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.     

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): 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.     

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.     

Dipole moments and statistical conformations of cyclic and linear dimethylsiloxane oligomers

The statistical conformations of cyclic dimethylsiloxane oligomers [(CH₃)₂SiO]_x with x in the range 4–10 have been studied by using rotational isomeric state models to describe the ‘cyclic’ conformations of the open chain molecules. Stringent criteria were used to select ‘cyclic’ conformations of the equivalent open chains based on the relative orientations and rotational states of their terminal skeletal bonds. The root-mean-square electric dipole moments $\text{〈μ}{}^2\text{〉}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and the temperature coefficients d $\text{ln}\text{〈μ}{}^2\text{〉}{}_0\text{dT}$ were calculated using a modified form of the rotational isomeric state model of Flory, Crescenzi and Mark. The calculated dipole moments are compared with some experimental values measured for cyclic oligomers in the undiluted state at 298 K. For the ‘cyclic’ conformations of the open chains the magnitude of the calculated temperature coefficients for x = 5–9 were found to be very nearly inversely proportional to the fraction of rotatable skeletal bonds occupying trans rotational states; a functional dependence opposite to that found for the open chains.     

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): 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.     

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.     

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(dimethylsiloxanes): 19. Glass transition temperatures and crystallization behaviour

Differential scanning calorimetry (d.s.c.) was used to investigate the thermal behaviour of cyclic and linear poly(dimethylsiloxanes) over the temperature range 103–298 K. Fractions of the polymers studied had number-average molar masses in the range 160 < M_n < 25 500 g mol^?1 and heterogeneity indices $\text{M}{}_{\mathrm{<mtext>w</mtext>}}\text{M}{}_{\mathrm{<mtext>n</mtext>}}\text{< 1.1}$ in most cases. D.s.c. was applied to measure the glass transition temperatures T_g cold crystallization temperatures T_c and polymer crystalline melting temperatures T_m of the oligomer and polymer fractions. Cyclic siloxanes [(CH₃)₂SiO]_x with number-average numbers of skeletal bonds n_n in the range 24 ≦ n_n ≦ 79 and linear siloxanes (CH₃)SiO[(CH₃)₂SiO]_ySi(CH₃)₃ with n_n in the range 10 ≦ n_n ≦ 40 were found not to crystallize. The T_g values of the linear siloxanes were found to be in agreement with values in the literature and they increased with increasing M_n. By contrast, the T_g values of the cyclics were found to decrease with increasing M_n.     

Polymerization of poly(dimethylsiloxane) macromers: 1. Copolymerization with styrene

The synthesis and characterization of methacrylate-ended macromers ($\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ 500 to 10 000) and their copolymerization with styrene (M₂) is described. The experimental errors in the values of the reactivity ratios r₁ render them meaningless. Values of r₂ can be determined with more precision and increase from 1.06 to 1.55 as the molecular weight of the macromer increases. This behaviour is due to steric effects, not diffusion-controlled propagation. It is shown that the assumptions that $\text{1 > r}{}_1\text{[}\text{M}{}_1\text{]}\text{[}\text{M}{}_2\text{]}$ and $\text{r}{}_2\text{>}\text{[}\text{M}{}_1\text{]}\text{[}\text{M}{}_2\text{]}$ are only valid for macromers of $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}\text{> ca. 10 000}$.     

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.     

Studies of cyclic and linear poly(dimethyl siloxanes): 9. Quasi-elastic light scattering and concentration dependences of diffusion coefficients

The concentration dependences of the diffusion coefficients (D) of linear and cyclic poly(dimethyl siloxanes) (PDMS) in toluene at 298K are reported. Three cyclic/linear pairs of fractions with molar masses in the range 300 to 23 500 g mol^?1 were used. The values of D obtained by quasielastic scattering were in good agreement with those measured by the classical boundary-spreading technique. Analysis of the concentration dependences in terms of the theory of Pyun and Fixman indicates that the solute molecules show a minimum of interpenetration in toluene at 298K.     

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.     

Synthesis of some organic poly(aminium phosphate)s: 4

Poly(aminium phosphate)s were prepared by precipitation from aqueous solution. The composition of these derivatives was established by analysing for nitrogen and phosphorus. Weight average molecular weights were determined by intrinsic viscosity determination. The intrinsic viscosity has been determined by replacing the usual extrapolation of specific viscosity to zero concentration ($\text{η}{}_{\mathrm{<mtext>sp</mtext>}}\text{C}$ vs. CO) with the extrapolation of linear transformation. G = AF + B where $\text{G =}\text{y}\text{α ? x}$, $\text{F =}\text{x}\text{α ? x}$ and α = x_M + x_m (where $\text{y =}\text{η}{}_{\mathrm{<mtext>sp</mtext>}}\text{C}$ and x_m and x_M denote concentration). The values for Huggins constants (k′ + k″) were also calculated and found to be characteristic of linear chain polymers. The R_g values for poly(aminium phosphate)s have been determined in New Ebel's solvent, by a paper chromatographic technique. A linear relationship between degree of polymerization and R_g values is indicative of the linear chain polymeric character of these derivatives. The polyelectrolyte behaviour of these polymers has also been established by conductivity measurements.     

Dielectric constants of coal-derived liquids and slurries with coal at 750 MHz

The real part of the complex dielectric constants of SRC-I recycle solvent, SRC-II naphtha, middle distillate and heavy distillate, and tetralin were measured over the temperature range of 23° to 140°C. Values were strongly temperature dependent, generally increasing with temperature and increasing in the sequence naphtha < heavy distillate < recycle solvent < middle distillate, and were related to the phenolic contents of the liquids. The temperature dependence was attributed to the viscosity which in turn affects the relaxation behaviour of the dipolar molecules in the liquid. Association-dissociation equilibria of the polar components also affect the dielectric constant. Measurements of slurries of the SRC-I recycle solvent with coal show that the real part of the dielectric constant, $\text{}\text{?}$g3′, is given by the Looyenga equation, $\text{}\text{?}\text{g3′ = [ε′}\text{1}\text{3}{}_2\text{+φ}{}_1\text{(ε′}\text{1}\text{3}{}_1\text{?ε′}\text{1}\text{3}{}_2\text{)]}{}^3$, where ε′₁ and ε′₂ are respectively the real parts of the dielectric constant of the coal and the solvent and φ₁ is the volume fraction of the coal.     

Dielectric constants of coal-water slurries at 750 MHz

Measurements of the real portion of the dielectric constant of coal-water slurries at 750MHz are reported. Slurries of 40–65wt% of either Illinois No. 6, Utah bituminous or Texas lignite coals over the temperature range 11–71 °C were studied. The dielectric constant was independent of coal type and particle size within experimental error. The measured values of dielectric constants agreed with those predicted by the Looyenga equation: $\text{?′}\text{= [?′}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}{}_2\text{+ φ(?′}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}{}_1\text{??′}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}{}_2\text{)]}{}^3$ where: $\text{?′}$, the mean value of the dielectric constant; ?′₁, the dielectric constant (3.8) of the dry coal; ?′₂, the dielectric constant of water; φ, the volume fraction of coal.     

Studies of cyclic and linear poly(dimethyl siloxanes): 8. Light scattering measurements in good and poor solvents

Weight average molar masses (M_w) and second virial coefficients (A₂) have been measured for linear and cyclic poly(dimethyl siloxane) (PDMS) fractions in toluene at 298K and for linear PDMS in bromocyclohexane at 301K. The values of M_w are compared with those deduced previously using gel permeation chromatography, broadly confirming the values already assigned to the fractions. The values of A₂ for linear PDMS in toluene are shown to be consistent with previously published values for oligomeric linear PDMS. The values of A₂ for cyclic PDMS approach those of linear PDMS for M_w<～1000 g mol^?1 and decrease more rapidly as M_w increases in approximate agreement with theoretical predictions. In addition, the conventional relations between A₂ and the expansion factor α_s are shown to be inapplicable at low molar mass.     

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.     

Random coil configuration of the polyformals (CH2O (CH2)yO-): 4. Dipole moments of poly(1,3-dioxocane) (y =5) and poly(1,3-dioxonane) (y = 6)

Samples of poly(1,3-dioxocane) [CH₂O(CH₂)₅O-] and poly(1,3-dioxonane) [CH₂O(CH₂)₆O-] were prepared by reacting paraformaldehyde with 1,5-pentanediol and 1,6-hexanediol, respectively. Fractions of both polymers, obtained by liquid-liquid precipitation separations, were studied in benzene solutions by means of dielectric constant measurements from 20 to 60°C. Mean-square dipole moments 〈μ²〉₀ thus obtained were compared with theoretical results based on rotational isomeric state models of the two chains. Very good agreement is obtained for the magnitudes of the dipole moments, and for their dependence on chain length and temperature. Values of the dipole moment ratio $\text{〈μ}{}^2\text{〉}{}_0\text{nm}{}^2$, where n is the number of bond dipoles of moment m, are essentially the same for the polyformals corresponding to y = 2,4,5, and 6. This indicates that even the very short CH₂CH₂ non-polar sequences strongly suppress the correlations between the polar oxymethylene CH₂OCH₂OCH₂ sequences in this type of chain. The configurational analysis also identifies the lowest energy conformations of poly(1,3-dioxocane) and poly(1,3-dioxonane), and they are found to be the conformations adopted by the chains in crystalline state.