Interaction of glycine with cationic, anionic, and nonionic surfactants at different temperatures: a volumetric, viscometric, refractive index, conductometric, and fluorescence probe study

A number of thermodynamic parameters viz. apparent molar volumes, ϕ _v , partial molar volumes, , transfer volumes, , Falkenhagen coefficients, A, Jones–Dole coefficients, B, free energies per mole of solute, , and per mole of solvent, , molar refraction, R _D , and limiting molar conductivity, , have been calculated by using the experimentally measured densities, ρ, viscosities, η, refractive indices, n _D , and specific conductivities, κ, data of glycine (0.02–0.10 m) in 0.01 m aqueous sodium dodecyl sulphate, cetyltrimethylammonium bromide, and triton X-100 (TX-100) solutions at 298.15, 303.15, 308.15, and 313.15 K. The above calculated parameters were found to be sensitive towards the interactions prevailing in the studied amino acid–surfactant–water systems. Moreover, fluorescence study using pyrene as a photophysical probe has also been carried out, the results of which support the conclusions obtained from other techniques.     

Linear polymers in nonhomogeneous flow fields. II. The cross-stream migration velocity

The cross-stream migration velocity v _⊥ is that part of the velocity of a particle which has no component in the direction of the undistrubed flow. In order to obtain v _⊥ for bead–spring model macromolecules, it is necessary to compute the trace of the matrix product \documentclass{article}\pagestyle{empty}\begin{document}$ \underline \ell \cdot \underline {{\rm \hat C}} $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \underline \ell $\end{document} denotes the migration matrix and \documentclass{article}\pagestyle{empty}\begin{document}$ \underline {{\rm \hat C}} $\end{document} is the modified Kramer's matrix. In this paper this is done via an eigenvalue calculation, where the eigenvalues are estimated by using the Rouse eigenfunctions. The results are then checked against the few known exact results and excellent agreement is found. It turns out that v _⊥ depends on the third power of the molecular weight for free-draining polymers. The dependence upon molecular weight becomes weaker with increasing hydrodynamic interaction until, in the nondraining limit, v _⊥ ∝ M^2.5. A simple yet accurate formula for v _⊥ is proposed. In conjunction with the results for D (of Part I), purely rotational flow fields are shown to be characterized by a single parameter, the particle Peclet number Pe. Up to a constant of order one (actually a function of the hydrodynamic interaction parameters h^* and h, which can vary only between 0.8 and 2.057), Pe depends only upon D, the mean-square equilibrium extension R, and q₀, the magnitude of the maximum shear rate for the flow.     

Separation of dextrans by gel permeation chromatography

The role of the intrinsic viscosity [η] as separation parameter in gel permeation chromatography (GPC) was studied for dextrans (from Leuconostoc mesenteroids B512) dissolved in water with deactivated silicagel (Porasil) as the column-filling material. For that purpose specific viscosities of dextran fractions eluted by GPC were measured as a function of the elution volume v. Provided that the elution volumes are corrected for zonal spreading, they are related to the intrinsic viscosities in an unambiguous way, probably reflecting a unique relationship between degree of branching and molecular weights. This was further investigated by developing an iteration method to prepare two calibration curves γ(v) and g(v), respectively, relating ln[\documentclass{article}\pagestyle{empty}\begin{document}$\left[ {\bar \eta } \right]$\end {document}] and InM (M is the molecular weight) to v. It required that the weight-average molecular weight M _w, the number-average molecular weight M _n, and the average intrinsic viscosity [\documentclass{article}\pagestyle{empty}\begin{document}$\left[ {\bar \eta } \right]$\end {document}] for a number of dextran samples (broad distributions) be previously known. The calibration curves found lead to consistent values of the above-mentioned averages. Moreover, they allow-establishment of the [\documentclass{article}\pagestyle{empty}\begin{document}$\left[ {\bar \eta } \right]$\end {document}]-M relationship over the range 5000 < M < 500,000.     

An entanglement model for the dependence of fracture surface energy on molecular weight

Over the last decade, empirical evidence has indicated that the effective surface energy γ associated with the fracture of noncrystalline is a linear function of the reciprocal of the viscosity–average molecular weight: \documentclass{article}\pagestyle{empty}\begin{document}$ \gamma = \gamma _\infty - b\bar M_v ^{ - 1} $\end{document}. For poly(methyl methacrylate), data of J. P. Berry, G. C. Berry and Fox show that gamma; ～ 0 at about the same value of M?_v that corresponds to the polymer chain-entanglement length. From this fact, we have developed an entanglement network model for fracture, that bears a resemblance to F. Bueche's entanglement model for the melt viscosity of bulk polymers. Our model allows for the expression of the previously empirical constants, γ_∞ and b, in terms of molecular parameters: \documentclass{article}\pagestyle{empty}\begin{document}$ {{\gamma _\infty = \gamma _{\rm s} A_{\rm s} Z_{\rm c} \rho _{\rm c} N_A } \mathord{\left/ {\vphantom {{\gamma _\infty = \gamma _{\rm s} A_{\rm s} Z_{\rm c} \rho _{\rm c} N_A } {\bar M_{\rm s} }}} \right. \kern-\nulldelimiterspace} {\bar M_{\rm s} }} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ b = 2({{\bar M_v } \mathord{\left/ {\vphantom {{\bar M_v } {\bar M_n }}} \right. \kern-\nulldelimiterspace} {\bar M_n }})\gamma _\infty M_{\rm f} $\end{document} where M?_n and M?_f are the number-average molecular weights of the polymer and of the free chain ends, M?_v is the viscosity-average molecular weight, γ_s is the average fracture-energy per entanglement in the craze volume, A_s is the average cross-sectional area of the polymer chain, Z_c and ρ_c are the thickness and density of crazed material on the fracture surface, respectively; M?_s is the average strand molecular weight between entanglements, and N_A is AvogadrO's number.     

Tensile stress and recoverable strain measurements on polystyrene melts. Interpretation of results in terms of rubberlike elasticity

Extensional tests at constant strain rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \varepsilon $\end{document} have been carried out on polystyrene melts with different molecular weight distributions at various temperatures and strain rates. The true tensile stress is found to be well approximated by the sum of two contributions: (1) a neo-Hookean expression involving the recoverable strain and (2) a contribution rapidly reaching a steady-state value. Two experimental parameters can be defined: an elasticity modulus \documentclass{article}\pagestyle{empty}\begin{document}$ G(\dot \varepsilon ) $\end{document} from (1) and a viscosity \documentclass{article}\pagestyle{empty}\begin{document}$ \eta _{\rm v} (\dot \varepsilon ) $\end{document} from (2). It is further shown that time-temperature equivalence applies not only to the stress but also to the recoverable strain and to G and η_v. The dependence of G and η_v on strain rate is then discussed. For high strain rates, G is close to the linear viscoelastic plateau modulus of PS melts and decreases with decreasing strain rate. The value of η_v is found to a good approximation to be equal to three times the shear viscosity taken at a shear rate equivalent to the elongational strain rate.     

Unicycle Graphs with Maximum Generalized Topological Indices

Let G be an unicycle graph and d _v the degree of the vertex v. In this paper, we investigate the following topological indices for an unicycle graph , , where m ≥ 2 is an integer. All unicycle graphs with the largest values of the three topological indices are characterized. This research is supported by the National Natural Science Foundation of China(10471037)and the Education Committee of Hunan Province(02C210)(04B047).     

Exact solution of the relativistic dynamics of a spin‐½ particle moving in a homogeneous magnetic field

The relativistic dynamics of one spin‐½ particle moving in a uniform magnetic field is described by the Hamiltonian $\mathbf{h}^{0}_{D}(\pi)=c\alpha\cdot\pi+\beta mc^{2}$. The discrete (and semidiscrete) eigenvalues and the corresponding eigenspinors are in principle known from the work of Dirac, Rabi, and Bloch. These are extensively reviewed here. Next, exact solutions are worked out for the recoil dynamics in relative coordinates, which involves the Hamiltonian $\mathbf{h}^{0}_{D}(-\mathbf{k})=-c\alpha\cdot\mathbf{k}+\beta mc^{2}$. Exact solutions are also explicitly calculated in the case where the spin‐½ particle has an anomalous magnetic moment such that its Hamiltonian is given by $\mathbf{h}_{D}(\pi)=\mathbf{h}^{0}_{D}(\pi)-\beta\mu_{\mathrm{ano}}\sigma\cdot\mathbf{B}$. Similar exact solutions are derived here when the recoiling particle has an anomalous magnetic moment, that is, the eigenvalues and eigenspinors of the Hamiltonian $\mathbf{h}_{D}(-\mathbf{k})=\mathbf{h}^{0}_{D}(-\mathbf{k})-\beta\mu_{\mathrm{ano}}\sigma\cdot\mathbf{B}$ are explicitly obtained. The diagonalized and separable form of the Hamiltonian h _D(π), written as $\tilde{\mathbf{h}}_{D}(\pi)$, has exceedingly simple forms of eigenspinors. Similarly, the diagonalized and separable form of the operator h _D(? k ), written as $\tilde{\mathbf{h}}_{D}(-\mathbf{k})$, has very simple eigenspinors. The importance of these exact solutions is that the eigenspinors can be used as bases in a calculation involving many spin‐½ particles placed in a uniform magnetic field. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 209–217, 2001     

Densities, Specific Heat Capacities, Apparent and Partial Molar Volumes and Heat Capacities of Glycine in?Aqueous Solutions of Formamide, Acetamide, and?N,N-Dimethylacetamide at T=298.15?K and?Ambient Pressure

Apparent molar volumes (V _2,φ ) and heat capacities (C _p2,φ ) of glycine in known concentrations (1.0, 2.0, 4.0, 6.0, and 8.0 mol⋅kg⁻¹) of aqueous formamide (FM), acetamide (AM), and N,N-dimethylacetamide (DMA) solutions at T=298.15 K have been calculated from relative density and specific heat capacity measurements. These measurements were completed using a vibrating-tube flow densimeter and a Picker flow microcalorimeter, respectively. The concentration dependences of the apparent molar data have been used to calculate standard partial molar properties. The latter values have been combined with previously published standard partial molar volumes and heat capacities for glycine in water to calculate volumes and heat capacities associated with the transfer of glycine from water to the investigated aqueous amide solutions, D[`(V)]<sub>2,tr</sub><sup>o</sup>\Delta\overline{V}_{\mathrm{2,tr}}^{\mathrm{o}} and D[`(C)]_p2,tr^o\Delta\overline{C}_{p\mathrm{2,tr}}^{\mathrm{o}} respectively. Calculated values for D[`(V)]<sub>2,tr</sub><sup>o</sup>\Delta\overline{V}_{\mathrm{2,tr}}^{\mathrm{o}} and D[`(C)]_p2,tr^o\Delta\overline{C}_{p\mathrm{2,tr}}^{\mathrm{o}} are positive for all investigated concentrations of aqueous FM and AM solutions. However, values for D[`(C)]_p2,tr^o\Delta\overline{C}_{p\mathrm{2,tr}}^{\mathrm{o}} associated with aqueous DMA solutions are found to be negative. The reported transfer properties increase with increasing co-solute (amide) concentration. This observation is discussed in terms of solute + co-solute interactions. The transfer properties have also been used to estimate interaction coefficients.     

Volumetric,Acoustic and Transport Properties of Metformin Hydrochloride Drug in Aqueous <Emphasis Type="SmallCaps">d</Emphasis>-Glucose Solutions at <Emphasis Type="Italic">T</Emphasis> = (298.15–318.15) K

Apparent molar volumes, apparent molar adiabatic compressibilities and viscosity B-coefficients for metformin hydrochloride in aqueous d-glucose solutions were determined from solution densities, sound velocities and viscosities measured at T = (298.15–318.15) K and at pressure p = 101 kPa as a function of the metformin hydrochloride concentrations. The standard partial molar volumes (\( \phi_{V}^{0} \)) and slopes (\( S_{V}^{*} \)) obtained from the Masson equation were interpreted in terms of solute–solvent and solute–solute interactions, respectively. Solution viscosities were analyzed using the Jones–Dole equation and the viscosity A and B coefficients discussed in terms of solute–solute and solute–solvent interactions, respectively. Adiabatic compressibility (\( \beta_{s} \)) and apparent molar adiabatic compressibility (\( \phi_{\kappa }^{{}} \)), limiting apparent molar adiabatic compressibility (\( \phi_{\kappa }^{0} \)) and experimental slopes (\( S_{\kappa }^{*} \)) were determined from sound velocity data. The standard volume of transfer (\( \Delta_{t} \phi_{V}^{0} \)), viscosity B-coefficients of transfer (\( \Delta_{t} B \)) and limiting apparent molar adiabatic compressibility of transfer (\( \Delta_{t} \phi_{\kappa }^{0} \)) of metformin hydrochloride from water to aqueous glucose solutions were derived to understand various interactions in the ternary solutions. The activation parameters of viscous flow for the studied solutions were calculated using transition state theory. Hepler’s coefficient \( (d\phi /dT)_{p} \) indicated the structure making ability of metformin hydrochloride in the ternary solutions.     

Effect of the excluded volume on specific rate of combination reactions between polymer radicals

The specific rate k_D for reaction between polymer radicals is formulated when the potential of average force on the basis of the excluded volume affects the motion of the polymer radicals. This rate is given by \documentclass{article}\pagestyle{empty}\begin{document}$ k_D = Fk_S \left( {{\rm with}\ {F} = \sum\limits_{s = 0}^\infty {{{[ ‐ 2(\alpha ^2 ‐ 1)]} \mathord{\left/ {\vphantom {{[ ‐ 2(\alpha ^2 ‐ 1)]} {(s + 1)^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern‐\nulldelimiterspace} 2}} }}} \right. \kern‐\nulldelimiterspace} {(s + 1)^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern‐\nulldelimiterspace} 2}} }}} } \right) $\end{document} where k_S is specific rate of reaction between radical chain ends and α is the average expansion of the polymer arising from the long-range effects. The effect of the excluded volume reduces k_D. F depends on the degree of polymerization of the polymer radical when α ≠ 1. These results are discussed in terms of the experimental data for very low polymer concentrations.     

The Radical Anions and Trianions of 1,8-Diphenylnaphthalene and of Some of its Derivatives Containing a Cyclophane Substructure

The radical anions of 1,8-diphenylnaphthalene ( 1 ) and its decadeuterio-(D₁₀- 1 ) and dimethyl-( 2 ) derivatives, as well as those of [2.0.0] (1,4)benzeno(1,8)naphthaleno(1,4)benzenophane ( 3 ) and its olefinic analogue ( 4 ) have been studied by ESR and ENDOR spectroscopy, At a variance with a previous report, the spin population in \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{-\kern-4pt {.}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {2}^{-\kern-4pt {.}} $\end{document} is to a great extent localized in the naphthalene moiety. A similar spin distribution is found for \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {3}^{-\kern-4pt {.}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {4}^{-\kern-4pt {.}} $\end{document}. The ground conformations of \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{-\kern-4pt {.}} $\end{document}-\documentclass{article}\pagestyle{empty}\begin{document}$ \rm {4}^{-\kern-4pt {.}} $\end{document} are chiral of C₂ symmetry. For \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{-\kern-4pt {.}} $\end{document}, an energy barrier between these conformations and the angle of twist about the bonds linking the naphthalene moiety with the phenyl substituents were estimated as ca. 50 kJ/mol and ca. 45°, respectively. The radical trianions of 1 , D₁₀- 1 , and 2 , have also been characterized by their hyperfine data. In \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{3-\kern-4pt {.}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {2}^{3-\kern-4pt {.}} $\end{document}, the bulk of the spin population resides in the two benzene rings so that these radical trianions can be regarded as the radical anions of ‘open-chain cyclophanes’ with a fused naphthalene π-system bearing almost two negative charges. The main features of the spin distribution in both \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{-\kern-4pt {.}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \rm {1}^{3-\kern-4pt {.}} $\end{document} are correctly predicted by an HMO model of 1 .     

Oligomeric proanthocyanidin glycosides ofRhodiola pamiroalaica

Two oligomeric proanthocyanidin glycosides have been isolated from the roots ofRhodiola pamiroalaica and their structures and relative configurations have been established: — RP-1 - and — RP-2. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 484–491, July–August, 1998.     

On zeroth-order general Randić index of conjugated unicyclic graphs

Let G be a graph and d _v denote the degree of the vertex v in G. The zeroth-order general Randić index of a graph is defined as where α is an arbitrary real number. In this paper, we investigate the zeroth-order general Randić index of conjugated unicyclic graphs G (i.e., unicyclic graphs with a perfect matching) and sharp lower and upper bounds are obtained for depending on α in different intervals.     

The standard transported entropy of chloride ion in H2O and D2O

Transported entropies of the chloride ion, , in H₂O and in D₂O at 25°C and at concentrations ranging from 0.001 to 0.04m have been determined from the measurements of the steady-state (final) thermoelectric powers of the silver-silver chloride thermocell. Experimental data was extrapolated to infinite dilution to obtain the standard transported entropy . The concentration dependence of is examined and the solvent-isotope effect on the transported entropy is investigated. Thermodynamic data on the entropy of transfer of chloride ion from H₂O to D₂O is used to estimate the difference of the standard ionic entropy of transport in H₂O and D₂O for chloride ion.     

Flow-dependent rejection of polystyrene from microporous membranes

Dilute solutions of polystyrene (molecular weight 1 × 10⁵?2 × 10⁷) in a mixed solvent of 90% carbon tetrachloride-10% methanol were filtered through track-etched porous mica membranes. The reflection coefficient σ, defined as the fraction of polymer held back by the membrane, was measured as a function of polymer size r_s, pore radius r_o, and solvent flow rate q through each pore. Polymer size was characterized by the Stokes-Einstein radius, as determined from diffusion coefficients measured by quasielastic light scattering, and chain relaxation times τ were estimated from measured intrinsic viscosities. In the case of chains whose unperturbed radius was smaller than the pore, σ depended on the ratio r_s/r_o in the manner predicted by a hard-sphere theory, as long as \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma \tau < < 1 $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} is the mean rate of strain of solvent at the pore entrance. However, when the polymer chains exceeded the pore in size, σ depended on flow rate and decreased from almost unity, at small q, toward zero at high q. The relationship between σ and q was nearly independent of polymer and pore size, consistent with a theory based on scaling concepts of how polymer chains deform at the entrance of a pore, but the reduction in σ as q increased was very gradual and did not exhibit the sharp transition predicted by the theory. We were able to empirically correlate all the data for σ when r_s > r_o by a single similarity variable \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = {{({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})} \mathord{\left/ {\vphantom {{({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})} {(\dot \gamma \tau)^n}}} \right. \kern-\nulldelimiterspace} {(\dot \gamma \tau)^n}} \sim ({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})^{1 - 3n} q^{- n} $\end{document}; a least-squares fit gave n = 0.33, showing that σ is insensitive to polymer size for large chains.     

Structures and formation of \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm C}_{{\rm 4}} {\rm H}_{{\rm 8}} } \right]_{}^{_.^ + } $\end{document} ions

Several \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm C}_{{\rm 4}} {\rm H}_{{\rm\ 8}} } \right]_{}^{_.^ + } $\end{document} ion isomers yield characteristic and distinguishable collisional activation spectra: \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm 1-butene} } \right]_{}^{_.^ + } $\end{document} and/or \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm 2-butene} } \right]_{}^{_.^ + } $\end{document} (a-b), \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm isobutene} } \right]_{}^{_.^ + } $\end{document} (c) and [cyclobutane]⁺ (e), while the collisional activation spectrum of \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm methylcyclopropane} } \right]_{}^{_.^ + } $\end{document} (d) could also arise from a combination of a-b and c. Although ready isomerization may occur for \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm C}_{{\rm 4}} {\rm H}_{{\rm 8}} } \right]_{}^{_.^ + } $\end{document} ions of higher internal energy, such as d or e → a, b, and/or c, the isomeric product ions identified from many precursors are consistent with previously postulated rearrangement mechanisms. 1,4-Eliminations of HX occur in 1-alkanols and, in part, 1-buthanethiol and 1-bromobutane. The collisional activation data are consistent with a substantial proportion of 1,3-elimination in 1- and 2-chlorobutane, although 1,2-elimination may also occur in the latter, and the formation of the methylcycloprpane ion from n-butyl vinyl ether and from n-butyl formate. Surprisingly, cyclohexane yields the \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm linear butene} } \right]_{}^{_.^ + } $\end{document} ions a-b, not \documentclass{article}\pagestyle{empty}\begin{document}$ \left[{{\rm cyclobutane} } \right]_{}^{_.^ + } $\end{document}, e.     

The Radical Anions of 1,2-diphenylcyclohexene and Structurally Related Compounds. Conformational ESR and ENDOR studies

ESR, ENDOR, and TRIPLE resonance studies have been performed on the radical anions of 1,2-diphenylcyclohex-1-ene ( 4 ), 1,2-di(perdeuteriophenyl)cyclohex-1-ene ((D₁₀) 4 ) the trans-configurated 3,4-diphenyl-8-oxabicyclo[4.3.0]non-3-ene ( 5 ) and its 2,2,5,5-tetradeuterio derivative (D₄) 5 , and 2,3-diphenyl-8,9,10-trinorborn-2-ene ( 6 ). The spectra of \documentclass{article}\pagestyle{empty}\begin{document}$ 4^{- \atop \dot{}} $\end{document} exhibit strong temperature dependence along with a specific broadening of ESR hyperfine lines and proton ENDOR signals. The coupling constant, which bears the main responsibility for these features, is that of the β-protons in the quasi-equatorial positions of the cyclohexene ring, and the experimental findings are readily rationlized in terms of relatively modest conformational changes without invoking the inversion of the half-chair form. The hyperfine data for the β-protons in \documentclass{article}\pagestyle{empty}\begin{document}$ 5^{- \atop \dot{}} $\end{document} closely resemble the corresponding low-temperature values for \documentclass{article}\pagestyle{empty}\begin{document}$ 4^{- \atop \dot{}} $\end{document}, However, the ‘unusual’ features observed for \documentclass{article}\pagestyle{empty}\begin{document}$ 4^{- \atop \dot{}} $\end{document} are absent in the ESR and ENDOR spectra of \documentclass{article}\pagestyle{empty}\begin{document}$ 5^{- \atop \dot{}} $\end{document}, because the half-chair conformation of the cyclohexene ring in \documentclass{article}\pagestyle{empty}\begin{document}$ 5^{- \atop \dot{}} $\end{document} is deprived of its flexibility. Although the boat form of this ring in \documentclass{article}\pagestyle{empty}\begin{document}$ 6^{- \atop \dot{}} $\end{document} is also rigid, the spectra of \documentclass{article}\pagestyle{empty}\begin{document}$ 6^{- \atop \dot{}} $\end{document} are temperature-dependent, due to an interconversion between two propeller-like conformations of the phenyl groups. The pertinent barrier is 30 ± 5 kJ ·mol^?1. An analogous interconversion presumably takes place in \documentclass{article}\pagestyle{empty}\begin{document}$ 4^{- \atop \dot{}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ 5^{- \atop \dot{}} $\end{document} as well, but, unlike \documentclass{article}\pagestyle{empty}\begin{document}$ 6^{- \atop \dot{}} $\end{document}, it is not amenable to experimental study.