Expanding the Origin of Stereocontrol in Propene Polymerization Catalysis

Predicting the propene stereoselectivity on transition metal catalysts: A daunting task for density functional theory

Thanks to recent developments in hardware and software, quantum chemical methods are increasingly used for interpreting the complex mechanisms underlying polymerization reaction by homogeneous catalysis. Unfortunately, the dimensions of even the smallest realistic models are too large to permit the use of state-of-the-art composite wave function methods. Under these circumstances, density functional theory still offers the best compromise between cost and accuracy. However, comprehensive benchmarks of different functionals are not yet available for this important research field. The main aim of the present paper is to fill this gap by performing an unbiased comparison of several density functionals and continuum solvent models for the stereo-control in the propylene polymerization on prototypical catalysts inducing different reaction mechanisms. While it was not possible to define a unique computational protocol providing the best results in all the situations, the B3PW91 functional in conjunction with D3 empirical dispersions and the solvent model density solvent model performs remarkably well for three out of the four investigated catalysts. Under such circumstances, it is recommended to compare the results delivered by different models when approaching additional classes of catalysts.

Atomistic Simulation of Hf-Pyridyl Amido-Catalyzed Chain Transfer Alkene Polymerization Reaction and Its Machine Learning for Extraction of Essential Descriptors: Effect of Microscopic Steric Hindrance on the Monomer Insertion Process

The microscopic effects of each substituent of the Hf catalyst and the growing polymer on the monomer insertion process were investigated for Hf-pyridyl amido-catalyzed coordinative chain transfer polymerization using the Red Moon method. Since the Hf catalyst has two reaction sites, cis- and trans-sites, we separately applied the appropriate analysis methods to each one, revealing that the naphthalene ring influenced monomer insertion at the cis-one, while the i-Pr group and the hexyl group of the adjacent 1-octene unit did the trans-one. It was interesting to find that the hexyl group of the 1-octene-inserted catalyst (oHfCat) pushes the naphthalene ring toward the cis-site and narrows the space at the cis-site, thus indirectly creating a steric hindrance to cis-insertions. Further, the relative position of the Hf catalyst and the growing polymer was found to be strongly influenced by the patterns of insertion reactions, i.e., cis- or trans-insertions. In particular, it was clarified that, after trans-insertions, the growing polymer on the Hf atom covers the cis-site, making cis-insertion less likely to occur. These studies reveal the microscopic effects of the catalyst substituents and the growing polymer on the catalyst during the polymerization reaction process; these microscopic analyses using the RM method should provide atomistic insights that are not easy to obtain experimentally for advanced catalyst design and polymerization control.

Accessing Functionalized Ultra-High Molecular Weight Poly(α-olefin)s via Hafnium-Mediated Highly Isospecific Copolymerization

Inspired by the favorable impact of heteroatom-containing groups in phenoxy-imine titanium and late transition metal catalysts, a series of novel pyridylamido hafnium catalysts bearing ─OMe (Cat-OMe), ─CF3 (Cat-CF3), and ─C6F5 (Cat-C6F5) substituents are designed and synthesized. Together with the established hafnium catalysts Cat-H and Cat-iPr by Dow/Symyx, these catalysts are applied in the polymerization of α-olefins, including 1-hexene, 1-octene, and 4M1P, as well as in the copolymerization of these α-olefins with a specifically designed polar monomer. The enhancement of polymer molecular weight derived from catalyst modification and the incorporation of polar monomers is discussed in detail. Notably, the new catalysts are all highly active for α-olefins polymerization, with catalyst Cat-CF3 producing isotactic polymers with the highest molecular weight (Mw = 1649 kg mol-1); in copolymerization with polar monomers, catalyst Cat-OMe yields isotactic copolymer with the highest molecular weight (Mw = 2990 kg mol-1). Interestingly, catalyst Cat-C6F5 bearing a ─C6F5 group in the N-aryl moiety gives rise to poly(α-olefin) with reduced stereoselectivity. The findings of this study underscore the potential of heteroatom-containing groups in the development of early transition metal catalysts and the synthesis of polymer with novel structures.

Revisiting Stereoselective Propene Polymerization Mechanisms: Insights through the Activation Strain Model

The stereoelectronic factors responsible for stereoselectivity in propene polymerization with several metallocene and post-metallocene transition metal catalysts have been revisited using a combined approach of DFT calculations, the Activation Strain Model, Natural Energy Decomposition Analysis and a molecular descriptor (%VBur). There are in most cases two different paths leading to the formation of stereoerrors (SE), and the classical model does not suffice to fully understand stereoregulation. Improving stereoselectivity requires raising the energies of both SE insertion transition states. Our analyses show that the degrees of deformation of the active site (catalyst+chain) and the prochiral monomer differ for these two paths, and between different catalyst classes. Based on such analyses we discuss: a) the subtle differences in SE formation between stereoselective catalysts with different ligand frameworks; b) the reason for exceptional stereoselectivity reported for a special ansa-metallocene catalyst; c) the (double) stereocontrol origin for isoselective catalysts; d) the electronic contribution for isoselective catalysts generating SE by a modification of the ligand wrapping mode during the polymerization. Although this study will not immediately suggest new catalyst structures, we believe that understanding stereoregulation in great detail will increase our chances of success.

Cocatalyst effects in Hf-catalysed olefin polymerization: taking well-defined Al-alkyl borate salts into account

Hafnium catalysts for olefin polymerization are often very sensitive to the nature of cocatalysts, especially if they contain "free" aluminium trialkyls. Herein, cocatalyst effects in Hf-catalysed propene polymerization are examined for four Hf catalysts belonging to the family of CS-symmetric (Hf-CS-Met) and C2-symmetric (Hf-C2-Met) metallocenes, as well as of octahedral (Hf-OOOO) and pentacoordinated (Hf-PyAm) "post-metallocenes". The performance of the recently developed {[iBu2(PhNMe2)Al]2(μ-H)}+[B(C6F5)4]- (AlHAl) cocatalyst is compared with that of established systems like methylalumoxane, phenol-modified methylalumoxane and trityl borate/tri-iso-butylaluminium. The worst catalytic performance is observed with MAO. Conversely, the best cocatalyst varies depending on the Hf catalyst used and the performance indicator of interest, highlighting the complexity and importance of selecting the right precatalyst/cocatalyst combination. AlHAl proved to be a suitable system for all catalysts tested and, in some cases, it provides the best performance in terms of productivity (e.g. with hafnocenes). Furthermore, it generally leads to high molecular weight polymers, also with catalysts enabling easy chain transfer to Al like Hf-PyAm. This suggests that AlHAl has a low tendency to form heterodinuclear adducts with the cationic active species, therefore preventing the formation of dormant sites and/or termination events by chain transfer to Al.

Ring Opening Polymerization of Six- and Eight-Membered Racemic Cyclic Esters for Biodegradable Materials

The low percentage of recyclability of the polymeric materials obtained by olefin transition metal (TM) polymerization catalysis has increased the interest in their substitution with more eco-friendly materials with reliable physical and mechanical properties. Among the variety of known biodegradable polymers, linear aliphatic polyesters produced by ring-opening polymerization (ROP) of cyclic esters occupy a prominent position. The polymer properties are highly dependent on the macromolecule microstructure, and the control of stereoselectivity is necessary for providing materials with precise and finely tuned properties. In this review, we aim to outline the main synthetic routes, the physical properties and also the applications of three commercially available biodegradable materials: Polylactic acid (PLA), Poly(Lactic-co-Glycolic Acid) (PLGA), and Poly(3-hydroxybutyrate) (P3HB), all of three easily accessible via ROP. In this framework, understanding the origin of enantioselectivity and the factors that determine it is then crucial for the development of materials with suitable thermal and mechanical properties.

A Computational Evaluation of the Steric and Electronic Contributions in Stereoselective Olefin Polymerization with Pyridylamido-Type Catalysts

A density functional theory (DFT) study combined with the steric maps of buried volume (%V_Bur) as molecular descriptors and an energy decomposition analysis through the ASM (activation strain model)-NEDA (natural energy decomposition analysis) approach were applied to investigate the origins of stereoselectivity for propene polymerization promoted by pyridylamido-type nonmetallocene systems. The relationships between the fine tuning of the ligand and the propene stereoregularity were rationalized (e.g., the metallacycle size, chemical nature of the bridge, and substituents at the ortho-position on the aniline moieties). The DFT calculations and %V_Bur steric maps reproduced the experimental trend: substituents on the bridge and on the ortho-positions of aniline fragments enhance the stereoselectivity. The ASM-NEDA analysis enabled the separation of the steric and electronic effects and revealed how subtle ligand modification may affect the stereoselectivity of the process.

(Pyridylamido)Hf(IV)-Catalyzed 1-Octene Polymerization Reaction Interwoven with the Structural Dynamics of the Ion-Pair-Active Species: Bridging from Microscopic Simulation to Chemical Kinetics with the Red Moon Method

We performed the atomistic simulation of 1-octene polymerization reaction catalyzed by the ionic pair (IP) consisting of the cationic active species of (pyridylamido)Hf(IV) catalyst, HfCat^Pn+, and different counteranions (CAs), B(C₆F₅)₄^- and MeB(C₆F₅)₃^-, at different monomer concentrations. Using a hybrid Monte Carlo/molecular dynamics method, that is, the Red Moon (RM) method, the reaction progress measured by the "RM cycle" was transformed into effective real time using the time transformation theory. Then, the degree of polymerization was found to be consistent with that in the chemical kinetics, a macroscopic theory, and experimental ones. Remarkably, the current simulation has revealed the different dynamical features in the polymerization behavior originating from the CA. Namely, the HfCat^Pn+-B(C₆F₅)₄^- IP mainly forms an outer-sphere IP (OSIP) throughout the polymerization. The HfCat^Pn+-MeB(C₆F₅)₃^- IP, on the other hand, forms an inner-sphere IP (ISIP) in the initial stage of polymerization, and the ratio of ISIP steeply drops after the first monomer insertion because the IP interaction is reduced by the steric hindrance between the inserted monomers and the CA. In conclusion, we have shown that the microscopic IP dynamics interwoven with the polymerization reaction can be computationally observed in the real-time domain by using the RM method. Therefore, our current work demonstrates the promising potential of the RM method in studying catalytic olefin polymerization and complex chemical reaction systems.

Chiral Polymers from Norbornenes Based on Renewable Chemical Feedstocks

Optically active polymers are of great interest as materials for dense enantioselective membranes, as well as chiral stationary phases for gas and liquid chromatography. Combining the versatility of norbornene chemistry and the advantages of chiral natural terpenes in one molecule will open up a facile route toward the synthesis of diverse optically active polymers. Herein, we prepared a set of new chiral monomers from cis-5-norbornene-2,3-dicarboxylic anhydride and chiral alcohols of various natures. Alcohols based on cyclic terpenes ((-)-menthol, (-)-borneol and pinanol), as well as commercially available alcohols (S-(-)-2-methylbutanol-1, S-(+)-3-octanol), were used. All the synthesized monomers were successfully involved in ring-opening metathesis polymerization, affording polymers in high yields (up to 96%) and with molecular weights in the range of 1.9 × 10⁵-5.8 × 10⁵ (M_w). The properties of the metathesis polymers obtained were studied by TGA and DSC analysis, WAXD, and circular dichroism spectroscopy. The polymers exhibited high thermal stability and good film-forming properties. Glass transition temperatures for the prepared polymers varied from -30 °C to +139 °C and, therefore, the state of the polymers changed from rubbery to glassy. The prepared polymers represent a new attractive platform of chiral polymeric materials for enantioselective membrane separation and chiral stationary phases for chromatography.

Unconventional Stereoerror Formation Mechanisms in Nonmetallocene Propene Polymerization Systems Revealed by DFT Calculations

An unconventional mechanism for the stereoerror formation in propene polymerization catalyzed by C₁-symmetric salalen-M systems (M = Zr, Hf) is suggested by DFT calculations. While propagation happens with the ligand in its fac-mer conformation, a change of ligand wrapping mode from fac-mer to fac-fac is the main source of the lower stereoselectivities obtained with Zr and Hf. This is different for the Ti analogues, where the ligand fac-mer wrapping mode does not play a role. Activation strain analysis indicates that the preference for a chain stationary mechanism of the Zr/Hf species is due to the energy required to distort the reactants (ΔE_Strain) rather than to their mutual interaction (ΔE_Int)_.

Structure and Morphology of Crystalline Syndiotactic Polypropylene-Polyethylene Block Copolymers

A study of the structure and morphology of diblock copolymers composed of crystallizable blocks of polyethylene (PE) and syndiotactic polypropylene (sPP) having different lengths is reported. In both analyzed samples, the PE block crystallizes first by cooling from the melt (at 130 °C) and the sPP block crystallizes after at a lower temperature. Small angle X-ray scattering (SAXS) recorded during cooling showed three correlation peaks at values of the scattering vector, q₁ = 0.12 nm⁻¹, q₂ = 0.24 nm⁻¹ and q₃ = 0.4 nm⁻¹, indicating development of a lamellar morphology, where lamellar domains of PE and sPP alternate, each domain containing stacks of crystalline lamellae of PE or sPP sandwiched by their own amorphous phase of PE or sPP. At temperatures higher than 120 °C, when only PE crystals are formed, the morphology is defined by the formation of stacks of PE lamellae (17 nm thick) alternating with amorphous layers and with a long period of nearly 52 nm. At lower temperatures, when crystals of sPP are also well-formed, the morphology is more complex. A model of the morphology at room temperature is proposed based on the correlation distances determined from the self-correlation functions extracted from the SAXS data. Lamellar domains of PE (41.5 nm thick) and sPP (8.2 nm thick) alternate, each domain containing stacks of crystalline lamellae sandwiched by their own amorphous phase, forming a global morphology having a total lamellar periodicity of 49.7 nm, characterized by alternating amorphous and crystalline layers, where the crystalline layers are alternatively made of stacks of PE lamellae (22 nm thick) and thinner sPP lamellae (only 3.5 nm thick).

Structure and morphology of isotactic polypropylene–polyethylene block copolymers prepared with living and stereoselective catalyst

Isotactic polypropylene–polyethylene block copolymers prepared with living and stereoselective catalyst allow linking incompatible crystalline polymers giving a lamellar morphology defined by competition between phase separation and crystallization.

Synthesis of Polymers Bearing a Chiral Backbone via Stereospecific Ionic Ring-Opening Polymerization of Chiral Donor-Acceptor Cyclopropanes

The stereospecific ionic ring-opening polymerization of various donor-acceptor cyclopropanes is reported. The chiral cyclopropane monomers are readily prepared with established methodology and stereospecific polymerization is best conducted with a catalytic amount of MgBr₂ serving as a Lewis acid and as an initiator. Polymers with molecular masses of up to 7800 g mol^-1 containing a stereocenter in every repeating unit are obtained and the substituents of the monomers can be readily varied to access a novel class of chiral polymers.

Syndiotactic PLA from meso-LA polymerization at the Al-chiral complex: a probe of DFT mechanistic insights

The mechanism(s) for the formation of syndiotactic PLA by the ROP of meso-LA by a chiral-Al-complex are disclosed by DFT calculations. The contributions toward stereoselectivity have been analyzed confirming the peculiar chiral recognition for stereocontrolled ROP polymerization.

Atomistic Simulation of the Polymerization Reaction by a (Pyridylamido)hafnium(IV) Catalyst: Counteranion Influence on the Reaction Rate and the Living Character of the Catalytic System

Atomistic simulation of the 1-octene polymerization reaction by a (pyridylamido)Hf(IV) catalyst was conducted on the basis of Red Moon (RM) methodology, focusing on the effect of the counteranions (CAs), MeB(C₆F₅)₃^-, and B(C₆F₅)₄^-, on the catalyst activity and chain termination reaction. We show that RM simulation reasonably reproduces the faster reaction rate with B(C₆F₅)₄^- than with MeB(C₆F₅)₃^-. Notably, the initiation of the polymerization reaction with MeB(C₆F₅)₃^- is comparatively slow due to the difficulty of the first insertion. Then, we investigated the free energy map of the ion pair (IP) structures consisting of each CA and the cationic (pyridylamido)Hf(IV) catalyst with the growing polymer chain (HfCat^Pn+), which determines the polymerization reaction rates, and found that HfCat^Pn+-MeB(C₆F₅)₃^- can keep forming "inner-sphere" IPs even after the polymer chain becomes sufficiently bulky, while HfCat^Pn+-B(C₆F₅)₄^- forms mostly "outer-sphere" IPs. Finally, we further tried to elucidate the origin of the broader molecular weight distribution (MWD) of the polymer experimentally produced with B(C₆F₅)₄^- than that with MeB(C₆F₅)₃^-. Then, through the trajectory analysis of the RM simulations, it was revealed that the chain termination reaction would be more sensitive to the IP structures than the monomer insertion reaction because the former involves a more constrained structure than the latter, which is likely to be a possible origin of the MWDs dependent on the CAs.

Progress in propylene homo- and copolymers using advanced transition metal catalyst systems

Recent progress on advanced transition metal catalysts for propylene polymerization and copolymerization are reviewed.

Preparation of Pyridylamido Hafnium Complexes for Coordinative Chain Transfer Polymerization

The pyridylamido hafnium complex (I) discovered at Dow is a flagship catalyst among postmetallocenes, which are used in the polyolefin industry for PO-chain growth from a chain transfer agent, dialkylzinc. In the present work, with the aim to block a possible deactivation process in prototype compound I, the corresponding derivatives were prepared. A series of pyridylamido Hf complexes were prepared by replacing the 2,6-diisopropylphenylamido part in I with various 2,6-R2C6H3N-moieties (R = cycloheptyl, cyclohexyl, cyclopentyl, 3-pentyl, ethyl, or Ph) or by replacing 2-iPrC6H4C(H)- in I with the simple PhC(H)-moiety. The isopropyl substituent in the 2-iPrC6H4C(H)-moiety influences not only the geometry of the structures (revealed by X-ray crystallography), but also catalytic performance. In the complexes bearing the 2-iPrC6H4C(H)-moiety, the chelation framework forms a plane; however, this framework is distorted in the complexes containing the PhC(H)-moiety. The ability to incorporate α-olefin decreased upon replacing 2-iPrC6H4C(H)-with the PhC(H)-moiety. The complexes carrying the 2,6-di(cycloheptyl)phenylamido or 2,6-di(cyclohexyl)phenylamido moiety (replacing the 2,6-diisopropylphenylamido part in I) showed somewhat higher activity with greater longevity than did prototype catalyst I.

Polystyrene Chain Growth Initiated from Dialkylzinc for Synthesis of Polyolefin-Polystyrene Block Copolymers

Polyolefins (POs) are the most abundant polymers. However, synthesis of PO-based block copolymers has only rarely been achieved. We aimed to synthesize various PO-based block copolymers by coordinative chain transfer polymerization (CCTP) followed by anionic polymerization in one-pot via conversion of the CCTP product (polyolefinyl)2Zn to polyolefinyl-Li. The addition of 2 equiv t-BuLi to (1-octyl)2Zn (a model compound of (polyolefinyl)2Zn) and selective removal or decomposition of (tBu)2Zn by evacuation or heating at 130 °C afforded 1-octyl-Li. Attempts to convert (polyolefinyl)2Zn to polyolefinyl-Li were unsuccessful. However, polystyrene (PS) chains were efficiently grown from (polyolefinyl)2Zn; the addition of styrene monomers after treatment with t-BuLi and pentamethyldiethylenetriamine (PMDTA) in the presence of residual olefin monomers afforded PO-block-PSs. Organolithium species that might be generated in the pot of t-BuLi, PMDTA, and olefin monomers, i.e., [Me2NCH2CH2N(Me)CH2CH2N(Me)CH2Li, Me2NCH2CH2N(Me)Li·(PMDTA), pentylallyl-Li⋅(PMDTA)], as well as PhLi⋅(PMDTA), were screened as initiators to grow PS chains from (1-hexyl)2Zn, as well as from (polyolefinyl)2Zn. Pentylallyl-Li⋅(PMDTA) was the best initiator. The Mn values increased substantially after the styrene polymerization with some generation of homo-PSs (27-29%). The Mn values of the extracted homo-PS suggested that PS chains were grown mainly from polyolefinyl groups in [(polyolefinyl)2(pentylallyl)Zn]-[Li⋅(PMDTA)]+ formed by pentylallyl-Li⋅(PMDTA) acting onto (polyolefinyl)2Zn.

Preparation of Half- and Post-Metallocene Hafnium Complexes with Tetrahydroquinoline and Tetrahydrophenanthroline Frameworks for Olefin Polymerization

Hafnium complexes have drawn attention for their application as post-metallocene catalysts with unique performance in olefin polymerization. In this work, a series of half-metallocene HfMe₂ complexes, bearing a tetrahydroquinoline framework, as well as a series of [N^amido,N,C^aryl]HfMe₂-type post-metallocene complexes, bearing a tetrahydrophenanthroline framework, were prepared; the structures of the prepared Hf complexes were unambiguously confirmed by X-ray crystallography. When the prepared complexes were reacted with anhydrous [(C₁₈H₃₇)₂N(H)Me]⁺[B(C₆F₅)₄]⁻, desired ion-pair complexes, in which (C₁₈H₃₇)₂NMe coordinated to the Hf center, were cleanly afforded. The activated complexes generated from the half-metallocene complexes were inactive for the copolymerization of ethylene/propylene, while those generated from post-metallocene complexes were active. Complex bearing bulky isopropyl substituents (12) exhibited the highest activity. However, the activity was approximately half that of the prototype pyridylamido-Hf Dow catalyst. The comonomer incorporation capability was also inferior to that of the pyridylamido-Hf Dow catalyst. However, 12 performed well in the coordinative chain transfer polymerization performed in the presence of (octyl)₂Zn, converting all the fed (octyl)₂Zn to (polyolefinyl)₂Zn with controlled lengths of the polyolefinyl chain.

Preparation of Pincer Hafnium Complexes for Olefin Polymerization

Pincer-type [C^naphthyl, N^pyridine, N^amido]HfMe₂ complex is a flagship among the post-metallocene catalysts. In this work, various pincer-type Hf-complexes were prepared for olefin polymerization. Pincer-type [N^amido, N^pyridine, N^amido]HfMe₂ complexes were prepared by reacting in situ generated HfMe₄ with the corresponding ligand precursors, and the structure of a complex bearing 2,6-Et₂C₆H₃N^amido moieties was confirmed by X-ray crystallography. When the ligand precursors of [(CH₃)R₂Si-C₅H₃N-C(H)PhN(H)Ar (R = Me or Ph, Ar = 2,6-diisopropylphenyl) were treated with in situ generated HfMe₄, pincer-type [C^silylmethyl, N^pyridine, N^amido]HfMe₂ complexes were afforded by formation of Hf-CH₂Si bond. Pincer-type [C^naphthyl, S^thiophene, N^amido]HfMe₂ complex, where the pyridine moiety in the flagship catalyst was replaced with a thiophene unit, was not generated when the corresponding ligand precursor was treated with HfMe₄. Instead, the [S^thiophene, N^amido]HfMe₃-type complex was obtained with no formation of the Hf-C^naphthyl bond. A series of pincer-type [C^naphthyl, N^pyridine, N^alkylamido]HfMe₂ complexes was prepared where the arylamido moiety in the flagship catalyst was replaced with alkylamido moieties (alkyl = iPr, cyclohexyl, tBu, adamantyl). Structures of the complexes bearing isopropylamido and adamantylamido moieties were confirmed by X-ray crystallography. Most of the complexes cleanly generated the desired ion-pair complexes when treated with an equivalent amount of [(C₁₈H₃₇)₂N(H)Me]⁺[B(C₆F₅)₄]⁻, which showed negligible activity in olefin polymerization. Some complexes bearing bulky substituents showed moderate activities, even though the desired ion-pair complexes were not cleanly afforded.

Atomistic chemical computation of Olefin polymerization reaction catalyzed by (pyridylamido)hafnium(IV) complex: Application of Red Moon simulation

We have realized the microscopic simulation of olefin polymerization, that is, the simulation of the catalytic polymerization (CP) reaction system composed of (pyridylamido)hafnium(IV) complex as the catalyst. For this purpose, we adopted Red Moon (RM) method, a novel molecular simulation method to simulate the complex reaction system. First, according to the previous research, with the help of the QM calculation, we proposed a model system and elementary processes and explained the theoretical treatment of the simulation by the RM method (the RM simulation). In addition, we also proposed a macroscopic simulation based on chemical kinetics simulation. Then, we performed two simulations and compared them in terms of the effective time evolution of the three macroscopic physical quantities, the number-average molecular weight M_n , the mass-average molecular weight M_w , and the molar-mass dispersity Đ_M . The comparison showed that the two simulations are in quantitative or partially qualitative agreement with each other. Therefore, it is concluded that the RM simulation could not only simulate the CP reaction process microscopically, but also it is connected essentially to reproduce the time evolution of the macroscopic physical quantities on the basis of its microscopic simulation data. © 2018 Wiley Periodicals, Inc.