Concentration dependence of chain dimensions and its role in gel chromatography

A theoretical model has been developed for the concentration effect in gel chromatography, i.e. the dependence of the elution volume V_e on the concentration of injected polymer c. On the basis of the theoretical relations of Yamakawa and Eizner for coil shrinkage with increasing concentration in the range of dilute polymer solutions, relations predicting the extent of the concentration effect have been derived. A comparison of the calculated and experimental data for polystyrene in tetrahydrofuran and toluene has shown that both theories slightly underestimate the extent of the concentration effect but qualitatively correctly describe its dependence on molecular mass M and on thermodynamic quality of an eluent given by the product A₂M, where A₂ is the second virial coefficient of the polymer-eluent system. The proposed model explains the recently established correlation between the slope of the concentration dependence of V_e and the thermodynamic quality of the eluent and theoretically accounts for the method for estimating the coefficient A₂ from gel chromatographic measurements. The possibility of using the measurements of concentration effects for examining the reliability of the theoretical relations for coil shrinkage with concentration in dilute polymer solution as well as for eventual semiempirical modification of these relations is examined.     

Zur unverträglichkeit von polymergemischen. 1. Lichtstreuungsmessungen am system polystyrol/polymethylmethacrylat/benzol

A polystyrene (PS) with M?_w = 9,7 · 10⁴ was investigated by means of light scattering in the isorefractive polymer/solvens-mixture polymethylmethacrylate (PMMA)/benzene. It was found, that the second osmotic virial coefficient A₂ of PS was strongly dependent on the average viscosimetric molecular weight M?_v and on the concentration of PMMA, but scarcely on the temperature in the range of 20°C to 60°C. The θ-Point, where A₂ is zero, was independent of the temperature within experimental error. By defining the PMMA concentration at the θ-Point as c_θ, and by reducing the measured PMMA concentration c to c/c_θ, an unequivocal relation was obtained between A₂ and c/c_θ, which is independent of molecular weight and molecular weight distribution of PMMA. PS shows a high second virial coefficient in dimer and trimer MMA as well as in non-hydrogenated and hydrogenated MMA. The investigated PS constitutes a θ-System in PMMA of a degree of polymerisation of P?_w, ～ 17without the use of benzene.     

The effects of the synthesis parameters on the xerogels structures and on the swelling parameters of the poly(methacrylic acid) hydrogels

Poly(methacrylic acid) hydrogels were synthesized. The effects of the synthesis parameters: the neutralization degree of methacrylic acid and the concentrations of monomer, crosslinker and initiator on the xerogels structural properties: the xerogel density (ρ_xg), the number average molar mass between the network crosslinks (M_c), the crosslink degree (ρ_c), the number of elastically effective chains totally induced in a perfect network per unit volume (V_e), the distance between the macromolecular chains (ξ) and the equilibrium swelling degree (SD_eq) and the swelling kinetics was investigated. As the concentrations of crosslinker, monomer and initiator increase, the value of ρ_xg, ρ_c and V_e increases and decreases the value of M_c, ξ and SD_eq. With the increase in the neutralization degree of methacrylic acid, the values of ρ_xg, M_c, ξ, SD_eq increase, while the ρ_c and V_e decrease. The xerogels structural properties, SD_eq and swelling kinetic parameters are mainly in power law form functional relationships with the synthesis parameters as well as with the xerogels crosslinking degree.     

Thermodynamic and hydrodynamic properties of polymer — tetrahydrofuran — water systems: 2. Gel chromatography of polystyrene

Chromatogram shapes, concentration effects and calibration curves in g.p.c. were studied for dry tetrahydrofuran and its mixtures with water up to 8.9 vol. %. Polystyrene reference materials were separated with silica-based column packings. The results can be generalized fairly well and lead to the conclusion that the gel chromatographic data are considerably influenced by humidity present in the eluent. Ghost-peaks appeared in the domain of high elution volumes (V_e) using mixed eluents. Simultaneously, the solute peaks changed their widths and the slope of the plot of V_eversus injected polymer concentration changed with water content. However, most important were the shifts in the polymer elution volumes that were caused by the complex of interactions in the system gel-mixed eluent-solute and depended on the amount of water present in eluent. Thus, the dry eluent is an inevitable condition for obtaining g.p.c. results of high precision and reproducibility. The use of a guard column filled with a sorbent strongly trapping water is proposed in g.p.c. with hygroscopic eluents. Similar precautions are to be considered for any admixture in the eluent, especially if its content cannot be kept constant and if its polarity differs substantially from the polarity of the eluent.     

Contribution of adsorption and partition to the separation mechanism in gel chromatography on inorganic carriers

Gel permeation chromatography (GPC) calibration curves log hydrodynamic volume versus elution volumes were obtained from a series of single and mixed eluents for polystyrene on inorganic carriers. The observed calibration shifts were interpreted as a result of adsorption and partition effects on elution volume V_e. Secondary contributions to the separation mechanism can be qualitatively described by means of thermodynamic relations from liquid adsorption (LSC) and liquid partition (LLC) chromatography using the solubility parameters of the eluents. The universal calibration procedure based on the hydrodynamic volume of the coils is directly applicable only for systems in which adsorption and partition is approximately the same.     

Elastic behavior of concentrated solutions of acrylonitrile copolymers

The elastic behavior of concentrated solution of acrylonitrile copolymer was investigated by the capillary end correction method. The results were as follows. (1) The shear stress is proportional to recoverable shear strain in accordance with Hooke's law below critical concentration; above a critical concentration, however, the shear modulus depends on shear stress. (2) The log–log plots of zero shear modulus against polymer concentration and molecular weight fall on two straight lines with different slopes. The intersection of lines is considered to be the onset of elastically deformable entanglement network. We denote this inflection point as (C_c)_e or (M_c)_e. (3) The log–log plot of viscosity against polymer concentration does not show a change of slope at the critical concentration (C_c)_e. (4) By the application of the kinetic theory of rubberlike elasticity to the pseudo-network structure of concentrated polymer solution, in the range of C_c < C < (C_c)_e or M_c < M < (M_c)_e, the number of chain entanglement per molecule is kept one; moreover, in the range of C > (C_c)_e, or M > (M_c)_e, the number of chain entanglement increases to three.     

Concentration dependence of static and hydrodynamic screening lengths for three different polymers in a variety of solvents

We have used small angle neutron scattering and dynamic light scattering to measure the static and hydrodynamic screening lengths of polystyrene, polymethylmethacrylate and polydimethylsiloxane solutions ranging from marginal to good solvent quality. A universal plot is found for the scaled static screening length when the concentration is scaled using the second virial coefficient in the way suggested by renormalization group theories. The same concentration units do not produce a universal plot for the hydrodynamic screening length at the molecular weights that we have studied (all around 1-2×10⁵ g/mol). However, when the concentration is expressed in terms of k_Dc, where k_D is the virial expansion coefficient for the cooperative diffusion coefficient and c is the concentration, most of the variation between different polymer-solvent combinations is eliminated. The ratio of hydrodynamic screening length to static screening length increases with concentration for all of the polymer solvent pairs studied, and its value differs for different polymer solvent pairs.     

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.     

Compatibility and neutron scattering studies of mixtures of polystyrene with poly(2,6-dimethyl 1,4-phenylene oxide) and its brominated derivatives

Several narrowly disperse polystyrenes (PS) were mixed with three series of random copolymers of 2,6-dimethyl phenylene oxide (also known as xylenyl ether (XE)) and 3-bromo-2,6-dimethyl phenylene oxide (BrXE), each series having a fixed chain length. The critical BrXE comonomer concentration necessary to induce phase separation, x_c′ was characterized for each blend series by a number of techniques. x_c was extrapolated to a value of about 0.5 at infinite chain lengths of each polymer of the blend. This finding supports the negative heat of mixing of PS with PXE reported by other workers. Small-angle neutron scattering studies were carried out using small amounts of perdeuteropolystyrene in several matrices for which single phase behaviour had been shown to exist. The radius of gyration R₂ and the second virial coefficient A₂ were greatest in the pure PXE matrix reflecting the goodness of this material as a ‘solvent’ for PS. In matrices containing $\text{50\%}\text{PS}\text{50\%}$ copolymer, A₂ extrapolated to zero at x_c ≥ 1 which was consistent with the phase behaviour of this series of blends.     

Diffusion of polystyrene in tetrahydrofuran

The diffusion of polystyrene in tetrahydrofuran has been studied by line width measurements in a laser light scattering spectrometer. The diffusion coefficient D has been determined as a function of concentration c for the molecular weight range of 2.04 × 10⁴ to 1.8 × 10⁶. At low concentration the relationship between D and c is linear to a very good approximation over a relatively large concentration region, as has also been found for some other systems. The molecular weight dependence of D, extrapolated to zero concentration, D₀ can be written as D₀ = k_TM^?b_w, where b = 0.564, in good agreement with thermodynamic predictions derived from intrinsic viscosity studies.     

Determination of polystyrene-carbon dioxide-decahydronaphthalene solution properties by high pressure dynamic light scattering

The diffusion coefficients of polystyrene (PS) in decahydronaphthalene (DHN) and in solutions of carbon dioxide (CO₂) and DHN were measured for dilute PS solutions over a range of temperatures and CO₂-DHN ratios using high pressure dynamic light scattering. Infinite dilution diffusion coefficients (D₀) of PS and dynamic second virial coefficients (k_D) were determined for essentially monodisperse 308 kDa PS. At a system pressure of 20.7 MPa, PS diffusion coefficients increased by a factor of 2.5, and the activation energy of diffusion decreased by approximately 16% when DHN was “expanded” with 44 mol% CO₂. However, the hydrodynamic radius of PS at a given temperature was not particularly sensitive to the CO₂ concentration. Solvent quality, as measured by k_D, decreased at higher CO₂ concentrations. The addition of CO₂ to polymer solutions may offer a way to “tune” the properties of the solution to facilitate the heterogeneous catalytic hydrogenation of polymers.     

Swelling of High Oil-Absorptive Network Based on 1-Octene and Isodecyl Acrylate Copolymers

Crosslinked 1-octene-isodecyl acrylate copolymers were synthesized and evaluated for oil-absorbency application. The copolymer was crosslinked at different concentrations of ethylene glycol diacrylate (EGDA) and ethylene glycol dimethacrylate (EGDMA) crosslinkers via catalytic initiation or by electron-beam irradiation at dose rate 80 kGy. The concentration of both crosslinkers was varied from 0.5% to 2%. The effect of crosslinking conditions, such as crosslinker concentration, method of polymerization and monomers concentration on conversion and gel fraction was examined through an oil-absorption test using petroleum crude oil. It was found that, the oil absorbency was influenced mainly by the degree of crosslinking and the hydrophobicity of the copolymer units. The final equilibrium oil content, volume fraction of polymer and swelling capacity were determined at 298 K. The effective crosslinking density V_e, the average molecular weight between the crosslinks M_c and the polymer-toluene interaction parameter were determined from stress–strain measurements. The crosslinking efficiencies of EGDA and EGDMA towards copolymers were determined.     

Craze microstructure and molecular entanglements in polystyrene-poly(phenylene oxide) blends

Polystyrene and poly(phenylene oxide) are miscible over the entire range of compositions. Thin films of five blends of high molecular weight polystyrene (PS) with high molecular weight poly(phenylene oxide) (PPO), and four blends of low molecular weight PS (whose molecular weight lies below its entanglement molecular weight M_e) with the same PPO have been prepared. Following bonding of these films to copper grids, crazes were grown by uniaxial straining in air. Suitable crazes were then observed by transmission electron microscopy. From microdensitometry of the image plates it is possible to measure the extension ratio λ_craze within crazes in the nine blends. These measured values are compared with predicted values of λ_max, computed from λ_max = I_ed, where I_e is the chain contour length between entanglements and d is the root mean square end-to-end distance for a chain of molecular weight M_e. For the high molecular weight PS blends λ_max depends on the entanglement properties of both PS and PPO chains. For the low molecular weight PS blends, the PS chains cannot form part of the entanglement network and the correct value of λ_max is obtained from appropriate scaling of the pure PPO value. Comparison of λ_craze and λ_max for both types of blends shows excellent agreement, demonstrating the importance of the entanglement network in determining craze parameters and hence the toughness of a given polymer.     

Determination of the molecular weight between cross-links of elastomeric stocks by tensile retraction measurements. II. Polyurethanes

Tensile retraction measurements of M_c were made on a variety of polyurethanes or polyurethane-ureas. These samples were prepared using a number of prepolymer MW and functionalities. In addition, the stoichiometry of the cure was allowed to range widely. In all cases, excellent linear correlation coefficients were obtained between the M_c and the A_max of the test. The slope and M_r (the value of M_c extrapolated to A_max = 1) determined from this was used to characterize the polymer. These data allowed the determination of χ for each of the different systems such that comparable values of M_c could be measured by swelling. Identical formulations cured at different temperatures were shown to have measurable differences in M_c, slope, and percentage set. These variations appear to relate to the perfection of the network and morphology of the hard domains.     

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.     

On the dynamics of the irreversible Michaelis-Menten reaction mechanism

The mass action kinetic model of the irreversible Michaelis-Menten reaction mechanism is mathematically intractable: an explicit analytical solution cannot be obtained. This difficulty is overcome by applying simplifying kinetic assumptions but a full understanding of their dynamic implications and applicability is not readily available. This paper shows how simple modal analysis can provide both a conceptually appealing insight into the reaction dynamics and justification of the commonly used quasi-steady-state and quasi-equilibrium assumptions.The key results are that the quasi-steady-state assumption is applicable when the initial enzyme concentration, e₀, is much smaller than the Michaelis constant, K_m, or when the initial substrate concentration, s₀, is much greater than K_m. These results show that the commonly accepted criterion e₀ < <s₀ is incomplete and should be decomposed into e₀ < <K_m and K_m <<s₀. The quasi-equilibrium assumption is valid when e₀ ⪢⪢ K_m and when the rate of product formation is much slower than reversion to the substrate from the intermediate state, or k₂ ⪢⪢ k₋₁. The important dimensionless parameter ratios characterizing the reaction dynamics are e₀/K_m, s₀/K_m and k₂/k₋₁.     

Temperature-composition phase diagrams of binary blends of block copolymer and homopolymer

The temperature-composition phase diagrams for six pairs of diblock copolymer and homopolymer are presented, putting emphasis on the effects of block copolymer composition and the molecular weight of added homopolymers. For the study, two polystyrene-block-polyisoprene (SI diblock) copolymers having lamellar or spherical microdomains, a polystyrene-block-polybutadiene (SB diblock) copolymer having lamellar microdomains, and a series of polystyrene (PS), polyisoprene (PI), and polybutadiene (PB) were used to prepare SI/PS, SI/PI, SB/PS, and SB/PB binary blends, via solvent casting, over a wide range of compositions. The shape of temperature-composition phase diagram of block copolymer/homopolymer blend is greatly affected by a small change in the ratio of the molecular weight of added homopolymer to the molecular weight of corresponding block (M_H,A/M_C,A or M_H,B/M_C,B) when the block copolymer is highly asymmetric in composition but only moderately even for a large change in M_H,A/M_C,A ratio when the block copolymer is symmetric or nearly symmetric in composition. The boundary between the mesophase (M₁) of block copolymer and the homogeneous phase (H) of block copolymer/homopolymer blend was determined using oscillatory shear rheometry, and the boundary between the homogeneous phase (H) and two-phase liquid mixture (L₁+L₂) with L₁ being disordered block copolymer and L₂ being macrophase-separated homopolymer was determined using cloud point measurement. It is found that the addition of PI to a lamella-forming SI diblock copolymer or the addition of PB to a lamella-forming SB diblock copolymer gives rise to disordered micelles (DM) having no long-range order, while the addition of PS to a lamella-forming SB diblock copolymer retains lamellar microdomain structure until microdomains disappear completely. Thus, the phase diagram of SI/PI or SB/PB blends looks more complicated than that of SI/PS or SB/PS blends.     

Scission of non-interpenetrating macromolecules in transient extensional flows

Solutions of the random coiling polymers; polystyrene, poly (methylmethacrylate), and sodium polystyrene sulfonate (NaPSS), all at concentrations well below the critical value for entanglement, were subjected to transient, high, elongational strain rates by passage from a cylinder through an orifice into a gently diverging section, driven by a piston at constant, high velocity over a short stroke. It is shown that a critical orifice flow velocity V_c. exists for each polymer species, above which scission of polymer molecules occurs creating new molecules. By gel permeation chromatography, the number of additional polymer molecules created per initial polymer molecule, the scission index, was determined as M _n,0/M _n – 1 where M _n is the number average molecular weight, and M _n,0 is the initial value thereof. V_c is found to vary as approximately M . Above V_c the scission index was found to be proportional to M , to the difference: orifice velocity V less V_c, and to the number of passes N of the polymer solution through the orifice. Expansion of NaPSS coils by reducing ionic strength of their aqueous solutions, at constant polymer molecular weight, decreases the scission index, The hypothesis is proposed that intramolecular entanglements are responsible for scission. The random coiling macromolecules in the solution cannot respond to the strain rate (imposed in ca, 100 microseconds) so as to avoid having internal sections, caught by loop entanglement, pulled to nearly full extension and thus broken.     

Virial coefficients of normal fluids

The force constants of the square-well potential for normal fluids were correlated in terms of the critical properties P_c, T_c, and the acentric factor ω, by means of a non-linear regression technique. The second virial coefficients, a total fo 100 points chosen uniformly with respect to P_r and ω from the compilation of Dymond, together with the compressibility factors, taken from the generalized tables of Pitzer. were employed in the correlation. The valid ranges of the correlation are 0.5 ?T_r ? 2·0 and 0 ? ρ_r ? 1·0. The calculated results for the second virial coefficients compare favourably with the generalized correlation of Pitzer and Curl. The calculated third virial and cross third virial coefficients, and the compressibility factors also agree well with the literature values.     

Adsorption equilibrium constants of methyl oleate and methyl linoleate in vapor phase on supported copper and nickel catalysts

Adsorption equilibrium constants for methyl oleate and methyl linoleate in vapor phase on supported copper and nickel catalysts have been determined using the technique of pulse gas chromatography. The results are discussed in relation to selectivity in fat hydrogenation. Notation: A, column cross-section, m₂ ; a_n,b_n, nth Fourier coefficients; c, concentration of adsorbate in bulk flow, mol/m³ ; c^* = c/ ∫ ₀ ^∞ cdt, normalized concentration of adsorbate in bulk flow; C_i, concentration of adsorbate in catalyst pores, mol/m³ ; c_a, concentration of adsorbate on catalyst surface, mol/kg; c_TOT, active area of catalyst as measured by hydrogen adsorption, mol/kg; D_e, effective diffusion coefficient of adsorbate in catalyst, m²/s; D_ea, axial dispersion coefficient based on void cross-section, m²/s; h_n, nth coefficient in Hermite polynomial expansion; H_n nth Hermite polynomial; ΔH_A, adsorption enthalpy, kJ/mol; ΔH_vap , heat of vaporization, kJ/moll; k_a, adsorption rate constant, m³/kgs;K_A, adsorption equilibrium constant, m³/kg; K₀ , preexponential factor defined in Eqn. 8, m³/kg; k_f, mass transfer coefficient, m/s; L, bed length, m; q, flow rate, m³/s; R, particle radius, m; R_g, gas constant; t, time, s; T, temperature, K; T_F, period of Fourier expansion, s; u = q/A, linear velocity, m/s; z, length coordinate in packed column, m. Greek symbols: δ(t), Dirac delta function; ∈_B, void fraction of bed; ∈_-p, particle void fraction, ρ_rp, particle density, kg/m³ ; ξ, radial coordinate in particle, m; μ₁, first absolute moment, μ₂, second central moment.