Polymer translational diffusion: 2. Non-theta solutions,polystyrene in butan-2-one

The diffusion of linear polystyrene under non-theta conditions in butan-2-one has been studied by Rayleigh light scattered linewidth measurements for the molecular weight range of 2.08 × 10⁶ to 8.7 × 10⁶ and as a function of concentration. By extrapolation of diffusion coefficient values to zero concentration we find that $\text{D}{}_0\text{= 5.5 × 10}{}^{\mathrm{?4}}\text{M}\text{?}{}^{\mathrm{?0.561}}{}_{\mathrm{w}}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$. The first order concentration dependence $\text{k}{}_{\mathrm{<mtext>d</mtext>}}\text{c}$ changes sign as the molecular weight increases, $\text{k}{}_{\mathrm{<mtext>d</mtext>}}$ being fairly small and negative at low molecular weights and increasingly positive above $\text{M}\text{?}{}_{\mathrm{w}}\text{?230 000}$.     

Properties of extremely high molecular weight polystyrene in solution

Extremely high molecular weight polystyrenes with a $\text{M}\text{?}{}_{\mathrm{w}}$ in the range 10.8 × 10⁶ to 2.2 × 10⁷ were prepared by emulsion polymerization initiated with a heterogeneous initiator at 30°C, which has a ‘living character’. Samples of polystyrene were characterized by light scattering and viscometry in toluene and benzene at 25°C, and in θ-solvent cyclohexane at 34.8°C. Also determined were the relationships of mean-square radius of gyration 〈s²〉 (m²) and the second virial coefficient A₂ (m³ mol kg^?2) on the molecular weight, which for toluene and benzene are described in equations: Toluene (25°C) $\text{〈s}{}^2\text{〉=1.59 × 10}{}^{\mathrm{?23}}\text{M}\text{?}{}_{\mathrm{w}}{}^{1.23}$; $\text{A}{}_2\text{=4.79 × 10}{}^{\mathrm{?3}}\text{M}\text{?}{}_{\mathrm{w}}{}^{\mathrm{?0.63}}$; Benzene (25°C) $\text{〈s}{}^2\text{〉=1.23 × 10}{}^{\mathrm{?22}}\text{M}\text{?}{}_{\mathrm{w}}{}^{1.20}$; $\text{A}{}_2\text{=2.59 × 10}{}^{\mathrm{?3}}\text{M}\text{?}{}_{\mathrm{w}}{}^{\mathrm{?0.59}}$. The parameters in the Mark-Houwink-Sakurada equation were established, for extremely high molecular weight polystyrene in toluene and in benzene, at 25°C into the form giving for $\text{[η] (}\text{m}{}^3\text{kg}{}^{\mathrm{?1}}\text{): [η] = 8.52 × 10}{}^{\mathrm{?5}}\text{M}\text{?}{}_{\mathrm{w}}{}^{0.61}$; $\text{[η] = 1.47 × 10}{}^{\mathrm{?4}}\text{M}\text{?}{}_{\mathrm{w}}{}^{0.56}$. The mentioned relations, as well as the obtained values of Flory parameter ?₀ and of ratio $\text{[η]}\text{M}\text{?}{}_{\mathrm{w}}{}^{0.5}$ were compared with solution properties of high molecular weight polystyrene with narrow molecular weight distribution prepared by anionic polymerization by Fukuda et al.     

Upper and lower critical solution temperatures in poly (ethylene glycol) solutions

Upper and lower critical solution temperatures have been determined for solutions of poly(ethylene glycol) in t-butyl acetate and water over the molecular weight range of M_η = 2.18 × 10³ to ～1020 × 10³. The phase diagram for solutions of poly(ethylene glycol) (M_η = 719 × 10³) in t-butyl acetate was expressed as the ‘hour glass’ type, while the phase diagram for solution of poly(ethylene glycol) (M_η = 2.18 × 10³ to ～2.29 × 10³) in water was expressed as the ‘closed loop’ type. The value of the pressure dependence of the lower critical solution temperature $\text{(}\text{d}\text{T}\text{d}\text{P}\text{)}{}_{\mathrm{c}}$ in the poly(ethylene glycol) (M_η = 1020 × 10³)/water system over the pressure range of 0 to ～50 atm was negligibly small and positive.     

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.     

The concentration dependence of the angular dissymmetry of light scattered by micellar solutions

A light scattering investigation was made of micelles formed from a polystyrene-poly(ethylene/propylene) two-block copolymer in n-nexane. n-Hexane is a selectively bad solvent for polystyrene and so polystyrene blocks formed the cores of the micelles. The light scattering measurements were made at 25°C for concentrations up to 0.015 g cm^?3. The dissymetry ratio ($\text{I}{}_{\mathrm{45°}}\text{I}{}_{\mathrm{135°}}$) was found to decrease with increase in concentration and it was below unity for measurements at c > 4.8 × 10^?3 g cm^?3. The effect of concentration on the dissymmetry ratio was predicted quite well by assuming the micelle packing could be described by radial distribution functions for hard spheres.     

Thermomechanical heat of deformation studies on cis-polybutadiene

Thermomechanical heat of torsional deformation measurements have been made on crosslinked cis-polybutadiene by means of a Calvet microcalorimeter operated at 30°C. When corrected for volume changes utilizing the Gaussian statistical theory of elasticity, the data gave a value for the relative energy contribution to the torsional couple, $\text{M}{}_{\mathrm{e}}\text{M}$, of 0.14 ± 0.02. Measurements were also made on a sample subjected to simple tensile deformations. The relative energy contribution to the tensile force ($\text{f}{}_{\mathrm{e}}\text{f}$) was found to agree within experimental error with the value obtained for $\text{M}{}_{\mathrm{e}}\text{M}$, and the two results gave an average value for din $\text{〈r}{}^2{}_0\text{〉}\text{d}\text{T}$ of 4.1 × 10^?4 K^?1.     

Effect of molecular weight on the refractive index increment of polystyrenes in solution

The variation of refractive index increment $\text{d}\text{n}\text{d}\text{c}$ with molecular weight has been studied using solutions of monodisperse polystyrenes (2000<M_w<4×10⁶) in benzene. The results are in good agreement with those obtained by several authors using other systems.We have shown that the linear relationship:

$\text{d}\text{n}\text{d}\text{c}\text{=}\text{d}\text{n}\text{d}\text{c}{}_{\mathrm{m}}\text{+}\text{K″}\text{Mn}$

where $\text{(}\text{d}\text{n}\text{d}\text{c)}{}_{\mathrm{m}}$ is the refractive index increment of the repeating unit and K″ a constant, holds only for low molecular weights. With the assumption of volume additivity, we have estimated quantitatively the linear portion of the curve, $\text{d}\text{n}\text{d}\text{c}\text{=f(}\text{1}\text{M}\text{)}$, observed for molecular weights below 20 000 as a function of polymer composition. Beyond this limit, the increase of $\text{d}\text{n}\text{d}\text{c}$ with molecular weight may be probably related to segment-segment interactions within the coil.     

Graft copolymers from azodicarboxylate-functional pre-polymers: 1. Synthesis of azodicarboxylate-functional polystyrene

A synthetic sequence is described for the preparation of polystyrenes in the molecular weight range ($\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$) 3 × 10³ to 2 × 10⁴ having terminal azodicarboxylate functionality with one functional group per polymer chain. The polymer end groups are characterized spectroscopically at each step in the synthetic sequence. The concentration of azodicarboxylate groups on the polymers is determined spectro-scopically and compared with the $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ of the polymers as calculated from initiator/monomer ratio or as measured by g.p.c. analysis.     

Crystallization and melt behaviour of isotactic poly(2-vinylpyridine)

The crystallization and melting behaviour of highly isotactic poly(2-vinylpyridine) (it-P2VP) with $\text{M}\text{?}{}_{\mathrm{<mtext>v</mtext>}}\text{= 4 × 10}{}^5$ has been studied by microscopy and d.s.c.. The maximum spherulitic growth rate was found to be 250 × 10^?3μm/min at a crystallization temperature T_c of 165°C. Experimental data could be described by the growth rate theory for small supercooling, by taking the appropriate value of 75 for the constant c₂ of the WLF equation. The chain-folded surface free energy σ_e, was estimated at 39.5 × 10^?3 J m^?2. The melting curves showed 1,2 or 3 melting endotherms. At large supercooling, crystallization from the melt produced a small melting endotherm just above T_c. This peak may originate from secondary crystallization of melt trapped within the spherulites. The next melting endotherm is related to the normal primary crystallization process. Its peak temperature increased linearly with T_c, yielding an extrapolated value for the equilibrium melting temperature T°_m of 212.5°C. At the normal values of T_c and heating rate a third endotherm appeared with a peak temperature that was independent of T_c, but rose with decreasing heating rate. From the effects of heating rate and partial scanning on the ratio of peak areas, it is concluded that this peak arises from secondary crystallization by continuous melting and recrystallization during the scan. This crystallization and melting behaviour of it-P2VP is very similar to that of isotactic polystyrene.     

Dynamics of macromolecular chains. 13C spin relaxation study of short-chain polystyrenes in deutero-chloroform solution

The results of T₁, T₂ and nuclear Overhauser effect (NOE) measurements on molecular weights 510–110 000 at weight fractions 0.05–0.60 in the title system suggest that previously neglected entanglement effects are highly significant for the reorientational processes in polymer chains and that previous T₂ estimates from bandwidths may be too low. T₂ is usually equal to T₁, and deviates only at high concentrations in these systems. The data can be represented by a double exponential reorientational correlation function of the form

$\text{G(τ)= A}\text{exp}\text{(}\text{? τ}\text{τ}{}_{\mathrm{A}}\text{) + B(}\text{? τ}\text{τ}{}_{\mathrm{B}}\text{)}$

where A + B = 1. The correlation times τ_A and τ_B are typically 1.5 × 10^?10 and 1.5 × 10^?9s, respectively. B increases with increasing concentration and molecular weight. The terminal phenyl group rotation is quite free in contrast to the backbone phenyls, and a spinning ratio above 15 has been estimated in a 60% solution for this group. Signal assignments and relaxation times (T₁) are given for 15 different ¹³C signals of these polymers at high concentrations.     

Self-diffusion of poly(ethylene oxide) in aqueous dextran solutions measured using FT-pulsed field gradient n.m.r.

Transport in ternary polymer₁, polymer₂, solvent systems has been investigated using an n.m.r. spin-echo technique. The dependence of the self-diffusion coefficient of poly(ethylene oxide) polymers on the concentration and molecular size of dextran in aqueous solution has been measured. Monodisperse poly(ethylene oxide) fractions ($\text{M}\text{?}{}_{\mathrm{w}}\text{=7.3×10}{}^4$, 2.8·10⁵ and 1.2·10⁶) and dextrans ($\text{M}\text{?}{}_{\mathrm{w}}\text{=2·10}{}^4$, 1·10⁵ and 5·10⁵) have been employed over a range of concentration up to the miscibility limit in each system. It is found that when the molecular size of the diffusant is commensurate with or exceeds that of the matrix polymer, a relationship of the form: $\text{(}\text{D}\text{D}{}_0\text{)}{}_{\mathrm{<mtext>PEO</mtext>}}\text{=}\text{exp}\text{?k(C[η])}$ is applicable, where C[η] refers to the dextran component and is considered to describe the extent of coil overlap in concentrated solution. ($\text{D}\text{D}{}_0$) is independent of the molecular size of the poly(ethylene oxide), at least in the range studied (M_w<300 000).     

Effect of molecular weight on crystallization isotherms of high molecular weight poly(ethylene oxide) fractions

Dilatometric crystallization isotherms have been determined for a set of poly(ethylene oxide) fractions ranging in molecular weight from 2 × 10⁴ to 1.6 × 10⁶. For a given fraction the isotherms obtained for different crystallization temperatures can be superimposed over most of the crystallization. For a given crystallization temperature the degree of crystallinity obtained in the primary stage of the crystallization varies greatly with molecular weight, and superimposition of the isotherms is not possible. Secondary crystallization processes are pronounced when the molecular weight ($\text{M}\text{?}{}_{\mathrm{v}}$) exceeds 10⁵.     

Influence of the molecular weight of poly(methyl methacrylate) on fracture morphology in notched tension

Specimens of poly(methyl methacrylate) (PMMA) were prepared by radiolysis of a polymer from an initial viscosity-average molecular weight ($\text{M}\text{?}{}_{\mathrm{v}}$) of 1.2 × 10⁶ down to 2.6 × 10³. At a molecular weight of 1 × 10⁵, abrupt changes in fracture morphology were observed correlating with a similarly abrupt decrease in fracture surface energy (γ). As the molecular weight was decreased further, the fracture morphology resembled more that of very brittle materials such as silicate glasses. Evidence was obtained that Wallner lines can influence the disposition of ribs but not their spacing. An empirical relationship was established between functions of rib spacing (r) and fracture surface energy.     

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.     

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.     

Effects of dextran molecular weight on graft copolymerization of dextran-methyl methacrylate

Effects of the molecular weight of dextran on its graft copolymerization with methyl methacrylate (MMA), initiated by ceric ammonium nitrate (CAN), have been investigated. The results indicate that grafting (%), graft polymerization (%) (ψ), the overall rate constant (k′) for consumption of Ce⁴⁺, and branch PMMA were influenced significantly by the molecular weight of the backbone polymer dextran. The number of branch PMMA chains per dextran molecule was 0.05 ～ 0.30 for $\text{M}\text{?}{}_{\mathrm{w}}$ 9000 dextran (D1), 0.35 ～ 0.55 for $\text{M}\text{?}{}_{\mathrm{w}}$ 61 000 (D2), and 0.8 ～ 1.6 for $\text{M}\text{?}{}_{\mathrm{w}}$ 196 000 (D3), respectively. The relationship between the rate of graft polymerization and $\text{M}\text{?}{}_{\mathrm{w}}$ (the weight-average molecular weight of dextran) was expressed by the equation: $\text{R}{}_{\mathrm{p}}\text{g = ?A}\text{log}\text{M}\text{?}{}_{\mathrm{w}}\text{+ B}$. Another linear relationship was obtained between In (100 ? ψ) and reaction time (t) for both D1 and D2 samples or In t for D3. Detailed kinetic analysis has been made on the basis of the latter relationship. Mechanical properties were also studied on the moulded sample plates of these copolymers.     

Thermoelastic and thermomechanical studies on natural rubber vulcanized in the swollen state

Three samples of natural rubber were crosslinked in n-decane solution. After the solvent had been removed, a thermodynamic investigation was made of the elastic behaviour of the samples in simple extension. Thermoelastic measurements at constant pressure and length were carried out on the first two samples. The third sample was subjected to a thermomechanical heat of extension study using a Calvet microcalorimeter. The experiments enabled the temperature coefficient of the mean-square unperturbed dimensions, 〈r²₀〉, to be derived. From the thermoelastic measurements average values for dln $\text{〈r}{}^2{}_0\text{d}\text{T}$ of (0.44 ± 0.08) × 10^?3deg^?1 and (0.38 ± 0.07) × 10^?3deg^?1 were obtained, whilst the thermomechanical measurements gave a value of (0.54 ± 0.04) × 10^?3deg^?1.     

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).     

Analysis of the temperature-time sequences for deactivating isothermal catalyst beds

A procedure is shown to determine the temperature-time sequences to keep the conversion at outlet of a fixed bed reactor subject to catalyst deactivati constant.The calculated sequences for different reaction systems follow the equation: t=$\text{k}{}_0$/k_0d$\text{E}\text{E}{}_{\mathrm{d}}$ exp($\text{E}{}_{\mathrm{d}}\text{RT}{}_0$/1.258×10⁵p_A^0.79{1-exp[$\text{E}{}_{\mathrm{d}}\text{R}$($\text{1}\text{T}$- $\text{1}\text{T}{}_0$)]}.From the analysis of the calculated sequences we have determined the values of the parameters of operation (space time, conversion and initial temperature) that give maximum values to the two functions which we sought to maximize, namely the time of operation and production.