Influence of Dispersion Forces and Ordering on the Compositions of

Oct 10, 2013 - Meghan E. Kern and David F. Watson*. Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New Yor...
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Influence of Dispersion Forces and Ordering on the Compositions of Mixed Monolayers of Alkanoic Acids on Nanocrystalline TiO2 Films Meghan E. Kern and David F. Watson* Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260-3000, United States S Supporting Information *

ABSTRACT: Lateral dispersion forces induce the ordering of n-alkanoic acids on nanocrystalline TiO2 films and cause the compositions of mixed monolayers to change. The equilibrium formation of single-component monolayers of n-alkanoic acids and 6-bromohexanoic acid (Br6A) on TiO2 was well-modeled by the Langmuir adsorption isotherm. Surface adduct formation constants were 103−104 M−1, and saturation amounts of adsorbates per projected surface area of TiO2 were on the order of 10−7 mol cm−2. The adsorption of n-heneicosanoic acid (21A) followed Langmuir kinetics, whereas the net rates of adsorption of shorter n-alkanoic acids and Br6A were slower than predicted by simple Langmuir kinetics, suggesting that desorption was non-negligible. At high surface coverages, n-alkanoic acids with 14 or more methylene groups formed ordered, crystalline monolayers, as evidenced by shifts of asymmetric and symmetric CH2 stretching bands in IR spectra. The extent of ordering was similar to that of self-assembled monolayers of alkanethiols on gold. The formation of ordered monolayers was wellmodeled by an idealized mechanism, in which adsorption and desorption followed Langmuir kinetics and ordering was first-order with respect to the fractional surface coverage of adsorbates. Dispersion forces and ordering affected the compositions of mixed monolayers of 21A and Br6A on TiO2 films that remained in contact with mixed coadsorption solutions. When the fractional surface coverage of 21A was sufficiently high to induce ordering, it displaced Br6A from TiO2. We propose that these compositional changes were driven by the stabilization of 21A via cohesive lateral dispersion forces. Our results reveal that mixed monolayers on nanocrystalline TiO2 films are dynamic and that noncovalent intermolecular interactions can profoundly influence their compositions and properties.

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INTRODUCTION The properties and reactivity of mixed monolayer-functionalized surfaces depend on the structure, functionalization, relative abundance, and spatial distribution of adsorbates.1−7 Therefore, mixed monolayer-functionalized surfaces and nanoparticles have been applied in sensing and recognition, catalysis, molecular electronics, and as substrates and building blocks for materials assembly.2,7−15 An ongoing challenge, however, is to control precisely the compositions of mixed monolayers, thereby enabling programmable functionality. Binary mixed monolayers are typically prepared by coadsorbing components from mixed solutions. Because of differences in the kinetics and thermodynamics of adsorption of components, the compositions of mixed monolayers often differ from the compositions of solutions from which they are prepared.16−23 Lateral interactions within monolayers can stabilize a given component or cause the formation of single-component domains within mixed monolayers.4,17,18,21,25 Our research group has studied binary mixed monolayers of thiol- and methyl-terminated alkanoic acids and related adsorbates on nanocrystalline TiO2 films.26−28 We found that the formation of disulfide bonds between terminal thiol groups of mercaptoalkanoic acids increases their stability and persistence on TiO2 relative to nonthiolated adsorbates through a mechanism analogous to the chelate effect.27,28 Disulfide © 2013 American Chemical Society

formation drives compositional changes, in which mercaptoalkanoic acids displace methyl-terminated adsorbates on time scales of several hours, well after the formation of full monolayers. Rates of compositional changes vary with solvation, sterics, and the relative abundance of components in coadsorption solutions.28 These previously reported experiments revealed that the formation of covalent bonds between adsorbates altered the compositions of mixed monolayers on TiO2 films. We reasoned that noncovalent intermolecular interactions might similarly influence the relative stability and inertness of adsorbates and drive compositional changes within mixed monolayers. Whitesides and co-workers’ related studies of mixed monolayers on gold provide precedent. They reported that long-chain alkanethiols adsorbed preferentially to gold relative to shorter-chain alkanethiols with identical terminal functional groups.17,18 The effect was attributed to cohesive interactions between alkyl chains and the poorer solubility of long-chain alkanethiols in the solvents used for adsorption. For some mixed monolayers, the mole fraction of longer alkanethiols increased with time, suggesting that initial compositions of monolayers were influenced by adsorption Received: August 8, 2013 Revised: October 7, 2013 Published: October 10, 2013 13797

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Figure 1. Representative IR spectra of TiO2 films that were functionalized with 11A (a) and 21A (b) by equilibrating with heptane solutions of varying concentrations.

ordered adsorbates as a function of time and concentration for various chain lengths and surrounding solvents. The rate and extent of ordering increased with alkyl chain length and surface coverage and varied with solvent. Having established that the longer n-alkanoic acids ordered on nanocrystalline TiO2 films, we evaluated the influence of dispersion forces on the compositions and compositional evolution of mixed monolayers. Under certain conditions, the ordering of long-chain nalkanoic acids led to their enrichment within monolayers, via displacement of Br6A, on time scales of several hours. Our results reveal that the mixed monolayers are dynamic, that noncovalent lateral interactions can alter the relative stabilities and persistences of adsorbates, and that these differences can induce compositional changes well after the initial formation of monolayers at saturation surface coverages.

kinetics and that monolayers then relaxed to thermodynamically controlled equilibrium compositions.17,18 We sought to evaluate the extent to which dispersion forces affect the compositions of mixed monolayers of alkanoic acids on highsurface-area TiO2 films. Our findings are reported in this article. Adsorbates with terminal alkyl chains are known to form ordered crystalline monolayers on gold;29−33 the native oxides of aluminum, copper, and silver;34−38 and porous and nonporous ZrO2 and TiO2 nanoparticles and thin films.39−42 Ordered monolayers of alkyl-terminated adsorbates are stabilized by lateral dispersion forces.29,34 The extent of ordering has been shown to increase with chain length and surface coverage.34,35,37,38,40,42 Ordering induces shifts of C−H stretching vibrations of alkyl chains. Maxima of asymmetric CH2 stretching (νa(CH2)) and symmetric CH2 stretching (νs(CH2)) bands of adsorbates within ordered monolayers are shifted lower by 5−10 cm−1 relative to the band maxima of adsorbates within disordered monolayers.29,32 The νa(CH2) and νs(CH2) maxima of ordered monolayers are similar to those of crystalline solid alkanes.43,44 Nanocrystalline TiO2 films are intriguing substrates with which to evaluate the influence of intermolecular interactions on compositions of mixed monolayers. First, they are porous. In our prior work, the low mobility of solutes within the pore structure of TiO2 films probably limited the rate of disulfideinduced compositional changes,28 enabling us to characterize compositional evolution in real time. Second, the films are several micrometers thick and support the adsorption of alkanoic acids and related adsorbates at saturation amounts per projected surface area of approximately 10−7 mol cm−2.26,28,45,47 TiO2 films functionalized with alkanoic acids at saturation coverages exhibit intense C−H stretching absorbances in transmission-mode IR absorption spectra.26,28 Measured absorbances are proportional to amounts of adsorbates. Thus, we expected that C−H stretching regions of vibrational spectra of TiO2 films functionalized with mixtures of alkanoic acids would reveal both the compositions of mixed monolayers and the extent of ordering of adsorbates via lateral dispersion forces. To aid in our understanding of the mixed monolayers, we first characterized the formation of single-component monolayers of methyl-terminated n-alkanoic acids of varying lengths and also 6-bromohexanoic acid (Br6A) on nanocrystalline TiO2 films. We quantified the surface coverages of disordered and

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EXPERIMENTAL SECTION

Nomenclature. Linear methyl-terminated n-alkanoic acids are hereafter referred to as “nA” where n equals the number of carbons in the alkanoic acid. Experimental Details in Supporting Information. Detailed descriptions of the acquisition of transmission-mode IR spectra, the determination of amounts of adsorbates on TiO2, and the commercial sources of reagents and solvents are in Appendix S1 of the Supporting Information. Synthesis of TiO2 Films. Nanocrystalline TiO2 films on glass microscope slides were synthesized as described previously by hydrolyzing titanium(IV) isopropoxide, concentrating the resulting sol, spreading the sol onto glass, and annealing.26,48 Projected surface areas of films were approximately 4 cm2. Our prior characterization revealed that films were 4.1 ± 0.9 μm thick and consisted of anatase TiO2 particles with an average diameter of 36 ± 6 nm.26,48 Equilibrium Binding of Single-Component Monolayers. A series of TiO2-coated glass slides were immersed into solutions of an n-alkanoic acid or Br6A in heptane, toluene, dichloromethane (DCM), or tetrahydrofuran (THF) at room temperature (22 °C). In a typical experiment, concentrations of n-alkanoic acid or Br6A ranged from 0.03 to 8 mM. Two slides were immersed back-to-back into 5.0 mL aliquots of each solution. Slides were removed from adsorption solutions after approximately 8 h of immersion. Slides were then rinsed by immersing for 2−5 s (while being moved back and forth) in approximately 20 mL of the neat solvent used for adsorption. This rinsing procedure typically removed 2−5% of n-alkanoic acids from TiO2 films.28 Films were stored in the dark until characterization by IR spectroscopy. 13798

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Figure 2. Equilibrium binding data for adsorption of 11A (a), 16A (b), and 21A (c) to TiO2 from heptane. Filled black circles represent total surface coverages (Γ), open red circles represent fractional surface coverages of disordered adsorbates (θd), and open blue triangles represent fractional surface coverages of ordered adsorbates (θo). Black lines are fits of Γ vs concentration data to the Langmuir adsorption isotherm. Insets show plots of C/Γ vs C and linear fits. Error bars are standard deviations relative to average values of Γ, θd, or θo from two TiO2 films at each concentration of nalkanoic acid.

Table 1. Parameters from Fitting Data from Equilibrium Binding and Adsorption Kinetics Experiments acid

solvent

Br6A 6A 11A 16A 18A 21A 21A 21A 21A

heptane heptane heptane heptane heptane heptane DCM toluene THF

Γ0a (mol cm−2) (3.75 (2.50 (3.44 (4.11 (4.10 (3.05 d d d

± ± ± ± ± ±

0.05) 0.04) 0.06) 0.05) 0.04) 0.07)

× × × × × ×

10−7 10−7 10−7 10−7 10−7 10−7

Kada (M−1) (1.3 (7.5 (3.8 (3.2 (2.8 (4.0 d d d

± ± ± ± ± ±

0.2) 0.8) 0.3) 0.3) 0.1) 0.3)

× × × × × ×

104 103 103 103 103 103

kadb (M−1 s−1)

kadc (M−1 s−1)

e e e e e 1.22 ± 0.09 1.9 ± 0.1 0.63 ± 0.02 e

f f f 3.3 5.9 1.3 7.1 4.3 f

kdc (s−1) f f f 1.4 6.9 0 1.5 5.2 f

× 10−3 × 10−3 × 10−2 × 10−3

koc (s−1) f f f 1.1 3.5 4.3 5.1 3.5 f

× × × × ×

10−3 10−3 10−3 10−3 10−3

a Two TiO2 films were immersed in each adsorption solution; standard deviations are from linear regression analysis of plots of average values of C/Γ vs C and 1/Γ vs 1/C. bkad values and standard deviations are from linear regression analysis of plots of average values of ln(1 − θt) vs t from 1 to 3 adsorption kinetics experiments in which 4 TiO2 films were functionalized at each adsorption time. cRate constants are from fits of plots of θd and θo vs t to eqs 9 and 10. dData were not modeled precisely by the Langmuir adsorption isotherm. eData were not modeled precisely by Langmuir adsorption kinetics. fAdsorbates underwent negligible ordering and were not fit to eqs 9 and 10.

Adsorption Kinetics for Single-Component Monolayers. In a typical experiment, 32 TiO2-coated glass slides were immersed together into 100 mL of a 1 mM solution of an n-alkanoic acid or Br6A in heptane, toluene, DCM, or THF at room temperature (22 °C). The slides were oriented vertically and were not in contact with each other. At each desired immersion time, ranging from 30 s to 1 h, four slides were removed from the adsorption solution and then rinsed with neat solvent as described above. Slides were dried in air and stored in the dark until characterization by IR spectroscopy. Preparation and Characterization of Mixed Monolayers on Nanocrystalline TiO2 Films. In a typical experiment, 32 TiO2-coated glass slides were immersed together into 100 mL of a mixed solution of an n-alkanoic acid and Br6A in heptane, toluene, DCM, or THF at room temperature (22 °C). The slides were oriented vertically and were not in contact with each other. The sum of the concentrations of adsorbates in all coadsorption solutions was 2 mM to ensure that saturation surface coverages of adsorbates were attained.26 At each desired immersion time, ranging from 5 min to 6 h, four slides were removed from the coadsorption solution. Slides were stored in the dark until characterization by IR spectroscopy.

adsorption of n-alkanoic acids and Br6A to TiO2 from heptane followed the Langmuir adsorption isotherm (Figure 2 and Figure S2 in Supporting Information).49 Surface adduct formation constants (Kad) and saturation surface coverages (Γ0) were extracted from the slopes of linear fits to plots of 1/Γ vs 1/C and C/Γ vs C, 46,50 respectively, where C is concentration of adsorbate in the solution (Table 1). Values of Γ0 ranged from approximately 2.5 × 10−7 to 4.1 × 10−7 mol cm−2, and values of Kad were on the order of 103−104 M−1. Values of both parameters are similar to reported values for alkanoic acids and other carboxylic acid-bearing adsorbates on nanocrystalline TiO2 films.26,28,45−47 Kad values for Br6A and 6A were 2−5-fold greater than for the longer n-alkanoic acids, which we attribute to their greater polarity and lower solubility in heptane. Equilibrium binding data for adsorption of 21A to TiO2 from toluene, DCM, and THF were not well-modeled by the Langmuir adsorption isotherm (Figure S2 in Supporting Information). When 21A was adsorbed from DCM or toluene, Γ saturated at approximately 2 × 10−7−3 × 10−7 mol cm−2; however, when 21A was adsorbed from THF, Γ saturated at only approximately 1.2 × 10−7 mol cm−2. We previously reported that THF adsorbed to nanocrystalline TiO2 films, presumably by coordination of its oxygen to Ti4+, but that it was displaced completely by oxalic acid when the concentration of oxalic acid in THF adsorption solutions was greater than 0.18 mM. 26 Thus, although THF may have adsorbed competitively to TiO2 from solutions containing the lowest concentrations of 21A, we expect that 21A displaced THF at

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RESULTS AND DISCUSSION Equilibrium Formation of Single-Component Monolayers. Equilibrium amounts of adsorbed n-alkanoic acids and Br6A per projected area of TiO2, hereafter referred to as “surface coverages” (Γ) of adsorbates, increased with the concentration of adsorption solutions, as evidenced by increasing absorbances in the C−H stretching region of IR spectra of functionalized TiO2 films (Figure 1 and Figure S1 in Supporting Information). Equilibrium binding data for the 13799

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the highest concentrations used in equilibrium binding experiments. The νa(CH2) and νs(CH2) bands in IR spectra of TiO2adsorbed 6A and Br6A did not vary with surface coverage and were unshifted relative to those of solvated 6A and Br6A (Figure S1 in Supporting Information); therefore, 6A and Br6A existed in disordered, liquid-like phases even at their highest surface coverages on TiO2.29,43 In contrast, the νa(CH2) and νs(CH2) bands of TiO2 films functionalized with 11A, 16A, 18A, and 21A varied significantly with surface coverage (Figure 1 and Figure S1 in Supporting Information). At the lowest surface coverages, νa(CH2) and νs(CH2) maxima were similar to those of the n-alkanoic acids in CCl4 solutions. As the surface coverages of these n-alkanoic acids increased, the νa(CH2) and νs(CH2) maxima shifted to lower wavenumbers, indicating that they formed increasingly ordered monolayers on TiO2 as the average lateral distance between adsorbates decreased.29,32,43,44 The νa(CH2) and νs(CH2) maxima of TiO2 films functionalized with 11A at saturation surface coverage were 2923 and 2852 cm−1, respectively, corresponding to 3−5 cm−1 shifts of these bands relative to solution spectra. The νa(CH2) and νs(CH2) maxima of films functionalized with 16A, 18A, and 21A at saturation coverages were 2917 and 2850 cm−1, respectively, corresponding to 10 and 5 cm−1 shifts relative to solution spectra. These νa(CH2) and νs(CH2) maxima are identical to those of crystalline solid alkanes43,44 and ordered crystalline monolayers of alkanethiols with 15 or more methylene groups on gold surfaces.29−31 Therefore, at saturation surface coverages, 16A, 18A, and 21A formed ordered monolayers on TiO2. Ordering was probably driven by cohesive lateral dispersion forces within monolayers, consistent with the observed increase of νa(CH2) and νs(CH2) maxima and decrease of ordering for the shorter adsorbates 11A, 6A, and Br6A. Similar dependences of ordering on chain length have been reported for alkanethiols on gold.29,31 To estimate the relative amounts of ordered and disordered n-alkanoic acids within monolayers of 16A, 18A, and 21A on TiO2, we fit measured IR spectra, in the C−H stretching region, to linear combinations of absorbances from ordered and disordered adsorbates. The method is described in detail in Appendix S2 of the Supporting Information. Spectral fits generated by this approach corresponded closely to measured C−H stretching regions of IR spectra of TiO 2 films functionalized with 16A, 18A, and 21A (Figure 3 and Figure S3 in Supporting Information). Corresponding plots of fractional surface coverages of n-alkanoic acids within disordered and ordered phases (θd and θo, respectively) vs concentration of the surrounding solution are overlaid with the equilibrium binding data in Figure 2 and in Figure S2 in Supporting Information. Surface coverages of disordered and ordered adsorbates (Γd and Γo, respectively) extracted from the fits were probably least accurate for 21A adsorbed from heptane because 21A had already undergone some ordering within just 30 s of adsorption from a 1 mM solution, as evidenced by broadening to lower wavenumbers of the νa(CH2) and νs(CH2) bands (Figure S3 in Supporting Information). Therefore, the reference extinction spectrum corresponding to ostensibly disordered 21A actually contained a contribution from ordered 21A, and our fits underestimated θo. Similarly, when 21A was adsorbed from THF, the monolayers consisted of mixtures of disordered and ordered 21A even at the highest surface coverages, as evidenced by the broad νa(CH2) and νs(CH2) bands with shoulders extending to higher wavenumbers than

Figure 3. Normalized average IR spectra (black solid lines) of TiO2 films that had equilibrated with solutions of 16A in heptane. Concentrations of 16A are indicated at the left of spectra; absorbance scale bars are on the right. Also plotted are simulated spectra from fitting to eq S2 (yellow solid lines), contributions from disordered 16A (red dashed lines) and ordered 16A (blue dashed lines), and residuals (measured minus fitted spectra, black dashed lines). Vertical black dashed lines show measured νa(CH2) and νs(CH2) maxima of TiO2 films that had equilibrated with solutions of 16A at the lowest and highest concentrations.

the band maxima (Figure S3 in Supporting Information). Therefore, the reference extinction spectrum corresponding to ordered 21A contained some contribution from disordered 21A, and our fits overestimated θo. Despite these complications associated with the adsorption of 21A from heptane and THF, our spectral fits revealed several trends pertaining to adsorption and ordering. For each adsorbate and each adsorption solvent, the lowest-coverage monolayers, which were prepared by equilibrating with solutions of n-alkanoic acids at concentrations of 0.0625 mM or less and contained adsorbates at Γ of 3 × 10−8−7 × 10−8 mol cm−2, were essentially completely disordered (Figures 2 and 3 and Figures S2 and S3 in Supporting Information). The first evidence of ordering occurred in monolayers with Γ of 5 × 10−8−1 × 10−7 mol cm−2, corresponding to total fractional surface coverages (θt, which equals the sum of θd and θo) of 0.2−0.4. Such monolayers were prepared by equilibration with solutions of n-alkanoic acids with concentrations of 0.125−0.25 mM. The mole fractions of disordered and ordered n-alkanoic acids within monolayers (χd and χo, respectively) were calculated from θd and θo: χd =

θd θd + θo

(1)

χo =

θo θd + θo

(2)

Plots of χd and χo vs the total surface coverage of n-alkanoic acid, which was determined from integrated C−H stretching absorbances (Figure 2 and Figure S2 in Supporting Information), reveal that monolayers of 16A and 18A became nearly completely ordered (χo > 0.9) only at the highest Γ values of approximately 3.5 × 10−7 mol cm−2 or more, whereas 13800

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Figure 4. χd and χo vs Γ from equilibrium binding data for 21A, 18A, and 16A adsorbed to TiO2 from heptane (a) and for 21A adsorbed to TiO2 from heptane, toluene, and DCM (b). The data sets are offset for clarity of presentation; horizontal grid lines correspond to χ = 0 for each data set. Error bars are standard deviations relative to average values of Γ and χd or χo from two TiO2 films at each concentration of n-alkanoic acid.

S2 in Supporting Information), which revealed that monolayers of 21A were only partially ordered and had subsaturation surface coverages at equilibrium with 1 mM solutions of 21A in THF. The adsorption of 21A to TiO2 from solutions in heptane, DCM, and toluene was well-modeled by Langmuir kinetics and the following differential and integrated rate laws:49,52

21A became nearly completely ordered at slightly lower coverages (Figure 4). The molar enthalpy of dispersion forces becomes more negative with increasing alkyl chain length,34 which probably induced ordering of 21A at slightly lower surface coverages than 18A or 16A. Adsorption Kinetics for the Formation of SingleComponent Monolayers. To characterize the kinetics of adsorption of n-alkanoic acids and Br6A, and of ordering of the longer n-alkanoic acids, on nanocrystalline TiO2 films, we acquired IR spectra of the films as a function of the time they were immersed in 1 mM solutions of n-alkanoic acids. This concentration was sufficient to yield monolayers at or near saturation surface coverages at equilibrium (Figure 2 and Figure S2 in Supporting Information), and adsorption was slow enough to follow using IR spectroscopy. For each adsorbate, the integrated C−H stretching absorbance (3000−2800 cm−1) increased with immersion time, corresponding to an increase of surface coverage (Figures S4 and S5 in Supporting Information). The νa(CH2) and νs(CH2) maxima of 6A and Br6A did not change with immersion time; thus, monolayers of 6A and Br6A were liquid-like and disordered at all adsorption times and surface coverages. In contrast, the νa(CH2) and νs(CH2) maxima of the longer n-alkanoic acids shifted to lower wavenumbers with increasing immersion time, indicating that the monolayers became more ordered as surface coverages increased.29,32,43,44 This transition from disordered to ordered monolayers with increasing adsorption time is qualitatively consistent with the mechanism by which octadecylphosphonic acid adsorbs to mica and sapphire at room temperature, as reported by Schwartz and co-workers.51 The νa(CH2) maxima of 11A and 16A shifted to 2925 and 2920 cm−1, respectively, with increasing surface coverage during the course of adsorption kinetics experiments; thus, monolayers of 11A and 16A were not fully ordered under these conditions. At the longest adsorption times, the νa(CH2) maxima of 18A adsorbed from heptane and of 21A adsorbed from heptane, DCM, and toluene were 2917 cm−1, indicating that the monolayers were essentially fully ordered. When 21A was adsorbed from THF, the νa(CH2) maximum shifted from 2928 to 2924 cm−1 over the course of adsorption kinetics experiments, indicating that monolayers formed from 1 mM adsorption solutions were only partially ordered even at the longest adsorption times. This result is consistent with our equilibrium binding data (Figure

dθt d(1 − θt ) =− = kadC(1 − θt) dt dt

(3)

ln(1 − θt) = −kadCt

(4)

where t is time, kad is the rate constant for adsorption, and values of θt were determined by dividing the average measured value of Γ at a given adsorption time by Γ0 (Table 1). Equations 3 and 4 are predicated on the assumption that the rate of desorption was negligible compared to the rate of adsorption. We previously reported that kinetics of adsorption of n-alkanoic acids to nanocrystalline TiO2 films are modeled precisely by these rate laws.28 These equations have also been used to model the adsorption of alkanethiols to gold and of metal complexes to platinum.52−56 For 21A adsorbed from heptane, DCM, and toluene, plots of ln(1 − θt) vs t were linear (Figure S5 in Supporting Information). Values of k ad determined from linear fits to the data were approximately 1 M−1 s−1 and varied minimally with solvent (Table 1). We previously reported that, for a given solvent, kad for adsorption of n-alkanoic acids was inversely proportional to the number of carbons in the alkyl chain.28 Our measured values of kad for 21A are lower than our reported values for shorter n-alkanoic acids and are in line with this chain-length dependence. The adsorption of 21A to TiO2 from THF and the adsorption of most other n-alkanoic acids to TiO2 from heptane were not modeled precisely by Langmuir adsorption kinetics. Plots of ln(1 − θt) vs t were nonlinear and became less negatively sloped at increasing adsorption times (Figure S5 in Supporting Information). Such deviation from linearity suggests that desorption of n-alkanoic acids was not negligible and reduced the net rate at which θt increased. In summary, only the data for adsorption of 21A from heptane, DCM, and toluene, followed simple Langmuir kinetics. Lateral dispersion forces were probably stronger for 21A than for the shorter n-alkanoic acids and may have stabilized 21A within monolayers and 13801

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Figure 5. Fractional surface coverages of disordered 21A (θd) and ordered 21A (θo) on TiO2 as a function of adsorption time from 1 mM solutions in heptane (a) and DCM (b). Error bars are standard deviations relative to average values of θd or θo from 1 to 3 adsorption kinetics experiments in which 4 TiO2 films were functionalized at each adsorption time. Superimposed on data are fits to eqs 9 and 10.

increased the activation barrier to desorption. This effect was minimized when 21A was adsorbed from THF, which yielded less-ordered monolayers (Figures S1 and S4 in Supporting Information), consistent with the poor fits of these data to Langmuir kinetics. To quantify the ordering of monolayers of n-alkanoic acids with increasing adsorption time, we fit measured IR spectra, in the C−H stretching region, of TiO2 films functionalized with 16A, 18A, and 21A (adsorbed from heptane, DCM, and toluene) to linear combinations of absorbances from ordered and disordered adsorbates (eq S2 in Supporting Information). Fits corresponded closely to measured spectra (Figure S6 in Supporting Information). At the shortest adsorption times, monolayers of 16A, 18A, and 21A were essentially completely disordered (Figure 5 and Figure S7 in Supporting Information). After an initial induction period of several minutes, θo increased with total surface coverage. In contrast, θd increased rapidly at short adsorption times, plateaued after 0.05−0.2 h, then decreased steadily, approaching zero at adsorption times of 0.5−1 h. Thus, the spectral fits reveal that the monolayers became more ordered as the surface coverages of 16A, 18A, and 21A increased, consistent with the measured shifts of νa(CH2) and νs(CH2) maxima to lower wavenumbers with time (Figure S6 in Supporting Information). Notably, θo increased more slowly for 16A than for 18A and 21A (Figure 5 and Figure S7 in Supporting Information), again suggesting that ordering was driven by dispersion forces that were stronger for the longer nalkanoic acids. The evolution of monolayers of n-alkanoic acids from disordered to ordered with increasing adsorption time and surface coverage is similar to the established two-stage adsorption of alkanethiols on gold, in which the rapid initial adsorption is followed by slower reorganization and formation of crystalline monolayers.54,57−59 Damos et al. reported differential and integrated rate laws for the two-stage adsorption of alkanethiols to gold.60 Following their logic, we assumed that the adsorption and ordering of 16A, 18A, and 21A proceeded via the following idealized mechanism:

[H3C−(CH 2)n −CO2−]d −TiO2 ko

→ [H3C−(CH 2)n −CO2−]o −TiO2

where kd is the rate constant for desorption, ko is the rate constant for ordering of adsorbates, and the subscripts “d” and “o” refer to disordered and ordered adsorbates, respectively. (We previously reported that n-alkanoic acids adsorb to TiO2 as deprotonated n-alkanoates.48) Assuming that adsorption and desorption follow Langmuir kinetics, that ordering is irreversible and first-order with respect to surface coverage of adsorbate, and that adsorbates within ordered phases do not desorb, then differential rate laws for the time-dependent changes of θd and θo are as follows:60 (7)

dθo = koθd dt

(8)

θd =

−kadC [exp(−kobs,1t ) − exp(−kobs,2t )] kobs,1 − kobs,2

θo =

⎡ k −kadC ⎢ o (1 − exp(−kobs,1t )) kobs,1 − kobs,2 ⎢⎣ kobs,1

−

⎤ (1 − exp(−kobs,2t ))⎥ ⎥⎦ kobs,1

(9)

ko

(10)

where kobs,1 =

kadC + kd + ko 2 +

kobs,2 =

kad kd

dθd = kadC(1 − θo) − (kadC + kd + ko)θd dt

The corresponding integrated rate laws are as follows:

H3C−(CH 2)n −CO2 H + TiO2 ⇄ [H3C−(CH 2)n −CO2−]d −TiO2 + H+

(6)

13802

(11)

kadC + kd + ko 2 −

(5)

⎛ kadC + kd + ko ⎞2 ⎜ ⎟ − kadkoC ⎝ ⎠ 2

⎛ kadC + kd + ko ⎞2 ⎜ ⎟ − kadkoC ⎝ ⎠ 2

(12)

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Figure 6. Average IR spectra of TiO2 films as a function of immersion time in mixed solutions of 21A and Br6A in heptane with total concentration of 2 mM and χ21A,soln of 0.3 (a) and 0.5 (b).

compositional evolution with time. We chose 21A because it exhibited significant ordering on TiO2. We chose Br6A because it did not order to any measurable extent on TiO2 and because it lacks a terminal methyl group; therefore, the C−H stretching bands of its IR spectrum differ significantly from those of 21A, simplifying the determination of mixed-monolayer compositions via spectral fitting. Mixed 21A−Br6A monolayers were prepared by immersing TiO2 films into mixed coadsorption solutions for times ranging from 2 min to 6 h. IR spectra were acquired to monitor changes in the surface coverages of adsorbates and the compositions of mixed monolayers as a function of time. In one experiment, the relative solute mole fraction of 21A (χ21A,soln) and the relative solute mole fraction of Br6A (χBr6A,soln) in heptane solutions were varied while the sum of their concentrations was fixed at 2 mM. Representative IR spectra are shown in Figure 6 for two sets of TiO2 films: one of which was immersed in heptane coadsorption solutions with χ21A,soln of 0.3 and the other of which was immersed in solutions with χ21A,soln of 0.5. The C−H stretching region of the spectra of TiO2 films immersed into the solution with χ21A,soln of 0.3 was nearly unchanged with immersion time (Figure 6a). Absorbances at the maxima of C−H stretching bands decreased by approximately 30% over 6 h, and the bands were unshifted. IR spectra of TiO2 films immersed into heptane coadsorption solutions with χ21A,soln of 0.4 were similar, exhibiting only a slight diminution of C−H stretching bands with time (Figure S8 in Supporting Information). In contrast, spectra of the films immersed into solutions with χ21A,soln of 0.5 changed dramatically with increasing immersion time (Figure 6b). Absorbances at maxima of the νa(CH2), νs(CH2), and asymmetric methyl stretching (νa(CH3)) bands increased by 4−5-fold over the course of 6 h of immersion, and the νa(CH2) band narrowed and shifted to lower wavenumbers. The νa(CH2) and νs(CH2) bands of 21A have higher molar absorption coefficients (ε) than those of Br6A (Table S1) due to the difference in chain lengths. Therefore, the spectral changes indicate that the total surface coverage of 21A (Γ21A,t) increased with time. When TiO2 films were immersed into coadsorption solutions with χ21A,soln of 0.6 and 0.7, IR spectra evolved similarly, indicating that Γ21A,t increased with time (Figure S8 in Supporting Information).

For 16A and 18A adsorbed from heptane and for 21A adsorbed from heptane, DCM, and toluene, plots of θd and θo vs t were fit simultaneously to eqs 9 and 10. Values of kad, kd, and ko were adjusted to minimize differences between the values of θd or θo obtained by fitting measured IR spectra to equation S2 (Supporting Information) and the values of θd or θo calculated from eqs 9 and 10. Fits were optimized by minimizing the sum of (1) the sums of the squares of differences between fitted and calculated θd values and (2) the sums of the squares of the differences between fitted and calculated θo values. The resulting time-dependent calculated values of θd and θo are superimposed on the plots of θd and θo (from spectral fitting) vs t in Figure 5 and in Figure S7 of the Supporting Information. The corresponding values of kad, kd, and ko are listed in Table 1. The time-dependent values of θd and θo generated by this procedure correspond closely to the values of θd and θo generated from IR spectral fitting, indicating that the idealized mechanism of eqs 5 and 6 accounts satisfactorily for the overall kinetics of adsorption, desorption, and ordering. Notably, the value of ko for 16A was approximately 3−5-fold less than the values of ko for 18A and 21A, consistent with the slower ordering of 16A as determined from spectral fitting (Figure S7 in Supporting Information). For 21A, the values of kad determined from fitting the data to eqs 9 and 10 were within an order of magnitude of the values of kad extracted from fits to Langmuir adsorption kinetics (eq 4 and Figure S5 in Supporting Information). Neither the values of kd nor the ratios of kad to kd varied systematically with alkyl chain length, despite variations in the linearity of plots of ln(1 − θt) vs t with chain length. Formation and Compositional Evolution of Mixed Monolayers on TiO2. Taken together, data from our equilibrium binding and adsorption kinetics experiments reveal that n-alkanoic acids with 14 or more methylene groups form ordered, crystalline monolayers on nanocrystalline TiO2 films at high surface coverages. Ordering is presumably driven by cohesive dispersion forces between alkyl chains. Having previously discovered that disulfide formation stabilized thiolated adsorbates and drove compositional changes within mixed monolayers,28 we sought to determine whether noncovalent lateral dispersion forces between adsorbates similarly affected mixed-monolayer compositions. To do so, we prepared mixed monolayers of Br6A and 21A and followed their 13803

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Figure 7. χBr6A,surf, χ21A,d,surf, and χ21A,o,surf on TiO2 as a function of immersion time in heptane coadsorption solutions with total concentration of 2 mM and χ21A,soln of 0.3 (a) and 0.5 (b). Error bars are standard deviations relative to average values of χBr6A,surf, χ21A,d,surf, or χ21A,o,surf from 2 to 4 TiO2 films for each adsorption time.

To quantify the compositions of mixed monolayers, we fit C−H stretching regions to linear combinations of absorbances from Br6A, disordered 21A, and ordered 21A: A(ν) = εBr6A (ν)ΓBr6A + εd(ν)Γ21A,d + εo(ν)Γ21A,o

in disordered and ordered phases containing roughly equal amounts of adsorbates. Notably, χBr6A,surf exceeded χBr6A,soln (and χ21A,t,surf was less than χ21A,soln) at all immersion times. The preferential adsorption of Br6A may have arisen from either thermodynamics, as the measured Kad value of Br6A was approximately 3.5-fold greater than that of 21A (Table 1), or kinetics, owing to the higher concentration of Br6A than 21A in the mixed coadsorption solutions (and the concentration dependence of the rate of adsorption (eq 3)). The compositions of mixed monolayers prepared from heptane coadsorption solutions with χ21A,soln of 0.5 changed significantly during the first 6 h of immersion (Figure 7 and Figure S10 in Supporting Information). For the first 10 min, ΓBr6A and Γ21A,t increased rapidly. The value of χ21A,d,surf initially exceeded χ21A,o,surf; however, 21A then underwent significant ordering, such that χ21A,d,surf decreased steadily to less than 0.05 after 2 h. The value of χ21A,o,surf increased throughout the 6 h experiments. From immersion times of 10 min onward, χ21A,t,surf increased while χBr6A,surf decreased (Figure 7). At the longest immersion times, χ21A,t,surf was greater than χBr6A,surf, and the mixed monolayers were enriched in 21A relative to the coadsorption solutions. Importantly, these compositional changes occurred after the Br6A and 21A had already achieved Γsum values of 2.5 × 10−7−3.5 × 10−7 mol cm−2, corresponding to the formation of full monolayers at saturation surface coverages. Mixed monolayers prepared from heptane coadsorption solutions with χ21A,soln of 0.6 and 0.7 also underwent compositional changes (Figures S9−S11 in Supporting Information). Within the first 1 h of immersion, χ21A,t,surf increased and χBr6A,surf decreased as 21A became more ordered. At the longest immersion times, χ21A,t,surf was greater than or equal to χ21A,soln. Our data reveal a correlation between the ordering of 21A and its enrichment within mixed monolayers on TiO2. We propose that lateral dispersion forces stabilized 21A on TiO2 by making more negative its enthalpy of adsorption. Thus, when χ21A,t,surf was sufficiently high to allow for significant lateral interactions and ordering, 21A became more stable than Br6A and displaced Br6A from TiO2. However, when χ21A,t,surf was below a certain threshold value, 21A underwent minimal ordering and Br6A predominated on TiO2. Because the initial values of χ21A,t,surf and χBr6A,surf depended on χ21A,soln and χ6BrA,soln, the extent of ordering of 21A and the compositions of

(13)

where A(ν) is the measured absorbance at a given wavenumber, εBr6A(ν), εd(ν), and εo(ν) are the molar absorption coefficients of TiO2-adsorbed Br6A, 21A within a disordered phase, and 21A within an ordered phase, at a given wavenumber; and ΓBr6A, Γ21A,d, and Γ21A,o are the surface coverages of Br6A, disordered 21A, and ordered 21A, respectively. We made the same assumptions and used the same spectral fitting procedure as described in Appendix S2 of the Supporting Information for fitting the IR spectra of single-component monolayers to eq S2. Mole fractions of Br6A, disordered 21A, and ordered 21A within the mixed monolayers on TiO2 (χBr6A,surf, χ21A,d,surf, and χ21A,o,surf, respectively) were calculated from ΓBr6A, Γ21A,d, and Γ21A,o: χi ,surf =

Γi ΓBr6A + Γ21A,d + Γ21A,o

(14)

where i equals Br6A, 21A,d, or 21A,o. Spectral fits generated by this approach corresponded closely to measured IR spectra of mixed monolayer-functionalized TiO2 films (Figure S9 in Supporting Information). For each of the different compositions of coadsorption solution, plots of ΓBr6A, Γ21A,d, Γ21A,o and the sum of the surface coverages of Br6A and 21A (Γsum) vs t are shown in Figure S10 of the Supporting Information. Corresponding plots of χBr6A,surf, χ21A,d,surf, and χ21A,o,surf vs t are presented in Figure 7 (for χ21A,soln of 0.3 and 0.5) and in Figure S11 of the Supporting Information (for χ21A,soln of 0.4, 0.6, and 0.7). Mixed monolayers prepared from heptane coadsorption solutions with χ21A,soln of 0.3 and 0.4 consisted primarily of Br6A at all immersion times (Figure 7 and Figures S10 and S11 in the Supporting Information). At the earliest immersion time of 5 min, χBr6A,surf was 2−3-fold greater than the total mole fraction of 21A on TiO2 (χ21A,t,surf); χBr6A,surf and then increased to approximately 0.8, or 4-fold greater than χ21A,t,surf. Compositions of these mixed monolayers were essentially invariant from immersion times of 10 min−6 h. Values of both χ21A,d,surf and χ21A,o,surf were approximately 0.1; thus, 21A existed 13804

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Supporting Information). In the latter mixed monolayers, 21A underwent significant ordering, and χ21A,surf was approximately 4-fold greater than χBr6A,surf at equilibrium. Thus, shortening the alkanoic acid from 19 to 4 methylene groups, and thereby decreasing the magnitude of dispersion forces and the extent of ordering, dramatically altered the composition and compositional evolution of mixed monolayers, such that Br6A predominated at equilibrium when coadsorbed with 6A. This result provides additional compelling evidence that the slow displacement of Br6A by 21A within mixed monolayers, when χ21A,t,surf was sufficiently high, was driven by the stabilization of 21A on TiO2 caused by lateral dispersion forces and ordering.

mixed monolayers varied greatly with compositions of coadsorption solutions. An alternative explanation involves a chelate-like kinetic effect. Cohesive dispersion forces between 21A may have retained desorbed 21A near the TiO2 surface, increasing its local concentration and accelerating its readsorption to TiO2. In a second experiment, we prepared mixed monolayers of 21A and Br6A from coadsorption solutions in DCM, toluene, and THF with χ21A,soln of 0.5. The mixed monolayers prepared from DCM and toluene solutions behaved similarly to those prepared from heptane (Figure S12 in Supporting Information). After an initial rapid increase of Γsum, 21A became almost completely ordered and slowly displaced Br6A from TiO2. At the longest immersion times, χ21A,t,surf exceeded χBr6A,surf and χ21A,soln. Thus, ordering of 21A was correlated with its enrichment within mixed 21A-Br6A monolayers. In contrast, when mixed monolayers were prepared from THF, 21A did not order to an appreciable extent (χ21A,o,surf was less than 0.1 at all immersion times), and Br6A predominated on TiO2 (Figure S12 in Supporting Information). Values of χ21A,t,surf and χBr6A,surf initially corresponded closely to χ21A,soln and χBr6A,soln, and then χBr6A,surf increased to approximately 0.75 after 4−6 h. The lack of ordering of 21A within these mixed monolayers is consistent with our equilibrium binding and adsorption kinetics data for single-component monolayers, which revealed that n-alkanoic acids underwent substantially less ordering when adsorbed from THF than when adsorbed from heptane, DCM, or toluene. The corresponding lack of compositional changes of mixed monolayers prepared from THF and the predominance of Br6A within these mixed monolayers, provide additional evidence that dispersion forces and ordering of 21A drive the time-dependent compositional changes of mixed monolayers prepared from the other solvents. Finally, we prepared mixed monolayers of 6A and Br6A on TiO2 to evaluate whether compositions of mixed monolayers depended on the length of the alkanoic acid and the extent of ordering. In a representative experiment, mixed 6A−Br6A monolayers were prepared by immersing TiO2 films into heptane coadsorption solutions with relative solute mole fraction of 6A (χ6A,soln) of 0.7 and χBr6A,soln of 0.3 for times ranging from 5 min to 6 h. Results are summarized in Figure S13 of the Supporting Information. IR spectra of mixed monolayer-functionalized films varied only minimally with immersion time. Compositions of mixed monolayers were determined by fitting the C−H stretching regions of IR spectra to linear combinations of absorbances from Br6A and 6A: A(ν) = εBr6A (ν)ΓBr6A + ε6A (ν)Γ6A

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CONCLUSIONS

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ASSOCIATED CONTENT

We have characterized single-component and mixed monolayers of n-alkanoic acids and Br6A on nanocrystalline TiO2 films. Measured IR spectra reveal that n-alkanoic acids with 14 or more methylene groups formed ordered, crystalline monolayers on the TiO2 films. The νa(CH2) and νs(CH2) maxima of TiO2 films functionalized with 16A, 18A, and 21A were identical to reported maxima for monolayers of alkanethiolates on gold and crystalline alkanes, indicating a similar degree of ordering and crystallinity despite the mesoporous morphology of the TiO2 substrate. The rate and extent of ordering of n-alkanoic acids increased with their length, suggesting that ordering was driven by lateral intermolecular dispersion forces within monolayers. IR spectra were modeled precisely as linear combinations of contributions from disordered and ordered adsorbates. The idealized mechanism presented in eqs 5 and 6 is satisfactory to model the kinetics of adsorption, desorption, and ordering. Dispersion forces and ordering governed compositions of mixed monolayers. The compositions of mixed 21A−Br6A monolayers varied significantly with time, solvent, and the relative amounts of adsorbates in coadsorption solutions. When mixed monolayers were prepared from heptane, DCM, or toluene and χ21A,soln was sufficiently high, 21A became increasingly ordered and displaced Br6A with time. When χ21A,soln was insufficiently high, or when the mixed monolayers were prepared from THF, 21A underwent substantially less ordering, compositions of mixed monolayers varied much less with time, and Br6A predominated on TiO2. Similarly, Br6A predominated when coadsorbed to TiO2 with 6A. To explain these effects, we proposed that cohesive dispersion forces between alkyl chains of 21A stabilize it on TiO2, ultimately causing it to displace Br6A within mixed monolayers that remain in contact with coadsorption solutions. Our results reveal that noncovalent intermolecular interactions between adsorbates can greatly affect the compositions, terminal functionalization, and properties of mixed monolayers on nanocrystalline TiO2 films. To prepare mixed monolayers with tightly controlled compositions requires careful consideration of such effects.

(15)

where ε6A(ν) is the molar absorption coefficient of 6A at a given wavenumber and Γ6A is the surface coverage of 6A. At the earliest immersion times, Γ6A and ΓBr6A were similar; subsequently, ΓBr6A increased while Γ6A remained essentially constant. At immersion times of 2 h or more, χBr6A,surf was approximately twice the mole fraction of 6A on the surface (χ6A,surf). Thus, the mixed monolayers were enriched in Br6A relative to the coadsorption solutions from which they were formed, probably due to the nearly 2-fold greater Kad value of Br6A relative to 6A (Table 1). The relative lack of compositional changes of these mixed 6A−Br6A monolayers, and the predominance of Br6A within the monolayers at all immersion times, differ markedly from mixed 21A−Br6A monolayers prepared from coadsorption solutions with χ21A,soln of 0.7 and χBr6A,soln of 0.3 (Figures S8−S11 in

S Supporting Information *

Measured and fitted IR spectra of single-component and mixed monolayers, equilibrium binding and adsorption kinetics data for single-component monolayers, and data showing the compositional evolution of various mixed monolayers. This material is available free of charge via the Internet at http:// pubs.acs.org. 13805

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AUTHOR INFORMATION

Corresponding Author

*E-mail dwatson3@buffalo.edu (D.F.W.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation (CHE-0645678). REFERENCES

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dx.doi.org/10.1021/la4030519 | Langmuir 2013, 29, 13797−13807