Foundations of the fluctuation theory of adsorption on microcrystalline particles

Tovbin, Yu. K.

doi:10.1134/s1990793110060229

Cited by 14 publications

(9 citation statements)

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“…Goal (a) will be achieved based on recent progress on the statistical thermodynamics of fluctuation. 10,13,[22][23][24][25][26] Unlike the previous approach, which proposed to evaluate higher order moments of correlation from adsorption, [27][28][29][30][31][32] our goal (b) is to elucidate the adsorbate-adsorbate interaction from an isotherm by extending KBIs applicable to surfaces. A previous attempt to apply KBIs to a surface structure was limited to liquid-vapour mixtures, which required experimental parameters on the solution surface structure.…”

Section: Introductionmentioning

confidence: 99%

Fluctuation adsorption theory: quantifying adsorbate–adsorbate interaction and interfacial phase transition from an isotherm

Shimizu

Matubayasi

2020

Phys. Chem. Chem. Phys.

247

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Section: Introductionmentioning

confidence: 99%

Fluctuation adsorption theory: quantifying adsorbate–adsorbate interaction and interfacial phase transition from an isotherm

Shimizu

Matubayasi

2020

Phys. Chem. Chem. Phys.

247

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“…9 shows the adsorption capacity variation of 5%CS-fMWCNT-HAP and 5%CS-fMWCNT-HAPSi at pH ¼ 7.5 and 0.5 g/l BSA concentration during the adsorption process. During the measurements the adsorption capacity showed a fluctuation caused by the "competition" between adsorption and desorption until the equilibrium was reached; this is a characteristic adsorption behaviour of nanomaterials and this phenomenon was reported and modelled by Tovbin et al [61]. The adsorption capacity variation during the measurement process for these composites was very similar.…”

Section: Adsorption Measurementsmentioning

confidence: 81%

Albumin adsorption study onto hydroxyapatite-multiwall carbon nanotube based composites

Czikó

Bogya

Paizs

et al. 2016

Materials Chemistry and Physics

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“…Let us find the conditions minimizing lnР({N q , N qp }) depending on independent variables Х (=N q , N qp , N qp ) and the second derivatives of lnP charac terizing the dispersion matrix of the Р({N q , N qp }) distribu tion function. For small sized particles, we must use symmetrical difference derivatives instead of usual differ ential derivatives [2,3]. The , = 0 extremum condition gives an equation for a local iso therm of adsorption, which relates the chemical potential of the system (μ q = μ + β -1 ln(J q )) determined by the thermostat to the number of molecules on each face N q (or the local filling degree θ q = N q /M q ),…”

Section: The Inclusion Of Density Fluctuations In the Theory Of Adsormentioning

confidence: 99%

“…For microcrystals, such studies are at the beginning stage. It was shown in [2][3][4][5] that density fluctuation effects become important for adsorption on small sized crystalline particles, and their role is fairly noticeable for nonuniform surfaces. The influ ence of intermolecular interactions on adsorption iso therms has currently been considered in the mean field approximation only [3,[6][7][8][9].…”

mentioning

confidence: 98%

“…It was shown in [2-5] that density fluctuation effects become important for adsorption on small sized crystalline particles, and their role is fairly noticeable for nonuniform surfaces. The influ ence of intermolecular interactions on adsorption iso therms has currently been considered in the mean field approximation only [3,[6][7][8][9]. This approximation fairly roughly described intermolecular interactions, and, in this work, more exact equations were con structed for taking interactions of molecules into account in the quasi chemical approximation describ ing direct correlations between molecules.…”

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confidence: 99%

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The inclusion of density fluctuations in the theory of adsorption of laterally interacting molecules on microcrystalline particles

Tovbin

2012

Russ. J. Phys. Chem.

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The theory of adsorption of macroscopic systems on nonuniform surfaces has been developed in consid erable detail using the lattice gas model (LGM) [1]. Lateral interactions between adsorbed molecules and surface nonuniformity strongly influence equilibrium adsorption characteristics (isotherms and heats of adsorption). For microcrystals, such studies are at the beginning stage. It was shown in [2-5] that density fluctuation effects become important for adsorption on small sized crystalline particles, and their role is fairly noticeable for nonuniform surfaces. The influ ence of intermolecular interactions on adsorption iso therms has currently been considered in the mean field approximation only [3,[6][7][8][9]. This approximation fairly roughly described intermolecular interactions, and, in this work, more exact equations were con structed for taking interactions of molecules into account in the quasi chemical approximation describ ing direct correlations between molecules.Let us consider a nonuniform crystal surface and describe adsorption using the LGM. We will analyze the distribution of molecules in a grand canonical ensemble (μ, М, T), where μ is the chemical potential of molecules in the volume phase; М is the total num ber of surface nodes consisting of regions with size M q ,; and t is the number of node types on the surface of a microcrystal. Each node can be either occupied or free. Let N q be the number of adsorbed molecules on nodes of type q. The number of free nodes of type q will be denoted byThe mean number of pairs of nodes of different types qp will be denoted by M qp . Pairs of nodes of dif ferent types are related as , where z q is the number of neighbors of a node of type q, and prime at the sum sign means the absence of the term with p = q, 1 ≤ p ≤ t. Let z qp be the number of nodes of type p neighboring nodes of type q. These numbers char acterize the local structure of a nonuniform surface. Their relation to the numbers of node pairs M qp of the qp type can be written as = or = , where is the Kronecker symbol. The total balance of pairs of nodes is written in the form of two sums, + .Let J q be the partition function of a particle in a node of type q, 1 ≤ q ≤ t, and J the partition function of a molecule in the gas phase. The other denotations are: μ = β -1 ln(βP/J), β = (kT) -1 , P is the gas phase pres sure, and ε q is the bond energy between a particle and a node of type q on the surface of the adsorbent. Lat eral interaction parameters ε qp depend on the type of the qp pair, 1 ≤ q, р ≤ t, on which two neighboring mol ecules are adsorbed.The equation for the partition function of a non uniform system in the quasi chemical approximation with taking into account interaction between the near est neighbors only is written as , where, .1 ' 2 t qp qq q q p M M z M = + = ∑ qp z / (1 ) qp qp q M M + Δ qp M /(1 ) qp q qp z M + Δ qp Δ 1 t qq q M = ∑ * 1 t qp qp M = ∑ 1 2 Q Q Q = , 1 , 0 1 q q q q q q t M M qq N N q Q Q = = = ∑ ∏ * 2 0 1 qp qp t M qp N qp Q Q = = = ∑ ∏ Abstract-Equations for the...

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Foundations of the fluctuation theory of adsorption on microcrystalline particles

Cited by 14 publications

References 2 publications

Fluctuation adsorption theory: quantifying adsorbate–adsorbate interaction and interfacial phase transition from an isotherm

Fluctuation adsorption theory: quantifying adsorbate–adsorbate interaction and interfacial phase transition from an isotherm

Albumin adsorption study onto hydroxyapatite-multiwall carbon nanotube based composites

The inclusion of density fluctuations in the theory of adsorption of laterally interacting molecules on microcrystalline particles

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