Studies of cyclic and linear poly(dimethyl siloxanes): 3. Neutron scattering measurements of the dimensions of ring and chain polymers

The dimensions of both cyclic and linear poly(dimethyl siloxanes) in dilute solution in benzene-d₆ have been measured by small-angle neutron scattering. The mean-square radii of gyration of the linear polymers are consistent with values predicted from published data, including experimental molar cyclization equilibrium constants. The average dimensions of the cyclic poly(dimethyl siloxanes) in fractions containing z-average numbers of bonds $\text{n}\text{?}{}_{\mathrm{z}}$ in the range $\text{130 <}\text{n}\text{?}{}_{\mathrm{z}}\text{< 550}$, were found to be considerably smaller than those of the corresponding linear polymers. The neutron scattering results give a value for the ratio of the z-average radii of gyration for linear and ring poly(dimethyl siloxanes) (containing the same number of monomer units) $\text{〈s}{}^2\text{〉}{}_{\mathrm{z,l}}\text{<s}{}^2\text{〉}{}_{\mathrm{z,r}}\text{= 1.9 ± 0.2}$. This ratio may be compared with the value of 2.0 predicted theoretically for ‘flexible’ high molecular weight linear and cyclic polymers, unperturbed by excluded volume effects.     

Small-angle neutron scattering studies of polyethylene crystallized at high pressure

The technique of small-angle neutron scattering (SANS) has been used to study the chain configuration in pressure crystallized polyethylene. Two narrow molecular weight fractions of deuterated molecules (PED) of M_w 23 000 and 54 000 were solution blended with a protonated matrix polymer of M_w 81 500. Although pressure crystallization was shown to have produced a clustering of the PED molecules, the radii of gyration $\text{〈}\text{S}{}^2\text{〉}{}_{\mathrm{z}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ were, nevertheless, shown to be consistent with a model in which the PED molecules possessed rod-like configurations. The predicted rod lengths were in close agreement with the molecular stem lengths of the PEH matrix polymer, which were independently determined by nitric acid etching. Furthermore, a doubling of the PED molecular weight produced no change in the value of $\text{〈S}{}^2\text{〉}{}_{\mathrm{z}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. This was interpreted in terms of a chain folding mechanism in which a molecule is bounded by the surfaces of a lamellar block and is therefore unable to increase its' rod length.     

Temperature and concentration dependence of diffusion coefficient in dilute solutions

Temperature and molecular weight dependence of k_D in D(C) = D(O) [1 + Ck_D], where D(C) is the diffusion coefficient for the density fluctuations in a dilute polymer solution, is investigated by first expressing D(C) as a function of the static structure factor S(q,C) within the framework of the Kirkwood-Riseman theory. The continuous transition of k_D from negative values under theta conditions to positive values in good solvents is calculated using various models for the intermolecular interaction potential and the results are presented graphically as function of a reduced variables $\text{S}\text{?}\text{R}{}_{\mathrm{H}}$ that combines both molecular weight and temperature effects. It is shown that the negative value of k_D at the theta temperature can be explained at least partially, in terms of an increase in the chain dimensions of two overlapping molecules. The concentration dependence of the self-diffusion coefficient is also discussed.     

Quasi-elastic light scattering: separability of effects of polydispersity and internal modes of motion

The influence of a size distribution on the angular dependence of the quasielastically scattered light is studied for (i) large hard spherical particles and (ii) large flexible chain molecules. For the spherical particles the angular dependence is shown to depend solely on the size distribution and the particle scattering factor. Combination of conventional elastic light scattering with quasielastic light scattering allows the determination of the z-average radii moments $\text{r}{}^{\mathrm{<mtext>n</mtext><mtext>?</mtext>}}{}_{\mathrm{z}}\text{(n = ?1, 1, 2, …)}$ which define the size distribution. Flexible chains — linear and branched ones — show in any case a linear dependence of the apparent diffusion constant $\text{D}{}_{\mathrm{app}}\text{=}\text{Г}\text{q}{}^2$ on $\text{q = (}\text{4π}\text{λ}\text{)}$ sin $\text{θ}\text{2}$, when q becomes large. This behaviour represents the flexibility of the spring-bead model with strong hydrodynamic interaction. The initial part on the other hand form a straight line when D_app is plotted against q². The intercept of this straight line is the z-average diffusion constant while the slope is proportional to the z-average mean square radius of gyration. Thus, the polydispersity can be estimated from D_z and 〈S²〉_z while the asymptote at large q-values is determined by the internal flexibility of the molecule.     

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.     

On the molecular weight determination of a poly(aryl-ether-ether-ketone) (PEEK)

Attempts have been made to determine the weight average molecular weight ($\text{M}\text{?}{}_{\mathrm{<mtext>W</mtext>}}$), the radius of gyration ($\text{R}\text{?}{}_{\mathrm{<mtext>G</mtext>}}$) and the second virial coefficient (A₂) of five samples of poly(ether-ether-ketone) (PEEK) by light scattering (LS) in concentrated sulphuric acid. Account has been taken of the sulphonation of the polymer. Correlations between LS-molecular weights, melt viscosities and intrinsic viscosities in sulphuric acid or in a $\text{50}\text{50}$ phenol-trichlorobenzene mixture have been established. Gel permeation chromatography (g.p.c.) analyses at 115°C have been performed in this latter solvent and two calibration methods were compared.     

I.r. study of solution-grown crystals of polyethylene: correlation with the model from neutron scattering

The crystal stem arrangement in solution-grown polyethylene crystals has been investigated by the mixed-crystal infra-red technique. Parallel neutron scattering measurements are reported separately. The behaviour of the CD₂ bending vibration is shown to be consistent with a model having 75% adjacent re-entry, 50% dilution of a molecule along the fold plane (110 direction) and a degree of superfolding equivalent to an average molecular weight ($\text{M}\text{?}{}_{\mathrm{w}}$) of 21 000 for each sheet. This is in agreement with results from neutron scattering, which have previously been interpreted using this model. Computer calculations of stem positions based on these parameters are used to calculate the distributions of doublet splittings for several molecular weights. The main features of low-temperature FTi.r. spectra as a function of molecular weight are reproduced in this way.     

Studies of cyclic and linear poly(dimethyl siloxanes):7. Diffusion behaviour in a poor solvent

The diffusion coefficients (D) of cyclic and linear poly(dimethylsiloxanes) (PDMS) have been measured in bromocyclohexane at 288 K and 301 K. Bromocyclohexane has previously been reported to be a θ-solvent for high molar mass linear PDMS at 301 K, but the hydrodynamic radii reported here apparently show the effects of molecular expansion at both temperatures. In addition, the hydrodynamic radii of both linear and cyclic PDMS are found to be insensitive to whether the solvent is toluene or bromocyclohexane. The ratio of friction coefficients $\text{f}{}_{\mathrm{r}}\text{f}{}_{\mathrm{l}}$ for the ring (r) and linear (l) molecules of the same number of segments (x) is in good agreement with the theoretical value of $\text{8}\text{3π}$ in the impermeable limit and with the experimental value found previously in toluene solution. As x decreases the ratio $\text{f}{}_{\mathrm{r}}\text{f}{}_{\mathrm{l}}$ tends to unity, illustrating the increasing importance of free-draining at low molar mass.     

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.     

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.     

Quasi-elastic light scattering from branched polymers: 1. Polyvinylacetate and polyvinylacetate—microgels prepared by emulsion polymerization

Emulsion polymerization of vinylacetate leads to branched polymers which at high monomer conversions form microgels of the shape and size of the latex particles. Quasielastic light scattering measurements from samples in the pre-gel state give at small q² a linear angular dependence of $\text{D}{}_{\mathrm{app}}\text{=}\text{Г}\text{q}{}^2$ which resembles that of randomly branched chain molecules, where Г is the decay constant of the time correlation function. Extrapolation of D_app towards zero scattering angle yields the translational diffusion constant D_z. The diffusion constant follows the molecular weight dependence D_z = 9.78 10^?5M_w^?0.478. The diffusion constant of the microgels, i.e. at molecular weights M_w > 14 10⁶, remains constant because of the finite and constant size of the latex particles. The coefficients k_f and k_D in the concentration dependence of the frictional and diffusion coefficients are related according to the equation $\text{k}{}_{\mathrm{D}}\text{= k}{}_{\mathrm{f}}\text{? 2A}{}_2\text{M}{}_{\mathrm{w}}\text{?}\text{v}\text{?}$ where A₂ is the second virial coefficient and v? the partial specific volume of the particle. The coefficient k_f is calculated from the experimentally determined quantities k_D, A₂ and M_w, and the result is compared with the theory by Pyun and Fixman. Accordingly the branched coils in the pre-gel state resemble soft spheres, but the microgels behave more like spheres of some rigidity.     

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).     

Polyethylene/deutero-polyethylene phase behaviour

A study of the phase behaviour of polyethylene/deuterated polyethylene (PEH/PED) has been carried out to address the question of phase segregation. The phase diagram has been determined by differential scanning calorimetry on carefully co-crystallized mixtures of PEH and PED that are of essentially the same molecular weight. The phase diagram for PEH/PED is compared with one determined for the model alkane system ($\text{C}{}_{36}\text{H}{}_{74}\text{C}{}_{36}\text{D}{}_{74}$) and both are found to be of the type expected for a system forming a series of continuous solid solutions with a narrow liquidus-solidus gap. The relevance of the PEH/PED phase diagram to neutron scattering results, which claim the observation of isotopically driven phase segregation, is discussed.     

Molecular weight distributions in novolactype phenol-formaldehyde polymerization

To model the reversible novolac polymerization, five reactive species A to E have been defined. Molecules having bound CH₂OH (Q_n) are distinguished from those without it (P_n) and it is assumed that molecules of Q_n do not have more than one bound CH₂OH group. A kinetic model has been written and, based upon it, balance equations for molecules of novolac polymer in batch reactors have been derived. Based upon our earlier studies, the phenomenon of molecular shielding has been neglected. As a result, the reactivities of the ortho and para positions of phenol which are available in the literature could be used. The kinetic model for the molecular weight distribution (MWD) of reversible novolac polymer formation thus involves only one parameter. The study of the MWD of novolac polymer reveals two very important design variables: the phenol-formaldehyde ratio, $\text{[P]}{}_0\text{[F]}{}_0$, in the feed and the vacuum applied on the reactor. As the $\text{[P]}{}_0\text{[F]}{}_0$ ratio is increased, the breadth of the distribution is found to increase and it undergoes a maximum at $\text{[P]}{}_0\text{[F]}{}_0\text{? 1.4}$ for the set of rate constants chosen. At this ratio, the chain length average molecular weight is also found to be the largest. Industrially, the $\text{[P]}{}_0\text{[F]}{}_0$ ratio used in producing novolac polymer is 1.67 and it is usually desired that the polymer be linear with minimal branching. On application of vacuum, for a given time of polymerization, the chain length molecular weight is found to increase when the results are compared with those of batch reactors. The breadth of the distribution is also found to reduce thus giving a lower polydispersity index of the polymer formed.     

Pseudo diffusion of nonvolatile metals in electro graphite

The apparent diffusion coefficients for Ti, V, Cr, Nb, Mo and Hf as carbides and for elementary Fe, Ni and Cu in electro graphite have been determined by means of an electron-microprobe analyzer. These pseudo diffusion coefficients were found to vary with the heat treatment time. However, after one hour these remain constant and follow the Arrhenius type of relation D = D₀exp(?Q/RT). The activation energy Q was nearly constant for the metals investigated. An attempt was made to correlate the frequency factor D₀ with the heat of formation $\text{ΔH}{}_{\mathrm{?}}{}^{298}$ of the corresponding carbides. A plot of log D₀vsΔH_f yielded two straight lines, one for the negative $\text{ΔH}{}_{\mathrm{?}}$, the other for positive $\text{ΔH}{}_{\mathrm{?}}$. This method was satisfactorily applied to predict the diffusion coefficients of Zr, Sb and Bi.     

Copoly(m,p-chloromethylstyrene-50% styrene): Copolymer molecular weights,fractionation and derivatization

Copolymerization of an equimolar mixture of m,p-chloromethylstyrene ($\text{M}$₁) and styrene ($\text{M}$₂) was carried out in chlorobenzene in the presence of AIBN at 80°C. Molecular weight analysis (by g.p.c.) of the resulting polymer samples was performed at various conversions. $\text{M}\text{?}{}_{\mathrm{<mtext>w</mtext>}}$, $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$, and ($\text{M}\text{?}{}_{\mathrm{<mtext>w</mtext>}}\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$) value of 21 300, 13 800 and 1.54 were obtained at 8.9% conversion. At higher conversions, the value of $\text{M}\text{?}{}_{\mathrm{<mtext>w</mtext>}}$ remained effectively constant while $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ decreased to 9200 at ca. 80% conversion, and then increased to 12 000 at about 100% conversion (16 h), and to 13 700 if the polymer solutions were maintained at 80°C for an additional 44 h. These results suggest that, although the termination step initially involves the combination of polymer radicals, at high conversions a large number of very low molecular weight, and unsaturated, polymer molecules are formed possibly by disproportionation involving polymer radicals and primary radicals. The unsaturated polymer molecules are subsequently polymerized by growing polymer radicals towards the end of the polymerization. It was noticed that further reaction occurred after complete depletion of monomer, involving radical attack on the unsaturated polymer molecules. Other reactions including chain transfer to polymer will also be important at high polymer concentrations. A copolymer of $\text{M}$₁ and $\text{M}$₂ was separated into four fractions on a preparative scale, and molecular weight analysis of the resulting polymer samples provided more evidence of the above interpretation. G.p.c. analysis of several derivatives of a copolymer of $\text{M}$₁ and $\text{M}$₂ showed that most molecular weights were much lower than that of the starting polymer. These results in some cases may reflect the chemical or dimensional changes introduced into the polymer molecules during derivatization.