Self-reporting and self-regulating liquid crystals

Abstract

Liquid crystals (LCs) are anisotropic fluids that combine the long-range order of crystals with the mobility of liquids^1,2. This combination of properties has been widely used to create reconfigurable materials that optically report information about their environment, such as changes in electric fields (smart-phone displays)³, temperature (thermometers)⁴ or mechanical shear⁵, and the arrival of chemical and biological stimuli (sensors)^6,7. An unmet need exists, however, for responsive materials that not only report their environment but also transform it through self-regulated chemical interactions. Here we show that a range of stimuli can trigger pulsatile (transient) or continuous release of microcargo (aqueous microdroplets or solid microparticles and their chemical contents) that is trapped initially within LCs. The resulting LC materials self-report and self-regulate their chemical response to targeted physical, chemical and biological events in ways that can be preprogrammed through an interplay of elastic, electrical double-layer, buoyant and shear forces in diverse geometries (such as wells, films and emulsion droplets). These LC materials can carry out complex functions that go beyond the capabilities of conventional materials used for controlled microcargo release, such as optically reporting a stimulus (for example, mechanical shear stresses generated by motile bacteria) and then responding in a self-regulated manner via a feedback loop (for example, to release the minimum amount of biocidal agent required to cause bacterial cell death).

Main

We use nematic phases as representative LCs. Nematic LC phases comprise molecules that assume a preferred orientation, called the director n¹. This leads to anisotropic optical properties (birefringence) and elasticity, the latter allowing energy to be stored in strained states of LCs at rest (for example, via bending, splaying or twisting)^1,2. When a dispersed microphase of an immiscible liquid, solid or gas (guest) is introduced into an LC host, the ordering of LCs around the guest microphase is determined by a competition between the elastic energy (KR) arising from the strain of the LC and an orientation-dependent interfacial energy at the LC–guest interface (WR²), where K is the Frank elastic constant of the LC, W is the surface-anchoring energy density and R is the radius of the guest^2,8,9. If WR² > KR (that is, R > K/W), the guest will elastically strain the LC and thus can generate a strong repulsive force (elastic repulsion, F_e) between the guest and the boundaries of the nematic LC (Fig. 1a)^10,11,12. The strain and associated topological defects will also mediate interactions between guest microphases, which can prevent contact or coalescence of liquid microphases^{10,11,12,13,14}. For typical nematic LCs formed from small organic molecules (thermotropic LCs), K ≈ 10⁻¹² N and W ≈ 10⁻⁶ J m⁻² (ref. ⁸); thus, K/W ≈ 1 µm and the associated elastic energy is about 2,400k_BT (Methods), where k_B is the Boltzmann constant and T is the temperature. In the absence of external forces, therefore, we predict that dispersed microphases with R ≥ K/W would be sequestered by elastic forces within a bulk nematic phase and prevented from escaping into the surrounding environment.

Fig. 1: Pulsatile ejection of microdroplets from LCs and accompanying LC optical responses, as triggered by N–I phase transitions.

a, Molecular structure of 5CB and optical micrograph (bright field) of an aqueous microdroplet (containing 9 mM of SDS and red tracer) in nematic 5CB with a reconstructed LC director profile. F_e1 is the repulsive elastic force acting between the aqueous microdroplet and the interface between the LC and the overlying aqueous phase. Scale bar, 10 µm. b, Illustration of a dispersion of aqueous microdroplets in an LC that is hosted in a mini-well and submerged under a bulk aqueous phase that is initially free of tracer. c, d, f, h, Sequential photographs of the LC-filled mini-well containing the initial N phase (c) and after N-to-I (d), N-to-I-to-N (f) and 10 phase transitions (h); see Supplementary Video 1. The phase transitions were triggered by heating and cooling between 25 °C and 50 °C. Scale bar, 3 mm. e, Mass of tracer released (solid line) from LC as a function of time before (black circles) and after N-to-I phase transition (red circles); the accompanying optical response of the LC is shown by the dashed line. The insets show micrographs of mini-wells (of diameter 3 mm) between crossed polars (top view). g, Mass of tracer released as a function of the number of phase transitions. Red and blue circles indicate mass released after N-to-I and I-to-N phase transitions, respectively. a.u., arbitrary units. i, Mass of tracer released after 20 phase transitions as a function of the microdroplet concentration (C_aq) initially in the LC. The data points show mean values and the error bars represent 1 s.d. (n > 3). j, k, Sequential micrographs showing the transport of small (dashed circles; R < R*), but not of large (solid circles; R > R*), microdroplets by a moving N–I interface (yellow arrows; v_NI = 10 µm s⁻¹) upon heating. Scale bar, 20 µm. l, Calculated net force ${F}_{{\rm{h}}}^{{\rm{net}}}(z)$ acting on a microdroplet (R = 1.5 µm) near an N–I interface. The insets show microdroplets for z ≥ R (red line), −R < z < R (blue line), and z ≤ −R (black line). Red and blue arrows indicate the forces that favour and oppose the ejection of microdroplets, respectively. F_e2 is the repulsive elastic force acting between the aqueous microdroplet dispersed in the N phase and the N–I interface, which is modified by the elastic force F_e* and interfacial tension force F_it when the aqueous microdroplet penetrates that N–I interface (Methods). m, Calculated dependence of R* on v_NI. The red dashed line indicates R* at v_NI = 10 µm s⁻¹, which coincides with the experimental conditions.

To demonstrate the elastic trapping of guest microphases in LCs, we dispersed aqueous microdroplets (0.5 µm ≤ R ≤ 3 µm) containing a model chemical solute (a red dye for visualization) and the surfactant sodium dodecyl sulphate (SDS) in nematic 4′-pentyl-4-biphenylcarbonitrile (5CB; Fig. 1a), and then filled a mini-well (3.5 mm in depth) with the dispersion (Fig. 1b). The SDS adsorbed at the interface between the aqueous microdroplets and the LC and aligned n perpendicular to the local droplet interface; this is called homeotropic anchoring⁷. Accordingly, each aqueous microdroplet was surrounded by a region of strained LCs that included a point topological defect (called a hyperbolic hedgehog^{10,11,12,13,14}; Fig. 1a). At the interface between the LC and the overlying bulk aqueous phase, the LC adopted a parallel orientation (planar anchoring), leading to a bright optical appearance of the system (left inset in Fig. 1e). As shown in Fig. 1c and Extended Data Fig. 1, the aqueous environment contacting the LC remained free of red tracer after four days at room temperature. This result is consistent with the effects of the elastic repulsion^10,11,12 of the guest microdroplets away from the interface between the LC and the overlying aqueous phase by a force F_e1 = −A²BπK[R/(h₁ + R)]⁴, where A is a numerical factor (A = 0 for R < K/W or for an isotropic phase^10,11), B is an anchoring-dependent constant (B = 3/4 and B = 1/2 for the parallel and perpendicular orientation, respectively, of n at the interface between the LCs and the bulk aqueous phase) and h₁ is the distance between the microdroplet surface and the LC interface to the bulk aqueous phase (Fig. 1a). The trapping of microdroplets within LCs was observed to occur regardless of the relative density of the microdroplets (ρ_aq) and the LCs (ρ_LC) because F_e1 is much larger than buoyant forces (F_b) at room temperature; for R = 3 µm and 5CB, |F_e1/F_b| > 500 at h₁/R < 1 (Methods).

Thermal and chemical stimuli can trigger optical responses in LCs via changes in LC ordering^2,4,6,7,8,15. For example, 5CB undergoes a first-order transition from a nematic (N) to an isotropic (I) phase at temperature ${T}_{{\rm{NI}}}^{5{\rm{CB}}}=35{}^{\circ }{\rm{C}}$. Alternatively, isothermal phase transitions can be induced by absorption of solutes¹⁶. We found that heating of 5CB containing microdroplets to T_h > 35 °C from below (through contact with a warm body) led not only to an N-to-I phase transition accompanied by an optical response of the LCs (bright to dark; see insets and dashed line in Fig. 1e), but also to the ejection of microdroplets and red tracer into the overlying aqueous environment (Fig. 1d and solid line in Fig. 1e). The release occurred irrespective of the relative magnitudes of ρ_aq and ρ_LC, including in conditions under which the microdroplets sediment downwards and away from the interface to the overlying aqueous environment (ρ_aq >ρ_LC). Surprisingly, the release was transient, coinciding with the time period of the phase transition (Fig. 1e). After the phase transition, we did not measure any additional release for a period of 24 h (Extended Data Fig. 1). A second pulse of solute was released when the system was cooled back to T_c = 25 °C to reform the birefringent N phase (Fig. 1f). We subsequently repeated the heating and cooling cycles and observed that, with each optical response, a well defined pulse of microdroplets was ejected into the overlying aqueous phase (Fig. 1g). After 20 cycles, the mass of solute dispensed into the aqueous environment was linearly proportional to the initial concentration of aqueous microdroplets, C_aq, in the LCs (Fig. 1h, i), revealing a high level of control. Thermal release was also conveniently initiated by ohmic heating of a thin, electrically resistive film supporting the LCs (Extended Data Fig. 1).

We determined that the pulsatile ejection of microdroplets accompanied the upward motion of the N–I interface towards the overlying aqueous environment (Extended Data Fig. 1). Microscopic observations revealed that repulsive elastic interactions between the aqueous microdroplets and the moving N–I interface pushed the microdroplets ahead of the interface in a manner that depended on the size of the microdroplets (Fig. 1j, k). Past studies¹⁷ have observed N–I interfaces to transport adsorbed colloids, but they have not reported the elastic levitation of colloids ahead of an N–I interface, as is required for triggering the release of the microdroplet shown in Fig. 1. The elastic force—evaluated as F_e2 =  + A²BπK(R/z)⁴, where B = 3/4 and z is the vertical position of the centre of the microdroplet relative to an N–I interface (z = 0)—elastically levitates the microdroplets to a height defined by the net force ${F}_{{\rm{h}}}^{{\rm{net}}}(z)=0$ above the N–I interface (see Fig. 1l and Methods)¹¹. In the absence of F_e2, the microdroplets will not be transported by the rising N–I interface. Microdroplets pushed by F_e2 ahead of the moving N–I interface also experience a downward Stokes drag force F_S = −6πη_LCv_aqR, where η_LC is the dynamic viscosity of the LC and v_aq is the velocity of the microdroplet¹⁸ (which is equal to the velocity v_NI of the moving N–I interface for microdroplets transported by the N–I interface). If F_S exceeds the maximum value of ${F}_{{\rm{h}}}^{{\rm{net}}}(z)$ (Fig. 1l), microdroplets break through the moving N–I interface. For (z–R)/R $\ll$ 1, F_e2 is independent of R, whereas F_S scales linearly with R; thus, for each value of v_NI, our model defines a critical microdroplet radius R* above which microdroplets are not transported by the moving N–I interface (Fig. 1m and Extended Data Fig. 2). Our model predicts R* = 10.2 µm for v_NI = 10 µm s⁻¹ (Fig. 1m), in good agreement with our experiments (Fig. 1j, k; R* = 10 ± 1 µm). Our model also predicts that microdroplets with R = 1.5 µm pushed by an N–I interface with v_NI = 10 µm s⁻¹ will be able to reach within 60 nm of the interface of an overlying aqueous phase. At this separation, attractive interfacial forces, such as van der Waals and electrical double-layer forces (see below), mediate the fusion of the microdroplets with the overlying aqueous phase (Extended Data Fig. 3).

Modified versions of the above-described elastostatic model can account for the ejection of microdroplets by the upward motion of the N–I interface during cooling (Methods and Extended Data Fig. 4). In addition, the model predicts that tuning of the elastic properties of the LC, which can be achieved using light¹⁹, temperature^19,20 and chemical additives^6,7,16, can trigger optical responses in LCs along with a continuous release of microdroplets; these predictions were verified by experiments (see Extended Data Figs. 5–7 and Methods).

The orientations of LCs respond to interfacial interactions, which can be modulated by the adsorption of specific synthetic and biological molecules, as well as chemical transformations (for example, enzymatic or photochemical) of adsorbed species^6,7. We found that specific interfacial events can introduce interactions (for example, interfacial charge interactions) that override the elastic trapping of microdroplets. For example, at room temperature, microdroplets containing anionic amphiphile (SDS) and solutes were elastically trapped within supported films of 5CB (thickness, 40 μm) immersed under an aqueous phase (Fig. 2a, d). The LC films have bright optical appearances due to the planar anchoring of the LCs at the interface to the bulk aqueous phase. However, addition of a cationic amphiphile (dodecyltrimethylammonium bromide; DTAB) to the bulk aqueous environment triggered an LC anchoring transition to a homeotropic orientation. The anchoring transition caused an optical response from the LC (bright to dark; see Fig. 2a, b) and the release of microdroplets into the overlying aqueous phase (Fig. 2a–g). By contrast, addition of anionic amphiphiles to the overlying aqueous phase did not trigger release of microdroplets (Fig. 2g). The rate of microdroplet release was correlated closely with the zeta potential, ζ, of the interface between the LC and aqueous phase, which is controlled by addition of charged amphiphiles (Fig. 2g, h). These observations indicate that release of microdroplets is triggered by electrical double-layer forces²¹ (F_edl) acting between the microdroplets and the interface between the LC and the bulk aqueous phase. These forces can overcome the elastic forces (F_e1) that trap the microdroplet initially. We evaluated the double-layer forces as ${F}_{{\rm{edl}}}=-4{\rm{\pi }}{\varepsilon }_{0}\varepsilon (R/\lambda ){({k}_{{\rm{B}}}T/{e}_{{\rm{c}}})}^{2}{Y}_{{\rm{p}}}{Y}_{{\rm{i}}}\hspace{2.77626pt}{{\rm{e}}}^{-{h}_{1}/\lambda }$, where λ is the Debye screening length, ε is the relative dielectric constant measured along the interface normal, ε₀ is the vacuum permittivity, e_c is the elementary charge, and Y_p and Y_i are the effective surface potentials of the microdroplet and the LC interface, respectively (see Methods). The calculated net force $\left({F}_{{\rm{i}}}^{{\rm{net}}}={F}_{{\rm{edl}}}+{F}_{{\rm{e1}}}\right)$ experienced by microdroplets near the LC interface confirmed that addition of DTAB generates an attractive F_edl that overcomes the repulsive F_e1 (Fig. 2i). We also found a strong correlation between ζ, F_edl and the microdroplet release rate (Extended Data Fig. 8). We examined the influence of microdroplet size (R) on ${F}_{{\rm{i}}}^{{\rm{net}}}$ and the experimental release of microdroplets. In the limit of h₁ ≪ R (close approach), larger microdroplets experience a larger attractive ${F}_{{\rm{i}}}^{{\rm{net}}}$ due to F_edl (in this limit, F_e1 is independent of R whereas F_edl scales linearly with R). Importantly, however, the distance dependence of F_e1 and F_edl leads to a repulsive kinetic barrier $\left({F}_{{\rm{i}}\ast }^{{\rm{net}}} < 0\right)$ that grows with R (Fig. 2i, j). Specifically, our model predicts that a kinetic barrier will prevent ejection of microdroplets with R > 2.3 µm. Our experimental observations confirmed the existence of the size-dependent kinetic barrier (Fig. 2k). The role of interfacial charge in triggering microdroplet release was also confirmed by experiments involving changes in pH and the adsorption of polyelectrolytes (Extended Data Fig. 8). In addition, we demonstrated that adsorption of anionic bacterial lipopolysaccharides (Extended Data Fig. 9) can introduce interfacial charge interactions that trigger changes in the optical appearance of LCs and the release of microdroplets containing anti-bacterial agents (for example, DTAB) from the LCs.

Fig. 2: Isothermal triggering of release of microdroplets dispersed in LCs by interfacial charge interactions.

a–f, Sequential micrographs (crossed polars, top view, a–c) and corresponding illustrations (side view, d–f) of an LC film (thickness 40 µm, hosted in a square grid) containing microdroplets (concentration C_SDS = 9 mM and red tracer) before (a, d) and after addition of the cationic amphiphile DTAB (10 mM) to the overlying aqueous phase, at 0 (b, e) and 60 min (c, f). P and A indicate the orientations of the polarizer and analyser, respectively. Red and blue arrows indicate the forces that favour (electrical double-layer force, F_edl) and oppose (elastic repulsion, F_e1) the ejection of microdroplets, respectively. Green (in e, f) and white (inset in f) circles with tails represent cationic (DTAB) and anionic (SDS) surfactants, respectively. Scale bar, 200 µm. g, Mass of tracer released from the LC following the addition of DTAB at concentrations C_DTAB = 2 mM (upside-down triangles), 5 mM (empty circles), 10 mM (triangles) or SDS at C_SDS = 5 mM (full circles) to the overlying aqueous phase. The symbols show mean values and the error bars are 1 s.d. (n > 5). h, Zeta potentials (ζ) of LC–aqueous interfaces without amphiphiles (white bar) and with SDS (grey bar) or DTAB (green bars). Data show mean values and the error bars are 1 s.d. (n > 3). i, Calculated net force $\left({F}_{{\rm{i}}}^{{\rm{net}}}={F}_{{\rm{edl}}}+{F}_{{\rm{e1}}}\right)$ acting on a microdroplet (C_SDS = 9 mM) with R = 1.5 µm (red), 3 µm (black) and 5 µm (blue) after the addition of DTAB (10 mM; solid lines) or SDS (5 mM, R = 1.5 µm; red dashed line) to the overlying aqueous phase, plotted as a function of h₁. The inset shows the corresponding elastic (F_e1; grey) and electrical double-layer (F_edl; orange dashed and solid lines are for C_SDS = 5 mM and C_DTAB = 10 mM in the overlying aqueous phase, respectively) forces for R = 1.5 µm. j, Magnitude $\left({F}_{{\rm{i}}* }^{{\rm{net}}}\right)$ of the kinetic barrier in i as a function of R. k, Measured fraction of microdroplets released with R = 1–2 µm, 2.5–3.5 µm and 4.5–5.5 µm. Data are mean values and error bars are 1 s.d. (n > 10).

Past studies^1,2,3,4,5 have demonstrated that interfacial shear stresses can change the orientations of LCs; here we show that this leads to changes in both F_edl(ε) and F_e1(B) due to the orientation dependence of ε and B, respectively. The orientation of the LC director changes when interfacial shear stresses exceed the elastic torque required to rotate the LC (which is approximately equal to K(∂²Ψ/∂d²), where Ψ is the angle of the LC director from the surface normal and d is distance from the LC interface¹⁵). For a typical nematic LC (K ≈ 10⁻¹² N), we calculate that an interfacial shear stress of 1 N m⁻² is sufficient to reorient the LC director within an interfacial layer with thickness of about 10⁻⁶ m (as seen in our experiments). In agreement with this calculation, we observed aqueous phases sheared at 10⁴ s⁻¹ to generate interfacial shear stresses of about 10 N m⁻² (the viscosity of water is 10⁻³ kg m⁻¹ s⁻¹) that triggered changes in the orientations and optical responses of LC films with initially homeotropic (Fig. 3a, b) or planar (Fig. 3c, d) orientations. When the initial orientation of the LC at its interface with the overlying aqueous phase was planar, we observed microdroplets containing cationic surfactant (with concentration C_DTAB = 2 mM) to be elastically trapped within the LC, consistent with our calculation that the attractive F_edl cannot overcome the repulsive F_e1 (solid lines in Fig. 3e, f); we evaluated F_edl and F_e1 using ε = 13.2, B = 3/4 and ζ = −42.5 mV  at the interface between the LC and the overlying aqueous phase (Fig. 2h). The presence of mechanical shear at the interface, however, caused the orientation of the LC to deviate from the initial planar orientation (Fig. 3c, d; see also Fig. 4), which changed the balance of orientation-dependent elastic and electrical double-layer forces. For the limiting case of a fluctuation to a perpendicular orientation (ε = 19.7 and B = 1/2), we calculated the increase in F_edl and decrease in F_e1 to be sufficient to trigger ejection of microdroplets (see dashed lines in Fig. 3e, f and Methods). This prediction was confirmed by experiments showing that microdroplet release was triggered by the interfacial shear stresses (> 10 N m⁻²) generated by shearing the overlying aqueous phase with a magnetic bar (Fig. 3g, h).

Fig. 3: Optical response of LCs and release of microdroplets from LCs, as triggered by interfacial shear stresses.

a–d, Optical response of LC films (of thickness 40 µm, hosted in a square grid supported on a treated-glass slide; crossed polars) with initially homeotropic (a, b; achieved using 2 mM SDS in the aqueous phase) or planar (c, d; surfactant-free aqueous phase) anchoring at the interface of the LCs with the overlying aqueous phase, before (a, c) and after (b, d) the introduction of interfacial shear stress via convection in the aqueous phase. Scale bar, 200 µm. e, f, Calculated F_edl (e; red lines), F_e1 (e; blue lines) and net force (f; black lines) for an aqueous microdroplet (R = 1.5 µm) containing C_DTAB = 2 mM (ζ = 90 mV; Fig. 2h), with planar (solid lines) or homeotropic (dashed lines) orientation of the LC at its interface (with ζ = −42.5 mV ) with the overlying aqueous phase. g, h, Sequential photographs showing the ejection of microdroplets (C_DTAB = 2 mM and red tracer) from the LCs, which is triggered by interfacial shear stresses, before (g) and after (h) stirring the overlying water with a magnetic bar for 30 min to generate an interfacial shear stress of about 10 N m⁻². Scale bar, 1 cm.

Fig. 4: Release of microcargo from LCs by the heat of a human finger or by motile bacteria that generate interfacial shear stresses and interact with microcargo in a self-regulated manner.

a–d, Schematic illustration (a) and sequential photographs (b–d) showing that the touch of a human finger can trigger a change in the Bragg diffraction of light and release of a well defined pulse of microdroplets (C_SDS = 2 mM and red tracer) from a cholesteric LC into the water (see Supplementary Video 2). Scale bar, 1 cm. e–h, Illustration (side view, e) and sequential photographs (side view, f–h) showing interfacial shear stresses generated by motile bacteria (10⁷–10⁸ E. coli cells per millilitre) triggering the self-regulated release of microdroplets containing anti-bacterial agent (C_DTAB = 2 mM and silver salts) and red tracer, before the arrival of bacteria (f), immediately after the arrival of motile bacteria (g; Supplementary Video 3) and two hours after the arrival of bacteria and following cell death (h). Scale bar, 40 µm. i, Optical responses and side views (crossed polars) of the LC interface corresponding to f–h. Scale bar, 10 µm.

Conventional materials used for controlled release of small or large molecules do not self-report triggering events, have not been shown to respond to the same combinations of physical, chemical and biological stimuli that we describe here, and do not permit programming of the diversity of dynamic responses (for example, pulsatile or continuous release), including self-regulating responses. For example, guided by the results shown in Fig. 1, we designed a cholesteric (chiral nematic)²² LC system that was triggered by the touch of a human finger (Fig. 4a–d; Supplementary Video 2). An N-to-I phase transition, which was designed to occur upon exposure to physiological temperature, triggered a change in the Bragg diffraction of light (as used in electronic paper³ and LC thermometers⁴), and elastic forces F_e2 generated ahead of the N–I interface ejected a precise dose of chemical microcargo (a dye for visualization and a cleaning agent). We note that the twisted LC within the cholesteric phase modifies the magnitude of F_e relative to an achiral nematic phase, but does not eliminate the force required to eject microcargo²³. The programmed release of precise doses of microcargo upon thermal activation differs from the behaviour of conventional materials that release chemical agents continuously upon thermal activation until the stimulus is removed or the agent reservoir is exhausted (for example, thermally responsive hydrogels²⁴ and lyotropic LC matrices²⁵). Current methods that release precise and repeated doses of active agent require the use of devices incorporating micrometre-scale chips, pumps, valves or flow channels²⁶. The LC response shown in Fig. 4a–d can also prevent the release of excess agent (minimizing waste or toxicity) and extend the lifetime of the material so that it can withstand repeated triggering events (for example, releasing cleaning agents from a touch screen by exposure to physiological temperature). The optical response of the LC also permits self-reporting of the triggering event, which can be used to signal the amount of agent released and the remaining useful lifetime of the material.

We also used the results shown in Figs. 2 and 3 to design self-reporting and self-regulating LC materials that are triggered by mechanical shear stresses generated by the swimming motion of motile bacteria (for example, Escherichia coli). As noted above, interfacial shear stresses of 1 N m⁻² can reorient an LC (see Fig. 3 and associated text) and generate LC interfacial velocities v _x of 10 µm s⁻¹ (calculated from viscous stresses of about α(∂v _x /∂d) within the LC film, where α is the LC effective viscosity, α ≈ 10⁻¹ kg m⁻¹ s⁻¹). We observed that the arrival of motile bacterial cells moving at 30–40 µm s⁻¹ triggered shear-induced changes in the orientation of the LC, leading to optical reporting of the presence of bacteria (Fig. 4i) and triggering of the release of microcargo of antibacterial agents (Fig. 4e–h; Supplementary Video 3) via changes in F_edl and F_e1 (see Fig. 3e, f). Non- (v _x  = 0 µm s⁻¹) or weakly motile bacteria (v _x  < 10 µm s⁻¹) generated insufficient shear stresses to trigger the LC (Extended Data Fig. 10). Whereas conventional controlled-release materials, used in areas such as healthcare, water purification and food safety, release active agents regardless of whether bacteria are present (which can lead to antibacterial resistance)²⁷ or not, our LC material designs are self-regulating; they do not release antibacterial agents in the absence of bacteria (Fig. 4f) and release only the minimum amount of biocidal agent required to kill the bacterial cells (Fig. 4g). Specifically, self-regulation involves a feedback loop in which the bacterial shear-triggered release of antibacterial agent causes cell death, which in turn eliminates the trigger and ends the release of antibacterial agent (Fig. 4h). In addition, the self-reporting function of the LC material signals the successful killing of the bacteria (Fig. 4i). To our knowledge, this is the first example of a material with the capability to provide a self-regulated release of chemoactive agents in response to mechanical forces generated by living cells.

Our results demonstrate that LC materials can be designed to report thermal, chemical and mechanical triggers and release microcargo in response to these triggers. Given the broad range of triggers and underlying colloidal interactions (for example, elastic, electrical double-layer and shear stresses) that are perturbed by these triggers, our results provide the basis for a highly versatile approach. For example, in addition to the results reported above, we have used LCs in free-standing forms, such as LC emulsion droplets (Extended Data Fig. 11). We have also designed LC systems that respond to combinations of stimuli (for example, thermal plus chemical), thus providing more selective responses than is possible with a single stimulus (Extended Data Fig. 11). We note that specific biological processes, including specific binding events²⁸ and interfacial enzymatic events²⁹, can lead to changes in interfacial charge, thus enabling the introduction of additional selectivity into the reporting and release of microcargo. Promising future directions include the use of magnetic or electric fields to modulate the responses and actions of LC systems, the use of other LC phases, such as smectic and edible lyotropic chromonic LCs³⁰ and the triggered release of solid microcargo from LCs (Extended Data Fig. 12).

Methods

Comparison of the magnitudes of elastic and thermal energies

The elastic interaction energy E_e between a microdroplet and the boundaries of the nematic LC (for example, the interfaces of N–overlying aqueous phase, N–glass, N–I) can be written as^10,11,12:

$${E}_{{\rm{e}}}={A}^{2}B{\rm{\pi }}K\frac{{R}^{4}}{{\left(h+R\right)}^{3}}$$

(1)

where A is a numerical factor (A = 2.04 for microdroplets of R > K/W with homeotropic anchoring in an N phase and A = 0 for microdroplets of R < K/W or in an I phase)¹⁰, B is the anchoring-dependent constant (B = 3/4 and B = 1/2 for planar and homeotropic anchoring, respectively, at the boundaries of nematic LCs), R is the radius of the guest microdroplet, h is the distance between a microdroplet surface and the nematic boundary and K = (K₁ + K₃)/2 is the Frank elastic constant of the LC, where K₁ and K₃ are elastic constants for splay and bend deformations, respectively¹. As a microdroplet approaches a nematic interface, E_e increases and exhibits a maximum at h = 0. Because K ≈ 10⁻¹² N for typical thermotropic LCs, the maximum elastic interaction energy ${E}_{{\rm{e}}}^{{\rm{\max }}}$ for a microdroplet with R = 1 µm and B = 3/4 is 9.8 × 10⁻¹⁸ J. k_BT = 4.1 × 10⁻²¹ J at T = 25 °C, and thus ${E}_{{\rm{e}}}^{{\rm{\max }}}=2,383{k}_{{\rm{B}}}T$.

Comparison of the magnitudes of elastic forces and buoyant forces

Based on equation (1), the elastic repulsive force F_e between a microdroplet and a nematic interface can be written as^10,11

$${F}_{{\rm{e}}}\approx \pm {A}^{2}B{\rm{\pi }}K{\left(\frac{R}{h+R}\right)}^{4}$$

(2)

F_e is valid for a microdroplet in an N phase and needs to be modified for a microdroplet at an N–I interface (see below). The maximum F_e is ${F}_{{\rm{e}}}^{{\rm{\max }}}={A}^{2}B{\rm{\pi }}K$ at h = 0 and the buoyant force F_b acting on a microdroplet in the LC is F_b = (4/3)πR³g(ρ_LC − ρ_aq). At 25 °C, K_5CB = 7.3 pN (ref. ³¹), K_E7 = 14.4 pN (ref. ³²), ρ_5CB = 1.010 g cm⁻³ (ref. ³³), and we measured ρ_E7 = 1.057 g cm⁻³, ρ_aq = 1.018 g cm⁻³ with red dye and ρ_aq = 1.012 g cm⁻³ with green dye. Therefore, for a microdroplet (red dye) of R = 3 µm and B = 3/4 in 5CB, we get ${F}_{{\rm{e}}}^{{\rm{\max }}}=8,072{F}_{{\rm{b}}}$ and for a microdroplet (green dye) of R = 4 µm and B = 3/4 in E7, we have ${F}_{{\rm{e}}}^{{\rm{\max }}}=1,194{F}_{{\rm{b}}}$.

Net force ${{\boldsymbol{F}}}_{{\bf{h}}}^{{\bf{net}}}{\boldsymbol{(}}{\boldsymbol{z}}{\boldsymbol{)}}$ upon heating (Fig. 1)

The net force ${F}_{{\rm{h}}}^{{\rm{net}}}(z)$ acting on a quasi-static microdroplet with respect to the distance z between the centre of the microdroplet and the N–I interface (z = 0) upon heating can be written as

$${F}_{{\rm{h,N}}}^{{\rm{net}}}(z)={\left[-{A}^{2}B{\rm{\pi }}K{\left(\frac{R}{{h}_{1}+R}\right)}^{4}\right]}_{{F}_{{\rm{e1}}}}+{\left[{A}^{2}B{\rm{\pi }}K{\left(\frac{R}{z}\right)}^{4}\right]}_{{F}_{{\rm{e2}}}}+{\left[\frac{4}{3}{\rm{\pi }}{R}^{3}g\left({\rho }_{{\rm{LC}}}-{\rho }_{{\rm{aq}}}\right)\right]}_{{F}_{{\rm{b}}}}$$

(3)

at z ≥ R (in the N phase; see Fig. 1l (i)),

$$\begin{array}{c}\hspace{-30pt}{F}_{{\rm{h,NI}}}^{{\rm{net}}}(z)={\left[-{A}^{2}B{\rm{\pi }}K\frac{1}{{\left({h}_{1}+\frac{z+R}{2}\right)}^{4}}{\left(\frac{z+R}{2}\right)}^{4}\right]}_{{F}_{{\rm{e1}}}}+{\left[{A}^{2}B{\rm{\pi }}K\right]}_{{F}_{{\rm{e2}}}}\\ \hspace{30pt}+{\left[\frac{4}{3}{\rm{\pi }}{R}^{3}g\left({\rho }_{{\rm{LC}}}-{\rho }_{{\rm{aq}}}\right)\right]}_{{F}_{{\rm{b}}}}+{\left[-2{\rm{\pi }}R{\sigma }_{{\rm{NI}}}\left(1-\frac{{z}^{2}}{{R}^{2}}\right)\right]}_{{F}_{{\rm{it}}}}\\ \hspace{30pt}+{\left[-\left(1+\frac{z}{R}\right)\left\{\alpha \left[WR+\frac{{\left(WR\right)}^{2}}{K}\right]+\beta K\right\}\right]}_{{F}_{{\rm{e}}\ast }}\end{array}$$

(4)

at –R < z < R (at the N–I interface; see Fig. 1l (ii)), and

$${F}_{{\rm{h,I}}}^{{\rm{net}}}(z)={\left[\frac{4}{3}{\rm{\pi }}{R}^{3}g\left({\rho }_{{\rm{LC}}}-{\rho }_{{\rm{aq}}}\right)\right]}_{{F}_{{\rm{b}}}}$$

(5)

at z ≤ −R (in the I phase; see Fig. 1l (iii)). In these equations, h₁ is the distance between the microdroplet surface and the interface between the LC and the overlying aqueous phase (Fig. 1a), α = 0 for R > K/W, A = β = 0 for R < K/W, and B = 3/4 (parallel orientation at nematic boundaries).

When a microdroplet (R > K/W; homeotropic anchoring) is in the N phase (z ≥ R), the net force ${F}_{{\rm{h}},{\rm{N}}}^{{\rm{n}}{\rm{e}}{\rm{t}}}(z)$ arises from F_b and F_e with^10,11 A = 2.04; see Fig. 1l (i). As the N–I interface (z = 0) approaches the microdroplet, ${F}_{{\rm{h,N}}}^{{\rm{net}}}(z)$ increases and becomes positive (upward) at z < z* (at z = z*, ${F}_{{\rm{h,N}}}^{{\rm{net}}}=0$) owing to the elastic repulsion from the N–I interface (F_e2 in equation (3)); z* = 17.0 µm for a microdroplet with R = 1.5 µm and h₁ = 1 mm in 5CB. This reveals that the microdroplet will be levitated at z = z* above the N–I interface. ${F}_{{\rm{h,N}}}^{{\rm{net}}}(z)$ shows a maximum at z = R (red curve in Fig. 1l).

When the microdroplet penetrates the N–I interface (–R < z < R; Fig. 1l (ii)), two additional forces are generated from the changes in interfacial tensions^17,34 (F_it) and elastic strain^17,35 (F_e*). These forces drive the microdroplets into the I phase (Fig. 1l (ii)); see separate sections on F_it and F_e* for additional detail. Additionally, F_e needs to be modified because the part of the microdroplet that protrudes into the I phase no longer strains the LC. Because R in equation (2) is the radius of a microdroplet in the N phase, for simplicity, we used (R + z)/2 for heating and (R – z)/2 for cooling as the effective radius of the part of each microdroplet in the N phase. We also need to take into account the decrease in the topological strength m of the microdroplet² from 1 to θ/π, where θ (0 ≤ θ ≤ π) is half of the central angle of the part of the microdroplet in the N phase; see Extended Data Fig. 4a (ii). Because the elastic interaction is proportional^1,2 to m², the numerical factor A in equation (4) can be described as A = 2.04 m = (2.04/π)cos⁻¹(−z/R). Consequently, ${F}_{{\rm{h,NI}}}^{{\rm{net}}}(z)$ decreases rapidly at –R < z < R (blue curve in Fig. 1l).

When the microdroplet is in the I phase (z ≤ −R; Fig. 1l (iii)), the net force ${F}_{{\rm{h,I}}}^{{\rm{net}}}(z)$ is composed of only F_b; A = 0 and thus F_e = 0. Therefore, the microdroplets in 5CB (ρ_5CB < ρ_aq) sink whereas the microdroplets in E7 (ρ_E7 > ρ_aq) rise.

Upon heating, the elastic repulsion from the N−I interface promotes release of the microdroplets (F_e2 in equation (3)). Therefore, the moving N–I interface can only transport microdroplets with R > K/W in the nematic phase (F_e2 ≠ 0). The interface passes through the microdroplets with R < K/W because F_e2 = 0.

Net force ${{\boldsymbol{F}}}_{{\bf{c}}}^{{\bf{net}}}{\boldsymbol{(}}{\boldsymbol{z}}{\boldsymbol{)}}$ upon cooling (Fig. 1)

The net force ${F}_{{\rm{c}}}^{{\rm{net}}}(z)$ acting on a quasi-static microdroplet with respect to z can be written as:

$${F}_{{\rm{c,I}}}^{{\rm{net}}}(z)={\left[\frac{4}{3}{\rm{\pi }}{R}^{3}g\left({\rho }_{{\rm{LC}}}-{\rho }_{{\rm{aq}}}\right)\right]}_{{F}_{{\rm{b}}}}$$

(6)

at z ≥ R (in the I phase; Extended Data Fig. 4a (i)),

$$\begin{array}{c}\hspace{-60pt}{F}_{{\rm{c,NI}}}^{{\rm{net}}}(z)={\left[{A}^{2}B{\rm{\pi }}K\frac{1}{{\left({h}_{2}+\frac{R-z}{2}\right)}^{4}}{\left(\frac{R-z}{2}\right)}^{4}\right]}_{{F}_{{\rm{e3}}}}+{\left[-{A}^{2}B{\rm{\pi }}K\right]}_{{F}_{{\rm{e2}}}}\\ \hspace{30pt}+{\left[\frac{4}{3}{\rm{\pi }}{R}^{3}g\left({\rho }_{{\rm{LC}}}-{\rho }_{{\rm{aq}}}\right)\right]}_{{F}_{{\rm{b}}}}+{\left[2{\rm{\pi }}R{\sigma }_{{\rm{NI}}}\left(1-\frac{{z}^{2}}{{R}^{2}}\right)\right]}_{{F}_{{\rm{it}}}}\\ \hspace{30pt}+{\left[\left(1-\frac{z}{R}\right)\left\{\alpha \left[WR+\frac{{\left(WR\right)}^{2}}{K}\right]+\beta K\right\}\right]}_{{F}_{{\rm{e}}\ast }}\end{array}$$

(7)

at –R < z < R (at the N–I interface; see Extended Data Fig. 4a (ii)), and

$$\begin{array}{l}{F}_{{\rm{c,N}}}^{{\rm{net}}}(z)={\left[{A}^{2}B{\rm{\pi }}K{\left(\frac{R}{{h}_{2}+R}\right)}^{4}\right]}_{{F}_{{\rm{e3}}}}+{\left[-{A}^{2}B{\rm{\pi }}K{\left(\frac{R}{z}\right)}^{4}\right]}_{{F}_{{\rm{e2}}}}+{\left[\frac{4}{3}{\rm{\pi }}{R}^{3}g\left({\rho }_{{\rm{LC}}}-{\rho }_{{\rm{aq}}}\right)\right]}_{{F}_{{\rm{b}}}}\end{array}$$

(8)

at z ≤ −R (in the N phase; see Extended Data Fig. 4a (iii)). In these equations, F_e3 is the upward elastic repulsion from an LC–glass interface and h₂ is the distance between a microdroplet surface and the LC–glass interface (Extended Data Fig. 5k). For R > K/W, A = (2.04/π) cos⁻¹(z/R) in equation (7) and A = 2.04 in equation (8); for R < K/W, A = 0; B = 3/4. In the I phase (z ≥ R; see Extended Data Fig. 4a (i)), aqueous microdroplets in 5CB sink because ρ_5CB < ρ_aq (that is, ${F}_{{\rm{c,I}}}^{{\rm{net}}}(z) < 0$).

In contrast to heating, the two additional forces (F_it and F_e*) at –R < z < R are directed upwards upon cooling (see Extended Data Fig. 4a (ii)); F_it > 0 and F_e* > 0. As a result, ${F}_{{\rm{c,NI}}}^{{\rm{net}}}(z)$ becomes positive and exhibits a maximum at –R < z < R (Extended Data Fig. 4a). Importantly, upon cooling F_it > 0 and F_e* > 0, regardless of R. This indicates that the cooling N–I interface can transport the microdroplets with both R > K/W and R < K/W (Extended Data Fig. 4b), whereas upon heating the interface cannot transport the microdroplets with R < K/W (because F_e = 0).

At z ≤ −R (N phase; see Extended Data Fig. 4a (iii)), the microdroplets with R > K/W are sequestered in a nematic bulk whereas the microdroplets with R < K/W sediment away from the N–I interface.

In Fig. 1c–i, v_NI upon both cooling and heating was 37 ± 3 µm s⁻¹, for which our model predicts the dispensing of microdroplets with K/W ≤ R ≤ 3 µm upon heating and 0.6 µm ≤ R ≤ 6 µm upon cooling. This prediction is consistent with our observation that the amount of tracer released upon cooling was greater than that released upon heating (Fig. 1g).

Interfacial tension force, F _it

When a microdroplet is near an interface dividing two immiscible fluids (N and I phase in our case), F_it arises to minimize the surface tension energy³⁴. Typically, microdroplets are stabilized at the interface between two immiscible fluids because the interface tensions are similar in magnitude to each other. In thermotropic LCs, however, the surface tension at the N–I interface (σ_NI) is much smaller than the surface tension at the interfaces between the aqueous solution and the N (σ_aq–N) or I (σ_aq–I) phases. In the case of 5CB, for example, at T = 35 °C, σ_aq–N ≈ 7 × 10^–3 J m^–2, σ_aq–I ≈ 6 × 10⁻³ J m^–2 and σ_NI ≈ 10⁻⁵ J m^–2 (σ_aq–N > σ_aq–I $\gg$ σ_NI)^33,36. As a result, the aqueous microdroplets at the N–I interface are expelled to the I phase³⁴. For simplicity, we assume that F_it is active only when the microdroplet contacts the N–I interface; F_it = 0 at |z| ≥ R.

Elastic force, F _e*

When a microdroplet penetrates the N–I interface (–R < z < R), the elastic force acting on the microdroplet is modified^17,35 by F_e*. Whereas F_e acts to keep microdroplets in the nematic phase, F_e* expels the microdroplets into the isotropic phase to minimize the elastic free energy. In the weak anchoring regime (R < K/W), F_e* originates from the anchoring of the director at the microdroplet surface and the director deformation in the bulk nematic phase, and can be written as

$${F}_{{\rm{e}}\ast }(R < K{\rm{/}}W)={\left[WR{f}_{1}(z{\rm{/}}R)\right]}_{{\rm{surface}}}+{\left[\frac{{\left(WR\right)}^{2}}{K}{f}_{1}(z{\rm{/}}R)\right]}_{{\rm{bulk}}}$$

(9)

where f₁(z/R) is a dimensionless function of the penetration depth (z/R) of a microdroplet into an N phase^17,35.

In the strong anchoring regime (R > K/W), F_e* is given by

$${F}_{{\rm{e}}\ast }(R > K{\rm{/}}W)={\left[K{f}_{2}(z{\rm{/}}R)\right]}_{{\rm{bulk}}}$$

(10)

where f₂(z/R) is also a dimensionless function^17,35. Andrienko et al.³⁷ found that the force acting on a particle passing through an N–I interface is linearly proportional to the penetration depth z/R. In our evaluation, therefore, we simplified the dimensionless functions to ${f}_{1}(z/R)=\alpha (\mp 1-z/R)$  and  ${f}_{2}(z/R)=\beta (\mp 1-z/R)$

where – and + denote N-to-I and I-to-N phase transitions, respectively.

Electrical double-layer interaction, F _edl (Figs. 2 and 3)

F_edl can be calculated as

$${F}_{{\rm{edl}}}=-4{\rm{\pi }}{\varepsilon }_{0}\varepsilon \frac{R}{\lambda }{\left(\frac{{k}_{{\rm{B}}}T}{{e}_{{\rm{c}}}}\right)}^{2}{Y}_{{\rm{p}}}{Y}_{{\rm{i}}}{{\rm{e}}}^{-h/\lambda }$$

(11)

where ε₀ is the vacuum permittivity, ε is the relative permittivity of the LC, e_c is the elementary charge, Y_p is the effective surface potential of the microdroplet, Y_i is the effective surface potential of the interface between the LCs and the overlying aqueous phase and λ is the Debye screening length²¹. λ, Y_p and Y_i can be written as

$$\begin{array}{l}\lambda =\sqrt{\frac{{\varepsilon }_{0}\varepsilon {k}_{{\rm{B}}}T}{2{e}_{{\rm{c}}}^{2}{N}_{{\rm{A}}}I}}\,\,{Y}_{{\rm{p}}}=\frac{8tanh\left(D{\zeta }_{{\rm{p}}}{e}_{{\rm{c}}}/{k}_{{\rm{B}}}T\right)}{1+\sqrt{1-\frac{2\left(R/\lambda \right)+1}{{\left((R/\lambda )+1\right)}^{2}}{tanh}^{2}\left(\frac{D{\zeta }_{{\rm{p}}}{e}_{{\rm{c}}}}{{k}_{{\rm{B}}}T}\right)}}\,\,\\ {Y}_{{\rm{i}}}=4tanh\left(\frac{D{\zeta }_{{\rm{i}}}{e}_{{\rm{c}}}}{{k}_{{\rm{B}}}T}\right)\end{array}$$

(12)

where N_A is the Avogadro constant (N_A = 6.02 × 10²³ mol^–1), I is the ionic strength of the LC, D is a numerical factor and ζ_p and ζ_i are the zeta potentials at the microdroplet surface and LC interface, respectively. In our evaluation, we used D values between 1 and 2 and I = 1.8 × 10^–5 mol m⁻³ (corresponding to λ ≈ 0.66 µm at the LC interface with planar anchoring); λ ≈ 1.5 µm in 5CB without added electrolyte³⁸. The range of D values reflects the fact that the surface potential (~|Dζ|) is typically greater than the corresponding zeta potential³⁹ (|ζ|). We note that the exact value of D does not change the conclusions of our model. The value of D will influence the calculated radius of the microdroplets above which the kinetic barrier $\left({F}_{{\rm{i}}\ast }^{{\rm{net}}}\right)$ will prevent release of the microdroplets. Because equation (11) is valid at h > λ and it tends to overpredict²¹ F_edl at h < λ, we only evaluated F_edl at h ≥ λ.

In Figs. 2 and 3, therefore, the net force ${F}_{{\rm{i}}}^{{\rm{net}}}$can be written as

$${F}_{{\rm{i}}}^{{\rm{net}}}={\left[-4{\rm{\pi }}{\varepsilon }_{0}\varepsilon \frac{R}{\lambda }{\left(\frac{{k}_{{\rm{B}}}T}{{e}_{{\rm{c}}}}\right)}^{2}{Y}_{{\rm{p}}}{Y}_{{\rm{i}}}{{\rm{e}}}^{-{h}_{1}{\rm{/}}\lambda }\right]}_{{F}_{{\rm{edl}}}}+{\left[-{\left(2.04\right)}^{2}B{\rm{\pi }}K{\left(\frac{R}{{h}_{1}+R}\right)}^{4}\right]}_{{F}_{{\rm{e1}}}}$$

(13)

As shown in Fig. 2a–c, microdroplets containing anionic SDS (C_SDS = 9 mM) elastically sequestered in LCs can be ejected by an upward F_edl (> 0) induced by the addition of cationic DTAB (C_DTAB = 10 mM) into an overlying phase; for a microdroplet of R = 1.5 µm in 5CB, F_edl = 9.2 pN and F_e1 = –6.2 pN at h₁ = 1 µm. As evidenced by the optical response shown in Fig. 2, SDS or DTAB causes an anchoring transition from a parallel to perpendicular orientation at the interface between the LCs and the overlying aqueous phase. Because the anchoring transition involves the variation of B and ε (for the parallel orientation B = 3/4 and $\varepsilon =\left({\varepsilon }_{\perp }+{\varepsilon }_{\parallel }\right)/2$, and for the perpendicular orientation B = 1/2 and $\varepsilon ={\varepsilon }_{\parallel }$), F_edl increases, whereas F_e1 decreases. For 5CB, ${\varepsilon }_{\perp }=6.7$ and ${\varepsilon }_{\parallel }=19.7$ at T = 25 °C and we used $\varepsilon =\left({\varepsilon }_{\perp }+{\varepsilon }_{\parallel }\right)/2=13.2$  for the parallel orientation at the interface between the LC and the overlying aqueous phase because the microdroplet interface exhibits homeotropic anchoring.

Ejection of microdroplets upon the convection or the arrival of motile bacteria (Figs. 3 and 4f–h)

In the system, the net force is also expressed by equation (13). Microdroplets with cationic DTAB (C_DTAB = 2 mM) have an upward F_edl but are elastically sequestered because F_edl cannot overcome F_e1 under planar anchoring at the interface between the LC and the overlying aqueous phase (solid lines in Fig. 3e, f); $\varepsilon =\left({\varepsilon }_{\perp }+{\varepsilon }_{\parallel }\right)/2=13.2$, B = 3/4, F_edl = 6.5 pN and F_e1 = −9.3 pN at h₁ = 1 µm for R = 1.5 µm. The introduction of convection or of the motile bacteria in the overlying phase, however, generates a dynamic fluctuation of the director orientation at the LC interface (Figs. 3a–d and 4i), leading to changes in both F_e1 and F_edl. If homeotropic anchoring is induced, for example, ε increases to 19.7 ($\varepsilon ={\varepsilon }_{\parallel }$, F_edl = 9.9 pN) from 13.2 (F_edl = 6.5 pN), while B decreases to 1/2 (F_e1 = −6.2 pN) from 3/4 (F_e1 = −9.3 pN). Consequently, an enhanced F_edl can override the reduced F_e1, enabling the ejection of microdroplets from the LC (dashed lines in Fig. 3e, f).

Continuous release of microdroplets through thermal tuning of the elastic properties of the LC (Extended Data Fig. 5)

To illustrate this point, we used a nematic LC called E7, with ρ_E7 > ρ_aq and ${T}_{{\rm{NI}}}^{{\rm{E}}7}$ = 60 °C. At 25 °C, aqueous microdroplets (0.5 µm ≤ R ≤ 4 µm) were elastically sequestered in E7 because F_e1/F_b = 1,194. Both thermal tuning of the elastic properties (at T < T_NI; Extended Data Figs. 5 and 7) and isothermal tuning of the elastic properties by partitioning solutes into the LC (Extended Data Fig. 6) led to continuous release of microdroplets sequestered in the LC into the overlying aqueous phase. By contrast, when exposed to the same thermal stimulus, 5CB showed pulsatile release of microdroplets (Extended Data Fig. 5e–i). The experiment and modelling revealed that release from E7 occurred when |F_e1| decreased below |F_b| (Extended Data Fig. 5k), which in turn depended on R, h and T (thermal) or C (solute). With E7 at T = 59 °C, we calculated this constraint to be satisfied for R > 22 µm (Extended Data Fig. 5l, m). Consistent with this prediction, we observed that individual LC microdroplets with R < 10 µm were not released. Large microdroplets with R > 22 µm, or clusters of LC microdroplets formed through LC-mediated elastic interactions^{10,11,12,13,14} with an effective radius of R > 22 µm, were released (Extended Data Fig. 7).

The net force ${F}_{{\rm{b}}}^{{\rm{net}}}$ acting on a guest microdroplet in a nematic phase comprises F_b and F_e (Extended Data Fig. 5k), and is calculated as

$${F}_{{\rm{b}}}^{{\rm{net}}}(z)={\left[-{A}^{2}B{\rm{\pi }}K{\left(\frac{R}{{h}_{1}+R}\right)}^{4}\right]}_{{F}_{{\rm{e}}1}}+{\left[{A}^{2}B{\rm{\pi }}K{\left(\frac{R}{{h}_{2}+R}\right)}^{4}\right]}_{{F}_{{\rm{e}}3}}+{\left[\frac{4}{3}{\rm{\pi }}{R}^{3}g\left({\rho }_{{\rm{LC}}}-{\rho }_{{\rm{aq}}}\right)\right]}_{{F}_{{\rm{b}}}}$$

(14)

where A = 2.04 and B = 3/4. Here, the upward forces are F_b (ρ_E7 > ρ_aq) and the elastic repulsion from the LC–glass interface (F_e3).

Parameters used in the calculations

For 5CB, at T = 25 °C we used K_5CB = 7.3 pN (ref. ³¹) and ρ_5CB = 1.010 g cm⁻³ (ref. ³³), and at T = 35 °C (= ${T}_{{\rm{NI}}}^{5{\rm{CB}}}$) we used K_5CB = 3 pN (ref. ³¹), ρ_5CB = 1.000 g cm⁻³ (ref. ³³), W = 10⁻⁶ J m⁻² (ref. ⁸) and η_5CB = 0.015 kg m⁻¹ s⁻¹ (ref. ⁴⁰). The σ_NI value of 5CB is 1.5 × 10⁻⁵ J m⁻² (ref. ³⁶). In our calculation, however, we used σ_NI = 1.5 × 10⁻⁶ J m⁻² because the surfactants added to the microdroplets reduce the surface tension^41,42,43. For E7, we used K_E7 = 14.4 pN (25 °C), 10.25 pN (40 °C), 7 pN (50 °C) and 2 pN (59 °C)³², and we measured ρ_E7 = 1.057 g cm⁻³ (25 °C), 1.045 g cm⁻³ (40 °C), 1.037 g cm⁻³ (50 °C) and 1.028 g cm⁻³ (59 °C). We chose α and β on the basis of the experimental results as α = 9.9 and β = 0 for R < K/W and α = 0, β = 4.4 for R > K/W. We used h₁ = h₂ = 1 mm for Fig. 1l and Extended Data Fig. 4, and h₁ + h₂ + 2 R = 3.5 mm (thickness of LC layer in mini-wells) for Extended Data Fig. 5. For red-dye microdroplets (Fig. 1l, m and Extended Data Fig. 4), we measured ρ_aq = 1.018 g cm⁻³ (25 °C) and 1.013 g cm⁻³ (35 °C). For green-dye microdroplets (Extended Data Fig. 5l, m), we measured ρ_aq = 1.012 g cm⁻³ (25 °C), 1.004 g cm⁻³ (40 °C), 0.996 g cm⁻³ (50 °C) and 0.987 g cm⁻³ (59 °C). In F_edl calculations, we used ζ =  + 108 (C_DTAB = 10 mM), + 90 (C_DTAB = 2 mM), −116 (C_SDS = 9 mM), −108.5 (C_SDS = 5 mM) and −42.5 mV (no surfactants).

Materials

Nematic liquid crystals, 5CB and E7, and the chiral dopant S-811 were purchased from HCCH (Jiangsu Hecheng Display Technology Co., Ltd). Water-soluble dyes that were used as tracers were purchased from MontBlanc. SDS, DTAB, dimethyloctadecyl[3-(trimethoxysilyl)propyl]ammonium chloride (DMOAP), FITC-dextran, silver acetate and lipopolysaccharides (LPS) were purchased form Sigma-Aldrich. Lysogeny broth was purchased from Becton, Dickinson and Company. Transmission electron microscopy (TEM) grids were purchased from Electron Microscopy Sciences. The polymeric alignment layer (PI2555) was purchased from HD Microsystems. A Sylgard 184 silicone elastomer kit for preparing polydimethylsiloxane (PDMS) was purchased from Dow Corning. Biopsy punches were obtained from Integra Miltex.

Preparation of LCs containing aqueous microdroplets

To stabilize the dispersions of aqueous microdroplets in the LCs, we first added either SDS or DTAB at a specified concentration to the aqueous solutions of water-soluble dyes (10 wt% with respect to aqueous solution). The aqueous solutions of dyes were emulsified into the nematic LCs (5CB or E7) by vortexing for 1 min at 3,000 revolutions per minute (r.p.m.) and sonication for 10 min. The volume fractions (v%) of aqueous microdroplets (C_aq) dispersed in the LCs were 20 v% for Figs. 1c–h and 2g (C_SDS = 9 mM), 0.5 v% for Fig. 1j–k (C_SDS = 9 mM), 5 v% for Fig. 2a–c (C_SDS = 9 mM), 10 v% for Fig. 3g, h and 4f–h (C_DTAB = 2 mM) and 10 v% for Fig. 4b–d (C_SDS = 2 mM). Each surfactant was present at a concentration below its critical micelle concentration.

Preparation of LC-filled mini-wells

Mini-wells were made of PDMS. Elastomer base and curing agent from a Sylgard elastomer kit were mixed in a ratio of 10:1. The mixture was then cured at 60 °C for 2 h. A cured PDMS disk with a diameter of 6 mm was obtained using a 6-mm biopsy punch. Subsequently, a cylindrical hole with a diameter of 3 mm was punched at the centre of the 6-mm-diameter disk using a second biopsy punch. The PDMS was treated with an oxygen plasma for 20 s and bonded to a glass substrate to create a mini-well with a depth of 3.5 mm. After fabrication, the mini-wells were stored for at least 3 days before filling with 18 µl of LCs containing guest microdroplets. Subsequently, the mini-wells were submerged into glass vials filled with 2 ml of aqueous solutions. If used within 3 days, the PDMS surface was sufficiently hydrophilic to allow water to spread between the LC phase and the PDMS surface.

Preparation of samples for microscopic observations

Experimental cells for microscopic observations were assembled from glass plates coated with a polyimide film (PI2555; Fig. 1j, k and Extended Data Fig. 2) or DMOAP (Fig. 4f–h and Extended Data Figs. 9b–e and 10), which caused planar and homeotropic alignment, respectively. PI2555 substrates were rubbed to achieve unidirectional alignment of n and were assembled in an anti-parallel fashion. The gaps (100–300 µm) between the plates were set by using double-sided tape. PI2555 cells were filled with the LCs containing microdroplets and then observed while either heating or cooling one edge of the optical cell to drive the N–I interface across the field of view. DMOAP cells were filled with aqueous solutions, followed by the LCs, and were then characterized using microscopy.

Preparation of LC films

As described in Figs. 2a–c and 3a–d (and Extended Data Figs. 3, 9f–i, 12), TEM grids were placed onto DMOAP-coated glass substrates and filled with LC containing the aqueous microdroplets. Subsequently, the films (40 µm in thickness) were submerged into aqueous baths. The DMOAP-coated glass was used to orient the LC perpendicular to the glass substrate and prevent penetration of the aqueous phase between the LC and the glass substrate.

Preparation of interfacial shear stresses (Fig. 3a–d, g and h)

As shown in Figs. 3a–d, the LC films were submerged into aqueous SDS (C_SDS = 2 mM; homeotropic anchoring at LC–aqueous interface, Fig. 3a) and pure water (planar anchoring at LC–aqueous interface, Fig. 3c). Subsequently, shear stresses were induced at the interface between the LC and the bulk aqueous phase by circulating the latter with a pipette. Figure 3g and h shows a mini-well filled with 5CB containing microdroplets being submerged into a water bath. Subsequently, shear stresses were induced at the interface between the LCs and the bulk aqueous phase by rotating a magnetic bar (700–800 r.p.m.).

Preparation of cholesteric LC (Fig. 4a–d)

20 wt% of chiral dopant (S-811) was dissolved in 5CB. The clearing temperature of the LC was measured to be T_NI = 27 °C.

Preparation of bacterial dispersions (Fig. 4f–h)

Escherichia coli (strain MG1655) were grown aerobically in 1 ml of lysogeny broth [1% (w/v) tryptone, 0.5% (w/v) yeast extract and 1% (w/v) NaCl] at temperature T = 37 °C with agitation (200 r.p.m.) for 12 h. To achieve motile bacteria, the culture was diluted into 2 ml of fresh lysogeny broth in a 1:100 ratio and the bacteria were grown again for 2 h (T = 37 °C, 200 r.p.m.). The density of bacteria in the resulting dispersion was 10⁷–10⁸ cells ml⁻¹.

Optical responses in Figs. 1e and 4i

The optical response shown in Fig. 1e is the intensity measured from the micrographs of mini-wells between crossed polarizers (insets in Fig. 1e). For the optical response in Fig. 4i, the transmittance at the LC–aqueous interface was averaged for every frame and the average values are plotted for 4 s for each sequence (Fig. 4f–h).

LC system with multiple stimuli (Extended Data Fig. 11)

In this system, the mechanisms leading to the release of microcargo are the same as those described in Fig. 1 (thermal stimulus) and 2 (chemical stimulus). Specifically, the net force acting on microdroplets in the LC is described by ${F}_{{\rm{edl}}}+{F}_{{\rm{h,N}}}^{{\rm{net}}}$ (see equations (3) and (11)) during heating and ${F}_{{\rm{edl}}}+{F}_{{\rm{c,NI}}}^{{\rm{net}}}$ (see equation (7)) during cooling. Because the sign and amplitude of F_edl can be manipulated by charged surfactants added into overlying aqueous phases, we predicted that the combination of thermal and chemical stimuli would enable selective release of two agents that are oppositely charged. To test this prediction, Wells 1 and 2 were filled with 5CB containing microdroplets (C_aq = 20 v%) doped with DTAB (C_DTAB = 9 mM, ζ > 0, and green tracer) and SDS (C_SDS = 9 mM, ζ < 0, and red tracer), respectively, and then were submerged into an aqueous SDS solution (3 mM, ζ < 0). Under these conditions, F_edl > 0 in Well 1 (ζ < 0 at the interface between the LCs and the overlying aqueous phase, but ζ > 0 at their interface with the microdroplets), while F_edl < 0 in Well 2 (ζ < 0 at both interfaces). Upon thermally triggering phase transitions (0th to 4th phase transitions, T_h = 50 °C and T_c = 25 °C), Well 1 released green tracer owing to the attractive F_edl and the elastic forces (F_e2 for heating, equation (3); elastic strain F_e* and interfacial tension F_it forces for cooling, equation (7)) generated by the motion of the N–I interface. By contrast, no release was observed from Well 2 because the attractive elastic forces did not override the repulsive F_edl. After four phase transitions, aqueous DTAB (C_DTAB = 3 mM) was introduced into the bath to reverse the charge at the interface between the LCs and the overlying aqueous phase from ζ < 0 to ζ > 0 (and thus F_edl < 0 in Well 1 and F_edl > 0 in Well 2). Consequently, the elastic forces were able to trigger the release of microcargo from Well 2 (F_edl > 0, red tracer) but not Well 1 (F_edl < 0, green tracer).

Temperature control

The temperature was controlled using a STC200 hot stage and a controller (Instec Inc.) with and accuracy of 0.1 °C. Both heating and cooling were achieved by circulation of cold water. The rate of temperature change was typically ± 15 °C min⁻¹.

Measurement for the mass of tracer released

6 µl of aqueous solution was collected from the baths contacting the LCs after each N–I phase transition (Fig. 1 and Extended Data Fig. 1i and 11f) or every 2–5 min (Fig. 2g and Extended Data Fig. 5j). Prior to collection of a sample, the baths were gently agitated to uniformly mix the tracer released from the LCs through the overlying aqueous solution. We estimated the mass of tracer released from the absorbance of the samples at a wavelength corresponding to peak tracer absorbance, which was measured using a NanoDrop 2000 (Thermo Scientific) spectrophotometer.

Zeta potential measurement

5CB (0.01 v% ≥ C_5CB ≥ 0.001 v%) was emulsified in aqueous solution (water or aqueous solutions of SDS or DTAB) using a homogenizer. The zeta potentials on the aqueous side of the LC–aqueous interface were measured using a Zetasizer Nano instrument (Malvern Instruments Ltd).

Additional observations on the transport of microdroplets by propagating N–I interfaces

We made two additional observations in the experiments shown in Fig. 1j, k and Extended Data Fig. 2. First, we observed single microdroplets or microdroplet clusters with R < R* to be transported initially by the moving N–I interface (denoted by dotted circles in Extended Data Fig. 2c, d, g and h). However, as the moving interface formed bigger clusters with R > R* by collecting additional microdroplets, we observed some microdroplets from the cluster to be left behind the interface, as illustrated in Extended Data Fig. 2i–l. West et al.¹⁷ observed similar behaviours with solid particles and attributed them to an increase in the effective radius of the particles due to aggregation. Importantly, this observation provides insight into why only a fraction of the microdroplets was released at each phase transition (Fig. 1g).

Second, we observed microdroplets to occasionally coalesce upon heating (denoted by white arrows in Extended Data Fig. 2c, d). Consequently, large microdroplets formed, which were observed to remain behind the moving N–I interface. This latter observation provides insight into why the amount of tracer released after 20 cycles corresponded to approximately 40% of the tracer loaded initially into the 5CB (Fig. 1i). Overall, these results indicate that the fraction of microdroplets released can be manipulated by tuning the clustering size and coalescence of microdroplets.

Data availability

The authors declare that the main data supporting the findings of this study are available within the paper and in Supplementary Information. Additional data are available from the corresponding author upon reasonable request.

Extended data figures and tables

Extended Data Fig. 1 Thermally triggered ejection of microdroplets.

a, b, Mass of tracer released from LCs (5CB) as a function of time, before (a) and after (b) an N-to-I phase transition (corresponds to Fig. 1). Black and red points indicate the mass released before and after an N–I phase transition, respectively. c–e, Sequential photographs of the release of microdroplets (C_SDS = 9 mM and red tracer) from the LC, which is triggered by phase transitions induced by resistive heating. We used C_aq = 20 v% and 30 V for heating (to T_h = 60 °C, d) and 0 V for cooling (to room temperature, e). Heating of the sample from below was achieved by passing a current through an indium-tin-oxide electrode coated on glass. The motion of the N–I interface was upward for both heating and cooling. f–h, Dependence of the direction of motion of the N–I interface on T_h and T_c. f, Optical images showing a propagation of the N–I interface across a mini-well filled with 5CB (containing no microdroplets) in an aqueous bath upon heating from T = 25 °C to T_h = 50 °C (N-to-I phase transition). Upon heating the sample from below, the interface moved upwards (towards the interface between the LCs and the overlying aqueous phase) regardless of T_h. g, Upward motion of the N–I interface upon cooling from T = 50 °C to T_c = 25 °C (I-to-N phase transition). h, Downward motion of the N–I interface upon cooling from T = 50 °C to T_c = 34 °C (I-to-N phase transition). Scale bars, 5 mm. i, Released mass of tracer as a function of the number of phase transitions with T_h = 50 °C and T_c = 34 °C; C_aq = 20 v% (C_SDS = 9 mM).

Extended Data Fig. 2 Behaviours of microdroplet clusters during passage of the N–I interface.

a–h, Sequential micrographs showing the behaviours of microdroplet clusters dispersed in an LC (5CB) during passage of an N–I interface upon an N-to-I (heating, a–d) and an I-to-N (cooling, e–h) phase transition. We used C_aq = 3 v% (C_SDS = 2 mM) and measured v_NI = 10 µm s⁻¹ for heating, v_NI = 35 µm s⁻¹ for cooling and R* ≈ 10 µm for both cases. Scale bar, 100 µm (see Methods, ‘Additional observations on the transport of microdroplets by propagating N–I interfaces’ for more details). Red and blue arrows indicate the direction of motion of the N–I interface. Solid and dotted circles indicate microdroplets with R > R* (= 10 µm) and R < R*, respectively. White arrows indicate microdroplets that coalesced while being transported by the moving N–I interface. We note that microdroplets with R < R* were left behind the N–I interface in c because they were shed from clusters, as illustrated in i–l. i–l, Illustration of a microdroplet cluster being transported by a moving N–I interface. i, Single microdroplets or microdroplet clusters with R < R* are transported by a moving N–I interface. j, As the moving interface collects more microdroplets, the microdroplet clusters formed at the interface increase in size. k, When the effective radius of a microdroplet cluster exceeds R*, the interface no longer transports the cluster. l, Because some of microdroplets from the cluster are left behind the N–I interface, the cluster becomes smaller than R* and thus is transported again by the interface. m–r, Evidence that microdroplets with R > R* are not transported by an N–I interface moving at high speed (v_NI = 100 µm s⁻¹) during N-to-I (m–o) and I-to-N (p–r) phase transitions. Here C_aq = 0.5 v% and C_SDS = 2 mM. Scale bar, 100 µm. The left (m, p) and right (o, r) columns show optical micrographs before and after passage of the N–I interface, respectively, and the middle column (n, q) shows micrographs taken during passage of the N–I interface. The positions of microdroplets before and after the passage of the N–I interface were unchanged, revealing that R > R* for the rapidly moving interface.

Extended Data Fig. 3 Transport of microdroplets by an N–I interface propagating across an LC film.

a–j, Sequential micrographs (a–e, top view) and corresponding illustrations (f–j, side view) of microdroplets transported by a moving N–I interface upon heating in an LC film (5CB, 40 µm in thickness). The focal plane is near the interface between the LC and the overlying water (red boxes in f and h). a, f, Microdroplets are dispersed initially in the LC bulk. b, g, When the bottom of the LC film is heated to T_h = 50 °C (> T_NI), the N-to-I transition first occurs at the LC–glass interface (denoted by the asterisk in b) and the N–I interface propagates upwards, towards the LC–water interface. c, h, Microdroplets that were out of focus (red dashed circles in a and f) move into focus, revealing that the moving interface transported the microdroplets towards the LC–water interface. d, i, As the N–I interface reaches the LC–water interface, the microdroplets disappear, consistent with their fusion with the overlying aqueous phase. e, j, After the phase transition, some microdroplets remain in the LC layer. k–n, Micrographs showing the decrease in the population of microdroplets in the LC at T = 25 °C; before any phase transitions (k) and after 2 (l), 4 (m) and 6 (n) phase transitions. Scale bars, 50 µm. P and A indicate the orientations of the polarizer and analyser, respectively. T_h = 50 °C, T_c = 25 °C, C_aq = 5 vol% (C_SDS = 9 mM) and v_NI = 8 µm s⁻¹.

Extended Data Fig. 4 Calculated net force ${{\boldsymbol{F}}}_{{\bf{c}}}^{{\bf{net}}}{\boldsymbol{(}}{\boldsymbol{z}}{\boldsymbol{)}}$ acting on a microdroplet and calculated dependence of R* on v_NI during an I-to-N phase transition (cooling).

a, ${F}_{{\rm{c}}}^{{\rm{net}}}(z)$ for a quasi-static microdroplet of R = 1.5 µm in 5CB. The insets show microdroplets at z ≥ R (black line; (i)), at –R < z < R (blue line; (ii)) and at z ≤ −R (red line; (iii)). b, Critical radius R* of a microdroplet as a function of v_NI upon cooling. See Methods for details.

Extended Data Fig. 5 Influence of LC phase behaviour and elastic properties on dynamics of release of dispersed microdroplets.

a–h, Sequential photographs showing continuous release (a–d) of dispersed microdroplets (green tracer and C_SDS = 2 mM) from a nematic LC (E7) in response to a thermal trigger ${T}_{{\rm{h}}} < {T}_{{\rm{NI}}}^{5{\rm{CB}}}$ (ρ_E7 > ρ_aq), and for pulsatile release of dispersed microdroplets (red tracer and C_SDS = 9 mM) from 5CB (ρ_5CB < ρ_aq, ${T}_{{\rm{h}}} > {T}_{{\rm{NI}}}^{5{\rm{CB}}}$) at 0 min (a, e), 15 min (b, f), 60 min (c, g) and 120 min (d, h) after heating of the baths from below to T_h = 59 °C. We used C_aq = 30 v% for a–d and C_aq = 20 v% for e–h. Scale bar, 5 mm. i, Corresponding time derivative of the released mass m of the tracer (dm/dt; t, time) for pulsatile (red line and circles) and continuous (green line and circles) release. j, Released mass of green tracers from E7 (continuous release) with respect to time at representative temperatures of T = 40 °C (blue triangles), 50 °C (circles) and 59 °C (red triangles). The data are mean values and the error bars are 1 s.d. (n = 5). k, Forces acting on an aqueous microdroplet in E7. l, m, Calculated net force ${F}_{{\rm{b}}}^{{\rm{net}}}$ acting on a microdroplet in E7 as a function of R at h₁ = 0 (l) and as a function of h₁ for R = 25 µm (m) at T = 40 °C (blue line), 50 °C (black line) and 59 °C (red line). See Methods for details.

Extended Data Fig. 6 Isothermal release of microdroplets from an LC by a solute-triggered N-to-I phase transition.

a–d, Sequential photographs of a solute-triggered N-to-I phase transition of 5CB at T = 25 °C $\left({T}_{{\rm{NI}}}^{5{\rm{CB}}}=35{}^{\circ }{\rm{C}}\right)$ at 0 h (a), 1 h (b), 2 h (c) and 3 h (d) after the addition of propanol to the overlying water. As the propanol diffused into the 5CB, an N-to-I transition occurred first at the interface between the LC and the aqueous solution and propagated into the LC bulk. e, Illustration of inverted mini-wells filled with 5CB containing microdroplets (red tracer), placed in baths containing pure water (left) and water containing propanol (C_propanol = 16 v%; right). f–h, Sequential photographs of the mini-wells at 0 min (f), 5 min (g) and 30 min (h) after the mini-wells were submerged into the baths; C_aq = 10 v% (C_SDS = 9 mM). Although F_b (ρ_LC < ρ_aq) promotes the release of tracers, no release of red tracers was observed in the left bath owing to strong elastic sequestration. In the right bath, however, the red tracers were continuously released as the elastic barrier was removed by the solute-induced N-to-I phase transition. Scale bars, 5 mm.

Extended Data Fig. 7 Influence of the size and clustering of microdroplets on release from the LC.

a–f, Optical micrographs of microdroplets (C_SDS = 2 mM and red tracer), with R = 9.5 µm (a–c) and 27 µm (d–f) in an LC (E7) at 25 °C (a, d), 50 °C (b, e) and 59 °C (c, f); ρ_E7 > ρ_aq and C_aq = 1 v%. Scale bars, 20 µm. The microdroplets were elastically trapped in the nematic LC bulk at 25 °C. As the temperature increased to 50 °C (R > 34 µm for release), the microdroplets moved upwards and into focus, but were not dispensed into the overlying water; the focal plane was near the interface between the LC and the overlying aqueous solution. At 59 °C (R > 23 µm for release), we observed the larger microdroplet (R = 27 µm) to escape into the overlying aqueous phase, whereas the smaller microdroplet (R = 9.5 µm) remained elastically trapped in the nematic bulk. This observation is in good agreement with our theoretical prediction (Extended Data Fig. 5l, m). g–i, Micrographs of the clustering of microdroplets at 0 min (g), 30 min (h) and 180 min (i) after they were dispersed in the LC; C_aq = 2 v% (C_SDS = 9 mM). Scale bar, 200 µm. j–o, Illustration (j) and sequential micrographs (k–o) of thermally triggered, continuous release of microdroplets (C_SDS = 9 mM and red tracer) from mini-wells filled with E7 containing microdroplets of different sizes, at 0 min (k), 7 min (l), 10 min (m), 12 min (n) and 15 min (o) after the baths were heated to T_h = 59 °C(< T_NI); ρ_E7 > ρ_aq (F_b > 0) and C_aq = 20 v%. Scale bar, 5 mm. The mini-well containing the larger microdroplets (left bath) exhibited a higher release rate due to the facile formation of microdroplet clusters with a radius higher than that for which ${F}_{{\rm{b}}}^{{\rm{net}}} > 0$, consistent with the theoretical model whose results are shown in Extended Data Fig. 5l, m.

Extended Data Fig. 8 Role of electrical double-layer interactions in the release of microdroplets from an LC.

a, Calculated repulsive elastic (F_e1, dashed line) and attractive electrical double-layer (F_edl, solid lines) forces acting on a microdroplet (C_SDS = 9 mM, R = 1.5 µm) as a function of h₁ following the addition of DTAB with C_DTAB = 10 mM (red), 5 mM (orange) and 2 mM (black) to the overlying aqueous phase. The inset shows the corresponding net forces $\left({F}_{{\rm{i}}}^{{\rm{net}}}={F}_{{\rm{e1}}}+{F}_{{\rm{edl}}}\right)$. b, ${F}_{{\rm{i}}}^{{\rm{net}}}$ near the interface between the LC and the overlying aqueous phase (h₁ = λ), and initial release rate of microdroplets (from 0 to 60 min in Fig. 2g) as a function of C_DTAB added into the overlying aqueous phase. c, Illustration of inverted mini-wells in baths with water (pH 7, left bath) and alkaline water (pH 13, right bath) at T = 45 °C (> T_NI). d, e, Sequential photographs of mini-wells filled with 5CB containing aqueous microdroplets (red tracer) at 0 min (b) and 60 min (c) after an N-to-I phase transition, with C_aq = 10 v% (C_SDS = 9 mM) and T_h = 50 °C. Scale bar, 5 mm. Because ρ_LC < ρ_aq (F_b < 0), tracers are continuously released from an isotropic phase of 5CB (F_e1 = 0) into the pure water (left bath). In the alkaline water (right bath), however, the release is suppressed because of the introduction of repulsive charge interactions between the LC interface in alkaline water (negatively charged) and SDS-containing aqueous microdroplets (negatively charged).

Extended Data Fig. 9 Triggering of the release of dispersed microdroplets by interfacial charge interactions of biological molecules.

a, Zeta potential ζ at LC–aqueous interface without (white bar) and with lipopolysaccharides (LPS; green bars) from Escherichia coli, or with DTAB (grey bar). The data are mean values and the error bars are 1 s.d. (n > 3). b–e, Micrographs (side view) showing the ejection of microdroplets (C_DTAB = 2 mM and red tracer) from LC (5CB) 30 min after addition of C_LPS = 0 mg ml⁻¹ (b), 1 mg ml⁻¹ (c), 2 mg ml⁻¹ (d) and 4 mg ml⁻¹ (e) to the overlying aqueous phase. f–i, Sequential micrographs (top view) showing the ejection of microdroplets before (f) and at 0 min (g), 15 min (h) and 30 min (i) after the addition of C_LPS = 4 mg ml⁻¹ into the overlying aqueous phase. Scale bars, 200 µm. P and A indicate the orientations of the polarizer and analyser, respectively. In the presence of LPS, microdroplets are ejected continuously from the LC, as evidenced by the release of red tracer (b–e) and the decrease in the population of aqueous microdroplets within the thin LC film (40 µm in thickness; f–i). The release rate is enhanced with an increase in C_LPS (b–e), consistent with release controlled by interfacial charge interactions.

Extended Data Fig. 10 Ejection of microdroplets from the LC by motile bacteria.

a–f, Sequential micrographs showing that microdroplets containing anti-bacterial agent (2 mM DTAB and 1 wt% silver acetate) are not ejected from the LC (5CB) in the absence of bacteria (a–c) and at 0 min (a, d), 15 min (b, e) and 30 min (c, f) after the arrival of weakly motile bacteria (d–f); C_aq = 10 v%. g–i, Sequential micrographs showing ejection of microdroplets from the LC at 0 min (g), 30 min (h) and 120 min (i) after the arrival of motile bacteria and subsequent bacterial death and aggregation. Scale bar, 40 µm. g, Motile bacteria generate shear stresses at the LC interfaces, triggering the release of microdroplets containing anti-bacterial agent. h, As the anti-bacterial agents are released, the bacteria become less motile. At 30 min, we observe dead bacteria and cessation of the triggered release due to the decrease in the number of motile bacteria. The amount of silver acetate released is 1–2 µg µl⁻¹. i, Two hours after the arrival of motile bacteria, only dead (non-motile) bacteria are observed.

Extended Data Fig. 11 LC systems with complex geometries and responsiveness to multiple stimuli.

a–c, Isothermal release of aqueous microdroplets (C_SDS = 9 mM and red tracer) from a large LC emulsion droplet (5CB) before (a) and at 50 s (b) and 80 s (c) after the addition of DTAB (10 mM) into surrounding aqueous phase; C_aq = 5 v%. Scale bar, 200 µm. The insets in a and b are optical micrographs (crossed polars) of the LC droplet, showing the optical response. d–f, Selective release of two agents, triggered by a combination of chemical and thermal stimuli (see Methods for details). d, In an aqueous SDS bath, the thermal stimulus triggers release of DTAB-doped microdroplets (green tracer) from Well 1, but not of SDS-doped microdroplets (red tracer) from Well 2 (1st to 4th phase transition; left inset in f). e, Addition of DTAB into the bath reverses the charge at the interface between the LCs and the overlying aqueous phase, thus enabling the ejection of microdroplets from Well 2, but not from Well 1 (5th to 8th phase transition; right inset in f). Red and blue points in f correspond to the released mass of tracers after N-to-I and I-to-N phase transitions, respectively. Scale bar, 5 mm.

Extended Data Fig. 12 Triggered release of water-soluble solid microparticles from an LC film.

a–f, Polarizing (a, d; top view) and fluorescence (b, e; top view) micrographs and schematic illustrations (c, f; side view) of an LC film at 25 °C in the initial N phase (a–c) and after six phase transitions (d–f) with T_h = 50 °C and T_c = 25 °C. Scale bar, 200 µm. The LC film (5CB, 40 µm in thickness) contained solid microparticles of FITC-dextran (1–2 wt%). Before any phase transition, a strong fluorescence signal was detected from the FITC-dextran microparticles that were sequestered in the LC film (b), but not from the water bath (g), indicating that the solid microparticles were trapped in the LC. After six N–I phase transitions, however, no fluorescence signal was detected from the LC (e), whereas the water bath showed a strong fluorescence signal (h). The inset in h shows the fluorescence intensity I_f from the bath as a function of the number of phase transitions.