Experiment and Theory of Low-Pressure Nitrogen Adsorption in

May 31, 2012 - We report experimental nitrogen adsorption isotherms of ... Adsorption in heterogeneous porous media: Hierarchical and composite solids...
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Experiment and Theory of Low-Pressure Nitrogen Adsorption in Organic Layers Supported or Grafted on Inorganic Adsorbents: Toward a Tool To Characterize Surfaces of Hybrid Organic/Inorganic Systems Anne Boutin,*,† Benoit Coasne,‡ Alain H. Fuchs,§ Anne Galarneau,‡ and Francesco Di Renzo‡ †

Laboratoire Pasteur, CNRS-ENS-UPMC, Département de Chimie, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France ‡ Institut Charles Gerhardt Montpellier, UMR 5253 CNRS/UM2/ENSCM/UM1, ENSCM, 8 rue de l’Ecole Normale, 34296 Montpellier Cedex 05, France § CNRS & Chimie ParisTech, 11 rue Pierre et Marie Curie, F-75005 Paris, France S Supporting Information *

ABSTRACT: We report experimental nitrogen adsorption isotherms of organicscoated silicas, which exhibit a low-pressure desorption branch that does not meet the adsorption branch upon emptying of the pores. To address the physical origin of such a hysteresis loop, we propose an equilibrium thermodynamic model that enables one to explain this phenomenon. The present model assumes that, upon adsorption, a small amount of nitrogen molecules penetrate within the organic layer and reach adsorption sites that are located on the inorganic surface, between the grafted or adsorbed organic molecules. The number of accessible adsorption sites thus varies with the increasing gas pressure, and then we assume that it stays constant upon desorption. Comparison with experimental data shows that our model captures the features of nitrogen adsorption on such hybrid organic/inorganic materials. In particular, in addition to predicting the shape of the adsorption isotherm, the model is able to estimate, with a reasonable number of adjustable parameters, the height of the lowpressure hysteresis loop and to assess in a qualitative fashion the local density of the organic chains at the surface of the material.

1. INTRODUCTION Increasing efforts are devoted to synthesizing and characterizing materials consisting of an organic layer supported on inorganic substrates as they are at the heart of both fundamental research and practical applications. In such hybrid materials, the organic layer can be either deposited (physical adsorption, electrostatic interaction) or grafted (through chemical bonding) on the surface of the inorganic substrate. The inorganic material consists of a planar or a porous substrate. From a fundamental point of view, hybrid systems such as those described above can be used to investigate properties of materials that contain an organic/ inorganic interface. From a practical point of view, hybrid organic/inorganic materials including organic groups grafted on porous materials can be used for several applications such as chromatography,1 separation chemistry, heterogeneous catalysis for fine chemicals production, organic or cationic pollutant removals,2−4 energy storage,5,6 as well as other applications7−9 as they combine a large surface area of the host porous substrate with the useful properties of the organic groups. To help and improve the design of new devices and processes, accurate characterization of these materials is crucial as their efficiency for a given desired process mainly depends on their interfacial properties.10,11 Low temperature adsorption measurements of simple fluids such as argon or nitrogen and water5 or mercury intrusion are routinely used to characterize porous © 2012 American Chemical Society

hybrid solids. Adsorbed amounts and capillary condensation or intrusion pressures are related to the geometrical properties of the porous matrix.12,13 In the Barrett, Joyner, and Halenda (BJH) method,14 the pore size distribution of porous hybrid materials is estimated from the adsorption/desorption isotherm using the Kelvin equation. Water intrusion−extrusion cycles for organicgrafted mesoporous materials also allow one to characterize the stability of the grafting procedure and the hydrophobic character of the resulting materials.5,6 Surface properties (specific surface area and typical surface energy) are usually assessed from adsorption experiments (prior to capillary condensation of the fluid) on the basis of the Brunauer, Emmett, and Teller (BET) method in which the fluid is assumed to uniformly cover the surface.15 The resulting CBET parameter evaluates the global interaction of nitrogen with the organic layer, but it does not allow a precise determination of the organic chains distribution over the inorganic surface. Among substrates that can be used for practical applications involving hybrid organic/inorganic systems, porous silicas constitute an important class of materials as they are composed of large pores of a simple geometry.16−18 Moreover, surface Received: March 19, 2012 Revised: May 26, 2012 Published: May 31, 2012 9526

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Article is organized as follows. Section 2 reports our experimental data for N2 physisorption on organics-coated silicas. Section 3 reports our simple thermodynamic model and the main information that can be gained by applying the model to adsorption/desorption data for organic layers supported at the surface of nonporous and porous materials. Section 4 contains some concluding remarks.

grafting of silica with organosilane groups allows one to play in an almost infinite way with the surface properties of these materials. Most of the grafted molecules are organic groups with tunable chain length or bulkiness, which allow for controlling the decrease of the average pore size. Moreover, the organic groups can be polar or nonpolar so that the degree of hydrophilicity or hydrophobicity of the surface can be tuned. Grafting of silica or deposit of an organic layer on inorganic surfaces raises the question of the general validity of the classical characterization methods mentioned above for the organic/inorganic class of materials. Indeed, as shown in this work, particular hysteresis loops, in which the desorption curve is nearly parallel to the adsorption curve and located at a slightly higher adsorbed amount, have been systematically observed in several classes of organic-coated materials: silica surfaces coated with a continuous layer of long-chain cationic surfactants,2 silica surfaces functionalized with hydrocarbon chains,5,19 or hydrocarbon chains bearing several kind of functional groups.20−22 Such a lowpressure hysteresis phenomenon has nothing to do with the wellknown irreversibility of capillary condensation in mesopores as it is observed at pressures below the lowest closure point of capillary condensation hysteresis (P/P0 = 0.42 for nitrogen at 77 K where P0 is the bulk saturating vapor pressure). This new and unexpected low-pressure hysteresis is a rather small amplitude effect, and one has to be very careful not to confuse it with more trivial instrumental issues. Yet, a careful examination of a certain number of studies of hybrid materials such as grafted mesoporous silicas, grafted silica nanoparticles, and assynthesized swelled MCM-41 type materials (with a layer of hexadecyltrimethylammonium electrostatically linked to the surface)1−3,5,6,23−27 has disclosed a systematic occurrence of a low-pressure nitrogen adsorption hysteresis. In addition, the socalled height of the hysteresis (which is defined as the difference in the adsorbed amounts between the adsorption and desorption branches taken at the same given pressure) increases linearly with the maximum pressure reached during the adsorption experiment. This definitely calls for a true physical effect rather than a straightforward experimental uncertainty. The aim of this Article is 2-fold. We first provide experimental N2 adsorption isotherm data of several organics-coated silicas in which the lack of reversibility of the adsorption−desorption cycles is observed. We then report a simple thermodynamic model that describes the main features of the experimental adsorption isotherms. The model is based on the following assumptions. Adsorption takes place (1) on the part of the inorganic surface that is free of organic groups and (2) on top of the organic-grafted or deposited molecules. Moreover, as gas pressure is increased, a small amount of nitrogen molecules penetrates within the organic layer and reaches adsorption sites that are located on the inorganic surface, between the grafted or deposited organic molecules. Starting from the maximum pressure reached upon adsorption, desorption takes place both from the grafted and from the ungrafted surfaces. In this model, the low-pressure hysteresis loop arises from the fact that nitrogen adsorbs in the organic layer at a pressure higher than the pressure at which they desorb. This provides a simple explanation why the desorption branch in the nitrogen adsorption isotherm is located slightly above the adsorption branch. Our simple model captures the essential features of adsorption experiments at the surface of organic/inorganic materials and could be used to gain useful insights such as the local organic chains density in hybrid materials obtained through different routes such as grafting, sol− gel synthesis, or organic layer deposition. The remainder of this

2. EXPERIMENTS 2.1. Materials and Methods. Hexadecyltrimethylammoniumtemplated MCM-41 silicas were prepared according to published procedures.28 In some cases, the templating micelles were swollen with different amounts of trimethylbenzene (TMB).2 Commercial silicas were also used such as silica gel Si60 purchased from Fluka and precipitated silica Levilite provided by CECA. Nitrogen sorption isotherms were performed at 77 K on as-synthesized and dried MCM-41 and swollen MCM-41 samples (after TMB evaporation) containing the surfactants with hexadecyl chains on their surface. Calcination of the MCM-41 materials was performed at 550 °C for 8 h in airflow to remove the surfactants. The calcined MCM-41 samples, as well as the commercial silicas, were silylated according to published procedures28 with alkylsilanes presenting different chain lengths: propyl, butyl, and octyl chains. The amounts of organic chains grafted on the surface of the materials or physically adsorbed through electrostatic interactions on the surface (in the case of as-synthesized MCM-41 materials) were evaluated by thermal gravimetric analysis. N2 sorption isotherms at 77 K were recorded on Micromeritics ASAP or Tristar devices equipped with secondary vacuum systems. The adsorption cells were equipped with filler rods and isothermal jackets. The saturation pressure of nitrogen was measured throughout the experiments. The effect of equilibration time was monitored by comparing experimental runs with average equilibration time for experimental points varying from 6 to 30 min. Prior to the adsorption experiment, the organics-free samples were outgassed at 523 K and the organics-bearing samples at 323 K until a static vacuum of 3 × 10−3 Torr. The amount of sample used in each measurement allowed a total surface area not lower than 35 m2 to be measured in each cell. The specific surface area of the different materials was evaluated by the BET method and pore volume by the αS method,12 while the pore size was evaluated by comparison with the predictions of the DFT method.29,30 2.2. Experimental Data. The N2 adsorption−desorption isotherm of the bare Si60 silica (Fluka) is reported in Figure 1a. The large hysteresis loop between P* = 0.5 and 0.8 (throughout this Article, the asterisk indicates that pressures are in reduced units with respect to the nitrogen bulk saturating vapor pressure, P0) is typical of capillary condensation (type IV isotherm) on an adsorbent with a broad distribution of mesopores. Figure 1b shows the same data but with a zoom in the low-pressure region: it can be clearly seen that below P* = 0.4, the desorption branch of the isotherm is perfectly superimposed on the adsorption branch. We also show in Figure 1 the nitrogen sorption isotherm of the same silica sample grafted with octyl chains (2.3 chains per nm2). Lining of the mesopores by the organics has not altered the type IV character of the sorption isotherm but leads to a decrease of the average pore diameter from 7.0 to 5.3 nm. Accordingly, the surface area has decreased from 500 to 300 m2/g and the pore volume from 0.68 to 0.31 cm3/g. Once capillary condensation has been completely reverted, the desorption branch of the isotherm below P* = 0.4 does not meet the adsorption branch. On the contrary, the desorption branch runs parallel to the adsorption branch in a significant range of pressure. Experimental evidence indicates that at very low pressure, as P* = 0 is approached, nitrogen is fully desorbed. If two consecutive adsorption/desorption cycles are carried out on the same sample without extracting the cell from the experimental device, the same extent of hysteresis is observed in the two runs. This effect leads us to believe that none of the nitrogen gas remains trapped when the vacuum treatment at the end of the cycle approaches P* = 0. In a general way, the variations in the extent of hysteresis measured in replicated experiments were lower than 10%. This level of repeatability was also observed for experiments replicated at different equilibration times. Variations of the equilibration time by a 9527

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Figure 3. Adsorption (void symbols) and desorption (filled symbols) isotherms of N2 at 77 K on a noncalcined MCM-41 silica still bearing the hexadecyltrimethylammonium templates. are still retained in the pores by electrostatic interaction between the ammonium groups of the surfactants and the charged silica surface. No steps of the adsorption curves corresponding to free mesopores are observed, and the αS-plot (see Figure S1, Supporting Information) indicates that no microporosity is present: the adsorption isotherm is type II in the IUPAC classification. The desorption branch of the sorption isotherm patently separates from the adsorption branch as the pressure decreases, and the adsorbate retained at P* = 0.15 along the desorption branch is 25% higher than the amount adsorbed at the same reduced pressure along the adsorption branch. It is well-known that molecules significantly larger than N2 can be dissolved in the hexadecyl chains layer lining the pores of MCM-41 and interact with the underlying surface.31 The large departure from reversibility of the sorption isotherm cycle on an adsorbent bearing about 50% mass of organics, like uncalcined MCM-41 (see Figure 3), suggests that adsorption of N2 in the organic layer plays some role in the phenomenon. If the height of the hysteresis was related to the dissolution of N2 molecules in the organic layer, the phenomenon would be expected to follow a Henry’s law-type linear dependence on vapor pressure. To verify this hypothesis, the height of the hysteresis was measured for adsorption−desorption cycles for different maximum pressures of adsorption. This experiment was performed with an as-synthesized and dried swollen MCM-41 (free of TMB) presenting a lining of hexadecyltrimethylammonium on the silica surface (stabilized by electrostatic interactions between ammonium head groups and charged silica surface) and featuring a pore size of 5.2 nm, a surface area of 211 m2/g, and a pore volume of 0.28 mL/g.2 Figure 4 shows the maximum height of the low-pressure hysteresis of the noncalcined swollen MCM41 silica as a function of the maximum relative pressure of the adsorption−desorption cycle reached upon adsorption. The graph

Figure 1. (a) Nitrogen adsorption (void symbols) and desorption (filled symbols) isotherms of N2 at 77 K of Si60 silica gel (Fluka) as bare silica (A, squares) and as octylsilane-grafted silica (B, circles). (b) Zoom on low-pressure data. factor 5 did not induce any significant variation of the extent of hysteresis, suggesting that the adsorption system can be considered as equilibrated at the time-scale of the measurements. Figure 2 shows the N2 sorption isotherm at 77 K of an octylsilanegrafted MCM-41 silica. The lining of the 3.7 nm mesopores of MCM-41

Figure 2. Adsorption (void symbols) and desorption (filled symbols) isotherms of N2 at 77 K of an octylsilane-grafted MCM-41 silica. with octyl chains has led to a decrease of the pore diameter: no type IV steps related to capillary condensation in the mesopores can be observed. The sorption isotherm is type I in the IUPAC classification, and the αS-plot (see Figure S1, Supporting Information) indicates a micropore volume of 0.10 cm3/g. Moreover, in this case, adsorption is not fully reversible; the figure clearly shows that the desorption branch of the isotherm gradually separates from the adsorption branch as the pressure decreases. Again, nitrogen is fully desorbed at P* = 0. The N2 sorption isotherm at 77 K of an as-synthesized and dried (noncalcined) MCM-41 silica is reported in Figure 3. The templates of the mesoporous material, hexadecyltrimethylammonium surfactants,

Figure 4. Height of the low-pressure hysteresis at P* = 0.16 on a hexadecyltrimethylammonium-bearing swollen MCM-41 as a function of the maximum relative pressure reached upon adsorption. 9528

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indeed suggests that the height of the hysteresis is roughly proportional to the maximum pressure at which nitrogen uptake has taken place. To further verify the role of absorption in the organic layer on the low-pressure hysteresis, the retention of excess adsorbate was measured

3. MODEL 3.1. Details. Let us consider a surface that is composed of n adsorption sites per unit of surface area (Figure 6). A fraction η of

Figure 6. Schematic view of the model. An inorganic surface (gray substrate) is partially covered with organic molecules (black lines). Upon adsorption, adsorption occurs on top of the grafted molecules (sites I, red spheres), on the sites of the uncovered surface (sites II, blue spheres). In addition, upon adsorption, the space between grafted molecules opens, and new adsorption sites at the pore surface become available for adsorption (sites III, green spheres).

the n sites is occupied by the presence of organic molecules, which can be either grafted or simply deposited on the surface. Upon adsorption, nitrogen molecules can adsorb both on top of the organic molecules ng = ηn sites (sites I in Figure 6) and on the available ns = (1 − η)n sites (sites II in Figure 6) of the bare surface. These two types of sites have different adsorption energies denoted εg and εs, respectively. Multilayer adsorption can occur on these two types of site with the same adsorption energy labeled ε. In addition to adsorption on the sites ns and ng, we consider that a number of nitrogen molecules can penetrate the organic layer and reach available adsorption sites at the pore surface (the green sites III in Figure 6). The latter adsorption process can be accounted for by the solubility of the nitrogen molecules in the organic chain layer. Once “dissolved” in the organic layer, we assume that a nitrogen molecule diffuses and reaches a surface site characterized by an adsorption energy εs (i.e., equal to that of a molecule directly adsorbed on the bare silica surface). While sites I and II are available for adsorption from the very beginning of the process, this is not the case for sites III. At zero pressure, these sites are hidden at the bottom of the organic layer. As gas pressure is increased, more sites III become available. We assume that, upon adsorption, the number nd of sites III increases linearly with pressure (on account of Henry’s law) as such sites appear once nitrogen molecules penetrate in the organic layer. In contrast, upon desorption, the number of available sites nd remains constant and equal to the maximum number of sites nd,max “created” (i.e., uncovered) upon adsorption at the maximum pressure Pmax* . Again, the asterisk indicates that pressures are in reduced units with respect to the nitrogen bulk saturating vapor pressure, P0. In this model, we assume that the process of molecular penetration/diffusion within the organic layer has the effect of uncovering new adsorption sites III on the inorganic surface. Once disclosed, these sites are amenable to the standard equilibrium thermodynamic adsorption/desorption laws. Thus, the overall process is entirely described by equilibrium thermodynamics considerations, rather than being driven by transport effects. In summary, upon adsorption, nd is proportional to P* and is also necessarily related to ng. We write:

Figure 5. Height of the hysteresis at P* = 0.2 for silica surfaces grafted with propyl ( ▲ ), butyl ( ■ ), octyl ( ◆ ) chains or bearing hexadecyltrimethylammonium cations (○) as a function of the surface density of the chains.

on adsorbent surfaces coated with different organic moieties. Figure 5 shows the height of the low-pressure hysteresis as a function of the density of organic chains on the surface of several kinds of organiccoated silicas: commercial silicas, MCM-41 and swollen MCM-41 samples silylated with propyl, butyl, and octyl chains, as well as noncalcined MCM-41 and swollen MCM-41 retaining surface-adsorbed hexadecyltrimethylammonium molecules. For the sake of comparison, the height of the hysteresis was measured at a reduced pressure P* = 0.2 for all physisorption cycles. Moreover, the excess adsorbate amounts are normalized to the surface area of the corresponding bare silica. It can be observed that silylation with propyl and butyl moieties brought no hysteresis in the adsorption−desorption cycles. Moreover, hysteresis loops are only observed when the organics coverage is high enough (surface density of chain greater than 0.8 nm2). As far as the height of the hysteresis on octyl-coated materials as a function of coverage is considered, adsorbate retention is not observed below a threshold coverage of about 0.9 chain per square nm2. At this value, a hysteresis loop appears, and retention of more than 0.15 N2 molecules per nm2 of silica surface is observed. The amount of excess adsorbate moderately increases as the organics coverage further increases. Figure 5 shows that adsorbed hexadecyltrimethylammonium molecules are at the origin of a hysteresis loop having a height similar to that generated by grafted octyl chains (if the two organics are compared at the same surface density of chains). As the hydrocarbon chain of hexadecyltrimethylammonium is twice as long as the octyl chain, the mass of the hydrocarbon chains at a given chain density is 2-fold in the case of hexadecyltrimethylammonium than in the case of octyl. If the low-pressure hysteresis only depended on a Henry’s law absorption of N2 in the hydrocarbon, the excess amount on the hexadecyltrimethylammonium-bearing surface would be twice that of the octyl-grafted surface, in disagreement with the experimental data. The latter result and the comparison between different organics reported in Figure 5 indicate that the presence of hysteresis essentially depends on the density of chains at the surface, provided that the organic chains are long enough. The observation of hysteresis for hydrocarbon chains of 8 or more carbon atoms suggests that only chains flexible enough to form a layer equivalent to a supported liquid phase are at the origin of the phenomenon. Moreover, the presence of low-pressure hysteresis seems independent of the curvature of the supporting surface as the porous silicas under study had average pore diameters spanning from micropores to mesopores larger than 10 nm.

nd = αP*ng

(1)

where the proportionality factor, α, is related to the solubility of the adsorbate within the organic layer. Upon desorption, nd is constant and equal to nd,max, and is related to the maximum pressure reached upon adsorption. We write: 9529

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nd,max = αP*max ng

(2)

Vs(P*), Vg(P*), and Vd(P*) are the volumes or numbers of nitrogen molecules adsorbed on the ns, ng, and nd sites, respectively. The total adsorbed volume V(P*) at a given pressure P* upon adsorption or desorption is simply given by the sum of the adsorbed volumes on the ns, ng, and nd sites: V (P*) = Vg(P*) + Vs(P*) + Vd(P*)

(3)

In our model, the hysteresis loop observed upon adsorption/ desorption isotherms is due to the fact that nd increases linearly with pressure upon adsorption, while it is constant upon desorption. Using our model and testing its predictions against experimental data requires a classical equation to describe each term of eq 3. One can choose any of the thermodynamic adsorption models available in the literature such as the Langmuir or BET model. In the present work, we selected the BET model, which allows describing multilayer adsorption for any adsorbate/adsorbent couple. In the following section, we consider both the case of a planar substrate and a cylindrical mesopore. While the use of a given adsorption theory (the BET theory in the present work) affects the quantitative predictions of the model, it must be emphasized that similar qualitative behavior and predictions would be observed with other adsorption models. 3.2. Adsorption/Desorption in an Organic Layer at the Surface of a Nonporous Substrate. We present here typical results obtained using our model for the adsorption/desorption process of an adsorbate on an organic layer supported on a nonporous substrate. In the BET theory, the adsorbed amount at a given pressure is related to the number of sites available for adsorption and the pressure P*: Vi(P*) =

n iC iP* (1 − P*)(1 + C iP* − P*)

Figure 7. (a) Theoretical nitrogen adsorption/desorption isotherm at 77 K on an organic layer supported onto a nonporous silica surface. The following values were used to calculate the data: Cs = Cd = 90, Cg = 20, and αη = 0.25. The red and blue lines are the adsorption and desorption data, respectively, as predicted with the present model. (b) Different contributions to the adsorption branch of the adsorption isotherm shown on the top panel: (s-blue) adsorbed amount on the bare silica surface, (g-black) adsorption on the top of the organic molecules, and (d-red) nitrogen molecules “dissolved” in the organic layer.

(4)

where i = g, s, d denotes the different possible adsorption sites of the adsorbate: at the top of the organic layer (g), at the bare silica surface (s), or dissolved within the organic layer (d). The constant Ci is related to the energy parameters εs, εg, ε, which have been defined previously. ⎛ε − ε⎞ C i = exp⎜ i ⎟ ⎝ kBT ⎠

following values: Cs = Cd = 90 and Cg = 20. Both the parameters α and η (the fraction of sites occupied by the presence of organic molecules) were arbitrarily fixed to 0.5. Actually, these two parameters cannot be determined independently within our model, and only their product αη can be known (see below, eq 6). Here, αη = 0.25. We also show in Figure 7b the different contributions of the different adsorption sites (s, g, d) to the adsorption branch: adsorbed on the bare silica surface, adsorbed on the top of the organic molecules, and molecules “dissolved” in the organic layer, respectively. In qualitative agreement with experimental nitrogen adsorption/desorption isotherms of materials featuring supported or grafted organic layers, the present model predicts that the adsorption/desorption isotherm on such a surface exhibits a hysteresis loop with parallel adsorption and desorption branches. Such a hysteresis loop spanning over the entire pressure range is of a different nature than capillary condensation hysteresis loops, which are located between the condensation and evaporation branches at well-defined pressures. The hysteresis height ΔV(P*) as a function of pressure P* can be readily estimated from the difference between the adsorbed amounts upon adsorption and desorption:

(5)

where T is the temperature and kB is Boltzmann’s constant. Using eq 4 to estimate the adsorbed amount of nitrogen on the supported organic layer (g), at the bare silica surface (s), and within the organic layer (d), one can estimate the total adsorbed amount at a given pressure through eq 3. We recall that in our model nd is different upon adsorption and desorption: nd = αP*ng upon adsorption and nd,max = αPmax*ng upon desorption. Figure 7a shows a typical calculated nitrogen adsorption/desorption isotherm at 77 K on an organic layer supported onto a silica surface. The number of nitrogen molecules adsorbed on the surface is expressed per nm2 for further comparison with experimental results. For this purpose, the adsorbed amounts have been divided by the total number of available sites n. Experimentally, C parameters of 90−110 are generally observed for N2 adsorption on pure silica surfaces. A much lower value of 20 is reported for completely silylated surfaces, as expected due to a lower interaction energy between the organic and the nitrogen molecule.32 On the basis of these experimental results, the adsorption isotherm shown in Figure 7 was obtained with the

ΔV (P*) =

αη(P*max − P*)CsP* (1 − P*)(1 + Cs − 1)P*)

(6)

We recall that Pmax* is the maximum pressure reached upon adsorption. As shown in eq 6, for a given Cs value and a given 9530

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pressure P*, ΔV(P*) varies in a linear way with Pmax*, α, and η. ΔV(P*) is proportional to both α and η so that the two variables cannot be fitted independently; that is, there exists an infinite set of values (α,η) such as αη = constant that can be used to fit the experimental data. As a result, in the rest of this section, we report data for several values of the product αη. In contrast, when comparing below with available experimental data for nitrogen adsorption/desorption on hybrid materials, only α will be adjusted as η is known for each sample that will be considered. Figure 8a shows the hysteresis height as a function of pressure P*

3.3. Adsorption/Desorption in an Organic Layer Supported on a Mesoporous Substrate. We now consider nitrogen adsorption/desorption in organic molecules supported in porous silica materials, which exhibit cylindrical mesopores. Let us consider a cylindrical pore of a diameter D and length L. The number of sites n is proportional to πDL. Considering the length δ of the grafted molecules, the number of adsorption sites ng available is proportional to π(D −2δ)ηL. As in the previous section, we used the BET theory to estimate the amount of nitrogen adsorbed on top of the supported organic molecules (g), the bare silica surface (s), and within the organic layer (d). Figure 9 shows the nitrogen adsorption/desorption isotherms

Figure 8. (a) Theoretical hysteresis height (difference between the adsorbed amounts upon desorption and adsorption at the same given pressure) in molec·nm−2 as a function of pressure P* for Pmax* = 0.99. (b) Theoretical hysteresis height at P* = 0.1 as a function of the maximum pressure reached upon adsorption. In both graphs, the blue, red, black, purple, and green curves correspond to αη = 0.1, 0.25, 0.5, 0.75, and 1, respectively.

Figure 9. Experimental nitrogen adsorption/desorption isotherms at 77 K on MCM-41 mesoporous silica grafted with dimethyloctylsilane for a maximum pressure Pmax* reached upon adsorption: (a) Pmax* = 0.25 and (b) Pmax* = 0.42. The open and closed symbols are the experimental adsorption and desorption data, respectively. The solid and dashed lines are the theoretical adsorption and desorption data, respectively.

predicted by our model for two maximum pressures Pmax* reached upon adsorption: Pmax* = 0.25 and 0.42. The latter data were adjusted against available experimental adsorption data, which were obtained for N2 adsorption/desorption isotherms at 77 K on octylsilane-grafted MCM-41 mesoporous silica. As can be seen in Figure 9, good agreement between the experimental data and our model was obtained for a set of parameters α = 0.27, η = 0.72 (i.e., αη = 0.1944), and ρ = 5.8 nm−2. The latter value, which corresponds to the surface density of nitrogen molecules adsorbed at the surface of the material, is consistent with what is expected on the basis of the molecular surface area for the nitrogen molecule: a = 0.16 nm2, which corresponds to a density of site of ρ = 1/a = 6.25 nm−2. The ρ parameter is only needed to obtain adsorbed quantities in molec/nm2 (ms =ρns and mg = ρng). Other parameters of the model, which are known for N2 adsorption on silica grafted with organic molecules, are Cs = Cd = 90, Cg = 25, and δ= 1 nm (the latter value corresponds to a reasonable value for the length of the octyl chains).

for nitrogen adsorption at 77 K on an organic layer supported onto a silica surface for a fixed value Pmax* of 0.99. Data for several values of the product αη are shown to estimate their effect on the hysteresis height. Except at their lower and upper closure points (P* = 0 and P* = Pmax*, respectively), the hysteresis height is nearly independent of pressure in agreement with experimental data for nitrogen adsorption isotherms on grafted silica materials. For the same coefficient α, the height of the hysteresis will increase with the fraction of organic materials present on the surface. We also show in Figure 8b the hysteresis height at P* = 0.1 as a function of the maximum pressure Pmax* reached upon adsorption. Again, we report data for several values of the product αη. The hysteresis height at P* = 0.1 increases in a linear way with Pmax*. This result is due to the fact that in our model the difference between the number of adsorption sites nd upon adsorption and desorption is an increasing linear function of Pmax*. 9531

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For the same parameters of our model, Figure 10 shows the height of the low-pressure hysteresis as a function of the

Figure 12. Low-pressure hysteresis height (expressed in molecule/nm2) taken at P* = 0.2 for different mesoporous silica materials grafted with octylsilane chains as a function of their pore size. For comparison, the hysteresis height has been calculated in molecules divided by the surface area of native silica materials (blue data) or of grafted silica (red data). The lines correspond to the predictions of the present model, while the symbols are the experimental data obtained for dimethyloctylsilane grafted on different mesoporous silicas.

Figure 10. Height of the low-pressure hysteresis (difference between the adsorbed volumes upon adsorption and desorption expressed in molecules/nm2) as a function of the maximum pressure Pmax* reached upon adsorption. The hysteresis height is taken at a pressure P* = 0.16. The straight line corresponds to the predictions of the present model, while the symbols are the experimental data obtained for dimethyloctylsilane grafted on MCM-41 mesoporous silica.

Very good agreement is found between the experimental and theoretical data, which shows that the present model captures the adsorption and desorption mechanisms of gas molecules within grafted or deposited organic layers at the surface of porous substrates. In particular, given that the data shown in Figure 12 are for different samples and that the low-pressure hysteresis effect is quite small, the agreement obtained between experiments and the present model is remarkable.

maximum pressure Pmax* reached upon adsorption. The hysteresis height is taken at a pressure P* = 0.16 as the difference between the adsorbed amounts of nitrogen upon desorption and adsorption. To further test our model against experimental data, we show in Figure 11 the height of the hysteresis as a function of

4. CONCLUSION This Article reports both experiments and a simple thermodynamic model of N2 adsorption on organics-coated silicas. The experimental adsorption isotherms exhibit a low-pressure hysteresis with the desorption branch that does not meet the adsorption branch after emptying of the pores. Such a hysteresis loop, in which the desorption curve lies nearly parallel to the adsorption curve at a slightly higher adsorbed amount, differs from hysteresis loops related to capillary condensation as it occurs at a pressure lower than the closure point of capillary condensation hysteresis. To address the physical origin of such unexplained hysteresis loops, we report a simple thermodynamic model, which provides a simple yet physically sound picture of the phenomena at play. In this model, we assume that nitrogen adsorbs within the organic layer in addition to the surface that is free of organic material and on the top of the organic layer. Upon adsorption, the number of sites nd available within the organic layer increases linearly with pressure (i.e., guest molecules dissolve into the organic layer according to a Henry’s law). In contrast, upon desorption, the number of available sites nd within the organic layer remains constant to the maximum number of sites nd,max uncovered upon adsorption at the maximum pressure. As a result, the hysteresis loop predicted in our model is due to the fact that the adsorption sites available within the organic layer increase linearly with pressure upon adsorption, while it is constant upon desorption. The present model, which is found to be in good agreement with experimental data, captures the essential features of adsorption experiments on hybrid organic− inorganic materials. In particular, the present model correctly predicts the shape of the adsorption isotherm. Thanks to the use of a minimum number of parameters (which can be estimated from simple experimental data), the present model could be used

Figure 11. Low-pressure hysteresis height as a function of pressure for different maximum pressures reached upon adsorption Pmax*: (blue) Pmax* = 0.25, (red) Pmax* = 0.42, and (black) Pmax* = 0.6. The experimental data (symbols) have been obtained for dimethyloctylsilane grafted on MCM-41 mesoporous silica.

pressure for different values of Pmax* = 0.25, 0.42, and 0.60. We also compared them to experimental data obtained from nitrogen adsorption/desorption isotherms at 77 K on MCM-41 mesoporous silica grafted with octyl chains. For all values of Pmax*, the theoretical predictions are in good agreement with the experimental data. Figure 12 shows the height of the hysteresis loop divided by the surface of the calcined material or the noncalcined material as a function of the pore diameter D. The hysteresis height is taken at a pressure P* = 0.2 and corresponds to the difference between the adsorbed amounts upon desorption and adsorption. Both theoretical and experimental data are reported for nitrogen adsorption/desorption at 77 K on octylsilane-grafted mesoporous silicas. 9532

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(8) Tokarev, A.; Grandjean, A.; Guari, Y.; Larionova, J.; Pflieger, R.; Guerin, C. Functionalized Porous Glass for the Removal and the Confinement of Ruthenium from Radioactive Solutions. J. Nucl. Mater. 2010, 400, 25. (9) Sepehrian, H.; Ghannadi-Maragheh, M.; Waqif-Husain, S.; Yavari, R.; Khanchi, A. R. Sorption Studies of Radionuclides on a Modified Mesoporous Cerium(IV) Silicate. J. Radioanal. Nucl. Chem. 2008, 275, 145. (10) Mahmoud, M. E.; Haggag, S. S.; Hegazi, A. H. Synthesis, Characterization, and Sorption Properties of Silica Gel-Immobilized Pyrimidine Derivative. J. Colloid Interface Sc 2006, 300, 94. (11) Ju, Y. H.; Webb, O. F.; Dai, S.; Lin, J. S.; Barnes, C. E. Synthesis and Characterization of Ordered Mesoporous Anion-Exchange Inorganic/Organic Hybrid Resins for Radionuclide Separation. Ind. Eng. Chem. Res. 2000, 39, 550. (12) Rouquerol, F.; Rouquerol, J.; Sing, K. S. W. Adsorption by Powders and Porous Solids; Academic Press: London, 1999. (13) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic Press: New York, 1982. (14) Barrett, E. P.; Joyner, L. G.; Halenda, P. P. The Determination of Pore Volume and Area Distributions in Porous Substances. I. Computations from Nitrogen Isotherms. J. Am. Chem. Soc. 1951, 73, 373. (15) Brunauer, S.; Emmett, P. H.; Teller, E. Adsorption of Gases in Multimolecular Layers. J. Am. Chem. Soc. 1938, 60, 309. (16) Corma, A. From Microporous to Mesoporous Molecular Sieve Materials and Their Use in Catalysis. Chem. Rev. 1997, 97, 2373. (17) Ciesla, U.; Schuth, F. Ordered Mesoporous Materials. Microporous Mesoporous Mater. 1999, 27, 131. (18) Soler-Illia, G. J.; de, A. A.; Sanchez, C.; Lebeau, B.; Patarin, J. Chemical Strategies To Design Textured Materials: from Microporous and Mesoporous Oxides to Nanonetworks and Hierarchical Structures. Chem. Rev. 2002, 102, 4093. (19) Jaroniec, C. P.; Kruk, M.; Jaroniec, M.; Sayari, A. Tailoring Surface and Structural Properties of MCM-41 Silicas by Bonding Organosilanes. J. Phys. Chem. B 1998, 102, 5503. (20) Ding, J.; Hudalla, C. J.; Cook, J. T.; Walsh, D. P.; Boissel, C. E.; Iraneta, P. C.; O’Gara, J. E. Synthesis and Surface Chemistry of Spherical Mesoporous Organic−Inorganic Hybrid Particles with an Integrated Alcohol Functionality on the Pore Surface. Chem. Mater. 2004, 16, 670. (21) Margolese, D.; Melero, J. A.; Christiansen, S. C.; Chmelka, B. F.; Stucky, G. D. Direct Syntheses of Ordered SBA-15 Mesoporous Silica Containing Sulfonic Acid Groups. Chem. Mater. 2000, 12, 2448. (22) Walcarius, A.; Delacôte, C. Rate of Access to the Binding Sites in Organically Modified Silicates. 3. Effect of Structure and Density of Functional Groups in Mesoporous Solids Obtained by the CoCondensation Route. Chem. Mater. 2003, 15, 4181. (23) Martin, T.; Galarneau, A.; Brunel, D.; Izard, V.; Hulea, H.; Blanc, A. C.; Abramson, S.; Di Renzo, F.; Fajula, F. Towards total Hydrophobisation of MCM-41-type silica Surface. Stud. Surf. Sci. Catal. 2001, 135, 4621. (24) Desplantier, D. Ph.D. Thesis, Montpellier, 2000. Iapichella, J. Ph.D. Thesis, Montpellier, 2006. (25) Iapichella, J.; Meneses, J.-M.; Beurroies, I.; Denoyel, R.; BayramHahn, Z.; Unger, K.; Galarneau, A. Characterization of Mesoporous Silica and Its Pseudomorphically Transformed Derivative by Gas and Liquid Adsorption. Microporous Mesoporous Mater. 2007, 102, 111. (26) Lassiaz, S.; Mutin, H.; Galarneau, A.; Trens, P.; Labarre, D.; Brunel, D. Organo-lined Alumina Surface from Covalent Attachment of Alkylphosphonate Chains in Aqueous Solution. New J. Chem. 2010, 34, 1424. (27) Lassiaz, S.; Galarneau, A.; Labarre, D.; Brunel, D.; Mutin, H. Modification of Silica by an Organic Monolayer in Aqueous Medium Using Octylphosphonic Acid and Aluminium Species. J. Mater. Chem. 2011, 21, 8199. (28) Brunel, D.; Cauvel, A.; Di Renzo, F.; Fajula, F.; Fubini, B.; Onida, B.; Garrone, E. Preferential Grafting of Alkoxysilane Coupling Agents on the Hydrophobic Portion of the Surface of Micelle-Templated Silica. New J. Chem. 2000, 24, 807.

to assess surface properties of hybrid systems consisting of an organic layer supported or grafted on inorganic substrates. Further work will be performed to use this model to better characterize the uniformity of an organic layer adsorbed or grafted on the surface of a porous material. In particular, given that the total number of organic molecules at the pore surface is known in the experiments, the present model could be used to determine the parameter α by fitting against the experimental adsorption data. The latter parameter provides a qualitative order parameter to describe the quality of the grafting or deposit of organic layers at the pore surface. For instance, low α values suggest that the number and surface density of organic layers are small so that the number of nitrogen molecules that can adsorb between them is small. In contrast, large α values would suggest that the number and surface density of organic layers are large (dense regions of organic chains) so that a large number of adsorbate molecules can adsorb between the chains.

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ASSOCIATED CONTENT

* Supporting Information S

αS-Plot of the octylsilane-grafted MCM-41 silica as well as noncalcined MCM-41. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +33 1 44 32 24 29. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Christine Biolley, Daniel Brunel, Delphine Desplantier-Giscard, Thierry Martin, and Julien Iapichella for technical support.

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REFERENCES

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