We exploit the temperaturedependence of the MLG electrical resistance to measure the local heatingof the QCL chip. The results are further validated through microprobephotoluminescence experiments, performed on the front-facet of theelectrically driven QCL. We extract a heterostructure cross-planeconductivity of k⊥= 10.2 W/m·K,in agreement with previous theoretical and experimental reports. Ourintegrated system endows THz QCLs with a fast (∼30 ms) temperaturesensor, providing a tool to reach full electrical and thermal controlon laser operation. This can be exploited, inter alia, to stabilizethe emission of THz frequency combs, with potential impact on quantumtechnologies and high-precision spectroscopy.The on-chip integration of two-dimensional nanomaterials,havingexceptional optical, electrical, and thermal properties, with terahertz(THz) quantum cascade lasers (QCLs) has recently led to wide spectraltuning, nonlinear high-harmonic generation, and pulse generation.Here, we transfer a large area (1 × 1 cm Here, heat extraction is hindered both by the large devicethermal resistance,k//) and cross-plane (k⊥) components being smaller than the thermal conductivitiesof the constituent bulk materials. This effect is more relevant interahertz (THz) frequency quantum cascade lasers (QCLs),20 where the narrow separation between the intersubbandlevels involved in the lasing transition (5–20 meV) may requireultrathin and abrupt barriers, which enhance the rate of phonon scatteringby interfaces, mainly in heterostructures with layer widths comparableor smaller than the phonon mean free path. These effects inherentlyinhibit the phonon transport and reduce the heat dissipation rate,as a consequence of the series of thermal boundary (Kapitza) resistancesarising at each interface between materials of different thermal andmechanical properties.16 Diffusive scatteringof phonons by interfaces17 in THz QCLssignificantly reduces k//, while the reduction of k⊥ ismostly due to scattering by interface roughness and alloy disorder.The heat conductivity is largely anisotropic,with both in-planespectroscopy.24 This technique providesa way to indirectly determine the lattice temperature (TL) by measuring the redshift of the PL peak when the heatsink temperature (THS) is increased,25 or when the AR is heated during laser operation(Joule heating). Importantly, microprobe PL spectroscopy gives a localmeasurement of TL and of the electronictemperature;23 thus, it constitutes a powerfultool to infer the thermal resistance,22 the facettemperature profile,16 and the heat flow25 through the semiconductor heterostructure, givingaccess to the thermal dynamics within the device. However, the implementationof PL spectroscopy to determine QCL temperature during operation requiresadditional and complex experimental setups, making impractical a real-timemonitoring of the local device heating during a specific application.The mostestablished method to monitor the AR heating during operationin mid-infrared (mid-IR)TL in QCLs include the following: analysis of the dependence of thethreshold current density on the heat sink temperature,26 or of the average laser power as a functionof the duty cycle,27 transient interferometricthermal mapping28 or all-electrical techniquesfor monitoring the lattice temperature by measuring the heating ofthe laser metallic top contact.30 This latter methodrequires independent electrical access to four leads and at leastfour bonding wires to be collinearly placed on the QCL top contact.This entails complex bonding schemes30 andcan be unpractical for specific device architectures, such as wirelasers31 or vertical emitting QCLs withtwo-dimensional photonic patterns,33 or for deviceapplications requiring radio frequency coupling to the laser, e.g.,injection-locked systems34 and dual-combschemes.36Alternative procedures to assess 37 So far, graphene has been also incorporated/combinedwith THz QCLs to achieve gate-tunable spectral control,38 modulate the radiation intensity,39 or to stabilize the operation of frequency combs40 through its fast saturable absorption dynamics.Its rich physics,41 along with its versatilityand fabrication flexibility, makes it a promising material platformfor integration with different on-chip electronic43 and photonic45 solid-state architectures, suchas CMOS,46 silicon on insulator (SOI),48 and SiN.49Here, we devise an integrated two-componentsystem that allowsmonitoring the QCL lattice temperature during operation, by simplyusing one additional electrical access. The devised chip comprisesa THz-frequency QCL and a graphene microthermometer, lithographicallypatterned adjacent to the laser ridge. Graphene field effect transistorsproved to be highly efficient radiation sensors in the far-infrared.R/RdT ≈ −1%/K), graphene is a promising candidatefor the realization of integrated thermometers. Negative TCR thermistorsare commonly used as on-chip temperature sensors for the thermal stabilizationof near-infrared laser diodes in combination with Peltier coolers.50 Thus, depending on the required operating temperaturerange, two-dimensional (2D) materials, preferably with high TCR , could be employed as on-chip thermistors in combination with electricallypumped semiconductor sources, such as mid-infrared GeSn/SiGeSn heterostructurelasers.53Therefore, despite therelatively weak temperature coefficientof resistance , are fabricated onsingle plasmon waveguides54 following theprocedure described in 2 layer, covering a surface of 300 × 800 μm2, is deposited by Ar sputtering on the bottom doped layerbetween each pair of laser bars to host and electrically isolate theintegrated thermometers.THz-frequency QCLs, based ona bound-to-continuum GaAs/AlSupporting Information . The TCR increases as afunction of thickness, especially for thicknesses larger than 5 layers.Using a 5/7-layer graphene results in the best compromise betweenbolometer performance and sample robustness that increase with thickness,and fabrication complexity and sample quality that degrades aftera large number of wet-transfer processes. Commercially available (GrapheneaInc.) SLG samples, grown on Cu via chemical vapor deposition (CVD),are sequentially transferred on top of each other using a wet-transfertechnique: A4-950K poly(methyl-methacrylate) polymer (PMMA) is spincoated at 2000 rpm on the surface of an SLG sample and then placedin a solution of 1 g of ammonium persulfate (1 g diluted in 40 mLof DI water) to etch the Cu substrate. Once the Cu etching is complete,the PMMA-SLG film is transferred in a beaker with DI water and thenlifted with a second Cu-graphene square to obtain an MLG sample. Thesample is left to dry, and finally the PMMA is removed with acetone.The final Cu substrate is eventually etched, and MLG is transferredon top of the QCL device. MLG channels of 30 × 100 μm2 are lithographically defined on the SiO2 patches,etched with oxygen plasma, and connected to two Cr/Au (10/150 nm)electrodes. Finally, the GaAs substrate is lapped down to a thicknessof ∼200 μm and back coated with a 10/50 nm Cr/Au metalliclayer to improve thermal coupling with the copper bar. Laser bars2.1 mm long and 200 μm wide are cleaved, mounted on a copperbar through a dedicated thermal InAg alloy (97%: 3%), and wire bonded.A scanning electron microscopy (SEM) image of a prototypical deviceis shown in Figure S2), which show a marginalthermal gradient (<1 °C) along the laser ridge.The integrated thermometer comprisesa stack (7 layers) of single-layergraphene (SLG). The resulting multilayer graphene (MLG) film is easierto manipulate and more stable during the transfer process with respectto SLG. The performance of different thermometers as a function ofthe number of layers is analyzed and reported in the ormation S1. The T–1, full width at half-maximum fwhm = 20 cm–1) and2D (POS(2D) = 2690 cm–1, fwhm = 37 cm–1) peaks.55 The 2D band is always single-peaked,less intense with respect to the G peak  = 1344 cm–1, fwhm = 67 cm–1) and D′ (POS(D′) = 1616 cm–1, fwhm = 24 cm–1) Raman peaks are observed. Thesefeatures, coming from defect-assisted Raman processes,58 reflect the disorder introduced during the multiple graphene-transfersteps.Micro Raman experiments are performed on the transferredMLG usinga confocal Raman spectrometer  equipped witha 532 nm laser in backscattering configuration. We use a 100×objective producing a laser spot size of ∼0.5 μm. TheRaman spectrum of the MLG thermometer, plotted in Rgr, whichis monitored with a lock-in amplifier (time constant 30 ms) over avoltage dividing circuit: the lock-in signal is VIN = VOUTRgr/(RLoad + Rgr), where VOUT is a sinewave with amplitude 40 mV and frequency fmod = 343 Hz, generated by the lock-in itself, and RLoad = 3.3 kΩ is chosen to be close to Rgr. A capacitor CD = 1 μFis added to the circuit to act as a dc-block on thethermometer line. Therefore, this architecture is able to keep continuoustrack of temperature variations through the dependence Rgr(T), with a time scale given by thelock-in time constant.The integrated laser-thermometer system 1c is engTHS is monitored by a silicon diode sensor and varied inthe range 6–300 K, through a tunable heater. V–J) and the light–currentdensity (L–J) characteristicsacquired while driving the QCL in pulsed mode  at THS = 15 K. The opticalsignal is further modulated with a 33 Hz square envelope to allowfor lock-in detection. The QCL has a threshold current density Jth = 115 A cm–2 anddelivers a maximum output power of 9 mW when biased at VQCL = 10.3 V, IQCL= 900 mA.This optical power is calibrated with a power meter  and corrected to account forthe transmittance (25% at ∼3 THz) of the high-density polyethylenecryostat window. The far-field intensity distribution is collectedwith a pyroelectric detector  at THS = 15 K when theQCL is driven in CW at 600 mA and 850 mA, respectively: the laseris single-mode (2.56 THz) above threshold and becomes progressivelymultimode when the current is increased, spanning a 110 GHz frequencyrange (2.60–2.71 THz).Rgr from THS, as shown in Rgr decreases when the heat-sink temperature is increased, indicatinga negative TCR and a thermally activated electrical transport, inagreement with previous findings on graphene thermistors.60 In the high-temperature limit (THS >80 K), Rgr follows an exponential dependenceon THS, given by the Arrhenius equation.60Rgr = R0 exp(B/THS), where R0 is the resistanceat infinite THS and B = Ea/2kB is the thermal index, with Ea activationenergy in the graphene layer and kB Boltzmannconstant. Rgr), asa function of 300/THS. From the linearfit to the data, in the range THS >80K, we find R0 = 698 ± 1 Ω, B = 17.6 ± 0.9 K, and Ea = 3.0 ± 0.1 meV; these thermal figures of merit are close tothose measured in printed multilayer graphene films, at room temperature.59 The Rgr(THS) curve can be used to determine the sensitivityof the graphene thermistor in terms of the TCR figure of merit: |TCR| ∼ 1% K–1 for THS < 30 K and progressively decreases to<0.1% K–1 for THS > 100 K (THS) to estimatethe accuracy (deviation from true temperature) of the graphene thermometerby calculating the standard deviation ΔT stemmingfrom the instrumental error ΔRgr in the Rgr(THS) calibration curve. Results are shown in T < 50 K and reaching ±12 K at room temperature. The accuracyincrease is caused by the reduction of the thermistor TCR at hightemperature.We then calibrate the graphenethermometer by measuring the thermoresistancecharacteristics, i.e., the dependence of  > 100 K 3c. We thRgr(THS) to monitor the temperatureof thegraphene thermometer (TG) during laseroperation. The QCL is driven in continuous wave (CW), while THS is kept at 15 K. TG asa function of the electrical power (Pe) dissipated in the QCL. TG grows linearlyfrom THS = 15 K to a maximum of 48 K,suggesting that the graphene thermometer is effectively measuringthe device temperature, whose dependence from the electrical poweris expected to be linear.23 From the linearfit to the TG(Pe) plot, we obtain a slope RTG = dTG/dPe = 3.86 K W–1.We then use the calibration curve TG extracted with thegraphene thermometer with the lattice temperature measured by meansof a microprobe PL technique (TPL). Forthis experiment, the QCL is mounted in the cold unit of a He flowmicrocryostat , with the laser facet facing thecryostat quartz window (1.5 mm thick). The cryostat is fixed belowthe objective  of a confocalRaman spectrometer , and the ∼1 μmfocal spot is aligned with the center of the QCL facet by means ofa motorized stage.We then compare –2, thus keeping the laser-induced electron heatingbelow ∼5 K.22 The laser excitationprovides the valence band holes needed to probe the electronic populationvia interband radiative recombination. We use the facet temperatureas a close estimate of the internal one due to the absence of nonradiativesurface electron–hole recombination processes in unipolar devices.PL spectra are acquired using a 1800 grooves/mmgrating and a 638nm laser whose optical power density is attenuated to <10 kWcmTHS in the range6.0–296 K. Each spectrum shows a main peak, located at an energy Ep, ascribed to band-to-band transitions betweenlevels in the injector miniband, where the vast majority of electronssit, and valence subbands, as typically retrieved in bound-to-continuumactive region designs. For THS < 20K, the PL spectra display four peaks, corresponding to free excitonsand impurity-bound excitons.62 As the temperatureis increased, the main peak redshifts as an effect of the temperature-inducedchange of the GaAs energy gap; this redshift can be used as a thermometricproperty to extract the calibration curve  = EP(0) – αTHS2/(β+ THS), which is typically used to describethe band gap shrinkage with temperature, obtaining EP(0) = (1.524 ± 0.0003) eV, α = (7.5 ±0.5) × 10–4 eV K–1 and β = (405 ± 45) K. The value of EP can in turn be used to extract the local lattice temperature(TPL) during laser operation, providedthat the calculated field-induced shift of the confinement energiesin the QCL active region is properly considered.21 The field-effect correction is relevant only below thethreshold for current-injection.on curve 4b, i.e.,Pe. THS is kept fixed at 15 K. When the laser is driven in CW, theactive region is Joule-heated and EP redshiftsas Pe increases. The color-map of thePL intensity as a function of energy and QCL driving current is reportedin 23 is marked with labels“1” and “2”; the excited laser level excitons4 are marked with label “3”; theupper miniband,64 which becomes progressivelypopulated with the applied electric field, is marked with “uM”; and the low-energy peaks at low QCL currents correspondto free excitons and impurity-bound excitons (marked with “exc”).The position of the main PL peak shifts with increasing current, asdescribed in Pe from0 to 8.8 W. The position of the lowest-energy peak is calculated byfitting the whole spectrum with a combination of Lorentzian and Lorentzian-exponentialfunctions.65 This procedure is repeatedfor each value of the QCL electrical power to determine the dependenceof EP, and in turn TPL, from Pe . The lattice temperature,extracted from micro-PL at the center of the laser facet, increaseslinearly with Pe, with RTL= 3.62 KW–1, similar to the valuemeasured by the graphene thermometer (RTG). The direct comparison between the error bars in We then collect a set of PL spectra while varyingthe QCL drivingcurrent, hence  from Pe 4e. The l67 measured while sweeping THS in the range of 10–45 K. The peakat ∼1.515 eV corresponds to the band-to-band (B–B) luminescenceof GaAs, i.e., the energy gap in the bulk, whereas the peak at ∼1.495eV is attributed to a band-to-acceptor (B–A) luminescence dueto residual carbon impurities, which typically create an acceptorlevel in GaAs.67 The intensity ratio (ρAB) between the B–A and B–B PL peaks is stronglydependent on the local temperature, providing an optimal observableto determine it. THS dependencies of theB–B energy (EBB) and ρAB. When THS is increased from10 to 45 K, ρAB decreases almost linearly from 1.1to 0.15, with a slope −0.027 K–1, whereas EBB decreases by just 2 meV, with an initialflat region that hampers a correct evaluation of T. We therefore exploit the calibration of ρAB(THS) to estimate the local temperature TPL at different positions in the GaAs substratewhen Pe = 9 W , TPL slowlydecreases following a linear trend with a slope of −4.6 K mm–1. From the fits to the data, we can infer a temperature∼40 K on the substrate top-surface at a position ∼200μm from the ridge corner .We then monitor, via micro-PL spectroscopy, the substratetemperatureduring laser operation. h∼35 μm 5d, approTb = 42.5 K, while at the facet center TPL = 48.5 K, with a bottom-to-center temperaturedifference ΔTbc = 6 K. Thus, ∼70%of the temperature increase with respect to THS takes place in the substrate. Assuming that the lateralheat extraction is suppressed in the laser ridge29 and using a one-dimensional model along the growth axis,we derive the relation ΔTbc = 1/4·(PeRL), from whichwe estimate the absolute thermal resistance of the QCL lattice RL= 2.7 K/W and a cross plane thermal conductivity k⊥= d/(RL·A) = 10.2 W/m·K, which isin agreement with previous results on similar heterostructures.68 We can thus decompose the total thermal resistance RTL into the contributions of the substrate and the activeregion, RTL = RS + RL/4, from which we estimate an absolutethermal resistance of the GaAs wafer RS = 2.95 K/W.The measured substrate heating reveals that thetemperature dropin the GaAs wafer plays a relevant role in the thermal managementof the device. Indeed, by using the results in Our experiments demonstrate that the on-chipintegrated graphenethermometer provides a reliable evaluation of the active region latticetemperature during laser operation, allowed by the optimal thermalcoupling between the laser ridge and the electrode between the ridgeson which the measurement relies.TG, measured by the graphenethermometer, is retrieved on a time scale given by the lock-in integrationtime constant (30 ms), enabling the active control of the QCL temperatureby measuring Rgr(T),rather than by the conventional control of THS. This can be exploited to directly stabilize TL and can be applied in different scenarios, e.g. in therealization of frequency stable THz QCL frequency combs, where thedependence of the intermode beatnote frequency Δν on theactive region temperature (∼ −5 MHz K–1)69 can lead to drifts in Δν,which are unavoidable if the temperature feedback to the control systemis given by THS.The value of 2) MLG , and monolithically mounted on a QCLchip. The scalability of the fabrication technique can allow, as afuture perspective, the realization of multiple thermometers, ideallyconnected to multiple local heaters and multiple QCL ridges for theparallel stabilization of the temperature all over the chip. We havehere adopted graphene for the ease of transfer and manipulation; however,the use of other 2D materials,70 aboveall with higher TCR52 is also promising and could providea larger temperature sensitivity thanks to steeper thermoresistancecharacteristics. Owing to the wide spectrum of thermoresistive 2Dmaterials,52 to the advancement of synthesisand transfer techniques,71 and to the generalcharacter of the proposed approach,50 itcan find application in several electrically pumped radiation sourcesoperating at different temperatures, such as THz and mid-IR QCLs,difference frequency generation QCL,72 andinfrared light-emitting diodes in single and large array configurations.In conclusion,we have demonstrated integrated graphene thermometers,based on transferred large-area (∼1 × 1 cmd = 12 μmthick active region is embedded between a doped ([Si] = 2.0 ×1018 cm–3) 700 nm thick GaAs bottom layerand a doped ([Si] = 5.0 × 1018 cm–3) 80 nm thick GaAs top contact layer. The laser bars are definedby means of optical UV lithography and wet etching of the active region(H2SO4:H2O2:H2O with proportion 5.5:4.5:25 mL). Top and bottom AuGe/Au (80/100nm on the top and 80/150 nm on the bottom) ohmic contacts are thenlithographically defined, thermally evaporated, and annealed at 400°C.The


As diffusion delivers nutrients over only ∼200 µm, refreshing flows through organoids are required to avoid necrosis at their cores; achieving this is a central challenge in the field. Our general aim is to develop a platform for culturing micro-organoids fed by appropriate flows that is accessible to bioscientists. As organs develop from layers of several cell types, our strategy is to seed different cells in thin modules (i.e. extra-cellular matrices in stronger scaffolds) in standard Petri dishes, stack modules in the required order, and overlay an immiscible fluorocarbon (FC40) to prevent evaporation. As FC40 is denser than medium, one might expect medium to float on FC40, but interfacial forces can be stronger than buoyancy ones; then, stacks remain attached to the bottom of dishes. After manually pipetting medium into the base of stacks, refreshing upward flows occur automatically , driven mainly by differences in hydrostatic pressure. Proof-of-concept experiments show that such flows support clonal growth of human embryonic kidney cells at expected rates, even though cells may lie hundreds of microns away from surrounding fluid walls of the two immiscible liquids.Organoids grow  Summary: Refreshing flows through organoids are required to avoid necrosis at their cores; we develop a platform for culturing micro-organoids fed by appropriate flows that is accessible to bioscientists. Moreover, prototyping should be rapid with, for example, modules being easily swapped in and out to test new conditions. Finally, the method should be accessible to bioscientists – which probably means organoids sit in standard Petri dishes where they can be fed with fresh media delivered through standard pipettes and imaged using microscopes found in biolabs.Thus far, cells have been grown in fluid-walled circuits on the two-dimensional (2D) surface of polystyrene Petri dishes ; we now We now describe a platform incorporating properties in this wish-list ; it is iin vivo from layers of different cell types under critical length constraints . This is counter-intuitive: one might expect less-dense medium to float on the denser fluorocarbon, but interfacial forces between dish and medium can be stronger than buoyancy ones. Where volumes are large and contact areas with the dish small, weights  are added on top of modules to prevent floatation.Interfacial and hydrostatic forces play critical roles in this workflow. For example, interfacial forces drive initial cell wicking and dispersal throughout modules . They alP, and interfacial forces working through differential wetting of polystyrene and steel by each liquid plus Laplace pressure. Thus, P is given by ρgh , and the pressure difference, ΔP, across any spherical medium:FC40 interface is given by the Young-Laplace equation and is 2γ/R . Consequently, in P required to force medium between washers increases as Rside shrinks, so Laplace pressure prevents seepage from the stack laterally as Rbot and Rside are so small.To illustrate the interplay between forces that are exploited, consider a stack of five stainless-steel washers with outer and inner diameters (ODs and IDs) of 10 and 5 mm (more relevant modules are used later). The stack is built manually by placing one washer on top of another in a standard polystyrene Petri dish, and medium pipetted into the middle of the stack. As these washers are not particularly flat or smooth, some medium seeps under the bottom washer and between others; nevertheless, most medium remains confined to the stack, held there by interfacial forces that are strong enough to prevent spreading throughout the dish. When FC40 is overlaid, medium remains in the stack A. The stRcap>Rbot and Rside , plus pores down to ∼11 µm  in air, wet the paper with medium, fill stacks, and overlay FC40; interfacial forces hold medium in the circuit Ai,ii. WhWe require that hydrogel-containing modules can be tessellated and aqueous continuity between them established; this proves to be easy. Thus, four blocks of agarose are assembled into abutting stacks B,C in Ai just bQ, of a fluid (dynamic viscosity µ) through a porous module of length L, permeability k, and cross-sectional area A; it depends on the pressure difference ΔP across that module, where ΔP=Q(µL/kA). Here, µL/kA is a resistance term, hydR; then, ΔhydP=QR . The circuit contains four input stacks with agarose:paper regulators (A1–A4) that feed the central stack B  unless stated otherwise. FC40 was from Acota , stainless-steel nuts and washers from a local hardware store  or Accu Ltd , Teflon washers from Washersdirect , tube magnets from Magnet Expert Ltd , monofilament nylon mesh  from Cadisch Precision Meshes Ltd , and natural silk mesh CQ15  from Bonfilt . Water-soluble dyes  are used where indicated.Liquids are sometimes delivered through blunt dispensing needles  connected via a PTFE tube  to syringe pumps . When high flow rates are used, needles sometimes have PTFE collars at their tips to prevent flow of inputted aqueous phase upwards . Needles are held in 3D-printed rectangular rods containing holes, and rods are surrounded by double-sided sticky tape so they can stick to the top sides of dishes. Before starting pumps, needles are lowered to contact prewetted filter papers in input stacks; after starting pumps, inputs are delivered to the filter paper, and then differences in hydrostatic pressure are the main drivers of flow through circuits).Images of dishes are taken using a digital SLR camera (Nikon D610). Bright-field, phase-contrast, and fluorescent images of modules are collected using a digital SLR camera (Nikon D7100) connected to an epi-fluorescent microscope  equipped with a CoolLED pe-100 combiner and 470 nm light source .Adherent HEK 293 are grown routinely in DMEM+10% FBS +1% penicillin plus streptomycin  – which is referred to as ‘medium’ throughout, and sub-cultured using trypsin . They were obtained from the departmental cell bank (which tests for mycoplasma prior to freezing), but they were not tested after thawing or authenticated in any way. Medium is supplemented with 10 mM HEPES when cells are grown in stacks. Geltrex was from ThermoFisher Scientific .Here, we describe general principles . (1) Polystyrene dishes  are used initially unless stated otherwise, as we thought their use would minimize aqueous flows around components sitting on a dish. However, these dishes became unavailable at one stage during the COVID-19 pandemic, and we found dishes treated for tissue-culture gave similar outcomes . (2) TheFor For For For For ∼240–440 µm) are cut into squares (10×10 mm). Squares are picked up with tweezers, dipped briefly into an ice-cold mixture of HEKs (1 volume at 106/ml)+Geltrex (1 volume)+medium with 10 mM HEPES (8 volumes) so the mixture wicks throughout, dropped immediately into 8 ml DMEM+10 mM HEPES (37°C) to set the gel, and submerged papers incubated overnight (37°C). This Geltrex concentration is too low to yield free-standing gels but forms a dilute gel in paper pores. Next day, live cells are imaged using one half of the LIVE/DEAD Viability/Cytotoxicity Kit for mammalian cells (ThermoFisher Scientific). The unused half exploits binding of Red-fluorescent Ethidium homodimer-1 to indicate loss of plasma membrane integrity, but the homodimer binds to paper giving a high background. The used half exploits calcein AM, a cell-permeant and non-fluorescent ester converted by living cells to green-fluorescent calcein. Thus, papers are rinsed briefly in PBS, incubated at room temperature in 1 µM calcein AM, and phase-contrast and fluorescence images  collected within 1–2 h of adding calcein. Controls are cells grown in submerged and unstacked papers (three per dish in 8 ml medium) for 5 or 10 days (they are fed by diffusion). Stacks are constructed (day 1) on filter-paper 1  are incubated  in a 50 ml centrifuge tube filled with equal volumes of PBS and H2O2 , meshes rinsed thoroughly in distilled water, air dried at room temperature, and cut into 10×10 mm squares. Meshes are filled with Geltrex as follows. The manufacturer recommends setting liquid ice-cold hydrogels by incubation at 37°C for 30 min; however, here we set gels by incubation in FC40 at 37°C, but pilot experiments showed a 30 min incubation reduced cloning efficiency (presumably because too much evaporation occurs from the nanoliter volume in each mesh chamber). Therefore, gelling time is reduced to 10 s, and FC40 is pre-saturated with water. Thus, 1 volume HEKs in medium (106/ml)+10 mM HEPES is mixed with nine volumes of ice-cold Geltrex+10 mM HEPES in a cryogenic vial  – chosen only because it is a small tube with a 10 mm diameter and so the width of the mesh. In contrast to the lower Geltrex concentration used in For For 2 incubator). Fourth, blue dye  is pipetted into each of A1–A4 at t=0, 15, 30, and 45 min (not twice daily); at t=60, the output reservoir is emptied, all FC40 removed, and the stack dismantled.For t=0, 25 µl blue dye (0.5 mg/ml resazurin in DMEM+10 mM HEPES) is pipetted into each input quadrant. At t=5 h, 140 µl is removed from the cap on stack B to restore the medium level so it again just fills the washer (indicating a flow rate of 140 µl/5 h); additionally, a total of 350 µl is added to the four quadrants. At t=20 h, 400 µl is removed from the cap to restore the medium level so it again just fills the washer (indicating a flow rate of 400 µl/15 h). At t=20 h, the output reservoir is emptied, all FC40 removed, and the stack dismantled. While we still seek better regulators and base papers, the ones used here are currently those of choice. Comparison of flows through an identical circuit with wider input quadrants (i.e. 2 mm) increases reservoir capacity and yields a higher flow rate (i.e. ∼235 µl/5 h). As PLA has a density of 1.24 g/cc, increasing reservoir width beyond 2 mm requires use of weights to prevent them from floating on FC40. Note also that PLA softens at ∼50°C, and so is sterilized using 70% ethanol (not by autoclaving).For For In principle, cloning efficiencies and growth rates can be calculated using images collected in the experiments illustrated in 10.1242/biolopen.059825_sup1Supplementary informationClick here for additional data file.


The flexible3D “sandwich” exhibits excellent long-term reliabilitywith >1000 cycles over a broad temperature range from −55°Cto 125 °C. This nanostructured thermal interface material cangreatly benefit a variety of electronic systems and devices by allowingthem to operate at lower temperatures or at the same temperature butwith higher performance and higher power density.Despite the recent advancements of passive and activecooling solutionsfor electronics, interfaces between materials have generally becomecrucial barriers for thermal transport because of intrinsic materialdissimilarity and surface roughness at interfaces. We demonstratea 3D graphene-nanowire “sandwich” thermal interfacethat enables an ultralow thermal resistance of ∼0.24 mm In microelectronics, the escalating integrationdensity in the last six decades has pushed forward the computing capabilitiesat the cost of rising heat dissipation across the device, circuit,and system levels.11 To date, the heat fluxes of high-powerelectronic devices and systems such as SiC high-electron-mobilitytransistors, solid-state lasers, and phased-array radars, can reachthe order of 1 kW/cm2.15 Heat rejection technology hasbeen playing a critical role in maintaining the Moore’s lawscaling in the microelectronics industry.16 Despite the recent advancements of passive and active cooling solutionsfor electronics, interfaces between materials are still the crucialbarriers for thermal transport because of the intrinsic material dissimilarityand surface roughness at interfaces. In many cases, thermal resistanceat interfaces can constitute more than 50% of the total thermal resistancefrom an electronic device to a cooling fluid.18Flexible electronics are transformingthe way that we interact with our environments.19 Thermal greases, epoxies and other polymer-basedcomposites have high compliance but struggle with low thermal conductivity.21 Large-scale high-aspect-ratio nanostructures, including carbon nanotubes(CNTs),26 nanowires (NWs),29 graphene,32 nanosheets,33 and nanofibers,34 have offereda promising platform for fabricating thermally conductive and mechanicallycompliant thermal interface materials. Nevertheless, since these nanostructuresare not intrinsically adhesive or solderable, physically bonding thesenanostructures to a target substrate with a continuous interface anda low contact resistance remains an outstanding challenge. Here, wedemonstrate a 3D nanostructured TIM on the basis of highly compliantand thermally conductive graphene-coated Cu nanowires (g-CuNWs) sandwichedbetween two Cu thin films. The whole structure is fully free-standing,soft, and flexible with a thickness of <40 μm and can beapplied to a broad range of flexible and warped surfaces in electronics have been widely employedtomechanically joint and thermally bridge the interfaces. To enablea wide range of applications in flexible electronics and microelectronics,the “ideal” thermal interface materials must simultaneouslypossess high thermal conductivity for minimizing thermal resistanceand high flexibility and compliance for adapting to soft and curvedsurfaces while accommodating the thermal stress derived from the mismatchof thermal expansion between two jointed materials. However, conventionalthermal interface materials, such as solders, greases, gels, and epoxies,cannot satisfy such demanding and stringent technical criteria. Soldersdisplay high thermal conductivity but feature poor mechanical compliance.ctronics1a. To thctronics1b.35 . For the Young’s modulus measurements, theload–partial unload method with controlled normal displacementis performed for 20 cycles . For the shear modulus measurements,we conduct standard scratch tests in which, after the probe tip contactsthe specimen surfaces, a normal displacement of 30 nm is exerted onthe samples to ensure full contact while the probe moves laterally(Fl/(AΔx), where F is the lateral force, Δx is the lateral displacement, l is thethickness of the sample, and A is the shearing areathat is determined by contact probe area. The measured shear moduliof bare CuNWs, g-CuNWs, and the 3D “sandwich” structureare 0.447 ± 0.275, 0.738 ± 0.236, and 1.044 ± 0.289MPa, respectively. Both the measured Young’s modulus (1.35MPa) and shear modulus (1.044 MPa) are about 4 orders of magnitudesmaller than those of solder alloys (10–20 GPa) and manifestthat the 3D graphene-nanowire “sandwich” structure hasa low stiffness like foams and polymers.In order to quantify the compliance of the 3D graphene-nanowire“sandwich” structure, we characterize its mechanicalproperties using a nanoindentor (Hysitron TI900 Triboindenter) andcompare it with the cases of bare CuNWs and g-CuNWs and the best fit from the heat transfer model give the thermal conductivityof CuNWs to be 65 ± 6 W/m·K, which is consistent with theestimation based on the ∼20% CuNW filling ratio . After the graphene deposition on theCuNW sample (the fitting is demonstrated as 2·K/W (Sample #1), ∼0.26mm2·K/W (Sample #2), and ∼0.24 mm2·K/W (Sample #3) .The ultralow thermal resistance (∼0.24 mm2·K/W)is about 1 order of magnitude smaller than that of conventional solders. It is worth noting that forthe three samples, the average thermal interface resistance (∼0.006mm2·K/W) between the g-CuNWs and their electroplatedCu cap layers is about 1 order of magnitude smaller than that betweenthe as-grown CuNWs and their original Cu base layers (∼0.04mm2·K/W), which demonstrates the excellent bondingof the g-CuNWs with the electroplated Cu layer.We implement the frequency-domain thermoreflectance(FDTR) methodto measure the thermal transport properties of the fabricated 3D graphene-nanowire“sandwich” structure. As shown in Supplementary Note S5 for detailed setup description).This controlled group of two assemblies is mounted on the same heaterwith an area of 35 mm × 20 mm and 50 W applied. Immediately afterthe heater is switched on, the top surface temperature of the assembliesis measured by an infrared camera. From the infrared temperature mapping(Supplementary Note S6 for detailedsetup description). As a control experiment, a similar assembly bya commercial thermal paste experiencing the same cycle is measured,as well. One thermal cycle includes a 2 min ramping up from −55°C to 125 °C, a 30 s dwelling, a 2 min ramping down from125 °C to −55 °C, and another 30 s dwelling, as shownin 43 is an indication oflong-term reliability, thus demonstrating the long-term reliabilityof the 3D graphene-nanowire “sandwich” thermal interface.Moreover, in comparison with the assembly integrated with the thermalpaste, the “sandwich” assembly possesses a higher temperaturerange, thereby indicating the higher through-plane thermal transport.To further demonstrate the superior performanceof the 3D graphene-nanowire“sandwich” thermal interface, in  mapping4e,f resuIn summary, we demonstrate a free-standing,paperlike, and flexible3D graphene-nanowire “sandwich” TIM that enables excellentsolderability and has ultrahigh mechanical compliance, like polymersand foams, with an ultralow thermal resistance about 1 order of magnitudesmaller than that of traditional solders. From temperature cyclingtests in a wide temperature range, the 3D “sandwich”shows good long-term reliability. Since most flexible electronics and microelectronics are solderable, the 3D“sandwich” TIM demonstrated in this work can be appliedto a broad range of flexible and curved surfaces in electronics foradvanced thermal management, energy conversion, and energy harvestingtechnologies.4/Ar = 1:19, 50 sccm).Following the PECVD synthesis, the copper electroplating was conductedagain, in which the copper was only deposited on the tip of the g-CuNWsto form an ∼8 μm thick continuous layer, labeled as “Cucap.” The “sandwich” structure was enabled tospread and bond with other substrates by electroplating thin tin layerson the top and the bottom of the material. Via trial and error, atin layer of 3–5 μm was determined sufficient to combinetwo relative rough surfaces. During assembly, it was sandwiched betweentwo substrates with a mild pressure applied and heated to the meltingpoint of tin (∼240 °C) for few seconds. The melted tinwas able to flow and conform to the roughness of the mating surfacesand join them together after cooling down. As opposed to the conventional≥20 μm soldering bond line thickness, the reason whysuch a thin tin layer can be used here is attributed to the flexiblenanowires that can readily conform to the major surface asperities,while the liquid tin only needs to fill the remaining tiny air voids.A thin layer of copper (∼2 μm), labeledas “Cu base,” was sputtered on the anodic aluminum oxide(AAO) template  to form a seed layer for the subsequent copper nanowireelectroplating. To have copper electrodeposited only from the openhole side, a sample holder that blocks the Cu base was exploited.In the copper electrolyte bath (Sigma-Aldrich), a square wave currentwas applied whereby the “on” time determines the coppernanowire length (∼20 μm). The AAO template was then dissolvedin KOH solution to release the nanowires. Concurrently, critical-pointdrying (CPD) was conducted to remove the solution, by such mannerthat the nanowire aggregation caused by liquid surface tension canbe avoided. Subsequently, the out-of-plane graphene was synthesizedon the copper nanowire arrays by PECVD method. A homemade fixturewas designed for holding the CuNWs/Cu base in the reaction gas flowcomposed of methane and argon  mapping . The representativepeaks in the Raman spectrum 2b, i.e.,Figure S11), from whichonly Cu was observed. After the removal of the AAO, however, CuNWswere quickly oxidized to form copper oxide and cuprous oxide, as illustratedby the XRD peaks at 36.5°, 42°, and 61.5° (The X-ray diffraction (XRD) spectroscopy(Empyrean) was used to investigate the composition of both CuNWs andg-CuNWs. A benchmark XRD spectrum of CuNWs embedded in the AAO wasalso performed S11, fromTo extract thermal properties from FDTR measurements, it is importantto know the specific heat of the material, including CuNWs and g-CuNWs.This property was quantified by exploiting the TA Instruments DiscoveryDSC250 Differential Scanning Calorimeter (DSC). Prior to the measurement,the CuNWs on Cu base and the g-CuNWs on Cu base samples were pressedand sealed in separate aluminum pans. The measurement scans were performedin the order of empty baseline, sapphire disk, and unknown samples.All of them experienced the same procedure: room temperature to 200°C with a ramp rate of 20 °C/min and isothermal for 10 min.Given the known masses of sapphire and the sample and the well-knownsapphire heat capacity, the heat capacity of the unknown materialscould be determined by the heat flow difference with the sapphire.As a result, the specific heat values of the CuNWs on the Cu baseand g-CuNWs on the Cu base were measured to be 0.31 and 0.3 J/g·K,respectively, at room temperature. After excluding the contributionfrom the Cu base layer, the specific heat values of the CuNWs andg-CuNWs were estimated to be 0.287 and 0.273 J/g·K. The densitywas evaluated on the basis of the mass and volume to determine thevolumetric specific heat of the CuNWs and g-CuNWs.


To assess the prevalence of dry eye disease (DED) in the Uyghur population in Hotan, Xinjiang, and to identify risk factors associated with this disorder.Between January and September of 2020, 5,121 Uyghur subjects aged 18 − 98 years from 105 villages were selected and studied cross-sectionally using a whole-group random sampling method in the Hotan area, Xinjiang, China. The Ocular Surface Disease Index questionnaire was used to collect subjective symptoms of DED and examine tear-film break-up times. The break up time and Schirmer’s test were used to collect objective signs, to determine the prevalence of DED and its risk factors.p < 0.05), but there was no significant difference in sex, presence of diabetes, or presence of hypertension (p > 0.05).A total of 5,121 subjects aged 18 − 98 years were recruited from the Uyghur population in the Hotan region of Xinjiang, China, for eye examinations and questionnaire surveys. A total of 40.6%  were diagnosed with DED, of which 38.3% were male and 41.9% were female. The prevalence of DED was the highest in subjects ≥ 65 years of age, with 47.8% in males and 53.3% in females. The lowest occurrence was in subjects 18 − 44 years of age, with 32.5% in males and 33.7% in females. Older age, tea drinking, and staying awake late were risk factors affecting the severity of DED prevalence (The prevalence of DED in the study population was 40.6%, and its prevalence was higher in females, when compared with males. The prevalence of dry eye also increased with age, and at an advanced age, female sex, smoking, staying awake late, and not exercising were risk factors for DED. The TFOS Dry Eye Workshop II (TFOS DEWS II) defines dry eye disease (DED) as a chronic ocular surface disease caused by multiple factors, involving an unstable tear film or imbalance in the ocular surface microenvironment due to abnormalities in the quality, quantity, and kinetics of tears, which can be accompanied by ocular surface inflammatory responses, tissue damage, and neurological abnormalities, resulting in multiple ocular discomfort and/or visual dysfunction . The preXinjiang is located in northwestern China, in the interior of the Asian and European continents, and has a distinct temperate continental climate due to its distance from the ocean, and being surrounded by high mountains that prevent easy access to oceanic air currents. In 2017, Yingying  reportedUyghur subjects aged ≥ 18 years of age in the Hotan area of Xinjiang were selected from January to September of 2020 using whole-group random sampling in villages. Inclusion criteria included: (1)ages ≥ 18 years; (2) Duration of residence > 1 year; (3)voluntary participation in the study; (4)signing an informed consent form. Exclusion criteria included: (1)those with skin diseases, such as Stevens-Johnson syndrome and Aspergillosis; (2)subjects wearing contact lenses;(3)subjects previously treated with ophthalmic surgery, such as refractive surgery, glaucoma, or cataract surgery;(4)subjects with active ocular surface diseases; and (5) patients who could not cooperate due to impaired consciousness, psychological disorders, or psychiatric disorders.(1)Questionnaire The Ocular Surface Disease Index (OSDI), which was translated into Uyghur, was used to analyze the distribution of main symptoms based upon the frequency of reported ocular discomforts. Each point was calculated according to the duration of the symptom, with 4 points for all the time, 3 points for most of the time, 2 points for half of the time, 1 point for a small part of the time, and 0 points for never occurring. The final OSDI score was calculated as /(number of questions answered × 4). The total OSDI score was 100, with a higher score suggesting a more serious ocular surface disease and less stable tear film. This scoring system has been shown to be efficient, objective, and accurate. The Schirmer’s test is a non-anesthetic test that reflects the secretory function of the main lacrimal gland . Fluorescein staining tear film breakup time (FBUT) is the most commonly used method in clinical practice. It must be performed at room temperature, under suitable humidity, and in a light-proof room. The standard test method involves applying 1% sodium fluorescein solution (2 μL) to the conjunctival sac with a sterile dropper, or to touch the lid margin of the lower eyelid with fluorescein paper moistened with antibiotic drops but without excess residual solution. The subject then blinks 3 ~ 4 times so that fluorescein is applied to the surface of the eye, with both eyes looking straight ahead. The results obtained in ≤ 5 s indicate whether the degree of dry eye is moderate to severe.The study complied with the dry eye diagnostic criteria in the Chinese Dry Eye Expert Consensus: Examination and Diagnosis (2020) :1. Patiep < 0.05 was considered a statistically significant difference.Excel 2016 software was used to establish the database, and SPSS statistical software for Windows, version 26.0  was used for statistical analysis. Data are expressed as percentages (%), and confidence intervals were calculated for the prevalence of dry eye and risk factors. Comparisons between groups were made using the chi-square test or Fisher’s exact test according to the conditions, and the associations between DED and its influencing factors were analyzed using the one-way chi-square test and multi-factor logistic regression. A value of A total of 5,121 Uyghur adult subjects were selected from the Hotan area, Xinjiang, China, with an average age of 51.7 ± 10.3 years, with the largest number of subjects in the 45 − 54 years age range, with 1,722 (33.6%) subjects in this age group. There were 1,905 (37.2%) males and 3,216 (62.8%) females; 2,462 (48.1%) drank tea, and 913 (17.8%) had late hours. A total of 913 (17.8%) had the habit of staying up late, 213 (4.2%) had diabetes mellitus, and 1,278 (25.0%) had hypertension. Table p < 0.05). With increasing age subjective symptoms (OSDI ≥ 13), objective sign1 (BUT ≤ 5), and objective sign2 (Schirmer’s test ≤ 5) of DED showed a trend toward greater severity and a higher prevalence of DED. By stratifying by sex, it was found that the subjective symptoms of DED (OSDI ≥ 13), objective signs of dry eye1 (BUT ≤ 5), objective signs of dry eye2 (Schirmer’s test ≤ 5), and the prevalence of DED differed among age groups in males and females , and the overall trend was consistent with dry eye symptoms becoming more severe with increasing age, as shown in Table Among 5,121 subjects, 3,515 (68.6%) had an OSDI questionnaire score ≥ 13, 2,368 (46.2%) had a BUT score ≤ 5, and 1,057 (20.6%) had a Schirmer’s test score ≤ 5, with 2,078 cases of dry eye with a prevalence of 40.6%. Subjective symptoms (OSDI ≥ 13), objective sign1 (BUT ≤ 5), objective sign2 (Schirmer’s test ≤ 5), and prevalence of DED significantly differed among age groups . In addition, the prevalence of DED was higher in the Uyghur population with those drinking tea, with late hours, and without regular exercise ; but there was no significant difference between the prevalence of DED in the diabetic population and the non-diabetic population (p > 0.05), and the prevalence of DED in the population with hypertension was significantly higher than that in the population without hypertension (p < 0.05) , but there was no significant difference among sexes, whether they had diabetes, and whether they had hypertension (p > 0.05), as shown in Table The 2,078 Uyghur subjects with DED were divided into mild dry eye, moderate dry eye, and severe dry eye according to OSDI scores, among which 1,789 subjects (86.1%) had mild dry eye, 267 (12.8%) moderate dry eye, and 22 subjects (1.1%) had severe dry eye. The severity of DED differed among age groups, whether they drank tea, and whether they had late hours , as shown in Fig. A multifactorial logistic regression analysis of DED showed that age, female , smoking  and late hours  were risk factors for DED. Exercise  was a protective factor for DED. The prevalence of DED increased with age, with those 45 − 54 years of age, 55 − 64 years of age, and those ≥ 65 years of age being 1.3 times (95% CI: 1.137 − 1.529), 1.6 times (95% CI: 1.373 − 1.901), and 2.2 times (95% CI: 1.801 − 2.654) more likely to develop dry eye than those 18 − 44 years of age, respectively. DED was not significantly associated with drinking tea, alcohol consumption, diabetes, or hypertension , which was higher than the prevalence of dry eye in Kashgar, Xinjiang, which was 27.8% , and sigIn the present study, we showed, using symptom data, that the overall prevalence of DED was 40.6%, while the prevalence of symptomatic DED  was 68.4%, a prevalence similar to 69% in Palestine , but higThe 2,078 Uyghur patients with DED were classified according to OSDI scores into mild dry eye, moderate dry eye, and severe dry eye, with 1,789 cases (86.1%) with mild dry eye, 267 cases (12.8%) with moderate dry eye, and 22 cases (1.1%) with severe dry eye. The variabilities in the severities of DED were associated with factors such as age, drinking tea, and late hours, with no significant difference in the distributions of sex, diabetes, or hypertension. The percentages of patients with mild DED decreased gradually with age, with the highest percentage of mild DED (91.6%) in those 18 − 44 years of age and the lowest percentage of mild DED (75.3%) in those ≥ 65 years, while the percentages of patients with moderate and DED showed a significant increasing trend with age. Our results indicated that subjects who smoked, had late hours, and did not exercise tended to have higher percentages of DED. One study reported a significant effect of green tea consumption on ocular tear film quality , yet anoThis is associated with the local consumption of greasy foods and less vegetables, and dyslipidemia is a high risk factor for DED. The prevalence of metabolic syndrome is high in Xinjiang, especially among ethnic minorities because of their special dietary patterns , 27. MetFinally, our study was based on a Uyghur population with a large sample size and included objective examinations and questionnaires. However, the study may have some limitations. The use of Schirmer’s test and FBUT examination were invasive, which may have affected the true state of tears and tear film, although a subsequent study included a dry eye analyzer to provide more objective data analysis and analysis of the Meibomian gland .In conclusion, the prevalence of DED was high among Uyghurs in the Hotan region of Xinjiang, and was especially common among elderly patients and females. Subjects in this region were not aware of the negative impact of DED on the visual quality and quality of life. With the increasing trends of aging and popularity of video terminals(VDT), the prevalence of DED in this region may increase. We therefore need to increase social awareness about DED to reduce modifiable risk factors (arid environment, high fat diet, and systemic diseases such as diabetes , 26, 27.


It is unknown how the patterns of negative and positive attentional biases in children predict fear of COVID-19, anxiety symptoms, and depression symptoms during the COVID-19 pandemic. The study identified profiles of negative and positive attentional biases in children and examined their association with emotional symptoms during the COVID-19 pandemic.264 children (girls: 53.8% and boys: 46.2%) of 9–10 years born in Hong Kong or mainland China from a primary school in Shenzhen, People’s Republic of China were involved in a two-wave longitudinal study. Children completed the COVID-19 Fear Scale, the Revised Child Anxiety and Depression Scale, and the Attention to Positive and Negative Information Scale to measure fear of COVID-19, anxiety and depression symptoms, and negative and positive attentional biases in classrooms. After six months, they completed the second assessment of fear of COVID-19, anxiety symptoms, and depression symptoms in classrooms. Latent profile analysis was conducted to reveal distinct profiles of attentional biases in children. A series of repeated MANOVA was performed to examine the association of profiles of attentional biases to fear of COVID-19, anxiety symptoms, and depression symptoms across 6 months.Three profiles of negative and positive attentional biases were revealed in children. Children with a “moderate positive and high negative attentional biases” profile had significantly higher fear of the COVID-19 pandemic, anxiety symptoms, and depression symptoms than children with a “high positive and moderate negative attentional biases” profile. Children with a “low positive and negative attentional biases” profile were not significantly different in fear of COVID-19, anxiety symptoms, and depression symptoms than those with the other two profiles.Patterns of negative and positive attentional biases were related to emotional symptoms during the COVID-19 pandemic. It might be important to consider children's overall patterns of negative and positive attentional biases to identify children at risk of higher emotional symptoms.The online version contains supplementary material available at 10.1186/s13034-023-00594-y. The COVID-19 pandemic might lead to an increase in the rate of emotional symptoms among children . PreviouLongitudinal studies that examine how the profiles of attentional preferences affect emotional symptoms during the COVID-19 pandemic are particularly scarce. Considering the importance of attentional bias in children’s development of internalizing symptoms, more research is needed to investigate how children’s overall patterns of attentional biases might affect the development of fear, anxiety symptoms, and depression symptoms during the COVID-19 pandemic. These findings would add to the literature what were the overall patterns of negative and positive attentional biases in children during the COVID-19 pandemic, and how these patterns of negative and positive attentional biases were associated with emotional symptoms during the COVID-19 pandemic. Such findings might also add to our understanding of whether psychologists should consider both negative and positive attentional biases simultaneously when investigating the development of emotional symptoms in children, especially during the COVID-19 pandemic.To address these research gaps, the present study aimed to reveal profiles of attentional biases and to examine how these profiles were associated with the development of fear of COVID-19, anxiety symptoms, and depression symptoms in children during the COVID-19 pandemic.Attentional bias refers to the cognitive tendency to shift attention toward negative or positive stimuli. Based on the cognitive models, negative attentional bias is the vulnerability factor for the development of anxiety symptoms and depression symptoms in children , 33. ResAttentional training that targeted negative attentional bias has shown efficacy in modifying self-esteem as an indicator of depression symptoms in 108 participants over 17 years old with mild or minimal depression symptoms  [During the COVID-19 pandemic, children around the age of 14.23 years (N = 195) recruited from the Netherlands might experience strong fear of COVID-19 infection which was the result of communication of threatening COVID-19-related information with parents . A meta-Profiles of negative and positive attentional biases depicted overall patterns of attentional preferences to negative and positive stimuli. Although negative attentional bias might be the opposite of positive attentional bias in terms of the affective valence of preferred stimuli, people might have low negative attentional bias and low positive attentional bias simultaneously. The presence of high negative and high positive attentional biases might predict lower emotional symptoms than those with high negative and low positive attentional biases. For example, a study with an unselected community sample of 270 adults (the mean age of 22 years) from the undergraduate student population and community forum has shown that attentional bias toward threats was linked to high self-report anxiety symptoms only in individuals with a tendency to attend away from positive information . Latent The current research recruited a sample of children from a primary school. The study aimed to 1) reveal distinct profiles of negative and positive attentional biases in children during the COVID-19 pandemic. Also, the study aimed to 2) reveal the relationship of profiles of attentional biases to fear of COVID-19, anxiety symptoms, and depression symptoms during the COVID-19 pandemic. The majority of existing studies have only investigated either negative attentional bias or positive attentional bias separately. No previous studies have used the latent profile analysis to investigate the effect of the overall patterns of attentional biases on children’s emotional symptoms during the COVID-19 pandemic. This study would be the first study that took a holistic approach to reveal profiles of attentional biases in children. Also, it would provide the first evidence from a longitudinal study for how profiles of attentional biases would affect fear of COVID-19, anxiety symptoms, and depression symptoms during the COVID-19 pandemic.Based on the previous evidence, distinct profiles of attentional biases would be revealed which might include profiles of “low negative and positive attentional bias”, “low negative and high positive attentional bias”, “high negative and low positive attentional bias” and “high negative and positive attentional bias”. Compared to the “high negative and positive attentional bias” profile, the “low negative attentional bias and high positive attentional bias” profile would predict low fear, anxiety symptoms, and depression symptoms during the COVID-19 pandemic. While compared to the “low negative and positive attentional bias” profile, the “high negative attentional bias and low positive attentional bias” profile would be related to more fear, anxiety symptoms, and depression symptoms in children during the COVID-19 pandemic.The study initially recruited a sample of middle-class 322 children from a primary school in Shenzhen, PRC. Children had similar social economic status and education levels. They were from middle-class families and had the same grade at the same school.Convenient sampling was used to recruit participants. First, public schools where children were normal Chinese students from middle-class families were selected. This population was chosen because the middle class is rapidly growing, and takes a significantly large proportion of the population in China . Then, iboys = 124 and N girls = 138) were input into analyses.Regarding gender distribution, 53.8% (N = 171) of participants were girls, and 46.2% (N = 147) were boys; three participants did not indicate their gender. The average age of the sample was 9.54 years, ranging from 9 to 10 years (SD = 0.505 years). Exclusion criteria were (1) not able to fluently speak and understand simplified Chinese, (2) having a diagnosis of psychological disorders or developmental disorders, and (3) birthplace outside of mainland China. 50 children were excluded from the study because they failed to meet the inclusion criteria. 8 children who failed to complete one of the self-report assessments were excluded from the research. Altogether, 58 students were excluded from the study. Consequently, data from 264 children . First, researchers assigned the informed consent and assent forms to students. After collecting the informed consent and assent forms from students, children completed the Attention to Positive and Negative Information Scale for approximately 30 min in the classrooms. Researchers answered questions regarding the scale from students in the classrooms.The present study was conducted from November 16th to November 30th, 2020, when the COVID-19 pandemic was ongoing. The prevention measures, including social distancing, were implemented during the period. Teachers in the primary school helped researchers disseminate informed consent forms and assent forms to parents and students. The signed informed consent and assent forms were collected one day before the date of data collection in the classrooms. Only children who signed the assent forms and obtained the signed informed consent forms from their parents participated in the study. On the data collection date, research assistants assigned a set of questionnaires to students during classes. The participants were informed that they could ask questions and withdraw from the study at any time without any consequence. The assessment of attentional biases was conducted concurrently with the first assessment of emotional symptoms at time one (T1) and before the second assessment of emotional symptoms at time two (T2). At time one, students completed a set of questionnaires for children to assess their negative and positive attentional biases, fear of COVID-19, anxiety symptoms, and depression symptoms for approximately 45 min in the classrooms. After approximately six months, students completed the questionnaire to assess their fear of COVID-19, anxiety symptoms, and depression symptoms at time two in the classrooms for approximately 45 min. In each assessment, a teacher and researcher were present to answer students’ questions and ensure the safety of students.The eight-item Chinese version of the Attention to Positive and Negative Information Scale (CAPNIS) was administered to children , 23. Thehttp://www.childfirst.ucla.edu/Resources.html). RCADS is a wildly used scale for childhood anxiety symptoms and depression symptoms. The 47 items of the scale can be grouped into the Anxiety Disorders and the Major Depression sub-scales, rated on a Likert scale from 0 to 3 . The scale of Anxiety Disorders has 37 items , and the scale of Major Depressive includes 10 items . An anxiety symptoms score and a depression symptoms score were calculated by summing up scores of the relevant items on the subscales of Anxiety Disorder and Major Depression, respectively. The scales showed excellent reliability with the current data .The Chinese version of the Revised Child Anxiety and Depression Scale  was usedFear of COVID-19 was measured by the COVID-19 Fear Scale (CFS). CFS was adapted from the Chinese version of the 18-item SARS Fear Scale . When adapting the CFS scale, three items were deleted from the original scale, because these items were only related to healthcare workers . Also, instead of SARS, participants were asked about their response to the COVID-19 pandemic in the COVID-19 Fear Scale.Participants were asked to rate on a 4-point Likert scale how much the statement is true in the face of the COVID-19 pandemic. 0 indicates "definitely false" and 3 indicates "definitely true." The sample item includes "Fear that I will be infected." Three items were excluded from CFS  because of their inapplicability to students. A CFS score was obtained by summing up scores from each item. The higher the CFS scores, the higher the fear of COVID-19. The scale demonstrated good internal consistency in the current study .Exploratory factor analysis was first performed to examine the structural validity of the Attention to Positive and Negative Information Scale with data from the preliminary study , the adjusted Lo–Mendell–Rubin likelihood ratio test (Adj. LMR), as well as the Bootstrapped Likelihood ratio test (BLRT), showed that a model with k number of groups was significantly better than a model with k-1 groups [Descriptive statistics were presented. Two-tailed Pearson’s partial correlation was investigated using SPSS version 22 to understand the association among psychological variables. Independent t-tests examined the gender differences in the psychological variables. Latent profile analyses were subsequently conducted to reveal profiles of negative and positive attentional biases in children with MPlus 7.4. With maximum likelihood estimation with robust standard error (MLR), heterogeneous profiles of attentional biases were revealed. The number of groups for the model was increased until the model was not significantly better than the model with one fewer group. Smaller values of the Bayesian Information Criterion (BIC) and Akaike information criteria (AIC), as well as the higher value of entropy, suggested a better model fit . The sig1 groups . Next, C1 groups , 18. The t (260) = 1.48, p = 0.14, positive attentional bias, t (260) = − 0.04, p = 0.97, and depression symptoms at T1, t (260) = 1.41, p = 0.16. Girls showed significantly higher anxiety symptoms at T1, t (260) = 3.13, p < 0.005, higher anxiety symptoms at T2, t (260) = 2.92, p < 0.005, and higher depression symptoms at T2, t (260) = 2.17, p < 0.05, than did boys. Also, girls were significantly higher in fear of COVID-19 at T1, t (257) = 2.12, p < 0.05, than boys. Girls were significantly higher in fear of COVID-19 at T2, t (256) = 2.92, p < 0.005. Refer to Table An independent t-test was performed with 262 participants to examine the difference between girls and boys in positive and negative attentional biases, fear of COVID-19, depression symptoms, and anxiety symptoms assessed at time one (T1) and time two (T2). Results revealed that girls and boys didn’t significantly differ in negative attentional bias,r = − 0.01, p = 0.82, negative attentional bias, r = 0.04, p = 0.57, anxiety symptoms at T1, r = − 0.04, p = 0.52, depression symptoms at T1, r = − 0.03, p = 0.61, anxiety symptoms at T2, r = − 0.03, p = 0.60, and depression symptoms at T2, r = − 0.02, p = 0.76.The Pearson’s partial correlation, controlling for gender revealed that age was not significantly associated with positive attentional bias, Higher anxiety symptoms at T1 and T2 were significantly related to higher depression symptoms at T1 and T2. They were also significantly associated with higher negative and lower positive attentional biases. Depression symptoms at T1 and T2 were positively and significantly associated with negative attentional bias; depression symptoms at T1 and T2 were negatively and significantly related to positive attentional bias. Higher fear of COVID-19 at T1 and T2 was associated with significantly higher anxiety symptoms and depression symptoms at T1 and T2. Also, higher fear of COVID-19 at T1 and T2 was significantly related to higher negative attentional bias. Higher fear of COVID-19 at T1 was significantly associated with lower positive attentional bias. Higher fear of COVID-19 at T2 was not significantly related to lower positive attentional bias. Higher anxiety symptoms at T1 were significantly related to higher anxiety symptoms at T2; higher depression symptoms at T1 were significantly related to higher depression symptoms at T2. Fear of COVID-19 at T1 was significantly related to higher fear of COVID-19 at T2. Negative attentional bias was not significantly associated with positive attentional bias. Refer to Table p values of VLMR, Adj. LMR and BLRT were insignificant for the four-class model, which suggested that the four-class model was not significantly better than the three-group model. Thus, the three-class model showed the best model fit.The fit indices for models with one to five groups were examined with a latent profile analysis , and was named as “low positive and negative attentional biases” profile . Class two had the highest positive attentional bias and moderate negative attentional bias , which was accordingly defined as the “high positive and moderate negative attentional biases” profile . Class three had a moderate positive attentional bias and high negative attentional bias , which was named the “moderate positive and high negative attentional biases” profile . Figure Class one had the lowest level of negative and positive attentional biases (Mean χ2 (2) = 0.23, p = 0.89, birthplace, χ2 (2) = 1.14, p = 0.57, and age groups (9 & 10 years), χ2 (2) = 1.24, p = 0.54. Refer to Table The three latent profiles were not significantly different in terms of gender, F  = 5.66, p < 0.001. The effect size was small, partial η2 = 0.042. Power for the effect of profiles on anxiety symptoms was as high as 0.86.The Bonferroni post hoc test showed that children with a “moderate positive and high negative attentional biases” profile had significantly higher anxiety symptoms  than children with a “high positive and moderate negative attentional biases” profile . Children with a “low positive and negative attentional biases” profile  were not significantly different in anxiety symptoms level from children with the other two profiles  = 6.43, p < 0.01. The effect size was small with partial η2 = 0.047. The between-subject effect had high calculated power of 0.90. Bonferroni post hoc test showed that children with a “moderate positive and high negative attentional biases” profile  had significantly higher depression symptoms than children with a “high positive and moderate negative attentional biases” profile . Children with a “low positive and negative attentional biases” profile  were not significantly different in depression symptoms from children with the other two profiles  = 6.43, p < 0.05. The effect size was small, partial η2 = 0.031. The calculated power for the effect of profiles on fear of COVID-19 was 0.72. The Bonferroni post hoc test showed that children with a “moderate positive and high negative attentional biases” profile  demonstrated significantly higher fear of COVID-19 than children with a “high positive and moderate negative attentional biases” profile . Children with a “low positive and negative attentional biases”  profile didn’t significantly differ in fear of COVID-19 from children with “moderate positive and high negative attentional biases” and “high positive and moderate negative attentional biases” , “high positive and moderate negative attentional biases” profile (38.5%), and “moderate positive and high negative attentional biases” profile (57.2%). Profiles of attentional biases showed a significant relationship with emotional symptoms over six months during the COVID-19 pandemic; the “moderate positive and high negative attentional biases” profile was related to significantly higher anxiety symptoms and depression symptoms than “high positive and moderate negative attentional biases” profile. The “low positive and negative attentional biases” profile was not significantly different from the other two profiles in emotional symptoms. Consistent with the findings, previous studies which measured negative attentional bias by behavioral tasks also found a positive association between negative attentional bias and emotional symptoms. , 16. TheMoreover, during the COVID-19 pandemic, negative attentional bias was related to higher health anxiety and higher COVID-19-related anxiety symptoms , 4. ThisThese were the first results identifying children’s patterns of attentional biases during the COVID-19 pandemic and their relationship with emotional symptoms. With latent profile analysis and the longitudinal design, the results added to the literature that it was important to consider negative and positive attentional biases simultaneously and to use profiles of attentional biases to predict the development of emotional symptoms during the COVID-19 pandemic. Evidence might provide significant implications for the cognitive model of emotional symptoms, suggesting that negative attentional bias was as important as positive attentional bias, and thus the overall patterns of negative and positive attentional bias might be more important than negative attentional bias alone.The current study revealed three profiles of positive and negative attentional biases in children during the COVID-19 pandemic. Over half of the children showed a “moderate positive and high negative attentional biases” profile (59.5%), and only a smaller number of children had a “low positive and negative attentional biases” profile (3.8%) or “high negative attentional bias and moderate positive attentional bias” profile (36.7%). Consistent with previous research, most children’s attentional bias towards negative stimuli tended to be moderate or high during the COVID-19 pandemic .


Diffusion of molecules in porous media is a criticalprocess thatis fundamental to numerous chemical, physical, and biological applications.The prevailing theoretical frameworks are challenged when explainingthe complex dynamics resulting from the highly tortuous host structureand strong guest–host interactions, especially when the poresize approximates the size of diffusing molecule. This study, usingmolecular dynamics, formulates a semiempirical model based on theoreticalconsiderations and factorization that offer an alternative view ofdiffusion and its link with the structure and behavior (sorption anddeformation) of material. By analyzing the intermittent dynamics ofwater, microscopic self-diffusion coefficients are predicted. Theapparent tortuosity, defined as the ratio of the bulk to the confinedself-diffusion coefficients, is found to depend quantitatively ona limited set of material parameters: heat of adsorption, elasticmodulus, and percolation probability, all of which are experimentallyaccessible. The proposed sorption–deformation–percolationmodel provides guidance on the understanding and fine-tuning of diffusion. The main measure of diffusion is the diffusioncoefficient, including intrinsic, tracer, corrected, transport, mutual,self, chemical, and collective diffusion coefficients, many of whichare clarified in Supplementary Note S1.Of note, this paper focuses on self-diffusion or, equivalently, tracerdiffusion.1Diffusion of molecules, 3 hopping,4 obstruction,5 and free volume,8 to hydrodynamic/friction,10etc. For dilute polymer solutions, e.g., hydrogels, diffusion theoriesare relatively well established, as fluid–solid interactionscan be reasonably neglected when pore size λ is much largerthan the diffusant size σ, λ ≫ σ. For example,the obstruction theory successfully predicts diffusion coefficientsin hydrogels by relating diffusion coefficients to the probabilityof finding a pore large enough to accommodate water molecules.5 In contrast, for the case of highly concentratedpolymer solutions, where λ ∼ σ, the fluid–solidinteraction force ζ becomes dominant as it roughly scales withthe reciprocal of the pore length scale ζ ∼ λ–1 . This strong fluid–solidinteraction force leads to rich dynamics including molecular sieving,single-file diffusion, and anomalous diffusion.10 In more detail, from a thermodynamical point of view, confinedwater displays a complex behavior as the interaction field generatedby the host medium induces dynamical heterogeneities . Fromag.,refs , 13)). ). 3 hopp15 and activation energy-based theories.16 Molecularsimulation studies have proved that free volume scaleslinearly with adsorbed amount.15 However,the experimental measurement of free volume remains sophisticated,involving positron annihilation lifetime spectroscopy,17 inverse gas chromatography,18etc.,19 combinedwith semiempirical interpretation. Though activation energy can bemore easily measured through temperature-dependent Arrhenius processes,21 the connection between pore structure and activation energy, bothrelevant to diffusion, is not straightforward. Moreover, the above-mentionedtheories do not consider the intermittent dynamics of the diffusant.Previous works employed tortuosity, defined as the ratio of self-diffusioncoefficient of bulk water to water diffusion coefficient in pores,ξ = Ds,w/Dμ, to phenomenologically describe the intermittent dynamics. From a fundamentalviewpoint, a microscopic explanation of tortuosity based on physicalparameters is still lacking.Besides the obstructiontheory, researchers proposed free volumeIn short, the strong fluid–solidinteraction and complexpore structure form together a nontrivial energy landscape impedingthe efforts of elucidating diffusion when the size of the pore, alsoreferred to as mesh opening or free volume, approximates the watermolecular size, λ ∼ σ. To tackle these important,yet unresolved, challenges, this study resorts to molecular dynamics(MD) to address water diffusion in a dense, sorptive, and deformablepolymer structure. We first segregate the microscopic diffusion coefficientfrom the overall diffusion coefficient through the stop-and-go formalism—whichis equivalent to the concept of intermittent Brownian motion—andthen rationalize the concept of tortuosity using simple material parametersinvolving pore structure, sorption, and deformation. Our approachprovides a unifying picture of the intermittent motion of water moleculesand of the quantification of complex diffusion landscape through physicallywell-defined material parameters. This model provides a way of predictingdiffusion coefficients from adsorption heat, elastic modulus, andpercolation probability.i.e., two types of hemicelluloses, arabinoglucoronoxylan (AGX) and galactoglucomannan(GGM), two types of lignins, uncondensed lignin (uLGN) and condensedlignin (cLGN), and their mixtures, mixture 1  and mixture 2 . These woodpolymers are chosen as model systems because they cover a broad rangeof water–polymer interaction strengths, pore structures, chainconnectivities, etc. More details about the molecularmodels are included in Supplementary Note S2 and our previous work.22 Moreover, waterdiffusion in wooden materials is relevant to ubiquitous wooden buildingconstruction, furniture, and artifacts, more specialized issues includingarcheological wood preservation,23 advancedwood-based iontronics devices,24etc. The moisture content, m, of the systemis defined as the ratio of the mass of water to the mass of the drypolymer. This study focuses on a moisture content range m = 0–0.3, corresponding to the normal range of moisture loadof wood exposed to atmospheric environments.25m ∼ 0.2.To study the diffusion of moleculesin dense, sorptive, and deformablenanoporous structures, diffusion of water in hydrophilic nanoporousbiopolymers is employed as a prototypical model. More specifically,six biopolymer systems are studied, 27 Molecular motion is characterized by mean square displacement (MSD).A sample MSD curve is included in Supplementary Note S3 . The MSD curve displays alternating segmentsof plateaus and slopes, corresponding to waiting and moving status,respectively. Diffusion is usually described using Einstein’s equationwhere particle diffusion is considered as a random walk resultingfrom stochastic collisions. In sorptive systems, however, water moleculesmove via a series of waiting—sometimes referred to as residence/stop/immobile—andmoving—relocation/go/mobile—events, alternatively identifiedas intermittent Brownian dynamics. Note S3 S1a. The 26 we define the time segment i, i.e., the time range ti < t < ti + 1, as waiting if the deviation from theaverage displacement is less than 0.1 nm (OH bond length), |r(t) – ⟨r⟩t | < 0.1 nm, t ∈ ,and the rate of change of its squared displacement ti+1 – ti is then averaged over all waiting segments and watermolecules, denoted as τw. The frequencyof status switching, ν, is normalized by thetotal simulation time ttot. Therefore,we have ttot = tw + tm = τwνttot + τmνttot, where ν–1 = τw + τm and τm is the moving time.26Following our previous work,ν asa function of moisture content m are shown in i.e., uLGN and cLGN, the switching frequencymonotonically decreases with moisture content. With the ongoing hydrationprocess, adsorption sites at the polymer surface are gradually occupiedby water molecules, and, therefore, the new water molecules in thesystem are gradually screened from adsorption at the occupied sitesand consequently remain mostly more mobile. For the same reason, withincreasing moisture content m, the waiting time τw decreases while the moving time τm increasesas shown in i.e., AGX, GGM, M1, andM2, displays a peak at intermediate moisture contents. This peak impliesa crossover from waiting-dominated mode to moving-dominated mode,meaning that water molecules mostly stay waiting at low moisture contentdue to sorption and are mostly moving at high moisture content.28 Here, ergodicity is implicitly invoked, meaningthat the number fractions of moving and waiting molecules are equalto the time fraction of moving and waiting phases, respectively. Thisassumption is confirmed by our simulation data.The resultsof switching frequency Dμ = D/(τmν).26 The factor τmν denotes the fraction of moving water or time withrespect to the total number of water or total time. The microscopicdiffusion coefficient Dμ and thefraction of moving water molecules τmv are shown in In the waitingstate, water molecules are trapped, thus displayinga nearly zero diffusion coefficient. The real displacement only occursduring the moving phases . The diffusion coefficient in the moving phase is referredto as microscopic diffusion coefficient D iscalculated as theslope of the Fickian regime of MSD averaged over all water moleculesand time origins (Supplementary Note S1).29 For all systems, the diffusion coefficientsincrease with increasing moisture content but remain lower than thebulk water self-diffusion coefficient Ds,w = 3.5 nm2 ns–1 (the bulk diffusioncoefficient was measured in a separate simulation). The cLGN and uLGNshow the highest diffusion coefficient, while GGM the lowest. M1 showsa diffusion coefficient lower than uLGN but higher than AGX, i.e., a mixing of its two components, andso does M2. We note that the diffusion coefficient of cLGN surgesat m ∼ 0.15 . One can invoke a linear relationshipbetween activation energy Ea of diffusionand heat of adsorption, Ea ∼ αQad .30 Therefore,taking the limit α = 1, an exponential relation between normalizeddiffusion coefficient can be employed, ξ–1 ∼ exp(−Qad/kBT), where kB and T denote the Boltzmann constant and temperature,respectively. This relation is shown to be valid, as seen in In the activation theory, the diffusion coefficientscales withthe activation energy D ∼ lp1/2.31 The persistence length of a worm-like chain is related to Young’smodulus E, cross-section area, and moment of inertia M, following the relation lp = EM/kBT.32 Therefore, the normalized diffusioncoefficient is also assumed to scale exponentially with Young’smodulus, ξ–1 ∼ exp[(E/E0)1/2], where E0 is simply assumed as 1 GPa to make the term betweenbrackets dimensionless. Figure S4 show the validityof the proposed exponential scaling.Yang and Chun derived the relation between diffusioncoefficientand polymer persistence length ln Supplementary Note S5. However, for some systems, e.g., cLGN, there exists a surge of diffusion coefficientsaround m ∼ 0.15, which is related to the occurrenceof percolation. The prediction above, which relies on two terms (heatof adsorption and elastic moduli), fails to include such a feature.It is thus necessary to introduce percolation into the model.The prediction of diffusioncoefficient based on heat of adsorptionand elastic moduli works relatively well, as shown in pp defined as the time interval during whichpercolation is occurring divided by the total simulation time, i.e., pp = ∫ δp(t)dt/∫ dt, where δp(ti) equals 1 or 0 whether or not the system percolatesat time ti, correspondingly(details in Supplementary Note S4). Thescaling between the normalized diffusion coefficient and percolationprobability pp is not a simple function.In analogy with heat of adsorption and modulus, we propose an exponentialscaling, ξ–1 ∼ exp(pp) . Inessence, percolation is a special type of structural feature thatis not represented by heat of adsorption and elastic modulus, whichsupports the inclusion of percolation as a separate factor. The percolationprobability is system size dependent. The size dependency is not consideredas a critical issue here because percolation probability will be pairedwith an adjustable parameter that incorporates in an effective mannerall unspecified effects including the size effect, shown below.In this study, percolation is quantified by the percolation probability 33 the above-mentioned factors are multiplied in the sorption–deformation–percolation(SDP) model:ai  is weight. We can also writeIn the spirit of tortuosity factorization,Figure S3 . A sensitivity analysis is carried out by omitting an arbitrarynumber of factors. The prediction is poor for any model with fewerfactors.The SDP model well describes the measurementsas shown in a0 =−0.572, aQ = −3.051, aE = −1.243, and ap = 0.466. The weights ai in the SDP model are dimensionlessnumbers, which are the first derivative of ln ξ–1 with respect to the corresponding property xi, ai = ∂ ln ξ–1/∂xi. The a0 is introduced to manifest all the influencing factors otherthan sorption, deformation, and percolation. When aQ is zero, the SDP model reduces to thedescription of a nonsorptive material. Unlike most previous diffusionstudies, which shun complexity by assuming negligible host–guestinteraction and pore length scale being much larger than the diffusantsize, here the SDP model tackles the challenge of diffusion in dense,sorptive, and deformable polymer materials.The weights are 34 In fact, our simulation shows that water in most systemsis mainly in the moving state, except for the strongly adsorbing material,GGM, whose heat of adsorption reaches ∼43 kJ mol–1. It is noted that the latent heat of water is not included, as weuse liquid water as the reference state (details in Supplementary Note S4). The proposed material parameters oftortuosity are also experimentally accessible: heat of adsorption Qad and Young’s modulus E can be measured via calorimetry and mechanical tests, respectively;the probability of percolation can be estimated by, for example, conductivityor capacitance. Preliminary validation of the SDP model based on literaturedata is included in Supplementary Note S6, where acceptable agreement between the predicted and measured diffusioncoefficient is shown.The SDP model canbe verified by experiments. The diffusion coefficientcan be measured via nuclear magnetic resonance (NMR). The waitingand moving statistics are accessible via experimental methods suchas differential scanning calorimetry (DSC) and NMR.35 In a highly confined porous system, it is difficultto distinguish residence modes. In fact, defining the surface, atthe nanoscale, can be a highly nontrivial task.Stop-and-go is a simple picture of watermotion in sorptive systems. There are other modes of (semi)residencesuch as surface diffusion where water is confined to a sorptive surfacebut is free to travel within the vicinity of the surface.While this studyfocuses on water diffusion, we believe that our framework can be extendedto other diffusants, such as hydrated ions and methane, as long asthe molecular size approximates the size of the free volume or porelength scale. Such a scenario has rarely been covered by previousstudies, however, is of significant academic and industrial relevance.For instance, most drugs have molecular sizes around 0.5–5nm, which are comparable to the pore length scale of the drug deliverysystems. Better control of drug release can be achieved by the rationaldesign of the structure of the host porous media under the guidanceof our model.The rigorous applicability of the SDP model toother polymer systemsremains to be verified by comprehensive studies of polymers with differentchemistry, structure, and conditions. The current study motivatesfurther studies by offering a concise physical picture of diffusion.i.e., heatof adsorption Qad, Young’s modulus E, and probability of percolation pp. We resort to MD simulations where the trajectories of individualwater molecules manifest the intermittent dynamics, which is causedby strong sorption interactions and highly tortuous pore space. Themicroscopic diffusion coefficient Dμ should be extracted from the measureddiffusion coefficient D by disregarding the waitingphases using the factor τmv, thefraction of moving water derived from single water molecule statistics.The microscopic diffusion coefficient, equivalently tortuosity ξ,is then predicted via three characteristic parameters of the porousmedia, i.e., Qad, E, and pp, each representinga fundamental physical aspect of the porous system, i.e., sorption, deformation, and percolating structure.The SDP model, therefore, provides guidelines for the comparison ofdiffusion in different polymers. The model may guide the design ofmaterials to achieve the desired diffusion property.This study offers a unifying picture ofwater diffusion withindense disordered deformable porous media and moreover describes thediffusion coefficient via a complete set of physically well-definedmaterial properties, 22 six differentpolymer systems are built. AGX consists of three types of monomers, i.e., 67% xylose, 20% glucuronoacid-xylose,and 13% arabinoxylose, which are randomly polymerized.28 GGM consists of two types of monomers, i.e., 25% glucose and 75% mannose branchedwith galactose side groups (∼8%).36 The uLGN is a linear homopolymer of coniferyl units.37 The cLGN is a randomly branched polymer of coniferylunits with 60% β-O-4 linkage and 40% 5–5′ linkage.38 In addition to the single-component systems,AGX and uLGN are randomly mixed, forming matrix 1 (M1) with a massratio of 1:2. Similarly GGM and cLGN randomly form M2 with a massratio of 7:4.42 The detailed dimensions and densities of polymer systems are listedin Following our previous work,43 and GROMOS53a6 united-atom force field44 in an isobaric–isothermalensemble realized by a velocity rescaling thermostat45 and a Berendsen barostat.46 Thesimulation time of each system is 100–1000 ns depending onthe time needed to reach the Fickian diffusion regime, i.e., where the MSD scales linearly with time. Sorptionis mimicked by the random insertion method. Following each successfulinsertion, energy minimization and 100 ps relaxation are carried out.22 More details are in Supplementary Note S2.A typical simulation system has a lateral size of∼5 nm,containing ∼10,000 atoms. The MD simulations are carried outusing the GROMACS 5.0 packagepp is defined as the time interval during whichpercolation is occurring divided by the total simulation time, i.e., pp = ∫δp(t) dt/∫ dt, where δp(ti) equals 1 or 0 when the system percolatesor not at time ti, correspondingly.Integral heat of adsorption is defined as Qad = Hp + Hwv – Hc)/nwater – Hlatent, where Hp, Hwv, Hc, nwater, and Hlatent are the enthalpies of dry polymer, watervapor, polymer–water mixture, the amount of water in moles,and latent heat of water, respectively. Hp and Hc are calculated with the definitionof enthalpy H = U + PV, where U, P, and V are directly measurable from MD. Hwv is taken as 4nwaterRT.28Hlatent takes the value of 40.68 kJ mol–1.47 The elastic constant, i.e., Young’s modulus, is determined from the linearregime of stress–strain curves of uniaxial tensile tests.22 Stepwise strains are applied with each stepstraining around 0.01% of the initial dimension until a total strainof ∼1%. Every strain step is followed by a relaxation run of100 ps, where the tension strain is maintained while the transversedirections are subjected to stress-free relaxation.Percolation probability