Small-angle x-ray scattering from solution of rodlike particles with length distribution

The scattering function of rods with a constant radius, 8 Å, and a length distribution of the Schulz–Zimm type was calculated on a computer as a model of helical synthetic polypeptide. The influence of length and length distribution on the scattered intensity of small-angle x-ray scattering was clarified. As length grows and length distribution broadens it is difficult to obtain reliable values of molecular weight and radius of gyration from a Zimm plot. The influence of length distribution on the mass per unit length, M_q, and the radius of gyration of the cross section, 〈S〉^1/2, from the Guinier plot of the cross-sectional factor decreases as the length increases, and reliable values of M_q and 〈S〉^1/2 can be obtained even for rods with wide distribution for rods more than 600 Å long. In particular, it is pointed out that the value of 〈S〉^1/2 is little influenced by length and length distribution.     

Dilute solution properties of a polybenzimidazole

Light scattering and viscometric studies have been carried out on dilute solutions of a polybenzimidazole in N,N-dimethylacetamide. The data, which span the molecular weight range 2.9 ≦ 10^?4M_w ≦ 23.3, and the temperature range 290 ≦ T/K ≦343, yield the dependence of the mean-square radius of gyration 〈s²〉_LS, the second virial coefficient A₂, and the intrinsic viscosity [η] on molecular weight M_w and temperature. The unperturbed mean-square radius 〈s〉_LS was calculated using experimental values of 〈s²〉_LS and A₂. It was found that excluded volume effects on 〈s²〉_LS are very small. The unperturbed hydrodynamic chain dimension 〈s〉_η was estimated by considering draining effects. A small value of the draining parameter was obtained. Analysis of the temperature dependence of A₂ and [eta;] leads to the conclusion that this system approaches a lower theta temperature with increasing temperature. The steric factor σ = 〈s〉/〈s〉f, based on the value of 〈s〉_f calculated for the polymer chain with free rotation, is nearly unity. Most of these properties can be interpreted in terms of long rotational units within the main chain.     

Structural analysis of aggregates formed by a thermoresponsive homopolymer in dilute aqueous solutions

The aqueous solution of a thermoresponsive polymer, poly[2‐(2‐ethoxy) ethoxyethyl vinyl ether] poly(EOEOVE), contains a tiny amount of large polymer aggregates at low polymer concentrations far below the lower critical solution temperature (～40 °C). The molar mass M_w,slow, radius of gyration 〈S²〉, and hydrodynamic radius R_H,slow of the aggregating component of poly(EOEOVE) were obtained by simultaneous static and dynamic light scattering as functions of the polymer concentration and temperature, while the weight fraction w_slow of the component was estimated by size‐exclusion chromatography. The M_w,slow dependencies of 〈S²〉 and R_H,slow, as well as the ratio 〈S²〉/R_H,slow, indicated that the poly(EOEOVE) aggregate takes a sparsely branched polymer‐like conformation. We have analyzed the structure of the aggregate, using the branched polymer model of random type. The M_w,slow dependence of 〈S²〉 obtained was favorably compared with this model with reasonable structural parameters. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1179–1187, 2006     

Simulation studies of branched polymer molecules

Monte Carlo simulation results are presented for lattice models of uniform stars (one branch point of functionality f = 3), combs (two branch points, ? = 3,3) and brushes (two branch points ? = 3,4 and ? = 3,5). We estimate the critical exponent γ(?), the ratio g(?) = 〈S(?)〉/〈S(1)〉 (where 〈S(?)〉 is the mean-square radius of gyration of a structure having ? branches and N monomers), and the meansquare end-to-end branch lengths, as a function of the number and arrangement of branches. Comparisons with theoretical predictions and experimental data are made where possible, leading to a test of some predictions, and a suggestion concerning future experiments.     

Characterization of poly(styrene-co-divinylbenzene) microgels

Tightly cross-linked poly(styrene-co-divinylbenzene) microgels with molecular weights in the range 10⁷ to 10⁸ g mole^?1 were studied in solution in dimethylformamide containing 7 g dm^?3 LiBr. Laser light scattering photon correlation spectroscopy (PCS) was used to measure z-average translational diffusion coefficients D?_z and dilute solution viscometry to measure intrinsic viscosities [η]; values of the equivalent hydrodynamic radii 〈R〉${}_{\text{η}}^{\text{?}}$ and 〈R_D^?1〉 were derived. Weight-average molecular weights M?_w and z-average mean-square radii of gyration 〈S²〉_z were determined by conventional light scattering. The microgels were investigated by gel permeation chromatography, and molecular weight data obtained using the [η]M calibration procedure were in satisfactory agreement with results obtained by electron microsocopy and conventional light scattering.     

Magnesium chloride-supported high-mileage catalysts for olefin polymerization XI. Determinations of poly(decene-1) molecular weight chain dimension and thermal transitions

Decene-1 was polymerized with the CW catalyst and fractionated by precipitation technique. Light-scattering and viscometric measurements on these fractions established the relationship [η] = 5.19 × 10^?3 M . The unperturbed mean square end-to-end distance is (〈R〉/M)^1/2 = (6.17 ± 0.34) × 10^?9. Light-scattering data is consistent with a relatively stiff molecule with length of L = 1.75 × 10^?5 cm for poly(decene-1) with MW = 397,000. Its mean square radius of gyration 〈R〉 is 2.79 × 10^?11 cm.² The ratio of L²/〈R〉 = 11 is close to the theoretical ratio of 12 for this kind of macromolecule.     

Influence of short-range interactions on the shape of an unperturbed polymer chain: polyethylene

The average instantaneous shape of an unperturbed polyethylene chain is studied with a Monte Carlo technique. Different short-range interactions in the polyethylene chain are considered. The shape is evaluated as the ratio 〈L〉:〈L〉:〈L〉, where L₁≤L₂≤L₃ are the orthogonal components in the system of principal axes of gyration. Differences are found for different interactions in short- and medium-length chains, while for long chains all ratios converge to a common limit, which is about 1:2.7:12.0 for polyethylene chains.     

Fractionation and characterization of a protein–polysaccharide complex from Pleurotus tuberregium sclerotia

A water‐soluble sample (TM4b), extracted from sclerotia of Pleurotus tuberregium, was analyzed using elemental analysis, one‐ and two‐dimensional ¹H and ¹³C NMR. The results indicated that TM4b was protein–polysaccharide complex, and the polysaccharide moiety was hyperbranched β‐D ‐glucan with residuals branched at C3, C2, C4, and C6 positions. A preparative size‐exclusion chromatography (SEC) column combined with nonsolvent addition method was used to fractionate TM4b, and nine fractions were obtained. Solution properties of TM4b in 0.15 M aqueous NaCl were studied using static laser light scattering and viscometry at 25 °C. The dependences of intrinsic viscosity ([η]) and radius of gyration (〈S²〉) on weight–average molecular weight (M_w) for TM4b in the M_w range from 1.89 × 10⁴ to 2.58 × 10⁶ were found to be [η] = 0.21M and 〈S²〉 = 3.63M. It indicated that TM4b existed as compact sphere conformation in the aqueous solution. Atomic force microscopy image further confirmed that the TM4b molecules exhibited globular shape in the solution. This work gave valuable information on fractionation and chain conformation characterization of the globular protein–polysaccharide complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2546–2554, 2007     

Conformation and dynamics of a self-avoiding sheet: Bond-fluctuation computer simulation

The conformation and dynamics of a self-avoiding sheet are analyzed by the bond-fluctuating Monte Carlo method. The mean-square displacement of the center of mass of the sheet and that of its center node (R) show asymptotic diffusive behavior. The segmental dynamics in short and long time regimes can be deduced from the motion of the center node described by the power law with μ ≃ 0.13 and ν ≃ ½, where C₁ and C₂ are fitting constants and t is the time. The radius of gyration, R_g, scales with the linear size, L_s, of the sheet as R_g ≃ N^γ with γ ≃ ½ and N = L, and this is consistent with the conformational analysis of open tethered membranes with excluded-volume constraints. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1041–1046, 2005     

Beyond the Planck–Benzinger thermal work function: New insights into the role of molecular switches in biology

The Planck‐Benzinger methodology provides a means of determining the innate temperature‐invariant enthalpy, ΔH°(T₀), thermal agitation energy, or the heat capacity integrals ∫ΔCp°(T)dT, and allows precise determination of 〈T_Cp〉, 〈T_h〉, 〈T_s〉, and 〈T_m〉. It is a method for evaluating [ΔH ? ΔH°(T₀)], the heat of reaction for biologic molecules at room temperature, and provides for a better understanding of cooperative thermodynamic compensation. The Planck‐Benzinger methodology demonstrates that macromolecular interactions will always exhibit a negative value of the Gibbs free energy change at a well‐defined temperature. It can be used for determination of the thermodynamic molecular switch, where there is a change of sign in ΔCp°(T)_reaction which determines the behavior patterns of the Gibbs free energy change. All interacting biologic systems that we have thus far examined using the Planck‐Benzinger approach point to the universality of this thermodynamic switch. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Improved expression of the mean-square radius of gyration, 2. Poly(1,1-disubstituted ethylene)s

The mean-square radius of gyration of poly(1,1-disubstituted ethylene)s is calculated according to a method already developed for poly(methyl methacrylate), poly(α-methylstyrene) and polyitaconate. During the derivation both the effect of side groups and the masses of skeletal atoms were taken into account. A hypothetical polymer chain was introduced, in which the mass of the substituents on every C^α was considered to be concentrated in their center of mass, and the virtual side bond vector runs from C^α to this center. The mean-square radius of gyration of poly(1,1-disubstituted ethylene)s consists of two parts, one of which is the mean-square radius of gyration of the hypothetical molecule described before and the other is related to the geometrical characteristics of the side groups. Numerical calculations indicated that the dependence of the mean-square radius of gyration of poly(1,1-disubstituted ethylene)s on the molecular weight is analogous to that of vinyl polymers, 〈S²〉 = aM^b, where a and b are constants characteristic of the polymer.     

Monte Carlo study of star-branched polymers on the tetrahedral lattice. I. Conformation of the macromolecule

The star-branched polymers on the tetrahedral lattice are studied by means of the Monte Carlo method. The influence of solvent quality on the dimensions of the coil is described for both linear and branched polymer systems of different functionality. It has been observed that the ratios of gyration radii 〈S²〉_b/〈S²〉_l are greater than those predicted theoretically for the random-flight model. The fourth reduced moment of S² distribution and the mean-square separation of the branch ends from the center of gravity have been also computed. The changes in segment arrangement in the coil with increasing number of branches have been observed.     

Configurational-conformational statistics of stereoirregular polystyrene

The dependence of the configurational-conformational characteristics, such as the mean-square end-to-end distance, the mean-square radius of gyration, and the temperature coefficient of the stereoirregular polystyrene chains on the fraction of meso dyads, P_m was investigated, using the periodic condition method. The calculation shows that polystyrene has the most compact chain when P_m = 0.7, and the temperature coefficient of the characteristic ratio of the mean-square end-to-end distance reaches the minimum, −0.89 × 10⁻³ K⁻¹, at P_m = 0.5. The theoretical result of the mean-square radius of gyration for atactic polystyrene, 〈S²〉^1/2 = 0.2245 M^0.5106 shows good agreement with the experimental measurement in both bulk amorphous state and θ-solvent.     

Theoretical studies of diamagnetic properties of the hydrogen molecule ion II. Effect of varying internuclear separation

The diamagnetic susceptibility χ and magnetic shielding σ for H are investigated in the range of internuclear separations R = 1.6 a.u. to R = 2.4 a.u. according to a previously reported technique. From this data values of 〈χ〉 and 〈σ〉, for which nuclear motion due to zero-point vibration and centrifugal stretching is taken into account, are calculated at 300°K. These averages are 〈χ〉 = ?0.3902 α²a and 〈σ〉 = 1.096 × 10^?5 c.g.s. units which are approximately 3.1% and 1.4% respectively, smaller than the equilibrium values.     

Laser ablation of AgSbS2 and cluster analysis by time‐of‐flight mass spectrometry

Thin films of AgSbS₂ are important for phase‐change memory applications. This solid is deposited by various techniques, such as metal organic chemical vapour deposition or laser ablation deposition, and the structure of AgSbS₂(s), as either amorphous or crystalline, is already well characterized. The pulsed laser ablation deposition (PLD) of solid AgSbS₂ is also used as a manufacturing process. However, the processes in plasma have not been well studied. We have studied the laser ablation of synthesized AgSbS₂(s) using a nitrogen laser of 337 nm and the clusters formed in the laser plume were identified. The ablation leads to the formation of various single charged ternary Ag_pSb_qS_r clusters. Negatively charged AgSbS, AgSb₂S, AgSb₂S, AgSb₂S and positively charged ternary AgSbS⁺, AgSb₂S⁺, AgSb₂S, AgSb₂S clusters were identified. The formation of several singly charged Ag⁺, Ag, Ag, Sb, Sb, S ions and binary Ag_pS_r clusters such as AgSb, Ag₃S^?, SbS (r = 1–5), Sb₂S^?, Sb₂S, Sb₃S (r = 1–4) and AgS, SbS⁺, SbS, Sb₂S⁺, Sb₂S, Sb₃S (r = 1–4), AgSb was also observed. The stoichiometry of the clusters was determined via isotopic envelope analysis and computer modeling. The relation of the composition of the clusters to the crystal structure of AgSbS₂ is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Dipole,quadrupole, octupole,and dipole–dipole–quandrupole polarizabilities and second hyperpolarizabilities at real and imaginary frequencies for helium in the 23S state: Dispersion-energy coefficients for interactions between He(23S) and H(12S), He(11S), He(23S), or H2(X1∑g+)

We have determined the dynamic dipole (α₁), quadrupole (α₂), octupole (α₃), and dipole–dipole–quadrupole (B) polarizabilities and the second hyperpolarizability tensor (γ) for the helium atom in its lowest triplet state (2³S). We have done so for both real and imaginary frequencies: in the former case, for a range of frequencies (ω) between zero and the first electronic-transition frequency, and in the latter case for a 32-point Gauss–Legendre grid running from zero to ?ω = 20 E_h. We have also determined the dispersion-energy coefficients C₆, C₈, and C₁₀ for the systems H(1²S)? He(2³S), He(1¹S)? He(2³S), and He(2³S)? He(2³S) and the C, C, C, C, and C coefficients for the interaction He(2³S)? H₂(X¹∑). Our values of the higher-order multipolar polarizabilities and of γ for the 2³S state of helium are, we believe, the first to be published. © 1993 John Wiley & Sons, Inc.     

Laser ablation of ternary As‐S‐Se glasses and time‐of‐flight mass spectrometric study

Ternary chalcogenide As‐S‐Se glasses, important for optics, computers, material science and technological applications, are often made by pulsed laser deposition (PLD) technology but the plasma composition formed during the process is mostly unknown. Therefore, the formation of clusters in a plasma plume from different glasses was followed by laser desorption ionization (LDI) or laser ablation (LA) time‐of‐flight mass spectrometry (TOF MS) in positive and negative ion modes. The LA of glasses of different composition leads to the formation of a number of binary As_pS_q, As_pSe_r and ternary As_pS_qSe_r singly charged clusters. Series of clusters with the ratio As:chalcogen = 3:3 (As₃S, As₃S₂Se⁺, As₃SSe), 3:4 (As₃S, As₃S₃Se⁺, As₃S₂Se, As₃SSe, As₃Se), 3:1 (As₃S⁺, As₃Se⁺), and 3:2 (As₃S, As₃SSe⁺, As₃Se), formed from both bulk and PLD‐deposited nano‐layer glass, were detected. The stoichiometry of the As_pS_qSe_r clusters was determined via isotopic envelope analysis and computer modeling. The structure of the clusters is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Light scattering studies of copolymers. 1. Soluble hemoglobin--dextran complexes

Complexes between dextrans of different molar mass and bovine hemoglobin were synthesized by two different methods. In the alkylation method three and in the dialdehyde method, two hemoglobins are coupled on average to one dextran molecule. In both cases, the soluble hemoglobin-dextran complexes reversibly bind and release oxygen; the oxygen affinity is greater than that of free hemoglobin. Static and dynamic light scattering was used to determine the average molar mass M_u, the radius of gyration 〈S〉, and the hydrodynamic radius R_h of both the complexes and the single dextrans. Interpretation of these data is complicated due to the fact that the complexes are copolymers. When appropriate approximations are made, the results indicate that the complexes have a spherical shape and an internal structure of a multiple-chain network, where several dextrans are linked together by the hemoglobins. The number of single dextrans per complex increases as the molar mass of the single dextrans is decreased. The increment is greater in the dialdehyde than in the alkylation method. The probable reason is that in the dialdehyde method one hemoglobin can connect many dextrans simultaneously while in the alkylation method a hemoglobin is able to link maximally two dextrans. The ratio of the radius of gyration to the hydrodynamic radius decreases as the temperature is increased. This suggests a decrease of the solvent penetration length for the complexes and can be interpreted on the basis of the Deutsch-Felderhof theory for porous spheres. © 1994 John Wiley & Sons, Inc.