Generalization of correlation between polymer glass transition Tg and an e.s.r. parameter T50G

The tumbling of five nitroxide spin probes (molecular weights between 172–486 g/mol) in a standard unfractionated polyisobutylene [$\text{M}\text{?}{}_{\mathrm{v}}\text{= (1.26 ± 0.18) × 10}{}^6\text{g/mol}$] has been studied by means of the electron spin resonance (e.s.r.) technique. The temperature at which the separation of the outermost peaks of the e.s.r. spectrum is 50 G (T_50G) attained a limiting value T′_50G = 330K at probe M_W = 332 g/mol. This temperature coincided with the temperature of the loss maximum of the merged glass transition (T_g) and segmental relaxations at the corresponding frequency (3 × 10⁷ Hz). A literature survey indicated that an analogous situation exists in the case of poly(vinylidene fluoride) and polyamide-6,10 while T′_50G values of poly(2,6-dimethyl phenylene oxide) and polycarbonate are correlated only to segmental relaxations of polymer chains. It is concluded that the equation:

$\text{T}{}_{\mathrm{<mtext>50</mtext><mtext>G</mtext>}}\text{= T}{}_{\mathrm{g}}\text{[1 + (}\text{exp}\text{T}{}_{\mathrm{g}}\text{/T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{?1}}\text{]}$

describes generally the temperature shift between glass transitions at low and high frequencies and can be applied to determine experimentally low frequency T_g values from T′_50G values if T_g and T < T_g relaxations (if any are present) are already merged at this temperature.     

Viscoelastic properties of poly(propylene glycols)

The relaxational and retardational properties of poly(propylene glycol) liquids, of nominal molecular weights 400 and 4000, are described. The viscoelastic behaviour of each liquid has been determined over a wide temperature range, using high frequency shear wave techniques operating at 30 and 454 MHz. It is found that the complex compliance $\text{J1(jω)}$ is described in terms of the viscosity ν, the limiting high frequency compliance J_∞, the retardational compliance J_r and a characteristic retardation time $\text{т}{}_{\mathrm{r}}$ by:

$\text{J}{}^1\text{(jω)=J}{}_{\mathrm{\infty }}\text{+}\text{1}\text{jωη}\text{+}\text{j}{}_{\mathrm{r}}\text{(1+jωτ}{}_{\mathrm{r}}\text{)}{}^{\mathrm{\beta }}$

where β is a parameter of the retardation time distribution.For the lower molecular weight liquid, $\text{J}{}_{\mathrm{r}}\text{J}{}_{\mathrm{\infty }}\text{= 17.4}$, β = 0.45 and $\text{т}{}_{\mathrm{r}}\text{т}{}_{\mathrm{m}}$ increases with decreasing temperature, reaching a limit of 170 near 0°C. This liquid shows no evidence of polymeric behaviour.For the other, $\text{J}{}_{\mathrm{r}}\text{J}{}_{\mathrm{\infty }}$, β = 0.76, $\text{т}{}_{\mathrm{r}}\text{т}{}_{\mathrm{m}}\text{= 15.4}$ and is constant over the temperature range investigated. The main difference between the two liquids appears as an additional retardational or relaxational process for the higher molecular weight material which occurs in the initial or low frequency part of the relaxation region. This process is characterized by a single time, but with relaxation time $\text{1}\text{7}$ and a stiffness 7 times the values calculated for the first Rouse mode of polymer chain motion.     

Role of electrostatic forces in the glass transition temperatures of ionic polymers

The glass transition temperatures of ionic polymers have been correlated with cohesive energy densities (CED). The CEDs of ionic polymers, such as ionene polymers, polyphosphates, and polyacrylates were calculated under the assumption that they could be approximated to the electrostatic energy of the system. The T_gs of ionic polymers could be conveniently expressed by the equation $\text{T}{}_{\mathrm{g}}\text{= K}{}_1\text{(CED)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ in which K₁ took a different value for each polymer system. This paper discusses the influence on T_g of the change in both the cohesive energy and the degree of freedom of segmental motion caused by the introduction of ionic characteristics in polymeric chains.     

Glass transition temperature of ideal polymeric networks

Measurements of the glass transition temperature (T_g) have been carried out on polystyrene networks prepared by the anionic copolymerization of styrene and divinylbenzene, and star-shaped polystyrene of varying functionality. The results show a linear variation of T_g versus $\text{M}\text{?}{}^{\mathrm{?1}}{}_{\mathrm{n}}$ in all cases. The value of the slope interpreted in terms of the free volume theory shows that the glass transition temperature depends closely on the average functionality of the crosslinks. In order to study the influence of free chains on the glass transition of crosslinked polymers a series of networks were contaminated with increasing ratios of linear polystyrene chains, slightly polydisperse.     

Statistical mechanical theories of the glass transition — a new perspective

The statistical mechanical functions of Gibbs and DiMarzio are briefly reviewed, and subsequent modifications of these equations by other workers are described. Then using computer analysis, three-dimensional representations of the two original expressions are developed to illustrate the overall multifunctional dependence. By recognizing that the free volume (V₀) is of secondary importance but that the ratio of the dimensionless parameter ($\text{β = ?}\text{ε}\text{k}\text{T}{}_{\mathrm{g}}$) is crucial, a reduced variables plot of $\text{T}{}_{\mathrm{g}}\text{T}{}_{\mathrm{g\infty }}$ versus $\text{10}{}^3\text{P}\text{?}$ is introduced. From a representative data sampling, the applicability of a single curvilinear function is established along with some initial observations.     

Effect of temperature and frequency in fatigue of polymers

The effects of frequency and temperature on fatigue crack propagation rate in poly(methyl methacrylate) and polycarbonate have been studied using centrally notched plate specimens cycled in tension between constant stress intensity limits. Crack growth was monitored at frequencies between 0.1 Hz and 100 Hz and at temperatures between ?60°C and 40°C. A linear relationship between the cyclic crack growth rate $\text{d}\text{(2a)}\text{d}\text{N}$ and appropriate levels of toughness, K, has been proposed: $\text{d}\text{(2a)}\text{d}\text{N}\text{= A?}{}^{\mathrm{\alpha }}$, where $\text{? =}\text{(λ ? λ}{}_{\mathrm{<mtext>th</mtext>}}\text{)}\text{(K}{}^2{}_{\mathrm{<mtext>1</mtext><mtext>C</mtext>}}\text{? K}{}^2{}_{\mathrm{<mtext>max</mtext>}}\text{)}$, λ = K²_max ? K²_min, λ_th is the threshold limit and A and α are constants. Also, the influence of mean stress intensity was briefly discussed.     

Synthesis of electroreactive polymers from poly (m,p-chloromethylstyrene) and copoly (m,p-chloromethylstyrene-styrene)

Polymerization, and copolymerization with styrene, of m,p-chloromethylstyrene have been carried out at 75°C, in chlorobenzene and in the presence of AIBN ($\text{[}\text{AIBN}\text{] ? 6 × 10}{}^{\mathrm{?2}}$, and $\text{12 × 10}{}^{\mathrm{?2}}\text{m}$, respectively). The polymer molecular weights, determined by g.p.c., are: $\text{M}\text{?}{}_{\mathrm{w}}\text{= 8670}$, $\text{M}\text{?}{}_{\mathrm{n}}\text{= 5860}$, and $\text{M}\text{?}{}_{\mathrm{w}}\text{/-M}{}_{\mathrm{n}}\text{= 1.48}$ for the homopolymer, poly(m,p-chloromethylstyrene), (1a); and $\text{M}\text{?}{}_{\mathrm{w}}\text{= 8805}$, $\text{M}\text{?}{}_{\mathrm{n}}\text{= 5144}$, and $\text{M}\text{?}{}_{\mathrm{w}}\text{/-M}{}_{\mathrm{n}}\text{= 1.71}$ for the copolymer, copoly(m,p-chloromethylstyrene-styrene), (2a). A series of phosphine derivatives of both 1a and 2a are prepared by the reaction of the polymers with either chlorodiphenylphosphine/lithium, or diphenylphosphine/potassium tert. butoxide. A number of other potentially electroreactive derivatives of 2a are obtained by reacting the polymer with 2-aminoanthraquinone, 3-N-methylamino-propionitrile, or 2-(2-aminoethyl) pyridine. The phosphinated polymers are reacted with bis-benzonitrilepalladium-(II) chloride to obtain a series of polymer-palladium(II) complexes containing 8.5–12.9% palladium. Similarly, reaction of the last-named bidentate polymeric ligand with cupric acetylacetonate, or cupric sulphate pentahydrate, produces polymer-copper(II) complexes having 5.8, or 3.3% copper, respectively. The inter/intra-chain nature of some of the side reactions during the derivatization of the chloromethylated polymers, and that of the complex formation between transition metal centres and macromolecular ligands, are briefly discussed in view of the experimental results.     

Isothermal crystallization of poly(ethylene-terephthalate) of low molecular weight by differential scanning calorimetry: 1. Crystallization kinetics

The isothermal crystallization of poly(ethylene-terephthalate) (PETP) fractions, from the melt, was investigated using differential scanning calorimetry (d.s.c.). The molecular weight range of the fractions was from 5300–11750. Crystallization temperatures were from 498–513 K. The dependence of molecular weight and undercooling on several crystallization parameters has been observed. Either maxima or minima appear at a molecular weight of about 9000, depending on the crystallization temperature. The activation energy values point to the possibility of different mechanisms of crystallization according to the chain length. A folded chain process for the higher $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ chains and an extended chain mechanism for the lower $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ chains. The values of the Avrami equation exponent n vary from 2–4 depending on the crystallization temperature; non-integer values are indicative of heterogeneous nucleation. The rate constant K depends on T_c and $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$, showing maxima related to the T_c used. The plot of log K either vs. (ΔT)^?1 and (ΔT)^?2 or $\text{T}{}_{\mathrm{<mtext>m</mtext>}}\text{T(ΔT)}$ and $\text{T}{}^2{}_{\mathrm{<mtext>m</mtext>}}\text{T(ΔT)}{}^2$ is linear in every case.     

Quantitative evaluation of the Gibbs—DiMarzio theory of the glass transition

The applicability of the Gibbs—DiMarzio (G—DM) theory of the glass transition (T_g) is quantitatively evaluated for PS, PVC, PαMS and PMMA. The analysis was conducted under the assumption that both the inter-/intramolecular energy ratio (r) and the effective chain segment density (n) remain constant while the fractional free volume at T_g(V₀) varies as a function of the reciprocal degree of polymerization ($\text{10}{}^3\text{P}\text{?}$). Based upon reduced parametric plots of $\text{T}{}_{\mathrm{<mtext>g</mtext>}}\text{T}{}_{\mathrm{<mtext>g\infty </mtext>}}$versus$\text{10}{}^3\text{P}\text{?}$, the results showed that the G-DM equations were satisfactory for PS and PVC but unsuccessful in the cases of PαMS and PMMA. For the former cases the analysis indicated that when 0.015 ? V₀ ? 0.045 optimum agreement occurred at n=1.80, r=10.5 and n=1.36, r=0.95, respectively. Although potential n, r values were obtained for PαMS when the allowable V₀ range was expanded to 0.010–0.050, none of these combinations satisfied all of the analytical requirements. No agreement for the PMMA data sets could be obtained even when this less stringent V₀ criterion was adopted. Attempts to improve this situation by incorporating ‘beads’ and ‘flexes’ into the statistical mechanical equations are also considered.     

Unperturbed dimensions of poly(phenyl acrylate)

Thirteen fractions of poly(phenyl acrylate) have been prepared with weight-average molecular weight ranging from 0.158 × 10⁶ to 2.57 × 10⁶ g mol^?1. The temperature coefficient of the unperturbed dimensions and the glass transition temperature were found to be ?1.8 × 10^?3 deg^?1 and 55.6°C respectively. Good accord was obtained among different methods for establishing θ-conditions of 11.5°C in ethyl lactate. From viscometry, osmometry and light scattering under θ-conditions, as well as in a good solvent, the unperturbed dimensions were determined via several procedures yielding a value of $\text{[〈r}{}^2\text{〉}{}_{\mathrm{0w}}\text{M}\text{?}{}_{\mathrm{w}}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 6.0 (±0.2) × 10}{}^{\mathrm{?9}}\text{cm g}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{mol}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. This corresponds to a steric factor υ = 2.37 (±0.08) and a characteristic ratio C_∞ = 11.3 (±0.8). The polymer chain is thus more rigid than poly(methyl acrylate), but less rigid than poly(phenyl methacrylate). With respect to its T_g and flexibility, poly(phenyl acrylate) bears a strong similarity to poly(benzyl methacrylate).     

Poly(ortho-vinylbenzophenone)

This article reports the synthesis and free radical polymerization of ortho-vinylbenzophenone. The glass transition temperature T_g of the homopolymer is 136°C. The products synthesized appeared to be atactic and amorphous. The Mark-Houwink constants for poly (o-vinylbenzophenone) in tetrahydrofuran are K = 4.2 × 10^?2 cm³ g^?1 and a = 0.765. The pre-exponential constant under theta conditions, K_θ, is estimated to be 5.93 × 10^?2 cm³ g^?1. The ratio of unperturbed dimensions of the actual polymer and free rotating analogue chain is 3.93, which is almost double that of polystyrene. The Flory-Huggins interaction parameter for poly $\text{(o-}\text{vinylbenzophenone}\text{)}\text{tetrahydrofuran}$ is 0.48 at room temperature. The $\text{k}{}_{\mathrm{<mtext>p</mtext>}}\text{k}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{<mtext>t</mtext>}}$ ratio at 60°C is $\text{1.1 × 10}{}^{\mathrm{?2}}\text{l}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{mol}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{s}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$. In free radical copolymerizations with styrene at 70°C, r₁ (o-vinylbenzophenone) = 1.216, r₂ = 0.751. This copolymerizations is virtually random.     

Dielectric properties of oligomers: 4. Dielectric properties of vinyl acetate and methyl methacrylate oligomers

Dielectric properties of vinyl acetate and methyl methacrylate oligomers were studied in order to compare the dielectric properties of an oligomer with those of the corresponding high polymers. The two oligomers showed asymmetric dielectric relaxations at room temperatures. The complex dielectric constants vs. angular frequencies for these oligomers were well represented by the Havriliak-Negami equation:

$\text{?}{}^{\mathrm{ast;}}\text{??}{}_{\mathrm{\infty }}\text{=}\text{?}{}_0\text{??}{}_{\mathrm{\infty }}\text{[1+(jωτ}{}_0\text{)}{}^{\mathrm{1?\alpha }}\text{]}{}^{\mathrm{\beta }}$

The distribution parameters (1 - α) and β of vinyl acetate and methyl methacrylate oligomer are almost equal to those of poly(vinyl acetate) and poly(methyl methacrylate), respectively. It was concluded that the distribution of relaxation times was independent of the molecular weight of the polymers.     

Viscometric behaviour of polystyrene in tetralin/cyclohexane mixtures

For solutions of polystyrene (M=10⁵–10⁶ g mol^?1), intrinsic viscosities [η] have been measured at 34.5°C, which is the θ temperature for the polymer in cyclohexane. The solvents comprised cyclohexane in admixture with a thermodynamically good solvent, 1,2,3,4-tetrahydronaphthalene (tetralin, TET) over the whole range of solvent composition. From an assessment of several extrapolation procedures, a value of 85 × 10^?3$\text{(±1 × 10}{}^{\mathrm{?3}}\text{)}\text{cm}{}^3\text{g}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}\text{mol}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ was obtained for K_θ (in the relationship $\text{[η] = K}{}_{\mathrm{\theta }}\text{M}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{α}{}^3$, where α is the expansion factor), thus yielding $\text{0.681}\text{A}\text{?}\text{g}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{mol}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, 2.25 and 10.2 for the unperturbed dimensions, steric factor σ and characteristic ratio C_∞ respectively. The value of K_θ was independent of solvent composition despite the finite excess free energy of mixing for the solvent components alone, which has been asserted elsewhere to affect K_θ. The present results, in conjunction with previous ones relating to 98.4°C, indicate a value of ?0.89 × 10^?3 deg^?1 for the temperature coefficient of the unperturbed dimensions.     

Viscosity of heparin in formamide and glycerol

The viscosity of heparin was examined in pure glycerol, formamide and in mixtures of the two solvents. This study confirms that the equation $\text{η}{}_{\mathrm{sp}}\text{c}\text{= [η]}{}_{\mathrm{\infty }}\text{[1 +}\text{k}\text{(c)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{]}$, where [η]_∞ is the shielded intrinsic viscosity, adequately describes the concentration dependence of the reduced viscosity of the polyelectrolyte, heparin. The [η]_∞ linearly increases with the dielectric constant of the solvent.     

Paramagnetische elektronenresonanz (EPR) in polykristallinen graphiten bei hohen temperaturen

EPR measurements were carried out on polycrystalline graphites in a temperature range of 300–1300 K. A special temperature unit permitted stable and interference-free adjustment of the sample temperature up to 1400 K (Fig. 1). The powdered samples based on natural (RWA) and an artificial extruded graphite (RWS) respectively were separated into grains of small size (≤ 3 μm), dispersed and evacuated, to avoid troublesome oxygen and skin-depth effects. It was possible to obtain the crystallite tensor components of the g-factor (Figs. 2, 3) and the crystallite line-width parameters (Fig. 4) from the asymmetrical powder spectrum by computer analysis, assuming an axial symmetry of the crystallites within the grains. One can thereby determine the average orientation of the crystallites within the grains, expressed by $\text{sin}{}^2\text{φ}$, where φ is the angle between the symmetry axis of the grain and the perpendicular on the basal plane of a crystallite. The anisotropy $\text{Δg = g}{}_3\text{? g}{}_1\text{= ?(}\text{1}\text{T}\text{)}$ of the graphites examined is smaller than that of a monocrystalline graphite (Fig. 3). The thermal variation of Δg, ΔH_⊥ and ΔH_∥ can be expressed by the phenomenological equations (4) and (6). But the physical meaning of the degeneracy temperatures T′ and T″ is not clear.A simplified model of the density of states was used for computing the susceptibility χ₀ of the free charge carriers (eqn (8) and Fig. 5). This corresponds with our measurements (Fig. 6). The susceptibility of the polycrystalline graphites is smaller than that of a mono-crystalline graphite. This may result from a slightly modified band structure, i.e. a smaller band overlap.     

Light-sensitive elastomers modified by 4-(N-dimethylmaleimido)-benzenesulphenyl chloride

New light-sensitive polymers were prepared by modification of four different elastomers with 4-(N-dimethylmaleimido)-benzenesulphenyl chloride (DMI-BSCI). Polydienes modified by DMI-BSCI form block copolymers. These polymers show a strong increase of the glass transition temperature T_g whereby the T_g increase of modified poly(octenamer) is much smaller. Higher modified polydienes have two T_g. Modified poly(octenamers) show a melting temperature dependence T_m on the content of trans double bonds which is characteristic of statistical copolymers. The ratio of rate constants with which trans- and cis-structures in poly(octenamer) are occupied by DMI-BSCI, is

$\text{k}{}_{\mathrm{trans}}\text{k}{}_{\mathrm{cis}}\text{= 0.34}$

     

Pulsed n.m.r. of cis-polyisoprene: 1

Proton spin-spin (T₂), and spin-lattice (T₁) relaxation time measurements are reported for six monodisperse cis-polyisoprenes ($\text{M}\text{?}{}_{\mathrm{n}}$ from 2000 to 200 000) over the temperature range from ?50° to 170°C. At low temperatures (?30° to 10°C) T₁ and T₂ are determined by the short range segmental motions but above 10°C T₂ is sensitive to the long range motions. When $\text{M}\text{?}{}_{\mathrm{n}}\text{? 30 000 T}{}_2$ becomes influenced by the presence of entanglements which produce a transient network structure and this confers on the spin-spin relaxation a pseudo-solid-like response. Similar behaviour is observed in crosslinked networks produced by irradiation. The results are discussed in terms of the types of motion occurring in amorphous polymers above T_g and the analogy with dynamic mechanical measurements is discussed.     

Interaction parameters in the n-undecane/butanone/poly(dimethyl siloxane) system

Intrinsic viscosities, [η], second virial coefficients, A₂, preferential solvation coefficients, λ, and binary interaction potential as measured by light scattering, g₁₂, for the system n-undecane(1)/butanone(2)/poly(dimethylsiloxane) (3) have been determined at 20.0°C. The system shows cosolvent character, as the inversion in λ and the maxima in A₂ and in [η], at $\text{ø}{}_{10}\text{?0.65}$, seem to indicate. (g₁₃ – sg₂₃) and the ternary interaction potential, g_T, and its derivatives on system composition, and , have been evaluated. Global interaction parameters, χ_m3, have also been evaluated and a critical analysis on the approximations usually followed for χ_m3 calculations is undertaken.