Dynamic and static light scattering by weakly ionized gels and solutions

Dynamic light scattering (DLS) and static light scattering (SLS) experiments have been performed on partially neutralized poly(acrylic acid) and poly(methacrylic acid) solutions and gels. The gels exhibit a non-ergodic behavior, much less marked however than that observed in neutral systems. By combining DLS and SLS, the fluctuating part of the light scattered from PAA gel was separated from the total scattered intensity and found to be almost equal to the intensity scattered by the solution. Also the diffusion coefficient associated with the dynamic fluctuation was found to be the same in the PAA gel and the PAA solution.     

Dynamic light scattering by optically anisotropic colloidal particles in polyacrylamide gels

The translational and rotational motions of optically anisotropic spherical particles embedded in cross-linked polyacrylamide gels is studied by dynamic light scattering. The particles are liquid crystal droplets solidified in the nematic phase. The amount of cross linkers is varied to cross the sol-gel transition where the system becomes nonergodic for both translational and rotational diffusion modes of the probes. The translational and rotational dynamic correlation functions are obtained by measuring the intensity correlation function between crossed polarizers in the parallel and perpendicular geometries. Data from nonergodic systems is analyzed using an extension, to include rotations, of the method of Pusey and van Megen [Physica A 157, 705 (1989)]. Both diffusion modes are observed to be arrested as the rigidity of the gel increases.     

Dynamic light scattering by permanent gels: Partial heterodyne and nonergodic medium methods for data evaluation

Four relationships between the intensity and field correlation functions have been used in the analysis of the measured intensity correlation function in dynamic light scattering for four different polymer gel samples. The evaluation of diffusion coefficients was performed using inverse Laplace transformation (ILT) and the cumulante method, respectively. The diffusion coefficients derived from the nonergodic medium method are almost the same as those from the partial heterodyne method when ILT is used. ILT can give similar results by all four procedures even when large baselines for the nonergodic medium method exist. The cumulants method leads to incorrect diffusion coefficients from the correlation functions derived using the nonergodic medium method.     

Theory of dynamic light scattering by polymers and gels

It is shown under very general conditions that the intermediate scattering function for the generalized Rouse—Zimm model always takes the simple form G(K, t) α exp[?K²(k_BT/f)t], when the scattering vector K becomes sufficiently large. (Here k_B is Boltzmann's constant, T is the absolute temperature and f is the individual bead friction factor.) A microscopic formulation for the bulk modulus and friction factor density of a gel network is incorporated into the viscoelastic continuum model of Tanaka et al. The resulting expression for the apparent long-wavelength diffusion coefficient of the gel is D_G = (k_BT/f)2(1 - 2/Φ), where Φ is the network functionality.     

Low-angle light scattering of ionotropic gels

Low-angle light-scattering patterns were obtained on ionotropic gels formed by the diffusion of Ca⁺⁺ into a polygalacturonate sol. Near the sol–gel boundary, diffraction patterns were obtained which indicated organized structures with repeating units of 1100, 250, and 12.5 μ. Microscopic investigations confirmed that at this gel boundary capillaries run parallel to each other and perpendicular to the direction of diffusion. The diameter of capillaries was 12 μ while their length was in the 1000 μ range. Short interconnecting capillaries were about 200–300 μ in length. Inside the gel, in the more highly crosslinked parts, a disorientation occurs during the aging process with the partial disappearance of capillaries. However, at the gel–sol and gel–semipermeable membrane boundaries, the highly organized structures remain even during prolonged aging. The kinetics of the gel formation was also investigated.     

Comparison between neutron and quasielastic light scattering by polyacrylamide gels

The authors describe small-angle neutron scattering measurements of the screening length ζ in polyacrylamide-water gels. Although these are inhomogeneous systems, the screening length is clearly observable and is in good numerical agreement with the relation E = 3kT/4πζ³, where E is the longitudinal elastic modulus of the gel obtained from measurements of the intensity of qu-asielastically scattered light. Static light scattering observations reveal a larger-scale (ca. 30 nm) superstructure in the gel.     

Dynamic fluctuations and spatial inhomogeneities in poly(N-isopropylacrylamide)/clay nanocomposite hydrogels studied by dynamic light scattering

The contributions of the dynamic fluctuations and the frozen-in inhomogeneities to the total light scattering intensity observed in poly(N-isopropylacrylamide)/clay nanocomposite hydrogels were analyzed by applying the nonergodic method proposed by Pusey and van Megen. Approximately 90% of the total scattering intensity corresponds to the frozen-in component. The scattering intensity of the fluctuating component is smaller by far than that of a pure clay suspension, indicating that the thermal fluctuations of the clay particles are largely suppressed upon network formation. Accordingly, the fluctuating component consists of two contributions: one due to the polymer chains and the other, smaller one representing the residual mobility of the clay particles. The latter depends on how tightly the clay particles are fixed in the network. The dynamic features of the nanocomposite hydrogels are described by two relaxation modes. The fast one is purely diffusive and can be related to a dynamic correlation length of 6-8 nm, which is similar to that of a corresponding polymer solution. The relaxation time of the slow mode varies appreciably with sample position even though the data had been treated with the nonergodic method.     

Dynamic light scattering by polyelectrolyte solutions

A generalized expression for the apparent diffusion coefficient (D_app) for macroions as a function of scattering vector (q) is developed. Mathematica®, a system of doing mathematics on a computer, was used to obtain the eigenvalues for a select set of polyion-electrolyte systems. It is shown that under the conditions of low electrolyte concentration D_app exhibits a marked q-dependence. The second part of this communication focuses on the so-called “ordinary-extraordinary” transition observed in some polyelectrolyte systems. The characteristic D_app versus electrolyte profile for this transition is compared with the “splitting” of relaxation times reported for many other polyelectrolyte systems. General problems associated with dynamic light scattering studies on macroion systems are discussed.     

Dynamic light scattering by non-ergodic media

The theory of dynamic light scattering (DLS) by non-ergodic media, systems such as polymeric gels whose density fluctuations are partially “frozen”, is discussed. We derive the relationship between the time-averaged time correlation function of the scattered intensity, the quantity measured in a single DLS experiment, and the ensemble-averaged correlation function of the sample's density fluctuations. The connection between DLS, speckle and the reciprocal-space structure of the medium is also discussed.     

Laser light scattering study of polyacrylamide gels

Laser light scattering experiments with polyacrylamide gels containing diffusing bovine plasma albumin are described. Complete heterodyne beating has not been assumed, and an account is given of a novel method for finding the degree of spectral broadening by scanning angles of scatter while measuring the temporal autocorrelation function. Results obtained by this method for polyacrylamide gels and un-cross-linked solutions in the absence of diffusing protein, are compared with those of other authors. In the presence of the protein there is a complex interaction between the diffusion coefficient of the protein and the coefficient associated with the diffusing fluctuations in segment density of polyacrylamide. The diffusing protein dominates at low gel concentrations, and the gel density fluctuations dominates at high gel concentrations. It is proposed that the protein preferentially occupies the less dense regions of the gel, so that at low gel concentrations, where it diffuses faster than the gel fluctuations, it tends to cancel them out, whereas at high gel concentrations where the protein is highly impeded by the gel structure, it tends to be carried along by the gel density fluctuations.     

Scattering structure factor of colloidal gels characterized by static light scattering, small-angle light scattering, and small-angle neutron scattering measurements

The scattering structure factor of a colloidal gel in a q range of 5 orders of magnitude has been determined by combining static light scattering, small-angle light scattering, and neutron scattering measurements. It exhibits simultaneously two types of structure information: a mass fractal scaling within the clusters that constitute the gel and a surface fractal scaling for length scales larger than that of the clusters. Such scattering behavior can be well interpreted by the pair-correlation function proposed in the literature to model an ideal structure constituted of mass fractal objects inside surface fractal objects.     

Dynamic light scattering studies of ionic and nonionic polymer gels with continuous and discontinuous volume transitions

We have performed dynamic light scattering experiments on poly(acrylamide)‐poly(acrylic acid) copolymer gels with controlled crosslink density and copolymer composition, by varying the temperature, amount and valency of added salt, pH, and solvent quality. Our systematic study provides several insights. The correlation length for the monomer density fluctuations, as inferred from the measured diffusion coefficient, is too small to be identified as the mesh size of the gel. The correlation length in an ionic gel, which is found to be smaller than that for an equivalent gel without ionization. Comparison of swelling ratio with the diffusion coefficient shows that these quantities are not simply geometrically related to each other. When a discontinuous volume phase transition is induced by gradually varying the solvent quality, the diffusion coefficient exhibits a pretransitional reduction by two orders of magnitude even before the gel collapse. These findings provoke a need for new theoretical approaches for describing the elastic modes of polyelectrolyte gels. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Quasielastic light scattering study of chemically crosslinked gelatin solutions and gels

Quasielastic light scattering measurements are reported for experiments performed on mixtures of gelatin and glutaraldehyde (GA) in the aqueous phase, where the gelatin concentration was fixed at 5 (w/v) and the GA concentration was varied from 1×10⁻⁵ to 1×10⁻³ (w/v). The dynamic structure factor, S(q,t), was deduced from the measured intensity autocorrelation function, g ₂(τ), with appropriate allowance for heterodyning detection in the gel phase. The S(q,t) data could be fitted to S(q,t)=Aexp(−D _f q ² t)+Bexp(−t/τ_c)^β, both in the sol (50 and 60 ^∘C) and gel states (25 and 40 ^∘C). The fast-mode diffusion coefficient, D _f showed almost negligible dependence on the concentration of the crosslinker GA; however, the resultant mesh size, ξ, of the crosslinked network exhibited strong temperature dependence, ξ∼(0.5−χ)^1/5exp(−A/RT) implying shrinkage of the network as the gel phase was approached. The slow-mode relaxation was characterized by the stretched exponential factor exp(−t/τ_c)^β. β was found to be independent of GA concentration but strongly dependent on the temperature as β=β₀+β₁ T+β₂ T ². The slow-mode relaxation time, τ_c, exhibited a maximum GA concentration dependence in the gel phase and at a given temperature we found τ_c(c)=τ₀+τ₁ c+τ₂ c ². Our results agree with the predictions of the Zimm model in the gel case but differ significantly for the sol state. Received: 25 May 1999 /Accepted in revised form: 27 July 1999     

Dynamic light scattering from spherical particles

The dynamic light scattering behavior of poly(butylmethacrylate) PBMA microgels and of kappa-casein micelles is compared with that from hard sphere latex particles. The latex particles and the kappa-casein micelles exhibited a single exponential decay of the time correlation function (TCF). For the microgels, progessively stronger deviations from a single exponential were observed as the scattering angle was made larger. These deviations are interpreted as being the result of internal modes of motion. From measurement of the first cumulant of the TCF, extrapolated towards zero angle, the translational diffusion coefficients D were determined, and the hydrodynamically effective radii were calculated via the Stokes-Einstein relationship. The ratio of the radius of gyration to the hydrodynamic radius was found to be?=0.775+0.012 for the latex particles, in good agreement with theory. The microgels, however, exhibit much lower?-parameters of 0.49 to 0.58, while the kappa-casein micelles showed the opposite behavior with values between 1.1 and 2.5. The results are interpreted on the basis of the DebyeBueche and Deutsch-Felderhof theory for porous spheres.     

Brillouin light scattering from poly(vinyl chloride) gels

The hypersonic velocity and attenuation in PVC gels have been measured as a function of gel network volume fraction, using the technique of Brillouin light scattering. The experimental data have been analysed using the full theory for the elastodynamics of gels proposed recently by Johnson. It has been found that for two asymptotic approximations of the dynamic damping factor the tortuosity parameter is nearly always less than unity, contrary to the theoretical expectation.     

Dynamic light scattering for characterization of latices

With photon correlation spectrometry the diffusion coefficients of colloid particles in highly diluted aqueous suspensions can be measured and average diameters and polydispersities of the samples can be determined. Electrokinetic and electroviscous effects caused by polarization of the electrostatic double layer influence the diffusion of the particles. The adsorption of macromolecules at the interfaces of the particles results in an increase of the hydrodynamic diameter and a decrease of the diffusion and sedimentation coefficients. The hydrodynamic thicknesses of the polymer layers can be evaluated. The thickness values and their dependences on adsorbed amount and molar mass can only be interpreted by the existence of long tails of the adsorbed macromolecules dangling from the interface into the solution. The resulting conformation model is supported by the new theory of Scheutjens-Fleer. Special importance have those tails for the interaction of particles and their stability and flocculation in disperse systems.     

Physical gels from PVC: molecular structure of pregels and gels by low-angle neutron scattering

In this paper we report on investigations into the short-range molecular structure of pregels (aggregates formed in dilute solutions) and gels as a function of ageing time, temperature and solvent type. In some solvents (diethyl oxalate and bromobenzene) it is found that the structure of the pregels is cylinder-like or ellipsoid-like. The structure is seen to be the same for the gels and the pregels in the investigated range of transfer momentum which leads us to conclude that the gels are probably fiber-like, a statement in agreement with the morphology observed by Yang and Geil. The fiber section is also about the same order of magnitude as that reported by these authors. Also, further evidence is given for the existence of a second type of physical knot, different from those formed by the more syndiotactic sequences. The validity of the molecular structures deduced from these experiments is discussed in the light of macroscopic properties such as compression modulus and swelling.     

Dynamic light scattering method of polymer solutions

The main features of dynamic light scattering are briefly outlined. The capability of this method to characterizing molar mass distributions and to distinguishing different molecular architectures is demonstrated with some examples. Special attention is given to the question of internal mobility and the spectrum of relaxation times. Recent results on asymptotic behavior are presented and discussed. Scaling behavior of the first cumulant with respect of space and of the time correlation function with respect of time (shape function) is found. All examples studied so far demonstrate the dynamic scaling of Zimm-Rouse chains, but the prefactors strongly depend on branching and crosslinking.     

Correction factors for sizing weakly anisotropic transparent fibers using light scattering

Correction factors defined as the ratio of the true size parameter and the size parameter deduced from Fraunhofer diffraction theory are presented for weakly anisotropic transparent fibers. These correction factors enable the Fraunhofer diffraction approximation to be used for sizing weakly anisotropic fibers from light-scattering measurements. Fibers in the diameter range 4–50 μm and refractive index range 1.45–1.56 are considered. It is shown that for fibers having birefringence ?0.005 ≤ Δm ≤ 0.01, the diameters may be obtained to within 9% accuracy if the fiber diameter lies between 4 and 50 μm.