Adsorption and Depletion Regimes of a Nonionic Surfactant in

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Adsorption and depletion regimes of a nonionic surfactant in hydrophilic mesopores: An experimental and simulation study Dirk Müter, Gernot Rother, Henry Bock, Martin Schoen, and Gerhard H. Findenegg Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b02262 • Publication Date (Web): 15 Aug 2017 Downloaded from http://pubs.acs.org on August 17, 2017

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Adsorption and Depletion Regimes of a Nonionic Surfactant in Hydrophilic Mesopores: An Experimental and Simulation Study Dirk Müter,a Gernot Rother,b,c Henry Bock,d* Martin Schoen,b and Gerhard H. Findeneggb* a

Nano-Science Center, Department of Chemistry, University of Copenhagen, Copenhagen,

Denmark b

Stranski Laboratory of Physical and Theoretical Chemistry, Department of Chemistry,

Technical University Berlin, 10623 Berlin, Germany c

Geochemistry & Interfacial Science Group, Chemical Sciences Division, Oak Ridge National

Laboratory, Oak Ridge, Tennessee 37831-6110, U.S.A. d

Institute of Chemical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, United

Kingdom

ACS Paragon Plus Environment

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ABSTRACT. Adsorption and aggregation of nonionic surfactants at oxide surfaces has been studied extensively in the past, but only for concentrations below and near the critical micelle concentration. Here we report an adsorption study of a short-chain surfactant (C6E3) in porous silica glass of different pore sizes (7.5 to 50 nm), covering a wide composition range up to 50 wt.-% in a temperature range from 20°C to the LCST. Aggregative adsorption is observed at low concentrations, but the excess concentration of C6E3 in the pores decreases and approaches zero at higher bulk concentrations. Strong depletion of surfactant (corresponding to enrichment of water in the pores) is observed in materials with wide pores at high bulk concentrations. We propose an explanation for the observed pore-size dependence of the azeotropic point. Mesoscale simulations based on dissipative particle dynamics (DPD) were performed to reveal the structural origin of this transition from the adsorption to the depletion regime. The simulated adsorption isotherms reproduce the behavior found in the 7.5 nm pores. The calculated bead density profiles indicate that the repulsive interaction of surfactant head groups causes a depletion of surfactant in the region around the corona of the surface micelles.

INTRODUCTION Adsorption of surfactants from aqueous solutions onto solid surfaces is of eminent importance for technological processes involving detergency, wetting, adhesion, and the stabilization of colloidal dispersions. Surfactant adsorption in narrow pores plays an important role in surfactantaided separation processes, such as membrane filtration1 or micellar-enhanced ultrafiltration.2 Nonionic surfactants are strongly adsorbed onto hydrophobic surfaces via hydrophobic interactions with the surfactant tails. Adsorption onto polar/hydrophilic surfaces involves more


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subtle interactions. For surfactants of the n-alkyl poly(oxyethylene) ether family (abbreviated as CnEm), hydrogen bonding of the ether groups to surface hydroxyl groups is believed to represent the dominant binding mechanism. Because the ether moieties of the surfactant heads and the surface hydroxyl groups both are strongly hydrated in water, the net interaction of a surfactant molecule with the surface is weak. Hence, very weak adsorption is observed at concentrations well below the critical micelle concentration (cmc).3 At higher concentrations, but still below the cmc, surfactant aggregation reminiscent of micelle formation can occur at the surface and lead to a sharp increase in adsorption.4,5 This aggregative adsorption behavior is exemplified by CnEm surfactants at hydrophilic silica surfaces.3,6,7,8,9 CnEm surfactants with short hydrophobic tails are miscible with water in all proportions at low temperatures, but phase separation occurs above a lower critical solution temperature (LCST) to coexisting water-rich and amphiphile-rich phases.10 A phenomenon closely connected with this phase behavior is the anomalous temperature dependence of the adsorption of CnEm surfactants: Whereas normally adsorption decreases with increasing temperature, aggregative adsorption of CnEm surfactants at hydrophilic surfaces increases with temperature.11,12 This behavior is attributed to a gradual dehydration of the surfactant heads (i.e., breaking of water– surfactant H-bonds) with increasing temperature, which renders the surfactant molecules less hydrophilic in water and thus favors phase separation and accumulation of surfactant at the surface. Two of the present authors have cooperated with Keith Gubbins in developing a theoretical model for this behavior13 and its experimental test.14 In the past, studies of surfactant adsorption focussed on the low-concentration region below and near the cmc, where the adsorption isotherms reach a plateau value. Recently we studied the adsorption of the weakly amphiphilic surfactant C6E3 in mesoporous silica glass up to much


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higher concentrations and observed a novel behavior.15 At concentrations above the cmc the adsorption, expressed as a surface excess of the surfactant, does not remain constant but gradually decreases and eventually becomes negative. A negative surface excess of the surfactant implies that water was enriched and the amphiphile depleted in the pores. The transition from preferential adsorption of surfactant to preferential adsorption of water marks a surface azeotropic point. The possibility of a surface azeotrope in adsorption from binary systems was predicted long ago16,17 for systems in which neither of the components is strongly preferred by the surface, and for temperatures close to a liquid/liquid phase separation. However, to our knowledge the recent work of Rother et al.15 was the first report of a surface azeotrope in an aqueous surfactant system. Thermodynamic and structural aspects of the self-assembly of nonionic surfactants in hydrophilic pores have been studied experimentally14,18,19 and by models based on classical thermodynamics20 or mean-field lattice theory.21 More recently, mesoscale simulation techniques including various variants of the dissipative particle dynamics (DPD) have been used

for

modeling aqueous solutions of nonionic surfactants in monolayers,22,23 micelles,24,25 and in confined

geometries.25,26,27,28,29

DPD simulations provide information

about

possible

morphologies of surfactant aggregates in confinement,26 but also about the distribution of surfactant molecules between the pore space and an external reservoir, i.e., the adsorption isotherm.28 Using this approach, Rother et al.15 showed that a layer of micellar aggregates formed near the surface of the pores can repel further amphiphile molecules from the surface region, thereby causing a decrease in adsorption and formation of a layer depleted in amphiphile at higher amphiphile concentrations.


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Although our recent study15 clearly demonstrated the existence of a surface azeotrope, it was desirable to confirm the unusual adsorption behavior at high amphiphile concentrations by adsorption measurements based on a different technique. Instead of the isothermal titration method used in the previous study we now derive adsorption isotherms from temperature scans of the equilibrium composition of the supernatant solution measured for a series of initial compositions of the bulk system.30,31 By this independent technique we can locate the azeotropic composition with higher confidence, and study the adsorption behavior up to the LCST. The simulation studies reported in this work focus on the dependence of the azeotropic composition on the pore diameter, and the influence of the parameter controlling the relative strength of surfactant head beads and water with the surface.

MATERIALS AND METHODS Materials Three controlled-pore glass (CPG10) materials with nominal mean pore sizes 75 Å, 240 Å and 500 Å were supplied by Fluka (Germany). We refer to these materials by their nominal pore size as CPG-75, CPG-240 and CPG-500. The materials CPG-75 and CPG-240 were characterized by nitrogen adsorption. Values of their BET specific surface area , total specific pore volume , mean pore diameter (BHJ, desorption branch), and hydraulic diameter are given in Table 1. The values for CPG-500 result from Hg porosimetry measurements as given by the producer. The CPG powders were cleaned by acid-treatment to remove soluble traces of the borate phase and adsorbed organic contaminants from the pore walls, and rinsed thoroughly with Milli-Q water until pH neutrality. Accordingly, differences in pH of the three materials resulting from the purification process can be excluded. Details of the purification method are given elsewhere.31


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The surfactant n-hexyl trioxyethylene (C6E3) supplied by Bachem (purity 99.5% by GC and 98.4% by elemental analysis) and milli-Q50 water was used to prepare the aqueous mixtures. < TABLE 1 here > Adsorption measurements Preferential adsorption from the binary mixture in the pores of the CPG materials was determined from the change in composition of the mixture before and after equilibration with the CPG. Measurements were made as a function of temperature for several samples of known initial compositions, characterized by the mass fraction of amphiphile . The shift in composition − after equilibration of the mixture with the adsorbent at temperature was determined using a sensitive differential refractometer (DR) as described elsewhere.30,31 The adsorbed amount is expressed by the mass-related reduced surface excess amount of the amphiphile per unit surface area,32

, =

,

(1)

where is the overall mass of the liquid mixture, and , respectively, the mass fraction of amphiphile in the initial mixture, and the mass fraction after equilibration at temperature with a mass of the adsorbent of specific surface area ; is the molar mass

of the amphiphile ( = 234,34 g/mol for C6E3).

represents the difference between the

amount of amphiphile actually present in the system ( = ⁄ ) and the amount !"#

= $ in a reference system of uniform composition throughout the entire mass

, expressed per unit surface area of the adsorbent (surface excess concentration). For a binary system (A + W) the surface excess concentrations of the two components are interrelated as


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%

= − ⁄%

, where % denotes the molar mass of water. For the present system

⁄% = 13.0. Mixtures (ca. 1cm3) of the desired initial mass fraction were prepared by weight directly in the sample compartment of the DR, and about 100-200 mg of the CPG powder was added, depending on the specific surface area of the material (Table 1). The pore volume amounted to 10-20 % of the total volume of liquid. The reference compartment of the DR contained pure water. At each experimental temperature the sample was equilibrated for ca. 2 h, with frequent brief magnetic stirring of the sample compartment to accelerate mass transfer. The equilibrium composition ( ) was then determined from the DR reading based on a calibration of the instrument for the experimental composition and temperature range. In this way, temperature scans of

, were obtained from 20 °C up to the phase separation

temperature at each chosen initial composition . Errors in

arise mostly from errors in the

determination of the compositions and , which are estimated respectively to ≤ 4x10-4 and ≤ 2x10-4. Hence, the error in the composition difference & = δ( − ) is ≤ 6x10-4. This

translates into a relative error in

up to 5% for

≈ 3 µmol/m2, and up to 15% for

≈ 1 µmol/m2. In addition, an error in the specific surface area of the CPG materials will

cause a systematic error in the values of

. Such errors are estimated to be < 5%. The

temperature scan method is believed to be more reliable than the isothermal titration method15 for determining adsorption at high amphiphile concentrations, as it avoids cumulative errors that can arise in the titration method. On the other hand, the present method has a lower concentration resolution than the titration method, and thus it is less suitable for resolving details of the adsorption isotherms in the low-concentration regime.


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Mesoscale simulations Mesoscale simulations of the adsorption of amphiphilic molecules in cylindrical pores were performed using the DPD method in the canonical ensemble (+,,, ) as described previously.15 The molecules were modelled as a chain of beads (H5T5) consisting of a block of five hydrophilic head beads (H) and five hydrophobic tail beads (T) of equal van der Waals diameter σ, joined by harmonic springs. The pores are simulated as smooth cylinders of radius - and length ., where - is defined as the distance from the pore center to the center of the smoothedout wall beads. The pores are directly connected to the bulk reservoir at both ends. The first 5/ of pore length are ignored in the analysis, giving . = 120/.28 The solvent is treated implicitly, which leads to effective and coarse-grained forces between all remaining interaction centers. The attractive T-T interaction is represented by the Lennard-Jones (LJ) (12-6) potential, and the repulsive H-H and H-T interactions by the soft-repulsive Weeks–Chandler–Andersen (WCA) potential.33 As reported earlier,25 this model surfactant aggregates to spherical micelles at a cmc = 5.2x10-5 molecules// 0 . The interaction of the hydrophilic pore wall with the surfactant head and tail beads is represented by the purely distance-dependent LJ (12-6) potential (H beads) and WCA potential (T beads). In both cases the origin of the potential is the position of the pore wall at -. The strength of both interactions is scaled by a factor 2 relative to the attractive T-T potential. 2 represents a key parameter in this study, as it quantifies the preference of the pore wall for the hydrophilic head beads relative to the (implicit) solvent. Adsorption isotherms were constructed by computing the numbers of molecules in the pore (+ ) and in the bulk reservoir (+3 ) at equilibrium for a set of total numbers of amphiphile molecules in the system. To make sure that equilibrium had been reached in the simulations, we


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observed the change in temperature, bulk concentration and mean aggregate size. Temperature, as regulated by the DPD approach reached a stable value (±1% of the target temperature of 0.72/56 ) within 105 simulation time steps. Bulk concentration became stable after 1–1.5x106 simulation time steps with deviations from the mean value being less than 2% at high bulk concentration. The mean aggregate size approaches a value of ~40 molecules for both adsorbed and free aggregates, which is consistent with our previous work28 in the same simulation time frame. Thus, equilibration time was set to 2.5x106 time steps at a total simulation runtime of 5x106 time steps. Adsorption isotherms are represented by the equilibrium concentration of amphiphile molecules in the pore, 7 = + ⁄, , or the excess concentration 7 − 73 , as a function of the bulk concentration 73 . For a comparison with experimental results we consider the surface excess concentration , given by the excess number of molecules per unit surface area relative to a reference system in which the entire pore volume contains fluid of bulk concentration, 8

= :+ − 73 , ;.

(2)

9

For a given porous matrix, is linearly related to the excess concentration as - − /⁄2 ? . and @ = 2>- − /⁄2 ..


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RESULTS Experimental findings < FIGURE 1 here > Adsorption from the binary system C6E3 + H2O in the three Controlled-Pore Glass materials CPG-75, CPG-240 and CPG-500 was studied in an extended composition range below and above the critical composition of the upper miscibility gap (A = 0.141) for temperatures from 20°C up to the phase separation temperature 3 at the respective composition. Results for the adsorption in CPG-240 at several initial compositions in a range 0.1 < < 0.5 are shown in Figure 1. Corresponding results for the adsorption in CPG-75 and CPG-500 are presented in Supporting Information. The temperature vs. composition diagram in Fig. 1(a) shows the composition ( ) of the supernatant solutions after equilibration with the adsorbent at a series of temperatures. The respective initial compositions are indicated by vertical lines. For the scans at compositions < 0.2 the equilibrium composition is lower than ( < ), which

from eq (1) implies that

is positive, i.e., the amphiphile is preferentially adsorbed at these

compositions. For the scans at compositions > 0.2 we find that > , implying that

is negative, i.e., water is preferentially adsorbed in this region. Closer inspection of Fig. 1(a) also shows that the temperature scans ( ) are not vertical, which means that adsorption exhibits some temperature dependence. This behavior is shown more distinctly in Fig. 1(b), where the

values of

obtained by eq (1) for the trajectories of Fig. 1(a) are plotted against temperature.

Each trajectory terminates at the respective liquid-liquid coexistence temperature 3 . At

temperatures near 3 ,

exhibits a significant temperature dependence, increasing with in

the water-rich region, but decreasing with increasing at higher amphiphile concentrations. < FIGURES 2 – 4 here >


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Based on the results as shown in Fig. 1, and temperature scans obtained for lower amphiphile

concentrations (see SI), adsorption isotherms

=

( ) were constructed for several

temperatures up to A . Isotherms for 20, 30, 40 and 44 °C in the three CPG materials are shown in Figures 2–4. These results confirm our recent finding15 of a transition from preferential adsorption of the amphiphile at low concentration to preferential adsorption of water at high concentration of the amphiphile. The composition of the surface azeotrope, B , exhibits a pronounced dependence on the pore size; namely, B is smallest in the material with the widest pores (CPG-500) and largest in the material with smallest pores (CPG-75). The values of B in CPG-500 and CPG-240 agree with our earlier results (for 20°C) obtained by the isothermal titration method.15 For CPG-75 we estimate the azeotrope composition by linear extrapolation of the existing data (see Fig. 2). The new value (B = 0.32 ± 0.01 at 20 °C) is larger than the one resulting from the titration measurements (B = 0.27) but is believed to be more reliable, as it is not affected by cumulative mixture composition errors of the titration method. In all materials B slightly increases with increasing temperature. This temperature dependence of B results

from the inverse temperature dependence of

in the region of aggregative adsorption, which

extends up to the azeotropic composition. < TABLE 2 here > The surface excess isotherms in CPG-240 and CPG-500 (Figs. 3 and 4) were measured up to amphiphile mass fractions well above the azeotropic point. They exhibit an extended linear region in the high-concentration regime, conforming to a relation

= − C

(4)


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where C is the magnitude of the slope in the linear region of the isotherm, and the surface excess extrapolated to = 0. Values of , C, and B = ⁄C for the 20 °C isotherms are given in Table 2. The corresponding values for CPG-75, extracted from the linear region of the isotherm below the surface azeotrope, are also included. The values of in Table 2 are similar to the plateau values of the adsorption isotherms of the amphiphile C8E4 in the same materials.14 A remarkable result of Table 2 is that the magnitude of the slope C increases by a factor 5 from CPG-75 to CPG-500. We return to this point in the Discussion.

For CPG-500 large negative values of

large surface excess of water (%

(up to -15 µmol/m2), corresponding to a very

≈ +200 µmol/m2), are found at bulk compositions

between 0.4 and 0.5 at 20°C. It appears that

range. (Note that a minimum in

is reaching its minimum in that composition

in the composition range B < < 1 is a direct

consequence of the surface azeotrope.) Negative values of

a wide composition range, reaching about -6 µmol/m2 (%

are also found in CPG-240 over

≈ +80 µmol/m2) at = 0.5. In this

case the minimum in the surface excess is not reached in the experimental composition range. For CPG-75 the situation is less clear, as our measurements did not extend to compositions above the surface azeotrope, and a few data points for 20°C close to the azeotrope may suggest leveling off without reaching an azeotrope. However, our earlier study15 clearly indicates a surface azeotrope and this is what we assume in this work by using extrapolation to determine the position of the azeotrope (see Fig. 2). Hence, the experimental study shows that with increasing pore size the surface azeotrope is moving to lower amphiphile concentrations and there is an increasing preference for water in the pores at compositions > B .


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Results from DPD DPD simulations were performed for H5T5 molecules in cylindrical pores of diameters in the range 24/ ≤ ≤ 56 /. As the micelles formed by H5T5 have a mean diameter of 10.5 /,25 the chosen pore diameters cover a range from 2.3 to 5.3 micelle diameters (see Table 3). < FIGURE 5 here > The influence of the adsorption parameter 2 on the adsorption of H5T5 was studied for one representative pore diameter, = 40 / (3.8 micelle diameters). Surface excess isotherms for different values of 2 are shown in Figure 5. The highest value (2 = 2.5) corresponds to strong preference of the pore wall for the head beads relative to the (implicit) water. In this case the adsorption isotherm exhibits a step at a concentration 73 = 3.5x10-5 / 0, indicating aggregative adsorption of the surfactant at a concentration below the bulk cmc = 5.2x10-5 / 0 28 (see inset in Fig. 5). Surface aggregation leads to a maximum surface excess of nearly 9x10-2 / ?. As the bulk concentration is further increased, gradually decreases but remains positive for bulk concentrations up to 3x10-2 / 0 studied in this work. Lowering the adsorption parameter 2 causes pronounced changes of the adsorption isotherm, namely a smaller initial slope and maximum surface excess, and disappearance of the inflection point. The adsorption isotherm for 2 = 1.5 can be represented by a Langmuir equation in the low-concentration region up to 5x10-4 / 0 (see inset in Fig. 5), and the maximum surface excess is reduced to 4x10-2 / ?. For 2 = 1.2 the adsorption isotherm exhibits a shallow maximum with < 1x10-2 / ?, and the surface excess changes from positive to negative at a bulk concentration 73B ≈1.5x10-2 / 0 . Eventually, at 2 = 1.0 a weak negative surface excess of the amphiphile is observed even at the lowest concentrations. < FIGURE 6 here >


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A comparison of the radial concentration profiles of the systems at 2 = 1.2 and 2 = 1.5 reveals the structural differences that lead to an azeotrope in one case but not in the other. Figure 6(a) shows radial concentration profiles FG of head beads, tail beads, and their sum for the two systems at a high bulk concentration. The two systems behave quite similar except for the region between the hydrophobic core of the admicelles and the pore wall. Here the concentration of directly adsorbed head beads is much higher in the 2 = 1.5 system, and thus the micelles can move somewhat closer to the pore wall than in the 2 = 1.2 system. The maximum in FG of tail beads at the pore center (see Fig. 6(a)) indicates micelles located near the pore center, which is peculiar for pores with = 40/ (see later). Fig. 6(b) shows histograms of the excess number of beads at a given distance from the pore center, &+G = HFG − F3 I&,G , with &,G = >.HG + &G ? − G ? I and &G = 0.125/. The histogram of the 2 = 1.5 system exhibits a pronounced peak near the pore walls, while in the 2 = 1.2 system &+G is mostly negative in this region. All other differences between the two systems are comparatively small. The integral excess number of beads in the region from the pore wall to a distance - − G from the wall, +- − G = ∑L! &+G , is shown in Fig. 6(c). In both systems +- − G has negative values at L small distances from the pore wall, but is significantly more negative in the 2 = 1.2 system, because of the more negative local excess concentration FG − F3 near the pore wall (Fig. 6b). As the distances from the pore wall increases, +- − G first increases steeply due to the high local density in the micellar cores, then decreases in the head group corona, and finally again increases in the core region of the pore, due to the presence of micelles in this region. A positive overall surface excess, +- = 7 − 73 , , is reached in the 2 = 1.5 system, but a negative overall surface excess in the 2 = 1.2 system. The difference in +- − G between the two systems (dashed curve in Fig. 6(c)) clearly demonstrates that the difference in surface excess


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concentration arises almost entirely from the different structure in the part of the head-group corona of the adsorbed micelles that lies nearest to the pore wall. < FIGURE 7 here > The influence of the pore size on the adsorption isotherm of H5T5 is shown in Figure 7. Here the adsorption parameter was fixed to a value of 2 = 1.5. Fig. 7(a) presents the mean concentration in the pore, 7 , as a function of the bulk concentration 73 . For all pore sizes studied a significant enrichment of amphiphile in the pore space is observed at low bulk concentrations. As the bulk concentration increases the concentration in the pore increases less, and 7 gradually approaches 73 . These trends can be seen more clearly in Fig. 7b, where the excess concentration in the pore, 7 − 73 , is plotted. For all pore sizes the excess concentration reaches a maximum at a bulk concentration 73 below 3x10-3/ 0, but the maximum value shows a pronounced dependence on pore size, being highest for the smallest pore and lowest for the largest pore. The decrease of 7 − 73 at concentrations above the adsorption maximum is steepest for the smallest pore ( = 24/), where it eventually leads to a sign inversion of the surface excess from positive to negative at 73B ≈ 2.5x10-2 / 0 . Fig. 7(b) suggests the existence of a surface azeotrope also for = 32/ at a similar concentration, and perhaps also for = 48/, but not for the intermediate pore size = 40/, for which 7 − 73 levels off at a positive value at the highest bulk concentrations. Results for = 56/ do not extend to such high concentrations but also appear to level off at positive values. Note that at concentrations near the maximum of the isotherms in Fig. 7(b) the adsorption is changing monotonically with pore size, whereas at higher concentrations it is not. This, as explained below, is related to micellar packing which takes effect only at high enough concentrations. < FIGURE 8 here >


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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For a comparison with the experimental results the surface excess concentration , defined by eq (2), is the appropriate quantity. Isotherms of for the given pore diameters are shown in Fig. 7(c). Because the surface excess amount is now normalized to the surface area of the pore, the

isotherms of do not exhibit the pronounced pore size dependence seen in 7 − 73 near

the maximum of the isotherms (Fig. 7(b)). Instead, a weak inverted pore size dependence appears at concentrations near the maximum of the isotherms, i.e., the smallest value of is found for the smallest pore. Fig. 7(c) suggests that at concentrations beyond the maximum in , pore-size specific effects come into play. For the pore sizes = 24σ, 32σ, and 48σ, the adsorption isotherms all appear to have an azeotrope, while for = 40σ and 56σ no azeotrope is observed. This behavior of the adsorption isotherms may be rationalized by the radial concentration profiles of head and tail beads, and of their sum, which are shown for four of these systems in Figure 8. The profiles for = 24σ, 32σ and 48σ exhibit a low-density central region, whereas the profile for = 40σ indicates a row of micelles near the pore center. It appears that in the latter system the pore size is just big enough to accommodate three micelles from wall to wall, whereas in all others the pore size is “slightly too big” for the micelles they contain, leading to an overall slightly lower amphiphile concentration (and an azeotrope) in the latter cases, and a slightly higher concentration (and no azeotrope) in the former. The concentration profiles for different bulk concentrations 73 shown in Figure 9 illustrate that micellar packing effects strongly affect the structure of the fluid in the core region and also the position of the adsorbed micelles at high bulk densities. Such packing effects are much less relevant at low concentrations where micelles interact only weakly. < FIGURE 9 here >


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Inspection of the radial concentration profiles in Fig. 8 shows that the structure of the liquid in pores of different size is quite similar, apart from the obvious differences caused by pore size and concomitant packing effects. In particular, the density of directly adsorbed head beads and the structure of the head group corona near the pore wall are nearly identical for the different pore sizes. This is not surprising as the interaction with the pore wall is the same in all cases and the pore curvature is small on the length scale of the individual bead. Above we have argued that this part of the system played a key role in the appearance of the azeotrope for 2 = 1.2, whereas the rest of the system made no decisive contribution. Thus, we expect these systems to differ only by packing effects, while curvature effects are introduced via the normalization to the pore surface area, which only for flat surfaces is identical to the size of the plane in which the surface micelles are located.

DISCUSSION Surface excess amounts in simulation and experiment The surface excess amounts considered in the experiments and simulations are defined in different ways, and this may affect the comparison of results obtained by the two methods. In the simulation, because of the implicit treatment of the solvent, the surface excess concentration given by eq (2) relates to a one-component fluid. This prescription of depends on the pore !"#

volume , via the number of amphiphile molecules in the reference state, +

= 76 , .

Accordingly, different definitions of , can cause large changes in at high bulk concentrations, and even affect the existence of the azeotrope. Our choice of the interaction potential of amphiphile beads with the pore wall implies an effective pore radius close to - − /⁄2. The influence on the surface excess isotherm of changing this definition of the pore radius by ± /⁄2


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is shown in Figure 10 for the case = 32/. If the effective pore radius is defined as - − /⁄2, the isotherm approaches an azeotrope at 76B ≈ 0.025/ 0 . With an effective pore radius defined as the nominal radius - the azeotrope would occur at a much lower concentration (0.017/ 0 ), while for an effective pore radius defined as - − / there may not be an azeotrope at all. As physically realistic values of the effective pore radius are unlikely to differ from our choice by more than ± /⁄10, the ambiguity of the azeotropic composition is much smaller than in the example of Figure 10. < FIGURE 10 here >

Contrary to , the reduced surface excess concentration

defined by eq (1) does not

directly depend on a definition of the pore volume or location of the solid/liquid interface. It represents the excess amount of amphiphile per unit area present in the actual system over and above that in a reference system containing the same total mass of mixture and in which the composition of the liquid phase is uniform, and equal to that of the bulk of the real system.32 This implies that in general the volume of the reference system, ,!"# , is different from that of the

actual system, so that

lacks a simple geometric interpretation. Here we focus on the

composition of the azeotropic point observed in the isotherms of

. As the actual system is

made up of the pore volume , and bulk volume ,3 , with mean densities Q and Q3 , the S9

condition that the two systems contain the same mass leads to ,!"# = , + ,3 + RS − 1U , . T

Hence, if Q = Q3 , we obtain ,!"# = , + ,3 , which is the condition implicit in the definition of the surface excess concentration by eq (2). Although equal densities Q and Q3 strictly does not imply equal composition of the mixture in the pores and in bulk, this will hold in good approximation for relatively wide pores. Accordingly, we may conclude that in these cases the


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composition of the azeotrope determined in the experiment relate to the same phenomenon as observed in the simulation.

Comparison of simulation and experiment < TABLE 3 here > In order to compare the simulation results with the experimental findings we have to adopt a criterion for corresponding pore sizes. Here we take the diameter of surfactant micelles in solution, V , as a mesoscopic scale bar, using V = 3.7 nm for C6E3 (from NMR self diffusion measurements)34,35 and V ≈ 10.5/ for micelles of H5T5 (DPD simulation).25,28 Values of the reduced pore diameter ⁄V studied in the simulation and for the three CPG materials are given in Table 3. It can be seen that, in units of ⁄V , the pore sizes studied in the simulation range from below to above the pore size of CPG-75, while CPG-240 and CPG-500 have considerably larger pores. Accordingly, results of the simulation may be compared with those for CPG-75, but not for CPG-240 and CPG-500. The surface excess isotherms of Fig. 7 and radial concentration profiles of Fig. 8 suggest that for the range of pores sizes covered by our simulation (2.3 ≤ ⁄V ≤ 5.3) the appearance of an azeotrope depends on whether the pore size is just large enough to accommodate 3 or 4 micelles from wall to wall, or if the pores are somewhat too large for the micelles they contain, causing a slightly lower mean concentration in the pore than in bulk, hence an azeotrope. In addition to this pore size effect, our simulations demonstrate that the appearance of an azeotrope depends on the adsorption parameter 2 . As illustrated for pore size = 40/ (⁄V = 3.8) in Figs. 5, the adsorption isotherm for 2 = 1.2 exhibits an azeotrope at a low bulk concentration (73B ≈ 0.015/ 0 ), while the isotherm for 2 = 1.5 levels off at a positive at higher bulk


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concentrations. With the radial concentration profiles in Fig. 6 this different behavior was traced back to a higher concentration of directly adsorbed head groups in the contact region of admicelles with the pore wall in the system with the higher adsorption parameter. These findings show that a surface azeotrope depends on both the adsorption strength of the surfactant head groups and on pore-size dependent micelle packing effects in the core of the pores. To compare the location of the surface azeotrope with the experimental findings we convert the concentration scale of the simulation to a volume fraction scale. The volume of a single H5T5 molecule is estimated to be 5√3/ 0 based on its volume in a hexagonal packing of cylinders. Accordingly, the concentration of the surface azeotrope found in the simulation with 2 = 1.5 for small pores, 73B ≈ 0.025/ 0 , corresponds to a volume fraction Y3B ≈ 0.22, and the value 73B ≈ 0.015/ 0 found for 2 = 1.2 in somewhat larger pores corresponds to Y3B ≈ 0.13. The azeotropic composition of the experimental study, B , may be converted to volume fraction with the relation Y = Q ⁄Q , where Q is the density of a mixture of mass fraction , and Q is the density of the pure amphiphile (0.964 g/cm3 for C6E3 at 20°C).36 As Q ⁄Q is close to 1 in the relevant composition range, we have YB ≈ B . Hence, for CPG-75 we find a volume fraction of the azeotrope YB ≈ 0.33, i.e. higher than the values obtained in the simulation. In conclusion, the surface excess isotherms for C6E3 + W in CPG-75 (⁄V = 2.8) (Fig. 2) and simulated isotherm for an equivalent pore size ( = 32/; ⁄V = 3.0) (Fig. 7(c)) indicate that the same overall effects prevail, i.e. preferential adsorption of the amphiphile followed by continuous decrease of the surface excess. An azeotropic point is reached in the experimental system and nearly reached in the simulation system. Hence, we may conclude that the simulations reproduce in a qualitative manner the adsorption behavior of C6E3 in CPG-75.


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Pore size dependence of azeotrope A key result of the experimental study is the pronounced shift of the azeotropic composition B with the pore size of the CPG materials (Table 2). This behavior can be rationalized on the basis of the simulation results which showed that the formation of a layer of admicelles at the pore wall is accompanied by zones depleted in amphiphile at the inner and outer rim of the admicelles, and that at higher bulk concentrations micellar packing effects and the concomitant development of depletion zones extends into the core of the pore space (Fig. 9). Based on these findings, a simple three-density-level model (admicelle layer, core region of pores, and bulk solution) is outlined in the Supporting Information. In the relevant composition range around the azeotrope the mean volume fraction of amphiphile in the admicelle layer is higher, that in the core region somewhat lower than in the bulk. This model leads to the following correlation for the azeotropic composition Y B with A ⁄ , the ratio of the core volume and overall pore volume: [

Y B = YZ − [\ YZ − YAB

(5)

9

< FIGURE 11 here > In eq (5), YZ represents the mean volume fraction of amphiphile in the admicelle layer, and YAB the mean volume fraction in the core region at the azeotropic composition. For cylindrical pores, the core volume is related to the pore radius - and the width of the admicelle layer V by A ⁄ = 1 − V ⁄- ? . Accordingly, for pores of diameter not much exceeding 2V, as in the case of CPG-75, the second term on the r.h.s. of eq (5) nearly vanishes and we expect Y B ≈ YZ . For larger pores the fraction of core volume A ⁄ increases and thus, according to eq (5), Y B decreases because YZ − YAB > 0. The volume fraction YZ is related to the limiting surface


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concentration of amphiphile in the adsorption layer, , by YZ = , ⁄V , where , is the molar volume of the amphiphile. Fig. 11 shows the experimental values of the azeotropic composition plotted as a function of A ⁄ with an assumed layer thickness V = 3 nm. It can be seen that Y B is not a linearly decreasing function of A ⁄ as would be expected if YZ − YAB was a constant independent of pore size. However, while YZ is expected to be independent or weakly dependent on pore size, the volume fraction YAB decreases with increasing pore size and thus the factor YZ − YAB in the second term of eq (5) will increase with the pore size. Accordingly, the azeotropic composition Y B is expected to decrease more strongly than linear as a function of A ⁄ , as it is indeed observed (Fig. 11). Hence, eq (5) accounts in a qualitative manner for the observed trend of the azeotropic composition as a function of pore size. The value of YZ obtained by extrapolation of the experimental azeotropic compositions to A ⁄ → 0 (Fig. 11) is consistent with an estimate of YZ =

, ⁄V = 0.324, based on a limiting surface

concentration of amphiphile = 4 µmol/m-2 and V = 3 nm. On the other hand, the model underlying eq (5) does not allow a quantitative estimate of YAB as a function of pore size, nor an extrapolation of the pore size dependence of Y B to larger pores and the limit A ⁄ → 1, corresponding to a flat surface. Indirect evidence for increasing depletion of amphiphile in pores of increasing size comes from the increasingly negative slope of the adsorption isotherms in the high concentration regime (see Table 2). As explained in SI, the slope of the adsorption isotherm in this high-concentration regime can be expressed by a layer thickness V^ that includes all adsorption and depletion effects, such that the rest of the pore volume (i.e., the central part not contained in the layer) contains bulk solution. Assuming cylindrical pores of radius - this model gives the following relation for V^ as a function of the isotherm slope C ACS Paragon Plus Environment

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_` L

= 1 − a1 −

73B 2 = 1.2 and 73 2 = 1.5 < 73B 2 = 1.5 : (a) radial bead concentration profiles; (b) excess number of beads profiles, i.e. the density profiles multiplied by the local volume; (c) integrated excess concentrations giving the accumulated number of beads in the pore (integration starting at the pore wall); the difference in the accumulated number of beads between the two cases is shown by the dashed line.


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Figure 7. Simulated surface excess isotherms for H5T5 in pores of different diameters, = 24/, 32/, 40/, 48/, 56/, with 2 = 1.5: (a) overall concentration of amphiphile in the pores 7 in comparison to the reference state 7 = 73 ; (b) excess concentration 7 − 73 in the pore; (c) surface excess concentration as defined by eq (2).


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Figure 8. Comparison of radial bead concentration profiles at 73 ≈ 0.023/ 0 for four different pore diameters as indicated in the figure: (a) head beads; (b) tail beads; (c) all beads; (d) integrated excess number of beads (integration starting at the pore wall) normalized with the pore surface area.


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Figure 9. Radial bead concentration profiles of the pore fluid in a pore of diameter = 40σ for increasing bulk concentration 73 . The density profiles illustrate the increasing importance of micelle packing effects that strongly affect the pore center but also the position of the adsorbed micelles.

Figure 10. Surface excess isotherms for the system of nominal diameter = 32/, with three different definitions of the effective pore radius, namely -, - − /⁄2 and - − /. The graphs demonstrate the sensitivity of the surface excess and the azeotrope to changes in the definition of the pore volume , .


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Figure 11. Correlation for the pore-size dependence of the azeotropic composition Y B according to eq (5): - is the (hydraulic) pore radius, A ⁄ the corresponding ratio of core volume to total pore volume (based on a layer thickness V = 3 nm). The symbols represent the experimental data (assuming that B = Y B ); the full line is a guide to the eye.

TOC


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TABLES

Table 1. Characteristics of the CPG materials a Material

m? /g

cm0 /g

CPG-75

170

CPG-240 CPG-500

nm

nm

0.58

10.3

6.8

91

1.06

35

23.2

69

1.50

50

43.4

Specific surface area , specific pore volume , mean pore diameter , and hydraulic diameter = 2 ⁄ . a

Table 2. Parameters of eq 4 for the linear region of the adsorption isotherms, and depletion layer thickness V^ calculated by eq 6. Materials

μmol/m?

C μmol/m?

B

9.3

0.323

1.3

V^ nm

CPG-75

3.0

CPG-240

4.0

20

0.20

2.8

CPG-500

5.5

45

0.12

6.5


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Table 3. Pore size expressed in units of a micelle diameter V Simulation

Experiment

⁄ V

Material

/ nm

⁄ V

24

2.3

CPG-75

10.3

2.8

32

3.0

CPG-240

35

9.5

40

3.7

CPG-500

50

13.5

48

4.6

56

5.3

/ /

ASSOCIATED CONTENT Supporting Information. Experimental temperature scans and surface excess graphs for the adsorption from C6E3 + W in CPG-75 and CPG-500. Correlation model for the pore size dependence of the azeotropic composition. AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] (G.H.F.) * E-mail: [email protected] (H.B.) ORCID Gerhard H. Findenegg: 0000-0002-8525-9905


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Notes The authors declare no competing financial interest. ACKNOWLEDGMENT It is a pleasure to dedicate this paper to Professor Keith E. Gubbins in celebrating his 80th birthday and in appreciation of long-standing professional and personal interactions. This work was supported by the German Research Foundation (DFG) in the framework of IRTG 1524 ‘Self-Assembled Soft Matter Nanostructures at Interfaces’. Analysis of experimental data and contribution to manuscript preparation by GR was supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy.

REFERENCES

(1) Jönsson, A.-S.; Jönsson, B. The influence of nonionic and ionic surfactants on hydrophobic and hydrophilic ultrafiltration membranes. J. Membr. Sci. 1991, 56, 49–76. (2) Nguyen, L. A. T.; Schwarze, M.; Schomäcker, R. Adsorption of nonionic surfactants from aqueous solution onto various ultrafiltration membranes. J. Membr. Sci. 2015, 493, 120–133. (3) Király, Z.; Börner, R. H. K.; Findenegg, G. H. Adsorption and aggregation of C8E4 and C8G1 nonionic surfactants on hydrophilic silica studied by calorimetry. Langmuir 1997, 13, 3308–3315.


35

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Page 36 of 51

(4) Levitz, P.: Van Damme, H. J. Fluorescence decay study of the adsorption of nonionic surfactants at the solid-liquid interface. J. Phys. Chem. 1986, 90, 1302–1310. (5) Levitz, P. Aggregative adsorption of nonionic surfactants onto hydrophilic solid/water interface. Relation with bulk micellization. Langmuir 1991, 7, 1595–1608. (6) Böhmer, M. R.; Koopal, L. K.; Janssen, R.; Lee, E. M.; Thomas, R. K.; Rennie A. R. Adsorption of nonionic surfactants on hydrophilic surfaces. An experimental and theoretical study on association in the adsorbed layer. Langmuir 1992, 8, 2228–2239. (7) Tiberg, F. Physical characterization of non-ionic surfactant layers adsorbed at hydrophilic and hydrophobic solid surfaces by time-resolved ellipsometry. J. Chem. Soc., Faraday Trans. 1996, 92, 531–538. (8) Qiao, Y.; Schönhoff, M.; Findenegg, G. H. 2H NMR investigation of the structure and dynamics of the nonionic surfactant C12E5 confined in controlled pore glass. Langmuir 2003, 19, 6160–6167. (9) Müter, D.; Shin, T.; Demé, B.; Fratzl, P.; Paris, O.; Findenegg, G. H. Surfactant selfassembly in cylindrical nanopores. J. Phys. Chem. Lett. 2010, 1, 1442–1446. (10) Strey, R. Water – nonionic surfactant systems and the effect of additives. Ber. Bunsenges. Phys. Chem. 1996, 100, 182–189. (11) Partyka, S.; Lindheimer, M.; Faucompre, B. Aggregate formation at the solid–liquid interface: The calorimetric evidence. Colloids Surf. A 1993, 76, 267–281.


36

Page 37 of 51

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(12) Seidel, J.; Wittrock, C.; Kohler, H.-H. Adsorption enthalpies of cationic and nonionic surfactants on silica gel. Microcalorimetric determination of adsorption enthalpies. Langmuir 1996, 12, 5557–5562. (13) Bock, H.; Gubbins, K. E. Anomalous temperature dependence of surfactant self-assembly from aqueous solution. Phys. Rev. Lett. 2004, 92, 135701–4. (14) Dietsch, O.; Eltekov, A.; Bock, H.; Gubbins, K. E.; Findenegg, G. H. Crossover from normal to inverse temperature dependence in the adsorption of nonionic surfactants at hydrophilic surfaces and pore walls. J. Phys. Chem. C 2007, 111, 16045–16054. (15) Rother, G.; Müter, D.; Bock, H.; Schoen, M.; Findenegg, G. H. From aggregative adsorption to surface depletion: Aqueous systems of CnEm amphiphiles at hydrophilic surfaces. Mol. Phys. 2017, 115, 1408–1416. (16) Everett, D. H. Thermodynamics of adsorption from solution. 2. Imperfect systems. Trans. Faraday Soc. 1965, 61, 2478–2495. (17) Telo da Gama, M. M.; Evans, R. Adsorption and wetting transitions at a model of the interface between a solid and a binary fluid mixture. Mol. Phys. 1983, 48, 687–714. (18) Giordano, F.; Denoyel, R.; Rouquerol, J. Influence of porosity on the adsorption of a nonionic surfactant in silica. Colloids Surf. A 1993, 71, 293–298. (19) Müter, D.; Shin. T.; Demé, B.; Fratzl, P.; Paris, O.; Findenegg, G. H. Surfactant selfassembly in cylindrical nanopores. J. Phys. Chem. Lett. 2010, 1, 1442–1446.


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Page 38 of 51

(20) Huinkink, H. P.; de Keizer, A.; Leermakers, F. A. M.; Lyklema, J. Adsorption of nonionic surfactants in hydrophilic cylindrical pores. 1. Thermodynamic analysis. Langmuir 1997, 13, 6452–6460. (21) Huinkink, H. P.; de Keizer, A.; Leermakers, F. A. M.; Lyklema, J. Adsorption of nonionic surfactants in hydrophilic cylindrical pores. 2. Mean field lattice calculations. Langmuir 1997, 13, 6618–6625. (22) Rekvig, L.; Hafskjold, B.; Smit B. Simulating the effect of surfactant structure on bending moduli of monolayers. J. Chem. Phys. 2004, 120, 4897–4905. (23) Suttipong, M.; Grady, B. P.; Striolo, A. Surfactants adsorption on crossing stripes and steps. Soft Matter 2017, 13, 862–874. (24) Pool, R.; Bolhuis, P. G. Can purely repulsive soft potentials predict micelle formation correctly? Phys. Chem. Chem. Phys. 2006, 8, 941–948. (25) Angelikopoulos, P.; Bock, H. Directed self-assembly of surfactants in carbon nanotube materials. J. Phys. Chem. B 2008, 112, 13793–13801. (26) Arai, N.; Yasuoka, K.; Zeng, X. C. Self-assembly of surfactants and polymorphic transition in nanotubes. J. Am. Chem. Soc. 2008, 130, 7916–7920. (27) Müter, D.; Angelikopoulos, P.; Bock, H. Angular dependence of surfactant-mediated forces between carbon nanotubes. J. Phys. Chem. B 2012, 116, 14869–14875. (28) Müter, D.; Widmann, M. A.; Bock, H. Surfactant self-assembly in cylindrical pores: Insights from mesoscale simulations. J. Phys. Chem. Lett. 2013, 4, 2153–2157.


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Page 39 of 51

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(29) Ren, Y.; Liu, B.; Kiryutina, T.; Xi, H.; Qian, Y. Investigation of structure formation mechanism of a mesoporous ZSM-5 zeolite by mesoscopic simulation. Chem. Phys. 2015, 448, 9–14. (30) Grüll H.; Woermann, D. Preferential adsorption on porous glass near the liquid/liquid coexistence curve of a binary liquid mixture. J. Chem. Phys. 1996, 105, 2527–2532. (31) Rother, G.; Woywod, D.; Schoen, M.; Findenegg, G. H. Confinement effect on the adsorption from a binary liquid system near liquid/liquid phase separation. J. Chem. Phys. 2004, 120, 11864–11873. (32) Everett, D. H. Adsorption at the solid/liquid interface, in: Colloid Science. Specialist Periodical Reports, vol. 1, The Chemical Society, London, 1973, chap. 2. (33) Weeks, J. D.; Chandler, D.; Andersen, H. C. Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 1971, 54, 5237–5247. (34) Ambrosone, L.; Costantino, L.; D’Errico, G.; Vitagliano, V. Thermodynamic and dynamic properties of micellar aggregates of nonionic surfactants with short hydrophobic tails. J. Colloid Interf. Sci. 1997, 190, 286–293. (35) Ortona, O.; Vitagliano, V.; Paduano, L.; Costantino, L. Microcalorimetric study of some short-chain nonionic surfactants. J. Colloid Interf. Sci. 1998, 203, 477-484. (36) Wieczorek, S. A. Thermodynamics of aqueous mixtures of polyoxyethene glycol monoethers. J. Chem. Thermodyn. 1992, 24, 129–138.


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