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Article Cite This: Langmuir 2018, 34, 12802−12808

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Analysis of Adsorbed Layers of Benzyldimethyldodecylammonium Bromide on Silica Particles in Water Using the Sorbent Mass Variation Method Shasha Jiang, Na Du, Shue Song, and Wanguo Hou* Key Laboratory of Colloid & Interface Chemistry (Ministry of Education), Shandong University, Jinan 250100, China

Langmuir 2018.34:12802-12808. Downloaded from pubs.acs.org by KAOHSIUNG MEDICAL UNIV on 11/06/18. For personal use only.

S Supporting Information *

ABSTRACT: A “sorbent mass variation” (SMV) method has been suggested to investigate the adsorption at solid−liquid interfaces, which can provide information on the adsorbed layer structure including its thickness and composition. However, there has been little research focused on the method, and therefore, it is essential to examine its general applicability. Herein, the adsorption of benzyldimethyldodecylammonium bromide (BDDABr), a cationic surfactant, on silica (SiO2) nanoparticles (with ∼12 and 24 nm in size, denoted as S-SiO2 and L-SiO2, respectively) in water was investigated using the SMV method. The adsorption isotherms all show a linearly declining tendency in the saturated adsorption regime, consistent with the prediction of the SMV model. The adsorption is interpreted to form noncomplete bilayers (or isolated admicelles). The thicknesses of the adsorbed bilayers on S-SiO2 and L-SiO2 are estimated to be ∼2.9 and 2.7 nm, respectively, and the volume fractions of BDDABr in the saturated adsorbed layers are 0.63 and 0.68, respectively. In addition, the change in the Gibbs free energy of the adsorption process is also analyzed, showing its spontaneous nature. This work demonstrates that the SMV method is available for investigation on the adsorption of surfactants at solid−liquid interfaces, which can provide information on the structure and formation thermodynamics of adsorbed layers.

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INTRODUCTION Adsorption of surfactants at solid−liquid interfaces has been extensively investigated owing to its fundamental and practical importance.1−3 For instance, surfactants may significantly affect the stability and rheology of colloid dispersions, which is closely related to the adsorption of the surfactants on the colloid particles.4−7 The surface modification of nanocelluloses using surfactants may enhance their dispersity in a fluid or in a solid matrix, thereby expanding their scope of application.3 Especially, interactions between nanoparticles and biomolecule aggregates (liposomes) or biological systems have recently received great attention because research on this aspect will help to develop “bionano” functional materials with great potential such as in biophysical, biomedical, and analytical applications and to understand the possible impact of nanoparticles on human health at the molecular level.2,8−11 In various applications of surfactants, the structure of adsorbed layers, including its composition, configuration, and thickness, on particle surfaces is critical. Many technologies such as atomic force microscopy,12 electron spin resonance spectroscopy,13 fluorescence spectroscopy,14 Raman spectroscopy,15 small-angle neutron scattering (SANS),16−18 ellipsometry,19 and neutron reflectivity (NR)20 have been used to estimate the adsorbed layer structure of surfactants at solid−liquid interfaces.1 Interestingly, Nagy21−24 developed a so-called “sorbent mass variation” (SMV) method to determine the © 2018 American Chemical Society

composition and thickness of adsorbed layers, only from the isotherm data obtained by simple adsorption measurements. Usually, an adsorption test is performed at a constant sorbent dosage with varying initial sorbate concentrations (Co) to determine the adsorption isotherm, namely, the change in the equilibrium adsorption (or surface excess) amount of sorbate (Γe) with the equilibrium (or remaining) concentration of the sorbate in bulk solution (Ce). This method may be called a “sorbent mass constant” (SMC) method, which can result in a series of isotherms at different given sorbent dosages. On the contrary, the SMV method suggests that the adsorption test is performed at a constant Co while varying sorbent dosages, which can result in a series of isotherms at different given Co.22,24 Theoretically, as an adsorption reaches saturation, the Γe as an excess amount should linearly decrease with an increase in Ce if the thickness and composition (or concentration) of adsorbed layers remain constant. On the basis of the SMV method, the information of adsorbed layer structures can be extracted from the intercept and slope of the linear decreasing segment in the Γe−Ce isotherm.22,24 Actually, the decrease in Γe with the increase of Ce is often observed in the isotherms reported in the literature,25−27 but it did not Received: August 9, 2018 Revised: October 5, 2018 Published: October 8, 2018 12802

DOI: 10.1021/acs.langmuir.8b02696 Langmuir 2018, 34, 12802−12808

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calculated from the difference between the initial and remaining (or equilibrium) concentrations. The relative errors for the sorbent mass, solution volume, and initial and equilibrium surfactant concentrations were less than 0.8%. Theoretical Basis. For clarity, the theoretical bases of the SMV method21−24 are summarized in the following. After mixing sorbent particles with a solution, adsorption of both the solvent and solute (sorbate) molecules may occur on the particles, forming an adsorbed layer at the solid−liquid interface. When the adsorption reaches equilibrium at given temperature (T) and pressure (P), the equilibrium adsorption (or surface excess) amount of the sorbate, Γe (mmol/g), can be calculated using the following equation

attract much attention. To the best of our knowledge, only Nagy et al.21−24 have published four papers on the SMV method so far, and only two systems, that is, 1-propanol/ activated carbon22,23 and sodium dodecyl sulfate (SDS)/ glutaric dialdehyde (GDA) cross-linking poly(vinyl alcohol) (PVA) hydrogel (GDA-c-PVA),24 have been studied using the SMV method. It is essential to examine the general applicability of the SMV method, as suggested by Nagy et al.24 In the present work, the adsorption of the cationic surfactant benzyldimethyldodecylammonium bromide (BDDABr) on silica (SiO2) nanoparticles in water was investigated using the SMV method. Special emphasis was placed on the structure of the adsorbed layers. Amorphous SiO2 is a widely used adsorbent,1,2,5,8−11,16−19,25 and the adsorbed layer structure of the nonionic surfactant alkyl polyoxyethylene ether (CnEOm) was investigated using SANS16−18 and ellipsometry.19 Benzyldimethyldodecylammonium halide (BDDA+X−, commonly X− = Cl− and Br−) is one kind of quaternary ammonium surfactants and widely applied in clinical, cosmetic, and industrial areas.28−31 However, research studies on the aggregation features of BDDA+X− at solid− liquid interfaces30,32,33 as well as in solutions29,34,35 are scarce. Harkot and Jańczuk30 studied the effect of BDDABr adsorption on the wetting of polytetrafluoroethylene and poly(methyl methacrylate) surfaces. Partyka group32,33 investigated the adsorption of BDDABr on SiO2 particles using the conventional batch method. More recently, we also investigated the adsorption of BDDABr on SiO2 nanoparticles in water and interestingly found that besides pH and temperature (T), the size of the SiO2 particles has an obvious influence on the adsorption.36 It is interesting to understand the adsorbed layer structure of the cationic surfactant on SiO2 nanoparticles in water. This work can provide a better understanding of surfactant adsorption at solid−liquid interfaces.

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Γe =

V (Cο − Ce) C − Ce = ο m cs

(1)

where V (L) is the volume of the solution, m (g) is the mass of the sorbent, Co and Ce (mmol/L) are the initial and equilibrium (remaining) concentrations of the sorbate in the bulk solution, respectively, and cs (g/L) is the sorbent dosage. According to the concept of surface excess, Γe is defined as the difference of the amount of solute in the adsorbed layer (per gram sorbent) minus that in the bulk solution of the same volume as the adsorbed layer. Assuming that adsorption causes no change in the total volume of the solution, Γe can be represented as Γe =

Val(Cal − Ce) = ks(Cal − Ce) m

(2)

where Val (L) is the volume of the adsorbed layer, Cal (mmol/L) is the concentration of the sorbate in the adsorbed layer, and ks (ks = Val/m, L/g) is the specific adsorption capacity of the sorbent. If ks and Cal remain constant (usually corresponding to saturated adsorption), Γe should linearly decrease with the increase of Ce. Therefore, ks and Cal can be extracted from the slope (ks) and intercept (ksCal) of the linear decreasing segment in the Γe−Ce isotherm. If the density of the adsorbed layer, ρal, and the specific surface area (As) of the sorbent are known, the thickness of the adsorbed layer, dal, can be estimated. From eqs 1 and 2, one has

EXPERIMENTAL SECTION

Ce =

Materials. BDDABr (≥97% for purity) was purchased from TCI, China, and used as received. The plot of surface tensions versus concentrations for the BDDABr solutions shows a minimum (Figure S1 in the Supporting Information), indicating surface-active impurities existing in the BDDABr sample, but the compositions of the impurities were not determined. Two high-purity (≥99.5%) SiO2 nanoparticle samples, with average diameters (Ds) of ∼12 and 24 nm (denoted as S-SiO2 and L-SiO2), respectively, were purchased from Macklin, China (notably, the size of L-SiO2 was overestimated to be ∼31 nm in our previous paper36). The Brunauer−Emmett−Teller specific surface areas (As) of S-SiO2 and L-SiO2 were 235 and 164 m2/g, respectively, determined by N2 adsorption−desorption at liquid nitrogen temperature.36 Ultrapure water with a resistivity of 18.25 MΩ·cm was obtained using a Hitech-Kflow water purification system (Hitech, China). Adsorption Experiment. The adsorption experiments were performed at free pH and 25 °C using a batch technique with the SMV method.22,24 Known masses (0.0125−1.75 g) of the adsorbents were added to 25 mL of test BDDABr solutions with given concentrations (10, 14, and 18 mM) in polyethylene centrifuge tubes. The centrifuge tubes were shaken using a thermostatic water bath shaker (Jiangsu Medical Instrument Factory, China) for 24 h at 25 ± 0.5 °C. The adsorption kinetic tests showed that the contact time of 24 h was sufficient to reach adsorption equilibrium. The adsorbent particles were then separated from the adsorption systems by centrifugation (GT16-3, Beijing Shidai Beili Centrifuge Co., Ltd., China) at 12 000 rpm for 30 min. The concentrations of BDDABr remaining in the resultant supernatants were determined using an UV−vis spectrometer (SP-4100, Shanghai Spectrum Instruments Co., Ltd., China) at 262 nm. The equilibrium adsorption amounts were

Cο − csksCal 1 − csks

(3)

and eq 2 can be rewritten as Cal =

Γe + Ce ks

(4)

The SMV method suggests that the adsorption tests are performed with varying cs at a constant Co, and the change in Ce with cs can thus be obtained. At cs → 0 for a given Co, the characteristic equilibrium adsorption amount (the adsorption amount in the limit of zero solid dosage), Γeo (mmol/g), can be obtained using the following equation21 ij dC yz Γ oe = − jjj e zzz j dcs z k {T , P , cs→ 0

(5)

Γoe

value can be obtained from the initial slope of the That is, the Ce−cs plot. Notably, Ce → Co at cs → 0 for a given Co. Therefore, eq 2 can be represented as Γoe = ks(Cal − Co). The plot of Γoe versus Co (or Ce) can be used to obtain the slope and intercept of the linear decreasing segment in the Γe−Ce isotherm. For an adsorption system at equilibrium, the chemical potentials (or activities) of each component (sorbate or solvent) in the adsorbed layer and in the bulk solution should be equal. Therefore, if the adsorbed layer composition is known, the surface activity coefficients of the components in the adsorbed layer can be calculated using the following equation23 xe, iγe, i γal, i = xal, i (6) 12803

DOI: 10.1021/acs.langmuir.8b02696 Langmuir 2018, 34, 12802−12808

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Langmuir where γal,i and xal,i are the activity coefficient and mole fraction of the component i (i = 1 for sorbate and 2 for solvent), respectively, in the adsorbed layer and γe,i and xe,i are the activity coefficient and mole fraction of the component i, respectively, in the bulk solution. An adsorption process can be regarded as a phase separation process, in which an initial homogeneous bulk phase with a concentration of Co is separated into two phases, namely, an interfacial phase (the adsorbed layer) with a concentration of Cal and an equilibrium bulk phase with a concentration of Ce. At adsorption equilibrium for a given system, the change in the Gibbs free energy accompanied by the phase separation process is

ΔGad = (ΔGal + ΔGe) − ΔGο

is often observed in the adsorption of surfactants on hydrophilic solid surfaces, and the critical concentration is usually called “critical surface aggregation concentration” (csac).1 At the csac, the cooperative adsorption, arising from the electrostatic interaction between oppositely charged solid surfaces and surfactants and the hydrophobic interaction between hydrocarbon chains of surfactants, begins to occur, thereby resulting in a sharp increase in Γe.1,37 Our data in Figure 1 suggest that the csac values of BDDABr on S-SiO2 and L-SiO2 are ∼4.8 and 2.7 mM, respectively, which are consistent with the SMC results.36 The critical micelle concentration (cmc) of BDDABr in bulk water was determined at 25 °C to be 5.56 mM.36 Therefore, the csac values obtained for S-SiO2 and L-SiO2 are located at 0.86 cmc and 0.49 cmc, respectively, similar to the literature reports (0.6−0.9 cmc).37,38 The Γe−Ce isotherms obtained using the SMV method may be called SMV isotherms. Figure 2 shows the SMV isotherms

(7)

where ΔGad is the Gibbs free energy change of the adsorptioninduced phase separation process and ΔGal, ΔGe, and ΔGo are the Gibbs free energy changes corresponding to the formation of the adsorbed layer solution, the equilibrium bulk solution, and the initial bulk solution, respectively. The change in the Gibbs free energy of the phase separation process per mole of initial bulk solution, ΔG*ad (J/ mol), can be represented as (see Section S1 in the Supporting Information)23 É ÅÄÅ ia y i a yÑÑÑ Å * = RT ÅÅÅÅxo,1 lnjjjj e,1 zzzz + xo,2 lnjjjj e,2 zzzzÑÑÑÑ ΔGad jj a zz jj a zzÑÑ ÅÅ (8) ÅÇÅ k o,1 { k o,2 {ÑÖÑ where xo,1 and xo,2 are the mole fractions of the sorbate and solvent in the initial bulk solution, respectively, ao,1 and ae,1 are the activities of the sorbate in the initial and equilibrium bulk solutions, respectively, ao,2 and ae,2 are the activities of the solvent in the initial and equilibrium bulk solutions, respectively, R is the gas constant [8.314 J/(mol K)], and T (K) is the absolute temperature.

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Figure 2. SMV isotherms for BDDABr adsorption on (A) S-SiO2 and (B) L-SiO2 at three initial concentrations. Lines are guides to the eye (with reference to ref 36). Red arrows indicate characteristic adsorption amounts.

RESULTS AND DISCUSSION SMV Isotherm. The adsorption of BDDABr on S-SiO2 and L-SiO2 in water was determined at 25 °C using the SMV method at three Co (10, 14, and 18 mM). Figure 1 shows the

at the three Co, in which the Γe data were obtained based on eq 1. In addition, the Γe values were obtained from the slopes of the linear decreasing parts of Ce−cs plots in low cs regimes (at cs → 0) based on eq 5, which are also shown in Figure 2 as marked by red arrows. The standard deviations of the obtained Γe values are lower than 3.1 μmol/g. Obviously, the three sets of Γe−Ce data obtained at the different Co fall almost on a single curve for each SiO2 sample. With increasing Ce (at Ce > csac), Γe has a sharp increase up to a maximum value and then slightly linearly decreases, which is consistent with the prediction of the SMV model. The maximum Γe should correspond to the saturated adsorption. For clarity, the maximum Γe corresponding to the saturated adsorption is denoted as Γe,m, and Ce corresponding to Γe,m is denoted as Ce,m. Γe,m and Ce,m for S-SiO2 are ∼409 μmol/g (or 1.74 μmol/ m2) and 7.4 mM, respectively, and those for L-SiO2 are ∼407 μmol/g (or 2.48 μmol/m2) and 7.8 mM, respectively, as shown in Figure 2. The Ce,m values observed for the two SiO2 samples are all higher than the cmc of BDDABr in bulk solution (5.56 mM), which is consistent with the SMC results.36 In addition, we noted that the adsorption (or SiO2 addition) causes a decrease in the pH of BDDABr solutions (Figure S2, Supporting Information). For the S-SiO2 system, the pH decreases from ∼6.0 to 5.0, and for the L-SiO2 system, the pH decreases from ∼6.0 to 3.2. In particular, the pH values of the S-SiO2 and L-SiO2 systems at saturated adsorption are 3.8 ± 0.2 and 5.2 ± 0.2, respectively. In our previous work,36 the pKa (Ka is the apparent dissociation constant) values of SSiO2 and L-SiO2 were estimated using acid−base titrations to be 9.43 and 9.57, respectively, and the deprotonation

Figure 1. BDDABr equilibrium concentration as a function of sorbent dosage for (A) S-SiO2 and (B) L-SiO2 at three initial concentrations. Symbols represent experimental data, and the red dotted lines are calculated with eq 3 assuming constant ks and Cal,m being 0.25 mL/g and 1.65 M for S-SiO2 and 0.23 mL/g and 1.78 M for L-SiO2, respectively.

change in Ce with cs at various given Co. With increasing cs, the Ce initially linearly (or almost linearly) decreases, followed by a slower (nonlinear) decrease, and finally reaches a constant value. With an increase in Co, the linear parts in the Ce−cs plots become longer. These results are similar to the reports of Nagy et al. for 1-propanol/activated carbon22,23 and SDS/GDA-cPVA systems.24 In addition, the constant minimum values of Ce observed in the high cs regime are independent of Co for each of the two SiO2 samples, showing that a significant adsorption of BDDABr on the SiO2 particles in water occurs only as Ce is higher than a critical value for a given SiO2. This phenomenon 12804

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determined using dynamic light scattering to be ca. 2.3 nm (Figure S3, Supporting Information). The fully extended length of BDDABr molecules is approximately 2.2 nm (Figure S4, Supporting Information). The result of the dal values being lower than the micelle size and even the fully extended length of BDDABr arises probably from the deviation of the assumed ideal perfect adsorbed layers from the real state of noncomplete adsorbed layers. If this is true, the apparent dal value should be corrected based on the surface coverage of adsorbed layers (αal). The surface site densities, Ns, of S-SiO2 and L-SiO2 are estimated to be ∼0.55 and 0.38 mmol/g, respectively, from the As of the SiO2 samples and the cross-sectional area of a hydrated BDDABr (∼0.71 nm2).36 The αal values at saturated bilayer adsorption for S-SiO2 and L-SiO2 can be estimated to be ∼0.36 and 0.52, respectively, based on the equation αal = Γe,m/2Ns. Therefore, the “real” thicknesses of the adsorbed layers (dal,r = dal/αal) on S-SiO2 and L-SiO2 may be estimated to be ∼2.9 ± 0.6 and 2.7 ± 0.3 nm, respectively, which are comparable with the literature values (2.0−6.6 nm).16−20,37−41 Notably, the so-obtained dal,r values are lower than the twice fully extended length of BDDABr (∼4.4 nm), suggesting that the BDDABr molecules in the bilayer structure are arranged with tilting or partial interdigitation of their tails.38 On the basis of eq 3, the change in Ce with cs can be obtained using the ks and Cal,m values, as shown in Figure 1. The calculated results at the low cs regime are in good agreement with the experimental data, suggesting that the soobtained ks and Cal,m values are reasonable. In addition, assuming ks is independent of Ce, the Cal values at various Ce can be calculated based on eq 4 and are shown in Figure 3. As

dissociation of surface hydroxyl groups for the SiO2 samples was found to obviously occur only at pH higher than ∼6. Therefore, it is reasonable to suggest that a cation exchange mechanism (between H+ of Si−OH and BDDA+) exists in the adsorption and that the obvious difference in Γe,m per unit area between the two SiO2 samples arises mainly from the difference in pH between the two systems. Notably, the differences in both the pH and Γe,m (in μmol/m2) between the two SiO2 systems result from the particle size effect.36 The above SMV isotherms indicate that Γe is a single-valued function of Ce under the studied conditions, which is similar to the report of Nagy et al. for the SDS/GDA-c-PVA system24 but different from that for the 1-propanol/activated carbon system.22 Nagy found that the adsorption of 1-propanol on activated carbon in water showed different maximum Γe values, depending on Co, namely, the maximum Γe decreases with a decrease in Co.22 That is to say, Γe is not a single-valued function of Ce and also related to Co or cs.22 From Nagy’s report,22 we note that the Co values showing lower maximum Γe values are all lower than the Ce,m value. On the basis of eq 2, one has ÑÉÑ ÅÄÅ ÑÑ ÅÅi ∂C y ij ∂Γe yz ij ∂Ce yz ÑÑ Å j z al jj z zz zz ÑÑ = ksÅÅÅjjj − jjj jj ∂c zzz z z j z j z Ñ Å c c ∂ ∂ ÅÅÅÇk s {T , P , ks k s {T , P , ksÑÑÑÖ k s {T , P , ks (9) In the case of Co < Ce,m, if the absolute value of (∂Cal/ ∂cs)T,P,ks is equal to or less than that of (∂Ce/∂cs)T,P,ks in a range of low cs (or high Ce), a constant Γe (at a low level) or a decrease in Γe with the increase of Ce will appear. Therefore, if the Co values used in the SMV experiments are all higher than the Ce,m value, only one maximum Γe (i.e., Γe,m) value will be observed, just as our current work and the work of Nagy et al. for the SDS/GDA-c-PVA system.24 However, if the Co values lower than Ce,m are used, maximum Γe values lower than Γe,m will be observed. Structure of the Adsorbed Layer. As adsorption reaches saturation, it can be reasonably assumed that Cal and ks no longer change with Ce. For clarity, Cal at saturated adsorption is denoted as Cal,m. On the basis of eq 2, ks and Cal,m can be estimated from the slope (−ks) and intercept (ksCal,m) of the linear decreasing part in the SMV isotherm (based on the Γoe − Co data, as shown in Figure 2). The ks values obtained for SSiO2 and L-SiO2 are ∼0.25 ± 0.05 and 0.23 ± 0.03 mL/g, respectively, and the Cal,m values obtained for the two samples are ∼1.65 ± 0.06 and 1.78 ± 0.06 M, respectively. Owing to the fact that the density of BDDABr (∼0.97 g/mL) is close to that of water, ρal is assumed to be the same as that of water (1 g/mL). The dal values can be estimated from the ks and As values to be ∼1.06 ± 0.21 and 1.40 ± 0.18 nm for S-SiO2 and L-SiO2, respectively, which are lower than the literature values (2.0−6.6 nm).16−20,37−41 It is worth noting that the so-obtained dal data are based on an assumption that a perfect adsorbed layer is evenly attached to the surface of solid particles and the adsorbed components (sorbates) are homogeneously distributed in the adsorbed layer. Actually, many previous research studies have demonstrated that the adsorption of cationic surfactants at SiO2− water interfaces can form a bilayer structure at Ce > cmc, and it usually consists of isolated surface micelles (isolated admicelles or noncomplete bilayers).1,33,36−38 Therefore, the dal data obtained here are apparent values. The average hydrodynamic diameter of the BDDABr micelles in bulk solution was

Figure 3. Concentrations of BDDABr in adsorbed layers as a function of equilibrium concentrations in bulk solutions for (A) S-SiO2 and (B) L-SiO2 at three initial concentrations. Lines are guides to the eye.

expected, Cal initially increases with the increase of Ce and then reaches a maximum constant value (i.e., the Cal,m value). Furthermore, from the so-obtained Cal,m values, the mole fractions (xal,m) of BDDABr in the saturated adsorbed layer for S-SiO2 and L-SiO2 can be calculated to be 0.029 ± 0.001 and 0.031 ± 0.001, respectively, corresponding to the volume fractions (Φal,m) being 0.63 ± 0.02 and 0.68 ± 0.02, respectively. These data are comparable with those reported in the literature (Φal,m 0.1−0.69).18,20,24,39 For clarity, Table 1 summarizes the parameter values of sorbents and adsorbed layer structures. Overall, our results indicate that the adsorption behavior of BDDABr on SiO2 nanoparticles in water accords with the prediction of the SMV method and that the SMV method can provide the structural information of the adsorbed layers. It is interesting to note that S-SiO2 shows a higher dal,r and a lower Φal,m in comparison with L-SiO2. This suggests that the affinity of high-curvature SiO2 for BDDABr is lower than that of low-curvature one, similar to our previous results obtained 12805

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be called a “phase separation” model, which was used to analyze our adsorption data. For the first time, this model has been applied to the adsorption of surfactants. Assuming the activity coefficients of BDDABr and water in bulk solutions all being unity, the ΔG*ad values at various cs and Ce were calculated using eq 8. Figure 5 shows the change in ΔG*ad with

Table 1. Characteristic Data of Sorbents and Adsorbed Layers sample

S-SiO2

L-SiO2

Ds (nm) As (m2/g) csac (mM) ks (mL/g) Cal,m (M) Φal,m dal (nm) αal dal,r (nm)

12 235 4.8 0.25 ± 0.05 1.65 ± 0.06 0.63 ± 0.02 1.06 ± 0.21 0.36 2.9 ± 0.6

24 164 2.7 0.23 ± 0.03 1.78 ± 0.06 0.68 ± 0.02 1.40 ± 0.18 0.52 2.7 ± 0.3

using the SMC method.36 In addition, Fragneto et al.39 found that the solid surface roughness has a significant effect on the properties of the adsorbed layer; the adsorbed amount (surface coverage) of hexadecyltrimethylammonium bromide (C16TAB) on rough silicon oxide surfaces was lower than that on smooth ones. This suggests that a high curvature (or low radius) for sorbent particles may lead to a low adsorption tendency. Our result obtained here seems to be consistent with the previous finding of Fragneto et al.39 Furthermore, owing to the curvature of solid surfaces having an effect on adsorption, the structures of adsorbed layers determined by ellipsometry, NR, etc., on large smooth surfaces of substrates37 might be different from those on the surfaces of small-sized particles. The SMV method can obtain information about the adsorbed layer structure on small-sized particles in solutions, which might be one of its advantages. Adsorption Thermodynamics. Activity Coefficient of BDDABr in Adsorbed Layers. On the basis of eq 6 and by assuming γe,1 = 1 (which may lead to a large error at Ce ≥ cmc), the activity coefficients of BDDABr in the adsorbed layers (γal,1) at various Cal can be calculated, as shown in Figure 4. γal,1 decreases with an increase in Cal. In addition, the γal,1

Figure 5. Dependence of Gibbs free energy change of adsorption per molar initial bulk solution with (A,B) sorbent dosage and (C,D) equilibrium concentration for (A,C) S-SiO2 and (B,D) L-SiO2 at three initial concentrations.

cs and Ce at the three Co for S-SiO2 and L-SiO2. All of the ΔG*ad values are negative, indicating the spontaneous nature of the adsorption processes. With increasing cs or Co, the absolute values of ΔGad * , |ΔGad * |, increase, suggesting the enhancement of spontaneous adsorption tendency. These results are consistent with the Nagy’s report.23 Note that the constant or slowly varying |ΔGad * | values in the high cs regime arise from the similar changes in Ce (or ao,i) values with cs. With increasing Ce at a given Co, the |ΔG*ad| value decreases, consistent with the results of the |ΔG*ad| changing with cs. This is because the increase in Ce corresponds to the decrease in cs for the SMV tests (at a fixed Co). In addition, it can be seen from Figure 5 that the |ΔG*ad| values of S-SiO2 are lower than those of L-SiO2, indicating that the affinity of high-curvature SiO2 for BDDABr is lower than that of low-curvature one.36 Overall, the phase separation model developed by Nagy23 may provide the thermodynamic information on adsorption processes, which may deepen the understanding of the adsorption phenomenon.

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Figure 4. Surface activity coefficients of BDDABr as a function of its concentrations inside adsorbed layers for S-SiO2 and L-SiO2 at three initial concentrations.

CONCLUSIONS The SMV method was used to determine the adsorption of the cationic surfactant BDDABr on two SiO2 samples (S-SiO2 and L-SiO2) in water. A linear decrease in Γe with an increase in Ce is observed on the adsorption isotherms, consistent with the prediction of the SMV model. The structural information on the adsorbed layers including their thickness and composition may be estimated from the SMV data. In addition, the change in the Gibbs free energy accompanied by the adsorption process can be analyzed using the phase separation model. Overall, our work demonstrates that the SMV method is available for investigation on the adsorption of surfactants at solid−liquid interfaces. SMV results can deepen the under-

values are much less than 1.0. These results are consistent with the previous reports.23 Such low γal,1 values observed here arise not only from the high Cal values but also more from the strong adsorption force of SiO2 for BDDABr. Furthermore, the γal,1 values obtained for S-SiO2 are higher than those for L-SiO2, suggesting that the adsorption force of S-SiO2 is lower than that of L-SiO2.36 Gibbs Free Energy Change. By considering an adsorption process as a solution-phase separation, Nagy23 suggested a calculation method for the Gibbs free energy change accompanied by the adsorption process. This method may 12806

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Langmuir

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standing of the adsorption phenomenon at solid−liquid interfaces.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.8b02696. Equilibrium surface tensions and micellar size distribution of BDDABr solutions, pH of adsorption systems, and molecular structure of BDDABr (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +86 531 88365460. Fax: +86 531 88364750. ORCID

Na Du: 0000-0003-2455-3497 Wanguo Hou: 0000-0003-1655-3593 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported financially by the National Natural Science Foundation of China (no. 21573133) and the Independent Innovation Foundation of Shandong University in China (no. 2016JC032).

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REFERENCES

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DOI: 10.1021/acs.langmuir.8b02696 Langmuir 2018, 34, 12802−12808