Rayleigh scattering from methane

Ackerson, Bruce J.; Straty, G. C.

doi:10.1063/1.436655

Cited by 34 publications

(45 citation statements)

References 21 publications

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“…Using both the Smoluchowski (33.1) and Langevin (33.2) approaches we derived a formal expression (3.13) for the time evolution of F(z) in a form which immediately lends itself to expansion in powers of the correlation delay time z. This result (3.13) has been obtained previously by several authors [31,32] who also pointed out the relevance of the adjoint Smoluchowski operator (equation (3.10)) in this context. In w 3.1 we also wrote down explicit expressions for the first two terms in the time series expansion of/;'(T); while the, term (3.17) was given by Zwanzig [31] some time ago, the z 2 term (3.18) appears to be new.…”

Section: Discussion and Summarysupporting

confidence: 64%

“…The z2 term in equation (3.24) has been discussed recently [11,40] for the case of a dilute suspension of ' hard-sphere' particles. In the simpler case where hydrodynamic interactions can be neglected, the first few terms in the power series expansions have also been used [41] to determine parameters in a memory function description of particle dynamics [32].…”

Section: Discussion and Summarymentioning

confidence: 99%

“…A more convenient procedure [31,32] is based on the use of the adjoint operator i, j = 1 r i OriJ J Or j" (3.10) (f'Of2) = --~ \Or, D~ (3.17) i,j=l Orj/ .=0 ~ (flO"fz)" (3.13) Note that such a short-time expansion is well-known in the theory of stochastic processes (see e.g.…”

Section: F(~) = ~ Dr N Drgfl(rg)fl(rn)exp[--~u(rg)]exp(o~) ~(R N-rg)mentioning

confidence: 99%

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Stochastic descriptions of the dynamics of interacting brownian particles

et al. 1986

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We review stochastic descriptions of the dynamics of colloidal particles, suspended in a liquid, which interact both directly and hydrodynamically. The equivalence of approaches based on Smoluchowski and Langevin equations is established. Particular attention is paid to the It6 and Stratonovich interpretations of stochastic differential equations with multiplicative noise. The short time behaviour of the correlation between two functions of particle position is discussed in some detail and compared with that found for a simple liquid. Finally the non-gaussian statistical properties of particle displacement are considered in the presence and absence of hydrodynamic interactions.

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Section: Discussion and Summarysupporting

confidence: 64%

Section: Discussion and Summarymentioning

confidence: 99%

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Stochastic descriptions of the dynamics of interacting brownian particles

et al. 1986

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“…After crossing the spinodal the diffusion coefficient becomes negative for small wave vectors, giving rise to spinodal decomposition. The following expression gives D in terms of the static structure factor S(k) and the hydrodynamic mobility function H(k): 15,16 where D 0 is the Stokes-Einstein diffusion coefficient. The static structure factor is given in eq 4, and the hydrodynamic mobility function is given by which is an ensemble average involving hydrodynamic interaction matrices D ij .…”

Section: Theorymentioning

confidence: 99%

“…The static structure factor is given in eq 4, and the hydrodynamic mobility function is given by which is an ensemble average involving hydrodynamic interaction matrices D ij . 15,16 Close to the spinodal this ensemble average is essentially an integral weighted by the total correlation function h(r), given by Without hydrodynamic interactions, the matrices D ij are simply given by in which δ ij is the Kronecker delta. Substituting this into eq 8, it follows that H(k) ) 1.…”

Section: Theorymentioning

confidence: 99%

Pretransitional Phenomena of a Colloid Polymer Mixture Studied with Static and Dynamic Light Scattering

1996

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A mixture of hard-sphere colloidal silica particles (radius 48 nm) and a nonadsorbing polymer (poly-(dimethylsiloxane), radius of gyration 23 nm) is studied by means of static and dynamic light scattering near the binodal. The spinodal is determined from an extrapolation of the diffusion coefficient as measured in the one-phase region, where it is essential to take the hydrodynamic interactions into account. The distance between the binodal and spinodal is small in the entire region so that it is difficult to locate the critical point accurately. The correlation length, measured with static light scattering, increases drastically on approaching the binodal. From these measurements the spinodal could be determined as well.For not yet understood reasons, there is a considerable discrepancy between the location of the spinodal as found from extrapolated dynamic and static light scattering data. I. IntroductionAttractive interactions between hard-sphere colloidal particles can be induced by adding nonadsorbing polymer. 1,2 This depletion-induced attraction can be tuned by the concentration and the size of the polymer. On increasing the attractive interactions, a phase separation will occur. The type of phase separation depends on the size ratio of the colloidal particles and the polymer. 3-10 Our interest in this article is focused on the experimental determination of the location of phase lines, relating to the gas-liquid transition (dilute and concentrated disordered phases).Light scattering studies, probing pretransitional phenomena, are performed to locate the spinodal. Although the spinodal cannot be measured directly, due to the existence of a metastable region between the binodal and spinodal, it is possible to measure quantities that change significantly in the stable region of the phase diagram due to the presence of the spinodal. The diffusion coefficient, for instance, vanishes at the spinodal. In the unstable region of the phase diagram, this diffusion coefficient is negative, giving rise to spinodal decomposition. This lowering of the diffusion coefficient in the vicinity of the spinodal is usually referred to as critical slowing down. In addition to a vanishing of the diffusion coefficient, the correlation length diverges at the spinodal, giving rise to critical opalescence. The correlation length is directly related to the small angle scattered intensity. 11 Phase separation into a dilute and a dense disordered colloidal phase is also found in adhesive hard-sphere suspensions. In addition, in adhesive hard-sphere suspensions a gel-line is found, 12,13 which seems to intersect with the critical point. 13 Such a gel-line is not observed in colloid polymer mixtures studied here, making the critical region better accessible for the study of critical phenomena. An essential difference between the two types of systems is that in colloid polymer mixtures the concentration of polymer sets the strength of the attractions, contrary to the adhesive hard-sphere system discussed in ref 13, where the temperature is...

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Hydrodynamic studies on benzethonium chloride micelles in dilute aqueous solution

Paradies

Hinze

Thies

1994

Ber Bunsenges Phys Chem

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Apparent micelle molecular weights, intrinsic viscosity, actual frictional coefficients and molal volumes have been determined for benzethonium chloride (BZCl) at 20°C in 0.01 M Tris-HCI, containing 0.01 M NaC1. The weight average molecular weight of BZCl was determined to 28000+ 1 500 by static light scattering, revealing an apparent aggregation number (ATapp) of 60-65. Average hydrodynamic dimensions of the BZCl micelle were obtained from measurements of sedimentation velocity, intrinsic viscosity and of the mutual diffusion coefficient above the CMC ( 8 . 4~ mol/l). By studying the autocorrelation function of light scattering of BZCl solutions above the CMC, the hydrodynamic and thermodynamic perturbations were determined. The dynamics of the micellar BZCl solutions are unperturbated by additions of polyhydric alcohols within the range of 10-40% (w/w). Above the CMC a classical hard-sphere behavior is derived from the volume fraction dependence of the scattered intensity for BZCI.The diffusivity data are consistent with a micellar hydrodynamic radius, R, of 25.5 A , with little or no growth of BZCl micelles upon increasing surfactant concentration evident between 0.01 M NaCl and 0.1 M NaCl at pH 7.5 (20°C).Applying the linear interaction theory we obtained theoretical fits to Dapp vs. BZCl concentrations over a region of low salt concentrations at pH 7.5 (20°C).

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Rayleigh scattering from methane

Cited by 34 publications

References 21 publications

Stochastic descriptions of the dynamics of interacting brownian particles

Stochastic descriptions of the dynamics of interacting brownian particles

Pretransitional Phenomena of a Colloid Polymer Mixture Studied with Static and Dynamic Light Scattering

Hydrodynamic studies on benzethonium chloride micelles in dilute aqueous solution

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