R2* using a single gradient‐recalled echo (GRE) measurement.To propose and validate an efficient method, based on a biophysically motivated signal model, for removing the orientation‐dependent part of R2*. The estimated parameters were compared to the classical, mono‐exponential decay model for R2* in a sample of an ex vivo human optic chiasm (OC). The OC was measured at 16 distinct orientations relative to the external magnetic field using GRE at 7T. To show that the proposed signal model can remove the orientation dependence of R2*, it was compared to the established phenomenological method for separating R2* into orientation‐dependent and ‐independent parts.The proposed method utilized a temporal second‐order approximation of the hollow‐cylinder‐fiber model, in which the parameter describing the linear signal decay corresponded to the orientation‐independent part of R2* into orientation‐dependent and ‐independent parts was verified. For the proposed model, no significant orientation dependence in the linear signal decay parameter was observed.Using the phenomenological method on the classical signal model, the well‐known separation of R2* using only a single GRE measurement.Since the proposed second‐order model features orientation‐dependent and ‐independent components at distinct temporal orders, it can be used to remove the orientation dependence of  Hence for GRE‐based R2* to be a robust qMRI parameter this effect needs to be controlled for.Quantitative MRI (qMRI) measures in the human brain are typically sensitive to multiple microstructural features at once, e.g., myelin and iron content.R2* can be quantified phenomenologically by partitioning R2* into an orientation‐independent, isotropic component R2,iso* and an orientation‐dependent, anisotropic component R2,aniso*(θ), describing the combined effect of bulk susceptibility and microstructure on R2*.R2* into isotropic and anisotropic components, either a large number of different orientations of the brain with respect to the external magnetic field have to be acquired,The orientation dependence of GRE‐based R2*. Unlike previous methods, our approach requires only GRE data acquired at a single, unknown orientation of the sample. The method is validated in a human postmortem sample of the optic chiasm (OC). Uncomplicated dissection from the postmortem brain and a straightforward anatomy of aligned retinal ganglion cell fibers inside the optic tracts (OTs) make the OC an ideal candidate for this purpose.Inspired by the HCFM, we propose here an efficient method for removing the orientation‐dependent part from 2TE is assumed to follow a mono‐exponential function, i.e. the logarithm of the signal may be written as α1=R2* denotes the apparent transverse relaxation rate, TE is the echo time and S(0) is the signal at TE = 0, given by the net magnetization and sensitivity of the MR system. The classical approach to estimating the apparent transverse relaxation rate R2* uses α1 in Equation α1=R2*(θ), where θ is the angle between local fiber orientation and direction of the external field of the MR scanner.R2*(θ) into orientation‐independent R2,iso* and orientation‐dependent R2,aniso*(θ) relaxation rates, the well‐known phenomenological model can be usedR2,aniso*(θ)∝sin4θ for the HCFM.Classically,itten as lnS(TE)=lTE) of the polynomial expansion of the logarithm of a more complex signal expression.However, Equation T2*. The HCFM signal is then assumed to be the sum of the remaining two compartments. Moreover, it is assumed that the static dephasing regime applies. Under these assumptions the HCFM signal simplifies to β1 is orientation‐independent, whereas β2 is orientation‐dependent, following a sin4θ function . To test our hypothesis, we therefore estimated not only the isotropic and anisotropic components in the first‐order coefficients , but also analyzed the second‐order coefficient β2 using a general orientation dependence in Equation kj,iso) and anisotropic contributions  to both first‐ and second‐order coefficients kj=α1,β1,β2, in analogy to previous studies.We derived a quadratic signal model inspired by the second‐order expansion of the signal predicted by the HCFM of parallel, hollow cylinders.ifies to lnS(TE)=l33.1θ0=0. However, it was assumed that the fibers in the left OT were also aligned implying that there is no need to model an additional phase offset in Equation π/2 was covered. The sphere was manually oriented according to the markings. The OC was scanned at each orientation using the gradient echo sequence described in the next subsection.For validating the proposed method in ex vivo white matter tissue, the orientation dependence of the GRE signal was assessed in an OC sample from a patient without diagnosis of neurological disease . The OC represents an ideal sample since the axons inside the optic tract (OT) form bundles of parallel fibers with a well‐defined direction θ relative to the main magnetic field. The OC was dissected from a brain provided by the body donation program (see Acknowledgments). The entire procedure of case recruitment, acquisition of the patient's personal data, the protocols and the informed consent forms, performing the autopsy, and handling the autopsy material have been approved by the responsible authorities . Following the standard Brain Bank procedures, the optic chiasm was immersion‐fixed in  in phosphate‐buffered saline (PBS) pH 7.4 with three changes of fixation solution on days 7, 14, and 21. In total, the OC remained in the fixation solution for 78 days. The OC was placed inside an acrylic sphere of 60 mm diameter filled with agarose (1.5% Biozym Plaque Agarose (low melting) in PBS + 0.1% sodium). The sphere was manually prepared with markings for 16 different orientations inside a spherical triangle as shown in Figure 3.2M = 16 echoes at equally spaced echo times TE = 3.4 to 53.5 ms (step size 3.34 ms). Further imaging parameters were: repetition time TR = 100 ms, FoV = 39 × 39 × 39 mm, matrix size 112 × 112 × 112, flip‐angle 23∘ and a bandwidth of 343 s-1/px resulting in 20:59 min total acquisition time for a single orientation of the sample.All MRI was performed at the Max Planck Institute for Human Cognitive and Brain Sciences on a 7T Siemens Magnetom MRI scanner  using a custom 2‐channel transmit/receive mini‐CP coil with a diameter of 60 mm. GRE signal decay was measured using a 3D gradient echo sequence with 3.3θ0=0 image using the 3D slicer software.θl were : 0, 38.7, 49.4, 53.7, 57.3, 59.1, 61.5, 72.6, 83.1, 83.6, 87.7, 88.3, 89.4, and 89.5. In the following the subscript l is suppressed, i.e. θ is used throughout.For estimating the angle between fibers and main magnetic field for each of the of 16 orientations, the gradient echo images corresponding to the first echo time were manually coregistered to the 3.4α1 from the classical model Equation β1,β2 from the proposed second‐order model Equation For analyses two regions‐of‐interest (ROI) were manually segmented in the left and right OT as shown in Figure 3.5t‐test on the residuals of α1 from Equation α1 from Equation α1,β1, and β2. In the first analysis, the relative contributions of the isotropic and anisotropic components of the model parameters were compared. For this comparison, mean values of the model parameters inside the ROIs were calculated. They were then separated into isotropic  and anisotropic  parts  according to the sinusoidal model introduced in Equation P‐values were obtained. In the second analysis, the parameters of both models Equation sin4θ using Matlab's corr function from the statistics toolbox yielding Pearson's ρ and a corresponding P‐value (P < 0.001 was considered significant).First, the left and right ROI were tested for any significant differences using a 4α1, β1, and β2 from Equations α1, which corresponded to the classical R2* clearly showed dependence on θ  of the coefficients 5TE suggested that orientation dependence should only be observed in the second order, while the linear term is expected to be orientation‐independent. Motivated by this prediction, we employed a second‐order polynomial in TE to fit the logarithm of the GRE‐MRI signal, and demonstrated that the coefficient of the first‐order term in TE described the orientation‐independent component of the apparent transverse relaxation rate R2,iso*, and the second‐order coefficient is related to R2,aniso*(θ).In this study, we have introduced a novel method to separate orientation‐dependent and ‐independent contributions to the GRE‐MRI signal decay using only a single GRE experiment. Our method was inspired by the predictions of the biophysical hollow‐cylinder‐fiber model of the GRE signal for short echo times.R2* at multiple sample orientations in the OTs of the ex vivo human OC sample. Mean values of parameters inside the ROIs . This observation was further supported by a correlation analysis of all coefficients α1,β1,β2 to the well‐known sin4θ‐dependence. Only the first‐order coefficient in the second‐order model, β1, showed no significant orientation dependence  were in accordance with previous findings in an ex vivo corpus callosum sample at 7T, Lee et al reported 6.4 ± 0.15 s-1,s-1 averaged over the left and right ROI  than observed in our study in the OC (average over the left and right ROI: 23±1.5s-1). One source for increased R2* could be due to the known R2 increase in aldehyde fixative solutions due to chemical exchange.R2 increase is related to the interaction between water and formaldehyde monomers.Moreover, our results for the magnitude of the anisotropic part of effective transverse relaxation P < 0.001) larger values only for R2,iso* (≈32s-1).In,T2*≈8 ms) is small compared to echo times typically employed in GRE.TE = 3.4 ms) is well within this range, a contribution of the fast‐relaxing water pools also cannot be excluded. Furthermore, it was demonstrated using simulations that apart from static sources of R2*, diffusion‐driven decoherence could lead to a sin4θ orientation dependence in R2.TE ≤ 36.8 ms were used, the results reported in Figure β1,  was below the sensitivity of this experiment.One limiting factor of this experiment is that the HCFM neglects the direct contribution of the myelin compartment. This is justified by observing that the volume fraction of myelin is much smaller than the volume fractions of axonal and extracellular spaces and, furthermore, the relaxation time of myelin T*≈8 ms isR2* is driven by local distortions of the magnetic field, affected by the isotropic and anisotropic bulk susceptibility distribution in the OC, as well as by anisotropic susceptibility resulting from the microscopic structure of the myelin sheaths, and to some extent, by exchange.TE.Another possible source of orientation dependence in the GRE signal is represented by the bulk magnetic susceptibility of the OC.R2* into orientation‐independent and dependent parts will depend on both the SNR and the degree of anisotropy of the susceptibility of the tissue.For in vivo application, it should be noted that the proposed method is only formally applicable in white matter consisting of parallel fibers, since the second‐order time dependence in the proposed signal model originates solely from parallel, hollow cylinders. Most voxels in the brain feature more complex fiber configurations than the parallel fibers assumed here, which will have to be accounted for in a revised model, e.g., by including fiber dispersionR2*. As compared to previous methods that separated R2* into an orientation‐dependent and ‐independent components,R2*, since it will help to reduce the impact of the orientation changes due to gyrifications.In the present study, we have introduced and validated an efficient method for removing the orientation‐dependent part of the GRE‐based FIGURE S1 Definitions of the white matter volume fractions in the HCFM and the g‐ratio FIGURE S2 Schematic of a hollow‐cylinder‐fiber in the static magnetic field of the MR scanner. The vectors n and v denote the direction of the magnetic field B0 of the MR scanner and the principal axis of the fiber, respectivelyClick here for additional data file.


In contrast, NPF reduces the number of CCN at updraft velocities < 0.2 m/s, and causes a direct aerosol radiative forcing of +0.15 W/m2. Hence, while HOM SOA contributes to climate cooling, NPF can result in climate warming over the Boreal forest.Over Boreal regions, monoterpenes emitted from the forest are the main precursors for secondary organic aerosol (SOA) formation and the primary driver of the growth of new aerosol particles to climatically important cloud condensation nuclei (CCN). Autoxidation of monoterpenes leads to rapid formation of Highly Oxygenated organic Molecules (HOM). We have developed the first model with near-explicit representation of atmospheric new particle formation (NPF) and HOM formation. The model can reproduce the observed NPF, HOM gas-phase composition and SOA formation over the Boreal forest. During the spring, HOM SOA formation increases the CCN concentration by ~10 % and causes a direct aerosol radiative forcing of −0.10 W/m Forests emit compounds into the atmosphere that are oxidized into highly oxygenated molecules that serve as precursors for cloud condensation nuclei–a process that impacts the climate, but is poorly represented in models. Here the authors create a new model that accurately depicts highly oxygenated molecule and climate dynamics over Boreal forests. In order for an organic vapour to contribute to the initial growth of new particles it needs to be an extremely low-volatility organic compound (ELVOC) or be very reactive at the particle surface or in the condensed phase6. When VOC react with oxidants, i.e. ozone (O3), hydroxyl radicals (OH) or nitrate radicals (NO3), peroxy radicals (RO2) are formed7. A fraction of these RO2 can autoxidize8 and finally react with other radicals to form either closed shell monomers or dimers9. Based on experimental19 and theoretical studies22 autoxidation can lead to very rapid  formation of highly oxygenated organic molecules (HOM), which are capable of driving initial nanoparticle growth23. HOM are formed efficiently from ozonolysis of monoterpenes with endocyclic double bonds (e.g. α-pinene and limonene) and also by monoterpenes oxidized by OH17. There is also experimental evidence that NO can suppress autoxidation9. However, until now we have been completely lacking a chemically sound but still computationally efficient mechanism that can be used in atmospheric chemistry transport models (CTMs) to simulate the contribution of HOM to the growth of new particles in the atmosphere.Atmospheric aerosol particles affect Earth’s radiation balance by scattering and absorbing solar radiation as well as by acting as cloud condensation nuclei (CCN) and thereby alter the optical properties and lifetime of clouds. The impact of volatile organic compounds (VOC) on the climate is still highly uncertain because of incomplete fundamental understanding of VOC emission rates, the oxidation of VOC and the contribution of the formed oxidation products to aerosol particle formation, particularly the growth of newly formed particles (1–2 nm in diameter) to CCN–9 Pa (~2.5 × 105 molecules cm−3)10. However, both functional group contribution methods25 and quantum chemical calculations indicate that most HOM monomers with ≤10 carbon atoms are not ELVOC6. Here, we define HOM as molecules with at least six oxygen atoms formed from peroxy radical autoxidation of VOC26. Organonitrates, which are formed when RO2 react with nitrogen oxide radicals (NO), can contain 6–7 oxygen atoms without involvement of peroxy radical autoxidation. Thus, in comparisons of modelled and observed total HOM organonitrate (HOM-NO3) concentrations, only species with at least eight oxygen atoms are considered (see Methods for a more detailed motivation).In some earlier publications, the term HOM was used interchangeably with the term ELVOC, inferring saturation vapour pressures below 1027 for production of HOM from monoterpenes and couple it to the Master Chemical Mechanism (MCMv3.3.1)29. PRAM has the potential to become a widely used mechanism for more realistic representations of HOM SOA formation in regional and global scale CTMs. We demonstrate a very good agreement between the modelled and measured gas-phase HOM composition, secondary organic aerosol (SOA) mass concentrations and new particle formation (NPF) over the Boreal forest, and apply the new model to explore the climatic implications of HOM. According to our model simulations both HOM SOA formation and NPF substantial impact the Boreal aerosol-cloud climate system. However, while HOM is contributing to climate cooling by increasing the number of CCN and the magnitude of the direct aerosol radiative forcing, NPF can result in net climate warming by decreasing the direct aerosol radiative forcing and by supressing the cloud droplet number concentrations at low to moderate cloud updraft velocities.In this work we develop the first comprehensive peroxy radical autoxidation mechanism (PRAM)α-pinene oxidation22, but is generalizable to other monoterpenes as well since it takes into account that different monoterpenes have different HOM yields upon oxidation with ozone or OH (see Methods and Supplementary Table 9 (see Methods).The PRAM was constrained based on theoretical and experimental work on 2 and HOM dimer concentrations for a wide range of α-pinene+O3 reaction rates, in the Jülich Plant Atmosphere Chamber (JPAC) , which leads to lower HOM yields at low temperatures. At 270 K, the modelled HOM molar yield from α-pinene ozonolysis is only ~2%, while at 289 K the yield is ~7%, in agreement with the observations from JPAC9 . In the JPAC experiments, however, the fraction of α-pinene reacting with NO3 was always less than 6%  Fig. . PRAM alAC) Fig. . For mosAC9 Fig. . The res32 and simulated SOA formation during an α-pinene ozonolysis experiment with ammonium sulfate (AS) seed particle addition9 (see Methods). According to the model simulations, ~50% of the SOA mass is formed from condensing HOM species ies Fig. .Fig. 2Hip0) estimated with the functional group contribution method SIMPOL24, using the estimated molecular properties assigned in the Supplementary Table p0 in the range 1.4 × 10−4–2.0 × 10−8 Pa. Therefore, their uptake onto the seed particles are at least partly limited by their volatility. According to our model simulations this likely explains why the closed shell HOM dimer fraction decreased when the seed particles were added to the chamber  are within the right order of magnitude in the model.The HOM dimers are most likely ELVOC, as indicated by their pure liquid saturation vapour pressures  in Finland  for the period 15–24 May 2013 (see Methods). Figure 2, closed shell HOM(g) monomers without nitrate functional groups, HOM(g) dimers and closed shell HOM(g) monomers with nitrate functional groups (HOM-NO3) at SMEAR II.To evaluate PRAM for atmospheric conditions we implemented it into the chemistry transport model (ADCHEM)R), the normalized mean bias (NMB) and the fraction of model predictions within a factor of two of the observations (FAC2). The HOM observations at SMEAR II have an estimated measurement uncertainty of approximately a factor of two9. Considering this, the modelled HOM concentrations are generally in good agreement with the observations. For the total and closed shell HOM monomers, the modelled concentrations are within a factor of two from the observations for 93% of the time . These discrepancies may partly occur because the observed RO2 concentrations in Fig. 2 termination reactions, which is manifested when the mechanism is applied for atmospheric conditions, but not during the pure α-pinene ozonolysis experiments in JPAC.The lowest correlation and highest normalized mean bias between the modelled and observed HOM species types are found for the peroxy radicals  and spring 2014 (15 April to 5 May), for a total of 31 days. For this purpose ADCHEM was run as a Lagrangian model along air mass trajectories arriving at SMEAR II with 3 h interval between each trajectory (see Methods).35, present day NPF can almost exclusively be explained by sulfuric acid (H2SO4) clustering with either ammonia (NH3) or organic compounds formed from OH-oxidation of monoterpenes37. In the present work we considered NPF involving sulfuric acid clustering with both ammonia and organic molecules. The NPF through neutral and ion-induced clustering of NH3 and H2SO4 molecules was modelled using the Atmospheric Cluster Dynamics Code (ACDC)38, which was dynamically coupled to the aerosol dynamics model of ADCHEM (see Methods). This is the first time that a module that explicitly simulates time-dependent molecular cluster formation is implemented directly into an atmospheric CTM.According to the latest global CTM simulations, which use state-of-the-art NPF parameterizations from the CLOUD chamber in CERN2SO4–organics pathway, a semi-empirical parameterization was applied (see Methods). This parameterization has been shown to adequately represent the NPF rate of nanoparticles with a diameter of 1.5 nm (J1.5) during real plant emission experiments in the JPAC smog chamber39 and at the rural Boreal forest station Pallas in Northern Finland34.For the sulfuric acid–organics induced NPF we could not use an explicit representation of the cluster formation as the exact participating compounds remain elusive. Therefore, in order to include the possible contribution of the HAs a complement to the control model run (CTRL), where we included all gas-phase chemistry and aerosol dynamics processes, we also performed four sensitivity test runs with: no HOM formation (NoHOM), no new particle formation (NoNPF), no new particle formation and no HOM formation (NoNPF-NoHOM), and only new particle formation via sulfuric acid clustering with ammonia. During spring 2013 the air masses reaching SMEAR II mainly originated from Russia and Eastern Finland, generally spending more than 2 days over the forest upwind SMEAR II. During spring 2014 the air masses mainly originated from the Arctic- and North Atlantic Ocean and spent less time over the forest upwind SMEAR II 3 and H2SO4 contributes to 91% of the total number of new particles formed at SMEAR II respectively. The remaining 9% can be attributed to the NPF of organics with H2SO4.With the CTRL setup, ADCHEM predicts the general trends in the observed particle number size distributions at SMEAR II with reasonable accuracy Fig.  and the 3-H2SO4 clusters in the mornings on 16 and 23 April, followed by several days of apparent particle growth and increasing organic aerosol (OA) mass at SMEAR II  . In order for particles to scatter light efficiently, they must have a diameter approximately equal to or larger than the wavelength of light. Therefore, mainly particles with diameters >200 nm scatter sunlight back into space and cause a negative RFARI. The RFARI caused by NPF and HOM SOA formation, during clear sky conditions (no clouds), were estimated using the radiative transfer module implemented in ADCHEM44 (see Methods).Apart from the indirect radiative forcing induced by the altered cloud droplet number concentrations and the optical properties of the clouds, NPF and HOM SOA formation can also influence the Radiative Forcing due to Aerosol–Radiation Interactions  are 1727 and 1629 cm−3, respectively. Without NPF PN25–1000 nm  = 533 cm−3 and without HOM formation PN25–1000 nm = 1308 cm−3.Table w) >1 m s−1  ≥ 0.66% , NPF reduces the number of CCN  where HOM increases the CCN concentrations by 8–12%  the condensation of HOM contributes to < 3% of the modelled CCN number concentration. The results from our detailed process-based model simulations are qualitatively consistent with the global model simulations performed by Jokinen et al.10, which concluded that ELVOC (i.e. HOM according to the definition of that study) have a very minor impact on the CCN at SSmax = 0.2% but clearly increase the number of CCN at SSmax = 1% over the Boreal forest.In contrast to NPF, HOM SOA formation increases the CCN concentrations for all updraft velocities. The largest impact is found at updraft velocities ≥0.3 m s12% Fig. . At w ≤ ARI becomes negative or positive. Figure ARI, with an average RFARI of −0.10;W m−2. NPF, on the other hand, almost always leads to positive RFARI, with an average value of +0.15 W m−2. The reason is that NPF indirectly causes a reduction in the number concentration of particles larger than ~170 nm in dry particle diameter  W m−2 (ref. 47).According to our model simulations the NPF at, and upwind from, SMEAR II can largely be explained by sulfuric acid clustering with ammonia. Sulfuric acid is mainly originating from anthropogenic SO19. In this work, we have developed and used the near explicit PRAM to provide a complete closure between the modelled and observed HOM concentrations at the Boreal forest station SMEAR II. This fundamental process knowledge is required to efficiently improve the representation of HOM SOA formation in atmospheric models. However, for most large-scale atmospheric model applications, PRAM and the SOA formation scheme used in this work may need to be reduced (simplified). Still, it is important that any reduced mechanism should be able to represent the non-linear SOA yield effects caused by different O3, OH, RO2, NOx, and temperature conditions. If the gas-phase chemistry mechanism (e.g. PRAM) can fulfil these requirements, the particle growth and/or SOA mass formation may be successfully parameterized by lumping the formed closed shell species into a volatility basis set framework34. This can reduce the number of condensable compounds from several hundreds to less than ten. PRAM explicitly treats RO2 + RO2 reactions between 94 RO2 from the MCMv3.3.1 chemistry and 17 PRAM specific RO2 7 reacts with the RO2 in PRAM using single collective rate coefficients. If the formed HOM dimers are only represented by two dimers, one for the HOM formed from monoterpene ozonolysis and one for dimers formed from OH-oxidation of monoterpenes the total number of reaction in PRAM is reduced from 1773 to 192 and the total number of species from 208 to 89  concentrations and SOA mass formation, both during smog chamber experiments and in the atmosphere. During typical spring-time conditions HOM SOA contributes to 18% of the modelled submicron particle mass at the SMEAR II station in Finland.w) in the range 0.3–5 m s−1, which corresponds to water vapour supersaturations between ~0.28% and ~0.84%. Furthermore, we estimate that the HOM SOA contributes to an average direct aerosol radiative forcing of −0.10  W m−2. Thus, biogenic HOM SOA formation most likely contributes to climate cooling over the Boreal forest, both with and without the presence of clouds.We show that the combination of NPF and particle growth by biogenic HOM SOA has a profound but complex impact on the aerosol-cloud-climate system over the Boreal forest. In spring the HOM SOA increases the number of CCN with ~10% at cloud updraft velocities  it will lead to optically thicker clouds and climate cooling. The combined effect of HOM formation and NPF over the Boreal forest is a substantial increase in the number concentration of CCN at cloud updraft velocities >0.2 m s−1. However, at clear sky conditions the negative radiative forcing from HOM SOA formation is offset by the positive radiative forcing caused by the NPF.The net climate impact (i.e. cooling or warming) caused by NPF over the Boreal forest is more complex, and varies depending on the amount and type of clouds. Our model simulations reveal that the observed NPF can to a large extent, be explained by sulfuric acid clustering with ammonia. In spring the NPF upwind of SMEAR II contributes to ≥50% of the number of CCN at cloud updraft velocities ≥3 m sWe demonstrate that the comprehensive PRAM mechanism may be substantially reduced. The reduced PRAM version can likely be used for realistic representations of HOM SOA formation in regional and global scale CTMs. However, before PRAM is used for large-scale CTM applications we recommend that the mechanism is evaluated also for other regions, e.g., over tropical forests and urban areas.27 for monoterpenes reacting with O3 or OH and coupled it to the Master Chemical Mechanism version 3.3.1 (MCMv3.3.1) using the Kinetic PreProcessor (KPP)48. Below we give a general description of the theory behind PRAM. In the 2 that are formed when monoterpenes are oxidized by O3 and OH in PRAM (Supplementary Table We have developed a PRAM2) autoxidation products (including HOM) formed from ozonolysis and OH-oxidation of monoterpenes. PRAM has been developed based on experimental and theoretical studies of α-pinene oxidized by O3 and OH22. However, for the atmospheric model simulations presented in this work we use PRAM as a general mechanism describing the autoxidation and formation of HOM from four different monoterpenes , by assigning species specific molar yields of formation of the first RO2 that initiates the autoxidation chain . According to quantum chemical calculations, the activation energies for autoxidation of different RO2 from α-pinene are between 22 and 29 kcal mol−1 (ref. 14). This leads to reduced autoxidation rates at low temperatures. PRAM presently uses temperature-dependent autoxidation rates corresponding to an activation energy barrier of 24 kcal mol−1 for all autoxidation reactions  and O−1 ref. 1. This le2 react with NO, HO2, or other peroxy radicals . When two peroxy radicals react with each other, the product(s) will either be alkoxy radicals (RO) (R6a), closed-shell monomers  or a dimer (R6d).2 + NO and RO2 + HO2 reactions, with values identical to MCMv3.3.1  replacing the peroxy radical group (–OO∙) (R5). For the RO2 + NO reactions the branching ratio between the channel forming organonitrate HOM (R2a) and the channel forming an alkoxy radical and NO2 (R2b) varies depending on the RO2 species. The RO formed from (R2b and R6a) is either rapidly isomerizing to a hydroxyl-substituted alkyl radical that further react with O2 and form a new RO2 species (R3a), form a closed-shell HOM monomer with an additional carbonyl group (R3b), or decompose and form more volatile species (R4)49. In the mechanism the fragmentation products from R4 are represented by the MCM species C717O2 (an RO2) and CH3COCH3 (acetone). PRAM assumes that all RO2 + RO2 reactions (R6) exclusively occur between RO2 formed from the PRAM autoxidation mechanism (R1) and in total 94 RO2 species formed in the MCMv3.3.1 chemical mechanism. These are all RO2 with 10, 9, or 8 carbon atoms originating from oxidation of α-pinene, β-pinene, and limonene in MCM.The autoxidation can be terminated by bimolecular reactions where the formed ROα-pinene is oxidized by O3 one of the two ring structures is broken but a cyclobutyl ring is left intact in the RO2 isomers (C10H15O4) that are formed. According to quantum chemical calculations by Kurtén et al.22 the cyclobutyl ring inhibits multiple autoxidation steps and prevents the first intramolecular H-shifts reactions rates to exceed 0.3 s−1 at 298 K. In PRAM we therefore assigned a rate constants of 0.3 s−1 at 298 K for the first H-shift reaction (R11 in 29) when the RO2 isomer, with the MCM name C107O2, react with NO, NO3 or other RO2 and form an alkoxy radical C107O that can isomerize and react with O2 and form a C10H15O5 peroxy radical named C108O2. In PRAM we therefore included the possibility of such additional HOM formation pathway for α-pinene, which is initiated by the reaction between C107O2 and other RO2  and a second slower pathway, e.g. that requires alkoxy radical formation via bimolecular reactions, is supported by the fact that the HOM yields reported from smog chamber experiments with 45 min reaction time9 are a factor of ~2 higher than the yields from flow tube experiments with 40 s reaction time10.When n R11 in . Kurtén s C10H15O that are2 + RO2 reactions range from 10−11 cm3 molecule−1 s−1 for acyl peroxy radicals to 6.7 × 10−15 cm3 molecule−1 s−1 for tertiary carbon peroxy radicals29. These rate coefficients are based on measured reaction rates of generally less oxygenated and smaller RO2 molecules than the RO2 in PRAM. PRAM uses RO2 + RO2 reaction rates leading to closed shell monomers in the range of 5 × 10−12 cm3 molecule−1 s−1 to 10−11 cm3 molecule−1 s−1 and RO2 + RO2 reaction rates leading to closed shell HOM dimers between 10−13 cm3 molecule−1 s−1 to 5 × 10−12 cm3 molecule−1 s−1, with the lowest values applied to the reactions involving the least oxygenated peroxy radicals and the highest values for the most oxygenated peroxy radicals ) in PRAM up or down with a factor of two. With k(RO2 +  RO2) × 0.5, the lifetime and concentration of RO2 increases. At an atmospheric relevant α-pinene + O3 reaction rate of 0.3 pptv s−1 and k(RO2 + RO2) × 0.5 the HOM RO2 concentrations become 60% higher, while with k(RO2 + RO2) × 2 the modelled HOM RO2 become 40% lower. At low α-pinene + O3 reaction rates the modelled closed shell HOM formation is limited by the formation of highly oxygenated RO2 via autoxidation and by the bimolecular termination reactions that lead to closed shell products. At conditions with high α-pinene + O3 reaction rates (high absolute RO2 concentrations) the closed shell HOM formation are primarely limited by the formation of the highly oxygenated RO2 and not by the bimolecular termination reactions. Instead, RO2 + RO2 reactions can cause termination of the autoxidation reaction chain before many of the RO2 become highly oxygenated. Thus, in the low RO2 concentration regime, higher k(RO2 + RO2) results in higher closed shell HOM concentrations, while in the high RO2 concentration regime, higher k(RO2 + RO2) results in lower closed shell HOM concentrations. This is why the modelled closed shell HOM concentrations (monomers and dimers) are slightly higher at α-pinene + O3 reaction rates <0.4 pptv s−1 but lower at α-pinene + O3 reaction rates >0.4 pptv s−1 in the k(RO2 + RO2) × 2 run compared to default PRAM setup (k(RO2 + RO2) × 1). The opposite trends can be seen for the k(RO2 + RO2) × 0.5 simulation. The HOM observations in JPAC indicate that the absolute closed shell HOM monomer and dimer yields decreases somewhat when the α-pinene + O3 reaction rates increases in the chamber. These results are consistent with the PRAM model simulations which uses k(RO2 + RO2) × 2. However, at atmospheric relevant α-pinene + O3 reaction rates <0.5 pptv s−1 the modelled closed shell HOM concentrations are relatively insensitive to the exact values of k(RO2 + RO2) . This activation energy is within the range of values suggested by Rissanen et al.14, which calculated EH-shift in the range of 90–120 kJ for different RO2 isomers formed from ozonolysis of α-pinene. The H-shift activation energy used as default in PRAM is higher than the EH-shift measured and calculated for peroxy radicals originating from several other VOCs, which generally are in the range 40–80 kJ51. However, Quéléver et al.52 recently showed that the observed HOM yields during α-pinene ozonolysis experiments in the AURA chamber was about 50 times lower at 273 K compared to 293 K. The AURA experiments were performed using an initial α-pinene and O3 concentrations of 50 and 100 ppb, respectively. This corresponds to an α-pinene + O3 reaction rate of ~10 pptv s−1. The results from Quéléver et al. indicate that the autoxidation reaction rates of RO2 formed from α-pinene ozonolysis must slow down considerably between 293 and 273 K. This, together with the presumably high absolute RO2 in the AURA experiments (i.e. short lifetime of RO2 with respect to RO2 + RO2 reactions) may at least partly explain the observed drastic drop in the HOM yield between 293 and 273 K52. With the default EH-shift of 100 kJ in PRAM, the modelled HOM molar yield at an α-pinene + O3 reaction rate of ~1 pptv s−1 increases from 2.3% to 9.0% between 270 and 310 K, while with EH-shift = 50 kJ the yield range between 4.4% and 8.3% and with EH-shift = 150 kJ the HOM molar yields range between 1.6% and 9.0% . Supplementary Fig. 2 + RO2 reaction rates and the H-shift activation energies. The small differences between the model sensitivity tests with different values of EH-shift is related to that the average surface temperatures at SMEAR II were 287.9 K for the simulated period.In Supplementary Fig. 2 that form HOM dimers  and the trajectory model for Aerosol Dynamics, gas and particle phase CHEMistry and radiative transfer (ADCHEM34). ADCHAM and ADCHEM use identical aerosol dynamics and gas-phase chemistry codes. They take into account Brownian coagulation and the condensation, dissolution, and evaporation of H2SO4, NH3, HNO3, and all organic oxidation products from Master Chemical Mechanism version 3.3.1 (MCM v.3.3.1) and from the PRAM mechanism (Supplementary Table p0) less than 10−2 Pa . p0 were estimated with the functional group contribution method SIMPOL24. For the peroxy radical autoxidation products the molecule properties provided in Supplementary Table p0.In this work we use the Aerosol Dynamics gas- and particle phase chemistry model for laboratory CHAMber studies ADCHAM3 and the k,iwall) for the JPAC smog chamber simulations were estimated based the experimentally derived HOM wall losses of HOM monomers9. HOM molecules with a molecular formula C10H16O8 have a first-order wall loss rate of 1/75 s−1 in JPAC9. In the model the individual HOM wall loss rates were estimated by multiplying the experimentally derived wall loss rate for C10H16O8 with the ratio between the molecular diffusion coefficient for C10H16O8 and the molecular diffusion coefficients for the other molecules (Di) 56. For JPAC where the walls are made out of glass, the release of semi-volatile non-reactive VOC back to the gas-phase from the walls Cwall is smaller than what generally is used for Teflon smog chamber walls. With a Cwall of 5 μmol m−3 ADCHAM is able to reproduce the observed SOA mass formation in JPAC . In and below cloud scavenging of aerosol particles and in-cloud sulfate aerosol formation and scavenging of SO2, H2O2, NH3, HNO3 and HCHO were also considered, analogous to Roldin et al.33. However, the model did not consider any cloud droplet aqueous phase chemistry or in- and below cloud scavenging of other organic molecules. The particle number size distributions are represented with 100 fixed size bins between 1.07 nm and 2.5 µm in dry diameter.In the present study we used ADCHEM as a one-dimensional column model consisting of 40 vertical layers, logarithmically spaced, with intervals increasing from 3 m at the surface to 100 m at the top of the model domain that extends up to 2500 m a. g. l. The main model time step was 30 s. The atmospheric diffusion equation is solved in the vertical direction using diffusion coefficients calculated with a slightly modified Grisogono scheme3-H2SO4 was modelled using the ACDC38, which solves the time evolution of a population of molecular clusters considering all possible collision and evaporation processes between the clusters and vapour molecules (in this case NH3 and H2SO4), as well as ionization and recombination by primary gas-phase ions, and cluster scavenging by larger aerosol particles. The NPF rate is obtained as the flux of stable clusters growing out of the size range simulated by ACDC.The NPF via NH2SO4 and NH3 vapours, the temperature, and the cluster scavenging rate obtained from the particle distribution simulated within ADCHEM. When the module is called, the ambient conditions are updated, and the time evolution of the cluster distribution is solved for the given time step. As output, the module gives the number of >1.07 nm particles that grew out of the ACDC size range during the simulated time interval. These newly-formed nanoparticles are assumed to behave like aerosol particles and are introduced into ADCHEM, which simulates the consecutive condensation growth, evaporation, and losses by coagulation and deposition.ACDC was implemented as an explicit molecular cluster dynamics module, in which the time-dependent cluster concentrations are monitored and updated at every time step. The ACDC module was combined to ADCHEM via an interface that takes as input the concentrations of H2SO4 and 5 NH3 molecules, with an approximate diameter of 1.07 nm. The rate constants related to cluster growth and evaporation were calculated as described by Olenius et al.38, using previously published quantum chemical data, computed at the B3LYP/CBSB7//RICC2/aug-cc-pV(T+d)Z level of theory, to calculate the cluster evaporation rates. Both electrically neutral and negatively and positively charged clusters were included, with ionization and recombination of molecules and clusters occurring through collisions with generic gas-phase ions O2− and H3O+38. The production rate of the generic ions was calculated as the sum of the ionization rate due to galactic cosmic rays and ionization caused by the decay of radon. The ionization rate due galactic cosmic was set to 1.7 cm−3 s−130. The radon concentration and radon induced ionization was modelled using the radon emission map and mean ionization rate formula from Zang et al.58. In average the modelled ion production rate was 3 cm−3 s−1 in the surface layer at the SMEAR II station. 2SO4 vapour, given by ADCHEM, according to the power-law formula by Lehtinen et al.59. In this formula, the parameter m was set to −1.6, corresponding to typical boundary layer conditions.The simulated clusters consist of up to 5 H2SO4 cluster formation was considered in ADCHEM using a semi-empirical parameterization  and entropy change (ΔS) for the critical cluster formation 41. The individual monoterpene emissions were estimated based on the measurements from 40 Scots pine trees around SMEAR II, which on average emit 43.7% α-pinene, 39.6% carene, 9% β-pinene, and 2.3% limonene62. In ADCHEM the three lowermost model layers at 0–3, 3–9, and 9–18 m are within the forest canopy at SMEAR II, and MEGAN simulates the BVOC emissions in each of these layers.The emissions of α-pinene, β-pinene, and limonene. However, since almost 40% of the monoterpenes emitted at SMEAR II is carene we include the initial oxidation reactions between carene and OH, O3 or NO3 in the gas-phase chemistry mechanism, and assume that the formed oxidation products are identical to the products formed from the α-pinene oxidation in MCMv3.3.1. This also means that we assume that carene forms HOM with the same yield and composition as α-pinene. Like α-pinene, carene has one endocyclic double bond and is therefore expected to have high HOM formation yields. However, future research is needed to obtain more detailed chemical information on carene processes.Of all monoterpenes MCMv3.3.1 only includes chemical mechanisms for 63 and a sea-to-air transfer velocity parameterization64. Anthropogenic emissions of NOx, SO2, CO, NH3, VOC with a resolution of 0.1° × 0.1° were retrieved from EMEP  database 65. Supplementary Table 66. Primary particle emission from ship traffic was parameterized based on the gas-phase emission of SO2 by using a conversion factor of 8.33 × 1014 particles/(g SO2)67. The size distribution of the primary particles from ships was estimated based on a study by Jonsson et al.68. Primary particle emissions of wind-generated marine aerosols were also included69. The model was initialized with an aerosol particle number concentration of 100 cm−3 in each vertical layer, with a unimodal lognormal particle number size distribution having a geometric mean diameter of 120 nm and a geometric standard deviation of 2. Ninety per cent and 10% of the dry particle volume in each size bin was assumed to be composed of non-volatile organic material and AS respectively.Gas-phase emission of dimethyl sulfide (DMS) in the marine boundary layer was estimated based on monthly mean seawater concentrations43 to calculate the number of activated cloud droplets and different predefine updraft velocities at SMEAR II. For the calculations we assume that all organic compounds (including HOM) are fully water soluble at the point of cloud droplet activation. As input we used the modelled aerosol particle properties in the surface layer from the CTRL, NoNPF and NoHOM runs from the periods 15–24 May 2013 and 15 April to 5 May 2014. The air parcels were assumed to start at the surface (0 m) with an initial relative humidity (RH) of 95% and rise to an altitude of 500 m with fixed predefined updraft velocities of 0.01, 0.02, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.5, 2.0, 3.0, 5.0 or 10 m s−1. With this setup the air gets supersaturated (RH > 100%) with respect to water vapour at ~115 m altitude and a fraction of the particles (the CCN) gets activated into cloud droplets. Depending on the updraft velocity the maximum cloud supersaturation (SSmax) is reached within a few metres to a few tens of metres above the cloud base . The RFARI caused by NPF and HOM SOA formation were estimated by calculating the difference in the modelled top of the atmosphere net downward shortwave radiation between the CTRL run and the NoNPF and NoHOM runs respectively.In order to estimate the direct aerosol radiative forcing at SMEAR II, caused by the NPF and HOM SOA formation upwind the station, we used the radiative transfer scheme implemented into ADCHEM2, O3, CO and total monoterpene at eight different altitudes between 4.2 and 125 m above ground level (a.g.l.), SO2 at 16.8 m and particle number size distributions for particles between 2.8 and 1000 nm in diameter. The particle number size distribution was assumed to be constant in the whole model domain (0–2500 m a.g.l). The modelled total monoterpene concentrations within the lowermost 125 m were scaled for each model time step in order to match the observed total monoterpene concentrations at SMEAR II. All other trace gas concentrations as well as the particle chemical composition and hygroscopic growth were calculated in order to provide the most realistic condensation losses of HOM and other condensable compounds.ADCHEM was implemented for simulations of aerosol particle and trace gas concentrations during 10 days in 2013 (15–24 May) and 21 days in 2014 (15 April to 5 May) at the SMEAR II field station in Finland . For the 2013 period, ADCHEM was first operated as a stationary column model at SMEAR II, with the purpose to evaluate the PRAM mechanism. ADCHEM was continuously reading in the observed concentrations of NO31. Unfortunately, only a few NPF events could be observed at SMEAR II during spring 2013. Thus, in order to be able to evaluate the HOM contribution to the growth of new particles of ~1 nm in diameter into the CCN size range, we also applied ADCHEM for a second period in spring 2014. During this period, NPF events with consecutive growth could be observed at more than 50% of the days ays Fig. . Both fo72, the Henry’s law coefficients (Hi) of the HOM species were estimated based on their pure liquid saturation vapour pressures  and their activity coefficients in an infinitesimally dilute aqueous solution (Eq. H is larger than ~108 M atm−1 the surface resistance become negligible compared to the aerodynamic- and quasilaminar resistances and the dry deposition is only limited by the atmospheric turbulence close to the surfaces. The activity coefficients (γi) were derived with the AIMOFAC model73, which is implemented into ADCHAM32. Hi from SIMPOL-AIOMFAC with the Hi computed using the BP-TZVPD-FINE parameterization in COSMOTherm74 76. The COSMO-calculation yields input files describing the screening charge surface (known as the σ-surface) of the molecule, which is converted into a distribution function (known as the σ-profile). In somewhat simplified terms, the σ-profile corresponds to the relative amount of the molecule’s surface with a certain polarity. The intermolecular electrostatic, hydrogen bonding, and van der Waals interactions between surface segments with different σ values (polarities) can then be computed within the COSMOTherm programme using various parameterizations, of which BP-TZVPD-FINE is the most advanced . Once the intra- and intermolecular interactions are thus described, the chemical potential of the HOM molecules in a water solution, and finally the Henry’s law coefficients, can be computed. Molecular conformations were generated using the systematic conformational search algorithm of the Spartan 14 program77 and the MMFF force-field. This yielded a few tens of conformers for C10H16O6iso2 and C10H16O6iso3, and about 1300 conformers for C10H16O6iso1. COSMO input files were then generated for all conformers of all three structures. (The input files for H2O are available in the COSMOTherm library.) The COSMOconf program (part of the same programme suite as COSMOTherm) was subsequently used to detect unique conformers , and to map the geometries of the conformers in the gas phase and in the solvent to ensure that each conformer in the solvent has a corresponding conformer in the gas phase. For the C10H16O6iso1 case, the 100 lowest-energy conformers were selected .In order to be able to calculate the dry deposition losses of HOM with the dry deposition resistance model in ADCHEMtion Eq. . In ADCHH from the two methods is less than one order of magnitude. However, for C10H16O6iso1 H is more than two orders of magnitude larger according to SIMPOL-AIMOFAC compared to the value derived with COSMOTherm using all 100 conformers. The large discrepancy between COSMOTherm and SIMPOL+AIMOFAC predictions for C10H16O6iso1 may be related to an overestimation of the strength of the intramolecular H-bonds of the molecule (relative to the intermolecular H-bonds with water) by COSMOTherm. A similar effect has been noted concerning HOM vapour pressures78. The two other molecules could be less affected by this due to steric constraints of the ring structures preventing or at least weakening some of the intramolecular H-bonding interactions. We tested this hypothesis by computing H values for all three species using only conformers with a minimal number of H-bonds . This approach was recently observed to improve agreement with experiments for saturation vapour pressures of two HOM-like isoprene oxidation products78. Using only conformers with a minimal number of H-bonds led to a significant increase in H for all three species, with the largest increases (around a factor of 300) surprisingly observed for C10H16O6iso2 and C10H18O6. This indicates that contrary to our hypothesis, intramolecular H-bonding interactions are, according to COSMOTherm, even stronger in these species than in C10H16O6iso1. As expected, the approach improved agreement with SIMPOL+AIMOFAC for C10H16O6iso1, though the agreement decreased for the other two cases. After correcting for the potential overestimation of intramolecular H-bonding, the COSMOTherm−predicted H values are well above 109 M atm−1 for all three studied species. Therefore, the approximately two order of magnitude uncertainty in the calculated H  is not crucial for the dry deposition losses of C10H16O6iso1 and most other peroxy radical autoxidation products listed in Supplementary Table For C10H16O6iso2 and C10H18O6 the difference between the 9. An identical CI-APi-TOF, described by Yan et al.31 were also used at SMEAR II during spring 2013 to measure the HOM and H2SO4 concentrations at ~2 m above ground level. The measured organonitrate concentration was represented by the sum of the species C10H15O5−12NO3 and the measured RO2 concentration was represented by the sum of the species C10H15O6−13, C9H13O8, and C9H13O10. We decided to not consider the observed organonitrates with six or seven oxygen atoms because a fraction of them may not be formed via peroxy radical autoxidation. For example, in MCM the compounds NC101O2 and NC102O2 with molecular formulas C10H15NO6 and C10H15NO7 are formed when α-pinene is reacting with NO3 followed by a second oxidation step involving OH. During the α-pinene + NOx ozonolysis experiments in JPAC, with low levels of NO3 radicals, C10H15NO6 and C10H15NO7 accounted for only ~3% of the total observed organonitrate concentrations in the gas-phase. However at SMEAR II they on average account for 26% of the observed total organonitrate concentrations. This illustrates that there are other mechanism than peroxy radical autoxidation that can lead to C10H15NO6 and C10H15NO7. Therefore we decided to only compare the modelled and measured HOM-NO3 with eight or more oxygen atoms, which most likely almost exclusively are formed via peroxy radical autoxidation.The HOM concentrations in the JPAC chamber were measured with a nitrate-ion-based chemical ionization atmospheric pressure-interface time-of-flight mass spectrometer (CI-APi-TOF)3− included) and the HOM dimers are all compounds with even mass in the range 452–590 u, except for some contamination peaks that were subtracted from the sum.The measured HOM monomers were calculated as all the compounds with even mass in the mass range of 290–450 u  ionization. General principles of AMS measurements, calibrations, modes of operation and data processing have been described comprehensively in previous work82.During spring 2013 the particle chemical composition at SMEAR II was measured with an ACSM83). For mass concentration calculations, the default relative ionization efficiency (RIE) values 1.1, 1.2, 1.3 and 1.4 for nitrate, sulfate, chloride and organics were applied. The RIE for ammonium was 2.65, as determined from the mass-based ionization efficiency calibration. After a comparison to the volume concentration from differential mobility particle sizer measurement, a particle collection efficiency factor of 0.85 was applied to account for the particle losses in the aerodynamic transmission lens and vaporizer.The AMS data were processed using Tof-AMS Data Analysis Toolkit SQUIRREL version 1.57H and PIKA version 1.16H in Igor Pro software . In addition, an improved-ambient elemental analysis was processed by using APES V1.06 (ref. 84.The monoterpene concentrations at SMEAR II were measured with proton transfer reaction mass spectrometry (PTR-MS) at eight different altitudes  according to the procedure described by Taipale et al.ARI values were calculated using the “mean” built in function in MATLAB® R2017b. The Pearson’s correlation coefficients (R) in Table NMB) between the modelled (M) and observed (O) HOM(g) concentrations in Table The mean diurnal HOM concentration trends in Fig. Supplementary InformationPeer Review File


The data in this paper are related to the research article entitled “Assessing the percentage of cork that a stopper should have from a mechanical perspective” . This data article contains data on the mechanical properties of different types of wine stoppers: 18 types of micro-agglomerated stoppers, three types of natural stoppers, and one type of co-extruded synthetic closure. Mechanical properties were evaluated with different analysis: Compression test for the maximum radial compression force, the young’s moduli and the diameter recovery, relaxation test for the relaxation force and the extraction test for the displacement force. Specifications tableValue of the data•Data show the mechanical properties of stoppers, which are valuable for assessing sealing performance of wine stoppers, through different tests that simulate the bottling process, the beginning of the sealing period and the extraction process.•These data can be used to compare the mechanical performance of different types of wine stoppers micro-agglomerated, natural and synthetic.•These data are suitable to support decision-making of producers and consumers in choosing suitable wine stoppers.1In the data, 2−3  and the densities 230, 290 y 350 kg·mOnce acclimatized (20 °C and 65% of relative humidity), stoppers were weighed and measured  using Mi2.1The maximum radial compression force  was measured using a Zwick universal testing machine (Zwick GmbH & Co.) with a 20,000 N load cell. A stress-strain curve was drawn from the data recorded and Young׳s modulus was calculated for each of the stoppers tested as the slope of the linear elastic portion of the stress-strain curve between 1% and 2% of the strain Diameter recovery was measured immediately after the compression test and again after 15 min, 1 h and 24 h after the test using a Mitutoyo ID-F150 digital vernier callipers.2.2As already reported in Sánchez González 2.3The displacement force 2.4All tests were carried out using the SAS software version 9.4 as already reported in Sánchez González


Inhomogeneous magnetization transfer (ihMT) is an emerging form of MRI contrast that may offer high specificity for myelinated tissue. Existing ihMT and pulsed MT sequences often use separate radiofrequency pulses for saturation and signal excitation. This study investigates the use of nonselective multiband radiofrequency pulses for simultaneous off‐resonance saturation and on‐resonance excitation specifically for generation of ihMT contrast within rapid steady‐state pulse sequences.A matrix‐based signal modeling approach was developed and applied for both balanced steady state free precession and spoiled gradient echo sequences, accounting specifically for multiband pulses. Phantom experiments were performed using a combination of balanced steady state free precession and spoiled gradient echo sequences, and compared with model fits. A human brain imaging exam was performed using balanced steady state free precession sequences to demonstrate the achieved contrast.A simple signal model derived assuming instantaneous radiofrequency pulses was shown to agree well with full integration of the governing equations and provided fits to phantom data for materials with strong ihMT contrast . In vivo ihMT ratio images showed the expected white matter contrast that has been seen by other ihMT investigations, and the observed ihMT ratios corresponded well with predictions.ihMT contrast can be generated by integrating multiband radiofrequency pulses directly into both spoiled gradient echo and balanced steady state free precession sequences, and the presented signal modeling approach can be used to understand the acquired signals. Existing work has focused on a preparation‐based paradigm in which saturation pulses are interleaved with readout periods for measurement, as illustrated by Figure The ihMT effect results in different observable MT characteristics when single or dual‐frequency off‐resonance irradiation are used during imaging. Novel pulse sequences incorporating either multiband or rapidly alternating single‐frequency saturation pulses have been proposed to generate ihMT weighted imagesIn this work, we explore the use of the proposed multiband sequence for generation of ihMT contrast and formulate a matrix‐based signal model for ihMT that may be used to directly calculate steady‐state signals for spoiled gradient echo (SPGR) and balanced steady state free precession (bSSFP) sequences when dipolar terms are present and multiband pulses are used. We investigate the validity of this matrix‐based model, compare predictions with phantom experiments, and present in vivo ihMT ratio images formed using the proposed sequences.22.1f and s, respectively. In this model, the (Zeeman) magnetization of the free water pool [MxfMyfMzf] interacts with (Zeeman) magnetization of the semisolid pool, written MZs. The semisolid pool has a very short transverse relaxation time (T2s≈10μs), so transverse components are typically excluded. The ihMT effect arises in some semisolids because of the presence of a dipolar interaction term (D) as well as Zeeman term (Z) in the quantum Hamiltonian. According to Provotorov theory as presented by Goldman,MZs and MDs, respectively; here we use the formalism adopted by Lee et alM=MxfMyfMzfMZsMDsT. The model has been further updated by Varma et alM=MxfMyfMzfMZs1MZs2MDs2T whose temporal evolution is governed by:The commonly used “binary spin bath” model for magnetization transfer effects divides tissue magnetization between free water and semisolids, labeled with superscripts time T2s≈0μs, so ttime T2s≈0μs, so tΛ and C describe evolution in the absence of RF:R1,2f are the free water relaxation rates (inverse of relaxation times); R1Zs and R1Ds are semisolid Zeeman and dipolar relaxation rates, respectively; Δω is the off‐resonance frequency; k is the exchange rate constant between free water and semisolid pools; and M0f and M0s are thermal equilibrium magnetizations for the free and semisolid pools, respectively. Note that, in this article, k represents the intrinsic exchange rate as opposed to a directional rate  as sometimes used in the literature .k and R1Zs are the same for pools s1 and s2, and use this formulation in this article. A more general version is given in the Appendix. Pools s1 and s2 occupy fractions 1-δ and δ, respectively, of the total semisolid compartment M0s and we adopt the convention M0f+M0s=1. Figure Matrices ce of RF:Λ=-R2fΔω0Δj is the (angular) frequency offset of the jth band and b{Δj;t} is the time domain pulse waveform associated with component frequency Δj. It then follows that matrix Ω describing interactions due to RF pulses may be written as:To handle multiband pulses, we explicitly decompose them into contributions from separate frequency bands:Ωfree is simply the Bloch equation for the free pool. For the multiband pulses used in this work, only the on‐resonance component b{0;t} need be considered. Ωsemi describes absorption by the semisolid pools and is explicitly written as a sum over frequency bands as suggested by GoldmanWj=πγ2b{Δj}2gΔj′,T2s, where gΔ,T2s is the absorption lineshape of the semisolid and T2s is its transverse relaxation time. The term Δj′≡Δj-Δω accounts for off‐resonance effects on the local absorption response; for simplicity, these have been neglected in this work and we have instead assumed that Δj′≈Δj. The term ωloc characterizes the strength of local field fluctuations, which relate to dipolar interactions; this may be derived from the second moment of the lineshape.Ωsemi is exactly as commonly used to describe “classic” MT effects; (ii) exchange between MZs2 and MDs2 is purely RF driven, while exchange between Mzf and MZs1,2 occurs continuously; (iii) coupling terms in Ωsemi are linear in Δj so equal off‐resonance RF power applied simultaneously at ±Δ (or at Δ=0) eliminates mixing between Zeeman and Dipolar components of s2 (this is the ihMT effect); (iv) MDs2 relaxes to a thermal equilibrium value of zero.There are a few properties to note for sequence modeling: (i) the first element of 2.2M˙=⟨Ω⟩M where ⟨Ω⟩ is the time average of Ω over pulse duration τ, with solution Mt+τ=RM(t) where R=exp⟨Ω⟩τ. The matrix exponential preserves the block diagonal form of Ω such that R consists of the normal rotation matrix for the free water in the upper left block, and a saturation matrix for the semisolid pool according to the mean square B1 of the pulse in the lower right block; this is exactly the approach taken for modeling of “classic” MT in rapid sequences.M˙=ΛM+C, which has the general solution Mt+TR=SMt+S-1Λ-1C for time period TR, where S=expΛTR. It is hence possible to write the following signal expressions for SPGR:The system of differential equations described above, referred to here as the Bloch‐McConnell‐Provotorov (BMP) equations, allow for MRI signal modeling of this system with arbitrary pulse sequences. Here, we consider rapid gradient echo sequences and make the common approximation that RF pulses act instantaneously. Under this approximation, the evolution during each pulse is Φ accounts for spoiling or phase cycling in each case. For SPGR, we assume perfect spoiling of transverse magnetization and so Φ=diag[001111] is used to remove transverse components after each TR; for bSSFP, we assume π phase cycling between successive pulses, hence Φ=diag[-1-11111]. The expression for SPGR gives the magnetization immediately after an RF pulse, while for bSSFP it is at the midpoint between 2 RF pulses. Equations M0s→0. Given that dipolar relaxation rates (R1Ds) are often very fast (time constants <10ms), we have also examined the validity of treating RF pulses instantaneously by comparing with full time integration of the BMP equations.The matrix 2.3M˙=AM+C, and then reformulated as:A and C ([0 0 0 0 0 0 0] in this case). The advantage of writing in this way is that the differential equation is homogeneous and the solution at any small time increment during which A~ is constant is M~t+Δt=exp(A~tΔt)M~(t). This may now be integrated over one TR period, with a small time‐step Δt allowing the shape of the RF pulse to be accounted for. The result is a single matrix that describes the evolution, such that:N=TR/Δt. The product must be evaluated by left multiplication of successive matrices. Phase cycling or forced “perfect” transverse spoiling can be added by incorporating matrix Φ into the product. The steady state solution requires that M~ is invariant after multiplication by X~— i.e., it is the eigenvector of X~ with an associated eigenvalue of 1. To remain consistent with Equations Ωsemi is evaluated by considering the time domain representation of the individual frequency bands b{Δj;t} that compose the multiband pulses.Time integration for these sequences is cumbersome because hundreds of TR periods are required to reach a steady state, so a more direct method was devised. Equation 3https://github.com/mriphysics/ihMT_steadystate, (hash 0db78e5 was used for the presented results). Phantom measurements are also available at the same site.In this article we explore the use of nonselective multiband RF pulses . A key parameter for quantifying saturation power is the mean square B1 (⟨B12⟩)B1rms) is a parameter easily accessible on many clinical MR systems. An SPGR or bSSFP sequence using single band excitation pulse b{0;t} has mean‐square B1 given byτ is the pulse duration. This can be turned into the required multiband pulse using modulation functions defined as follows:β quantifies the ratio of off‐resonant to on‐resonant power, calculated by⟨B12⟩TOT is the desired total mean square B1 such that the whole sequence B1rms≡√⟨B12⟩TOT. These expressions allow flexible design of multiband pulses that reach a required target total B1rms within a given pulse sequence; this depends on the properties of the pulse but also the sequence TR. All presented data used Gaussian pulse shapes for the single band pulses with time‐bandwidth‐product 2.26. For brevity, we will refer to single band pulses as 1B, 2 bands as 2B (or 2+B/2−B if distinction between sign of offset is important) and 3 bands as 3B. Function gen_MB_pulse.m in the accompanying code is an example implementation for generating these.Multiband pulses with power spectra illustrated by Figure 3.2R1f=1.54s-1, R1Zs=1s-1, R1Ds=154s-1, T2s=12.5μs, k=65s-1, M0s=0.147, δ=0.65; R2f=12.5s-1 was taken from Sled and Pike.Signal simulations were performed for white matter using parameters based on measurements of human internal capsule taken from Mchinda et al3.2.1τ, TR, B1rms, flip angle, Δ). The effect of long‐term dipolar order was assessed by modifying the white matter parameters to include a case with δ=0 (no “dipolar” pool) and δ=1 (whole semisolid pool contains “dipolar” component). The “ihMT difference” is defined as ΔihMT=S2B-S3B where S2B is the signal from the 2B acquisition, etc. The “ihMT ratio” is then defined as ihMTR=ΔihMTS1B; similarly the MT ratio is defined as MTR=S1B-S2BS1B. To account for asymmetry induced by chemical shift of the semisolid line, the definition S2B=12(S2+B+S2-B) is used for analysis of in vivo data. This is not necessary for numerical simulations because the line is centered on the water resonance in simulations. Because the single band images S1B are used as a reference for calculating both MTR and ihMTR, it is important to note that these images will also contain on‐resonance MT effects . In general, the contrast in the S1B image is influenced by MT and obviously also by free water relaxation effects. It should not necessarily be expected that MTR and ihMTR measured by steady‐state sequences would be directly comparable to those obtained by other methods.Signal simulations were performed for short TR sequences using 1B, 2B, and 3B pulses and a range of other sequence parameters ; chemically cross‐linked bovine serum albumin ; and off the shelf hair conditioner . The MnCl2 phantom is not expected to exhibit any MT effect; BSA is a model substance for human tissue MT effects,A phantom consisting of 4 sample tubes immersed in a bath of water for susceptibility matching was imaged on a Philips  1.5T Ingenia MR system. The samples included: water doped with MnClτ = 2.2 ms, Δ/2π = 8 kHz, isotropic resolution 1.5 × 1.5 × 1.5 mm3, no parallel imaging acceleration, time per scan 57 s. A total of 64 images were obtained using flip angles 10° to 80° (steps of 10°) for bSSFP, and 2° to 16° (steps of 2°) for SPGR, and then for each of these using 1B, 2+B, 2−B, and 3B excitation pulses. All multiband pulses were computed for B1rms=4.2μT, whereas the single band pulses used only the on‐resonance component of these pulses, and so had variable B1rms over the range of flip angles. The data were analyzed by averaging the signal from each sample tube over a range of 45 mm along the length of each tube; segmentation was performed automatically using k‐means clustering using all images as the feature space.The phantom was imaged using a series of bSSFP and SPGR sequences, all with TR = 5 ms, echo time = 2.5 ms, S2+B and S2-B were averaged before fitting because the model does not distinguish these. For SPGR sequences, Equation e-TER2f to account for transverse relaxation at the echo time, here using the approximation that R2f∗≈R2f. For bSSFP sequences, the Bieri‐Scheffler correction for finite pulse duration was applied. Matlab's fmincon optimization function was used with the interior point algorithm selected. Upper and lower bounds were used to constrain fits to plausible values; in each case, a range of bounds and initial starting points were tried out and the best fitting solutions in terms of normalized root mean square error (NRMSE) are reported. Uncertainties were computed by residual bootstrapping using 500 re‐samplings for each fit. All phantom data were fit using a Gaussian lineshape function, because this was empirically found to yield the lowest NRMSE in all cases. A full set of fitting bounds used for generating the presented data is given in Supporting Information Table The signal models  was imaged on the same Philips 1.5T MR system, after giving written informed consent in line with local governance rules. Balanced SSFP images were acquired with flip angle 30°, TR = 5 ms, echo time = 2.5 ms, 44.1τ = 2 ms, Δ/2π = 7 kHz, B1rms=5μT over a range of flip angles (as described above the single band pulses have variable B1rms). The “white matter” tissue parameters were used except that δ was set to 0 and 1 to examine extreme cases. For δ = 0, we see no difference between 2 or 3 band RF excitation; both lead to a strong reduction of signal compared with single band excitation, shaded blue. When δ = 1, signal S3B is clearly lower than S2B. This is expected because the 3B excitation decouples the dipolar ordered pool, leading to more efficient saturation of the semisolid Zeeman magnetization. Supporting Information Figure ΔihMT and ihMTR as functions of flip angle for the δ=1 case, showing that ihMTR is predicted to be in the order of 10% for bSSFP at lower flip angles, and similar for the SPGR around the Ernst angle.Figure B1rms=5μT, TR = 5 ms, τ = 2 ms, Δ/2π = 7 kHz, using white matter tissue parameters. Results are very similar for SPGR, but systematic differences exist for bSSFP that are resolved with application of the Bieri‐Scheffler correction. The right‐hand panels of Figure T1Ds (<1 ms) and long τ. The Bieri‐Scheffler correction was hence applied to all other bSSFP signal predictions presented in this study including Figure Figure 4.22 tube do not. The HC and PL161 samples additionally show an ihMTR of around 15%, suggesting they exhibit dipolar order effects. Figure 2 phantom is expected to show no difference between any of the excitation pulse types and the best fit was obtained with M0s fixed at zero. Small discrepancies in the bSSFP data can be attributed to off‐resonance distortion from an air bubble in this sample, visible on Figure Figure +B, 2−B, or 3B excitation, suggesting the absence of both ihMT effects and MT asymmetry; the best fit was achieved when constraining δ to be fixed at zero. For PL161, the best fit was obtained when δ was fixed to 1; however, for HC, a slightly improved fit was found when δ was allowed to vary. Uncertainty analysis also showed that some parameter estimates for HC are less precise than the others; this finding reflects instability of the model fitting, but also it should be noted that the residual bootstrapping method used is less valid for the situation with nonrandom structure in the residuals. Supporting Information Figure The BSA phantom showed no large difference in signals from 24.3ΔihMT occurs at flip angle ~30° and offset ~8 kHz for τ = 2 ms and B1rms=5μT, which is the maximum allowed within SAR constraints on the MR system used here. Figure B1rms would continue to increase the contrast. Parts C and D show ihMTR instead; here the peak value occurs at a lower flip angle but this is because the reference single band image has a lower signal at that flip angle. Setting the parameters to maximize ΔihMT maximizes the effect size relative to the total magnetization; ihMTR in the region of 5% is then expected for white matter.Results from phantom experiments indicated that similar ihMTR can be obtained using both bSSFP and SPGR, but contrast‐to‐noise ratio is higher for the former. We, therefore, focused on bSSFP imaging in vivo and sought to optimize acquisition parameters for the white matter tissue parameters listed in Section B1rms for a fixed τ the peak B1 needed  increases as TR increases. This is because reducing TR leads to an increase in B1rms for a given RF pulse, as the same energy is delivered at a higher rate. Increasing pulse duration reduces this maximum, but also reduces B1rms and may necessitate an increase in readout bandwidth, affecting signal‐to‐noise ratio. The human imaging protocol was designed based upon these considerations. Figure Figure 5Ωsemi in Equation This work has demonstrated inhomogeneous MT contrast in steady‐state gradient echo sequences using multiband pulses. Typical ihMT sequences use a saturation preparation step followed by a readout step. The combined multiband approach instead uses the same RF pulse to both excite free water and provide saturation of semisolid magnetization. This study presents theory for modeling the resulting signals, designing the RF pulses, and experimental validation in phantoms and in vivo. The behavior of bSSFP and SPGR sequences is exemplified by Figure The mathematical signal model used in this work was developed by Varma and co‐authors over many publications.τ≳T1Ds. The fact that differences only occur with 2B pulses is a clear indication that this is due to the dipolar terms, because these are excluded for 1B and 3B. It is also reasonable that errors would occur when τ is not small compared with T1Ds because we would then not properly account for relaxation of the dipolar pool during saturation. In particular, the commonly used instantaneous pulse approximation was used to simplify the calculations, and accuracy was investigated by comparing with full time integration. It may be expected that this approximation would fail for ihMT because the dipolar relaxation times are typically of the order of a few milliseconds, not much greater than the RF pulse durations or indeed the TRs examined. However, we found that the approximation does hold for SPGR sequences in general, with appreciable differences only when 2B pulses are used with duration R2f to account for the fact that the magnetization spends less than the full TR period in the transverse plane. Although derived for a standard Bloch equation model, it is perhaps interesting that this correction still holds here. An explanation for this may come from the original study,For bSSFP, there are much larger discrepancies associated with the instantaneous approximation, however, these largely vanish when the Bieri‐Scheffler correctionAnother contribution of this work is the development of the efficient eigenvector based direct integration method. The method is similar to other approaches proposed for quantitative MTT1Ds = 20.7 ms agrees with that of Swanson et al,1 shortening agent; however, all values appear plausible. Of interest, the estimated T1Zs was in the 100‐ to 200‐ms range for the phantoms with MT effects, which is quite far from the typically assumed 1 s used by many in the literature.Phantom experiments showed that this model can achieve good fits to data, with PL161 the most relevant model for ihMT also studied by others+B and 2−B for PL161, suggesting very little asymmetry of the absorption line. The fits for HC have slightly larger NRMSE (2.4%), primarily due to a poor fit for the SPGR measurements; a potential explanation for this is that this substance may contain extra unmodeled magnetization pools. We generally observed a high degree of degeneracy in fitting for all phantoms with MT effects. In particular, this was true for the T1 of free and semisolid compartments, exchange rate, and fraction δ. We hence limit our conclusions only to the fact that the model does fit the observed data well with plausible parameters, and do not claim that this experiment constitutes a proper quantitative measurement of these parameters. An obvious extension to better explore the lineshape properties would be to add measurements at different frequency offsets, for example. Note that, while some parameters were fixed for fitting, the reported solutions were the ones that led to the lowest NRMSE in each case .Figure 1 is a function of B1rms , for example. This is limited by B1rms, which increases directly with SAR; indeed, one motivation for conducting experiments at 1.5T is that these scanners can typically access much larger B1rms than higher field systems.In addition to the potential for steady‐state relaxometry, rapid gradient echo sequences, particularly bSSFP, offer high signal‐to‐noise ratio per unit time and can generate high Measured ihMTRs by our method are of the order of a few percent, which are lower than those measured by other methods,6Steady‐state imaging sequences generating inhomogeneous MT contrast have been demonstrated using spatially nonselective multiband RF excitation pulses. A matrix‐based approach for quantifying steady‐state signals was developed and demonstrated to provide good fits to phantom data, and to make good predictions for observed contrast in in vivo human brain images using balanced SSFP.FIGURE S1 Top,ΔihMT for bSSFP and SPGR as a function of flip angle for the δ=1 case plotted in Figure ΔihMT is shown as a percentage of the overall M0 which was arbitrarily fixed as 1.0 in this work. Middle, ihMTR for the same data, here shown as a percentage of the signal from the equivalent single band image (i.e. % of S1B). Close to 10% is achieved for both bSSFP and SPGR at lower flip angles. Bottom, the multiband pulses used in this work were computed to maintain the total B1rms; hence, increasing the on‐resonance flip angle results in a reduction of the total off‐resonance saturation power ⟩) that creates ihMT contrast. This plot shows √⟨B12(Δ≠0)⟩ for the flip angles used to make this figure ⟩) is larger than the gap between the curve and the 5μT line because the RMS values add in quadratureFIGURE S2 MTR and ihMTR as a function of flip angle, derived from the data plotted in Figure TABLE S1 Upper and lower fit bounds (UB/LB) for each parameterClick here for additional data file.


Thermobifida fusca have emerged as promising biocatalysts for an eco‐friendly PET recycling process. In this study, postconsumer PET food packaging containers are treated with TfCut2 and show weight losses of more than 50% after 96 h of incubation at 70 °C. Differential scanning calorimetry analysis indicates that the high linear degradation rates observed in the first 72 h of incubation is due to the high hydrolysis susceptibility of the mobile amorphous fraction (MAF) of PET. The physical aging process of PET occurring at 70 °C is shown to gradually convert MAF to polymer microstructures with limited accessibility to enzymatic hydrolysis. Analysis of the chain‐length distribution of degraded PET by nuclear magnetic resonance spectroscopy reveals that MAF is rapidly hydrolyzed via a combinatorial exo‐ and endo‐type degradation mechanism whereas the remaining PET microstructures are slowly degraded only by endo‐type chain scission causing no detectable weight loss. Hence, efficient thermostable biocatalysts are required to overcome the competitive physical aging process for the complete degradation of postconsumer PET materials close to the glass transition temperature of PET.Polyethylene terephthalate (PET) is the most important mass‐produced thermoplastic polyester used as a packaging material. Recently, thermophilic polyester hydrolases such as TfCut2 from  Untreated and partially hydrolyzed polymer samples were analyzed by differential scanning calorimetry, Fourier‐transform infrared spectroscopy, nuclear magnetic resonance spectroscopy, and scanning electron microscopy. The extent of the enzymatic degradation of the different amorphous and crystalline microstructures of the polymer as well as the effects of a physical aging process of the PET polymer during incubation with the enzyme at 70 °C was evaluated.Many previous studies assessed only the degree of crystallinity after an enzymatic PET degradation and compared with an untreated control while the change of the polymer properties during the enzymatic hydrolysis has remained unexplained. In this study, we used a thermostable recombinant polyester hydrolase expressed in 22.1Thermobifida fusca cutinase TfCut2 was overexpressed in B. subtilis and obtained as the only dominant protein in the cell‐free culture supernatant after 42 h of cultivation at 37 °C . Compared to the previously reported expression of a highly similar enzyme TfH (99% sequence identity to TfCut2) in Bacillus megaterium,B. subtilis thereby enabling a straightforward purification of the recombinant enzyme by a single size exclusion chromatography step to yield a highly pure enzyme preparation . When amorphous GF‐PET  chips were hydrolyzed with TfCut2 at various temperatures for 24 h, the degradation performance was shown to be dependent on the expression hosts used  spectroscopy were 80.7 ± 0.3 °C and 76.6 ± 0.3 °C, respectively, suggesting a more stable overall structure and superior thermostability of the former. Considering the extracellular nature of TfCut2, the secretory expression using B. subtilis was regarded as a more favorable condition for its stable folding compared to the reducing intracellular milieu in E. coli.Recombinant ed Figure1a. A w2.2In this study, the weight loss of bulky PET materials after enzymatic hydrolysis was determined to evaluate the degradation performance. These values indicated the depolymerization of the PET polymers into monomers such as terephthalic acid (TPA) and ethylene glycol (EG) as well as their mono‐ and di‐esters, the release of which could be easily monitored by reversed phased high performance liquid chromatography (HPLC) and correlated with the weight loss determined with the same sample.FigureB. subtilis expressed TfCut2 at 70 °C revealed different degradation performance. In the first 24 h of degradation, weight losses of CP‐PET (15.3 ± 1.5%) and GF‐PET (22.3 ± 0.9%) chips sampled from different parts of the packages and films were detected corresponding to absolute weight losses of 4.8 ± 0.5 mg and 9.9 ± 0.1 mg, respectively. In contrast, AP‐PET chips showed a different biodegradability depending on the origin of the chips sampled from different parts of the packages. Weight losses of the chips were detected in a broad range from 0.3% to 18.9%, corresponding to a maximum absolute weight loss of 7.3 mg  applied to all PET samples, the amorphous GF‐PET showed the highest biodegradability.As shown in FigureThe time course of the enzymatic degradation during a reaction time of 168 h at 70 °C is shown in Figure 2.3t = 0 h) revealed a glass transition temperature (Tg) between 75 and 79 °C overlayed by an endothermic signal and a cold crystallization temperature (Tcc) between 130 and 138 °C as indicated by an exothermic peak in this temperature range  among more than ten samples also showed a Tg1 of 78 °C and a Tg2 of 80 °C  has a chain mobility similar to the purely amorphous polymer whereas a rigid amorphous fraction  shows a lower chain mobility due to its presence within the intraspherulitic or interlamellar regions in close vicinity to the crystalline domains. The presence of RAF in semicrystalline aromatic polyesters has been described by Menczel and Wunderlich in the 1980s.Tg2 than GF‐PET suggested that the latter has less ordered microstructures. This can be further verified by the lower Tcc of postconsumer PET samples between 126 °C and 130 °C determined compared to GF‐PET which is more amorphous and thus requires higher temperatures to initiate the cold crystallization.Tg to higher values and the disappearance of the lower glass transition peaks was observed after treatment of the PET samples both in the presence and absence of the enzyme  and 4.49  ppm were assigned to the protons of the two oxydiethylenic methylenes.[qv: 28a] Diethylene glycol can form during the PET synthesis, and enters subsequently into the growing polyester chains resulting in the formation of an oxydiethylene unit.[qv: 28b] The corresponding chain defects lower the glass transition temperature of PET and the extent of its crystalline microstructures.1H integrals for oxydiethylene and terephthalate units, mole fraction of the former of ≈2.99% and 2.91% were calculated for the AP‐PET and CP‐PET samples, respectively. Consistently, previous studies have shown oxydiethylene units in the same fraction value ranges in other commercial PET samples.The NMR spectra of the postconsumer PET samples AP‐PET and CP‐PET at different stages of enzymatic degradation are shown in Figure n Figure b. In comenes.qv: a Diethyl1H signal appearing as a triplet at δH of 4.0 ppm  of 161.7 and 166.7 was obtained for AP‐PET and CP‐PET, respectively, corresponding to an apparent number average molecular weight (M¯n) of 31 500 and 31 000 g mol−1, respectively, by applying the molecular weight of 192.2 g mol−1 of a single PET repeating unit. These values are in the same order of magnitude of M¯n of PET samples determined previously by size exclusion chromatography.[12b] although a release of hydrolysis monomersA relatively weak but well‐resolved 2.5FigureAnalysis of the AP‐ and CP‐PET samples by scanning electron microscopy (SEM) showed drastic changes in their surface morphology following an incubation with the enzyme Figure6. The 3B. subtilis, two different postconsumer PET packaging materials could be efficiently degraded as indicated by an apparent weight loss of up to 50% after incubation at 70 °C for 96 h. DSC analysis confirmed the presence of a MAF fraction of the PET which was more accessible to enzymatic hydrolysis and a RAF fraction which was more difficult to be hydrolyzed by the enzyme. The occurrence of RAF fractions was considered to be related to the presence of neighboring crystalline microstructures in the polymer as a result of a strain‐induced crystallization during the thermoforming manufacturing process of the packaging. During hydrolysis at 70 °C, a transition of MAF to RAF as a result of a physical aging process was observed which resulted in drastically decreased degradation rates during further incubation. An apparent relationship was observed between the amount of the crystalline microstructures in the PET samples and the corresponding degradation rates indicating a preferential hydrolysis of the MAF by the polyester hydrolase TfCut2. A physical aging process observed by incubation of the PET materials at 70 °C negatively influenced their enzymatic degradation. An NMR‐based approach was established to estimate the changes of the apparent degree of polymerization of the PET samples. The results suggested the presence of a combination of exo‐ and endo‐type chain scissions in the MAF whereas the RAF and the remaining crystalline microstructures of PET could be cleaved only in an endo‐type manner and at a much lower rate without concomitant weight losses.Using a recombinant bacterial polyester hydrolase TfCut2 expressed in Our findings suggest that thermostable polyester hydrolases with high hydrolysis efficiency against both amorphous and crystalline PET are required, not only aiming to the general low energy and time costs of the biorecycling process but also to reduce the conversion loss caused by the decreased polymer degradability as a result of the accompanying physical aging of PET during the enzymatic degradation.4Construction of Plasmids and Bacterial Strains: B. subtilis strain RH 11496 was obtained by transformation with the plasmid pDATfCut2 as described previously.tfcut2 gene, which encodes the Thermobifida fusca cutinase TfCut2,[qv: 15b] with optimized codon usage for B. subtilis introducing complementary sequences to the 3′‐ends with a melting temperature (Tm) above 50 °C. AccuPrime Pfx DNA Polymerase  was used for DNA amplification by PCR following manufacturer's instructions. Amplified products were purified using the Wizard SV gel purification kit  and were fused by using the Gibson assembly kit . The product was directly used to transform competent cells of the intermediate host B. subtilis DB104Recombinant Enzyme Production, Purification, and Characterization: For the B. subtilis strain RH 11496 used in this study, cultivations of the seed cultures were carried out at 37 °C and 180 rpm in shaking flasks. The first preculture was prepared as an overnight culture of one colony from a lysogeny broth agar plate  with suitable antibiotics. The secondary inoculum was cultured from 5% (v/v) of the primary inoculum. For the fermentations carried out, the secondary seed cultures were used as an exponentially growing culture to inoculate 0.5 L fermenters with an inoculum size of 3.75% (v/v). The composition of the media used was as described previously.3 and H2SO4 during the fermentation process of 42 h. The initial aeration and agitation rates were 0.5 vessel volume per minute (vvm) and 1200 rpm. Samples were taken over the entire fermentation process after a cultivation time of 2, 5, 16, 18, 20, 22, and 42 h. After a centrifugation for 15 min at 4500 rpm, the culture supernatant was used for the activity measurement and analyzed by sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS PAGE). The hydrolytic activity was assayed using para‐nitrolphenyl acetate as a substrate. One unit of hydrolytic activity was defined as the amount of enzyme required to produce 1 µmol of p‐nitrophenol per min at 20 °C and pH = 7.0. Purification of the recombinant TfCut2 was carried out by size exclusion chromatography (SEC) as described before.[qv: 15a]E. coli BL21(DE3) and the subsequent purification sequentially by immobilized metal ion affinity chromatography and SEC was performed as described before.[qv: 15b]Recombinant expression of TfCut2 in −6m of purified enzymes were dissolved in 50 × 10−3m sodium borate buffer (pH 8.0) in quartz cuvettes with a path length of 2 mm . The thermal unfolding process was monitored by the ellipticity changes at 220 nm as a function of temperature from 55 to 95 °C in 0.5 °C steps.The thermal unfolding processes of purified enzymes were investigated by CD spectroscopy using a Jasco J‐715 spectropolarimeter . 10 × 10Enzymatic Hydrolysis of the PET Materials: Amorphous PET film with a thickness of 250 µm was purchased from Goodfellow Ltd. . Postconsumer PET packaging containers for fresh fruit and vegetables obtained from Agripack  and Carton Pack  were also used. Fourier transform infrared spectroscopy (FTIR) measurements of all three PET types were performed in ATR  mode with the FTIR spectrometer Vector 22  and a diamond crystal . The spectra were obtained in the wavenumber range of 550–4000 cm−1 using a spectral resolution of 2 cm−1 .2 with an average weight of 38.9, 31.1, and 44.2 mg for AP‐, CP‐, and GF‐PET, respectively, were placed in a 2 mL reaction vial containing 1.8 mL of K2HPO4/Cl  and 1 nmol cm−2 of purified TfCut2. Degradation was performed by shaking the reaction vials on a thermoshaker TS1  at 70 °C and 1000 rpm. The reaction was stopped by cooling the samples on ice. PET chips were washed and dried as described previously and subjected to gravimetric determination of the weight loss.PET chips of 3 × 0.5 cmDSC Analysis of the PET Materials: Differential scanning calorimetry was performed using a DSC 8500 calorimeter  using ≈4–5 mg of a dry PET sample. A heating rate of 10 °C min−1 was applied for the temperature range from −20 to 300 °C. The glass transition temperature (Tg), the cold crystallization temperature (Tcc), and the melting point (Tm) of various PET samples were obtained using the first heating scan. The initial fraction crystallinity X0 was calculated according toX0 is the initial crystallinity, X∞ is the complete crystallinity, ΔHm is the melting enthalpy, and ΔHcc is the cold crystallization enthalpy. ΔHm0(Tm) is the melting enthalpy of pure crystalline PET at the melting temperature of 140 J g−1.ΔHm0(Tcc) is the melting enthalpy of pure crystalline PET at the temperature of cold crystallization, which can be calculated according to Equation Cp is the difference of the heat capacity of amorphous and crystalline PET of 0.17 J g−1 K−1.NMR Analysis of the PET Materials: The enzyme‐treated PET samples and untreated control samples were dissolved in hexafluoroisopropanol  and stored at room temperature over 120 h for a complete dissolution. The PET solutions with a final concentration of 7.14 µg µL−1 were used for the NMR analysis. 5 µL of each PET solution was pipetted into a 5 mm NMR tube and mixed with 80 µL chloroform‐d  containing 0.05% (v/v) tetramethylsilane (TMS) as an internal standard . The solvent residual signal of CDCl3 calibrated on the TMS scale was used as a reference .1H solution NMR experiments were performed with a Bruker DRX‐600 NB spectrometer equipped with a 5 mm TXI probe  at 290.3 ± 0.1 K. An optimized 1H 90° pulse of 6.0 µs and a spectral width of 12.02 kHz was employed. The data were recorded with 256 or 1024 scans and a recycle delay of 15 s. A twofold zero‐filled to 128k points and an exponential line broadening of 0.2 Hz was applied to data processing. The baseline was corrected manually afterward. Processed data were analyzed with MestReNova 12.0.0 software . For determination of the 1H signal of the β CH2 protons for the hydroxyl end group, its 13C satellite at the low‐field side was not involved in the calculation due to their heavily overlapping with the strong main signal of the CH proton in HFIP (a septet centered at 4.41 ppm).All SEM Analysis of the PET Materials: The surface morphology of PET samples were determined by SEM  with samples coated with a thin (30 nm) chromium film using a Z400 sputter system .The authors declare no conflict of interest.SupplementaryClick here for additional data file.