The typology of the American metropolis: monocentricity, polycentricity, or generalized dispersion?

<p>Although the spatial structure of employment in large US metropolitan regions is a well-researched topic, few studies focus on medium-sized and small US metropolitan regions. Consequently, there is no overall typology relating small-to-medium urban form to employment distribution. We address this gap by investigating the spatial structure of employment in 356 metropolitan regions. We conceptualize six typologies based on three categories that have overlapping properties: “monocentricity,” “polycentricity,” and “generalized dispersion.” The study has three main findings. First, the three types of urban form that we identify as “hybrid” outnumber the three “pure” types by almost four to one. Second, job dispersion is a dominant characteristic in almost 70% of all metropolitan statistical areas (MSAs) (including the hybrid types), and polycentricity (56.7% of MSAs) is somewhat more common than monocentricity. Third, there is a strong relationship between population size and density. The population of medium-sized metropolitan areas is generally more dispersed than that of small and large metropolitan areas. Polycentricy emerges mostly in large metropolitan regions, while monocentrity is found in both small and large metropolitan regions.</p

C–H Bond Activation and Isoprene Polymerization by Rare-Earth-Metal Tetramethylaluminate Complexes Bearing Formamidinato N‑Ancillary Ligands

The bimetallic formamidinate complexes Ln­(Form)­(AlMe₄)₂ (Ln = Y, Form (ArNCHNAr) = EtForm (Ar = 2,6-Et₂C₆H₃), MesForm (Ar = 2,4,6-Me₃C₆H₂), DippForm (Ar = 2,6-<i>i</i>Pr₂C₆H₃), <i>t</i>BuForm (Ar = 2-<i>t</i>BuC₆H₄); Ln = La, Form = DippForm, <i>t</i>BuForm) were obtained in high yield by protonolysis reactions between formamidines (FormH) and homoleptic rare-earth-metal tetramethylaluminates Ln­(AlMe₄)₃. Y­(Form)­(AlMe₄)₂ (Form = EtForm, DippForm) were also prepared by treatment of Y­(Form)­[N­(SiHMe₂)₂]₂(thf) with trimethylaluminum after the former were prepared by the protonolysis of Y­[N­(SiHMe₂)₂]₃(thf)₂ complexes with EtFormH or DippFormH. The monomeric six-coordinate complexes Ln­(Form)­(AlMe₄)₂ (Ln = Y, Form = EtForm, MesForm, DippForm, <i>t</i>BuForm; Ln = La, Form = DippForm, <i>t</i>BuForm) show similar molecular structures with distorted-octahedral geometry and bidentate (N,N′) Form and AlMe₄ ligands. The complex [La­(EtFormAlMe₃)­(AlMe₄)₂]­(C₇H₈)_1.5 from a protonolysis reaction between La­(AlMe₄)₃ and EtFormH has the EtForm ligand adopting a configuration in which one nitrogen and one aryl substituent are coordinated to the eight-coordinate lanthanum center in an η¹(N):η⁶(arene) manner. From the reaction of La­(AlMe₄)₃ with MesFormH, C–H bond activation of an <i>o</i>-methyl group of the mesityl moiety occurred, yielding [La­{η¹(N):η⁶(Ar)-Me₂CH₂FormAlMe₃}­(AlMe₃)­(AlMe₄)]­[La­(Me₂CH₂FormAlMe₃)­(AlMe₃)­(AlMe₄)]­(C₆H₁₄)_1.5 (Me₂CH₂Form = MesForm-H­(<i>o</i>-Me)), in which two linkage isomers of Me₂CH₂Form were observed. Investigations were carried out on the compounds [Ln­(Form)­(AlMe₄)₂] (Ln = Y, La; Form = EtForm, DippForm) as precatalysts activated by [Ph₃C]­[B­(C₆F₅)₄] or [PhNMe₂H]­[B­(C₆F₅)₄] in isoprene polymerization. While the lanthanum complexes showed narrower molecular weight distributions (PDI < 1.2), a stereodirecting role was evidenced for the cocatalysts (trityl borate, maximum 87% trans-1,4-selectivity; anilinium borate, maximum 82% cis-1,4-selectivity)