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.     

Branched poly(ethylene terephthalate) correlations between viscosimetric properties and polymerization parameters

Samples of poly(ethylene terephthalate) (PET) modified with small amounts of trimesic acid groups and hence containing long chain branching have been prepared. From the content of trifunctional modifier and from the experimental value of the extent of reaction, the weight-average molecular weight $\text{M}\text{?}{}_{\mathrm{w}}$ and branching density $\text{B}\text{?}{}_{\mathrm{w}}$ have been calculated, assuming that all the end-groups are equally reactive and intramolecular reactions are absent. The values of $\text{M}\text{?}{}_{\mathrm{w}}$ and $\text{B}\text{?}{}_{\mathrm{w}}$ have been correlated with the experimental values of intrinsic viscosity [η] and the Newtonian melt viscosity η₀. General relations of the following type have been obtained:

$\text{f}{}_1\text{([η],}\text{M}{}_{\mathrm{w}}\text{,}\text{B}{}_{\mathrm{w}}\text{) = 0; f}{}_2\text{(η}{}_0\text{,}\text{M}{}_{\mathrm{w}}\text{,}\text{B}{}_{\mathrm{w}}\text{) =0; f}{}_3\text{(η}{}_0\text{, [η],}\text{B}{}_{\mathrm{w}}\text{) = 0; f}{}_4\text{(η}{}_0\text{, [η],}\text{M}{}_{\mathrm{w}}\text{) = 0;}$

In particular, [η] and η₀ increase on increasing $\text{M}\text{?}{}_{\mathrm{w}}$ and decrease on increasing $\text{B}\text{?}{}_{\mathrm{w}}$, but, at equal [η] values, η₀ increases with $\text{B}\text{?}{}_{\mathrm{w}}$. Through the last relation, the reliability limits of which should be experimentally checked, and from measurements of [η] and η₀, it is possible to calculate $\text{M}\text{?}{}_{\mathrm{w}}$ of a branched PET.     

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.     

Molecular weight distribution and stereoregularity of polypropylenes obtained with Ti(OC4H9)4Al2(C2H5)3Cl3 catalyst system

The effects of temperature and catalyst homogeneity on the molecular weight distribution (MWD) and stereochemical regulation of polypropylenes produced by $\text{Ti(OC}{}_4\text{H}{}_9\text{)}{}_4\text{Al}{}_2\text{(}\text{C}{}_2\text{H}{}_5\text{)}{}_3\text{Cl}{}_3$ system have been investigated. The MWD of polymers obtained at temperatures below 21°C were unimodal and narrow ($\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{?2.0}$), whereas those obtained at temperatures higher than 31°C were bimodal with one narrow distribution and the other broad one ($\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{=18}$) at higher molecular weights. The existence of two different types of catalyst, one soluble with homogeneous catalytic centres and the other insoluble with heterogeneous catalytic centres was found in the polymerization at 41°C. At temperatures below 21°C only soluble catalyst was present and produced isotactic polypropylenes with [m]=0.65. The isospecific nature of soluble titanium-based catalyst is greatly contrasted to the syndiospecific nature of soluble vanadium-based catalyst.     

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).     

Differences in the molecular weight and the temperature dependences of self-diffusion and zero shear viscosity in linear polyethylene and hydrogenated polybutadiene

Within the context of a generalized coupling model we can support the hypothesis that, while the mode of relaxation for self diffusion (D) and shear flow (η) are the same, the entanglement interactions are different. We assume that there are two distinct coupling parameters n_D and n_η for self diffusion and shear flow respectively. The model predicts the molecular weight and temperature dependences to be scaled by the relevant coupling parameters as:

for melts with Arrhenius temperature dependences. We have found that n_n=0.43 and 0.42 for polyethylene (PE) and hydrogenated polybutadiene (HPB) which scale η as M^3.5 and M^3.4. Also the apparent flow activation energies $\text{E1}{}_{\mathrm{a}}$ of 6.35 kcal mole^?1 for PE and 7.2 kcal mol^?1 for HPB scale to primitive activation energies E_a of 3.6 and 4.2 kcal mole^?1 for PE and HPB respectively. On the other hand the M^?2 dependence of D results in n_D=1/3. Then the reported activation energies for self-diffusion in PE and HPB of 5.49 and 6.2 kcal mole^?1 scale to primitive activation energies of 3.7 and 4.1 kcal mole^?1, respectively.     

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.     

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 $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}\text{> ca. 10 000}$.     

Self and mutual diffusion measurements in dilute and semi-dilute polystyrene solutions

Self diffusion coefficients have been obtained for polystyrene ($\text{M}\text{?}{}_{\mathrm{w}}\text{= 37 000}$) solutions in toluene (D₈) and cyclohexane (D₁₂) by the pulsed field gradient n.m.r. technique at 303 K. Mutual diffusion coefficients have been obtained by photon correlation spectroscopy (p.c.s.). In a poor solvent (cyclohexane) both techniques show a similar trend of a monotonic decrease in the diffusion coefficient with increasing concentration of polymer. However, in a good solvent (toluene) n.m.r. shows a monotonic decrease in the diffusion coefficient whereas p.c.s. shows an increase. The results are discussed in terms of self and mutual diffusion processes.     

Sedimentation velocity measurements close to the upper critical solution temperature and at θ-conditions: polystyrene in cyclopentane over a large concentration interval

Sedimentation velocity measurements on polystyrene (M = 110 000) in cyclopentane over an extended concentration region and from 5°C (close to the upper critical solution temperature) to 40°C are reported. The concentration dependence parameter (k_s)_w increases from 2 to 5°C to 27 at 40°C. For all temperatures except 5°C, $\text{s}{}_0\text{s}$ vs. w[η]_w shows an upward curvature at w[η]_w ≈ 1; at 5°C, on the other hand, $\text{s}{}_0\text{s}$ is independent of concentration over the region considered. Furthermore, measurements have also been performed at 20°C (θ-conditions) over a large concentration interval for the molecular weights M = 20 400, 390 000 and 950 000. The parameters s₀ and (k_s)_w were both found to be proportional to $\text{M}\text{?}{}^{\mathrm{1/2}}{}_{\mathrm{w}}$. In the ‘hydrodynamically normalized’ plot $\text{s}{}_0\text{s}$ vs. w[η]_w the sedimentation behaviour can approximately be represented by a single curve for all the molecular weights.     

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.     

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.     

Elution and molecular weight parameters in exclusion chromatography

The mode of the chromatogram is inadequate for characterizing experimental elution curves, which are generally dissymmetrical. It is also dependent on axial diffusion. When the molecular weight distribution is defined either by the generalized exponential function or by the log-normal function, simulation of elution at finite resolution shows that the calibration curve at infinite resolution, independent of the flow rate of the carrier fluid, is approximated validly by correlating the first moment of the chromatogram (MEV) with the geometrical compound average $\text{(}\text{M}\text{?}{}_{\mathrm{n}}\text{M}\text{?}{}_{\mathrm{w}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= M}{}_0$. The concentration effect seems to be controlled by a double extrapolation procedure defined by (1) treatment of the chromatograms using the calibration curve at zero concentration ($\text{In}\text{M}{}_0\text{versus}\text{lim}\text{c→o}\text{MEV}$), and (2) linear extrapolation to infinite dilution of the calculated molecular weight averages.     

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.     

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

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.     

Solid and liquid state relaxations in spin-labelled poly)ethylene glycol) at high temperatures (T>Tg)

Free and covalently bonded (esterified) nitroxyl radicals experienced in poly(ethylene glycols) (PEG; $\text{M}\text{?}{}_{\mathrm{n}}$ 200–22 000) at temperatures T >T_g several different isotropic rotational relaxation regions. As a first approximation it was assumed, that in the polyglycols $\text{M}\text{?}{}_{\mathrm{n}}\text{? 1000}$ there are at least three rotational relaxation regions: the liquid state (I), the melting state (II) and the solid state (III). The existence of the fourth region, the frozen solid state (IV), was also concluded. The existence of the relaxation region (II) indicated the close interaction between radicals and the crystalline phase. The order of rotational activation energies (E_a) was E^II_a >E^III_a >E^I_a >E^IV_a ($\text{M}\text{?}{}_{\mathrm{n}}\text{? 1000}$). In the polymer melts (I) E_a values of free and bonded radicals first diminished as a consequence of the decrease of the end group effect and they achieved constant high molecular weight values (～15 and 25 kJ respectively). E_a changed in the solid state as a function of $\text{M}\text{?}{}_{\mathrm{n}}$ principally in the same manner except of the higher numerical values (～40 kJ).E_a of free and covalently bonded radicals in the transition region (II) gained a maximum at $\text{M}\text{?}{}_{\mathrm{n}}$ 1550 (125 and 170 kJ) and another at $\text{M}\text{?}{}_{\mathrm{n}}\text{> 9500}$ (130 and 165 kJ) expressing the high degree of order in these polymers in the solid state.The results obtained correlated well with the proton magnetic resonance measurements but they did not correlate with the amorphous dielectric relaxation measurements.It was concluded that the following factors may affect the rotational relaxations of nitroxyl radicals in PEG: the free volume of the polymer, the crystallinity, the chain packing and the end-group effect. The segmental character of the relaxation process was clearly indicated.     

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.