Size-Dependent Thermodynamics and Kinetics of Adsorption on

Article Cite This: Langmuir XXXX, XXX, XXX−XXX

pubs.acs.org/Langmuir

Size-Dependent Thermodynamics and Kinetics of Adsorption on Nanoparticles: A Theoretical and Experimental Study Zixiang Cui, Juan Zhang, Yongqiang Xue,* and Huijuan Duan Department of Applied Chemistry, Taiyuan University of Technology, 030024 Taiyuan, China ABSTRACT: Owing to their excellent adsorption properties compared with those of the corresponding bulk materials, nanoparticles have been widely applied in many fields. Their properties depend on the thermodynamics and kinetics of adsorption, which depend on the particle size. In this paper, we present universal theories of the thermodynamics and kinetics for nanoadsorption that have been developed over the past few years. Theoretically, we have derived relationships between the adsorption thermodynamic properties and the particle size, as well as those between the adsorption kinetic parameters and the particle size. Moreover, we discuss the regularities and mechanisms of influence of the particle size on the thermodynamics and kinetics of adsorption. Experimentally, taking the adsorption of methyl orange on nano-CeO2 in aqueous solution as a system, we have studied the size-dependent thermodynamics and kinetics of the system, and the size dependences were confirmed to be consistent with the theoretical relationships. The results indicate that particle size has a significant effect on the thermodynamic properties and kinetic parameters of adsorption: with decreasing particle size of nano-CeO2, the adsorption equilibrium constant K⊖ and the adsorption ⊖ rate constant k increase, while the molar Gibbs free energy of adsorption ΔadsG⊖ m , the molar adsorption entropy ΔadsSm , the molar adsorption enthalpy ΔadsH⊖ , the adsorption activation energy E , and the adsorption pre-exponential factor A all decrease. m a ⊖ ⊖ Indeed, ln K⊖, ΔadsG⊖ m , ΔadsSm , ΔadsHm , ln k, Ea, and ln A are each linearly related to the reciprocal of particle size. Furthermore, ⊖ ⊖ thermodynamically, ΔadsG⊖ m and ln K are influenced by the molar surface area and the difference in surface tensions, ΔadsSm is influenced by the molar surface area and the difference in temperature coefficients of surface tension, and ΔadsH⊖ is influenced by m the molar surface area, the difference in surface tensions, and the difference in temperature coefficients of surface tension. Kinetically, Ea is influenced by the partial molar surface enthalpy of the nanoadsorbent, ln A is influenced by the partial molar surface entropy, and ln k is influenced by the partial molar surface Gibbs energy. The theories can quantitatively describe adsorption behavior on nanoparticles, explain the regularities and mechanisms of influence of particle size, and provide guidance for the research and application of nanoadsorption. et al.19 established that the adsorption energy for the adsorption of CO on Au nanoparticles decreased with decreasing particle size. In theoretical studies, Lu et al.20 and Zhang et al.21 derived the relationship between the adsorption equilibrium constants of two different particle sizes and concluded that this parameter increased with decreasing particle size, but the precise effect regularities of particle size on adsorption thermodynamic properties remained unclear. Previously, our group developed the size-dependent thermodynamics of nanoadsorption to understand the general adsorption regularities.22 However, the definitions of the chemical potentials of the surface phases of both the nanoparticles28 and the adsorption product are not exact, and the standard state of chemical potential of adsorption product is defined as the saturated state, such that the thermodynamic equations derived

1. INTRODUCTION Nanoparticles have excellent adsorption properties compared with the corresponding bulk materials.1 For example, for the adsorption of monocarboxylic acids and dicarboxylic acids on nano-TiO2, the adsorption equilibrium constant of a 6 nm particle is 60 times larger than that of a 16 nm particle.2 Nanoparticles have been widely applied in hydrometallurgy,3,4 catalysis,5,6 sewage treatment, and air purification.7 Their sizedependent adsorption properties will clearly relate to their sizedependent catalytic performances.8,9 Thus, understanding how size affects their adsorption properties is a hot topic in nanoadsorption research.10−13 The excellent adsorption properties depend on the thermodynamics and kinetics of adsorption on nanoparticles. With regard to thermodynamics, numerous studies have been carried out to determine adsorption capacities, which have shown that with decreasing particle size, the adsorption capacity of nanoparticles increases significantly.14−18 However, there have only been a few studies on the effect of size on the adsorption thermodynamic properties of nanoparticles. Pursell © XXXX American Chemical Society

Received: November 30, 2017 Revised: February 4, 2018 Published: February 19, 2018 A

DOI: 10.1021/acs.langmuir.7b04097 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir Thus, eq 3 can be expressed as

are only applicable to the saturated state. Thus, we have sought to solve these problems in this study. In terms of kinetics, as mentioned in previous reports, with decreasing particle size, the adsorption rate increases,23,24 the adsorption rate constant increases,25 the adsorption activation energy decreases,26 and the adsorption pre-exponential factor decreases.27 However, quantitative regularities concerning the effect of particle size on the kinetic parameters of adsorption are not fully clear. Our group has studied the relationships between adsorption kinetic parameters and particle size,27 but these were not precise, as the effect of particle size on the volume of nanoparticles was neglected. Moreover, relations in the adsorption kinetic parameters between nanoparticles and corresponding bulk materials were not obtained. Therefore, it is necessary to perfect the kinetics of nanoadsorption theoretically and experimentally. In this paper, we theoretically deduce generalized and precise relationships between the thermodynamic properties and the kinetic parameters of adsorption and the particle size in solution. Moreover, the influence mechanism of particle size on the thermodynamic properties and kinetic parameters are also discussed. Thermodynamic properties and kinetic parameters for the adsorption of methyl orange (MO) on nano-CeO2 of different particle sizes have been determined experimentally, and the size dependences of these properties are also summarized.

μ N = μ Nb +

μP = μ Nb + μBs + μs

dμBs = RT d ln

μBs = μBs sat + RT ln

3σNVN r

(7)

ΓB Γ sat B

(8)

where the superscript “sat” denotes a saturated state. 2.1.4. Chemical Potential of the Interface. 3σNVN r

μs =

(1)

(9)

where σN is the interface tension when the adsorption capacity is ΓB and VN is the molar volume of the nanoparticle. Substituting eqs 8 and 9 into eq 6, we obtain μP = μ Nb + μBs sat + RT ln

(2)

ΓB 3σNVN sat + ΓB r

(10)

2.1.5. Molar Gibbs Free Energy of Adsorption. From eq 1, the molar Gibbs free energy of the adsorption process can be expressed as ΔadsGm = μP − μB − μ N

(11)

Introducing eqs 2, 5, and 10 into eq 11, we obtain ΔadsGm = ΔadsGm⊖ + RT ln J

(12)

in which ΔadsGm⊖ = ΔadsGmb⊖ + ΔadsGms⊖

(3)

where μbN and μsN are the chemical potentials of the bulk phase and the surface phase of the pure nanoadsorbent in the standard state and the superscripts “b” and “s” denote the bulk phase and the surface phase, respectively. For the adsorption of spherical nanoparticles without holes, the partial molar surface Gibbs free energy (surface chemical potential) is equal to the molar surface Gibbs free energy,28 that is μ Ns = Gsm =

ΓB [Γ]

where ΓB is the number of moles of adsorbate adsorbed on unit mass of the nanoparticles and [Γ] is the unit of ΓB in mol/kg. By integrating eq 7 from μsBsat to μsB and from Γsat B to ΓB, we obtain

where μB(l) is the chemical potential of the adsorbate in solution, μ⊖ B (l) is the standard chemical potential of the adsorbate in solution, aB is the activity of the adsorbate in solution, R is the universal gas constant (8.314 J·mol−1·K−1), T is the absolute temperature, and the superscript “⊖” denotes the standard state. 2.1.2. Chemical Potential of the Pure Nanoadsorbent (N). The chemical potential of the nanoadsorbent is composed of the bulk part and the interfacial part and can be written as

μ N = μ Nb + μ Ns

(6)

At a certain temperature, μsB is related to the amount of adsorbed adsorbate. Its chemical potential can be obtained according to the definition of general chemical potential:

where B(aq) is an adsorbate in solution, N(s) is a pure nanoadsorbent with radius r, and P(s) is an adsorption product formed by adsorbing B on the surface of the nanoparticle. 2.1.1. Chemical Potential of the Adsorbate (B) in Solution. μB (l) = μB⊖ (l) + RT ln aB

(5)

where σ*N is the surface tension of pure nanoparticles. 2.1.3. Chemical Potential of the Adsorption Product P. The chemical potential of the adsorption product P can be composed of those of three phases: that of the nanoparticle bulk phase, that of B adsorbed on the particle surface, μsB, and that of the interface, μs:

2. NANOADSORPTION THEORY 2.1. Nanoadsorption Thermodynamics in Solution. A nanoadsorption process from solution can be expressed as B(aq) + N(s) ⇌ P(s)

3σN*VN r

ΔadsGms⊖ = μs − μ Ns = (σN − σN*) J=

ΓB/Γ sat B aB

(13)

3VN r

(14)

(15)

For adsorption on the corresponding bulk material, the expression is ΔadsGmb = ΔadsGmb⊖ + RT ln J

(4)

(16)

ΔadsGb⊖ m

where is the standard molar adsorption Gibbs free energy of the bulk phase. Equation 12 can be expressed as follows:

where σN, r, and VN are the surface tension, radius, and molar volume of the nanoparticles, respectively. B


Article

Langmuir ΔadsGm = ΔadsGmb + ΔadsGms = ΔadsGmb + (σN − σN*)

3VN r

2.1.8. Molar Enthalpy for Adsorption. If the influence of particle size on the volume is neglected, eq 20 can be obtained by substituting eq 17 into ΔH = −T2[∂(ΔG/T)/∂T]p:

(17)

⎡ ∂(ΔadsGm /T ) ⎤ ΔadsHm = −T 2⎢ ⎥ ⎣ ⎦p ∂T

where ΔadsGbm and ΔadsGsm are the molar adsorption Gibbs free energies of the bulk and surface phases. It can be seen from eq 17 that the influence of particle size on ΔadsGm depends on ΔadsGsm, which is proportional to (σN − σ*N) and the molar surface area (3VN/r). Because there is a decrease in surface tension after adsorption, which means that σN is smaller than σN*, the molar Gibbs free energy of adsorption becomes much more negative with decreasing particle size. That is to say, the adsorption tendency increases with decreasing particle size. 2.1.6. Adsorption Equilibrium Constant. When an adsorption reaches equilibrium, ΔadsGm = 0, σN = σ∞ N , and J = b K. Because ΔabsGb⊖ = −RT ln K , eq 17 can be written as m ln

3V K = (σN* − σN∞) N b RTr K

= ΔadsHmb +

(20)

It can be seen from eq 20 that the influence of particle size on the molar enthalpy for adsorption depends on the sign of [(∂σN/∂T)p − (∂σN*/∂T)p]. Because σN − σN* < 0, if the sign is positive, the molar entropy decreases with decreasing radius of the nanoparticles. However, if the sign is negative, it is unclear whether the molar enthalpy will increase or decrease with decreasing radius of the nanoparticles. When the mean radius of the nanoparticles is larger than 10 nm, ΔadsHm shows a linear relationship with the reciprocal of particle size. In a similar way, we can delineate the nanoadsorption thermodynamics in the gas phase. If the relative fugacity is used in place of the activity, the nanoadsorption thermodynamic relationships of solution adsorption will be changed into those for the gas phase. Indeed, the effects of particle size on the adsorption thermodynamic properties in the gas phase should be identical to those for liquid-phase adsorption. 2.2. Nanoadsorption Kinetics. 2.2.1. Adsorption Activation Energy. Basic Assumption 1.27 We assume that an intermediate transition state of an activated complex is involved in the process of adsorption, that transition-state theory for chemical reactions is applicable to the nanoadsorption process, and that the activated complex is not affected by particle size. It is represented by C‡ (the superscript “‡” denotes the transition state). The activation energy can be expressed as follows:

(18)

where K and Kb are the equilibrium constants of adsorption on nanoparticles and the corresponding bulk material, respectively, and the superscript “∞” denotes an equilibrium state. It can be estimated that for generic nanoparticles (σN* − σ∞ N) is on the order of 10−1−100 J·m−2,29 VN = 10−5−10−4 (M = 10−2−10−1 kg·mol−1, ρ = 103 kg·m−3, VN = M ), R = 10 J·mol−1· ρ

K−1, and T = 102 K, respectively. Thus, the magnitude of K/Kb for adsorption on spherical nanoparticles of different sizes can be calculated using eq 18. When r is 10−9 m, K/Kb is 20−1043, and when r is 10−6 m, K/Kb is 1−1.4. That is to say, when the radius of particles reaches the micron level, K for microparticles is equal to Kb. It can be seen from eq 18 that K is influenced by the molar surface area and the difference in surface tension between the preadsorption state and adsorption equilibrium. When the mean radius of the nanoparticles is larger than 10 nm, the influence of particle size on the surface tension is negligible.30−32 The surface tension of the pure nanoparticles can be regarded as constant, and the saturated adsorption capacity of per unit area is constant, hence σ∞ * − σ∞ N and (σN N) ∞ are also constant. At a given temperature, σN* − σN > 0, and K decreases with decreasing particle size. Its logarithm should show a linear relationship with the reciprocal of particle size. 2.1.7. Molar Entropy for Adsorption. If the influence of particle size on the volume is neglected, eq 19 can be obtained by substituting eq 17 into ΔS = −(∂ΔG/∂T)p:

Ea = Δ‡Hm + nRT

(21)

where n is a constant, equal to 2 for gas-phase adsorption and 1 for adsorption in solution.33 Δ‡Hm is the activation enthalpy for the nanoadsorption process. It can be expressed as Δ‡Hm = HC‡ − HN − HB

(22)

where HC‡ is the partial molar enthalpy for the activated complex, HN is the partial molar enthalpy for the nanoadsorbent, and HB is the partial molar enthalpy for the adsorbate. The partial molar enthalpy of nanoparticles comprises a bulk phase part and a surface phase part, and is expressed as follows:

⎛ ∂ΔG b ⎞ ⎛ ∂ΔGms ⎞ ⎛ ∂ΔGm ⎞ m ⎟⎟ − ⎜ ⎟ = −⎜⎜ ΔadsSm = −⎜ ⎟ ⎝ ∂T ⎠ p ⎝ ∂T ⎠ p ⎝ ∂T ⎠ p ⎡ ⎛ ∂σ * ⎞ ⎤ 3V ⎛ ∂σ ⎞ = ΔadsSmb − N ⎢⎜ N ⎟ − ⎜ N ⎟ ⎥ r ⎢⎣⎝ ∂T ⎠ p ⎝ ∂T ⎠ ⎥⎦ p

⎧ ⎡⎛ ⎛ ∂σ * ⎞ ⎤⎫ ⎪ 3VN ⎪ ∂σ ⎞ ⎨(σN − σN*) − T ⎢⎜ N ⎟ − ⎜ N ⎟ ⎥⎬ ⎪ ⎪ ⎝ ⎠ ⎢ ⎥ r ⎩ ⎣ ∂T P ⎝ ∂T ⎠P⎦⎭

HN = HNb + HNs

(23)

Basic Assumption 2.27 We assume that the transition state in a nanoadsorption process is the same as that in the corresponding bulk adsorption process. (19)

HC‡ = HCb‡

It can be seen from eq 19 that the influence of particle size on the molar entropy of adsorption depends on the sign of [(∂σN/∂T)p − (∂σN*/∂T)p], and this difference is relevant to the adsorption system. If the sign is positive, the molar entropy decreases with decreasing radius of the nanoparticles. On the contrary, if the sign is negative, the molar entropy increases with decreasing radius of the nanoparticles.

(24)

Equation 22 can then be changed into eq 25: Δ‡Hm = HCb‡ − HNb − HB − HNs = Δ‡Hmb − HNs

(25)

If the nanoparticles are spherical without inner holes, the partial molar enthalpy for the surface phase HsN can be expressed as follows: C


Article

Langmuir HNs =

3hsVN r

partial molar surface entropy increases with decreasing particle size. According to transition-state theory,

(26)

s

where h and VN are the specific surface enthalpy and the molar volume, respectively. Introducing eqs 25 and 26 into eq 21, we obtain s

Ea = Δ‡Hmb + nRT − HNs = Eab − HNs = Eab −

3h VN r (27)

1 ‡ b (Δ Sm − S Ns) + C1 R ⎧ ⎡ ⎤⎫ ⎪ 3V ⎛ ∂σ ⎞ 1⎪ 2 = ⎨Δ‡Smb + N ⎢⎜ N ⎟ + σNαN ⎥⎬ + C1 ⎥⎦⎪ R⎪ r ⎢⎣⎝ ∂T ⎠ p 3 ⎩ ⎭

ln A =

where is the adsorption activation energy for the corresponding bulk material. It can be seen from eq 27 that the adsorption activation energy for nanoparticles is larger than that for the bulk material. The adsorption activation energy of nanoparticles decreases with decreasing particle size and shows a linear relationship with the reciprocal of particle radius. The effect of particle size on the adsorption activation energy is thus caused by the partial molar surface enthalpy of the nanoparticles. 2.2.2. Pre-exponential Factor for Nanoadsorption. Expressions for the activation Gibbs energy and the activation entropy for the nanoadsorption process can be written as

Δ‡Gm = Δ‡Gmb − G Ns

(28)

Δ‡Sm = Δ‡Smb − S Ns

(29)

(35)

A pre-exponential factor for the bulk adsorption material can be obtained: ln Ab =

ln A = ln Ab −

ln

(31)

⎡ ⎤ ⎛ ∂Δ‡G ⎞ 3V ⎛ ∂σ ⎞ 2 m ⎟⎟ = Δ‡Smb + N ⎢⎜ N ⎟ + σNαN ⎥ Δ‡Sm = −⎜⎜ ⎥⎦ r ⎢⎣⎝ ∂T ⎠ p 3 ⎝ ∂T ⎠ p

where αN is the volume expansion coefficient, which is defined as the ratio of the change in volume and its volume at 0 °C when the temperature changes by 1 °C. Equations 29 and 32 can be combined to give

(∂σN/∂T)p < 0. Therefore,

( )

+

2 σ α 3 N N

ln k =

1 1 s (HNs − TS Ns) + C2 = G N + C2 RT RT

(39)

ln k =

⎧ ⎫ ⎡⎛ ⎤⎪ 3VN ⎪ s ∂σ ⎞ 2 ⎨h + T ⎢⎜ N ⎟ + σNαN ⎥⎬ + C2 ⎢⎣⎝ ∂T ⎠ p ⎥⎦⎪ RTr ⎪ 3 ⎩ ⎭

(40)

where k is the adsorption rate constant. When r → ∞, we obtain

C2 = ln k b

(41)

Equations 39 and 40 can be changed into

(33)

The orders of magnitude for σ,34 α,35,38 and (∂σ/∂T)p36,37 are 100 J/m2, 10−5 K−1, and 10−4 J·m−2·K−1, respectively, and ∂σN ∂T p

(38)

or

(32)

⎤ ⎡ 3V ⎛ ∂σ ⎞ 2 = − N ⎢⎜ N ⎟ + σNαN ⎥ ⎥⎦ r ⎢⎣⎝ ∂T ⎠ p 3

⎡ ⎤ 3VN ⎢⎛ ∂σN ⎞ 1 s 2 A ⎥ ⎜ ⎟ = − S = + σ α N N N ⎥⎦ 3 R Rr ⎢⎣⎝ ∂T ⎠ p Ab

It can be seen from eq 37 that the pre-exponential factor is influenced by the partial molar surface entropy, and that the pre-exponential factor for the nanoparticles is smaller than that for the bulk material. It decreases with decreasing particle size. When the radius of the nanoparticles is larger than 10 nm, the influence of particle size on the surface tension is negligible, and there is a linear relationship between the logarithm of the adsorption pre-exponential factor and the reciprocal of the radius of the nanoadsorbent. 2.2.3. Adsorption Rate Constant. Basic Assumption 3.27 We assume that nanoadsorption kinetics follows the Arrhenius equation ln k = ln A − Ea/RT. Introducing eqs 27 and 37 into this expression, we obtain

Equation 32 is obtained by differentiating eq 31 with respect to temperature:

S Ns

⎤ ⎡ 3V ⎛ ∂σ ⎞ 1 s 2 S N = ln Ab + N ⎢⎜ N ⎟ + σNαN ⎥ ⎥⎦ R Rr ⎢⎣⎝ ∂T ⎠ p 3

or

(30)

3σNVN r

(36)

(37)

where σN is the surface tension of the spherical nanoparticles. Equation 28 changes into Δ‡Gm = Δ‡Gmb −

1 ‡ b Δ Sm + C1 R

Equation 37 is obtained by substituting eq 36 into eq 35:

where Δ‡Gm and Δ‡Sm are the activation Gibbs energy and the activation entropy for the nanoparticles, respectively. Δ‡Gbm and Δ‡Sbm denote the activation Gibbs energy and the activation entropy for the bulk material, respectively. GsN and SsN are the partial molar Gibbs surface energy and partial molar surface entropy for the nanoparticles, respectively. For spherical nanoparticles without inner holes, the partial molar Gibbs energy for the surface phase can be expressed as follows:

3σNVN r

(34)

where C1 is a constant related only to temperature. Introducing eq 32 into eq 34, we obtain

Eab

G Ns =

Δ‡Sm + C1 R

ln A =

ln

is negative and the

s 3σVN G NP k = = b RT RTr k

(42)

or D


Article

Langmuir ⎧ ⎫ ⎡⎛ ⎤⎪ 3VN ⎪ s ∂σN ⎞ 2 ⎢ ⎥ ⎨ ⎬ ⎜ ⎟ h +T ln k = ln k + + σNαN ⎢⎣⎝ ∂T ⎠ p ⎥⎦⎪ RTr ⎪ 3 ⎩ ⎭

SEM (JEOL JSM-6701F). As shown in Figure 2, it consisted of approximately spherical particles. 3.3. Adsorption Experiments: Determination of Experimental Adsorption Data. Adsorption experiments were carried out in batches in a constant-temperature water-bath oscillator with a fixed concentration (14.81 mg/L, pH 6.5) of aqueous methyl orange (MO) solution. Nano-CeO2 (10 mg) of a certain particle size and MO solution (10 mL) were combined in a 100 mL brown conical flask. The suspensions were stirred in the dark at selected temperatures of 298, 308, 318, 328, and 338 K, respectively. At fixed time intervals, samples were withdrawn, centrifuged, and analyzed on a TU-1901 double-beam UV/vis/NIR spectrophotometer at 462 nm. 3.4. Calculation of Adsorption Kinetic Parameters. (1) The instantaneous adsorption capacity qt can be calculated by eq 44:

b

(43)

It is estimated that for generic nanoparticles, σN is on the order of 10−2 J·m−2, (∂σN/∂T)p = 10−4 J·m−2·K−1,36,37 T = 102 K, αN = 10−5 K−1,35,38 and hs = 10−1 J·m−2, such that the value of [hs + T((∂σN/∂T)p + 2σNαN/3)] in eq 43 is positive. The adsorption rate constant on nanoparticles is larger than that on the bulk material. Therefore, as the size of the nanoparticles is decreased, the adsorption rate constant increases. Moreover, when the mean radius of the nanoparticles is larger than 10 nm, the logarithm of the adsorption rate constant shows a linear relationship with the reciprocal of particle radius. It is clear from eqs 39 and 42 that the rate constant for nanoadsorption is related to the partial molar Gibbs energy. With the increase of partial molar Gibbs energy, the adsorption rate constant increases. The above theories of thermodynamics and kinetics are applicable to the adsorption of solid spherical nanoparticles without holes in the gas phase or in solution. Moreover, the thermodynamic and kinetic equations of adsorption of nanoparticles with other morphologies can be derived similarly.

V (c0 − ct) (44) m where qt is the instantaneous adsorption capacity, c0 and ct are the initial and instantaneous concentrations, respectively, V is the volume of MO solution, and m is the mass of adsorbent. (2) Pseudo-first-order kinetics39 and pseudo-second-order kinetics40 can be expressed as follows: qt =

qt = qe(1 − e−k1t )

(45)

t t 1 = + qt qe k 2qe 2

3. EXPERIMENTAL SECTION

(46) where k1 is the pseudo-first-order adsorption rate constant, k2 is the pseudo-second-order adsorption rate constant, and qe is the equilibrium adsorption capacity. From the slopes (1/qe) and intercepts (1/(k2qe2)) of fitted plots of t/qt versus t, the corresponding adsorption rate constants at different temperatures can be obtained. (3) Assuming that nanoadsorption kinetics follows the Arrhenius equation, applying eqs 47 and (48, we can derive the adsorption kinetic parameters.

3.1. Preparation of Nano-CeO2. Ce(NO3)3·6H2O (6.5 g) was dissolved in distilled water (30 mL). The resulting solution was added dropwise to the requisite amount of ammonium hydroxide mixed with a certain volume of ethylene glycol at 328 K. The mixture was then diluted to 120 mL with distilled water. After stirring for 30 min at room temperature, the resulting Ce(OH)3 suspension was transferred to a 200 mL stainless autoclave and kept at 373 K for 24 h. The precipitate was separated by centrifugation, and then dried and calcined. Subsequently, nano-CeO2 samples with different particle sizes were obtained by controlling the amount of ammonia added, the amount of ethylene glycol, and the calcination temperature. 3.2. Characterization of Nano-CeO2. The particle sizes of the samples were measured by means of a Shimadzu 6000 X-ray diffractometer (Cu Kα radiation, λ = 0.154 178 nm). It can be seen from Figure 1 that the diffraction peaks corresponded to the (111), (200), (220), (311), (222), (400), (331), and (420) planes of the cubic fluorite structure. On the basis of the diffraction angles and halfwidth data, the average sizes of the nanoparticles were calculated as 38.1, 43.8, 49.1, 53.2, 58.4, and 63.4 nm, respectively, by using Scherrer’s formula. The morphology of the ceria was inspected by

⎛ −E ⎞ k = A exp⎜ a ⎟ ⎝ RT ⎠

(47)

Ea (48) RT According to eq 48, the adsorption activation energies and adsorption pre-exponential factors can be calculated from the slopes and intercepts of fitted plots of ln k versus T−1. 3.5. Calculation of Thermodynamic Properties of Adsorption. ln k = ln A −

(1) Considering a reversible adsorption process, the standard equilibrium constant K can be expressed as

K=

c0 − ce ce

(49)

where ce is the equilibrium concentration. (2) The standard molar adsorption Gibbs energy can be calculated as follows:

ΔadsGm⊖ = − RT ln K

(50)

Linear regression of ΔadsG⊖ m against T should yield a good linear relationship. The average values of the standard molar entropy and the standard molar enthalpy can then be obtained from the slopes and intercepts of the linear fitting of ΔadsG⊖ m versus T at different particle sizes by applying eq 51.

ΔadsGm⊖ = ΔadsHm⊖ − T ΔadsSm⊖

Figure 1. XRD patterns of nano-CeO2 with different diameters. E

(51) DOI: 10.1021/acs.langmuir.7b04097 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir

Figure 2. SEM images of nano-CeO2 with different diameters.

Table 1. Correlation Coefficients of the Pseudo-First-Order and Pseudo-Second-Order Kinetic Equations 298 K 2

308 K

318 K

328 K

338 K

(R ) d/ nm

pseudofirst-order

pseudosecond-order

pseudofirst-order

pseudosecond-order

pseudofirst-order

pseudosecond-order

pseudofirst-order

pseudosecond-order

pseudofirst-order

pseudosecond-order

38.1 43.8 49.1 53.2 58.4 63.4

0.8727 0.6559 0.6529 0.6235 0.6926 0.8515

0.9990 0.9973 0.9962 0.9971 0.9902 0.9973

0.9531 0.7834 0.7238 0.6993 0.5443 0.9031

0.9998 0.9996 0.9996 0.9990 0.9978 0.9986

0.9927 0.8630 0.7448 0.7404 0.8446 0.9031

0.9998 0.9998 0.9998 0.9998 0.9994 0.9991

0.9915 0.8146 0.8456 0.7613 0.8275 0.8868

0.9999 0.9999 0.9999 0.9998 0.9999 0.9991

0.9969 0.7537 0.8451 0.8246 0.9432 0.9096

0.9999 0.9999 1.0000 1.0000 0.9999 0.9996

4. RESULTS AND DISCUSSION 4.1. Particle-Size Dependence of the Kinetic Parameters for Adsorption of MO on Nano-CeO2. 4.1.1. Effect of Particle Size on the Adsorption Kinetic Order. The correlation coefficients of the pseudo-first-order and pseudo-second-order kinetic equations were calculated according to eqs 45 and 46 and are listed in Table 1. From Table 1, it can be seen that adsorption of MO on nano-CeO2 of different sizes in aqueous solution could be well fitted by the pseudo-second-order adsorption kinetic equation, with linear correlation coefficients R2 > 0.99. Attempted fitting of the data by the pseudo-first-order adsorption kinetic equation led to inferior correlation coefficients R2 < 0.99, indicating that the kinetic data for MO adsorption on nanoCeO2 in aqueous solution are in accordance with a pseudosecond adsorption kinetic model under these conditions. Hence, it would appear that particle size has little effect on the kinetic order of the adsorption. Kinetic data for the adsorption of MO on nano-CeO2 of different particle sizes at 298 K were calculated, and plots of t/qt versus t are shown in Figure 3. Good linear relationships were obtained, further corroborating that particle size has little effect on the kinetic order of the adsorption. 4.1.2. Effect of Particle Size on Adsorption Rate Constant. The slope and intercept of each fitted line in Figure 3 were calculated, from which the corresponding adsorption rate constants k could be obtained. The relationships between the

Figure 3. Fitted lines for the pseudo-second-order kinetic equation for the adsorption of MO on nano-CeO2 of different particle sizes at 35 °C.

logarithms of the adsorption rate constants and the reciprocals of the particle diameters are shown in Figure 4. Good linear relationships are evident for this adsorption system. At the same temperature, as the particle size is decreased, the adsorption rate constant increases, which is mainly due to the high surface Gibbs energy of the nanoparticles. From eq 42, it is clear that the surface Gibbs energy will gradually increase with decreasing particle size, thus increasing the adsorption rate. In a previous literature report,27 the adsorption of benzene on nano-MgO was studied, and it F


Article

Langmuir

Figure 4. Plots of the logarithms of the adsorption rate constants against the reciprocals of the diameters of nano-CeO2 particles at different temperatures.

Figure 6. Relationship between the adsorption activation energies and the reciprocals of particle diameter of nano-CeO2.

was found that the logarithm of the adsorption rate constant showed a good linear relationship with the reciprocal of the particle size, consistent with our findings here. 4.1.3. Effects of Particle Size on Adsorption Activation Energy and Pre-Exponential Factor. Plots of ln k versus T−1 for different particle sizes are shown in Figure 5.

that of activated becomes smaller, showing the reduction of the adsorption activation energy. The relationship between the logarithms of the preexponential factors and the reciprocals of particle size is plotted in Figure 7.

Figure 7. Relationship between the logarithms of the pre-exponential factors and the reciprocals of the diameters of nano-CeO2.

Figure 5. Plots of logarithms of the adsorption rate constants versus reciprocals of temperature on nano-CeO2 of different diameters.

It can be seen that the adsorption pre-exponential factor decreases with decreasing particle size, which is mainly due to the surface entropy of the nanoparticles. From eq 33, it is evident that the surface entropy increases with decreasing particle size. Furthermore, the logarithms of the adsorption preexponential factors show a linear relationship with the reciprocal of particle size, consistent with eq 37. A previous literature report27 on the adsorption of benzene on nano-MgO showed a similar trend. 4.2. Particle-Size Dependence of Thermodynamic Properties for the Adsorption of MO on Nano-CeO2. 4.2.1. Particle-Size Dependence of the Adsorption Equilibrium Constant. Table 2 gives the logarithms of the standard equilibrium constants for adsorption of MO on nano-CeO2 of different particle sizes at different temperatures. The relationships between the logarithms of the standard equilibrium constants and the particle sizes at each temperature are plotted in Figure 8.

It can be seen that the logarithms of the adsorption rate constants show good linear relationships with the reciprocals of the respective temperatures. This indicates that the kinetics of nanoadsorption follows the Arrhenius equation, and that assumption 3 of the kinetic theory of adsorption is applicable. According to eq 48, the adsorption activation energies and the pre-exponential factors were calculated from the slopes and intercepts of the fitted lines in Figure 5. The relationship between the adsorption activation energies and the reciprocals of the particle size is shown in Figure 6. A good linear relationship is again apparent. With decreasing particle size, the adsorption activation energy decreases, consistent with previous literature findings.41 This can also be attributed to the effect of the surface enthalpy of the nanoparticles, in accordance with eq 27. Together with eq 26, this shows that the surface enthalpy increases with decreasing particle size, such that the total energy of the particles will increase. So the difference between the energy of particles and G


Article

Langmuir

Table 2. Logarithms of the Standard Equilibrium Constants of MO on Nano-CeO2 of Different Particle Sizes at Different Temperatures ln K d/nm

d−1/nm−1

298 K

308 K

318 K

328 K

338 K

38.1 43.8 49.1 53.2 58.4 63.4

0.02625 0.02283 0.02037 0.01880 0.01712 0.01577

0.8039 0.3631 −0.1717 −0.7315 −1.1775 −1.4719

0.5918 0.2033 −0.2726 −0.8068 −1.2684 −1.5468

0.4741 0.0386 −0.3901 −0.9206 −1.3860 −1.6321

0.2584 −0.0855 −0.5133 −0.9965 −1.4407 −1.6795

0.0847 −0.1991 −0.6359 −1.1161 −1.5033 −1.7140

Figure 8. Relationships between the logarithms of the standard equilibrium constants and the reciprocals of the diameters of nanoCeO2 at different temperatures.

Figure 9. Relationships between the standard Gibbs free energies and the reciprocals of the diameters of nano-CeO2 at different temperatures.

It can be seen from Figure 8 that the standard adsorption equilibrium constants for CeO2 of different particle sizes decreased with increasing temperature, showing the process to be exothermic. With decreasing particle size, the standard adsorption equilibrium constant measured at different temperatures increased, and linear relationships with the reciprocal of particle size were obtained. This was because decreasing the particle size of the nano-CeO2 led to increases in the specific surface area and the contact area between nano-CeO2 and the MO, increasing the adsorption capacity. This experimental result is consistent with that predicted by eq 18, with the logarithm of K being linearly related to the reciprocal of particle size. In a previous literature report,22 the adsorptions of Cu2+ on nano-ZnO and of Ag+ on nano-TiO2 of different sizes were studied. The equilibrium constants and standard molar Gibbs free energies at a constant temperature significantly increased with decreasing nanoparticle diameter, consistent with the trends observed here. 4.2.2. Effect of Particle Size on the Standard Molar Gibbs Free Energy of Adsorption. From Figure 9, it is evident that there are good linear relationships between the standard molar Gibbs free energy changes and the reciprocals of the particle diameters. With decreasing particle diameter, the values of ΔadsG⊖ m measured at different temperatures decrease, indicating increasing adsorption. This is in accordance with eq 17. For a fixed diameter of nano-CeO2, ΔadsG⊖ m gradually increases with increasing temperature. From the formula ΔS = −(∂ΔG/∂T)p, we can deduce that the adsorption entropy is negative. 4.2.3. Effects of Particle Size on Standard Molar Enthalpy and Standard Molar Entropy for Adsorption. Figure 10 shows plots of the standard molar Gibbs free energies for particles of

Figure 10. Relationships between standard Gibbs free energies and temperature for nano-CeO2 of different particle sizes.

different sizes at different temperatures. The calculated values ⊖ of ΔadsH⊖ m and ΔadsSm from linear fittings and regressions of these plots using eq 51 are listed in Table 3. The negative values of the standard molar enthalpies indicate that the adsorption is exothermic. The negative values of the standard molar entropies show that the adsorption is an entropy-decreasing process, which is consistent with the analysis in section 4.2.2. It can also be deduced that the adsorption is driven by enthalpy. Figures 11 and 12 show that the standard molar enthalpies and standard molar entropies of the adsorption are both functions of the reciprocal of particle size, with good linear relationships between them. This can be explained by eqs 19 H


Article

Langmuir

constant K⊖ increases and the molar Gibbs free energy of adsorption ΔadsG⊖ m decreases. However, the influences ⊖ of particle size on ΔadsS⊖ m and ΔadsHm depend on the sign of [(∂σN/∂T)p − (∂σN*/∂T)p], and its value is relevant to the adsorption system. For the adsorption of methyl orange on nano-CeO2, with decreasing particle size, ⊖ ΔadsS⊖ m and ΔadsHm both decrease. The mechanism of influence of particle size on the thermodynamic proper⊖ ties is that ΔadsG⊖ m and ln K are influenced by the molar surface area and the difference in surface tensions, ΔadsS⊖ m is influenced by the molar surface area and the difference in temperature coefficients of surface tension, and ΔadsH⊖ m is influenced by the molar surface area, the difference in surface tensions, and the difference in temperature coefficients of surface tension. (2) The particle size has a significant effect on the kinetics of nanoadsorption. With decreasing particle size of nanoCeO2, the adsorption rate constant k increases, and the adsorption activation energy Ea and the adsorption preexponential factor A decrease. ln k, Ea, and ln A are each linearly related to the reciprocal of particle size. The mechanism of particle size influence on the kinetic parameters is that Ea is influenced by the partial molar surface enthalpy of the nanoadsorbent, ln A is influenced by the partial molar surface entropy, and ln k is influenced by the partial molar surface Gibbs energy. The theories can quantitatively describe adsorption behavior on nanoparticles, explain the regularities and mechanisms of influence of particle size, and provide guidance for the research and application of nanoadsorption.

Table 3. Variations in Standard Molar Adsorption Enthalpies and Entropies on Nano-CeO2 of Different Particle Sizes d/nm

d−1/nm−1

−1 ΔadsH⊖ m /(kJ·mol )

−1 −1 ΔadsS⊖ m /(J·mol ·K )

38.1 43.8 49.1 53.2 58.4 63.4

0.02625 0.02283 0.02037 0.01880 0.01712 0.01577

−14.886 −11.834 −9.834 −8.066 −6.888 −5.149

−43.20 −36.74 −34.27 −33.00 −32.96 −29.59

Figure 11. Relationship between the standard molar enthalpy and the reciprocal of the diameter of nano-CeO2.

■

AUTHOR INFORMATION

Corresponding Author

*Y. Xue. E-mail: [email protected]. ORCID

Zixiang Cui: 0000-0002-7894-9019 Yongqiang Xue: 0000-0002-5707-2596 Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS The project is supported by the National Natural Science Foundation of China (Nos. 21573157 and 21373147)

Figure 12. Relationship between the standard molar entropy and the reciprocal of the diameter of nano-CeO2.

REFERENCES

(1) Guardia, P.; Labarta, A.; Batlle, X. Tuning the Size, the Shape, and the Magnetic Properties of Iron Oxide Nanoparticles. J. Phys. Chem. C 2011, 115, 390−396. (2) Penn, R. L.; Zhang, H. Z.; Banfield, J. F. Adsorption of organic acids to titania surfaces: Particle Size Dependence. Book of Abstracts, 217th ACS National Meeting, March 21−25, 1999, Anaheim, CA, USA, 1999. (3) Zhang, L.; Zhu, Y.; Li, H.; Liu, N.; Liu, X.; Guo, X. Kinetic and Thermodynamic Studies of Adsorption of Gallium(Iii) on Nano-TiO2. Rare Met. 2010, 29, 16−20. (4) X, M.; Grass, E.; Prof, Y. Z.; X, D.; Butcher, R.; X, J.; Dr, Y. P.; Dr, Y. L.; Dr, H. B.; X, K.; et al. A Reactive Oxide Overlayer on Rhodium Nanoparticles during CO Oxidation and Its Size Dependence Studied by in Situ Ambient-Pressure X-ray Photoelectron Spectroscopy. Angew. Chem., Int. Ed. 2008, 47, 8893−8896. (5) Wilson, O. M.; Knecht, M. R.; Garcia-Martinez, J. C.; Crooks, R. M. Effect of Pd Nanoparticle Size on the Catalytic Hydrogenation of Allyl Alcohol. J. Am. Chem. Soc. 2006, 128, 4510−4511.

and 20. The influences of particle size on the molar entropy and enthalpy of adsorption depend on the sign of [(∂σN/∂T)p − (∂σN*/∂T)p]. Because the molar enthalpy and enthalpy for the adsorption of MO on nano-CeO2 decreased with decreasing particle size, [(∂σN/∂T)p − (∂σ*N/∂T)p] > 0.

5. CONCLUSIONS The effects of nanoparticle size on adsorption thermodynamics and kinetics have been investigated theoretically and experimentally. The experimental results of nanoadsorption are consistent with the theory, and the following conclusions can be drawn. (1) Particle size of nanoparticles has a significant effect on the thermodynamic properties of nanoadsorption. With decreasing particle size, the adsorption equilibrium I


Article

Langmuir (6) Xu, Z.; Xiao, F. S.; Purnell, S. K.; Alexeev, O.; Kawi, S.; Deutsch, S. E.; Gates, B. C. Size-Dependent Catalytic Activity of Supported Metal Clusters. Nature 1994, 372, 346−348. (7) Shen, Y. F.; Tang, J.; Nie, Z. H.; Wang, Y. D.; Ren, Y.; Zuo, L. Preparation and Application of Magnetic Fe3O4 Nanoparticles for Wastewater Purification. Sep. Purif. Technol. 2009, 68, 312−319. (8) Zhou, X.; Xu, W.; Liu, G.; Panda, D.; Chen, P. Size-Dependent Catalytic Activity and Dynamics of Gold Nanoparticles at the SingleMolecule Level. J. Am. Chem. Soc. 2010, 132, 138−146. (9) Murzin, D. Y. Thermodynamic Analysis of Nanoparticle Size Effect on Catalytic Kinetics. Chem. Eng. Sci. 2009, 64, 1046−1052. (10) Chen, Z.; Zhuang, Z.; Cao, Q.; Pan, X.; Guan, X.; Lin, Z. Adsorption-Induced Crystallization Of U-Rich Nanocrystals on NanoMg(OH)(2) And The Aqueous Uranyl Enrichment. ACS Appl. Mater. Interfaces 2014, 6, 1301−1305. (11) Cao, C. Y.; Qu, J.; Yan, W. S.; Zhu, J. F.; Wu, Z. Y.; Song, W. G. Low-Cost Synthesis of Flowerlike α-Fe2O3 Nanostructures for Heavy Metal Ion Removal: Adsorption Property and Mechanism. Langmuir 2012, 28, 4573−4579. (12) Qu, Z.; Yan, L.; Li, L.; Xu, J.; Liu, M.; Li, Z.; Yan, N. Ultraeffective ZnS Nanocrystals Sorbent for Mercury(II) Removal Based on Size-Dependent Cation Exchange. ACS Appl. Mater. Interfaces 2014, 6, 18026. (13) Liu, Y.; Zhong, K.; Luo, K.; Gao, M.; Pan, H.; Wang, Q. SizeDependent Kinetic Enhancement in Hydrogen Absorption and Desorption of the Li−Mg−N−H System. J. Am. Chem. Soc. 2009, 131, 1862−1870. (14) Auffan, M.; Rose, J.; Proux, O.; Borschneck, D.; Masion, A.; Chaurand, P.; Hazemann, J.; Chaneac, C.; Jolivet, J.; Mark, R. W. Enhanced Adsorption of Arsenic onto Maghemites Nanoparticles: As(III) as a Probe of the Surface Structure and Heterogeneity. Langmuir 2008, 24, 3215−3222. (15) Yean, S.; Cong, L.; Yavuz, C. T.; Mayo, J. T.; Yu, W. W.; Kan, A. T.; Colvin, V. L.; Tomson, M. B. Effect of magnetite particle size on adsorption and desorption of arsenite and arsenate. J. Mater. Res. 2005, 20, 3255−3264. (16) Madden, A. S.; M, F. H., Jr; Luxton, T. P. Insights for sizedependent reactivity of hematite nanomineral surfaces through Cu2+ sorption. Geochim. Cosmochim. Acta 2006, 70, 4095−4104. (17) Gao, Y.; Wahi, R.; Kan, A. T.; Falkner, J. C.; Colvin, V. L.; Tomson, M. B. Adsorption of Cadmium on Anatase NanoparticlesEffect of Crystal Size and pH. Langmuir 2004, 20, 9585−9593. (18) Yang, L.; Dadwhal, M.; Shahrivari, Z.; Ostwal, M.; Liu, P. K. T.; Sahimi, M.; Tsotsis, T. T. Adsorption of Arsenic on Layered Double Hydroxides: Effect of the Particle Size. Ind. Eng. Chem. Res. 2006, 45, 4742−4751. (19) Pursell, C. J.; Chandler, B. D.; Manzoli, M.; Boccuzzi, F. CO Adsorption on Supported Gold Nanoparticle Catalysts: Application of the Temkin Model. J. Phys. Chem. C 2012, 116, 11117−11125. (20) Lu, H. M.; Wen, Z.; Jiang, Q. Size Dependent Adsorption On Nanocrystal Surfaces. Chem. Phys. 2005, 309, 303−307. (21) Zhang, H. Z.; PennR, L.; HamersR, J.; Banfield, J. F. Enhanced Adsorption of Molecules on Surfaces of Nanocrystalline Particles. J. Phys. Chem. B 1999, 103, 4656−4662. (22) Wen, Y. Z.; Xue, Y. Q.; Cui, Z. X.; Wang, Y. Thermodynamics of Nanoadsorption from Solution: Theoretical and Experimental Research. J. Chem. Thermodyn. 2015, 80, 112−118. (23) Rehrmann, J. A.; Jonas, L. A.Dependence of Gas Adsorption Rates on Carbon Granule Size and Linear Flow Velocity. Carbon 1978, 16, 47−51. (24) Norberg, N. S.; Arthur, T. S.; Fredrick, S. J.; Prieto, A. L. SizeDependent Hydrogen Storage Properties of Mg Nanocrystals Prepared from Solution. J. Am. Chem. Soc. 2011, 133, 10679. (25) Zhang, M.; Akbulut, M. Adsorption, Desorption, and Removal of Polymeric Nanomedicine on and from Cellulose Surfaces: Effect Of Size. Langmuir 2011, 27, 12550−12559. (26) Wang, H.; Shadman, F. Effect of Particle Size on the Adsorption and Desorption Properties of Oxide Nanoparticles. AIChE J. 2013, 59, 1502−1510.

(27) Wang, S.; Wen, Y.; Cui, Z.; Xue, Y. Size Dependence Of Adsorption Kinetics Of Nano-MgO: A Theoretical and Experimental Study. J. Nanopart. Res. 2016, 18, 15. (28) Zhang, Z.; Fu, Q.; Xue, Y.; Cui, Z.; Wang, S. S. Theoretical and Experimental Researches of Size-Dependent Surface Thermodynamic Properties of Nano-vaterite. J. Phys. Chem. C 2016, 120, 21652. (29) Yaws, C. L. Chemical Properties Handbook, 1st ed.; World Publishing Corporation: Beijing, 1999. (30) Cui, Z. X.; Zhao, M. Z.; Lai, W. P.; Xue, Y. Q. Thermodynamics of Size Effect on Phase Transition Temperatures of Dispersed Phases. J. Phys. Chem. C 2011, 115, 22796−22803. (31) Xue, Y. Q.; Yang, X. C.; Cui, Z. X.; Lai, W. P. The Effect of Microdroplet Size on the Surface Tension and Tolman Length. J. Phys. Chem. B 2011, 115, 109−112. (32) Samsonov, V. M.; Shcherbakov, L. M.; Novoselov, A. R.; Lebedev, A. V. Investigation of the Microdrop Surface Tension and the Linear Tension of the Wetting Perimeter on the Basis of Similarity Concepts and the Thermodynamic Perturbation Theory. Colloids Surf., A 1999, 160, 117−121. (33) Atkins, P W; Paula, J D. Atkins’ Physical Chemistry; Higher Education Press: Beijing, 2006; p 961. (34) Nanda, K. K. Bulk Cohesive Energy and Surface Tension From the Size-Dependent Evaporation Study of Nanoparticles. Appl. Phys. Lett. 2005, 87, 021909. (35) Yang, C. C.; Xiao, M. X.; Li, W.; Jiang, Q. Size Effects on Debye Temperature, Einstein Temperature, and Volume Thermal Expansion Coefficient of Nanocrystals. Solid State Commun. 2006, 139, 148−152. (36) Sdobnyakov, N. Y.; Samsonov, V. M. On the Size Dependenceof Surface Tension in the Temperature Range from Melting Point to Critical Point. Cent. Eur. J. Phys. 2005, 3, 247−257. (37) Tanaka, T.; Hara, S. Thermodynamic Evaluation of NanoParticle Binary Alloy Phase Diagrams. Z. Metallkd. 2001, 92, 1236− 1241. (38) Perry, R. H.; Green, D W. Perry’s Chemical Engineering Handbook, 8th ed.; McGraw-Hill Professional: New York, 2008. (39) Kannan, N.; Sundaram, M. M. Kinetics and Mechanism of Removal of Methylene Blue by Adsorption on Various CarbonsA Comparative Study. Dyes Pigm. 2001, 51, 25−40. (40) Ho, Y. S.; Wase, D. A. J.; Forster, C. F. Kinetic Studies of Competitive Heavy Metal Adsorption by Sphagnum Moss Peat. Environ. Technol. 1996, 17, 71−77. (41) Zhang, Y.; Yang, Y.; Han, H.; Yang, M.; Wang, L.; Zhang, Y.; Jiang, Z.; Li, C. Ultra-Deep Desulfurization Via Reactive Adsorption on Ni/Zno: the Effect of ZnO Particle Size on the Adsorption Performance. Appl. Catal., B 2012, 119−120, 13−19.

J


Size-Dependent Thermodynamics and Kinetics of Adsorption on

Recommend Documents