Atmospheric dust loadings play a crucial role in the global climate system. Southern South America is a key dust source, however, dust deposition rates remain poorly quantified since the last glacial termination (~17 kyr ago), an important timeframe to anticipate future climate changes. Here we use isotope and element geochemistry in a peat archive from Tierra del Fuego, to reconstruct atmospheric dust fluxes and associated environmental and westerly wind changes for the past 16.2 kyr. Dust depositions were elevated during the Antarctic Cold Reversal (ACR) and second half of the Younger Dryas (YD) stadial, originating from the glacial Beagle Channel valley. This increase was most probably associated with a strengthening of the westerlies during both periods as dust source areas were already available before the onset of the dust peaks and remained present throughout. Congruent with glacier advances across Patagonia, this dust record indicates an overall strengthening of the wind belt during the ACR. On the other hand, we argue that the YD dust peak is linked to strong and poleward shifted westerlies. The close interplay between dust fluxes and climatic changes demonstrates that atmospheric circulation was essential in generating and sustaining present-day interglacial conditions. The timing and nature of paleoclimatic changes in southern South America since the last glacial are still a matter of debate. A major issue is the reconstruction of changes in the intensity and latitudinal position of the southern westerly wind (SWW) belt as it exerts an important control on the Southern Hemisphere’s and global climate2318To investigate the dustiness of Tierra del Fuego during the late-glacial - Holocene, we sampled an ombrotrophic mire  located on the south coast of Isla Grande de Tierra del Fuego along the Beagle Channel . OmbrotrThe total dust accumulation rate shown in Apart from mineral dust, tephra layers are omnipresent in paleorecords from PatagoniaTo further trace the origin of the atmospheric dust, we determined the neodymium isotopic composition of a selection of peat samples across the intervals with increased ADD . EpsilonGlacier fluctuations have been suggested as an important dust generating process in South Patagonia14Although the Beagle Channel became progressively ice-free west of Harberton since ~17.8 cal kyr BP4After a brief episode of low dust fallout, a second dust peak was recorded from ~12.1 to 11.6 cal kyr BP, coinciding with the second half of the Younger Dryas  and southwest (50–55 °S) Patagonia, indicating an overall strengthening of the westerlies223118O values measured in the Botuverá cave in southern Brazil  towards the equator, pushing the westerlies southwards towards Antarctical 27 °S, 36, generl 27 °S, , explainl 27 °S, 34. Accor−2 yr−1, in Tierra del Fuego during the ACR and YD, the majority did not reach Antarctica. Furthermore, besides the spike at 12.9 cal kyr BP in the Antarctic dust record , which is most valuable for understanding and modelling dust dynamics.−1 and mean annual temperature is 6 °C. The bog surface is dominated by Sphagnum magellanicum with a sparse cover of Marsippospermum grandiflorum and Empetrum rubrum. The present-day landscape of this region was mainly shaped by outlet glaciers of the Upper Pleistocene Darwin Cordillera ice cap: the Beagle Channel and Lake Fagnano glaciers besides alpine glaciers from the Fuegian Andes. Upon deglaciation, peatlands developed in small lakes and ponds in local drumlin fields, such as the Harberton area15The Harberton bog  is one of the numerous mires located on the south coast of Isla Grande de Tierra del Fuego, along the Beagle Channel. Mean annual rainfall is around 600 mm yrPeat cores were recovered from Harberton bog in 2012 by means of a stainless steel Wardenaar corer2 and humic/fulvic acid), dried, combusted and graphitised14C ages were calculated14C dates of the peat samples and a tephra layer of the Hudson volcano  1 ml of H202 was added to react for 6 h at room temperature; (3) 2 ml of 16 M HNO3 was added and left at 90 °C for 2 days to finalize the digestion. After each step, samples were evaporated to dryness. Finally, the samples were dissolved in 2 ml of 35% HNO3, transferred into 15 ml polypropylene tubes , and further diluted with Milli-Q water up to 14 ml. Major elements  concentrations were determined by inductively coupled plasma optical emission spectroscopy . Trace elements  concentrations were determined by quadrupole inductively coupled plasma mass spectrometry  at the Observatoire Midi Pyrenees . The ICP-MS was calibrated using a synthetic multi-element standard, which was run every 8 samples, while an In-Re solution was used as an internal standard. The analytical performance was assessed by analyzing 3 international certified reference materials: SRM1947 (peach leaves), SRM1515 (apple leaves) and GBW-07063 (bush branches and leaves). The results are reported in A total of 205 bulk peat samples (at a ~5 cm resolution) were processed for element geochemistry. First, each sample was freeze-dried and powdered using an agate mortar. Subsequently, 100 mg of each sample was acid digested in Teflon beakers. The following digestion procedure was applied to each sample3 and HF. The accuracy and reproducibility of the digestion procedure regarding Nd concentrations, determined by repeat analyses of the international certified standard GBW-07063 (n = 3), was better than 10%. Each sample was subsampled in order to make sure that a mass of 250 ng Nd was present in the sample that was loaded onto the columns.Fifteen peat samples and 1 till sample were selected for neodymium (Nd) isotope analyses. To reduce complications associated with organic material during the separation process, 400 mg of bulk peat sample (100 mg for the till sample) was dry ashed in a furnace at 550 °C for 5 hours. Subsequently the samples were acid digested using a mixture of concentrated HNO−1.Nd was separated from the matrix using a two-column ion-exchange technique. First, the rare earth elements (REE) were extracted from the sample using a cation exchange column (Bio-Rad poly-prep) packed with ~2 ml of Dowex AG50W-X8 resin (200–400 mesh). Then, Nd was isolated from the other REE by reversed phase chromatographyObservatoire Midi Pyrénées . 143Nd/144Nd ratios were determined as the average of 150 ratios normalized to 146Nd/144Nd = 0.7219 to correct for instrumental-induced mass fractionation. The international standard La Jolla  Finnigan MAT 261 (static mode) at −2 yr−1) are calculated for each sample based on the REE concentrations measured in the peat samples using the following equations:Dust AR (g mi the of the concentrations (μg g−1) of the REE in sample i and ∑[REE]UCC the sum of the REE concentrations in the upper continental crust (148 μg/g−1) and density (g cm−3) are given in with ∑[REE] 148 μg/g. Peat ARi−XAvg)/Xstd with, Xi the concentration of element i, Xavg the average concentration of all samples for element i and Xstd is the respective standard deviation. Both transformations rescale the data and hence open the closed system of concentrations5354Principal component analysis (PCA) was performed using SPSSStatistics 20 software using a varimax rotation to reduce dimensionality within the dataset. Based on the co-variance between the variables , a number of components are extracted explaining the total variance within the dataset. In practice this means that the components will contain elements that show similar variation, in this case similar concentration-depth profiles. Before analysis all data were first log transformed (log10) and subsequently converted to z-scores to account for the compositional nature of the data. The latter are calculated as follows z = .


The demonstrated ability to recordfull polarization information over a broad wavelength range and to quantify theintrinsic plasmon polarimetry characteristics via Mueller matrixinverse analysis should lead to a novel route towards quantitativeunderstanding, analysis/interpretation of a number of intricate plasmonic effectsand may also prove useful towards development of polarization-controlled novelsensing schemes.Information on the polarization properties of scattered light from plasmonic systemsare of paramount importance due to fundamental interest and potential applications.However, such studies are severely compromised due to the experimental difficultiesin recording full polarization response of plasmonic nanostructures. Here, we reporton a novel Mueller matrix spectroscopic system capable of acquiring completepolarization information from single isolated plasmonic nanoparticle/nanostructure.The outstanding issues pertaining to reliable measurements of full4 × 4 spectroscopic scattering Mueller matricesfrom single nanoparticle/nanostructures are overcome by integrating an efficientMueller matrix measurement scheme and a robust eigenvalue calibration method with adark-field microscopic spectroscopy arrangement. Feasibility of  Initial exploration of this ‘comprehensiveplasmon polarimetry platform’ on gold nanorods demonstrates thepromise of the Mueller matrix-derived plasmon polarimetry parameters as novelexperimental metrics for studying a number of interesting plasmonic effects. Anillustrative example is presented on how such information can be utilized to probe,manipulate, and controllably tune the interference of the neighboring resonant modes and the resulting spectralline shape of the plasmonic system via polarization control.Despite the wealth of interesting effects that can be probed using spectral scatteringMueller matrices of plasmonic nanostructures/nanoparticles, its experimental realizationremains to be an outstanding challenge. The challenges include: (1) the scatteringsignal from plasmonic nanostructures is rather weak and is often swamped by the largebackground unscattered light, (2) recording of full Mueller matrix over a broadwavelength range simultaneously in combination with the corresponding spatial maps by itself is a formidable task, (3) this is confoundedfurther by the fact polarimetric measurements on plasmonic nanostructures oftennecessitates use of high numerical aperture (NA) microscopic setting, (4) challenges inanalysis and quantification of the measured polarization signals or images andcomplexities in understanding and interpreting the plasmon polarimetry results. In orderto address these outstanding challenges, in this paper, we present a novel experimentalsystem that integrates a Mueller matrix measurement scheme with dark-field microscope torecord full 4 × 4 spectroscopic scattering Muellermatrices from a single isolated nanoparticle/nanostructure. The dark field microscopicarrangement facilitates detection of weak scattering signal from the plasmonicnanostructures and has been previously explored for scattering spectroscopic studies onnanoparticles/nanostructures3132comprehensive plasmon polarimetry platform, comprising of (a) dark-fieldMueller matrix spectroscopic microscopy experimental system and (b) Mueller matrixinverse analysis models(shown in M(λ) from single isolated plasmonicnanoparticle/nanostructure and other samples. The results of these studies arepresented here. Specifically, we (i) briefly describe the Mueller matrixconstruction scheme and the inverse analysis approach, (ii) presentthe results of system calibration and (iii) describe the results of spectralMueller matrix measurements and inverse analysis on single isolated plasmonicgold (Au) nanorod samples. The potential utility of such quantitative Mueller matrixpolarimetry on plasmonic system is also illustrated and discussed in thiscontext.A shown in , wasexpϑ = 35°,70°, 105° and 140°) with respect to the axisof P1. These four sets of Stokes vectors(4 × 1 vector) are grouped as column vectorsto form the 4 × 4 generator matrixW.Similarly, the four elliptical analyzer basis states are obtained by changingthe fast axis of QWP2 to the corresponding four angles . The analyzer states areanalogously written as a 4 × 4 analyzermatrix A. The sixteen sequential intensity measurements (at anywavelength) are grouped in a 4 × 4 matrixMi, which is related to A, W matricesand the sample Mueller matrix M as,The 4 × 4 spectral Mueller matrices wereconstructed by combining sixteen spectrally resolved intensity measurements(spectra) for four different combinations of the optimized ellipticalpolarization state generator (using the PSG unit) and analyzer (using the PSAunit) basis states  were decided based onthisM can be determined fromexperimental Mi, by using theoretical forms ofWand A matrices (obtained by using the standard Mueller matricesof the polarizer and the quarter waveplates). However, this is confounded by– (1) the complex nature of the polarization transformation due tothe high NA imaging geometry leading to significant changes in theW(λ) and A(λ) matrices; (2) theW(λ) and A(λ) matrices may varysignificantly with wavelength due to the non-ideal behavior of the polarizingoptics over the wavelength range. We tackled these issues using a robusteigenvalue calibration method, which takes care of the spectral polarizationresponses of the polarization state generator, analyzer units, the focusing andthe detection systems (imaging geometry) by determining the exact experimentalforms of the W(λ) and A(λ) matricesW(λ) andA(λ) matrices are determined by performing measurements on aset of ideal calibrating samples (pure diattenuators (polarizers) and retarders(waveplates)). The specifics of the various steps of this method can be foundelsewhere (see Supplementary information)34The optimal generator and the analyzer basis states were obtained viaoptimization of the ratio of the smallest to the largest singular values of theindividual square matrices inverse analysis on the experimental Mueller matrices usingPolar decomposition method, which is a reliable and widely used approach forsolving the inverse problem in polarimetryIn general, plasmonic samples may exhibit all the polarimetry effects, namely,diattenuation, retardance and depolarization. These may contribute in a complexinterrelated way to the Mueller matrix elements, masking potentially interestinginformation and hindering their interpretation. This issue was addressed byperforming MΔ, MR andMD describe the depolarizing effects, theretardance effect (both linear and circular), and the diattenuation effect(linear and circular) of the medium, respectively (shown in MDR here. Note that the scattering matrix (definedin a given scattering plane) for regular shaped scatterer is generallynon-depolarizing and represents a preferentially oriented diattenuating retarderMueller matrix for a chosen scattering plane MΔ in MDR). The intrinsic sample polarizationinformation is therefore contained in the resulting (non-depolarizing)diattenuating retarder matrix MDR, which is subjectedto further analysis (results presented subsequently).Here, shown in . The latd) and linear retardance(δ) are quantified as36Once decomposed, the constituent polarimetry parameters depolarization(Δ), linear diattenuation  nanorod samples, as described subsequently.Note that we have not considered circular diattenuation and circularbirefringence effects due to the W(λ) andA(λ) matrices, as demonstrated in W(λ) and A(λ) matrices inδ) and linear diattenuation (d) ofthe quarter waveplate and the linear polarizer (respectively) were determinedfrom their experimental Mueller matrices (using d ~ 0.98 (overλ = 500–700 nm) arein good agreement with the expected ideal values (d = 1 for linearpolarizer). Based on these and calibration studies on various other referencesamples, the measurement strategy appears valid for performing accurate sampleMueller matrix measurements despite numerous complexities associated with thehigh NA microscopic imaging geometry that too over a broad wavelength range. Theability to record full 4 × 4 spectroscopicMueller matrices in the dark-field configuration and to quantify theintrinsic sample polarimetry characteristics bodes well forquantitative polarimetric investigations on plasmonicnanoparticles/nanostructures, which is our primary goal.The results of the eigenvalue calibration on reference samples (linear polarizeras pure diattenuator and achromatic quarter waveplate as pure retarder) aresummarized in es using  and are M(λ) exhibit several interesting spectral trends (M(λ)with essentially all sixteen non-zero matrix elements underscore the fact thateven a single isolated plasmonic Au nanorod exhibit all the elementarypolarimetry characteristics , thushighlighting the need for Mueller matrix inverse analysis. Theconsiderably low magnitudes of the diagonal elements imply overall strong depolarizing natureof the scattered light. Non-zero intensities of the elements in the first rowand the first column, on the otherhand, is a manifestation of the linear diattenuation effect. Strong signature ofthe linear retardance effect is also evident from significant intensities of theoff-diagonal elements in the lower 3 × 3block of M(λ). The spectral trends of the effects are gleaned further and becomemore evident in the decomposed (using MΔ(λ) (MDR(λ) (MΔ(λ) (MDR (which containsintrinsic sample polarization information) can therefore be used to reliablyextract the scattering-induced diattenuation and the retardance effects, and mayalso be relevant for further analysis on the polarized component of thescattered light.l trends . The comed using  basismang MΔ(λ)  and the  (MDR(λ) . The obs) (MΔ(λ)  that des) (MΔ(λ) . The resd(λ) and linear retardanceδ(λ) parameters are displayed. Whereas themagnitude of d(λ) peaks at the wavelengths corresponding tothe two orthogonal dipolar plasmon resonances, themagnitude of δ(λ) attains its maximum value atthe spectral overlap region of the two resonances(λ ~ 575 nm). Forcomparison, the theoretically computed (using T-matrix approachd(λ) andδ(λ) parameters for a preferentially orientedAu nanorod  under plane waveexcitation, are displayed in d(λ) andδ(λ) parameters are in good agreement to thecorresponding theoretical predictions. The corresponding wavelength dependenceof the derived depolarization coefficient Δ(λ) is shownin the inset of λ), the twoorthogonally polarized amplitude scattering matrix elements (representing thescattered fields) of the nanorod can be modeled as sl∝αl cos θand st ∝αt, whereαl andαt are the longitudinal and thetransverse dipolar plasmonpolarizabilities, respectively, andθ is the scattering angled and the linear retardance δ parametersare linked to the two competing resonant polarizabilities as28Interestingly, despite such high NA imaging geometry, the intrinsic spectralcharacteristics of the linear diattenuation and the retardance effects of singleplasmonic nanorod are preserved. This is illustrated in δ is directly related to the phase difference between thetwo orthogonal dipolar plasmon polarizabilities . The diattenuation, on theother hand, is primarily determined by the relative strengths of the twoorthogonal dipolar plasmon polarizabilities(|αl| and|αt|).Information on the relative strengths and phase differences between the tworesonant plasmon polarizabilities are therefore characteristically encoded inthe d(λ) and δ(λ) parameters,respectively. Note that in the dipolar approximation, the magnitude ofδ does not depend on the polar scattering angleθ or angle of excitation (exclusively related to thephase difference between the two intrinsic plasmon modes). The magnitude of theparameter d would however, weakly depend on the scattering angleθ also (thus on the choice of the excitation/scatteringdirection) because of the cos2 θfactor associated with dipolar scattering. In conformity with this, while thecomputed δ parameters for the Au nano-rod shows no angulardependence, the magnitude of d varies weakly with increasing forwardscattering angle θ . The magnitude of the derived δ(λ)parameter is accordingly reasonably close to the theoretical prediction forpreferentially oriented Au nano-rod under plane wave excitation (d(λ) parameter,on the other hand, is lower than the corresponding theoretical predictions(d(λ) andδ(λ) parameters are retained because these aredirectly linked to the relative strengths of the orthogonal dipolar plasmonpolarizabilities and phase difference between them, respectively.As apparent from citation . The magdictions, as averd(λ) andδ(λ) parameters may open-up interesting newavenues for the analysis/interpretation of the interference of the neighboringmodes in coupled plasmonic structures. An illustrative example of this for theAu nanorod is demonstrated in Idet(λ)) with +45°analyzer basis state (denoted by P) and that without any analyzer(polarization-blind detection). For the sake of comparison, the spectral lineshapes of Idet(λ)  ~ |sl(λ)|2 + |st(λ)|2).Projection of the scattered light into +45° linear polarizationbasis detection, on the other hand, leads to contribution of the interferencesignal [M33(λ)/M44(λ)]in addition to the scattered intensity contributions of the two individualplasmon modes[|sl(λ)|2 + |st(λ)|2].The appearance of the interference signal leads to distinct changes in thespectral line shape, manifesting as an asymmetry in the resulting line shape(Iint(λ) is separately shown (in relativeunits) in the inset of M(λ) and the derived d(λ) andδ(λ) polarization parameters for probing,manipulating and controllably tuning the spectral interference effect in asimplest possible plasmonic system. Its potential applications on more complexcoupled plasmonic structures  and retardanceδ(λ) effects from single isolated plasmonic Aunanorod, as quantified via Mueller matrix inverse analysis. It is demonstratedfurther that these Mueller matrix-derived plasmon polarimetry parameters,d(λ) and δ(λ) encode potentiallyvaluable information on the relative strengths (amplitudes) and phases of competingneighboring resonant modes in plasmonic structures. These polarimetry parameterstherefore hold considerable promise as novel experimental metrics for theanalysis/interpretation of a number of interesting plasmonic effects; for instance,these can be used to probe, manipulate and tune the interference of the neighboringmodes in complex coupled plasmonic structures, to study SOITo summarize, a novel experimental system is developed for the recording of full4 × 4 spectroscopic scattering Mueller matricesfrom single isolated plasmonic nanoparticle/nanostructure. The system overcomes theoutstanding issues pertaining to reliable measurements of weak scatteringpolarization signals from nanoparticle/nanostructures over broad spectral range thattoo in high NA imaging geometry, by integrating an efficient Mueller matrixmeasurement scheme and a robust eigenvalue calibration method with a dark-fieldmicroscopic spectroscopy arrangement. Feasibility of The experimental system shown in  is capabW(λ) and A(λ) matrices (overλ = 400–700 nm).Secondly, this measurement scheme is independent of the polarization response ofthe spectrometer (detector) and the source, since it uses fixed linearpolarizers at both the excitation  and the detection end. Finally, the entire experimental system is automated usingLabview for easier and faster data acquisition. The system is capable ofrecording the spectroscopic Mueller matrices by using the spectrometer.The salient advantages of the experimental system are worth a brief mention.First of all, the issues pertaining to polarization measurements over broadspectral range and the polarization transformation due to the high NA imaginggeometry are tackled by determining the actual experimentaletal.4.3H2O), L-ascorbic acid, silver nitrate(AgNO3) sodium borohydride (NaBH4) and CTAB(cetyltrimethylammonium bromide) were procured from Sigma-Aldrich. The entirereaction was carried out in two parts at room temperature. In the first part, wesynthesized the seed solution by mixing both 5 mL of 0.2 MolCTAB and5 ml of 0.5 mMol HAuCl4 solutions. Then0.6 ml of ice-cold 0.01 Mol NaBH4 was added to the abovemixture under continuous stirring for 5 min which produces seedsolution with nanoparticles of size less than 10 nm. The second partis about the preparation of growth solution where we would like to grow Aunanorods from the existing nanoparticles in seed solution. Growth solution isprepared by mixing 5 ml of 0.2 Mol CTAB, 5 ml of1 mMol HAuCl4, 150 μl of 0.0064Mol AgNO3, and 85 μl of 0.0788 Mol L-ascorbicacid. To obtain the required size of Au nanorods, 36 μlof seed solution was mixed with the growth solution under continuous stirringfor 1 hour. Au nanorod images were recorded by a Zeiss SUPRA55VP-Field Emission Scanning Electron Microscope (FE-SEM) by spin coating the Aunanorod solution on a clean silicon (100) substrate. For the Mueller matrixspectroscopic and imaging studies, the samples were diluted as required and thenfixed on a glass cover slip by spin coating , which was then kept at the sample stage of the dark-field microscopicarrangement.Gold (Au) nanorods were synthesized as described in the literature by Babak How to cite this article: Chandel, S. et al. Complete polarizationcharacterization of single plasmonic nanoparticle enabled by a novel Dark-fieldMueller matrix spectroscopy system. Sci. Rep. 6, 26466; doi:10.1038/srep26466 (2016).


The production of multiscale architectures is of significant interest in materials science, and the integration of those structures could provide a breakthrough for various applications. Here we report a simple yet versatile strategy that allows for the LEGO-like integrations of microscale membranes by quantitatively controlling the oxygen inhibition effects of ultraviolet-curable materials, leading to multilevel multiscale architectures. The spatial control of oxygen concentration induces different curing contrasts in a resin allowing the selective imprinting and bonding at different sides of a membrane, which enables LEGO-like integration together with the multiscale pattern formation. Utilizing the method, the multilevel multiscale Nafion membranes are prepared and applied to polymer electrolyte membrane fuel cell. Our multiscale membrane fuel cell demonstrates significant enhancement of performance while ensuring mechanical robustness. The performance enhancement is caused by the combined effect of the decrease of membrane resistance and the increase of the electrochemical active surface area. Multiplex lithography is a technique that can be used to fabricate complex soft materials. Here, the authors develop a method to prepare multilevel multiscale structures and demonstrate its application on polymer electrolyte membrane fuel cells which display decreased membrane resistance and increased electrochemical active surface area. Soft lithography, a rapid prototyping of structures geared for both the microscale and nanoscale, is a collection of versatile techniques that allow for the development of novel structures and their incorporation into advanced applications with the aid of flexible, elastomeric stamps234689111415Complex hierarchical microarchitectures have emerged181914212223−2) onto the membrane.The basic concept of multiplex lithography is illustrated in α. Then, in our method, only the top part of the resin could be forced to contain higher oxygen concentration so that CC becomes α′ using micro-ebb tide (will be explained later), while the bottom part remains the same as α. This resin brick having different CCs at the top and bottom is the MCB as defined earlier. Then, the imprinting is performed at the top part of MCB while the bonding (or stacking) of the other membrane is performed at the bottom, which finally yields multilevel multiscale structures.The first step of multiplex lithography is the fabrication of a MCB by slightly curing the PUA resin between two permeable PDMS layers  at the top surface because droplets placed initially at overlapped OIL regions (#3) should have high oxygen concentration that strongly inhibits the ultraviolet reaction while the bottom part maintains the same CC of α . Monolithic integration (or bonding) is performed on the bottom of the brick having CC ∼α (CC ∼55%) by placing it onto a pre-patterned PUA having 800-nm holes with CC ∼β (CC ∼60%) while imprinting is done on the top having CC ∼α′ (CC ∼45%) by pressing permeable PDMS mould having 800-nm pillars. The SEM image in α′) allows imprinting and is further cured to result in the intermediate CC (β′) with a slow curing speed shown as a red curve in β′ even after the second ultraviolet exposure. On the other hand, at the bottom part of MCB with an intermediate CC∼α experiences bonding and during ultraviolet exposure, the bottom part also becomes cured further, but follows the black curve (higher curing speed) shown in β after complete bonding between MCB and PUA brick occurs. The black box of β′), bonding of the other MCB is possible. In +) from the anode to the cathode in the PEMFC (272829303234L1>L2>L3), where L1 is the original thickness of the membrane  and L3 (∼10 μm)L2 and L3) affected the reduced membrane resistance, while the region of L1 ensured mechanical robustness. From the three-level multiscale architecture, we reduced the membrane resistances of Nafion by ∼16% from the original Nafion membrane , while the case of Nafion211 (t ∼25 μm) shows high stress concentration region near side grips. This result supports the robustness of our multiscale membrane.We carried out stress–strain measurements to examine the mechanical strength of our multiscale Nafion membrane and compared with the conventional flat cases, Nafion 212 membrane with thickness of ∼50 μm, and Nafion 211 membrane with thickness of ∼25 μm . The res−2, see 2/O2 (or H2/air), this MEA exhibited much improved performance compared with a conventional one as shown in −2 under additional pressure (150 kPa) following the conditions of the US Department of Energy (DOE)342/O2 conditions under ambient pressure. The enhancement is mainly due to the aforementioned reduced membrane resistance and the enlarged electrochemically active area, which is dependent but not proportionally increased by the increment of geometrical surface area of Nafion membranes  with multiscale Nafion membrane and the enhancement of ECSA was also observed from the CV test. The ECSA for our multiscale membrane was as much as 1.2-fold compared with that of the flat, which was not proportionally matched with the increment of geometrical surface area (1.96-fold than that of the flat one). This is mainly due to the fact that the only Pt/C catalysts that contacts onto the Nafion membrane affects the enhancement in ECSA and the Pt/C agglomerates that do not contact the membrane surface would not contribute to the increase of ECSA. Therefore, for ambient case, ∼20% increase of ECSA and 16% reduction in membrane resistance for our multilevel multiscale case well explain ∼40% increase of maximum power density. For the pressurized case, it is known that additional pressure induces enhanced transport of oxygen to the reaction sites in the cathodic active layerTo quantitatively explain the effect of reduced membrane resistance and increased active surface area, both electrochemical impedance spectroscopy−1 at room temperature for 5,000 cycles with fully humidified H2/N2 gases supplied to anode and cathode, respectively (in accordance with DOE condition2/O2 (H2/air) conditions under ambient pressure and ∼9.5% (∼16.1%) in the case of H2/O2 (H2/air) conditions under outlet pressure of 150 kPa. There was no breakdown of the system even with long-term electrochemical stress. However, after ADT test, performances of both MEA cases with flat and multiscale membranes were decreased as shown in We also performed accelerated durability testing (ADT) to confirm the robustness of our multiscale MEA and address if there is a risk of chemical short between the anode and cathode. The ADTs were conducted using CV method in the potential range of 0.05–1.20 V versus RHE and with a scan rate of 100 mV sSummarizing, we report a novel multiplex lithography that can manufacture multilevel multiscale architectures. To do this, we utilized oxygen inhibition effects on ultraviolet-curable resin by controlling the spatial distribution of oxygen concentration in the resin. This deliberate control of spatial oxygen concentration enables to induce different curing contrasts in different parts of the resin leading to MCBs. Three different regions having different oxygen concentrations are developed in the resin using highly permeable PDMS stamp and blanket. High-concentration region allows us to imprinting, while intermediate region provides bonding and low-concentration region as a frame work, which explains how LEGO-like integration of micrometre membranes in our method is possible together with versatile multiscale pattern formation. The multiplex lithography was applied to make multiscale Nafion membrane, which not only showed higher fuel cell performance caused by the combination of the effects of lower membrane resistance and larger ECSA than the conventional flat membrane, but also provided the robustness of the membrane.λ=250–400 nm) under an applied pressure (25 g cm−2 ∼1 kg cm−2) after achieving conformal contact. After the removal of the upper and lower PDMS moulds, a flexible, free-standing MCB via the micro-ebb-tide phenomena was obtained.A small amount of hydrophilic resin  was dispensed dropwise onto a patterned PDMS mould (see more details in α-phase) of the membrane, and the nanopatterned PDMS mould was placed onto the less cured face (α′-phase) of the membrane. Then, the sandwich assembly was exposed to ultraviolet light  with hydraulic pressure (6–8 kg cm−2) in a vacuum chamber (5 × 10−2 torr) after forming conformal contact. After removal of the PDMS moulds, a multiscale two-level PUA311 hole pattern array was obtained via a simultaneous bonding and imprinting process. The same process was conducted with different microsized membranes to obtain the trilevel PUA311 hole patterned master. After preparation of the master, a mixture of base and curing agents (10:1 w/w) of Sylgard 184 PDMS elastomer was poured onto the patterned masters and cured at 70 °C for 2 h. The cured PDMS replica was peeled off from the master and cut before use.A prepared brick was uniformly placed onto a nanopatterned PUA311 mould contacting the most cured face (−2) and temperature (∼120 °C) for 30 min. After cooling down to room temperature, the patterned Nafion membrane was peeled off the PDMS mould and kept in a deionized water container for ∼12 h.The Nafion 212 membrane  was uniformly placed onto an as-prepared multiscale PDMS mould and glass substrate. Then, the sandwich assembly was imprinted under hydraulic pressure −WPET). As shown below, we made a calibration curve for the deposited amount of Pt as a function of a catalyst ink volume from which we chose the loading of 0.12 mg cm−2 based on the DOE condition. The catalyst-coated membranes were dried at room temperature for 12 h and situated between the anode and cathode gas diffusion layers  without a hot press process. The active geometric areas of the MEAs were 5.0 cm2.A catalyst slurries for the anode and cathode catalyst layer were fabricated by mixing 40 wt.% Pt/C , Nafion ionomer solution and 2-propanol . Multiscale and flat Nafion membranes were used after the pretreatment. They were boiled in 3% hydrogen peroxide solution and rinsed in deionized water. Thereafter, the membranes were soaked in 0.5 M HFourier transform infrared (FTIR) spectroscopy spectra were obtained using Vertex 70 with FTIR spectrometer (BRUCKER) to monitor the degree of photopolymerization of PUA as a function of the ultraviolet exposure time. The curing contrast or conversion ratio was calculated asI810]0 and [I810]t are the signal intensities at time=0 and t, respectively.where [How to cite this article: Cho, H. et al. Multiplex lithography for multilevel multiscale architectures and its application to polymer electrolyte membrane fuel cell. Nat. Commun. 6:8484 doi: 10.1038/ncomms9484 (2015).Supplementary Figures 1-17, Supplementary Tables 1-3, Supplementary Notes 1-3 and Supplementary MethodsMovement of the PUA micro ebb tides toward the neighboring PUA brick due to the low affinity for the hydrophobic PDMS surface.Dewetting of the PUA droplet on the disintegrated flat PDMS layer after short UV exposure of the sandwich-like PDMS assembly.


In this article, we define the fractional Mellin transform by using Riemann–Liouville fractional integral operator and Caputo fractional derivative of order  According to Flajolet et al. , Hjalmart et al.  and somet et al. .Flajolet et al.f(x) be locally Lebesgue integrable over f(x) is defined by(The largest open strip Letf(x) be integrable with fundamental stripIfcis such thatandis integrable, then the equalityholds almost everywhere. Moreover, iff(x) is continuous, then equality holds everywhere onLetfbe Mellin transformable function defined onIf differentiation under the integral sign is allowed, then we have(1)(2)(3)(4)For more information readers may refer to Butzer and Jansche , A real function f(x) is defined as:The Riemann–Liouville fractional derivative operator of order PodlubnyPodlubny The Riemin particular Some properties of Riemann–Liouville fractional operatorIf CaputoCaputo The CapuIfthen the following two properties hold(1)(2)Fractional Cauchy’s integral formula) (Jumarie N integer. For every r. Then f (z) is actually infinitely  be Mellin transformable function onwherethen(1)(2)(3)The result is obtained by applying Mellin transform to both sides of the first property (1) in Theorem 3 (2)We apply Mellin transform on the part (2) in Theorem 3, then we obtain (3)x-integral becomes Now,we are applying Mellin transform of Letfbe Mellin transformable defined on(2)Continuing by the induction, then the results in Theorem 5 can be extended to further fractional derivatives as the following theorem:Letfbe Mellin transformable function onandfis a fractional derivative function for allthen:By using the same technique in above theorem, Mellin transform of fractional integral can be yielded as the following formula:Letfbe Mellin transformable defined onthenBy the same way as in Theorem 5, the next result follows:Solve the problem:By applying the Mellin transform to both side and on using the Theorem 7 we havef(x) explicitly as the solutionBy solving the equation and applying the inverse Mellin transform by using complex inversion integral in order to cover the Letand holomorphic on the stripSt. In additionfis Mellin transformable function, thenwhereandSt contains the circle s.We set First of all, for Secondly, we apply fractional Cauchy’s integral formula when By another application of fractional Cauchy’s integral formula, we obtainTherefore, the proof of Theorem 8 is fulfilled. Let f(x) be Delta function, Let If  formula  turns to formula  in Theor(i)if (ii)if In the Example 2,(i)if ettinger ,(ii)if  in Graf  when \doIn the Example 3,For special cases we have the following:Letbe Mellin transform of the functionf(x) inwherethen(1)(2)The result is given directly from Theorem 6 then we obtain (2)Also we apply the formula in Theorem 6 part by part as the following: From  and 2)  2) we obIn this paper, some properties of fractional calculus are proposed by applying Mellin integral transform, and some applications are also given. Further, the results in fractional sense by using Mellin transform are in agreement with ordinary way in the existing literature. In fact, Mellin integral transform and its inverse are powerful to solve some kinds of fractional equations with variable coefficients, that will be a future study.


We identify the microscopic transport mechanisms, and find facile vacancy-assisted migration of iodide ions with an activation energy of 0.6 eV, in good agreement with the kinetic measurements. The results of this combined computational and experimental study suggest that hybrid halide perovskites are mixed ionic–electronic conductors, a finding that has major implications for solar cell device architectures.Solar cells based on organic–inorganic halide perovskites have recently shown rapidly rising power conversion efficiencies, but exhibit unusual behaviour such as current–voltage hysteresis and a low-frequency giant dielectric response. Ionic transport has been suggested to be an important factor contributing to these effects; however, the chemical origin of this transport and the mobile species are unclear. Here, the activation energies for ionic migration in methylammonium lead iodide (CH Understanding the mechanism of ionic transport in organic–inorganic halide perovskites is crucial for the design of future solar cells. Here, Eames et al. undertake a combined experimental and computational study to elucidate the ion conducting species and help rationalize the unusual behaviour observed in these perovskite-based devices. The ABX3 perovskite-type structure, illustrated in 6 octahedra with the methylammonium cation (CH3NH3+) occupying the central A site and surrounded by 12 nearest-neighbour iodide ions.Solar cell materials based on organo-lead halide perovskites are attracting extraordinary attention on account of the rapid rise in their solar-to-electricity conversion efficiencies12343) exhibit high ionic conductivity mediated by defect species , making them useful in applications such as solid oxide fuel cells333 and CsPbCl3) have reported low activation energies for the migration of halide-ion vacancies3536Inorganic perovskite oxides have been intensively researched for decades in connection with a rich variety of solid-state magnetic, ferroelectric and conduction properties. In particular, it is well known that numerous perovskite oxides  behaviour, and indicate high carrier mobility and long minority-carrier diffusion lengths101113141516173NH3PbI3  vacancies create shallow donor or acceptor levels. Recent simulation work3NH3PbI3 with low formation energies for Schottky-type defects associated with anion and cation vacancies, shown in the following reaction in the Kröger–Vink notation for the full Schottky defect,Previous electronic structure calculations have been used to examine band structures, spin–orbit coupling and intrinsic defects in CHbI3 refs , 50, 51.3NH3PbI3 lattice, V indicates a vacancy, subscripts the ionic species and superscripts the effective defect charge (a dot for each positive charge and prime for each negative charge); recent results−, Pb2+ and CH3NH3+ vacancies at room temperature, which could support vacancy-mediated diffusion.where nil represents the perfect CH3NH3PbI3 using first-principles techniques combined with kinetic experiments monitoring the photocurrent relaxation of devices, extending our previous work on hybrid perovskites394033−, Pb2+ and CH3NH3+ ions, and compared these values directly with kinetic data extracted from a working CH3NH3PbI3 solar cell. The results support a mechanism of vacancy-mediated ion diffusion, pointing to mixed ionic–electronic conduction in these hybrid perovskites. The implications for perovskite solar cell operation and stability are discussed.Macroscopic conductivity or diffusion experiments, however, have so far not enabled the mobile defect species or the atomistic transport mechanism to be identified. Here, we investigate key issues related to intrinsic defect migration in CH3 perovskite structure, vacancy-mediated diffusion is the most common process, which is further supported for CH3NH3PbI3 by the ease of formation of Schottky disorder (reaction (1)), with an intrinsic concentration of I−, Pb2+ and CH3NH3+ vacancies predicted to exceed 0.4% at room temperatureIt is well established that the mobile ionic species in the solid state is associated with some type of vacancy or interstitial defect, the concentration of which is controlled by intrinsic Schottky and Frenkel defect reactions, non-stoichiometry or aliovalent doping3334− migration along an octahedron edge; (ii) Pb2+ migration along the diagonal (<110> directions) of the cubic unit cell; (iii) CH3NH3+ migration into a neighbouring vacant A-site cage. Energy profiles for these mechanisms were mapped out by performing a series of transition-state calculations between adjacent equivalent sites. Particular care has to be taken to ensure the starting and end point configurations are well converged to avoid anomalously low migration energies. This approach allows the energy barrier to ion migration to be determined, and has been used successfully in previous studies on oxide-ion, proton and metal-ion migration in perovskite oxides52In this study, three vacancy transport mechanisms involving conventional hopping between neighbouring positions ; this value is probably at the lower limit since we have considered the ideal migration path normal to the unit cell face. In addition, neutron diffraction3NH3+ ion at room temperature, which is likely to further inhibit long-range transport. 2+ vacancy migration, suggesting an immobile Pb sublattice. This result is consistent with the thermodynamic stability of the inorganic lead iodide sublattice of the perovskite structure. The high activation energy for Pb2+ transport also suggests that such cation diffusion is likely to be rate controlling for crystal growth processes.The migration activation energies for the three mechanisms are reported in 12 Hz for ionic species at a temperature of 320 K, we estimate a diffusion coefficient of 10−12 cm2 s−1 for I− ions, which is four orders of magnitude higher than the value of 10−16 cm2 s−1 for CH3NH3+, suggesting negligible diffusion of CH3NH3+ ions. These results clearly indicate that hybrid halide perovskites are mixed ionic–electronic conductors with iodide ions as the majority ionic carriers. A key factor for ionic conductivity will be the level of intrinsic iodide ion vacancies in the material, which will be sensitive to the synthesis conditions (equilibrium or non-equilibrium) and thermal processing routes. It is recognized that, as in binary lead halides, there are stability and photodecomposition issues with these hybrid lead perovskites12From the calculated activation energies a diffusion coefficient can be estimated. Assuming a Boltzmann-like barrier-hopping process with a typical attempt frequency of 103. Similar mechanisms may feature in related hybrid halide perovskites.With regard to mechanistic features, it is often assumed that the migrating ion takes the shortest path between adjacent sites, that is, a direct linear jump. However, detailed analysis of the migration paths for the iodide ion vacancy mechanism reveals a small deviation from the linear route involving a curved path between iodine sites, with the saddle point slightly bowed away from the neighbouring Pb ion 353633+ and Pb2+ vacancies  are higher than the measured values, confirming that significant migration of these ions is unlikely at the temperatures and timescales examined.The measured activation energies for hysteresis, 0.60–0.68 eV, are very close to the value calculated for the migration of iodide ion vacancies, 0.58 eV. Our measured and calculated values are also compatible with experimental ionic conductivity studies of inorganic perovskites, which have reported similar activation energies for halide-ion vacancy conduction in perovskite halides  is of the order of 30 nm. The corresponding drift distance in this time due to an electric field that might be found in a device of this thickness (1 V dropped uniformly across 500 nm) is around 80 nm. As an example, the change in potential across a layer of accumulated vacancies of thickness w of 10 nm yields a value of ≈0.6 V, using the relation qw2N/(2ɛ0ɛr) assuming a relative permittivity (ɛr) of 24 and 0.4% Schottky defects (N≈1.6 × 1019 cm−3) at room temperatureThe diffusion length of an iodide vacancy on the timescale of a photocurrent relaxation at room temperature (around 10 s) using our estimated diffusion coefficient . Although this investigation is not exhaustive in terms of possible polarization phenomena and direct observation of ion migration, it does highlight a crucial area for further work on this fascinating system. Indeed, large-scale molecular dynamics simulations could be used to explore diffusion mechanisms and defect association effects, while isotope diffusion measurements would provide a direct probe for determining the extent of ion transport in these materials.3NH3PbI3. We find facile vacancy-assisted diffusion of iodide ions, with good agreement with activation energies derived from kinetic measurements on a CH3NH3PbI3-based solar cell. A key factor influencing the conduction of iodide ions (as the majority ionic carriers) will be the levels of intrinsic iodide ion vacancies in the material, which will be sensitive to the fabrication conditions and sample thermal history.Our combined computational and experimental study has provided new atomic-scale insights into the ion transport mechanisms operating in the hybrid perovskite CHOur study provides a framework for understanding ionic transport phenomena in organic–inorganic halide perovskites, including the influence of the migration of iodide ion vacancies to and from interfaces in solar cell devices. Such ion migration has been suggested as a factor contributing to their unusual behaviour, including current–voltage hysteresis and a giant dielectric response at low frequencies. The picture emerging is that hybrid halide perovskites are mixed ionic–electronic conductors. This behaviour has major repercussions for interpreting solar cell device performance and degradation pathways, and for the design of future architectures.3NH3PbI3 perovskite structure and energies were calculated using density functional theory methods  in agreement with Raman and neutron scattering. We obtained an average lattice parameter of 6.28 Å for CH3NH3PbI3, in good agreement with the observed values of 6.28–6.32 Å from X-ray and neutron diffraction experiments -coated glass  was patterned by etching with zinc powder and 2 M HCl, cleaned with deionized H2O, isoproponal and heated at 450 °C for 30 min. A dense titanium dioxide (∼80 nm) blocking layer (d-TiO2) was deposited on SnO2:F glass substrates via spray pyrolysis and heated at 450 °C for 30 min−1) onto the substrate and dried at room temperature for 30 min before heating at 90 °C for 3 h in a glove box. Studies suggest that negligible chloride remains in the film following this preparation. The resulting CH3NH3PbI3 perovskite film thickness was ∼500 nm. A solution of 61.6 mM spiro-OMeTAD, 55 mM tBP and 26 mM LiTFSI in dry chlorobenzene was then spun onto the perovskite, as above, to create the hole-transporting layer. A gold electrode was evaporated onto this with an active area of 0.08 cm2. The cell was sealed in the glove box using a glass coverslip and a surlyn gasket.Methylammonium lead iodide solar cells were fabricated using a modification of standard recipesChronophotoampereometry measurements were made using the TRACER system15Jsc) towards equilibrium  after reverse bias was found to be well fit by a double exponential function:Empirically, the rise in the photocurrent  for the fast and slow phases of the rise and J1 and J2 are constants. The decay of the photocurrent towards equilibrium was observed to have a more complicated functional form with a shoulder in the decay at early times. The tail of this decay could be well fit by a single exponential function:where k3 is the rate constant for the decay and J3 is a constant. As discussed in the main text, we hypothesize that these phenomenological rates of photocurrent relaxation  are related to the formation or removal of energetic barriers in the material, which change the efficiency of photogenerated charge carrier collectionwhere T) from 263 to 323 K, representative of device-operating temperatures but below the tetragonal-to-cubic phase transition. Associated activation energies (EA) were determined by fitting the expression ln[k]=C—EA/(kBT) to an Arrhenius plot of the rate (k) data, where C is a constant and kB is Boltzmann's constant. Although the activation energies are derived from the rates of photocurrent relaxation, they are likely to be related to the underlying mechanism that causes the change in photocurrent.The barriers result from the motion of ionic charge to or from the interfaces following a change in the electric field across the device caused by switching the bias voltage state. Measurements were taken as a function of temperature .


Type 2 diabetes mellitus (T2DM) is a progressive disease resulting from increasing insulin resistance and reduced pancreatic β-cell insulin secretion. Ectonucleotide pyrophosphatase/phosphodiesterase 1 (ENPP1) inhibits insulin signalling and may contribute to the pathogenesis of T2DM. Others have found elevated ENPP1 levels in muscle, fat, and skin tissues from insulin resistant individuals, but similar data on liver ENPP1 is lacking. The purpose of this study was to compare expression and protein concentrations of ENPP1 in liver between patients with and without T2DM.Roux-en-Y gastric bypass surgery (RYGB) results in remission of insulin resistance and T2DM thus presenting an opportunity to examine some critical aspects of these conditions. We measured liver ENPP1 gene and protein expression in individuals with or without T2DM at RYGB and on average 17 (±5.6) months later.We found liver ENPP1 protein abundance was lower in individuals with T2DM than in those with normal glucose tolerance, and increased after RYGB surgery in those individuals who had remission of T2DM. ENPP1 positively correlated with insulin sensitivity at the liver (as measured by HOMA-IR), which is contrary to what others have reported in other insulin target tissues.Liver ENPP1 expression in T2DM is the reverse of that expected based on expression in other tissues and is likely due to the unique role the liver has in insulin clearance. The work presented here adds another dimension to the role of ENPP1, and supports the hypothesis that ENPP1 may act as a natural modulator of insulin signalling in the liver.The online version of this article (doi:10.1186/s12876-014-0222-x) contains supplementary material, which is available to authorized users. Type 2 diabetes mellitus (T2DM) is a multifactorial disease that results from increasing insulin resistance and relative loss of pancreatic β-cell function. It has reached epidemic proportions world-wide, with incidence predicted to increase from ~285 million in 2010 to ~552 million by the year 2030 ,7.Several molecules inhibit insulin signaling through the insulin receptor (INSR) and may contribute to pathogenesis of insulin resistance . One of Roux-en-Y gastric bypass surgery can induce acute remission of diabetes before any substantial weight loss occurs –21. InsuIn this study, our primary aim was to examine ENPP1 levels in liver tissue taken at RYGB surgery and later after remission of diabetes. We hypothesized that liver ENPP1 levels would be higher in individuals with T2DM and would decrease after remission of diabetes.We examined ENPP1 protein and mRNA expression using liver tissue taken from individuals who underwent open RYGB surgery as described in detail by our group elsewhere . All patFifty five individuals, from a tissue bank of 448, were included in this study based on presence or absence of diabetes and availability of cryogenically stored liver tissue. The study group included those who had: normal glucose tolerance (NGT group: n = 19), impaired glucose tolerance (IGT group: n = 9), and type 2 diabetes (T2DM group: n = 27)  [Clinical data on all patients was collected prior RYGB surgery and included: weight, height, body mass index, glycated haemoglobin (HbA1c), fasting plasma glucose, and fasting plasma insulin. Diagnosis of T2DM was established by either 1) prior documentation of diagnosis and/or receipt of treatment for T2DM or 2) diagnosis based of an oral glucose tolerance test (OGTT) routinely performed in all patients without a known history of diabetes (plasma glucose > 11.1 mmol/l at 2 hours). Impaired glucose tolerance was also diagnosed using the OGTT (plasma glucose > 7.8 and < 11.0 mmol/l at 2 hours). Individuals with T2DM were further classified as: previously unrecognized, diet controlled, needing oral hypoglycaemic drugs or insulin taking. For those individuals who had a second liver biopsy, weight, body mass index, HbA1c, fasting plasma glucose and fasting plasma insulin were measured within 2 months of the second surgery. Remission of T2DM was defined according to recommendations of Buse surgery) .All patients undertook a 12 hour fast prior to blood collection for biochemical tests. Fasting was either self-administered or administered during the hospital stay. Clinical biochemistry testing was conducted by Aotea Pathology  while testing for insulin was undertaken at Canterbury Health Laboratories .Homeostasis model assessment (HOMA) was used to estimate insulin resistance . HOMA-IRTotal RNA was extracted using TRIzol® (Life Technologies) as per the manufacturer’s instructions. Briefly, 2-3 mg of frozen liver tissue was pulverized under liquid nitrogen and 800 μl of TRIzol® was added to the resultant powder which was then homogenised with an Omni Tissue Homogenizer . 200 μl of chloroform was added to separate the mixture into a red phenol-chloroform phase, an interphase and an RNA containing colourless upper aqueous phase. The aqueous phase was collected and total RNA was precipitated with isopropyl alcohol and GlycoBlue (50 μg/mL) (Life Technologies). The resultant RNA pellet was washed with 75% ethanol, air dried and re-suspended in 20 μl DEPC-treated water. RNA was stored at −80°C prior to quality control and use in first strand cDNA synthesis. Quality and quantity of RNA was analyzed on the 2100 Agilent Bioanalyzer, using the Agilent RNA 600 Nano kit and BioSizing software (Agilent Technologies).-∆∆Ct). Eukaryotic 18S rRNA  was used as the reference gene.Total RNA was reverse transcribed using the SuperScript Vilo cDNA synthesis kit (Life Technologies) according to the manufacturer instructions. 1 μg of RNA was added to a 20 μl reaction mixture and the resulting cDNA was diluted 1:10 and stored at −20°C prior to use in RT-qPCR reactions. EXPRESS qPCR SuperMix (Life Technologies) and TaqMan Gene Expression Assays (ENPP1/PC-1 Hs 01054040_m1- Applied Biosystems) were used for all RT-qPCR reactions which were conducted on an ABI 7300 Real-Time PCR System (Applied Biosystems). Each sample was run in triplicate and each time a threshold cycle (Ct) was obtained using the 7300 Sequence Detection Software 1.3.1. The average of all three replicates for a particular sample was calculated and used in subsequent data analysis. Changes in gene expression were expressed as relative amount normalised to a reference gene and as fold change, both of which were calculated using the RQ method , 30 mM TrisCl, 7 M urea, 2 M thiourea and 4% (w/v) CHAPS) for 45 minutes on ice, with vigorous vortexing every 15 minutes. The mixture was centrifuged at 14000 g for 10 minutes to remove any insoluble material. The supernatant was aliquoted for storage at −80°C. Protein was quantified using Bradford reagent (Bio Rad) on a Bio-Rad Benchmark microplate reader .sum of the intensities of the pixels within a defined volume boundary × pixel area (intensity units × mm2). Local background subtraction was used to facilitate background correction. Protein relative abundance was calculated by normalizing the volume of the ENPP1 band to the volume of the Actin band.An E-PAGE 48 well protein electrophoresis system was used to resolve protein samples on pre-cast E-PAGE 48 well 8% gels (20-300 kDa separation range) (Life Technologies) under denaturing conditions. Two separate gels were run, the first with 39 samples from the RYGB only group and the second containing 13 sets of samples from the patients who had repeat operations. Results for the RYGB comparison from the second gel were combined with the first for analysis purposes. SeeBlue Plus2 Pre-stained Standard (Life technologies) and MagicMark XP Western Protein Standard (Life technologies) were used as molecular weights to assess protein migration during electrophoresis and western blotting respectively. Protein was transferred onto Hybond-P PVDF membrane (Amersham) and blocked with 5% skim milk powder in TBS-Tween at 4°C overnight. Membranes were probed for 2 h at room temperature with monoclonal ENPP1/PC-1  , or mono-ΔCt RT-qPCR data between each study group. Consequently gene expression data was expressed as both 2-ΔCt in graphical form, whereas the fold change for significant differences was reported in text. Statistical analysis of protein abundance was performed on the value generated from normalisation of band intensity to the loading control.Statistical analysis was performed on 2Normal distribution of all groups to be compared was tested with Kolmogorov-Smirnov test. Non-normally distributed data was log transformed to comply with parametric test assumptions. Pre-post comparisons were carried out using a paired t-test. ANOVA with Bonferroni correction was used to test significance between groups. The Pearson product–moment correlation coefficient was used to test the strength and significance of association between variables. An alpha level of 0.05 was set as the significance threshold. All analysis was performed using Minitab 15. Graphical visualization was performed using GraphPad Prism 5.2) and there were no statistically significant differences in BMI between any of the groups. The T2DM group was significantly older than the NGT group, likely owing to the chronic and progressive nature of the disease. Mean fasting plasma glucose and HbA1c levels were normal in the NGT group, and slightly raised in the IGT group. However there were no statistically significant differences between the NGT and IGT group in any of the parameters measured at RYGB surgery. The T2DM group had significantly higher  HbA1c and fasting glucose levels than the NGT group. Although insulin resistance was present in varying severity in all groups, the T2DM group were the most insulin resistant as they had the highest mean fasting plasma insulin concentration and HOMA-IR values, which was only significantly different between the T2DM and the NGT group .We measured levels of ENPP1 mRNA expression and protein abundance in individuals with and without T2DM and again after resolution of insulin resistance and remission of T2DM. Table We found that liver ENPP1 gene expression was −1.5 (95% CI −6.2 to 2.8) fold lower in the T2DM group when compared to the NGT group  or T2DM (rsT2DM group) at RYGB and at a second operation 17 months later. Table Figure ENPP1 may contribute to insulin resistance through its inhibitory action on insulin signalling. Although others have studied ENPP1 in various human tissues  –12, relaFrom the current literature on ENPP1 we expected that its levels would be high in individuals with T2DM and decrease after remission of the disease. Surprisingly, liver ENPP1 mRNA and protein was lower in individuals with T2DM in comparison to individuals with normal glucose tolerance Figure A.However, ENPP1 mRNA expression did not change significantly after remission of diabetes, even though individuals with T2DM had lower expression than those with normal glucose tolerance at RYGB surgery. This is likely caused by post transcriptional processing as insulin has been shown to affect liver ENPP1 protein abundance without changing its gene expression , which iet al. have shown no change in muscle ENPP1 content in morbidly obese humans after bariatric surgery where there had been a measured increase in insulin sensitivity [Although our data do not agree with studies that have associated increased ENPP1 content in muscle and adipose tissue with insulin resistance –13, thersitivity . In a Zusitivity . Even thsitivity , others sitivity ,34.et al. have suggested ENPP1 may act as a natural desensitiser of insulin signalling because of insulin’s ability to stimulate ENPP1 post-translational processing and recruitment to the plasma cell membrane [We suspect that the conflicting evidence reported in the literature and our own data presented here is due to the varied roles muscle, fat, and liver tissues have in regulating insulin action. The liver has a crucial role in regulating the systemic insulin concentration by hepatic insulin clearance . It is tmembrane . Our datet al. reported previously that metformin treatment can influence ENPP1 activity in lymphocytes from individuals with diabetes [et al. who have also shown that metformin does not affect ENPP1 mRNA levels in lymphocytes [However, there are some limitations to the data presented here. Stefanovic diabetes , while hphocytes . Repeat In this study, we have shown a reverse ENPP1 pattern to that previously described in muscle and adipose tissue of insulin resistant individuals. Liver ENPP1 protein abundance was lower in the liver of individuals with T2DM in comparison to individuals with normal glucose tolerance and increased after remission of T2DM. We believe this is likely due to the role of the liver in insulin processing, and our data is in agreement with the previously supposed hypothesis that ENPP1 is a natural regulator of insulin signalling strength. The decreased levels of liver ENPP1 during hyperglycaemic conditions such as diabetes may be a compensatory response to increase insulin signalling and regain control of glucose homeostasis. Although our work does not discount the possibility that ENPP1 contributes to insulin resistance, it does add another dimension that will have to be considered in future work exploring the influence ENPP1 has on liver insulin signalling.


Scientific Reports5: Article number: 1159510.1038/srep11595; published online: 06302015; updated: 09282015This Article contains typographical errors.In the caption of Figure 4,“k|| refers to the Κ-Γ-Κ direction in the reciprocal space of 2Te3 film.”should read:// refers to the Κ-Γ-Κ direction in the reciprocal space of 2Te3 film.”“kIn the Discussion section,“As the Te layer thickness increases, we do not detect obvious changes in the band dispersion or doping level nor do we detect a Te-derived metallic band, but the Dirac surface states of the TI gradually fade as the interface between the TI and capping layer move beyond the probe depth of our VUV ARPES experiments, which is ~1 nm below the surface.”should read:“As the Te layer thickness increases, we do not detect obvious changes in the band dispersion or doping level nor do we detect a Te-derived metallic band, but the Dirac surface states of the TI gradually fade as the interface between the TI and capping layer move beyond the probe depth of our VUV ARPES experiments (hv = 21.21 eV), which is ~1 nm below the surface.”


The term mesocrystal has been widely used to describe crystals that form by oriented assembly, and that exhibit nanoparticle substructures. Using calcite crystals co-precipitated with polymers as a suitable test case, this article looks critically at the concept of mesocrystals. Here we demonstrate that the data commonly used to assign mesocrystal structure may be frequently misinterpreted, and that these calcite/polymer crystals do not have nanoparticle substructures. Although morphologies suggest the presence of nanoparticles, these are only present on the crystal surface. High surface areas are only recorded for crystals freshly removed from solution and are again attributed to a thin shell of nanoparticles on a solid calcite core. Line broadening in powder X-ray diffraction spectra is due to lattice strain only, precluding the existence of a nanoparticle sub-structure. Finally, study of the formation mechanism provides no evidence for crystalline precursor particles. A re-evaluation of existing literature on some mesocrystals may therefore be required. The term mesocrystal describes three-dimensional crystals formed by oriented assembly and that exhibit nanoparticle substructures. Here, the authors perform detailed structural analyses on synthetic calcium carbonate/polymer crystals, and show that common signatures used to assign mesocrystals may be unreliable. Indeed, it is now known that single crystals of many materials including TiO2/SnO2  that were precipitated in the presence of polymer additives1718192122232425Following early demonstrations of crystal growth by oriented assembly, this concept was extended to the formation of larger, three-dimensional crystals, where these were designated as ‘mesocrystals’. The term mesocrystal was first applied to calcite and vaterite crystals  data using the Scherrer equation, we demonstrate that both of these approaches may be insufficient and unsafe. We then examine the mechanism of formation of these calcite mesocrystals, and show that modifications in the crystal morphology only occur at later stages of growth. An amorphous calcium carbonate (ACC) precursor phase is also not a pre-requisite to the development of classic mesocrystal morphologies. Finally, electron backscatter diffraction (EBSD) is used to investigate the microstructures of synthetic mesocrystals, revealing a sector-like mosaic structure that contrasts markedly with the uniform nanostructure seen for a biogenic mesocrystal—a sea urchin spine3 was precipitated in the presence of the polymeric additives poly (PSS-MA) and poly  PS-MA; , where t) PS-MA; . These c crystal 2829, andθ, and assuming that these effects are simply additive on the FWHM and integral breath. Notably, in the analyses presented here, both methods validate each other by showing the same trends  and calcite/PSS-MA, seeded calcite/PSS-MA and calcite/PS-MA crystals was carried out, where the recorded patterns were modelled using a Rietveld refinement, Williamson–Hall plots and the Scherrer equation. The results are presented in 2+ calcite crystals, which are widely described as single crystals in which Co2+ is substituted for Ca2+ in the latticey axis at a small negative value. As the intercept is inversely proportional to the domain size, a large negative-domain size is returned. Application of the Scherrer equation, in contrast, yielded domain sizes of 92 nm as broadening arising from lattice strain is attributed to reduced domain sizes. These diffraction data are therefore fully consistent with the description of a single crystal exhibiting considerable lattice strain.A detailed synchrotron PXRD analysis of the structures of control samples  and strain  is dominated by a steep linear decay, owing to the large external facets of the powder grains, whereas smaller nanostructural features within the mineral particles give rise to a bent curve shape in regime 2. More detailed analysis of the scattering profile obtained from the calcite/PS-MA crystals based on a modified Guinier law shows that the nanostructural heterogeneities within these particles can be described as dilute platelets with average thicknesses of ≈2.9 nm , the profiles show a linear decay that corresponds to smooth interfaces. A full evaluation of the SAXS data is provided in the Supplementary Note 2.Additional information on the internal structures of the calcite samples was obtained using SAXS. The Co-calcite gave rise to a scattering profile consistent with little structural complexity, as shown by its similarity to that of a control calcite sample . The min ≈2.9 nm . This wo2+]=5 mM and [PSS-MA]=125 μg ml−1 is shown in 2+]=1.25 mM and [PSS-MA]=125 μg ml−1) were also single crystals but displayed some differences in structure and comprised two distinct regions, namely a central core that appeared smooth and a rougher outer layer , where samples were prepared immediately after removal of the crystals from solution. A large thin section cut through a crystal grown under conditions  ratios and a low supersaturation, surface poisoning by the polymer additive will become more significantConsidering then the mechanism of formation of the calcite/polymer crystals, our data again provides no evidence for the assembly of crystalline precursor particles. In showing that calcite rhombohedra form before the characteristic ‘mesocrystal’ morphologies, and that these morphologies can also develop on overgrowth of calcite seed crystals, we demonstrate that the shape is not defined at nucleation. Instead, a morphological transition does not occur until the rhombohedra reach sizes of 0.5–1 μm. This can be explained by the change in the solution conditions with time. The morphologies of calcite crystals precipitated in the presence of soluble additives are determined by both kinetic and thermodynamic factors, where changes in the shape and separations of the atomic terraces dictate the macroscopic changes in the crystal morphology593 particles with morphologies identical to reported vaterite mesocrystals can be formed below the ACC supersaturation level and in the absence of additives through control of the supersaturation aloneACC has also been frequently observed at early stages of formation of calcite/polymer mesocrystals, suggesting that ACC may be an essential precursor phase. Indeed, growth of crystals by transformation of an amorphous precursor phase has marked parallels with the formation of biogenic mesocrystals such as sea urchin spines3 but also other types of mesocrystals are re-examined, especially where assembly-based formation mechanisms have been proposed.In conclusion, the detailed analysis of calcite crystals presented here provides a clear demonstration that great care needs to be taken when classifying particles as mesocrystals. Indeed, while observations of nanoparticulate surface structures, high surface areas, line broadening of PXRD spectra and characteristic morphologies are all routinely used to assign mesocrystal structure, none of these provide stand alone evidence for the nanoparticulate sub-structure that is now considered to define a mesocrystal2·2H2O, (NH4)2CO3 and CoCl2·6H2O were purchased from Sigma-Aldrich and were used without further purification. PSS-MA and PS-MA were purchased from Sigma-Aldrich and were used after purification by dialysis against copious amounts of water for 2 days to remove impurities, followed by freeze-drying.CaCl3 was precipitated using either the ammonium carbonate diffusion method or by a double decomposition method (precipitation from a metastable solution) where equal volumes of [(NH4)2CO3]=1–100 mM solution and [CaCl2·2H2O]=0.2–5 mM solution were added in a Petri dish and then incubated at room temperature for 24 h. Of these, the ammonium carbonate method was principally used, and was used unless stated otherwise.Calcium carbonate was precipitated in the presence of the soluble anionic block copolymers PSS, PSS-MA and PS-MA. Two precipitation methods were used, such that CaCO3 was precipitated in the presence of the polymers in a polystyrene dish containing 10 ml of solution. Glass substrates were cleaned by soaking in Piranha solution (70:30 H2SO4:H2O2) before use, and were placed at the base of the dish. Stock solutions of polymers were added to a solution of [CaCl2·2H2O]=0.5–5 mM to form final solutions with polymer concentrations of 50–300 μg ml−1. Precipitation of CaCO3 was then initiated by placing the dish in a sealed desiccator containing a glass Petri dish of (NH4)2CO3 (5 g), which was covered with a piece of parafilm pierced four times with a needle. Crystallization was typically allowed to proceed for 1–2 days (unless stated otherwise). Following this period, the glass slides supporting the CaCO3 crystals were removed from the solutions, washed with Millipore water and dried in air.CaCO3 was also co-precipitated with cobalt (II) ions using the Kitano method2 gas was bubbled through a saturated suspension of CaCO3 for 3–4 h before filtering  to remove any undissolved CaCO3 particles. CO2 gas was then bubbled through the solution for a further 10–20 min. CoCl2·6H2O was then added to the prepared Kitano solution to give a final Co(II) concentration of 0.01–2 mM, and precipitation was induced by opening the prepared solution to air to allow escape of CO2 gasFor comparison with the crystals generated in the presence of copolymers, CaCO2·2H2O and the desired soluble polymer, and precipitation was carried out via ammonium diffusion for 1 day, before isolating from solution. The overgrown crystals were then scraped from the substrate using a razor blade, dispersed in epoxy resin and subsequently cured on a silicon wafer. The specimen was then mechanically polished and was examined using optical microscopy and SEM.Overgrowth experiments were performed on seed calcite crystals either 3–5 μm or 10–30 μm in size. Rhombohedral calcite seed crystals were precipitated on mica or glass substrates using the ammonia diffusion method as described above. After brief washing and drying, the substrates supporting the crystals were transferred to a solution of 2.5 mM CaClλ≤255 nm, hν>4.8 eV) through a circular quartz photomask at a constant distance of 2 cm for 1 h. The mask was patterned with an array of 100–200 μm diameter circles with centre-to-centre spacings of 100 μm. Photocleaved alkylthiols were then displaced by back-filling in dichloromethane solutions of 0.1 mM mercaptohexadecanoic acid  for 1 h at 4 °C, before rinsing thoroughly in deionized water  and drying under a nitrogen gas stream.Experiments were performed using established methods3 precipitation was then carried out within a sealed chamber in which the humidity was controlled at 100%. A solution of [CaCl2·2H2O]=1.25–5 mM and [PSS-MA]=125–500 μg ml−1 was poured over a freshly prepared substrate, resulting in the formation of picolitre-volume droplets on the hydrophilic domains. The substrate was then placed in the equilibrated humidity chamber along with 0.1 g solid ammonium carbonate, and precipitation was allowed to proceed for up to 30 min, before removing the substrate, washing with ethanol and air-drying. Different growth stages were assessed by analysing particles present within different droplets at the same time, and over a range of times.CaCOThe supersaturations of the crystallization solutions were calculated using visual MinteQ software, where the supersaturation index is defined as:Ksp=solubility constant, Ksp =10−8.48 and Ksp (ACC)=10−6.39.where IAP=ion activity product, 2+ concentrations in the reaction solutions containing PSS-MA polymers were measured with a Ca2+ ion-selective electrode (Metrohm). All solutions were freshly prepared before each experiment using fresh Milli-Q water (resistivity 18.2 MΩ cm at 20 °C) and the electrode was calibrated with four standard CaCl2·2H2O solutions with concentrations in the range 0.5–10 mM. The desired concentrations of pure CaCl2·2H2O solutions were first measured, then CaCl2·2H2O solutions containing PSS-MA polymer were measured after stirring for 30 min. The (Davies-extended) Debye–Huckel equation was used to convert the measured Ca2+ activities into concentrations for determination of the activity coefficients.The actual Ca3 particles were analysed using SEM, high-resolution TEM (HRTEM), optical microscopy, Raman microscopy, infrared spectroscopy, thermogravimetric analysis, surface area analysis (BET), atomic absorption spectroscopy and EBSD. Selected samples were also analysed using synchrotron PXRD and SAXS. For SEM, particles were typically transferred onto glass coverslips that were subsequently mounted on aluminium stubs using carbon sticky pads. Samples were then coated with 5 nm Pt/Pd using an Agar High Resolution Sputter Coater and were examined using a LEO 1530 Gemini FEG-SEM operating at 3 kV using an in-lens detector mode. For TEM analysis, an FEI Tecnai TF20 FEG-TEM fitted with Oxford Instruments INCA 350 EDX system/80 mm X-Max SDD detector and Gatan Orius SC600A CCD camera operating at 200 kV was used. Raman microscopy and infrared spectroscopy were used to further confirm the polymorph and internal structure change of crystal particles with Raman being carried out using a Renishaw 2000 Raman microscope operating with a 785-nm diode laser, and infrared being performed with a PerkinElmer ATR-IR. The Co content of samples was analysed using a PerkinElmer Atomic Absorption Spectrometer, AAnalyst 400 with an air-acetylene flame after dissolving samples in dilute HNO3.The CaCO2 absorption with a Micromeritics-TriStar 3000 after degassing for 2 h and/or heating up to 80 or 300 °C. The surface area was calculated from the linear part of the BET plot while the pore-size distribution was determined using the Barrer–Jovner–Halenda model. For multi point (5 point) BET measurements, the data were treated according to the absorption isotherm given in Surface area analysis was conducted using NP=partial vapour pressure of adsorbate gas in equilibrium with the surface at 77.4 K (boiling point of liquid nitrogen), in pascals, Po=saturated pressure of adsorbate gas, in pascals, V=volume of gas adsorbed at standard temperature and pressure (273.15 K and atmospheric pressure (1.013 × 105 Pa)), in millilitres, Vm=volume of gas adsorbed at standard temperature and pressure to produce an apparent monolayer on the sample surface, in millilitres, C=dimensionless constant that is related to the enthalpy of adsorption of the adsorbate gas on the powder sample.where V was measured at each of 5 values of P/Po. Then, the BET value:A value of P/Po according to r2 is not <0.995 from the resulting linear plot, where the slope and intercepts are obtained as:was plotted against Vm is calculated as:From this value, Vm determined, the total surface area St is calculated by the equation:From the value of Nav=6.022 × 1023, Am=0.162 nm2, Mv=22 414 mlS is obtained as:Finally, the specific surface area m=the mass of sample used.where Images of the lattice structure of the calcite particles were obtained using HRTEM imaging of thin sections prepared by FIB Milling . FIB to electron transparency was performed using an FEI Dual Beam system equipped with a 30 kV Ga beam and a field emission electron gun operated at 5 kV. The samples were then analysed with a FEI Tecnai TF20 FEG-TEM fitted with an Oxford Instruments INCA 350 EDX system/80 mm X-Max SDD detector and a Gatan Orius SC600A CCD camera operating at 200 kV. In order to minimize electron beam related damage during the recording of images and diffraction patterns recording, a 10-μm condenser lens and the smallest spot size were used.in situ heating of specimens to temperatures of 100, 200 and 300 °C for 30 min using an internal heater.The high-resolution PXRD measurements were carried out at the dedicated high-resolution powder diffraction beamline (I11) at the Diamond Synchrotron Radiation Facility . The beamline is equipped with a crystal monochromator  and a crystal analyser at the incident and diffracted beams, respectively. The optics of the diffracted beam consists of nine (111) Si crystal analysers and the use of the advanced analysing optics yielded diffraction spectra of superior quality that exhibited intense and extremely narrow diffraction peaks with an instrumental contribution to the peak widths not exceeding 0.004° ref. . Instrumθ=3–150°. Strain and size analysis was performed using both Rietveld analysis and line profile analysis. In order to quantify the broadening, Williamson–Hall plots were also prepared. Using this technique, B cosθ was plotted against sinθ for the {104}, {001} and {100} families of planes. The average microstrains and size effects (or coherence lengths) of each sample were determined from the gradient and intercept of the plot, respectively.The structural parameters were refined by Rietveld analysis both using GSAS and using PANalytical X’Pert HighScore Plus software. There was no evidence of amorphous material, as indicated by a flat baseline in the entire range 2At least 20 reflection peaks were refined using a Pseudo-Voigt function and the size and strain analysis was plotted using the Caglioti equationU parameter contains the information about the strain broadening, whereas the W parameter corrects for a possible size broadening. Microstrain and size are then obtained using the following algorithm:The Microstrain is described by:Crystallite size is described by:Φ to describe the peak shape variation. These numbers can be determined for single peaks as well as for a whole range of peaks. The algorithm then empirically deconvolutes the profile into a Gaussian and a Lorentzian integral breadth: This is defined as net peak area/peak height, and is equal to a rectangle with the same height and the same area as the net peak area; FWHM (2θ) is defined as the full-width at half-maximum intensity of the peaks. The universal shape parameter is defined as FWHM/integral breadth. The sample contribution to the total broadening is calculated using an empirical convolution of the Gaussian and the Lorentzian parts, where the Lorentzian broadening (BL) is given as:The XRD data was also analysed by combining a Williamson–Hall plot with line profile analysis. This method uses the integral breadth as a measure of the peak width and the universal shape factor BL):The Gaussian broadening  is then obtained from the slope (=4 × strain)The crystallite size (Å) is obtained from:K=1 was used.A shape factor of The crystal size was also estimated using the Scherrer equation:B=FWHM or integral breadth and a shape factor (or Scherrer constant) of K=1 was applied.The integral breadth and FWHM as a measure of the peak width of selected peaks were used in the Scherrer equation. The individual peaks were fitted by line profile fitting as described above.2+-doped calcite, seeded calcite/PSS-MA crystals and calcite/PS-MA crystals) were recorded using a Nanostar Instrument  equipped with a single-photon counting area detector . The X-ray generator provided radiation with a wavelength of λ=1.54 Å (Cu–Kα) and was operated at 40 kV and 35 mA, while a parabolically bent graded multilayer (Göbel mirror) was used to ensure a parallel and monochromatic X-ray beam. All specimens were measured in borosilicate glass capillaries at a sample-detector distance of 105 cm. Scattering data for the polymer-containing particles were additionally recorded at a smaller sample-detector distance of 26 cm in order to cover a larger range of accessible values for the scattering vector Q. The integrated profiles of the scattering intensity versus the modulus of the scattering vector Q (Q=4π·sin(2θ)/λ), where 2θ is the scattering angle and λ represents the wavelength of the incident beam) were corrected for instrument-related background and sample transmission as well as scattering attributable to the sample container. The Laue background (ILaue) obtained from a Porod fit of the profiles (P being the Porod constant) was subtracted from the data. For the crystal/polymer samples a T-parameter analysis was performed according to the method described by Fratzl et al.Q limit , data points in this Q-range were not included in the trapezoidal integration of the Kratky curve (I(Q) Q2 versus Q), but were approximated by a rectangle curve.SAXS profiles of powdered samples . The surface of the sample was then coated with 4–6 nm of carbon. EBSD maps were obtained at 15 and 20 kV on a FEG-SEM (JEOL JSM 6400) equipped with an Oxford Instruments NordlysNano EBSD detector and interpreted by CHANNEL 5 EBSD software.Y.-Y.K. led the experimental work, preparing samples and carrying out TEM, BET and XRD analyses; A.S.S. performed the SAXS experiments, analysed the SAXS data and participated in sample preparation for EBSD; J.I. participated in the BET study of surface areas, whereas A.N.K. carried out the FIB preparation of samples and assisted with the BET analysis; C.C.T. provided access to Beamline I11 at Diamond and assisted with the XRD experiments; G.H. assisted with analysis and discussion of the XRD data; E.G. and W.W.S. performed the EBSD studies and analyses; N.B.J.H. performed early studies that inspired this work; F.C.M. originated and supervised the project. All authors contributed to the preparation of the manuscript.How to cite this article: Kim, Y.-Y. et al. A critical analysis of calcium carbonate mesocrystals. Nat. Commun. 5:4341 doi: 10.1038/ncomms5341 (2014).Supplementary Figures 1-9, Supplementary Tables 1-4, Supplementary Notes 1-2 and Supplementary References