Estimation of the standard entropy change on complete reduction of oxide MmOn

The standard entropy change ΔS° for the reduction of nonmagnetic, nonconducting oxides, $\text{M}{}_{\mathrm{m}}\text{O}{}_{\mathrm{n}}\text{(}\text{s}\text{) = mM(}\text{s}\text{) + (}\text{n}\text{2}\text{)}\text{O}{}_2\text{(g)}$, has been estimated as a function of m, n, and temperature T from motional entropies of oxygen molecules and vibrational entropies of solid phases. An available formula of ΔS°_calc = a · m + b · n with constant a and b based on effective Debye temperatures, θ_M = 165 K for M and θ_OX = 540 K for M_mO_n, agrees well with the observed ΔS°_obs for M₂O, MO, M₂O₃, MO₂, M₂O₅, and MO₃ in the temperature range T = 300 – 1300 K. Possible electronic entropy corrections are applied to ΔS°_calc for M₂O₇ and MO₄.     

Dependence of polymer specific volume on molecular characteristics

Linear and branched bisphenol A polycarbonate (PC) samples were characterized by their average molecular weights, $\text{M}{}_{\mathrm{<mtext>n</mtext>}}$ and $\text{M}{}_{\mathrm{<mtext>w</mtext>}}$, polydispersity degree $\text{q =}\text{M}{}_{\mathrm{<mtext>w</mtext>}}\text{/}\text{M}{}_{\mathrm{<mtext>n</mtext>}}$, and branching degree g_v. The weight fraction of microgel was also determined for branched samples. The samples were amorphized and densities were measured at 23°C to obtain the values of specific volume, v_sp. The dependence of v_sp on molecular characteristics is described by the multivariable power function $\text{Δv}{}_{\mathrm{<mtext>sp</mtext>}}\text{=}\text{A}{}_{\mathrm{sp}}\text{M}{}_{\mathrm{<mtext>x</mtext>}}{}^{\mathrm{<mtext>a</mtext>}}\text{q}{}^{\mathrm{<mtext>apx</mtext>}}\text{g}{}_{\mathrm{<mtext>v</mtext>}}{}^{\mathrm{<mtext>ab</mtext>}}$, where Δv_sp = v_sp ? v_sp,∞, and A_sp, a, a_px and a_b are constants. It has been confirmed that a = ?1, a_pn = 0 and a_pw = 1. It has also been found that the branching exponent a_b significantly depends on microgel content. The relationships found for PC should, in principle, be valid for other polymers. Examples based on literature data are given for linear polyethylene and polydimethylsiloxane.     

Determination of the vapour pressures of o-, m-, and p-dinitrobenzene by the torsion-effusion method

The vaporization of o-, m-, and p-dinitrobenzenes was investigated by means of the torsion-effusion method and the selected equations for vapour pressure p as a function of temperature T are:

$\text{o-dinitrobenzene: log}{}_{10}\text{(}\text{p}\text{atm}\text{)=(7.03±0.34)?(4270±120)}\text{K}\text{T}\text{,m-dinitrobenzene: log}{}_{10}\text{(}\text{p}\text{atm}\text{)=(7.66±0.28)?(4400±100)}\text{K}\text{T}\text{,p-dinitrobenzene: log}{}_{10}\text{(}\text{p}\text{atm}\text{)=(8.34±0.34)?(4860±120)}\text{K}\text{T}$

The sublimation enthalpies ΔH^o(o-, 298.15 K) = (21.0 ± 0.5) kcal_th mol^?1, ΔH^o(m-, 298.15 K) = (20.8 ± 0.2) kcal_th mol^?1, and ΔH^o(p-, 298.15 K) = (23.0 ± 0.6) kcal_th mol^?1, are also derived by means of the second- and third-law treatments of the results.     

Nonstoichiometry and defect structure of the perovskite-type oxides La1−xSrxFeO3−°

In order to elucidate the defect structure of the perovskite-type oxide solid solution La_1?xSr_xFeO_3?δ (x = 0.0, 0.1, 0.25, 0.4, and 0.6), the nonstoichiometry, δ, was measured as a function of oxygen partial pressure, P_O2, at temperatures up to 1200°C by means of the thermogravimetric method. Below 200°C and in an atmosphere of P_O2 ≥ 0.13 atm, δ in La_1?xSr_xFeO_3?δ was found to be close to 0. With decreasing log P_O2, δ increased and asymptotically reached $\text{x}\text{2}$. The value corresponding to $\text{δ =}\text{x}\text{2}$ was about ?10 at 1000°C. With further decrease in log P_O2, δ slightly increased. For LaFeO_3?δ, the observed δ values were as small as <0.015. It was found that the relation between δ and log P_O2 is interpreted on the basis of the defect equilibrium among Sr′_La (or V?_La for the case of LaFeO_3?δ), V^··_O, Fe′_Fe, and Fe^·_Fe. Calculations were made for the equilibrium constants K_ox of the reaction

$\text{1}\text{2}\text{O}{}_2\text{(g) + V}{}^{\mathrm{··}}{}_{\mathrm{o}}\text{+ 2Fe}{}^{\mathrm{x}}{}_{\mathrm{Fe}}\text{= O}{}^{\mathrm{x}}{}_{\mathrm{o}}\text{+ 2Fe}{}^{\mathrm{·}}{}_{\mathrm{Fe}}$

and K_i for the reaction

$\text{2Fe}{}^{\mathrm{x}}{}_{\mathrm{Fe}}\text{= Fe}{}^{\mathrm{\prime }}{}_{\mathrm{Fe}}\text{+ Fe}{}^{\mathrm{·}}{}_{\mathrm{Fe·}}$

Using these constants, the defect concentrations were calculated as functions of P_O2, temperature, and composition x. The present results are discussed with respect to previously reported results of conductivity measurements.     

Mutual solubility of n-butanol + water under high pressures

The mutual solubilities of {xCH₃CH₂CH₂CH₂OH+(1-x)H₂O} have been determined over the temperature range 302.95 to 397.75 K at pressures up to 2450 atm. An increase in temperature and pressure results in a contraction of the immiscibility region. The results obtained for the critical solution properties are: T_o(U.C.S.T.) = 397.85 K and x_o = 0.110 at 1 atm; $\text{(}\text{dT}{}_{\mathrm{o}}\text{d}\text{p}\text{) = ?(12.0±0.5)×10}{}^{\mathrm{?3}}\text{K atm}{}^{\mathrm{?1}}$ at p < 400 atm and $\text{(}\text{dT}{}_{\mathrm{o}}\text{d}\text{p}\text{) = ?(7.0±0.7)×10}{}^{\mathrm{?3}}\text{K atm}{}^{\mathrm{?1}}$ at 800 atm < p < 2500 atm; $\text{(}\text{dx}{}_{\mathrm{o}}\text{d}\text{T}\text{) = ?(4.0±0.5)×10}{}^{\mathrm{?4}}\text{K}{}^{\mathrm{?1}}$.     

Détermination des constantes de la relation de Mark-Houwink et des caractéristiques d'un polymère à partir d'un échantillon polymoléculaire—I.: Méthode expérimentale, étalonnage et exploitation des résultats application au polystyrène

We report here a method which affords the magnitude of the characteristic parameters of a macromolecular chain starting from a polydisperse sample. A statistical treatment of viscosity measurements made on the small fractions of a GPC elution wave enables us to assign to each of them its $\text{M}{}_{\mathrm{n}}$ value. By numerical calculations it is then possible on the one hand to evaluate the Mark-Houwink constants, $\text{M}{}_{\mathrm{n}}\text{and}\text{M}{}_{\mathrm{w}}$, the f(M) function and on the other hand to estimate according to a hydrodynamic model, the unperturbed geometrical dimensions. The method is tested for polystyrene samples under conditions which allow the dissolution of many polymers, viz in tetrachloroethane (TCE) at 50° and N-methylpyrrolidone at 85°.     

Dilute solution properties of poly(N-vinyl-3,6-dibromo carbazole)—III. Phase equilibrium studies

The phase relationships of poly(N-vinyl-3,6-dibromo carbazole) (PVK-3, 6-Br₂) were examined for four solvents, viz, o-chlorophenol, p-chloro-m-cresol, o-dichlorobenzene and bromobenzene. Upper critical solution temperatures (UCST) have been determined for solutions of PVK-3,6-Br, fractions in o-chlorophenol and p-chloro-m-cresol over the molecular weight range $\text{M}{}_{\mathrm{<mtext>w</mtext>}}\text{× 10}{}^{\mathrm{?4}}\text{= 125.0}\text{to}\text{4.8}$. The Flory temperature, θ, obtained from UCST for the PVK-3,6-Br₂/o-chlorophenol and PVK-3,6-Br₂/p-chloro-m-cresol systems are 66.0 and 112.9°C, respectively. The θ-temperatures were checked against molecular weight and viscosity data to determine the Mark-Houwink equations for these two theta solvents, with satisfactory agreement. The relations are

$\text{[ν] = 27.5}{}_4\text{× 10}{}^{\mathrm{?10}}\text{×}\text{M}{}^{0.50}{}_{\mathrm{<mtext>w</mtext>}}\text{(o-}\text{chlorophenol}\text{, 60.0°}\text{C}$

$\text{[ν] = 30.2}{}_4\text{× 10}{}^{\mathrm{?10}}\text{×}\text{M}{}^{0.50}{}_{\mathrm{<mtext>w</mtext>}}\text{(p-}\text{chloro}\text{-m}\text{cresol}\text{, 112.9°}\text{C}$

The characteristic ratio C_∞ = 〈R²〉₀/nl² was found to be 16.6 in o-chlorophenol at 60.0°C and 17.6 in p-chloro-m-cresol at 112.9°C. The value of the characteristic ratio C_∞ of PVK-3,6-Br₂ is of the same order of that for poly(N-vinyl carbazole). This indicates that the bromine atoms at the 3 and 6 (meta) positions have only an inappreciable effect on the hindering potential for rotation about the CC bond. This agreement of C_∞ for both polymers may also be taken as indicating that the effect of interaction between polar groups at the m-position on the hindering potential for rotation is small. The phase diagrams of PVK-3,6-Br₂ obtained in o-dichlorobenzene and bromobenzene seem to be characteristic of organized phase structures such as those found in systems exhibiting thermoreversible gelation. Light scattering measurement on PVK-3,6-Br₂ dissolved in o-dichlorobenzene, a gelation promoting solvent, and tetrahydrofuran, a very good solvent, strongly indicate that the macromolecular species in o-dichlorobenzene contain some extent supermolecular structures (aggregates, association of chain segments, etc.). These characteristic structures of PVK-3,6-Br₂ in o-dichlorobenzene and bromobenzene at 25°C are also characterized by high values of the Huggins' constant k′; for tetrahydrofuran solutions, the k′ values were in the range normally found for many good solvent-polymer systems.     

Thermophysical properties of the intermetallic Mn3MN perovskites III. Heat capacity of the solid solution Mn3.2Ga0.8N

The heat capacity of the solid solution Mn_3.2Ga_0.8N was measured between 5 to 330 K by adiabatic calorimetry. A sharp anomaly with first-order character was detected at T_A = (160.5±0.5) K, corresponding to a magnetic rearrangement and a lattice expansion. No sharp anomaly was observed at T_c ≈ 260 K where the magnetic ordering takes place; instead, a smooth shoulder was detected. The thermodynamic functions at 298.15 K are $\text{C}{}_{\mathrm{<mtext>p,</mtext><mtext>m</mtext>}}\text{R}\text{= 15.16}$, $\text{S}{}_{\mathrm{m}}{}^{\mathrm{o}}\text{R}\text{= 18.57}$, $\text{{H}{}_{\mathrm{m}}{}^{\mathrm{o}}\text{(T)?H}{}_{\mathrm{m}}{}^{\mathrm{o}}\text{(0)}}\text{R}\text{= 2896}\text{K}$, $\text{?{G}{}_{\mathrm{m}}{}^{\mathrm{o}}\text{(T)?H}{}_{\mathrm{m}}{}^{\mathrm{o}}\text{(0)}}\text{RT}\text{= 8.85}$. At low temperatures the coefficient for the linear electronic contribution to the heat capacity was derived: γ = (0.031±0.003) J·K^?2·mol^?1. Moreover, the different contributions to the heat capacity were obtained and the electronic origin of the phase transitions was established.     

Heat capacity and thermodynamic functions of CsCrCl3 and RbCrCl3. Structural phase transitions

We present the heat capacities measured by adiabatic calorimetry from 6 to 350 K, and by differential scanning calorimetry from 300 to 500 K, of CsCrCl₃ and RbCrCl₃. A first-order transition at T_c = (171.1±0.1) K was detected for CsCrCl₃. The RbCrCl₃ showed at T_c = (193.3±0.1) K a transition with thermal hysteresis at temperatures just below the maximum. At T₁ = (440±10) K a continuous transition was also detected. Furthermore, at T_N ≈ 16 K, and for both compounds, a small bump due to magnetic long-range ordering was observed. The thermodynamic functions at 298.15 K are

     

11.

General approach to polymer properties dependent on molecular characteristics     

Z. Dobkowski 《European Polymer Journal》1981,17(11):1131-1144

The general equation

where P is a polymer property, Π is the sign of product, A is a constant, v_i is the ith variable and a_i is the exponent of ith variable, has been proposed for the dependence of some polymer properties on molecular weight, molecular weight distribution and long-chain branching. The data confirming the proposed equation have been taken from published theoretical and experimental papers on intrinsic viscosity, melt viscosity and glass transition temperature, as well as on viscosity of polymer solutions. Examples of application are given.     

12.

A theory of viscosity of dilute and moderately concentrated polymer solutions     

V.P. Budtov 《European Polymer Journal》1981,17(2):191-195

A model theory of viscosity η for moderately concentrated polymer solutions is based on the assumption of a “local viscosity” effect and intermolecular hydrodynamic and thermodynamic interactions. It is shown that η is given by

$\text{η = η}{}_{\mathrm{o}}\text{{1 + γc[η]}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{·}\text{exp}\text{H}{}_{\mathrm{o}}\text{RT}\text{aø}\text{1 ? aø}$

where γ is 0–0.4 and depends on the quality of the solvent, a varies between 0,4 and 0.8 and depends on the fraction of the “free volume” of the systems, H₀ is the activation energy of the solvent and π is the polymer volume concentration. The dependence of η and “activation energy” of π and T for various molecular weights and qualities of solvents is described quantitatively. Anomalous dependences of [η] and of η on M for low polymer are obtained. An expression for η is proposed:

$\text{η}\text{η}{}_{\mathrm{o}}{}^{\mathrm{<mtext>1\; ?\; 2</mtext><mtext>K</mtext>}}\text{= {1 + (1 ? 2K)c[η]}F(π)}$

where K is the Huggins-Martin coefficient and F(π) = 1 for most solutions when T is > T_g. For poor solvents the H vs c curve (where H is the activation energy of η of solution) has a minimum value at moderate concentrations. For good solvents, H depends slightly on the molecular weight according to an empirical equation:

$\text{H = H}{}_{\mathrm{o}}\text{+}\text{660}\text{α}{}^3\text{1}\text{n}\text{η}\text{η}{}_{\mathrm{o}}$

Expressions are given from the viscosities of solutions of miscible and also solutions of immiscible polymers.     

13.

K_xP₂W₂O₁₆: A bronze with a tunnel structure built up from PO₄ tetrahedra and WO₆ octahedra     

J.P. Giroult  M. Goreaud  Ph. Labbe  B. Raveau 《Journal of solid state chemistry》1982,44(3):407-414

The structure of a $\text{K}{}_{\mathrm{x}}\text{P}{}_2\text{W}{}_4\text{O}{}_{16}\text{(x ? 0.4)}$ crystal was established by X-ray analysis. The solution in the cell of symmetry $\text{P2}{}_1\text{m}$, with a = 6.6702(5), b = 5.3228(8), c = 8.9091(8) Å, β = 100.546(7)°, Z = 1, has led to R = 0.033 and R_w = 0.036 for 2155 reflections with $\text{σ(I)}\text{I}\text{≤ 0.333}$. This structure can be described as two octahedra-wide ReO₃-type slabs connected through “planes” of PO₄ tetrahedra. A new structural family K_xP₂W_2nO_6n+4 can be foreseen which is closely related to the orthorhombic P₄W₈O₃₂ and the monoclinic Rb_xP₈W_8nO_24n+16 series.     

14.

Nouveaux thiochlorures de molybdène(II): Mo₆Cl₁₀Y (Y = S,Se, Te): Structure et propriétés magnétiques et électriques     

C. Perrin  M. Sergent  F. Le Traon  A. Le Traon 《Journal of solid state chemistry》1978,25(2):197-204

The thiochlorides Mo₆Cl₁₀Y (Y = S, Se, Te) have been prepared; they are isostructural with Nb₆I₁₁, space group Pccn, and have four formula units per unit cell. The X-ray structure of Mo₆Cl₁₀Se has been determined from three-dimensional single-crystal counter data and refined to a final R value of 0.053 for 3350 independent reflections. The most important result concerning this structure is a statistical distribution of the Se atom on the unit (Mo₆X′₈) with $\text{X′ ?}\text{7}\text{8}\text{Cl}\text{+}\text{1}\text{8}\text{Se}$: so the compound Mo₆Cl₁₀Se must be formulated $\text{(Mo}{}_6\text{Cl}{}_7\text{Se)Cl}{}_{\mathrm{<mtext>4</mtext><mtext>2</mtext>}}\text{Cl}{}_{\mathrm{<mtext>2</mtext><mtext>2</mtext>}}$. The diamagnetic and dielectric behavior of these new thiochlorides is discussed.     

15.

On rheological properties of polydisperse polymers     

A.Ya. Malkin  N.K. Blinova  G.V. Vinogradov  M.P. Zabugina  O.Yu. Sabsai  V.C. Shalganova  I.Yu. Kirchevskaya  V.P. Shatalov 《European Polymer Journal》1974,10(5):445-451

An investigation has been carried out into the effect of the fractional composition on the rheological (flow and elastic) properties of a system, using mixtures of polybutadienes with narrow molecularweight distribution (MWD). For mixtures of high-molecular-weight components, the initial Newtonian viscosity is determined by the weight-average molecular weight: $\text{η}{}_0\text{～}\text{M}{}^{\mathrm{\alpha }}{}_{\mathrm{<mtext>w</mtext>}}$; when low-molecular weight components are introduced, it is also determined by the MWD moment ratio. The characteristic relaxation time of a system is determined by the z-average molecular weight: , and in the general case α₁ ≠ α. A new model has been proposed to explain the non-Newtonian phenomenon as a consequence of the existence of a molecular-weight distribution. According to this model, as the shear rate increases the high-molecular-weight components gradually (at their critical rates) pass over to the high-elastic state. Therefore, at high shear rates, their contribution to viscous losses of a polydisperse polymer is associated with their behaviour as a viscoelastic filler in a viscous liquid.     

16.

The thermal polymerization of styrene at temperatures up to 250°     

W.I. Bengough  G.B. Park 《European Polymer Journal》1978,14(11):889-894

The kinetics of the thermal polymerization of styrene have been studied over the range 60–250°. The overall energy of activation was 86 ± 2 kJ/mole, a value identical to that obtained for the thermal polymerization of styrene in diethyl adipate. As expected, the molecular weight of the polymer decreases with increase in the temperature of the polymerization, and the ratio $\text{M}{}_{\mathrm{<mtext>w</mtext>}}\text{M}{}_{\mathrm{<mtext>n</mtext>}}$ becomes greater than 2 for polymer formed at above 140°. The plot of log ($\text{1}\text{M}{}_{\mathrm{<mtext>n</mtext>}}$) against (absolute temperature)^?1 can be represented by two straight lines yielding 24.5 and 32,0 kJ/mole for the activation energies at temperatures below 120° and above 140°, respectively. The former value is in keeping with the molecular weight being controlled by chain transfer with monomer; the latter value would be that expected if the termination process controls the molecular weight of the polymer. Mark Houwink relationships between intrinsic viscosity and $\text{M}$_n and $\text{M}$_w have been found to apply to polymer samples when the molecular weight averages were determined by osmometry and by light scattering. However, deviations were found for low molecular weight material when measured using gel permeation chromatography. The K values were considerably lower, and the α values higher than reported in the literature.     

17.

Polymérisation cationique du chloro-1 butadiène et copolymérisation avec l'isobutène     

F. Harzallah  M. Tardi  A. Polton  P. Sigwalt 《European Polymer Journal》1984,20(2):163-170

The cationic homopolymerization of 1-chlorobutadiene and its copolymerization with isobutene have been carried out in dichloromethane solution. The catalyst-cocatalyst pairs used were AlEt₂Cl-(CH₃)₃CCl and AlEtCl₂-(CH₃)₃CCl. In the latter case, the use of (CH₃)₃CCl was not necessary. According to experimental conditions, high molecular weight copolymers ($\text{M}{}_{\mathrm{n}}\text{= 200,000}$) insoluble in CH₂Cl₂, or soluble low polymers ($\text{M}{}_{\mathrm{n}}\text{= 20,000}$) were obtained. Homopoly-1-chlorobutadienes were soluble low molecular weight polymers ($\text{M}{}_{\mathrm{n}}\text{= 10,000}$). The 1-chlorobutadiene units in the polymers are nearly exclusively 3,4 (mainly trans). Consequently, this method is not convenient to prepare elastomers with a 1,4 structure similar to that of chlorinated butyl rubber.     

18.

Etude cristallochimique des phases de type perovskite du systeme Th_0.25 NbO₃NaNbO₃     

M. Labeau  J.C. Joubert 《Journal of solid state chemistry》1978,25(4):347-353

The compound Th_0.25 NbO₃ melts congruently at 1390°C. Single crystals obtained by slow cooling from the melt are transparent and show uniaxial optical properties. A single-crystal X-ray analysis confirms the tetragonal cell found by Kovba and Trunov from a powder data and gives a = 3.90 Å and c = 7.85 Å. No systematic absence of the hkl reflections is observed on precession films. The relative intensities of the main reflections are characteristic of a perovskite-like arrangement ABO₃ whose large dodecahedral A sites are only partly occupied. Several domains have been found in the perovskite-type solid solution (1 ? x) Th_0.25NbO₃-x NaNbO₃. For 0 ? x ? 0.5 the phases have a tetragonal cell with $\text{a ? a}{}_0$ and $\text{c ? 2a}{}_0$ as in pure Th_0.25 NbO₃. When 0.6 ? x ? 0.8 the corresponding phases crystallize with a small cubic cell ($\text{a}{}_0\text{? 3.9}$Å), while phases with 0.9 ? x ? 1 have an orthorhombic cell ($\text{a ? 2}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{a}{}_0\text{, b ? 2}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{a}{}_0\text{, c ? a}{}_0$).     

19.

Proprietes dielectriques d'une serie de polyoxyethylene (POE) presentant des masses moleculaires lentement variables ($\text{200 ≤}\text{M}{}_{\mathrm{w}}\text{≤ 4 × 10}{}^6$)     

Françoise Decossas  André Moliton  Eve Marchal 《European Polymer Journal》1982,18(12):1073-1084

In this paper, we present dielectric results for samples of POE (polyethyleneoxyde) divided into three classes. Compounds of low molecular weight ($\text{M}{}_{\mathrm{w}}\text{< 1000}$) show very weak absorption at lower temperatures. At higher temperatures (below the melting point), there appears a very important peak (stronger for lower $\text{M}{}_{\mathrm{w}}$) which corresponds to the supercooled phase. Compounds of intermediate molecular weight ($\text{1000 ≤}\text{M}{}_{\mathrm{w}}\text{≤ 10}{}^5$) show a β relaxation near 250 K (bis$\text{M}{}_{\mathrm{w}}\text{? 3000}$) which is due to the movement of chain-ends in the amorphous phase. This process increases with the importance of that part of the structure formed of shorter lamellae, thus explaining the marked diminution of this absorption for higher molecular weight compounds (the shorter lamellae cannot be obtained for $\text{M}{}_{\mathrm{w}}\text{> 4000}$). The α relaxation (obtained for T > 300 K) is perturbed by an important conduction; however, we have found a peak and a shoulder at lower frequencies, due to shorter and longer lamellae respectively. The shoulder is also present for high molecular weight compounds ($\text{M}{}_{\mathrm{w}}\text{≥ 0.1–10}{}^6$). At lower temperatures, they display a very broad γ absorption, superposed at higher frequencies with a β relaxation. The nature of this β relaxation is different from that observed for the intermediate molecular weight compounds.     

20.

Etude des volumes specifiques partiels de polystyrenes-modeles—Influence de la masse moleculaire et de la nature des groupements terminaux     

Jeanne Francois  Françoise Candau 《European Polymer Journal》1973,9(12):1355-1367

It is well known that the apparent specific volume η₂ of a polymer may be expressed by the following relationship: $\text{η}{}_2\text{= η}{}_{\mathrm{m}}\text{+ K/}\text{M}{}_{\mathrm{n}}$ where M?_n is the number-average molecular weight of the polymer, η_m the specific volume of the infinite polymer, and K a constant. We have shown that this relationship is valid for low molecular weight polystyrenes ($\text{M}{}_{\mathrm{n}}\text{< 4·10}{}^4$) with different end-groups, independently of the nature of the solvent. The K values (and variations with the solvent and with the nature of the end-groups) may be predicted through simple calculations proposed here. We conclude that η_m does not represent the specific volume of the infinite polymer, since we observe a rapid decrease of η₂ for increasing M (when $\text{M}{}_{\mathrm{n}}\text{< 4·10}{}^4$). The decrease is much greater than expected from the relationship $\text{η}{}_2\text{= ? (1/}\text{M}\text{)}$.     

	$\text{C}{}_{\mathrm{<mtext>p,</mtext><mtext>m</mtext>}}\text{R}$	$\text{S}{}_{\mathrm{m}}{}^{\mathrm{o}}\text{R}$	$\text{{H}{}_{\mathrm{m}}{}^{\mathrm{o}}\text{(T)?H}{}_{\mathrm{m}}{}^{\mathrm{o}}\text{(0)}}\text{R}\text{K}$	$\text{?{G}{}_{\mathrm{m}}{}^{\mathrm{o}}\text{(T)?H}{}_{\mathrm{m}}{}^{\mathrm{o}}\text{(0}}\text{RT}$
CsCrCl3	15.38	26.49	3503.2	14.735
RbCrCl3	15.76	25.99	3556.8	14.384

General approach to polymer properties dependent on molecular characteristics

The general equation

where P is a polymer property, Π is the sign of product, A is a constant, v_i is the ith variable and a_i is the exponent of ith variable, has been proposed for the dependence of some polymer properties on molecular weight, molecular weight distribution and long-chain branching. The data confirming the proposed equation have been taken from published theoretical and experimental papers on intrinsic viscosity, melt viscosity and glass transition temperature, as well as on viscosity of polymer solutions. Examples of application are given.     

A theory of viscosity of dilute and moderately concentrated polymer solutions

A model theory of viscosity η for moderately concentrated polymer solutions is based on the assumption of a “local viscosity” effect and intermolecular hydrodynamic and thermodynamic interactions. It is shown that η is given by

$\text{η = η}{}_{\mathrm{o}}\text{{1 + γc[η]}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{·}\text{exp}\text{H}{}_{\mathrm{o}}\text{RT}\text{aø}\text{1 ? aø}$

where γ is 0–0.4 and depends on the quality of the solvent, a varies between 0,4 and 0.8 and depends on the fraction of the “free volume” of the systems, H₀ is the activation energy of the solvent and π is the polymer volume concentration. The dependence of η and “activation energy” of π and T for various molecular weights and qualities of solvents is described quantitatively. Anomalous dependences of [η] and of η on M for low polymer are obtained. An expression for η is proposed:

$\text{η}\text{η}{}_{\mathrm{o}}{}^{\mathrm{<mtext>1\; ?\; 2</mtext><mtext>K</mtext>}}\text{= {1 + (1 ? 2K)c[η]}F(π)}$

where K is the Huggins-Martin coefficient and F(π) = 1 for most solutions when T is > T_g. For poor solvents the H vs c curve (where H is the activation energy of η of solution) has a minimum value at moderate concentrations. For good solvents, H depends slightly on the molecular weight according to an empirical equation:

$\text{H = H}{}_{\mathrm{o}}\text{+}\text{660}\text{α}{}^3\text{1}\text{n}\text{η}\text{η}{}_{\mathrm{o}}$

Expressions are given from the viscosities of solutions of miscible and also solutions of immiscible polymers.     

KxP2W2O16: A bronze with a tunnel structure built up from PO4 tetrahedra and WO6 octahedra

The structure of a $\text{K}{}_{\mathrm{x}}\text{P}{}_2\text{W}{}_4\text{O}{}_{16}\text{(x ? 0.4)}$ crystal was established by X-ray analysis. The solution in the cell of symmetry $\text{P2}{}_1\text{m}$, with a = 6.6702(5), b = 5.3228(8), c = 8.9091(8) Å, β = 100.546(7)°, Z = 1, has led to R = 0.033 and R_w = 0.036 for 2155 reflections with $\text{σ(I)}\text{I}\text{≤ 0.333}$. This structure can be described as two octahedra-wide ReO₃-type slabs connected through “planes” of PO₄ tetrahedra. A new structural family K_xP₂W_2nO_6n+4 can be foreseen which is closely related to the orthorhombic P₄W₈O₃₂ and the monoclinic Rb_xP₈W_8nO_24n+16 series.     

Nouveaux thiochlorures de molybdène(II): Mo6Cl10Y (Y = S,Se, Te): Structure et propriétés magnétiques et électriques

The thiochlorides Mo₆Cl₁₀Y (Y = S, Se, Te) have been prepared; they are isostructural with Nb₆I₁₁, space group Pccn, and have four formula units per unit cell. The X-ray structure of Mo₆Cl₁₀Se has been determined from three-dimensional single-crystal counter data and refined to a final R value of 0.053 for 3350 independent reflections. The most important result concerning this structure is a statistical distribution of the Se atom on the unit (Mo₆X′₈) with $\text{X′ ?}\text{7}\text{8}\text{Cl}\text{+}\text{1}\text{8}\text{Se}$: so the compound Mo₆Cl₁₀Se must be formulated $\text{(Mo}{}_6\text{Cl}{}_7\text{Se)Cl}{}_{\mathrm{<mtext>4</mtext><mtext>2</mtext>}}\text{Cl}{}_{\mathrm{<mtext>2</mtext><mtext>2</mtext>}}$. The diamagnetic and dielectric behavior of these new thiochlorides is discussed.     

On rheological properties of polydisperse polymers

An investigation has been carried out into the effect of the fractional composition on the rheological (flow and elastic) properties of a system, using mixtures of polybutadienes with narrow molecularweight distribution (MWD). For mixtures of high-molecular-weight components, the initial Newtonian viscosity is determined by the weight-average molecular weight: $\text{η}{}_0\text{～}\text{M}{}^{\mathrm{\alpha }}{}_{\mathrm{<mtext>w</mtext>}}$; when low-molecular weight components are introduced, it is also determined by the MWD moment ratio. The characteristic relaxation time of a system is determined by the z-average molecular weight: , and in the general case α₁ ≠ α. A new model has been proposed to explain the non-Newtonian phenomenon as a consequence of the existence of a molecular-weight distribution. According to this model, as the shear rate increases the high-molecular-weight components gradually (at their critical rates) pass over to the high-elastic state. Therefore, at high shear rates, their contribution to viscous losses of a polydisperse polymer is associated with their behaviour as a viscoelastic filler in a viscous liquid.     

The thermal polymerization of styrene at temperatures up to 250°

The kinetics of the thermal polymerization of styrene have been studied over the range 60–250°. The overall energy of activation was 86 ± 2 kJ/mole, a value identical to that obtained for the thermal polymerization of styrene in diethyl adipate. As expected, the molecular weight of the polymer decreases with increase in the temperature of the polymerization, and the ratio $\text{M}{}_{\mathrm{<mtext>w</mtext>}}\text{M}{}_{\mathrm{<mtext>n</mtext>}}$ becomes greater than 2 for polymer formed at above 140°. The plot of log ($\text{1}\text{M}{}_{\mathrm{<mtext>n</mtext>}}$) against (absolute temperature)^?1 can be represented by two straight lines yielding 24.5 and 32,0 kJ/mole for the activation energies at temperatures below 120° and above 140°, respectively. The former value is in keeping with the molecular weight being controlled by chain transfer with monomer; the latter value would be that expected if the termination process controls the molecular weight of the polymer. Mark Houwink relationships between intrinsic viscosity and $\text{M}$_n and $\text{M}$_w have been found to apply to polymer samples when the molecular weight averages were determined by osmometry and by light scattering. However, deviations were found for low molecular weight material when measured using gel permeation chromatography. The K values were considerably lower, and the α values higher than reported in the literature.     

Polymérisation cationique du chloro-1 butadiène et copolymérisation avec l'isobutène

The cationic homopolymerization of 1-chlorobutadiene and its copolymerization with isobutene have been carried out in dichloromethane solution. The catalyst-cocatalyst pairs used were AlEt₂Cl-(CH₃)₃CCl and AlEtCl₂-(CH₃)₃CCl. In the latter case, the use of (CH₃)₃CCl was not necessary. According to experimental conditions, high molecular weight copolymers ($\text{M}{}_{\mathrm{n}}\text{= 200,000}$) insoluble in CH₂Cl₂, or soluble low polymers ($\text{M}{}_{\mathrm{n}}\text{= 20,000}$) were obtained. Homopoly-1-chlorobutadienes were soluble low molecular weight polymers ($\text{M}{}_{\mathrm{n}}\text{= 10,000}$). The 1-chlorobutadiene units in the polymers are nearly exclusively 3,4 (mainly trans). Consequently, this method is not convenient to prepare elastomers with a 1,4 structure similar to that of chlorinated butyl rubber.     

Etude cristallochimique des phases de type perovskite du systeme Th0.25 NbO3NaNbO3

The compound Th_0.25 NbO₃ melts congruently at 1390°C. Single crystals obtained by slow cooling from the melt are transparent and show uniaxial optical properties. A single-crystal X-ray analysis confirms the tetragonal cell found by Kovba and Trunov from a powder data and gives a = 3.90 Å and c = 7.85 Å. No systematic absence of the hkl reflections is observed on precession films. The relative intensities of the main reflections are characteristic of a perovskite-like arrangement ABO₃ whose large dodecahedral A sites are only partly occupied. Several domains have been found in the perovskite-type solid solution (1 ? x) Th_0.25NbO₃-x NaNbO₃. For 0 ? x ? 0.5 the phases have a tetragonal cell with $\text{a ? a}{}_0$ and $\text{c ? 2a}{}_0$ as in pure Th_0.25 NbO₃. When 0.6 ? x ? 0.8 the corresponding phases crystallize with a small cubic cell ($\text{a}{}_0\text{? 3.9}$Å), while phases with 0.9 ? x ? 1 have an orthorhombic cell ($\text{a ? 2}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{a}{}_0\text{, b ? 2}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{a}{}_0\text{, c ? a}{}_0$).     

Proprietes dielectriques d'une serie de polyoxyethylene (POE) presentant des masses moleculaires lentement variables (200 ≤ Mw ≤ 4 × 106)

In this paper, we present dielectric results for samples of POE (polyethyleneoxyde) divided into three classes. Compounds of low molecular weight ($\text{M}{}_{\mathrm{w}}\text{< 1000}$) show very weak absorption at lower temperatures. At higher temperatures (below the melting point), there appears a very important peak (stronger for lower $\text{M}{}_{\mathrm{w}}$) which corresponds to the supercooled phase. Compounds of intermediate molecular weight ($\text{1000 ≤}\text{M}{}_{\mathrm{w}}\text{≤ 10}{}^5$) show a β relaxation near 250 K (bis$\text{M}{}_{\mathrm{w}}\text{? 3000}$) which is due to the movement of chain-ends in the amorphous phase. This process increases with the importance of that part of the structure formed of shorter lamellae, thus explaining the marked diminution of this absorption for higher molecular weight compounds (the shorter lamellae cannot be obtained for $\text{M}{}_{\mathrm{w}}\text{> 4000}$). The α relaxation (obtained for T > 300 K) is perturbed by an important conduction; however, we have found a peak and a shoulder at lower frequencies, due to shorter and longer lamellae respectively. The shoulder is also present for high molecular weight compounds ($\text{M}{}_{\mathrm{w}}\text{≥ 0.1–10}{}^6$). At lower temperatures, they display a very broad γ absorption, superposed at higher frequencies with a β relaxation. The nature of this β relaxation is different from that observed for the intermediate molecular weight compounds.     

Etude des volumes specifiques partiels de polystyrenes-modeles—Influence de la masse moleculaire et de la nature des groupements terminaux

It is well known that the apparent specific volume η₂ of a polymer may be expressed by the following relationship: $\text{η}{}_2\text{= η}{}_{\mathrm{m}}\text{+ K/}\text{M}{}_{\mathrm{n}}$ where M?_n is the number-average molecular weight of the polymer, η_m the specific volume of the infinite polymer, and K a constant. We have shown that this relationship is valid for low molecular weight polystyrenes ($\text{M}{}_{\mathrm{n}}\text{< 4·10}{}^4$) with different end-groups, independently of the nature of the solvent. The K values (and variations with the solvent and with the nature of the end-groups) may be predicted through simple calculations proposed here. We conclude that η_m does not represent the specific volume of the infinite polymer, since we observe a rapid decrease of η₂ for increasing M (when $\text{M}{}_{\mathrm{n}}\text{< 4·10}{}^4$). The decrease is much greater than expected from the relationship $\text{η}{}_2\text{= ? (1/}\text{M}\text{)}$.