Order-parameter profile at long distances in an adsorbed binary liquid mixture near criticality

Schlossman, Mark L.; Wu, Xiao-Lun; Franck, Carl

doi:10.1103/physrevb.31.1478

Cited by 53 publications

(20 citation statements)

References 15 publications

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“…Experimental studies of CA in binary-liquid mixtures have been carried out mainly by optical methods, e.g. , ellipsometry [5 -7], reflectometry [8], and fluorescence measurements [9]. From the analyses of the fluorescence measurements, it was estimated that p/ v = 0.3 -0.6 [9].…”

Section: Probing the Universal Critical-adsorption Profile By Neutronmentioning

confidence: 99%

Probing the Universal Critical-Adsorption Profile by Neutron Reflectometry

et al. 1995

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We present the results of a neutron-reflectivity study of the universal critical-adsorption profile near the liquid-vapor interface of a binary-liquid mixture (methanol + deuterated cyclohexane) near criticality. As the critical temperature is approached from the one-phase region, we observed an abrupt decrease in the intensity of the specularly reflected neutron beam near the total-reflection edge. By interpreting the observation as the expected neutron-reflectivity discontinuity associated with a slowly decaying power-law profile, we evaluated the power-law exponent (p/v = 0.50~0.05). PACS numbers: 68.35.Rh, 61.12. -q, 68.10.Jy P(x) = Ppx~~' as x 0, P e ' asx~~, where P p and P are amplitudes. A recent field theoretical calculation of CA suggests Po = 0.94~0.05 [3]. The theoretically expected exponent for the 3D Ising model is P/v = (d -2 + il)/2 = 0.52, where il is a critical exponent and d is the dimension of space. Experimental studies of CA in binary-liquid mixtures have been carried out mainly by optical methods, e.g. , ellipsometry [5 -7], reflectometry [8], and fluorescence measurements [9]. From the analyses of the fluorescence measurements, it was estimated that p/ v = 0.3 -0.6 [9]. In addition, the optical reflectivity and ellipticity measurements yielded the exponents for the first moment of the concentration profile [8] and the adsorption excess amount [6]. Although the results of these studies seemed to agree with the scaling theory, to our knowledge no accurate determination of both the exponent and the After Fisher and de Gennes' original work on the scaling theory of critical adsorption (CA) [1], it is now generally accepted that [2], for systems belonging to the 3D Ising universality class near criticality, such asa binary-liquid mixture near its critical temperature T" the order parameter at a normal distance z from a planar interface deviates from its equilibrium bulk value according to the following scaling law:for z greater than a molecular length. Here t is the reduced temperature (T -T,)/T"mo and p are the amplitude and the critical exponent of the bulk twophase coexistence curve, respectively [3], $(t) is the bulk correlation length defined in the exponential form of the density-density correlation function, and diverges as g(t) = got near criticality. The order parameter is defined as the deviation of the volume fraction @(z) of the preferentially adsorbed component from its bulk value, i.e. , m(z) = @(z) -@(~). The scaling theory suggests that the universal scaling function P(x) should satisfy the following conditions [3,4]:(3) amplitudes from direct probing of the adsorption profile has been reported.Thus we set out to use neutron reflectometry [10], which in principle has nanometer resolution [11],to study CA. The purpose of this Letter is to demonstrate that, under certain conditions (see below), important profile information can be obtained from analyses of neutron-reAectivity data near the total reflection edge (TRE).The underlying physics in the new approach adopted in this work ...

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Section: Probing the Universal Critical-adsorption Profile By Neutronmentioning

confidence: 99%

Probing the Universal Critical-Adsorption Profile by Neutron Reflectometry

et al. 1995

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“…However, they are strictly only applicable in the one phase region because neither of these equations reduce to Eq. ͑6͒, applicable in the two phase region, in the limit of large x. Liu and Fisher found that the universal crossover length scale c + / P ϱ+ Ӎ 1.2 in the one phase region by comparison with the evanescent-wave reflectometry results of Schlossman et al 17 and ellipsometry results of Schmidt and Moldover. 14 Theoretical estimates for the actual functional form of P͑x͒ have been derived in three dimensions using renormalization group 22 ͑RG͒ ͑to first order in ⑀ =4−d͒, Monte Carlo simulations ͑MC͒, 23 and local functional theory.…”

Section: ͑7͒mentioning

confidence: 92%

“…͑2͒ and ͑3͒, stimulated a significant experimental effort using a variety of experimental techniques, including ellipsometry, 12-15 evanescent-wave reflectometry, 16,17 light scattering, 18 and volumetry 19 to elucidate the functional form of P͑x͒. Ellipsometry provides a direct measure of ⌫ ͑at least far from T c ͒, 20 while the other techniques provide other ͑integral͒ measures over P͑x͒.…”

Section: ͑7͒mentioning

confidence: 99%

“…Ellipsometry provides a direct measure of ⌫ ͑at least far from T c ͒, 20 while the other techniques provide other ͑integral͒ measures over P͑x͒. [16][17][18] The variation of P͑x͒ with x ͑which is hidden inside these universal integrals͒ can only be ascertained indirectly by getting sufficiently close to T c ͑t Շ 10 −3 ͒ where is sufficiently large so that, for the optical measurements, interference effects provide a nonlinear measure of P͑x͒ via a solution of Maxwell's equations.…”

Section: ͑7͒mentioning

confidence: 99%

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Comparison of critical adsorption scaling functions obtained from neutron reflectometry and ellipsometry

Brown

Law

Satija

et al. 2007

The Journal of Chemical Physics

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Carpenter et al. [Phys. Rev. E 59, 5655 (1999); 61, 532 (2000)] managed to explain ellipsometric critical adsorption data collected from the liquid-vapor interface of four different critical binary liquid mixtures near their demixing critical temperature using a single model. This was the first time a single universal function had been found which could quantitatively describe the surface critical behavior of many different mixtures. There have also been various attempts to investigate this surface critical behavior using neutron and x-ray reflectometries. Results have been mixed and have often been at variance with Carpenter et al. In this paper, the authors show that neutron reflectometry data collected from a crystalline quartz-critical mixture interface, specifically deuterated water plus 3-methylpyridine, can be quantitatively explained using the model of Carpenter et al. derived from ellipsometric data.

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“…But if these particles prefer to attract strongly one polymer of the crosslinked mixture near the spinodal temperature (critical adsorption [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]), one assists to their aggregation in the non-preferred phase. This colloidal flocculation is due to a long-ranged induced potential, called critical Casimir potential we want to compute.…”

Section: Introductionmentioning

confidence: 99%

Casimir Force between Nanoparticles Immersed in a Crosslinked Polymer Blend

Fassi¹,

Benhamou²,

Boughou³

et al. 2010

Acta Phys. Pol. A

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We consider a crosslinked polymer blend made of two polymers of different chemical nature. We suppose that such a system incorporates small colloidal particles, which prefer to be attracted by one polymer, close to the spinodal temperature. This is the so-called critical adsorption. As assumption, the particle diameter, d 0 , is considered to be small enough in comparison with the size of microdomains (mesh size) ξ * ∼ an 1/2 , with a -the monomer size and n -the number of monomers between consecutive crosslinks. The critical fluctuations of the crosslinked polymer mixture induce a pair-potential between particles located in the non-preferred phase. The purpose is the determination of the Casimir pair-potential, U2(r), as a function of the interparticle distance r. To achieve calculations, use is made of an extended de Gennes field theory that takes into account the colloid-polymer interactions. Within the framework of this theory, we first show that the pair-particle is attractive. Second, we find for this potential the exact form:, with the known universal amplitudes AH > 0 and BH > 0 (the Hamaker constants). This expression clearly shows that the pair-potential differs from its homologue with no crosslinks only by the two exponential factors exp(−r/ξ * ) and exp(−2r/ξ * ). The main conclusion is that the presence of reticulations reduces substantially the Casimir effect in crosslinked polymer blends.

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Order-parameter profile at long distances in an adsorbed binary liquid mixture near criticality

Cited by 53 publications

References 15 publications

Probing the Universal Critical-Adsorption Profile by Neutron Reflectometry

Probing the Universal Critical-Adsorption Profile by Neutron Reflectometry

Comparison of critical adsorption scaling functions obtained from neutron reflectometry and ellipsometry

Casimir Force between Nanoparticles Immersed in a Crosslinked Polymer Blend

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