Solvent self-diffusion in semidilute polystyrene solutions. Pulsed-gradient spin-echo measurements on a standard Fourier transform n.m.r. spectrometer

Measurements of solvent self-diffusion coefficients in the systems polystyrene/dichloromethane and polystyrene/cyclopentane recorded on a standard Fourier transform n.m.r. spectrometer are reported. The ratio $\text{D}{}_{\mathrm{s}}\text{D}{}_{\mathrm{s,0}}$ was found to decrease linearly with increasing volume fraction of polystyrene, over the interval studied (ø_PS<0.27), for both systems. For PS/cyclopentane an increase in temperature from 12.5°C (close to UCST) to 40°C was not found to alter the concentration dependence of the ratio $\text{D}{}_{\mathrm{s}}\text{D}{}_{\mathrm{s,0}}$ significantly.     

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.     

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).     

Studies of cyclic and linear poly(dimethyl siloxanes): 12. Observation of diffusion behaviour by quasielastic neutron scattering

High resolution neutron scattering experiments have been used to observe the diffusive motion of low molecular weight linear and cyclic poly(dimethyl siloxane) molecules in dilute solution in deuterated benzene. Diffusion coefficients (D) and hydrodynamic radii (R_H) have been compared with values obtained by light scattering for higher molecular weight samples and with radii of gyration (R_g) obtained by small-angle neutron scattering. While the ratio $\text{D}{}_{\mathrm{<mtext>ring</mtext>}}\text{D}{}_{\mathrm{<mtext>chain</mtext>}}$ is close to the predicted value of 0.85, the ratio $\text{R}{}_{\mathrm{g}}\text{R}{}_{\mathrm{<mtext>H</mtext>}}$ falls below the theoretical value for both ring and chain molecules. The scattering curves show effects arising from both centre of mass diffusion and internal molecular motion, and the observed inverse correlation times are compared with calculated behaviour as a function of scattering vector, Q.     

Cyclization dynamics of polymers: 9. The effect of polymer concentration on the slowest internal relaxation mode of a labelled polystyrene chain

A combination of steady-state and fluorescence decay techniques permits one to measure the dynamics of end-to-end cyclization of a polymer chain substituted at both ends with pyrene groups. In the limit of low concentration, the rate constant for cyclization, k_cy, can be identified with the slowest relaxation rate $\text{τ}{}_1{}^{\mathrm{?1}}$ of a Rouse—Zimm chain. Experiments are reported which allow k_cy to be examined for two chain lengths of polystyrene substituted on both ends with pyrene groups. These chains have $\text{M}\text{?}{}_{\mathrm{n}}\text{= 9200}$ and 25 000 ($\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{? 1.15}$). Added unlabelled polystyrene polymer [PS] causes $\text{k}\text{?}{}_{\mathrm{<mtext>cy</mtext>}}$ to decrease in cyclohexane just above the θ-temperature, whereas in toluene, a good solvent, k_cy is largely unaffected, even at [PS] concentrations of 50 wt%. These results are explained in terms of frictional effects—hydrodynamic screening—dominating in the poor solvent, whereas other factors tend to have offsetting effects in the good solvent.     

Diffusion in polyacrylamide gels

Using a novel sorption technique, the diffusion of some series of solutes in polyacrylamide gels has been investigated with regard to: (a) molecular size of solute; (b) concentration of solute and gel polymer; and (c) temperature. The approach used also yields the partition coefficient pertaining to sorption equilibrium. The ratio, $\text{D}\text{D}{}_{\mathrm{o}}$, where D_o refers to diffusion in the pure solvent, is found to reflect in part the characteristic interactions between solute and gel polymer. The temperature results indicate that the apparent activation energy for solute diffusion is approximately independent of the polymeric component for dilute gels.     

Self diffusion of small molecules in aqueous solution of poly(vinylpyrrolidone)

The self-diffusion coefficients of small penetrants were measured in aqueous solutions at varying concentrations of poly(vinylpyrrolidone). Measurements have been performed using the n.m.r. pulsed-gradient spin-echo (PGSE) technique and the classical gradient diffusion (CGD) method, modified for ternary systems. A good agreement was found between the two, confirming the validity of the latter. The results have been quantitatively analysed by a free-volume approach adapted for diffusion of a solute in moderately concentrated polymer solutions. From this model a linear relationship is predicted between ln $\text{D}\text{D}{}_{\mathrm{<mtext>o</mtext>}}$ and ?^?1, the reciprocal volume fraction of solvent, which was also found experimentally for all diffusants studied. An enhanced concentration dependence of penetrant diffusion with increasing size of the diffusing molecules was observed. These findings are in agreement with predictions from the free-volume theory.     

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.     

Flow microcalorimetry on dilute polymer solutions

A flow microcalorimeter designed to measure the heat of mixing of dilute polymer solutions is described. The instrument is sensitive to steady state heating rates of ～10 μJ/sec. Measurements of heats of mixing of solutions of differing concentrations of n-hexane and cyclohexane are reported and are compared with recommended data of McGlashan and Stoeckli. Values of:

$\text{K}{}_1\text{=}\text{lim}\text{V}{}_2\text{→ 0}$

$\text{(}\text{H}\text{?}{}_1\text{?}\text{H}\text{?}{}^0{}_1\text{RTv}{}^2{}_2$ are obtained for four polymer—solvent systems: polyisobutylene—benzene, 0.22; polystyrene (PS)—cyclohexane, 0.33; PS—n-butyl acetate, ?0.06 all at 25°C; and PS—toluene, ?0.05 at 40°C. Various theoretical calculations of second virial coefficients A₂ made with use of the calorimetric data are compared with previously measured A₂ for the first two mixtures.     

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.     

Ultramicroscopy of association colloids formed from block copolymers

Ultramicroscopy studies have been made of micelle formation by two poly(styrene)-poly(isoprene) block copolymers in organic solvents (N,N-dimethylacetamide and n-decane respectively) and a poly(l-glutamic acid)-poly(l-leucine) block copolymer in an aqueous solution of 0.2M NaCl at pH = 4.0. The technique provides a method of determining the number-average translational diffusion coefficient) $\text{D}\text{?}{}_{\mathrm{n}}$, of association colloids and leads, via the Stokes-Einstein relation, to a measure of the number-average of the reciprocal hydrodynamic radius $\text{(R}{}_{\mathrm{<mtext>D</mtext><mtext>?</mtext>}}{}^1\text{)}{}_{\mathrm{n}}$ for spherical particles. Particles having a radius less than approximately 30 nm were too small to be detected by the technique.The ultramicroscopy results were compared with data obtained by laser light scattering photon correlation spectroscopy which provides a measure of the z-average translational diffusion coefficient. $\text{D}\text{?}{}_{\mathrm{z}}$. An additional comparison was made by carrying out measurements on two well-characterized poly(styrene/divinyl benzene) latices.     

Characterization of oligo-poly(dimethylsiloxanes) and their solutions in toluene

A commercial sample of poly(dimethylsiloxane) [PDMS] has been subjected to vacuum distillation, yielding five fractions of $\text{M}\text{?}{}_{\mathrm{n}}$ ranging from 481 to 1132 g mol^?1. These have been characterized at different temperatures with respect to density, refractive index, coefficient of isothermal compressibility, light scattering depolarization ratio and Rayleigh ratio. Similar measurements were made on pure toluene and PDMS/toluene mixtures over the whole composition range for each fraction. For these solutions, linearity in light scattering plots held up to PDMS concentrations of ～0.2 g cm^?3, yielding $\text{M}\text{?}{}_{\mathrm{w}}$ (500–1176 g mol^?1) and large positive values of the second virial coefficient, A₂. In contrast to the findings of others, there was no evidence for association. Data recast in a form in which toluene was regarded as solute and PDMS as solvent gave negative values of A₂. The Mark-Houwink constants for oligomeric PDMS in toluene at 25°C have also been determined. The properties of oligo-PDMS and solutions in toluene are discussed in relation to those of high molecular weight PDMS′     

Low-angle laser light scattering from polystyrene solutions: intensity measurements and photon correlation spectroscopy

Light scattering measurements have been made on polystyrenes with a range of molecular weights in toluene and for one polystyrene with a range of molecular weights in toluene and for one polystyrene in a range of solvents including a theta solvent. Intensity data were used to calculate second virial coefficients and molecular weights, whilst photon correlation spectroscopy was used to calculate diffusion coefficients. All measurements were made at 30°C and at a scattering angle of ca.4°. The data were used to examine current theories of polymer diffusion and the relation between hydrodynamic radius (R_H) and radius of gyrations ($\text{〈s}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$). The results support accepted theories of polymer diffusion, but suggest that the relation between R_H and $\text{〈s}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ requires further analysis.     

Verification of the Maxwell–Stefan theory for tracer diffusion in zeolites

Using the Maxwell–Stefan theory for diffusion we derive a simple formula to relate the tracer (i.e. self) diffusivity D¹ and Maxwell–Stefan (MS), or jump, diffusivity $\text{D}\text{–}$. The presence of the interchange coefficient $\text{D}\text{–}{}_{\mathrm{ij}}$ in the MS formulation causes the self diffusivity to be lower than the jump diffusivity. Assuming the interchange coefficient to be given by $\text{D}\text{–}$/F we derive:$\text{D}{}^1\text{=}\text{D}\text{–}\text{1+Fθ}$where F is a factor to take account of topology effects within the zeolite matrix.The validity of the MS formulation is established by performing kinetic Monte Carlo simulations for diffusion of methane, perfluoromethane, 2-methylhexane and iso-butane in silicalite. Furthermore, it is shown that the exchange coefficient $\text{D}\text{–}{}_{\mathrm{ij}}$ is a quantification of correlation effects during the hopping of molecules. For iso-butane, the isotherm inflection leads to a sharp inflection in the diffusion behaviour. The influence of molecular repulsive forces on the loading dependence of the jump and self-diffusivities is also discussed with the aid of published Molecular Dynamics simulations for methane.     

Synthesis and solution properties of comb polystyrenes

A new method for the synthesis of comb shaped polystyrenes of predetermined structure is described. Silicon-chlorine bonds are introduced into the backbone polystyrene by reaction of SiMe₂Cl₂ with hydrolysed styrene/vinyl acetate copolymers and coupled with polystyryl-lithium in benzene. From a common backbone polymer a series of comb polymers are prepared that have a constant number of branches but vary in branch length. The $\text{M}{}_{\mathrm{w}}\text{M}{}_{\mathrm{n}}$ of the whole comb polymers is about 1.3. The comb polymers with high branch density show θ (A₂) temperatures lower than that for linear polystyrene. The radius of gyration at θ (A₂) [〈S²〉_{θ (A2)}] is always larger than calculated from random flight statistics. For comb polymers with 20–30 branches increases with λ^?0.46 where λ is the fraction of polymer in the backbone. The intrinsic viscosities of the comb polystyrenes at θ (A₂) are equal to that of the parent backbone polymer when λ > 0.25 and increase only little when λ becomes equal to 0.1. Similar behaviour is found in toluene. Intrinsic viscosities in cyclohexane at 35°C show a complex pattern because of the θ-temperature variation.     

Activated diffusion of methane from coals at elevated pressures

Diffusion of methane from three coals ranging in rank from anthracite to HVA bituminous has been studied at initial methane pressures up to about 2.76 MPa (400 psi). Unsteady-state diffusion conditions existed, the methane pressure within the coal particle decreasing with time while the methane pressure outside the particles remained at atmospheric. The diffusion parameter $\text{D}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{r}{}_0$ increased with increasing methane concentration at high values of methane sorption. Diffusion was activated but the exact magnitude of the activation energy is uncertain owing to the suspected contribution of the heat of sorption to the temperature coefficient. $\text{D}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{r}{}_0$ increased with decreasing particle size of coal studied, but r₀ is clearly less than the particle radius.     

Novel excimer fluorescence method for monitoring polymerization: 1. Polymerization of methyl methacrylate

An excimer is formed by the association of an excited molecule with another molecule in its ground state. Such an excimer is characterized by a broad structureless fluorescence which is shifted to longer wavelengths compared to the fluorescence spectrum of the isolated molecule. Intramolecular excimer fluorescence has been observed in solutions of pyrene-labelled alkanes such as 1,3-bis-(1-pyrene)propane and 1,10-bis-(1-pyrene)decane.We have measured the solvent-viscosity dependence of the intensity ratio $\text{F}{}_{\mathrm{<mtext>M</mtext>}}\text{F}{}_{\mathrm{<mtext>D</mtext>}}$ for solutions of these pyrene-labelled alkanes in mixed solvents made of ethyl acetate and glycerol tripropionate. Here F_M and F_D are, respectively, the fluorescence intensity of the unassociated pyrene groups and that of the intramolecularly formed pyrene excimers. We have found that for each of the two pyrene-labelled alkanes, the ratio $\text{F}{}_{\mathrm{<mtext>M</mtext>}}\text{F}{}_{\mathrm{<mtext>D</mtext>}}$ increases with the increase in solvent viscosity. Further, we have shown that by adding a trace amount of 1,3-bis-(1-pyrene)propane or 1,10-bis-(1-pyrene)decanee to a polymerizing system, we can measure the ratio $\text{F}{}_{\mathrm{<mtext>M</mtext>}}\text{F}{}_{\mathrm{<mtext>D</mtext>}}$ to monitor in situ the polymerization reaction. polymerization;