Zum Einfluß der PR3‐Liganden auf Bildung und Eigenschaften der Phosphinophosphiniden‐Komplexe [{η2‐tBu2P–P}Pt(PR3)2] und [{η2‐tBu2P1–P2}Pt(P3R3)(P4R′3)]

Coordination Chemistry of P‐rich Phosphanes and Silylphosphanes XXI The Influence of the PR₃ Ligands on Formation and Properties of the Phosphinophosphinidene Complexes [{η²‐^tBu₂P–P}Pt(PR₃)₂] and [{η²‐^tBu₂P¹–P²}Pt(P³R₃)(P⁴R′₃)] (R₃P)₂PtCl₂ and C₂H₄ yield the compounds [{η²‐C₂H₄}Pt(PR₃)₂] (PR₃ = PMe₃, PEt₃, PPhEt₂, PPh₂Et, PPh₂Me, PPh₂ⁱPr, PPh₂^tBu and P(p‐Tol)₃); which react with ^tBu₂P–P=PMe^tBu₂ to give the phosphinophosphinidene complexes [{η²‐^tBu₂P–P}Pt(PMe₃)₂], [{η²‐^tBu₂P–P}Pt(PEt₃)₂], [{η²‐^tBu₂P–P}Pt(PPhEt₂)₂], [{η²‐^tBu₂P–P}Pt(PPh₂Et)₂], [{η²‐^tBu₂P–P}Pt(PPh₂Me)₂], [{η²‐^tBu₂P–P}Pt(PPh₂ⁱPr], [{η²‐^tBu₂P–P}Pt(PPh₂^tBu)₂] and [{η²‐^tBu₂P–P}Pt(P(p‐Tol)₃)₂]. [{η²‐^tBu₂P–P}Pt(PPh₃)₂] reacts with PMe₃ and PEt₃ as well as with ^tBu₂PMe, PⁱPr₃ and P(c‐Hex)₃ by substituting one PPh₃ ligand to give [{η²‐^tBu₂P¹–P²}Pt(P³Me₃)(P⁴Ph₃)], [{η²‐^tBu₂P¹–P²}Pt(P³Ph₃)(P⁴Me₃)], [{η²‐^tBu₂P¹–P²}Pt(P³Et₃)(P⁴Ph₃)], [{η²‐^tBu₂P¹–P²}Pt(P³Me^tBu₂)(P⁴Ph₃)], [{η²‐^tBu₂P¹–P²}Pt(P³ⁱPr₃)(P⁴Ph₃)] and [{η²‐^tBu₂P¹–P²}Pt(P³(c‐Hex)₃)(P⁴Ph₃)]. With ^tBu₂PMe, [{η²‐^tBu₂P–P}Pt(P(p‐Tol)₃)₂] forms [{η²‐^tBu₂P¹–P²}Pt(P³Me^tBu₂)(P⁴(p‐Tol)₃)]. The NMR data of the compounds are given and discussed with respect to the influence of the PR₃ ligands.     

Bildung und Struktur des [{η2‐tBu2P–P}Pt(PHtBu2)(PPh3)]

Coordination Chemistry of P‐rich Phosphanes and Silylphosphanes. XX Formation and Structure of [{η²‐^tBu₂P–P}Pt(PH^tBu₂)(PPh₃)] [{η²‐^tBu₂P¹–P²}Pt(P³Ph₃)(P⁴Ph₃)] ( 2 ) reacts with ^tBu₂PH exchanging only the P³Ph₃ group to give [{η²‐^tBu₂P¹–P²}Pt(P³H^tBu₂)(P⁴Ph₃)] ( 1 ). The crystal stucture determination of 1 together with its ³¹P{¹H} NMR data allow for an unequivocal assignment of the coupling constants in related Pt complexes. 1 crystallizes in the triclinic space group P1 (no. 2) with a = 1030.33(15), b = 1244.46(19), c = 1604.1(3) pm, α = 86.565(17)°, β = 80.344(18)°, γ = 74.729(17)°.     

On the (im)possibility of evaluating correct individual rate constants of chain propagation kp and chain termination kt by combining kp2/kt and kp/kt data for chain‐length dependent termination

On the basis of simulated data two ways of evaluating individual rate constants by combining k_p²/k_t and k_p /k_t (k_p , k_t = rate constants of chain propagation and termination, respectively) were checked considering the chain‐length dependence of k_t. The first way tried to make use of the fact that pseudostationary polymerization yields data for k_p²/k_t as well as for k_p /k_t referring to the very same experiment, in the second way k_p²/k_t (from steady state experiments) and k_p/k_t data referring to the same mean length of the terminating radical chains were compared. In the first case no meaningful data at all could be obtained because different averages of k_t are operative in the expressions for k_p /k_t and k_p²/k_t. In spite of the comparatively small difference between these two averages (≈15% only) this makes the method collapse. The second way, which can be regarded as an intelligent modification of the “classical” method of determining individual rate constants, at least succeeded in reproducing the correct order of magnitude of the individual rate constants. However, although stationary and pseudostationary experiments independently could be shown to return the same k_t for the same average chain‐length of terminating radicals within extremely narrow limits no reasonable chain‐length dependence of k_t could be derived in this way. The reason is an extreme sensitivity of the pair of equations for k_p/k_t and k_p²/k_t towards small errors and inconsistencies which renders the method unsuccessful even for the high quality simulation data and most probably makes it even collapse for real data. This casts a characteristic light on the unsatisfactory situation with respect to individual rate constants determined in the classical way, regardless of a chain‐length dependence of termination. As a consequence, all efforts of establishing the chain‐length dependence of k_t are recommended to avoid this way and should rather resort to methods based on inserting a directly determined k_p into the equations characteristic of k_p²/k_t or k_p/k_t, properly considering the chain‐length dependent character of k_t.     

Moment Sets of Bell–Shaped Distributions: Extreme Points,Extremal Decomposition and Chebysheff Inequalities

The paper deals with sets of distributions which are given by moment conditions and convex constraints on derivatives of their cumulative distribution functions. A general albeit simple method for the study of their extremal structure, extremal decomposition and topological or measure theoretical properties is developed. Its power is demonstrated by the application to bell–shaped distributions. Extreme points of their moment sets are characterized completely (thus filling a gap in the previous theory) and inequalities of Chebysheff type are derived by means of general integral representation theorems.     

Pair distribution function and related properties of star‐branched chains

Pair configurations of linear and star‐branched chains with F = 4, 8 and 12 arms embedded in the tetrahedral lattice were investigated. Pair data were determined by exact enumeration of all possible pair configurations. When the separation between two (linear) chains reached zero (r → 0) the pair distribution function g (r) read ≈ 0.15 for athermal and ≈ 0.6 for theta conditions in full accordance with former work. For star‐branched chains, g (r) approached a value zero at small separations for both thermodynamic conditions and the range of g (r) = 0 increased with an increase of the number of arms. As a consequence, the characteristic maximum of g (r) for theta conditions was the more pronounced the larger the number of arms. For stars, the extent to which mean squared dimensions and shape parameters depend on intermolecular distance was similar to that of linear chains, at least in the region of intermediate and large intermolecular separations. Transformation of the data into a concentration dependence revealed that with an increase in concentration, the dimensions decreased in the case of athermal solvents while they increased for θ‐solvents regardless of the functionality given.     

Lattice Monte Carlo investigations on copolymer systems, 1. Diblock copolymers

Symmetric diblock copolymers in dilute solution were examined by means of Monte Carlo simulations on a cubic lattice with respect to chain- and block dimensions, shape, local structure and number of contacts. The solvent was either a common good one, a common θ-solvent or a selective one for the two blocks. In all cases, repulsive interactions are operative between the blocks. In addition, the underlying homopolymers (athermal and θ) were divided into two parts (and treated as a block copolymer) for comparison. Chain-length was varied from 40 to 1280 segments leading to the expected values for the critical exponent 2v ≈ 1.2 for good solvent quality and 2v ≈ 1.0 for θ-solvent. Copolymers in a selective solvent scale with an intermediate exponent, 2v ≈ 1.13. The deviation of the mean squared dimensions of the copolymers from the sum of those of two homopolymers of the same length and for the same solvent quality as the blocks is largest for block copolymers in a common θ-solvent (where it exceeds 20%), while the blocks themselves have mostly the same dimensions as their underlying homopolymers of equal length. The shape of the copolymers, expressed by the parameter δ (asphericity) becomes more rod-like with increasing chain-length if there are (compact) θ-blocks in the molecule which are subject to mutual repulsive interaction. In these cases, θ exceeds the value of the homopolymers in the limit of infinite chain-length. The number of contacts per segment approaches a limiting value with increasing chain-length which is ≈0.20 for athermal chains and athermal blocks. For θ-chains and θ-blocks, a limiting value is not yet reached within the range of chainlengths investigated. The number of contacts per segment between two different blocks quickly tends to zero with increasing chain-length.