Determination of chain stiffness and polydispersity from static light-scattering

Chain stiffness is often difficult to distinguish from molecular polydisperity. Both effects cause a downturn of the angular dependence at large q² (q = (4π/λ)sin θ/2) in a Zimm plot. A quick estimation of polydisperity becomes possible from a bending rod (BR) plot in which lim (c → 0) qRθ/Kc is plotted against q(〈S²〉_z)^1/2 = u. Flexible and semiflexible chains show a maximum whose position is shifted from u_max = 1.41 for monodisperse chains towards larger values as polydispersity is increased, while simultaneously, the maximum height is lowered. Stiff chains display a constant plateau at large q, its value is πM_L where M_L is the linear mass density. Using Koyama's theory, the number of Kuhn segments can be determined from the ratio of the maximum height to the plateau height, if the polydispersity index z = (M_w/M_n ? 1)^?1 is known. Thus, if the weight-average molecular weight M_w, is known, the contour length L_w, the number of Kuhn segments (N_k)_w, the Kuhn segment length l_k and the polydispersity of the stiff chains can be determined. The influence of excluded volume is shown to have no effect on this set of data. The reliability of this set can be cross-checked with the mean-square radius of gyration 〈s²〉_z which can be calculated from the Benoit-Doty equation for polydisperse chains. Rigid and slightly bending rods exhibit no maximum in the BR plot, and the effect of polydispersity can no longer be distinguished from a slight flexibility if only static scattering techniques are applied.     

Characterization of a single sample of an unknown polymer by size exclusion chromatography

The relationship between viscosity constants, k', a and K_η from the equations of Huggins and Mark-Kuhn-Houwink has been considered. It is shown, theoretically, that the sum of k' and a must be constant for all flexible-chain macromolecules irrespective of the solvent used. On this basis, a combination of chromatography and viscometry measurements can be used to characterize a new species. The method has been applied to the new polymer, poly[methyl(pyridin-3-yl) siloxane] ( 1 ) where no suitable calibration standards are available. The value of a, k', and K_η for 1 has been calculated. The calculated constants enabled an estimation of different average molecular weights (M_nM_wM_z) and polydispersity (M_w/M_n) from a minimum of experimental data. The new method is general and can be applied to any homogeneous linear flexible-chain nondraining macromolecule.     

Interaction features of cerium (III) and europium (III) acetate and pivalate with monoethanolamine

The composition of mixed-ligand complexes of cerium (III) and europium (III) acetates and pivalates with monoethanolamine (MEA) depends on the synthesis conditions and the nature of carboxylate ligand. We prepared solid complexes [Ln(Piv)₃(MEA) _x ], where Ln = Ce, Eu; HPiv-2,2-dimethylpropionic (pivalic) acid; x = 1, 1.5, and gel-like hydroxocomplexes [Ln(Carb) _{n − x − y} ,(NO₃) _x (OH) _y (MEA) _w (H₂O) _z ], where Ln = Ce, n = 4; Ln = Eu, n = 3; HCarb is acetic acid (HAcet) or HPiv. The values of the coefficients x, y, w, and z depend on the synthesis conditions and heat treatment. Prepared compounds were characterized by IR and ¹H NMR spectroscopies, elemental and thermal analyses, and MALDI-MS. The ESI-MS method was used to characterize the processes occurring in the solutions.     

Multimerization: Association and aggregation. XIII. Concentration dependence of apparent average molecular weights of a poly-disperse associating polymer in a theta solvent

Analytical expressions are derived for the concentration dependences of different apparent average (n,w,z) molecular weights for two types (end-to-end and segment-to-segment) of open association of polymolecular unimers. The open association is defined as an association leading to an unlimited number of multimer species. The type of association depends upon the number of associogenic sites per unimer molecule: for the end-to-end type this number is constant, whereas for the segment-to-segment type it is proportional to the degree of polymerization of the unimer. For the end-to-end association, a simple relation exists between the polydispersity (M?_r)_w/(M?_r)_n of the mul-timer and the association number r and the polymolecularity (M?_I)_w/(M?_I)_n of the unimers: (M?_r)_w/(M?_r)_n = 1 + r^?1[(M?_I)_w/(M?_I)_n ? 1]. The z-average and higher averages of the r-mers may be lower than the corresponding averages of the unimers. In the theta-state, (M?_n)_app,Θ and (M?_w)_app,Θ are linear functions of c/(M?_n)_app,Θ, whereas a more complicated relation exists for the apparent higher averages. For the segment-to-segment association, both (M?_w)_app,Θ and (M?_z)_app,Θ are linear function of the weight concentration c, whereas no closed expression could be found for (M?_n)_app,Θ. For the polydispersities of multimers one finds (M?_I)_z/(M?_r)_w = 1 + r^?1[(M?_I)_z/(M?_I)_w ? 1], and, in the special case of a Schulz-Zimm distribution of unimer molecular weights, (M?_r)_n/(M?_r)_w = 1 + r^?1[(M?_I)_n/(M?_I)_w ? 1].     

Effect of molecular weight on non-isothermal decomposition kinetics of hydroxyl terminated polybutadiene

Hydroxyl terminated polybutadiene prepared by free radical polymerization was fractionated by a solvent-nonsolvent precipitation method. The fractions were characterized by gel permeation chromatography for their molecular weight averages (¯M _n,¯M_w and¯M _z) and dispersities. The kinetic parameters, viz., energy of activationE and preexponential factorA for the thermal decomposition of the fractions were computed from their TG data, using four nonisothermal integral equations. Quantitative correlations between the kinetic constants and the molecular weight parameters were derived for the first time for HTPB as:E (or InA)=k ₁–k₂/¯M_n (or ¯M _w or ¯M _z) and the trend is explained on the basis of the kinetic compensation effect.

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Zusammenfassung Mittels eines Löser-Nichtlöserverfahrens wurde ein durch Radikalpolymerisation hergestelltes, Hydroxyl-endständiges Polybutadien fraktioniert. Das mittlere Molekulargewicht (¯M _n, ¯M_w and¯M _z) und der Dispersionsgrad der einzelnen Fraktionen wurden durch Gelchromatograpie charakterisiert. Die kinetischen Parameter, d.h. die Aktivierungsenergie E und der präexponentielle FaktorA wurden auf der Basis der TG Daten unter Zuhilfenahme von vier nichtisothermen Integralgleichungen berechnet. Zum ersten Male konnte für HTPB ein quantitativer Zusammenhang zwischen den kinetischen Konstanten und den Molekulargewichtparametern gefunden werden:E (order InA)=k ₁–k₂/¯M_n (order¯M _w order¯M _z). Diese Tendenz wurde auf der Basis des kinetischen Kompensationseffektes gedeutet.

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We thank Dr. K. V. C. Rao, Mr. M. R. Kurup and Director, VSSC for their kind permission to publish this paper.     

Hybrid Polyoxotungstates as Functional Comonomers in New Cross‐Linked Catalytic Polymers for Sustainable Oxidation with Hydrogen Peroxide

Anchoring terminal octenyl tails on molecular polyoxotungstates yield polymerizable organic–inorganic monomers with formula [{CH₂?CH(CH₂)₆Si}_xO_ySiW_wO_z]^4? [x=2, w=11, y=1, z=39 ( 1 ); x=2, w=10, y=1, z=36 ( 2 ); and x=4, w=9, y=3, z=34 ( 3 )]. These molecular hybrids can use aqueous hydrogen peroxide to catalyze the selective oxidation of organic sulfides in CH₃CN. Copolymerization of 1 – 3 with methyl methacrylate and ethylene glycol dimethacrylate leads to porous materials with a homogeneous distribution of the functional monomers, as indicated by converging evidence from FTIR spectroscopy and electronic microscopy. The catalytic polymers activate hydrogen peroxide for oxygen transfer, as demonstrated by the quantitative and selective oxidation of methyl p‐tolyl sulfide, which was screened as model substrate. The hybrid material containing monomer 2 was also tested in n‐octane to evaluate its potential for the oxidation and removal of dibenzothiophene, a well‐known gasoline contaminant.     

Octanol/water partitioning simulation by RP‐HPLC for structurally diverse acidic drugs: Comparison of three columns in the presence and absence of n‐octanol as the mobile phase additive

The advantageous effect of n‐octanol as a mobile phase additive for lipophilicity assessment of structurally diverse acidic drugs both in the neutral and ionized form was explored. Two RP C₁₈ columns, ABZ⁺ and Aquasil, were used for the determination of logk_w indices, and the results were compared with those previously reported on a base‐deactivated silica column. At pH 2.5, the use of n‐octanol‐saturated buffer as the mobile phase aqueous component led to high‐quality 1:1 correlation between logk_w and logP for the ABZ⁺ column, while inferior statistics were obtained for Aquasil. At physiological pH, the correlations were significantly improved if strongly ionized acidic drugs were treated separately from weakly ionized ones. In the latter case, 1:1 correlations between logD_7.4 and logk_w^oct indices were obtained in the presence of 0.25% n‐octanol. Concerning strongly ionized compounds, adequate correlations were established under the same conditions; however, slopes were significantly lower than unity, while large negative intercepts were obtained. According to the absolute difference (diff = logD_7.4–logk_w) pattern, base‐deactivated silica showed a better performance than ABZ⁺, however, the latter seems more efficient for the lipophilicity assessment of highly lipophilic acidic compounds. Aquasil may be the column of choice if logD_7.4<3 with the limitation, however, that very hydrophilic compounds cannot be measured.     

The solution phase characterization of poly(ferrocenyldimethylsilane)s by small‐angle neutron scattering

A series of monodisperse (M_w/M_n < 1.1) poly(ferrocenyldimethylsilane)s was prepared with number‐averaged degrees of polymerization, 〈z〉_n, of 9, 33, 206, and 506 ( 2 – 5 , respectively), as determined by gel permeation chromatography (GPC). The polymers were studied by small‐angle neutron scattering (SANS) in solution with the aim of obtaining the radius of gyration, R_g, the weight‐averaged molecular weight, M_w, and the polydispersity index, M_w/M_n. Data were collected over the range 0.008 < Q/Å^?1 < 0.5 and for a series of concentrations (weight fraction, w = 0.0063, 0.0125, 0.025, and 0.05). The scattered intensity, I(Q), was fitted to a model based on a Schultz–Zimm distribution of isolated chains with excluded volume. A comparison of the molecular weight and size data determined by GPC and SANS indicated an acceptable agreement between the values for R_g, M_w and M_w/M_n. The results of this study demonstrate the potential utility of SANS to fully characterize metallopolymers, and other polymer systems where traditional methods cannot be applied. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4011–4020     

Molecular weight distribution in radiation-induced polymerization. I. γ-radiation-induced free-radical polymerization of liquid styrene

The kinetics of γ-radiation-induced free-radical polymerization of styrene were studied over the temperature range 0–50°C at radiation intensities of 9.5 × 10⁴, 3.1 × 10⁵, 4.0 × 10⁵, and 1.0 × 10⁶ rad/hr. The overall rate of polymerization was found to be proportional to the 0.44–0.49 power of radiation intensity, and the overall activation energy for the radiation-induced free-radical polymerization of styrene was 6.0–6.3 kcal/mole. Values of the kinetic constants, k_p²/k_t and k_trm/k_p, were calculated from the overall polymerization rates and the number-average molecular weights. Gelpermeation chromatography was used to determine the number-average molecular weight M?_n, the weight-average molecular weight M?_w, and the polydispersity ratio M?_w/M?_n, of the product polystyrene. The polydispersity ratios of the radiation-polymerized polystyrene were found to lie between 1.80 and 2.00. Significant differences were observed in the polydispersity ratios of chemically initiated and radiation-induced polystyrenes. The radiation chemical yield, G(styrene), was calculated to be 0.5–0.8.     

Non-newtonian behavior of polymers with log-normal molecular weight distribution

By choosing suitable approximations to Bueche's function, it is possible to calculate the viscosity versus shear stress for log-normal molecularly distributed linear polymers. For bulk polymers the mixing rules M?_w, M?_w, M?_z are considered. For values of η/η0 > 0.1 and heterogeneities with M?_w/M?_n > 1.5 the result obtained with any mixing rule is η/η0 = erfc [(1/delta;) log (M₀Q^h/aK)], where a = π²/6_pRT and where the δ and K values are dependent on the heterogeneity ratio Q = M?_w/M?_n and on the type of mixing rule; on the other hand, the h value is independent of the heterogeneity, but depends on the mixing rule. Most experimental data should fit the M?_w mixing rule as one would expect from the zero shear stress mixing rule. Experimental data are compared with the theoretical results.     

Effect of the Cationic Form of a Fiban K-1 Fibrous Sulfo Cation Exchanger on the Degree of Reduction and Activity of Palladium in the Oxidation of Hydrogen

The effect of the nature of the exchanged cation M ^z+ (M ^z+ = Li⁺, Na⁺, Rb⁺, Cs⁺, Mg²⁺, Ca²⁺, and Ba²⁺) of a Fiban K-1 fibrous sulfo cation exchanger on the degree of reduction of the immobilized complex cations [Pd(NH₃)₄]²⁺ to Pd⁰ was studied. A linear correlation was found between the degree of palladium reduction and the difference of the relative electronegativities of atoms that participate in the O–M ^z+ bond. The activity of the catalysts in the oxidation of H₂ depends on the degree of palladium reduction.     

Molecular weights and molecular weight distribution of polymers by equilibrium ultracentrifugation. Part I. Average molecular weights

From the sedimentation-diffusion equilibria of some polymer solutions the average molecular weights M?_n, M?_w, M?_z, and M?_z+1 have been determined in different ways. In particular, the applicability of Fujita's method, which utilizes concentration gradient values at the midpoint of the solution column at a number of rotor speeds, was examined. It appears that if the gradients at some other places in the column are also used, a smaller range of rotor speeds suffices. This method is generally applicable for determining the average molecular weights specified above.     

Synthesis of macrocycles by the ring‐crossover reaction of a cyclic dithioester

The ring‐crossover polymerization of cyclic dithioester 1 was performed in the presence of quaternary onium salts as catalysts at 70–150 °C for 24 h in NMP. It was found that predictable cyclic polymers with the same repeating structures as 1 were obtained with M_ns in the range between 700 and 3,500, quantitatively. It was observed that intermolecular and intramolecular thioester‐exchange reactions proceeded between cyclic monomer 1 and resulting cyclic polymers under thermodynamic control to give a lower‐molecular‐weight cyclic polymer with a lower polydispersity ratio (M_n = 2,400, M_w/M_n = 1.70). © 2006Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 680–687, 2007     

Determination of optimized blending fractions for particle size distributions or molecular weight distributions involving various physical properties

It has been shown in this study that the effects of particle size distribution or molecular weight distribution on selected physical properties can be related by a generalized blending approach that involves similar equations. The blending equations developed involve different z-fractions where z = 3 for volume blending of spherical particles, or z = 2 for surface blending of spherical particles, or z = 1 for the weight blending of molecular weights. This new analysis approach addresses the magnitude of the ratios of particle size averages, D_x/D_y, or ratios of molecular weight averages, M_x/M_y, as well as the location of this maximum, the level of distribution information available for the starting materials, and the type of z-fraction blending. To illustrate this approach suspension viscosity/concentration data was used to show how the D_x/D_y ratio could be introduced successfully to analyze latex volume blending where z = 3. In addition, the maximum steady-state elastic compliance, J_e, as a function of weighted blends (z = 1) of two different molecular weights of polyisobutylene was shown to fit the simple equation J_e = 1.187 (M₃/M₂) (M₄/M₁) reasonably well. © 1995 John Wiley & Sons, Inc.     

Fluorescence.detected X-band epr spectroscopy of the photosynthetic bacterial triplet state

The X-band FDMR spectrum of the bacterial triplet in reduced Rhodopseudomonas sphaeroides at 5 K has been obtained. Pure S-T₀ mixing is sufficient and k_z <k_x,k_y necessary to explain the polarization pattern and intensity ratios. The kinetic fluorescence response is sigmoidal due to the second-order kinetics of antenna-reaction center energy transfer.     

Application of the inner product technique to double-well potentials in three-dimensional quantum systems by expanding the potential functions around their minima

Energy eigenvalues of double-well potentials for three-dimensional systems are calculated by means of an expansion of the potential function V(x,y,z;Z²,λ,a_IJ)=-Z²[x²+y²+z²] +λ{x⁴+y⁴+z⁴+2a_IJ[x²y²+x²z²+y²z²]} around its minimum, using the inner product technique, for various values of perturbation parameters Z²,λ and a_IJ. Some of the results calculated by this technique are compared with results obtained by other methods. This revised version was published online in July 2006 with corrections to the Cover Date.     

Molecular weights and molecular weight distribution of polymers by equilibrium ultracentrifugation. Part II. Molecular weight distribution

A method has been developed for determining the molecular weight distribution of a polymer sample from the sedimentation–diffusion equilibrium data for a solution under pseudo-ideal conditions. From some theoretical examples it appears that the method works well and that the molecular weight distribution can be determined with a reasonable degree of resolution. From three polymer samples (polyethylene, polystyrene, and polycaprolactam) the molecular weight distribution was determined in this way. The average molecular weights, M?_n, M?_w, M?_z, and M _z+1, calculated from these distribution functions agree well with those calculated directly from the equilibrium data.     

Comment on Numerical Treatment of GPC Data

Abstract

The numerical treatment of a chromatogram to obtain the various molecular weight averages is discussed. The method used by Cooper and Matzinger to calculate the influence of the number of data points on M_n and M_w, is criticized. Another model function is proposed. Calculations then show that the results obtained for M_n, M_w and M_z are approaching the theoretical values more and more by increasing the number of data points as it should be expected. This is in contradiction with the results of Cooper and Matzinger. The influence of the base-line correction is evaluated too.     

Polymer Polydispersity Effect on Depletion Interaction between Colloidal Particles

The effect of polymer polydispersity on the polymer‐induced interaction between colloidal particles due to non‐adsorbing ideal chains is investigated. An analytical theory is developed for the polymer‐segment density between two plates and in the space surrounding two spheres by extending a recently proposed superposition approximation to include polymer polydispersity. Monte Carlo computer simulations were made to test the validity of the analytical theory. The polymer densities predicted by the superposition approximation are in reasonable agreement with simulation results for the polydisperse case. The simulations show that depletion leads to a size fractionation of the polymers. It is shown that size polydispersity has a small effect on the interaction between two parallel plates but a more significant effect on the interaction between two spheres. The range of the potential increases and the contact potential drops with increasing polydispersity.

Polymer‐segment density as a function of y for three values of x, as indicated, in the space surrounding two colloidal spheres with radius R = R_g0 and h = 0.48R_g0. Symbols are the MC results: polydisperse polymer (○; z = 1) and monodisperse polymer (•) samples. Curves are the predictions of the product‐function approximation for monodisperse polymer (solid lines) and polydisperse polymer (z = 1, dashed lines).