The unperturbed molecular dimensions of poly(ethylene oxide) in aqueous solutions from intrinsic viscosity measurements and the evaluation of the theta temperature

Intrinsic viscosity measurements were carried out on five well characterized fractions of poly(ethylene oxide) in aqueous solutions at 24.9°, 34.9°, and 45.5°C. The Stockmayer-Fixman extrapolation was applied to the data: it yields the unperturbed dimensions K₀ of the chain. The unperturbed root-mean-square end-to-end distance $\text{〈}\text{R}\text{?}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_0$ calculated for the polymer fractions in water indicate that the polymer molecules are expanded in this solvent as the temperature is raised. The temperature coefficient of unperturbed dimension, $\text{d In}\text{〈}\text{R}\text{?}{}^2\text{〉}{}_0\text{d}\text{t}\text{= 0.024}\text{K}{}^{\mathrm{?1}}$, calculated for poly(ethylene oxide) in water using the present data is about 100 times higher than the literature values of 0.23 (±0.02) × 10^?3 K^?1 and 0.2 (±0.2) × 10^?3 K^?1, respectively, obtained from force-temperature (‘thermoelastic’) measurements on elongated networks of the polymer in the amorphouse state and form viscosity measurements on this polymer in benzene. A value of θ=108.3°C was obtained from the temperature dependence of the interaction parameter B in the Stockmayer-Fixman equation.     

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.     

Comparison of the unperturbed dimension of polystyrene for endothermal and exothermal heats of dilution within the same system

Light scattering measurements for two samples of polystyrene (I, M_w = 2.15 × 10⁵; II, M_w = 2.5 × 10⁶) were performed in the iso-refractive mixed solvent dimethoxymethane-diethyl ether. For sample I the temperature dependence of the second osmotic virial coefficient A₂ was determined for three constant compositions of the mixed solvent. In the range ?30° to +25°C the three curves run practically parallel and exhibit a maximum at approximately ?10°C. For the volume fraction of 0.7 diethyl ether in the mixed solvent, an endothermal theta-temperature θ₊ was found at ?27.0° ± 1.5°C and θ_?, the exothermal theta-temperature, at ?5.0 ± 1°C. The investigation of sample II in the abovementioned solvent confirmed the observed θ_?-temperature and displayed a higher exothermicity compared with I. Similarly to the temperature variation of A₂, the chain dimensions of II, determined from the angular dependence of the scattered light, run through a maximum. The unperturbed dimensions in the mixed solvent are found to be: $\text{r}{}_{\mathrm{w}}\text{= 448 ± 5}\text{A}\text{?}$ at θ₊ = ?27°C and $\text{r}{}_{\mathrm{w}}\text{= 443 ± 5}\text{A}\text{?}$ at θ_? = ?5°C, as compared with $\text{r}{}_{\mathrm{w}}\text{= 420 ± 10}\text{A}\text{?}$ at θ₊ = +33°C in cyclohexene. The inter-relation of the chain expansion coefficient and A₂ is quantitatively described by the Zimm-Stockmayer-Fixman equation over the entire range of heats of dilution.     

Characterization of poly(1,4-phenyleneterephthalamide) in concentrated sulphuric acid: 1. Static and dynamic properties

Laser light scattering including angular dependence of total integrated scattered intensity and of the spectral distribution has been used to characterize five samples of poly(1,4-phenylene terephthalamide), PPTA (commercially known as Kevlar), of different molecular weights in 96% sulphuric acid and 0.1 NK₂SO₄. The data are supplemented by intrinsic viscosity measurements used to detect the possible effects of association, by differential refractometry providing a measure of the refractive index increments in mixed solvents (H₂O, H₂SO₄ and K₂SO₄) and by spectrophotometry for the extinction coefficient needed in the correction of attenuation in light scattering studies. The results show 〈D〉Z = 2.11 × 10^?5$\text{M}\text{?}{}_{\mathrm{<mtext>W</mtext>}}{}^{\mathrm{?0.75}}\text{cm}{}^{\mathrm{?2}}\text{s}{}^{\mathrm{?1}}$ in reasonable agreement with an average of many of the published intrinsic viscosity data obeying [η] = 1.09 × 10?3 M_w^1.25 ml g^?1 and _w expressed in g mol^?1.     

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.     

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.     

Poly(ethyl acrylate) in dilute solution

Poly(ethyl acrylate) (PEA), solution polymerized in methyl ethyl ketone by free radical initiation, was fractionated and the fractions were characterized by light scattering, viscometry and osmometry. Fractions obtained were in the molecular weight range of 0·3 × 10⁶ to 1·6 × 10⁶ with a polydispersity of 1.40. The following Mark-Houwink relations were established:

$\text{[η]}{}^{\mathrm{<mtext>35°</mtext><mtext>C</mtext>}}{}_{\mathrm{<mtext>acetone</mtext>}}\text{=4·15×10}{}^{\mathrm{?2}}\text{M}{}^{\mathrm{0?61}}{}_{\mathrm{W}}$

$\text{[η]}{}^{\mathrm{<mtext>35°</mtext><mtext>C</mtext>}}{}_{\mathrm{<mtext>MEK</mtext>}}\text{=2·03×10}{}^{\mathrm{?2}}\text{M}{}^{\mathrm{0?66}}{}_{\mathrm{W}}$

$\text{[η]}{}^{\mathrm{<mtext>39.5°</mtext><mtext>C</mtext>}}{}_{\mathrm{<mtext>n-propanal</mtext>}}\text{=7·89×10}{}^{\mathrm{?2}}\text{M}{}^{\mathrm{0?50}}{}_{\mathrm{W}}$

It was found that n-propanol at 39.5°C was a theta solvent for poly(ethyl acrylate) and that acetone was a poor solvent compared to methyl ethyl ketone. A relation between the molecular dimension and the molecular weight was established. It was observed that the chain dimensions of poly(ethyl acrylate) and poly(butyl acrylate) were considerably larger than poly(ethyl methacrylate) and poly(butyl methacrylate) respectively. The validity of various extrapolation procedures that have been proposed for calculating the unperturbed dimensions have been examined. The steric factor for PEA was 2·16 compared to 2·10 for poly(ethyl methacrylate). Root mean square end-to-end distances were calculated from the Debye-Bueche and Kirkwood-Riseman methods and compared with the experimental values.     

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.     

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).     

Solution properties and chain flexibility of polythiolmethacrylates: 1. Poly(phenyl thiolmethacrylate) and poly(O-methyl phenyl thiolmethacrylate)

Dilute solution properties of poly(phenyl thiolmethacrylate) (PTPh) and poly(o-methylphenyl-thiolmethacrylate) (PTMPh) were studied by gel permeation chromatography, light scattering, osmotic pressure and viscosity measurements in different solvents. Relations between intrinsic viscosity [η], z-average root-mean-square end-to-end distance $\text{(}\text{r}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and molecular weight $\text{M}\text{?}{}_{\mathrm{w}}$ were established. The unperturbed dimensions were calculated by different methods using $\text{M}\text{?}{}_{\mathrm{w}}$ and [η]. PTPh (σ = 2.26) and PTMPh (σ = 2.27) have practically the same flexibility, but both are more flexible than poly(phenyl methacrylate) (σ = 2.50). In our opinion, this is due to the change in the local intramolecular interaction and the higher flexibility of the sulphur-containing side group.     

Poly(sulphopropylbetaines): 2. Dilute solution properties

Solution properties of a series of aromatic ($\text{5 × 10}{}^3\text{<}\text{M}\text{?}{}_{\mathrm{w}}\text{< 2.5 × 10}{}^5$) and aliphatic ($\text{10}{}^6\text{<}\text{M}\text{?}{}_{\mathrm{w}}\text{< 1.2 × 10}{}^7$) poly(sulphopropylbetaines) have been investigated by examining three complementary phenomena: (a) solubility in organic protic solvents; (b) water solubility promoted by various (cloud point titrations), with special emphasis on the influence of the anion polarizability and a comparison between Na⁺ and Ca⁺⁺; (c) hydrodynamic and morphological properties in aqueous NaCl solutions at 25°C, as derived from the Mark-Houwink-Sakurada relations. Chain expansion is a slightly increasing function of the NaCl concentration (≤1 M) but it remains, however, relatively low, even for high molecular weights (α_η < 1.15). With respect to the polymeric amino precursors, the zwitterionic group

enhances chain rigidity (steric factor σ), as a result of its steric hindrance and specific dipolar interactions between neighbouring units.     

Studies of cyclic and linear poly(dimethyl siloxanes): 10. Calculations of radii of gyration

A Monte Carlo method has been devised for calculating the conformation-dependent properties of cyclic poly(dimethyl siloxanes) (PDMS), using Flory, Crescenzi and Mark's rotational isomeric state model. Calculated values of the mean-square radii of gyration 〈s²_r〉 of ring molecules unperturbed by excluded volume effects and containing 8–100 skeletal atoms are compared with the 〈s²_l〉 values for the corresponding unperturbed chain molecules. Exact enumeration methods were also employed for rings $\text{[(}\text{CH}{}_3\text{)}{}_2\text{SiO}\text{]}{}_{\mathrm{<mtext>w</mtext><mtext>2</mtext>}}$ with w ? 24 and the results found to be in close agreement with those obtained by the Monte Carlo method. The ratio $\text{〈s}{}^2{}_{\mathrm{l}}\text{〉}\text{〈s}{}^2{}_{\mathrm{r}}\text{〉}$ was found to attain limiting values close to 2.0 for w > 30, in agreement with theoretical predictions.     

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 $\text{M}\text{?}{}_{\mathrm{w}}\text{?230 000}$.     

Small-angle neutron scattering studies of isotropic polypropylene

Small-angle neutron scattering studies have been made of molten and crystalline polypropylene using samples containing small amounts of deuterated polypropylene in a protonated polypropylene matrix. The specimens were characterized by small- and wide-angle X-ray scattering to determine the d-spacing and the degree of crystallinity χ and by gel permeation chromatography to determine molecular weight, M_w, and molecular weight distribution. The degree of crystallinity was varied from 0.5 to 0.7, the d-spacing from 120 to 250 Å and the molecular weight from 34 000 to 1 540 000. Clustering was not observed. The radius of gyration $\text{〈s}{}^2\text{〉}{}_{\mathrm{w}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ of the tagged molecules was approximately proportional to $\text{M}{}_{\mathrm{w}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and almost independent of d and χ. In the melt similar values were obtained which are, within experimental uncertainties, the same as in a θ-solution. For 〈s²〉_wk²? 1 the scattering law approaches a k^?2 dependence. The results are discussed with reference to the chain-folded model but a fit cannot be obtained over all molecular weights. A simple random coil model fits the neutron scattering data partly but this does not explain the origin of the d-spacing.     

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.     

Pressure dependence of upper critical solution temperatures in the polystyrene - cyclohexane system

The pressure dependence of the upper critical solution temperature $\text{(}\text{d}\text{T}\text{d}\text{p}\text{)}{}_{\mathrm{c}}$ in the polystyrene-cyclohexane system has been measured over the pressure range of 1 to 50 atm. The value of $\text{(}\text{d}\text{T}\text{d}\text{p}\text{)}{}_{\mathrm{c}}$ determined over the molecular weight (M_w) range of 3.7 × 10⁴ to ～145 × 10⁴ greatly depends on the molecular weight of polystyrene. The value of $\text{(}\text{d}\text{T}\text{d}\text{p}\text{)}{}_{\mathrm{c}}$ for a polystyrene solution of low molecular weight (M_w = 3.7 × 10⁴) is positive (3.14 × 10^?3 degree atm^?1), while the values are negative (?0.52 × 10^?3～?5.64 × 10^?3 degree atm^?) for solutions of polystyrene over the high molecular weight range of 11 × 10⁴ to ～145 × 10⁴. The Patterson-Delmas theory of the corresponding state and the newer Flory theory have been used to explain this behaviour.     

A calculation of the elastic constant c33 of a graphite crystal as a function of temperature

A calculation is presented of the elastic constant C₃₃ of a graphite crystal as a function of temperature up to 2500 K, taking into account the anharmonic contribution and the changes in interlayer interactions due to the large lattice thermal expansion. Parametric variations in the theory show that the anharmonic contribution to C₃₃ depends principally on the parameter ($\text{?}{}^2\text{C}{}_{33}\text{?e}{}^2{}_{\mathrm{zz}}$) Comparison of theoretical results with the experimental data, which is mainly from neutron scattering experiments, shows that the data can be accounted for if ($\text{?}{}^2\text{C}{}_{33}\text{?e}{}^2{}_{\mathrm{zz}}$) lies in the range 7–10 × 10¹³ dynes/cm². A theoretical estimate of ($\text{?}{}^2\text{C}{}_{33}\text{?e}{}^2{}_{\mathrm{zz}}$) based on Lennard-Jones potentials between atoms in adjacent basal planes gives a value of 9·07 × 10¹³ dynes/cm².     

Solution properties of poly(propylene sulphide)

Poly(propylene sulphide) (PPS) initiated by cadmium bis(phenyl allyl thiolate) was fractionated from benzene-methanol, and the fractions were examined by viscosity, osmotic pressure and light scattering determinations. Gel permeation chromatography with Styragel columns was found unsatisfactory in tetrahydrofuran (THF) and toluene at room temperature. Polymer stored in the dark at room temperature underwent a very slow degradation which broadened the distribution in the fractions. The following quantitative relationships were found at 25°C:

Extrapolations to derive the unperturbed coil dimensions indicate a possible, but doubtful, solvent effect. The value derived from the θ-mixture gives $\text{A = 696 × 10}{}^{\mathrm{?11}}\text{cm mol}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{g}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ and a steric factor σ = 1.49, consistent with a high ‘chain flexibility’ expected from the relatively long C-S-C linkages.