets within the capsules .
while the majority of the caged 
 lc droplets appeared to be spherical , 
 we also observed a subpopulation of nonspherical , asymmetric droplets 
 ( approximately one in four droplets was asymmetric ; see discussion below for a further analysis of shape ) .
figure 4d shows an example of two capsules that contain 
 nonspherical lc droplets . in these images
, it appears that the lc 
 has partially wet the inner surface of the capsules , causing the droplets 
 to distort to asymmetric lemonlike shapes .
droplets that assumed this 
 asymmetric shape , however , still exhibited birefringent textures that 
 closely resembled those of the spherical droplets .
we conclude that 
 the lc ordering in these cases is a distorted bipolar configuration 
 ( figure 4d ) , with the two boojums located close 
 to the contact line defined by the lc  polymer interface . here
, 
 we also note that the shape of the polymeric capsules did not appear 
 to be perturbed by partial wetting of the inner surface of the capsule 
 by the lc .
previous studies have shown that addition of surfactants 
 to aqueous 
 dispersions of lc droplets can trigger a bipolar - to - radial ordering 
 transition within the droplets .
inspired by these results , 
 we investigated the response of lc droplets confined within dadm capsules 
 to model anionic and cationic surfactants ( sodium dodecyl sulfate 
 ( sds ) and dodecyl trimethylammonium bromide ( dtab ) ) .
the first section 
 below describes lc wetting transitions within amphiphilic capsules 
 induced by sds and dtab , and the second section describes changes 
 in the internal ordering that occur in response to each of the two 
 surfactants .
we note that the highest concentrations of surfactant 
 used in the experiments described below were less than the critical 
 micelle concentrations to avoid the solubilization of the lc .
bright - field 
 ( top row ) , polarized light ( middle row , crossed polarizers ) , 
 and fluorescence ( bottom row ) micrographs of representative regions 
 showing lc ordering and wetting in partially filled capsules as a 
 function of increasing sds concentration ( indicated below each column ) . 

labels above each column indicate the internal ordering of the lc 
 at each concentration .
figure 5 shows the appearance of lc 
 droplets 
 within dadm capsules upon exposure to increasing concentrations of 
 sds .
an inspection of figure 5 reveals that 
 the addition of sds caused a continuous decrease in the contact angle 
 (  ) of the lc on the inner surfaces of the capsules ( see figure 6 for the definition of  and values of  
 measured from bright - field micrographs ) , resulting in a change in 
 the shape of the lc droplet .
figures 5 and 6 , when combined , first reveal that low concentrations 
 of sds ( 0.050.25 mm ) caused the lc droplets to adopt 
 a convex lens shape (   130  10 ) . at moderate 
 sds concentrations ( 0.251 mm ) , we observed hemispherically 
 shaped lc droplets (   89  5 ) , with approximately 
 planar ( low curvature or a large radius of curvature ( rc ) , see discussion below ) lc  aqueous 
 interfaces inside the capsules .
we note that the shape ( and internal 
 ordering ) of the lc droplets was not homogeneous within a sample ; 
 for example , at 0.25 mm sds , we observed both lens - shaped droplets 
 and nearly hemispherical droplets .
( see also figure 
 s3 for information regarding the distribution of  for 
 samples in water or at different surfactant concentrations . )
lastly , 
 at higher sds concentrations ( 0.510 mm ) , we observed 
 a large population of droplets that adopted a concave lc 
aqueous 
 interface within the capsules (  < 85 ; measurements 
 on these samples were difficult because the angle was occluded by 
 the lc when the interface was concave ; see also a representative video 
 included in the si ) .
these observations 
 of a continuous change in the contact angle of the lc droplet on the 
 inner wall of the polymeric capsule suggest that the interaction of 
 sds with the capsule walls triggered this wetting transition .
plot of contact 
 angles of caged lc droplets on the interiors of 
 polymeric microcapsules as a function of sds concentration ( number 
 of droplets measured n > 30 for each data point ) . 

in contrast to the above - described influence of sds on the 
 wetting 
 of lc on capsule walls , we did not observe a substantial change in 
 the shape or wetting of lc droplets in the presence of dtab ( see figure 7 ; the average  increased from 157  
 11 in water to 162  10 in 10 mm dtab ; see also the si for histograms of  ) .
in contrast to 
 our results using sds , this result suggests that dtab permeates but 
 does not adsorb to the wall of the capsule to an extent that it leads 
 to measurable changes in the contact angle , likely because of the 
 positive charge of the dimethylamine functional groups decorating 
 the outer walls of the dadm capsules .
bright - field ( top row ) , polarized light 
 ( middle row , crossed polarizers ) , 
 and fluorescence ( bottom row ) micrographs of representative regions 
 showing lc ordering and wetting within partially filled capsules as 
 a function of increasing dtab concentration ( indicated below each 
 column ) .
labels above each column indicate the internal ordering of 
 the lc at each concentration .
concurrent with the surfactant - induced wetting transitions 
 on the 
 inner surfaces of the capsules , we observed the ordering of the lc 
 within the droplets to change with the addition of sds and dtab ( middle 
 row of images in figures 5 and 7 ) .
as discussed above , the encapsulated lc droplets exhibited 
 bipolar ordering in water ( i.e. , no surfactant , see figure 4 ) .
when dtab was added to an aqueous dispersion 
 of encapsulated lc droplets , we observed very little change in the 
 shapes of the droplets ( figure 7 ) , and the 
 sequence of internal configurational states that we observed was similar 
 to that of free lc droplets .
the states observed include ( i ) saturn - ring 
 disclination line - containing states ( at 2.5 mm dtab ) , ( ii ) preradial 
 configurations with a single point defect on the surface ( from 2.5 
 to 5 mm ) , and ( iii ) radial configurations ( from 5 to 10 mm ) .
we note , 
 in particular , that the appearance of the radial configuration is 
 consistent with very weak interactions between the lc droplets and 
 the inner surfaces of the capsules .
past studies have noted that the 
 contact of lc droplets with surfaces often pins the configurational 
 state of lc droplets at high surfactant concentration in the preradial 
 state .
next , we characterized the 
 ordering states of the lc within the 
 lens- and hemispherical - shaped lc droplets (   85127 ) 
 that formed in the presence of sds .
figure 8a  d shows selected lc droplets in the presence of 0.25 mm 
 sds (   90 ) . we interpret the optical appearance 
 of these droplets to indicate that they possess ordering consistent 
 with an axial or saturn - ring configuration in which the axis of symmetry 
 of the lc ordering follows the axis of symmetry of the droplet shape . 

we note that this optical texture is observed 
 for lens - shaped droplets in the presence of 0.05 mm sds ( figure 5 ) , and it is also observed in samples at higher 
 concentrations of sds ( up to 1.0 mm ) .
as seen from a side view ( figure 8c , d ) , this director profile exhibits a disclination 
 line near the planar interface such that the profile resembles that 
 of a saturn - ring configuration .
( see figure s4 for images of bare e7 droplets with saturn - ring and radial configurations . )
schematic 
 director profiles ( left column ) with corresponding bright - field 
 ( middle column ) and polarized light ( right column , crossed polarizers 
 indicated by white arrows ) micrographs of ( a ) top , ( b ) tilted , and 
 ( c , d ) side views ( at different angles with respect to the polarizer / analyzer ) 
 of hemispherical lc droplets contained within dadm capsules in 0.25 
 mm sds .
( e , f ) side views at different angles of hemispherical lc 
 droplets in 1 mm sds .
( g , h ) schematics show possible director configurations 
 for inhomogeneous boundary conditions . additionally , the top view ( figure 8a ) of 
 the hemispherical droplets has four white lobes surrounding a dark 
 cross , consistent with the axial symmetry indicated in figure 8 .
as the sds concentration 
 was increased , the lc droplets transitioned to an internal configuration 
 that resembled a deformed radial droplet ( figure 8e , f , 1 mm sds , see also the video in the si ) with a point defect clearly visible in the bright - field 
 and polarized light micrographs .
we note that another possible director 
 configuration that is consistent with the micrographs is shown in 
 figure 8 g , as further discussed below .
the key results of the study reported in this article relate to 
 the response of caged lc droplets to surfactants .
in contrast to free 
 lc droplets , where sds and dtab trigger qualitatively similar configurational 
 transitions and cause a minimal change in shape , we observed dadm - caged 
 lc droplets to undergo wetting transitions in the presence of sds 
 but not dtab .
the change in droplet shape that accompanied the wetting 
 transition resulted in differential effects of the two surfactants 
 on the internal configurations of the lc within the droplets .
we emphasize 
 that this situation also differs from past reports that examined the 
 anchoring of lcs confined to capillaries ( diameter  10200 
 nm ) , microgrooves , silica 
 pores , polymer - dispersed cavities , and so forth 
 because the internal volumes of those structures were completely filled 
 with lc .
( thus , changes in shape were not observed ; see ref ( 34 ) for one exception . ) below , 
 we discuss in more detail the coupled wetting transitions and ordering 
 transitions described in this article . to provide insight into 
 the wetting transitions , we calculated 
 the shapes of the caged droplets by solving the laplace equation under 
 the assumption that gravity and the elasticity of the lc have a negligible 
 influence on shape .
the neglect of gravity is justified by an evaluation 
 of the bond number , calculated as bo = gl/ , where  is the 
 difference in densities of the fluid phases , g is 
 the acceleration due to gravity , l is the characteristic 
 length ( for which we use the droplet radius ) , and  is the interfacial 
 tension . for our experimental system
as noted above , we also neglect 
 the effect of the elasticity of the lc on the shape of the lc droplets 
 since the ratio of the elastic energy to the surface energy , given 
 as k/v ( where k is either the splay or bend elastic constant and k  10 n ) , is 10 for our experimental system .
aqueous 
 interface will have constant curvature within the caged lc droplets , 
 as predicted by the laplace equation under the above - stated conditions .
figure 9a shows the shapes of lc 
 droplets on ( i ) planar surfaces and ( ii ) the curved interior surfaces 
 of the microcapsules , both calculated as a function of  [ and 
 by assuming that the capsules are rigid ( see experimental observations 
 above ) and of constant size ] . for these calculations
, we used a volume 
 of lc that corresponded to 40% of the interior of the capsule 
 volume ( also consistent with the experiments reported in this article ) . 
 to enable comparisons of the lc droplet behavior on a flat substrate 
 and in a spherical cavity
, figure 9b shows 
 a plot of the interfacial area between the lc and polymer ( i.e. , the 
 wall of the capsule or the surface of the flat substrate ) and between 
 the lc and aqueous phase , both as a function of . finally , 
 figure 9c shows the radii of curvature of the 
 lc  aqueous interfaces , plotted as a function of  for 
 the two geometries . from figure 9a 
first , an inspection of figure 9b reveals 
 that , within a spherical cavity defined by the polymer capsule , there 
 exists a crossover at which the interfacial area between the lc and 
 polymer capsule exceeds the interfacial area of the lc  aqueous 
 interface . for the lc volume and capsule size used in our calculations , 

this occurs at   130. in contrast , on a planar 
 surface , the interfacial area between the droplet and supporting substrate 
 is always less than the aqueous interface .
we also note that , on a 
 planar substrate , the areas of the two interfaces of the lc droplets 
 approach each other only in the limit of   0. 
 in this limit , a thin film of infinite area is predicted . in contrast , 
 however , in a spherical cavity , a thin film of finite thickness ( 0.5 
 m thick , as shown in figure 9a ) is formed 
 on the interior surface of the capsule wall in the limit of  
  0. from this result , we conclude that the caging of 
 droplets within capsules provides , in general , the basis of a versatile 
 method for control of the relative interfacial areas of liquids that 
 is not possible on flat surfaces .
( a ) calculated shapes for lc droplets 
 of constant volume ( using 
 the average experimental volume ) with varying contact angle for two 
 geometries : ( i ) on a flat surface and ( ii ) within a spherical cavity 
 equal in size to the dadm capsules in water .
black lines represent 
 the flat surface or spherical cavity , and blue lines represent the 
 lc  aqueous interface .
axes are square , with the grid on the x axis marking 10 m ( each droplet is plotted with 
 centers 10 m apart ) , and contact angles are used to label the x axis .
( b ) graph of interfacial areas ; interfaces are indicated 
 within the legend . ( c ) graph of the radius of curvature ( rc ) of the lc  aqueous interface for each geometry . 

( d ) shapes plotted for a constant contact angle of 90 for varying 
 volumes of lc , denoted on the plot relative to v , 
 the average volume measured experimentally .
the second set of observations that we make from figure 9 relates to the radius of curvature ( rc ) of the lc interface .
specifically , an examination of 
 figure 9c reveals that the caging of lc droplets 
 within capsules leads to radii of curvature of the lc interfaces that 
 are strikingly different from those on planar substrates .
in particular , 
 as the contact angle of the lc with the capsule wall approaches 84 , 
 we calculate rc of the lc  aqueous 
 interface to diverge to positive or negative infinity .
( see also experimental 
 observations in figure 5 . ) in contrast , the rc of lc on a planar interface diverges only 
 in the limit of   0. this fundamental difference 
 in the behavior of rc is significant , 
 as rc dictates the laplace pressure difference , 
  = pin  pout  = 2/rc , across the interface of the droplet .
thus , rc also affects the chemical potential of the lc inside a droplet , 
 which is given by i(rc ) = i( ) + 
 2vi / rc , where i( ) is the chemical potential of species i with a flat interface and vi is the molar volume of species i. in particular , we note that for all 
 contact angles ( figure 9c ) , the rc of the lc  aqueous interface for lc contained 
 within a spherical cavity is either negative ( at  < 84 ) 
 or larger ( 84 <  < 180 ) than that of the 
 lc on a flat surface .
this observation , when combined with the influence 
 of the laplace pressure on the chemical potential of the lc , leads 
 us to conclude that the chemical potential of caged lc is lower than 
 that of an lc droplet on a flat surface .
if two such droplets were 
 present in a system , then we would predict that ostwald ripening would 
 cause the growth of the encapsulated droplet at the expense of decreasing 
 the size ( and rc ) of the droplet of the 
 same volume on a flat surface .
the effects of changes in droplet volume 
 for caged lc droplets and lc droplets supported on flat surfaces are 
 shown in figure 9d ( for constant  = 
 90 ) .
for caged droplets , an increase in volume leads to an increase 
 in rc before turning negative .
significantly , 
 the chemical potential of the lc in the caged droplet decreases more 
 rapidly with increasing volume as compared to droplets on flat surfaces . 

this observation leads us to predict that capsules containing droplets 
 with rc < 0 will be stable with respect 
 to both uncaged droplets as well as bulk lc .
a second key result 
 reported in this article is that the wetting 
 transitions described above are coupled to changes in the internal 
 ordering and topological defects of the lc . in order to discuss this 
 coupling
, two key concepts need to be introduced , namely , the topological 
 charge of defects and the euler characteristic of closed surfaces . the topological charge ( n ) of a defect
is related to the number of times the lc 
 director rotates through all possible angles encountered on a surface 
 that encompasses the defect .
for example , in the case of a bipolar 
 droplet , a topological charge of n = + 1/2 is assigned 
 to each of the boojum defects by placing a hemispherical surface around 
 the boojum and evaluating the director orientations . for the case 
 of a radial droplet with a central point defect ,
the defect can be surrounded by a spherical surface that encounters 
 all possible angles of the director , and it therefore has a topological 
 charge of n = + 1 . for droplets in transition states 
 that connect the bipolar and radial configurations of spherical lc 
 droplets and possess uniform boundary conditions ( the tilt angle with 
 respect to the surface normal is the same everywhere on the droplet 
 surface ) , gauss s theorem requires the conservation of topological 
 charge . for example , the transition state that comprises a saturn - ring 
 disclination line located slightly inside the surface of the droplet 
 must have a topological charge of + 1 ( it can be encompassed by a spherical 
 surface that encounters all orientations of the lc director ) . another 
 commonly encountered transition state that lies between the bipolar 
 and radial configurations is the preradial configuration with a topological 
 charge of n = + 1 .
the above - described discussion 
 addresses the well - studied case 
 of configurational transitions in spherical droplets whereas the experiments 
 reported in this article address the more complicated situation where 
 changes in the shapes of the lc droplets accompany internal configurational 
 transitions . to address this situation
the euler characteristic of a sphere , and any 
 surface that can smoothly be transformed into a sphere ( e.g. , a football 
 and a bowl are both topologically equivalent to a sphere ) , is two .
this result is useful because , for uniform boundary conditions , 
 the sum of the topological charges ( n ) must be half 
 of the euler characteristic of a closed surface .
this 
 leads us to conclude that the euler characteristic of the caged lc 
 droplet shapes observed in our experiments is unaltered as compared 
 to that of spherical droplets because all shapes observed for the 
 caged lc droplets can be smoothly transformed into a sphere .
thus , 
 the wetting transitions reported in this article do not change the 
 conservation of topological charge discussed in the context of past 
 studies of free ( spherical ) droplets . specifically , 
 for lc droplets exposed to sds ( figures 5 and 8) , the wetting transition results in multiple shapes 
 ( lenses , hemispheres , and concave hemispheres ) , all of which are smooth 
 deformations of a spherical surface .
thus , if the boundary conditions 
 are uniform at all surfaces of the lc , then the internal configurations 
 of the lc in the presence of sds will be topologically equivalent 
 to bipolar , axial / saturn - ring , and radial configurations ( schematics 
 in figures 4 and 8a  f ) .
whether the anchoring of the lc at all surfaces of the caged droplets 
 is uniform , however , remains to be established .
it is possible that 
 the caged lc droplets possess inhomogeneous anchoring , for example , 
 due to differential adsorption of sds between the lc 
aqueous 
 interface or the lc  polymer interface ( figure 8g , h ) . in this scenario , due to
inhomogeneous anchoring , the 
 relationship of the topological charge and the euler characteristic 
 is changed from that discussed above .
the topological charges , however , 
 will still satisfy gauss s theorem and will be determined by 
 the specific profile of the director at the surfaces of the lc droplets . 
 in figure 8g ,
h , we present two possible director 
 configurations in the caged lc droplets that are consistent with the 
 nonuniform anchoring of the lc at its surfaces . in each case
polymer 
 interface , providing a net topological charge of + 1/2 ( see above ) . 
 as noted in the results section , the lc anchoring 
 shown schematically in figure 8 g is consistent 
 with the experimental observations shown in the micrographs in figure 8e , f .
however , we do not observe birefringent textures 
 that are consistent with the configuration in figure 8h .
we end by noting that in the limit of   
 0 the complete 
 wetting of lc on the inner surface of the capsule would lead to the 
 formation of a shell of lc .
this transition , although not yet observed 
 in our experiments , leads to the creation of a new surface and thus 
 the shell possesses an euler characteristic of + 4 ( and thus a topological 
 charge of + 2 ) . for additional discussion of this geometry
, we refer 
 the reader to studies of lc shells created from double emulsions .
in 
 summary , the key advances reported in this article are two - fold . 
 first , we provide insight into the physical processes that underlie 
 the formation of caged lc droplets contained within cross - linked polymer 
 multilayer capsules .
we demonstrate that dadm capsules swell reversibly 
 and that the extent of swelling correlates with the dielectric constant 
 of the solvent .
this result suggests principles by which the extent 
 of filling of the capsules can be systematically varied in future 
 studies .
we emphasize that the partial filling of the capsules reported 
 here underlies our observations of the lc wetting transitions .
the 
 second key advance involves surfactant - induced changes in both the 
 wetting and ordering of caged lc droplets . whereas the effects of 
 dtab and sds on the internal ordering of free lc droplets are similar
, 
 we reveal that the two surfactants trigger strikingly different wetting 
 and configurational transitions when the lc droplets are caged within 
 the polymeric capsules .
specifically , the addition of anionic sds 
 resulted in a progression of complex droplet shapes as the contact 
 angle of the lc on the inner surfaces of the capsules decreased ; in 
 contrast , no significant change in droplet shape was observed upon 
 addition of cationic surfactant dtab .
although additional measurements 
 are needed to quantify the orientation of the lc at the surfaces of 
 the complex shapes formed by the caged lc in the presence of the sds , 
 under the assumption of uniform anchoring the various internal states 
 of the droplets are topologically equivalent to axial and radial configurations 
 ( i.e. , consistent with the conservation of topological charge ) .
although 
 topologically equivalent to free droplets , the contributions that 
 surface anchoring , lc elasticity , and topological defects make to 
 the free energy of caged lc droplets will differ from those of free 
 droplets . as a result , caged lc droplets offer the promise of new 
 and versatile sources for the design of lc - droplet - based responsive 
 soft matter that can not be realized in dispersions of free droplets . 

we also note that the physics of caged lc droplets is conceptually 
 similar to that of liquid - crystalline dna toroids confined in viral 
 capsids . as such , caged lc droplets may 
 offer the basis of a model system for understanding some aspects of 
 dna packing in viruses .
 we 
 report a study of the wetting and ordering of thermotropic liquid 
 crystal ( lc ) droplets that are trapped ( or  caged  ) 
 within micrometer - sized cationic polymeric microcapsules dispersed 
 in aqueous solutions of surfactants . when they were initially dispersed 
 in water , we observed caged , nearly spherical droplets of e7 , a nematic 
 lc mixture , to occupy 40% of the interior volume of the polymeric 
 capsules [ diameter of 6.7  0.3 m , formed via covalent 
 layer - by - layer assembly of branched polyethylenimine and poly(2-vinyl-4,4-dimethylazlactone ) ] 
 and to contact the interior surface of the capsule wall at an angle 
 of 157  11. the internal ordering of lc within 
 the droplets corresponded to the so - called bipolar configuration ( distorted 
 by contact with the capsule walls ) . while the effects of dodecyltrimethylammonium 
 bromide ( dtab ) and sodium dodecyl sulfate ( sds ) on the internal ordering 
 of  free  lc droplets are similar , we observed the two 
 surfactants to trigger strikingly different wetting and configurational 
 transitions when lc droplets were caged within polymeric capsules . 
 specifically , upon addition of sds to the aqueous phase , we observed 
 the contact angles (  ) of caged lc on the interior surface of 
 the capsule to decrease , resulting in a progression of complex droplet 
 shapes , including lenses (   130  10 ) , hemispheres 
 (   89  5 ) , and concave hemispheres (  
 < 85 ) . the wetting transitions induced by sds also resulted 
 in changes in the internal ordering of the lc to yield states topologically 
 equivalent to axial and radial configurations . 
 although topologically 
 equivalent to free droplets , the contributions that surface anchoring , 
 lc elasticity , and topological defects make to the free energy of 
 caged lc droplets differ from those of free droplets . 
 overall , these 
 results and others reported herein lead us to conclude that caged 
 lc droplets offer a platform for new designs of lc - droplet - based responsive 
 soft matter that can not be realized in dispersions of free droplets . 
Introduction
Experimental Section
Results
Discussion
Conclusions