Studies of cyclic and linear poly(dimethyl siloxanes): 5. Diffusion behaviour in dilute solution

The diffusion coefficients of cyclic and linear oligomeric and polymeric dimethyl siloxanes, containing number-average numbers of skeletal bonds in the range $\text{6 <}\text{n}\text{?}{}_{\mathrm{n}}\text{< 650}$, have been measured in toluene solution at 298K. Impermeable diffusion behaviour was observed for all the siloxanes studied, in agreement with previous findings for ethylene oxide and hexamethylene oxide oligomers and polymers. The ratio of the friction coefficients $\text{f}{}_{\mathrm{r}}\text{f}{}_{\mathrm{l}}$ for the ring (r) and linear (l) dimethyl siloxanes was found to be $\text{8}\text{3κ}$ (within the limits of experimental error) over the whole range of molecular weights studied. Values of the expansion factor α_f for the linear poly(dimethyl siloxanes) (obtained from the diffusion measurements) were found to be approximately equal to the corresponding values for α_η (found previously by viscometric studies) for small values of the excluded volume parameter z; and α_f was larger than α_η for large z, as predicted by first-order perturbation theory. Mean-square radii of gyration 〈s²_G〉 were calculated from the diffusion data for both cyclic and linear poly(dimethyl siloxanes) assuming Gaussian statistics, and found to be in good agreement with the corresponding values obtained by neutron scattering. However, the values of 〈s²_G,l〉 for the short chain poly(dimethyl siloxanes) did not agree with the corresponding values of 〈s²_O,l〉, calculated using the rotational isomeric state model of Flory, Crescenzi and Mark. This discrepancy is thought to arise from deviations from Gaussian behaviour, and considerably better agreement between experiment and theory was achieved by using appropriate values of a function ψ_l(x), which relates radii of gyration and impermeable hydrodynamic diffusion radii.     

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.     

Determination of type and width of a size distribution from the z-averages of the radii moments rnz

Relationships are given between the z-average radii moments $\text{r}\text{?}{}^{\mathrm{n}}{}_{\mathrm{z}}$ and the common moments $\text{r}\text{?}{}^{\mathrm{n}}$ of a size distribution. Instructions are given for finding the type and width of a size distribution from measurements of the $\text{r}\text{?}{}^{\mathrm{n}}{}_{\mathrm{z}}$ moments.     

Studies of cyclic and linear poly(dimethyl siloxanes): 2. Preparative gel permeation chromatography

A preparative gel permeation chromatographic (g.p.c.) instrument has been constructed and used to separate broad fractions of cyclic poly(dimethyl siloxanes) into sharp fractions with heterogeneity indices $\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{= 1.05 ± 0.02}$. The number-average molecular weights $\text{M}\text{?}{}_{\mathrm{n}}$ of the cyclic polymer fractions obtained were as high as 50 000, corresponding to number-average numbers of skeletal bonds $\text{n}\text{?}{}_{\mathrm{n}}$ up to 1300. The concentrations of linear poly(dimethyl siloxanes) in all but the highest molecular weight cyclic polymer fractions prepared are believed to be negligible. The preparative g.p.c. instrument was also used to obtain some sharp fractions of linear poly(dimethyl siloxanes).     

Studies of cyclic and linear poly(dimethyl siloxanes): 14. Particle scattering functions

Particle scattering functions P(Q) (where Q represents the wave vector), have been calculated using a Monte Carlo method for cyclic and linear poly(dimethyl siloxanes) (PDMS) containing up to 100 skeletal bonds. A maximum is found in the Kratky plot at $\text{u (=Q〈s}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)≈2.0}$ for cyclic PDMS (with root-mean-square radii of gyration $\text{〈s}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) and this is in satisfactory agreement with the analytical calculations of Casassa and of Burchard and Schmidt. In addition, other clearly-defined maxima are found at u≈5.0 for PDMS ring molecules with less than ≈40 skeletal atoms. These maxima are believed to be characteristic of small cyclic molecules as they are also predicted for small polymethylene rings. Comparisons are made with experimental small-angle neutron scattering (SANS) data for cyclic and linear PDMS. A single maximum in the experimental Kratky plot at u≈2.0 is found for PDMS ring molecules with an average of 550 skeletal atoms. The experimental data for cyclic PDMS are in better agreement with the Monte Carlo calculations of P(u) than with analytical predictions up to u≈2.0.     

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.     

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.     

Studies of cyclic and linear poly(dimethyl siloxanes): 13. Static dielectric measurements and dipole moments

The static dielectric permittivities, refractive indices and densities of undiluted oligomeric cyclic and linear dimethyl siloxanes and narrow fractions of cyclic and linear poly(dimethyl siloxanes) have been measured for number-average molar masses M?_n in the range $\text{160 <}\text{M}\text{?}{}_{\mathrm{n}}\text{< 7700}$ at temperatures from 298 to 313 K. Measured total dielectric polarizations have been resolved into their electronic, atomic and orientation components and dipole moments have been derived. The dipole moments of cyclic oligomers ((CH₃)₂SiO)_x (for example, with x = 4, 5) are markedly lower than the dipole moments of the corresponding linear oligomers containing the same number of siloxane bonds. However, for x ? 10, the dipole moments of cyclic dimethyl siloxanes are identical, within experimental error, to those of the corresponding linear dimethyl siloxanes. Measured static dielectric permittivities of the dimethyl siloxanes and poly(dimethyl siloxanes) in solution in cyclohexane are markedly different from the corresponding values for the undiluted siloxanes. These differences are interpreted as resulting from the specific solvent effects.     

Studies of cyclic and linear poly(dimethyl siloxanes): 1. Limiting viscosity number-molecular weight relationships

The limiting viscosity numbers of ten cyclic and ten linear poly(dimethyl siloxane) fractions have been measured in a π-solvent (butanone at 293K) and in two ‘good’ solvents (toluene and cyclohexane at 298K). The dimethyl siloxane fractions studied were in the molecular weight range $\text{800 <}\text{M}\text{?}{}_{\mathrm{w}}\text{< 17 000}$. The data obtained are compared with related studies published in the literature. The ratio of the limiting viscosity numbers [η]_r and [η]_l of the cyclic and linear poly(dimethyl siloxanes) with $\text{M}\text{?}{}_{\mathrm{w}}\text{> 2500}$ was found to be 0.67 in butanone at 293K. This value is identical (within experimental error) to the theoretical ratio $\text{[η]}{}_{\mathrm{r}}\text{[η]}{}_{\mathrm{l}}\text{= 0.66}$ predicted by Bloomfield and Zimm and others for ring and chain polymers in π-solvents. The ratio $\text{[η]}{}_{\mathrm{r}}\text{[η]}{}_{\mathrm{l}}$ was found to be somewhat smaller for the higher molecular weight polymers in the ‘good’ solvents.     

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.     

Studies of cyclic and linear poly(dimethyl-siloxanes): 11. Shapes of ring and chain molecules

The equilibrium shapes of cyclic and linear poly(dimethyl siloxane) (PDMS) molecules have been investigated using Flory, Crescenzi and Mark's rotational isomeric state model, together with a Monte Carlo method described previously. The principal axes of the equivalent ellipsoids have been computed and the major change on ring formation was found to be a reduction in the longest axis of the ellipsoid. This result is in agreement with previous studies of other ring molecules. The shapes of the cyclics $\text{[(}\text{CH}{}_3\text{)}{}_2\text{SiO}\text{]}{}_{\mathrm{<mtext>w</mtext><mtext>2</mtext>}}$ in the region w=20 are disc-like and this observation is related to the different bond angles at silicon and oxygen atoms. Bulk densities and refractive indices of PDMS rings are discussed in relation to the calculated molecular shapes. Histograms are used to illustrate the proportional frequency functions of the radii of gyration and their components s_x, s_y and s_z.     

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.     

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.     

Studies of cyclic and linear poly(dimethyl siloxanes). 4. Bulk viscosities

The bulk viscosities η of over fifty sharp fractions of cyclic and linear poly(dimethyl siloxanes) in the weight-average molecular weight range $\text{500 <}\text{M}\text{?}{}_2\text{< 25 000}$ have been measured at 298 K using a cone- and-plate microviscometer. In the Iow molecular weight region $\text{M}\text{?}{}_{\mathrm{W}}\text{< 1000}$) the η values for the cyclics were found to be at least three times as large as the values for the corresponding chain molecules. By contrast, in the highest molecular weight region ($\text{M}\text{?}{}_{\mathrm{W}}\text{> 16 000}$), the η values for the cyclics were approximately one-half those for the corresponding linears. Cyclics and linears containing about one hundred skeletal bonds were found to have similar bulk viscosities. The temperature dependence of the bulk viscosities of eighteen of the cyclic and linear fractions were investigated, and the relationship $\text{η = A}\text{exp}\text{(}\text{E}{}_{\mathrm{<mtext>visc</mtext>}}\text{RT}\text{)}$ was used to deduce values for the energies of activation for viscous flow E_visc and the constants A.     

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.     

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.     

Universal relation for polymer crystallization rates from the melt

Analysis of spherulitic growth rate data for a number of linear polymers has shown that the temperature at maximum growth rate, $\text{T}{}^1$, is related to the glass transition temperature, T_g, through the empirical equation, $\text{T}{}^1\text{= 1.26 T}{}_{\mathrm{g}}$. The universal master curve for the temperature dependence of the growth rate of crystals from the melt in reduced Gandica—Magill coordinates, $\text{ln}\text{(}\text{G}\text{G}{}^1\text{) =}\text{f(T ? T}{}_{\mathrm{\infty }}\text{)}\text{(T}{}_{\mathrm{m}}\text{? T}{}_{\mathrm{\infty }}\text{)}$, is possible only on the condition that the following empirical equation holds: $\text{0.26 =}\text{T}{}_{\mathrm{\infty }}\text{T}{}_{\mathrm{g}}\text{?}\text{T}{}_{\mathrm{\infty }}\text{T}{}_{\mathrm{m}}$. Finally, limits of variation of the ‘conformational’ contribution to the excess entropy, and of the free volume fraction at $\text{T}{}^1$ were evaluated for some polymers.     

The θ-behaviour of heterogeneous macromolecules

A polymer chain consisting of N_r segments with a repulsive interaction (binary cluster integral β_r) and N_a ? N_r segments with a stronger, attractive and pairwise saturable interaction (β_a), which is at the averaged θ-point N²_rβ_r + N²_aβ_a = 0 deviations from the predictions of the two parameter theory: $\text{α}{}^2{}_{\mathrm{<mtext>R</mtext>}}\text{? 1 ～ δz}{}_{\mathrm{<mtext>r</mtext>}}\text{< 0}$ and A₂ ～ δz_r > 0 with $\text{δz}{}_{\mathrm{<mtext>r</mtext>}}\text{～ β}{}_{\mathrm{<mtext>r</mtext>}}\text{(}\text{N}{}_{\mathrm{<mtext>a</mtext>}}\text{N}{}_{\mathrm{<mtext>r</mtext>}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. It is shown that the deviations from the universal behaviour are due to the existence of an intermediate length scale $\text{～}\text{N}{}_{\mathrm{<mtext>a</mtext>}}\text{N}{}_{\mathrm{<mtext>r</mtext>}}$.     

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).