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.     

The molecular weight average obtained by combining quasielastic light-scattering and intrinsic viscosity measurements

For “monodisperse”, randomly coiled macromolecules, we find that the molecular weight, intrinsic viscosity, and diffusion coefficient are accurately related by This equation holds for denatured proteins in 6M GuHCl(aq) as well as for narrow polystyrene fractions in tetrahydrofuran. For a Schulz distribution of molecular weights, the weight measured from combining diffusion and viscosity data is closely approximated by These equations are verified with measurements of wide molecular distributions of polystyrene in toluene and data from the literature. These relations provide a rapid, nondestructive method to determine a well-specified molecular weight average of small quantities of polymers in a wide diversity of solvents using quasielastic light scattering techniques to evaluate polymer diffusion coefficients.     

Low-angle laser light scattering from polystyrene solutions: intensity measurements and photon correlation spectroscopy

Light scattering measurements have been made on polystyrenes with a range of molecular weights in toluene and for one polystyrene with a range of molecular weights in toluene and for one polystyrene in a range of solvents including a theta solvent. Intensity data were used to calculate second virial coefficients and molecular weights, whilst photon correlation spectroscopy was used to calculate diffusion coefficients. All measurements were made at 30°C and at a scattering angle of ca.4°. The data were used to examine current theories of polymer diffusion and the relation between hydrodynamic radius (R_H) and radius of gyrations ($\text{〈s}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$). The results support accepted theories of polymer diffusion, but suggest that the relation between R_H and $\text{〈s}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ requires further analysis.     

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.     

Quasi-elastic light scattering: separability of effects of polydispersity and internal modes of motion

The influence of a size distribution on the angular dependence of the quasielastically scattered light is studied for (i) large hard spherical particles and (ii) large flexible chain molecules. For the spherical particles the angular dependence is shown to depend solely on the size distribution and the particle scattering factor. Combination of conventional elastic light scattering with quasielastic light scattering allows the determination of the z-average radii moments $\text{r}{}^{\mathrm{<mtext>n</mtext><mtext>?</mtext>}}{}_{\mathrm{z}}\text{(n = ?1, 1, 2, …)}$ which define the size distribution. Flexible chains — linear and branched ones — show in any case a linear dependence of the apparent diffusion constant $\text{D}{}_{\mathrm{app}}\text{=}\text{Г}\text{q}{}^2$ on $\text{q = (}\text{4π}\text{λ}\text{)}$ sin $\text{θ}\text{2}$, when q becomes large. This behaviour represents the flexibility of the spring-bead model with strong hydrodynamic interaction. The initial part on the other hand form a straight line when D_app is plotted against q². The intercept of this straight line is the z-average diffusion constant while the slope is proportional to the z-average mean square radius of gyration. Thus, the polydispersity can be estimated from D_z and 〈S²〉_z while the asymptote at large q-values is determined by the internal flexibility of the molecule.     

Influence of temperature,molecular weight,and polydispersity of polystyrene on interfacial tension between low‐density polyethylene and polystyrene

In this work, the influence of temperature, molecular weight, and polydispersity of polystyrene on interfacial tension between low‐density polyethylene (LDPE) and polystyrene (PS) was evaluated using the pendant drop method. It was shown that interfacial tension between LDPE and PS decreases with increasing temperature for all LDPE–PS pairs studied. The temperature coefficient (∂γ/∂T) (where λ is interfacial tension and T is temperature) was higher for lower molecular weight and larger polydispersity of PS. The interfacial tension between LDPE and PS at a temperature of 202°C increased when the molecular weight of polystyrene was varied from 13,000 to 30,000. When the molecular weight of PS was further increased, the interfacial tension was shown to level off. The effect of polydispersity on interfacial tension between PS and LDPE, at a temperature of 202°C, was studied using PS with a constant‐number average molecular weight and varying polydispersity. The interfacial tension was shown to decrease with increasing polydispersity. However, the influence of polydispersity was lower for PS of higher molecular weight. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 2423–2431, 1999     

Molecular weight distributions of standard polystyrene samples by GPC and by sedimentation velocity analysis

In precision gel permeation chromatographic (GPC) work, the spreading (zone spreading) characteristics of the instrument must be calibrated. Standard samples of anionic polystyrene have been used for this purpose. The molecular weight distributions of these standard samples, nevertheless, have not been determined carefully. In this work, several standard polystyrene samples obtained from Pressure Chemical Company were examined by GPC and by sedimentation velocity analysis. The results show that (1) the high molecular weight polystyrene samples have skewed molecular weight distributions as has been suspected and that (2) the present data treatment technique for GPC is effective for these very narrow-distribution samples.     

Synthesis and characterization of the narrow polydispersity fullerene-end-capped polystyrene

Summary A living free radical polymerization process was adopted to synthesize a narrow polydispersity fullerene-end-capped polystyrene(NPFECPS). The UV-Vis, DSC, GPC demonstrated that fullerene(C₆₀) was chemically bonded to polystyrene successfully, and C₆₀ was almost monosubstituted. The NPFECPS can be dissolved in a variety of solvents, such as THF, toluene, trichloromethane, and so on. The good photoconductivity is also found for NPFECPS.     

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.     

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.     

Molecular weight dependency of refractive index increment of polystyrene determined by uniform oligomers

Molecular weight dependency of a specific UV absorption coefficient of polystyrene in solution was determined by supercritical fluid chromatography applied to equimolar and equimass mixtures of uniform polystyrenes whose degree of polymerization was n = 1 to 40. From the ratio between the response from a UV detector and that from a refractometer, we determined the refractive index increment dn/dc as a function of molecular weight for polystyrene in tetrahydrofuran at the wavelength λ = 633 nm. We found that dn/dc is well expressed as a linear function of the reciprocal of molecular weight for uniform polystyrenes. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 1101–1106, 2004     

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.     

Kinetics of polycondensation of urea with formaldehyde. Molecular weight distribution,average molecular weight,and polydispersity parameters

The molecular weight distribution, molecular weight averages M _n, M _w, M _z, polydisperisty coefficient, statistic standard deviation of number and weight distribution, and Hoseman–Schramek index of the polycondensates of urea with formaldehyde have been estimated. The properties of this solution were obtained by the help of the combination of the following methods: GPC, VPO, turbidimetric titration, and fractional precipitation. The course of the polycondensation described was formally divided in the following stages: (1) formation of methylolated urea derivates and of the lowest oligomers, (2) decrease in the content of methylol urea and in the content of the lowest oligomers with M < 200, and production of soluble molecules between 10³ and 10⁴, and (3) formation of insoluble products.     

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%.     

Magnetic birefringence of polystyrene sulphonate: Molecular weight and concentration dependence

The specific Cotton-Mouton constant of water solutions of PSS-Na⁺ of different molecular weight have been measured at concentrations below 2% in the absence and presence of added salt. A bare persistence length q=12 Å is found from the high ionic-strength molecular weight and concentration independent value. The molecular weight and concentration dependence at low ionic-strength is discussed in terms of the electrostatic contribution to the persistence length and the structure of semidilute polyelectrolyte solutions.     

Static and dynamic light scattering from polystyrene/cyclohexane/toluene solutions

Summary Static and dynamic light scattering data from polystyrene in cyclohexane and toluene mixed solvent are reported. It is found from the Zimm plot analysis of the static data that if the subtraction of solvent signal is made properly then, the results are consistent with those in toluene indicating a preferential adsorption of the good solvent. Contin analysis of the dynamic data yields two modes unlike the dynamics of polystyrene in single solvent solutions which exhibit a single mode at all polymer concentrations covered here. A possible interpretation of the fast and slow modes is given. Keywords: Mixed Solvent; Dilute Polymer Solution; Preferential Adsorption; Static and Dynamic Light Scattering; Relaxation Modes. Received: 28 May 1999/Accepted: 8 September 1999     

Molecular weight distribution in a polymer film degraded by light

An explicit expression is derived for the weight distribution function of polymer molecules in a photodegraded film. A most probable weight distribution of linear molecules is assumed initially present; normally incident, monochromatic light obeying a single Beer-Lambert absorption relation is the photolyzing radiation. The dependence of the weight distribution upon the film's optical thickness and the integrated incident light flux is illustrated by curves computed according to the derived functions. Predicted gel permeation chromatograms are indicated.     

Molecular weight and molecular weight distribution from dynamic measurements of polymer melts

A method for determining the molecular weight distribution (MWD) of a polymer melt has been developed using the dynamic elastic modulus (G'), plateau modulus (G), and zero shear complex viscosity (η). The cumulative MWD was found to be proportional to a plot of (G'/G)^0.5 vs. measurement frequency (ω). Frequency (ω) was found to be inversely proportional to (MW)^3.4, as expected. Results were scaled to absolute values using the empirical relationship η ∝ (M?_w)^3.4, where M?_w is the weight-average MW. M?_w, M?_n (number-average MW) and M?_w/M?_n calculated from melt measurements were found to agree with size exclusion chromatography usually well within 10 percent for broad and bimodal distribution samples. M?_w/M?_n tended to be approximately 20 percent higher for narrow distribution samples (M?_w/M?_n < 1.2) because we did not account for a finite distribution of relaxation times from a collection of monodisperse polymer chains. We also did not account for the plasticizing effect of short chains mixed with long ones which caused peak positions to be closer together for Theological vs, size exclusive chromatography (SEC) determinations of MW for bimodal distribution blends.     

A study of mass transport of linear polystyrene in polyethyl methacrylate gel by dynamic light scattering

Mass [i.e., linear polystyrene (PS) probe] transports in polyethyl methacrylate (PEMA) gels with ethylene dimethacrylate (EDMA) as crosslinker were studied by dynamic light scattering (DLS). For PEMA gels in toluene, we have established that it is a very well matched system, so that it is very convenient to study the mass transport of the PS macromolecule in such a system. Experiments show that the obstruction effects of PEMA gels for the mass transport of PS are obvious. Reasonably, the lower the gel obstruction for mass transport, the higher the diffusion coefficient D_t of PS in gel. Moreover, the larger the molecular weight of PS, the greater the obstruction effect of the gel. Furthermore, we traced quantitatively the evolution of D_t of PS during the crosslinking copolymerization of PEMA. The results show that, after the reaction, the obstacle for mass transport in the gel develops gradually. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 2062–2066, 2002     

Dynamic light scattering studies on random cross-linking of polystyrene in semi-dilute solution

The random cross-linking of appropriately functionalized polystyrene in semi-dilute toluene solution (c = 0.01–0.05 g/mL) was studied by time-dependent measurements of dynamic light scattering. Macroscopic gelation occurred from concentrations as low as 0.02 g/mL. The gelation time, determined from the first appearance of fluctuations of the scattering intensity and the initial amplitude of the intensity correlation function (ICF), decreases markedly from about 100 min to 10 min with an increase of polymer concentration or cross-linker content. After the gel point, the ICFs display a characteristic power-law decay. The power-law exponent, n = 0.75 ± 0.06, does not change with (i) extent of reaction, (ii) polymer concentration, and (iii) cross-linker concentration, within the inspected ranges. This universal behavior is traced back to the fact that gelation took place as a result of random cross-linking of existent macromolecules, whose state of solution does not change markedly during conversion.