Dynamic light scattering and viscoelasticity of semidilute polystyrene/cyclohexane solutions

In the present work, dynamic light scattering (DLS) measurements from polystyrene in cyclohexane semidilute solutions were carried out at 60 °C with scattering angles varied from 30° to 120°. The correlation functions were analyzed with the double KWW function and the CONTIN program. The amplitude of the fast mode A_f of the field correlation function g¹(t) was used to calculate the longitudinal stress modulus M_o using Wang’s theory. A comparison between M_o calculated from DLS data and the shear stress modulus G obtained from mechanical measurement was made.     

Viscoelastic characterization of moderately concentrated polystyrene solutions by dynamic light scattering

The dynamic light scattering measurements were performed for moderately concentrated entangled solutions of atactic polystyrene in benzene (BZ) at 25.0 °C, in cyclohexane (CH) at 34.5 °C (Θ), and in diethyl malonate (DEM) at 35.0 °C (Θ) to characterize their viscoelastic properties. The results have shown that while the mutual diffusion coefficient D increases in the BZ solutions and decreases in the CH and DEM solutions with increasing polymer mass concentration c, the friction coefficient ζ for the three solutions increases with c showing the same power-law behavior irrespective of the weight-average molecular weight M_w and solvent quality. It has been found that the instantaneous longitudinal modulus L₀ for the CH and DEM solutions increases in proportion to c², obeying the familiar relation for the plateau value (4/3)G_N of the longitudinal stress relaxation modulus, but the L₀ values for these solutions are somewhat smaller than the values predicted from the relation. The terminal relaxation time τ_m for the two Θ solvent systems has been found to follow the power-law τ_m∝c^2.7, showing good correspondence to the relation established by rheological measurements.     

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.     

Real-time dynamic light scattering on gelation and vitrification

The time-resolved dynamic light scattering has been employed to investigate gelation of divinylbenzene (DVB; branched chains) and vitrification of styrene (St; linear chains) during radical polymerization in bulk. The intensity correlation function (ICF) was obtained every 30 s during polymerization process. The DVB system exhibited a power law behavior in ICF characteristic of gelation threshold, which was followed by vitrification. In the case of St, two relaxation modes appeared before vitrification, which were assigned to be the cooperative and the slow relaxation modes.     

Dynamic light scattering and small-angle neutron scattering studies on phenolic resin solutions

Solution properties of unfractionated phenolic resins prepared by polycondensation of phenol and formaldehyde using oxalic acid as a catalyst were investigated by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The hydrodynamic radius, obtained by DLS experiments with 1 vol % solution in acetone, and the correlation length, ξ, of the Ornstein-Zernike equation, obtained by SANS experiments with 10 vol % solution in tetrahydrofuran, obey a power-law relation as a function of z-average molecular weight estimated by gel permeation chromatography, with scaling exponents of 0.57 and 0.27, respectively. These behaviors are unaffected by polymerization conditions, such as initial phenol-to-formaldehyde molar ratio in the range from 0.9 to 1.5, catalyst concentration with oxalic acid-to-phenol molar ratio from 0.01 to 0.1, and reaction time within the period in which the polymer remains soluble. SANS curves for polymers prepared under different conditions are sufficiently superimposed onto a single curve with the reduced variables, ξ⁻²I(q) and ξq. These results indicate that unfractionated phenolic resins have a self-similar structure with respect to the molecular weight.     

Characterization of spatial inhomogeneities and dynamic properties of random cross-linked polystyrene networks by dynamic light scattering

The network inhomogeneity and the cooperative motion of the network chains of random cross-linked poly(styrene-co-maleic anhydride) gels were investigated by dynamic light scattering. Measurements were performed for gels in the preparation state as well as in the swelling equilibrium. Network inhomogeneities and cooperative motion were analyzed at varying the cross-linker concentration and the polymer volume fraction. While the cross-linker concentration has only a minor influence on the inhomogeneity and the diffusion constant D_coop, the polymer volume fraction clearly influences both measured properties. The concentration dependence of D_coop can be well described by a power law, as known for semi-dilute polymer solutions. In the preparation state the networks appear homogeneous, exhibiting dynamic contributions to the scattering intensity of 70-90%. Swollen to equilibrium stage, significant heterogeneities emerge, reducing the dynamic contributions to 10-20%.     

[NCO]/[OH] and acryl-polyol concentration dependence of the gelation process and the microstructure analysis of polyurethane resin by dynamic light scattering

The gelation process and the microstructure after the gelation of polyurethane resin consisting of acryl-polyol and polyisocyanate was investigated by dynamic light scattering (DLS) as a function of stoichiometric ratio, [NCO]/[OH], and the concentration of acryl-polyol, C_polyol. The following conclusions were obtained. First, the sol-gel transition was explained by the so-called site-bond percolation theory. Here polyol groups act as site-occupants, and isocyanate groups act as chemical cross-linkers. Second, the scattering inhomogeneities increased rather gradually around the gelation point, which are the characteristics of the gelation process not from monomeric but from oligomer units. Third, at the gelation point, the characteristic decay time of the fast mode, τ_fast, decreased, and the fraction of the collective diffusion mode, A, increased with [NCO]/[OH], which are due to introduction of cross-linking and/or increase of the rigidity of the network. Finally, the ensemble average scattering intensities, 〈I〉_E, the static inhomogeneities, 〈I_C〉_E, the time-average dynamic fluctuating component, 〈I_F〉_T and the collective diffusion coefficient, D, showed remarkable dependence not only on C_polyol but also on [NCO]/[OH]. These are due to the competition between the cross-linking and the progress of micro-phase separation.     

Dynamic light scattering of dilute PVA-borax aqueous solutions

Poly(vinyl alcohol)-borate (PVA-borate) complexes in dilute aqueous solutions were investigated by dynamic light scattering (DLS). Two relaxation modes obtained, were scattering vector-q² dependent and diffusive. The amplitude of slow mode was independent of borax concentration. In the very dilute PVA concentration regime ( [PVA] < 5 g/L), the PVA di-diol-borate complexation was dominated by intra-molecular reaction, and the fast mode correlation length ς_f which corresponds to the polymer chain dimension increased rapidly with borax concentrations lower than 0.06 M, and reached an asymptote in the higher borax concentration regime. However, for a dilute PVA aqueous solution with higher PVA content (i.e., [PVA] = 9 g/L), both intra-and inter-molecular PVA di-diol-borate complexations might happen. The chain expansion and shrinkage of PVA-borate complex with increasing borax concentration was observed due to the balance between the electrostatic repulsion of the charged diol-borate complexes and the intra-molecular crosslink induced by the intra-molecular di-diol-borate complexation.     

Dynamic light scattering studies on the aggregation behavior of tributyl phosphate and straight chain dialkyl amides during thorium extraction

Dynamic light scattering (DLS) studies were carried out to investigate the aggregation behavior of 1.1 M solutions of tributyl phosphate (TBP), N,N-dihexyl octanamide (DHOA) and of N,N-dihexyl decanamide (DHDA) in n-dodecane equilibrated with varying concentrations of nitric acid (0.1–6 M) and of Th (10–200 g/L). There was a gradual increase in thorium extraction with increased aqueous phase acidities. A significant enhancement in the aggregate sizes was observed with increasing concentration of thorium in the organic phase. The effect of 1-octanol as phase modifier was also investigated on the aggregation behavior of extracted species for TBP system.     

Dynamic light scattering measurements of polystyrene in semidilute theta solutions

Measurements of the co-operative diffusion coefficient, D_c, and a centre of mass translational diffusion coefficient, D_s, have been made by dynamic light scattering for the polystyrene-cyclohexane theta system as a function of molecular weight and concentration. For semidilute solutions it is established that D_s∝N^?2c^?3 which is in agreement with the predictions from scaling arguments for the self-diffusion coefficient. However, if the co-operative mode is interpreted by D_c∝N^xc^y, the results of 0 < x < 0.7 and 0 < y < 0.5 are in disagreement with scaling predictions of D_c∝N⁰c¹. A discussion of the assumptions and potential shortcomings of the blob model which is used in the derivation of the power law predictions and the dynamic scattering equations is included. In addition, monomeric friction coefficients have been obtained from the D_s results within the framework of Doi-Edwards model. A comparison is made of the concentration dependence of the monomeric friction coefficient from the present data to that from similar experiments on a good solvent (tetrahydrofuran) system and from shear relaxation modulus measurements on the polystyrene in Aroclor 1248.     

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.     

Scaling laws and polystyrene networks: a quasi-elastic light scattering study

Randomly crosslinked networks with a range of crosslink densities were prepared by γ-irradiation. Quasielastic light scattering measurements were made on the gels swollen to equilibrium in cyclohexane at 308, 318 and 333 K. The longitudinal osmotic modulus M_os was obtained from the intensity of the dynamically scattered light, and the cooperative diffusion coefficient D_c calculated from the relaxation rate of the autocorrelation function. The concentration dependence of these parameters at the theta temperature was found to be consistent with the scaling predictions, but at higher temperatures where excluded volume conditions prevail, deviations from scaling behaviour were observed. These discrepancies are probably caused by defects in the network structure.     

Diffusion of poly(ethylene oxide) in semidilute aqueous solution: Dynamic light scattering and gradient diffusion

Gradient diffusion measurements and dynamic light scattering data are presented for semidilute aqueous solutions of narrow distribution (molecular weight M: 2.5 × 10⁴ – 1.2 × 10⁶) poly(ethylene oxide) fractions. Resolution of the time correlation function using bimodal analysis gave: (a) a fast mode, identical within experimental error to the classical gradient diffusion values; (b) a slow mode, interpreted as reflecting the translational motions of clusters of entangled chains. The results are similar to those found for other aqueous polymer systems, probably reflecting the ease with which association occurs between extended, polar, chains.     

Small-angle light scattering studies of poly(N-vinylcarbazole)

Morphology of PVK samples cast from various solvents (cyclohexanone, tetrahydrofuran, benzene) and crystallized on a glass surface, was studied by means of SALS. Results show existence of rod-like elements forming a morphology with nonrandom correlations of orientations. This morphology is practically independent of crystallization conditions.     

Dynamic light scattering measurements on the polystyrene/ethyl acetate system at semi-dilute concentrations as a function of temperature

Summary Measurements of autocorrelation functions extending over a broad time range are reported for a sample of polystyrene in ethyl acetate as a function of temperature between –44°C (-temperature) and 70°C. The corresponding spectra of decay times are obtained by two mathematical methods. The existence of three dynamic processes is shown and their temperature and angular behaviour is studied.     

Laser light scattering studies of ternary polymer solutions

Ternary polymer solutions [polystyrene and poly(methylvinylether) dissolved in a single solvent] have been studied to investigate the thermodynamic compatibility of the polymers and the solvents, and also to facilitate the investigation of the self-diffusion of polystyrene to greater polymer concentration. Both good and poor quality solvents have been used in this study. The self-diffusion coefficient of the polystyrene has been measured by dynamic light scattering and by pulsed field gradient NMR where appropriate. The self-diffusion data are also used to critically examine the recent theoretical developments in this field. Important confirmation of theory has been demonstrated for good solvent solutions and intriguing discrepancies have been discovered for poor solvent solutions.     

Light scattering study on the dynamic behaviour of cellulose inclusion complex in LiOH/urea aqueous solution

In our previous study, the rapid dissolution of cellulose in alkali/urea aqueous solution at low temperature induced by a dynamic self-assembly process has been demonstrated [1]. The cellulose solution was meta-stable, and its stability could be influenced by system fluctuations (temperature, concentration or time). In the present work, cellulose dissolved in 4.6wt% LiOH/15.0wt% urea aqueous solution pre-cooled to −12 °C was studied by means of dynamic light scattering (DLS). The results revealed that cellulose existed as single inclusion complexes (ICs) associated with LiOH and urea hydrate which could surround the ICs at their surface. And the ICs were stiff, as revealed by results from transmission electron microscopy (TEM) and light scattering (LS). When there was a system fluctuation, the self-association of cellulose with each other took place, resulted from the destruction of the urea shell, and leading to the aggregation of the ICs. For that reason, the ICs stability could be evaluated by the aggregation behaviour. In our findings, the hydrodynamic radius (R_h,app) for the cellulose dispersion in dilute solution shifted to higher values with an increase of the temperature, the concentration or the storage time, indicating an IC aggregation phenomenon.     

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.     

Characterization of magnetic nanoparticle by dynamic light scattering

Here we provide a complete review on the use of dynamic light scattering (DLS) to study the size distribution and colloidal stability of magnetic nanoparticles (MNPs). The mathematical analysis involved in obtaining size information from the correlation function and the calculation of Z-average are introduced. Contributions from various variables, such as surface coating, size differences, and concentration of particles, are elaborated within the context of measurement data. Comparison with other sizing techniques, such as transmission electron microscopy and dark-field microscopy, revealed both the advantages and disadvantages of DLS in measuring the size of magnetic nanoparticles. The self-assembly process of MNP with anisotropic structure can also be monitored effectively by DLS.     

Phase separation in randomly charged polystyrene sulphonate ionomer solutions

The dynamics of randomly charged polystyrene caesium-sulfonate ionomers in semi-dilute solutions were studied using a combination of dynamic light scattering (DLS), small angle neutron scattering (SANS), and bulk rheology. The samples were studied in toluene solutions where the aggregation of the dipolar groups is favoured. Evidence of aggregation in dilute solution is found using DLS and SANS with both the hydrodynamic and static radius of gyration indicating that there is a contraction of the chains due to intra-chain attractive forces. SANS experiments demonstrate the evolution of the aggregates into a network structure as a function of polymer concentration. The association process is caused by the dipolar attraction between the charged groups and introduces two static correlation lengths in the mesh structure of the network; the standard semi-dilute mesh size (ξ=1.12c^{−0.72±0.03}) and an inhomogeneity length (Ξ=24c^0.58±0.05) due to micro-phase separation. The scaling of the amplitudes of the correlation lengths I₁(0)∼c^{−0.33±0.07} and I₂(0)∼c^2.0±0.4 are consistent with good solvent conditions and micro-phase separation, respectively. An imposed shear causes the break up of the micro-phase separated micellar system with a characteristic yield stress for the Bingham step-like shear thinning.