Ultracentrifuge study of critically branched polycondensates, 4. Hinge point analysis and higher average molecular weights

Model polycondensates of 1,10-decanediol and 1,3,5-benzenetriacetic acid stabilised by means of diazodiphenylmethane and ketene are utilised to extend further our understanding of the critically branched state and to investigate possible contributions of the ultracentrifuge to the study of highly polydisperse macromolecules in non-ideal, dilute solutions. By way of computerised curve fitting, the concentration gradient curve is obtained from its concentration profile in the ultracentrifuge cell. From this the weight average molecular weight M?₁ is calculated by the hinge point method. It is also confirmed that values of the two next higher moments of the molecular weight distribution, viz. M?_2/1 and M?_3/2 (i.e. M_z and M_z+1) can hardly be distinguished from infinity for these samples. Application of the hinge point method to systems of high polydispersity is found both theoretically and experimentally to furnish M?₁ after a dual extrapolation of the measured M? against the generalised speed parameter λ and the initial concentration c⁰. It is found theoretically that for estimation of the higher molecular weight moments, plots of M? M? and M? M? M? (not merely M? and M?) must be extrapolated against the same variables, i.e. λ and c⁰. The quantitative results thus obtained are discussed in the context of previous results on these materials. They are compared with the classical theory for random f-functional polycondensates and statistical cut-off effects on the high molecular weight tail of distribution are assessed.     

Liquid crystalline polyacrylates containing biphenyl and chiral terminal groups in the side chain, 2. Influence of the nature of the chiral group

Acrylate monomers with a chiral group have been synthesized bearing a propyl, isopropyl or benzyl substituent on the asymmetric carbon. All of the monomers are crystalline. Above their melting point, they give a clear, isotropic melt. The corresponding polymers have been prepared by free radical polymerization. They were examined by differential scanning calorimetry, optical microscopy and X-ray diffraction. They were found to show a reproducible liquid-crystal behavior. On cooling from the isotropic state, S_A, S (or S) and crystal-like (probably S_H or S_H′) phases become evident. Our results do not preclude the existence of a S phase between the S_A and S phases. It is noteworthy that polyacrylates of the same series but with side chains terminated by a chiral group bearing a methyl substituent exhibit S_A, S_B and crystal-like (probably S_E) phases.     

Effect of molecular weight distribution of the original polymer on separation characteristics in successive solutional fractionation

An attempt has been made to clarify the effect of molecular weight distribution (MWD) in the original polymer on the separation characteristics in successive solutional fractionation (SSF) and comparisons were made with successive precipitational fractionation (SPF). Polymers with Schulz-Zimm distribution and Wesslau distribution of the degree of polymerization (ratio of the weight- to number-average degree of polymerization, X?/X? = 2 to 5) were brought into solution, and cooled to cause precipitation according to the modified simulative procedure of Kamide and Sugamiya, based on the Flory-Huggins's theory of dilute solutions of polymers. No double-peak distributions were observed in the fractions obtained by SSF under the conditions which give double-peak distributions in the case of SPF. The minimum value of X?_w in the fractions obtained in a given run is almost the same for SSF and SPF, the minimum increasing with decreasing X?/X? (the suffix zero denoting the original polymer). The ratio X?_w/X?_n in the fractions is not greatly influenced by X?/X? except for the first few fractions. The standard deviation σ′ of the MWD in the fractions decreases with increasing X?/X? in an initial stage, while this situation is reversed in the later stages. In general SSF furnishes sharp fractions regardless of X?/X?.     

Cationic polymerization of cyclic sulfides. IV. Determination of the structure and concentration of the propagating species during the polymerization of 3,3-dimethylthietane by 300 mhz nmr spectroscopy

For atactic as well as for isotactic copolymers of propylene with 1-pentene, styrene, or vinyl chloride the unperturbed dimensions, 〈r〉/nl², have been evaluated using the rotational isomeric state model of FLORY. The chemical composition has been varied over the whole range. 〈r〉/nl² turns out to be lower than an average of the corresponding homopolymer values for all copolymers, if the mol fractions of the components are weighted. The sequence lenth distribution–being characterized by the product r_A · r_B of the copolymerization parameters–has only little influence on 〈r〉/nl², especially for r_A · r_B < 1.     

Influence des traitements thermiques à l'état fondu sur les cinétiques de cristallisation du poly(oxyméthylène)

The influence of the temperature of the melt T₁ on the kinetics and the morphology of a semicrystalline polymer (poly(oxymethylene)) was investigated using thermal analysis and optical microscopy. The thermodynamic melting point T and the enthalpy of melting at thermodynamical equilibrium ΔH were determined by extrapolation of the graphs T_f = f(T_c) and ΔH_f = f(T_c); (T = 198°C, ΔH = 251 J/g). For different temperatures of the melt (T₁ = 185°C, 195°C, 205°C), isothermal and non-isothermal crystallizations were analysed using the Avrami and Ozawa equations. Nucleation and spherulitic growth in this polymer were studied by using optical microscopy at elevated temperatures. Using different analyses, we observed initial nucleation followed by spherulite growth with the following influence of the temperature of the melt on the distribution and the number of spherulites: T₁ < T produces many small spherulites; T₁ > T gives rise to few large spherulites.     

Stereokontrolle. IV. Konstitutionseinflüsse bei radikalischen Polymerisationen

A compensation effect exists between the quantities (ΔH ? ΔH) and (ΔS ? ΔS) in the free radical polymerization of a monomer in different solvents ΔH, ΔH, ΔS, and ΔS are the activation enthalpies and entropies, resp. for the formation of isotactic and syndiotactic dyads. The quantities ΔΔH and T₀ are by definition independent of the temperature of polymerization and other polymerization conditions and thus a pair of constants characteristic for each monomer. A linear relationship between ΔΔH and T₀ has been found for acrylic and vinyl monomers each. Both true activation and conformational effects seem to be responsible for the stereocontrol in free radical polymerizations.     

Viscosity-molecular weight relationships for low molecular weight polymers. II. Poly(vinyl acetate) and poly(methyl methacrylate)

[η]/M?_n relationships at 25°C. have been found for low molecular weight fractions of poly(vinyl acetate) (PV Ac) in chlorobenzene and poly(methyl methacrylate) (PMMA) in toluene. The PMMA used contains about 75% of syndiotactic form. Due to the difficulties of PMMA fractionation, the constants in the equation [η] = K M? refer to an average degree of polydispersity equal to M?_w/M?_n = 1.2. For both PVAc and PMMA there is a range of molecular weight where a = 0.5; in these ranges [η] is practically indistinguishable from [η]Θ.     

Intrinsic viscosity versus molecular weight relationship of polystyrene in cis-decahydronaphthalene

Intrinsic viscosities [η] and mean-square radii of gyration 〈R〉 of a polymer homologous series of commercially available narrow-molecular-weight-distribution polystyrene (PS) samples in a molecular-weight range of 800 up to 24 · 10⁶ were determined in cis-decahydronaphthalene at 25°C by light-scattering and viscosity measurements. These dilute solution properties were compared with those for PS in the good solvent toluene, in the constitutional isomer trans-decahydronaphthalene both at 25°C and in cyclohexane at 34,5°C as a theta-system.     

Stereokontrolle. VI. Zum mechanismus der radikalischen polymerisation von methylmethacrylat

Methylmethacrylate has been polymerized by free radicals in bulk and in 14 different solvents at temperatures between ?5 and +120°C. The tacticity of the polymethylmethacrylates depends on temperature, solvent and initial monomer concentration. The stereocontrol follows at least a MARKOFF first order statistics. A general compensation effect exists between the difference (ΔH ? ΔH) of two activation enthalpies and the corresponding differences (ΔS ? ΔS) of activation entropies, independent of monomer concentration and solvent (a, b = i/i, i/s, s/i, s/s). The compensation temperature T₀ is independent of the mode of dyad formation. The compensation enthalpy ΔΔH is the highest for the difference between the formation of an isotactic and a syndiotactic dyad at a given syndiotactic dyad (s/i vs. s/s). The compensation enthalpy equals practically zero for the process i/i vs. i/s. At the compensation temperature, isotactic dyads are preferentially formed at isotactic dyads and syndiotactic at syndiotactic dyads. The tendency to form heterotactic triads does not increase in all solvents with increasing temperature.     

Graph theory of configurational and viscoelastic properties of polymers, 6. The square radii distribution functions of copolymer chains

The general expression of square radii distribution functions for copolymer chains is derived in this paper. Particularly, the distribution function of the sum of two random orthogonal components, S, for cyclic AB alternate block copolymer chains is derived, and it can be reduced to the case of cyclic homopolymer chain when δ = m_A/m_B = 1.     

Photoconductivities of poly[γ-(β-N-carbazolylethyl)-L-glutamate] and its charge-transfer complex with 2,4,7-trinitrofluorenone

Poly[γ-(β-N-carbazolylethyl)-L -glutamate] (PCLG) was prepared by polymerizing the monomer which was synthesized by adapting the NCA method to a reaction product between L -glutamic acid and N-(β-hydroxyethyl)carbazole. PCLG films were prepared on a quartz Nesa (In₂O₃) plate by casting technique. The charge-transfer complex could be successfully formed only near the surface of the PCLG film by immersing the PCLG film into either a benzene or a methyl ethyl ketone solution of 2,4,7-trinitrofluorenone (TNF), since both benzene and methyl ethyl ketone were poor solvents for PCLG and suitable solvents for TNF. A photocell was formed by depositing a translucent gold electrode with vaccum evaporation onto the immersed film. For a small content of TNF in both the immersed films and the homogeneously mixed films of PCLG with TNF, the photocurrent of PCLG was successfully sensitized by TNF, but the sensitized photocurrents retained the relation I>I in a similar way as the photocurrent of PCLG alone, where I was the photocurrent under illumination onto the positive Au electrode and vice versa. On the other hand, as the TNF content increased, I became remarkably greater than I. The PCLG polymer, therefore, can behave as a p-type photoconductor, while the well-doped PCLG-TNF complex can behave as an n-type photoconductor.     

Extent of reaction,monomer conversion,and polymer yield in polycondensations

The extent of reaction of functional groups (p_A), the extent of conversion of monomer molecules (q_M), the true relative polymer yield (y_p), the constitutional repeating unit-based apparent relative polymer yield (y), and the monomer-based apparent relative polymer yield (y) are defined and their interrelationships given. The use of y instead of y_p overestimates the true yield, except in the limit of high degrees of polymerization. Use of y, on the other hand, always underestimates the true yield, especially at infinite degrees of polymerization. The correct expression for the calculation of the mass fraction of i-mers in reactants with a Schulz-Flory “most probable” distribution is given and shown to become identical with the usual approximation in the limit of vanishingly small mass of the leaving molecule.     

Approaches towards a comprehensive theory of the cationic polymerisation of olefins

Some of the factors which influence, or must be contained in, a Comprehensive Theory of the cationic polymerisation of olefins are discussed from new points of view, starting from the author's new theory concerning initiation by metal halides. Alleged determinations of the rate constant k are criticised because they ignored two equilibria which make the concentration of growing polymer chains [P] in general less than the nominal concentration, c₀, of initiator. One of them is a binary ionogenic equilibrium involving metal halide MtX_n and polymer halide P_nX. The other is between metal halide and olefin. An equation relating [P] to c₀ is deduced which takes account of these equilibria. The importance of the second equilibrium is illustrated by the way in which it provides simple explanations of hitherto obscure phenomena. Some of these arise during the interaction of aluminium halides with olefins in different circumstances, others concern the different interactions which can take place between titanium tetrachloride and 1,1-diphenylethylene. The fact that titanium tetrachloride appears to be able to initiate without co-initiator in some systems, but requires one in others is explained by the self-ionisation of the metal halide and the effects of impurities.     

Cationic polymerization of cyclic sulfides

The mechanism of the cationic polymerization of cyclic sulfides, initiated with triethyloxonium salts is reported. Differences due to changing the counter-ion from BF to SbCl are discussed. Initiation consists of the alkylation of monomer forming a cyclic sulfonium ion which is the active species in the propagating step. A generally occurring termination reaction is the formation of non-strained (linear or cyclic) sulfonium ions. In the case of epithiopropane (propylene sulfide) these can slowly re-initiate the polymerization by an intramolecular reaction forming the 3-membered cyclic sulfonium salt. This re-initiation is not possible with the thietanes because of the greater difficulty to form 4-membered cyclic sulfonium salts. When SbCl is the counter-ion, an additional, more drastic termination can occur most probably by reaction of the growing chain with the counter-ion, thereby forming an alkyl chloride and SbCl₅. After the polymerization of propylene sulfide with BF as the counter-ion, the polymer degrades to low molecular weight oligomers, predominantly the cyclic tetramer. This degradation is a back-biting reaction occuring via sulfonium salts. With SbCl as the anion, the sulfonium salts are destroyed by the termination reaction and degradation does not occur. It was possible to follow the concentration of the growing species (4-membered cyclic sulfonium salt) during the polymerization of 3,3-dimethylthietane by means of 300 MHz NMR spectroscopy. By measuring the rate constants of propagation for different initiator concentrations or in the presence of different amounts of an indifferent electrolyte, it was possible to calculate separate rate constants for propagation via free ions (k) and via ion-pairs (k). The ratio k/k was about 60 when BF was the anion and 35 when it was SbCl.     

Cationic polymerization of N-vinylcarbazole by tropylium salts at low temperatures

Cationic polymerizations of N-vinylcarbazole (NVC) in methylene dichloride containing approximately 1% nitromethane were studied by adiabatic calorimetry at temperatures between ?40 and ?70°C. Tropylium salts containing AsF, SbF and SbCl counterions were used as initiators. Reaction halflives ranged from 2 to 80 seconds and first-order plots displayed induction periods. Evidence indicated that the majority of the initiator was consumed, permitting estimation of propagation rate constants. For polymerizations involving the SbF counterion, these rate constants were found to be relatively insensitive to the concentration of initiator or excess anion and the conclusion is drawn that paired and unpaired PNVC⁺ SbF ions have similar reactivities at low temperatures. Correlation of the present results with those from previous work at 20 and 0°C yielded an Arrhenius exponential factor for propagation by unpaired ions of 30±9 kJ mol^?1. The degree of polymerization approached the ratio [M]₀/[1]₀ at ?70°C. At higher temperatures, molecular weights appeared to be governed by transfer reactions. The absence of significant chlorine content in polymer samples precluded the possibility of chain transfer to solvent.     

Static and dynamic light scattering studies of dextran from leuconostoc mesenteroides in the dilute region

Dextrans with mass-average molar masses 8.10⁴ g/mol ? M?_w ? 10⁸ g/mol have been studied in water by means of static and dynamic light scattering at different temperatures. Static light scattering (SLS) yields the z-average mean-square radius of gyration, 〈S²〉_z and the second virial coefficient A₂. It is found that the dependences of 〈S²〉 and A₂ on the mass-average molar mass, M?_w, can be well described by the power laws 〈S²〉 = K_S · M? and A₂ = K_A · M?. The exponent v_s is independent of the temperature T, while v_A decreases as T is raised. Dynamic light scattering (DLS) yields the apparent diffusion coefficient, D_app (q,c), and the hydrodynamic radius, R_h, where q is the wave vector and c the polymer concentration. For small q, a plot of D_app (q, c) versus q² · 〈S²〉_z gives a straight line. The intercept represents the centre-of-mass translational diffusion coefficient. Its dependence on the concentration, c, can be well simulated by the relation $ D_{\rm z} (c) = D_{{\rm z,}0} \left[ {1 + k_{{\rm D},2} \cdot c} \right] $. Here k_{D, 2} is the second hydrodynamic virial coefficient and D_z,0 the z-average of the translational diffusion coefficient at infinite dilution. The analysis of the k_D,2 -data shows that dextran molecules behave rather as interpenetrable than as non-interpenetrable spheres. The density p = (3 M?_w)/(N_A · 4 π R) proves to be a measure for the degree of penetration; p decreases with increasing M?_w, indicating that penetration becomes easier at higher molar masses.     

Kinetics of the anionic polymerization of ϵ-caprolactone with K+ · (dibenzo-18-crown-6 ether) counterion. Propagation via macroions and macroion pairs

Following our earlier work on the polymerization of lactones involving crowned cations, kinetics of the anionic polymerization of ?-caprolactone (?CL) with K⁺ · (dibenzo-18-crown-6 ether) (K⁺DB18C6) counterion was studied calorimetrically in THF solution in the temperature range from 0 to 20°C. Dissociation constants of CH₃(CH₂)₅O^?K⁺DB18C6, modelling the active centers, were determined conductometrically: K_D (20°C) = 7,7 · 10^?5 mol · dm^?3, ΔH = 9,3 ± 0,2 kJ · mol^?1, ΔS = ?47 ± 2J · mol^?1 · K^?1. From kinetic measurements and from measurements of the dissociation constant of CH₃(CH₂)₅O^? K⁺DB18C6, rate constants of propagation via macroions and via macroion pairs were determined. Activation parameters for propagation via these species are equal to: ΔH = 39,2 ± 0,2 kJ · mol^?1, ΔS = ?63 ± 1 J · mol^?1 · K^?1, ΔH = 13,7 ± 0,1 kJ · mol^?1, ΔS = ?185 ± 2 J · mol^?1 · K^?1. At 20°C, k = 3,50 · 10² dm³ · mol^?1 · s^?1 and k = 5,2 dm³ · mol^?1 · s^?1. Due to the large difference of ΔH^≠ for propagation via macroions and macroion pairs (vide supra), the isokinetic point (k = k) would appear at ?65°C.     

Iodine-poly(vinyl alcohol) interactions, 2. Anomalous slow quenching of the chromophore after extraction of free iodine with carbon tetrachloride

An equilibrium blue colored solution containing poly(vinyl alcohol) (PVA)-iodine-boric acid was prepared at 5°C. With increasing PVA concentration, at the same concentration of iodine, the absorption band of the chromophore I (λ_max = 650 nm, band D) linearly increased and the intensities of the bands for both I^? (λ_max = 226 nm, band A) and I (λ_max = 290 nm, band B) decreased. The band due to another iodide species (λ_max = 355 nm, band C), tentatively assigned to I · I₂, remained unchanged. Three solutions with different PVA concentration were then extracted with the same volume of carbon tetrachloride to remove I₂ present in the system. It was found that the chomophore due to I gradually decays with repeated extractions. After one extraction the change of the absorbance of I with time was measured at 5°C. In the system with a high PVA concentration the chromophore recovers the equilibrium within three days without losing much intensity, while in the systems with lower PVA concentration recovering of equilibrium takes more than four days with a considerable loss of chromophore. In the latter case, free I₂ extracted is supplied by the decomposition of polyiodide ions to I^?. Analysis of the rate of re-equilibration of iodine species revealed two reaction processes: one is a reaction involving free iodine species in an aqueous environment and the other is a slow reaction involving the polyiodide ions bound in a PVA cage.     

α,ω-dichloropoly(2-methylpropene) as an inifer: A modification to the Kennedy-Smith mechanism

Experimental details are given of attempts to enumerate the binary ionogenic equilibria (B.I.E.) of 1-chloro-1-methylethylbenzene ( 1 )/BCl₃, 1,4-bis(1-chloro-1-methylethyl)benzene ( 2 )/BCl₃ and 1,3,5-tris(1-chloro-1-methylethyl)benzene ( 3 )/BCl₃ in CH₂Cl₂. Due to chemical reaction (dimerisation or polymerisation) no experimental values for the B.I.E. constants could be obtained. A Born-Haber cycle is constructed to estimate the relative sequence of the overall B.I.E. constants. A similar treatment for 2-chloro-2methylpropane as a thermodynamic model for α,ω-dichloropoly(2-methylpropene) ( 4 ) suggests that the overall B.I.E. constant for these polymers is somewhat smaller than those for 1 and 2 but greater than that for 3 . Using 2 /BCl₃ as initiator for the polymerisation of 2-methylpropene (IB) it is shown, that the degree of polymerisation of 4 can be controlled within the limits 10 < DP < 100. It is shown that 4 can also act as an initiator for the polymerisation of IB, that these polymerisations involve only free ion propagation and, from a kinetic analysis of these polymerisations, that: (k)²/k = 12 1 · mol^?1 · s^?1, k = 1,2 · 10^?3 l · mol^?1 · s^?1, k [P] = 1,7 · 10^?3 s^?1, and k/(k K) = 102. The same analysis demonstrates that the self-ionisation of BCl₃ can be neglected in terms of any influence on the molar mass of the products. Experiments are also described which show that 2-chloro-2-methylpropane is not suitable as a substitute initiator for IB, but that 2-chloro-2,4,4-trimethylpentane is a useful model for 4 as an initiator for the polymerisation of IB.     

Excluded volume effects in dilute solutions of linear polystyrene

The second virial coefficient A₂ and the limiting viscosity number [η] were obtained for polystyrene solutions in toluene, in 1.2-dichloroethane and in methylethyl ketone over a molecular weight interval of 0.33 < M_w · 10^?5 < 65 at 35°C from light scattering and viscosity measurements. The relations in the form of α ? αⁿ = k₁z for the viscosity expansion factor α_η and α^p ? α^q = k₂z for the expansion factor α deduced from A₂ were studied, where m, n, k₁, p, q, and k₂ are constants independent of the interaction parameter z = (4π)^?3/2BA^?3M^1/2. The constants m, n, and p, q were determined from the molecular weight dependence of [η] and A₂. The value of the polymer-solvent interaction parameter B, with which the constants k₁ and k₂ were obtained, was determined so that the calculated value of 2A₂/N₀B goes to unity as z goes to zero. Here, N₀ is the AVOGADRO number. The viscosity data at high molecular weight was explained by the relation α ? α = 0.85z. The expansion factor deduced from A₂ in the good solvent was described by the relation α⁵ ? α² = 1.05z. A₂M^1/2A^?3α^?3 was practically constant over a wide range of z.