Small-angle neutron scattering studies of isotropic polypropylene

Small-angle neutron scattering studies have been made of molten and crystalline polypropylene using samples containing small amounts of deuterated polypropylene in a protonated polypropylene matrix. The specimens were characterized by small- and wide-angle X-ray scattering to determine the d-spacing and the degree of crystallinity χ and by gel permeation chromatography to determine molecular weight, M_w, and molecular weight distribution. The degree of crystallinity was varied from 0.5 to 0.7, the d-spacing from 120 to 250 Å and the molecular weight from 34 000 to 1 540 000. Clustering was not observed. The radius of gyration $\text{〈s}{}^2\text{〉}{}_{\mathrm{w}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ of the tagged molecules was approximately proportional to $\text{M}{}_{\mathrm{w}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and almost independent of d and χ. In the melt similar values were obtained which are, within experimental uncertainties, the same as in a θ-solution. For 〈s²〉_wk²? 1 the scattering law approaches a k^?2 dependence. The results are discussed with reference to the chain-folded model but a fit cannot be obtained over all molecular weights. A simple random coil model fits the neutron scattering data partly but this does not explain the origin of the d-spacing.     

Theory of slow,steady state crack growth in polymer glasses

Cracks in polymer glasses can grow slowly preceded by a craze, a narrow zone of plastic cavitation. The craze widens by drawing more polymer from its surfaces into its fibrils but the fibrils themselves fail by local creep. When the crack tip moves at velocity v the loading at the crack tip can be described by a local stress intensity factor K which is the sum of the ‘apparent’ stress intensity factor K_A and a plastic contribution K_p (usually negative). K_p is found to be $\text{?KP(K)}\text{v}$ where P(K) is an integral over the craze boundary displacement law. Fibril failure by local creep leads to a power law, v ∞ K^m. From these relations K and v can be determined as a function of K_A. The plot of K vs. K_A is multiple-valued with a stable branch (at high K) and an unstable branch (at low K) separated by a minimum value of K_A which represents a threshold for stable, steady state crack growth. There is also a v threshold, below which cracks will not grow steadily. These predictions, the form of the v?K_A curve and implications for slip-stick crack growth are compared with recent experiments.     

Effect of molecular weight on the partial specific volume of polystyrenes in solution

The partial specific volume $\text{v}\text{?}{}_2$ of linear and branched polystyrenes has been measured as a function of molecular weight (1300<M_w<9×10⁶). In the low molecular weight range, the effect of end-groups is predominant. In the high molecular weight range (M_w > about 20 000), we have detected small but significant variations due to the intramolecular segment-segment contacts within the coil. We have proposed an empirical relation between $\text{v}\text{?}{}_2$ and the segment density of the macromolecule; this relation has been confirmed using highly branched polystyrenes. These results relative to dissolved polystyrenes are compared to experimental data obtained by different authors on pure liquid polystyrenes at different temperatures. Starting from simple additivity rules and from the known chemical composition of liquid polymers, we have shown that the variation of specific volume with high molecular weights is due to some phenomenon different from an effect of chain-ends.     

Study of the conformational rigidity of polyelectrolytes by elastic neutron scattering: 2. Molecular dimensions and conformation of poly(methacrylic acid)

Elastic neutron scattering at small angles allows the radius of gyration of a PMA sample of molecular weight M_v ～ 13000 to be measured in highly dilute solution; the variation of this parameter with concentration and charge density to be followed, and the viscometric results to be confirmed. The scattered intensity is proportional to q^?2(q = momentum transfer) for the highest concentrations studied, which correspond to a Gaussian distribution function of the sub units of the chain, and to q^?1 at the lowest concentrations, of which it is concluded that the polyion is then a zig-zag with only a few subunits.     

Polymerization of propylene catalyzed by α-diimine nickel complexes/methylaluminoxane: catalytic behavior and polymer properties

α-Diimine nickel dibromide complexes of dibromo[N,N’-bis(2,6-diisopropylphenyl)-2,3-butanediimine]nickel(II) (A) and dibromo[N,N’-(phenanthrene-9,10-diylidene)bis(2,6-diisopropylaniline)]nickel(II) (B) were synthesized under controlled conditions. The catalysts A, B and mixed of 1:1 weight ratio of them (C) were activated by methylaluminoxane and were used for propylene polymerization in a semi-batch reactor. In study of the catalytic systems behavior, activities, glass transition temperature (T _g) and viscosity average molecular weight (M _v) values related to the catalyst C were between those related to the catalysts A and B under same conditions. The highest and the lowest molecular weights of the obtained polymers were produced by the catalysts B and A which were about 80,000 and 70,000 (g/mol) under same conditions, respectively. The T _g of polypropylenes produced by the catalysts was about ?34 °C. The resulting polymers had similar behavior with ethylene-propylene copolymer which it could be due to formation of ethylene-type units in the polymer chain.     

Electrophoresis of functionalized microgels: morphological insights

The electrophoretic mobility of thermosensitive poly(N-isopropylacrylamide) (PNIPAM) microgels, functionalized to contain the same bulk carboxylic acid content using acrylic acid (AA), methacrylic acid (MAA), vinylacetic acid (VAA) and acrylamide hydrolyzed in situ (H-AM), is fit to the soft particle mobility model developed by Ohshima. Good model fits were achieved for experimental mobility data as a function of both ionic strength and temperature. The model deconvolutes the underlying contributions to soft particle mobility, identifying large morphology differences between microgels with similar absolute mobility values (i.e. AA-NIPAM and VAA-NIPAM). The differences in the predicted morphologies can be correlated to the physical properties of the carboxylic acid-containing comonomers and independent light scattering data. Theoretical softness models significantly overestimate the best-fit softness of the microgels but give reasonable estimates of how the softness changes as a function of temperature. Based on simultaneous comparisons of the best-fit softness, volumetric charge density, mobility, and particle size profiles, functionalized microgels appear to deswell primarily through a consecutive core-shell mechanism.     

Investigation of the complexation of proteins with neutral water soluble polymers through model analysis method

In the current research, the complexation of bovine serum albumin (BSA) with poly(N-isopropylacrylamide) (PNIPAM) is studied in an aqueous system (pH 7) which contains NaCl as its supporting salt, and based on the electric charge conservation law a mathematical model used to quantitatively characterize the complexation between proteins and neutral polymers is established. This model, which is set up on the assumptions that there exists a dynamic equilibrium of absorption and desorption among free proteins, complexes and free polymers in the aqueous complex system and the complexation sizes of proteins with neutral water soluble polymers are not uniform, better reveals the actual state of complexation. By means of dynamic light scattering (DLS), fluorescence spectrophotometer and zeta potential analyzer, all necessary parameters of the mathematical model have been acquired accurately without destroying the dynamic equilibrium of the aqueous complex system. The calculated results demonstrate that, with the rise of mixing ratio (r_mixing, molar ratio of PNIPAM to BSA), both the average number of bound BSA per PNIPAM (n_b) and the diameters of complexes (R_h) decrease gradually, while the zeta potential (ζ) and the concentration of free PNIPAM ([PNIPAM]_free) increase. In addition, the average number of PNIPAM in the complexes (φ) and the molecular weight of the complexes (M_w) can also be calculated by this mathematical model. The changing pattern of M_w with r_mixing is in accordance with the results of static light scattering (SLS). This analysis method, which interprets the interaction between neutral polymers and proteins in an aqueous system, is a new way to calculate the complex parameters and study the complexation mechanism between proteins and polymers.     

Physical nature of complex structural relaxation in polysiloxane - PMpTS: α and α′ relaxations

Structural relaxation processes in poly(methyl-para-tolyl-siloxane) (PMpTS) polymers of three molecular weights were studied using dynamic light scattering. Two relaxation processes: the usual α and an additional slow one α′ were observed and studied as function of temperature and molecular weight. Contrary to the structural relaxation, we find that in a plot T-T_g the relaxation times for the α′ process for all molecular weights do not collapse to a single curve. For one of the samples the light scattering correlation functions were compared with the corresponding functions obtained by means of mechanical relaxation, dielectric spectroscopy and computer simulations. The simulations show that the bimodal distribution, i.e. the α relaxation and the slow (α′) process are contained in the correlation functions of most of the probes (optical anisotropy, dipole moment, chain bond, density) in agreement with experimental observations.     

Rheology of core cross-linked star polymers

The rheological characterization for a set of structurally diverse core cross-linked star (CCS) polymers is presented. The influence of arm molecular weight (M_w(arm)) and CCS polymer molecular weight (M_w(CCSP)) on the steady- and dynamic-shear properties determined by plate rheometry will be discussed. Both these parameters dramatically affect the CCS polymer solution properties and determine its “molecular softness”; a key feature of star polymers. Data from light scattering and capillary viscometry analysis are also presented to relate the dimensional configuration of the CCS polymers to their rheological properties. The methodology for tuning the structure of the CCS polymer is provided and the implications on solution properties are discussed.     

Microstructure and rheological properties of pH-responsive core-shell particles

The microstructure and rheological properties of core-shell pH-responsive microgels consisting of poly(methyl methacrylate) (PMMA) particles grafted with a soft layer of methacrylic acid-ethyl acrylate (MAA-EA) cross-linked with di-allyl phthalate (DAP) were examined using dynamic light scattering and rheological techniques. The validity and limitation of the semi-empirical approach to model charged soft microgel particles developed by our group were tested on this core-shell system. The viscosity data for three different core-shell particles showed excellent agreement with the modified Krieger-Dougherty (K-D) model. Good agreement was also observed when our semi-empirical approach was compared against a theoretical model, which confirmed the validity of the semi-empirical approach to model charged soft particles. In addition, we confirmed that the new scaling law which relates the swelling ratio Q of microgels as a function of neutralization degree, α, average number of monomers between two cross-links, N_x, molar fraction of acidic units, y and concentration of mobile counter-ions, CK⁺ and C⁺Na, represented as (Nx/c₀)(CK⁺+C⁺Na)Q+Q2/3 is proportional to yN_xα. All the core-shell data at varying ionic strength and mobile counter-ions concentrations fall onto a master curve.     

Characterization of poly(1,4-phenyleneterephthalamide) in concentrated sulphuric acid. 2: Determination of molecular weight distributions

By combining static and dynamic properties (M_w, A₂, k_dR_g and R_h) of poly(1,4-phenyleneterephthalamide), PPTA (commercially known as Kevlar), with a detailed analysis of measured time correlation functions at different scattering angles in dilute solution, we have been able to estimate the molecular weight dependence of the radius of gyration, R_g(M), the persistence length ? ($\text{≈ 290}\text{A}\text{?}$), and the molecular weight distribution (M_z:M_w:M_n ≈ 6.2:1.8:1) using an unfractionated PPTA sample (M_w = 4.3 × 10⁴ g/mole). Laplace inversion of the time correlation function was accomplished independently by means of two different algorithms: the singular value decomposition technique with discrete multi-exponentials to approximate the normalized characteristic linewidth distribution function G(г) and the method of regularization whereby a linearized smoothing operator was used. The non-intrusive laser light scattering technique permits us to characterize, for the first time, the molecular weight distribution of PPTA which has been difficult to perform by means of other more established methods, such as size exclusion chromatography, because of the corrosive nature of solvents used in preparing PPTA solutions.     

The structure of vitreous carbon from wide angle and low angle x-ray diffraction

Both wide angle and low angle X-ray diffraction patterns have been measured for a sample of vitreous carbon which has been subjected to a maximum heat-treatment of 1800°C. The wide angle scattering was used to calculate a radial distribution function, which showed that the basic atomic arrangement was that of hexagonal graphite like sheets with no graphitic registration between the sheets. The low angle scattering pattern was interpreted in terms of a theory due to Debye, and an exponential correlation function was found to be a reasonable approximation for representing the electron density fluctuations giving rise to this scattering. The electron density fluctuations originate from pores in the matrix with a mean chord intercept length of ? 8 Å. The mean chord intercept for the matrix is ? 16 Å in reasonable agreement with “crystallite sizes” $\text{L}{}_{\mathrm{c}}\text{? 15}\text{A}\text{?}$ and $\text{L}{}_{\mathrm{a}}\text{? 22}\text{A}\text{?}$, calculated from the Scherrer equation. L_c should be interpreted as a distance between pores, and L_a as a defect distance in the matrix rather than indicating sharp crystallite boundaries.     

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.     

Time‐resolved small‐angle X‐ray scattering study of void fraction evolution in high‐density polyethylene during stress unloading and strain recovery

By means of time‐resolved small‐angle X‐ray scattering, we developed an analysis methodology to assess the void volume fraction ?_v in high‐density polyethylene (HDPE) during tensile testing. The specimens were first drawn up to different imposed strains, and subsequently were subjected to stress unloading and strain recovery stages. During the loading stage, ?_v progressively increased with the strain level, starting from a well‐defined onset strain prior to the yield point. In particular, ?_v reached a maximum of 8.75 vol% for a strain of 12.5% in the case of a HDPE grade with a molecular weight of 105 000 g mol^?1. Stress unloading and strain recovery caused a decrease in ?_v attained at the end of the loading stage. For a HDPE grade with a molecular weight of 55 000 g mol^?1, ?_v was more important during the loading stage and the decrease in ?_v was less marked during the stress unloading stage when compared to the HDPE with molecular weight of 105 000 g mol^?1. The residual and reversible components of void volume fraction were revealed. © 2015 Society of Chemical Industry     

Determination of molecular weight and molecular sizes of polymers by high temperature gel permeation chromatography with a static and dynamic laser light scattering detector

Flow-mode static and dynamic laser light scattering (SLS/DLS) studies of polymers, including polystyrene, polyethylene, polypropylene and poly(dimethylsiloxane) (PDMS), in 1,2,4-trichlorobenzene (TCB) at 150 °C were performed on a high temperature gel permeation chromatography (GPC) coupled with a SLS/DLS detector. Both absolute molecular weight (M) and molecular sizes (radius of gyration, R_g and hydrodynamic radius, R_h) of polymers eluting from the GPC columns were obtained simultaneously. The conformation of different polymers in TCB at 150 °C were discussed according to the scaling relationships between R_g, R_h and M and the ρ-ratio (ρ=R_g/R_h). Flow-mode DLS results of PDMS were verified by batch-mode DLS study of the same sample. The presented technique was proved to be a convenient and quick method to study the shape and conformation of polymers in solution at high temperature. However, the flow-mode DLS was only applicable for high molecular weight polymers with a higher refractive index increment such as PDMS.     

Estimation of molecular weight averages from intrinsic viscosity

The weight-average molecular weight is estimated by an extrapolation technique based on a linear relation between the viscosity-average molecular weight M_v and a Mark–Houwink–Sakurada constant. This method may also be used to assess the unperturbed dimensions of polymers. If the M_v data are known with high accuracy, then the straight line may be stretched to reach the number-average molecular weight confidently. The slope of the linear plot is associated with the molecular weight distribution and as such can be utilized to compute the polydispersity index.     

A method for estimating both the solubility parameters and molar volumes of liquids

The solubility parameters and molar volumes of substances can be used, in conjunction with suitable theory, to provide estimates of the thermodynamic properties of solutions; the solubility characteristics of polymer-solvent systems and the estimation of the equilibrium uptake of liquids by polymers are examples of the type of practical problems that are amenable to treatment. For low molecular weight liquids, the solubility parameter, δ, is conveniently calculated using the expression δ = (ΔE_v/V)½, where ΔE_v is the energy of vaporization at a given temperature and V is the corresponding molar volume which is calculated from the known values of molecular weight and density. For high molecular weight polymers, the volatility is much too low for ΔE_v to be obtained directly and hence recourse must be made to indirect methods for estimating δ for these materials. One such widely used method is based on Small's additive group “molar-attraction constants” which when summed allow the estimation of δ from a knowledge of the structural formula of the material; however, the density must still be determined experimentally. The proposed method of estimating δ, also based on group additive constants is believed to be superior to Small's method for two reasons: (1) the contribution of a much larger number of functional groups have been evaluated, and (2) the method requires only a knowledge of the structural formula of the compound.     

Structure of polystyrene glasses

Wide-angle X-ray scattering from both unoriented and axially deformed glassy polystyrenes (atactic and quenched isotactic) is compared with that calculated for isolated molecules in different conformations. No satisfactory fit is obtained. It is apparent that the scattering beyond $\text{s=1.0}\text{A}\text{?}{}^{\mathrm{?1}}$ is very similar to that from benzene and styrene, having a large contribution from contacts between phenyl groups attached to neighbouring molecules which are not represented in a single chain model. The only significant difference between the scattering of the polymer and the two low molecular weight liquids is that there is a small peak at $\text{s=0.75}\text{A}\text{?}{}^{\mathrm{?1}}$ (0.62 Å^?1 for the isotactic glass) which forms on polymerization and was first reported by Katz in 1927. For drawn samples the peak intensifies on the equator and apparently represents interchain correlations. However, in comparison with those of other non-crystalline polymers this interchain peak is weak, at a surprisingly low scattering angle in relation to the expected spacing of the chains and shows a very significant increase in intensity with increasing temperature. A model is proposed in which the phenyl groups segregate on a molecular scale to form stacks; there are fewer stacks than chain backbones and they have a low electron density core which expands considerably in relation to its small diameter as the sample temperature increases. The model accounts for the position and temperature sensitivity of the interchain ‘polymerization’ peak. It also shows some similarities to the organization of isotactic molecules in the crystalline state. The stacks of phenyl groups contribute to the X-ray pattern as if they were flexible superchains. The cylindrical distribution function derived from the scattering pattern of the oriented polymer indicates that the phenyl groups are in register in all directions over distances of the order of several chain diameters.     

Microgelation of unsaturated polyester resins in the presence of poly(vinyl acetate) by static and dynamic light scattering

The partially cured unsaturated polyester (UPE)/styrene resins with various degrees of conversion lower than gel conversion blended with PVAc and 2‐fluorotoluene solvent were investigated using both static and dynamic light scattering (SLS and DLS). The solvent (i.e., 2‐fluorotoluene) is isorefractive with PVAc; thus, one sees only primary and partially cured UPEs in light‐scattering experiments. DLS was used to follow the variations of primary UPE and UPE microgel particle sizes, and SLS was used to follow the variations of UPE molecular weight, second virial coefficient (A₂), anisosymmetry (ρ_v), and differential index refraction (dn/dC) with degree of UPE conversion and PVAc concentration. The experimental data showed that, at a fixed degree of UPE/styrene conversion, increasing PVAc concentration in the UPE/styrene system caused decreases in dn/dC, A₂, ρ_v, and particle sizes of UPE microgels. These results suggest that mixing PVAc into UPE/styrene resins causes an increase in the compactness of UPE coils and favors intramolecular UPE/styrene cyclization in the early stage of curing. Thus A₂, ρ_v, and particle sizes of microgels decreased with increasing PVAc concentration. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 1439–1449, 2001     

Distribution analyses of multi-modal dynamic light scattering data

A method of data analysis for dynamic light scattering is proposed to evaluate the weight fraction, w(R_h), of a small amount of large aggregates in a dilute solution, where R_h is the hydrodynamic radius. We examined the time-correlation function of scattering intensity for model multi-modal systems, i.e., mixtures of latex solutions having different particle sizes and of polystyrene standard solutions having different molecular weights, by properly taking into account the unknown fractions, w(R_h), and scattering intensities of individual components. We derived an equation to evaluate the weight fractions of the components. The validity of this method was verified by successfully reconstructing the observed correlation functions having fast and slow modes. As a demonstration, the fraction of aggregates in a thermosensitive polymer solution in water was evaluated as a function of temperature.