The heat of solution of CaCO3, to form dissolved CO2, was obtained by a new technique and a modified calculation which served to include the heat of vaporization of the gas escaping in the reaction and resulted in a higher value than those obtained by Wells and Tayıor and by Bäckström in determinations representing only partial solution of CO2. The results obtained were:kj/molekcal/mole2O3·CaCO3·10.68H2O3CaO·Al Heat of formation  from elements, −1956   2O  from reactants and H−18.9N HCl Heat of solution in 2−532.9−127.42O3·6H2O3CaO·AlN HCl Heat of solution in 2−576.6−137.83CaCON HCl Heat of solution in 2−35.0−8.4The heat of formation of 3CaO·Al Turriziani and Schippa [2 pressures below the partial pressure of CO2 in air [Hydrated calcium aluminate monocarbonate, 3CaO·AlAs part of a continuing investigation of the thermochemical properties of substances occurring in hydraulic cements and their reaction products, the heat of formation of hydrated calcium aluminate monocarbonate has been determined.2O3·CaCO3·11H2O is an idealized formula in which the number of moles of H2O has been rounded off. This compound, as with many similar compounds encountered in portland cement chemistry, does not always have a definite water content. The actual water content in the samples prepared varied from 10.58 to 10.88. The average figure of 10.68H2O was used in the calculations.It should be noted that the formula 3CaO·AlMeasurements were made of the heat evolved at 25 °C in the reaction2O (2.00N HCl at 25 °C). The heats of formation of the reactants were taken from Circular 500 [The heat of solution of each of the reactants and of the product of this reaction was measured in HCl·26.61Hular 500  of the NAll calculations in this paper are based on the 1957 atomic weight table, and on the thermochemical calorie, defined as exactly 4.184 absolute joules.2O3·CaCO3·11H2O, were prepared and studied. Their properties and details of their preparation are listed in 2O3 and 1.2 g CaO per liter, is metastable and becomes cloudy soon after its maximum concentration is reached. It was filtered quickly and the filtrate used immediately to prepare the monocarbonate compound. A sample of the filtrate was taken at the same time to determine the concentration of CaO and Al2O3. Eight to nine liters of saturated Ca(OH)2 solution were added to 2 liters of the calcium aluminate solution, the mixture stirred a few seconds, after which 3.50 to 3.75 g Na2CO3 in 250 ml of water was added slowly with continued stirring. After the mixture had been allowed to stand about 2 months, the precipitate was filtered off and dried over saturated MgCl2 solution (33% relative humidity) until the ignition loss was constant (requiring about 2 months).Three samples, two of which closely approached the stoichiometric composition 3CaO·Al2 during every step of the process including preparation of the reagents, mixing, filtration, and drying. These precautions are described in another publication [Precautions were taken to exclude atmospheric COlication .α radiation. The patterns, one of which has been published [X-ray diffraction patterns of the samples were obtained by the powder method on a Geiger-counter diffractometer with copper Kublished , agree cublished .The oxide composition of the samples was obtained by chemical analysis. The designation and calculation of the amounts of compounds present as impurities was based on the chemical analysis and optical microscopic examination.2O3·6H2O, was prepared by autoclaving 3CaO·Al2O3 at 150 °C for several days, according to the method of Thorvaldson, Brown, and Peaker [2O3·5.859H2O (plus 0.007 mole CaCO3 per mole as impurity). The anhydrous aluminate had been prepared by repeated heating of lime and alumina with intervening moistening of the material to aid in dispersing the CaO, as described by the same authors.Tricalcium aluminate hydrate, 3CaO·Al3 to adhere to the glass funnel through which samples were normally introduced into the calorimeter.Low-alkali reagent calcium carbonate was used. The reagent was moistened with 3 percent of its weight of distilled water, pelleted at 4,000 psi, and dried at 110 °C to constant weight. This treatment served to agglomerate the fine particles and decrease (but not completely eliminate) the tendency of the CaCO3 was largely calcite. Since the difference between the heats of formation of calcite and aragonite [3 would have no effect on the results of the heat-of-solution determinations.The CaCOragonite  is small4H2O (2.00N HCl at 25 °C). A precision calorimeter, described by Newman [3. For this compound an improved calorimeter was used, which is shown in 3. Thermal equilibrium in the calorimeter is reached much sooner than in the older design, which featured a heavy cover and large temperature lags. The sample is introduced through opening C, either by means of a funnel or in a glass bulb as indicated by the dashed lines in the drawing. The glass bulb was used with CaCO3, as described in section 2.5. The entire calorimeter assembly, except for the bulb or funnel and for the outer supporting ring, is made of platinum. The calorimeter otherwise is similar to the earlier design. Opening D is fitted with an electric heater for calibration purposes and for setting the initial temperature range, and opening E contains the resistance thermometer. The calorimeter is placed inside an air jacket and the jacket-calorimeter assembly is submerged in a constant-temperature water bath controlled to ±0.005 °C.The heats of solution of the compounds were determined in HCl·26.61y Newman , was use3 were used with 740 g of acid (corresponding to 0.18 g in 600 g acid), and 0.7 g of hydrated tricalcium aluminate was added to the acid before the addition of CaCO3. These quantities are required by the stoichiometry of Since it was inconvenient to prepare the calcium aluminate monocarbonate in large quantities, 1–g samples of the compound were used with the normal quantity of acid (600 g) for the older calorimeter. With the newer calorimeter, 0.2–g samples of CaCO2O3·6H2O, the sample size was 0.2 to 0.4 g. These determinations had been made previously to calculate the heat of formation of calcium aluminate trisulfate  [2O instead of HCl·20H2O, thermo chemical calories  instead of 20° calories , and a final temperature of 25 °C instead of 20°, the result is 373.1 cal/g. The difference, 2.7 cal/g, or 1.0 kcal/mole, is in the wrong direction to be attributed to differences in sample size. There is thus no measurable dilution effect due to variations in sample size. The value obtained with the smaller samples was therefore used.In the determination of the heat of solution of 3CaO·Aluminate) . In accoN HCl [The heat effect of adding the 4.68 moles of water appearing in 3 presents problems because of the evolution of CO2 when the sample is dissolved in acid. Two reactions take place:2 from solution is endothermic; an uncertain amount of heat is lost depending on how much CO2 escapes. (b) The CO2 gas carries with it some of the sensible heat produced by 2 gas is lost as well. All these effects produce low results for the heat of solution and an inaccurate final rating period for the calculation of thermal leakage.The determination of the heat of solution of CaCO3 both in HCl saturated with CO2 and in HCl not saturated with CO2. A smaller heat of solution is obtained in the first solvent because all the CO2 escapes. The second solvent retains some of the CO2 and gives a larger value. Working with 1.5-g samples in 640 g of CO2-saturated 2N HCl, Wells and Taylor [H = 59.2 cal/g CaO or 33.2 cal/g CaCO3  at 25 °C. Working with 10-g samples in 800 g of CO2-saturated N HCl at the same temperature, Bäckström obtained 3.26 kcal/mole [Various investigators have attacked the first difficulty by determining the heat of solution of CaCOd Taylor  obtained2, principally because the sample and acid weights were different, resulting in different ratios of CO2 dissolved in the acid to CO2 escaping from the calorimeter in each case. Wells and Taylor, using 2N HCl at 25 °C and the same relative weights as for CO2-saturated HCl, obtained a heat of solution of –ΔH = 105.0 cal/g CaO or 58.9 cal/g CaCO3 . Bäckström, using N HCl at 25 °C and the same relative weights he had used before, obtained 4.50 kcal/mole.The agreement between these two investigators was not as good when the HCl was not saturated with CON HCl not saturated with CO2. It was therefore necessary to determine the heat of solution of the CaCO3 in the same acid and to adopt a sample size that would result in the same concentration of CO2 as for the aluminate carbonate. A CaCO3 sample of 0.2 g does not release enough CO2 to saturate 740 g of 2N HCl at 25 °C.  Theref3 into a calorimeter through a funnel because it adheres to the glass and forms lumps at the bottom of the funnel stem, even after the pressure treatment described in section 2.3. It was therefore introduced in a glass bulb . It then falls as CO2 is evolved, approaching a constant value. A first-order decay lawθ represents the corrected temperature rise at any time ft, θ the final temperature rise. From this relationship it is possible to calculate θ0, the corrected temperature rise at zero time when no CO2 has escaped. This rise, multiplied by the heat capacity of the calorimeter, is taken as the true heat of solution of CaCO3 in 2N HCl in accordance with The corrected rises obtained in this manner for a typical calorimeter run are plotted against time (open circles) in 2 was reduced by covering the sample of CaCO3 in the bulb with a few milliliters of distilled water. Any bubbles rising in the bulb stem give up their sensible heat to the water. At the same time, the water pushes the sample directly into the calorimeter acid, causing most of the bubbles to escape through the acid surrounding the bulb. Thermal equilibrium is thereby facilitated. Blank runs were made to determine the energy of dilution of the acid with the small quantity of water. The tendency of sensible heat to escape with the COThe heats of solution obtained on the preparations of calcium aluminate monocarbonate were corrected for the small quantities of impurities present. The heats of solution of the preparations and the corrected heats of solution of the pure monocarbonates themselves are summarized in 2O3·5.859H2O and CaCO3, are shown in The heats of solution of the reactants, 3CaO·AlThe heat capacities obtained in the calorimeter calibrations are listed in Additional data from the heat-of-solution determinations are shown in The calculation of the composition of a sample and of the heat of solution of the pure aluminate carbonate present in a sample is shown in the H=226.36±0.562O.The spread for the heat of solution of the three preparations is 4.51 cal/g before correction for impurities. After correction, the spread is 1.73 cal/g. The average corrected heat of solution of the three samples is –Δ3 was higher  than the values of Wells and Taylor  [2. The accuracy of the higher figure obtained in this work may be checked in two different ways.The heat of solution eventually determined for the CaCOgher –ΔH=3.6 cal/g9 cal/g) , obtaine3 which is to be checked:H9=—37.9 kcal/mole.From the heats of formation of the three compounds in 2 (g) as a reactant instead, and from the heat of vaporization of CO2 from solution, both values obtained from Bäckström’s work [2 (g) → CaCO3 (c)CaO (c) +COH10 = −42.6Δ2 (aq) → CO2 (g)   COH11 = + 4.9ΔH9 = −37.7ΔFrom the heat of the same reaction, but with COm’s work , 12:CaO2 from NBS Circular 500 [H11 is calculated to be +4.64. If this figure is added to Bäckström’s value for ΔH10, ΔH9 becomes −38.0.If the heat-of-formation figures for COular 500  are used3 in 2N HCl, based on Wells and Taylor’s value for CaO of −46.7 kcal/mole. [3 obtained in this work, ΔH9=−38.3 kcal/mole.From the heats of solution of CaO and CaCOal/mole.  and the The heat of the reaction3 in 2N HCl not saturated with CO2 from the heat of solution in CO2-saturated acid and from the heat of vaporization of CO2 from solution (ΔH11). To Wells and Taylor’s value of −3.32 [N HCl not CO2-saturated. This compares with −8.4 kcal/mole determined in this work.A second check on the value reported here may be made by calculating the heat of solution of CaCOof −3.32  or Bäcksof −3.32  for the of −3.32  to obtai2 has dissolved at the start. Some of the CO2 may, however, be evolved as a gas almost immediately without preliminary solution. The result obtained by this technique may therefore still be somewhat low. An error in the opposite direction results from the fact that the solution of the CaCO3 takes place in finite time so that the extrapolation should really be made to some point between zero time and 1 min.There may still be a residual error in this determination. The corrected temperature rise extrapolated analytically to zero time represents the correct enthalpy change for 2O3·CaCO3·nH2O was not materially different when determined by ordinary methods or by the technique used for CaCO3. This is attributed to the fact that the aluminate monocarbonate is slower to react with acid, and the CO2 is released more slowly. Chemical equilibrium is presumably obtained more easily, with complete solution of the CO2. The difference in activity is further evidence that CO2 is bound differently in the monocarbonate than in CaCO3, as concluded from differential thermal analysis and infrared patterns by Carlson and Berman [The heat of solution of 3CaO·AlThe heat of the reaction—ΔH = 20.23 kcal/mole 3CaO·Al2O3·CaCO3·10.68H2O.The heat of reaction  is the sH=−1.36 kcal/mole 3CaO·Al2O3 [H=20.23 −1.36 = 18.87 kcal, for the equationThis correction is found by adding to the heat of reaction for 2O3·6H2O= −13293= −288.452O= −319.72H3CaO·Al2O3·CaCO3·10.68H2O from these reactantsΔ= −18.872O3·CaCO3·10.68H2O= −1956 kcal/moleThe heat of formation of the calcium aluminate monocarbonate is the sum of the heat effect of The calculated uncertainty of this result, based on a standard deviation for the heat of solution of 0.38 kcal/mole for the aluminate carbonate, 0.12 for the tricalcium aluminate hydrate, and 0.05 for the calcium carbonate, is 0.40 kcal/mole. This value does not include the uncertainty in the heat of formation of the reactants, which is certainly of the order of 1 kcal/mole for the hydrated tricalcium aluminate, nor the uncertainties due to chemical analysis.2O3·CaCO3·10.68H2O in 2.00N HCl at 25 °C. Calculations were made of the heat of formation of this compound from 3CaO·Al2O3·6H2O, CaCO3, and H2O; and from the elements. A new technique was employed to determine the heat of solution of CaCO3, in which most of the sensible heat lost by escaping CO2 gas was retained by improved thermal equilibrium between the solution and the gas. By a modified type of calculation, the heat of solution determined included the latent heat of the evolved gas as well. The heat of solution thus calculated is greater than values obtained for CaCO3 by Wells and Taylor and by Bäckström in determinations in which only part of the CO2 went into solution. It is consistent with other thermochemical data in the literature.Determinations were made of the heat of solution of 3CaO·Al


Compound 1 features a hat‐shaped structure with the parent wheel‐shaped {Mo150} being capped by a {Mo30} unit on one side. Similarly, 2 exhibits an elliptical lanthanide‐doped wheel {Mo120Ce6} that is sealed by a {Mo10} unit on one side. Moreover, the observation of the parent uncapped {Mo150} and {Mo120Ce6} clusters as minor products during the synthesis of 1 and 2 strongly suggests that the molecular growth process can be initialized from {Mo150} and {Mo120Ce6} in solution, respectively.Understanding the process of the self‐assembly of gigantic polyoxometalates and their subsequent molecular growth, by the addition of capping moieties onto the oxo‐frameworks, is critical for the development of the designed assembly of complex high‐nuclearity cluster species, yet such processes remain far from being understood. Herein we describe the molecular growth from {Mo Herein, we report two novel MB clusters {Mo180} (1) and {Mo130Ce6} (2) constructed via the molecular growth from {Mo150} and {Mo120Ce6}, respectively. Compounds 1 and 2 exhibit unprecedented half‐closed structural motifs arising from the asymmetric growth of cap‐like {Mo30} and {Mo10} units present on just one side of {Mo150} and {Mo120Ce6}, respectively . Compounds 1–2 can be formulated as [Eqs. Compound  as Eqs. :(1)Na4, composed of 17 {Mo8} units, 15 {Mo2} units, and 14 {Mo1} units .The single‐crystal X‐ray structural analysis reveals that 1 a resembles that of half of a {Mo368} cluster.6} units as shown in Figure 368} cluster are shown tiled in three layers (A–C) with an 8‐8‐4 arrangement. The 8 pentagons in layer B stack between 8 pentagons in layer A and each pentagon in layer C further pack between 4 pairs of pentagons in layer B. Therefore, the general rule is that pentagons in three layers are connected in a ratio of 2:2:1  in Figure 2} units on {Mo150}, indicating that both the brim and cap of 1 a have adjusted their structures to dissatisfy the non‐defect‐based {Mo154} and the 3.5 pentagons to promote the formation of 1 a. Similar to that of {Mo368}, symmetry breaking occurs between layer B and C in 1 a, and the local symmetry of {Mo150} dramatically reduces from ideal Dd7 to Cs in the cap. Accordingly, the positively curved interior surfaces of {Mo150} transform to negative curvatures in the cap. There are two domains of negative curvatures formed between {Mo2} units and {Mo6} pentagons in layer B and C  as the candidate.III, PrIII, and EuIII ions to replace {Mo2} units on the parent {Mo154}. The resulting LMB generally exhibits smaller dodecameric or decameric frameworks in comparison with tetradecameric {Mo154}. Since the LnIII ions are significantly smaller than {Mo2} unit, the substitution of the {Mo2} units with LnIII ions causes the contraction of the wheel, and consequently increases the curvature on the inner surface of the ring. Therefore, the incorporation of lanthanide ions not only adjusts the available number of {Mo2} units but also tunes the curvature and size of the MB. With this in mind, we envision that LMBs may provide a great chance to cap “species” differently from the iso‐POMs such as {Mo150} and {Mo176}.The successful synthesis of compound 2. Single‐crystal X‐ray structure analysis reveals that 2 crystalizes in space group Pnma and features an elliptical ring structure of {Mo120Ce6} capped by a {Mo10} unit on one side . From the crystal structure, the ideal composition of cap fragment should be {Mo11}, however, the central pentagonal Mo atoms could be disordered equally on two positions with the total occupancy of one, so the actual formula of the cap is {Mo10} .III ions on 2 a adopt a 4‐connected mode and stay localised at the two ends of the wheel creating an oval‐shaped {Mo120Ce6}, thus providing a suitable pocket on one side to support the growth of the elliptical {Mo10} moiety. It is therefore reasonable to speculate that if the connecting modes and the positions of LnIII ions on the wheels could be manipulated in a controlled manner, then LMB with a variety of curvatures, shapes and sizes could be produced to not only enrich the structural library of LMB, but also provide more chances to use them as “functional building blocks”.It appears that the Ce1 and 2 can only be achieved under quite specific conditions. More precisely, 1 must be synthesized in very dilute solution; increasing the concentration of the starting materials or altering the reducing agents will result in the formation of a series of l‐ornithine functionalized MBs, such as {Mo150}, {Mo148}, and {Mo146}, owing to the faster crystallization rate.150} together with 1. Based on this, we postulate the self‐assembly of 1 occurs as follows: Firstly, the basic building blocks of {Mo8}, {Mo2}, and {Mo1} aggregate into l‐ornithine functionalized {Mo150}. Owing to the dilute conditions, {Mo150} does not precipitate from solution, but instead reacts with the “active species” in solution to initialize molecular growth. In this situation, three {Mo8} units of the {Mo30} gradually build‐up on the {Mo150}, and the molecular growth is finally terminated by the two edge‐sharing {Mo2} units , although sometimes minor amounts of {Mo120Ce6}‐a could also be identified by microscope owing to its distinct crystal morphology and unit‐cell checking as well. We propose that oxalic acid serves as a transient anion template, or provides supramolecular interactions, such as hydrogen bonding, to promote the encapsulation of {Mo10} during the assembly process. In view of this we therefore speculate a potential pathway for the self‐assembly of 2. In the absence of oxalic acid, {Mo120Ce6}‐a is produced as the major product, but with the aid of oxalic acid, {Mo120Ce6}, the parent MB framework of 2 a, is formed in solution and then serves as parent scaffold to trap the {Mo10} cap on one side  should be addressed to the authors.SupplementaryClick here for additional data file.


R2* and R2 measurements showed a significant dependence on the bifurcation and rotation angles in several scenarios using different vessel diameters, orientations, diffusion rates, and susceptibility values. The angular dependence of R2* and R2 using the CFM could potentially be exploited as a tool to differentiate between normal and tumor vessels. The CFM can also serve as the elementary building block to simulate a capillary network reflecting realistic topological features.Brain vasculature is conventionally represented as straight cylinders when simulating blood oxygenation level dependent (BOLD) contrast effects in functional magnetic resonance imaging (fMRI). In reality, the vasculature is more complicated with branching and coiling especially in tumors. Diffusion and susceptibility changes can also introduce variations in the relaxation mechanisms within tumors. This study introduces a simple cylinder fork model (CFM) and investigates the effects of vessel topology, diffusion, and susceptibility on the transverse relaxation rates R2* and R2. Simulations using Monte Carlo methods were performed to quantify R2* and R2 by manipulating the CFM at different orientations, bifurcation angles, and rotation angles. Other parameters of the CFM were chosen based on physiologically relevant values: vessel diameters (~2‒10 µm), diffusion rates (1 × 10 Despite its widespread use as a tool in neuroscience, the physiological changes that underlie the BOLD effect have not been completely elucidated. In particular, the specific characteristics that affect the transverse relaxation rate changes (∆R2* and ∆R2), due to variation in blood volume and oxygenation in the brain vasculature occurring in active brain tissue, have not been fully characterized. Several studies have probed into this relationship by studying the effect of perturber geometry by assuming spheres or infinite cylinders oriented randomly to explore susceptibility contrast mechanisms8. Other studies have attempted to explore the use of microvasculature models to depict a more realistic in vivo scenario of the brain vasculature and its influence of vascular morphology effect on BOLD contrast11. In reality, however, the cortical vasculature is more complicated with meshwork geometry that contains a multitude of microscopic patterns and scales19.Nearly three decades ago, Ogawa et al. to include sinuous branches, glomerular loops, brush bristle and star-like appearances of vessel networks, and right angle penetration of vessels12. Motti et al. also described the stirrup, T-, and Y-morphology of vessels13. In tumorous tissue, the blood vessel network topology changes drastically, not only with increased vessel size and length, but also with increased tortuosity, sinusoidal branching, loops, bifurcations and trifurcations19. All these topographical traits can be generalized as possessing angular characteristics which become more distinct in tumorous tissue compared to normal tissue. Hence, exploring the idea that the shape and angular orientation of vessels can have an influence on the transverse relaxation rates (R2* and R2) could provide some useful insight.The morphology and spatial arrangement of blood vessel networks in the brain exhibit certain design patterns that result in efficient delivery of oxygen and nutrients to the neural tissue. Some of these patterns have been described by Duvernoy 4. Thus, R2* and R2 will depend upon the diffusion coefficient of spins that are within the vicinity of the induced field inhomogeneities due to the presence of vessels. The extent of effect will also depend upon the correlation time (τD) compared to the Larmor frequency variation (∆ω) at the vessel perturber surface3. For a vessel, these quantities are defined as:R is the radius of the vessel, D is the water diffusion coefficient (or diffusion rate), γ is the gyromagnetic ratio, and Beq(R) is the equatorial magnetic field evaluated on the vessel surface. The values of the τD and ∆ω will determine whether the diffusion rate falls in the motional averaged regime (MAR) or the static dephasing regime (SDR).The diffusion of protons due to random Brownian motion through magnetic field inhomogeneities is another factor that contributes to phase coherence changes and affects the transverse relaxation rates∆ω∙τD < 1), both R2* and R2 are equal and given by21:f is the vessel volume fraction. For a large vessel size, relaxation is independent of the vessel radius and reaches an upper limit. In the SDR (satisfying ∆ω∙τD > 1), R2* is given by22:For a small vessel radius or equivalently fast diffusion rates, in the MAR (satisfying τCP) is reduced for large vessels, the RF pulses become more effective and partial refocusing occurs causing R2 to decrease compared to R2*. In this regime, known as the echo-limited regime , where τCP = TE/2, R2 is given by24:x = ∆ω∙τCP. Since the state of water diffusion differs between normal and tumorous tissue25, studying the effect of diffusion, in combination with the vessel angular characteristics mentioned earlier, on R2* and R2 could further help characterize BOLD contrast effects.As the radiofrequency (RF) pulse spacing  bifMonte Carlo methods were used to quantify R2* and R2 for cylindrical fork perturbers with different bifurcation and rotation angles, vessel sizes, susceptibility values, orientations relative to magnetic field, and diffusion rates of protons. Scripts in MATLAB  were used to generate all aspects of this simulation study.The vasculature was modeled using a cylinder fork model (CFM) composed of a straight trunk (prior to bifurcation) of at least half cube length with the bifurcating segments emanating in the other half of the cube. The cube was designed with 64 µm sides and incorporated cylinder fork segments Fig.  between 26 which allowed faster computation of the field variations. Signal generation was initiated by placing a proton at a random location outside the vessels to simulate extravascular signal. Each proton took 50 steps between a pair of 90° and 180° pulses distributed using a Gaussian distribution with zero mean and standard deviation D is the diffusion rate and each time step Δt = 0.1 ms. This one-dimensional step was repeated along the orthogonal directions to generate the displacement vector. The random walk of 40,000 protons was maintained outside the vessels assuming impermeability of the CFM. The phase accumulated by each proton during every step was calculated as γ·ΔB·Δt where γ is the gyromagnetic ratio and ΔB is the calculated magnetic field from the susceptibility map.Magnetic field perturbations were calculated using a forward 3D Fourier transform of the susceptibility distribution of the CFM28: (i) true vessel diameters of 2.8, 5.6 and 8.6 µm; (ii) diffusion rates (D) of 1 × 10−9, 1 × 10−10 and 1 × 10−11 m2/s; (iii) susceptibility values (χ) of 3 × 10−8, 1 × 10−7, and 4 × 10−7 in cgs units (or multiplied by 4π for SI units).The simulations were performed with the following parameters based on previously reported studiesR2* and R2 were calculated by linear least-square fitting of log signal intensity versus volume fraction. The R-squared values of all fittings were very high (~0.9). Relaxation rates per volume fraction unit were used to remove the dependence on vessel lengths and emphasize the role of the bifurcation and rotation angles (β and ϕ) on R2* and R2 while comparing the different simulation parameters.p < 0.05 was considered significant. All p-values corresponding to the ANOVA test for each graph are indicated in the respective graph inlets in all figures. Detailed statistical information are presented in the Supplemental Information for each figure.Two-way analysis of variance (ANOVA) test was performed to check for any significant effect of β and ϕ on the relaxation rates for the various simulation parameters. A value of The datasets generated and analyzed during this study are available from the corresponding author on reasonable request.Figure Figure Data in Fig. Similar ANOVA analysis was performed with regard to the effect of vessel size on R2 relationship with the rotation angle, which reveals that: (i) a significant effect of vessel size on R2 was observed for all orientations and bifurcation angles, and; (ii) a significant effect of rotation angle on R2 was observed in most bifurcation angles for Orientations 2 and 3; orientation 1 did not show significant effects for most bifurcation angles.−7). At this higher susceptibility value, in addition to increased R2* values for all cases, R2* vs. ϕ plots overlapped very closely for the two lower diffusion rates at the two larger vessel sizes at bifurcation angles of 0° and 45°. At a bifurcation angle of 90°, R2* vs. ϕ plots for all three diffusion rates overlapped each other for the two larger vessel sizes. ANOVA results showed: (i) significant effect of diffusion rate on R2* for all vessel sizes and bifurcation angles at both susceptibility values, and; (ii) significant effect of rotation angle on R2* at both susceptibility values for most of the two larger vessel sizes; the smallest vessel size did not show significance for most of the cases.Figure −7). In both Orientations 1 and 3, increasing the susceptibility value caused an increase in R2* values for all cases. At the higher susceptibility value, R2* vs. β plots overlapped very closely for the two lower diffusion rates and two larger vessel sizes at all rotation angles in both orientations. In Orientation 3 at the rotation angle of 90°, R2* vs. β plots for all three diffusion rates overlapped each other for the two larger vessel sizes. ANOVA results showed: (i) significant effect of diffusion rate on R2* for all vessel sizes and bifurcation angles at both susceptibility values in both orientations except for the higher susceptibility value in Orientation 3 with the two larger vessel sizes at the rotation angle of 90°, and; (ii) significant effect of bifurcation angle on R2* at both susceptibility values for most of the two larger vessel sizes in both orientations; for the smallest vessel size, however, more significances were observed in Orientation 3 compared to Orientation 1 for most rotation angles at both susceptibility values.Figure −11 m2/s to 1 × 10−10 m2/s caused an increase in R2 values, but then an increase from 1 × 10−10 m2/s to 1 × 10−9 m2/s caused a decrease in R2 values. An increase in susceptibility values caused an increase in R2 values for all cases. For both R2 vs. ϕ and R2 vs. β plots and for all susceptibility values in both Orientations 1 and 3, an increase in vessel size caused a general increase in R2 values for the highest diffusion rate. The two lower diffusion rates showed a decrease in R2 values with increasing vessel size. Increasing the vessel size also increased the R2 gap between the highest diffusion rate and the lower two diffusion rates. R2 gap between the two lower diffusion rates decreased with increasing vessel size. ANOVA results showed: (i) significant effect of diffusion rate on R2 for all vessel sizes and susceptibility values for both bifurcation and rotation angles in both orientations; (ii) no significant effect of the rotation angle on R2 in Orientation 1; however, in Orientation 3, significance was mainly observed at the smallest vessel size, and; (iii) no significant effect of the bifurcation angle on R2 in Orientation 1 except at the smallest vessel size and lowest susceptibility value; however, in Orientation 3, significance was mainly observed at the smallest vessel size.Figure τD) in Orientations 1, 2, and 3 and at susceptibility values of 3 × 10−8, 1 × 10−7, and 4 × 10−7 cgs units. The plotted R2* and R2 values are the mean values taken across all the bifurcation and rotation angles  to show the overall effect of τD on R2* and R2. Orientations 2 and 3 show nearly identical profiles. When τD is short (<0.01 s), little difference is seen between R2* and R2. As τD is increased, R2 reaches a peak and then begins to decrease, while R2* keeps increasing and approaches a static limit. With increasing susceptibility: (i) R2 peak value increases and shifts slightly to the left in all three orientations, and; (ii) R2* values increase with more fluctuation at higher τD values near the static limit, more so in Orientation 1 compared to Orientations 2 and 3. These fluctuations are due to the averaging of R2* over different bifurcation and rotation angles.Figure 29. The CFM structure presented in this study captures the basic angular characteristics of vascular architecture using the vessel orientation relative to the magnetic field, and the vessel bifurcation and rotation angles. To understand the effect of each of these angular variations on R2* and R2, vessel forks were simulated in different orientations and modelled with respect to realistic cortical vasculature measurements.When simulating BOLD contrast effects in fMRI, most researchers make the general assumption that the brain vasculature is represented as 2D or 3D infinite long cylinders to simulate BOLD signal changes6 astrocytoma cells that were implanted in rats19. This diameter range covered the lumen diameters that were observed in normal, peritumoral, and tumor microvessels both in the brain and muscle tissue19. These values also agree with the lower-end vessel diameters observed in different brain tumor grades in patients30. For computation efficiency and fitting the vessel size with the appropriate volume fraction in the voxel space, 128 × 128 × 128 matrix was used. The susceptibility values were chosen between 0 and 0.6 × 10−6 cgs units to cover a wide range of biologically relevant contrast agent concentrations4. The largest diffusion rate of 1 × 10−9 m2/s was chosen based on the typical value reported for the cerebral cortex28. The other two lower diffusion rates span the range of expected diffusion rates in tissue3.Vessel diameters were chosen in the capillary range from ~2‒10 µm based on morphometric data from normal tissue and CBifurcation and rotation angles were chosen between 0° and 90° to simplify the model, since larger angles would yield predictable results based on the 0°‒90° range. The three orientations studied in this model covered all three dimensions of the vessel topography. Depending on the chosen geometry, Orientations 2 and 3 showed almost a mirror effect for R2* and R2 with the bifurcation and rotation angles Figs ‒S5; hencτD) within the MAR up to τD = 0.01 s , at a rotation angle ϕ = 0°, the vessel exhibits a T-shape when the bifurcation angle β = 90°. This scenario presents the maximum disturbance in the local field caused by the interaction of B0 and vessel geometry, hence yielding larger R2* and R2 values :The R2* and R2 patterns observed in all the scenarios presented in this study are an outcome of the resultant field inhomogeneities caused due to the interaction of the respective vessel topology with the Bues Figs ‒S5. We cR is the vessel radius, r is the distance of proton from the cylinder axis, and φ is the rotation angle ϕ from our nomenclature. For a bifurcation angle β = 90° (at θ = φ = 0°), a contribution from the fork segments to the orientation angle θ will be made through the sin2θ term while the trunk segment will be oriented at θ = 0°, and hence making no contribution. The total contribution will, therefore, be non-zero unlike the case for a straight segment .where Δχ is the susceptibility difference between the intra- and extra-cylindrical space, 2a, a∙(1 + 2√2), and 3a, respectively, where 2a is the voxel size. Another normalization process takes place with respect to the diameter of the vessel which must also be taken into account for our results. When normalization is removed (as is routinely presented) from the data of Fig. Care must be exercised when interpreting Fig. The larger two vessel sizes showed more significant effects of bifurcation and rotation angles on R2* compared to the smallest vessel size in both the susceptibility values in Orientation 1 Figs  and S7. 2. This indicates that the transition from the MAR into the ELR , which occurs at ∆ω∙τD ≈ 1, is satisfied for ∆ω = 51 rad/s, a value consistent with susceptibility values. The agreement of the transverse relaxation rates behavior with the correlation time using the CFM compared to previous studies4, further validates the use of this model to develop realistic cortical vasculature patterns.Unlike R2*, in Orientation 1, nearly all the vessel sizes did not show a significant effect of the bifurcation and rotation angles on R2 for all susceptibility cases Fig. . In Orie30), the differences would be more vivid given that we were able to see differences just within the capillary range. The simulations also demonstrated that at certain bifurcation and rotation angles, the larger vessel sizes showed clear separation between the higher and lower diffusion rates at high vessel susceptibilities. This can potentially reflect a physiological scenario where with larger diameters (tumorous tissue) and increased susceptibility (presence of contrast agent) can delineate the relaxation rates in relation to the bifurcation and rotation angles as being either in the MAR  or in the SDR/ELR . Since the apparent diffusion coefficient (ADC) is known to be lower, which corresponds to lower diffusion rates, in low-grade tumors25, the quantifications presented herein using the CFM could be further explored and exploited to potentially differentiate normal vessels from tumor vessels based on a combination of diffusion rates and bifurcation and rotation angles. Some discussion in regards to model limitations and improvements have been included in the Supplementary Information.In summary, R2* and R2 measurements indicated a clear dependence on the bifurcation and rotation angles in scenarios using different orientations, diffusion rates, susceptibility values and vessel diameters in the capillary range. Presumably, at higher vessel diameters  level arising from arbitrary microvascular morphologies such as those typically exhibited in angiogenesis. The motivation for such approach was that differences in ∆R2* contrast observed in brain tumor angiogenesis 33 can be due to different vascular morphology of brain tumors compared to healthy brain tissue 34. Abnormal vascular phenotypes have been implicated in neuropathologies ranging from Alzheimer’s35 disease to brain tumors37 while cerebral vasculature is central to understanding the hemodynamics of novel therapies in the brain38.In order to evaluate tumor angiogenesis using MRI techniques, it is absolutely necessary to better understand the role of many morphological, biophysical, and experimental factors. To achieve this goal, computational modeling of susceptibility-induced MR contrast has been employed for a long timeOur work presents a novel vascular model that attempts to more accurately explain and predict MR signal changes and its critical dependence on 3D vessel architecture. The CFM model uniquely: 1) separates the effects of various vessel-specific morphological parameters  through the introduction of the fork concept, and; 2) offers a building block for MR signal source that can be combined with other similar or different blocks to take into account the complex morphology exhibited by a brain tumor. The design of the model uniquely offers a number of adjustable parameters that can be independently optimized to simulate the susceptibility-induced MR contrast. This feature makes the CFM uniquely suited to model complex vessel architecture such as exhibited by tumors. Furthermore, this approach will allow the investigation of an arbitrary and often complex vascular architecture and not be restricted by limitations seen in traditional models such as parallel, infinitely long cylindrical vessels, or non-overlapping magnetic fields.Supplementary Information


This bio‐inspired architecture allows a highly active Co2+ electronic structure for an efficient oxygen evolution reaction (OER) at the atomic scale, ultrahigh surface area (371 m2 g−1) for interfacial electrochemical reaction at the nanoscale, and enhanced transport of charge and electrolyte over CoOx nanotube building blocks at the microscale. Consequently, this CoOx nanosheet/nanotube heterostructure demonstrates a record‐high OER performance based on cobalt compounds reported so far, with an onset potential of ≈1.46 V versus reversible hydrogen electrode (RHE), a current density of 51.2 mA cm−2 at 1.65 V versus RHE, and a Tafel slope of 75 mV dec−1. Using the CoOx nanosheet/nanotube catalyst and a Pt‐mesh, a full water splitting cell with a 1.5‐V battery is also demonstrated.Plant leaves represent a unique 2D/1D heterostructure for enhanced surface reaction and efficient mass transport. Inspired by plant leaves, a 2D/1D CoO Third, at the microscale, the assembly of individual building blocks into an interlacing, conducting and highly porous architecture can benefit efficient mass transport of electrolytes, high electric conductivity and structural stability.Previous research efforts in design and optimization of Co‐based OER catalysts can be generally categorized into three scale levels. First, at the atomic scale, the tuning of cobalt oxidation state,x 2D/1D heterostructure, composed of ultrathin CoOx nanosheets that are further assembled into a nanotube structure, which enables simultaneous structural optimization over different length scales for superior OER activity , providing an excellent electronic structure for the OER reaction.x nanosheets over the Cu2O nanowire template surface precludes the homogeneous nucleation of CoOx in solution as well as the accumulation of nanosheet thickness, thus resulting in an ultrathin nanosheet assembly with high density and large surface area. Moreover, these few‐layered CoOx nanosheets are assembled into nanotubes of tens of micrometer long, which are further interlaced into a large 3D, porous framework for efficient charge and ion transport. This CoOx nanosheet/nanotube heterostructure has an ultrahigh surface area of 371 m2 g−1 ever obtained for CoOx, and, demonstrates the best OER performance based on cobalt compounds reported so far. A low onset potential of ≈1.46 V versus reversible hydrogen electrode (RHE) has been obtained, substantially better than most of the previously reported OER catalysts, with a record‐high current density of 51.2 mA cm−2 at 1.65 V versus RHE. Furthermore, using a single 1.5‐V AAA battery as input, a full water splitting cell that couples the CoOx OER catalyst and a Pt‐mesh hydrogen evolution reaction (HER) catalyst has been demonstrated.As a classical example of nature evolution, the plant leaves represent a unique heterostructure beneficial for their biofunctions. Typically, each leaf is grown into a thin 2D morphology with optimized surface area and reduced overpacking between their neighbors, which favors for enhanced light absorption and surface reactions. Meanwhile, the existence of 1D, hollow tubular structures under the leaf arrays allows for efficient transport of water and nutrition towards the leaves for their reactions and biofunctions. Inspired by the plant leaf structure, herein, we demonstrate the realization of a CoOty Figure1a. Fir2x nanosheet/nanotube structure is synthesized by a two‐step solution approach, in which Cu2O nanowire templates are first obtained via a solution‐based 1D crystal growth method, followed by in situ etching of Cu2O nanowire core and regrowth of Co(OH)2 nanosheets over the nanowire template surface  that both prevents Cu(OH)2 precipitation and reduce the free Cu2+ concentration, thus lowering the supersaturation and promoting the dislocation‐driven growth of nanowires. Afterwards, Co(OH)2 nanotubes are formed by using a coordination etching and precipitation method,2O nanowires are served as the sacrificial template, and Na2S2O3 and CoCl2 are used as coordination etching agent and cobalt precursor, respectively. The chemical reaction is described as2S2O3 is added into Cu2O suspension, S2O32− starts to coordinate and etch Cu2O by forming a soluble complex [Cu2(S2O3)x]x2–2, and OH− ions are released from this etching process 2 is precipitated in a nanosheet morphology 2 nanosheets are continuously grown over the surface of the original Cu2O nanowires, with a constrained nanosheet thicknesses and a high density. These ultrathin Co(OH)2 nanosheets are further self‐assembled into a nanotube morphology, in which the original Cu2O nanowire templates are etched and formed the hollow interior. These hierarchical CoOx nanosheet/nanotube structures are further entangled to form a highly porous, conducting framework. After dehydration in vacuum (samples designated as CoOx‐vacuum) or in air (samples designated as CoOx‐air), the hierarchical CoOx nanosheet/nanotube structures are obtained.The hierarchical CoO2O nanowires are uniform, with an average diameter of 100–200 nm and a length of 20–50 μm , confirming that the as‐synthesized nanowires are high‐quality Cu2O . The uniform nanowire morphology and high quality of Cu2O make it an excellent template to build hierarchical micronanostructures.The as‐synthesized Cuμm Figure2a. Tra2O nanowire templates in a mixed solution of Na2S2O3 and CoCl2, the color of the solution dispersion changes from yellow to green, and the product can be deposited into any arbitrary substrate to form a continuous film with a uniform surface morphology . Scanning electron microscopy (SEM) images show that the exterior diameter of the obtained CoOx nanotubes is about 200 nm , similar to that of the nanowire templates. No nanowire morphology is observed in the obtained nanotubes  spectroscopy pattern shows some Cu impurities are remaining in the CoOx nanotubes, with a Co to Cu atomic ratio of about 8:1 . High‐resolution TEM images show that these nanotubes are constructed by thin nanosheets, with thickness less than 1 nm , which is a synchrotron technique for studying the electronic and chemical structures of materials.x‐air and CoOx‐vacuum samples were recorded in the total electron yield (TEY) mode .x‐vacuum sample, which is ascribed to the crystal‐field redistribution by the Co2+ octahedral structure (designated as Co2+ Oh).2+ Oh structure can play an important role in the enhanced OER activity of the electrocatalyst.x‐air and CoOx‐vacuum samples, which is associated to the Co 3d‐O 2p interaction.x‐air and CoOx‐vacuum samples have some Co3+ species. Two shoulder peaks are observed at 530.7 and 534 eV .The electronic structure of CoOde Figure3a, whih  and CoO‐Td (zincblende) structures for water oxidation reaction, and both the total densities of states (DOS) and the projected densities of states (PDOS) of the Oh and Td structures are plotted , suggesting that electrons in Oh structures are easier to be excited into the conduction band than that of Td structures. In addition, the partial charge densities of the Oh structure is calculated, which exhibits a more delocalized profile than that of the Td structure  of the Co2+ Oh structure is 0.46 eV smaller than that of Co2+ Td structure, further indicating the higher capability of losing electrons from the Oh structure than the Td structure. As the molecular mechanisms of water oxidation at Co sites involve reaction cycles among Co2+, Co3+, and Co4+ oxidation sites,2+ Oh structure with a smaller energy barrier can significantly facilitate the electron transfer process for water oxidation reaction. Our XAS experimental results have shown the existence of Co2+ Oh, which are different from most of the previous reported OER catalysts with Co2+ Td structures,x‐vacuum catalyst demonstrate even better OER activity than the CoOx‐air sample, which can be attributed to the higher Co2+ Oh concentration in the CoOx‐vacuum catalyst (as shown by the XAS data). These Co2+ Oh sites will transform into Co2+ Td when the CoOx‐vacuum samples are heated in oxygen, further supporting our hypothesis of optimizing the Co2+ Oh concentration.Density functional theory (DFT) calculations are applied to compare the electronic structures of CoO‐Od Figure c. The vae Figure d, so thex samples (both dried in air and in vacuum) are first tested by cyclic voltammograms (CVs) between 0.75 and 1.55 V (vs RHE)  is negatively shifted for 40 mV compared to that of the CoOx‐air sample (blue curve). When the potential reaches above 1.45 V, a sharp increase of oxidation current occurs for both samples, due to the water splitting.The electrochemical behaviors of CoOE) Figure4a. Thex nanosheet/nanotube structures (both dried in air and in vacuum) are then evaluated by linear sweep voltammetry (LSV) between 1.10 and 1.70 V versus RHE  is much smaller than CoOx, suggesting a negligible electrochemical interference resulted from the remaining Cu2O impurity. The IrOx nanoparticle has the lowest onset potential of ≈1.41 V versus RHE (brown curve), while its current density at higher potentials is still much lower than both of the CoOx samples. The CoOx‐vacuum nanosheet/nanotube catalyst exhibits the best OER performance among all these samples. The current density at 1.65 V versus RHE reaches 51.2 mA cm−2, which is 1.6 times higher than that of the CoOx‐air catalyst (31.5 mA cm−2) and 4.5 times higher than that of IrOx nanoparticles (11.5 mA cm−2). The onset potentials of the CoOx‐vacuum and CoOx‐air catalysts are 1.46 and 1.48 V, respectively, which are substantial lower than almost all of the previously reported CoOx OER catalystsThe OER activity of the hierarchical CoOE Figure b. For cox nanosheet/nanotube structures are displayed, in comparison with the IrOx nanoparticles , suggesting more efficient charge transfer on these nanotubes. Furthermore, the electrocatalytic stability of the CoOx‐vacuum and the CoOx‐air catalysts are evaluated by chronoamperometry measurement . The comparison of the LSV curves recorded in 0.1 m KOH and in 1 m KOH shows that the onset potentials are nearly identical, while the current density observed in 0.1 m KOH is ≈70% of that observed in 1 m KOH. This is probably attributed to a lower OH− concentration in the electrolyte, which is consistent with previous reports.To compare with other reported OER catalysts, the OER activity of the CoOx‐vacuum catalyst is further investigated to demonstrate the efficient mass transport within such a hierarchical structure. The LSV curves of the CoOx‐vacuum catalyst, with different mass loading of 0.068, 0.136 and 0.204 mg cm−2, are displayed .Moreover, the mass loading effect of the CoOx nanosheet/nanotube framework can be attributed to its unique atomic and nanoscale structures, as well as the 3D assembled architecture. First, at the atomic scale, the Co2+ ions located at octahedral sites (Co2+ Oh) exhibit better OER activity than Co2+ at tetrahedral sites (Co2+ Td), as demonstrated by the DFT calculations. Second, the CoOx nanosheet/nanotube heterostructure offers a unique building block for simultaneous optimization of high surface area and efficient 1D charge transport behavior. Distinct from the conventional, direct synthesis of CoOx from Co2+ and OH− precursors, the use of Cu2O nanowire sacrificial templates allows for controlled, slow release of OH− anions close to the surface of Cu2O, thus resulting in the replacement/growth of Co(OH)2 on the template surface and avoiding the fast homogeneous nucleation of Co(OH)2 in the solution. Importantly, the thin diameter of Cu2O nanowire templates is only sufficient to sustain the replacement reaction under a limited level in different positions of the nanowire surface, resulting in the ultrathin thickness (≈1 nm) of the grown Co(OH)2 nanosheets. Consequently, an ultrahigh surface area of 371 m2 g−1 is obtained, substantially larger than previously reported CoOx nanoparticles (111 m2 g−1),2 g−1),2 g−1)2 g−1).2O nanowire template leads to the formation of the nanotube structure that are further interlaced into a 3D framework, which not only favors the 1D electron transport over the nanosheet/nanotube heterostructure surface, but also facilitates the electrolyte diffusion inside the hollow nanotubes as well as between adjacent nanotubes.The much enhanced OER catalytic activity of the hierarchical CoOarticles 1 m2 g−1,x nanosheet/nanotube catalyst can produce ≈1 mA cm−2 current density at 1.50 V versus RHE, which remains 65% after 8000 s stability test  water and ethanol repeatedly for three times, and dried in a 45 °C oven to obtain the Cu2O nanowires. The hierarchical CoOx nanosheet/nanotube structures were synthesized by using a coordinating etching and precipitating method. Typically, 200 mg of Cu2O nanowires and 68 mg of CoCl2·6H2O were dispersed in 200 mL of water and 200 mL of ethanol to form a suspension. Then 160 mL of Na2S2O3 (1 m) was added into the suspension dropwise. The color of the Cu2O solution is obscure orange. After excessive amount of Na2S2O3 was added into the solution, the color of the solution turned from light orange to transparent green at the initial 5 min, and we kept stirring for 30 min to convert most of Cu2O into Co(OH)2. The product was collected by centrifugation, washed by DI water and ethanol repeatedly for three times and dried at 80 °C in vacuum or air to get the hierarchical CoOx nanosheet/nanotube structures. The IrOx nanoparticle catalysts were synthesized as follows. A 300 mL of sodium hexachloroiridate(IV) hexahydrate solution (1 × 10−3m) was mixed with 3 mL of potassium hydroxide (0.1 m) and heated in 90 °C for 6 h. The products were collected by centrifugation, washed with DI water and ethanol repeatedly for three times, and then dried in the air.DFT Calculations: All calculations reported in this work were performed by using the Vienna ab initio simulation package (VASP)Ueff (U −J) values of 6 eV were applied for Co 3d states. Both rocksalt CoO and zincblende CoO are used 2 × 2 × 2 super cells, with 8 × 8 × 8 mesh of k‐points. All atoms were fully relaxed with the energy convergence tolerance of 10−6 eV atom−1 and the final force on each atom was <0.01 eV Å−1. The work function is defined as the energy of the vacuum level with respect to Fermi level of the system, which is calculated from VASP. Both rocksalt CoO(111) and zincblende CoO(111) surfaces were modeled using symmetric slabs with vacuum widths of 15 Å for work function calculations.OER Catalytic Measurement: The electrochemical measurements were performed with a CHI 660D electrochemistry workstation . The electrolyte was 1 m KOH, which was deaerated with high‐purity Ar prior to and throughout all the measurements. The working electrode was a thin layer of Nafion‐impregnated catalyst cast on a glassy carbon rotating disk electrode . The catalyst solution was prepared by mixing 1 mL of C2H5OH, 2 mg of catalyst and 120 μL of Nafion, and then pipetted onto a freshly polished GC–RDE to achieve the desired catalyst loading . A Pt gauze and a saturated calomel electrode electrode were used as the counter and reference electrodes, respectively. The GC–RDE was controlled at 1000 rpm by a speed regulator  to exclude the interference of generated oxygen bubbles at electrode surface. The scan rate for CV and LSV was kept at 5 mV s−1. All the electrochemical measurements were iR‐compensated and carried out at 25 ± 1 °C. The electrochemical tests in Figures S5 and S6, Supporting Information were tested in 0.1 m KOH presaturated by O2. The internal resistance Rs was determined from Nyquist plot and all the electrochemical measurements were iR‐compensated at ≈80% of the Rs and carried out at 25 ± 1 °C.As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.SupplementaryClick here for additional data file.


The results indicate the possibility of realizing topological quantum phase transition in SrSn2As2 single crystal and obtaining different exotic quantum states.Topological materials with exotic quantum properties are promising candidates for quantum spin electronics. Different classes of topological materials, including Weyl semimetal, topological superconductor, topological insulator and Axion insulator, etc., can be connected to each other via quantum phase transition. For example, it is believed that a trivial band insulator can be twisted into topological phase by increasing spin-orbital coupling or changing the parameters of crystal lattice. With the results of LDA calculation and measurement by angle-resolved photoemission spectroscopy (ARPES), we demonstrate in this work that the electronic structure of SrSn This field has enjoyed rapid development in recent years thanks to the well agreement and effective mutual promotion between experimental observation and theoretical calculation. In recent two years, the experimental discovery of three-dimensional (3D) Dirac semimetal, Weyl semimetal and hourglass fermion follows soon after the theoretical predications12. Among the families of topological materials, topological insulator is a novel state of matter. It has an energy gap in the bulk like ordinary insulators but gapless Dirac fermionic states on the boundaries. This intriguing feature makes it a potential candidate for spintronic devices due to the special spin properties of the surface state13. It is known that trivial band insulator can be tuned into topological insulator through a topological quantum phase transition by modulating the spin-orbital coupling or lattice parameters14. Band inversion is the key process in the transition, during which the energy gap between the valence bands and conduction bands becomes smaller and smaller until closed as shown in Fig. 18. Thus the investigation of materials near the topological critical point will not only help us understand the nature of topological quantum phase transition but also provide new ideas for finding Dirac semimetal materials.Topological materials attract much attention because of their exotic characters including non-trivial Dirac surface state, magnetic monopole Fermi arc and so on15, ZrTe522, Ca2PtO423, Au2Pb25, Bi4X427, Bi2Te2Se28 and so on. Most of them have been studied intensively. SrSn2As2 has been predicted to be a candidate for new 3D Dirac semimetal because it is naturally near the critical point. This prediction is based on the general design principles for predicting 3D Dirac semimetals from charge-balanced semiconductors with symmetry considerations28. The question now is whether the real SrSn2As2 single crystal is normal insulator, Dirac semimetal or topological insulator, and what factors can drive the phase transition. With these questions we systematically investigate the electronic states of SrSn2As2 single crystal. The ARPES results show the feature of band inversion around Γ point, which is evidence of strong topological insulator state. The experimental results are successfully reproduced by our LDA calculation. By modifying the exchange potential, the ordinary insulator state is also realized in the calculation. Our study shows that the single crystal SrSn2As2 is probably a new topological insulator near the topological critical point.Till now several materials have been predicted to be near the critical point, such as CdTe/GdTe quantum well with specific thickness2As2 crystals can be regarded as a superlattice consisting of alternating stacking of SrAs2 and Sn layers characterized by space group R-3m h (166) as shown in Fig. 2As2 recorded on the in-situ cleaved sample. On the enlarged spectrum shown in the inset of Fig. 4d and 5d peaks, meaning that the Sn atoms are on the cleaved surface.SrSn2As2, we performed ab-inito calculations within the framework of density function theory (DFT) using the VASP30. Spin-orbit coupling is taken into account self-consistently. We display the band structure along high symmetry line around Γ in Fig. pz orbit and As pz orbit. The band inversion results in a nontrivial topological Z2 index of ν0 = 1 according to the Z2 classification31. This result indicates that the single crystal of SrSn2As2 is a strong topological insulator with band inversion similar to the Bi2Se3 family32. But when we redo the calculation with the modified Becke-Johnson exchange potential (mBJ)33, the topological state is different as shown in Fig. 2As2 is near the topological critical point.In order to understand the topological band structure of SrSn2As2, we performed systematic ARPES measurement on the 001 surface. Figure hv = 22 eV and T = 25 K. We can see the 3-fold Fermi surfaces around Γ and dumb-bell like Fermi surfaces at BZ boundary. The band structure along high symmetry line labeled as “cut” with red line in Fig. EF, the inner one marked as α is an electron band, the outer ones marked as β and γ are hole-like bands. α and β band contribute to two small Fermi surface pockets around BZ center marked as α BFS (bulk Fermi surface) and β BFS in Fig. −1 and 0.06 Å−1, and the Fermi vector of β band also changes between 0.35 Å−1 and 0.30 Å−1 periodically. The γ band remains the same within our resolution. According to the variation period of α and β bands along photon energy, we can fit the hv versus kz curve very well in Fig. Vo = 12.2 eV and lattice parameter c′ = 26.728/2 Å. It should be noted that the c’ used here is half of the lattice constant c because there are two equivalent layers in one unit-cell along z direction as shown in Fig. kz = 0 and kz = π/c respectively. The band structure contains only one ‘M′ shape valance band near Fermi level around Γ. On kz = 0 plane, the bottom of the valance band at Γ point (marked as B1) is around 0.1 eV below EF. while on kz = π/c plane, the bottom (marked as B2) shifts down to around 1.2 eV below EF (the other bottom above marked as B3 results from hybridization of conduction band and the neighbor band below it). In order to reproduce the experimental data, in the kz = 0 plane we shift the LDA calculated valence bands up about 0.3 eV, and the calculated conductance bands down about 0.19 eV, the agreement between them is much better than before in Fig. kz = π plane, all the bands below EF are valence bands, when they are shifted up about 0.45 eV, the consistence becomes very well. The different shifting directions of valence bands and conductance bands indicate that the main cause of the discrepancy between the calculation and the experiment is the underestimation of the inversion size between the valence and conduction bands in calculations, which is a common shortcoming of LDA or GGA calculations in semiconductors. Considering the underestimation of the band gap by GGA, we have checked the band inversion carefully. The band topology of the occupied states is invariant even if the band inversion is underestimated. Further calculation information shows that α band is an inverted band contributed by Sn pz orbit and β band is contributed by As pz orbit.To study the electronic structure and topological character of SrSnkz dependent data, now let’s focus on the surface states along K-Γ-K. In order to identify the surface states, we display the calculated surface states of SrSn2As2 (001) surface in Fig. After discussing the EF comes from α band and β band. From Fig. 35. For bands consisting of different orbital components, the curves of photoelectron intensity versus photon energy usually have different shapes. We can see in Fig. 2As2. In our calculation, if the crossing happens, the gap will be open considering SOC, resulting in nontrivial Berry phase around the inverted Fermi surface pockets. Thus, we can draw the conclusion that the α band is evidence of band inversion texture.The greatest contribution to the texture of band inversion near 2As2 and observed the texture of band inversion and topological surface states. Our experiment results are reproduced by the calculation. The calculation suggests that single crystal SrSn2As2 is near the topological critical point between trivial insulator and a strong topological insulator. In the calculation using modified Becke-Johnson exchange potential the trivial insulator state appears. The direct evidence of band inversion from ARPES data indicates the probable strong topological insulator state of this crystal. Our studies provide the evidence for a new topological material near topological critical point, which is a potential material for further studies on topological quantum phase transition in the future.In summary, we investigated the electronic structure of SrSn2As2 were grown by the solid-state reactions. Stoichiometric amounts of Sr , Sn  and As  were sealed in an sealed quartz ampoule backfilled with about 0.2 atm high pure argon and placed in a furnace. Typical temperature gradient from 850 °C to 650 °C was applied. After seven days, bulk single crystals were obtained. The elemental compositions were checked by Oxford X-max energy dispersive X-ray spectroscopy (EDX) analysis in a Hitachi S-4800 scanning electron microscope. The atom percentage ratio between Sr, Sn and As is 1:2:2 with the error bar less than 1%, which is within the systematic error. We also conducted Hall conductivity measurement to check the carrier concentration, and the result indicates that the sample is not considerably hole-doped.Single crystals of SrSnin situ and measured in a temperature range between 20 and 50 K in a vacuum better than 5 × 10−11 Torr.ARPES measurements were performed at the “Dreamline” beamline of the Shanghai Synchrotron Radiation Facility (SSRF) with a Scienta D80 analyzer. The energy and angular resolutions were set to 15–30 meV and 0.2°, respectively. The samples for ARPES measurements were cleaved ab initio simulation package (VASP)30 is employed for first-principles calculations. The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof type36 is used for the exchange-correlation potential. Spin-orbit coupling (SOC) is taken into account self-consistently. The k-point sampling grids for different structures have been tested to be dense enough. The atomic structure and the lattice constants a = b = 4.204 Å, and c = 26.728 Å are adapted in our calculations37.The Vienna


We theoretically characterize the performance of the pairwise correlations (PCs) from multiple quantum correlated beams based on the cascaded four-wave mixing (FWM) processes. The presence of the PCs with quantum corre- lation in these systems can be verified by calculating the degree of intensity difference squeezing for any pair of all the output fields. The quantum correlation characteristics of all the PCs under different cascaded schemes are also discussed in detail and the repulsion effect between PCs in these cascaded FWM processes is theoretically predicted. Our results open the way for the classification and application of quantum states generated from the cascaded FWM processes. Quantum correlation shared between multiple quantum correlated beams is important for fundamental quantum mechanicsGk . The theoretical predictions can give a rough estimation of the obtained experimental results.Four-wave mixing (FWM) process in a hot rubidium (Rb) vapor910111213141516171819202122231 of Firstly, we give a simple description of the single FWM scheme. FWM is a nonlinear process in which two pump photons can convert to one signal photon and one idler photon, or vice versa. In the cellG1 is the power gain of the FWM process. i = 1, 2’)) for the beams where DS), i. e., the ratio of the variance of the correlated beams to the variance at the standard quantum limit (SQL)26where kth  scheme , the asymmetrical cascaded scheme (2) and the symmetrical cascaded scheme (3), the ith  beam and the jth  beam in the scheme. Var (A) = 〈A2〉 − 〈A〉2 denotes the variance of A. G1 is always larger than 1, the PC with quantum correlation of the two beams can be easily obtained in the experiment. However, the DSs of the single beams here This corresponds to a linear increase in the noise on both the signal and idler beams as gain is increased. Thus the beams 1) as the seed for the second FWM process (cell2) in Fig. 1(a)Secondly, compared to the above mentioned single FWM scheme, here we construct the asymmetrical cascaded scheme in G1 and G2 are the power gains for the cell1 and cell2 respectively. The optical intensities ) for the individual beams where DS of the triple beams  when we set G1 = 1 and G2 = 1 respectively, corresponding to the cases of G1 = 1, the PC between the thermal states G2 = 1, the PC between the thermal states G2 on the boundary , the stronger the quantum correlation between beams G1 > 3), the stronger the quantum correlation between beams PC between G2 = 2 − 1/G1, meaning that the quantum fluctuation of intensity difference of two thermal states can be equal to the one of two coherent states with equal powers. Except that, G2 = 2 − 1/G1) is shown as the red line denoted as  in 1, G2 > 1. In this sense, there isn’t any quantum correlation between beams G1 and G2 since PC between G2 − 1) and 2G1 − 1 for G1 and G2 are set to equal to 1 respectively, corresponding to the cases of G1 = 1, the PC between the thermal states G2 = 1, the PC between the thermal states G1 < G2) is shown in magenta denoted as  in G1 < G2 gives G1 less than G2. This is not difficult to figure out if one looks at the functional form of G1 < G2), the existence of quantum correlation between beams 1 will provide the correlation between them and cell2 will destroy their quantum correlation by adding extra vacuum noise, thus cell1 and cell2 can be viewed as the correlation mechanism provider and decorrelation mechanism provider respectively, thus the larger G1 and smaller G2 are preferred for the PC between beams 1 will generate a thermal state 2 will make them quantum correlated through the FWM process. In this case, cell1 and cell2 can be viewed as the decorrelation mechanism provider and correlation mechanism provider respectively, thus the smaller G1 and larger G2 are preferred for the PC between beams The simplified results, i. e., 1/(22 when G1 = 2.9 (cell1 gain in the experiment) in G2 which is consistent with G2 > 1.33 which is consistent with the boundary of 2 = 1.66 which is consistent with G2 = 2 − 1/G1 in G2 > 2.9 which is consistent with In order to give a summary of the theoretical predictions of A, B, C and D are the measured DSs between E is the corresponding normalized SQLs for traces A ~ D (See the methods). The experimental results show 10Log as the seed for the second FWM process (cell2) and the idler beam as the seed for the third FWM process (cell3) in Finally, we construct the following symmetrical cascaded scheme as shown in G1, G2 are the power gains of cell1, cell2 (cell3) respectively. Here we assume that the two FWM processes in the cell2 and cell3 have the same power gains for simplicity. The optical intensities ) for the individual beams where DS of the quadruple beams (2G2 − 1) > 1, i. e., G1 > 1 or G2 > 1. Next let us analyze all the possible PCs in this scheme and the triple correlations can also be obtained from the expressions of the PCs in the asymmetrical cascaded FWM scheme, for example, the DS for the triple beams  in PC between G1, G2 > 1 as shown in the contour plot of G1, G2 > 1. The absence of PC between G2 is always more than or equal to 1. This can be easily found if one looks at the functional form of 1, G2 > 1. As discussed above, for this symmetric cascaded scheme, there are three possible PCs with quantum correlation, namely 1 will provide the correlation between them while cell2 and cell3 will destroy their quantum correlation by adding extra vacuum noise, thus cell1, cell2 (cell3) can be viewed as the correlation mechanism provider and decorrelation mechanism provider respectively, thus the larger G1 and smaller G2 are preferred for the PC between beams 1 will generate two thermal states which will destroy their quantum correlation by adding extra vacuum noise into the system while the cell3 (cell2) will make them quantum correlated through the FWM processes. In this case, cell1, cell3 (cell2) can be viewed as the decorrelation mechanism provider and correlation mechanism provider respectively, thus the smaller G1 and larger G2 are preferred for the PC between beams The PC with quantum correlation between beams A) B) C) D) E) F) 2 when G1 = 2.94 (cell1 gain in the experiment) in A) can be enhanced with the increasing of G2 which is consistent with B) will be larger than 1 as long as G2 > 1.67 which is consistent with the boundary (G2 = 2 − 1/G1) in D) will be smaller than 1 as long as G2 > 2.9 which is consistent with C), E) and F) are also consistent with Here we also give a summary of the theoretical predictions of A, B, C, D and E are the measured DSs between A ~ E (See the methods). The experimental results show 10Log Quantum enhancement. The DS of the quadruple beams in the symmetrical cascaded scheme  has quanIn summary, we have theoretically characterized the performance of the PCs from the multiple quantum correlated beams and analyzed the dependence of all the PCs on the system intensity gains based on two different cascaded FWM processes. For both cases, we have theoretically predicted the so called repulsion effect of quantum correlation between the PCs of the cascaded systems. Our results presented here can be applied to the classification and application of the quantum states generated from the cascaded FWM processes.i = 1, 2, 3, and 4) from the cascaded FWM processes are sent to the photodetectors and their noise power values Ni  are measured. One beam is subtracted from the other beam in the pairwise beams and thus the intensity-difference squeezing shared by the pairwise beams is measured. In addition, the SQL of the measured pairwise beams can be measured in this way by using a beam in a coherent state with a power equal to the total power of the measured pairwise beams impinging on the photodetectors. We then split it with a 50/50 beamsplitter, direct the obtained beams into two photodetectors. and record the noise power of the differential photocurrent. This balanced detection system makes it possible to cancel all the sources of classical noise and obtain a measure of the SQL.The output beams How to cite this article: Wang, H. et al. Characterization of Pairwise Correlations from Multiple Quantum Correlated Beams Generated from Cascaded Four-Wave Mixing Processes. Sci. Rep.7, 40410; doi: 10.1038/srep40410 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.